Elasto-plastic fatigue crack growth analysis of plane problems in the presence of flaws using XFEM

doi:10.1007/s11709-015-0305-y

Frontiers of Structural and Civil Engineering

2015, Vol. 9

Issue (4): 420-440 https://doi.org/10.1007/s11709-015-0305-y

本期目录

Elasto-plastic fatigue crack growth analysis of plane problems in the presence of flaws using XFEM

Sachin KUMAR,A. S. SHEDBALE,I. V. SINGH(

),B. K. MISHRA

Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee 247667, India

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Abstract：

In this paper, elasto-plastic XFEM simulations have been performed to evaluate the fatigue life of plane crack problems in the presence of various defects. The stress-strain response of the material is modeled by Ramberg-Osgood equation. The von-Mises failure criterion has been used with isotropic hardening. The J-integral for two fracture modes (mode-I and mode-II) is obtained by decomposing the displacement and stress fields into their symmetric and antisymmetric parts, then individual stress intensity factors are extracted from J-integral. The fatigue life obtained by EPFM is found quite close to that obtained by LEFM.

Key words： XFEM von-Mises yield criterion isotropic hardening fatigue crack growth J-integral

收稿日期: 2015-03-30 出版日期: 2015-11-26

Corresponding Author(s): I. V. SINGH

引用本文:

. [J]. Frontiers of Structural and Civil Engineering, 2015, 9(4): 420-440.
Sachin KUMAR,A. S. SHEDBALE,I. V. SINGH,B. K. MISHRA. Elasto-plastic fatigue crack growth analysis of plane problems in the presence of flaws using XFEM. Front. Struct. Civ. Eng., 2015, 9(4): 420-440.

链接本文:

https://academic.hep.com.cn/fsce/CN/10.1007/s11709-015-0305-y
https://academic.hep.com.cn/fsce/CN/Y2015/V9/I4/420

