메뉴 건너뛰기




Volumn 57, Issue 2, 2009, Pages 342-368

Laws of crack motion and phase-field models of fracture

Author keywords

Anisotropy; Eshelby tensor; Fracture; Herring torque; Phase field

Indexed keywords

ANISOTROPY; BRITTLENESS; CRACK PROPAGATION; CRACK TIPS; CRACKS; FORECASTING; FRACTURE; FRACTURE MECHANICS; MATHEMATICAL MODELS; MAXIMUM PRINCIPLE; STRENGTH OF MATERIALS; SURFACE CHEMISTRY; SURFACE TENSION; TENSORS; THEOREM PROVING; TORQUE;

EID: 58149189884     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2008.10.012     Document Type: Article
Times cited : (365)

References (44)
  • 1
    • 79961076832 scopus 로고    scopus 로고
    • Generalized Griffith criterion for dynamic fracture and the stability of crack motion at high velocities
    • Adda-Bedia M., Arias R., Ben Amar M., and Lund F. Generalized Griffith criterion for dynamic fracture and the stability of crack motion at high velocities. Phys. Rev. E 60 (1999) 2366-2376
    • (1999) Phys. Rev. E , vol.60 , pp. 2366-2376
    • Adda-Bedia, M.1    Arias, R.2    Ben Amar, M.3    Lund, F.4
  • 2
    • 34748925841 scopus 로고
    • Approximation of functionals depending on jumps by elliptic functionals via gamma-convergence
    • Ambrosio L., and Tortorelli V. Approximation of functionals depending on jumps by elliptic functionals via gamma-convergence. Commun. Pure Appl. Math. 43 8 (1990) 999-1036
    • (1990) Commun. Pure Appl. Math. , vol.43 , Issue.8 , pp. 999-1036
    • Ambrosio, L.1    Tortorelli, V.2
  • 3
    • 0026715730 scopus 로고
    • Crack path in plane situations. 2. Detailed form of the expansion of the stress intensity factors
    • Amestoy M., and Leblond J. Crack path in plane situations. 2. Detailed form of the expansion of the stress intensity factors. Int. J. Solids Struct. 29 4 (1992) 465-501
    • (1992) Int. J. Solids Struct. , vol.29 , Issue.4 , pp. 465-501
    • Amestoy, M.1    Leblond, J.2
  • 4
    • 0034227516 scopus 로고    scopus 로고
    • Continuum field description of crack propagation
    • Aranson I., Kalatsky V., and Vinokur V. Continuum field description of crack propagation. Phys. Rev. Lett. 85 (2000) 118-121
    • (2000) Phys. Rev. Lett. , vol.85 , pp. 118-121
    • Aranson, I.1    Kalatsky, V.2    Vinokur, V.3
  • 5
    • 46749148254 scopus 로고
    • On brittle cracks under longitudinal shear
    • Barenblatt G., and Cherepanov G. On brittle cracks under longitudinal shear. PMM 25 (1961) 1110-1119
    • (1961) PMM , vol.25 , pp. 1110-1119
    • Barenblatt, G.1    Cherepanov, G.2
  • 6
    • 0033891792 scopus 로고    scopus 로고
    • Numerical experiments in revisited brittle fracture
    • Bourdin B., Francfort G., and Marigo J. Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48 4 (2000) 797-826
    • (2000) J. Mech. Phys. Solids , vol.48 , Issue.4 , pp. 797-826
    • Bourdin, B.1    Francfort, G.2    Marigo, J.3
  • 7
    • 4244003287 scopus 로고    scopus 로고
    • Surface instabilities in cracks
    • Brener E.A., and Marchenko V.I. Surface instabilities in cracks. Phys. Rev. Lett. 81 (1998) 5141-5144
    • (1998) Phys. Rev. Lett. , vol.81 , pp. 5141-5144
    • Brener, E.A.1    Marchenko, V.I.2
  • 9
    • 58149199178 scopus 로고    scopus 로고
    • Corson, F., Adda-Bedia, M., Henry, H., Katzav, E., 2008. Thermal fracture as a framework for crack propagation law. cond-mat.mtrl-sci 0801.2101.
    • Corson, F., Adda-Bedia, M., Henry, H., Katzav, E., 2008. Thermal fracture as a framework for crack propagation law. cond-mat.mtrl-sci 0801.2101.
  • 10
    • 33745451119 scopus 로고
    • Slightly curved or kinked cracks
    • Cotterell B., and Rice J. Slightly curved or kinked cracks. Int. J. Fract. 16 2 (1980) 155-169
    • (1980) Int. J. Fract. , vol.16 , Issue.2 , pp. 155-169
    • Cotterell, B.1    Rice, J.2
  • 13
    • 0001826268 scopus 로고
    • The force on an elastic singularity
    • Eshelby J. The force on an elastic singularity. Philos. Trans. Roy. Soc. (London) A 244 877 (1951) 87-112
    • (1951) Philos. Trans. Roy. Soc. (London) A , vol.244 , Issue.877 , pp. 87-112
    • Eshelby, J.1
  • 14
    • 0016576296 scopus 로고
    • Elastic energy-momentum tensor
    • Eshelby J. Elastic energy-momentum tensor. J. Elasticity 5 3-4 (1975) 321-335
