Perturbation approaches of a planar crack in linear elastic fracture mechanics: A review

Journal of the Mechanics and Physics of Solids

Volumn 59, Issue 2, 2011, Pages 121-144

  Lazarus, V ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Brittle fracture; Crack front deformations; Fatigue; LEFM; Perturbation approach

Indexed keywords

CIRCULAR FRONTS; COALESCENCE OF CRACKS; CRACK FRONTS; CRACK SHAPE; FATIGUE; FRACTURE PROPERTY; HETEROGENEOUS MEDIA; HOMOGENEOUS MEDIA; LEFM; LENGTH SCALE; LINEAR-ELASTIC FRACTURE MECHANICS; NONLINEARITIES; PERTURBATION APPROACH; PERTURBATION METHOD; PLANAR CRACKS; QUASI-STATIC; REALISTIC GEOMETRY; STRAIGHT CRACK;

BRITTLENESS; COALESCENCE; CRACKS; DEFORMATION; FRACTURE MECHANICS; PERTURBATION TECHNIQUES; STRESS INTENSITY FACTORS;

BRITTLE FRACTURE;

EID: 78651322736     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2010.12.006     Document Type: Review

References (130)

1. M. Adda-Bedia, and L. Mahadevan Crack-front instability in a confined elastic film Proceedings of the Royal Society AMathematical Physical and Engineering Sciences 462 2075 2006 3233 3251
2. M. Amestoy, and J.-B. Leblond Crack paths in plane situationsII. Detailed form of the expansion of the stress intensity factors International Journal of Solids and Structures 29 1992 465 501
3. T.L. Anderson Fracture Mechanics: Fundamentals and Applications 1991 CRC Press Inc., Boca Raton, USA
4. Atkinson, B.K., 1987. Fracture Mechanics of Rock. Academic Press Geology Series.
5. A. Aydin, and D.D. Pollard Progress in understanding jointing over the past century Geological Society of America Bulletin 100 1988 1181 1204
6. Barabsi, A.-L., Stanley, H.E., 1995. Fractal Concepts in Surface Growth.
7. Z.P. Bazant, and L. Cedolin Stability of Structures: Elastic, Inelastic, Fracture, and Damage Theories New ed. (February 14, 2003) 2003 Dover Publications
8. A. Benallal, and J.-J. Marigo Bifurcation and stability issues in gradient theories with softening Modelling and Simulation in Materials Science and Engineering 15 2007 S283 S295
9. J. Bercial-Velez, Y. Antipov, and A. Movchan High-order asymptotics and perturbation problems for 3d interfacial cracks Journal of the Mechanics and Physics of Solids 53 5 2005 1128 1162
10. D. Bonamy Intermittency and roughening in the failure of brittle heterogeneous materials Journal of Physics D: Applied Physics 42 21 2009 214014 (21p)
11. E. Bouchbinder, A. Livne, and J. Fineberg Weakly nonlinear fracture mechanics: experiments and theory International Journal of Fracture 162 1 2010 3 20
12. B. Bourdin, G. Francfort, and J.-J. Marigo The variational approach to fracture Journal of Elasticity 91 1 2008 5 148
13. B. Bourdin, G.A. Francfort, and J.J. Marigo Numerical experiments in revisited brittle fracture Journal of the Mechanics and Physics of Solids 48 4 2000 797 826
14. A.F. Bower, and M. Ortiz Solution of three-dimensional crack problems by a finite perturbation method Journal of the Mechanics and Physics of Solids 38 4 1990 443 480
15. A.F. Bower, and M. Ortiz A three-dimensional analysis of crack trapping and bridging by tough particles Journal of the Mechanics and Physics of Solids 39 6 1991 815 858
16. A.F. Bower, and M. Ortiz An analysis of crack trapping by residual stresses in brittle solids Transactions of the ASME. Journal of Applied Mechanics 60 1 1993 175 182
17. K.B. Broberg Cracks and Fracture 1999 Academic Press
18. B. Budiansky, J.C. Amazigo, and A.G. Evans Small-scale crack bridging and the fracture toughness of particulate-reinforced ceramics Journal of the Mechanics and Physics of Solids 36 2 1988 167 187
