journal article·2021-05

Fatigue crack separation and merging simulation using the smoothed particle hydrodynamics

Koki Tazoe, Genki Yagawa

International Journal of Fracture· Volume 229· Issue 1
Publisher page

Abstract

The present paper proposes a new computational method for the fatigue crack propagation in a metallic structure using the smoothed particle hydrodynamics (SPH). First, we discuss how to model the crack front line with C0 continuous elements called chained crack front lines, which resemble those that were experimentally observed. In the second, the detailed algorithm for the chained crack front line is proposed and implemented into the fatigue crack propagation analysis program based on the SPH named as SPH-Fatigue. Third, the present method is applied to the fatigue crack propagation problems with crack separation and merging phenomena, such as the crack propagation passing through a hole or passing through a slit in a T-joint structure. The calculated results show an excellent agreement with time-dependent crack shapes experimentally obtained. We conclude that the idea of chained crack front line discussed in this paper is useful to estimate the time dependent crack shape of real materials and structures.
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Research context

OpenAlex topics: Fluid Dynamics Simulations and Interactions · Numerical methods in engineering · Geotechnical Engineering and Underground Structures

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References (50)

Show source-provided references
1. Aghahosseini A, Khosravifard A, Bui TQ (2019) Efficient analysis of dynamic fracture mechanics in various media by a novel meshfree approach. Theor Appl Fract Mech 99:161–176. https://doi.org/10.1016/j.tafmec.2018.12.00210.1016/j.tafmec.2018.12.002 ↗
2. Ashari SE, Mohammadi S (2011) Delamination analysis of composites by new orthotropic biomaterial extended finite element method. Int J Numer Methods Eng 86:1507–1543. https://doi.org/10.1002/nme.311410.1002/nme.3114 ↗
3. ASTM E647-13a (1992) Standard Test Method for Measurement of Fatigue Crack Growth Rates. Am. Soc. Test. Mater 3(1):674–701
4. Batra RC, Zhang GM (2007) Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method. Comput Mech 40:531–546. https://doi.org/10.1007/s00466-006-0124-z10.1007/s00466-006-0124-z ↗
5. Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int J Numer Methods Eng 45(5):601–620. https://doi.org/10.1002/(SICI)1097-0207(19990620)45:53c601::AID-NME5983e3.0.CO;2-S10.1002/(SICI)1097-0207(19990620)45:53c601::AID-NME5983e3.0.CO;2-S ↗
6. Belytschko T, Lu YY, Gu L (1994) Element-free Galerkin methods. Int J Numer Methods Eng 47(2):229–256. https://doi.org/10.1002/nme.162037020510.1002/nme.1620370205 ↗
7. Belytschko T, Gu L, Lu YY (1994) Fracture and crack growth by element free Galerkin methods. Model Simul Mater Sci Eng 2(3A):519–534. https://doi.org/10.1088/0965-0393/2/3a/00710.1088/0965-0393/2/3a/007 ↗
8. Belytschko T, Lu YY, Gu L (1995) Crack propagation by element-free Galerkin methods. Eng Fracture Mech 51(2):295–315. https://doi.org/10.1016/0013-7944(94)00153-910.1016/0013-7944(94)00153-9 ↗
