id sid tid token lemma pos aiti-14372 1 1 microsoft microsoft PROPN aiti-14372 1 2 word word NOUN aiti-14372 1 3 aiti#14372 aiti#14372 PROPN aiti-14372 1 4 20250526 20250526 NUM aiti-14372 1 5 ( ( PUNCT aiti-14372 1 6 update update NOUN aiti-14372 1 7 header header NOUN aiti-14372 1 8 information information NOUN aiti-14372 1 9 ) ) PUNCT aiti-14372 1 10 advances advance NOUN aiti-14372 1 11 in in ADP aiti-14372 1 12 technology technology NOUN aiti-14372 1 13 innovation innovation NOUN aiti-14372 1 14 , , PUNCT aiti-14372 1 15 vol vol NOUN aiti-14372 1 16 . . PROPN aiti-14372 1 17 10 10 NUM aiti-14372 1 18 , , PUNCT aiti-14372 1 19 no no INTJ aiti-14372 1 20 . . NOUN aiti-14372 1 21 3 3 NUM aiti-14372 1 22 , , PUNCT aiti-14372 1 23 2025 2025 NUM aiti-14372 1 24 , , PUNCT aiti-14372 1 25 pp pp ADJ aiti-14372 1 26 . . PUNCT aiti-14372 2 1 238 238 NUM aiti-14372 2 2 - - SYM aiti-14372 2 3 253 253 NUM aiti-14372 2 4 a a DET aiti-14372 2 5 modified modify VERB aiti-14372 2 6 exponential exponential ADJ aiti-14372 2 7 model model NOUN aiti-14372 2 8 for for ADP aiti-14372 2 9 predicting predict VERB aiti-14372 2 10 the the DET aiti-14372 2 11 fatigue fatigue NOUN aiti-14372 2 12 crack crack VERB aiti-14372 2 13 growth growth NOUN aiti-14372 2 14 rate rate NOUN aiti-14372 2 15 in in ADP aiti-14372 2 16 a a DET aiti-14372 2 17 pipeline pipeline NOUN aiti-14372 2 18 steel steel NOUN aiti-14372 2 19 under under ADP aiti-14372 2 20 pure pure ADJ aiti-14372 2 21 bending bend VERB aiti-14372 2 22 sergei sergei PROPN aiti-14372 2 23 sherbakov1 sherbakov1 PROPN aiti-14372 2 24 , , PUNCT aiti-14372 2 25 pawan pawan PROPN aiti-14372 2 26 kumar1 kumar1 PROPN aiti-14372 2 27 , , PUNCT aiti-14372 2 28 * * PROPN aiti-14372 2 29 , , PUNCT aiti-14372 2 30 daria daria PROPN aiti-14372 2 31 podgayskaya1 podgayskaya1 PROPN aiti-14372 2 32 , , PUNCT aiti-14372 2 33 pavel pavel PROPN aiti-14372 2 34 poliakov2 poliakov2 PROPN aiti-14372 2 35 , , PUNCT aiti-14372 2 36 vasilii vasilii NOUN aiti-14372 2 37 dobrianskii2 dobrianskii2 NOUN aiti-14372 2 38 , , PUNCT aiti-14372 2 39 vishwanatha vishwanatha PROPN aiti-14372 2 40 h h PROPN aiti-14372 2 41 m3 m3 PROPN aiti-14372 2 42 1joint 1joint PROPN aiti-14372 2 43 institute institute NOUN aiti-14372 2 44 of of ADP aiti-14372 2 45 mechanical mechanical ADJ aiti-14372 2 46 engineering engineering NOUN aiti-14372 2 47 of of ADP aiti-14372 2 48 the the DET aiti-14372 2 49 national national PROPN aiti-14372 2 50 academy academy PROPN aiti-14372 2 51 of of ADP aiti-14372 2 52 sciences sciences PROPN aiti-14372 2 53 of of ADP aiti-14372 2 54 belarus belarus PROPN aiti-14372 2 55 , , PUNCT aiti-14372 2 56 minsk minsk PROPN aiti-14372 2 57 , , PUNCT aiti-14372 2 58 belarus belarus PROPN aiti-14372 2 59 2moscow 2moscow NUM aiti-14372 2 60 aviation aviation NOUN aiti-14372 2 61 institute institute NOUN aiti-14372 2 62 ( ( PUNCT aiti-14372 2 63 national national PROPN aiti-14372 2 64 research research PROPN aiti-14372 2 65 university university PROPN aiti-14372 2 66 ) ) PUNCT aiti-14372 2 67 , , PUNCT aiti-14372 2 68 moscow moscow PROPN aiti-14372 2 69 , , PUNCT aiti-14372 2 70 russia russia PROPN aiti-14372 2 71 3department 3department NUM aiti-14372 2 72 of of ADP aiti-14372 2 73 mechanical mechanical ADJ aiti-14372 2 74 and and CCONJ aiti-14372 2 75 industrial industrial ADJ aiti-14372 2 76 engineering engineering NOUN aiti-14372 2 77 , , PUNCT aiti-14372 2 78 manipal manipal PROPN aiti-14372 2 79 institute institute PROPN aiti-14372 2 80 of of ADP aiti-14372 2 81 technology technology PROPN aiti-14372 2 82 , , PUNCT aiti-14372 2 83 manipal manipal PROPN aiti-14372 2 84 academy academy PROPN aiti-14372 2 85 of of ADP aiti-14372 2 86 higher high ADJ aiti-14372 2 87 education education NOUN aiti-14372 2 88 , , PUNCT aiti-14372 2 89 manipal manipal PROPN aiti-14372 2 90 , , PUNCT aiti-14372 2 91 india india PROPN aiti-14372 2 92 received receive VERB aiti-14372 2 93 08 08 NUM aiti-14372 2 94 october october PROPN aiti-14372 2 95 2024 2024 NUM aiti-14372 2 96 ; ; PUNCT aiti-14372 2 97 received receive VERB aiti-14372 2 98 in in ADP aiti-14372 2 99 revised revise VERB aiti-14372 2 100 form form NOUN aiti-14372 2 101 09 09 NUM aiti-14372 2 102 february february NOUN aiti-14372 2 103 2025 2025 NUM aiti-14372 2 104 ; ; PUNCT aiti-14372 2 105 accepted accept VERB aiti-14372 2 106 13 13 NUM aiti-14372 2 107 march march NOUN aiti-14372 2 108 2025 2025 NUM aiti-14372 2 109 doi doi NOUN aiti-14372 2 110 : : PUNCT aiti-14372 2 111 https://doi.org/10.46604/aiti.2024.14372 https://doi.org/10.46604/aiti.2024.14372 PROPN aiti-14372 2 112 abstract abstract NOUN aiti-14372 2 113 the the DET aiti-14372 2 114 present present ADJ aiti-14372 2 115 work work NOUN aiti-14372 2 116 proposes propose VERB aiti-14372 2 117 a a DET aiti-14372 2 118 fatigue fatigue NOUN aiti-14372 2 119 crack crack VERB aiti-14372 2 120 growth growth NOUN aiti-14372 2 121 rate rate NOUN aiti-14372 2 122 ( ( PUNCT aiti-14372 2 123 fcgr fcgr NOUN aiti-14372 2 124 ) ) PUNCT aiti-14372 2 125 model model NOUN aiti-14372 2 126 for for ADP aiti-14372 2 127 steel steel NOUN aiti-14372 2 128 pipelines pipeline NOUN aiti-14372 2 129 subjected subject VERB aiti-14372 2 130 to to ADP aiti-14372 2 131 sinusoidal sinusoidal ADJ aiti-14372 2 132 loading loading NOUN aiti-14372 2 133 using use VERB aiti-14372 2 134 a a DET aiti-14372 2 135 modified modify VERB aiti-14372 2 136 exponential exponential ADJ aiti-14372 2 137 function function NOUN aiti-14372 2 138 . . PUNCT aiti-14372 3 1 the the DET aiti-14372 3 2 modification modification NOUN aiti-14372 3 3 in in ADP aiti-14372 3 4 the the DET aiti-14372 3 5 exponential exponential ADJ aiti-14372 3 6 function function NOUN aiti-14372 3 7 is be AUX aiti-14372 3 8 made make VERB aiti-14372 3 9 for for ADP aiti-14372 3 10 the the DET aiti-14372 3 11 non non ADJ aiti-14372 3 12 - - ADJ aiti-14372 3 13 dimensional dimensional ADJ aiti-14372 3 14 parameter parameter NOUN aiti-14372 3 15 using use VERB aiti-14372 3 16 the the DET aiti-14372 3 17 stress stress NOUN aiti-14372 3 18 intensity intensity NOUN aiti-14372 3 19 range range NOUN aiti-14372 3 20 ( ( PUNCT aiti-14372 3 21 Ξ΄k Ξ΄k ADP aiti-14372 3 22 ) ) PUNCT aiti-14372 3 23 as as ADP aiti-14372 3 24 the the DET aiti-14372 3 25 crack crack NOUN aiti-14372 3 26 driving driving NOUN aiti-14372 3 27 force force NOUN aiti-14372 3 28 . . PUNCT aiti-14372 4 1 the the DET aiti-14372 4 2 acceptable acceptable ADJ aiti-14372 4 3 values value NOUN aiti-14372 4 4 of of ADP aiti-14372 4 5 Ξ΄k Ξ΄k PRON aiti-14372 4 6 for for ADP aiti-14372 4 7 fcgr fcgr NOUN aiti-14372 4 8 in in ADP aiti-14372 4 9 stage stage NOUN aiti-14372 4 10 - - PUNCT aiti-14372 4 11 i i PRON aiti-14372 4 12 ranged range VERB aiti-14372 4 13 between between ADP aiti-14372 4 14 17.45 17.45 NUM aiti-14372 4 15 - - SYM aiti-14372 4 16 20.46 20.46 NUM aiti-14372 4 17 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 4 18 , , PUNCT aiti-14372 4 19 between between ADP aiti-14372 4 20 20.46 20.46 NUM aiti-14372 4 21 - - SYM aiti-14372 4 22 21.41 21.41 NUM aiti-14372 4 23 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 4 24 for for ADP aiti-14372 4 25 stage stage NOUN aiti-14372 4 26 - - PUNCT aiti-14372 4 27 ii ii NOUN aiti-14372 4 28 , , PUNCT aiti-14372 4 29 and and CCONJ aiti-14372 4 30 between between ADP aiti-14372 4 31 21.41 21.41 NUM aiti-14372 4 32 - - SYM aiti-14372 4 33 21.98 21.98 NUM aiti-14372 4 34 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 4 35 for for ADP aiti-14372 4 36 stage stage NOUN aiti-14372 4 37 - - PUNCT aiti-14372 4 38 iii iii NOUN aiti-14372 4 39 . . PUNCT aiti-14372 5 1 a a DET aiti-14372 5 2 new new ADJ aiti-14372 5 3 correlation correlation NOUN aiti-14372 5 4 is be AUX aiti-14372 5 5 also also ADV aiti-14372 5 6 developed develop VERB aiti-14372 5 7 between between ADP aiti-14372 5 8 the the DET aiti-14372 5 9 specific specific ADJ aiti-14372 5 10 growth growth NOUN aiti-14372 5 11 rate rate NOUN aiti-14372 5 12 and and CCONJ aiti-14372 5 13 the the DET aiti-14372 5 14 non non ADJ aiti-14372 5 15 - - ADJ aiti-14372 5 16 dimensional dimensional ADJ aiti-14372 5 17 number number NOUN aiti-14372 5 18 . . PUNCT aiti-14372 6 1 the the DET aiti-14372 6 2 modified modify VERB aiti-14372 6 3 exponential exponential ADJ aiti-14372 6 4 function function NOUN aiti-14372 6 5 predicted predict VERB aiti-14372 6 6 the the DET aiti-14372 6 7 fcgr fcgr NOUN aiti-14372 6 8 within within ADP aiti-14372 6 9 the the DET aiti-14372 6 10 acceptable acceptable ADJ aiti-14372 6 11 values value NOUN aiti-14372 6 12 for for ADP aiti-14372 6 13 all all DET aiti-14372 6 14 three three NUM aiti-14372 6 15 stages stage NOUN aiti-14372 6 16 in in ADP aiti-14372 6 17 the the DET aiti-14372 6 18 radial radial ADJ aiti-14372 6 19 direction direction NOUN aiti-14372 6 20 . . PUNCT aiti-14372 7 1 it it PRON aiti-14372 7 2 shows show VERB aiti-14372 7 3 the the DET aiti-14372 7 4 best good ADJ aiti-14372 7 5 performance performance NOUN aiti-14372 7 6 for for ADP aiti-14372 7 7 stage stage NOUN aiti-14372 7 8 - - PUNCT aiti-14372 7 9 i i PRON aiti-14372 7 10 of of ADP aiti-14372 7 11 fcgr fcgr NOUN aiti-14372 7 12 and and CCONJ aiti-14372 7 13 the the DET aiti-14372 7 14 lowest low ADJ aiti-14372 7 15 for for ADP aiti-14372 7 16 stage stage NOUN aiti-14372 7 17 - - PUNCT aiti-14372 7 18 iii iii NOUN aiti-14372 7 19 . . PUNCT aiti-14372 8 1 the the DET aiti-14372 8 2 microstructure microstructure NOUN aiti-14372 8 3 envisages envisage VERB aiti-14372 8 4 shallowed shallow VERB aiti-14372 8 5 microvoids microvoid NOUN aiti-14372 8 6 , , PUNCT aiti-14372 8 7 while while SCONJ aiti-14372 8 8 the the DET aiti-14372 8 9 striations striation NOUN aiti-14372 8 10 and and CCONJ aiti-14372 8 11 secondary secondary ADJ aiti-14372 8 12 cracks crack NOUN aiti-14372 8 13 are be AUX aiti-14372 8 14 mostly mostly ADV aiti-14372 8 15 perpendicular perpendicular ADJ aiti-14372 8 16 to to ADP aiti-14372 8 17 the the DET aiti-14372 8 18 fcg fcg PROPN aiti-14372 8 19 direction direction NOUN aiti-14372 8 20 . . PUNCT aiti-14372 9 1 keywords keyword NOUN aiti-14372 9 2 : : PUNCT aiti-14372 9 3 exponential exponential ADJ aiti-14372 9 4 function function NOUN aiti-14372 9 5 , , PUNCT aiti-14372 9 6 specific specific ADJ aiti-14372 9 7 growth growth NOUN aiti-14372 9 8 rate rate NOUN aiti-14372 9 9 , , PUNCT aiti-14372 9 10 fatigue fatigue NOUN aiti-14372 9 11 crack crack NOUN aiti-14372 9 12 , , PUNCT aiti-14372 9 13 stress stress NOUN aiti-14372 9 14 intensity intensity NOUN aiti-14372 9 15 factor factor NOUN aiti-14372 9 16 , , PUNCT aiti-14372 9 17 sdg sdg NOUN aiti-14372 9 18 9 9 NUM aiti-14372 9 19 1 1 NUM aiti-14372 9 20 . . PUNCT aiti-14372 9 21 introduction introduction NOUN aiti-14372 9 22 fatigue fatigue NOUN aiti-14372 9 23 failure failure NOUN aiti-14372 9 24 of of ADP aiti-14372 9 25 steel steel NOUN aiti-14372 9 26 pipes pipe NOUN aiti-14372 9 27 is be AUX aiti-14372 9 28 one one NUM aiti-14372 9 29 of of ADP aiti-14372 9 30 the the DET aiti-14372 9 31 most most ADV aiti-14372 9 32 important important ADJ aiti-14372 9 33 design design NOUN aiti-14372 9 34 criteria criterion NOUN aiti-14372 9 35 in in ADP aiti-14372 9 36 pipeline pipeline NOUN aiti-14372 9 37 engineering engineering NOUN aiti-14372 9 38 . . PUNCT aiti-14372 10 1 the the DET aiti-14372 10 2 steel steel NOUN aiti-14372 10 3 pipes pipe NOUN aiti-14372 10 4 are be AUX aiti-14372 10 5 used use VERB aiti-14372 10 6 to to PART aiti-14372 10 7 transport transport VERB aiti-14372 10 8 fluids fluid NOUN aiti-14372 10 9 in in ADP aiti-14372 10 10 the the DET aiti-14372 10 11 petrochemical petrochemical NOUN aiti-14372 10 12 , , PUNCT aiti-14372 10 13 aerospace aerospace NOUN aiti-14372 10 14 , , PUNCT aiti-14372 10 15 automobile automobile NOUN aiti-14372 10 16 , , PUNCT aiti-14372 10 17 and and CCONJ aiti-14372 10 18 chemical chemical NOUN aiti-14372 10 19 industries industry NOUN aiti-14372 11 1 [ [ X aiti-14372 11 2 1 1 NUM aiti-14372 11 3 ] ] PUNCT aiti-14372 11 4 . . PUNCT aiti-14372 12 1 the the DET aiti-14372 12 2 change change NOUN aiti-14372 12 3 in in ADP aiti-14372 12 4 pressure pressure NOUN aiti-14372 12 5 and and CCONJ aiti-14372 12 6 external external ADJ aiti-14372 12 7 loading loading NOUN aiti-14372 12 8 during during ADP aiti-14372 12 9 service service NOUN aiti-14372 12 10 envisages envisage VERB aiti-14372 12 11 a a DET aiti-14372 12 12 sinusoidal sinusoidal ADJ aiti-14372 12 13 loading loading NOUN aiti-14372 12 14 , , PUNCT aiti-14372 12 15 which which PRON aiti-14372 12 16 makes make VERB aiti-14372 12 17 the the DET aiti-14372 12 18 steel steel NOUN aiti-14372 12 19 pipes pipe NOUN aiti-14372 12 20 susceptible susceptible ADJ aiti-14372 12 21 to to ADP aiti-14372 12 22 fatigue fatigue NOUN aiti-14372 12 23 failure failure NOUN aiti-14372 12 24 [ [ X aiti-14372 12 25 2 2 NUM aiti-14372 12 26 ] ] PUNCT aiti-14372 12 27 . . PUNCT aiti-14372 13 1 therefore therefore ADV aiti-14372 13 2 , , PUNCT aiti-14372 13 3 fatigue fatigue NOUN aiti-14372 13 4 crack crack NOUN aiti-14372 13 5 growth growth NOUN aiti-14372 13 6 ( ( PUNCT aiti-14372 13 7 fcg fcg NOUN aiti-14372 13 8 ) ) PUNCT aiti-14372 13 9 is be AUX aiti-14372 13 10 a a DET aiti-14372 13 11 vital vital ADJ aiti-14372 13 12 failure failure NOUN aiti-14372 13 13 phenomenon phenomenon NOUN aiti-14372 13 14 in in ADP aiti-14372 13 15 pipeline pipeline NOUN aiti-14372 13 16 steel steel NOUN aiti-14372 13 17 due due ADP aiti-14372 13 18 to to ADP aiti-14372 13 19 the the DET aiti-14372 13 20 vibrational vibrational ADJ aiti-14372 13 21 nature nature NOUN aiti-14372 13 22 of of ADP aiti-14372 13 23 fluid fluid ADJ aiti-14372 13 24 and and CCONJ aiti-14372 13 25 operational operational ADJ aiti-14372 13 26 environment environment NOUN aiti-14372 13 27 [ [ X aiti-14372 13 28 3 3 NUM aiti-14372 13 29 ] ] PUNCT aiti-14372 13 30 . . PUNCT aiti-14372 14 1 it it PRON aiti-14372 14 2 is be AUX aiti-14372 14 3 quite quite ADV aiti-14372 14 4 possible possible ADJ aiti-14372 14 5 that that SCONJ aiti-14372 14 6 during during ADP aiti-14372 14 7 a a DET aiti-14372 14 8 significant significant ADJ aiti-14372 14 9 service service NOUN aiti-14372 14 10 time time NOUN aiti-14372 14 11 , , PUNCT aiti-14372 14 12 a a DET aiti-14372 14 13 microcrack microcrack NOUN aiti-14372 14 14 can can AUX aiti-14372 14 15 be be AUX aiti-14372 14 16 generated generate VERB aiti-14372 14 17 in in ADP aiti-14372 14 18 the the DET aiti-14372 14 19 pipeline pipeline NOUN aiti-14372 14 20 surface surface NOUN aiti-14372 14 21 , , PUNCT aiti-14372 14 22 which which PRON aiti-14372 14 23 acts act VERB aiti-14372 14 24 as as ADP aiti-14372 14 25 a a DET aiti-14372 14 26 stress stress NOUN aiti-14372 14 27 accumulator accumulator NOUN aiti-14372 14 28 in in ADP aiti-14372 14 29 its its PRON aiti-14372 14 30 vicinity vicinity NOUN aiti-14372 14 31 , , PUNCT aiti-14372 14 32 and and CCONJ aiti-14372 14 33 once once ADV aiti-14372 14 34 threshold threshold NOUN aiti-14372 14 35 stresses stress NOUN aiti-14372 14 36 accumulate accumulate VERB aiti-14372 14 37 , , PUNCT aiti-14372 14 38 it it PRON aiti-14372 14 39 results result VERB aiti-14372 14 40 in in ADP aiti-14372 14 41 fcg fcg PROPN aiti-14372 14 42 [ [ X aiti-14372 14 43 4 4 NUM aiti-14372 14 44 - - SYM aiti-14372 14 45 5 5 NUM aiti-14372 14 46 ] ] PUNCT aiti-14372 14 47 . . PUNCT aiti-14372 15 1 it it PRON aiti-14372 15 2 is be AUX aiti-14372 15 3 also also ADV aiti-14372 15 4 possible possible ADJ aiti-14372 15 5 that that SCONJ aiti-14372 15 6 a a DET aiti-14372 15 7 new new ADJ aiti-14372 15 8 crack crack NOUN aiti-14372 15 9 can can AUX aiti-14372 15 10 generate generate VERB aiti-14372 15 11 and and CCONJ aiti-14372 15 12 change change VERB aiti-14372 15 13 the the DET aiti-14372 15 14 stress stress NOUN aiti-14372 15 15 field field NOUN aiti-14372 15 16 locally locally ADV aiti-14372 15 17 , , PUNCT aiti-14372 15 18 providing provide VERB aiti-14372 15 19 the the DET aiti-14372 15 20 required require VERB aiti-14372 15 21 localized localized ADJ aiti-14372 15 22 stresses stress NOUN aiti-14372 15 23 for for ADP aiti-14372 15 24 multiple multiple ADJ aiti-14372 15 25 / / SYM aiti-14372 15 26 or or CCONJ aiti-14372 15 27 new new ADJ aiti-14372 15 28 crack crack NOUN aiti-14372 15 29 propagation propagation NOUN aiti-14372 15 30 . . PUNCT aiti-14372 16 1 one one NUM aiti-14372 16 2 of of ADP aiti-14372 16 3 the the DET aiti-14372 16 4 driving drive VERB aiti-14372 16 5 forces force NOUN aiti-14372 16 6 in in ADP aiti-14372 16 7 such such ADJ aiti-14372 16 8 failure failure NOUN aiti-14372 16 9 is be AUX aiti-14372 16 10 stress stress ADJ aiti-14372 16 11 intensity intensity NOUN aiti-14372 16 12 . . PUNCT aiti-14372 17 1 in in ADP aiti-14372 17 2 general general ADJ aiti-14372 17 3 , , PUNCT aiti-14372 17 4 the the DET aiti-14372 17 5 stress stress NOUN aiti-14372 17 6 intensity intensity NOUN aiti-14372 17 7 is be AUX aiti-14372 17 8 not not PART aiti-14372 17 9 defined define VERB aiti-14372 17 10 for for ADP aiti-14372 17 11 certain certain ADJ aiti-14372 17 12 crack crack NOUN aiti-14372 17 13 geometries geometry NOUN aiti-14372 17 14 ( ( PUNCT aiti-14372 17 15 solid solid ADJ aiti-14372 17 16 or or CCONJ aiti-14372 17 17 tubular tubular ADJ aiti-14372 17 18 ) ) PUNCT aiti-14372 17 19 of of ADP aiti-14372 17 20 pipes pipe NOUN aiti-14372 17 21 , , PUNCT aiti-14372 17 22 as as SCONJ aiti-14372 17 23 the the DET aiti-14372 17 24 pipeline pipeline NOUN aiti-14372 17 25 is be AUX aiti-14372 17 26 not not PART aiti-14372 17 27 a a DET aiti-14372 17 28 standard standard ADJ aiti-14372 17 29 geometry geometry NOUN aiti-14372 17 30 for for ADP aiti-14372 17 31 fatigue fatigue NOUN aiti-14372 17 32 crack crack NOUN aiti-14372 17 33 experimentations experimentation NOUN aiti-14372 17 34 and and CCONJ aiti-14372 17 35 simulations simulation NOUN aiti-14372 18 1 [ [ X aiti-14372 18 2 6 6 NUM aiti-14372 18 3 - - SYM aiti-14372 18 4 7 7 NUM aiti-14372 18 5 ] ] PUNCT aiti-14372 18 6 . . PUNCT aiti-14372 19 1 the the DET aiti-14372 19 2 varying vary VERB aiti-14372 19 3 thickness thickness NOUN aiti-14372 19 4 of of ADP aiti-14372 19 5 different different ADJ aiti-14372 19 6 pipes pipe NOUN aiti-14372 19 7 makes make VERB aiti-14372 19 8 it it PRON aiti-14372 19 9 even even ADV aiti-14372 19 10 more more ADV aiti-14372 19 11 difficult difficult ADJ aiti-14372 19 12 to to PART aiti-14372 19 13 consider consider VERB aiti-14372 19 14 different different ADJ aiti-14372 19 15 loading loading NOUN aiti-14372 19 16 conditions condition NOUN aiti-14372 19 17 and and CCONJ aiti-14372 19 18 applications application NOUN aiti-14372 19 19 [ [ X aiti-14372 19 20 8 8 NUM aiti-14372 19 21 - - SYM aiti-14372 19 22 9 9 NUM aiti-14372 19 23 ] ] PUNCT aiti-14372 19 24 . . PUNCT aiti-14372 20 1 also also ADV aiti-14372 20 2 , , PUNCT aiti-14372 20 3 the the DET aiti-14372 20 4 initial initial ADJ aiti-14372 20 5 microcrack microcrack NOUN aiti-14372 20 6 in in ADP aiti-14372 20 7 pipes pipe NOUN aiti-14372 20 8 can can AUX aiti-14372 20 9 be be AUX aiti-14372 20 10 of of ADP aiti-14372 20 11 part part NOUN aiti-14372 20 12 - - PUNCT aiti-14372 20 13 through through ADP aiti-14372 20 14 type type NOUN aiti-14372 20 15 or or CCONJ aiti-14372 20 16 throughthe throughthe ADJ aiti-14372 20 17 - - PUNCT aiti-14372 20 18 thickness thickness NOUN aiti-14372 20 19 dominant dominant ADJ aiti-14372 20 20 type type NOUN aiti-14372 20 21 , , PUNCT aiti-14372 20 22 yet yet CCONJ aiti-14372 20 23 the the DET aiti-14372 20 24 crack crack NOUN aiti-14372 20 25 propagation propagation NOUN aiti-14372 20 26 characteristics characteristic NOUN aiti-14372 20 27 of of ADP aiti-14372 20 28 such such ADJ aiti-14372 20 29 pipe pipe NOUN aiti-14372 20 30 geometries geometry NOUN aiti-14372 20 31 remain remain VERB aiti-14372 20 32 unknown unknown ADJ aiti-14372 20 33 . . PUNCT aiti-14372 21 1 * * PUNCT aiti-14372 21 2 corresponding correspond VERB aiti-14372 21 3 author author NOUN aiti-14372 21 4 . . PUNCT aiti-14372 22 1 e e X aiti-14372 22 2 - - NOUN aiti-14372 22 3 mail mail NOUN aiti-14372 22 4 address address NOUN aiti-14372 22 5 : : PUNCT aiti-14372 22 6 kumarpawan@mail.ru kumarpawan@mail.ru VERB aiti-14372 22 7 advances advance NOUN aiti-14372 22 8 in in ADP aiti-14372 22 9 technology technology NOUN aiti-14372 22 10 innovation innovation NOUN aiti-14372 22 11 , , PUNCT aiti-14372 22 12 vol vol NOUN aiti-14372 22 13 . . PROPN aiti-14372 23 1 10 10 NUM aiti-14372 23 2 , , PUNCT aiti-14372 23 3 no no INTJ aiti-14372 23 4 . . NOUN aiti-14372 23 5 3 3 NUM aiti-14372 23 6 , , PUNCT aiti-14372 23 7 2025 2025 NUM aiti-14372 23 8 , , PUNCT aiti-14372 23 9 pp pp ADJ aiti-14372 23 10 . . PUNCT aiti-14372 24 1 238 238 NUM aiti-14372 24 2 - - SYM aiti-14372 24 3 253 253 NUM aiti-14372 24 4 239 239 NUM aiti-14372 24 5 to to PART aiti-14372 24 6 address address VERB aiti-14372 24 7 such such ADJ aiti-14372 24 8 phenomena phenomenon NOUN aiti-14372 24 9 of of ADP aiti-14372 24 10 fatigue fatigue NOUN aiti-14372 24 11 crack crack VERB aiti-14372 24 12 propagation propagation NOUN aiti-14372 24 13 in in ADP aiti-14372 24 14 steel steel NOUN aiti-14372 24 15 pipes pipe NOUN aiti-14372 24 16 , , PUNCT aiti-14372 24 17 different different ADJ aiti-14372 24 18 fcg fcg NOUN aiti-14372 24 19 models model NOUN aiti-14372 24 20 were be AUX aiti-14372 24 21 developed develop VERB aiti-14372 24 22 considering consider VERB aiti-14372 24 23 external external ADJ aiti-14372 24 24 sinusoidal sinusoidal NOUN aiti-14372 24 25 load load NOUN aiti-14372 24 26 , , PUNCT aiti-14372 24 27 the the DET aiti-14372 24 28 effect effect NOUN aiti-14372 24 29 of of ADP aiti-14372 24 30 inclusion inclusion NOUN aiti-14372 24 31 , , PUNCT aiti-14372 24 32 and and CCONJ aiti-14372 24 33 the the DET aiti-14372 24 34 environmental environmental ADJ aiti-14372 24 35 effect effect NOUN aiti-14372 24 36 [ [ X aiti-14372 24 37 10 10 NUM aiti-14372 24 38 - - SYM aiti-14372 24 39 12 12 NUM aiti-14372 24 40 ] ] PUNCT aiti-14372 24 41 . . PUNCT aiti-14372 25 1 these these DET aiti-14372 25 2 models model NOUN aiti-14372 25 3 were be AUX aiti-14372 25 4 based base VERB aiti-14372 25 5 on on ADP aiti-14372 25 6 several several ADJ aiti-14372 25 7 approaches approach NOUN aiti-14372 25 8 , , PUNCT aiti-14372 25 9 including include VERB aiti-14372 25 10 finite finite ADJ aiti-14372 25 11 element element NOUN aiti-14372 25 12 analysis analysis NOUN aiti-14372 25 13 , , PUNCT aiti-14372 25 14 mathematical mathematical ADJ aiti-14372 25 15 modeling modeling NOUN aiti-14372 25 16 , , PUNCT aiti-14372 25 17 and and CCONJ aiti-14372 25 18 descriptive descriptive ADJ aiti-14372 25 19 analysis analysis NOUN aiti-14372 25 20 . . PUNCT aiti-14372 26 1 teng teng PROPN aiti-14372 26 2 an an DET aiti-14372 26 3 et et PROPN aiti-14372 26 4 al al PROPN aiti-14372 26 5 . . PROPN aiti-14372 26 6 calculated calculate VERB aiti-14372 26 7 the the DET aiti-14372 26 8 fcg fcg PROPN aiti-14372 26 9 of of ADP aiti-14372 26 10 x80 x80 PROPN aiti-14372 26 11 grades grade NOUN aiti-14372 26 12 of of ADP aiti-14372 26 13 pipeline pipeline NOUN aiti-14372 26 14 steel steel NOUN aiti-14372 26 15 , , PUNCT aiti-14372 26 16 considering consider VERB aiti-14372 26 17 the the DET aiti-14372 26 18 hydrogen hydrogen NOUN aiti-14372 26 19 pressure pressure NOUN aiti-14372 26 20 [ [ X aiti-14372 26 21 13 13 NUM aiti-14372 26 22 ] ] PUNCT aiti-14372 26 23 . . PUNCT aiti-14372 27 1 they they PRON aiti-14372 27 2 reported report VERB aiti-14372 27 3 a a DET aiti-14372 27 4 reduced reduced ADJ aiti-14372 27 5 fatigue fatigue NOUN aiti-14372 27 6 due due ADP aiti-14372 27 7 to to ADP aiti-14372 27 8 hydrogenaccelerated hydrogenaccelerate VERB aiti-14372 27 9 crack crack NOUN aiti-14372 27 10 propagation propagation NOUN aiti-14372 27 11 . . PUNCT aiti-14372 28 1 in in ADP aiti-14372 28 2 a a DET aiti-14372 28 3 similar similar ADJ aiti-14372 28 4 study study NOUN aiti-14372 28 5 , , PUNCT aiti-14372 28 6 fatoba fatoba PROPN aiti-14372 28 7 et et PROPN aiti-14372 28 8 al al PROPN aiti-14372 28 9 . . PROPN aiti-14372 28 10 studied study VERB aiti-14372 28 11 the the DET aiti-14372 28 12 low low ADJ aiti-14372 28 13 - - PUNCT aiti-14372 28 14 cycle cycle NOUN aiti-14372 28 15 fatigue fatigue NOUN aiti-14372 28 16 behavior behavior NOUN aiti-14372 28 17 of of ADP aiti-14372 28 18 api5l api5l PROPN aiti-14372 28 19 x65 x65 PROPN aiti-14372 28 20 pipeline pipeline NOUN aiti-14372 28 21 steel steel NOUN aiti-14372 28 22 under under ADP aiti-14372 28 23 completely completely ADV aiti-14372 28 24 reversed reverse VERB aiti-14372 28 25 strain strain NOUN aiti-14372 28 26 - - PUNCT aiti-14372 28 27 controlled control VERB aiti-14372 28 28 situations situation NOUN aiti-14372 28 29 at at ADP aiti-14372 28 30 ambient ambient ADJ aiti-14372 28 31 temperature temperature NOUN aiti-14372 28 32 and and CCONJ aiti-14372 28 33 reported report VERB aiti-14372 28 34 a a DET aiti-14372 28 35 decrease decrease NOUN aiti-14372 28 36 in in ADP aiti-14372 28 37 fatigue fatigue NOUN aiti-14372 28 38 life life NOUN aiti-14372 28 39 with with ADP aiti-14372 28 40 increasing increase VERB aiti-14372 28 41 plastic plastic ADJ aiti-14372 28 42 strain strain NOUN aiti-14372 28 43 amplitude amplitude NOUN aiti-14372 28 44 [ [ X aiti-14372 28 45 14 14 NUM aiti-14372 28 46 ] ] PUNCT aiti-14372 28 47 . . PUNCT aiti-14372 29 1 jiang jiang PROPN aiti-14372 29 2 et et PROPN aiti-14372 29 3 al al PROPN aiti-14372 29 4 . . PROPN aiti-14372 29 5 also also ADV aiti-14372 29 6 reported report VERB aiti-14372 29 7 that that SCONJ aiti-14372 29 8 fcg fcg PROPN aiti-14372 29 9 is be AUX aiti-14372 29 10 mostly mostly ADV aiti-14372 29 11 dependent dependent ADJ aiti-14372 29 12 on on ADP aiti-14372 29 13 stress stress NOUN aiti-14372 29 14 intensity intensity NOUN aiti-14372 29 15 range range NOUN aiti-14372 29 16 and and CCONJ aiti-14372 29 17 reported report VERB aiti-14372 29 18 an an DET aiti-14372 29 19 increasing increase VERB aiti-14372 29 20 fcg fcg NOUN aiti-14372 29 21 [ [ X aiti-14372 29 22 15 15 NUM aiti-14372 29 23 ] ] PUNCT aiti-14372 29 24 . . PUNCT aiti-14372 30 1 in in SCONJ aiti-14372 30 2 addition addition NOUN aiti-14372 30 3 to to ADP aiti-14372 30 4 fatigue fatigue NOUN aiti-14372 30 5 load load NOUN aiti-14372 30 6 , , PUNCT aiti-14372 30 7 bonab bonab PROPN aiti-14372 30 8 et et PROPN aiti-14372 30 9 al al PROPN aiti-14372 30 10 . . PROPN aiti-14372 30 11 considered consider VERB aiti-14372 30 12 the the DET aiti-14372 30 13 influence influence NOUN aiti-14372 30 14 of of ADP aiti-14372 30 15 microstructure microstructure NOUN aiti-14372 30 16 on on ADP aiti-14372 30 17 fcg fcg PROPN aiti-14372 30 18 in in ADP aiti-14372 30 19 api api NOUN aiti-14372 30 20 x65 x65 PROPN aiti-14372 30 21 pipeline pipeline PROPN aiti-14372 30 22 steel steel NOUN aiti-14372 30 23 . . PUNCT aiti-14372 31 1 they they PRON aiti-14372 31 2 studied study VERB aiti-14372 31 3 a a DET aiti-14372 31 4 non non ADJ aiti-14372 31 5 - - ADJ aiti-14372 31 6 metallic metallic ADJ aiti-14372 31 7 inclusion inclusion NOUN aiti-14372 31 8 and and CCONJ aiti-14372 31 9 reported report VERB aiti-14372 31 10 crack crack NOUN aiti-14372 31 11 nucleation nucleation NOUN aiti-14372 31 12 after after ADP aiti-14372 31 13 a a DET aiti-14372 31 14 significant significant ADJ aiti-14372 31 15 number number NOUN aiti-14372 31 16 of of ADP aiti-14372 31 17 loading loading NOUN aiti-14372 31 18 cycles cycle NOUN aiti-14372 31 19 [ [ X aiti-14372 31 20 16 16 NUM aiti-14372 31 21 ] ] PUNCT aiti-14372 31 22 . . PUNCT aiti-14372 32 1 in in ADP aiti-14372 32 2 a a DET aiti-14372 32 3 similar similar ADJ aiti-14372 32 4 work work NOUN aiti-14372 32 5 , , PUNCT aiti-14372 32 6 the the DET aiti-14372 32 7 authors author NOUN aiti-14372 32 8 have have AUX aiti-14372 32 9 also also ADV aiti-14372 32 10 studied study VERB aiti-14372 32 11 features feature NOUN aiti-14372 32 12 of of ADP aiti-14372 32 13 intergranular intergranular NOUN aiti-14372 32 14 and and CCONJ aiti-14372 32 15 trans trans ADJ aiti-14372 32 16 - - ADJ aiti-14372 32 17 granular granular ADJ aiti-14372 32 18 fcg fcg NOUN aiti-14372 32 19 and and CCONJ aiti-14372 32 20 observed observe VERB aiti-14372 32 21 an an DET aiti-14372 32 22 accretion accretion NOUN aiti-14372 32 23 of of ADP aiti-14372 32 24 Οƒ3 Οƒ3 ADJ aiti-14372 32 25 boundaries boundary NOUN aiti-14372 32 26 around around ADP aiti-14372 32 27 the the DET aiti-14372 32 28 fatigue fatigue NOUN aiti-14372 32 29 microcracks microcrack NOUN aiti-14372 32 30 as as ADP aiti-14372 32 31 high high ADJ aiti-14372 32 32 - - PUNCT aiti-14372 32 33 energy energy NOUN aiti-14372 32 34 boundaries boundary NOUN aiti-14372 32 35 [ [ X aiti-14372 32 36 17 17 NUM aiti-14372 32 37 ] ] PUNCT aiti-14372 32 38 . . PUNCT aiti-14372 33 1 apart apart ADV aiti-14372 33 2 from from ADP aiti-14372 33 3 external external ADJ aiti-14372 33 4 loading loading NOUN aiti-14372 33 5 and and CCONJ aiti-14372 33 6 inclusion inclusion NOUN aiti-14372 33 7 , , PUNCT aiti-14372 33 8 the the DET aiti-14372 33 9 environmental environmental ADJ aiti-14372 33 10 effect effect NOUN aiti-14372 33 11 on on ADP aiti-14372 33 12 fcg fcg PROPN aiti-14372 33 13 was be AUX aiti-14372 33 14 also also ADV aiti-14372 33 15 studied study VERB aiti-14372 33 16 . . PUNCT aiti-14372 34 1 ronevich ronevich PROPN aiti-14372 34 2 et et PROPN aiti-14372 34 3 al al PROPN aiti-14372 34 4 . . PROPN aiti-14372 35 1 considered consider VERB aiti-14372 35 2 the the DET aiti-14372 35 3 effect effect NOUN aiti-14372 35 4 of of ADP aiti-14372 35 5 microstructure microstructure ADJ aiti-14372 35 6 banding banding NOUN aiti-14372 35 7 on on ADP aiti-14372 35 8 hydrogen hydrogen NOUN aiti-14372 35 9 - - PUNCT aiti-14372 35 10 abetted abet VERB aiti-14372 35 11 fcg fcg NOUN aiti-14372 35 12 in in ADP aiti-14372 35 13 x65 x65 NOUN aiti-14372 35 14 pipeline pipeline NOUN aiti-14372 35 15 steels steel NOUN aiti-14372 35 16 [ [ X aiti-14372 35 17 18 18 NUM aiti-14372 35 18 ] ] PUNCT aiti-14372 35 19 . . PUNCT aiti-14372 36 1 in in ADP aiti-14372 36 2 a a DET aiti-14372 36 3 similar similar ADJ aiti-14372 36 4 work work NOUN aiti-14372 36 5 , , PUNCT aiti-14372 36 6 slifka slifka VERB aiti-14372 36 7 et et PROPN aiti-14372 36 8 al al PROPN aiti-14372 36 9 . . PROPN aiti-14372 37 1 also also ADV aiti-14372 37 2 studied study VERB aiti-14372 37 3 the the DET aiti-14372 37 4 influence influence NOUN aiti-14372 37 5 of of ADP aiti-14372 37 6 microstructure microstructure NOUN aiti-14372 37 7 on on ADP aiti-14372 37 8 the the DET aiti-14372 37 9 hydrogen hydrogen NOUN aiti-14372 37 10 - - PUNCT aiti-14372 37 11 assisted assist VERB aiti-14372 37 12 fcg fcg NOUN aiti-14372 37 13 in in ADP aiti-14372 37 14 pipeline pipeline NOUN aiti-14372 37 15 steel steel NOUN aiti-14372 37 16 and and CCONJ aiti-14372 37 17 reported report VERB aiti-14372 37 18 the the DET aiti-14372 37 19 effect effect NOUN aiti-14372 37 20 of of ADP aiti-14372 37 21 different different ADJ aiti-14372 37 22 microstructures microstructure NOUN aiti-14372 37 23 , , PUNCT aiti-14372 37 24 considering consider VERB aiti-14372 37 25 the the DET aiti-14372 37 26 emphasis emphasis NOUN aiti-14372 37 27 on on ADP aiti-14372 37 28 the the DET aiti-14372 37 29 low low ADJ aiti-14372 37 30 Ξ΄k Ξ΄k PROPN aiti-14372 37 31 regime regime NOUN aiti-14372 37 32 [ [ X aiti-14372 37 33 19 19 NUM aiti-14372 37 34 ] ] PUNCT aiti-14372 37 35 . . PUNCT aiti-14372 38 1 igwemezie igwemezie PROPN aiti-14372 38 2 et et PROPN aiti-14372 38 3 al al PROPN aiti-14372 38 4 . . PROPN aiti-14372 38 5 also also ADV aiti-14372 38 6 studied study VERB aiti-14372 38 7 the the DET aiti-14372 38 8 influence influence NOUN aiti-14372 38 9 of of ADP aiti-14372 38 10 microstructure microstructure NOUN aiti-14372 38 11 on on ADP aiti-14372 38 12 fcgr fcgr NOUN aiti-14372 38 13 in in ADP aiti-14372 38 14 marine marine ADJ aiti-14372 38 15 steels steel NOUN aiti-14372 38 16 , , PUNCT aiti-14372 38 17 considering consider VERB aiti-14372 38 18 the the DET aiti-14372 38 19 paris paris PROPN aiti-14372 38 20 region region NOUN aiti-14372 38 21 of of ADP aiti-14372 38 22 fcg fcg PROPN aiti-14372 38 23 . . PUNCT aiti-14372 39 1 the the DET aiti-14372 39 2 authors author NOUN aiti-14372 39 3 reported report VERB aiti-14372 39 4 that that SCONJ aiti-14372 39 5 the the DET aiti-14372 39 6 crack crack NOUN aiti-14372 39 7 tip tip NOUN aiti-14372 39 8 diversion diversion NOUN aiti-14372 39 9 , , PUNCT aiti-14372 39 10 crack crack VERB aiti-14372 39 11 front front ADJ aiti-14372 39 12 bifurcation bifurcation NOUN aiti-14372 39 13 , , PUNCT aiti-14372 39 14 and and CCONJ aiti-14372 39 15 metal metal NOUN aiti-14372 39 16 crumb crumb NOUN aiti-14372 39 17 formation formation NOUN aiti-14372 39 18 affect affect VERB aiti-14372 39 19 the the DET aiti-14372 39 20 fcgr fcgr NOUN aiti-14372 39 21 [ [ X aiti-14372 39 22 20 20 NUM aiti-14372 39 23 ] ] PUNCT aiti-14372 39 24 . . PUNCT aiti-14372 40 1 sahu sahu PROPN aiti-14372 40 2 et et PROPN aiti-14372 40 3 al al PROPN aiti-14372 40 4 . . PROPN aiti-14372 40 5 predicted predict VERB aiti-14372 40 6 fcgr fcgr NOUN aiti-14372 40 7 for for ADP aiti-14372 40 8 tp316l tp316l PROPN aiti-14372 40 9 stainless stainless ADJ aiti-14372 40 10 steel steel NOUN aiti-14372 40 11 pipe pipe NOUN aiti-14372 40 12 in in ADP aiti-14372 40 13 the the DET aiti-14372 40 14 circumferential circumferential ADJ aiti-14372 40 15 direction direction NOUN aiti-14372 40 16 [ [ X aiti-14372 40 17 21 21 NUM aiti-14372 40 18 ] ] PUNCT aiti-14372 40 19 . . PUNCT aiti-14372 41 1 however however ADV aiti-14372 41 2 , , PUNCT aiti-14372 41 3 they they PRON aiti-14372 41 4 did do AUX aiti-14372 41 5 not not PART aiti-14372 41 6 consider consider VERB aiti-14372 41 7 different different ADJ aiti-14372 41 8 stages stage NOUN aiti-14372 41 9 of of ADP aiti-14372 41 10 fcgr fcgr NOUN aiti-14372 41 11 for for ADP aiti-14372 41 12 modeling modeling NOUN aiti-14372 41 13 . . PUNCT aiti-14372 42 1 it it PRON aiti-14372 42 2 is be AUX aiti-14372 42 3 believed believe VERB aiti-14372 42 4 that that SCONJ aiti-14372 42 5 the the DET aiti-14372 42 6 fatigue fatigue NOUN aiti-14372 42 7 failure failure NOUN aiti-14372 42 8 in in ADP aiti-14372 42 9 pipes pipe NOUN aiti-14372 42 10 is be AUX aiti-14372 42 11 more more ADV aiti-14372 42 12 significant significant ADJ aiti-14372 42 13 in in ADP aiti-14372 42 14 the the DET aiti-14372 42 15 radial radial ADJ aiti-14372 42 16 direction direction NOUN aiti-14372 42 17 and and CCONJ aiti-14372 42 18 that that SCONJ aiti-14372 42 19 a a DET aiti-14372 42 20 break break NOUN aiti-14372 42 21 - - PUNCT aiti-14372 42 22 before before ADP aiti-14372 42 23 - - PUNCT aiti-14372 42 24 leak leak NOUN aiti-14372 42 25 model model NOUN aiti-14372 42 26 is be AUX aiti-14372 42 27 more more ADV aiti-14372 42 28 relevant relevant ADJ aiti-14372 42 29 and and CCONJ aiti-14372 42 30 practical practical ADJ aiti-14372 42 31 for for ADP aiti-14372 42 32 applications application NOUN aiti-14372 42 33 . . PUNCT aiti-14372 43 1 in in ADP aiti-14372 43 2 earlier early ADJ aiti-14372 43 3 work work NOUN aiti-14372 43 4 , , PUNCT aiti-14372 43 5 kumar kumar PROPN aiti-14372 43 6 et et PROPN aiti-14372 43 7 al al PROPN aiti-14372 43 8 . . PROPN aiti-14372 43 9 used use VERB aiti-14372 43 10 an an DET aiti-14372 43 11 exponential exponential ADJ aiti-14372 43 12 model model NOUN aiti-14372 43 13 , , PUNCT aiti-14372 43 14 the the DET aiti-14372 43 15 gamma gamma NOUN aiti-14372 43 16 function function NOUN aiti-14372 43 17 , , PUNCT aiti-14372 43 18 and and CCONJ aiti-14372 43 19 finite finite ADJ aiti-14372 43 20 element element NOUN aiti-14372 43 21 analysis analysis NOUN aiti-14372 43 22 to to PART aiti-14372 43 23 predict predict VERB aiti-14372 43 24 fcgr fcgr NOUN aiti-14372 43 25 in in ADP aiti-14372 43 26 tp316l tp316l PROPN aiti-14372 43 27 stainless stainless ADJ aiti-14372 43 28 steel steel NOUN aiti-14372 43 29 pipe pipe NOUN aiti-14372 43 30 specimens specimen NOUN aiti-14372 44 1 [ [ X aiti-14372 44 2 22 22 NUM aiti-14372 44 3 - - SYM aiti-14372 44 4 24 24 NUM aiti-14372 44 5 ] ] PUNCT aiti-14372 44 6 . . PUNCT aiti-14372 45 1 however however ADV aiti-14372 45 2 , , PUNCT aiti-14372 45 3 the the DET aiti-14372 45 4 modeling modeling NOUN aiti-14372 45 5 was be AUX aiti-14372 45 6 carried carry VERB aiti-14372 45 7 out out ADP aiti-14372 45 8 without without ADP aiti-14372 45 9 considering consider VERB aiti-14372 45 10 the the DET aiti-14372 45 11 different different ADJ aiti-14372 45 12 stages stage NOUN aiti-14372 45 13 of of ADP aiti-14372 45 14 fcgr fcgr NOUN aiti-14372 45 15 . . PUNCT aiti-14372 46 1 also also ADV aiti-14372 46 2 , , PUNCT aiti-14372 46 3 the the DET aiti-14372 46 4 prediction prediction NOUN aiti-14372 46 5 of of ADP aiti-14372 46 6 the the DET aiti-14372 46 7 fcgr fcgr NOUN aiti-14372 46 8 was be AUX aiti-14372 46 9 only only ADV aiti-14372 46 10 for for ADP aiti-14372 46 11 the the DET aiti-14372 46 12 initial initial ADJ aiti-14372 46 13 crack crack NOUN aiti-14372 46 14 propagation propagation NOUN aiti-14372 46 15 . . PUNCT aiti-14372 47 1 the the DET aiti-14372 47 2 model model NOUN aiti-14372 47 3 did do AUX aiti-14372 47 4 not not PART aiti-14372 47 5 address address VERB aiti-14372 47 6 the the DET aiti-14372 47 7 fcgr fcgr NOUN aiti-14372 47 8 when when SCONJ aiti-14372 47 9 the the DET aiti-14372 47 10 crack crack NOUN aiti-14372 47 11 propagation propagation NOUN aiti-14372 47 12 was be AUX aiti-14372 47 13 accelerated accelerate VERB aiti-14372 47 14 with with ADP aiti-14372 47 15 the the DET aiti-14372 47 16 number number NOUN aiti-14372 47 17 of of ADP aiti-14372 47 18 cycles cycle NOUN aiti-14372 47 19 . . PUNCT aiti-14372 48 1 therefore therefore ADV aiti-14372 48 2 , , PUNCT aiti-14372 48 3 it it PRON aiti-14372 48 4 is be AUX aiti-14372 48 5 still still ADV aiti-14372 48 6 unknown unknown ADJ aiti-14372 48 7 whether whether SCONJ aiti-14372 48 8 the the DET aiti-14372 48 9 fcgr fcgr NOUN aiti-14372 48 10 is be AUX aiti-14372 48 11 in in ADP aiti-14372 48 12 accelerated accelerate VERB aiti-14372 48 13 stages stage NOUN aiti-14372 48 14 , , PUNCT aiti-14372 48 15 and and CCONJ aiti-14372 48 16 the the DET aiti-14372 48 17 corresponding correspond VERB aiti-14372 48 18 modeling modeling NOUN aiti-14372 48 19 formulation formulation NOUN aiti-14372 48 20 has have VERB aiti-14372 48 21 yet yet ADV aiti-14372 48 22 to to PART aiti-14372 48 23 be be AUX aiti-14372 48 24 defined define VERB aiti-14372 48 25 . . PUNCT aiti-14372 49 1 further far ADV aiti-14372 49 2 , , PUNCT aiti-14372 49 3 they they PRON aiti-14372 49 4 did do AUX aiti-14372 49 5 not not PART aiti-14372 49 6 address address VERB aiti-14372 49 7 the the DET aiti-14372 49 8 microstructural microstructural ADJ aiti-14372 49 9 features feature NOUN aiti-14372 49 10 of of ADP aiti-14372 49 11 the the DET aiti-14372 49 12 fatigue fatigue NOUN aiti-14372 49 13 - - PUNCT aiti-14372 49 14 fracture fracture NOUN aiti-14372 49 15 surfaces surface NOUN aiti-14372 49 16 . . PUNCT aiti-14372 50 1 hence hence ADV aiti-14372 50 2 , , PUNCT aiti-14372 50 3 it it PRON aiti-14372 50 4 is be AUX aiti-14372 50 5 believed believe VERB aiti-14372 50 6 that that SCONJ aiti-14372 50 7 a a DET aiti-14372 50 8 more more ADV aiti-14372 50 9 comprehensive comprehensive ADJ aiti-14372 50 10 analysis analysis NOUN aiti-14372 50 11 and and CCONJ aiti-14372 50 12 modifications modification NOUN aiti-14372 50 13 are be AUX aiti-14372 50 14 required require VERB aiti-14372 50 15 so so SCONJ aiti-14372 50 16 that that SCONJ aiti-14372 50 17 the the DET aiti-14372 50 18 fcgr fcgr NOUN aiti-14372 50 19 can can AUX aiti-14372 50 20 be be AUX aiti-14372 50 21 predicted predict VERB aiti-14372 50 22 not not PART aiti-14372 50 23 only only ADV aiti-14372 50 24 for for ADP aiti-14372 50 25 the the DET aiti-14372 50 26 initial initial ADJ aiti-14372 50 27 stage stage NOUN aiti-14372 50 28 but but CCONJ aiti-14372 50 29 also also ADV aiti-14372 50 30 for for ADP aiti-14372 50 31 all all DET aiti-14372 50 32 three three NUM aiti-14372 50 33 stages stage NOUN aiti-14372 50 34 of of ADP aiti-14372 50 35 fcg fcg NOUN aiti-14372 50 36 . . PUNCT aiti-14372 51 1 the the DET aiti-14372 51 2 relationship relationship NOUN aiti-14372 51 3 between between ADP aiti-14372 51 4 the the DET aiti-14372 51 5 specific specific ADJ aiti-14372 51 6 growth growth NOUN aiti-14372 51 7 rate rate NOUN aiti-14372 51 8 and and CCONJ aiti-14372 51 9 the the DET aiti-14372 51 10 non non ADJ aiti-14372 51 11 - - ADJ aiti-14372 51 12 dimensional dimensional ADJ aiti-14372 51 13 number number NOUN aiti-14372 51 14 also also ADV aiti-14372 51 15 needs need VERB aiti-14372 51 16 to to PART aiti-14372 51 17 be be AUX aiti-14372 51 18 addressed address VERB aiti-14372 51 19 . . PUNCT aiti-14372 52 1 the the DET aiti-14372 52 2 effect effect NOUN aiti-14372 52 3 of of ADP aiti-14372 52 4 stress stress ADJ aiti-14372 52 5 accumulation accumulation NOUN aiti-14372 52 6 on on ADP aiti-14372 52 7 the the DET aiti-14372 52 8 fatigue fatigue NOUN aiti-14372 52 9 - - PUNCT aiti-14372 52 10 fracture fracture NOUN aiti-14372 52 11 surface surface NOUN aiti-14372 52 12 features feature NOUN aiti-14372 52 13 also also ADV aiti-14372 52 14 needed need VERB aiti-14372 52 15 to to PART aiti-14372 52 16 be be AUX aiti-14372 52 17 analyzed analyze VERB aiti-14372 52 18 . . PUNCT aiti-14372 53 1 therefore therefore ADV aiti-14372 53 2 , , PUNCT aiti-14372 53 3 in in ADP aiti-14372 53 4 the the DET aiti-14372 53 5 present present ADJ aiti-14372 53 6 work work NOUN aiti-14372 53 7 , , PUNCT aiti-14372 53 8 a a DET aiti-14372 53 9 modified modify VERB aiti-14372 53 10 exponential exponential ADJ aiti-14372 53 11 model model NOUN aiti-14372 53 12 is be AUX aiti-14372 53 13 developed develop VERB aiti-14372 53 14 for for ADP aiti-14372 53 15 fatigue fatigue NOUN aiti-14372 53 16 crack crack NOUN aiti-14372 53 17 propagation propagation NOUN aiti-14372 53 18 in in ADP aiti-14372 53 19 through through ADP aiti-14372 53 20 - - PUNCT aiti-14372 53 21 the the DET aiti-14372 53 22 - - PUNCT aiti-14372 53 23 thickness thickness NOUN aiti-14372 53 24 pipe pipe NOUN aiti-14372 53 25 walls wall NOUN aiti-14372 53 26 to to PART aiti-14372 53 27 predict predict VERB aiti-14372 53 28 the the DET aiti-14372 53 29 fcgr fcgr NOUN aiti-14372 53 30 in in ADP aiti-14372 53 31 all all DET aiti-14372 53 32 three three NUM aiti-14372 53 33 distinct distinct ADJ aiti-14372 53 34 stages stage NOUN aiti-14372 53 35 . . PUNCT aiti-14372 54 1 a a DET aiti-14372 54 2 relationship relationship NOUN aiti-14372 54 3 between between ADP aiti-14372 54 4 a a DET aiti-14372 54 5 specific specific ADJ aiti-14372 54 6 growth growth NOUN aiti-14372 54 7 rate rate NOUN aiti-14372 54 8 and and CCONJ aiti-14372 54 9 the the DET aiti-14372 54 10 non non ADJ aiti-14372 54 11 - - ADJ aiti-14372 54 12 dimensional dimensional ADJ aiti-14372 54 13 number number NOUN aiti-14372 54 14 is be AUX aiti-14372 54 15 established establish VERB aiti-14372 54 16 . . PUNCT aiti-14372 55 1 the the DET aiti-14372 55 2 predicted predict VERB aiti-14372 55 3 model model NOUN aiti-14372 55 4 is be AUX aiti-14372 55 5 validated validate VERB aiti-14372 55 6 through through ADP aiti-14372 55 7 the the DET aiti-14372 55 8 experimental experimental ADJ aiti-14372 55 9 data datum NOUN aiti-14372 55 10 obtained obtain VERB aiti-14372 55 11 from from ADP aiti-14372 55 12 a a DET aiti-14372 55 13 four four NUM aiti-14372 55 14 - - PUNCT aiti-14372 55 15 point point NOUN aiti-14372 55 16 bending bend VERB aiti-14372 55 17 test test NOUN aiti-14372 55 18 conducted conduct VERB aiti-14372 55 19 at at ADP aiti-14372 55 20 ambient ambient ADJ aiti-14372 55 21 temperature temperature NOUN aiti-14372 55 22 . . PUNCT aiti-14372 56 1 the the DET aiti-14372 56 2 performance performance NOUN aiti-14372 56 3 of of ADP aiti-14372 56 4 the the DET aiti-14372 56 5 model model NOUN aiti-14372 56 6 is be AUX aiti-14372 56 7 analyzed analyze VERB aiti-14372 56 8 using use VERB aiti-14372 56 9 statistical statistical ADJ aiti-14372 56 10 methods method NOUN aiti-14372 56 11 like like ADP aiti-14372 56 12 mean mean VERB aiti-14372 56 13 absolute absolute ADJ aiti-14372 56 14 error error NOUN aiti-14372 56 15 ( ( PUNCT aiti-14372 56 16 mae mae PROPN aiti-14372 56 17 ) ) PUNCT aiti-14372 56 18 , , PUNCT aiti-14372 56 19 mean mean VERB aiti-14372 56 20 squared square VERB aiti-14372 56 21 error error NOUN aiti-14372 56 22 ( ( PUNCT aiti-14372 56 23 mse mse NOUN aiti-14372 56 24 ) ) PUNCT aiti-14372 56 25 , , PUNCT aiti-14372 56 26 root root NOUN aiti-14372 56 27 mean mean VERB aiti-14372 56 28 square square ADJ aiti-14372 56 29 error error NOUN aiti-14372 56 30 ( ( PUNCT aiti-14372 56 31 rmse rmse NOUN aiti-14372 56 32 ) ) PUNCT aiti-14372 56 33 , , PUNCT aiti-14372 56 34 mean mean VERB aiti-14372 56 35 prediction prediction NOUN aiti-14372 56 36 ratio ratio NOUN aiti-14372 56 37 ( ( PUNCT aiti-14372 56 38 mpr mpr NOUN aiti-14372 56 39 ) ) PUNCT aiti-14372 56 40 , , PUNCT aiti-14372 56 41 mean mean VERB aiti-14372 56 42 % % NOUN aiti-14372 56 43 deviation deviation NOUN aiti-14372 56 44 , , PUNCT aiti-14372 56 45 and and CCONJ aiti-14372 56 46 coefficient coefficient NOUN aiti-14372 56 47 of of ADP aiti-14372 56 48 determination determination NOUN aiti-14372 56 49 ( ( PUNCT aiti-14372 56 50 r2 r2 PROPN aiti-14372 56 51 ) ) PUNCT aiti-14372 56 52 , , PUNCT aiti-14372 56 53 followed follow VERB aiti-14372 56 54 by by ADP aiti-14372 56 55 error error NOUN aiti-14372 56 56 band band NOUN aiti-14372 56 57 scatter scatter NOUN aiti-14372 56 58 analysis analysis NOUN aiti-14372 56 59 . . PUNCT aiti-14372 57 1 the the DET aiti-14372 57 2 microstructural microstructural ADJ aiti-14372 57 3 features feature NOUN aiti-14372 57 4 of of ADP aiti-14372 57 5 the the DET aiti-14372 57 6 fatigue fatigue NOUN aiti-14372 57 7 - - PUNCT aiti-14372 57 8 fractured fracture VERB aiti-14372 57 9 surface surface NOUN aiti-14372 57 10 are be AUX aiti-14372 57 11 studied study VERB aiti-14372 57 12 using use VERB aiti-14372 57 13 standard standard ADJ aiti-14372 57 14 microscopy microscopy NOUN aiti-14372 57 15 characterization characterization NOUN aiti-14372 57 16 . . PUNCT aiti-14372 58 1 2 2 X aiti-14372 58 2 . . X aiti-14372 58 3 materials material NOUN aiti-14372 58 4 and and CCONJ aiti-14372 58 5 methodology methodology NOUN aiti-14372 58 6 the the DET aiti-14372 58 7 tp316l tp316l PROPN aiti-14372 58 8 stainless stainless ADJ aiti-14372 58 9 steel steel NOUN aiti-14372 58 10 pipe pipe NOUN aiti-14372 58 11 was be AUX aiti-14372 58 12 deformed deform VERB aiti-14372 58 13 to to ADP aiti-14372 58 14 large large ADJ aiti-14372 58 15 - - PUNCT aiti-14372 58 16 scale scale NOUN aiti-14372 58 17 plastic plastic NOUN aiti-14372 58 18 deformation deformation NOUN aiti-14372 58 19 under under ADP aiti-14372 58 20 pure pure ADJ aiti-14372 58 21 bending bending NOUN aiti-14372 58 22 using use VERB aiti-14372 58 23 a a DET aiti-14372 58 24 servohydraulic servohydraulic ADJ aiti-14372 58 25 dynamic dynamic ADJ aiti-14372 58 26 testing testing NOUN aiti-14372 58 27 apparatus apparatus NOUN aiti-14372 58 28 ( ( PUNCT aiti-14372 58 29 instron instron PROPN aiti-14372 58 30 8800 8800 NUM aiti-14372 58 31 ) ) PUNCT aiti-14372 58 32 . . PUNCT aiti-14372 59 1 the the DET aiti-14372 59 2 four four NUM aiti-14372 59 3 - - PUNCT aiti-14372 59 4 point point NOUN aiti-14372 59 5 bending bend VERB aiti-14372 59 6 test test NOUN aiti-14372 59 7 setup setup NOUN aiti-14372 59 8 and and CCONJ aiti-14372 59 9 the the DET aiti-14372 59 10 pipe pipe NOUN aiti-14372 59 11 specimen speciman NOUN aiti-14372 59 12 with with ADP aiti-14372 59 13 a a DET aiti-14372 59 14 centrally centrally ADV aiti-14372 59 15 attached attach VERB aiti-14372 59 16 crack crack NOUN aiti-14372 59 17 opening open VERB aiti-14372 59 18 displacement displacement NOUN aiti-14372 59 19 ( ( PUNCT aiti-14372 59 20 cod cod NOUN aiti-14372 59 21 ) ) PUNCT aiti-14372 59 22 gauge gauge NOUN aiti-14372 59 23 on on ADP aiti-14372 59 24 a a DET aiti-14372 59 25 servo servo NOUN aiti-14372 59 26 - - PUNCT aiti-14372 59 27 hydraulic hydraulic ADJ aiti-14372 59 28 universal universal ADJ aiti-14372 59 29 testing testing NOUN aiti-14372 59 30 apparatus apparatus NOUN aiti-14372 59 31 ( ( PUNCT aiti-14372 59 32 instron instron PROPN aiti-14372 59 33 8800 8800 NUM aiti-14372 59 34 ) ) PUNCT aiti-14372 59 35 are be AUX aiti-14372 59 36 shown show VERB aiti-14372 59 37 in in ADP aiti-14372 59 38 fig fig NOUN aiti-14372 59 39 . . PUNCT aiti-14372 60 1 1 1 NUM aiti-14372 61 1 [ [ SYM aiti-14372 61 2 22 22 NUM aiti-14372 61 3 - - SYM aiti-14372 61 4 23 23 NUM aiti-14372 61 5 ] ] PUNCT aiti-14372 61 6 . . PUNCT aiti-14372 62 1 however however ADV aiti-14372 62 2 , , PUNCT aiti-14372 62 3 the the DET aiti-14372 62 4 representation representation NOUN aiti-14372 62 5 of of ADP aiti-14372 62 6 the the DET aiti-14372 62 7 cross cross ADJ aiti-14372 62 8 - - ADJ aiti-14372 62 9 sectional sectional ADJ aiti-14372 62 10 view view NOUN aiti-14372 62 11 of of ADP aiti-14372 62 12 the the DET aiti-14372 62 13 pipe pipe NOUN aiti-14372 62 14 specimen speciman NOUN aiti-14372 62 15 and and CCONJ aiti-14372 62 16 constant constant ADJ aiti-14372 62 17 amplitude amplitude NOUN aiti-14372 62 18 loading loading NOUN aiti-14372 62 19 advances advance NOUN aiti-14372 62 20 in in ADP aiti-14372 62 21 technology technology NOUN aiti-14372 62 22 innovation innovation NOUN aiti-14372 62 23 , , PUNCT aiti-14372 62 24 vol vol NOUN aiti-14372 62 25 . . PROPN aiti-14372 62 26 10 10 NUM aiti-14372 62 27 , , PUNCT aiti-14372 62 28 no no INTJ aiti-14372 62 29 . . NOUN aiti-14372 62 30 3 3 NUM aiti-14372 62 31 , , PUNCT aiti-14372 62 32 2025 2025 NUM aiti-14372 62 33 , , PUNCT aiti-14372 62 34 pp pp ADJ aiti-14372 62 35 . . PUNCT aiti-14372 63 1 238 238 NUM aiti-14372 63 2 - - SYM aiti-14372 63 3 253 253 NUM aiti-14372 63 4 240 240 NUM aiti-14372 63 5 condition condition NOUN aiti-14372 63 6 is be AUX aiti-14372 63 7 shown show VERB aiti-14372 63 8 in in ADP aiti-14372 63 9 fig fig NOUN aiti-14372 63 10 . . PUNCT aiti-14372 64 1 2 2 NUM aiti-14372 64 2 and and CCONJ aiti-14372 64 3 fig fig NOUN aiti-14372 64 4 . . PUNCT aiti-14372 65 1 3 3 NUM aiti-14372 65 2 , , PUNCT aiti-14372 65 3 respectively respectively ADV aiti-14372 65 4 . . PUNCT aiti-14372 66 1 the the DET aiti-14372 66 2 specimen speciman NOUN aiti-14372 66 3 dimensions dimension NOUN aiti-14372 66 4 exhibiting exhibit VERB aiti-14372 66 5 inner inner ADJ aiti-14372 66 6 radius radius NOUN aiti-14372 66 7 , , PUNCT aiti-14372 66 8 outer outer ADJ aiti-14372 66 9 radius radius NOUN aiti-14372 66 10 , , PUNCT aiti-14372 66 11 thickness thickness NOUN aiti-14372 66 12 ( ( PUNCT aiti-14372 66 13 in in ADP aiti-14372 66 14 the the DET aiti-14372 66 15 radial radial ADJ aiti-14372 66 16 direction direction NOUN aiti-14372 66 17 ) ) PUNCT aiti-14372 66 18 , , PUNCT aiti-14372 66 19 span span NOUN aiti-14372 66 20 of of ADP aiti-14372 66 21 the the DET aiti-14372 66 22 support support NOUN aiti-14372 66 23 rollers roller NOUN aiti-14372 66 24 , , PUNCT aiti-14372 66 25 span span NOUN aiti-14372 66 26 of of ADP aiti-14372 66 27 the the DET aiti-14372 66 28 load load NOUN aiti-14372 66 29 rollers roller NOUN aiti-14372 66 30 , , PUNCT aiti-14372 66 31 and and CCONJ aiti-14372 66 32 the the DET aiti-14372 66 33 end end NOUN aiti-14372 66 34 clearance clearance NOUN aiti-14372 66 35 are be AUX aiti-14372 66 36 presented present VERB aiti-14372 66 37 in in ADP aiti-14372 66 38 table table NOUN aiti-14372 66 39 1 1 NUM aiti-14372 66 40 . . PUNCT aiti-14372 67 1 the the DET aiti-14372 67 2 mechanical mechanical ADJ aiti-14372 67 3 properties property NOUN aiti-14372 67 4 of of ADP aiti-14372 67 5 the the DET aiti-14372 67 6 tp316l tp316l PROPN aiti-14372 67 7 stainless stainless ADJ aiti-14372 67 8 steel steel NOUN aiti-14372 67 9 are be AUX aiti-14372 67 10 presented present VERB aiti-14372 67 11 in in ADP aiti-14372 67 12 table table NOUN aiti-14372 67 13 2 2 NUM aiti-14372 67 14 . . PUNCT aiti-14372 67 15 fig fig NOUN aiti-14372 67 16 . . PUNCT aiti-14372 68 1 1 1 NUM aiti-14372 68 2 four four NUM aiti-14372 68 3 - - PUNCT aiti-14372 68 4 point point NOUN aiti-14372 68 5 bending bend VERB aiti-14372 68 6 test test NOUN aiti-14372 68 7 setup setup NOUN aiti-14372 68 8 the the DET aiti-14372 68 9 four four NUM aiti-14372 68 10 - - PUNCT aiti-14372 68 11 point point NOUN aiti-14372 68 12 bending bend VERB aiti-14372 68 13 test test NOUN aiti-14372 68 14 was be AUX aiti-14372 68 15 conducted conduct VERB aiti-14372 68 16 considering consider VERB aiti-14372 68 17 a a DET aiti-14372 68 18 sinusoidal sinusoidal ADJ aiti-14372 68 19 load load NOUN aiti-14372 68 20 of of ADP aiti-14372 68 21 22.5 22.5 NUM aiti-14372 68 22 kn kn NOUN aiti-14372 68 23 , , PUNCT aiti-14372 68 24 a a DET aiti-14372 68 25 stress stress NOUN aiti-14372 68 26 ratio ratio NOUN aiti-14372 68 27 of of ADP aiti-14372 68 28 0.1 0.1 NUM aiti-14372 68 29 , , PUNCT aiti-14372 68 30 and and CCONJ aiti-14372 68 31 a a DET aiti-14372 68 32 frequency frequency NOUN aiti-14372 68 33 of of ADP aiti-14372 68 34 4 4 NUM aiti-14372 68 35 hz hz ADJ aiti-14372 68 36 was be AUX aiti-14372 68 37 applied apply VERB aiti-14372 68 38 to to ADP aiti-14372 68 39 the the DET aiti-14372 68 40 specimen speciman NOUN aiti-14372 68 41 . . PUNCT aiti-14372 69 1 the the DET aiti-14372 69 2 four four NUM aiti-14372 69 3 - - PUNCT aiti-14372 69 4 point point NOUN aiti-14372 69 5 bending bend VERB aiti-14372 69 6 test test NOUN aiti-14372 69 7 was be AUX aiti-14372 69 8 conducted conduct VERB aiti-14372 69 9 at at ADP aiti-14372 69 10 ambient ambient ADJ aiti-14372 69 11 temperature temperature NOUN aiti-14372 69 12 . . PUNCT aiti-14372 70 1 the the DET aiti-14372 70 2 distance distance NOUN aiti-14372 70 3 of of ADP aiti-14372 70 4 the the DET aiti-14372 70 5 load load NOUN aiti-14372 70 6 line line NOUN aiti-14372 70 7 and and CCONJ aiti-14372 70 8 reaction reaction NOUN aiti-14372 70 9 force force NOUN aiti-14372 70 10 was be AUX aiti-14372 70 11 110 110 NUM aiti-14372 70 12 mm mm NOUN aiti-14372 70 13 and and CCONJ aiti-14372 70 14 225 225 NUM aiti-14372 70 15 mm mm NOUN aiti-14372 70 16 , , PUNCT aiti-14372 70 17 respectively respectively ADV aiti-14372 70 18 , , PUNCT aiti-14372 70 19 from from ADP aiti-14372 70 20 the the DET aiti-14372 70 21 center center NOUN aiti-14372 70 22 of of ADP aiti-14372 70 23 the the DET aiti-14372 70 24 pre pre NOUN aiti-14372 70 25 - - NOUN aiti-14372 70 26 notch notch ADJ aiti-14372 70 27 . . PUNCT aiti-14372 71 1 the the DET aiti-14372 71 2 pre pre ADJ aiti-14372 71 3 - - ADJ aiti-14372 71 4 notch notch ADJ aiti-14372 71 5 had have VERB aiti-14372 71 6 a a DET aiti-14372 71 7 semi semi ADJ aiti-14372 71 8 - - ADJ aiti-14372 71 9 elliptical elliptical ADJ aiti-14372 71 10 geometry geometry NOUN aiti-14372 71 11 with with ADP aiti-14372 71 12 the the DET aiti-14372 71 13 length length NOUN aiti-14372 71 14 of of ADP aiti-14372 71 15 the the DET aiti-14372 71 16 major major ADJ aiti-14372 71 17 axis axis NOUN aiti-14372 71 18 22.96 22.96 NUM aiti-14372 71 19 mm mm NOUN aiti-14372 71 20 , , PUNCT aiti-14372 71 21 and and CCONJ aiti-14372 71 22 the the DET aiti-14372 71 23 semi semi ADJ aiti-14372 71 24 - - ADJ aiti-14372 71 25 minor minor ADJ aiti-14372 71 26 axis axis NOUN aiti-14372 71 27 ( ( PUNCT aiti-14372 71 28 in in ADP aiti-14372 71 29 the the DET aiti-14372 71 30 radial radial ADJ aiti-14372 71 31 direction direction NOUN aiti-14372 71 32 of of ADP aiti-14372 71 33 the the DET aiti-14372 71 34 pipe pipe NOUN aiti-14372 71 35 ) ) PUNCT aiti-14372 71 36 2.28 2.28 NUM aiti-14372 71 37 mm mm NOUN aiti-14372 71 38 . . PUNCT aiti-14372 71 39 fig fig NOUN aiti-14372 71 40 . . PUNCT aiti-14372 72 1 2 2 NUM aiti-14372 72 2 cross cross ADJ aiti-14372 72 3 - - ADJ aiti-14372 72 4 sectional sectional ADJ aiti-14372 72 5 view view NOUN aiti-14372 72 6 of of ADP aiti-14372 72 7 the the DET aiti-14372 72 8 pipe pipe NOUN aiti-14372 72 9 specimen speciman NOUN aiti-14372 72 10 fig fig NOUN aiti-14372 72 11 . . PUNCT aiti-14372 73 1 3 3 NUM aiti-14372 73 2 constant constant ADJ aiti-14372 73 3 amplitude amplitude NOUN aiti-14372 73 4 loading loading NOUN aiti-14372 73 5 condition condition NOUN aiti-14372 73 6 in in ADP aiti-14372 73 7 four four NUM aiti-14372 73 8 - - PUNCT aiti-14372 73 9 point point NOUN aiti-14372 73 10 bending bending NOUN aiti-14372 73 11 advances advance NOUN aiti-14372 73 12 in in ADP aiti-14372 73 13 technology technology NOUN aiti-14372 73 14 innovation innovation NOUN aiti-14372 73 15 , , PUNCT aiti-14372 73 16 vol vol NOUN aiti-14372 73 17 . . PROPN aiti-14372 73 18 10 10 NUM aiti-14372 73 19 , , PUNCT aiti-14372 73 20 no no INTJ aiti-14372 73 21 . . NOUN aiti-14372 73 22 3 3 NUM aiti-14372 73 23 , , PUNCT aiti-14372 73 24 2025 2025 NUM aiti-14372 73 25 , , PUNCT aiti-14372 73 26 pp pp ADJ aiti-14372 73 27 . . PUNCT aiti-14372 74 1 238 238 NUM aiti-14372 74 2 - - SYM aiti-14372 74 3 253 253 NUM aiti-14372 74 4 241 241 NUM aiti-14372 74 5 the the DET aiti-14372 74 6 fcg fcg PROPN aiti-14372 74 7 data datum NOUN aiti-14372 74 8 in in ADP aiti-14372 74 9 terms term NOUN aiti-14372 74 10 of of ADP aiti-14372 74 11 crack crack NOUN aiti-14372 74 12 length length NOUN aiti-14372 74 13 ( ( PUNCT aiti-14372 74 14 a a NOUN aiti-14372 74 15 ) ) PUNCT aiti-14372 74 16 and and CCONJ aiti-14372 74 17 number number NOUN aiti-14372 74 18 of of ADP aiti-14372 74 19 loading loading NOUN aiti-14372 74 20 cycles cycle NOUN aiti-14372 74 21 ( ( PUNCT aiti-14372 74 22 n n CCONJ aiti-14372 74 23 ) ) PUNCT aiti-14372 74 24 was be AUX aiti-14372 74 25 monitored monitor VERB aiti-14372 74 26 using use VERB aiti-14372 74 27 a a DET aiti-14372 74 28 crack crack NOUN aiti-14372 74 29 opening open VERB aiti-14372 74 30 displacement displacement NOUN aiti-14372 74 31 ( ( PUNCT aiti-14372 74 32 cod cod NOUN aiti-14372 74 33 ) ) PUNCT aiti-14372 74 34 gauge gauge NOUN aiti-14372 74 35 and and CCONJ aiti-14372 74 36 processor processor NOUN aiti-14372 74 37 . . PUNCT aiti-14372 75 1 the the DET aiti-14372 75 2 cod cod NOUN aiti-14372 75 3 gauge gauge NOUN aiti-14372 75 4 was be AUX aiti-14372 75 5 mounted mount VERB aiti-14372 75 6 at at ADP aiti-14372 75 7 the the DET aiti-14372 75 8 crack crack NOUN aiti-14372 75 9 mouth mouth NOUN aiti-14372 75 10 with with ADP aiti-14372 75 11 suitable suitable ADJ aiti-14372 75 12 knife knife NOUN aiti-14372 75 13 edges edge NOUN aiti-14372 75 14 . . PUNCT aiti-14372 76 1 since since SCONJ aiti-14372 76 2 there there PRON aiti-14372 76 3 is be VERB aiti-14372 76 4 no no DET aiti-14372 76 5 direct direct ADJ aiti-14372 76 6 crack crack NOUN aiti-14372 76 7 - - PUNCT aiti-14372 76 8 compliance compliance NOUN aiti-14372 76 9 correlation correlation NOUN aiti-14372 76 10 available available ADJ aiti-14372 76 11 for for ADP aiti-14372 76 12 the the DET aiti-14372 76 13 measurement measurement NOUN aiti-14372 76 14 of of ADP aiti-14372 76 15 the the DET aiti-14372 76 16 fcg fcg NOUN aiti-14372 76 17 in in ADP aiti-14372 76 18 part part NOUN aiti-14372 76 19 - - PUNCT aiti-14372 76 20 through through ADP aiti-14372 76 21 cracked crack VERB aiti-14372 76 22 pipes pipe NOUN aiti-14372 76 23 , , PUNCT aiti-14372 76 24 the the DET aiti-14372 76 25 cod cod NOUN aiti-14372 76 26 gauge gauge NOUN aiti-14372 76 27 was be AUX aiti-14372 76 28 calibrated calibrate VERB aiti-14372 76 29 to to PART aiti-14372 76 30 find find VERB aiti-14372 76 31 the the DET aiti-14372 76 32 correlation correlation NOUN aiti-14372 76 33 between between ADP aiti-14372 76 34 radial radial ADJ aiti-14372 76 35 crack crack NOUN aiti-14372 76 36 lengths length NOUN aiti-14372 76 37 and and CCONJ aiti-14372 76 38 Ξ΄cod Ξ΄cod NOUN aiti-14372 76 39 output output NOUN aiti-14372 77 1 [ [ X aiti-14372 77 2 22 22 NUM aiti-14372 77 3 - - SYM aiti-14372 77 4 23 23 NUM aiti-14372 77 5 ] ] PUNCT aiti-14372 77 6 . . PUNCT aiti-14372 78 1 the the DET aiti-14372 78 2 calibration calibration NOUN aiti-14372 78 3 curves curve NOUN aiti-14372 78 4 thus thus ADV aiti-14372 78 5 obtained obtain VERB aiti-14372 78 6 have have AUX aiti-14372 78 7 been be AUX aiti-14372 78 8 utilized utilize VERB aiti-14372 78 9 for for ADP aiti-14372 78 10 the the DET aiti-14372 78 11 indirect indirect ADJ aiti-14372 78 12 measurement measurement NOUN aiti-14372 78 13 of of ADP aiti-14372 78 14 the the DET aiti-14372 78 15 crack crack NOUN aiti-14372 78 16 lengths length NOUN aiti-14372 78 17 in in ADP aiti-14372 78 18 the the DET aiti-14372 78 19 radial radial ADJ aiti-14372 78 20 direction direction NOUN aiti-14372 78 21 . . PUNCT aiti-14372 79 1 the the DET aiti-14372 79 2 microstructural microstructural ADJ aiti-14372 79 3 characterization characterization NOUN aiti-14372 79 4 of of ADP aiti-14372 79 5 the the DET aiti-14372 79 6 fatigue fatigue NOUN aiti-14372 79 7 - - PUNCT aiti-14372 79 8 fractured fracture VERB aiti-14372 79 9 pipe pipe NOUN aiti-14372 79 10 specimen speciman NOUN aiti-14372 79 11 was be AUX aiti-14372 79 12 carried carry VERB aiti-14372 79 13 out out ADP aiti-14372 79 14 using use VERB aiti-14372 79 15 a a DET aiti-14372 79 16 jeol jeol PROPN aiti-14372 79 17 jsm-6480 jsm-6480 NOUN aiti-14372 80 1 lv lv PROPN aiti-14372 80 2 scanning scan VERB aiti-14372 80 3 electron electron NOUN aiti-14372 80 4 microscope microscope NOUN aiti-14372 80 5 ( ( PUNCT aiti-14372 80 6 sem sem NOUN aiti-14372 80 7 ) ) PUNCT aiti-14372 80 8 . . PUNCT aiti-14372 81 1 the the DET aiti-14372 81 2 samples sample NOUN aiti-14372 81 3 for for ADP aiti-14372 81 4 sem sem ADJ aiti-14372 81 5 analysis analysis NOUN aiti-14372 81 6 were be AUX aiti-14372 81 7 prepared prepare VERB aiti-14372 81 8 as as ADP aiti-14372 81 9 per per ADP aiti-14372 81 10 the the DET aiti-14372 81 11 regular regular ADJ aiti-14372 81 12 metallographic metallographic ADJ aiti-14372 81 13 procedures procedure NOUN aiti-14372 81 14 . . PUNCT aiti-14372 82 1 the the DET aiti-14372 82 2 mounted mount VERB aiti-14372 82 3 samples sample NOUN aiti-14372 82 4 were be AUX aiti-14372 82 5 mechanically mechanically ADV aiti-14372 82 6 polished polished ADJ aiti-14372 82 7 using use VERB aiti-14372 82 8 the the DET aiti-14372 82 9 emery emery NOUN aiti-14372 82 10 papers paper NOUN aiti-14372 82 11 with with ADP aiti-14372 82 12 grit grit NOUN aiti-14372 82 13 levels level NOUN aiti-14372 82 14 ranging range VERB aiti-14372 82 15 from from ADP aiti-14372 82 16 100 100 NUM aiti-14372 82 17 - - SYM aiti-14372 82 18 500 500 NUM aiti-14372 82 19 Β΅m Β΅m NOUN aiti-14372 82 20 , , PUNCT aiti-14372 82 21 followed follow VERB aiti-14372 82 22 by by ADP aiti-14372 82 23 cloth cloth NOUN aiti-14372 82 24 polishing polishing NOUN aiti-14372 82 25 using use VERB aiti-14372 82 26 a a DET aiti-14372 82 27 tegrapol tegrapol NOUN aiti-14372 82 28 polishing polish VERB aiti-14372 82 29 apparatus apparatus NOUN aiti-14372 82 30 . . PUNCT aiti-14372 83 1 the the DET aiti-14372 83 2 polishing polish VERB aiti-14372 83 3 grit grit NOUN aiti-14372 83 4 in in ADP aiti-14372 83 5 the the DET aiti-14372 83 6 size size NOUN aiti-14372 83 7 sequence sequence NOUN aiti-14372 83 8 of of ADP aiti-14372 83 9 9 9 NUM aiti-14372 83 10 Β΅ Β΅ NOUN aiti-14372 83 11 , , PUNCT aiti-14372 83 12 3 3 NUM aiti-14372 83 13 Β΅ Β΅ NUM aiti-14372 83 14 , , PUNCT aiti-14372 83 15 and and CCONJ aiti-14372 83 16 1 1 NUM aiti-14372 83 17 Β΅ Β΅ NOUN aiti-14372 83 18 was be AUX aiti-14372 83 19 used use VERB aiti-14372 83 20 for for ADP aiti-14372 83 21 mechanical mechanical ADJ aiti-14372 83 22 polishing polishing NOUN aiti-14372 83 23 . . PUNCT aiti-14372 84 1 table table NOUN aiti-14372 84 2 1 1 NUM aiti-14372 84 3 specimen speciman NOUN aiti-14372 84 4 dimensions dimension NOUN aiti-14372 84 5 [ [ X aiti-14372 84 6 22 22 NUM aiti-14372 84 7 - - SYM aiti-14372 84 8 23 23 NUM aiti-14372 84 9 ] ] PUNCT aiti-14372 84 10 outer outer ADJ aiti-14372 84 11 radius radius NOUN aiti-14372 84 12 ( ( PUNCT aiti-14372 84 13 ro ro NOUN aiti-14372 84 14 ) ) PUNCT aiti-14372 84 15 inner inner ADJ aiti-14372 84 16 radius radius NOUN aiti-14372 84 17 ( ( PUNCT aiti-14372 84 18 ri ri NOUN aiti-14372 84 19 ) ) PUNCT aiti-14372 84 20 thickness thickness NOUN aiti-14372 84 21 ( ( PUNCT aiti-14372 84 22 t t NOUN aiti-14372 84 23 ) ) PUNCT aiti-14372 84 24 span span NOUN aiti-14372 84 25 of of ADP aiti-14372 84 26 the the DET aiti-14372 84 27 support support NOUN aiti-14372 84 28 rollers roller NOUN aiti-14372 84 29 span span NOUN aiti-14372 84 30 of of ADP aiti-14372 84 31 the the DET aiti-14372 84 32 load load NOUN aiti-14372 84 33 rollers roller NOUN aiti-14372 84 34 end end NOUN aiti-14372 84 35 clearance clearance NOUN aiti-14372 84 36 30 30 NUM aiti-14372 84 37 mm mm NOUN aiti-14372 84 38 21 21 NUM aiti-14372 84 39 mm mm NOUN aiti-14372 84 40 9 9 NUM aiti-14372 84 41 mm mm NOUN aiti-14372 84 42 450 450 NUM aiti-14372 84 43 mm mm NOUN aiti-14372 84 44 220 220 NUM aiti-14372 84 45 mm mm NOUN aiti-14372 84 46 25 25 NUM aiti-14372 84 47 mm mm NOUN aiti-14372 84 48 table table NOUN aiti-14372 84 49 2 2 NUM aiti-14372 84 50 mechanical mechanical ADJ aiti-14372 84 51 properties property NOUN aiti-14372 84 52 of of ADP aiti-14372 84 53 tp tp ADP aiti-14372 84 54 316l 316l NUM aiti-14372 84 55 stainless stainless ADJ aiti-14372 84 56 steel steel NOUN aiti-14372 85 1 [ [ X aiti-14372 85 2 22 22 NUM aiti-14372 85 3 - - SYM aiti-14372 85 4 23 23 NUM aiti-14372 85 5 ] ] PUNCT aiti-14372 85 6 material material NOUN aiti-14372 85 7 modulus modulus NOUN aiti-14372 85 8 of of ADP aiti-14372 85 9 elasticity elasticity NOUN aiti-14372 85 10 ( ( PUNCT aiti-14372 85 11 e e NOUN aiti-14372 85 12 ) ) PUNCT aiti-14372 85 13 poisson poisson PROPN aiti-14372 85 14 ’s ’s PART aiti-14372 85 15 ratio ratio NOUN aiti-14372 85 16 ( ( PUNCT aiti-14372 85 17 Β΅ Β΅ NOUN aiti-14372 85 18 ) ) PUNCT aiti-14372 85 19 yield yield NOUN aiti-14372 85 20 strength strength NOUN aiti-14372 85 21 ( ( PUNCT aiti-14372 85 22 Οƒys Οƒys PROPN aiti-14372 85 23 ) ) PUNCT aiti-14372 85 24 ultimate ultimate ADJ aiti-14372 85 25 tensile tensile NOUN aiti-14372 85 26 strength strength NOUN aiti-14372 85 27 ( ( PUNCT aiti-14372 85 28 Οƒut Οƒut NOUN aiti-14372 85 29 ) ) PUNCT aiti-14372 85 30 316l 316l PROPN aiti-14372 85 31 stainless stainless ADJ aiti-14372 85 32 steel steel NOUN aiti-14372 85 33 220 220 NUM aiti-14372 85 34 gpa gpa PROPN aiti-14372 85 35 0.3 0.3 NUM aiti-14372 85 36 366 366 NUM aiti-14372 85 37 mpa mpa NOUN aiti-14372 85 38 611 611 NUM aiti-14372 85 39 mpa mpa NOUN aiti-14372 85 40 3 3 NUM aiti-14372 85 41 . . NOUN aiti-14372 85 42 results result NOUN aiti-14372 85 43 and and CCONJ aiti-14372 85 44 discussion discussion NOUN aiti-14372 85 45 this this DET aiti-14372 85 46 section section NOUN aiti-14372 85 47 describes describe VERB aiti-14372 85 48 the the DET aiti-14372 85 49 stress stress NOUN aiti-14372 85 50 intensity intensity NOUN aiti-14372 85 51 factor factor NOUN aiti-14372 85 52 and and CCONJ aiti-14372 85 53 its its PRON aiti-14372 85 54 influence influence NOUN aiti-14372 85 55 on on ADP aiti-14372 85 56 crack crack NOUN aiti-14372 85 57 propagation propagation NOUN aiti-14372 85 58 . . PUNCT aiti-14372 86 1 the the DET aiti-14372 86 2 fatigue fatigue NOUN aiti-14372 86 3 crack crack VERB aiti-14372 86 4 growth growth NOUN aiti-14372 86 5 rates rate NOUN aiti-14372 86 6 in in ADP aiti-14372 86 7 stagesi stagesi PROPN aiti-14372 86 8 , , PUNCT aiti-14372 86 9 ii ii PROPN aiti-14372 86 10 , , PUNCT aiti-14372 86 11 and and CCONJ aiti-14372 86 12 iii iii NOUN aiti-14372 86 13 are be AUX aiti-14372 86 14 defined define VERB aiti-14372 86 15 . . PUNCT aiti-14372 87 1 the the DET aiti-14372 87 2 modelling modelling NOUN aiti-14372 87 3 of of ADP aiti-14372 87 4 fcgr fcgr NOUN aiti-14372 87 5 for for ADP aiti-14372 87 6 all all DET aiti-14372 87 7 three three NUM aiti-14372 87 8 stages stage NOUN aiti-14372 87 9 is be AUX aiti-14372 87 10 formulated formulate VERB aiti-14372 87 11 with with ADP aiti-14372 87 12 a a DET aiti-14372 87 13 modification modification NOUN aiti-14372 87 14 to to ADP aiti-14372 87 15 the the DET aiti-14372 87 16 exponential exponential ADJ aiti-14372 87 17 function function NOUN aiti-14372 87 18 . . PUNCT aiti-14372 88 1 it it PRON aiti-14372 88 2 is be AUX aiti-14372 88 3 then then ADV aiti-14372 88 4 followed follow VERB aiti-14372 88 5 by by ADP aiti-14372 88 6 a a DET aiti-14372 88 7 performance performance NOUN aiti-14372 88 8 evaluation evaluation NOUN aiti-14372 88 9 and and CCONJ aiti-14372 88 10 comparison comparison NOUN aiti-14372 88 11 with with ADP aiti-14372 88 12 earlier early ADJ aiti-14372 88 13 developed develop VERB aiti-14372 88 14 models model NOUN aiti-14372 88 15 . . PUNCT aiti-14372 89 1 the the DET aiti-14372 89 2 microstructural microstructural ADJ aiti-14372 89 3 features feature NOUN aiti-14372 89 4 are be AUX aiti-14372 89 5 discussed discuss VERB aiti-14372 89 6 to to PART aiti-14372 89 7 characterize characterize VERB aiti-14372 89 8 fatigue fatigue NOUN aiti-14372 89 9 crack crack NOUN aiti-14372 89 10 propagation propagation NOUN aiti-14372 89 11 . . PUNCT aiti-14372 90 1 3.1 3.1 NUM aiti-14372 90 2 . . PUNCT aiti-14372 90 3 stress stress NOUN aiti-14372 90 4 intensity intensity NOUN aiti-14372 90 5 factor factor NOUN aiti-14372 90 6 and and CCONJ aiti-14372 90 7 crack crack VERB aiti-14372 90 8 propagation propagation NOUN aiti-14372 90 9 the the DET aiti-14372 90 10 fcg fcg PROPN aiti-14372 90 11 data datum NOUN aiti-14372 90 12 was be AUX aiti-14372 90 13 generated generate VERB aiti-14372 90 14 using use VERB aiti-14372 90 15 the the DET aiti-14372 90 16 instron instron PROPN aiti-14372 90 17 8800 8800 NUM aiti-14372 90 18 apparatus apparatus NOUN aiti-14372 90 19 . . PUNCT aiti-14372 91 1 the the DET aiti-14372 91 2 increase increase NOUN aiti-14372 91 3 in in ADP aiti-14372 91 4 a a PRON aiti-14372 91 5 with with ADP aiti-14372 91 6 n n NUM aiti-14372 91 7 was be AUX aiti-14372 91 8 recorded record VERB aiti-14372 91 9 . . PUNCT aiti-14372 92 1 the the DET aiti-14372 92 2 stress stress NOUN aiti-14372 92 3 intensity intensity NOUN aiti-14372 92 4 factor factor NOUN aiti-14372 92 5 ( ( PUNCT aiti-14372 92 6 k k NOUN aiti-14372 92 7 ) ) PUNCT aiti-14372 92 8 , , PUNCT aiti-14372 92 9 considering consider VERB aiti-14372 92 10 the the DET aiti-14372 92 11 mean mean NOUN aiti-14372 92 12 of of ADP aiti-14372 92 13 5 5 NUM aiti-14372 92 14 specimens specimen NOUN aiti-14372 92 15 under under ADP aiti-14372 92 16 pure pure ADJ aiti-14372 92 17 bending bending NOUN aiti-14372 92 18 , , PUNCT aiti-14372 92 19 with with ADP aiti-14372 92 20 corresponding correspond VERB aiti-14372 92 21 a a PRON aiti-14372 92 22 and and CCONJ aiti-14372 92 23 n n CCONJ aiti-14372 92 24 , , PUNCT aiti-14372 92 25 is be AUX aiti-14372 92 26 shown show VERB aiti-14372 92 27 in in ADP aiti-14372 92 28 fig fig NOUN aiti-14372 92 29 . . PUNCT aiti-14372 93 1 4 4 X aiti-14372 93 2 . . X aiti-14372 93 3 the the DET aiti-14372 93 4 theoretical theoretical ADJ aiti-14372 93 5 k k PROPN aiti-14372 93 6 indexes index NOUN aiti-14372 93 7 the the DET aiti-14372 93 8 pre pre ADJ aiti-14372 93 9 - - ADJ aiti-14372 93 10 notch notch ADJ aiti-14372 93 11 stress stress NOUN aiti-14372 93 12 field field NOUN aiti-14372 93 13 singularity singularity NOUN aiti-14372 93 14 by by ADP aiti-14372 93 15 delineating delineate VERB aiti-14372 93 16 the the DET aiti-14372 93 17 stress stress NOUN aiti-14372 93 18 field field NOUN aiti-14372 93 19 in in ADP aiti-14372 93 20 the the DET aiti-14372 93 21 vicinity vicinity NOUN aiti-14372 93 22 of of ADP aiti-14372 93 23 the the DET aiti-14372 93 24 pre pre NOUN aiti-14372 93 25 - - NOUN aiti-14372 93 26 notch notch ADJ aiti-14372 93 27 where where SCONJ aiti-14372 93 28 the the DET aiti-14372 93 29 singularity singularity NOUN aiti-14372 93 30 occurred occur VERB aiti-14372 93 31 . . PUNCT aiti-14372 94 1 in in ADP aiti-14372 94 2 other other ADJ aiti-14372 94 3 words word NOUN aiti-14372 94 4 , , PUNCT aiti-14372 94 5 k k PROPN aiti-14372 94 6 predicted predict VERB aiti-14372 94 7 the the DET aiti-14372 94 8 state state NOUN aiti-14372 94 9 of of ADP aiti-14372 94 10 stress stress NOUN aiti-14372 94 11 near near ADP aiti-14372 94 12 the the DET aiti-14372 94 13 vicinity vicinity NOUN aiti-14372 94 14 of of ADP aiti-14372 94 15 the the DET aiti-14372 94 16 pre pre NOUN aiti-14372 94 17 - - NOUN aiti-14372 94 18 notch notch ADJ aiti-14372 94 19 ( ( PUNCT aiti-14372 94 20 which which PRON aiti-14372 94 21 was be AUX aiti-14372 94 22 at at ADP aiti-14372 94 23 the the DET aiti-14372 94 24 center center NOUN aiti-14372 94 25 of of ADP aiti-14372 94 26 the the DET aiti-14372 94 27 specimen speciman NOUN aiti-14372 94 28 with with ADP aiti-14372 94 29 a a DET aiti-14372 94 30 semi semi ADJ aiti-14372 94 31 - - ADJ aiti-14372 94 32 elliptical elliptical ADJ aiti-14372 94 33 geometry geometry NOUN aiti-14372 94 34 ) ) PUNCT aiti-14372 94 35 . . PUNCT aiti-14372 95 1 the the DET aiti-14372 95 2 theoretical theoretical ADJ aiti-14372 95 3 k k PROPN aiti-14372 95 4 depends depend VERB aiti-14372 95 5 on on ADP aiti-14372 95 6 the the DET aiti-14372 95 7 geometry geometry NOUN aiti-14372 95 8 of of ADP aiti-14372 95 9 the the DET aiti-14372 95 10 crack crack NOUN aiti-14372 95 11 , , PUNCT aiti-14372 95 12 the the DET aiti-14372 95 13 geometry geometry NOUN aiti-14372 95 14 of of ADP aiti-14372 95 15 the the DET aiti-14372 95 16 specimen speciman NOUN aiti-14372 95 17 , , PUNCT aiti-14372 95 18 structural structural ADJ aiti-14372 95 19 constraints constraint NOUN aiti-14372 95 20 , , PUNCT aiti-14372 95 21 and and CCONJ aiti-14372 95 22 loading loading NOUN aiti-14372 95 23 conditions condition NOUN aiti-14372 95 24 . . PUNCT aiti-14372 96 1 the the DET aiti-14372 96 2 k k PROPN aiti-14372 96 3 was be AUX aiti-14372 96 4 calculated calculate VERB aiti-14372 96 5 using use VERB aiti-14372 96 6 the the DET aiti-14372 96 7 methodology methodology NOUN aiti-14372 96 8 provided provide VERB aiti-14372 96 9 by by ADP aiti-14372 96 10 laham laham PROPN aiti-14372 96 11 et et PROPN aiti-14372 96 12 al al PROPN aiti-14372 96 13 . . PUNCT aiti-14372 97 1 [ [ X aiti-14372 97 2 25 25 NUM aiti-14372 97 3 ] ] PUNCT aiti-14372 97 4 . . PUNCT aiti-14372 98 1 the the DET aiti-14372 98 2 geometrical geometrical ADJ aiti-14372 98 3 functions function NOUN aiti-14372 98 4 ( ( PUNCT aiti-14372 98 5 𝑓 𝑓 PRON aiti-14372 98 6 and and CCONJ aiti-14372 98 7 𝑓 𝑓 X aiti-14372 98 8 ) ) PUNCT aiti-14372 98 9 were be AUX aiti-14372 98 10 extra extra ADJ aiti-14372 98 11 - - VERB aiti-14372 98 12 plotted plot VERB aiti-14372 98 13 for for ADP aiti-14372 98 14 the the DET aiti-14372 98 15 pipe pipe NOUN aiti-14372 98 16 specimen speciman NOUN aiti-14372 98 17 and and CCONJ aiti-14372 98 18 elliptical elliptical ADJ aiti-14372 98 19 crack crack NOUN aiti-14372 98 20 geometries geometry NOUN aiti-14372 98 21 . . PUNCT aiti-14372 99 1 the the DET aiti-14372 99 2 theoretical theoretical ADJ aiti-14372 99 3 k k PROPN aiti-14372 99 4 is be AUX aiti-14372 99 5 given give VERB aiti-14372 99 6 by by ADP aiti-14372 99 7 eq eq PROPN aiti-14372 99 8 . . PUNCT aiti-14372 100 1 ( ( PUNCT aiti-14372 100 2 1 1 NUM aiti-14372 100 3 ) ) PUNCT aiti-14372 100 4 . . PUNCT aiti-14372 101 1 3 3 NUM aiti-14372 101 2 1 1 NUM aiti-14372 101 3 2 2 NUM aiti-14372 101 4 2i 2i NUM aiti-14372 101 5 i i PRON aiti-14372 101 6 t t NOUN aiti-14372 101 7 t t PROPN aiti-14372 101 8 bg bg PROPN aiti-14372 101 9 bgi bgi PROPN aiti-14372 101 10 r r NOUN aiti-14372 101 11 ra ra PROPN aiti-14372 101 12 c c PROPN aiti-14372 102 1 a a DET aiti-14372 102 2 c c X aiti-14372 102 3 k k PROPN aiti-14372 102 4 a a PRON aiti-14372 102 5 f f X aiti-14372 102 6 f f PROPN aiti-14372 102 7 t t PROPN aiti-14372 102 8 a a DET aiti-14372 102 9 t t PROPN aiti-14372 102 10 t t PROPN aiti-14372 102 11 a a DET aiti-14372 102 12 t t PROPN aiti-14372 102 13   PROPN aiti-14372 102 14   PROPN aiti-14372 102 15   PROPN aiti-14372 102 16 ο€½ ο€½ PROPN aiti-14372 102 17   NOUN aiti-14372 102 18 οƒΆο€½ οƒΆο€½ PROPN aiti-14372 102 19 ο‚΄ ο‚΄ PROPN aiti-14372 102 20 ο‚΄ ο‚΄ PROPN aiti-14372 102 21 ο‚΄ ο‚΄ PROPN aiti-14372 102 22 ο‚΄ ο‚΄ PROPN aiti-14372 102 23   PROPN aiti-14372 102 24 ο‚΄ ο‚΄ PROPN aiti-14372 102 25 ο‚΄ ο‚΄ PROPN aiti-14372 102 26 ο‚΄ ο‚΄ PROPN aiti-14372 102 27   NUM aiti-14372 102 28 οƒ· οƒ· PROPN aiti-14372 102 29   PROPN aiti-14372 102 30 οƒΈ οƒΈ NOUN aiti-14372 102 31 οƒ₯ οƒ₯ X aiti-14372 102 32 ( ( PUNCT aiti-14372 102 33 1 1 X aiti-14372 102 34 ) ) PUNCT aiti-14372 102 35 where where SCONJ aiti-14372 102 36 𝜎 𝜎 PROPN aiti-14372 102 37 is be AUX aiti-14372 102 38 bending bend VERB aiti-14372 102 39 stress stress NOUN aiti-14372 102 40 , , PUNCT aiti-14372 102 41 𝜎 𝜎 PROPN aiti-14372 102 42 is be AUX aiti-14372 102 43 axis axis ADJ aiti-14372 102 44 - - PUNCT aiti-14372 102 45 symmetrical symmetrical ADJ aiti-14372 102 46 stress stress NOUN aiti-14372 102 47 ( ( PUNCT aiti-14372 102 48 zero zero NUM aiti-14372 102 49 in in ADP aiti-14372 102 50 the the DET aiti-14372 102 51 current current ADJ aiti-14372 102 52 case case NOUN aiti-14372 102 53 ) ) PUNCT aiti-14372 102 54 , , PUNCT aiti-14372 102 55 a a PRON aiti-14372 102 56 is be AUX aiti-14372 102 57 the the DET aiti-14372 102 58 depth depth NOUN aiti-14372 102 59 of of ADP aiti-14372 102 60 the the DET aiti-14372 102 61 elliptical elliptical ADJ aiti-14372 102 62 defect defect NOUN aiti-14372 102 63 / / SYM aiti-14372 102 64 length length NOUN aiti-14372 102 65 of of ADP aiti-14372 102 66 the the DET aiti-14372 102 67 semi semi ADJ aiti-14372 102 68 - - ADJ aiti-14372 102 69 minor minor ADJ aiti-14372 102 70 axis axis NOUN aiti-14372 102 71 , , PUNCT aiti-14372 102 72 t t PROPN aiti-14372 102 73 is be AUX aiti-14372 102 74 the the DET aiti-14372 102 75 thickness thickness NOUN aiti-14372 102 76 of of ADP aiti-14372 102 77 the the DET aiti-14372 102 78 pipe pipe NOUN aiti-14372 102 79 , , PUNCT aiti-14372 102 80 2c 2c NOUN aiti-14372 102 81 is be AUX aiti-14372 102 82 the the DET aiti-14372 102 83 length length NOUN aiti-14372 102 84 of of ADP aiti-14372 102 85 the the DET aiti-14372 102 86 major major ADJ aiti-14372 102 87 axis axis NOUN aiti-14372 102 88 , , PUNCT aiti-14372 102 89 and and CCONJ aiti-14372 102 90 ri ri PROPN aiti-14372 102 91 is be AUX aiti-14372 102 92 the the DET aiti-14372 102 93 internal internal ADJ aiti-14372 102 94 radius radius NOUN aiti-14372 102 95 of of ADP aiti-14372 102 96 the the DET aiti-14372 102 97 pipe pipe NOUN aiti-14372 102 98 . . PUNCT aiti-14372 103 1 the the DET aiti-14372 103 2 first first ADJ aiti-14372 103 3 computable computable ADJ aiti-14372 103 4 a a PRON aiti-14372 103 5 of of ADP aiti-14372 103 6 0.87 0.87 NUM aiti-14372 103 