Phase field modeling of crack propagation

Philosophical Magazine

Volumn 91, Issue 1, 2011, Pages 75-95

  Spatschek, Robert ^a   Brener, Efim ^b   Karma, Alain ^c  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b FORSCHUNGSZENTRUM JÜLICH   (Germany)

^c NORTHEASTERN UNIVERSITY   (United States)

Author keywords

crack branching; fracture; phase field modeling; sharp interface limit

Indexed keywords

BRANCHING INSTABILITIES; BRITTLE MATERIALS; CONTINUUM FIELDS; CRACK BRANCHING; CRACK DYNAMICS; CRACK PATHS; DYNAMICAL BEHAVIORS; FAILURE PROCESS; FRONT TRACKING; LINEAR ELASTICITY; MATERIAL INTERFACES; MATERIALS FAILURE; MESOSCALE; PHASE FIELD METHODS; PHASE FIELD MODELING; PHASE FIELD MODELS; PHASE TRANSFORMATION; PHYSICS OF FAILURES; SCALE SELECTION; SHARP INTERFACE; TIME-SCALES;

CRACK PROPAGATION; CRACK TIPS; ELASTICITY; MATERIALS SCIENCE; SOLID SOLUTIONS;

PHASE INTERFACES;

EID: 78249237887     PISSN: 14786435     EISSN: 14786443     Source Type: Journal    
DOI: 10.1080/14786431003773015     Document Type: Article

References (113)