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1	Wolf E. Fatigue crack closure under cyclic tension. Engineering Fracture Mechanics, 1970, 2(1): 37–45
2	Guo W, Wang C H, Rose L R F. Influence of cross-sectional thickness on fatigue crack growth. Fatigue & Fracture of Engineering Materials & Structure, 1999, 22(5): 437–444
3	de Matos P F P, Nowell D. Experimental and numerical investigation of thickness effects in plasticity-induced fatigue crack closure. International Journal of Fatigue, 2009, 31(11–12): 1795–1804
4	Antunes F V, Branco R, Costa J D, Rodrigues M. Plasticity induced crack closure in middle-crack tension specimen: Numerical versus experimental. Fatigue & Fracture of Engineering Materials & Structure, 2010, 33(10): 673–686
5	Newman J C Jr. A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading. ASTM STP 748, Philadelphia, PA, 1981, 53–84
6	Budiansky B, Hutchinson J W. Analysis of closure in fatigue crack growth. ASME Journal of Applied Mechanics, 1992, 42: 389–400
7	Newman J C Jr. Finite element analysis of fatigue crack closure. ASTM STP 590, Philadelphia, PA, 1976, 281–301
8	Blom A F, Holm D K. An experimental and numerical study of crack closure. Engineering Fracture Mechanics, 1985, 22(6): 997–1011
9	McClung R C, Thacker B H, Roy S. Finite element visualization of fatigue crack closure in plane stress and plane strain. International Journal of Fracture, 1991, 50: 27–49
10	Solanki K, Daniewicz S R, Newman J C Jr. Finite element modeling of plasticity-induced crack closure with emphasis on geometry and mesh refinement effects. Engineering Fracture Mechanics, 2003, 70(12): 1475–1489
11	Alizadeh H, Hills D A, de Matos P F P, Nowell D, Pavier M J, Paynter R J, Smith D J, Simandjuntak S. A comparison of two and three-dimensional analysis of fatigue crack closure. International Journal of Fatigue, 2007, 29(2): 222–231
12	Ellyin F, Ozah F. The effect of material model in describing mechanism of plasticity-induced crack closure under variable cyclic loading. International Journal of Fracture, 2007, 143(1): 15–33
13	Toribio J, Kharin V. Finite-deformation analysis of the crack-tip fields under cyclic loading. International Journal of Solids and Structures, 2009, 46(9): 1937–1952
14	Cheung S, Luxmoore A R. A finite element analysis of stable crack growth in an aluminium alloy. Engineering Fracture Mechanics, 2003, 70(9): 1153–1169
15	Yan A M, Nguyen-Dang H. Multiple-cracked fatigue crack growth by BEM. Computational Mechanics, 1995, 16(5): 273–280
16	Yan X. A boundary element modeling of fatigue crack growth in a plane elastic plate. Mechanics Research Communications, 2006, 33(4): 470–481
17	Belytschko T, Gu L, Lu Y Y. Fracture and crack growth by element-free Galerkin methods. Modelling and Simulation in Materials Science and Engineering, 1994, 2(3A): 519–534
18	Belytschko T, Lu Y Y, Gu L. Crack propagation by element-free Galerkin methods. Engineering Fracture Mechanics, 1995, 51(2): 295–315
19	Duflot M, Nguyen-Dang H. Fatigue crack growth analysis by an enriched meshless method. Journal of Computational and Applied Mathematics, 2004, 168(1–2): 155–164
20	Rabczuk T, Belytschko T. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799
21	Rabczuk T, Areias P M A, Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. International Journal for Numerical Methods in Engineering, 2007, 72(5): 524–548
22	Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495
23	Rabczuk T, Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering, 2008, 197(6–8): 641–658
24	Bordas S, Rabczuk T, Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engineering Fracture Mechanics, 2008, 75(5): 943–960
25	Nguyen V P, Rabczuk T, Bordas S, Duflot M. Meshless methods: A review and computer implementation aspects. Mathematics and Computers in Simulation, 2008, 79(3): 763–813
26	Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 1999, 45(5): 601–620
27	Stolarska M, Chopp D, Moes N, Belytschko T. Modeling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering, 2001, 51(8): 943–960
28	Sukumar N, Chopp D L, Moes N, Belytschko T. Modeling of holes and inclusions by level sets in the extended finite element method. Computer Methods in Applied Mechanics and Engineering, 2001, 190(46–47): 6183–6200
29	Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
30	Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49
31	Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
32	Rabczuk T, Zi G, Gerstenberger A, Wall W A. A new crack tip element for the phantom-node method with arbitrary cohesive cracks. International Journal for Numerical Methods in Engineering, 2008, 75(5): 577–599
33	Bordas S P A, Rabczuk T, Hung N X, Nguyen V P, Natarajan S, Bog T, Quan D M, Hiep N V. Strain smoothing in FEM and XFEM. Computers & Structures, 2010, 88(23–24): 1419–1443
34	Bordas S P A, Natarajan S, Kerfriden P, Augarde C E, Mahapatra D R, Rabczuk T, Pont S D. On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM). International Journal for Numerical Methods in Engineering, 2011, 86(4–5): 637–666
35	Budarapu P R, Gracie R, Yang S W, Zhuang X, Rabczuk T. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143
36	Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57
37	Bhardwaj G, Singh I V, Mishra B K. Stochastic fatigue crack growth simulation of interfacial crack in bi-layered FGMs using XIGA. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 186–229
38	Kumar S, Singh I V, Mishra B K, Rabczuk T. Modeling and simulation of kinked cracks by virtual node XFEM. Computer Methods in Applied Mechanics and Engineering, 2015, 283: 1425–1466
39	Singh I V, Mishra B K, Bhattacharya S, Patil R U. The numerical simulation of fatigue crack growth using extended finite element method. International Journal of Fatigue, 2012, 36(1): 109–119
40	Dolbow J, Moes N, Belytschko T. An extended finite element method for modelling crack growth with frictional contact. Computer Methods in Applied Mechanics and Engineering, 2001, 190(51–52): 6825–6846