7 mm mm NOUN aiti-14372 103 8 was be AUX aiti-14372 103 9 detected detect VERB aiti-14372 103 10 at at ADP aiti-14372 103 11 a a DET aiti-14372 103 12 loading loading NOUN aiti-14372 103 13 cycle cycle NOUN aiti-14372 103 14 of of ADP aiti-14372 103 15 60530 60530 NUM aiti-14372 103 16 . . PUNCT aiti-14372 104 1 in in ADP aiti-14372 104 2 the the DET aiti-14372 104 3 current current ADJ aiti-14372 104 4 work work NOUN aiti-14372 104 5 , , PUNCT aiti-14372 104 6 the the DET aiti-14372 104 7 n n NOUN aiti-14372 104 8 for for ADP aiti-14372 104 9 the the DET aiti-14372 104 10 first first ADJ aiti-14372 104 11 appearance appearance NOUN aiti-14372 104 12 of of ADP aiti-14372 104 13 a a PRON aiti-14372 104 14 was be AUX aiti-14372 104 15 considered consider VERB aiti-14372 104 16 as as ADP aiti-14372 104 17 the the DET aiti-14372 104 18 start start NOUN aiti-14372 104 19 of of ADP aiti-14372 104 20 the the DET aiti-14372 104 21 loading loading NOUN aiti-14372 104 22 cycle cycle NOUN aiti-14372 104 23 . . PUNCT aiti-14372 105 1 this this DET aiti-14372 105 2 premise premise NOUN aiti-14372 105 3 was be AUX aiti-14372 105 4 considered consider VERB aiti-14372 105 5 for for ADP aiti-14372 105 6 plastic plastic ADJ aiti-14372 105 7 behavior behavior NOUN aiti-14372 105 8 and and CCONJ aiti-14372 105 9 eliminated eliminate VERB aiti-14372 105 10 all all DET aiti-14372 105 11 linear linear NOUN aiti-14372 105 12 advances advance NOUN aiti-14372 105 13 in in ADP aiti-14372 105 14 technology technology NOUN aiti-14372 105 15 innovation innovation NOUN aiti-14372 105 16 , , PUNCT aiti-14372 105 17 vol vol NOUN aiti-14372 105 18 . . PROPN aiti-14372 106 1 10 10 NUM aiti-14372 106 2 , , PUNCT aiti-14372 106 3 no no INTJ aiti-14372 106 4 . . NOUN aiti-14372 106 5 3 3 NUM aiti-14372 106 6 , , PUNCT aiti-14372 106 7 2025 2025 NUM aiti-14372 106 8 , , PUNCT aiti-14372 106 9 pp pp ADJ aiti-14372 106 10 . . PUNCT aiti-14372 107 1 238 238 NUM aiti-14372 107 2 - - SYM aiti-14372 107 3 253 253 NUM aiti-14372 107 4 242 242 NUM aiti-14372 107 5 elastic elastic ADJ aiti-14372 107 6 deformation deformation NOUN aiti-14372 107 7 . . PUNCT aiti-14372 108 1 fig fig NOUN aiti-14372 108 2 . . PUNCT aiti-14372 109 1 4(a 4(a NUM aiti-14372 109 2 ) ) PUNCT aiti-14372 109 3 describes describe VERB aiti-14372 109 4 variation variation NOUN aiti-14372 109 5 in in ADP aiti-14372 109 6 k k PROPN aiti-14372 109 7 with with ADP aiti-14372 109 8 a. a. NOUN aiti-14372 109 9 the the DET aiti-14372 109 10 curve curve NOUN aiti-14372 109 11 shows show VERB aiti-14372 109 12 a a DET aiti-14372 109 13 typical typical ADJ aiti-14372 109 14 k k NOUN aiti-14372 109 15 - - PUNCT aiti-14372 109 16 a a DET aiti-14372 109 17 variation variation NOUN aiti-14372 109 18 for for ADP aiti-14372 109 19 fcg fcg NOUN aiti-14372 109 20 [ [ X aiti-14372 109 21 26 26 NUM aiti-14372 109 22 ] ] PUNCT aiti-14372 109 23 . . PUNCT aiti-14372 110 1 the the DET aiti-14372 110 2 slope slope NOUN aiti-14372 110 3 of of ADP aiti-14372 110 4 the the DET aiti-14372 110 5 curve curve NOUN aiti-14372 110 6 decreases decrease VERB aiti-14372 110 7 with with ADP aiti-14372 110 8 the the DET aiti-14372 110 9 a a DET aiti-14372 110 10 continuously continuously ADV aiti-14372 110 11 . . PUNCT aiti-14372 111 1 in in ADP aiti-14372 111 2 other other ADJ aiti-14372 111 3 words word NOUN aiti-14372 111 4 , , PUNCT aiti-14372 111 5 initially initially ADV aiti-14372 111 6 , , PUNCT aiti-14372 111 7 for for ADP aiti-14372 111 8 a a DET aiti-14372 111 9 small small ADJ aiti-14372 111 10 increment increment NOUN aiti-14372 111 11 in in ADP aiti-14372 111 12 a a PRON aiti-14372 111 13 , , PUNCT aiti-14372 111 14 the the DET aiti-14372 111 15 corresponding corresponding ADJ aiti-14372 111 16 increase increase NOUN aiti-14372 111 17 in in ADP aiti-14372 111 18 k k PROPN aiti-14372 111 19 was be AUX aiti-14372 111 20 greater great ADJ aiti-14372 111 21 . . PUNCT aiti-14372 112 1 for for ADP aiti-14372 112 2 further far ADV aiti-14372 112 3 crack crack VERB aiti-14372 112 4 propagation propagation NOUN aiti-14372 112 5 , , PUNCT aiti-14372 112 6 the the DET aiti-14372 112 7 slope slope NOUN aiti-14372 112 8 decreases decrease VERB aiti-14372 112 9 , , PUNCT aiti-14372 112 10 which which PRON aiti-14372 112 11 means mean VERB aiti-14372 112 12 a a DET aiti-14372 112 13 lower low ADJ aiti-14372 112 14 incremental incremental NOUN aiti-14372 112 15 k k PROPN aiti-14372 112 16 was be AUX aiti-14372 112 17 required require VERB aiti-14372 112 18 for for ADP aiti-14372 112 19 the the DET aiti-14372 112 20 corresponding corresponding ADJ aiti-14372 112 21 increment increment NOUN aiti-14372 112 22 in in ADP aiti-14372 112 23 a. a. NOUN aiti-14372 112 24 therefore therefore ADV aiti-14372 112 25 , , PUNCT aiti-14372 112 26 it it PRON aiti-14372 112 27 envisages envisage VERB aiti-14372 112 28 a a DET aiti-14372 112 29 preceding precede VERB aiti-14372 112 30 crack crack NOUN aiti-14372 112 31 that that PRON aiti-14372 112 32 changes change VERB aiti-14372 112 33 the the DET aiti-14372 112 34 stress stress NOUN aiti-14372 112 35 field field NOUN aiti-14372 112 36 near near ADP aiti-14372 112 37 the the DET aiti-14372 112 38 vicinity vicinity NOUN aiti-14372 112 39 of of ADP aiti-14372 112 40 the the DET aiti-14372 112 41 crack crack NOUN aiti-14372 112 42 tip tip NOUN aiti-14372 112 43 , , PUNCT aiti-14372 112 44 and and CCONJ aiti-14372 112 45 envisages envisage VERB aiti-14372 112 46 a a DET aiti-14372 112 47 new new ADJ aiti-14372 112 48 crack crack NOUN aiti-14372 112 49 to to PART aiti-14372 112 50 be be AUX aiti-14372 112 51 less less ADV aiti-14372 112 52 resistant resistant ADJ aiti-14372 112 53 to to ADP aiti-14372 112 54 external external ADJ aiti-14372 112 55 bending bending NOUN aiti-14372 112 56 [ [ X aiti-14372 112 57 27 27 NUM aiti-14372 112 58 ] ] PUNCT aiti-14372 112 59 . . PUNCT aiti-14372 113 1 this this DET aiti-14372 113 2 nature nature NOUN aiti-14372 113 3 continued continue VERB aiti-14372 113 4 till till SCONJ aiti-14372 113 5 the the DET aiti-14372 113 6 complete complete ADJ aiti-14372 113 7 failure failure NOUN aiti-14372 113 8 of of ADP aiti-14372 113 9 the the DET aiti-14372 113 10 sample sample NOUN aiti-14372 113 11 . . PUNCT aiti-14372 114 1 it it PRON aiti-14372 114 2 is be AUX aiti-14372 114 3 to to PART aiti-14372 114 4 be be AUX aiti-14372 114 5 noted note VERB aiti-14372 114 6 that that SCONJ aiti-14372 114 7 the the DET aiti-14372 114 8 slope slope NOUN aiti-14372 114 9 of of ADP aiti-14372 114 10 the the DET aiti-14372 114 11 k k NOUN aiti-14372 114 12 - - PUNCT aiti-14372 114 13 a a DET aiti-14372 114 14 curve curve NOUN aiti-14372 114 15 after after ADP aiti-14372 114 16 a a DET aiti-14372 114 17 preceding precede VERB aiti-14372 114 18 crack crack NOUN aiti-14372 114 19 length length NOUN aiti-14372 114 20 of of ADP aiti-14372 114 21 4 4 NUM aiti-14372 114 22 mm mm NOUN aiti-14372 114 23 decreased decrease VERB aiti-14372 114 24 significantly significantly ADV aiti-14372 114 25 as as SCONJ aiti-14372 114 26 compared compare VERB aiti-14372 114 27 to to ADP aiti-14372 114 28 the the DET aiti-14372 114 29 slope slope NOUN aiti-14372 114 30 at at ADP aiti-14372 114 31 the the DET aiti-14372 114 32 initiation initiation NOUN aiti-14372 114 33 of of ADP aiti-14372 114 34 the the DET aiti-14372 114 35 crack crack NOUN aiti-14372 114 36 ( ( PUNCT aiti-14372 114 37 when when SCONJ aiti-14372 114 38 a=0.85 a=0.85 ADV aiti-14372 114 39 mm mm NOUN aiti-14372 114 40 ) ) PUNCT aiti-14372 114 41 . . PUNCT aiti-14372 115 1 the the DET aiti-14372 115 2 variation variation NOUN aiti-14372 115 3 in in ADP aiti-14372 115 4 k k PROPN aiti-14372 115 5 with with ADP aiti-14372 115 6 n n PROPN aiti-14372 115 7 is be AUX aiti-14372 115 8 shown show VERB aiti-14372 115 9 in in ADP aiti-14372 115 10 fig fig NOUN aiti-14372 115 11 . . PUNCT aiti-14372 116 1 4(b 4(b NUM aiti-14372 116 2 ) ) PUNCT aiti-14372 116 3 . . PUNCT aiti-14372 117 1 the the DET aiti-14372 117 2 nature nature NOUN aiti-14372 117 3 of of ADP aiti-14372 117 4 the the DET aiti-14372 117 5 plot plot NOUN aiti-14372 117 6 shows show VERB aiti-14372 117 7 a a DET aiti-14372 117 8 typical typical ADJ aiti-14372 117 9 k k ADJ aiti-14372 117 10 - - PUNCT aiti-14372 117 11 n n NOUN aiti-14372 117 12 curve curve NOUN aiti-14372 117 13 [ [ X aiti-14372 117 14 28 28 NUM aiti-14372 117 15 ] ] PUNCT aiti-14372 117 16 . . PUNCT aiti-14372 118 1 in in ADP aiti-14372 118 2 contrast contrast NOUN aiti-14372 118 3 to to ADP aiti-14372 118 4 the the DET aiti-14372 118 5 k k NOUN aiti-14372 118 6 - - PUNCT aiti-14372 118 7 a a DET aiti-14372 118 8 curve curve NOUN aiti-14372 118 9 , , PUNCT aiti-14372 118 10 the the DET aiti-14372 118 11 slope slope NOUN aiti-14372 118 12 of of ADP aiti-14372 118 13 the the DET aiti-14372 118 14 k k PROPN aiti-14372 118 15 - - PUNCT aiti-14372 118 16 n n PRON aiti-14372 118 17 curve curve NOUN aiti-14372 118 18 increases increase NOUN aiti-14372 118 19 continuously continuously ADV aiti-14372 118 20 till till SCONJ aiti-14372 118 21 the the DET aiti-14372 118 22 fracture fracture NOUN aiti-14372 118 23 . . PUNCT aiti-14372 119 1 initially initially ADV aiti-14372 119 2 , , PUNCT aiti-14372 119 3 a a DET aiti-14372 119 4 higher high ADJ aiti-14372 119 5 n n NOUN aiti-14372 119 6 is be AUX aiti-14372 119 7 required require VERB aiti-14372 119 8 for for ADP aiti-14372 119 9 a a DET aiti-14372 119 10 small small ADJ aiti-14372 119 11 increase increase NOUN aiti-14372 119 12 in in ADP aiti-14372 119 13 k k PROPN aiti-14372 119 14 , , PUNCT aiti-14372 119 15 which which PRON aiti-14372 119 16 indicates indicate VERB aiti-14372 119 17 that that SCONJ aiti-14372 119 18 the the DET aiti-14372 119 19 initial initial ADJ aiti-14372 119 20 crack crack NOUN aiti-14372 119 21 propagation propagation NOUN aiti-14372 119 22 required require VERB aiti-14372 119 23 a a DET aiti-14372 119 24 large large ADJ aiti-14372 119 25 accumulation accumulation NOUN aiti-14372 119 26 of of ADP aiti-14372 119 27 external external ADJ aiti-14372 119 28 bending bending NOUN aiti-14372 119 29 stresses stress NOUN aiti-14372 119 30 ( ( PUNCT aiti-14372 119 31 using use VERB aiti-14372 119 32 higher high ADJ aiti-14372 119 33 n n NOUN aiti-14372 119 34 ) ) PUNCT aiti-14372 119 35 . . PUNCT aiti-14372 120 1 with with ADP aiti-14372 120 2 the the DET aiti-14372 120 3 crack crack NOUN aiti-14372 120 4 propagation propagation NOUN aiti-14372 120 5 and and CCONJ aiti-14372 120 6 accumulation accumulation NOUN aiti-14372 120 7 of of ADP aiti-14372 120 8 external external ADJ aiti-14372 120 9 bending bending NOUN aiti-14372 120 10 stresses stress NOUN aiti-14372 120 11 , , PUNCT aiti-14372 120 12 the the DET aiti-14372 120 13 subsequent subsequent ADJ aiti-14372 120 14 requirement requirement NOUN aiti-14372 120 15 of of ADP aiti-14372 120 16 n n PROPN aiti-14372 120 17 for for ADP aiti-14372 120 18 an an DET aiti-14372 120 19 incremental incremental ADJ aiti-14372 121 1 k k PROPN aiti-14372 121 2 decreased decrease VERB aiti-14372 121 3 . . PUNCT aiti-14372 122 1 it it PRON aiti-14372 122 2 is be AUX aiti-14372 122 3 suggested suggest VERB aiti-14372 122 4 that that SCONJ aiti-14372 122 5 the the DET aiti-14372 122 6 preceding precede VERB aiti-14372 122 7 bending bend VERB aiti-14372 122 8 stress stress ADJ aiti-14372 122 9 accumulation accumulation NOUN aiti-14372 122 10 made make VERB aiti-14372 122 11 the the DET aiti-14372 122 12 crack crack NOUN aiti-14372 122 13 tip tip NOUN aiti-14372 122 14 more more ADV aiti-14372 122 15 susceptible susceptible ADJ aiti-14372 122 16 to to ADP aiti-14372 122 17 propagating propagate VERB aiti-14372 122 18 ( ( PUNCT aiti-14372 122 19 growing grow VERB aiti-14372 122 20 ) ) PUNCT aiti-14372 122 21 . . PUNCT aiti-14372 123 1 a a DET aiti-14372 123 2 much much ADV aiti-14372 123 3 higher high ADJ aiti-14372 123 4 slope slope NOUN aiti-14372 123 5 of of ADP aiti-14372 123 6 the the DET aiti-14372 123 7 k k PROPN aiti-14372 123 8 - - PUNCT aiti-14372 123 9 n n PRON aiti-14372 123 10 curve curve NOUN aiti-14372 123 11 after after SCONJ aiti-14372 123 12 n n PRON aiti-14372 123 13 reaches reach VERB aiti-14372 123 14 60,000 60,000 NUM aiti-14372 123 15 envisages envisage VERB aiti-14372 123 16 a a DET aiti-14372 123 17 highly highly ADV aiti-14372 123 18 plastic plastic ADJ aiti-14372 123 19 deformation deformation NOUN aiti-14372 123 20 state state NOUN aiti-14372 123 21 , , PUNCT aiti-14372 123 22 which which PRON aiti-14372 123 23 eventually eventually ADV aiti-14372 123 24 leads lead VERB aiti-14372 123 25 to to ADP aiti-14372 123 26 the the DET aiti-14372 123 27 fracture fracture NOUN aiti-14372 123 28 of of ADP aiti-14372 123 29 the the DET aiti-14372 123 30 specimen speciman NOUN aiti-14372 123 31 . . PUNCT aiti-14372 124 1 ( ( PUNCT aiti-14372 124 2 a a X aiti-14372 124 3 ) ) PUNCT aiti-14372 124 4 k k NOUN aiti-14372 124 5 vs vs ADP aiti-14372 124 6 a a DET aiti-14372 124 7 graph graph NOUN aiti-14372 124 8 ( ( PUNCT aiti-14372 124 9 b b NOUN aiti-14372 124 10 ) ) PUNCT aiti-14372 124 11 k k NOUN aiti-14372 124 12 vs vs ADP aiti-14372 124 13 n n PRON aiti-14372 124 14 graph graph NOUN aiti-14372 124 15 fig fig NOUN aiti-14372 124 16 . . PUNCT aiti-14372 125 1 4 4 NUM aiti-14372 125 2 the the DET aiti-14372 125 3 variation variation NOUN aiti-14372 125 4 in in ADP aiti-14372 125 5 k k PROPN aiti-14372 125 6 with with ADP aiti-14372 125 7 a a PRON aiti-14372 125 8 and and CCONJ aiti-14372 125 9 n n PRON aiti-14372 125 10 3.2 3.2 NUM aiti-14372 125 11 . . PUNCT aiti-14372 126 1 fcgr fcgr VERB aiti-14372 126 2 the the DET aiti-14372 126 3 fcgr fcgr NOUN aiti-14372 126 4 provides provide VERB aiti-14372 126 5 the the DET aiti-14372 126 6 features feature NOUN aiti-14372 126 7 of of ADP aiti-14372 126 8 crack crack NOUN aiti-14372 126 9 propagation propagation NOUN aiti-14372 126 10 . . PUNCT aiti-14372 127 1 it it PRON aiti-14372 127 2 is be AUX aiti-14372 127 3 the the DET aiti-14372 127 4 rate rate NOUN aiti-14372 127 5 of of ADP aiti-14372 127 6 change change NOUN aiti-14372 127 7 of of ADP aiti-14372 127 8 a a PRON aiti-14372 127 9 with with ADP aiti-14372 127 10 n n CCONJ aiti-14372 127 11 ; ; PUNCT aiti-14372 127 12 in in ADP aiti-14372 127 13 other other ADJ aiti-14372 127 14 words word NOUN aiti-14372 127 15 , , PUNCT aiti-14372 127 16 it it PRON aiti-14372 127 17 provides provide VERB aiti-14372 127 18 an an DET aiti-14372 127 19 idea idea NOUN aiti-14372 127 20 of of ADP aiti-14372 127 21 incremental incremental NOUN aiti-14372 127 22 a a PRON aiti-14372 127 23 in in ADP aiti-14372 127 24 a a DET aiti-14372 127 25 given give VERB aiti-14372 127 26 interval interval NOUN aiti-14372 127 27 of of ADP aiti-14372 127 28 n. n. NOUN aiti-14372 127 29 the the DET aiti-14372 127 30 variations variation NOUN aiti-14372 127 31 of of ADP aiti-14372 127 32 da da PROPN aiti-14372 127 33 / / SYM aiti-14372 127 34 dn dn NOUN aiti-14372 127 35 with with ADP aiti-14372 127 36 Ξ΄k Ξ΄k ADP aiti-14372 127 37 , , PUNCT aiti-14372 127 38 a a PRON aiti-14372 127 39 , , PUNCT aiti-14372 127 40 and and CCONJ aiti-14372 127 41 n n PRON aiti-14372 127 42 are be AUX aiti-14372 127 43 presented present VERB aiti-14372 127 44 in in ADP aiti-14372 127 45 figs fig NOUN aiti-14372 127 46 . . PUNCT aiti-14372 128 1 5 5 NUM aiti-14372 128 2 , , PUNCT aiti-14372 128 3 6 6 NUM aiti-14372 128 4 , , PUNCT aiti-14372 128 5 and and CCONJ aiti-14372 128 6 7 7 NUM aiti-14372 128 7 , , PUNCT aiti-14372 128 8 respectively respectively ADV aiti-14372 128 9 . . PUNCT aiti-14372 129 1 based base VERB aiti-14372 129 2 on on ADP aiti-14372 129 3 the the DET aiti-14372 129 4 nature nature NOUN aiti-14372 129 5 of of ADP aiti-14372 129 6 fcgr fcgr NOUN aiti-14372 129 7 , , PUNCT aiti-14372 129 8 it it PRON aiti-14372 129 9 is be AUX aiti-14372 129 10 categorized categorize VERB aiti-14372 129 11 into into ADP aiti-14372 129 12 three three NUM aiti-14372 129 13 discrete discrete ADJ aiti-14372 129 14 stages stage NOUN aiti-14372 129 15 : : PUNCT aiti-14372 129 16 stage stage NOUN aiti-14372 129 17 - - PUNCT aiti-14372 129 18 i i NOUN aiti-14372 129 19 , , PUNCT aiti-14372 129 20 stage stage NOUN aiti-14372 129 21 - - PUNCT aiti-14372 129 22 ii ii NOUN aiti-14372 129 23 , , PUNCT aiti-14372 129 24 and and CCONJ aiti-14372 129 25 stage stage NOUN aiti-14372 129 26 - - PUNCT aiti-14372 129 27 iii iii NOUN aiti-14372 129 28 for for ADP aiti-14372 129 29 the the DET aiti-14372 129 30 present present ADJ aiti-14372 129 31 investigation investigation NOUN aiti-14372 129 32 . . PUNCT aiti-14372 130 1 the the DET aiti-14372 130 2 three three NUM aiti-14372 130 3 distinct distinct ADJ aiti-14372 130 4 stages stage NOUN aiti-14372 130 5 characterize characterize VERB aiti-14372 130 6 fcgr fcgr NOUN aiti-14372 130 7 . . PUNCT aiti-14372 131 1 3.2.1 3.2.1 NUM aiti-14372 131 2 . . PUNCT aiti-14372 131 3 fcgr fcgr NOUN aiti-14372 131 4 in in ADP aiti-14372 131 5 stage stage NOUN aiti-14372 131 6 - - PUNCT aiti-14372 131 7 i i PRON aiti-14372 131 8 as as SCONJ aiti-14372 131 9 shown show VERB aiti-14372 131 10 in in ADP aiti-14372 131 11 fig fig NOUN aiti-14372 131 12 . . PUNCT aiti-14372 132 1 5 5 NUM aiti-14372 132 2 , , PUNCT aiti-14372 132 3 the the DET aiti-14372 132 4 stage stage NOUN aiti-14372 132 5 - - PUNCT aiti-14372 132 6 i i PRON aiti-14372 132 7 of of ADP aiti-14372 132 8 fcgr fcgr NOUN aiti-14372 132 9 is be AUX aiti-14372 132 10 in in ADP aiti-14372 132 11 the the DET aiti-14372 132 12 threshold threshold NOUN aiti-14372 132 13 Ξ΄k Ξ΄k ADP aiti-14372 132 14 range range NOUN aiti-14372 132 15 17.45 17.45 NUM aiti-14372 132 16 - - SYM aiti-14372 132 17 20.46 20.46 NUM aiti-14372 132 18 π‘€π‘ƒπ‘Žβˆšπ‘š. π‘€π‘ƒπ‘Žβˆšπ‘š. NOUN aiti-14372 132 19 the the DET aiti-14372 132 20 appearance appearance NOUN aiti-14372 132 21 of of ADP aiti-14372 132 22 the the DET aiti-14372 132 23 first first ADJ aiti-14372 132 24 crack crack NOUN aiti-14372 132 25 is be AUX aiti-14372 132 26 observed observe VERB aiti-14372 132 27 at at ADP aiti-14372 132 28 Ξ΄k Ξ΄k ADP aiti-14372 132 29 = = NOUN aiti-14372 132 30 17.45 17.45 NUM aiti-14372 132 31 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 132 32 , , PUNCT aiti-14372 132 33 and and CCONJ aiti-14372 132 34 the the DET aiti-14372 132 35 slope slope NOUN aiti-14372 132 36 increases increase VERB aiti-14372 132 37 gradually gradually ADV aiti-14372 132 38 up up ADP aiti-14372 132 39 to to ADP aiti-14372 132 40 Ξ΄k Ξ΄k ADP aiti-14372 132 41 = = NOUN aiti-14372 132 42 20.46 20.46 NUM aiti-14372 132 43 π‘€π‘ƒπ‘Žβˆšπ‘š. π‘€π‘ƒπ‘Žβˆšπ‘š. VERB aiti-14372 132 44 the the DET aiti-14372 132 45 initiation initiation NOUN aiti-14372 132 46 of of ADP aiti-14372 132 47 the the DET aiti-14372 132 48 first first ADJ aiti-14372 132 49 crack crack NOUN aiti-14372 132 50 required require VERB aiti-14372 132 51 a a DET aiti-14372 132 52 critical critical ADJ aiti-14372 132 53 accumulation accumulation NOUN aiti-14372 132 54 of of ADP aiti-14372 132 55 bending bend VERB aiti-14372 132 56 stresses stress NOUN aiti-14372 132 57 near near ADP aiti-14372 132 58 the the DET aiti-14372 132 59 vicinity vicinity NOUN aiti-14372 132 60 of of ADP aiti-14372 132 61 the the DET aiti-14372 132 62 crack crack NOUN aiti-14372 132 63 tip tip NOUN aiti-14372 132 64 , , PUNCT aiti-14372 132 65 which which PRON aiti-14372 132 66 was be AUX aiti-14372 132 67 provided provide VERB aiti-14372 132 68 by by ADP aiti-14372 132 69 the the DET aiti-14372 132 70 threshold threshold NOUN aiti-14372 132 71 Ξ΄k Ξ΄k ADP aiti-14372 132 72 [ [ X aiti-14372 132 73 29 29 NUM aiti-14372 132 74 ] ] PUNCT aiti-14372 132 75 . . PUNCT aiti-14372 133 1 the the DET aiti-14372 133 2 da da PROPN aiti-14372 133 3 / / SYM aiti-14372 133 4 dn dn NOUN aiti-14372 133 5 versus versus ADP aiti-14372 133 6 Ξ΄k Ξ΄k ADP aiti-14372 133 7 curve curve NOUN aiti-14372 133 8 is be AUX aiti-14372 133 9 detrimental detrimental ADJ aiti-14372 133 10 to to PART aiti-14372 133 11 fcg fcg VERB aiti-14372 133 12 studies study NOUN aiti-14372 133 13 [ [ X aiti-14372 133 14 27 27 NUM aiti-14372 133 15 ] ] PUNCT aiti-14372 133 16 . . PUNCT aiti-14372 134 1 the the DET aiti-14372 134 2 Ξ΄k Ξ΄k PROPN aiti-14372 134 3 provided provide VERB aiti-14372 134 4 the the DET aiti-14372 134 5 driving drive VERB aiti-14372 134 6 force force NOUN aiti-14372 134 7 for for ADP aiti-14372 134 8 fcg fcg NOUN aiti-14372 134 9 , , PUNCT aiti-14372 134 10 which which PRON aiti-14372 134 11 is be AUX aiti-14372 134 12 proportional proportional ADJ aiti-14372 134 13 to to ADP aiti-14372 134 14 applied apply VERB aiti-14372 134 15 bending bend VERB aiti-14372 134 16 stress stress NOUN aiti-14372 134 17 and and CCONJ aiti-14372 134 18 the the DET aiti-14372 134 19 square square ADJ aiti-14372 134 20 root root NOUN aiti-14372 134 21 of of ADP aiti-14372 134 22 a a DET aiti-14372 134 23 ( ( PUNCT aiti-14372 134 24 equation equation NOUN aiti-14372 134 25 1 1 NUM aiti-14372 134 26 ) ) PUNCT aiti-14372 134 27 . . PUNCT aiti-14372 135 1 the the DET aiti-14372 135 2 slowly slowly ADV aiti-14372 135 3 increasing increase VERB aiti-14372 135 4 slope slope NOUN aiti-14372 135 5 of of ADP aiti-14372 135 6 the the DET aiti-14372 135 7 da da PROPN aiti-14372 135 8 / / SYM aiti-14372 135 9 dn dn NOUN aiti-14372 135 10 versus versus ADP aiti-14372 135 11 Ξ΄k Ξ΄k ADJ aiti-14372 135 12 curve curve NOUN aiti-14372 135 13 in in ADP aiti-14372 135 14 stage stage NOUN aiti-14372 135 15 - - PUNCT aiti-14372 135 16 i i PRON aiti-14372 135 17 envisages envisage VERB aiti-14372 135 18 that that SCONJ aiti-14372 135 19 a a DET aiti-14372 135 20 higher high ADJ aiti-14372 135 21 crack crack NOUN aiti-14372 135 22 driving driving NOUN aiti-14372 135 23 force force NOUN aiti-14372 135 24 was be AUX aiti-14372 135 25 required require VERB aiti-14372 135 26 initially initially ADV aiti-14372 135 27 . . PUNCT aiti-14372 136 1 this this PRON aiti-14372 136 2 is be AUX aiti-14372 136 3 the the DET aiti-14372 136 4 region region NOUN aiti-14372 136 5 where where SCONJ aiti-14372 136 6 the the DET aiti-14372 136 7 crack crack NOUN aiti-14372 136 8 resisting resist VERB aiti-14372 136 9 parameter parameter NOUN aiti-14372 136 10 ( ( PUNCT aiti-14372 136 11 kc kc PROPN aiti-14372 136 12 ) ) PUNCT aiti-14372 136 13 and and CCONJ aiti-14372 136 14 materials material NOUN aiti-14372 136 15 property property NOUN aiti-14372 136 16 ( ( PUNCT aiti-14372 136 17 stiffness stiffness NOUN aiti-14372 136 18 , , PUNCT aiti-14372 136 19 e e NOUN aiti-14372 136 20 ) ) PUNCT aiti-14372 136 21 oppose oppose VERB aiti-14372 136 22 the the DET aiti-14372 136 23 crack crack NOUN aiti-14372 136 24 driving driving NOUN aiti-14372 136 25 force force NOUN aiti-14372 136 26 ( ( PUNCT aiti-14372 136 27 Ξ΄k Ξ΄k ADP aiti-14372 136 28 ) ) PUNCT aiti-14372 136 29 at at ADP aiti-14372 136 30 best good ADJ aiti-14372 136 31 after after ADP aiti-14372 136 32 the the DET aiti-14372 136 33 threshold threshold NOUN aiti-14372 136 34 Ξ΄k Ξ΄k VERB aiti-14372 136 35 . . PUNCT aiti-14372 137 1 it it PRON aiti-14372 137 2 required require VERB aiti-14372 137 3 a a DET aiti-14372 137 4 higher high ADJ aiti-14372 137 5 Ξ΄k Ξ΄k X aiti-14372 137 6 for for ADP aiti-14372 137 7 a a DET aiti-14372 137 8 small small ADJ aiti-14372 137 9 increment increment NOUN aiti-14372 137 10 in in ADP aiti-14372 137 11 the the DET aiti-14372 137 12 da da PROPN aiti-14372 137 13 / / SYM aiti-14372 137 14 dn dn PROPN aiti-14372 137 15 . . PUNCT aiti-14372 138 1 the the DET aiti-14372 138 2 fcgr fcgr NOUN aiti-14372 138 3 versus versus ADP aiti-14372 138 4 a a DET aiti-14372 138 5 curve curve NOUN aiti-14372 138 6 is be AUX aiti-14372 138 7 shown show VERB aiti-14372 138 8 in in ADP aiti-14372 138 9 fig fig NOUN aiti-14372 138 10 . . PUNCT aiti-14372 139 1 6 6 NUM aiti-14372 139 2 . . X aiti-14372 140 1 1.90e+01 1.90e+01 NUM aiti-14372 140 2 2.00e+01 2.00e+01 NUM aiti-14372 140 3 2.10e+01 2.10e+01 NUM aiti-14372 140 4 2.20e+01 2.20e+01 NUM aiti-14372 140 5 2.30e+01 2.30e+01 NUM aiti-14372 141 1 2.40e+01 2.40e+01 NUM aiti-14372 141 2 2.50e+01 2.50e+01 NUM aiti-14372 141 3 0 0 NUM aiti-14372 141 4 1 1 NUM aiti-14372 141 5 2 2 NUM aiti-14372 141 6 3 3 NUM aiti-14372 141 7 4 4 NUM aiti-14372 141 8 5 5 NUM aiti-14372 141 9 6 6 NUM aiti-14372 141 10 k k NOUN aiti-14372 141 11 ( ( PUNCT aiti-14372 141 12 𝑀 𝑀 NOUN aiti-14372 141 13 𝑃 𝑃 VERB aiti-14372 141 14 π‘Ž π‘Ž NOUN aiti-14372 141 15 βˆšπ‘š βˆšπ‘š NOUN aiti-14372 141 16 ) ) PUNCT aiti-14372 141 17 a a PRON aiti-14372 141 18 ( ( PUNCT aiti-14372 141 19 mm mm NOUN aiti-14372 141 20 ) ) PUNCT aiti-14372 141 21 1.90e+01 1.90e+01 PROPN aiti-14372 141 22 2.00e+01 2.00e+01 NUM aiti-14372 142 1 2.10e+01 2.10e+01 NUM aiti-14372 142 2 2.20e+01 2.20e+01 NUM aiti-14372 142 3 2.30e+01 2.30e+01 NUM aiti-14372 143 1 2.40e+01 2.40e+01 NUM aiti-14372 143 2 2.50e+01 2.50e+01 NUM aiti-14372 143 3 0 0 NUM aiti-14372 143 4 20000 20000 NUM aiti-14372 143 5 40000 40000 NUM aiti-14372 143 6 60000 60000 NUM aiti-14372 143 7 80000 80000 NUM aiti-14372 143 8 k k NOUN aiti-14372 143 9 ( ( PUNCT aiti-14372 143 10 𝑀 𝑀 NOUN aiti-14372 143 11 𝑃 𝑃 VERB aiti-14372 143 12 π‘Ž π‘Ž NOUN aiti-14372 143 13 βˆšπ‘š βˆšπ‘š NOUN aiti-14372 143 14 ) ) PUNCT aiti-14372 144 1 n n PRON aiti-14372 144 2 advances advance NOUN aiti-14372 144 3 in in ADP aiti-14372 144 4 technology technology NOUN aiti-14372 144 5 innovation innovation NOUN aiti-14372 144 6 , , PUNCT aiti-14372 144 7 vol vol NOUN aiti-14372 144 8 . . PROPN aiti-14372 144 9 10 10 NUM aiti-14372 144 10 , , PUNCT aiti-14372 144 11 no no INTJ aiti-14372 144 12 . . NOUN aiti-14372 144 13 3 3 NUM aiti-14372 144 14 , , PUNCT aiti-14372 144 15 2025 2025 NUM aiti-14372 144 16 , , PUNCT aiti-14372 144 17 pp pp ADJ aiti-14372 144 18 . . PUNCT aiti-14372 145 1 238 238 NUM aiti-14372 145 2 - - SYM aiti-14372 145 3 253 253 NUM aiti-14372 145 4 243 243 NUM aiti-14372 145 5 the the DET aiti-14372 145 6 stage stage NOUN aiti-14372 145 7 - - PUNCT aiti-14372 145 8 i i PRON aiti-14372 145 9 of of ADP aiti-14372 145 10 fcgr fcgr NOUN aiti-14372 145 11 is be AUX aiti-14372 145 12 in in ADP aiti-14372 145 13 the the DET aiti-14372 145 14 crack crack NOUN aiti-14372 145 15 length length NOUN aiti-14372 145 16 , , PUNCT aiti-14372 145 17 a a DET aiti-14372 145 18 , , PUNCT aiti-14372 145 19 range range NOUN aiti-14372 145 20 of of ADP aiti-14372 145 21 0.8 0.8 NUM aiti-14372 145 22 - - SYM aiti-14372 145 23 2.8 2.8 NUM aiti-14372 145 24 mm mm NOUN aiti-14372 145 25 . . PUNCT aiti-14372 146 1 it it PRON aiti-14372 146 2 is be AUX aiti-14372 146 3 observed observe VERB aiti-14372 146 4 that that SCONJ aiti-14372 146 5 the the DET aiti-14372 146 6 slope slope NOUN aiti-14372 146 7 of of ADP aiti-14372 146 8 da da PROPN aiti-14372 146 9 / / SYM aiti-14372 146 10 dn dn NOUN aiti-14372 146 11 versus versus ADP aiti-14372 146 12 a a DET aiti-14372 146 13 curve curve NOUN aiti-14372 146 14 increases increase NOUN aiti-14372 146 15 gradually gradually ADV aiti-14372 146 16 , , PUNCT aiti-14372 146 17 indicating indicate VERB aiti-14372 146 18 that that SCONJ aiti-14372 146 19 a a DET aiti-14372 146 20 higher high ADJ aiti-14372 146 21 number number NOUN aiti-14372 146 22 of of ADP aiti-14372 146 23 loading loading NOUN aiti-14372 146 24 cycles cycle NOUN aiti-14372 146 25 is be AUX aiti-14372 146 26 required require VERB aiti-14372 146 27 for for ADP aiti-14372 146 28 a a DET aiti-14372 146 29 small small ADJ aiti-14372 146 30 increment increment NOUN aiti-14372 146 31 in in ADP aiti-14372 146 32 crack crack NOUN aiti-14372 146 33 length length NOUN aiti-14372 146 34 in in ADP aiti-14372 146 35 the the DET aiti-14372 146 36 region region NOUN aiti-14372 146 37 . . PUNCT aiti-14372 147 1 the the DET aiti-14372 147 2 same same ADJ aiti-14372 147 3 is be AUX aiti-14372 147 4 also also ADV aiti-14372 147 5 evident evident ADJ aiti-14372 147 6 from from ADP aiti-14372 147 7 the the DET aiti-14372 147 8 da da PROPN aiti-14372 147 9 / / SYM aiti-14372 147 10 dn dn NOUN aiti-14372 147 11 versus versus ADP aiti-14372 147 12 n n PRON aiti-14372 147 13 curve curve NOUN aiti-14372 147 14 , , PUNCT aiti-14372 147 15 shown show VERB aiti-14372 147 16 in in ADP aiti-14372 147 17 fig fig NOUN aiti-14372 147 18 . . PUNCT aiti-14372 148 1 7 7 X aiti-14372 148 2 . . X aiti-14372 148 3 the the DET aiti-14372 148 4 range range NOUN aiti-14372 148 5 of of ADP aiti-14372 148 6 n n PRON aiti-14372 148 7 for for ADP aiti-14372 148 8 stage stage NOUN aiti-14372 148 9 - - PUNCT aiti-14372 148 10 i i PRON aiti-14372 148 11 of of ADP aiti-14372 148 12 fcgr fcgr NOUN aiti-14372 148 13 is be AUX aiti-14372 148 14 observed observe VERB aiti-14372 148 15 between between ADP aiti-14372 148 16 0 0 NUM aiti-14372 148 17 - - SYM aiti-14372 148 18 44419 44419 NUM aiti-14372 148 19 , , PUNCT aiti-14372 148 20 in in ADP aiti-14372 148 21 the the DET aiti-14372 148 22 plastic plastic ADJ aiti-14372 148 23 region region NOUN aiti-14372 148 24 . . PUNCT aiti-14372 149 1 3.2.2 3.2.2 X aiti-14372 149 2 . . PUNCT aiti-14372 149 3 fcgr fcgr NOUN aiti-14372 149 4 in in ADP aiti-14372 149 5 stage stage NOUN aiti-14372 149 6 - - PUNCT aiti-14372 149 7 ii ii NOUN aiti-14372 149 8 from from ADP aiti-14372 149 9 fig fig NOUN aiti-14372 149 10 . . PUNCT aiti-14372 150 1 5 5 NUM aiti-14372 150 2 , , PUNCT aiti-14372 150 3 the the DET aiti-14372 150 4 stage stage NOUN aiti-14372 150 5 - - PUNCT aiti-14372 150 6 ii ii NOUN aiti-14372 150 7 of of ADP aiti-14372 150 8 fcgr fcgr NOUN aiti-14372 150 9 is be AUX aiti-14372 150 10 observed observe VERB aiti-14372 150 11 in in ADP aiti-14372 150 12 the the DET aiti-14372 150 13 Ξ΄k Ξ΄k PROPN aiti-14372 150 14 range range NOUN aiti-14372 150 15 20.46 20.46 NUM aiti-14372 150 16 - - SYM aiti-14372 150 17 21.41 21.41 NUM aiti-14372 150 18 π‘€π‘ƒπ‘Žβˆšπ‘š. π‘€π‘ƒπ‘Žβˆšπ‘š. NOUN aiti-14372 150 19 in in ADP aiti-14372 150 20 this this DET aiti-14372 150 21 range range NOUN aiti-14372 150 22 , , PUNCT aiti-14372 150 23 the the DET aiti-14372 150 24 slope slope NOUN aiti-14372 150 25 of of ADP aiti-14372 150 26 da da PROPN aiti-14372 150 27 / / SYM aiti-14372 150 28 dn dn NOUN aiti-14372 150 29 versus versus ADP aiti-14372 150 30 Ξ΄k Ξ΄k X aiti-14372 150 31 increases increase NOUN aiti-14372 150 32 significantly significantly ADV aiti-14372 150 33 . . PUNCT aiti-14372 151 1 in in ADP aiti-14372 151 2 other other ADJ aiti-14372 151 3 words word NOUN aiti-14372 151 4 , , PUNCT aiti-14372 151 5 the the DET aiti-14372 151 6 crack crack NOUN aiti-14372 151 7 driving driving NOUN aiti-14372 151 8 force force NOUN aiti-14372 151 9 Ξ΄k Ξ΄k ADP aiti-14372 151 10 decreases decrease NOUN aiti-14372 151 11 with with ADP aiti-14372 151 12 increasing increase VERB aiti-14372 151 13 a. a. NOUN aiti-14372 151 14 it it PRON aiti-14372 151 15 is be AUX aiti-14372 151 16 suggested suggest VERB aiti-14372 151 17 that that SCONJ aiti-14372 151 18 the the DET aiti-14372 151 19 bending bend VERB aiti-14372 151 20 stress stress ADJ aiti-14372 151 21 accumulation accumulation NOUN aiti-14372 151 22 in in ADP aiti-14372 151 23 the the DET aiti-14372 151 24 previous previous ADJ aiti-14372 151 25 stage stage NOUN aiti-14372 151 26 played play VERB aiti-14372 151 27 a a DET aiti-14372 151 28 significant significant ADJ aiti-14372 151 29 role role NOUN aiti-14372 151 30 in in ADP aiti-14372 151 31 reducing reduce VERB aiti-14372 151 32 the the DET aiti-14372 151 33 required require VERB aiti-14372 151 34 drive drive NOUN aiti-14372 151 35 force force NOUN aiti-14372 151 36 for for ADP aiti-14372 151 37 fcg fcg NOUN aiti-14372 151 38 . . PUNCT aiti-14372 152 1 it it PRON aiti-14372 152 2 indicates indicate VERB aiti-14372 152 3 that that SCONJ aiti-14372 152 4 the the DET aiti-14372 152 5 crack crack NOUN aiti-14372 152 6 softening softening NOUN aiti-14372 152 7 accelerates accelerate VERB aiti-14372 152 8 as as SCONJ aiti-14372 152 9 compared compare VERB aiti-14372 152 10 to to ADP aiti-14372 152 11 the the DET aiti-14372 152 12 previous previous ADJ aiti-14372 152 13 stage stage NOUN aiti-14372 152 14 . . PUNCT aiti-14372 153 1 the the DET aiti-14372 153 2 increasing increase VERB aiti-14372 153 3 slope slope NOUN aiti-14372 153 4 of of ADP aiti-14372 153 5 fcgr fcgr NOUN aiti-14372 153 6 between between ADP aiti-14372 153 7 2.84.15 2.84.15 NUM aiti-14372 153 8 mm mm PROPN aiti-14372 153 9 envisages envisage VERB aiti-14372 153 10 that that SCONJ aiti-14372 153 11 a a DET aiti-14372 153 12 comparatively comparatively ADV aiti-14372 153 13 lower low ADJ aiti-14372 153 14 number number NOUN aiti-14372 153 15 of of ADP aiti-14372 153 16 n n NUM aiti-14372 153 17 was be AUX aiti-14372 153 18 required require VERB aiti-14372 153 19 for for ADP aiti-14372 153 20 a a DET aiti-14372 153 21 corresponding corresponding ADJ aiti-14372 153 22 increase increase NOUN aiti-14372 153 23 in in ADP aiti-14372 153 24 a a PRON aiti-14372 153 25 as as ADP aiti-14372 153 26 compared compare VERB aiti-14372 153 27 to to ADP aiti-14372 153 28 stage stage NOUN aiti-14372 153 29 - - PUNCT aiti-14372 153 30 i i PRON aiti-14372 153 31 , , PUNCT aiti-14372 153 32 as as SCONJ aiti-14372 153 33 shown show VERB aiti-14372 153 34 in in ADP aiti-14372 153 35 fig fig NOUN aiti-14372 153 36 . . PUNCT aiti-14372 154 1 6 6 NUM aiti-14372 154 2 . . X aiti-14372 155 1 the the DET aiti-14372 155 2 hypothesis hypothesis NOUN aiti-14372 155 3 of of ADP aiti-14372 155 4 the the DET aiti-14372 155 5 lower low ADJ aiti-14372 155 6 n n NOUN aiti-14372 155 7 was be AUX aiti-14372 155 8 confirmed confirm VERB aiti-14372 155 9 from from ADP aiti-14372 155 10 the the DET aiti-14372 155 11 slopes slope NOUN aiti-14372 155 12 of of ADP aiti-14372 155 13 fcgr fcgr NOUN aiti-14372 155 14 versus versus ADP aiti-14372 155 15 n n CCONJ aiti-14372 155 16 in in ADP aiti-14372 155 17 stage stage NOUN aiti-14372 155 18 - - PUNCT aiti-14372 155 19 ii ii NOUN aiti-14372 155 20 , , PUNCT aiti-14372 155 21 as as SCONJ aiti-14372 155 22 shown show VERB aiti-14372 155 23 in in ADP aiti-14372 155 24 fig fig NOUN aiti-14372 155 25 . . PUNCT aiti-14372 156 1 7 7 X aiti-14372 156 2 . . X aiti-14372 156 3 the the DET aiti-14372 156 4 n n NOUN aiti-14372 156 5 for for ADP aiti-14372 156 6 stage stage NOUN aiti-14372 156 7 - - PUNCT aiti-14372 156 8 ii ii NOUN aiti-14372 156 9 of of ADP aiti-14372 156 10 fcgr fcgr NOUN aiti-14372 156 11 was be AUX aiti-14372 156 12 from from ADP aiti-14372 156 13 44419 44419 NUM aiti-14372 156 14 - - SYM aiti-14372 156 15 60106 60106 NUM aiti-14372 156 16 . . PUNCT aiti-14372 157 1 3.2.3 3.2.3 X aiti-14372 157 2 . . X aiti-14372 157 3 fcgr fcgr NOUN aiti-14372 157 4 in in ADP aiti-14372 157 5 stage stage NOUN aiti-14372 157 6 - - PUNCT aiti-14372 157 7 iii iii NOUN aiti-14372 157 8 the the DET aiti-14372 157 9 stage stage NOUN aiti-14372 157 10 - - PUNCT aiti-14372 157 11 iii iii NOUN aiti-14372 157 12 of of ADP aiti-14372 157 13 fcgr fcgr NOUN aiti-14372 157 14 showed show VERB aiti-14372 157 15 an an DET aiti-14372 157 16 accelerated accelerated ADJ aiti-14372 157 17 crack crack NOUN aiti-14372 157 18 growth growth NOUN aiti-14372 157 19 . . PUNCT aiti-14372 158 1 the the DET aiti-14372 158 2 slope slope NOUN aiti-14372 158 3 of of ADP aiti-14372 158 4 da da PROPN aiti-14372 158 5 / / SYM aiti-14372 158 6 dn dn NOUN aiti-14372 158 7 versus versus ADP aiti-14372 158 8 Ξ΄k Ξ΄k INTJ aiti-14372 158 9 increased increase VERB aiti-14372 158 10 vigorously vigorously ADV aiti-14372 158 11 . . PUNCT aiti-14372 159 1 it it PRON aiti-14372 159 2 means mean VERB aiti-14372 159 3 , , PUNCT aiti-14372 159 4 the the DET aiti-14372 159 5 driving drive VERB aiti-14372 159 6 force force NOUN aiti-14372 159 7 required require VERB aiti-14372 159 8 for for ADP aiti-14372 159 9 an an DET aiti-14372 159 10 existing exist VERB aiti-14372 159 11 crack crack NOUN aiti-14372 159 12 ( ( PUNCT aiti-14372 159 13 in in ADP aiti-14372 159 14 the the DET aiti-14372 159 15 previous previous ADJ aiti-14372 159 16 stage stage NOUN aiti-14372 159 17 - - PUNCT aiti-14372 159 18 ii ii NOUN aiti-14372 159 19 ) ) PUNCT aiti-14372 159 20 to to PART aiti-14372 159 21 propagate propagate VERB aiti-14372 159 22 was be AUX aiti-14372 159 23 highly highly ADV aiti-14372 159 24 reduced reduce VERB aiti-14372 159 25 , , PUNCT aiti-14372 159 26 and and CCONJ aiti-14372 159 27 an an DET aiti-14372 159 28 accelerated accelerated ADJ aiti-14372 159 29 fcg fcg NOUN aiti-14372 159 30 occurred occur VERB aiti-14372 159 31 with with ADP aiti-14372 159 32 a a DET aiti-14372 159 33 lower low ADJ aiti-14372 159 34 increase increase NOUN aiti-14372 159 35 in in ADP aiti-14372 159 36 Ξ΄k Ξ΄k PROPN aiti-14372 159 37 . . PUNCT aiti-14372 160 1 as as SCONJ aiti-14372 160 2 shown show VERB aiti-14372 160 3 in in ADP aiti-14372 160 4 fig fig NOUN aiti-14372 160 5 . . PUNCT aiti-14372 161 1 5 5 NUM aiti-14372 161 2 , , PUNCT aiti-14372 161 3 the the DET aiti-14372 161 4 stage stage NOUN aiti-14372 161 5 - - PUNCT aiti-14372 161 6 iii iii NOUN aiti-14372 161 7 of of ADP aiti-14372 161 8 fcgr fcgr NOUN aiti-14372 161 9 is be AUX aiti-14372 161 10 in in ADP aiti-14372 161 11 the the DET aiti-14372 161 12 Ξ΄k Ξ΄k ADJ aiti-14372 161 13 range range NOUN aiti-14372 161 14 21.41 21.41 NUM aiti-14372 161 15 - - SYM aiti-14372 161 16 21.98 21.98 NUM aiti-14372 161 17 π‘€π‘ƒπ‘Žβˆšπ‘š. π‘€π‘ƒπ‘Žβˆšπ‘š. NOUN aiti-14372 161 18 as as SCONJ aiti-14372 161 19 shown show VERB aiti-14372 161 20 in in ADP aiti-14372 161 21 figs fig NOUN aiti-14372 161 22 . . PUNCT aiti-14372 162 1 6 6 NUM aiti-14372 162 2 and and CCONJ aiti-14372 162 3 7 7 NUM aiti-14372 162 4 , , PUNCT aiti-14372 162 5 a a DET aiti-14372 162 6 much much ADV aiti-14372 162 7 lower low ADJ aiti-14372 162 8 number number NOUN aiti-14372 162 9 of of ADP aiti-14372 162 10 loading loading NOUN aiti-14372 162 11 cycles cycle NOUN aiti-14372 162 12 was be AUX aiti-14372 162 13 required require VERB aiti-14372 162 14 for for ADP aiti-14372 162 15 a a DET aiti-14372 162 16 corresponding correspond VERB aiti-14372 162 17 crack crack NOUN aiti-14372 162 18 propagation propagation NOUN aiti-14372 162 19 and and CCONJ aiti-14372 162 20 hence hence ADV aiti-14372 162 21 , , PUNCT aiti-14372 162 22 da da ADJ aiti-14372 162 23 / / SYM aiti-14372 162 24 dn dn NOUN aiti-14372 162 25 increases increase VERB aiti-14372 162 26 rapidly rapidly ADV aiti-14372 162 27 for for ADP aiti-14372 162 28 a a DET aiti-14372 162 29 given give VERB aiti-14372 162 30 a a PRON aiti-14372 162 31 and and CCONJ aiti-14372 162 32 n. n. NOUN aiti-14372 162 33 it it PRON aiti-14372 162 34 is be AUX aiti-14372 162 35 suggested suggest VERB aiti-14372 162 36 that that SCONJ aiti-14372 162 37 in in ADP aiti-14372 162 38 this this DET aiti-14372 162 39 region region NOUN aiti-14372 162 40 , , PUNCT aiti-14372 162 41 the the DET aiti-14372 162 42 crack crack NOUN aiti-14372 162 43 driving driving NOUN aiti-14372 162 44 force force NOUN aiti-14372 162 45 ( ( PUNCT aiti-14372 162 46 Ξ΄k Ξ΄k VERB aiti-14372 162 47 ) ) PUNCT aiti-14372 162 48 was be AUX aiti-14372 162 49 subjugated subjugate VERB aiti-14372 162 50 to to ADP aiti-14372 162 51 the the DET aiti-14372 162 52 crack crack NOUN aiti-14372 162 53 resisting resist VERB aiti-14372 162 54 parameter parameter NOUN aiti-14372 162 55 ( ( PUNCT aiti-14372 162 56 kc kc PROPN aiti-14372 162 57 ) ) PUNCT aiti-14372 162 58 and and CCONJ aiti-14372 162 59 material material NOUN aiti-14372 162 60 properties property