1. B. Lawn, Fracture in Brittle Solids, 2nd ed., Cambridge University Press, Cambridge, 1993.
2. M. Marder and J. Fineberg, Phys. Today 49(1996) p. 24.
3. J. S. Langer, Directions in Condensed Matter, in Models of Pattern Formation in First-Order Phase Transitions, G. Grinstein and G. Mazenko, eds., World Scientific, Singapore, 1986, p. 164.
4. J. B. Collins and H. Levine, Phys. Rev. B 31(1985) p. 6119.
5. L. Q. Chen, Ann. Rev. Mater. Res. 32(2002) p. 113.
6. A. Karma, Phase field modeling, in Handbook of Materials Modeling. Volume I: Methods and Models, S. Yip, ed., Springer, Netherlands, 2005, p. 2087.
7. I. Steinbach, Model. Simul. Mater. Sci. Eng. 17(2009) p. 073001.
8. J. A. Warren, R. Kobayashi, A. E. Lobovsky and W. C. Carter, Acta Mater. 51(2003) p. 6035.
9. L. B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge, 1998.
10. K. B. Broberg, Cracks and Fracture, Academic Press, New York, 1999.
11. J. R. Rice, Mathematical analysis in the mechanics of fracture, in Fracture: An Advanced Treatise, H. Liebowitz, ed., Academic, New York, 1968, p. 191.
12. M. Adda-Bedia and M. Ben Amar, Phys. Rev. Lett. 76(1996) p. 1497.
13. M. Adda-Bedia, R. Arias, M. Ben Amar and F. Lund, Phys. Rev. Lett. 82(1999) p. 2314.
14. S. Ramanathan and D. S. Fisher, Phys. Rev. Lett. 79(1997) p. 877.
15. J. A. Hauch, D. Holland, M. P. Marder and H. L. Swinney, Phys. Rev. Lett. 82(1999) p. 3823.
16. E. Sharon, S. P. Gross and J. Fineberg, Phys. Rev. Lett. 74(1995) p. 5096.
17. E. Sharon, S. P. Gross and J. Fineberg, Phys. Rev. Lett. 76(1996) p. 2117.
18. J. Fineberg, S. P. Gross, M. Marder and H. L. Swinney, Phys. Rev. Lett. 67(1991) p. 457.
19. P. Daguier, S. Henaux, E. Bouchaud and F. Creuzet, Phys. Rev. e 53(1996) p. 5637.
20. E. Sharon and J. Fineberg, Nature 397(1999) p. 333.
21. J. F. Boudet, S. Ciliberto and V. Steinberg, Europhys. Lett. 30(1995) p. 337.
22. J. Boudet, S. Ciliberto and V. Steinberg, J. Phys. II France 6(1996) p. 1493.
23. J. Fineberg and M. Marder, Phys. Rep. 313(1999) p. 1.
24. F. F. Abraham, Phys. Rev. Lett. 77(1996) p. 869.
25. S. J. Zhou, D. M. Beazley, P. S. Lomdahl and B. L. Holian, Phys. Rev. Lett. 78(1997) p. 479.
26. R. K. Kalia, A. Nakano, K. Tsuruta and P. Vashishta, Phys. Rev. Lett. 78(1997) p. 689.
27. F. Cleri, S. Yip, D. Wolf and S. R. Phillpot, Phys. Rev. Lett. 79(1997) p. 1309.
28. Special Issue on Dynamic Fracture Analysis, Comp. Sci. Eng., Vol. 1(1999).
29. A. Hellemans, Science 281(1998) p. 943.
30. D. A. Kessler and H. Levine, Phys. Rev. e 68(2003) p. 036118.
31. M. Marder and S. Gross, J. Mech. Phys. Solids 43(1995) p. 1.
32. D. Chopp, Level set extentions, flows and crack propagation, in PDE and Level Sets: Algorithmic Approaches to Static and Motion Imagery, J. S. Suri and S. Laximinarayan, eds., Springer-Verlag, Berlin, 2002, p. 31.
33. Y. Wang and J. Li, Acta Mater. 58(2010) p. 1212.
34. A. Griffith, Phil. Trans. Roy. Soc. (London) A 221(1920) p. 163.
35. J. B. Rundle and W. Klein, Phys. Rev. Lett. 63(1989) p. 171.
36. M. William, J. Appl. Mech. 24(1957) p. 109.
37. G. Irwin, J. Appl. Mech. 24(1957) p. 361.
38. S. Ogata, J. Li, N. Hirosaki, Y. Shibutani and S. Yip, Phys. Rev. B 70(2004) p. 104104.
39. I. S. Aranson, V. A. Kalatsky and V. M. Vinokur, Phys. Rev. Lett. 85(2000) p. 118.
40. A. Karma, D. A. Kessler and H. Levine, Phys. Rev. Lett. 87(2001) p. 045501.
41. A. Karma and A. E. Lobkovsky, Phys. Rev. Lett. 92(2004) p. 245510.
42. M. Adda-Bedia, J. Mech. Phys. Solids 52(2004) p. 1407.
43. H. Henry and H. Levine, Phys. Rev. Lett. 93(2004) p. 105504.
44. R. D. Deegan, P. J. Petersan, M. Marder and H. L. Swinney, Phys. Rev. Lett. 88(2001) p. 014304.
45. H. Henry, Europhys. Lett. 83(2008) p. 16004.
46. E. Sharon and J. Fineberg, Phys. Rev. B 54(1996) p. 7128.
47. M. Adda-Bedia, J. Mech. Phys. Solids 53(2005) p. 227.
48. E. Katzav, M. Adda-Bedia and R. Arias, Internat. J. Fract. 143(2007) p. 245.
49. C. Kuhn and R. Müller, Proc. Appl. Math. Mech. 8(2008) p. 10223.
50. V. I. Marconi and E. A. Jagla, Phys. Rev. e 71(2005) p. 036110.
51. L. O. Eastgate, J. P. Sethna, M. Rauscher, T. Cretegny, C. S. Chen and C. R. Myers, Phys. Rev. e 65(2002) p. 036117.
52. D. N. Bhate, A. Kumar and A. F. Bower, J. Appl. Phys. 87(2000) p. 1712.
53. R. Goldstein and R. Salganik, Internat. J. Fract. 10(1974) p. 507.
54. B. Cotterell and J. R. Rice, Int. J. Fract. 16(1980) p. 155.
55. G. E. Oleaga, J. Mech. Phys. Solids 49(2001) p. 2273.