    • (1975) J. Elasticity , vol.5 , Issue.3-4 , pp. 321-335
    • Eshelby, J.1
  • 15
    • 0032139947 scopus 로고    scopus 로고
    • Revisiting brittle fracture as an energy minimization problem
    • Francfort G., and Marigo J. Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46 8 (1998) 1319-1342
    • (1998) J. Mech. Phys. Solids , vol.46 , Issue.8 , pp. 1319-1342
    • Francfort, G.1    Marigo, J.2
  • 16
    • 0016349897 scopus 로고
    • Brittle-fracture of solids with arbitrary cracks
    • Goldstein R., and Salganik R. Brittle-fracture of solids with arbitrary cracks. Int. J. Fract. 10 4 (1974) 507-523
    • (1974) Int. J. Fract. , vol.10 , Issue.4 , pp. 507-523
    • Goldstein, R.1    Salganik, R.2
  • 17
    • 0000357002 scopus 로고
    • The phenomena of rupture and flows in solids
    • Griffith A. The phenomena of rupture and flows in solids. Philos. Trans. Roy. Soc. (London) A 221 (1920) 163-198
    • (1920) Philos. Trans. Roy. Soc. (London) A , vol.221 , pp. 163-198
    • Griffith, A.1
  • 18
    • 0032141457 scopus 로고    scopus 로고
    • Configurational forces and a constitutive theory for crack propagation that allows for kinking and curving
    • Gurtin M., and Podio-Guidugli P. Configurational forces and a constitutive theory for crack propagation that allows for kinking and curving. J. Mech. Phys. Solids 46 8 (1998) 1343-1378
    • (1998) J. Mech. Phys. Solids , vol.46 , Issue.8 , pp. 1343-1378
    • Gurtin, M.1    Podio-Guidugli, P.2
  • 19
    • 28844450634 scopus 로고    scopus 로고
    • Crack path prediction in anisotropic brittle materials
    • Hakim V., and Karma A. Crack path prediction in anisotropic brittle materials. Phys. Rev. Lett. 95 (2005) 235501
    • (2005) Phys. Rev. Lett. , vol.95 , pp. 235501
    • Hakim, V.1    Karma, A.2
  • 21
    • 79051469848 scopus 로고    scopus 로고
    • Study of the branching instability using a phase field model of inplane crack propagation
    • Henry H. Study of the branching instability using a phase field model of inplane crack propagation. Europhys. Lett. 83 (2008) 16004
    • (2008) Europhys. Lett. , vol.83 , pp. 16004
    • Henry, H.1
  • 22
    • 19544384902 scopus 로고    scopus 로고
    • Dynamic instabilities of fracture under biaxial strain using a phase field model
    • Henry H., and Levine H. Dynamic instabilities of fracture under biaxial strain using a phase field model. Phys. Rev. Lett. 93 (2004) 105504
    • (2004) Phys. Rev. Lett. , vol.93 , pp. 105504
    • Henry, H.1    Levine, H.2
  • 23
    • 58149178221 scopus 로고    scopus 로고
    • Herring, C., 1951. in: Kingston, W.E. (Ed.), The Physics of Powder Metallurgy. McGraw-Hill, New York.
    • Herring, C., 1951. in: Kingston, W.E. (Ed.), The Physics of Powder Metallurgy. McGraw-Hill, New York.
  • 24
    • 0001470808 scopus 로고    scopus 로고
    • Hodgdon, J.A., Sethna, J.P., 1993. Derivation of a general 3-dimensional crack propagation law-a generalization of the principle of local symmetry. Phys. Rev. B 47, 4831-4840.
    • Hodgdon, J.A., Sethna, J.P., 1993. Derivation of a general 3-dimensional crack propagation law-a generalization of the principle of local symmetry. Phys. Rev. B 47, 4831-4840.
  • 25
    • 71149121504 scopus 로고
    • Mixed mode cracking in layered materials
    • Hutchinson J.W., and Suo Z. Mixed mode cracking in layered materials. Adv. Appl. Mech. 29 (1992) 63-191
    • (1992) Adv. Appl. Mech. , vol.29 , pp. 63-191
    • Hutchinson, J.W.1    Suo, Z.2
  • 26
    • 58149197204 scopus 로고    scopus 로고
    • Irwin, G., 1957. J. Appl. Mech. 24, 361.
    • Irwin, G., 1957. J. Appl. Mech. 24, 361.
  • 27
    • 3242721550 scopus 로고    scopus 로고
    • Unsteady crack motion and branching in a phase-field model of brittle fracture
    • Karma A., and Lobkovsky A. Unsteady crack motion and branching in a phase-field model of brittle fracture. Phys. Rev. Lett. 92 (2004) 245510
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 245510
    • Karma, A.1    Lobkovsky, A.2
  • 28
    • 4244131779 scopus 로고    scopus 로고
    • Phase-field model of mode III dynamic fracture
