Al-khwarizmi!! Engineering!!! Journal Al-Khwarizmi Engineering Journal, Vol.4 , No.1 , pp 58-!67 (2008!) ! ! Impact Energy of 100Cr6 under low different velocities Prof. Dr. Hussain. J. Al-Alkawi Electromechanical Eng. Dept. University of Technology Lec. Dr. Khansaa D. Al- Shamari Electromechanical Eng. Dept University of Technology (Received 11 Julay2006 ; accepted 24 September 2007) Abstract: This study has been undertaken to postulate the mechanism of impact test at low velocities. Thin-walled tubes of 100Cr6 were deformed under axial compression. In the present work there are seven velocities (4.429,4.652,5.240,5.600,5.942,6.264, 6.569) m\sec were applied to show how they effect the load, change in length, also the kinetic energy. However, the comparison between the obtained results and the other studies (Alexandar[3] , Abramowicz[4], Ayad[5]) was made the present work and Ayad data show good agreement. Load, change in length, kinetic energy were determined to understand the impact test. Keywords: Impact Energy Introduction: The use of thin-walled tubes collapsing plastically in axial compre-ssion is one of the most efficient means of energy absorption. These tubes are small in volume, easy to fabricate in weight, cheap, and stable during crushing. The crushing of thin tubes is a process by which the kinetic energy can be absorbed for example in vehicle cursh. The criterion upon which many energy absorbing devices are based, is that these devices undergo a large amount of plastic deformation before total collapse [1]. The active absorbing element of an energy absorption system can assume several common shapes such as tubes, honey combs, frusta, strips and rods. When impact velocity is less than 30 m/s, the impact is low speed impact. Buckling under a low velocity can be considered as a quasi-static behavior. While impact velocities larger than 30 m/s cause stresses above the yield stress of the material, the impact is high speed impact. Thin tubes deforms in one of the following modes [2]. (i) Column or Euler buckling. (ii) Concertina or like axisy-mmetric buckling. (iii) Diamond buckling. (iv) Tearing of the tubes. (v) Brittle fracture or shuttering. (vi) Uniform compression. Fig(1): Thin tube deform,(a) diamond mode type buckling, (b) concertina mode type buckling, (c) invert tubes showmen (left) External, inside-out, inversion (right), Internal , outside-in, inversion, (d) Tearing failure [2]. Many articles have been published on the static and dynamic crushing of circular tubes [1, 2]. The pioneer work of Alexander [3] and Abramowicz [4] of circular and square tubes under dynamic conditions. Alexander [3] was the first to present a mathematical model of crushing phenomena for thin walled tubular specimens, calculating the mean crushing force of tubes and collapsing in the axisymmetric or concertina mode. While Abramowicz and Jones [4] have improved the Alexander model by modifying the effective crushing distance and the effect of material strain rate under dynamic loading. In this article. Three models namely Alexander [3], Abramowicz [4] and Ayad [5], Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÒÖ were using thin-walled tubes which were made from 100Cr6 steel tested under different velocities impact. Literature Review: Abramoswicz [4] focuses on the range of dynamic load which give rise to a quasi-static crushing response. A series of axial crushing tests on steel circular cylindrical tubes loaded either statica-lly, or dynamically, is reported and compared with various theoretical predictions and empirical relations: A modified version of Alexander's [3] theoretical solution for axisymmetric, or concertina, deformations, which includes a correction for the effective crushing distance, gives good agreem-ent with the mean of experimental static crushing loads. Guillow and Grezbieta [6] tested 6060 aluminum alloy tubes with different range of (D/t), Internal diameter to thickness ratio from 10-450. It was found that the behavior of thin walled tubes can be described by the empirical formula. 