56. E. A. Brener and V. I. Marchenko, Phys. Rev. Lett. 81(1998) p. 5141.
57. G. A. Francfort and J. J. Marigo, J. Mech. Phys. Solids 46(1998) p. 1319.
58. B. Bourdin, G. A. Francfort and J. J. Marigo, J. Mech. Phys. Solids 48(2000) p. 797.
59. J. A. Hodgdon and J. P. Sethna, Phys. Rev. B 47(1993) p. 4831.
60. M. Marder, Europhys. Lett. 66(2004) p. 364.
61. V. Hakim and A. Karma, Phys. Rev. Lett. 95(2005) p. 235501.
62. V. Hakim and A. Karma, J. Mech. Phys. Solids 57(2009) p. 342.
63. J. R. Rice, J. Appl. Mech. 35(1968) p. 379.
64. J. Eshelby, J. Elasticity 5(1975) p. 321.
65. C. Herring, in The Physics of Powder Metallurgy, W. E. Kingston, ed., McGraw-Hill, New York, 1951, p. 143.
66. J. W. Hutchinson and Z. Suo, Adv. Appl. Mech. 29(1992) p. 63.
67. M. Amestoy and J. Leblond, Internat. J. Solids Struct. 29(1992) p. 465.
68. G. I. Barenblatt and G. P. Cherepanov, J. Appl. Math. Mech. 25(1961) p. 1110.
69. F. Corson, M. Adda-Bedia, H. Henry and E. Katzav, Internat. J. Fract. 158(2009) p. 1.
70. Y. M. Jin, Y. U. Wang and A. G. Khachaturyan, Phil. Mag. 83(2003) p. 1587.
71. Y. Wang, H. Wang, L. Q. Chen and A. G. Khachaturyan, J. Am. Ceram. Soc. 76(1993) p. 3029.
72. Y. L. Bouar, A. Loiseau and A. G. Khachaturyan, Acta Mater. 46(1998) p. 2777.
73. S. Y. Hu and L. Q. Chen, Acta Mater. 49(2001) p. 463.
74. Y. Wang and A. G. Khachaturyan, Acta Mater. 45(1997) p. 759.
75. Y. M. Jin, A. Artemev and A. G. Khachaturyan, Acta Mater. 49(2001) p. 2309.
76. Y. M. Jin and A. G. Khachaturyan, Phil. Mag. Lett. 81(2001) p. 607.
77. Y. U. Wang, Y. M. Jin, A. M. Cuitino and A. G. Khachaturyan, Acta Mater. 49(2001) p. 1847.
78. A. G. Khachaturyan, S. Semenovskaya and T. Tsakalakos, Phys. Rev. B 52(1995) p. 15909.
79. Y. U. Wang, Y. M. Jin and A. G. Khachaturyan, J. Appl. Phys. 92(2002) p. 1351.
80. B. Bilby and J. D. Eshelbyin, in Fracture: An Advanced Treatise, H. Liebowitz, ed., Academic Press, New York, 1968, p. 99.
81. Y. U. Wang, Y. M. Jin and A. G. Khachaturyan, Acta Mater. 51(2003) p. 4209.
82. Y. M. Jin, Y. U. Wang and A. G. Khachaturyan, Appl. Phys. Lett. 79(2001) p. 3071.
83. Y. U. Wang, Y. M. Jin and A. G. Khachaturyan, J. Appl. Phys. 91(2002) p. 6435.
84. Y. C. Song, A. K. Soh and Y. Ni, J. Phys. D Appl. Phys. 40(2007) p. 1175.
85. J. Wang and T. Y. Zhang, Acta Mater. 55(2007) p. 2465.
86. X. Ma, S. Shi, C. Woo and L. Chen, Mech. Mater. 38(2006) p. 3.
87. K. R. Elder and M. Grant, Phys. Rev. e 70(2004) p. 051605.
88. P. Stefanovic, M. Haataja and N. Provatas, Phys. Rev. Lett. 96(2006) p. 225504.
89. R. J. Asaro and W. A. Tiller, Metall. Trans. 3(1972) p. 1789.
90. M. A. Grinfeld, Sov. Phys. Dokl. 31(1986) p. 831.
91. W. H. Yang and D. J. Srolovitz, Phys. Rev. Lett. 71(1993) p. 1593.
92. C. H. Chiu and H. Gao, Int. J. Solids Struct. 30(1993) p. 2983.
93. K. Kassner and C. Misbah, Europhys. Lett. 28(1994) p. 245.
94. K. Kassner and C. Misbah, Europhys. Lett. 46(1999) p. 217.
95. J. Muller and M. Grant, Phys. Rev. Lett. 82(1999) p. 1736.
96. P. Kohlert, K. Kassner and C. Misbah, Eur. Phys. J. B Cond. Matter Complex Syst. 35(2003) p. 493.
97. K. Kassner, C. Misbah, J. Müller, J. Kappey and P. Kohlert, Phys. Rev. e 63(2001) p. 036117.
98. A. Ratz, A. Ribalta and A. Voigt, J. Comput. Phys. 214(2006) p. 187.
99. C. Gugenberger, R. Spatschek and K. Kassner, Phys. Rev. e 78(2008) p. 016703.
100. K. A. Wu and P. W. Voorhees, Phys. Rev. B 80(2009) p. 125408.
101. R. Spatschek and E. A. Brener, Phys. Rev. e 64(2001) p. 046120.
102. E. A. Brener and R. Spatschek, Phys. Rev. e 67(2003) p. 016112.
103. R. Spatschek, M. Hartmann, E. Brener, H. Muller-Krumbhaar and K. Kassner, Phys. Rev. Lett. 96(2006) p. 015502.
104. D. Pilipenko, R. Spatschek, E. A. Brener and H. Muller-Krumbhaar, Phys. Rev. Lett. 98(2007) p. 015503.
105. R. Spatschek, C. Muller-Gugenberger, E. Brener and B. Nestler, Phys. Rev. e 75(2007) p. 066111.
106. R. Spatschek, E. A. Brener and D. Pilipenko, Phys. Rev. Lett. 101(2008) p. 205501.
107. E. A. Brener, M. Fleck, D. Pilipenko and R. Spatschek; in preparation.
108. T. S. Lo, A. Pomyalov, I. Procaccia and J. Zylberg, Phys. Rev. e 78(2008) p. 027101.
109. F. Rosch and H. R. Trebin, Europhys. Lett. 85(2009) p. 56002.
110. E. Bouchbinder, Phys. Rev. Lett. 103(2009) p. 164301.
111. E. Bouchbinder, A. Livne and J. Fineberg, Phys. Rev. Lett. 101(2008) p. 264302.
112. A. Livne, E. Bouchbinder and J. Fineberg, Phys. Rev. Lett. 101(2008) p. 264301.
113. A. Pons and A. Karma, Nature 464(2010) p. 85.