19. H.F. Bueckner A novel principle for the computation of stress intensity factors Zeitschrift fur Angewandte Mathematik und Mechanik 50 9 1970 529 546
20. H.F. Bueckner Weight functions and fundamental fields for the penny-shaped and the half-plane crack in three-space International Journal of Solids and Structures 23 1 1987 57 93
21. G. Caginalp, and P. Fife Phase field methods for interfacial boundaries Physical Review B 33 1986 7792 7794
22. A. Chambolle, G. Francfort, and J.-J. Marigo When and how do cracks propagate? Journal of the Mechanics and Physics of Solids 57 9 2009 1614 1622
23. M. Ciavarella, M. Paggi, and A. Carpinteri One, no one, and one hundred thousand crack propagation laws: a generalized barenblatt and botvina dimensional analysis approach to fatigue crack growth Journal of the Mechanics and Physics of Solids 56 12 2008 3416 3432
24. J.B. Collins, and H. Levine Diffuse interface model of diffusion-limited crystal growth Physical Review B 31 1985 6119 6122
25. M.L. Cooke, and D.D. Pollard Fracture propagation paths under mixed mode loading within rectangular blocks of polymethyl methacrylate Journal of Geophysical Research 101 B2 1996 3387 3400
26. F. Corson, M. Adda-Bedia, H. Henry, and E. Katzav Thermal fracture as a framework for quasi-static crack propagation International Journal of Fracture 158 1 2009 1 14
27. B. Cotterell, and J.R. Rice Slightly curved or kinked cracks International Journal of Fracture 16 2 1980 155 169
28. P. Daguier, E. Bouchaud, and G. Lapasset Roughness of a crack front pinned by microstructural obstacles EPL (Europhysics Letters) 31 7 1995 367 372
29. D. Dalmas, E. Barthel, and D. Vandembroucq Crack front pinning by design in planar heterogeneous interfaces Journal of the Mechanics and Physics of Solids 57 3 2009 446 457
30. A. Delaplace, J. Schmittbuhl, and K.J. Maløy High resolution description of a crack front in a heterogeneous plexiglas block Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics) 60 2 1999 1337 1343
31. V. Doquet, and G. Bertolino Local approach to fatigue cracks bifurcation International Journal of Fatigue 30 5 2008 942 950
32. P.G. Drazin Nonlinear Systems 1992 Press Syndicate of the University of Cambridge Cambridge
33. G. Erdogan, and P. Paris A critical analysis of crack propagation laws ASME Journal of Basic Engineering Transactions 85 1963 528 534
34. G. Erdogan, and G.C. Sih On the crack extension in plates under plane loading and transverse shear ASME J. Basic Eng. 85 1963 519 527
35. F. Family, and T. Vicsek Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model Journal of Physics A: Mathematical and General 18 2 1985 L75
36. E. Favier, V. Lazarus, and J.-B. Leblond Coplanar propagation paths of 3D cracks in infinite bodies loaded in shear International Journal of Solids and Structures 43 78 2006 2091 2109
37. E. Favier, V. Lazarus, and J.-B. Leblond Statistics of the deformation of the front of a tunnel-crack propagating in some inhomogeneous medium Journal of the Mechanics and Physics of Solids 54 7 2006 1449 1478
38. J. Fineberg, and M. Marder Instability in dynamic fracture Physics ReportsReview Section of Physics Letters 313 12 1999 2 108
39. D.S. Fisher, K. Dahmen, S. Ramanathan, and Y. Ben-Zion Statistics of earthquakes in simple models of heterogeneous faults Physical Review Letters 78 25 1997 4885 4888
40. N. Fleck, K. Kang, and M. Ashby Overview no. 112: the cyclic properties of engineering materials Acta Metallurgica et Materialia 42 2 1994 365 381