32.0)(3.72 t D Mp Fav  ------------ (1) where: Fav: average crushing force. Mp: plastic moment per unit length. Also it was found that the ratio of Fmax/Fav increased substantially with an increase in the D/t ratio. Huang and Lu [7] presented an axisymmetric crushing behavior of metal tubes subjected to quasi-static axial loads. Based on the experimental results and finite element analysis, a theoretical model is developed by introducing the concept of effective plastic hinge length which is proportional to tube thickness. Seitzberger and Willminger [8] investigated steel alloy of different types of cross-sections (square, hexa-gonal, octagonal) which are fully or partially filled with aluminum foam. The results of the parameter studies confirm with the experimental observa-tions for given tube/filler combinations and the foam is a major parameter in the design of the collapse models. Ayad Arab [5] studied the variety speed impact for thin walled cylinder made from 2024-T351 Aluminum alloy. A proposed mathematical model was presented based on the experim-ental data. This model can predicted the mean load, variation of load and deformation for static and dynamic conditions by falling axial mass with different velocities impact. The effect of folding parameter (m) and size of fold (h) on mean load and deformation have been studied. Experimental Work A series of 12 axial crushing tests was conducted on circular tubes specimens loaded either statically or dynamically. This section presents the experimental work done using 100Cr6 steel which is widly used in structures and in many industrial of automobiles. Mechanical Properties: Table (1) illustrates the mechanical properties of the metal used while Fig (2) shows the relation between the stress and strain (tensile test). Chemical Composition: Table (2) shows the chemical compos-ition of 100Cr6 in weight percentage. Microstructure Evaluation: A computerized optical microscopy was used to examine the microstru-cture of the sample. Photo micrographs was taken for sample which was examined by optical microscopy as shown in Fig (3). Specimens Preparation: Circular sectioned steel alloy tubes formed by a deep drawing process were used. These tubes were cut to equal lengths by cutter machine. Fig. (4) shows the shape and dimensions of the specimens used in this study [9]. Test Rig: The test rig used is described in details in reference [10]. Experimental Results: The results recorded are divided into two groupes static and dynamic as follows: Static Compressive Test: A load of 2.5 ton at 1 mm/min head speed is chosen in order to compare the results with Ref. [8] who used the same condition of Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÍ testing. The purpose of doing the test is to obtain the mode of deformation. The results are given in Table (3), and Table (4) gives the results at failure. The energy absorbed was calculated using the equation : (Pm f ).(L f) = E -----------------------(2) where : Lf : deformation at failure (mm) . Pmf : mean load at failure (KN). E:Energy absorbed by the specimen(J). Impact test results: 12 specimens are tested at different speeds (4.429 - 6.569 ) by using a mass of (14.55 kg) at different heights. The results can be illustrated in table (5). 