NOUN aiti-14372 162 61 ( ( PUNCT aiti-14372 162 62 stiffness stiffness NOUN aiti-14372 162 63 , , PUNCT aiti-14372 162 64 e e NOUN aiti-14372 162 65 ) ) PUNCT aiti-14372 162 66 . . PUNCT aiti-14372 163 1 the the DET aiti-14372 163 2 stage stage NOUN aiti-14372 163 3 - - PUNCT aiti-14372 163 4 iii iii NOUN aiti-14372 163 5 was be AUX aiti-14372 163 6 characterized characterize VERB aiti-14372 163 7 in in ADP aiti-14372 163 8 the the DET aiti-14372 163 9 a a DET aiti-14372 163 10 range4.15 range4.15 NOUN aiti-14372 163 11 - - SYM aiti-14372 163 12 4.75 4.75 NUM aiti-14372 163 13 mm mm NOUN aiti-14372 163 14 and and CCONJ aiti-14372 163 15 a a DET aiti-14372 163 16 corresponding corresponding ADJ aiti-14372 163 17 n n CCONJ aiti-14372 163 18 60106 60106 NUM aiti-14372 163 19 - - SYM aiti-14372 163 20 63014 63014 NUM aiti-14372 163 21 . . PUNCT aiti-14372 164 1 after after ADP aiti-14372 164 2 a a DET aiti-14372 164 3 Ξ΄k Ξ΄k PROPN aiti-14372 164 4 of of ADP aiti-14372 164 5 21.98 21.98 NUM aiti-14372 164 6 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 164 7 , , PUNCT aiti-14372 164 8 a a PRON aiti-14372 164 9 of of ADP aiti-14372 164 10 4.75 4.75 NUM aiti-14372 164 11 mm mm NOUN aiti-14372 164 12 , , PUNCT aiti-14372 164 13 and and CCONJ aiti-14372 164 14 n n PRON aiti-14372 164 15 63014 63014 NUM aiti-14372 164 16 , , PUNCT aiti-14372 164 17 the the DET aiti-14372 164 18 fcgr fcgr NOUN aiti-14372 164 19 is be AUX aiti-14372 164 20 highly highly ADV aiti-14372 164 21 accelerated accelerate VERB aiti-14372 164 22 , , PUNCT aiti-14372 164 23 and and CCONJ aiti-14372 164 24 the the DET aiti-14372 164 25 material material NOUN aiti-14372 164 26 reaches reach VERB aiti-14372 164 27 the the DET aiti-14372 164 28 tri tri ADJ aiti-14372 164 29 - - ADJ aiti-14372 164 30 axial axial ADJ aiti-14372 164 31 stresses stress NOUN aiti-14372 164 32 envisaging envisage VERB aiti-14372 164 33 necking neck VERB aiti-14372 164 34 phenomena phenomenon NOUN aiti-14372 164 35 that that SCONJ aiti-14372 164 36 eventually eventually ADV aiti-14372 164 37 led lead VERB aiti-14372 164 38 to to ADP aiti-14372 164 39 the the DET aiti-14372 164 40 catastrophic catastrophic ADJ aiti-14372 164 41 failure failure NOUN aiti-14372 164 42 of of ADP aiti-14372 164 43 the the DET aiti-14372 164 44 material material NOUN aiti-14372 164 45 [ [ X aiti-14372 164 46 21 21 NUM aiti-14372 164 47 , , PUNCT aiti-14372 164 48 27 27 NUM aiti-14372 164 49 ] ] PUNCT aiti-14372 164 50 . . PUNCT aiti-14372 165 1 the the DET aiti-14372 165 2 next next ADJ aiti-14372 165 3 stage stage NOUN aiti-14372 165 4 of of ADP aiti-14372 165 5 fcg fcg NOUN aiti-14372 165 6 after after ADP aiti-14372 165 7 4.75 4.75 NUM aiti-14372 165 8 mm mm NOUN aiti-14372 165 9 of of ADP aiti-14372 165 10 crack crack NOUN aiti-14372 165 11 length length NOUN aiti-14372 165 12 ( ( PUNCT aiti-14372 165 13 which which PRON aiti-14372 165 14 was be AUX aiti-14372 165 15 7.03 7.03 NUM aiti-14372 165 16 mm mm NOUN aiti-14372 165 17 considering consider VERB aiti-14372 165 18 the the DET aiti-14372 165 19 pre pre ADJ aiti-14372 165 20 - - ADJ aiti-14372 165 21 notch notch ADJ aiti-14372 165 22 length length NOUN aiti-14372 165 23 ) ) PUNCT aiti-14372 165 24 up up ADP aiti-14372 165 25 to to ADP aiti-14372 165 26 the the DET aiti-14372 165 27 radial radial ADJ aiti-14372 165 28 thickness thickness NOUN aiti-14372 165 29 of of ADP aiti-14372 165 30 pipe pipe NOUN aiti-14372 165 31 ( ( PUNCT aiti-14372 165 32 equal equal ADJ aiti-14372 165 33 to to ADP aiti-14372 165 34 9 9 NUM aiti-14372 165 35 mm mm NOUN aiti-14372 165 36 ) ) PUNCT aiti-14372 165 37 was be AUX aiti-14372 165 38 not not PART aiti-14372 165 39 considered consider VERB aiti-14372 165 40 for for ADP aiti-14372 165 41 fcgr fcgr NOUN aiti-14372 165 42 modelling modelling NOUN aiti-14372 165 43 due due ADP aiti-14372 165 44 to to ADP aiti-14372 165 45 the the DET aiti-14372 165 46 limitation limitation NOUN aiti-14372 165 47 of of ADP aiti-14372 165 48 the the DET aiti-14372 165 49 modified modify VERB aiti-14372 165 50 exponential exponential ADJ aiti-14372 165 51 function function NOUN aiti-14372 165 52 , , PUNCT aiti-14372 165 53 stress stress NOUN aiti-14372 165 54 - - PUNCT aiti-14372 165 55 triaxiality triaxiality NOUN aiti-14372 165 56 in in ADP aiti-14372 165 57 the the DET aiti-14372 165 58 vicinity vicinity NOUN aiti-14372 165 59 of of ADP aiti-14372 165 60 crack crack NOUN aiti-14372 165 61 , , PUNCT aiti-14372 165 62 and and CCONJ aiti-14372 165 63 requirement requirement NOUN aiti-14372 165 64 of of ADP aiti-14372 165 65 complex complex ADJ aiti-14372 165 66 mathematical mathematical ADJ aiti-14372 165 67 expressions expression NOUN aiti-14372 165 68 . . PUNCT aiti-14372 166 1 based base VERB aiti-14372 166 2 on on ADP aiti-14372 166 3 the the DET aiti-14372 166 4 above above ADJ aiti-14372 166 5 discussion discussion NOUN aiti-14372 166 6 , , PUNCT aiti-14372 166 7 the the DET aiti-14372 166 8 boundary boundary ADJ aiti-14372 166 9 conditions condition NOUN aiti-14372 166 10 and and CCONJ aiti-14372 166 11 fcgr fcgr VERB aiti-14372 166 12 for for ADP aiti-14372 166 13 all all DET aiti-14372 166 14 three three NUM aiti-14372 166 15 stages stage NOUN aiti-14372 166 16 are be AUX aiti-14372 166 17 shown show VERB aiti-14372 166 18 in in ADP aiti-14372 166 19 table table NOUN aiti-14372 166 20 3 3 NUM aiti-14372 166 21 . . PUNCT aiti-14372 166 22 table table NOUN aiti-14372 166 23 3 3 NUM aiti-14372 166 24 boundary boundary ADJ aiti-14372 166 25 conditions condition NOUN aiti-14372 166 26 and and CCONJ aiti-14372 166 27 fcgr fcgr VERB aiti-14372 166 28 for for ADP aiti-14372 166 29 all all DET aiti-14372 166 30 three three NUM aiti-14372 166 31 stages stage NOUN aiti-14372 166 32 stage stage NOUN aiti-14372 166 33 of of ADP aiti-14372 166 34 fcgr fcgr NOUN aiti-14372 166 35 boundary boundary ADJ aiti-14372 166 36 condition condition NOUN aiti-14372 166 37 phenomena phenomenon NOUN aiti-14372 166 38 of of ADP aiti-14372 166 39 fcgr fcgr NOUN aiti-14372 166 40 i i PRON aiti-14372 166 41   ADJ aiti-14372 166 42   ADP aiti-14372 166 43 stage stage NOUN aiti-14372 166 44 - - PUNCT aiti-14372 166 45 i i PRON aiti-14372 166 46 0.85 0.85 NUM aiti-14372 166 47 , , PUNCT aiti-14372 166 48 2.80 2.80 NUM aiti-14372 166 49 ; ; PUNCT aiti-14372 166 50 17.45 17.45 NUM aiti-14372 166 51 , , PUNCT aiti-14372 166 52 20.46 20.46 NUM aiti-14372 166 53 fcgr fcgr NOUN aiti-14372 166 54 a a DET aiti-14372 166 55 mm mm INTJ aiti-14372 166 56 mm mm INTJ aiti-14372 167 1 k k PROPN aiti-14372 167 2 mpa mpa PROPN aiti-14372 167 3 m m PROPN aiti-14372 167 4 mpa mpa PROPN aiti-14372 167 5 m m PROPN aiti-14372 167 6 ο€½ ο€½ PROPN aiti-14372 167 7   PROPN aiti-14372 167 8   PUNCT aiti-14372 167 9   PROPN aiti-14372 167 10   PROPN aiti-14372 167 11 the the DET aiti-14372 167 12 cracks crack NOUN aiti-14372 167 13 resisting resist VERB aiti-14372 167 14 parameter parameter NOUN aiti-14372 167 15 ( ( PUNCT aiti-14372 167 16 kc kc PROPN aiti-14372 167 17 ) ) PUNCT aiti-14372 167 18 and and CCONJ aiti-14372 167 19 materials material NOUN aiti-14372 167 20 property property NOUN aiti-14372 167 21 ( ( PUNCT aiti-14372 167 22 stiffness stiffness NOUN aiti-14372 167 23 , , PUNCT aiti-14372 167 24 e e NOUN aiti-14372 167 25 ) ) PUNCT aiti-14372 167 26 oppose oppose VERB aiti-14372 167 27 the the DET aiti-14372 167 28 crack crack NOUN aiti-14372 167 29 driving driving NOUN aiti-14372 167 30 force force NOUN aiti-14372 167 31 ( ( PUNCT aiti-14372 167 32 Ξ΄k Ξ΄k ADP aiti-14372 167 33 ) ) PUNCT aiti-14372 167 34 at at ADP aiti-14372 167 35 best good ADJ aiti-14372 167 36 after after ADP aiti-14372 167 37 the the DET aiti-14372 167 38 threshold threshold NOUN aiti-14372 167 39 Ξ΄k Ξ΄k PROPN aiti-14372 167 40 . . PROPN aiti-14372 167 41 ii ii PROPN aiti-14372 167 42   PROPN aiti-14372 167 43   NOUN aiti-14372 167 44 stage stage NOUN aiti-14372 167 45 - - PUNCT aiti-14372 167 46 ii ii NOUN aiti-14372 167 47 2.80 2.80 NUM aiti-14372 167 48 , , PUNCT aiti-14372 167 49 4.15 4.15 NUM aiti-14372 167 50 ; ; PUNCT aiti-14372 167 51 20.46 20.46 NUM aiti-14372 167 52 , , PUNCT aiti-14372 167 53 21.41 21.41 NUM aiti-14372 167 54 fcgr fcgr NOUN aiti-14372 167 55 a a DET aiti-14372 167 56 mm mm INTJ aiti-14372 167 57 mm mm INTJ aiti-14372 168 1 k k PROPN aiti-14372 168 2 mpa mpa PROPN aiti-14372 168 3 m m PROPN aiti-14372 168 4 mpa mpa PROPN aiti-14372 168 5 m m PROPN aiti-14372 168 6 ο€½ ο€½ PROPN aiti-14372 168 7   PROPN aiti-14372 168 8   PUNCT aiti-14372 168 9   PROPN aiti-14372 168 10   PROPN aiti-14372 168 11 the the DET aiti-14372 168 12 driving drive VERB aiti-14372 168 13 force force NOUN aiti-14372 168 14 Ξ΄k Ξ΄k PROPN aiti-14372 168 15 was be AUX aiti-14372 168 16 decreased decrease VERB aiti-14372 168 17 with with ADP aiti-14372 168 18 increasing increase VERB aiti-14372 168 19 a. a. NOUN aiti-14372 168 20 iii iii PROPN aiti-14372 168 21   PROPN aiti-14372 168 22   NOUN aiti-14372 168 23 stage stage NOUN aiti-14372 168 24 - - PUNCT aiti-14372 168 25 iii iii NUM aiti-14372 168 26 4.15 4.15 NUM aiti-14372 168 27 , , PUNCT aiti-14372 168 28 4.75 4.75 NUM aiti-14372 168 29 ; ; PUNCT aiti-14372 168 30 21.41 21.41 NUM aiti-14372 168 31 , , PUNCT aiti-14372 168 32 21.98 21.98 NUM aiti-14372 168 33 fcgr fcgr NOUN aiti-14372 168 34 a a DET aiti-14372 168 35 mm mm INTJ aiti-14372 168 36 mm mm INTJ aiti-14372 169 1 k k PROPN aiti-14372 169 2 mpa mpa PROPN aiti-14372 169 3 m m PROPN aiti-14372 169 4 mpa mpa PROPN aiti-14372 169 5 m m PROPN aiti-14372 169 6 ο€½ ο€½ PROPN aiti-14372 169 7   PROPN aiti-14372 169 8   PUNCT aiti-14372 169 9   PROPN aiti-14372 169 10   PROPN aiti-14372 169 11 the the DET aiti-14372 169 12 driving drive VERB aiti-14372 169 13 force force NOUN aiti-14372 169 14 ( ( PUNCT aiti-14372 169 15 Ξ΄k Ξ΄k VERB aiti-14372 169 16 ) ) PUNCT aiti-14372 169 17 was be AUX aiti-14372 169 18 subjugated subjugate VERB aiti-14372 169 19 to to ADP aiti-14372 169 20 the the DET aiti-14372 169 21 crack crack NOUN aiti-14372 169 22 resisting resist VERB aiti-14372 169 23 parameter parameter NOUN aiti-14372 169 24 ( ( PUNCT aiti-14372 169 25 kc kc PROPN aiti-14372 169 26 ) ) PUNCT aiti-14372 169 27 and and CCONJ aiti-14372 169 28 material material NOUN aiti-14372 169 29 property property NOUN aiti-14372 169 30 ( ( PUNCT aiti-14372 169 31 stiffness stiffness NOUN aiti-14372 169 32 , , PUNCT aiti-14372 169 33 e e NOUN aiti-14372 169 34 ) ) PUNCT aiti-14372 169 35 . . PUNCT aiti-14372 170 1 advances advance NOUN aiti-14372 170 2 in in ADP aiti-14372 170 3 technology technology NOUN aiti-14372 170 4 innovation innovation NOUN aiti-14372 170 5 , , PUNCT aiti-14372 170 6 vol vol NOUN aiti-14372 170 7 . . PROPN aiti-14372 171 1 10 10 NUM aiti-14372 171 2 , , PUNCT aiti-14372 171 3 no no INTJ aiti-14372 171 4 . . NOUN aiti-14372 171 5 3 3 NUM aiti-14372 171 6 , , PUNCT aiti-14372 171 7 2025 2025 NUM aiti-14372 171 8 , , PUNCT aiti-14372 171 9 pp pp ADJ aiti-14372 171 10 . . PUNCT aiti-14372 172 1 238 238 NUM aiti-14372 172 2 - - SYM aiti-14372 172 3 253 253 NUM aiti-14372 172 4 244 244 NUM aiti-14372 172 5 fig fig NOUN aiti-14372 172 6 . . PUNCT aiti-14372 173 1 5 5 NUM aiti-14372 173 2 fcgr fcgr NOUN aiti-14372 173 3 versus versus ADP aiti-14372 173 4 Ξ΄k Ξ΄k PROPN aiti-14372 173 5 for for ADP aiti-14372 173 6 stages stage NOUN aiti-14372 173 7 - - PUNCT aiti-14372 173 8 i i PRON aiti-14372 173 9 , , PUNCT aiti-14372 173 10 ii ii PROPN aiti-14372 173 11 , , PUNCT aiti-14372 173 12 and and CCONJ aiti-14372 173 13 iii iii X aiti-14372 173 14 fig fig NOUN aiti-14372 173 15 . . PUNCT aiti-14372 174 1 6 6 NUM aiti-14372 174 2 fcgr fcgr NOUN aiti-14372 174 3 versus versus ADP aiti-14372 174 4 a a PRON aiti-14372 174 5 for for ADP aiti-14372 174 6 stages stage NOUN aiti-14372 174 7 - - PUNCT aiti-14372 174 8 i i PRON aiti-14372 174 9 , , PUNCT aiti-14372 174 10 ii ii PROPN aiti-14372 174 11 , , PUNCT aiti-14372 174 12 and and CCONJ aiti-14372 174 13 iii iii X aiti-14372 174 14 fig fig NOUN aiti-14372 174 15 . . PUNCT aiti-14372 175 1 7 7 NUM aiti-14372 175 2 fcgr fcgr NOUN aiti-14372 175 3 versus versus ADP aiti-14372 175 4 n n CCONJ aiti-14372 175 5 for for ADP aiti-14372 175 6 stages stage NOUN aiti-14372 175 7 - - PUNCT aiti-14372 175 8 i i PRON aiti-14372 175 9 , , PUNCT aiti-14372 175 10 ii ii PROPN aiti-14372 175 11 , , PUNCT aiti-14372 175 12 and and CCONJ aiti-14372 175 13 iii iii NUM aiti-14372 175 14 4 4 NUM aiti-14372 175 15 . . X aiti-14372 175 16 modelling modelling NOUN aiti-14372 175 17 of of ADP aiti-14372 175 18 fcgr fcgr NOUN aiti-14372 175 19 using use VERB aiti-14372 175 20 a a DET aiti-14372 175 21 modified modify VERB aiti-14372 175 22 exponential exponential ADJ aiti-14372 175 23 function function NOUN aiti-14372 175 24 the the DET aiti-14372 175 25 model model NOUN aiti-14372 175 26 considered consider VERB aiti-14372 175 27 the the DET aiti-14372 175 28 crack crack NOUN aiti-14372 175 29 driving driving NOUN aiti-14372 175 30 force force NOUN aiti-14372 175 31 and and CCONJ aiti-14372 175 32 crack crack VERB aiti-14372 175 33 resisting resist VERB aiti-14372 175 34 parameters parameter NOUN aiti-14372 175 35 to to PART aiti-14372 175 36 characterize characterize VERB aiti-14372 175 37 the the DET aiti-14372 175 38 nature nature NOUN aiti-14372 175 39 of of ADP aiti-14372 175 40 da da PROPN aiti-14372 175 41 / / SYM aiti-14372 175 42 dn dn NOUN aiti-14372 175 43 and and CCONJ aiti-14372 175 44 then then ADV aiti-14372 175 45 predicted predict VERB aiti-14372 175 46 the the DET aiti-14372 175 47 fcgr fcgr NOUN aiti-14372 175 48 . . PUNCT aiti-14372 176 1 the the DET aiti-14372 176 2 specific specific ADJ aiti-14372 176 3 growth growth NOUN aiti-14372 176 4 rate rate NOUN aiti-14372 176 5 is be AUX aiti-14372 176 6 discussed discuss VERB aiti-14372 176 7 for for ADP aiti-14372 176 8 all all DET aiti-14372 176 9 the the DET aiti-14372 176 10 stages stage NOUN aiti-14372 176 11 . . PUNCT aiti-14372 177 1 then then ADV aiti-14372 177 2 , , PUNCT aiti-14372 177 3 the the DET aiti-14372 177 4 modifications modification NOUN aiti-14372 177 5 made make VERB aiti-14372 177 6 to to ADP aiti-14372 177 7 the the DET aiti-14372 177 8 exponential exponential ADJ aiti-14372 177 9 function function NOUN aiti-14372 177 10 are be AUX aiti-14372 177 11 discussed discuss VERB aiti-14372 177 12 . . PUNCT aiti-14372 178 1 4.1 4.1 NUM aiti-14372 178 2 formulation formulation NOUN aiti-14372 178 3 of of ADP aiti-14372 178 4 the the DET aiti-14372 178 5 modified modify VERB aiti-14372 178 6 exponential exponential NOUN aiti-14372 178 7 function function NOUN aiti-14372 178 8 the the DET aiti-14372 178 9 hypothesis hypothesis NOUN aiti-14372 178 10 of of ADP aiti-14372 178 11 a a DET aiti-14372 178 12 given give VERB aiti-14372 178 13 mathematical mathematical ADJ aiti-14372 178 14 function function NOUN aiti-14372 178 15 is be AUX aiti-14372 178 16 proportional proportional ADJ aiti-14372 178 17 to to ADP aiti-14372 178 18 the the DET aiti-14372 178 19 speed speed NOUN aiti-14372 178 20 at at ADP aiti-14372 178 21 which which PRON aiti-14372 178 22 the the DET aiti-14372 178 23 function function NOUN aiti-14372 178 24 rises rise VERB aiti-14372 178 25 , , PUNCT aiti-14372 178 26 as as SCONJ aiti-14372 178 27 defined define VERB aiti-14372 178 28 by by ADP aiti-14372 178 29 the the DET aiti-14372 178 30 exponential exponential ADJ aiti-14372 178 31 function function NOUN aiti-14372 178 32 given give VERB aiti-14372 178 33 below below ADP aiti-14372 178 34 ( ( PUNCT aiti-14372 178 35 ) ) PUNCT aiti-14372 178 36 rt rt INTJ aiti-14372 178 37 op op NOUN aiti-14372 178 38 t t PROPN aiti-14372 178 39 p p PROPN aiti-14372 178 40 eο€½ eο€½ PROPN aiti-14372 178 41 ( ( PUNCT aiti-14372 178 42 2 2 NUM aiti-14372 178 43 ) ) PUNCT aiti-14372 178 44 where where SCONJ aiti-14372 178 45 p p NOUN aiti-14372 178 46 is be AUX aiti-14372 178 47 population population NOUN aiti-14372 178 48 , , PUNCT aiti-14372 178 49 𝑃 𝑃 PROPN aiti-14372 178 50 is be AUX aiti-14372 178 51 the the DET aiti-14372 178 52 initial initial ADJ aiti-14372 178 53 population population NOUN aiti-14372 178 54 , , PUNCT aiti-14372 178 55 t t PROPN aiti-14372 178 56 is be AUX aiti-14372 178 57 the the DET aiti-14372 178 58 time time NOUN aiti-14372 178 59 , , PUNCT aiti-14372 178 60 and and CCONJ aiti-14372 178 61 the the DET aiti-14372 178 62 quantity quantity NOUN aiti-14372 178 63 r r NOUN aiti-14372 178 64 in in ADP aiti-14372 178 65 the the DET aiti-14372 178 66 above above ADJ aiti-14372 178 67 equation equation NOUN aiti-14372 178 68 is be AUX aiti-14372 178 69 the the DET aiti-14372 178 70 malthusian malthusian ADJ aiti-14372 178 71 parameter parameter NOUN aiti-14372 178 72 or or CCONJ aiti-14372 178 73 specific specific ADJ aiti-14372 178 74 growth growth NOUN aiti-14372 178 75 rate rate NOUN aiti-14372 178 76 . . PUNCT aiti-14372 179 1 the the DET aiti-14372 179 2 eq eq NOUN aiti-14372 179 3 . . PUNCT aiti-14372 180 1 ( ( PUNCT aiti-14372 180 2 1 1 X aiti-14372 180 3 ) ) PUNCT aiti-14372 180 4 has have AUX aiti-14372 180 5 been be AUX aiti-14372 180 6 modified modify VERB aiti-14372 180 7 by by ADP aiti-14372 180 8 kumar kumar PROPN aiti-14372 180 9 et et PROPN aiti-14372 180 10 al al PROPN aiti-14372 180 11 . . PUNCT aiti-14372 181 1 to to PART aiti-14372 181 2 calculate calculate VERB aiti-14372 181 3 a a PRON aiti-14372 181 4 for for ADP aiti-14372 181 5 a a DET aiti-14372 181 6 given give VERB aiti-14372 181 7 n. n. NOUN aiti-14372 181 8 the the DET aiti-14372 181 9 modified modify VERB aiti-14372 181 10 equation equation NOUN aiti-14372 181 11 can can AUX aiti-14372 181 12 be be AUX aiti-14372 181 13 obtained obtain VERB aiti-14372 181 14 by by ADP aiti-14372 181 15 [ [ PUNCT aiti-14372 181 16 22 22 NUM aiti-14372 181 17 - - SYM aiti-14372 181 18 23 23 NUM aiti-14372 181 19 ] ] PUNCT aiti-14372 181 20 . . PUNCT aiti-14372 182 1 ( ( PUNCT aiti-14372 182 2 ) ) PUNCT aiti-14372 182 3 ijm ijm PROPN aiti-14372 182 4 j j PROPN aiti-14372 182 5 i i PRON aiti-14372 182 6 j j PROPN aiti-14372 182 7 ia ia PROPN aiti-14372 182 8 a a PROPN aiti-14372 182 9 e e PROPN aiti-14372 182 10 n n CCONJ aiti-14372 182 11 nο€½ nο€½ PROPN aiti-14372 182 12 ο€­ ο€­ NOUN aiti-14372 182 13 ( ( PUNCT aiti-14372 182 14 3 3 NUM aiti-14372 182 15 ) ) PUNCT aiti-14372 182 16 where where SCONJ aiti-14372 182 17 , , PUNCT aiti-14372 182 18 for for ADP aiti-14372 182 19 a a DET aiti-14372 182 20 given give VERB aiti-14372 182 21 interval interval NOUN aiti-14372 182 22 ( ( PUNCT aiti-14372 182 23 i i PROPN aiti-14372 182 24 , , PUNCT aiti-14372 182 25 j j PROPN aiti-14372 182 26 ) ) PUNCT aiti-14372 182 27 , , PUNCT aiti-14372 182 28 π‘Ž π‘Ž NOUN aiti-14372 182 29 is be AUX aiti-14372 182 30 the the DET aiti-14372 182 31 final final ADJ aiti-14372 182 32 crack crack NOUN aiti-14372 182 33 length length NOUN aiti-14372 182 34 , , PUNCT aiti-14372 182 35 π‘Ž π‘Ž NOUN aiti-14372 182 36 is be AUX aiti-14372 182 37 the the DET aiti-14372 182 38 initial initial ADJ aiti-14372 182 39 crack crack NOUN aiti-14372 182 40 length length NOUN aiti-14372 182 41 , , PUNCT aiti-14372 182 42 𝑁 𝑁 PROPN aiti-14372 182 43 βˆ’ βˆ’ NOUN aiti-14372 182 44 𝑁 𝑁 PROPN aiti-14372 182 45 is be AUX aiti-14372 182 46 the the DET aiti-14372 182 47 load load NOUN aiti-14372 182 48 cycle cycle NOUN aiti-14372 182 49 interval interval NOUN aiti-14372 182 50 , , PUNCT aiti-14372 182 51 and and CCONJ aiti-14372 182 52 π‘š π‘š PROPN aiti-14372 182 53 is be AUX aiti-14372 182 54 the the DET aiti-14372 182 55 specific specific ADJ aiti-14372 182 56 growth growth NOUN aiti-14372 182 57 rate rate NOUN aiti-14372 182 58 . . PUNCT aiti-14372 183 1 the the DET aiti-14372 183 2 π‘š π‘š PROPN aiti-14372 183 3 can can AUX aiti-14372 183 4 be be AUX aiti-14372 183 5 calculated calculate VERB aiti-14372 183 6 by by ADP aiti-14372 183 7 ln ln PROPN aiti-14372 183 8 j j PROPN aiti-14372 184 1 i i PRON aiti-14372 184 2 ij ij INTJ aiti-14372 184 3 j j PROPN aiti-14372 185 1 i i PRON aiti-14372 185 2 a a DET aiti-14372 185 3 a a DET aiti-14372 185 4 m m NOUN aiti-14372 185 5 n n ADP aiti-14372 185 6 n n PRON aiti-14372 185 7   NOUN aiti-14372 186 1 οƒΆ οƒΆ PROPN aiti-14372 186 2   PROPN aiti-14372 186 3 οƒ· οƒ· PROPN aiti-14372 187 1   ADJ aiti-14372 187 2 οƒΈο€½ οƒΈο€½ PROPN aiti-14372 187 3 ο€­ ο€­ NOUN aiti-14372 187 4 ( ( PUNCT aiti-14372 187 5 4 4 NUM aiti-14372 187 6 ) ) PUNCT aiti-14372 187 7 advances advance NOUN aiti-14372 187 8 in in ADP aiti-14372 187 9 technology technology NOUN aiti-14372 187 10 innovation innovation NOUN aiti-14372 187 11 , , PUNCT aiti-14372 187 12 vol vol NOUN aiti-14372 187 13 . . PROPN aiti-14372 187 14 10 10 NUM aiti-14372 187 15 , , PUNCT aiti-14372 187 16 no no INTJ aiti-14372 187 17 . . NOUN aiti-14372 187 18 3 3 NUM aiti-14372 187 19 , , PUNCT aiti-14372 187 20 2025 2025 NUM aiti-14372 187 21 , , PUNCT aiti-14372 187 22 pp pp ADJ aiti-14372 187 23 . . PUNCT aiti-14372 188 1 238 238 NUM aiti-14372 188 2 - - SYM aiti-14372 188 3 253 253 NUM aiti-14372 188 4 245 245 NUM aiti-14372 188 5 in in ADP aiti-14372 188 6 the the DET aiti-14372 188 7 present present ADJ aiti-14372 188 8 work work NOUN aiti-14372 188 9 , , PUNCT aiti-14372 188 10 the the DET aiti-14372 188 11 specific specific ADJ aiti-14372 188 12 growth growth NOUN aiti-14372 188 13 rate rate NOUN aiti-14372 188 14 mij mij NOUN aiti-14372 188 15 is be AUX aiti-14372 188 16 modified modify VERB aiti-14372 188 17 and and CCONJ aiti-14372 188 18 correlated correlate VERB aiti-14372 188 19 with with ADP aiti-14372 188 20 a a DET aiti-14372 188 21 non non ADJ aiti-14372 188 22 - - ADJ aiti-14372 188 23 dimensional dimensional ADJ aiti-14372 188 24 number number NOUN aiti-14372 188 25 n n CCONJ aiti-14372 188 26 as as SCONJ aiti-14372 188 27 given give VERB aiti-14372 188 28 in in ADP aiti-14372 188 29 eq eq ADP aiti-14372 188 30 . . PUNCT aiti-14372 189 1 ( ( PUNCT aiti-14372 189 2 5 5 NUM aiti-14372 189 3 ) ) PUNCT aiti-14372 189 4 2 2 NUM aiti-14372 189 5 m m NOUN aiti-14372 189 6 an an DET aiti-14372 189 7 bn bn ADJ aiti-14372 189 8 cο€½ cο€½ NOUN aiti-14372 189 9   ADV aiti-14372 189 10   X aiti-14372 189 11 ( ( PUNCT aiti-14372 189 12 5 5 NUM aiti-14372 189 13 ) ) PUNCT aiti-14372 189 14 where where SCONJ aiti-14372 189 15 n n PRON aiti-14372 189 16 was be AUX aiti-14372 189 17 correlated correlate VERB aiti-14372 189 18 with with ADP aiti-14372 189 19 two two NUM aiti-14372 189 20 crack crack NOUN aiti-14372 189 21 driving driving NOUN aiti-14372 189 22 forces force NOUN aiti-14372 189 23 , , PUNCT aiti-14372 189 24 Ξ΄k Ξ΄k PUNCT aiti-14372 189 25 and and CCONJ aiti-14372 189 26 maximum maximum ADJ aiti-14372 189 27 stress stress NOUN aiti-14372 189 28 intensity intensity NOUN aiti-14372 189 29 factor factor NOUN aiti-14372 189 30 ( ( PUNCT aiti-14372 189 31 kmax kmax PROPN aiti-14372 189 32 ) ) PUNCT aiti-14372 189 33 , , PUNCT aiti-14372 189 34 as as ADV aiti-14372 189 35 well well ADV aiti-14372 189 36 as as ADP aiti-14372 189 37 material material ADJ aiti-14372 189 38 parameters parameter NOUN aiti-14372 189 39 , , PUNCT aiti-14372 189 40 fracture fracture ADJ aiti-14372 189 41 toughness toughness NOUN aiti-14372 189 42 ( ( PUNCT aiti-14372 189 43 kc kc PROPN aiti-14372 189 44 ) ) PUNCT aiti-14372 189 45 , , PUNCT aiti-14372 189 46 stiffness stiffness NOUN aiti-14372 189 47 ( ( PUNCT aiti-14372 189 48 e e NOUN aiti-14372 189 49 ) ) PUNCT aiti-14372 189 50 , , PUNCT aiti-14372 189 51 and and CCONJ aiti-14372 189 52 yield yield VERB aiti-14372 189 53 stress stress NOUN aiti-14372 189 54 ( ( PUNCT aiti-14372 189 55 Οƒys Οƒys PROPN aiti-14372 189 56 ) ) PUNCT aiti-14372 189 57 . . PUNCT aiti-14372 190 1 the the DET aiti-14372 190 2 above above ADJ aiti-14372 190 3 equation equation NOUN aiti-14372 190 4 has have AUX aiti-14372 190 5 been be AUX aiti-14372 190 6 modified modify VERB aiti-14372 190 7 to to ADP aiti-14372 190 8 a a DET aiti-14372 190 9 2nd 2nd ADJ aiti-14372 190 10 degree degree NOUN aiti-14372 190 11 polynomial polynomial NOUN aiti-14372 190 12 for for ADP aiti-14372 190 13 the the DET aiti-14372 190 14 present present ADJ aiti-14372 190 15 study study NOUN aiti-14372 190 16 . . PUNCT aiti-14372 191 1 however however ADV aiti-14372 191 2 , , PUNCT aiti-14372 191 3 in in ADP aiti-14372 191 4 the the DET aiti-14372 191 5 previous previous ADJ aiti-14372 191 6 exponential exponential ADJ aiti-14372 191 7 model model NOUN aiti-14372 191 8 , , PUNCT aiti-14372 191 9 it it PRON aiti-14372 191 10 was be AUX aiti-14372 191 11 a a DET aiti-14372 191 12 3rd 3rd ADJ aiti-14372 191 13 degree degree NOUN aiti-14372 191 14 polynomial polynomial ADJ aiti-14372 191 15 . . PUNCT aiti-14372 192 1 in in ADP aiti-14372 192 2 the the DET aiti-14372 192 3 present present ADJ aiti-14372 192 4 work work NOUN aiti-14372 192 5 , , PUNCT aiti-14372 192 6 the the DET aiti-14372 192 7 modified modified ADJ aiti-14372 192 8 non non ADJ aiti-14372 192 9 - - ADJ aiti-14372 192 10 dimensional dimensional ADJ aiti-14372 192 11 parameter parameter NOUN aiti-14372 192 12 n n PRON aiti-14372 192 13 can can AUX aiti-14372 192 14 be be AUX aiti-14372 192 15 represented represent VERB aiti-14372 192 16 by by ADP aiti-14372 192 17 max max PROPN aiti-14372 192 18 ys ys PROPN aiti-14372 193 1 c c PROPN aiti-14372 193 2 c c PROPN aiti-14372 193 3 kk kk PROPN aiti-14372 194 1 n n PROPN aiti-14372 194 2 k k PROPN aiti-14372 194 3 k k PROPN aiti-14372 194 4 e e PROPN aiti-14372 194 5   PROPN aiti-14372 195 1 ο€½ ο€½ PROPN aiti-14372 195 2 ο‚΄ ο‚΄ PROPN aiti-14372 195 3 ο‚΄ ο‚΄ PROPN aiti-14372 195 4 ( ( PUNCT aiti-14372 195 5 6 6 NUM aiti-14372 195 6 ) ) PUNCT aiti-14372 195 7 the the DET aiti-14372 195 8 above above ADJ aiti-14372 195 9 equation equation NOUN aiti-14372 195 10 has have AUX aiti-14372 195 11 been be AUX aiti-14372 195 12 modified modify VERB aiti-14372 195 13 as as ADP aiti-14372 195 14 a a DET aiti-14372 195 15 monomial monomial NOUN aiti-14372 195 16 . . PUNCT aiti-14372 196 1 however however ADV aiti-14372 196 2 , , PUNCT aiti-14372 196 3 in in ADP aiti-14372 196 4 the the DET aiti-14372 196 5 previous previous ADJ aiti-14372 196 6 exponential exponential ADJ aiti-14372 196 7 model model NOUN aiti-14372 196 8 , , PUNCT aiti-14372 196 9 it it PRON aiti-14372 196 10 was be AUX aiti-14372 196 11 an an DET aiti-14372 196 12 equation equation NOUN aiti-14372 196 13 with with ADP aiti-14372 196 14 a a DET aiti-14372 196 15 fractional fractional ADJ aiti-14372 196 16 power power NOUN aiti-14372 196 17 of of ADP aiti-14372 196 18 0.25 0.25 NUM aiti-14372 196 19 . . PUNCT aiti-14372 197 1 the the DET aiti-14372 197 2 constants constant NOUN aiti-14372 197 3 ( ( PUNCT aiti-14372 197 4 a a DET aiti-14372 197 5 , , PUNCT aiti-14372 197 6 b b NOUN aiti-14372 197 7 , , PUNCT aiti-14372 197 8 and and CCONJ aiti-14372 197 9 c c X aiti-14372 197 10 ) ) PUNCT aiti-14372 197 11 were be AUX aiti-14372 197 12 calculated calculate VERB aiti-14372 197 13 for for ADP aiti-14372 197 14 stages stage NOUN aiti-14372 197 15 - - PUNCT aiti-14372 197 16 i i PRON aiti-14372 197 17 , , PUNCT aiti-14372 197 18 ii ii PROPN aiti-14372 197 19 , , PUNCT aiti-14372 197 20 and and CCONJ aiti-14372 197 21 iii iii X aiti-14372 197 22 of of ADP aiti-14372 197 23 fcgr fcgr NOUN aiti-14372 197 24 and and CCONJ aiti-14372 197 25 the the DET aiti-14372 197 26 subsequent subsequent ADJ aiti-14372 197 27 π‘š π‘š X aiti-14372 197 28 and and CCONJ aiti-14372 197 29 the the DET aiti-14372 197 30 predicted predict VERB aiti-14372 197 31 number number NOUN aiti-14372 197 32 of of ADP aiti-14372 197 33 loading loading NOUN aiti-14372 197 34 cycles cycle NOUN aiti-14372 197 35 ( ( PUNCT aiti-14372 197 36 𝑁 𝑁 PROPN aiti-14372 197 37 ) ) PUNCT aiti-14372 197 38 can can AUX aiti-14372 197 39 be be AUX aiti-14372 197 40 calculated calculate VERB aiti-14372 197 41 by by ADP aiti-14372 197 42 ln ln PROPN aiti-14372 197 43 j j PROPN aiti-14372 197 44 ip ip PROPN aiti-14372 197 45 j j NOUN aiti-14372 198 1 i i PRON aiti-14372 198 2 ij ij VERB aiti-14372 198 3 a a DET aiti-14372 198 4 a a DET aiti-14372 198 5 n n CCONJ aiti-14372 198 6 n n NOUN aiti-14372 198 7 m m PROPN aiti-14372 198 8   NOUN aiti-14372 199 1 οƒΆ οƒΆ PROPN aiti-14372 200 1   PROPN aiti-14372 201 1 οƒ· οƒ· PROPN aiti-14372 202 1   PROPN aiti-14372 202 2 οƒΈο€½ οƒΈο€½ PROPN aiti-14372 202 3   PUNCT aiti-14372 202 4 ( ( PUNCT aiti-14372 202 5 7 7 X aiti-14372 202 6 ) ) SYM aiti-14372 202 7 4.2 4.2 NUM aiti-14372 202 8 calculation calculation NOUN aiti-14372 202 9 of of ADP aiti-14372 202 10 π‘š π‘š PROPN aiti-14372 202 11 and and CCONJ aiti-14372 202 12 the the DET aiti-14372 202 13 curve curve NOUN aiti-14372 202 14 fitting fitting ADJ aiti-14372 202 15 constant constant ADJ aiti-14372 202 16 for for ADP aiti-14372 202 17 stagesi stagesi NOUN aiti-14372 202 18 , , PUNCT aiti-14372 202 19 ii ii PROPN aiti-14372 202 20 , , PUNCT aiti-14372 202 21 and and CCONJ aiti-14372 202 22 iii iii X aiti-14372 202 23 of of ADP aiti-14372 202 24 fcg fcg PROPN aiti-14372 202 25 the the DET aiti-14372 202 26 specific specific ADJ aiti-14372 202 27 growth growth NOUN aiti-14372 202 28 rate rate NOUN aiti-14372 202 29 π‘š π‘š PROPN aiti-14372 202 30 defined define VERB aiti-14372 202 31 in in ADP aiti-14372 202 32 eq eq ADP aiti-14372 202 33 . . PUNCT aiti-14372 203 1 ( ( PUNCT aiti-14372 203 2 4 4 X aiti-14372 203 3 ) ) PUNCT aiti-14372 203 4 was be AUX aiti-14372 203 5 plotted plot VERB aiti-14372 203 6 with with ADP aiti-14372 203 7 the the DET aiti-14372 203 8 non non ADJ aiti-14372 203 9 - - ADJ aiti-14372 203 10 dimensional dimensional ADJ aiti-14372 203 11 number number NOUN aiti-14372 203 12 n n CCONJ aiti-14372 203 13 ( ( PUNCT aiti-14372 203 14 defined define VERB aiti-14372 203 15 in in ADP aiti-14372 203 16 eq eq ADP aiti-14372 203 17 . . PUNCT aiti-14372 204 1 ( ( PUNCT aiti-14372 204 2 6 6 NUM aiti-14372 204 3 ) ) PUNCT aiti-14372 204 4 ) ) PUNCT aiti-14372 204 5 . . PUNCT aiti-14372 205 1 this this DET aiti-14372 205 2 graph graph NOUN aiti-14372 205 3 provided provide VERB aiti-14372 205 4 the the DET aiti-14372 205 5 relationship relationship NOUN aiti-14372 205 6 between between ADP aiti-14372 205 7 fcg fcg PROPN aiti-14372 205 8 characteristics characteristic NOUN aiti-14372 205 9 with with ADP aiti-14372 205 10 crack crack NOUN aiti-14372 205 11 driving driving NOUN aiti-14372 205 12 force force NOUN aiti-14372 205 13 and and CCONJ aiti-14372 205 14 material material NOUN aiti-14372 205 15 properties property NOUN aiti-14372 205 16 . . PUNCT aiti-14372 206 1 the the DET aiti-14372 206 2 curve curve NOUN aiti-14372 206 3 was be AUX aiti-14372 206 4 fitted fit VERB aiti-14372 206 5 with with ADP aiti-14372 206 6 a a DET aiti-14372 206 7 polynomial polynomial ADJ aiti-14372 206 8 equation equation NOUN aiti-14372 206 9 ( ( PUNCT aiti-14372 206 10 given give VERB aiti-14372 206 11 in in ADP aiti-14372 206 12 eq eq ADP aiti-14372 206 13 . . PUNCT aiti-14372 207 1 ( ( PUNCT aiti-14372 207 2 5 5 NUM aiti-14372 207 3 ) ) PUNCT aiti-14372 207 4 for for ADP aiti-14372 207 5 stages stage NOUN aiti-14372 207 6 - - PUNCT aiti-14372 207 7 i i PRON aiti-14372 207 8 , , PUNCT aiti-14372 207 9 ii ii PROPN aiti-14372 207 10 , , PUNCT aiti-14372 207 11 and and CCONJ aiti-14372 207 12 iii iii X aiti-14372 207 13 of of ADP aiti-14372 207 14 fcgr fcgr NOUN aiti-14372 207 15 . . PUNCT aiti-14372 208 1 the the DET aiti-14372 208 2 curve curve NOUN aiti-14372 208 3 - - PUNCT aiti-14372 208 4 fitting fit VERB aiti-14372 208 5 constants constant NOUN aiti-14372 208 6 are be AUX aiti-14372 208 7 presented present VERB aiti-14372 208 8 in in ADP aiti-14372 208 9 table table NOUN aiti-14372 208 10 4 4 NUM aiti-14372 208 11 . . PUNCT aiti-14372 209 1 figs fig NOUN aiti-14372 209 2 . . PUNCT aiti-14372 210 1 8 8 NUM aiti-14372 210 2 , , PUNCT aiti-14372 210 3 9 9 NUM aiti-14372 210 4 , , PUNCT aiti-14372 210 5 and and CCONJ aiti-14372 210 6 10 10 NUM aiti-14372 210 7 provide provide VERB aiti-14372 210 8 the the DET aiti-14372 210 9 variation variation NOUN aiti-14372 210 10 of of ADP aiti-14372 210 11 the the DET aiti-14372 210 12 specific specific ADJ aiti-14372 210 13 growth growth NOUN aiti-14372 210 14 rate rate NOUN aiti-14372 210 15 with with ADP aiti-14372 210 16 the the DET aiti-14372 210 17 crack crack NOUN aiti-14372 210 18 driving driving NOUN aiti-14372 210 19 force force NOUN aiti-14372 210 20 and and CCONJ aiti-14372 210 21 crack crack VERB aiti-14372 210 22 resistive resistive ADJ aiti-14372 210 23 parameters parameter NOUN aiti-14372 210 24 . . PUNCT aiti-14372 211 1 in in ADP aiti-14372 211 2 stage stage NOUN aiti-14372 211 3 - - PUNCT aiti-14372 211 4 i i PRON aiti-14372 211 5 of of ADP aiti-14372 211 6 fcgr fcgr NOUN aiti-14372 211 7 ( ( PUNCT aiti-14372 211 8 fig fig NOUN aiti-14372 211 9 . . PUNCT aiti-14372 211 10 8) 8) NUM aiti-14372 211 11 , , PUNCT aiti-14372 211 12 the the DET aiti-14372 211 13 decreasing decrease VERB aiti-14372 211 14 slope slope NOUN aiti-14372 211 15 envisages envisage VERB aiti-14372 211 16 the the DET aiti-14372 211 17 emancipation emancipation NOUN aiti-14372 211 18 of of ADP aiti-14372 211 19 the the DET aiti-14372 211 20 combined combined ADJ aiti-14372 211 21 effect effect NOUN aiti-14372 211 22 of of ADP aiti-14372 211 23 crack crack NOUN aiti-14372 211 24 driving driving NOUN aiti-14372 211 25 force force NOUN aiti-14372 211 26 and and CCONJ aiti-14372 211 27 crack crack VERB aiti-14372 211 28 resistance resistance NOUN aiti-14372 211 29 parameter parameter NOUN aiti-14372 211 30 . . PUNCT aiti-14372 212 1 this this PRON aiti-14372 212 2 suggests suggest VERB aiti-14372 212 3 that that SCONJ aiti-14372 212 4 the the DET aiti-14372 212 5 crack crack NOUN aiti-14372 212 6 propagation propagation NOUN aiti-14372 212 7 was be AUX aiti-14372 212 8 slow slow ADJ aiti-14372 212 9 with with ADP aiti-14372 212 10 the the DET aiti-14372 212 11 n n NOUN aiti-14372 212 12 during during ADP aiti-14372 212 13 the the DET aiti-14372 212 14 initial initial ADJ aiti-14372 212 15 stage stage NOUN aiti-14372 212 16 of of ADP aiti-14372 212 17 fcg fcg PROPN aiti-14372 212 18 . . PUNCT aiti-14372 213 1 however however ADV aiti-14372 213 2 , , PUNCT aiti-14372 213 3 once once ADV aiti-14372 213 4 a a DET aiti-14372 213 5 sufficient sufficient ADJ aiti-14372 213 6 amount amount NOUN aiti-14372 213 7 of of ADP aiti-14372 213 8 stress stress ADJ aiti-14372 213 9 intensification intensification NOUN aiti-14372 213 10 near near ADP aiti-14372 213 11 the the DET aiti-14372 213 12 vicinity vicinity NOUN aiti-14372 213 13 of of ADP aiti-14372 213 14 the the DET aiti-14372 213 15 crack crack NOUN aiti-14372 213 16 tip tip NOUN aiti-14372 213 17 occurred occur VERB aiti-14372 213 18 , , PUNCT aiti-14372 213 19 the the DET aiti-14372 213 20 slope slope NOUN aiti-14372 213 21 of of ADP aiti-14372 213 22 specific specific ADJ aiti-14372 213 23 crack crack NOUN aiti-14372 213 24 growth growth NOUN aiti-14372 213 25 rate rate NOUN aiti-14372 213 26 versus versus ADP aiti-14372 213 27 non non ADJ aiti-14372 213 28 - - ADJ aiti-14372 213 29 dimensional dimensional ADJ aiti-14372 213 30 number number NOUN aiti-14372 213 31 n n NOUN aiti-14372 213 32 increases increase NOUN aiti-14372 213 33 as as SCONJ aiti-14372 213 34 shown show VERB aiti-14372 213 35 for for ADP aiti-14372 213 36 stages stage NOUN aiti-14372 213 37 - - PUNCT aiti-14372 213 38 ii ii NOUN aiti-14372 213 39 and and CCONJ aiti-14372 213 40 iii iii NUM aiti-14372 213 41 of of ADP aiti-14372 213 42 fcgr fcgr NOUN aiti-14372 213 43 in in ADP aiti-14372 213 44 figs fig NOUN aiti-14372 213 45 . . PUNCT aiti-14372 214 1 9 9 NUM aiti-14372 214 2 and and CCONJ aiti-14372 214 3 10 10 NUM aiti-14372 214 4 . . PUNCT aiti-14372 215 1 such such DET aiti-14372 215 2 an an DET aiti-14372 215 3 increase increase NOUN aiti-14372 215 4 depicts depict VERB aiti-14372 215 5 the the DET aiti-14372 215 6 dominance dominance NOUN aiti-14372 215 7 of of ADP aiti-14372 215 8 the the DET aiti-14372 215 9 effect effect NOUN aiti-14372 215 10 of of ADP aiti-14372 215 11 the the DET aiti-14372 215 12 crack crack NOUN aiti-14372 215 13 driving driving NOUN aiti-14372 215 14 force force NOUN aiti-14372 215 15 over over ADP aiti-14372 215 16 the the DET aiti-14372 215 17 crack crack NOUN aiti-14372 215 18 resistance resistance NOUN aiti-14372 215 19 parameters parameter NOUN aiti-14372 215 20 . . PUNCT aiti-14372 216 1 it it PRON aiti-14372 216 2 also also ADV aiti-14372 216 3 indicated indicate VERB aiti-14372 216 4 an an DET aiti-14372 216 5 accelerated accelerate VERB aiti-14372 216 6 crack crack NOUN aiti-14372 216 7 propagation propagation NOUN aiti-14372 216 8 with with ADP aiti-14372 216 9 the the DET aiti-14372 216 10 number number NOUN aiti-14372 216 11 of of ADP aiti-14372 216 12 n. n. NOUN aiti-14372 216 13 the the DET aiti-14372 216 14 different different ADJ aiti-14372 216 15 natures nature NOUN aiti-14372 216 16 of of ADP aiti-14372 216 17 the the DET aiti-14372 216 18 slopes slope NOUN aiti-14372 216 19 in in ADP aiti-14372 216 20 stages stage NOUN aiti-14372 216 21 - - PUNCT aiti-14372 216 22 i i PRON aiti-14372 216 23 , , PUNCT aiti-14372 216 24 ii ii PROPN aiti-14372 216 25 , , PUNCT aiti-14372 216 26 and and CCONJ aiti-14372 216 27 iii iii NUM aiti-14372 216 28 characterized characterize VERB aiti-14372 216 29 the the DET aiti-14372 216 30 nature nature NOUN aiti-14372 216 31 of of ADP aiti-14372 216 32 fcg fcg PROPN aiti-14372 216 33 in in ADP aiti-14372 216 34 the the DET aiti-14372 216 35 respective respective ADJ aiti-14372 216 36 stages stage NOUN aiti-14372 216 37 . . PUNCT aiti-14372 217 1 table table NOUN aiti-14372 217 2 4 4 NUM aiti-14372 217 3 curve curve NOUN aiti-14372 217 4 fitting fitting ADJ aiti-14372 217 5 constants constant NOUN aiti-14372 217 6 for for ADP aiti-14372 217 7 stages stage NOUN aiti-14372 217 8 - - PUNCT aiti-14372 217 9 i i PRON aiti-14372 217 10 , , PUNCT aiti-14372 217 11 ii ii PROPN aiti-14372 217 12 , , PUNCT aiti-14372 217 13 and and CCONJ aiti-14372 217 14 iii iii X aiti-14372 217 15 of of ADP aiti-14372 217 16 fcg fcg PROPN aiti-14372 217 17 stage stage NOUN aiti-14372 217 18 of of ADP aiti-14372 217 19 fcg fcg PROPN aiti-14372 217 20 a a DET aiti-14372 217 21 b b NOUN aiti-14372 217 22 c c NOUN aiti-14372 217 23 stage stage NOUN aiti-14372 217 24 - - PUNCT aiti-14372 217 25 i i NOUN aiti-14372 217 26 7989107.2800 7989107.2800 NUM aiti-14372 218 1 βˆ’91.4011 βˆ’91.4011 PROPN aiti-14372 218 2 0.0002 0.0002 NUM aiti-14372 218 3 stage stage NOUN aiti-14372 218 4 - - PUNCT aiti-14372 218 5 ii ii NOUN aiti-14372 218 6 33838863.5100 33838863.5100 NUM aiti-14372 218 7 βˆ’413.1787 βˆ’413.1787 NOUN aiti-14372 218 8 0.0012 0.0012 NUM aiti-14372 218 9 stage stage NOUN aiti-14372 218 10 - - PUNCT aiti-14372 218 11 iii iii NUM aiti-14372 218 12 1116368244.00 1116368244.00 NUM aiti-14372 218 13 βˆ’15001.6072 βˆ’15001.6072 NOUN aiti-14372 218 14 0.0504 0.0504 NUM aiti-14372 218 15 fig fig NOUN aiti-14372 218 16 . . PUNCT aiti-14372 218 17 8 8 NUM aiti-14372 218 18 specific specific ADJ aiti-14372 218 19 growth growth NOUN aiti-14372 218 20 rate rate NOUN aiti-14372 218 21 versus versus ADP aiti-14372 218 22 n n NOUN aiti-14372 218 23 for for ADP aiti-14372 218 24 stage stage NOUN aiti-14372 218 25 - - PUNCT aiti-14372 218 26 i i PRON aiti-14372 218 27 of of ADP aiti-14372 218 28 fcg fcg PROPN aiti-14372 218 29 y y PROPN aiti-14372 218 30 = = PUNCT aiti-14372 