9. Bhowmick S, Liu GR (2018) A phase-field modeling for brittle fracture and crack propagation based on the cell-based smoothed finite element method. Eng Fracture Mech 204:369–387. https://doi.org/10.1016/j.engfracmech.2018.10.02610.1016/j.engfracmech.2018.10.026 ↗
10. Bhowmick S, Liu GR (2018) Three dimensional CS-FEM phase-field modeling technique for brittle fracture in elastic solids. Comput Methods Fracture 8(12):2488–2507. https://doi.org/10.3390/app812248810.3390/app8122488 ↗
11. Chopp DL, Sukumar N (2003) Fatigue crack propagation of multiple coplanar cracks with the coupled extended finite element/fast marching method. Int J Eng Sci 41(8):845–869. https://doi.org/10.1016/S0020-7225(02)00322-110.1016/S0020-7225(02)00322-1 ↗
12. Colombo D (2012) An implicit geometrical approach to level sets update for 3D non planar X-FEM crack propagation. Comput Methods Appl Mech Eng 237–240:39–50. https://doi.org/10.1016/j.cma.2012.04.02010.1016/j.cma.2012.04.020 ↗
13. Colombo D, Massin P (2011) Fast and robust level set update for 3D non-planar X-FEM crack propagation modelling. Comput Methods Appl Mech Eng 200:2160–2180. https://doi.org/10.1016/j.cma.2011.03.01410.1016/j.cma.2011.03.014 ↗
14. Dassault Systèmes (2015) Abaqus 6.14 analysis user’s manual
15. Fish J, Markolefas S, Guttal R, Nayak P (1994) On adaptive multilevel superposition of finite element meshes for linear elastostatics. Appl Numer Math 14(1–3):135–164. https://doi.org/10.1016/0168-9274(94)90023-X10.1016/0168-9274(94)90023-X ↗
16. Géniaut S, Massin P, Moës N (2007) A stable 3d contact formulation for cracks using X-FEM. Euro J Comput Mech 16(2):259–275. https://doi.org/10.3166/remn.16.259-27510.3166/remn.16.259-275 ↗
17. Giner E, Sukumar N, Tarancón JE, Fuenmayor FJ (2009) An Abaqus implementation of the extended finite element method. Eng Fracture Mech 76:347–368. https://doi.org/10.1016/j.engfracmech.2008.10.01510.1016/j.engfracmech.2008.10.015 ↗
18. Gravouil A, Moës N, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets-part II: level set update. Int J Numer Methods Eng 53:2569–2586. https://doi.org/10.1002/nme.43010.1002/nme.430 ↗
19. Hušek M, Kala J, Hokeš F, Král P (2016) Influence of SPH regularity and parameters in dynamic fracture phenomena. Procedia Eng 161:489–496. https://doi.org/10.1016/j.proeng.2016.08.67110.1016/j.proeng.2016.08.671 ↗
20. Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–36410.1115/1.4011547 ↗
21. Japan Ship Technology Research Association (1979) Ship research summary report SR169:137-147 (in Japanese). http://www.jstra.jp/html/PDF/SR169-5303.pdf. Accessed 16 Oct, 2020
22. Kashfi M, Ghazi A, Ghavamian A (2014) Numerical study on fracture patterns and crack growth on concrete under impact loading. Proceedings of the WCCM11 conference; 2014 July 20–25; Barcelona, Spain. IACM. https://www.researchgate.net/publication/288824909_Numerical_study_on_fracture_patterns_and_crack_growth_on_concrete_under_impact_loading. Accessed 16 October 2020
23. Kikuchi M, Takahashi M, Wada Y, Li Y (2008) Fatigue crack growth simulation using S-version FEM-2nd report: study on interaction of two parallel cracks. Trans JSME A 74(745):1243-1248. https://doi.org/10.1299/kikaia.74.1243(in Japanese)10.1299/kikaia.74.1243 ↗