1) The velocity of the dropping mass was measured experimentally by the test rig end compared with the calculated velocity using the equation: V = gH2 Where : H is the height of the dropping mass . The error of the results was about 5%. (H was taken from 1-2.2 m). And g = 9.81 m/sec². 2) The failure deformation (Lf ) was measured from the specimen at failure 3) The dynamic mean load ( Pm ) was calculated from the equation: (Pm)dynamic = K.E/Lf = mV²/2Lf Where: m is weight of the falling body = 14.55 kg Figure (5) represents the increasing in the velocity leads to increase in the load as it is shown obviously in Abramowicz test [4] which the increment in the load is a higher than in the others, while this increment in the present work, Alexandar [3] and Ayad [5] is small . Most of the relationships seems to be horizontally linear. This is return to that the sample of Abramowicz which was obtained for steel show that the relation between the load and the velocity curve extremely according to the:  206.0113.11 Vpm  and its lead to give higher slope than in another's. Figure (6) represents the results of L/L which was plotted as a function of V, It is seen that the relation of present work is extremely close to Ayad work [5] and far from Alexandar, Abramowicz work. These relations have the same slops when they are linear proportionality. From figure (7), it is found that L/L varying with the kinetic energy, and give the same conclusions which were obtained by L/L and V, this is return to that the kinetic energy extremely related with velocity as : K=1/2mV² , hence the results are the same at which obtained between L/L and V. Conclusions: The behavior of 100Cr6 thin – walled tube under dynamic Impact loading takes the followings : A\ The mp increases with increases in velocity V and takes a relation close to Abramowicz and Ayad models . B\ The variation of the ratio L/L against velocity V is taken the trend of Ayad model while Alexandar and Abramowicz are far away from the present results. Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÎ !! Fig. (1) Shows the most types of deformation of thin-walled tubes. 0.03 0.08 0.13 0.18 0.230.00 0.05 0.10 0.15 0.20 0.25 10 30 50 70 90 0 20 40 60 80 100 St re ss ( M pa ) Strain Fig. (2): Relationship between stress and strain !! Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÏ ÓÎ Fig. (3): Microstructure of the 100 Cr6 with Mg ( 270X ) t=1mm L =30mm 18mm Fig. (4) : shape and specimen dimensions Fig. (Ò) : Relationship between load and velocity !! Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÐ Fig. (6) : Relationship between deformation and velocity. Fig. (7) : Relationship between deformation and kinetic energy. !! !! !!K(J) Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÑ Table (1) mechanical properties of 100Cr6 y (MPa) u (MPa) Elong.% Brinell Hardness G (Gpa) E (Gpa) µ K 310 840 7.2 211 88.46 230 0.3 287.5 The above data is the average of three readings. Table (2) Chemical Composition of the material used. C Mn Si P S Cr Ni Mo Cu Fe% 1.05 0.40 0.23 0.016 0.009 1.77 0.07 0.03 0.17 96.122 * The above analyses was done by Thermo ARL 3460!º º OE SPECTROMETER. Table (3) static compressive test for 100Cr6 Load (KN) L (mm) Load (KN) L (mm) Load (KN) L (mm) Load (KN) L (mm) 14.0 17 15 13 0.057 0.122 0.22 0.31 10 7 11 13 16 0.44 0.51 0.62 0.78 1.000 14.5 12 10 16 18 17 1.1 1.2 1.5 1.8 2.1 2.3 14 13 11 10 18 19 20 8 10 11 13 14 17 18 failure Table (4) static results at failure Failure E (J) L f (mm) Pm f (KN) Mode Complete damage of specimen 252 18 14 Concertina buckling Table (5) Dynamic results of 100Cr6 under 14.55 kg Spec.No V(m\s) Lf (mm) Pm (KN) H (m) Mode of def.* 4 4.429 8 17.838 1 C 5 4.652 12.5 12.595 1.2 C 6 5.24 14.8 13.496 1.4 C 7 5.6 15.7 14.531 1.6 C 8 5.942 17.2 14.933 1.8 C 9 6.264 18.4 15.513 2 C 10 6.569 19.7 15.935 2.2 C 11 6.569 20.4 15.388 2.2 C 12 6.569 20.1 15.161 2.2 C 13 6.569 20.5 15.463 2.2 C 14 6.569 20.3 15.312 2.2 C 15 6.569 20 15.086 2.2 C Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÒ T ab le ( 6) s ho w s th e co m pa ri so n be tw ee n th re e re fe re nc es [3 ], [ 4] , [ 5] w ith th e cu rr en t w or k. Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÓ References [1] Reid S.R. Drew S. L. and karing J.E. “Energy absorbing capacities of metal” Inter. Journal of Mech. SCi. 1983, 25, Page 649-667. [2] Karagiozovaa, D. and Norman J.C. “Inertia effects in axis-symmetrically deformed cylindrical shells under axial impact” Internal report, Liverpool University, UK. 2000 [3] Alexander, J. M. “An approximate analysis of the collaps of thin cylindrical shells under axial loading” Q. J. Mech. Appl. Math 1960 pp (1-10). [4] Abramowicz W. and Jones, N. “Dynamic axial crushing of circular tubes” Int. J. Impact 1984, Page 263. [5]Ayad Arab, K. “Variety speed impact of thin walled circular tubes” MSC Thesis, university of AL-Anbar (2005). [6] Guillow, S.R. and Grzebieta, R. H. “Quasi- static” axial compression of thin-walled circular aluminum tubes” I. J. Mech. Sci. Vol. 43, 2001 pp.2103-2123. [7] Huang, X. and Lu, G. “Axisymmetric progressive crushing of circular tubes” I.J. crashworthiness Vol.8. 2002 pp-87-95 [8] Seitzberger, M. and Willminger, S. “Application of plastic collapse mechanisms for the axial crushing analysis of tubular steel structures filled with aluminum foam” Int. J. crashworthiness, 2001 pp (165-176). [9] Jones, N. and Abramowicz, W. (1985) “Static and dynamic axial curshing of circular and square tubes” Proc. Metal forming and Impact Mech. Pergoman Press oxford 1985. [10] Al-Badrany, Ayad Aied “Energy absorption capacity of thin metallic tubes” MSC. Thesis, Al-Anbar University 2005. Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) ÓÔ !!! ! Ž!!! ! !! !Œ!! !œ!100Cr6!! Ž!!! ! !! ! Ž! !! !! ! ! !! š!!! خنساء داود سلمان الشمري. دحسین جاسم محمد العلكاوي . د قسم الھندسة الكھرومیكانیكیة قسم الھندسة الكھرومیكانیكیة الجامعة التكنولوجیة الجامعة التكنولوجیة :الخالصة استخدمت عینات أنبوبیة قصیرة رقیقة المقطع من . مختلفة سرع منخفضةأجریت ھذه الدراسة لتخمین آلیة اختبار الصدمة عند وقد تم تشویھ العینات تحت تأثیر قوة ضغط أحادیة المحور في ھذه الدراسة تم تسلیط سبع سرع 100Cr6معدن الفوالذ من نوع )4.429 ,4.652 ,5.240 ,5.600 ,5.942 ,6.264 ,6.569 m\sec (الطاقة , التغیر في الطول , القوة لبیان تأثیرھا على . الحركیة الدراسة ). Alexandar[3] , Abramowicz[4] , Ayad[5])وبناًء على ذلك أجریت مقارنة بین الدراسة الحالیة ودراسات اخرى ة الحركیة لفھم آلیة االختبار الطاق, التغیر في أبعاد العینة, لقد تم حساب القوة الالزمة. Ayad[5]الحالیة تتوافق بشكل جید مع دراسة ) .اختبار الصدمة ( المستخدم 0 . 0 3 0 . 0 8 0 . 1 3 0 . 1 8 0 . 2 3 0 . 0 0 0 . 0 5 0 . 1 0 0 . 1 5 0 . 2 0 0 . 2 5 1 0 3 0 5 0 7 0 9 0 0 2 0 4 0 6 0 8 0 1 0 0 0.030.080.130.180.230.000.050.100.150.200.25 10 30 50 70 900 20 40 60 80100 32 . 0 ) ( 3 . 72 t D Mp Fav = gH 2 ( ) 2 06 . 0 1 13 . 11 V p m + = m p Waheed S. Mohammed Al-khwarizmi Engineering Journal, Vol.4 , No. 1 PP 58-67 (2008) Al-khwarizmi Engineering Journal Al-Khwarizmi Engineering Journal, Vol.4 , No.1 , pp 58- 67 (2008 ) Impact Energy of 100Cr6 under low different velocities Prof. Dr. Hussain. J. Al-Alkawi Electromechanical Eng. Dept. University of Technology Lec. Dr. Khansaa D. Al- Shamari Electromechanical Eng. Dept University of Technology (Received 11 Julay2006 ; accepted 24 September 2007) Abstract: This study has been undertaken to postulate the mechanism of impact test at low velocities. Thin-walled tubes of 100Cr6 were deformed under axial compression. In the present work there are seven velocities (4.429,4.652,5.240,5.600,5.942,6.264, 6.569) m\sec were applied to show how they effect the load, change in length, also the kinetic energy. However, the comparison between the obtained results and the other studies (Alexandar[3] , Abramowicz[4], Ayad[5]) was made the present work and Ayad data show good agreement. Load, change in length, kinetic energy were determined to understand the impact test. Keywords: Impact Energy Introduction: The use of thin-walled tubes collapsing plastically in axial compre-ssion is one of the most efficient means of energy absorption. These tubes are small in volume, easy to fabricate in weight, cheap, and stable during crushing. The crushing of thin tubes is a process by which the kinetic energy can be absorbed for example in vehicle cursh. The criterion upon which many energy absorbing devices are based, is that these devices undergo a large amount of plastic deformation before total collapse [1]. The active absorbing element of an energy absorption system