219 1 7989107.283x2 7989107.283x2 NUM aiti-14372 219 2 91.40113054x 91.40113054x NUM aiti-14372 220 1 + + CCONJ aiti-14372 220 2 0.000282919 0.000282919 NUM aiti-14372 220 3 rΒ² rΒ² NOUN aiti-14372 220 4 = = SYM aiti-14372 220 5 0.996503434 0.996503434 NUM aiti-14372 220 6 1.50e-05 1.50e-05 NUM aiti-14372 220 7 2.00e-05 2.00e-05 NUM aiti-14372 220 8 2.50e-05 2.50e-05 NUM aiti-14372 220 9 3.00e-05 3.00e-05 NUM aiti-14372 220 10 3.50e-05 3.50e-05 NUM aiti-14372 220 11 4.00e-05 4.00e-05 NUM aiti-14372 220 12 4.00e-06 4.00e-06 NUM aiti-14372 220 13 4.50e-06 4.50e-06 NUM aiti-14372 220 14 5.00e-06 5.00e-06 NUM aiti-14372 220 15 5.50e-06 5.50e-06 NUM aiti-14372 220 16 6.00e-06 6.00e-06 NUM aiti-14372 220 17 6.50e-06 6.50e-06 NUM aiti-14372 220 18 sp sp ADP aiti-14372 220 19 ec ec PROPN aiti-14372 220 20 if if SCONJ aiti-14372 220 21 ic ic PROPN aiti-14372 220 22 g g PROPN aiti-14372 220 23 ro ro PROPN aiti-14372 220 24 w w X aiti-14372 220 25 th th NOUN aiti-14372 220 26 r r NOUN aiti-14372 220 27 at at ADP aiti-14372 220 28 e e NOUN aiti-14372 220 29 , , PUNCT aiti-14372 220 30 m m VERB aiti-14372 220 31 non non ADJ aiti-14372 220 32 - - ADJ aiti-14372 220 33 dimensional dimensional ADJ aiti-14372 220 34 number number NOUN aiti-14372 220 35 , , PUNCT aiti-14372 220 36 n n CCONJ aiti-14372 220 37 satge satge NOUN aiti-14372 220 38 - - PUNCT aiti-14372 220 39 i i PRON aiti-14372 220 40 of of ADP aiti-14372 220 41 fcg fcg PROPN aiti-14372 220 42 advances advance NOUN aiti-14372 220 43 in in ADP aiti-14372 220 44 technology technology NOUN aiti-14372 220 45 innovation innovation NOUN aiti-14372 220 46 , , PUNCT aiti-14372 220 47 vol vol NOUN aiti-14372 220 48 . . PROPN aiti-14372 221 1 10 10 NUM aiti-14372 221 2 , , PUNCT aiti-14372 221 3 no no INTJ aiti-14372 221 4 . . NOUN aiti-14372 221 5 3 3 NUM aiti-14372 221 6 , , PUNCT aiti-14372 221 7 2025 2025 NUM aiti-14372 221 8 , , PUNCT aiti-14372 221 9 pp pp ADJ aiti-14372 221 10 . . PUNCT aiti-14372 222 1 238 238 NUM aiti-14372 222 2 - - SYM aiti-14372 222 3 253 253 NUM aiti-14372 222 4 246 246 NUM aiti-14372 222 5 fig fig NOUN aiti-14372 222 6 . . PUNCT aiti-14372 223 1 9 9 NUM aiti-14372 223 2 specific specific ADJ aiti-14372 223 3 growth growth NOUN aiti-14372 223 4 rate rate NOUN aiti-14372 223 5 versus versus ADP aiti-14372 223 6 n n CCONJ aiti-14372 223 7 for for ADP aiti-14372 223 8 stages stage NOUN aiti-14372 223 9 - - PUNCT aiti-14372 223 10 ii ii NOUN aiti-14372 223 11 of of ADP aiti-14372 223 12 fcg fcg PROPN aiti-14372 223 13 fig fig PROPN aiti-14372 223 14 . . PUNCT aiti-14372 224 1 10 10 NUM aiti-14372 224 2 specific specific ADJ aiti-14372 224 3 growth growth NOUN aiti-14372 224 4 rate rate NOUN aiti-14372 224 5 versus versus ADP aiti-14372 224 6 n n NOUN aiti-14372 224 7 for for ADP aiti-14372 224 8 stage stage NOUN aiti-14372 224 9 - - PUNCT aiti-14372 224 10 iii iii NOUN aiti-14372 224 11 of of ADP aiti-14372 224 12 fcg fcg PROPN aiti-14372 224 13 4.3 4.3 NUM aiti-14372 224 14 prediction prediction NOUN aiti-14372 224 15 of of ADP aiti-14372 224 16 fcgr fcgr NOUN aiti-14372 224 17 using use VERB aiti-14372 224 18 a a DET aiti-14372 224 19 modified modify VERB aiti-14372 224 20 exponential exponential ADJ aiti-14372 224 21 function function NOUN aiti-14372 224 22 and and CCONJ aiti-14372 224 23 specific specific ADJ aiti-14372 224 24 growth growth NOUN aiti-14372 224 25 rate rate NOUN aiti-14372 224 26 the the DET aiti-14372 224 27 modified modify VERB aiti-14372 224 28 exponential exponential ADJ aiti-14372 224 29 function function NOUN aiti-14372 224 30 and and CCONJ aiti-14372 224 31 specific specific ADJ aiti-14372 224 32 growth growth NOUN aiti-14372 224 33 rate rate NOUN aiti-14372 224 34 were be AUX aiti-14372 224 35 formulated formulate VERB aiti-14372 224 36 considering consider VERB aiti-14372 224 37 the the DET aiti-14372 224 38 experimental experimental ADJ aiti-14372 224 39 data datum NOUN aiti-14372 224 40 of of ADP aiti-14372 224 41 5 5 NUM aiti-14372 224 42 samples sample NOUN aiti-14372 224 43 , , PUNCT aiti-14372 224 44 followed follow VERB aiti-14372 224 45 by by ADP aiti-14372 224 46 validation validation NOUN aiti-14372 224 47 of of ADP aiti-14372 224 48 the the DET aiti-14372 224 49 model model NOUN aiti-14372 224 50 using use VERB aiti-14372 224 51 the the DET aiti-14372 224 52 6th 6th ADJ aiti-14372 224 53 sample sample NOUN aiti-14372 224 54 . . PUNCT aiti-14372 225 1 the the DET aiti-14372 225 2 n n PROPN aiti-14372 225 3 was be AUX aiti-14372 225 4 predicted predict VERB aiti-14372 225 5 using use VERB aiti-14372 225 6 eq eq ADP aiti-14372 225 7 . . PUNCT aiti-14372 226 1 ( ( PUNCT aiti-14372 226 2 7 7 NUM aiti-14372 226 3 ) ) PUNCT aiti-14372 226 4 , , PUNCT aiti-14372 226 5 and and CCONJ aiti-14372 226 6 then then ADV aiti-14372 226 7 the the DET aiti-14372 226 8 values value NOUN aiti-14372 226 9 of of ADP aiti-14372 226 10 da da PROPN aiti-14372 226 11 / / SYM aiti-14372 226 12 dn dn PROPN aiti-14372 226 13 were be AUX aiti-14372 226 14 calculated calculate VERB aiti-14372 226 15 . . PUNCT aiti-14372 227 1 the the DET aiti-14372 227 2 fcgr fcgr NOUN aiti-14372 227 3 was be AUX aiti-14372 227 4 plotted plot VERB aiti-14372 227 5 against against ADP aiti-14372 227 6 Ξ΄k Ξ΄k PRON aiti-14372 227 7 for for ADP aiti-14372 227 8 stages stage NOUN aiti-14372 227 9 - - PUNCT aiti-14372 227 10 i i PRON aiti-14372 227 11 , , PUNCT aiti-14372 227 12 ii ii PROPN aiti-14372 227 13 , , PUNCT aiti-14372 227 14 and and CCONJ aiti-14372 227 15 iii iii NOUN aiti-14372 227 16 as as SCONJ aiti-14372 227 17 shown show VERB aiti-14372 227 18 in in ADP aiti-14372 227 19 figs fig NOUN aiti-14372 227 20 . . PUNCT aiti-14372 228 1 11 11 NUM aiti-14372 228 2 , , PUNCT aiti-14372 228 3 12 12 NUM aiti-14372 228 4 , , PUNCT aiti-14372 228 5 and and CCONJ aiti-14372 228 6 13 13 NUM aiti-14372 228 7 , , PUNCT aiti-14372 228 8 respectively respectively ADV aiti-14372 228 9 . . PUNCT aiti-14372 229 1 fig fig NOUN aiti-14372 229 2 . . PUNCT aiti-14372 230 1 11 11 NUM aiti-14372 230 2 fcgr fcgr NOUN aiti-14372 230 3 in in ADP aiti-14372 230 4 stage stage NOUN aiti-14372 230 5 - - PUNCT aiti-14372 230 6 i i PRON aiti-14372 230 7 fig fig NOUN aiti-14372 230 8 . . PUNCT aiti-14372 231 1 12 12 NUM aiti-14372 231 2 fcgr fcgr NOUN aiti-14372 231 3 in in ADP aiti-14372 231 4 stage stage NOUN aiti-14372 231 5 - - PUNCT aiti-14372 231 6 ii ii NOUN aiti-14372 231 7 fig fig NOUN aiti-14372 231 8 . . PUNCT aiti-14372 232 1 13 13 NUM aiti-14372 232 2 fcgr fcgr NOUN aiti-14372 232 3 in in ADP aiti-14372 232 4 stage stage NOUN aiti-14372 232 5 - - PUNCT aiti-14372 232 6 iii iii NOUN aiti-14372 232 7 the the DET aiti-14372 232 8 modelling modelling NOUN aiti-14372 232 9 agreed agree VERB aiti-14372 232 10 with with ADP aiti-14372 232 11 the the DET aiti-14372 232 12 experimental experimental ADJ aiti-14372 232 13 data datum NOUN aiti-14372 232 14 . . PUNCT aiti-14372 233 1 however however ADV aiti-14372 233 2 , , PUNCT aiti-14372 233 3 the the DET aiti-14372 233 4 accuracy accuracy NOUN aiti-14372 233 5 and and CCONJ aiti-14372 233 6 performance performance NOUN aiti-14372 233 7 studies study NOUN aiti-14372 233 8 of of ADP aiti-14372 233 9 the the DET aiti-14372 233 10 model model NOUN aiti-14372 233 11 required require VERB aiti-14372 233 12 statistical statistical ADJ aiti-14372 233 13 analysis analysis NOUN aiti-14372 233 14 for for ADP aiti-14372 233 15 quantification quantification NOUN aiti-14372 233 16 . . PUNCT aiti-14372 234 1 it it PRON aiti-14372 234 2 is be AUX aiti-14372 234 3 also also ADV aiti-14372 234 4 observed observe VERB aiti-14372 234 5 that that SCONJ aiti-14372 234 6 the the DET aiti-14372 234 7 predicted predict VERB aiti-14372 234 8 fcgr fcgr NOUN aiti-14372 234 9 in in ADP aiti-14372 234 10 all all DET aiti-14372 234 11 three three NUM aiti-14372 234 12 stages stage NOUN aiti-14372 234 13 provided provide VERB aiti-14372 234 14 a a DET aiti-14372 234 15 higher high ADJ aiti-14372 234 16 value value NOUN aiti-14372 234 17 as as SCONJ aiti-14372 234 18 compared compare VERB aiti-14372 234 19 to to ADP aiti-14372 234 20 the the DET aiti-14372 234 21 experimental experimental ADJ aiti-14372 234 22 data datum NOUN aiti-14372 234 23 . . PUNCT aiti-14372 235 1 in in ADP aiti-14372 235 2 other other ADJ aiti-14372 235 3 words word NOUN aiti-14372 235 4 , , PUNCT aiti-14372 235 5 the the DET aiti-14372 235 6 model model NOUN aiti-14372 235 7 overestimates overestimate VERB aiti-14372 235 8 the the DET aiti-14372 235 9 materials material NOUN aiti-14372 235 10 ’ ' PUNCT aiti-14372 235 11 properties property NOUN aiti-14372 235 12 and and CCONJ aiti-14372 235 13 geometry geometry NOUN aiti-14372 235 14 . . PUNCT aiti-14372 236 1 4.4 4.4 NUM aiti-14372 236 2 modification modification NOUN aiti-14372 236 3 in in ADP aiti-14372 236 4 the the DET aiti-14372 236 5 exponential exponential ADJ aiti-14372 236 6 function function NOUN aiti-14372 236 7 in in ADP aiti-14372 236 8 the the DET aiti-14372 236 9 previous previous ADJ aiti-14372 236 10 work work NOUN aiti-14372 236 11 , , PUNCT aiti-14372 236 12 the the DET aiti-14372 236 13 non non ADJ aiti-14372 236 14 - - ADJ aiti-14372 236 15 dimensional dimensional ADJ aiti-14372 236 16 parameter parameter NOUN aiti-14372 236 17 n n NUM aiti-14372 236 18 is be AUX aiti-14372 236 19 defined define VERB aiti-14372 236 20 as as ADP aiti-14372 236 21 [ [ X aiti-14372 236 22 22 22 NUM aiti-14372 236 23 ] ] PUNCT aiti-14372 236 24 : : PUNCT aiti-14372 237 1   NOUN aiti-14372 237 2 0.25 0.25 NUM aiti-14372 237 3 max max NOUN aiti-14372 237 4 earlier early ADJ aiti-14372 237 5 model model NOUN aiti-14372 238 1 ys ys PROPN aiti-14372 239 1 c c PROPN aiti-14372 239 2 c c PROPN aiti-14372 239 3 kk kk PROPN aiti-14372 240 1 n n PROPN aiti-14372 240 2 k k PROPN aiti-14372 240 3 k k PROPN aiti-14372 240 4 e e PROPN aiti-14372 240 5   PROPN aiti-14372 240 6 οƒΉ οƒΉ NOUN aiti-14372 240 7 ο€½ ο€½ PROPN aiti-14372 240 8 ο‚΄ ο‚΄ INTJ aiti-14372 240 9 ο‚΄οƒͺ ο‚΄οƒͺ PROPN aiti-14372 240 10 οƒΊ οƒΊ NOUN aiti-14372 240 11   PROPN aiti-14372 240 12   PROPN aiti-14372 240 13 ( ( PUNCT aiti-14372 240 14 8) 8) NUM aiti-14372 240 15 y y NOUN aiti-14372 240 16 = = SYM aiti-14372 241 1 33838863.51x2 33838863.51x2 PROPN aiti-14372 241 2 413.1787744x 413.1787744x NOUN aiti-14372 241 3 + + CCONJ aiti-14372 241 4 0.001283286 0.001283286 NUM aiti-14372 241 5 rΒ² rΒ² NOUN aiti-14372 241 6 = = PUNCT aiti-14372 241 7 0.990202666 0.990202666 NUM aiti-14372 241 8 1.50e-05 1.50e-05 NUM aiti-14372 241 9 2.00e-05 2.00e-05 NUM aiti-14372 241 10 2.50e-05 2.50e-05 NUM aiti-14372 241 11 3.00e-05 3.00e-05 NUM aiti-14372 241 12 3.50e-05 3.50e-05 NUM aiti-14372 241 13 4.00e-05 4.00e-05 NUM aiti-14372 241 14 5.80e-06 5.80e-06 NUM aiti-14372 241 15 6.00e-06 6.00e-06 NUM aiti-14372 241 16 6.20e-06 6.20e-06 NUM aiti-14372 241 17 6.40e-06 6.40e-06 NUM aiti-14372 241 18 6.60e-06 6.60e-06 NUM aiti-14372 241 19 6.80e-06 6.80e-06 NUM aiti-14372 241 20 sp sp ADP aiti-14372 241 21 ec ec PROPN aiti-14372 241 22 if if SCONJ aiti-14372 241 23 ic ic PROPN aiti-14372 241 24 g g PROPN aiti-14372 241 25 ro ro PROPN aiti-14372 241 26 w w X aiti-14372 241 27 th th NOUN aiti-14372 241 28 r r NOUN aiti-14372 241 29 at at ADP aiti-14372 241 30 e e NOUN aiti-14372 241 31 , , PUNCT aiti-14372 241 32 m m VERB aiti-14372 241 33 non non ADJ aiti-14372 241 34 - - ADJ aiti-14372 241 35 dimensional dimensional ADJ aiti-14372 241 36 number number NOUN aiti-14372 241 37 , , PUNCT aiti-14372 241 38 n n PRON aiti-14372 241 39 stage stage NOUN aiti-14372 241 40 - - PUNCT aiti-14372 241 41 ii ii NOUN aiti-14372 241 42 of of ADP aiti-14372 241 43 fcg fcg PROPN aiti-14372 241 44 y y PROPN aiti-14372 242 1 = = SYM aiti-14372 243 1 1116368244x2 1116368244x2 PROPN aiti-14372 244 1 15001.60729x 15001.60729x NUM aiti-14372 245 1 + + NUM aiti-14372 245 2 0.050434881 0.050434881 NUM aiti-14372 245 3 rΒ² rΒ² NOUN aiti-14372 245 4 = = PUNCT aiti-14372 245 5 0.993584987 0.993584987 NUM aiti-14372 245 6 0.00e+00 0.00e+00 NUM aiti-14372 245 7 2.00e-05 2.00e-05 NUM aiti-14372 245 8 4.00e-05 4.00e-05 NUM aiti-14372 245 9 6.00e-05 6.00e-05 NUM aiti-14372 245 10 8.00e-05 8.00e-05 NUM aiti-14372 245 11 1.00e-04 1.00e-04 NUM aiti-14372 245 12 6.70e-06 6.70e-06 NUM aiti-14372 245 13 6.75e-06 6.75e-06 NUM aiti-14372 245 14 6.80e-06 6.80e-06 NUM aiti-14372 245 15 6.85e-06 6.85e-06 NUM aiti-14372 245 16 6.90e-06 6.90e-06 NUM aiti-14372 245 17 6.95e-06 6.95e-06 NUM aiti-14372 245 18 sp sp ADP aiti-14372 245 19 ec ec PROPN aiti-14372 245 20 if if SCONJ aiti-14372 245 21 ic ic PROPN aiti-14372 245 22 g g PROPN aiti-14372 245 23 ro ro PROPN aiti-14372 245 24 w w X aiti-14372 245 25 th th NOUN aiti-14372 245 26 r r NOUN aiti-14372 245 27 at at ADP aiti-14372 245 28 e e NOUN aiti-14372 245 29 , , PUNCT aiti-14372 245 30 m m VERB aiti-14372 245 31 non non ADJ aiti-14372 245 32 - - ADJ aiti-14372 245 33 dimensional dimensional ADJ aiti-14372 245 34 number number NOUN aiti-14372 245 35 , , PUNCT aiti-14372 245 36 n n PRON aiti-14372 245 37 stage stage NOUN aiti-14372 245 38 - - PUNCT aiti-14372 245 39 iii iii NOUN aiti-14372 245 40 of of ADP aiti-14372 245 41 fcg fcg PROPN aiti-14372 245 42 5.00e-05 5.00e-05 NUM aiti-14372 245 43 5.50e-05 5.50e-05 NUM aiti-14372 246 1 6.00e-05 6.00e-05 NUM aiti-14372 246 2 6.50e-05 6.50e-05 NUM aiti-14372 246 3 7.00e-05 7.00e-05 NUM aiti-14372 246 4 7.50e-05 7.50e-05 NUM aiti-14372 246 5 8.00e-05 8.00e-05 NUM aiti-14372 246 6 8.50e-05 8.50e-05 NUM aiti-14372 246 7 17.5 17.5 NUM aiti-14372 246 8 18.5 18.5 NUM aiti-14372 246 9 19.5 19.5 NUM aiti-14372 246 10 20.5 20.5 NUM aiti-14372 246 11 21.5 21.5 NUM aiti-14372 246 12 da da NOUN aiti-14372 246 13 /d /d PUNCT aiti-14372 246 14 n n PROPN aiti-14372 246 15 ( ( PUNCT aiti-14372 246 16 m m VERB aiti-14372 246 17 m m VERB aiti-14372 246 18 /c /c PUNCT aiti-14372 246 19 yc yc X aiti-14372 246 20 le le X aiti-14372 246 21 ) ) PUNCT aiti-14372 246 22 βˆ†k βˆ†k PROPN aiti-14372 246 23 ( ( PUNCT aiti-14372 246 24 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 246 25 ) ) PUNCT aiti-14372 246 26 stage stage NOUN aiti-14372 246 27 - - PUNCT aiti-14372 246 28 i i PRON aiti-14372 246 29 of of ADP aiti-14372 246 30 fcgr fcgr NOUN aiti-14372 246 31 da da PROPN aiti-14372 246 32 / / SYM aiti-14372 246 33 dn dn PROPN aiti-14372 246 34 ( ( PUNCT aiti-14372 246 35 experimental experimental ADJ aiti-14372 246 36 ) ) PUNCT aiti-14372 246 37 da da PROPN aiti-14372 246 38 / / SYM aiti-14372 246 39 dn dn PROPN aiti-14372 246 40 ( ( PUNCT aiti-14372 246 41 predicted predict VERB aiti-14372 246 42 ) ) PUNCT aiti-14372 247 1 8.00e-05 8.00e-05 NUM aiti-14372 247 2 8.50e-05 8.50e-05 NUM aiti-14372 247 3 9.00e-05 9.00e-05 NUM aiti-14372 247 4 9.50e-05 9.50e-05 NUM aiti-14372 247 5 1.00e-04 1.00e-04 NUM aiti-14372 247 6 1.05e-04 1.05e-04 NUM aiti-14372 247 7 20.5 20.5 NUM aiti-14372 247 8 20.7 20.7 NUM aiti-14372 247 9 20.9 20.9 NUM aiti-14372 247 10 21.1 21.1 NUM aiti-14372 247 11 21.3 21.3 NUM aiti-14372 247 12 21.5 21.5 NUM aiti-14372 247 13 da da NOUN aiti-14372 247 14 /d /d PUNCT aiti-14372 247 15 n n PROPN aiti-14372 247 16 ( ( PUNCT aiti-14372 247 17 m m VERB aiti-14372 247 18 m m VERB aiti-14372 247 19 /c /c PUNCT aiti-14372 247 20 yc yc X aiti-14372 247 21 le le X aiti-14372 247 22 ) ) PUNCT aiti-14372 247 23 βˆ†k βˆ†k PROPN aiti-14372 247 24 ( ( PUNCT aiti-14372 247 25 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 247 26 ) ) PUNCT aiti-14372 247 27 stage stage NOUN aiti-14372 247 28 - - PUNCT aiti-14372 247 29 ii ii NOUN aiti-14372 247 30 of of ADP aiti-14372 247 31 fcgr fcgr PROPN aiti-14372 247 32 da da PROPN aiti-14372 247 33 / / SYM aiti-14372 247 34 dn dn PROPN aiti-14372 247 35 ( ( PUNCT aiti-14372 247 36 experimental experimental ADJ aiti-14372 247 37 ) ) PUNCT aiti-14372 247 38 da da PROPN aiti-14372 247 39 / / SYM aiti-14372 247 40 dn dn PROPN aiti-14372 247 41 ( ( PUNCT aiti-14372 247 42 predicted predict VERB aiti-14372 247 43 ) ) PUNCT aiti-14372 247 44 1.10e-04 1.10e-04 NUM aiti-14372 247 45 1.15e-04 1.15e-04 NUM aiti-14372 247 46 1.20e-04 1.20e-04 NUM aiti-14372 247 47 1.25e-04 1.25e-04 NUM aiti-14372 247 48 1.30e-04 1.30e-04 NUM aiti-14372 247 49 1.35e-04 1.35e-04 NUM aiti-14372 247 50 1.40e-04 1.40e-04 NUM aiti-14372 247 51 21.7 21.7 NUM aiti-14372 247 52 21.75 21.75 NUM aiti-14372 247 53 21.8 21.8 NUM aiti-14372 247 54 21.85 21.85 NUM aiti-14372 247 55 21.9 21.9 NUM aiti-14372 247 56 21.95 21.95 NUM aiti-14372 247 57 22 22 NUM aiti-14372 247 58 da da NOUN aiti-14372 247 59 /d /d PUNCT aiti-14372 247 60 n n PROPN aiti-14372 247 61 ( ( PUNCT aiti-14372 247 62 m m VERB aiti-14372 247 63 m m VERB aiti-14372 247 64 /c /c PUNCT aiti-14372 247 65 yc yc X aiti-14372 247 66 le le X aiti-14372 247 67 ) ) PUNCT aiti-14372 247 68 βˆ†k βˆ†k PROPN aiti-14372 247 69 ( ( PUNCT aiti-14372 247 70 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 247 71 ) ) PUNCT aiti-14372 247 72 stage stage NOUN aiti-14372 247 73 - - PUNCT aiti-14372 247 74 iii iii NOUN aiti-14372 247 75 of of ADP aiti-14372 247 76 fcgr fcgr NOUN aiti-14372 247 77 da da PROPN aiti-14372 247 78 / / SYM aiti-14372 247 79 dn dn PROPN aiti-14372 247 80 ( ( PUNCT aiti-14372 247 81 experimental experimental ADJ aiti-14372 247 82 ) ) PUNCT aiti-14372 247 83 da da PROPN aiti-14372 247 84 / / SYM aiti-14372 247 85 dn dn PROPN aiti-14372 247 86 ( ( PUNCT aiti-14372 247 87 predicted predict VERB aiti-14372 247 88 ) ) PUNCT aiti-14372 247 89 advances advance NOUN aiti-14372 247 90 in in ADP aiti-14372 247 91 technology technology NOUN aiti-14372 247 92 innovation innovation NOUN aiti-14372 247 93 , , PUNCT aiti-14372 247 94 vol vol NOUN aiti-14372 247 95 . . PROPN aiti-14372 248 1 10 10 NUM aiti-14372 248 2 , , PUNCT aiti-14372 248 3 no no INTJ aiti-14372 248 4 . . NOUN aiti-14372 248 5 3 3 NUM aiti-14372 248 6 , , PUNCT aiti-14372 248 7 2025 2025 NUM aiti-14372 248 8 , , PUNCT aiti-14372 248 9 pp pp ADJ aiti-14372 248 10 . . PUNCT aiti-14372 249 1 238 238 NUM aiti-14372 249 2 - - SYM aiti-14372 249 3 253 253 NUM aiti-14372 249 4 247 247 NUM aiti-14372 249 5 however however ADV aiti-14372 249 6 , , PUNCT aiti-14372 249 7 in in ADP aiti-14372 249 8 the the DET aiti-14372 249 9 present present ADJ aiti-14372 249 10 work work NOUN aiti-14372 249 11 , , PUNCT aiti-14372 249 12 the the DET aiti-14372 249 13 formulation formulation NOUN aiti-14372 249 14 of of ADP aiti-14372 249 15 the the DET aiti-14372 249 16 non non ADJ aiti-14372 249 17 - - ADJ aiti-14372 249 18 dimensional dimensional ADJ aiti-14372 249 19 number number NOUN aiti-14372 249 20 has have AUX aiti-14372 249 21 been be AUX aiti-14372 249 22 modified modify VERB aiti-14372 249 23 . . PUNCT aiti-14372 250 1 one one NUM aiti-14372 250 2 of of ADP aiti-14372 250 3 the the DET aiti-14372 250 4 crack crack NOUN aiti-14372 250 5 driving drive VERB aiti-14372 250 6 forces force NOUN aiti-14372 250 7 used use VERB aiti-14372 250 8 in in ADP aiti-14372 250 9 the the DET aiti-14372 250 10 previous previous ADJ aiti-14372 250 11 work work NOUN aiti-14372 250 12 was be AUX aiti-14372 250 13 stress stress NOUN aiti-14372 250 14 intensity intensity NOUN aiti-14372 250 15 ( ( PUNCT aiti-14372 250 16 k k NOUN aiti-14372 250 17 ) ) PUNCT aiti-14372 250 18 . . PUNCT aiti-14372 251 1 however however ADV aiti-14372 251 2 , , PUNCT aiti-14372 251 3 it it PRON aiti-14372 251 4 was be AUX aiti-14372 251 5 felt feel VERB aiti-14372 251 6 that that SCONJ aiti-14372 251 7 , , PUNCT aiti-14372 251 8 rather rather ADV aiti-14372 251 9 than than ADP aiti-14372 251 10 k k PROPN aiti-14372 251 11 , , PUNCT aiti-14372 251 12 it it PRON aiti-14372 251 13 was be AUX aiti-14372 251 14 the the DET aiti-14372 251 15 stress stress NOUN aiti-14372 251 16 intensity intensity NOUN aiti-14372 251 17 change change NOUN aiti-14372 251 18 ( ( PUNCT aiti-14372 251 19 Ξ΄k Ξ΄k ADP aiti-14372 251 20 ) ) PUNCT aiti-14372 251 21 that that PRON aiti-14372 251 22 provided provide VERB aiti-14372 251 23 the the DET aiti-14372 251 24 crack crack NOUN aiti-14372 251 25 driving driving NOUN aiti-14372 251 26 force force NOUN aiti-14372 251 27 for for ADP aiti-14372 251 28 distinct distinct ADJ aiti-14372 251 29 stages stage NOUN aiti-14372 251 30 of of ADP aiti-14372 251 31 fcgr fcgr NOUN aiti-14372 251 32 . . PUNCT aiti-14372 252 1 also also ADV aiti-14372 252 2 , , PUNCT aiti-14372 252 3 the the DET aiti-14372 252 4 exponent exponent NOUN aiti-14372 252 5 0.25 0.25 NUM aiti-14372 252 6 was be AUX aiti-14372 252 7 changed change VERB aiti-14372 252 8 to to ADP aiti-14372 252 9 1 1 NUM aiti-14372 252 10 . . PUNCT aiti-14372 253 1 therefore therefore ADV aiti-14372 253 2 , , PUNCT aiti-14372 253 3 the the DET aiti-14372 253 4 modified modified ADJ aiti-14372 253 5 non non ADJ aiti-14372 253 6 - - ADJ aiti-14372 253 7 dimensional dimensional ADJ aiti-14372 253 8 parameter parameter NOUN aiti-14372 253 9 n n PRON aiti-14372 253 10 can can AUX aiti-14372 253 11 be be AUX aiti-14372 253 12 computed compute VERB aiti-14372 253 13 by by ADP aiti-14372 253 14   PROPN aiti-14372 253 15 max max PROPN aiti-14372 253 16 modified modify VERB aiti-14372 253 17 model model NOUN aiti-14372 254 1 ys ys PROPN aiti-14372 254 2 c c PROPN aiti-14372 254 3 c c PROPN aiti-14372 254 4 kk kk PROPN aiti-14372 255 1 n n PROPN aiti-14372 255 2 k k PROPN aiti-14372 255 3 k k PROPN aiti-14372 255 4 e e PROPN aiti-14372 255 5   PROPN aiti-14372 256 1 ο€½ ο€½ PROPN aiti-14372 256 2 ο‚΄ ο‚΄ PROPN aiti-14372 256 3 ο‚΄ ο‚΄ PROPN aiti-14372 256 4 ( ( PUNCT aiti-14372 256 5 9 9 NUM aiti-14372 256 6 ) ) PUNCT aiti-14372 256 7 another another DET aiti-14372 256 8 modification modification NOUN aiti-14372 256 9 introduced introduce VERB aiti-14372 256 10 was be AUX aiti-14372 256 11 the the DET aiti-14372 256 12 correlation correlation NOUN aiti-14372 256 13 between between ADP aiti-14372 256 14 the the DET aiti-14372 256 15 specific specific ADJ aiti-14372 256 16 growth growth NOUN aiti-14372 256 17 rate rate NOUN aiti-14372 256 18 m m PROPN aiti-14372 256 19 and and CCONJ aiti-14372 256 20 the the DET aiti-14372 256 21 non non ADJ aiti-14372 256 22 - - ADJ aiti-14372 256 23 dimensional dimensional ADJ aiti-14372 256 24 number number NOUN aiti-14372 256 25 n. n. NOUN aiti-14372 256 26 in in ADP aiti-14372 256 27 the the DET aiti-14372 256 28 previous previous ADJ aiti-14372 256 29 work work NOUN aiti-14372 256 30 , , PUNCT aiti-14372 256 31 the the DET aiti-14372 256 32 correlation correlation NOUN aiti-14372 256 33 can can AUX aiti-14372 256 34 be be AUX aiti-14372 256 35 calculated calculate VERB aiti-14372 256 36 using use VERB aiti-14372 256 37 the the DET aiti-14372 256 38 3 3 NUM aiti-14372 256 39 - - PUNCT aiti-14372 256 40 degree degree NOUN aiti-14372 256 41 polynomial polynomial NOUN aiti-14372 256 42 below below ADP aiti-14372 256 43 [ [ X aiti-14372 256 44 22 22 NUM aiti-14372 256 45 ] ] PUNCT aiti-14372 256 46 : : PUNCT aiti-14372 256 47   NOUN aiti-14372 256 48 3 3 NUM aiti-14372 256 49 2 2 NUM aiti-14372 256 50 earlier early ADJ aiti-14372 256 51 model model NOUN aiti-14372 256 52 m m VERB aiti-14372 256 53 an an DET aiti-14372 256 54 bn bn INTJ aiti-14372 256 55 cn cn PROPN aiti-14372 256 56 dο€½ dο€½ PROPN aiti-14372 256 57   PROPN aiti-14372 256 58   PUNCT aiti-14372 256 59   X aiti-14372 256 60 ( ( PUNCT aiti-14372 256 61 10 10 NUM aiti-14372 256 62 ) ) PUNCT aiti-14372 256 63 however however ADV aiti-14372 256 64 , , PUNCT aiti-14372 256 65 in in ADP aiti-14372 256 66 the the DET aiti-14372 256 67 current current ADJ aiti-14372 256 68 work work NOUN aiti-14372 256 69 , , PUNCT aiti-14372 256 70 the the DET aiti-14372 256 71 correlation correlation NOUN aiti-14372 256 72 can can AUX aiti-14372 256 73 be be AUX aiti-14372 256 74 computed compute VERB aiti-14372 256 75 by by ADP aiti-14372 256 76   PROPN aiti-14372 256 77 2 2 NUM aiti-14372 256 78 modified modify VERB aiti-14372 256 79 model model NOUN aiti-14372 256 80 m m VERB aiti-14372 256 81 an an DET aiti-14372 256 82 bn bn ADJ aiti-14372 256 83 cο€½ cο€½ NOUN aiti-14372 256 84   ADV aiti-14372 256 85   X aiti-14372 256 86 ( ( PUNCT aiti-14372 256 87 11 11 NUM aiti-14372 256 88 ) ) PUNCT aiti-14372 256 89 one one NUM aiti-14372 256 90 of of ADP aiti-14372 256 91 the the DET aiti-14372 256 92 modifications modification NOUN aiti-14372 256 93 done do VERB aiti-14372 256 94 in in ADP aiti-14372 256 95 the the DET aiti-14372 256 96 present present ADJ aiti-14372 256 97 work work NOUN aiti-14372 256 98 is be AUX aiti-14372 256 99 to to PART aiti-14372 256 100 predict predict VERB aiti-14372 256 101 the the DET aiti-14372 256 102 fcgr fcgr NOUN aiti-14372 256 103 in in ADP aiti-14372 256 104 a a DET aiti-14372 256 105 wider wide ADJ aiti-14372 256 106 range range NOUN aiti-14372 256 107 for for ADP aiti-14372 256 108 the the DET aiti-14372 256 109 through through ADP aiti-14372 256 110 - - PUNCT aiti-14372 256 111 the the DET aiti-14372 256 112 - - PUNCT aiti-14372 256 113 thickness thickness NOUN aiti-14372 256 114 direction direction NOUN aiti-14372 256 115 of of ADP aiti-14372 256 116 the the DET aiti-14372 256 117 pipe pipe NOUN aiti-14372 256 118 . . PUNCT aiti-14372 257 1 the the DET aiti-14372 257 2 limits limit NOUN aiti-14372 257 3 of of ADP aiti-14372 257 4 the the DET aiti-14372 257 5 earlier early ADJ aiti-14372 257 6 model model NOUN aiti-14372 257 7 and and CCONJ aiti-14372 257 8 the the DET aiti-14372 257 9 modified modify VERB aiti-14372 257 10 model model NOUN aiti-14372 257 11 are be AUX aiti-14372 257 12 presented present VERB aiti-14372 257 13 as as ADP aiti-14372 257 14 0.85 0.85 NUM aiti-14372 257 15 2.95 2.95 NUM aiti-14372 257 16 0.85 0.85 NUM aiti-14372 257 17 4.75 4.75 NUM aiti-14372 258 1 lim lim PROPN aiti-14372 258 2 lim lim PROPN aiti-14372 258 3 mm mm INTJ aiti-14372 259 1 mm mm INTJ aiti-14372 260 1 mm mm INTJ aiti-14372 260 2 mm mm NOUN aiti-14372 260 3 crack crack NOUN aiti-14372 260 4 length length NOUN aiti-14372 260 5 modified modify VERB aiti-14372 260 6 model model NOUN aiti-14372 260 7 crack crack NOUN aiti-14372 260 8 length length NOUN aiti-14372 260 9   X aiti-14372 260 10 ( ( PUNCT aiti-14372 260 11 12 12 NUM aiti-14372 260 12 ) ) PUNCT aiti-14372 260 13 17.45 17.45 NUM aiti-14372 260 14 20.62 20.62 NUM aiti-14372 260 15 17.45 17.45 NUM aiti-14372 260 16 21.98 21.98 NUM aiti-14372 261 1 lim lim PROPN aiti-14372 261 2 lim lim PROPN aiti-14372 262 1 mpa mpa PROPN aiti-14372 263 1 m m PROPN aiti-14372 264 1 mpa mpa PROPN aiti-14372 264 2 m m PROPN aiti-14372 264 3 mpa mpa PROPN aiti-14372 264 4 m m PROPN aiti-14372 264 5 mpa mpa PROPN aiti-14372 264 6 m m PROPN aiti-14372 264 7 k k PROPN aiti-14372 264 8 modified modify VERB aiti-14372 264 9 model model NOUN aiti-14372 264 10 k k PROPN aiti-14372 264 11 ο€­ ο€­ PROPN aiti-14372 264 12 ο€­ ο€­ PROPN aiti-14372 264 13   NOUN aiti-14372 264 14   PUNCT aiti-14372 264 15   X aiti-14372 264 16 ( ( PUNCT aiti-14372 264 17 13 13 NUM aiti-14372 264 18 ) ) PUNCT aiti-14372 264 19 4.5 4.5 NUM aiti-14372 264 20 performance performance NOUN aiti-14372 264 21 of of ADP aiti-14372 264 22 model model NOUN aiti-14372 264 23 the the DET aiti-14372 264 24 performance performance NOUN aiti-14372 264 25 of of ADP aiti-14372 264 26 the the DET aiti-14372 264 27 model model NOUN aiti-14372 264 28 was be AUX aiti-14372 264 29 analyzed analyze VERB aiti-14372 264 30 using use VERB aiti-14372 264 31 statistical statistical ADJ aiti-14372 264 32 methods method NOUN aiti-14372 264 33 like like ADP aiti-14372 264 34 mean mean VERB aiti-14372 264 35 absolute absolute ADJ aiti-14372 264 36 error error NOUN aiti-14372 264 37 ( ( PUNCT aiti-14372 264 38 mae mae PROPN aiti-14372 264 39 ) ) PUNCT aiti-14372 264 40 , , PUNCT aiti-14372 264 41 mean mean VERB aiti-14372 264 42 squared square VERB aiti-14372 264 43 error error NOUN aiti-14372 264 44 ( ( PUNCT aiti-14372 264 45 mse mse NOUN aiti-14372 264 46 ) ) PUNCT aiti-14372 264 47 , , PUNCT aiti-14372 264 48 root root NOUN aiti-14372 264 49 mean mean VERB aiti-14372 264 50 square square ADJ aiti-14372 264 51 error error NOUN aiti-14372 264 52 ( ( PUNCT aiti-14372 264 53 rmse rmse NOUN aiti-14372 264 54 ) ) PUNCT aiti-14372 264 55 , , PUNCT aiti-14372 264 56 mean mean VERB aiti-14372 264 57 prediction prediction NOUN aiti-14372 264 58 ratio ratio NOUN aiti-14372 264 59 ( ( PUNCT aiti-14372 264 60 mpr mpr NOUN aiti-14372 264 61 ) ) PUNCT aiti-14372 264 62 , , PUNCT aiti-14372 264 63 mean mean VERB aiti-14372 264 64 % % NOUN aiti-14372 264 65 deviation deviation NOUN aiti-14372 264 66 , , PUNCT aiti-14372 264 67 and and CCONJ aiti-14372 264 68 coefficient coefficient NOUN aiti-14372 264 69 of of ADP aiti-14372 264 70 determination determination NOUN aiti-14372 264 71 ( ( PUNCT aiti-14372 264 72 r2 r2 PROPN aiti-14372 264 73 ) ) PUNCT aiti-14372 264 74 . . PUNCT aiti-14372 265 1 the the DET aiti-14372 265 2 different different ADJ aiti-14372 265 3 statistical statistical ADJ aiti-14372 265 4 methods method NOUN aiti-14372 265 5 are be AUX aiti-14372 265 6 expressed express VERB aiti-14372 265 7 as as ADP aiti-14372 265 8   PROPN aiti-14372 265 9   PROPN aiti-14372 265 10   PROPN aiti-14372 265 11   PROPN aiti-14372 265 12 1 1 NUM aiti-14372 265 13 1 1 NUM aiti-14372 265 14 n n NOUN aiti-14372 265 15 i i PRON aiti-14372 265 16 experimental experimental ADJ aiti-14372 265 17 data datum NOUN aiti-14372 265 18 predicted predict VERB aiti-14372 265 19 valuei valuei PROPN aiti-14372 265 20 in in ADP aiti-14372 265 21 mae mae PROPN aiti-14372 265 22 ο€½ ο€½ PROPN aiti-14372 266 1 ο€½ ο€½ PROPN aiti-14372 266 2 οƒ₯ οƒ₯ X aiti-14372 266 3 ( ( PUNCT aiti-14372 266 4 14 14 NUM aiti-14372 266 5 ) ) PUNCT aiti-14372 266 6   PROPN aiti-14372 266 7   PROPN aiti-14372 266 8   PROPN aiti-14372 266 9   NOUN aiti-14372 266 10   PROPN aiti-14372 266 11 1 1 NUM aiti-14372 266 12 21 21 NUM aiti-14372 266 13 n n NOUN aiti-14372 266 14 i i PRON aiti-14372 266 15 experimental experimental ADJ aiti-14372 266 16 data datum NOUN aiti-14372 266 17 predicted predict VERB aiti-14372 266 18 valuei valuei PROPN aiti-14372 266 19 in in ADP aiti-14372 266 20 mse mse PROPN aiti-14372 267 1 ο€½ ο€½ PROPN aiti-14372 267 2 ο€½ ο€½ PROPN aiti-14372 267 3 οƒ₯ οƒ₯ X aiti-14372 267 4 ( ( PUNCT aiti-14372 267 5 15 15 NUM aiti-14372 267 6 ) ) PUNCT aiti-14372 267 7 rmse rmse NOUN aiti-14372 268 1 mseο€½ mseο€½ PROPN aiti-14372 268 2 ( ( PUNCT aiti-14372 268 3 16 16 NUM aiti-14372 268 4 ) ) PUNCT aiti-14372 268 5   NOUN aiti-14372 268 6   SYM aiti-14372 268 7   NOUN aiti-14372 268 8 1 1 VERB aiti-14372 268 9 1 1 NUM aiti-14372 268 10 n n NOUN aiti-14372 268 11 i i PRON aiti-14372 268 12 experimental experimental ADJ aiti-14372 268 13 data datum NOUN aiti-14372 269 1 i i PRON aiti-14372 269 2 n n VERB aiti-14372 269 3 predicted predict VERB aiti-14372 269 4 value value NOUN aiti-14372 269 5 i i PRON aiti-14372 269 6 mpr mpr VERB aiti-14372 270 1 ο€½ ο€½ NOUN aiti-14372 270 2 ο€½ ο€½ PROPN aiti-14372 270 3 οƒ₯ οƒ₯ X aiti-14372 270 4 ( ( PUNCT aiti-14372 270 5 17 17 NUM aiti-14372 270 6 ) ) PUNCT aiti-14372 270 7   PROPN aiti-14372 271 1   PROPN aiti-14372 271 2   PROPN aiti-14372 271 3   PROPN aiti-14372 271 4   NOUN aiti-14372 271 5 1 1 AUX aiti-14372 271 6 exp1 exp1 VERB aiti-14372 271 7 100 100 NUM aiti-14372 271 8 exp exp NOUN aiti-14372 272 1 n n NOUN aiti-14372 273 1 i i PRON aiti-14372 273 2 erimental erimental ADJ aiti-14372 273 3 data datum NOUN aiti-14372 273 4 predicted predict VERB aiti-14372 273 5 valuei valuei PROPN aiti-14372 273 6 i i PRON aiti-14372 273 7 n n NUM aiti-14372 273 8 erimental erimental ADJ aiti-14372 273 9 data datum NOUN aiti-14372 273 10 i i PRON aiti-14372 273 11 mean% mean% NOUN aiti-14372 273 12 deviation deviation NOUN aiti-14372 273 13 ο€½ ο€½ PROPN aiti-14372 273 14 ο€­ ο€­ PROPN aiti-14372 273 15 ο‚΄ο€½ ο‚΄ο€½ NOUN aiti-14372 273 16 οƒ₯ οƒ₯ X aiti-14372 273 17 ( ( PUNCT aiti-14372 273 18 18 18 NUM aiti-14372 273 19 ) ) SYM aiti-14372 273 20 2 2 NUM aiti-14372 273 21 1 1 NUM aiti-14372 273 22 sum sum NOUN aiti-14372 273 23 of of ADP aiti-14372 273 24 square square ADJ aiti-14372 273 25 error error NOUN aiti-14372 273 26 sum sum NOUN aiti-14372 273 27 of of ADP aiti-14372 273 28 squares square NOUN aiti-14372 273 29 total total ADJ aiti-14372 273 30 r r NOUN aiti-14372 273 31 ο€½ ο€½ PROPN aiti-14372 273 32 ο€­ ο€­ NOUN aiti-14372 273 33 ( ( PUNCT aiti-14372 273 34 19 19 NUM aiti-14372 273 35 ) ) PUNCT aiti-14372 273 36 the the DET aiti-14372 273 37 quantitative quantitative ADJ aiti-14372 273 38 analysis analysis NOUN aiti-14372 273 39 of of ADP aiti-14372 273 40 the the DET aiti-14372 273 41 model model NOUN aiti-14372 273 42 is be AUX aiti-14372 273 43 shown show VERB aiti-14372 273 44 in in ADP aiti-14372 273 45 table table NOUN aiti-14372 273 46 5 5 NUM aiti-14372 273 47 . . PUNCT aiti-14372 274 1 the the DET aiti-14372 274 2 model model NOUN aiti-14372 274 3 showed show VERB aiti-14372 274 4 the the DET aiti-14372 274 5 lowest low ADJ aiti-14372 274 6 ( ( PUNCT aiti-14372 274 7 and and CCONJ aiti-14372 274 8 the the DET aiti-14372 274 9 best good ADJ aiti-14372 274 10 ) ) PUNCT aiti-14372 274 11 value value NOUN aiti-14372 274 12 of of ADP aiti-14372 274 13 mae mae PROPN aiti-14372 274 14 , , PUNCT aiti-14372 274 15 mse mse PROPN aiti-14372 274 16 , , PUNCT aiti-14372 274 17 and and CCONJ aiti-14372 274 18 rmse rmse NOUN aiti-14372 274 19 for for ADP aiti-14372 274 20 stage stage NOUN aiti-14372 274 21 - - PUNCT aiti-14372 274 22 i i PRON aiti-14372 274 23 of of ADP aiti-14372 274 24 fcgr fcgr NOUN aiti-14372 274 25 and and CCONJ aiti-14372 274 26 the the DET aiti-14372 274 27 highest high ADJ aiti-14372 274 28 for for ADP aiti-14372 274 29 stage stage NOUN aiti-14372 274 30 - - PUNCT aiti-14372 274 31 iii iii NOUN aiti-14372 274 32 . . PUNCT aiti-14372 275 1 however however ADV aiti-14372 275 2 , , PUNCT aiti-14372 275 3 the the DET aiti-14372 275 4 performance performance NOUN aiti-14372 275 5 of of ADP aiti-14372 275 6 the the DET aiti-14372 275 7 model model NOUN aiti-14372 275 8 was be AUX aiti-14372 275 9 within within ADP aiti-14372 275 10 the the DET aiti-14372 275 11 acceptable acceptable ADJ aiti-14372 275 12 values value NOUN aiti-14372 275 13 for for ADP aiti-14372 275 14 all all DET aiti-14372 275 15 three three NUM aiti-14372 275 16 stages stage NOUN aiti-14372 275 17 . . PUNCT aiti-14372 276 1 for for ADP aiti-14372 276 2 stages stage NOUN aiti-14372 276 3 - - PUNCT aiti-14372 276 4 i i PRON aiti-14372 276 5 and and CCONJ aiti-14372 276 6 ii ii PROPN aiti-14372 276 7 , , PUNCT aiti-14372 276 8 modelling model VERB aiti-14372 276 9 provided provide VERB aiti-14372 276 10 the the DET aiti-14372 276 11 best good ADJ aiti-14372 276 12 results result NOUN aiti-14372 276 13 ; ; PUNCT aiti-14372 276 14 however however ADV aiti-14372 276 15 , , PUNCT aiti-14372 276 16 for for ADP aiti-14372 276 17 stage stage NOUN aiti-14372 276 18 - - PUNCT aiti-14372 276 19 iii iii NOUN aiti-14372 276 20 , , PUNCT aiti-14372 276 21 modelling modelling NOUN aiti-14372 276 22 was be AUX aiti-14372 276 23 comparatively comparatively ADV aiti-14372 276 24 conservative conservative ADJ aiti-14372 276 25 , , PUNCT aiti-14372 276 26 but but CCONJ aiti-14372 276 27 still still ADV aiti-14372 276 28 in in ADP aiti-14372 276 29 the the DET aiti-14372 276 30 acceptable acceptable ADJ aiti-14372 276 31 range range NOUN aiti-14372 276 32 . . PUNCT aiti-14372 277 1 it it PRON aiti-14372 277 2 is be AUX aiti-14372 277 3 suggested suggest VERB aiti-14372 277 4 that that SCONJ aiti-14372 277 5 the the DET aiti-14372 277 6 modified modify VERB aiti-14372 277 7 exponential exponential ADJ aiti-14372 277 8 function function NOUN aiti-14372 277 9 and and CCONJ aiti-14372 277 10 specific specific ADJ aiti-14372 277 11 growth growth NOUN aiti-14372 277 12 rate rate NOUN aiti-14372 277 13 depict depict VERB aiti-14372 277 14 the the DET aiti-14372 277 15 slopes slope NOUN aiti-14372 277 16 of of ADP aiti-14372 277 17 da da PROPN aiti-14372 277 18 / / SYM aiti-14372 277 19 dn dn PROPN aiti-14372 277 20 versus versus ADP aiti-14372 277 21 the the DET aiti-14372 277 22 Ξ΄k Ξ΄k PROPN aiti-14372 277 23 curve curve NOUN aiti-14372 277 24 precisely precisely ADV aiti-14372 277 25 , , PUNCT aiti-14372 277 26 where where SCONJ aiti-14372 277 27 the the DET aiti-14372 277 28 fcgr fcgr NOUN aiti-14372 277 29 was be AUX aiti-14372 277 30 initially initially ADV aiti-14372 277 31 slow slow ADJ aiti-14372 277 32 during during ADP aiti-14372 277 33 stagei stagei NOUN aiti-14372 277 34 and and CCONJ aiti-14372 277 35 accelerated accelerate VERB aiti-14372 277 36 during during ADP aiti-14372 277 37 stage stage NOUN aiti-14372 277 38 - - PUNCT aiti-14372 277 39 ii ii NOUN aiti-14372 277 40 . . PUNCT aiti-14372 278 1 when when SCONJ aiti-14372 278 2 the the DET aiti-14372 278 3 crack crack NOUN aiti-14372 278 4 fcgr fcgr NOUN aiti-14372 278 5 was be AUX aiti-14372 278 6 highly highly ADV aiti-14372 278 7 accelerated accelerate VERB aiti-14372 278 8 , , PUNCT aiti-14372 278 9 the the DET aiti-14372 278 10 model model NOUN aiti-14372 278 11 depicted depict VERB aiti-14372 278 12 a a DET aiti-14372 278 13 fall fall NOUN aiti-14372 278 14 in in ADP aiti-14372 278 15 the the DET aiti-14372 278 16 performance performance NOUN aiti-14372 278 17 . . PUNCT aiti-14372 279 1 advances advance NOUN aiti-14372 279 2 in in ADP aiti-14372 279 3 technology technology NOUN aiti-14372 279 4 innovation innovation NOUN aiti-14372 279 5 , , PUNCT aiti-14372 279 6 vol vol NOUN aiti-14372 279 7 . . PROPN aiti-14372 280 1 10 10 NUM aiti-14372 280 2 , , PUNCT aiti-14372 280 3 no no INTJ aiti-14372 280 4 . . NOUN aiti-14372 280 5 3 3 NUM aiti-14372 280 6 , , PUNCT aiti-14372 280 7 2025 2025 NUM aiti-14372 280 8 , , PUNCT aiti-14372 280 9 pp pp ADJ aiti-14372 280 10 . . PUNCT aiti-14372 281 1 238 238 NUM aiti-14372 281 2 - - SYM aiti-14372 281 3 253 253 NUM aiti-14372 281 4 248 248 NUM aiti-14372 281 5 the the DET aiti-14372 281 6 mpr mpr NOUN aiti-14372 281 7 , , PUNCT aiti-14372 281 8 mean mean VERB aiti-14372 281 9 % % NOUN aiti-14372 281 10 deviation deviation NOUN aiti-14372 281 11 , , PUNCT aiti-14372 281 12 and and CCONJ aiti-14372 281 13 r2 r2 PROPN aiti-14372 281 14 in in ADP aiti-14372 281 15 stage stage NOUN aiti-14372 281 16 - - PUNCT aiti-14372 281 17 i i PRON aiti-14372 281 18 of of ADP aiti-14372 281 19 fcgr fcgr NOUN aiti-14372 281 20 showed show VERB aiti-14372 281 21 the the DET aiti-14372 281 22 best good ADJ aiti-14372 281 23 performance performance NOUN aiti-14372 281 24 . . PUNCT aiti-14372 282 1 an an DET aiti-14372 282 2 r2 r2 NOUN aiti-14372 282 3 of of ADP aiti-14372 282 4 0.998 0.998 NUM aiti-14372 282 5 and and CCONJ aiti-14372 282 6 0.997 0.997 NUM aiti-14372 282 7 in in ADP aiti-14372 282 8 stages stage NOUN aiti-14372 282 9 - - PUNCT aiti-14372 282 10 i i PRON aiti-14372 282 11 and and CCONJ aiti-14372 282 12 ii ii PROPN aiti-14372 282 13 indicated indicate VERB aiti-14372 282 14 that that SCONJ aiti-14372 282 15 the the DET aiti-14372 282 16 hypothesis hypothesis NOUN aiti-14372 282 17 of of ADP aiti-14372 282 18 the the DET aiti-14372 282 19 use use NOUN aiti-14372 282 20 of of ADP aiti-14372 282 21 a a DET aiti-14372 282 22 modified modify VERB aiti-14372 282 23 exponential exponential ADJ aiti-14372 282 24 function function NOUN aiti-14372 282 25 and and CCONJ aiti-14372 282 26 specific specific ADJ aiti-14372 282 27 growth growth NOUN aiti-14372 282 28 rate rate NOUN aiti-14372 282 29 to to PART