41. G.A. Francfort, and J.J. Marigo Revisiting brittle fracture as an energy minimization problem Journal of the Mechanics and Physics of Solids 46 1998 1319 1342
42. L. Freund Crack propagation in an elastic solid subjected to general loadingi. Constant rate of extension Journal of the Mechanics and Physics of Solids 20 3 1972 129 140
43. L. Freund Crack propagation in an elastic solid subjected to general loadingii. Non-uniform rate of extension Journal of the Mechanics and Physics of Solids 20 3 1972 141 152
44. L. Freund Crack propagation in an elastic solid subjected to general loadingiii. Stress wave loading Journal of the Mechanics and Physics of Solids 21 2 1973 47 61
45. L.B. Freund Crack propagation in an elastic solid subjected to general loadingiv. Obliquely incident stress pulse Journal of the Mechanics and Physics of Solids 22 3 1974 137 146
46. L.B. Freund Substrate curvature due to thin film mismatch strain in the nonlinear deformation range Journal of the Mechanics and Physics of Solids 48 67 2000 1159 1174
47. H. Gao Nearly circular shear mode cracks International Journal of Solids and Structures 24 2 1988 177 193
48. H. Gao, and J.R. Rice Shear stress intensity factors for planar crack with slightly curved front ASME Journal of Applied Mechanics 53 4 1986 774 778 (Pubitemid 17495483)
49. H. Gao, and J.R. Rice Nearly circular connections of elastic half spaces ASME Journal of Applied Mechanics 54 4 1987 627 634
50. H. Gao, and J.R. Rice Somewhat circular tensile cracks International Journal of Fracture 33 3 1987 155 174
51. H. Gao, and J.R. Rice A first-order perturbation analysis of crack trapping by arrays of obstacles Transactions of the ASME 56 1989 828 836
52. H. Gao, J.R. Rice, and J. Lee Penetration of a quasi-statically slipping crack into a seismogenic zone of heterogeneous fracture resistance Journal of Geophysical Research 96 B13 1991 21535 21548
53. G. Gauthier, V. Lazarus, and L. Pauchard Shrinkage star-shaped cracks: explaining the transition from 90 degrees to 120 degrees Europhysics Letters 89 2010 26002
54. A. Ghatak, and M.K. Chaudhury Adhesion-induced instability patterns in thin confined elastic film Langmuir 19 7 2003 2621 2631
55. L. Goehring, L. Mahadevan, and S.W. Morris Nonequilibrium scale selection mechanism for columnar jointing Proceedings of the National Academy of Sciences 106 2 2009 387 392
56. R.V. Goldstein, and R.L. Salganik Brittle fracture of solides with arbitrary cracks Int. J. Fract. 10 1974 507 523
57. A.A. Griffith The phenomena of rupture and flow in solids Philosophical Transactions of the Royal Society of London 221 1920 163 198
58. M. Grob, J. Schmittbuhl, R. Toussaint, L. Rivera, S. Santucci, and K.J. Maloy Quake catalogs from an optical monitoring of an interfacial crack propagation Pure and Applied Geophysics 166 57 2009 777 799
59. V. Hakim, and A. Karma Laws of crack motion and phase-field models of fracture Journal of the Mechanics and Physics of Solids 57 2 2009 342 368
60. A. Hansen, and J. Schmittbuhl Origin of the universal roughness exponent of brittle fracture surfaces: stress-weighted percolation in the damage zone Physical Review Letters 90 4 2003 045504/1 4
61. H. Henry, and H. Levine Dynamic instabilities of fracture under biaxial strain using a phase field model Physical Review Letters 93 10 2004 105504
62. D. Hull Tilting cracks: the evolution of fracture surface topology in brittle solids International Journal of Fracture 62 2 1993 119 138