41	Moes N, Gravouil A, Belytschko T. Non-planar 3D crack growth with the extended finite element and level set−Part I: Mechanical model. International Journal for Numerical Methods in Engineering, 2002, 53: 2549–2568
42	Pathak H, Singh A, Singh I V, Yadav S K. A simple and efficient XFEM approach for 3-D cracks simulations. International Journal of Fracture, 2013, 181(2): 189–208
43	Rethore J, Gravouil A, Combescure A. An energy-conserving scheme for dynamic crack growth using the extended finite element method. International Journal for Numerical Methods in Engineering, 2005, 63(5): 631–659
44	Kumar S, Singh I V, Mishra B K, Singh A. New enrichments in XFEM to model dynamic crack response of 2-D elastic solids. International Journal of Impact Engineering, 2015
45	Natarajan S, Baiz P M, Bordas S, Rabczuk T, Kerfriden P. Natural frequencies of cracked functionally graded material plates by the extended finite element method. Composite Structures, 2011, 93(11): 3082–3092
46	Baiz P M, Natarajan S, Bordas S P A, Kerfriden P, Rabczuk T. Linear buckling analysis of cracked plates by SFEM and XFEM. Journal of Mechanics of Materials and Structures, 2011, 6(9–10): 1213–1238
47	Vu-Bac N, Nguyen-Xuan H, Chen L, Bordas S, Kerfriden P, Simpson R N, Liu G R, Rabczuk T. A Node-based smoothed extended finite element method (NS-XFEM) for fracture analysis, CMES. Computer Modeling in Engineering & Sciences, 2011, 73: 331–356
48	Chen L, Rabczuk T, Bordas S P A, Liu G R, Zeng K Y, Kerfriden P. Extended finite element method with edge-based strain smoothing (Esm-XFEM) for linear elastic crack growth. Computer Methods in Applied Mechanics and Engineering, 2012, 209–212: 250–265
49	Legrain G, Moes N, Verron E. Stress analysis around crack tips in finite strain problems using the extended finite element method. International Journal for Numerical Methods in Engineering, 200<?Pub Caret?>5, 63: 209–314
50	Ji H, Chopp D, Dolbow J E. A hybrid finite element/level set method for modelling phase transformation. International Journal for Numerical Methods in Engineering, 2002, 54(8): 1209–1233
51	Elguedj T, Gravouil A, Combescure A. A mixed augmented Lagrangian-extended finite element method for modeling elastic-plastic fatigue crack growth with unilateral contact. International Journal for Numerical Methods in Engineering, 2007, 71(13): 1569–1597
52	Kumar S, Singh I V, Mishra B K. XFEM simulation of stable crack growth using J-R curve under finite strain plasticity. International Journal of Mechanics and Materials in Design, 2014, 10(2): 165–177
53	Budarapu P R, Gracie R, Bordas S P A, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148
54	Yang S W, Budarapu P R, Mahapatra D R, Bordas S P A, Zi G, Rabczuk T. A meshless adaptive multiscale method for fracture. Computational Materials Science, 2015, 96: 382–395
55	Nanthakumar S S, Lahmer T, Rabczuk T. Detection of multiple flaws in piezoelectric structures using XFEM and level sets. Computer Methods in Applied Mechanics and Engineering, 2014, 275: 98–112
56	Kumar S, Singh I V, Mishra B K. A multigrid coupled (FE-EFG) approach to simulate fatigue crack growth in heterogeneous materials. Theoretical and Applied Fracture Mechanics, 2014, 72: 121–135
57	Kumar S, Singh I V, Mishra B K. A homogenized XFEM approach to simulate fatigue crack growth problems. Computers & Structures, 2015, 150: 1–22
58	Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464
59	Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535
60	Hinton E, Owen D. Finite Element in Plasticity. Pineridge Press Limited, 1980, 215–265
61	Moes N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 1999, 46: 131–150
62	Bland D R. The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids, 1957, 6(1): 71–78
63	Fries T P. A corrected XFEM approximation without problems in blending elements. International Journal for Numerical Methods in Engineering, 2008, 75(5): 503–532
64	McClung R C, Sehitoglu H. On the finite element analysis of fatigue crack closure-1. Basic modeling issues. Engineering Fracture Mechanics, 1983, 33(2): 237–252
65	McClung R C, Sehitoglu H. On the finite element analysis of fatigue crack closure-2. Numerical results. Engineering Fracture Mechanics, 1983, 33(2): 253–257
66	Solanki K, Daniewicz S R, Newman J C Jr. A new methodology for computing crack opening values from finite element analyses. Engineering Fracture Mechanics, 2004, 71(7–8): 1165–1175
67	Elguedj T, Gravouil A, Combescure A. Appropriate extended functions for XFEM simulation of plastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering, 2006, 195(7–8): 501–515
68	Hutchinson J W. Singular behavior at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids, 1968, 16(1): 13–31
69	Rice J R, Rosengren G F. Plane strain deformation near a crack tip in a power-law hardening material. Journal of the Mechanics and Physics of Solids, 1968, 16(1): 1–2
70	Li F Z, Shih C F, Needleman A. A comparison of methods for calculating energy release rates. Engineering Fracture Mechanics, 1985, 21(2): 405–421
71	Ishikawa H. A finite element analysis of stress intensity factors for combined tensile and shear loading by only a virtual crack extension. International Journal of Fracture, 1980, 16(5): 243– 246
72	Bui H D. Associated path independent J-integrals for separating mixed modes. Journal of the Mechanics and Physics of Solids, 1983, 6(6): 439–448
73	Erdogan F, Sih G. On the crack extension in plates under plane loading and transverse shear. Journal of Basic Engineering, 1963, 85(4): 519–527
74	de Matos P F P, Nowell D. On the accurate assessment of crack opening and closing stresses in plasticity-induced fatigue crack closure problems. Engineering Fracture Mechanics, 2007, 74(10): 1579–1601
75	Antunes F V, Chegini A G, Correia L, Branco R. Numerical study of contact forces for crack closure analysis. International Journal of Solids and Structures, 2014, 51(6): 1330–1339
76	Paris P C, Gomez M P, Anderson W E. A rational analytic theory of fatigue. Trend in Engineering, 1961, 13: 9–14

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