24. Kikuchi M, Wada Y, Takahashi M, Li Y (2008) Fatigue crack growth simulation using S$$-$$version FEM. Adv Mater Res 33(37):133–138. https://doi.org/10.4028/www.scientific.net/AMR.33-37.13310.4028/www.scientific.net/AMR.33-37.133 ↗
25. Kikuchi M, Wada Y, Utsunomiya A, Suyama H (2009) Fatigue crack growth simulation using S$$-$$version FEM-3rd report: Fatigue of 3D surface crack. Trans JSME A 75(755):142-148. https://doi.org/10.1299/kikaia.75.918(in Japanese)10.1299/kikaia.75.918 ↗
26. Liu GR, Nourbakhshnia N, Zhang YW (2009) A novel singular ES-FEM method for simulating singular stress fields near the crack tips for linear fracture problems. Eng Fracture Mech 78(6):863–876. https://doi.org/10.1016/j.engfracmech.2009.11.00410.1016/j.engfracmech.2009.11.004 ↗
27. Liu GR, Chen L, Nguyen-Thoi T, Zeng KY, Zhang GY (2010) A novel singular node-based smoothed finite element method (NS-FEM) for upper bound solutions of fracture problems. Int J Numer Meth Eng 83(11):1466–1497. https://doi.org/10.1002/nme.286810.1002/nme.2868 ↗
28. Lucy LB (1977) A numerical approach to the testing of the fission hypothesis. Astronom J 8:1013–1024. https://doi.org/10.1086/11216410.1086/112164 ↗
29. Maeda K, Tanaka S, Takei T (2017) Bifurcation and unification of fatigue cracks by X-FEM. Proceedings of the 30th CMD conference; 2017 Sep 16–18; Tokushima, Japan. JSME (in Japanese. https://doi.org/10.1299/jsmecmd.2017.30.32710.1299/jsmecmd.2017.30.327 ↗
30. Massin P, Ferté G, Moët N (2015) 3D crack propagation with XFEM cohesive elements. Proceedings of the SMiRT-23 conference; 2015 Aug 10-14; Manchester, UK. IASMiRT. https://pdfs.semanticscholar.org/3cb0/49cc572a96b19be8d6092d3dc037da5f8bfc.pdf. Accessed 16 Oct, 2020
31. Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150. https://doi.org/10.1002/(SICI)1097-0207(19990910)46:13c131::AID-NME7263e3.0.CO;2-J10.1002/(SICI)1097-0207(19990910)46:13c131::AID-NME7263e3.0.CO;2-J ↗
32. Moës N, Gravouil A, Belytschko T (2002) Non-planar 3D crack growth by the extended finite element and level sets-part I: mechanical model. Int J Numer Methods Eng 53:2549–2568. https://doi.org/10.1002/nme.42910.1002/nme.429 ↗
33. Nagashima T, Sawada M (2012) Two-dimensional crack analyses by XFEM using crack tip elements. Trans JSME A 78(796):1642-1655. https://doi.org/10.1299/kikaia.78.1642(in Japanese)10.1299/kikaia.78.1642 ↗
34. Nguyen-Xuan H, Liu GR, Nourbakhshnia N, Chen L (2012) A novel singular ES-FEM for crack growth simulation. Eng Fracture Mech 84:41–66. https://doi.org/10.1016/j.engfracmech.2012.01.00110.1016/j.engfracmech.2012.01.001 ↗
35. Nguyen-Xuan H, Liu GR, Bordas S, Natarajan S, Rabczuk T (2013) An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order. Comput Meth Appl Mech Eng 253:252–273. https://doi.org/10.1016/j.cma.2012.07.01710.1016/j.cma.2012.07.017 ↗
36. Nishioka T, Lee H, Won Y, Fujimoto T (2012) Evaluation of fatigue crack growth behavior in materials with lubricating oil holes. J JIME 47(5):89-94. https://doi.org/10.5988/jime.47.723(in Japanese)10.5988/jime.47.723 ↗
37. Paris P, Erdogan F (1963) A critical analysis of crack propagation laws. J Basic Eng 85(4):528–534. https://doi.org/10.1115/1.365690010.1115/1.3656900 ↗