aiti-14372 282 30 predict predict VERB aiti-14372 282 31 the the DET aiti-14372 282 32 fcgr fcgr NOUN aiti-14372 282 33 agreed agree VERB aiti-14372 282 34 with with ADP aiti-14372 282 35 the the DET aiti-14372 282 36 experimental experimental ADJ aiti-14372 282 37 outcomes outcome NOUN aiti-14372 282 38 . . PUNCT aiti-14372 283 1 the the DET aiti-14372 283 2 performance performance NOUN aiti-14372 283 3 of of ADP aiti-14372 283 4 the the DET aiti-14372 283 5 model model NOUN aiti-14372 283 6 dropped drop VERB aiti-14372 283 7 to to ADP aiti-14372 283 8 a a DET aiti-14372 283 9 value value NOUN aiti-14372 283 10 of of ADP aiti-14372 283 11 0.969 0.969 NUM aiti-14372 283 12 for for ADP aiti-14372 283 13 r2 r2 PROPN aiti-14372 283 14 in in ADP aiti-14372 283 15 stageiii stageiii NOUN aiti-14372 283 16 of of ADP aiti-14372 283 17 fcgr fcgr NOUN aiti-14372 283 18 . . PUNCT aiti-14372 284 1 when when SCONJ aiti-14372 284 2 the the DET aiti-14372 284 3 fcgr fcgr NOUN aiti-14372 284 4 was be AUX aiti-14372 284 5 highly highly ADV aiti-14372 284 6 accelerated accelerate VERB aiti-14372 284 7 , , PUNCT aiti-14372 284 8 the the DET aiti-14372 284 9 modified modify VERB aiti-14372 284 10 exponential exponential ADJ aiti-14372 284 11 function function NOUN aiti-14372 284 12 became become VERB aiti-14372 284 13 conservative conservative ADJ aiti-14372 284 14 and and CCONJ aiti-14372 284 15 showed show VERB aiti-14372 284 16 a a DET aiti-14372 284 17 lower low ADJ aiti-14372 284 18 performance performance NOUN aiti-14372 284 19 as as ADP aiti-14372 284 20 compared compare VERB aiti-14372 284 21 to to ADP aiti-14372 284 22 stages stage NOUN aiti-14372 284 23 - - PUNCT aiti-14372 284 24 i i PRON aiti-14372 284 25 and and CCONJ aiti-14372 284 26 ii ii PROPN aiti-14372 284 27 . . PUNCT aiti-14372 285 1 a a DET aiti-14372 285 2 mean mean ADJ aiti-14372 285 3 prediction prediction NOUN aiti-14372 285 4 ratio ratio NOUN aiti-14372 285 5 of of ADP aiti-14372 285 6 < < X aiti-14372 285 7 1 1 NUM aiti-14372 285 8 for for ADP aiti-14372 285 9 all all DET aiti-14372 285 10 three three NUM aiti-14372 285 11 stages stage NOUN aiti-14372 285 12 of of ADP aiti-14372 285 13 fcgr fcgr NOUN aiti-14372 285 14 depicted depict VERB aiti-14372 285 15 that that SCONJ aiti-14372 285 16 the the DET aiti-14372 285 17 model model NOUN aiti-14372 285 18 performance performance NOUN aiti-14372 285 19 was be AUX aiti-14372 285 20 on on ADP aiti-14372 285 21 the the DET aiti-14372 285 22 higher high ADJ aiti-14372 285 23 side side NOUN aiti-14372 285 24 of of ADP aiti-14372 285 25 the the DET aiti-14372 285 26 experimental experimental ADJ aiti-14372 285 27 data datum NOUN aiti-14372 285 28 . . PUNCT aiti-14372 286 1 in in ADP aiti-14372 286 2 other other ADJ aiti-14372 286 3 words word NOUN aiti-14372 286 4 , , PUNCT aiti-14372 286 5 the the DET aiti-14372 286 6 predicted predict VERB aiti-14372 286 7 values value NOUN aiti-14372 286 8 of of ADP aiti-14372 286 9 da da PROPN aiti-14372 286 10 / / SYM aiti-14372 286 11 dn dn NOUN aiti-14372 286 12 were be AUX aiti-14372 286 13 greater great ADJ aiti-14372 286 14 than than ADP aiti-14372 286 15 the the DET aiti-14372 286 16 experimental experimental ADJ aiti-14372 286 17 values value NOUN aiti-14372 286 18 . . PUNCT aiti-14372 287 1 table table NOUN aiti-14372 287 2 5 5 NUM aiti-14372 287 3 performance performance NOUN aiti-14372 287 4 of of ADP aiti-14372 287 5 the the DET aiti-14372 287 6 model model NOUN aiti-14372 287 7 for for ADP aiti-14372 287 8 the the DET aiti-14372 287 9 prediction prediction NOUN aiti-14372 287 10 of of ADP aiti-14372 287 11 fcgr fcgr NOUN aiti-14372 287 12 as as ADP aiti-14372 287 13 a a DET aiti-14372 287 14 function function NOUN aiti-14372 287 15 of of ADP aiti-14372 287 16 Ξ΄k Ξ΄k DET aiti-14372 287 17 stage stage NOUN aiti-14372 287 18 of of ADP aiti-14372 287 19 fcgr fcgr NOUN aiti-14372 287 20 mae mae PROPN aiti-14372 287 21 mse mse PROPN aiti-14372 287 22 rmse rmse PROPN aiti-14372 287 23 mpr mpr PROPN aiti-14372 287 24 mean mean NOUN aiti-14372 287 25 % % NOUN aiti-14372 287 26 deviation deviation NOUN aiti-14372 287 27 r2 r2 NOUN aiti-14372 287 28 stage stage NOUN aiti-14372 287 29 - - PUNCT aiti-14372 287 30 i i PRON aiti-14372 287 31 1.13812eβˆ’06 1.13812eβˆ’06 NUM aiti-14372 288 1 1.41535eβˆ’12 1.41535eβˆ’12 NUM aiti-14372 288 2 1.18969eβˆ’06 1.18969eβˆ’06 NUM aiti-14372 288 3 0.983 0.983 NUM aiti-14372 288 4 1.664 1.664 NUM aiti-14372 288 5 0.998 0.998 NUM aiti-14372 288 6 stage stage NOUN aiti-14372 288 7 - - PUNCT aiti-14372 288 8 ii ii NOUN aiti-14372 288 9 1.9169eβˆ’06 1.9169eβˆ’06 NUM aiti-14372 288 10 4.12088eβˆ’12 4.12088eβˆ’12 NUM aiti-14372 288 11 2.02999eβˆ’06 2.02999eβˆ’06 NUM aiti-14372 288 12 0.979 0.979 NUM aiti-14372 288 13 2.075 2.075 NUM aiti-14372 288 14 0.997 0.997 NUM aiti-14372 288 15 stage stage NOUN aiti-14372 288 16 - - PUNCT aiti-14372 288 17 iii iii NUM aiti-14372 288 18 3.30524eβˆ’06 3.30524eβˆ’06 NUM aiti-14372 288 19 1.27444eβˆ’11 1.27444eβˆ’11 NUM aiti-14372 288 20 3.56993eβˆ’06 3.56993eβˆ’06 NUM aiti-14372 288 21 0.974 0.974 NUM aiti-14372 288 22 2.655 2.655 NUM aiti-14372 288 23 0.969 0.969 NUM aiti-14372 288 24 the the DET aiti-14372 288 25 error error NOUN aiti-14372 288 26 band band NOUN aiti-14372 288 27 scatter scatter NOUN aiti-14372 288 28 analysis analysis NOUN aiti-14372 288 29 was be AUX aiti-14372 288 30 carried carry VERB aiti-14372 288 31 out out ADP aiti-14372 288 32 for for ADP aiti-14372 288 33 the the DET aiti-14372 288 34 predicted predict VERB aiti-14372 288 35 and and CCONJ aiti-14372 288 36 experimental experimental ADJ aiti-14372 288 37 results result NOUN aiti-14372 288 38 of of ADP aiti-14372 288 39 fcgr fcgr NOUN aiti-14372 288 40 for for ADP aiti-14372 288 41 stages stage NOUN aiti-14372 288 42 - - PUNCT aiti-14372 288 43 i i PRON aiti-14372 288 44 , , PUNCT aiti-14372 288 45 ii ii PROPN aiti-14372 288 46 , , PUNCT aiti-14372 288 47 and and CCONJ aiti-14372 288 48 ii ii X aiti-14372 288 49 . . PUNCT aiti-14372 289 1 the the DET aiti-14372 289 2 results result NOUN aiti-14372 289 3 of of ADP aiti-14372 289 4 the the DET aiti-14372 289 5 analysis analysis NOUN aiti-14372 289 6 are be AUX aiti-14372 289 7 shown show VERB aiti-14372 289 8 in in ADP aiti-14372 289 9 figs fig NOUN aiti-14372 289 10 . . PUNCT aiti-14372 290 1 14 14 NUM aiti-14372 290 2 , , PUNCT aiti-14372 290 3 15 15 NUM aiti-14372 290 4 , , PUNCT aiti-14372 290 5 and and CCONJ aiti-14372 290 6 16 16 NUM aiti-14372 290 7 , , PUNCT aiti-14372 290 8 respectively respectively ADV aiti-14372 290 9 . . PUNCT aiti-14372 291 1 the the DET aiti-14372 291 2 error error NOUN aiti-14372 291 3 band band NOUN aiti-14372 291 4 scatter scatter NOUN aiti-14372 291 5 was be AUX aiti-14372 291 6 considered consider VERB aiti-14372 291 7 on on ADP aiti-14372 291 8 the the DET aiti-14372 291 9 positive positive ADJ aiti-14372 291 10 side side NOUN aiti-14372 291 11 of of ADP aiti-14372 291 12 the the DET aiti-14372 291 13 perfect perfect ADJ aiti-14372 291 14 fit fit NOUN aiti-14372 291 15 because because SCONJ aiti-14372 291 16 the the DET aiti-14372 291 17 predicted predict VERB aiti-14372 291 18 values value NOUN aiti-14372 291 19 were be AUX aiti-14372 291 20 on on ADP aiti-14372 291 21 the the DET aiti-14372 291 22 higher high ADJ aiti-14372 291 23 side side NOUN aiti-14372 291 24 of of ADP aiti-14372 291 25 the the DET aiti-14372 291 26 experimental experimental ADJ aiti-14372 291 27 data datum NOUN aiti-14372 291 28 . . PUNCT aiti-14372 292 1 the the DET aiti-14372 292 2 error error NOUN aiti-14372 292 3 band band NOUN aiti-14372 292 4 for for ADP aiti-14372 292 5 stagesi stagesi NOUN aiti-14372 292 6 , , PUNCT aiti-14372 292 7 ii ii PROPN aiti-14372 292 8 , , PUNCT aiti-14372 292 9 and and CCONJ aiti-14372 292 10 iii iii NOUN aiti-14372 292 11 falls fall VERB aiti-14372 292 12 on on ADP aiti-14372 292 13 the the DET aiti-14372 292 14 positive positive ADJ aiti-14372 292 15 side side NOUN aiti-14372 292 16 by by ADP aiti-14372 292 17 0.034 0.034 NUM aiti-14372 292 18 , , PUNCT aiti-14372 292 19 0.035 0.035 NUM aiti-14372 292 20 , , PUNCT aiti-14372 292 21 and and CCONJ aiti-14372 292 22 0.043 0.043 NUM aiti-14372 292 23 % % NOUN aiti-14372 292 24 of of ADP aiti-14372 292 25 the the DET aiti-14372 292 26 perfect perfect ADJ aiti-14372 292 27 fit fit PROPN aiti-14372 292 28 . . PUNCT aiti-14372 293 1 fig fig NOUN aiti-14372 293 2 . . PUNCT aiti-14372 294 1 14 14 NUM aiti-14372 294 2 error error NOUN aiti-14372 294 3 band band NOUN aiti-14372 294 4 scatter scatter NOUN aiti-14372 294 5 for for ADP aiti-14372 294 6 stage stage NOUN aiti-14372 294 7 - - PUNCT aiti-14372 294 8 i i PRON aiti-14372 294 9 of of ADP aiti-14372 294 10 fcgr fcgr NOUN aiti-14372 294 11 fig fig NOUN aiti-14372 294 12 . . PUNCT aiti-14372 295 1 15 15 NUM aiti-14372 295 2 error error NOUN aiti-14372 295 3 band band NOUN aiti-14372 295 4 scatter scatter NOUN aiti-14372 295 5 for for ADP aiti-14372 295 6 stage stage NOUN aiti-14372 295 7 - - PUNCT aiti-14372 295 8 ii ii NOUN aiti-14372 295 9 of of ADP aiti-14372 295 10 fcgr fcgr PROPN aiti-14372 295 11 fig fig PROPN aiti-14372 295 12 . . PUNCT aiti-14372 296 1 16 16 NUM aiti-14372 296 2 error error NOUN aiti-14372 296 3 band band NOUN aiti-14372 296 4 scatter scatter NOUN aiti-14372 296 5 for for ADP aiti-14372 296 6 stage stage NOUN aiti-14372 296 7 - - PUNCT aiti-14372 296 8 iii iii NOUN aiti-14372 296 9 of of ADP aiti-14372 296 10 fcgr fcgr NOUN aiti-14372 296 11 4.6 4.6 NUM aiti-14372 296 12 comparison comparison NOUN aiti-14372 296 13 of of ADP aiti-14372 296 14 the the DET aiti-14372 296 15 performance performance NOUN aiti-14372 296 16 of of ADP aiti-14372 296 17 the the DET aiti-14372 296 18 model model NOUN aiti-14372 296 19 with with ADP aiti-14372 296 20 earlier early ADJ aiti-14372 296 21 developed develop VERB aiti-14372 296 22 models model NOUN aiti-14372 296 23 the the DET aiti-14372 296 24 performance performance NOUN aiti-14372 296 25 of of ADP aiti-14372 296 26 the the DET aiti-14372 296 27 modified modify VERB aiti-14372 296 28 exponential exponential ADJ aiti-14372 296 29 function function NOUN aiti-14372 296 30 in in ADP aiti-14372 296 31 the the DET aiti-14372 296 32 present present ADJ aiti-14372 296 33 work work NOUN aiti-14372 296 34 was be AUX aiti-14372 296 35 compared compare VERB aiti-14372 296 36 with with ADP aiti-14372 296 37 previous previous ADJ aiti-14372 296 38 models model NOUN aiti-14372 296 39 developed develop VERB aiti-14372 296 40 in in ADP aiti-14372 296 41 earlier early ADJ aiti-14372 296 42 work work NOUN aiti-14372 296 43 [ [ X aiti-14372 296 44 22 22 NUM aiti-14372 296 45 ] ] PUNCT aiti-14372 296 46 . . PUNCT aiti-14372 297 1 the the DET aiti-14372 297 2 earlier early ADJ aiti-14372 297 3 models model NOUN aiti-14372 297 4 only only ADV aiti-14372 297 5 predicted predict VERB aiti-14372 297 6 fcgr fcgr NOUN aiti-14372 297 7 for for ADP aiti-14372 297 8 stage stage NOUN aiti-14372 297 9 - - PUNCT aiti-14372 297 10 i. i. NOUN aiti-14372 297 11 although although SCONJ aiti-14372 297 12 the the DET aiti-14372 297 13 present present ADJ aiti-14372 297 14 work work NOUN aiti-14372 297 15 predicted predict VERB aiti-14372 297 16 fcgr fcgr NOUN aiti-14372 297 17 for for ADP aiti-14372 297 18 all all DET aiti-14372 297 19 three three NUM aiti-14372 297 20 stages stage NOUN aiti-14372 297 21 , , PUNCT aiti-14372 297 22 only only ADV aiti-14372 297 23 the the DET aiti-14372 297 24 stage stage NOUN aiti-14372 297 25 - - PUNCT aiti-14372 297 26 i i PRON aiti-14372 297 27 of of ADP aiti-14372 297 28 fcgr fcgr NOUN aiti-14372 297 29 prediction prediction NOUN aiti-14372 297 30 performance performance NOUN aiti-14372 297 31 has have AUX aiti-14372 297 32 been be AUX aiti-14372 297 33 compared compare VERB aiti-14372 297 34 and and CCONJ aiti-14372 297 35 presented present VERB aiti-14372 297 36 in in ADP aiti-14372 297 37 table table NOUN aiti-14372 297 38 6 6 NUM aiti-14372 297 39 . . PUNCT aiti-14372 298 1 there there PRON aiti-14372 298 2 was be VERB aiti-14372 298 3 a a DET aiti-14372 298 4 significant significant ADJ aiti-14372 298 5 advancement advancement NOUN aiti-14372 298 6 in in ADP aiti-14372 298 7 the the DET aiti-14372 298 8 performance performance NOUN aiti-14372 298 9 observed observe VERB aiti-14372 298 10 for for ADP aiti-14372 298 11 the the DET aiti-14372 298 12 modified modify VERB aiti-14372 298 13 exponential exponential ADJ aiti-14372 298 14 function function NOUN aiti-14372 298 15 as as ADP aiti-14372 298 16 compared compare VERB aiti-14372 298 17 to to ADP aiti-14372 298 18 the the DET aiti-14372 298 19 earlier early ADJ aiti-14372 298 20 5.00e-05 5.00e-05 NUM aiti-14372 298 21 5.50e-05 5.50e-05 NUM aiti-14372 298 22 6.00e-05 6.00e-05 NUM aiti-14372 298 23 6.50e-05 6.50e-05 NUM aiti-14372 298 24 7.00e-05 7.00e-05 NUM aiti-14372 298 25 7.50e-05 7.50e-05 NUM aiti-14372 298 26 8.00e-05 8.00e-05 NUM aiti-14372 298 27 8.50e-05 8.50e-05 NUM aiti-14372 298 28 5.00e-05 5.00e-05 NUM aiti-14372 298 29 6.00e-05 6.00e-05 NUM aiti-14372 298 30 7.00e-05 7.00e-05 NUM aiti-14372 298 31 8.00e-05 8.00e-05 NUM aiti-14372 298 32 9.00e-05 9.00e-05 NUM aiti-14372 298 33 da da NOUN aiti-14372 298 34 /d /d PUNCT aiti-14372 298 35 n n CCONJ aiti-14372 298 36 ( ( PUNCT aiti-14372 298 37 pr pr INTJ aiti-14372 298 38 ed ed NOUN aiti-14372 298 39 ic ic INTJ aiti-14372 298 40 te te PROPN aiti-14372 298 41 d d PROPN aiti-14372 298 42 ) ) PUNCT aiti-14372 298 43 da da ADJ aiti-14372 298 44 / / SYM aiti-14372 298 45 dn dn PROPN aiti-14372 298 46 ( ( PUNCT aiti-14372 298 47 experimental experimental ADJ aiti-14372 298 48 ) ) PUNCT aiti-14372 298 49 da da PROPN aiti-14372 298 50 / / SYM aiti-14372 298 51 dn dn PROPN aiti-14372 298 52 ( ( PUNCT aiti-14372 298 53 predicted predict VERB aiti-14372 298 54 ) ) PUNCT aiti-14372 298 55 0.035 0.035 NUM aiti-14372 298 56 % % NOUN aiti-14372 298 57 fit fit ADJ aiti-14372 298 58 perfect perfect ADJ aiti-14372 298 59 fit fit ADJ aiti-14372 298 60 8.00e-05 8.00e-05 NUM aiti-14372 298 61 8.50e-05 8.50e-05 NUM aiti-14372 298 62 9.00e-05 9.00e-05 NUM aiti-14372 298 63 9.50e-05 9.50e-05 NUM aiti-14372 298 64 1.00e-04 1.00e-04 NUM aiti-14372 298 65 1.05e-04 1.05e-04 NUM aiti-14372 298 66 1.10e-04 1.10e-04 NUM aiti-14372 298 67 8.00e-05 8.00e-05 NUM aiti-14372 298 68 9.00e-05 9.00e-05 NUM aiti-14372 298 69 1.00e-04 1.00e-04 NUM aiti-14372 298 70 1.10e-04 1.10e-04 NUM aiti-14372 298 71 da da NOUN aiti-14372 298 72 /d /d PUNCT aiti-14372 298 73 n n PROPN aiti-14372 298 74 ( ( PUNCT aiti-14372 298 75 p p X aiti-14372 298 76 re re ADP aiti-14372 298 77 di di X aiti-14372 298 78 ct ct PROPN aiti-14372 298 79 ed ed PROPN aiti-14372 298 80 ) ) PUNCT aiti-14372 298 81 da da PROPN aiti-14372 298 82 / / SYM aiti-14372 298 83 dn dn PROPN aiti-14372 298 84 ( ( PUNCT aiti-14372 298 85 experimental experimental ADJ aiti-14372 298 86 ) ) PUNCT aiti-14372 298 87 da da PROPN aiti-14372 298 88 / / SYM aiti-14372 298 89 dn dn PROPN aiti-14372 298 90 ( ( PUNCT aiti-14372 298 91 predicted predict VERB aiti-14372 298 92 ) ) PUNCT aiti-14372 298 93 0.034 0.034 NUM aiti-14372 298 94 % % NOUN aiti-14372 298 95 fit fit ADJ aiti-14372 298 96 perfect perfect ADJ aiti-14372 298 97 fit fit ADJ aiti-14372 298 98 1.10e-04 1.10e-04 NUM aiti-14372 298 99 1.15e-04 1.15e-04 NUM aiti-14372 298 100 1.20e-04 1.20e-04 NUM aiti-14372 298 101 1.25e-04 1.25e-04 NUM aiti-14372 298 102 1.30e-04 1.30e-04 NUM aiti-14372 298 103 1.35e-04 1.35e-04 NUM aiti-14372 298 104 1.40e-04 1.40e-04 NUM aiti-14372 298 105 1.10e-04 1.10e-04 NUM aiti-14372 298 106 1.20e-04 1.20e-04 NUM aiti-14372 298 107 1.30e-04 1.30e-04 NUM aiti-14372 298 108 1.40e-04 1.40e-04 NUM aiti-14372 298 109 da da X aiti-14372 298 110 /d /d PUNCT aiti-14372 298 111 n n CCONJ aiti-14372 298 112 ( ( PUNCT aiti-14372 298 113 pr pr INTJ aiti-14372 298 114 ed ed NOUN aiti-14372 298 115 ic ic INTJ aiti-14372 298 116 te te PROPN aiti-14372 298 117 d d PROPN aiti-14372 298 118 ) ) PUNCT aiti-14372 298 119 da da ADJ aiti-14372 298 120 / / SYM aiti-14372 298 121 dn dn PROPN aiti-14372 298 122 ( ( PUNCT aiti-14372 298 123 experimental experimental ADJ aiti-14372 298 124 ) ) PUNCT aiti-14372 298 125 da da PROPN aiti-14372 298 126 / / SYM aiti-14372 298 127 dn dn PROPN aiti-14372 298 128 ( ( PUNCT aiti-14372 298 129 predicted predict VERB aiti-14372 298 130 ) ) PUNCT aiti-14372 298 131 0.043 0.043 NUM aiti-14372 298 132 % % NOUN aiti-14372 298 133 fit fit ADJ aiti-14372 298 134 perfect perfect ADJ aiti-14372 298 135 fit fit ADJ aiti-14372 298 136 advances advance NOUN aiti-14372 298 137 in in ADP aiti-14372 298 138 technology technology NOUN aiti-14372 298 139 innovation innovation NOUN aiti-14372 298 140 , , PUNCT aiti-14372 298 141 vol vol NOUN aiti-14372 298 142 . . PROPN aiti-14372 298 143 10 10 NUM aiti-14372 298 144 , , PUNCT aiti-14372 298 145 no no INTJ aiti-14372 298 146 . . NOUN aiti-14372 298 147 3 3 NUM aiti-14372 298 148 , , PUNCT aiti-14372 298 149 2025 2025 NUM aiti-14372 298 150 , , PUNCT aiti-14372 298 151 pp pp ADJ aiti-14372 298 152 . . PUNCT aiti-14372 299 1 238 238 NUM aiti-14372 299 2 - - SYM aiti-14372 299 3 253 253 NUM aiti-14372 299 4 249 249 NUM aiti-14372 299 5 exponential exponential ADJ aiti-14372 299 6 model model NOUN aiti-14372 299 7 for for ADP aiti-14372 299 8 mae mae PROPN aiti-14372 299 9 , , PUNCT aiti-14372 299 10 mse mse PROPN aiti-14372 299 11 , , PUNCT aiti-14372 299 12 rmse rmse NOUN aiti-14372 299 13 , , PUNCT aiti-14372 299 14 mpr mpr NOUN aiti-14372 299 15 , , PUNCT aiti-14372 299 16 and and CCONJ aiti-14372 299 17 mean mean VERB aiti-14372 299 18 % % NOUN aiti-14372 299 19 deviation deviation NOUN aiti-14372 299 20 . . PUNCT aiti-14372 300 1 however however ADV aiti-14372 300 2 , , PUNCT aiti-14372 300 3 the the DET aiti-14372 300 4 coefficient coefficient NOUN aiti-14372 300 5 of of ADP aiti-14372 300 6 determination determination NOUN aiti-14372 300 7 ( ( PUNCT aiti-14372 300 8 r2 r2 PROPN aiti-14372 300 9 ) ) PUNCT aiti-14372 300 10 was be AUX aiti-14372 300 11 similar similar ADJ aiti-14372 300 12 for for ADP aiti-14372 300 13 both both DET aiti-14372 300 14 models model NOUN aiti-14372 300 15 . . PUNCT aiti-14372 301 1 on on ADP aiti-14372 301 2 the the DET aiti-14372 301 3 other other ADJ aiti-14372 301 4 hand hand NOUN aiti-14372 301 5 , , PUNCT aiti-14372 301 6 in in ADP aiti-14372 301 7 comparison comparison NOUN aiti-14372 301 8 with with ADP aiti-14372 301 9 the the DET aiti-14372 301 10 gamma gamma NOUN aiti-14372 301 11 mode mode NOUN aiti-14372 301 12 [ [ X aiti-14372 301 13 23 23 NUM aiti-14372 301 14 ] ] PUNCT aiti-14372 301 15 , , PUNCT aiti-14372 301 16 the the DET aiti-14372 301 17 gamma gamma NOUN aiti-14372 301 18 function function NOUN aiti-14372 301 19 performed perform VERB aiti-14372 301 20 marginally marginally ADV aiti-14372 301 21 better well ADV aiti-14372 301 22 for for ADP aiti-14372 301 23 mae mae PROPN aiti-14372 301 24 , , PUNCT aiti-14372 301 25 mse mse PROPN aiti-14372 301 26 , , PUNCT aiti-14372 301 27 and and CCONJ aiti-14372 301 28 rmse rmse ADJ aiti-14372 301 29 performance performance NOUN aiti-14372 301 30 and and CCONJ aiti-14372 301 31 significantly significantly ADV aiti-14372 301 32 better well ADV aiti-14372 301 33 for for ADP aiti-14372 301 34 mean mean ADJ aiti-14372 301 35 % % NOUN aiti-14372 301 36 deviation deviation NOUN aiti-14372 301 37 , , PUNCT aiti-14372 301 38 while while SCONJ aiti-14372 301 39 the the DET aiti-14372 301 40 mpr mpr NOUN aiti-14372 301 41 and and CCONJ aiti-14372 301 42 r2 r2 PROPN aiti-14372 301 43 were be AUX aiti-14372 301 44 similar similar ADJ aiti-14372 301 45 to to ADP aiti-14372 301 46 the the DET aiti-14372 301 47 current current ADJ aiti-14372 301 48 work work NOUN aiti-14372 301 49 ’s ’s PART aiti-14372 301 50 model model NOUN aiti-14372 301 51 . . PUNCT aiti-14372 302 1 table table NOUN aiti-14372 302 2 6 6 NUM aiti-14372 302 3 performance performance NOUN aiti-14372 302 4 of of ADP aiti-14372 302 5 the the DET aiti-14372 302 6 model model NOUN aiti-14372 302 7 model model PROPN aiti-14372 302 8 type type PROPN aiti-14372 302 9 mae mae PROPN aiti-14372 302 10 mse mse PROPN aiti-14372 302 11 rmse rmse PROPN aiti-14372 302 12 mpr mpr PROPN aiti-14372 302 13 mean mean NOUN aiti-14372 302 14 % % NOUN aiti-14372 302 15 deviation deviation NOUN aiti-14372 302 16 r2 r2 NOUN aiti-14372 302 17 modified modify VERB aiti-14372 302 18 exponential exponential ADJ aiti-14372 302 19 function function NOUN aiti-14372 302 20 1.13812eβˆ’06 1.13812eβˆ’06 NUM aiti-14372 302 21 1.41535eβˆ’12 1.41535eβˆ’12 NUM aiti-14372 303 1 1.18969eβˆ’06 1.18969eβˆ’06 NUM aiti-14372 303 2 0.983 0.983 NUM aiti-14372 303 3 1.664 1.664 NUM aiti-14372 303 4 0.998 0.998 NUM aiti-14372 303 5 earlier early ADJ aiti-14372 303 6 exponential exponential ADJ aiti-14372 303 7 model model NOUN aiti-14372 303 8 9.07eβˆ’06 9.07eβˆ’06 PROPN aiti-14372 303 9 8.14eβˆ’11 8.14eβˆ’11 ADP aiti-14372 303 10 9.02eβˆ’06 9.02eβˆ’06 PROPN aiti-14372 303 11 0.83 0.83 NUM aiti-14372 303 12 10.14 10.14 NUM aiti-14372 303 13 0.995 0.995 NUM aiti-14372 303 14 gamma gamma NOUN aiti-14372 303 15 function function NOUN aiti-14372 303 16 1.23113eβˆ’06 1.23113eβˆ’06 NUM aiti-14372 303 17 1.88896eβˆ’12 1.88896eβˆ’12 NUM aiti-14372 304 1 1.37439eβˆ’06 1.37439eβˆ’06 NUM aiti-14372 304 2 0.99 0.99 NUM aiti-14372 304 3 0.30 0.30 NUM aiti-14372 304 4 1.02 1.02 NUM aiti-14372 304 5 for for ADP aiti-14372 304 6 the the DET aiti-14372 304 7 specific specific ADJ aiti-14372 304 8 grades grade NOUN aiti-14372 304 9 of of ADP aiti-14372 304 10 material material NOUN aiti-14372 304 11 and and CCONJ aiti-14372 304 12 loading loading NOUN aiti-14372 304 13 conditions condition NOUN aiti-14372 304 14 used use VERB aiti-14372 304 15 in in ADP aiti-14372 304 16 the the DET aiti-14372 304 17 present present ADJ aiti-14372 304 18 work work NOUN aiti-14372 305 1 , , PUNCT aiti-14372 305 2 the the DET aiti-14372 305 3 dataset dataset NOUN aiti-14372 305 4 is be AUX aiti-14372 305 5 not not PART aiti-14372 305 6 available available ADJ aiti-14372 305 7 for for ADP aiti-14372 305 8 comparison comparison NOUN aiti-14372 305 9 with with ADP aiti-14372 305 10 models model NOUN aiti-14372 305 11 developed develop VERB aiti-14372 305 12 by by ADP aiti-14372 305 13 other other ADJ aiti-14372 305 14 researchers researcher NOUN aiti-14372 305 15 . . PUNCT aiti-14372 306 1 hence hence ADV aiti-14372 306 2 , , PUNCT aiti-14372 306 3 the the DET aiti-14372 306 4 modified modify VERB aiti-14372 306 5 exponential exponential ADJ aiti-14372 306 6 function function NOUN aiti-14372 306 7 discussed discuss VERB aiti-14372 306 8 here here ADV aiti-14372 306 9 was be AUX aiti-14372 306 10 compared compare VERB aiti-14372 306 11 with with ADP aiti-14372 306 12 the the DET aiti-14372 306 13 paris paris PROPN aiti-14372 306 14 equation equation NOUN aiti-14372 306 15 [ [ X aiti-14372 306 16 20 20 NUM aiti-14372 306 17 ] ] PUNCT aiti-14372 306 18 . . PUNCT aiti-14372 307 1 the the DET aiti-14372 307 2 stage stage NOUN aiti-14372 307 3 - - PUNCT aiti-14372 307 4 ii ii NOUN aiti-14372 307 5 of of ADP aiti-14372 307 6 any any DET aiti-14372 307 7 fcg fcg NOUN aiti-14372 307 8 curve curve NOUN aiti-14372 307 9 depicts depict VERB aiti-14372 307 10 the the DET aiti-14372 307 11 paris paris PROPN aiti-14372 307 12 region region NOUN aiti-14372 307 13 and and CCONJ aiti-14372 307 14 its its PRON aiti-14372 307 15 law law NOUN aiti-14372 307 16 . . PUNCT aiti-14372 308 1 therefore therefore ADV aiti-14372 308 2 , , PUNCT aiti-14372 308 3 the the DET aiti-14372 308 4 modified modify VERB aiti-14372 308 5 exponential exponential ADJ aiti-14372 308 6 function function NOUN aiti-14372 308 7 was be AUX aiti-14372 308 8 compared compare VERB aiti-14372 308 9 for for ADP aiti-14372 308 10 this this DET aiti-14372 308 11 stage stage NOUN aiti-14372 308 12 specifically specifically ADV aiti-14372 308 13 . . PUNCT aiti-14372 309 1 the the DET aiti-14372 309 2 paris paris PROPN aiti-14372 309 3 curve curve NOUN aiti-14372 309 4 fitting fitting ADJ aiti-14372 309 5 is be AUX aiti-14372 309 6 shown show VERB aiti-14372 309 7 in in ADP aiti-14372 309 8 fig fig NOUN aiti-14372 309 9 . . PUNCT aiti-14372 310 1 17 17 NUM aiti-14372 310 2 . . PUNCT aiti-14372 311 1 the the DET aiti-14372 311 2 curve curve NOUN aiti-14372 311 3 fitting fitting ADJ aiti-14372 311 4 equations equation NOUN aiti-14372 311 5 given give VERB aiti-14372 311 6 in in ADP aiti-14372 311 7 red red ADJ aiti-14372 311 8 and and CCONJ aiti-14372 311 9 green green ADJ aiti-14372 311 10 colors color NOUN aiti-14372 311 11 , , PUNCT aiti-14372 311 12 in in ADP aiti-14372 311 13 fig fig NOUN aiti-14372 311 14 . . PUNCT aiti-14372 311 15 17 17 NUM aiti-14372 311 16 , , PUNCT aiti-14372 311 17 represent represent VERB aiti-14372 311 18 the the DET aiti-14372 311 19 experimental experimental ADJ aiti-14372 311 20 and and CCONJ aiti-14372 311 21 modified modify VERB aiti-14372 311 22 exponential exponential ADJ aiti-14372 311 23 model model NOUN aiti-14372 311 24 , , PUNCT aiti-14372 311 25 respectively respectively ADV aiti-14372 311 26 . . PUNCT aiti-14372 312 1 the the DET aiti-14372 312 2 materials material NOUN aiti-14372 312 3 constants constant NOUN aiti-14372 312 4 ( ( PUNCT aiti-14372 312 5 c c NOUN aiti-14372 312 6 and and CCONJ aiti-14372 312 7 n n CCONJ aiti-14372 312 8 ) ) PUNCT aiti-14372 312 9 are be AUX aiti-14372 312 10 obtained obtain VERB aiti-14372 312 11 using use VERB aiti-14372 312 12 eq eq ADP aiti-14372 312 13 . . PUNCT aiti-14372 313 1 ( ( PUNCT aiti-14372 313 2 20 20 NUM aiti-14372 313 3 ) ) PUNCT aiti-14372 313 4 , , PUNCT aiti-14372 313 5 and and CCONJ aiti-14372 313 6 the the DET aiti-14372 313 7 goodness goodness NOUN aiti-14372 313 8 of of ADP aiti-14372 313 9 fit fit NOUN aiti-14372 313 10 is be AUX aiti-14372 313 11 presented present VERB aiti-14372 313 12 in in ADP aiti-14372 313 13 table table NOUN aiti-14372 313 14 7 7 NUM aiti-14372 313 15 . . PUNCT aiti-14372 314 1 nda nda PROPN aiti-14372 314 2 c c PROPN aiti-14372 315 1 k k PROPN aiti-14372 315 2 dn dn PROPN aiti-14372 315 3 ο€½ ο€½ PROPN aiti-14372 315 4   NOUN aiti-14372 315 5 ( ( PUNCT aiti-14372 315 6 20 20 NUM aiti-14372 315 7 ) ) PUNCT aiti-14372 315 8 where where SCONJ aiti-14372 315 9 c c NOUN aiti-14372 315 10 and and CCONJ aiti-14372 315 11 n n PROPN aiti-14372 315 12 are be AUX aiti-14372 315 13 material material ADJ aiti-14372 315 14 constants constant NOUN aiti-14372 315 15 that that PRON aiti-14372 315 16 depend depend VERB aiti-14372 315 17 upon upon SCONJ aiti-14372 315 18 the the DET aiti-14372 315 19 environment environment NOUN aiti-14372 315 20 , , PUNCT aiti-14372 315 21 frequency frequency NOUN aiti-14372 315 22 , , PUNCT aiti-14372 315 23 temperature temperature NOUN aiti-14372 315 24 , , PUNCT aiti-14372 315 25 and and CCONJ aiti-14372 315 26 stress stress NOUN aiti-14372 315 27 ratio ratio NOUN aiti-14372 315 28 . . PUNCT aiti-14372 316 1 the the DET aiti-14372 316 2 a a NOUN aiti-14372 316 3 and and CCONJ aiti-14372 316 4 n n NUM aiti-14372 316 5 are be AUX aiti-14372 316 6 crack crack NOUN aiti-14372 316 7 length length NOUN aiti-14372 316 8 and and CCONJ aiti-14372 316 9 number number NOUN aiti-14372 316 10 of of ADP aiti-14372 316 11 cycles cycle NOUN aiti-14372 316 12 , , PUNCT aiti-14372 316 13 respectively respectively ADV aiti-14372 316 14 . . PUNCT aiti-14372 317 1 fig fig NOUN aiti-14372 317 2 . . PUNCT aiti-14372 318 1 17 17 NUM aiti-14372 318 2 fcgr fcgr NOUN aiti-14372 318 3 curve curve NOUN aiti-14372 318 4 in in ADP aiti-14372 318 5 the the DET aiti-14372 318 6 paris paris PROPN aiti-14372 318 7 region region PROPN aiti-14372 318 8 table table NOUN aiti-14372 318 9 7 7 NUM aiti-14372 318 10 constants constant NOUN aiti-14372 318 11 of of ADP aiti-14372 318 12 the the DET aiti-14372 318 13 paris paris PROPN aiti-14372 318 14 equation equation NOUN aiti-14372 318 15 and and CCONJ aiti-14372 318 16 goodness goodness NOUN aiti-14372 318 17 of of ADP aiti-14372 318 18 fit fit ADJ aiti-14372 318 19 type type NOUN aiti-14372 318 20 of of ADP aiti-14372 318 21 model model NOUN aiti-14372 318 22 c c PROPN aiti-14372 318 23 n n PRON aiti-14372 318 24 goodness goodness NOUN aiti-14372 318 25 of of ADP aiti-14372 318 26 fit fit ADJ aiti-14372 318 27 modified modify VERB aiti-14372 318 28 exponential exponential ADJ aiti-14372 318 29 function function NOUN aiti-14372 318 30 4e-07 4e-07 NUM aiti-14372 318 31 0.2592 0.2592 NUM aiti-14372 318 32 0.994 0.994 NUM aiti-14372 318 33 paris paris PROPN aiti-14372 318 34 model model NOUN aiti-14372 318 35 2e-07 2e-07 PROPN aiti-14372 318 36 0.2821 0.2821 NUM aiti-14372 318 37 0.999 0.999 NUM aiti-14372 318 38 5 5 NUM aiti-14372 318 39 . . PUNCT aiti-14372 318 40 microstructure microstructure ADJ aiti-14372 318 41 analysis analysis NOUN aiti-14372 318 42 the the DET aiti-14372 318 43 image image NOUN aiti-14372 318 44 of of ADP aiti-14372 318 45 the the DET aiti-14372 318 46 fatigue fatigue NOUN aiti-14372 318 47 - - PUNCT aiti-14372 318 48 fracture fracture NOUN aiti-14372 318 49 cross cross NOUN aiti-14372 318 50 - - NOUN aiti-14372 318 51 section section NOUN aiti-14372 318 52 of of ADP aiti-14372 318 53 the the DET aiti-14372 318 54 pipe pipe NOUN aiti-14372 318 55 specimen speciman NOUN aiti-14372 318 56 is be AUX aiti-14372 318 57 shown show VERB aiti-14372 318 58 in in ADP aiti-14372 318 59 fig fig NOUN aiti-14372 318 60 . . PUNCT aiti-14372 319 1 18 18 NUM aiti-14372 319 2 . . PUNCT aiti-14372 320 1 the the DET aiti-14372 320 2 green green ADJ aiti-14372 320 3 , , PUNCT aiti-14372 320 4 blue blue ADJ aiti-14372 320 5 , , PUNCT aiti-14372 320 6 and and CCONJ aiti-14372 320 7 black black ADJ aiti-14372 320 8 arrow arrow NOUN aiti-14372 320 9 indicates indicate VERB aiti-14372 320 10 the the DET aiti-14372 320 11 pre pre NOUN aiti-14372 320 12 - - ADJ aiti-14372 320 13 notch notch ADJ aiti-14372 320 14 , , PUNCT aiti-14372 320 15 fatigue fatigue NOUN aiti-14372 320 16 - - PUNCT aiti-14372 320 17 fractured fracture VERB aiti-14372 320 18 surface surface NOUN aiti-14372 320 19 , , PUNCT aiti-14372 320 20 and and CCONJ aiti-14372 320 21 machined machine VERB aiti-14372 320 22 part part NOUN aiti-14372 320 23 , , PUNCT aiti-14372 320 24 respectively respectively ADV aiti-14372 320 25 . . PUNCT aiti-14372 321 1 a a DET aiti-14372 321 2 granular granular ADJ aiti-14372 321 3 microstructure microstructure NOUN aiti-14372 321 4 ( ( PUNCT aiti-14372 321 5 indicated indicate VERB aiti-14372 321 6 by by ADP aiti-14372 321 7 blue blue ADJ aiti-14372 321 8 arrow arrow NOUN aiti-14372 321 9 ) ) PUNCT aiti-14372 321 10 , , PUNCT aiti-14372 321 11 which which PRON aiti-14372 321 12 is be AUX aiti-14372 321 13 completely completely ADV aiti-14372 321 14 different different ADJ aiti-14372 321 15 from from ADP aiti-14372 321 16 the the DET aiti-14372 321 17 non non ADJ aiti-14372 321 18 - - ADJ aiti-14372 321 19 fatigue fatigue ADJ aiti-14372 321 20 surface surface NOUN aiti-14372 321 21 , , PUNCT aiti-14372 321 22 is be AUX aiti-14372 321 23 observed observe VERB aiti-14372 321 24 . . PUNCT aiti-14372 322 1 the the DET aiti-14372 322 2 granular granular ADJ aiti-14372 322 3 surface surface NOUN aiti-14372 322 4 morphology morphology NOUN aiti-14372 322 5 characteristics characteristic NOUN aiti-14372 322 6 of of ADP aiti-14372 322 7 the the DET aiti-14372 322 8 fatigue fatigue NOUN aiti-14372 322 9 - - PUNCT aiti-14372 322 10 fractured fracture VERB aiti-14372 322 11 surface surface NOUN aiti-14372 322 12 were be AUX aiti-14372 322 13 in in ADP aiti-14372 322 14 line line NOUN aiti-14372 322 15 with with ADP aiti-14372 322 16 earlier early ADJ aiti-14372 322 17 reports report NOUN aiti-14372 322 18 [ [ X aiti-14372 322 19 27 27 NUM aiti-14372 322 20 ] ] PUNCT aiti-14372 322 21 . . PUNCT aiti-14372 323 1 it it PRON aiti-14372 323 2 is be AUX aiti-14372 323 3 suggested suggest VERB aiti-14372 323 4 that that SCONJ aiti-14372 323 5 the the DET aiti-14372 323 6 Ξ΄k Ξ΄k PROPN aiti-14372 323 7 provides provide VERB aiti-14372 323 8 the the DET aiti-14372 323 9 necessary necessary ADJ aiti-14372 323 10 crack crack NOUN aiti-14372 323 11 driving driving NOUN aiti-14372 323 12 force force NOUN aiti-14372 323 13 . . PUNCT aiti-14372 324 1 fcg fcg PROPN aiti-14372 324 2 microstructural microstructural ADJ aiti-14372 324 3 fractography fractography NOUN aiti-14372 324 4 features feature NOUN aiti-14372 324 5 envisage envisage VERB aiti-14372 324 6 the the DET aiti-14372 324 7 crack crack NOUN aiti-14372 324 8 growth growth NOUN aiti-14372 324 9 mechanism mechanism NOUN aiti-14372 324 10 of of ADP aiti-14372 324 11 the the DET aiti-14372 324 12 material material NOUN aiti-14372 324 13 due due ADP aiti-14372 324 14 to to ADP aiti-14372 324 15 the the DET aiti-14372 324 16 stress stress NOUN aiti-14372 324 17 accumulation accumulation NOUN aiti-14372 324 18 on on ADP aiti-14372 324 19 the the DET aiti-14372 324 20 surface surface NOUN aiti-14372 324 21 for for ADP aiti-14372 324 22 a a DET aiti-14372 324 23 given give VERB aiti-14372 324 24 n. n. NOUN aiti-14372 324 25 the the DET aiti-14372 324 26 fcg fcg PROPN aiti-14372 324 27 microstructural microstructural PROPN aiti-14372 324 28 features feature NOUN aiti-14372 324 29 are be AUX aiti-14372 324 30 characteristics characteristic NOUN aiti-14372 324 31 of of ADP aiti-14372 324 32 pure pure ADJ aiti-14372 324 33 y y PROPN aiti-14372 324 34 = = SYM aiti-14372 324 35 4e-07e0.2592x 4e-07e0.2592x PROPN aiti-14372 324 36 rΒ² rΒ² NOUN aiti-14372 324 37 = = PUNCT aiti-14372 325 1 0.9947 0.9947 NUM aiti-14372 325 2 y y X aiti-14372 325 3 = = SYM aiti-14372 325 4 2e-07e0.2821x 2e-07e0.2821x PROPN aiti-14372 326 1 rΒ² rΒ² NOUN aiti-14372 326 2 = = PUNCT aiti-14372 326 3 0.9997 0.9997 NUM aiti-14372 326 4 8.00e-05 8.00e-05 NUM aiti-14372 326 5 8.50e-05 8.50e-05 NUM aiti-14372 326 6 9.00e-05 9.00e-05 NUM aiti-14372 326 7 9.50e-05 9.50e-05 NUM aiti-14372 326 8 1.00e-04 1.00e-04 NUM aiti-14372 326 9 1.05e-04 1.05e-04 NUM aiti-14372 326 10 20.5 20.5 NUM aiti-14372 326 11 20.7 20.7 NUM aiti-14372 326 12 20.9 20.9 NUM aiti-14372 326 13 21.1 21.1 NUM aiti-14372 326 14 21.3 21.3 NUM aiti-14372 326 15 21.5 21.5 NUM aiti-14372 326 16 da da NOUN aiti-14372 326 17 /d /d PUNCT aiti-14372 326 18 n n PROPN aiti-14372 326 19 ( ( PUNCT aiti-14372 326 20 m m VERB aiti-14372 326 21 m m VERB aiti-14372 326 22 /c /c PUNCT aiti-14372 326 23 yc yc X aiti-14372 326 24 le le X aiti-14372 326 25 ) ) PUNCT aiti-14372 326 26 βˆ†k βˆ†k PROPN aiti-14372 326 27 ( ( PUNCT aiti-14372 326 28 mpa*m^0.5 mpa*m^0.5 NOUN aiti-14372 326 29 ) ) PUNCT aiti-14372 326 30 da da ADJ aiti-14372 326 31 / / SYM aiti-14372 326 32 dn dn PROPN aiti-14372 326 33 ( ( PUNCT aiti-14372 326 34 experimental experimental ADJ aiti-14372 326 35 ) ) PUNCT aiti-14372 326 36 da da PROPN aiti-14372 326 37 / / SYM aiti-14372 326 38 dn dn PROPN aiti-14372 326 39 ( ( PUNCT aiti-14372 326 40 predicted predict VERB aiti-14372 326 41 ) ) PUNCT aiti-14372 326 42 expon expon ADV aiti-14372 326 43 . . PUNCT aiti-14372 327 1 ( ( PUNCT aiti-14372 327 2 da da NOUN aiti-14372 327 3 / / SYM aiti-14372 327 4 dn dn PROPN aiti-14372 327 5 ( ( PUNCT aiti-14372 327 6 experimental experimental ADJ aiti-14372 327 7 ) ) PUNCT aiti-14372 327 8 ) ) PUNCT aiti-14372 327 9 expon expon ADV aiti-14372 327 10 . . PUNCT aiti-14372 328 1 ( ( PUNCT aiti-14372 328 2 da da NOUN aiti-14372 328 3 / / SYM aiti-14372 328 4 dn dn PROPN aiti-14372 328 5 ( ( PUNCT aiti-14372 328 6 predicted predict VERB aiti-14372 328 7 ) ) PUNCT aiti-14372 328 8 ) ) PUNCT aiti-14372 328 9 advances advance NOUN aiti-14372 328 10 in in ADP aiti-14372 328 11 technology technology NOUN aiti-14372 328 12 innovation innovation NOUN aiti-14372 328 13 , , PUNCT aiti-14372 328 14 vol vol NOUN aiti-14372 328 15 . . PROPN aiti-14372 329 1 10 10 NUM aiti-14372 329 2 , , PUNCT aiti-14372 329 3 no no INTJ aiti-14372 329 4 . . NOUN aiti-14372 329 5 3 3 NUM aiti-14372 329 6 , , PUNCT aiti-14372 329 7 2025 2025 NUM aiti-14372 329 8 , , PUNCT aiti-14372 329 9 pp pp ADJ aiti-14372 329 10 . . PUNCT aiti-14372 330 1 238 238 NUM aiti-14372 330 2 - - SYM aiti-14372 330 3 253 253 NUM aiti-14372 330 4 250 250 NUM aiti-14372 330 5 bending bending NOUN aiti-14372 330 6 and and CCONJ aiti-14372 330 7 the the DET aiti-14372 330 8 initial initial ADJ aiti-14372 330 9 microstructure microstructure NOUN aiti-14372 330 10 of of ADP aiti-14372 330 11 the the DET aiti-14372 330 12 material material NOUN aiti-14372 330 13 [ [ X aiti-14372 330 14 27 27 NUM aiti-14372 330 15 ] ] PUNCT aiti-14372 330 16 . . PUNCT aiti-14372 331 1 in in ADP aiti-14372 331 2 the the DET aiti-14372 331 3 case case NOUN aiti-14372 331 4 of of ADP aiti-14372 331 5 pipeline pipeline NOUN aiti-14372 331 6 steel steel NOUN aiti-14372 331 7 , , PUNCT aiti-14372 331 8 the the DET aiti-14372 331 9 fcg fcg NOUN aiti-14372 331 10 wear wear NOUN aiti-14372 331 11 was be AUX aiti-14372 331 12 influenced influence VERB aiti-14372 331 13 by by ADP aiti-14372 331 14 the the DET aiti-14372 331 15 formation formation NOUN aiti-14372 331 16 of of ADP aiti-14372 331 17 surface surface NOUN aiti-14372 331 18 and and CCONJ aiti-14372 331 19 sub sub ADJ aiti-14372 331 20 - - ADJ aiti-14372 331 21 surface surface ADJ aiti-14372 331 22 cracks crack NOUN aiti-14372 331 23 after after SCONJ aiti-14372 331 24 sufficient sufficient ADJ aiti-14372 331 25 plastic plastic NOUN aiti-14372 331 26 deformation deformation NOUN aiti-14372 331 27 led lead VERB aiti-14372 331 28 to to ADP aiti-14372 331 29 severe severe ADJ aiti-14372 331 30 damage damage NOUN aiti-14372 331 31 . . PUNCT aiti-14372 332 1 the the DET aiti-14372 332 2 surface surface NOUN aiti-14372 332 3 wear wear NOUN aiti-14372 332 4 was be AUX aiti-14372 332 5 characterized characterize VERB aiti-14372 332 6 by by ADP aiti-14372 332 7 the the DET aiti-14372 332 8 method method NOUN aiti-14372 332 9 of of ADP aiti-14372 332 10 crack crack NOUN aiti-14372 332 11 propagation propagation NOUN aiti-14372 332 12 , , PUNCT aiti-14372 332 13 which which PRON aiti-14372 332 14 was be AUX aiti-14372 332 15 induced induce VERB aiti-14372 332 16 by by ADP aiti-14372 332 17 plastic plastic ADJ aiti-14372 332 18 deformation deformation NOUN aiti-14372 332 19 , , PUNCT aiti-14372 332 20 envisaging envisage VERB aiti-14372 332 21 the the DET aiti-14372 332 22 amendment amendment NOUN aiti-14372 332 23 of of ADP aiti-14372 332 24 the the DET aiti-14372 332 25 microstructure microstructure NOUN aiti-14372 332 26 of of ADP aiti-14372 332 27 the the DET aiti-14372 332 28 fractured fractured ADJ aiti-14372 332 29 surface surface NOUN aiti-14372 332 30 , , PUNCT aiti-14372 332 31 distressing distress VERB aiti-14372 332 32 the the DET aiti-14372 332 33 fcg fcg NOUN aiti-14372 332 34 wear wear VERB aiti-14372 332 35 procedures procedure NOUN aiti-14372 332 36 . . PUNCT aiti-14372 333 1 fig fig NOUN aiti-14372 333 2 . . PUNCT aiti-14372 334 1 18 18 NUM aiti-14372 334 2 the the DET aiti-14372 334 3 image image NOUN aiti-14372 334 4 of of ADP aiti-14372 334 5 the the DET aiti-14372 334 6 fatigue fatigue NOUN aiti-14372 334 7 - - PUNCT aiti-14372 334 8 fracture fracture NOUN aiti-14372 334 9 cross cross NOUN aiti-14372 334 10 - - NOUN aiti-14372 334 11 section section NOUN aiti-14372 334 12 the the DET aiti-14372 334 13 sem sem NOUN aiti-14372 334 14 microstructure microstructure NOUN aiti-14372 334 15 is be AUX aiti-14372 334 16 shown show