63. G.R. Irwin Analysis of stresses and strains near the end of a crack traversing a plate Journal of Applied Mechanics 24 1957 361 364
64. G.R. Irwin Fracture Handbuch der Physik vol. IV 1958 Springer Berlin
65. M. Kardar Nonequilibrium dynamics of interfaces and lines Physics ReportsReview Section of Physics Letters 301 13 1998 85 112
66. A. Karma, D.A. Kessler, and H. Levine Phase-field model of mode III dynamic fracture Physical Review Letters 87 2001 045501
67. M.K. Kassir, and G. Sih Three Dimensional Crack Problems 1975 Nordhoff International Publishing Leyden, The Netherlands
68. E. Katzav, and M. Adda-Bedia Roughness of tensile crack fronts in heterogenous materials Europhysics Letters 76 3 2006 450 456
69. B. Kostrov On the crack propagation with variable velocity International Journal of Fracture 11 1975 47 56
70. G. Lancioni, and G. Royer-Carfagni The variational approach to fracture mechanics. A practical application to the French Panthon in Paris Journal of elasticity 95 12 2009 1 30
71. F.F. Lange The interaction of a crack front with a second-phase dispersion Philosophical Magazine 22 179 1970
72. V. Lazarus Brittle fracture and fatigue propagation paths of 3D plane cracks under uniform remote tensile loading International Journal of Fracture 122 12 2003 23 46
73. V. Lazarus, F.-G. Buchholz, M. Fulland, and J. Wiebesiek Comparison of predictions by mode II or mode III criteria on crack front twisting in three or four point bending experiments International Journal of Fracture 153 2008 141 151
74. V. Lazarus, and J.-B. Leblond Crack paths under mixed mode (IIII) or (IIIIII) loadings Comptes Rendus de l'Acadmie des Sciences, Srie II (Mcanique, Physique, Astronomie) 326 3 1998 171 177
75. V. Lazarus, and J.-B. Leblond Three-dimensional crack-face weight functions for the semi-infinite interface crack. I. Variation of the stress intensity factors due to some small perturbation of the crack front Journal of the Mechanics and Physics of Solids 46 3 1998 489 511
76. V. Lazarus, and J.-B. Leblond Crack front stability for a tunnel-crack propagating along its plane in mode 23 Comptes Rendus de l'Acadmie des Sciences Paris, Serie II (Mecanique, Physique, Astronomie) 330 6 2002 437 443
77. V. Lazarus, and J.-B. Leblond In-plane perturbation of the tunnel-crack under shear loading. I: bifurcation and stability of the straight configuration of the front International Journal of Solids and Structures 39 17 2002 4421 4436
78. V. Lazarus, and J.-B. Leblond In-plane perturbation of the tunnel-crack under shear loading. II: determination of the fundamental kernel International Journal of Solids and Structures 39 17 2002 4437 4455
79. V. Lazarus, J.-B. Leblond, and S.-E. Mouchrif Crack front rotation and segmentation in mixed mode IIII or IIIIIIpart I: calculation of stress intensity factor Journal of the Mechanics and Physics of Solids 49 7 2001 1399 1420
80. V. Lazarus, J.-B. Leblond, and S.-E. Mouchrif Crack front rotation and segmentation in mixed mode IIII or IIIIIIpart II: comparison with experiments Journal of the Mechanics and Physics of Solids 49 7 2001 1421 1443 (Pubitemid 32471279)
81. Lazarus, V., Gauthier, G., Pauchard, L., Maurini, C., Valdivia, C., 2009. Basalt columns and crack formation during directional drying of colloidal suspensions in capillary tubes. In: Proceedings of the 12th International Conference on Fracture (ICF12), July, Ottawa (Canada).
82. Leblond, J., Karma, A., Lazarus, V., A theoretical analysis of crack front instability in mode IIII. Journal of the Mechanics and Physics of Solids, submitted.