38. Shi J, Chopp D, Lua J, Sukumar N, Belytschko T (2010) Abaqus implementation of extended finite element method using a level set representation of three-dimensional fatigue crack growth and life predictions. Eng Fracture Mech 77:2840–2863. https://doi.org/10.1016/j.engfracmech.2010.06.00910.1016/j.engfracmech.2010.06.009 ↗
39. Sukumar N, Chopp DL, Moran B (2003) Extended finite element method and fast marching method for three-dimensional fatigue crack propagation. Eng Fracture Mech 70:29–48. https://doi.org/10.1016/S0013-7944(02)00032-210.1016/S0013-7944(02)00032-2 ↗
40. Sukumar N, Huang ZY, Prévost JH, Suo Z (2004) Partition of unity enrichment for bimaterial interface cracks. Int J Numer Methods Eng 59:1075–1102. https://doi.org/10.1002/nme.90210.1002/nme.902 ↗
41. Sukumar N, Chopp DL, Béchet E, Moës N (2008) Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method. Int J Numer Methods Eng 76:727–748. https://doi.org/10.1002/nme.234410.1002/nme.2344 ↗
42. Tazoe K, Hamada S, Noguchi H (2017) Fatigue crack growth behavior of JIS SCM440 steel near fatigue threshold in 9 MPa hydrogen gas environment. Int J Hydrog Energy 42(18):13158–13170. https://doi.org/10.1016/j.ijhydene.2017.03.22310.1016/j.ijhydene.2017.03.223 ↗
43. Tazoe K, Tanaka H, Oka M, Yagawa G (2020) Near-threshold fatigue crack propagation without oxide-induced crack closure. Sci Rep 10:7926. https://doi.org/10.1038/s41598-020-64915-310.1038/s41598-020-64915-3 ↗
44. Tazoe K, Tanaka H, Oka M, Yagawa G (2020) An approach for fatigue crack propagation analysis by smoothed particle hydrodynamics method. Strength Fracture Complex 12:127–133. https://doi.org/10.3233/SFC-19024210.3233/SFC-190242 ↗
45. Tazoe K, Tanaka H, Oka M, Yagawa G (2020) Analyses of fatigue crack propagation with smoothed particle hydrodynamics method. Eng Fracture Mech 224:106819. https://doi.org/10.1016/j.engfracmech.2019.10681910.1016/j.engfracmech.2019.106819 ↗
46. Tazoe K, Oda Y, Noguchi H (2012) Hydrogen gas effects on the fatigue crack growth behavior of Cr-Mo steel CT specimen in extremely low rate range. Proceedings of the ECF19 conference; 2012 Aug 26-31; Kazan, Russian Federation. ESIS. https://kyushu-u.pure.elsevier.com/en/publications/hydrogen-gas-effects-on-the-fatigue-crack-growth-behavior-of-cr-m. Accessed 16 Oct, 2020
47. Uchibori C J, Sakuyama S, Sakai Y, Su-I T, Watanabe T, Yamagata N (2014) Solder crack simulation using SPH particle method with sub-modeling technique. Proceedings of the international conference on electronics packaging & iMAPS all Asia conference; 2014 Apr 23–25; Toyama, Japan. IEEE. https://doi.org/10.1109/ICEP.2014.682673010.1109/ICEP.2014.6826730 ↗
48. Wu SC, Zhang SQ, Xu ZW (2016) Thermal crack growth-based fatigue life prediction due to braking for a high-speed railway brake disc. Int J Fatigue 87:359–369. https://doi.org/10.1016/j.ijfatigue.2016.02.02410.1016/j.ijfatigue.2016.02.024 ↗
49. Yagawa G, Furukawa T (2000) Recent developments of free mesh method. Int J Numer Methods Eng 47(8):1419–1443. https://doi.org/10.1002/(SICI)1097-0207(20000320)47:83c1419::AID-NME8373e3.0.CO;2-E10.1002/(SICI)1097-0207(20000320)47:83c1419::AID-NME8373e3.0.CO;2-E ↗
50. Yagawa G, Yamada T (1996) Free mesh method: a new meshless finite element method. Comput Mech 18(5):383–386. https://doi.org/10.1007/BF0037613410.1007/BF00376134 ↗