Microsoft Word - numero_36_art_5 Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 46 Focused on Fracture Mechanics in Central and East Europe Fatigue life prediction of casing welded pipes by using the extended finite element method Ljubica Lazić Vulićević, Aleksandar Rajić High Technical School of Professional Studies, Đorđa Stratimirovića 39, Zrenjanin, Serbia Aleksandar Grbović Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade, Serbia Aleksandar Sedmak Faculty of Mechanical Engineering, Kraljice Marije 16, Belgrade, Serbia asedmak@mas.bg.ac.rs Živče Šarkočević High Technical School of Professional Studies, Zvecan, Serbia ABSTRACT. The extended finite element (XFEM) method has been used to simulate fatigue crack growth in casing pipe, made of API J55 steel by high-frequency welding, in order estimate its structural integrity and life. Based on the critical value of stress intensity factor KIc, measured in different regions of welded joint, the crack was located in the base metal as the region with the lowest resistance to crack initiation and propagation. The XFEM was first applied to the 3 point bending specimens to verify numerical results with the experimental ones. After successful verification, the XFEM was used to simulate fatigue crack growth, position axially in the pipe, and estimate its remaining life. KEYWORDS. XFEM; Seam casing pipes; Axial surface crack; Fatigue crack growth; Remaining life. INTRODUCTION n order to keep pipeline safe and reliable in operation, its fatigue life estimation is of utmost importance, [1]. Toward this aim, extensive experimental and numerical investigation is needed. In this paper the extended finite element method (XFEM) has been used for modeling and analysis of crack propagation in a seam casing pipe made of API J55 steel by high-frequency (HF) contact welding, but only after its verification, based on the comparison of the xFEM results with experimental results obtained on the standard three-point bending specimen. RESISTANCE TO CRACK GROWTH OF API J55 odified CT specimens with thickness d = 6.98 mm (equal to the pipe wall thickness) have been used to evaluate critical values of fracture mechanics parameters (JIc, KIc), and the critical crack length, ac, as shown in more details in [2] for new and exploited pipes. Here only results obtained for exploited pipe are shown in Tab. 1. I M Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 47 Specimen Temperature [°C] JIc [kN/m] KIc [MPam] ac [mm] BM-NR-E 20 35.8 91.4 14.4 HAZ-NW-E 48.5 106.4 19.6 WM-NW-E 45.7 103.3 18.5 Table 1: The values of JIc KIc and ac - pipe taken from service. Based on the obtained values of KIc for the base metal (BM), heat-affected-zone (HAZ) and weld metal (WM), one can conclude that the BM has the lowest resistance to crack initiation and propagation. VERIFICATION OF THE METHOD USING EXPERIMENTAL RESULTS OBTAINED ON STANDARD SPECIMEN he XFEM is relatively new method of numerical simulation and it has to be verified by experimental results, [3]. For this purpose the results from experimental testing and from numerical simulation using XFEM, both carried out on the standard Charpy specimen, were compared. The specimen is made of API J55 steel, the same steel as the pipe is made of. The three-point-bending test was conducted on standard Charpy specimen made from BM, since it has the lowest resistance to crack initiation and propagation. The test was conducted on high-frequency pulsator RUMUL- CRACKTRONIC at the room temperature providing relation between the crack length, a, and the number of cycles N. A finite element model of the Charpy specimen was created using the Abaqus software. Mesh was refined around the initial crack, as shown in Fig. 1. Figure 1: Standard Charpy specimen: dimensions of the specimen and 3D model obtained using Abaqus software. The crack growth to its critical size was simulated by using Paris equation:    d dN        1.12 ma pm pC K C ap p where da/dN [m/cycles] is the fatigue crack growth, ΔK [MPam] the stress intensity factor range, Cp and mp material parameters, which have the following value in this paper: Cp=2.1110-15, exponent mp=6.166, [2]. T Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 48 The initial crack length used in the analysis was 2 mm. The growing crack was incremented at steps of 0.16 mm (chosen by the software) and 28 steps were performed. The first step in 3D analysis using XFEM was crack “opening” (Fig. 2). In this step stresses in the specimen are