VERB aiti-14372 334 17 in in ADP aiti-14372 334 18 fig fig NOUN aiti-14372 334 19 . . PUNCT aiti-14372 335 1 19 19 NUM aiti-14372 335 2 . . PUNCT aiti-14372 336 1 it it PRON aiti-14372 336 2 is be AUX aiti-14372 336 3 suggested suggest VERB aiti-14372 336 4 that that SCONJ aiti-14372 336 5 these these DET aiti-14372 336 6 crack crack NOUN aiti-14372 336 7 initiation initiation NOUN aiti-14372 336 8 sites site NOUN aiti-14372 336 9 were be AUX aiti-14372 336 10 generated generate VERB aiti-14372 336 11 during during ADP aiti-14372 336 12 the the DET aiti-14372 336 13 fcg fcg PROPN aiti-14372 336 14 test test NOUN aiti-14372 336 15 once once ADV aiti-14372 336 16 a a DET aiti-14372 336 17 sufficient sufficient ADJ aiti-14372 336 18 crack crack NOUN aiti-14372 336 19 driving driving NOUN aiti-14372 336 20 force force NOUN aiti-14372 336 21 ( ( PUNCT aiti-14372 336 22 Ξ΄k Ξ΄k VERB aiti-14372 336 23 ) ) PUNCT aiti-14372 336 24 was be AUX aiti-14372 336 25 achieved achieve VERB aiti-14372 336 26 . . PUNCT aiti-14372 337 1 the the DET aiti-14372 337 2 crack crack NOUN aiti-14372 337 3 driving driving NOUN aiti-14372 337 4 force force NOUN aiti-14372 337 5 then then ADV aiti-14372 337 6 provides provide VERB aiti-14372 337 7 sufficient sufficient ADJ aiti-14372 337 8 energy energy NOUN aiti-14372 337 9 to to PART aiti-14372 337 10 generate generate VERB aiti-14372 337 11 dislocations dislocation NOUN aiti-14372 337 12 in in ADP aiti-14372 337 13 grain grain NOUN aiti-14372 337 14 interiors interior NOUN aiti-14372 337 15 . . PUNCT aiti-14372 338 1 similar similar ADJ aiti-14372 338 2 phenomena phenomenon NOUN aiti-14372 338 3 were be AUX aiti-14372 338 4 reported report VERB aiti-14372 338 5 by by ADP aiti-14372 338 6 kung kung PROPN aiti-14372 338 7 et et PROPN aiti-14372 338 8 al al PROPN aiti-14372 338 9 . . PROPN aiti-14372 338 10 , , PUNCT aiti-14372 338 11 stating state VERB aiti-14372 338 12 that that SCONJ aiti-14372 338 13 the the DET aiti-14372 338 14 preliminary preliminary ADJ aiti-14372 338 15 fcg fcg NOUN aiti-14372 338 16 cracks crack NOUN aiti-14372 338 17 were be AUX aiti-14372 338 18 generated generate VERB aiti-14372 338 19 in in ADP aiti-14372 338 20 the the DET aiti-14372 338 21 grain grain NOUN aiti-14372 338 22 interior interior NOUN aiti-14372 338 23 [ [ X aiti-14372 338 24 27 27 NUM aiti-14372 338 25 ] ] PUNCT aiti-14372 338 26 . . PUNCT aiti-14372 339 1 these these DET aiti-14372 339 2 dislocations dislocation NOUN aiti-14372 339 3 are be AUX aiti-14372 339 4 then then ADV aiti-14372 339 5 converted convert VERB aiti-14372 339 6 into into ADP aiti-14372 339 7 microvoids microvoid NOUN aiti-14372 339 8 with with ADP aiti-14372 339 9 increasing increase VERB aiti-14372 339 10 n n VERB aiti-14372 339 11 as as SCONJ aiti-14372 339 12 shown show VERB aiti-14372 339 13 in in ADP aiti-14372 339 14 fig fig NOUN aiti-14372 339 15 . . PUNCT aiti-14372 340 1 19(a 19(a NUM aiti-14372 340 2 ) ) PUNCT aiti-14372 340 3 . . PUNCT aiti-14372 341 1 several several ADJ aiti-14372 341 2 microvoids microvoid NOUN aiti-14372 341 3 were be AUX aiti-14372 341 4 generated generate VERB aiti-14372 341 5 , , PUNCT aiti-14372 341 6 suggesting suggest VERB aiti-14372 341 7 high high ADJ aiti-14372 341 8 - - PUNCT aiti-14372 341 9 energy energy NOUN aiti-14372 341 10 sites site NOUN aiti-14372 341 11 . . PUNCT aiti-14372 342 1 it it PRON aiti-14372 342 2 was be AUX aiti-14372 342 3 also also ADV aiti-14372 342 4 observed observe VERB aiti-14372 342 5 that that SCONJ aiti-14372 342 6 these these DET aiti-14372 342 7 microvoids microvoid NOUN aiti-14372 342 8 were be AUX aiti-14372 342 9 shallowed shallow VERB aiti-14372 342 10 , , PUNCT aiti-14372 342 11 indicating indicate VERB aiti-14372 342 12 an an DET aiti-14372 342 13 acceleration acceleration NOUN aiti-14372 342 14 in in ADP aiti-14372 342 15 crack crack NOUN aiti-14372 342 16 growth growth NOUN aiti-14372 342 17 . . PUNCT aiti-14372 343 1 the the DET aiti-14372 343 2 microstructural microstructural ADJ aiti-14372 343 3 features feature NOUN aiti-14372 343 4 , , PUNCT aiti-14372 343 5 including include VERB aiti-14372 343 6 striations striation NOUN aiti-14372 343 7 and and CCONJ aiti-14372 343 8 secondary secondary ADJ aiti-14372 343 9 cracks crack NOUN aiti-14372 343 10 , , PUNCT aiti-14372 343 11 were be AUX aiti-14372 343 12 also also ADV aiti-14372 343 13 observed observe VERB aiti-14372 343 14 as as SCONJ aiti-14372 343 15 shown show VERB aiti-14372 343 16 in in ADP aiti-14372 343 17 figs fig NOUN aiti-14372 343 18 . . PUNCT aiti-14372 344 1 19(b 19(b NUM aiti-14372 344 2 ) ) PUNCT aiti-14372 344 3 and and CCONJ aiti-14372 344 4 ( ( PUNCT aiti-14372 344 5 c c NOUN aiti-14372 344 6 ) ) PUNCT aiti-14372 344 7 , , PUNCT aiti-14372 344 8 respectively respectively ADV aiti-14372 344 9 . . PUNCT aiti-14372 345 1 moving move VERB aiti-14372 345 2 along along ADP aiti-14372 345 3 the the DET aiti-14372 345 4 radial radial ADJ aiti-14372 345 5 direction direction NOUN aiti-14372 345 6 towards towards ADP aiti-14372 345 7 the the DET aiti-14372 345 8 inner inner ADJ aiti-14372 345 9 surface surface NOUN aiti-14372 345 10 of of ADP aiti-14372 345 11 the the DET aiti-14372 345 12 pipe pipe NOUN aiti-14372 345 13 , , PUNCT aiti-14372 345 14 the the DET aiti-14372 345 15 striations striation NOUN aiti-14372 345 16 were be AUX aiti-14372 345 17 perceived perceive VERB aiti-14372 345 18 at at ADP aiti-14372 345 19 a a DET aiti-14372 345 20 few few ADJ aiti-14372 345 21 locations location NOUN aiti-14372 345 22 . . PUNCT aiti-14372 346 1 these these DET aiti-14372 346 2 striations striation NOUN aiti-14372 346 3 were be AUX aiti-14372 346 4 mostly mostly ADV aiti-14372 346 5 oriented orient VERB aiti-14372 346 6 upright upright ADJ aiti-14372 346 7 to to ADP aiti-14372 346 8 the the DET aiti-14372 346 9 fcg fcg PROPN aiti-14372 346 10 direction direction NOUN aiti-14372 346 11 and and CCONJ aiti-14372 346 12 close close ADJ aiti-14372 346 13 to to ADP aiti-14372 346 14 the the DET aiti-14372 346 15 inner inner ADJ aiti-14372 346 16 wall wall NOUN aiti-14372 346 17 of of ADP aiti-14372 346 18 the the DET aiti-14372 346 19 pipe pipe NOUN aiti-14372 346 20 . . PUNCT aiti-14372 347 1 ( ( PUNCT aiti-14372 347 2 a a X aiti-14372 347 3 ) ) PUNCT aiti-14372 347 4 microvoids microvoid NOUN aiti-14372 347 5 ( ( PUNCT aiti-14372 347 6 b b NOUN aiti-14372 347 7 ) ) PUNCT aiti-14372 347 8 striations striation NOUN aiti-14372 347 9 ( ( PUNCT aiti-14372 347 10 c c X aiti-14372 347 11 ) ) PUNCT aiti-14372 347 12 secondary secondary ADJ aiti-14372 347 13 crack crack NOUN aiti-14372 347 14 fig fig NOUN aiti-14372 347 15 . . PUNCT aiti-14372 348 1 19 19 NUM aiti-14372 348 2 microstructure microstructure NOUN aiti-14372 348 3 of of ADP aiti-14372 348 4 fatigue fatigue NOUN aiti-14372 348 5 - - PUNCT aiti-14372 348 6 fractured fracture VERB aiti-14372 348 7 surface surface NOUN aiti-14372 348 8 advances advance NOUN aiti-14372 348 9 in in ADP aiti-14372 348 10 technology technology NOUN aiti-14372 348 11 innovation innovation NOUN aiti-14372 348 12 , , PUNCT aiti-14372 348 13 vol vol NOUN aiti-14372 348 14 . . PROPN aiti-14372 348 15 10 10 NUM aiti-14372 348 16 , , PUNCT aiti-14372 348 17 no no INTJ aiti-14372 348 18 . . NOUN aiti-14372 348 19 3 3 NUM aiti-14372 348 20 , , PUNCT aiti-14372 348 21 2025 2025 NUM aiti-14372 348 22 , , PUNCT aiti-14372 348 23 pp pp ADJ aiti-14372 348 24 . . PUNCT aiti-14372 349 1 238 238 NUM aiti-14372 349 2 - - SYM aiti-14372 349 3 253 253 NUM aiti-14372 349 4 251 251 NUM aiti-14372 349 5 it it PRON aiti-14372 349 6 is be AUX aiti-14372 349 7 suggested suggest VERB aiti-14372 349 8 that that SCONJ aiti-14372 349 9 these these DET aiti-14372 349 10 striations striation NOUN aiti-14372 349 11 envisage envisage VERB aiti-14372 349 12 the the DET aiti-14372 349 13 parting parting NOUN aiti-14372 349 14 of of ADP aiti-14372 349 15 damage damage NOUN aiti-14372 349 16 accumulation accumulation NOUN aiti-14372 349 17 and and CCONJ aiti-14372 349 18 crack crack NOUN aiti-14372 349 19 - - PUNCT aiti-14372 349 20 tip tip NOUN aiti-14372 349 21 fracture fracture NOUN aiti-14372 349 22 steps step NOUN aiti-14372 349 23 for for ADP aiti-14372 349 24 crack crack NOUN aiti-14372 349 25 advancement advancement NOUN aiti-14372 349 26 as as ADP aiti-14372 349 27 an an DET aiti-14372 349 28 outcome outcome NOUN aiti-14372 349 29 of of ADP aiti-14372 349 30 continuous continuous ADJ aiti-14372 349 31 cyclic cyclic ADJ aiti-14372 349 32 loading loading NOUN aiti-14372 349 33 [ [ X aiti-14372 349 34 27 27 NUM aiti-14372 349 35 ] ] PUNCT aiti-14372 349 36 . . PUNCT aiti-14372 350 1 the the DET aiti-14372 350 2 section section NOUN aiti-14372 350 3 on on ADP aiti-14372 350 4 strain strain NOUN aiti-14372 350 5 accumulation accumulation NOUN aiti-14372 350 6 influences influence VERB aiti-14372 350 7 the the DET aiti-14372 350 8 critical critical ADJ aiti-14372 350 9 boundary boundary NOUN aiti-14372 350 10 and and CCONJ aiti-14372 350 11 is be AUX aiti-14372 350 12 well well ADV aiti-14372 350 13 - - PUNCT aiti-14372 350 14 thought think VERB aiti-14372 350 15 - - PUNCT aiti-14372 350 16 out out NOUN aiti-14372 350 17 , , PUNCT aiti-14372 350 18 the the DET aiti-14372 350 19 feeble feeble ADJ aiti-14372 350 20 point point NOUN aiti-14372 350 21 at at ADP aiti-14372 350 22 which which PRON aiti-14372 350 23 the the DET aiti-14372 350 24 fcg fcg PROPN aiti-14372 350 25 initiation initiation NOUN aiti-14372 350 26 took take VERB aiti-14372 350 27 place place NOUN aiti-14372 350 28 . . PUNCT aiti-14372 351 1 it it PRON aiti-14372 351 2 is be AUX aiti-14372 351 3 suggested suggest VERB aiti-14372 351 4 that that SCONJ aiti-14372 351 5 the the DET aiti-14372 351 6 fcg fcg PROPN aiti-14372 351 7 crack crack VERB aiti-14372 351 8 spreads spread NOUN aiti-14372 351 9 along along ADP aiti-14372 351 10 the the DET aiti-14372 351 11 orientation orientation NOUN aiti-14372 351 12 of of ADP aiti-14372 351 13 the the DET aiti-14372 351 14 feeble feeble ADJ aiti-14372 351 15 planes plane NOUN aiti-14372 351 16 or or CCONJ aiti-14372 351 17 dislocation dislocation NOUN aiti-14372 351 18 cell cell NOUN aiti-14372 351 19 boundaries boundary NOUN aiti-14372 351 20 , , PUNCT aiti-14372 351 21 principal principal NOUN aiti-14372 351 22 to to ADP aiti-14372 351 23 the the DET aiti-14372 351 24 formation formation NOUN aiti-14372 351 25 of of ADP aiti-14372 351 26 the the DET aiti-14372 351 27 primary primary ADJ aiti-14372 351 28 crack crack NOUN aiti-14372 351 29 . . PUNCT aiti-14372 352 1 the the DET aiti-14372 352 2 primary primary ADJ aiti-14372 352 3 crack crack NOUN aiti-14372 352 4 , , PUNCT aiti-14372 352 5 on on ADP aiti-14372 352 6 further further ADJ aiti-14372 352 7 strain strain NOUN aiti-14372 352 8 accumulation accumulation NOUN aiti-14372 352 9 , , PUNCT aiti-14372 352 10 develops develop VERB aiti-14372 352 11 into into ADP aiti-14372 352 12 the the DET aiti-14372 352 13 secondary secondary ADJ aiti-14372 352 14 cracks crack NOUN aiti-14372 352 15 as as SCONJ aiti-14372 352 16 shown show VERB aiti-14372 352 17 in in ADP aiti-14372 352 18 fig fig NOUN aiti-14372 352 19 . . PUNCT aiti-14372 353 1 19(c 19(c NUM aiti-14372 353 2 ) ) PUNCT aiti-14372 353 3 . . PUNCT aiti-14372 354 1 these these DET aiti-14372 354 2 secondary secondary ADJ aiti-14372 354 3 cracks crack NOUN aiti-14372 354 4 are be AUX aiti-14372 354 5 designed design VERB aiti-14372 354 6 on on ADP aiti-14372 354 7 the the DET aiti-14372 354 8 sub sub NOUN aiti-14372 354 9 - - NOUN aiti-14372 354 10 surface surface NOUN aiti-14372 354 11 of of ADP aiti-14372 354 12 the the DET aiti-14372 354 13 specimen speciman NOUN aiti-14372 354 14 and and CCONJ aiti-14372 354 15 bend bend VERB aiti-14372 354 16 along along ADP aiti-14372 354 17 the the DET aiti-14372 354 18 weaker weak ADJ aiti-14372 354 19 plane plane NOUN aiti-14372 354 20 near near ADP aiti-14372 354 21 the the DET aiti-14372 354 22 surface surface NOUN aiti-14372 354 23 . . PUNCT aiti-14372 355 1 6 6 X aiti-14372 355 2 . . X aiti-14372 355 3 conclusions conclusion NOUN aiti-14372 355 4 an an DET aiti-14372 355 5 exponential exponential ADJ aiti-14372 355 6 fatigue fatigue NOUN aiti-14372 355 7 crack crack NOUN aiti-14372 355 8 growth growth NOUN aiti-14372 355 9 model model NOUN aiti-14372 355 10 was be AUX aiti-14372 355 11 developed develop VERB aiti-14372 355 12 using use VERB aiti-14372 355 13 a a DET aiti-14372 355 14 modified modify VERB aiti-14372 355 15 specific specific ADJ aiti-14372 355 16 growth growth NOUN aiti-14372 355 17 rate rate NOUN aiti-14372 355 18 for for ADP aiti-14372 355 19 three three NUM aiti-14372 355 20 distinct distinct ADJ aiti-14372 355 21 stages stage NOUN aiti-14372 355 22 of of ADP aiti-14372 355 23 fcgr fcgr NOUN aiti-14372 355 24 for for ADP aiti-14372 355 25 tp tp PROPN aiti-14372 355 26 316l 316l NUM aiti-14372 355 27 stainless stainless ADJ aiti-14372 355 28 steel steel NOUN aiti-14372 355 29 pipe pipe NOUN aiti-14372 355 30 . . PUNCT aiti-14372 356 1 the the DET aiti-14372 356 2 model model NOUN aiti-14372 356 3 was be AUX aiti-14372 356 4 validated validate VERB aiti-14372 356 5 through through ADP aiti-14372 356 6 a a DET aiti-14372 356 7 comparative comparative ADJ aiti-14372 356 8 study study NOUN aiti-14372 356 9 of of ADP aiti-14372 356 10 predicted predict VERB aiti-14372 356 11 results result NOUN aiti-14372 356 12 against against ADP aiti-14372 356 13 experimental experimental ADJ aiti-14372 356 14 data datum NOUN aiti-14372 356 15 . . PUNCT aiti-14372 357 1 the the DET aiti-14372 357 2 performance performance NOUN aiti-14372 357 3 of of ADP aiti-14372 357 4 the the DET aiti-14372 357 5 proposed propose VERB aiti-14372 357 6 model model NOUN aiti-14372 357 7 was be AUX aiti-14372 357 8 analyzed analyze VERB aiti-14372 357 9 using use VERB aiti-14372 357 10 statistical statistical ADJ aiti-14372 357 11 methods method NOUN aiti-14372 357 12 . . PUNCT aiti-14372 358 1 the the DET aiti-14372 358 2 following follow VERB aiti-14372 358 3 are be AUX aiti-14372 358 4 the the DET aiti-14372 358 5 important important ADJ aiti-14372 358 6 conclusions conclusion NOUN aiti-14372 358 7 drawn draw VERB aiti-14372 358 8 from from ADP aiti-14372 358 9 the the DET aiti-14372 358 10 present present ADJ aiti-14372 358 11 study study NOUN aiti-14372 358 12 : : PUNCT aiti-14372 358 13 ( ( PUNCT aiti-14372 358 14 1 1 X aiti-14372 358 15 ) ) PUNCT aiti-14372 358 16 the the DET aiti-14372 358 17 specific specific ADJ aiti-14372 358 18 growth growth NOUN aiti-14372 358 19 rate rate NOUN aiti-14372 358 20 in in ADP aiti-14372 358 21 the the DET aiti-14372 358 22 modified modify VERB aiti-14372 358 23 form form NOUN aiti-14372 358 24 of of ADP aiti-14372 358 25 2 2 NUM aiti-14372 358 26 1 1 NUM aiti-14372 358 27 max max PROPN aiti-14372 358 28 maxys maxys NOUN aiti-14372 358 29 ys ys INTJ aiti-14372 359 1 ij ij INTJ aiti-14372 360 1 c c NOUN aiti-14372 360 2 c c NOUN aiti-14372 360 3 c c NOUN aiti-14372 361 1 c c X aiti-14372 361 2 k k PROPN aiti-14372 362 1 kk kk PROPN aiti-14372 362 2 k k PROPN aiti-14372 362 3 m m VERB aiti-14372 362 4 a a DET aiti-14372 362 5 b b X aiti-14372 362 6 c c X aiti-14372 362 7 k k PROPN aiti-14372 362 8 k k PROPN aiti-14372 362 9 e e PROPN aiti-14372 362 10 k k PROPN aiti-14372 362 11 k k PROPN aiti-14372 362 12 e e PROPN aiti-14372 362 13   PROPN aiti-14372 362 14   PROPN aiti-14372 362 15 οƒΉ οƒΉ ADJ aiti-14372 362 16   PROPN aiti-14372 362 17   PROPN aiti-14372 362 18   NOUN aiti-14372 363 1 ο€½ ο€½ NUM aiti-14372 363 2 ο‚΄ ο‚΄ PROPN aiti-14372 364 1 ο‚΄ ο‚΄ PROPN aiti-14372 364 2   PROPN aiti-14372 364 3 ο‚΄ ο‚΄ PROPN aiti-14372 364 4 ο‚΄ ο‚΄ PROPN aiti-14372 364 5 οƒͺ οƒͺ PROPN aiti-14372 364 6 οƒΊ οƒΊ PROPN aiti-14372 364 7 οƒͺ οƒͺ NOUN aiti-14372 364 8 οƒΊ οƒΊ NOUN aiti-14372 364 9   NOUN aiti-14372 364 10   PROPN aiti-14372 364 11   NOUN aiti-14372 364 12   PROPN aiti-14372 364 13 simulated simulate VERB aiti-14372 364 14 the the DET aiti-14372 364 15 crack crack NOUN aiti-14372 364 16 driving driving NOUN aiti-14372 364 17 force force NOUN aiti-14372 364 18 and and CCONJ aiti-14372 364 19 crack crack VERB aiti-14372 364 20 resistive resistive ADJ aiti-14372 364 21 parameters parameter NOUN aiti-14372 364 22 in in ADP aiti-14372 364 23 all all DET aiti-14372 364 24 three three NUM aiti-14372 364 25 stages stage NOUN aiti-14372 364 26 with with ADP aiti-14372 364 27 different different ADJ aiti-14372 364 28 curve curve NOUN aiti-14372 364 29 fitting fitting ADJ aiti-14372 364 30 constants constant NOUN aiti-14372 364 31 . . PUNCT aiti-14372 365 1 additionally additionally ADV aiti-14372 365 2 , , PUNCT aiti-14372 365 3 the the DET aiti-14372 365 4 modified modify VERB aiti-14372 365 5 exponential exponential ADJ aiti-14372 365 6 function function NOUN aiti-14372 365 7 in in ADP aiti-14372 365 8 the the DET aiti-14372 365 9 form form NOUN aiti-14372 365 10 of of ADP aiti-14372 365 11 ( ( PUNCT aiti-14372 365 12 ) ) PUNCT aiti-14372 365 13 ijm ijm PROPN aiti-14372 365 14 j j PROPN aiti-14372 366 1 i i PRON aiti-14372 366 2 j j PROPN aiti-14372 366 3 ia ia PROPN aiti-14372 366 4 a a PROPN aiti-14372 366 5 n n PRON aiti-14372 366 6 nο€½ nο€½ PROPN aiti-14372 366 7 ο€­ ο€­ PROPN aiti-14372 366 8 predicted predict VERB aiti-14372 366 9 the the DET aiti-14372 366 10 da da PROPN aiti-14372 366 11 / / SYM aiti-14372 366 12 dn dn NOUN aiti-14372 366 13 with with ADP aiti-14372 366 14 a a DET aiti-14372 366 15 given give VERB aiti-14372 366 16 Ξ΄k Ξ΄k PRON aiti-14372 366 17 in in ADP aiti-14372 366 18 stages stage NOUN aiti-14372 366 19 - - PUNCT aiti-14372 366 20 i i PRON aiti-14372 366 21 , , PUNCT aiti-14372 366 22 ii ii PROPN aiti-14372 366 23 , , PUNCT aiti-14372 366 24 and and CCONJ aiti-14372 366 25 iii iii X aiti-14372 366 26 of of ADP aiti-14372 366 27 fcgr fcgr NOUN aiti-14372 366 28 . . PUNCT aiti-14372 367 1 ( ( PUNCT aiti-14372 367 2 2 2 X aiti-14372 367 3 ) ) PUNCT aiti-14372 367 4 stage stage NOUN aiti-14372 367 5 - - PUNCT aiti-14372 367 6 i i PRON aiti-14372 367 7 of of ADP aiti-14372 367 8 fcgr fcgr NOUN aiti-14372 367 9 was be AUX aiti-14372 367 10 from from ADP aiti-14372 367 11 the the DET aiti-14372 367 12 threshold threshold NOUN aiti-14372 367 13 sif sif NOUN aiti-14372 367 14 range range NOUN aiti-14372 367 15 ( ( PUNCT aiti-14372 367 16 17.45 17.45 NUM aiti-14372 367 17 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 367 18 ) ) PUNCT aiti-14372 367 19 to to ADP aiti-14372 367 20 the the DET aiti-14372 367 21 value value NOUN aiti-14372 367 22 of of ADP aiti-14372 367 23 Ξ΄k Ξ΄k PROPN aiti-14372 367 24 ( ( PUNCT aiti-14372 367 25 20.46 20.46 NUM aiti-14372 367 26 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š NOUN aiti-14372 367 27 ) ) PUNCT aiti-14372 367 28 , , PUNCT aiti-14372 367 29 up up ADP aiti-14372 367 30 to to PART aiti-14372 367 31 which which DET aiti-14372 367 32 fcgr fcgr NOUN aiti-14372 367 33 slope slope NOUN aiti-14372 367 34 was be AUX aiti-14372 367 35 increasing increase VERB aiti-14372 367 36 slowly slowly ADV aiti-14372 367 37 . . PUNCT aiti-14372 368 1 stage stage NOUN aiti-14372 368 2 - - PUNCT aiti-14372 368 3 ii ii NOUN aiti-14372 368 4 of of ADP aiti-14372 368 5 fcgr fcgr NOUN aiti-14372 368 6 was be AUX aiti-14372 368 7 Ξ΄k Ξ΄k ADP aiti-14372 368 8 range range NOUN aiti-14372 368 9 20.46 20.46 NUM aiti-14372 368 10 - - SYM aiti-14372 368 11 21.41 21.41 NUM aiti-14372 368 12 π‘€π‘ƒπ‘Žβˆšπ‘š π‘€π‘ƒπ‘Žβˆšπ‘š PROPN aiti-14372 368 13 , , PUNCT aiti-14372 368 14 which which PRON aiti-14372 368 15 was be AUX aiti-14372 368 16 the the DET aiti-14372 368 17 stage stage NOUN aiti-14372 368 18 where where SCONJ aiti-14372 368 19 the the DET aiti-14372 368 20 slope slope NOUN aiti-14372 368 21 of of ADP aiti-14372 368 22 da da PROPN aiti-14372 368 23 / / SYM aiti-14372 368 24 dn dn NOUN aiti-14372 368 25 versus versus ADP aiti-14372 368 26 Ξ΄k Ξ΄k PROPN aiti-14372 368 27 was be AUX aiti-14372 368 28 significantly significantly ADV aiti-14372 368 29 increased increase VERB aiti-14372 368 30 . . PUNCT aiti-14372 369 1 ( ( PUNCT aiti-14372 369 2 3 3 X aiti-14372 369 3 ) ) PUNCT aiti-14372 369 4 in in ADP aiti-14372 369 5 stage stage NOUN aiti-14372 369 6 - - PUNCT aiti-14372 369 7 iii iii NOUN aiti-14372 369 8 of of ADP aiti-14372 369 9 fcgr fcgr NOUN aiti-14372 369 10 , , PUNCT aiti-14372 369 11 the the DET aiti-14372 369 12 driving drive VERB aiti-14372 369 13 force force NOUN aiti-14372 369 14 required require VERB aiti-14372 369 15 for for ADP aiti-14372 369 16 an an DET aiti-14372 369 17 existing exist VERB aiti-14372 369 18 crack crack NOUN aiti-14372 369 19 ( ( PUNCT aiti-14372 369 20 in in ADP aiti-14372 369 21 stage stage PROPN aiti-14372 369 22 ii ii PROPN aiti-14372 369 23 ) ) PUNCT aiti-14372 369 24 to to PART aiti-14372 369 25 propagate propagate VERB aiti-14372 369 26 was be AUX aiti-14372 369 27 reduced reduce VERB aiti-14372 369 28 significantly significantly ADV aiti-14372 369 29 , , PUNCT aiti-14372 369 30 and and CCONJ aiti-14372 369 31 an an DET aiti-14372 369 32 accelerated accelerate VERB aiti-14372 369 33 crack crack NOUN aiti-14372 369 34 propagation propagation NOUN aiti-14372 369 35 occurred occur VERB aiti-14372 369 36 with with ADP aiti-14372 369 37 a a DET aiti-14372 369 38 lower low ADJ aiti-14372 369 39 increase increase NOUN aiti-14372 369 40 in in ADP aiti-14372 369 41 Ξ΄k Ξ΄k PROPN aiti-14372 369 42 . . NOUN aiti-14372 369 43 stage stage NOUN aiti-14372 369 44 - - PUNCT aiti-14372 369 45 iii iii NOUN aiti-14372 369 46 of of ADP aiti-14372 369 47 fcgr fcgr NOUN aiti-14372 369 48 was be AUX aiti-14372 369 49 for for ADP aiti-14372 369 50 the the DET aiti-14372 369 51 Ξ΄k Ξ΄k PROPN aiti-14372 369 52 range range NOUN aiti-14372 369 53 21.41 21.41 NUM aiti-14372 369 54 - - SYM aiti-14372 369 55 21.98 21.98 NUM aiti-14372 369 56 π‘€π‘ƒπ‘Žβˆšπ‘š. π‘€π‘ƒπ‘Žβˆšπ‘š. NOUN aiti-14372 369 57 ( ( PUNCT aiti-14372 369 58 4 4 NUM aiti-14372 369 59 ) ) PUNCT aiti-14372 369 60 the the DET aiti-14372 369 61 model model NOUN aiti-14372 369 62 showed show VERB aiti-14372 369 63 the the DET aiti-14372 369 64 lowest low ADJ aiti-14372 369 65 ( ( PUNCT aiti-14372 369 66 also also ADV aiti-14372 369 67 the the DET aiti-14372 369 68 best good ADJ aiti-14372 369 69 ) ) PUNCT aiti-14372 369 70 value value NOUN aiti-14372 369 71 of of ADP aiti-14372 369 72 mae mae PROPN aiti-14372 369 73 , , PUNCT aiti-14372 369 74 mse mse PROPN aiti-14372 369 75 , , PUNCT aiti-14372 369 76 and and CCONJ aiti-14372 369 77 rmse rmse NOUN aiti-14372 369 78 for for ADP aiti-14372 369 79 stage stage NOUN aiti-14372 369 80 - - PUNCT aiti-14372 369 81 i i PRON aiti-14372 369 82 of of ADP aiti-14372 369 83 fcgr fcgr NOUN aiti-14372 369 84 and and CCONJ aiti-14372 369 85 the the DET aiti-14372 369 86 highest high ADJ aiti-14372 369 87 value value NOUN aiti-14372 369 88 for for ADP aiti-14372 369 89 stage stage NOUN aiti-14372 369 90 - - PUNCT aiti-14372 369 91 iii iii NOUN aiti-14372 369 92 . . PUNCT aiti-14372 370 1 the the DET aiti-14372 370 2 mpr mpr NOUN aiti-14372 370 3 , , PUNCT aiti-14372 370 4 mean mean VERB aiti-14372 370 5 % % NOUN aiti-14372 370 6 deviation deviation NOUN aiti-14372 370 7 , , PUNCT aiti-14372 370 8 and and CCONJ aiti-14372 370 9 r2 r2 PROPN aiti-14372 370 10 in in ADP aiti-14372 370 11 stage stage NOUN aiti-14372 370 12 - - PUNCT aiti-14372 370 13 i i PRON aiti-14372 370 14 of of ADP aiti-14372 370 15 fcgr fcgr NOUN aiti-14372 370 16 showed show VERB aiti-14372 370 17 the the DET aiti-14372 370 18 best good ADJ aiti-14372 370 19 performance performance NOUN aiti-14372 370 20 . . PUNCT aiti-14372 371 1 the the DET aiti-14372 371 2 performance performance NOUN aiti-14372 371 3 of of ADP aiti-14372 371 4 the the DET aiti-14372 371 5 model model NOUN aiti-14372 371 6 dropped drop VERB aiti-14372 371 7 to to ADP aiti-14372 371 8 a a DET aiti-14372 371 9 value value NOUN aiti-14372 371 10 of of ADP aiti-14372 371 11 0.969 0.969 NUM aiti-14372 371 12 for for ADP aiti-14372 371 13 r2 r2 PROPN aiti-14372 371 14 in in ADP aiti-14372 371 15 stage stage NOUN aiti-14372 371 16 - - PUNCT aiti-14372 371 17 iii iii NOUN aiti-14372 371 18 of of ADP aiti-14372 371 19 fcgr fcgr NOUN aiti-14372 371 20 . . PUNCT aiti-14372 372 1 the the DET aiti-14372 372 2 error error NOUN aiti-14372 372 3 band band NOUN aiti-14372 372 4 scatter scatter NOUN aiti-14372 372 5 for for ADP aiti-14372 372 6 stages stage NOUN aiti-14372 372 7 - - PUNCT aiti-14372 372 8 i i PRON aiti-14372 372 9 , , PUNCT aiti-14372 372 10 ii ii PROPN aiti-14372 372 11 , , PUNCT aiti-14372 372 12 and and CCONJ aiti-14372 372 13 iii iii NOUN aiti-14372 372 14 falls fall VERB aiti-14372 372 15 on on ADP aiti-14372 372 16 the the DET aiti-14372 372 17 positive positive ADJ aiti-14372 372 18 side side NOUN aiti-14372 372 19 of of ADP aiti-14372 372 20 the the DET aiti-14372 372 21 perfect perfect ADJ aiti-14372 372 22 fit fit NOUN aiti-14372 372 23 . . PUNCT aiti-14372 373 1 ( ( PUNCT aiti-14372 373 2 5 5 X aiti-14372 373 3 ) ) PUNCT aiti-14372 373 4 the the DET aiti-14372 373 5 microstructural microstructural NOUN aiti-14372 373 6 features feature VERB aiti-14372 373 7 envisage envisage VERB aiti-14372 373 8 striations striation NOUN aiti-14372 373 9 and and CCONJ aiti-14372 373 10 secondary secondary ADJ aiti-14372 373 11 cracks crack NOUN aiti-14372 373 12 ; ; PUNCT aiti-14372 373 13 while while SCONJ aiti-14372 373 14 moving move VERB aiti-14372 373 15 along along ADP aiti-14372 373 16 the the DET aiti-14372 373 17 radial radial ADJ aiti-14372 373 18 direction direction NOUN aiti-14372 373 19 towards towards ADP aiti-14372 373 20 the the DET aiti-14372 373 21 inner inner ADJ aiti-14372 373 22 surface surface NOUN aiti-14372 373 23 of of ADP aiti-14372 373 24 the the DET aiti-14372 373 25 pipe pipe NOUN aiti-14372 373 26 , , PUNCT aiti-14372 373 27 the the DET aiti-14372 373 28 striations striation NOUN aiti-14372 373 29 were be AUX aiti-14372 373 30 perceived perceive VERB aiti-14372 373 31 at at ADP aiti-14372 373 32 a a DET aiti-14372 373 33 few few ADJ aiti-14372 373 34 locations location NOUN aiti-14372 373 35 . . PUNCT aiti-14372 374 1 these these DET aiti-14372 374 2 striations striation NOUN aiti-14372 374 3 were be AUX aiti-14372 374 4 mostly mostly ADV aiti-14372 374 5 preoccupied preoccupy VERB aiti-14372 374 6 with with ADP aiti-14372 374 7 being be AUX aiti-14372 374 8 upright upright ADJ aiti-14372 374 9 to to ADP aiti-14372 374 10 the the DET aiti-14372 374 11 fcg fcg PROPN aiti-14372 374 12 direction direction NOUN aiti-14372 374 13 and and CCONJ aiti-14372 374 14 close close ADJ aiti-14372 374 15 to to ADP aiti-14372 374 16 the the DET aiti-14372 374 17 inner inner ADJ aiti-14372 374 18 wall wall NOUN aiti-14372 374 19 of of ADP aiti-14372 374 20 the the DET aiti-14372 374 21 pipe pipe NOUN aiti-14372 374 22 . . PUNCT aiti-14372 375 1 acknowledgment acknowledgment NOUN aiti-14372 375 2 the the DET aiti-14372 375 3 authors author NOUN aiti-14372 375 4 wish wish VERB aiti-14372 375 5 to to PART aiti-14372 375 6 acknowledge acknowledge VERB aiti-14372 375 7 the the DET aiti-14372 375 8 state state NOUN aiti-14372 375 9 scientific scientific ADJ aiti-14372 375 10 institution institution NOUN aiti-14372 375 11 β€” β€” PUNCT aiti-14372 375 12 the the DET aiti-14372 375 13 joint joint ADJ aiti-14372 375 14 institute institute NOUN aiti-14372 375 15 of of ADP aiti-14372 375 16 mechanical mechanical ADJ aiti-14372 375 17 engineering engineering NOUN aiti-14372 375 18 of of ADP aiti-14372 375 19 the the DET aiti-14372 375 20 national national PROPN aiti-14372 375 21 academy academy PROPN aiti-14372 375 22 of of ADP aiti-14372 375 23 sciences sciences PROPN aiti-14372 375 24 of of ADP aiti-14372 375 25 belarus belarus PROPN aiti-14372 375 26 . . PUNCT aiti-14372 376 1 funding fund VERB aiti-14372 376 2 this this DET aiti-14372 376 3 work work NOUN aiti-14372 376 4 was be AUX aiti-14372 376 5 carried carry VERB aiti-14372 376 6 out out ADP aiti-14372 376 7 with with ADP aiti-14372 376 8 the the DET aiti-14372 376 9 support support NOUN aiti-14372 376 10 of of ADP aiti-14372 376 11 the the DET aiti-14372 376 12 belarusian belarusian ADJ aiti-14372 376 13 republican republican PROPN aiti-14372 376 14 foundation foundation PROPN aiti-14372 376 15 for for ADP aiti-14372 376 16 fundamental fundamental ADJ aiti-14372 376 17 research research NOUN aiti-14372 376 18 ( ( PUNCT aiti-14372 376 19 project project NOUN aiti-14372 376 20 number number NOUN aiti-14372 376 21 : : PUNCT aiti-14372 376 22 t23rnf-125 t23rnf-125 NOUN aiti-14372 376 23 ) ) PUNCT aiti-14372 376 24 and and CCONJ aiti-14372 376 25 the the DET aiti-14372 376 26 russian russian PROPN aiti-14372 376 27 science science PROPN aiti-14372 376 28 foundation foundation PROPN aiti-14372 376 29 ( ( PUNCT aiti-14372 376 30 grant grant PROPN aiti-14372 376 31 number number NOUN aiti-14372 376 32 : : PUNCT aiti-14372 376 33 23 23 NUM aiti-14372 376 34 - - SYM aiti-14372 376 35 49 49 NUM aiti-14372 376 36 - - PUNCT aiti-14372 376 37 10061 10061 NUM aiti-14372 376 38 ) ) PUNCT aiti-14372 376 39 . . PUNCT aiti-14372 377 1 conflicts conflict NOUN aiti-14372 377 2 of of ADP aiti-14372 377 3 interest interest NOUN aiti-14372 377 4 the the DET aiti-14372 377 5 authors author NOUN aiti-14372 377 6 declare declare VERB aiti-14372 377 7 no no DET aiti-14372 377 8 conflict conflict NOUN aiti-14372 377 9 of of ADP aiti-14372 377 10 interest interest NOUN aiti-14372 377 11 . . PUNCT aiti-14372 378 1 advances advance NOUN aiti-14372 378 2 in in ADP aiti-14372 378 3 technology technology NOUN aiti-14372 378 4 innovation innovation NOUN aiti-14372 378 5 , , PUNCT aiti-14372 378 6 vol vol NOUN aiti-14372 378 7 . . PROPN aiti-14372 379 1 10 10 NUM aiti-14372 379 2 , , PUNCT aiti-14372 379 3 no no INTJ aiti-14372 379 4 . . NOUN aiti-14372 379 5 3 3 NUM aiti-14372 379 6 , , PUNCT aiti-14372 379 7 2025 2025 NUM aiti-14372 379 8 , , PUNCT aiti-14372 379 9 pp pp ADJ aiti-14372 379 10 . . PUNCT aiti-14372 380 1 238 238 NUM aiti-14372 380 2 - - SYM aiti-14372 380 3 253 253 NUM aiti-14372 380 4 252 252 NUM aiti-14372 380 5 references reference NOUN aiti-14372 380 6 [ [ X aiti-14372 380 7 1 1 NUM aiti-14372 380 8 ] ] PUNCT aiti-14372 380 9 j. j. PROPN aiti-14372 380 10 wanjun wanjun PROPN aiti-14372 380 11 , , PUNCT aiti-14372 380 12 w. w. PROPN aiti-14372 380 13 jinfu jinfu PROPN aiti-14372 380 14 , , PUNCT aiti-14372 380 15 n. n. PROPN aiti-14372 380 16 cunhou cunhou PROPN aiti-14372 380 17 , , PUNCT aiti-14372 380 18 and and CCONJ aiti-14372 380 19 p. p. PROPN aiti-14372 380 20 xiaofei xiaofei PROPN aiti-14372 380 21 , , PUNCT aiti-14372 380 22 β€œ " PUNCT aiti-14372 380 23 application application NOUN aiti-14372 380 24 of of ADP aiti-14372 380 25 austenitic austenitic ADJ aiti-14372 380 26 stainless stainless ADJ aiti-14372 380 27 steel steel NOUN aiti-14372 380 28 pipe pipe NOUN aiti-14372 380 29 in in ADP aiti-14372 380 30 petrochemical petrochemical NOUN aiti-14372 380 31 units unit NOUN aiti-14372 380 32 , , PUNCT aiti-14372 380 33 ” " PUNCT aiti-14372 380 34 petroleum petroleum NOUN aiti-14372 380 35 refinery refinery NOUN aiti-14372 380 36 engineering engineering NOUN aiti-14372 380 37 , , PUNCT aiti-14372 380 38 vol vol NOUN aiti-14372 380 39 . . PROPN aiti-14372 381 1 53 53 NUM aiti-14372 381 2 , , PUNCT aiti-14372 381 3 no no INTJ aiti-14372 381 4 . . NOUN aiti-14372 381 5 9 9 NUM aiti-14372 381 6 . . X aiti-14372 382 1 pp pp ADJ aiti-14372 382 2 . . PUNCT aiti-14372 383 1 35 35 NUM aiti-14372 383 2 - - SYM aiti-14372 383 3 37 37 NUM aiti-14372 383 4 , , PUNCT aiti-14372 383 5 2023 2023 NUM aiti-14372 383 6 . . PUNCT aiti-14372 384 1 [ [ X aiti-14372 384 2 2 2 X aiti-14372 384 3 ] ] PUNCT aiti-14372 384 4 s. s. PROPN aiti-14372 384 5 vishnuvardhan vishnuvardhan ADV aiti-14372 384 6 et et PROPN aiti-14372 384 7 al al PROPN aiti-14372 384 8 . . PROPN aiti-14372 384 9 , , PUNCT aiti-14372 384 10 β€œ " PUNCT aiti-14372 384 11 fatigue fatigue NOUN aiti-14372 384 12 ratcheting ratchet VERB aiti-14372 384 13 studies study NOUN aiti-14372 384 14 on on ADP aiti-14372 384 15 tp304 tp304 PROPN aiti-14372 384 16 ln ln ADJ aiti-14372 384 17 stainless stainless ADJ aiti-14372 384 18 steel steel NOUN aiti-14372 384 19 straight straight ADJ aiti-14372 384 20 pipes pipe NOUN aiti-14372 384 21 , , PUNCT aiti-14372 384 22 ” " PUNCT aiti-14372 384 23 procedia procedia NOUN aiti-14372 384 24 engineering engineering NOUN aiti-14372 384 25 , , PUNCT aiti-14372 384 26 vol vol NOUN aiti-14372 384 27 . . PROPN aiti-14372 384 28 2 2 NUM aiti-14372 384 29 , , PUNCT aiti-14372 384 30 no no INTJ aiti-14372 384 31 . . NOUN aiti-14372 384 32 1 1 NUM aiti-14372 384 33 , , PUNCT aiti-14372 384 34 pp pp ADJ aiti-14372 384 35 . . PUNCT aiti-14372 385 1 2209 2209 NUM aiti-14372 385 2 - - SYM aiti-14372 385 3 2218 2218 NUM aiti-14372 385 4 , , PUNCT aiti-14372 385 5 2010 2010 NUM aiti-14372 385 6 . . PUNCT aiti-14372 386 1 [ [ X aiti-14372 386 2 3 3 NUM aiti-14372 386 3 ] ] PUNCT aiti-14372 386 4 a. a. PROPN aiti-14372 386 5 b. b. PROPN aiti-14372 386 6 radwan radwan PROPN aiti-14372 386 7 , , PUNCT aiti-14372 386 8 a. a. NOUN aiti-14372 386 9 m. m. PROPN aiti-14372 386 10 abdullah abdullah PROPN aiti-14372 386 11 , , PUNCT aiti-14372 386 12 h. h. PROPN aiti-14372 386 13 j. j. PROPN aiti-14372 386 14 roven roven PROPN aiti-14372 386 15 , , PUNCT aiti-14372 386 16 a. a. PROPN aiti-14372 386 17 m. m. PROPN aiti-14372 386 18 mohamed mohamed PROPN aiti-14372 386 19 , , PUNCT aiti-14372 386 20 and and CCONJ aiti-14372 386 21 s. s. PROPN aiti-14372 386 22 k. k. PROPN aiti-14372 387 1 mobbassar mobbassar PROPN aiti-14372 387 2 hassan hassan PROPN aiti-14372 387 3 , , PUNCT aiti-14372 387 4 β€œ " PUNCT aiti-14372 387 5 failure failure NOUN aiti-14372 387 6 analysis analysis NOUN aiti-14372 387 7 of of ADP aiti-14372 387 8 316l 316l NUM aiti-14372 387 9 air air NOUN aiti-14372 387 10 cooler cooler NOUN aiti-14372 387 11 stainless stainless ADJ aiti-14372 387 12 steel steel NOUN aiti-14372 387 13 tube tube NOUN aiti-14372 387 14 in in ADP aiti-14372 387 15 a a DET aiti-14372 387 16 natural natural ADJ aiti-14372 387 17 gas gas NOUN aiti-14372 387 18 production production NOUN aiti-14372 387 19 field field NOUN aiti-14372 387 20 , , PUNCT aiti-14372 387 21 ” " PUNCT aiti-14372 387 22 international international ADJ aiti-14372 387 23 journal journal NOUN aiti-14372 387 24 of of ADP aiti-14372 387 25 electrochemical electrochemical ADJ aiti-14372 387 26 science science NOUN aiti-14372 387 27 , , PUNCT aiti-14372 387 28 vol vol NOUN aiti-14372 387 29 . . PROPN aiti-14372 387 30 10 10 NUM aiti-14372 387 31 , , PUNCT aiti-14372 387 32 no no INTJ aiti-14372 387 33 . . NOUN aiti-14372 387 34 9 9 NUM aiti-14372 387 35 , , PUNCT aiti-14372 387 36 pp pp ADJ aiti-14372 387 37 . . PUNCT aiti-14372 388 1 7606 7606 NUM aiti-14372 388 2 - - SYM aiti-14372 388 3 7621 7621 NUM aiti-14372 388 4 , , PUNCT aiti-14372 388 5 2015 2015 NUM aiti-14372 388 6 . . PUNCT aiti-14372 389 1 [ [ X aiti-14372 389 2 4 4 NUM aiti-14372 389 3 ] ] PUNCT aiti-14372 389 4 m. m. NOUN aiti-14372 389 5 puiggali puiggali PROPN aiti-14372 389 6 , , PUNCT aiti-14372 389 7 s. s. PROPN aiti-14372 389 8 rousserie rousserie PROPN aiti-14372 389 9 , , PUNCT aiti-14372 389 10 and and CCONJ aiti-14372 389 11 m. m. NOUN aiti-14372 389 12 touzet touzet NOUN aiti-14372 389 13 , , PUNCT aiti-14372 389 14 β€œ " PUNCT aiti-14372 389 15 fatigue fatigue NOUN aiti-14372 389 16 crack crack VERB aiti-14372 389 17 initiation initiation NOUN aiti-14372 389 18 on on ADP aiti-14372 389 19 low low ADJ aiti-14372 389 20 - - PUNCT aiti-14372 389 21 carbon carbon NOUN aiti-14372 389 22 steel steel NOUN aiti-14372 389 23 pipes pipe NOUN aiti-14372 389 24 in in ADP aiti-14372 389 25 a a DET aiti-14372 389 26 near near ADV aiti-14372 389 27 - - PUNCT aiti-14372 389 28 neutral neutral ADJ aiti-14372 389 29 - - PUNCT aiti-14372 389 30 ph ph NOUN aiti-14372 389 31 environment environment NOUN aiti-14372 389 32 under under ADP aiti-14372 389 33 potential potential ADJ aiti-14372 389 34 control control NOUN aiti-14372 389 35 conditions condition NOUN aiti-14372 389 36 , , PUNCT aiti-14372 389 37 ” " PUNCT aiti-14372 389 38 corrosion corrosion NOUN aiti-14372 389 39 , , PUNCT aiti-14372 389 40 vol vol NOUN aiti-14372 389 41 . . PROPN aiti-14372 390 1 58 58 NUM aiti-14372 390 2 , , PUNCT aiti-14372 390 3 no no INTJ aiti-14372 390 4 . . NOUN aiti-14372 390 5 11 11 NUM aiti-14372 390 6 , , PUNCT aiti-14372 390 7 2002 2002 NUM aiti-14372 390 8 . . PUNCT aiti-14372 391 1 [ [ X aiti-14372 391 2 5 5 NUM aiti-14372 391 3 ] ] PUNCT aiti-14372 391 4 x. x. NOUN aiti-14372 391 5 guo guo PROPN aiti-14372 391 6 , , PUNCT aiti-14372 391 7 d. d. PROPN aiti-14372 391 8 zhang zhang PROPN aiti-14372 391 9 , , PUNCT aiti-14372 391 10 and and CCONJ aiti-14372 391 11 j. j. PROPN aiti-14372 391 12 zhang zhang PROPN aiti-14372 391 13 , , PUNCT aiti-14372 391 14 β€œ " PUNCT aiti-14372 391 15 detection detection NOUN aiti-14372 391 16 of of ADP aiti-14372 391 17 fatigue fatigue NOUN aiti-14372 391 18 - - PUNCT aiti-14372 391 19 induced induce VERB aiti-14372 391 20 microcracks microcrack NOUN aiti-14372 391 21 in in ADP aiti-14372 391 22 a a DET aiti-14372 391 23 pipe pipe NOUN aiti-14372 391 24 by by ADP aiti-14372 391 25 using use VERB aiti-14372 391 26 time time NOUN aiti-14372 391 27 - - PUNCT aiti-14372 391 28 reversed reverse VERB aiti-14372 391 29 nonlinear nonlinear ADJ aiti-14372 391 30 guided guide VERB aiti-14372 391 31 waves wave NOUN aiti-14372 391 32 : : PUNCT aiti-14372 391 33 a a DET aiti-14372 391 34 three three NUM aiti-14372 391 35 - - PUNCT aiti-14372 391 36 dimensional dimensional ADJ aiti-14372 391 37 model model NOUN aiti-14372 391 38 study study NOUN aiti-14372 391 39 , , PUNCT aiti-14372 391 40 ” " PUNCT aiti-14372 391 41 ultrasonics ultrasonic NOUN aiti-14372 391 42 , , PUNCT aiti-14372 391 43 vol vol NOUN aiti-14372 391 44 . . PROPN aiti-14372 391 45 52 52 NUM aiti-14372 391 46 , , PUNCT aiti-14372 391 47 no no INTJ aiti-14372 391 48 . . NOUN aiti-14372 391 49 7 7 NUM aiti-14372 391 50 , , PUNCT aiti-14372 391 51 pp pp ADJ aiti-14372 391 52 . . PUNCT aiti-14372 392 1 912 912 NUM aiti-14372 392 2 - - SYM aiti-14372 392 3 919 919 NUM aiti-14372 392 4 , , PUNCT aiti-14372 392 5 2012 2012 NUM aiti-14372 392 6 . . PUNCT aiti-14372 393 1 [ [ X aiti-14372 393 2 6 6 NUM aiti-14372 393 3 ] ] PUNCT aiti-14372 393 4 a. a. PROPN aiti-14372 393 5 h. h. PROPN aiti-14372 393 6 noroozi noroozi PROPN aiti-14372 393 7 , , PUNCT aiti-14372 393 8 g. g. PROPN aiti-14372 393 9 glinka glinka PROPN aiti-14372 393 10 , , PUNCT aiti-14372 393 11 and and CCONJ aiti-14372 393 12 s. s. PROPN aiti-14372 393 13 lambert lambert PROPN aiti-14372 393 14 , , PUNCT aiti-14372 393 15 β€œ " PUNCT aiti-14372 393 16 a a DET aiti-14372 393 17 study study NOUN aiti-14372 393 18 of of ADP aiti-14372 393 19 the the DET aiti-14372 393 20 stress stress NOUN aiti-14372 393 21 ratio ratio NOUN aiti-14372 393 22 effects effect NOUN aiti-14372 393 23 on on ADP aiti-14372 393 24 fatigue fatigue NOUN aiti-14372 393 25 crack crack NOUN aiti-14372 393 26 growth growth NOUN aiti-14372 393 27 using use VERB aiti-14372 393 28 the the DET aiti-14372 393 29 unified unified ADJ aiti-14372 393 30 two two NUM aiti-14372 393 31 - - PUNCT aiti-14372 393 32 parameter parameter NOUN aiti-14372 393 33 fatigue fatigue NOUN aiti-14372 393 34 crack crack VERB aiti-14372 393 