83. J.-B. Leblond Crack paths in plane situationsI. General form of the expansion of the stress intensity factors International Journal of Solids and Structures 25 1989 1311 1325
84. J.-B. Leblond Crack paths in three-dimensional elastic solids. I: two-term expansion of the stress intensity factorsapplication to crack path stability in hydraulic fracturing International Journal of Solids and Structures 36 1 1999 79 103
85. J.-B. Leblond, V. Lazarus, and S.-E. Mouchrif Crack paths in three-dimensional elastic solids. II. Three-term expansion of the stress intensity factorsapplications and perspectives International Journal of Solids and Structures 36 1 1999 105 142
86. J.-B. Leblond, and D. Leguillon Asymptotic behavior of stress intensity factors near an angular point of a crack front European Journal of Mechanics, A/Solids 18 1 1999 135 145
87. J.-B. Leblond, S.-E. Mouchrif, and G. Perrin The tensile tunnel-crack with a slightly wavy front International Journal of Solids and Structures 33 14 1996 1995 2022
88. L. Legrand, and J.B. Leblond Evolution of the shape of the fronts of a pair of semi-infinite cracks during their coplanar coalescence Zeitschrift fr Angewandte Mathematik und Mechanik 90 1011 2010 821 836
89. L. Legrand, and J.-B. Leblond In-plane perturbation of a system of two coplanar slit-cracksII: case of a large distance between the outer crack fronts International Journal of Solids and Structures 47 2010 3504 3512
90. B. Lin, M. Mear, and K. Ravi-Chandar Criterion for initiation of cracks under mixed-mode I III loading International Journal of Fracture 165 2010 175 188
91. Y. Liu, and J. Rice Aseismic slip transients emerge spontaneously in three-dimensional rate and state modeling of subduction earthquake sequences Journal of Geophysical ResearchSolid Earth 110 B8 2005
92. K. Maloy, and J. Schmittbuhl Dynamical event during slow crack propagation Physical Review Letters 87 10 2001 105502/14
93. K.P. Meade, and L.M. Keer On the problem of a pair of point forces applied to the faces of a semi-infinite plane crack Journal of Elasticity 14 1 1984 3 14
94. J. Morrissey, and J. Rice Crack front waves Journal of the Mechanics and Physics of Solids 46 3 1998 467 487
95. J. Morrissey, and J. Rice Perturbative simulations of cracks front waves J. Mech. Phys. Solids 48 67 2000 1229 1251
96. A.B. Movchan, H. Gao, and J.R. Willis On perturbations of plane cracks International Journal of Solids and Structures 35 2627 1998 3419 3453
97. T. Mower, and A. Argon Experimental investigations of crack trapping in brittle heterogeneous solids Mechanics of Materials 19 4 1995 343 364
98. Q.-S. Nguyen Stability and Nonlinear Solid Mechanics 2000 John Wiley
99. O. Obrezanova, A. Movchan, and J. Willis Dynamic stability of a propagating crack Journal of the Mechanics and Physics of Solids 50 12 2002 2637 2668
100. O. Obrezanova, A. Movchan, and J. Willis Stability of an advancing crack to small perturbation of its path Journal of the Mechanics and Physics of Solids 50 1 2002 57 80
101. P. Paris, M. Gomez, and W. Anderson A rational analytic theory of fatigue Trends in Engineering 13 1961 94
102. G. Perrin, and J.R. Rice Disordering of a dynamic planar crack front in a model elastic medium of randomly variable toughness Journal of the Mechanics and Physics of Solids 42 6 1994 1047 1064
103. A. Piccolroaz, G. Mishuris, and A.B. Movchan Evaluation of the LazarusLeblond constants in the asymptotic model of the interfacial wavy crack Journal of the Mechanics and Physics of Solids 55 8 2007 1575 1600
104. N. Pindra, V. Lazarus, and J.-B. Leblond The deformation of the front of a 3d interface crack propagating quasistatically in a medium with random fracture properties Journal of the Mechanics and Physics of Solids 56 4 2008 1269 1295
105. N. Pindra, V. Lazarus, and J.-B. Leblond Geometrical disorder of the fronts of a tunnel-crack propagating in shear in some heterogeneous medium Journal of the Mechanics and Physics of Solids 58 2010 281 299
106. N. Pindra, V. Lazarus, and J.-B. Leblond In-plane perturbation of a system of two coplanar slit-cracksI: case of arbitrarily spaced crack fronts International Journal of Solids and Structures 47 2010 3489 3503
107. A.J. Pons, and A. Karma Helical crack-front instability in mixed-mode fracture Nature 464 2010 85 89
108. J. Qian, and A. Fatemi Mixed mode fatigue crack growth: a literature survey Engineering Fracture Mechanics 55 6 1996 969
109. S. Ramanathan, and D.S. Fisher Dynamics and instabilities of planar tensile cracks in heterogeneous media Physical Review Letters 79 5 1997 877 880
110. K. Ravi-Chandar Dynamic fracture of nominally brittle materials International Journal of Fracture 90 12 1998 83 102
111. J. Rice, Y. Ben-Zion, and K. Kim 3-Dimensional perturbation solution for a dynamic planar crack moving unsteadily in a model elastic solid Journal of the Mechanics and Physics of Solids 42 5 1994 813 843
112. J.R. Rice Some remarks on elastic crack-tip stress fields International Journal of Solids and Structures 8 6 1972 751 758
113. J.R. Rice First-order variation in elastic fields due to variation in location of a planar crack front ASME Journal of Applied Mechanics 52 3 1985 571 579
114. Rice, J.R., 1988. Crack fronts trapped by arrays of obstacles: Solutions based on linear perturbation theory. In: Rosakis, A.J., Ravi-Chandar, K., Rajapakse, Y. (Eds.), Analytical, Numerical and Experimental Aspects of Three Dimensional Fracture Processes, vol. 91. ASME Applied Mechanics Division, American Society of Mechanical Engineers, New York, pp. 175184.