obtained, as well as stress intensity factors (SIFs) at the crack tip. Based on that, Morfeo/Crack for Abaqus, computes the SIFs for mode I, II and III, for every step of the crack propagation, and the corresponding crack growth. Fig. 2 shows crack at beginning (1st step- crack opening), Fig. 3, after 8th step, while Fig. 4 shows the crack after the 27th step. Figure 2: Step one - crack opening and Von Mises stresses at crack tip. Figure 3: Crack length after 8th step. Figure 4: Crack length after 27th step. The SIF values at the crack tip determine the appropriate crack growth increment. This procedure was performed in 28 steps in order to simulate incremental crack growth. Values obtained in Abaqus for the 16th crack growth step are shown in Tab. 1, indicating SIF values Keq, KI, KII, and KIII) in the last four columns. As expected, crack growth was characterized by KI, since values of KII and KIII are negligible. Therefore, data for all crack growth steps is given only for Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 49 KI, Tab. 2, including its average, minimum and maximum values along the crack front. Tab. 2 also shows number of point in each crack growth step, being between 66 and 68. Curvilinear abscissa along the crack front [mm] x front coordinate [mm] y front coordinate [mm] z front coordinate [mm] Keq [MPa√m] KI [MPa√m] KII [MPa√m] KIII [MPa√m] 0.000 0.033 0.781 0.035 67.4 67.3 -0.1 0.8 0.151 0.031 0.791 0.187 67.4 67.3 -0.1 0.7 0.293 0.028 0.801 0.328 67.4 67.4 -0.1 0.7 0.445 0.025 0.815 0.479 67.5 67.4 -0.1 0.6 0.585 0.023 0.828 0.618 67.5 67.4 -0.1 0.5 0.716 0.021 0.841 0.749 67.5 67.4 -0.2 0.5 0.855 0.018 0.853 0.887 67.5 67.4 -0.2 0.4 Table 2: Values for Keq, KI, KII, and KIII in the 16th crack growth step. SIF for mod I, KI [MPam] step Crack length a [mm] Number of points of the crack front max min average value 1 2.00 66 28.09 26.34 27.60 2 2.15 68 29.63 27.93 29.08 3 2.31 66 30.97 29.50 30.60 4 2.47 68 32.44 31.46 32.16 5 2.65 68 34.34 33.81 34.04 6 2.84 66 36.42 35.82 36.22 7 3.03 68 37.84 37.39 37.68 8 3.22 68 40.22 39.77 39.99 9 3.42 66 42.97 42.62 42.82 10 3.61 68 44.93 44.58 44.83 11 3.80 68 47.99 47.49 47.75 12 3.96 66 51.62 51.19 51.46 13 4.19 68 54.40 54.15 54.30 14 4.39 68 58.43 57.91 58.17 15 4.58 66 63.43 63.07 63.25 16 4.78 68 67.45 67.19 67.33 17 4.98 68 73.02 72.59 72.80 18 5.18 66 80.30 79.84 80.10 19 5.38 68 86.26 85.91 86.11 20 5.58 68 94.77 94.09 94.40 21 5.78 66 106.00 105.16 105.58 22 5.98 68 115.78 115.07 115.48 23 6.18 66 129.66 128.21 128.72 24 6.37 66 148.40 146.73 147.56 25 6.58 68 165.09 164.01 164.37 26 6.78 68 190.23 187.30 188.21 27 6.98 66 225.71 222.78 223.74 28 7.18 68 261.11 257.68 258.90 Table 3: Values for KI for all steps (28) growth. Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 50 Chart in Fig. 5 shows very similar behavior of experimentally tested specimen and its 3D numerical simulation. Beyond 106 cycles very small number of cycles to collapse is left, and in this area two curves are exactly the same. Generally speaking, one can say that experimental and numerical results agree well, with some differences which require further investigation. 0 1 2 3 4 5 6 7 8 0 200000 400000 600000 800000 1000000 1200000 number of cycles N c ra c k le n g th a [ m m ] XFEM test Figure 5: Comparing curves from experiment and 3D simulation. FATIGUE LIFE PREDICTIONS OF PIPES WITH AXIAL SURFACE CRACK he main technical characteristics of the oil rigs from where the observed pipe are as follows, [4]:  layer pressure (Kp-31): maximum=10.01 [MPa], minimum=7.89 [MPa],  layer temperature: T=65 [°C],  number of strokes of pump rod: nPR=9.6 [min-1]. The geometry used in simulations is pipe with axial surface crack in the base metal (BM), Fig. 6. The pipe is made of API J55. On the outer surface of the pipe there is an initial axial surface crack with dimensions: a=3.5 mm and 2c=200 mm. The wall thickness is 6.98 mm. Figure 6: Geometry of pipe. A finite element model of the pipe was created using the Abaqus software. The initial crack length used in the analysis was 200 mm, and it was 3.5 mm deep (the wall thickness is 6.98 mm). Mesh was refined around the initial crack, and a uniform template of elements was used. The growing crack was incremented at steps of 0.2 mm. The first step was crack opening, and after that, the crack was growing through the inner side of wall, in radial and axial direction, while, in 7th step, it becomes through-wall crack. Fig. 7 shows the crack growth at beginning (1st step - crack opening), whereas Fig. 8 shows crack growth after 7th step when the crack “breaks” through the wall. Afterwards, crack grows in axial direction only T Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 51 through inner side of the wall, and “outer” initial crack remains the same as it was in the beginning of simulation, until 64th step, when “inner” and “outer” crack become equal, 200 mm long, and it has become complete through-wall crack, Fig. 9. Further crack growth is in axial direction until the final step of 3D simulation, when the crack is 209.42 mm long. Fig. 10 shows 3D chart of “inner” and “outer” crack growing. Figure 7: Step 1 - crack opening and Von Mises stresses at crack tips. Figure 8: The 7th step – crack became through-wall and stresses around the crack. Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 52 Figure 9: Step 64 when “inner” and “outer” crack going to be equal (crack length is 200 mm) and stresses around the crack. Figure 10: The 3D chart of “inner” and “outer” crack growing. The prediction of crack growth rate and residual strength of pipe demands accurate calculation of stress intensity factors (SIFs), which determine the appropriate crack growth increment for the crack. This calculation was performed 100 times in order to simulate incremental crack growth. The obtained relationship between equivalent stress intensity factor Keq and crack length a, Fig. 11, shows tendency of increasing Keq with increased crack length a, while the crack was reached up to 210 mm. The fastest increase of Keq, as expected, was before the seventh step, when crack penetrated the pipe wall. The chart in Fig. 12 shows the obtained relationship between steps and number of cycles. After the 7th step, when the crack penetrates the pipe wall, the number of cycles becomes significantly lower and remains at about the same values until the final step. The chart in the Fig. 13 shows the obtained relationship between the crack length a [mm] and the total number of cycles N. For crack growth from initial crack length until final length of 209.42 mm, 10548 cycles are necessary. Obviously, the most of them occur until the seventh step, in which the crack becomes through-wall crack (8606 cycles), while the further cracks growth requires a very small number of cycles. Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 53 0 1000 2000 3000 4000 5000 6000 7000 8000 0 20 40 60 80 100 120 step of propagation K e q [ M P a m m 1/ 2 ] Figure 11: Relationship between equivalent stress intensity factor Keq and propagation step. 1 10 100 1000 10000 0 20 40 60 80 100 120 Step cy cl es n u m b er l o g N Figure 12: Obtained relationship between steps and number of cycles. 0 50 100 150 200 250 0 2000 4000 6000 8000 10000 12000 Number of cycles N C ra c k le n g th a [ m m ] Figure 13: Relationship between crack length a and number of cycles N using 3D simulation. CONCLUSION ased on the presented results, one can conclude that experimental and numerical results agree well, with some differences which require further investigation. Therefore, the obtained stress intensity factor histories can be used to predict fatigue crack growth rates. B Lj. L. Vulićević et alii, Frattura ed Integrità Strutturale, 36 (2016) 46-54; DOI: 10.3221/IGF-ESIS.36.05 54 Based on the obtained values for KIc for the BM, HAZ and WM, one can conclude that the BM has the lowest resistance to crack initiation and propagation. The fatigue crack simulation for a surface crack in BM, with depth approximately half of the thickness (3.5 vs. 6.98 mm), and initial length 200 mm, indicated 8606 cycles needed for crack to grow through the whole thickness, and 10548 cycles to grow up to the final length of 209.42 mm, i.e. relatively fast growth once it became through-wall crack. REFERENCES [1] Gubeljak N., Predan J., Kozak D., Leak-Before-Break Analysis of a Pressurizer - Estimation of the Elastic-Plastic Semi-elliptical Through Wall Crack Opening Displacement. Structural Integrity and Life. 12(1) (2012) 31-37. [2] Lazić V.-Lj., Arsić, M., Šarkoćević, Ž., Sedmak, A., Rakin, M., Structural life assessment of oil rig pipes made of API J55 steel by high frequency welding, Technical Gazette, 20(6) (2013) 1091-1094. [3] Belytschko, T., Lu, Y. Y., Gu, I. L., Element-free Galerkin methods, International Journal for Numerical Methods in Engineering, 37 (1994) 229. << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. 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