can assume several common shapes such as tubes, honey combs, frusta, strips and rods. When impact velocity is less than 30 m/s, the impact is low speed impact. Buckling under a low velocity can be considered as a quasi-static behavior. While impact velocities larger than 30 m/s cause stresses above the yield stress of the material, the impact is high speed impact. Thin tubes deforms in one of the following modes [2]. (i) Column or Euler buckling. (ii) Concertina or like axisy-mmetric buckling. (iii) Diamond buckling. (iv) Tearing of the tubes. (v) Brittle fracture or shuttering. (vi) Uniform compression. Fig(1): Thin tube deform,(a) diamond mode type buckling, (b) concertina mode type buckling, (c) invert tubes showmen (left) External, inside-out, inversion (right), Internal , outside-in, inversion, (d) Tearing failure [2]. Many articles have been published on the static and dynamic crushing of circular tubes [1, 2]. The pioneer work of Alexander [3] and Abramowicz [4] of circular and square tubes under dynamic conditions. Alexander [3] was the first to present a mathematical model of crushing phenomena for thin walled tubular specimens, calculating the mean crushing force of tubes and collapsing in the axisymmetric or concertina mode. While Abramowicz and Jones [4] have improved the Alexander model by modifying the effective crushing distance and the effect of material strain rate under dynamic loading. In this article. Three models namely Alexander [3], Abramowicz [4] and Ayad [5], were using thin-walled tubes which were made from 100Cr6 steel tested under different velocities impact. Literature Review: Abramoswicz [4] focuses on the range of dynamic load which give rise to a quasi-static crushing response. A series of axial crushing tests on steel circular cylindrical tubes loaded either statica-lly, or dynamically, is reported and compared with various theoretical predictions and empirical relations: A modified version of Alexander's [3] theoretical solution for axisymmetric, or concertina, deformations, which includes a correction for the effective crushing distance, gives good agreem-ent with the mean of experimental static crushing loads. Guillow and Grezbieta [6] tested 6060 aluminum alloy tubes with different range of (D/t), Internal diameter to thickness ratio from 10-450. It was found that the behavior of thin walled tubes can be described by the empirical formula. ------------ (1) where: Fav: average crushing force. Mp: plastic moment per unit length. Also it was found that the ratio of Fmax/Fav increased substantially with an increase in the D/t ratio. Huang and Lu [7] presented an axisymmetric crushing behavior of metal tubes subjected to quasi-static axial loads. Based on the experimental results and finite element analysis, a theoretical model is developed by introducing the concept of effective plastic hinge length which is proportional to tube thickness. Seitzberger and Willminger [8] investigated steel alloy of different types of cross-sections (square, hexa-gonal, octagonal) which are fully or partially filled with aluminum foam. The results of the parameter studies confirm with the experimental observa-tions for given tube/filler combinations and the foam is a major parameter in the design of the collapse models. Ayad Arab [5] studied the variety speed impact for thin walled cylinder made from 2024-T351 Aluminum alloy. A proposed mathematical model was presented based on the experim-ental data. This model can predicted the mean load, variation of load and deformation for static and dynamic conditions by falling axial mass with different velocities impact. The effect of folding parameter (m) and size of fold (h) on mean load and deformation have been studied. Experimental Work A series of 12 axial crushing tests was conducted on circular tubes specimens loaded either statically or dynamically. This section presents the experimental work done using 100Cr6 steel which is widly used in