    • Karma A., Kessler D., and Levine H. Phase-field model of mode III dynamic fracture. Phys. Rev. Lett. 8704 (2001) 045501
    • (2001) Phys. Rev. Lett. , vol.8704 , pp. 045501
    • Karma, A.1    Kessler, D.2    Levine, H.3
  • 29
    • 34248210707 scopus 로고    scopus 로고
    • Theory of dynamic crack branching in brittle materials
    • Katzav E., Adda-Bedia M., and Arias R. Theory of dynamic crack branching in brittle materials. Int. J. Fract. 143 (2007) 245-271
    • (2007) Int. J. Fract. , vol.143 , pp. 245-271
    • Katzav, E.1    Adda-Bedia, M.2    Arias, R.3
  • 31
    • 58149194237 scopus 로고    scopus 로고
    • Leblond, J., 2005. Private communication.
    • Leblond, J., 2005. Private communication.
  • 32
    • 41349093713 scopus 로고    scopus 로고
    • Diffuse interface approach to brittle fracture
    • Marconi V., and Jagla E. Diffuse interface approach to brittle fracture. Phys. Rev. E 71 (2005) 036110
    • (2005) Phys. Rev. E , vol.71 , pp. 036110
    • Marconi, V.1    Jagla, E.2
  • 33
    • 2442604351 scopus 로고    scopus 로고
    • Cracks cleave crystals
    • Marder M. Cracks cleave crystals. Europhys. Lett. 66 3 (2004) 364-370
    • (2004) Europhys. Lett. , vol.66 , Issue.3 , pp. 364-370
    • Marder, M.1
  • 34
    • 33747600198 scopus 로고    scopus 로고
    • Effect of atoms on brittle fracture
    • Marder M. Effect of atoms on brittle fracture. Int. J. Fract. 130 (2004) 517-555
    • (2004) Int. J. Fract. , vol.130 , pp. 517-555
    • Marder, M.1
  • 35
    • 84990602490 scopus 로고
    • Optimal approximations by piecewise smooth functions and associated variational-problems
    • Mumford D., and Shah J. Optimal approximations by piecewise smooth functions and associated variational-problems. Commun. Pure Appl. Math. 42 5 (1989) 577-685
    • (1989) Commun. Pure Appl. Math. , vol.42 , Issue.5 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 36
    • 58149183297 scopus 로고    scopus 로고
    • Noether, E., 1918. Invariante Variationsprobleme. Nachr. v. d. Ges. d. Wiss. zu Göttingen, pp. 235-257.
    • Noether, E., 1918. Invariante Variationsprobleme. Nachr. v. d. Ges. d. Wiss. zu Göttingen, pp. 235-257.
  • 37
    • 0035479782 scopus 로고    scopus 로고
    • Remarks on a basic law for dynamic crack propagation
    • Oleaga G. Remarks on a basic law for dynamic crack propagation. J. Mech. Phys. Solids 49 10 (2001) 2273-2306
    • (2001) J. Mech. Phys. Solids , vol.49 , Issue.10 , pp. 2273-2306
    • Oleaga, G.1
  • 38
    • 58149201775 scopus 로고    scopus 로고
    • Pons, A., Karma, A., 2008, in preparation.
    • Pons, A., Karma, A., 2008, in preparation.
  • 39
    • 84980287971 scopus 로고
    • A path independent integral and approximate analysis of strain concentration by notches and cracks
    • Rice J. A path independent integral and approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35 2 (1968) 379
    • (1968) J. Appl. Mech. , vol.35 , Issue.2 , pp. 379
    • Rice, J.1
  • 40
    • 85009646506 scopus 로고
    • Stress distribution near internal crack tips for longitudinal shear problems
    • Sih G. Stress distribution near internal crack tips for longitudinal shear problems. J. Appl. Mech. 32 1 (1965) 51
    • (1965) J. Appl. Mech. , vol.32 , Issue.1 , pp. 51
    • Sih, G.1
  • 41
    • 0000013148 scopus 로고
    • Formation of fracture "lances" in glass
    • Sommer E. Formation of fracture "lances" in glass. Eng. Fract. Mech. 1 (1969) 539-546
    • (1969) Eng. Fract. Mech. , vol.1 , pp. 539-546
    • Sommer, E.1
  • 43
    • 0036677426 scopus 로고    scopus 로고
    • Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid
    • Wang Y., Jin Y., and Khachaturyan A. Phase field microelasticity theory and modeling of elastically and structurally inhomogeneous solid. J. Appl. Phys. 92 3 (2002) 1351-1360
    • (2002) J. Appl. Phys. , vol.92 , Issue.3 , pp. 1351-1360
    • Wang, Y.1    Jin, Y.2    Khachaturyan, A.3
  • 44
    • 85137171003 scopus 로고
    • On the stress distribution at the base of a stationary crack
    • William M. On the stress distribution at the base of a stationary crack. J. Appl. Mech. 24 (1957) 109-114
    • (1957) J. Appl. Mech. , vol.24 , pp. 109-114
    • William, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.