115. Rice, J.R., 1989. Weight function theory for three-dimensional elastic crack analysis. In: Wei, R.P., Gangloff, R.P. (Eds.), Fracture Mechanics: Perspectives and Directions (Twentieth Symposium). American Society for Testing and Materials STP 1020, Philadelphia, USA, pp. 2957.
116. A. Rosso, and W. Krauth Roughness at the depinning threshold for a long-range elastic string Physical Review E 65 2 2002 025101
117. S. Roux, D. Vandembroucq, and F. Hild Effective toughness of heterogeneous brittle materials European Journal of MechanicsA/Solids 22 5 2003 743 749
118. Santucci, S., Grob, M., Toussaint, R., Schmittbuhl, J., Hansen, A., Mløy, K.J., 2009. Crackling dynamics during the failure of heterogeneous material: Optical and acoustic tracking of slow interfacial crack growth. In: 12th International Conference on Fracture (ICF12), Ottawa, Canada, July.
119. J. Schmittbuhl, A. Delaplace, K.J. Mløy, H. Perfettini, and J.P. Vilotte Slow crack propagation and slip correlations Pure and Applied Geophysics 160 56 2003 961 976
120. J. Schmittbuhl, A. Hansen, and G. Batrouni Roughness of interfacial crack fronts: stress-weighted percolation in the damage zone Physical Review Letters 90 4 2003 045505/1 4
121. J. Schmittbuhl, and K.J. Maløy Direct observation of a self-affine crack propagation Physical Review Letters 78 20 1997 3888 3891
122. J. Schmittbuhl, S. Roux, J.P. Vilotte, and K.-J. Maloy Interfacial crack pinning: effect of nonlocal interactions Physical Review Letters 74 10 1995 1787 1790
123. J. Schmittbuhl, and J.-P. Vilotte Interfacial crack front wandering: influence of quenched noise correlations Physica A 270 12 1999 42 56
124. E. Sharon, and J. Fineberg Confirming the continuum theory of dynamic brittle fracture for fast cracks Nature 397 6717 1999 333 335
125. M. Stallybrass On the concentrated loading of certain elastic half-space problems and related external crack problems. A new approach International Journal of Engineering Science 19 8 1981 1123 1144
126. H. Tada, P.C. Paris, and G.R. Irwin The Stress Analysis of Cracks Handbook 1973 Del Research Corporation Hellertown, USA
127. A.P. Vieira, S. Jose, J. Andrade, and H.J. Herrmann Subcritical crack growth: The microscopic origin of Paris' law Physical Review Letters 100 19 2008 195503 (origine physic de la loi de Paris)
128. J. Willis, and A. Movchan Three-dimensional dynamic perturbation of a propagating crack Journal of the Mechanics and Physics of Solids 45 4 1997 591 610
129. J.R. Willis, and A.B. Movchan Dynamic weight-functions for a moving crack. 1. Mode-I loading Journal of the Mechanics and Physics of Solids 43 3 1995 319 341
130. S. Woolfries, and J.R. Willis Perturbation of a dynamic planar crack moving in a model elastic solid Journal of the Mechanics and Physics of Solids 47 8 1999 1633 1661