structures and in many industrial of automobiles. Mechanical Properties: Table (1) illustrates the mechanical properties of the metal used while Fig (2) shows the relation between the stress and strain (tensile test). Chemical Composition: Table (2) shows the chemical compos-ition of 100Cr6 in weight percentage. Microstructure Evaluation: A computerized optical microscopy was used to examine the microstru-cture of the sample. Photo micrographs was taken for sample which was examined by optical microscopy as shown in Fig (3). Specimens Preparation: Circular sectioned steel alloy tubes formed by a deep drawing process were used. These tubes were cut to equal lengths by cutter machine. Fig. (4) shows the shape and dimensions of the specimens used in this study [9]. Test Rig: The test rig used is described in details in reference [10]. Experimental Results: The results recorded are divided into two groupes static and dynamic as follows: Static Compressive Test: A load of 2.5 ton at 1 mm/min head speed is chosen in order to compare the results with Ref. [8] who used the same condition of testing. The purpose of doing the test is to obtain the mode of deformation. The results are given in Table (3), and Table (4) gives the results at failure. The energy absorbed was calculated using the equation : (Pm f ).((L f) = E -----------------------(2) where : (Lf : deformation at failure (mm) . Pmf : mean load at failure (KN). E:Energy absorbed by the specimen(J). Impact test results: 12 specimens are tested at different speeds (4.429 - 6.569 ) by using a mass of (14.55 kg) at different heights. The results can be illustrated in table (5). 1) The velocity of the dropping mass was measured experimentally by the test rig end compared with the calculated velocity using the equation: V = Where : H is the height of the dropping mass . The error of the results was about 5%. (H was taken from 1-2.2 m). And g = 9.81 m/sec². 2) The failure deformation ((Lf ) was measured from the specimen at failure 3) The dynamic mean load ( Pm ) was calculated from the equation: (Pm)dynamic = K.E/(Lf = mV²/2(Lf Where: m is weight of the falling body = 14.55 kg Figure (5) represents the increasing in the velocity leads to increase in the load as it is shown obviously in Abramowicz test [4] which the increment in the load is a higher than in the others, while this increment in the present work, Alexandar [3] and Ayad [5] is small . Most of the relationships seems to be horizontally linear. This is return to that the sample of Abramowicz which was obtained for steel show that the relation between the load and the velocity curve extremely according to the: and its lead to give higher slope than in another's. Figure (6) represents the results of (L/L which was plotted as a function of V, It is seen that the relation of present work is extremely close to Ayad work [5] and far from Alexandar, Abramowicz work. These relations have the same slops when they are linear proportionality. From figure (7), it is found that (L/L varying with the kinetic energy, and give the same conclusions which were obtained by (L/L and V, this is return to that the kinetic energy extremely related with velocity as : K=1/2mV² , hence the results are the same at which obtained between (L/L and V. Conclusions: The behavior of 100Cr6 thin – walled tube under dynamic Impact loading takes the followings : A\ The increases with increases in velocity V and takes a relation close to Abramowicz and Ayad models . B\ The variation of the ratio (L/L against velocity V is taken the trend of Ayad model while Alexandar and Abramowicz are far away from the present results. 61 Table (1) mechanical properties of 100Cr6 (y (MPa) (u (MPa) Elong.