35 growth growth NOUN aiti-14372 393 36 driving driving NOUN aiti-14372 393 37 force force NOUN aiti-14372 393 38 , , PUNCT aiti-14372 393 39 ” " PUNCT aiti-14372 393 40 international international ADJ aiti-14372 393 41 journal journal NOUN aiti-14372 393 42 of of ADP aiti-14372 393 43 fatigue fatigue NOUN aiti-14372 393 44 , , PUNCT aiti-14372 393 45 vol vol NOUN aiti-14372 393 46 . . PROPN aiti-14372 393 47 29 29 NUM aiti-14372 393 48 , , PUNCT aiti-14372 393 49 no no INTJ aiti-14372 393 50 . . NOUN aiti-14372 393 51 9 9 NUM aiti-14372 393 52 - - SYM aiti-14372 393 53 11 11 NUM aiti-14372 393 54 , , PUNCT aiti-14372 393 55 pp pp ADJ aiti-14372 393 56 . . PUNCT aiti-14372 394 1 1616 1616 NUM aiti-14372 394 2 - - SYM aiti-14372 394 3 1633 1633 NUM aiti-14372 394 4 , , PUNCT aiti-14372 394 5 2007 2007 NUM aiti-14372 394 6 . . PUNCT aiti-14372 395 1 [ [ X aiti-14372 395 2 7 7 NUM aiti-14372 395 3 ] ] PUNCT aiti-14372 395 4 a. a. NOUN aiti-14372 395 5 h. h. PROPN aiti-14372 395 6 noroozi noroozi PROPN aiti-14372 395 7 , , PUNCT aiti-14372 395 8 g. g. PROPN aiti-14372 395 9 glinka glinka PROPN aiti-14372 395 10 , , PUNCT aiti-14372 395 11 and and CCONJ aiti-14372 395 12 s. s. PROPN aiti-14372 395 13 lambert lambert PROPN aiti-14372 395 14 , , PUNCT aiti-14372 395 15 β€œ " PUNCT aiti-14372 395 16 prediction prediction NOUN aiti-14372 395 17 of of ADP aiti-14372 395 18 fatigue fatigue NOUN aiti-14372 395 19 crack crack VERB aiti-14372 395 20 growth growth NOUN aiti-14372 395 21 under under ADP aiti-14372 395 22 constant constant ADJ aiti-14372 395 23 amplitude amplitude NOUN aiti-14372 395 24 loading loading NOUN aiti-14372 395 25 and and CCONJ aiti-14372 395 26 a a DET aiti-14372 395 27 single single ADJ aiti-14372 395 28 overload overload NOUN aiti-14372 395 29 based base VERB aiti-14372 395 30 on on ADP aiti-14372 395 31 elasto elasto NOUN aiti-14372 395 32 - - PUNCT aiti-14372 395 33 plastic plastic NOUN aiti-14372 395 34 crack crack NOUN aiti-14372 395 35 tip tip NOUN aiti-14372 395 36 stresses stress NOUN aiti-14372 395 37 and and CCONJ aiti-14372 395 38 strains strain NOUN aiti-14372 395 39 , , PUNCT aiti-14372 395 40 ” " PUNCT aiti-14372 395 41 engineering engineering NOUN aiti-14372 395 42 fracture fracture NOUN aiti-14372 395 43 mechanics mechanic NOUN aiti-14372 395 44 , , PUNCT aiti-14372 395 45 vol vol NOUN aiti-14372 395 46 . . PROPN aiti-14372 395 47 75 75 NUM aiti-14372 395 48 , , PUNCT aiti-14372 395 49 no no INTJ aiti-14372 395 50 . . NOUN aiti-14372 395 51 2 2 NUM aiti-14372 395 52 , , PUNCT aiti-14372 395 53 pp pp ADJ aiti-14372 395 54 . . PUNCT aiti-14372 396 1 188 188 NUM aiti-14372 396 2 - - SYM aiti-14372 396 3 206 206 NUM aiti-14372 396 4 , , PUNCT aiti-14372 396 5 2008 2008 NUM aiti-14372 396 6 . . PUNCT aiti-14372 397 1 [ [ X aiti-14372 397 2 8 8 NUM aiti-14372 397 3 ] ] PUNCT aiti-14372 398 1 p. p. NOUN aiti-14372 398 2 k. k. PROPN aiti-14372 399 1 singh singh PROPN aiti-14372 399 2 et et PROPN aiti-14372 399 3 al al PROPN aiti-14372 399 4 . . PROPN aiti-14372 399 5 , , PUNCT aiti-14372 399 6 β€œ " PUNCT aiti-14372 399 7 fatigue fatigue NOUN aiti-14372 399 8 studies study NOUN aiti-14372 399 9 on on ADP aiti-14372 399 10 carbon carbon NOUN aiti-14372 399 11 steel steel NOUN aiti-14372 399 12 piping piping NOUN aiti-14372 399 13 materials material NOUN aiti-14372 399 14 and and CCONJ aiti-14372 399 15 components component NOUN aiti-14372 399 16 : : PUNCT aiti-14372 399 17 indian indian ADJ aiti-14372 399 18 phwrs phwrs NOUN aiti-14372 399 19 , , PUNCT aiti-14372 399 20 ” " PUNCT aiti-14372 399 21 nuclear nuclear ADJ aiti-14372 399 22 engineering engineering NOUN aiti-14372 399 23 and and CCONJ aiti-14372 399 24 design design NOUN aiti-14372 399 25 , , PUNCT aiti-14372 399 26 vol vol NOUN aiti-14372 399 27 . . PROPN aiti-14372 400 1 238 238 NUM aiti-14372 400 2 , , PUNCT aiti-14372 400 3 no no INTJ aiti-14372 400 4 . . NOUN aiti-14372 400 5 4 4 NUM aiti-14372 400 6 , , PUNCT aiti-14372 400 7 pp pp ADJ aiti-14372 400 8 . . PUNCT aiti-14372 401 1 801 801 NUM aiti-14372 401 2 - - NUM aiti-14372 401 3 813 813 NUM aiti-14372 401 4 , , PUNCT aiti-14372 401 5 2008 2008 NUM aiti-14372 401 6 . . PUNCT aiti-14372 402 1 [ [ X aiti-14372 402 2 9 9 X aiti-14372 402 3 ] ] PUNCT aiti-14372 402 4 t. t. PROPN aiti-14372 402 5 hassan hassan PROPN aiti-14372 402 6 , , PUNCT aiti-14372 402 7 m. m. PROPN aiti-14372 402 8 rahman rahman PROPN aiti-14372 402 9 , , PUNCT aiti-14372 402 10 and and CCONJ aiti-14372 402 11 s. s. PROPN aiti-14372 402 12 bari bari PROPN aiti-14372 402 13 , , PUNCT aiti-14372 402 14 β€œ " PUNCT aiti-14372 402 15 low low ADJ aiti-14372 402 16 - - PUNCT aiti-14372 402 17 cycle cycle NOUN aiti-14372 402 18 fatigue fatigue NOUN aiti-14372 402 19 and and CCONJ aiti-14372 402 20 ratcheting ratchet VERB aiti-14372 402 21 responses response NOUN aiti-14372 402 22 of of ADP aiti-14372 402 23 elbow elbow NOUN aiti-14372 402 24 piping pipe VERB aiti-14372 402 25 components component NOUN aiti-14372 402 26 , , PUNCT aiti-14372 402 27 ” " PUNCT aiti-14372 402 28 journal journal NOUN aiti-14372 402 29 of of ADP aiti-14372 402 30 pressure pressure NOUN aiti-14372 402 31 vessel vessel NOUN aiti-14372 402 32 technology technology NOUN aiti-14372 402 33 , , PUNCT aiti-14372 402 34 vol vol NOUN aiti-14372 402 35 . . PROPN aiti-14372 402 36 137 137 NUM aiti-14372 402 37 , , PUNCT aiti-14372 402 38 no no INTJ aiti-14372 402 39 . . NOUN aiti-14372 402 40 3 3 NUM aiti-14372 402 41 , , PUNCT aiti-14372 402 42 article article NOUN aiti-14372 402 43 no no NOUN aiti-14372 402 44 . . PROPN aiti-14372 402 45 031010 031010 NUM aiti-14372 402 46 , , PUNCT aiti-14372 402 47 2015 2015 NUM aiti-14372 402 48 . . PUNCT aiti-14372 403 1 [ [ X aiti-14372 403 2 10 10 NUM aiti-14372 403 3 ] ] X aiti-14372 403 4 h. h. PROPN aiti-14372 403 5 shirazi shirazi PROPN aiti-14372 403 6 , , PUNCT aiti-14372 403 7 s. s. PROPN aiti-14372 403 8 wang wang PROPN aiti-14372 403 9 , , PUNCT aiti-14372 403 10 w. w. PROPN aiti-14372 403 11 chen chen PROPN aiti-14372 403 12 , , PUNCT aiti-14372 403 13 and and CCONJ aiti-14372 403 14 r. r. PROPN aiti-14372 403 15 eadie eadie PROPN aiti-14372 403 16 , , PUNCT aiti-14372 403 17 β€œ " PUNCT aiti-14372 403 18 pipeline pipeline NOUN aiti-14372 403 19 circumferential circumferential ADJ aiti-14372 403 20 corrosion corrosion NOUN aiti-14372 403 21 fatigue fatigue NOUN aiti-14372 403 22 failure failure NOUN aiti-14372 403 23 under under ADP aiti-14372 403 24 the the DET aiti-14372 403 25 influence influence NOUN aiti-14372 403 26 of of ADP aiti-14372 403 27 bending bend VERB aiti-14372 403 28 residual residual ADJ aiti-14372 403 29 stress stress NOUN aiti-14372 403 30 in in ADP aiti-14372 403 31 the the DET aiti-14372 403 32 near near ADV aiti-14372 403 33 - - PUNCT aiti-14372 403 34 neutral neutral ADJ aiti-14372 403 35 ph ph ADJ aiti-14372 403 36 environment environment NOUN aiti-14372 403 37 , , PUNCT aiti-14372 403 38 ” " PUNCT aiti-14372 403 39 engineering engineering NOUN aiti-14372 403 40 failure failure NOUN aiti-14372 403 41 analysis analysis NOUN aiti-14372 403 42 , , PUNCT aiti-14372 403 43 vol vol NOUN aiti-14372 403 44 . . PROPN aiti-14372 403 45 166 166 NUM aiti-14372 403 46 , , PUNCT aiti-14372 403 47 pp pp ADJ aiti-14372 403 48 . . PUNCT aiti-14372 403 49 108887 108887 NUM aiti-14372 403 50 , , PUNCT aiti-14372 403 51 2024 2024 NUM aiti-14372 403 52 . . PUNCT aiti-14372 404 1 [ [ X aiti-14372 404 2 11 11 NUM aiti-14372 404 3 ] ] X aiti-14372 404 4 w. w. PROPN aiti-14372 404 5 liang liang PROPN aiti-14372 404 6 , , PUNCT aiti-14372 404 7 m. m. PROPN aiti-14372 404 8 lou lou PROPN aiti-14372 404 9 , , PUNCT aiti-14372 404 10 c. c. PROPN aiti-14372 404 11 zhang zhang PROPN aiti-14372 404 12 , , PUNCT aiti-14372 404 13 d. d. PROPN aiti-14372 404 14 zhao zhao PROPN aiti-14372 404 15 , , PUNCT aiti-14372 404 16 d. d. PROPN aiti-14372 404 17 yang yang PROPN aiti-14372 404 18 , , PUNCT aiti-14372 404 19 and and CCONJ aiti-14372 404 20 y. y. PROPN aiti-14372 404 21 wang wang PROPN aiti-14372 404 22 , , PUNCT aiti-14372 404 23 β€œ " PUNCT aiti-14372 404 24 experimental experimental ADJ aiti-14372 404 25 investigation investigation NOUN aiti-14372 404 26 and and CCONJ aiti-14372 404 27 phenomenological phenomenological ADJ aiti-14372 404 28 modeling modeling NOUN aiti-14372 404 29 of of ADP aiti-14372 404 30 fatigue fatigue NOUN aiti-14372 404 31 crack crack VERB aiti-14372 404 32 growth growth NOUN aiti-14372 404 33 in in ADP aiti-14372 404 34 x80 x80 PROPN aiti-14372 404 35 pipeline pipeline NOUN aiti-14372 404 36 steel steel NOUN aiti-14372 404 37 under under ADP aiti-14372 404 38 random random ADJ aiti-14372 404 39 loading loading NOUN aiti-14372 404 40 , , PUNCT aiti-14372 404 41 ” " PUNCT aiti-14372 404 42 international international ADJ aiti-14372 404 43 journal journal NOUN aiti-14372 404 44 of of ADP aiti-14372 404 45 fatigue fatigue NOUN aiti-14372 404 46 , , PUNCT aiti-14372 404 47 vol vol NOUN aiti-14372 404 48 . . PROPN aiti-14372 404 49 182 182 NUM aiti-14372 404 50 , , PUNCT aiti-14372 404 51 pp pp ADJ aiti-14372 404 52 . . PUNCT aiti-14372 404 53 108169 108169 NUM aiti-14372 404 54 , , PUNCT aiti-14372 404 55 2024 2024 NUM aiti-14372 404 56 . . PUNCT aiti-14372 405 1 [ [ X aiti-14372 405 2 12 12 NUM aiti-14372 405 3 ] ] PUNCT aiti-14372 405 4 z. z. PROPN aiti-14372 405 5 lin lin PROPN aiti-14372 405 6 et et PROPN aiti-14372 405 7 al al PROPN aiti-14372 405 8 . . PROPN aiti-14372 405 9 , , PUNCT aiti-14372 405 10 β€œ " PUNCT aiti-14372 405 11 the the DET aiti-14372 405 12 dependence dependence NOUN aiti-14372 405 13 of of ADP aiti-14372 405 14 fatigue fatigue NOUN aiti-14372 405 15 property property NOUN aiti-14372 405 16 on on ADP aiti-14372 405 17 applied apply VERB aiti-14372 405 18 stress stress NOUN aiti-14372 405 19 in in ADP aiti-14372 405 20 x80 x80 PROPN aiti-14372 405 21 pipeline pipeline NOUN aiti-14372 405 22 steel steel NOUN aiti-14372 405 23 notched notch VERB aiti-14372 405 24 specimens specimen NOUN aiti-14372 405 25 in in ADP aiti-14372 405 26 hydrogen hydrogen NOUN aiti-14372 405 27 gas gas NOUN aiti-14372 405 28 environment environment NOUN aiti-14372 405 29 , , PUNCT aiti-14372 405 30 ” " PUNCT aiti-14372 405 31 international international ADJ aiti-14372 405 32 journal journal NOUN aiti-14372 405 33 of of ADP aiti-14372 405 34 fatigue fatigue NOUN aiti-14372 405 35 , , PUNCT aiti-14372 405 36 vol vol NOUN aiti-14372 405 37 . . PROPN aiti-14372 405 38 183 183 NUM aiti-14372 405 39 , , PUNCT aiti-14372 405 40 pp pp ADJ aiti-14372 405 41 . . PUNCT aiti-14372 405 42 108222 108222 NUM aiti-14372 405 43 , , PUNCT aiti-14372 405 44 2024 2024 NUM aiti-14372 405 45 . . PUNCT aiti-14372 406 1 [ [ X aiti-14372 406 2 13 13 NUM aiti-14372 406 3 ] ] PUNCT aiti-14372 406 4 t. t. PROPN aiti-14372 406 5 an an PROPN aiti-14372 406 6 , , PUNCT aiti-14372 406 7 h. h. PROPN aiti-14372 406 8 peng peng PROPN aiti-14372 406 9 , , PUNCT aiti-14372 406 10 p. p. PROPN aiti-14372 406 11 bai bai PROPN aiti-14372 406 12 , , PUNCT aiti-14372 406 13 s. s. PROPN aiti-14372 406 14 zheng zheng PROPN aiti-14372 406 15 , , PUNCT aiti-14372 406 16 x. x. PROPN aiti-14372 406 17 wen wen PROPN aiti-14372 406 18 , , PUNCT aiti-14372 406 19 and and CCONJ aiti-14372 406 20 l. l. PROPN aiti-14372 406 21 zhang zhang PROPN aiti-14372 406 22 , , PUNCT aiti-14372 406 23 β€œ " PUNCT aiti-14372 406 24 influence influence NOUN aiti-14372 406 25 of of ADP aiti-14372 406 26 hydrogen hydrogen NOUN aiti-14372 406 27 pressure pressure NOUN aiti-14372 406 28 on on ADP aiti-14372 406 29 fatigue fatigue NOUN aiti-14372 406 30 properties property NOUN aiti-14372 406 31 of of ADP aiti-14372 406 32 x80 x80 PROPN aiti-14372 406 33 pipeline pipeline PROPN aiti-14372 406 34 steel steel NOUN aiti-14372 406 35 , , PUNCT aiti-14372 406 36 ” " PUNCT aiti-14372 406 37 international international ADJ aiti-14372 406 38 journal journal NOUN aiti-14372 406 39 of of ADP aiti-14372 406 40 hydrogen hydrogen NOUN aiti-14372 406 41 energy energy NOUN aiti-14372 406 42 , , PUNCT aiti-14372 406 43 vol vol NOUN aiti-14372 406 44 . . PROPN aiti-14372 406 45 42 42 NUM aiti-14372 406 46 , , PUNCT aiti-14372 406 47 no no INTJ aiti-14372 406 48 . . NOUN aiti-14372 406 49 23 23 NUM aiti-14372 406 50 , , PUNCT aiti-14372 406 51 pp pp ADJ aiti-14372 406 52 . . PUNCT aiti-14372 407 1 15669 15669 NUM aiti-14372 407 2 - - SYM aiti-14372 407 3 15678 15678 NUM aiti-14372 407 4 , , PUNCT aiti-14372 407 5 2017 2017 NUM aiti-14372 407 6 . . PUNCT aiti-14372 408 1 [ [ X aiti-14372 408 2 14 14 NUM aiti-14372 408 3 ] ] X aiti-14372 408 4 o. o. PROPN aiti-14372 408 5 fatoba fatoba PROPN aiti-14372 408 6 and and CCONJ aiti-14372 408 7 r. r. PROPN aiti-14372 408 8 akid akid PROPN aiti-14372 408 9 , , PUNCT aiti-14372 408 10 β€œ " PUNCT aiti-14372 408 11 low low ADJ aiti-14372 408 12 cycle cycle NOUN aiti-14372 408 13 fatigue fatigue NOUN aiti-14372 408 14 behaviour behaviour NOUN aiti-14372 408 15 of of ADP aiti-14372 408 16 api api NOUN aiti-14372 408 17 5l 5l PROPN aiti-14372 408 18 x65 x65 NOUN aiti-14372 408 19 pipeline pipeline NOUN aiti-14372 408 20 steel steel NOUN aiti-14372 408 21 at at ADP aiti-14372 408 22 room room NOUN aiti-14372 408 23 temperature temperature NOUN aiti-14372 408 24 , , PUNCT aiti-14372 408 25 ” " PUNCT aiti-14372 408 26 procedia procedia NOUN aiti-14372 408 27 engineering engineering NOUN aiti-14372 408 28 , , PUNCT aiti-14372 408 29 vol vol NOUN aiti-14372 408 30 . . PROPN aiti-14372 408 31 74 74 NUM aiti-14372 408 32 , , PUNCT aiti-14372 408 33 pp pp ADJ aiti-14372 408 34 . . PUNCT aiti-14372 409 1 279 279 NUM aiti-14372 409 2 - - SYM aiti-14372 409 3 286 286 NUM aiti-14372 409 4 , , PUNCT aiti-14372 409 5 2014 2014 NUM aiti-14372 409 6 . . PUNCT aiti-14372 410 1 [ [ X aiti-14372 410 2 15 15 NUM aiti-14372 410 3 ] ] X aiti-14372 410 4 y. y. PROPN aiti-14372 410 5 jiang jiang PROPN aiti-14372 410 6 and and CCONJ aiti-14372 410 7 m. m. PROPN aiti-14372 410 8 chen chen PROPN aiti-14372 410 9 , , PUNCT aiti-14372 410 10 β€œ " PUNCT aiti-14372 410 11 researches research VERB aiti-14372 410 12 on on ADP aiti-14372 410 13 the the DET aiti-14372 410 14 fatigue fatigue NOUN aiti-14372 410 15 crack crack VERB aiti-14372 410 16 propagation propagation NOUN aiti-14372 410 17 of of ADP aiti-14372 410 18 pipeline pipeline NOUN aiti-14372 410 19 steel steel NOUN aiti-14372 410 20 , , PUNCT aiti-14372 410 21 ” " PUNCT aiti-14372 410 22 energy energy NOUN aiti-14372 410 23 procedia procedia NOUN aiti-14372 410 24 , , PUNCT aiti-14372 410 25 vol vol NOUN aiti-14372 410 26 . . PROPN aiti-14372 410 27 14 14 NUM aiti-14372 410 28 , , PUNCT aiti-14372 410 29 pp pp ADJ aiti-14372 410 30 . . PUNCT aiti-14372 411 1 524 524 NUM aiti-14372 411 2 - - SYM aiti-14372 411 3 528 528 NUM aiti-14372 411 4 , , PUNCT aiti-14372 411 5 2012 2012 NUM aiti-14372 411 6 . . PUNCT aiti-14372 412 1 [ [ X aiti-14372 412 2 16 16 NUM aiti-14372 412 3 ] ] PUNCT aiti-14372 412 4 m. m. NOUN aiti-14372 412 5 a. a. NOUN aiti-14372 412 6 mohtadi mohtadi PROPN aiti-14372 412 7 - - PUNCT aiti-14372 412 8 bonab bonab NOUN aiti-14372 412 9 , , PUNCT aiti-14372 412 10 m. m. NOUN aiti-14372 412 11 eskandari eskandari PROPN aiti-14372 412 12 , , PUNCT aiti-14372 412 13 h. h. PROPN aiti-14372 412 14 ghaednia ghaednia PROPN aiti-14372 412 15 , , PUNCT aiti-14372 412 16 and and CCONJ aiti-14372 412 17 s. s. PROPN aiti-14372 412 18 das das PROPN aiti-14372 412 19 , , PUNCT aiti-14372 412 20 β€œ " PUNCT aiti-14372 412 21 effect effect NOUN aiti-14372 412 22 of of ADP aiti-14372 412 23 microstructural microstructural ADJ aiti-14372 412 24 parameters parameter NOUN aiti-14372 412 25 on on ADP aiti-14372 412 26 fatigue fatigue NOUN aiti-14372 412 27 crack crack NOUN aiti-14372 412 28 propagation propagation NOUN aiti-14372 412 29 in in ADP aiti-14372 412 30 an an DET aiti-14372 412 31 api api NOUN aiti-14372 412 32 x65 x65 NOUN aiti-14372 412 33 pipeline pipeline PROPN aiti-14372 412 34 steel steel NOUN aiti-14372 412 35 , , PUNCT aiti-14372 412 36 ” " PUNCT aiti-14372 412 37 journal journal NOUN aiti-14372 412 38 of of ADP aiti-14372 412 39 materials material NOUN aiti-14372 412 40 engineering engineering NOUN aiti-14372 412 41 and and CCONJ aiti-14372 412 42 performance performance NOUN aiti-14372 412 43 , , PUNCT aiti-14372 412 44 vol vol NOUN aiti-14372 412 45 . . PROPN aiti-14372 412 46 25 25 NUM aiti-14372 412 47 , , PUNCT aiti-14372 412 48 no no INTJ aiti-14372 412 49 . . NOUN aiti-14372 412 50 11 11 NUM aiti-14372 412 51 , , PUNCT aiti-14372 412 52 pp pp ADJ aiti-14372 412 53 . . PUNCT aiti-14372 412 54 49334940 49334940 NUM aiti-14372 412 55 , , PUNCT aiti-14372 412 56 2016 2016 NUM aiti-14372 412 57 . . PUNCT aiti-14372 413 1 [ [ X aiti-14372 413 2 17 17 NUM aiti-14372 413 3 ] ] PUNCT aiti-14372 413 4 m. m. NOUN aiti-14372 413 5 a. a. NOUN aiti-14372 413 6 mohtadi mohtadi PROPN aiti-14372 413 7 - - PUNCT aiti-14372 413 8 bonab bonab NOUN aiti-14372 413 9 , , PUNCT aiti-14372 413 10 m. m. NOUN aiti-14372 413 11 eskandari eskandari PROPN aiti-14372 413 12 , , PUNCT aiti-14372 413 13 m. m. NOUN aiti-14372 413 14 sanayei sanayei NOUN aiti-14372 413 15 , , PUNCT aiti-14372 413 16 and and CCONJ aiti-14372 413 17 s. s. PROPN aiti-14372 413 18 das das PROPN aiti-14372 413 19 , , PUNCT aiti-14372 413 20 β€œ " PUNCT aiti-14372 413 21 microstructural microstructural ADJ aiti-14372 413 22 aspects aspect NOUN aiti-14372 413 23 of of ADP aiti-14372 413 24 intergranular intergranular NOUN aiti-14372 413 25 and and CCONJ aiti-14372 413 26 transgranular transgranular ADJ aiti-14372 413 27 crack crack VERB aiti-14372 413 28 propagation propagation NOUN aiti-14372 413 29 in in ADP aiti-14372 413 30 an an DET aiti-14372 413 31 api api NOUN aiti-14372 413 32 x65 x65 NOUN aiti-14372 413 33 steel steel NOUN aiti-14372 413 34 pipeline pipeline NOUN aiti-14372 413 35 related relate VERB aiti-14372 413 36 to to ADP aiti-14372 413 37 fatigue fatigue NOUN aiti-14372 413 38 failure failure NOUN aiti-14372 413 39 , , PUNCT aiti-14372 413 40 ” " PUNCT aiti-14372 413 41 engineering engineering NOUN aiti-14372 413 42 failure failure NOUN aiti-14372 413 43 analysis analysis NOUN aiti-14372 413 44 , , PUNCT aiti-14372 413 45 vol vol NOUN aiti-14372 413 46 . . PROPN aiti-14372 413 47 94 94 NUM aiti-14372 413 48 , , PUNCT aiti-14372 413 49 pp pp ADJ aiti-14372 413 50 . . PUNCT aiti-14372 414 1 214 214 NUM aiti-14372 414 2 - - SYM aiti-14372 414 3 225 225 NUM aiti-14372 414 4 , , PUNCT aiti-14372 414 5 2018 2018 NUM aiti-14372 414 6 . . PUNCT aiti-14372 415 1 [ [ X aiti-14372 415 2 18 18 NUM aiti-14372 415 3 ] ] PUNCT aiti-14372 415 4 j. j. PROPN aiti-14372 415 5 a. a. PROPN aiti-14372 415 6 ronevich ronevich PROPN aiti-14372 415 7 , , PUNCT aiti-14372 415 8 b. b. PROPN aiti-14372 415 9 p. p. PROPN aiti-14372 415 10 somerday somerday NOUN aiti-14372 415 11 , , PUNCT aiti-14372 415 12 and and CCONJ aiti-14372 415 13 c. c. PROPN aiti-14372 415 14 w. w. PROPN aiti-14372 415 15 san san PROPN aiti-14372 415 16 marchi marchi PROPN aiti-14372 415 17 , , PUNCT aiti-14372 415 18 β€œ " PUNCT aiti-14372 415 19 effects effect NOUN aiti-14372 415 20 of of ADP aiti-14372 415 21 microstructure microstructure ADJ aiti-14372 415 22 banding banding NOUN aiti-14372 415 23 on on ADP aiti-14372 415 24 hydrogen hydrogen NOUN aiti-14372 415 25 - - PUNCT aiti-14372 415 26 assisted assist VERB aiti-14372 415 27 fatigue fatigue NOUN aiti-14372 415 28 crack crack VERB aiti-14372 415 29 growth growth NOUN aiti-14372 415 30 in in ADP aiti-14372 415 31 x65 x65 NOUN aiti-14372 415 32 pipeline pipeline NOUN aiti-14372 415 33 steels steel NOUN aiti-14372 415 34 , , PUNCT aiti-14372 415 35 ” " PUNCT aiti-14372 415 36 international international ADJ aiti-14372 415 37 journal journal NOUN aiti-14372 415 38 of of ADP aiti-14372 415 39 fatigue fatigue NOUN aiti-14372 415 40 , , PUNCT aiti-14372 415 41 vol vol NOUN aiti-14372 415 42 . . PROPN aiti-14372 415 43 82 82 NUM aiti-14372 415 44 , , PUNCT aiti-14372 415 45 pp pp ADJ aiti-14372 415 46 . . PUNCT aiti-14372 416 1 497 497 NUM aiti-14372 416 2 - - SYM aiti-14372 416 3 504 504 NUM aiti-14372 416 4 , , PUNCT aiti-14372 416 5 2016 2016 NUM aiti-14372 416 6 . . PUNCT aiti-14372 417 1 [ [ X aiti-14372 417 2 19 19 NUM aiti-14372 417 3 ] ] X aiti-14372 417 4 a. a. NOUN aiti-14372 417 5 j. j. PROPN aiti-14372 417 6 slifka slifka VERB aiti-14372 417 7 et et PROPN aiti-14372 417 8 al al PROPN aiti-14372 417 9 . . PROPN aiti-14372 417 10 , , PUNCT aiti-14372 417 11 β€œ " PUNCT aiti-14372 417 12 the the DET aiti-14372 417 13 effect effect NOUN aiti-14372 417 14 of of ADP aiti-14372 417 15 microstructure microstructure NOUN aiti-14372 417 16 on on ADP aiti-14372 417 17 the the DET aiti-14372 417 18 hydrogen hydrogen NOUN aiti-14372 417 19 - - PUNCT aiti-14372 417 20 assisted assist VERB aiti-14372 417 21 fatigue fatigue NOUN aiti-14372 417 22 of of ADP aiti-14372 417 23 pipeline pipeline NOUN aiti-14372 417 24 steels steel NOUN aiti-14372 417 25 , , PUNCT aiti-14372 417 26 ” " PUNCT aiti-14372 417 27 proceedings proceeding NOUN aiti-14372 417 28 of of ADP aiti-14372 417 29 american american ADJ aiti-14372 417 30 society society NOUN aiti-14372 417 31 of of ADP aiti-14372 417 32 mechanical mechanical ADJ aiti-14372 417 33 engineers engineer NOUN aiti-14372 417 34 , , PUNCT aiti-14372 417 35 pressure pressure NOUN aiti-14372 417 36 vessels vessel NOUN aiti-14372 417 37 and and CCONJ aiti-14372 417 38 piping piping NOUN aiti-14372 417 39 division division NOUN aiti-14372 417 40 ( ( PUNCT aiti-14372 417 41 publication publication NOUN aiti-14372 417 42 ) ) PUNCT aiti-14372 417 43 pvp pvp NOUN aiti-14372 417 44 , , PUNCT aiti-14372 417 45 vol vol NOUN aiti-14372 417 46 . . PROPN aiti-14372 417 47 6 6 NUM aiti-14372 417 48 , , PUNCT aiti-14372 417 49 asme asme PROPN aiti-14372 417 50 press press PROPN aiti-14372 417 51 , , PUNCT aiti-14372 417 52 2013 2013 NUM aiti-14372 417 53 . . PUNCT aiti-14372 418 1 [ [ X aiti-14372 418 2 20 20 NUM aiti-14372 418 3 ] ] X aiti-14372 418 4 v. v. PROPN aiti-14372 418 5 igwemezie igwemezie PROPN aiti-14372 418 6 , , PUNCT aiti-14372 418 7 a. a. NOUN aiti-14372 418 8 mehmanparast mehmanparast NOUN aiti-14372 418 9 , , PUNCT aiti-14372 418 10 and and CCONJ aiti-14372 418 11 f. f. PROPN aiti-14372 418 12 brennan brennan PROPN aiti-14372 418 13 , , PUNCT aiti-14372 418 14 β€œ " PUNCT aiti-14372 418 15 the the DET aiti-14372 418 16 influence influence NOUN aiti-14372 418 17 of of ADP aiti-14372 418 18 microstructure microstructure NOUN aiti-14372 418 19 on on ADP aiti-14372 418 20 the the DET aiti-14372 418 21 fatigue fatigue NOUN aiti-14372 418 22 crack crack VERB aiti-14372 418 23 growth growth NOUN aiti-14372 418 24 rate rate NOUN aiti-14372 418 25 in in ADP aiti-14372 418 26 marine marine ADJ aiti-14372 418 27 steels steel NOUN aiti-14372 418 28 in in ADP aiti-14372 418 29 the the DET aiti-14372 418 30 paris paris PROPN aiti-14372 418 31 region region NOUN aiti-14372 418 32 , , PUNCT aiti-14372 418 33 ” " PUNCT aiti-14372 418 34 fatigue fatigue NOUN aiti-14372 418 35 & & CCONJ aiti-14372 418 36 fracture fracture PROPN aiti-14372 418 37 of of ADP aiti-14372 418 38 engineering engineering NOUN aiti-14372 418 39 materials material NOUN aiti-14372 418 40 & & CCONJ aiti-14372 418 41 structures structure NOUN aiti-14372 418 42 , , PUNCT aiti-14372 418 43 vol vol NOUN aiti-14372 418 44 . . PROPN aiti-14372 418 45 43 43 NUM aiti-14372 418 46 , , PUNCT aiti-14372 418 47 no no INTJ aiti-14372 418 48 . . NOUN aiti-14372 418 49 10 10 NUM aiti-14372 418 50 , , PUNCT aiti-14372 418 51 pp pp ADJ aiti-14372 418 52 . . PUNCT aiti-14372 419 1 2416 2416 NUM aiti-14372 419 2 - - SYM aiti-14372 419 3 2440 2440 NUM aiti-14372 419 4 , , PUNCT aiti-14372 419 5 2020 2020 NUM aiti-14372 419 6 . . PUNCT aiti-14372 420 1 advances advance NOUN aiti-14372 420 2 in in ADP aiti-14372 420 3 technology technology NOUN aiti-14372 420 4 innovation innovation NOUN aiti-14372 420 5 , , PUNCT aiti-14372 420 6 vol vol NOUN aiti-14372 420 7 . . PROPN aiti-14372 421 1 10 10 NUM aiti-14372 421 2 , , PUNCT aiti-14372 421 3 no no INTJ aiti-14372 421 4 . . NOUN aiti-14372 421 5 3 3 NUM aiti-14372 421 6 , , PUNCT aiti-14372 421 7 2025 2025 NUM aiti-14372 421 8 , , PUNCT aiti-14372 421 9 pp pp ADJ aiti-14372 421 10 . . PUNCT aiti-14372 422 1 238 238 NUM aiti-14372 422 2 - - SYM aiti-14372 422 3 253 253 NUM aiti-14372 422 4 253 253 NUM aiti-14372 422 5 [ [ X aiti-14372 422 6 21 21 NUM aiti-14372 422 7 ] ] PUNCT aiti-14372 422 8 v. v. PROPN aiti-14372 422 9 k. k. PROPN aiti-14372 422 10 sahu sahu PROPN aiti-14372 422 11 , , PUNCT aiti-14372 422 12 p. p. PROPN aiti-14372 422 13 k. k. PROPN aiti-14372 422 14 ray ray PROPN aiti-14372 422 15 , , PUNCT aiti-14372 422 16 and and CCONJ aiti-14372 422 17 b. b. PROPN aiti-14372 422 18 b. b. PROPN aiti-14372 422 19 verma verma PROPN aiti-14372 422 20 , , PUNCT aiti-14372 422 21 β€œ " PUNCT aiti-14372 422 22 experimental experimental ADJ aiti-14372 422 23 fatigue fatigue NOUN aiti-14372 422 24 crack crack VERB aiti-14372 422 25 growth growth NOUN aiti-14372 422 26 analysis analysis NOUN aiti-14372 422 27 and and CCONJ aiti-14372 422 28 modelling modelling NOUN aiti-14372 422 29 in in ADP aiti-14372 422 30 part part NOUN aiti-14372 422 31 - - PUNCT aiti-14372 422 32 through through ADP aiti-14372 422 33 circumferentially circumferentially ADV aiti-14372 422 34 pre pre ADJ aiti-14372 422 35 - - ADJ aiti-14372 422 36 cracked cracked ADJ aiti-14372 422 37 pipes pipe NOUN aiti-14372 422 38 under under ADP aiti-14372 422 39 pure pure ADJ aiti-14372 422 40 bending bending NOUN aiti-14372 422 41 load load NOUN aiti-14372 422 42 , , PUNCT aiti-14372 422 43 ” " PUNCT aiti-14372 422 44 fatigue fatigue NOUN aiti-14372 422 45 & & CCONJ aiti-14372 422 46 fracture fracture PROPN aiti-14372 422 47 of of ADP aiti-14372 422 48 engineering engineering NOUN aiti-14372 422 49 materials material NOUN aiti-14372 422 50 & & CCONJ aiti-14372 422 51 structures structure NOUN aiti-14372 422 52 , , PUNCT aiti-14372 422 53 vol vol NOUN aiti-14372 422 54 . . PROPN aiti-14372 422 55 40 40 NUM aiti-14372 422 56 , , PUNCT aiti-14372 422 57 no no INTJ aiti-14372 422 58 . . NOUN aiti-14372 422 59 7 7 NUM aiti-14372 422 60 , , PUNCT aiti-14372 422 61 pp pp ADJ aiti-14372 422 62 . . PUNCT aiti-14372 423 1 1154 1154 NUM aiti-14372 423 2 - - SYM aiti-14372 423 3 1163 1163 NUM aiti-14372 423 4 , , PUNCT aiti-14372 423 5 2017 2017 NUM aiti-14372 423 6 . . PUNCT aiti-14372 424 1 [ [ X aiti-14372 424 2 22 22 NUM aiti-14372 424 3 ] ] PUNCT aiti-14372 424 4 p. p. PROPN aiti-14372 424 5 kumar kumar PROPN aiti-14372 424 6 , , PUNCT aiti-14372 424 7 h. h. PROPN aiti-14372 424 8 patel patel PROPN aiti-14372 424 9 , , PUNCT aiti-14372 424 10 p. p. PROPN aiti-14372 424 11 k. k. PROPN aiti-14372 424 12 ray ray PROPN aiti-14372 424 13 , , PUNCT aiti-14372 424 14 b. b. PROPN aiti-14372 424 15 b.verma b.verma PROPN aiti-14372 424 16 , , PUNCT aiti-14372 424 17 " " PUNCT aiti-14372 424 18 calibration calibration NOUN aiti-14372 424 19 of of ADP aiti-14372 424 20 cod cod NOUN aiti-14372 424 21 gauge gauge NOUN aiti-14372 424 22 and and CCONJ aiti-14372 424 23 determination determination NOUN aiti-14372 424 24 of of ADP aiti-14372 424 25 crack crack NOUN aiti-14372 424 26 profile profile NOUN aiti-14372 424 27 for for ADP aiti-14372 424 28 prediction prediction NOUN aiti-14372 424 29 of of ADP aiti-14372 424 30 through through ADP aiti-14372 424 31 the the DET aiti-14372 424 32 thickness thickness NOUN aiti-14372 424 33 fatigue fatigue NOUN aiti-14372 424 34 crack crack VERB aiti-14372 424 35 growth growth NOUN aiti-14372 424 36 in in ADP aiti-14372 424 37 pipes pipe NOUN aiti-14372 424 38 using use VERB aiti-14372 424 39 exponential exponential ADJ aiti-14372 424 40 function function NOUN aiti-14372 424 41 , , PUNCT aiti-14372 424 42 " " PUNCT aiti-14372 424 43 mechanics mechanic NOUN aiti-14372 424 44 , , PUNCT aiti-14372 424 45 materials material NOUN aiti-14372 424 46 science science NOUN aiti-14372 424 47 & & CCONJ aiti-14372 424 48 engineering engineering PROPN aiti-14372 424 49 , , PUNCT aiti-14372 424 50 no no INTJ aiti-14372 424 51 . . NOUN aiti-14372 424 52 9 9 NUM aiti-14372 424 53 , , PUNCT aiti-14372 424 54 2016 2016 NUM aiti-14372 424 55 . . PUNCT aiti-14372 425 1 [ [ X aiti-14372 425 2 23 23 NUM aiti-14372 425 3 ] ] PUNCT aiti-14372 425 4 p. p. PROPN aiti-14372 425 5 kumar kumar PROPN aiti-14372 425 6 , , PUNCT aiti-14372 425 7 v. v. PROPN aiti-14372 425 8 k. k. PROPN aiti-14372 425 9 sahu sahu PROPN aiti-14372 425 10 , , PUNCT aiti-14372 425 11 p. p. PROPN aiti-14372 425 12 k. k. PROPN aiti-14372 425 13 ray ray PROPN aiti-14372 425 14 , , PUNCT aiti-14372 425 15 b. b. PROPN aiti-14372 425 16 b. b. PROPN aiti-14372 425 17 verma verma PROPN aiti-14372 425 18 , , PUNCT aiti-14372 425 19 " " PUNCT aiti-14372 425 20 modelling modelling NOUN aiti-14372 425 21 of of ADP aiti-14372 425 22 fatigue fatigue NOUN aiti-14372 425 23 crack crack VERB aiti-14372 425 24 propagation propagation NOUN aiti-14372 425 25 in in ADP aiti-14372 425 26 part part NOUN aiti-14372 425 27 - - PUNCT aiti-14372 425 28 through through ADP aiti-14372 425 29 cracked crack VERB aiti-14372 425 30 pipes pipe NOUN aiti-14372 425 31 using use VERB aiti-14372 425 32 gamma gamma NOUN aiti-14372 425 33 function function NOUN aiti-14372 425 34 , , PUNCT aiti-14372 425 35 " " PUNCT aiti-14372 425 36 mechanics mechanic NOUN aiti-14372 425 37 , , PUNCT aiti-14372 425 38 materials material NOUN aiti-14372 425 39 science science NOUN aiti-14372 425 40 & & CCONJ aiti-14372 425 41 engineering engineering PROPN aiti-14372 425 42 , , PUNCT aiti-14372 425 43 no no INTJ aiti-14372 425 44 . . NOUN aiti-14372 425 45 9 9 NUM aiti-14372 425 46 , , PUNCT aiti-14372 425 47 2016 2016 NUM aiti-14372 425 48 . . PUNCT aiti-14372 426 1 [ [ X aiti-14372 426 2 24 24 NUM aiti-14372 426 3 ] ] PUNCT aiti-14372 426 4 p. p. PROPN aiti-14372 426 5 kumar kumar PROPN aiti-14372 426 6 , , PUNCT aiti-14372 426 7 m. m. PROPN aiti-14372 426 8 e. e. PROPN aiti-14372 426 9 makhatha makhatha PROPN aiti-14372 426 10 , , PUNCT aiti-14372 426 11 s. s. PROPN aiti-14372 426 12 sengupta sengupta PROPN aiti-14372 426 13 , , PUNCT aiti-14372 426 14 and and CCONJ aiti-14372 426 15 a. a. PROPN aiti-14372 426 16 k. k. PROPN aiti-14372 426 17 dutt dutt PROPN aiti-14372 426 18 , , PUNCT aiti-14372 426 19 β€œ " PUNCT aiti-14372 426 20 prediction prediction NOUN aiti-14372 426 21 of of ADP aiti-14372 426 22 the the DET aiti-14372 426 23 propagation propagation NOUN aiti-14372 426 24 of of ADP aiti-14372 426 25 fatigue fatigue NOUN aiti-14372 426 26 cracks crack NOUN aiti-14372 426 27 in in ADP aiti-14372 426 28 partthrough partthrough NOUN aiti-14372 426 29 cracked crack VERB aiti-14372 426 30 pipes pipe NOUN aiti-14372 426 31 with with ADP aiti-14372 426 32 casca casca NOUN aiti-14372 426 33 and and CCONJ aiti-14372 426 34 franc2d franc2d NOUN aiti-14372 426 35 , , PUNCT aiti-14372 426 36 ” " PUNCT aiti-14372 426 37 transactions transaction NOUN aiti-14372 426 38 of of ADP aiti-14372 426 39 the the DET aiti-14372 426 40 indian indian PROPN aiti-14372 426 41 institute institute PROPN aiti-14372 426 42 of of ADP aiti-14372 426 43 metals metal NOUN aiti-14372 426 44 , , PUNCT aiti-14372 426 45 vol vol NOUN aiti-14372 426 46 . . PROPN aiti-14372 426 47 73 73 NUM aiti-14372 426 48 , , PUNCT aiti-14372 426 49 no no INTJ aiti-14372 426 50 . . NOUN aiti-14372 426 51 6 6 NUM aiti-14372 426 52 , , PUNCT aiti-14372 426 53 pp pp ADJ aiti-14372 426 54 . . PUNCT aiti-14372 427 1 1417 1417 NUM aiti-14372 427 2 - - SYM aiti-14372 427 3 1420 1420 NUM aiti-14372 427 4 , , PUNCT aiti-14372 427 5 2020 2020 NUM aiti-14372 427 6 . . PUNCT aiti-14372 428 1 [ [ X aiti-14372 428 2 25 25 NUM aiti-14372 428 3 ] ] PUNCT aiti-14372 428 4 s. s. PROPN aiti-14372 428 5 al al PROPN aiti-14372 428 6 laham laham PROPN aiti-14372 428 7 and and CCONJ aiti-14372 428 8 s. s. PROPN aiti-14372 428 9 i. i. PROPN aiti-14372 428 10 branch branch PROPN aiti-14372 428 11 , , PUNCT aiti-14372 428 12 stress stress NOUN aiti-14372 428 13 intensity intensity NOUN aiti-14372 428 14 factor factor NOUN aiti-14372 428 15 and and CCONJ aiti-14372 428 16 limit limit VERB aiti-14372 428 17 load load NOUN aiti-14372 428 18 handbook handbook NOUN aiti-14372 428 19 , , PUNCT aiti-14372 428 20 vol vol NOUN aiti-14372 428 21 . . PROPN aiti-14372 429 1 3 3 NUM aiti-14372 429 2 . . X aiti-14372 429 3 british british ADJ aiti-14372 429 4 energy energy NOUN aiti-14372 429 5 generation generation NOUN aiti-14372 429 6 limited limit VERB aiti-14372 429 7 , , PUNCT aiti-14372 429 8 gloucester gloucester NOUN aiti-14372 429 9 , , PUNCT aiti-14372 429 10 uk uk PROPN aiti-14372 429 11 , , PUNCT aiti-14372 429 12 1998 1998 NUM aiti-14372 429 13 . . PUNCT aiti-14372 430 1 [ [ X aiti-14372 430 2 26 26 NUM aiti-14372 430 3 ] ] PUNCT aiti-14372 430 4 a. a. NOUN aiti-14372 430 5 albedah albedah PROPN aiti-14372 430 6 , , PUNCT aiti-14372 430 7 b. b. PROPN aiti-14372 430 8 bachir bachir PROPN aiti-14372 430 9 bouiadjra bouiadjra PROPN aiti-14372 430 10 , , PUNCT aiti-14372 430 11 l. l. PROPN aiti-14372 430 12 aminallah aminallah PROPN aiti-14372 430 13 , , PUNCT aiti-14372 430 14 m. m. NOUN aiti-14372 430 15 es es NOUN aiti-14372 430 16 - - PUNCT aiti-14372 430 17 saheb saheb NOUN aiti-14372 430 18 , , PUNCT aiti-14372 430 19 and and CCONJ aiti-14372 430 20 f. f. PROPN aiti-14372 430 21 benyahia benyahia PROPN aiti-14372 430 22 , , PUNCT aiti-14372 430 23 β€œ " PUNCT aiti-14372 430 24 numerical numerical ADJ aiti-14372 430 25 analysis analysis NOUN aiti-14372 430 26 of of ADP aiti-14372 430 27 the the DET aiti-14372 430 28 effect effect NOUN aiti-14372 430 29 of of ADP aiti-14372 430 30 thermal thermal ADJ aiti-14372 430 31 residual residual ADJ aiti-14372 430 32 stresses stress NOUN aiti-14372 430 33 on on ADP aiti-14372 430 34 the the DET aiti-14372 430 35 performances performance NOUN aiti-14372 430 36 of of ADP aiti-14372 430 37 bonded bond VERB aiti-14372 430 38 composite composite ADJ aiti-14372 430 39 repairs repair NOUN aiti-14372 430 40 in in ADP aiti-14372 430 41 aircraft aircraft NOUN aiti-14372 430 42 structures structure NOUN aiti-14372 430 43 , , PUNCT aiti-14372 430 44 ” " PUNCT aiti-14372 430 45 composites composite VERB aiti-14372 430 46 part part NOUN aiti-14372 430 47 b b NOUN aiti-14372 430 48 : : PUNCT aiti-14372 430 49 engineering engineering NOUN aiti-14372 430 50 , , PUNCT aiti-14372 430 51 vol vol NOUN aiti-14372 430 52 . . PROPN aiti-14372 431 1 42 42 NUM aiti-14372 431 2 , , PUNCT aiti-14372 431 3 no no INTJ aiti-14372 431 4 . . NOUN aiti-14372 431 5 3 3 NUM aiti-14372 431 6 , , PUNCT aiti-14372 431 7 pp pp ADJ aiti-14372 431 8 . . PUNCT aiti-14372 432 1 511 511 NUM aiti-14372 432 2 - - SYM aiti-14372 432 3 516 516 NUM aiti-14372 432 4 , , PUNCT aiti-14372 432 5 2011 2011 NUM aiti-14372 432 6 . . PUNCT aiti-14372 433 1 [ [ X aiti-14372 433 2 27 27 NUM aiti-14372 433 3 ] ] PUNCT aiti-14372 433 4 t. t. PROPN aiti-14372 433 5 l. l. PROPN aiti-14372 433 6 anderson anderson PROPN aiti-14372 433 7 , , PUNCT aiti-14372 433 8 fracture fracture PROPN aiti-14372 433 9 mechanics mechanic NOUN aiti-14372 433 10 : : PUNCT aiti-14372 433 11 fundamentals fundamental NOUN aiti-14372 433 12 and and CCONJ aiti-14372 433 13 applications application NOUN aiti-14372 433 14 , , PUNCT aiti-14372 433 15 4th 4th ADJ aiti-14372 433 16 ed ed NOUN aiti-14372 433 17 . . PUNCT aiti-14372 434 1 boca boca PROPN aiti-14372 434 2 raton raton PROPN aiti-14372 434 3 , , PUNCT aiti-14372 434 4 fl fl PROPN aiti-14372 434 5 : : PUNCT aiti-14372 434 6 crc crc NOUN aiti-14372 434 7 press press NOUN aiti-14372 434 8 , , PUNCT aiti-14372 434 9 2017 2017 NUM aiti-14372 434 10 . . PUNCT aiti-14372 435 1 [ [ X aiti-14372 435 2 28 28 NUM aiti-14372 435 3 ] ] X aiti-14372 435 4 c. c. PROPN aiti-14372 435 5 m. m. PROPN aiti-14372 435 6 roşca roşca PROPN aiti-14372 435 7 , , PUNCT aiti-14372 435 8 vΓ’lcu vΓ’lcu NOUN aiti-14372 435 9 β€― β€― SPACE aiti-14372 435 10 ; ; PUNCT aiti-14372 435 11 miriΕ£oiu miriΕ£oiu ADJ aiti-14372 435 12 , , PUNCT aiti-14372 435 13 β€œ " PUNCT aiti-14372 435 14 fnk fnk VERB aiti-14372 435 15 model model NOUN aiti-14372 435 16 of of ADP aiti-14372 435 17 cracking crack VERB aiti-14372 435 18 rate rate NOUN aiti-14372 435 19 calculus calculus NOUN aiti-14372 435 20 for for ADP aiti-14372 435 21 a a DET aiti-14372 435 22 variable variable ADJ aiti-14372 435 23 asymmetry asymmetry NOUN aiti-14372 435 24 coefficient coefficient NOUN aiti-14372 435 25 , , PUNCT aiti-14372 435 26 ” " PUNCT aiti-14372 435 27 acta acta PROPN aiti-14372 435 28 universitatis universitatis PROPN aiti-14372 435 29 cibiniensis cibiniensis NOUN aiti-14372 435 30 , , PUNCT aiti-14372 435 31 vol vol NOUN aiti-14372 435 32 . . PROPN aiti-14372 436 1 69 69 NUM aiti-14372 436 2 , , PUNCT aiti-14372 436 3 no no INTJ aiti-14372 436 4 . . NOUN aiti-14372 436 5 1 1 NUM aiti-14372 436 6 , , PUNCT aiti-14372 436 7 pp pp ADJ aiti-14372 436 8 . . PUNCT aiti-14372 437 1 72 72 NUM aiti-14372 437 2 - - SYM aiti-14372 437 3 81 81 NUM aiti-14372 437 4 , , PUNCT aiti-14372 437 5 2017 2017 NUM aiti-14372 437 6 . . PUNCT aiti-14372 438 1 [ [ X aiti-14372 438 2 29 29 NUM aiti-14372 438 3 ] ] PUNCT aiti-14372 438 4 w. w. PROPN aiti-14372 438 5 f. f. PROPN aiti-14372 438 6 gale gale PROPN aiti-14372 438 7 and and CCONJ aiti-14372 438 8 t. t. PROPN aiti-14372 438 9 c. c. PROPN aiti-14372 438 10 totemeier totemeier NOUN aiti-14372 438 11 , , PUNCT aiti-14372 438 12 eds eds PROPN aiti-14372 438 13 . . PROPN aiti-14372 438 14 , , PUNCT aiti-14372 438 15 smithells smithell VERB aiti-14372 438 16 metals metal NOUN aiti-14372 438 17 reference reference NOUN aiti-14372 438 18 book book NOUN aiti-14372 438 19 , , PUNCT aiti-14372 438 20 8th 8th ADJ aiti-14372 438 21 ed ed NOUN aiti-14372 438 22 . . PUNCT aiti-14372 439 1 butterworth butterworth PROPN aiti-14372 439 2 - - PUNCT aiti-14372 439 3 heinemann heinemann PROPN aiti-14372 439 4 , , PUNCT aiti-14372 439 5 2003 2003 NUM aiti-14372 439 6 . . PUNCT aiti-14372 440 1 copyright copyright NOUN aiti-14372 440 2 Β© Β© PROPN aiti-14372 440 3 by by ADP aiti-14372 440 4 the the DET aiti-14372 440 5 authors author NOUN aiti-14372 440 6 . . PUNCT aiti-14372 441 1 licensee licensee PROPN aiti-14372 441 2 taeti taeti PROPN aiti-14372 441 3 , , PUNCT aiti-14372 441 4 taiwan taiwan PROPN aiti-14372 441 5 . . PUNCT aiti-14372 442 1 this this DET aiti-14372 442 2 article article NOUN aiti-14372 442 3 is be AUX aiti-14372 442 4 an an DET aiti-14372 442 5 open open ADJ aiti-14372 442 6 access access NOUN aiti-14372 442 7 article article NOUN aiti-14372 442 8 distributed distribute VERB aiti-14372 442 9 under under ADP aiti-14372 442 10 the the DET aiti-14372 442 11 terms term NOUN aiti-14372 442 12 and and CCONJ aiti-14372 442 13 conditions condition NOUN aiti-14372 442 14 of of ADP aiti-14372 442 15 the the DET aiti-14372 442 16 creative creative ADJ aiti-14372 442 17 commons common NOUN aiti-14372 442 18 attribution attribution NOUN aiti-14372 442 19 ( ( PUNCT aiti-14372 442 20 cc cc NOUN aiti-14372 442 21 by by ADP aiti-14372 442 22 - - PUNCT aiti-14372 442 23 nc nc NOUN aiti-14372 442 24 ) ) PUNCT aiti-14372 442 25 license license NOUN aiti-14372 442 26 ( ( PUNCT aiti-14372 442 27 https://creativecommons.org/licenses/by-nc/4.0/ https://creativecommons.org/licenses/by-nc/4.0/ NOUN aiti-14372 442 28 ) ) PUNCT aiti-14372 442 29 . . PUNCT