% Brinell Hardness G (Gpa) E (Gpa) µ K 310 840 7.2 211 88.46 230 0.3 287.5 The above data is the average of three readings. Table (2) Chemical Composition of the material used. C Mn Si P S Cr Ni Mo Cu Fe% 1.05 0.40 0.23 0.016 0.009 1.77 0.07 0.03 0.17 96.122 * The above analyses was done by Thermo ARL 3460ــ OE SPECTROMETER. Table (3) static compressive test for 100Cr6 Load (KN) (L (mm) Load (KN) (L (mm) Load (KN) (L (mm) Load (KN) (L (mm) 14.0 17 15 13 0.057 0.122 0.22 0.31 10 7 11 13 16 0.44 0.51 0.62 0.78 1.000 14.5 12 10 16 18 17 1.1 1.2 1.5 1.8 2.1 2.3 14 13 11 10 18 19 20 8 10 11 13 14 17 18 failure Table (4) static results at failure Failure E (J) (L f (mm) Pm f (KN) Mode Complete damage of specimen 252 18 14 Concertina buckling Table (5) Dynamic results of 100Cr6 under 14.55 kg Spec.No V(m\s) (Lf (mm) Pm (KN) H (m) Mode of def.* 4 4.429 8 17.838 1 C 5 4.652 12.5 12.595 1.2 C 6 5.24 14.8 13.496 1.4 C 7 5.6 15.7 14.531 1.6 C 8 5.942 17.2 14.933 1.8 C 9 6.264 18.4 15.513 2 C 10 6.569 19.7 15.935 2.2 C 11 6.569 20.4 15.388 2.2 C 12 6.569 20.1 15.161 2.2 C 13 6.569 20.5 15.463 2.2 C 14 6.569 20.3 15.312 2.2 C 15 6.569 20 15.086 2.2 C References [1] Reid S.R. Drew S. L. and karing J.E. “Energy absorbing capacities of metal” Inter. Journal of Mech. SCi. 1983, 25, Page 649-667. [2] Karagiozovaa, D. and Norman J.C. “Inertia effects in axis-symmetrically deformed cylindrical shells under axial impact” Internal report, Liverpool University, UK. 2000 [3] Alexander, J. M. “An approximate analysis of the collaps of thin cylindrical shells under axial loading” Q. J. Mech. Appl. Math 1960 pp (1-10). [4] Abramowicz W. and Jones, N. “Dynamic axial crushing of circular tubes” Int. J. Impact 1984, Page 263. [5]Ayad Arab, K. “Variety speed impact of thin walled circular tubes” MSC Thesis, university of AL-Anbar (2005). [6] Guillow, S.R. and Grzebieta, R. H. “Quasi-static” axial compression of thin-walled circular aluminum tubes” I. J. Mech. Sci. Vol. 43, 2001 pp.2103-2123. [7] Huang, X. and Lu, G. “Axisymmetric progressive crushing of circular tubes” I.J. crashworthiness Vol.8. 2002 pp-87-95 [8] Seitzberger, M. and Willminger, S. “Application of plastic collapse mechanisms for the axial crushing analysis of tubular steel structures filled with aluminum foam” Int. J. crashworthiness, 2001 pp (165-176). [9] Jones, N. and Abramowicz, W. (1985) “Static and dynamic axial curshing of circular and square tubes” Proc. Metal forming and Impact Mech. Pergoman Press oxford 1985. [10] Al-Badrany, Ayad Aied “Energy absorption capacity of thin metallic tubes” MSC. Thesis, Al-Anbar University 2005. طاقة الصدمة لفولاذ 100Cr6 تحت سرع منخفضة مختلفة د. حسين جاسم محمد العلكاوي د. خنساء داود سلمان الشمري قسم الهندسة الكهروميكانيكية قسم الهندسة الكهروميكانيكية الجامعة التكنولوجية الجامعة التكنولوجية الخلاصة: أجريت هذه الدراسة لتخمين آلية اختبار الصدمة عند سرع منخفضة مختلفة . استخدمت عينات أنبوبية قصيرة رقيقة المقطع من معدن الفولاذ من نوع 100Cr6 وقد تم تشويه العينات تحت تأثير قوة ضغط أحادية المحور في هذه الدراسة تم تسليط سبع سرع (4.429 , 4.652 , 5.240 , 5.600 , 5.942 , 6.264 , 6.569 m\sec ) لبيان تأثيرها على القوة , التغير في الطول , الطاقة الحركية . وبناءً على ذلك أجريت مقارنة بين الدراسة الحالية ودراسات اخرى (Alexandar[3] , Abramowicz[4] , Ayad[5] ). الدراسة الحالية تتوافق بشكل جيد مع دراسة Ayad[5] . لقد تم حساب القوة اللازمة, التغير في أبعاد العينة, الطاقة الحركية لفهم آلية الاختبار المستخدم ( اختبار الصدمة ) . � EMBED PBrush ��� � Fig. (1) Shows the most types of deformation of thin-walled tubes. Stress (Mpa) � Fig. (2): Relationship between stress and strain Strain Fig. (3): Microstructure of the 100 Cr6 with Mg ( 270X ) t=1mm L =30mm 18mm Fig. (4) : shape and specimen dimensions �EMBED PBrush��� Fig. (5) : Relationship between load and velocity �EMBED PBrush��� Fig. (6) : Relationship between deformation and velocity. K(J) �EMBED PBrush��� Fig. (7) : Relationship between deformation and kinetic energy. Table (6) shows the comparison between three references [3], [4], [5] with the current work. 68 60 _1256459126.unknown _1256459129.unknown _1264194191.unknown _1256459127.unknown _1256459121 _1256459123 _1256459125.unknown _1256459122 _1256459111 _1256459114 _1256459118 _1173207870