The integr al-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions,in which the displacement discontinuities across the crack faces are the unknowns to be determined.The interface is parallel to both the planes of isotropy.The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method.The stress intensity factors were expressed in terms of the displaceme nt discontinuities.In the non-oscillatory case,the hyper-singular bo undary integral-differential equations werere duced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.
Hutchinson J W, Suo Z. Mixed-mode cracking in layered materials[J].Advances in Applied Mechanics,1992,29:63—191.
[2]
Ting T C T.Anisotropic Elasticity: Theory and Applications[M].New York:Oxford University Press,1996.
[3]
Choi S T, Shin H, Earmme Y Y. On the unified approach to anisotropic and isotropic elasticity for singularity, interface and crack in dissimilar media[J].Internat J Solids Structure,2003,40(6):1411—1431. doi: 10.1016/S0020-7683(02)00671-6
[4]
Keer L M, Chen S H, Comninou M.The interface penny-shaped crack reconsidered[J].Internat J Eng Sci,1978,16(10):765—772. doi: 10.1016/0020-7225(78)90009-5
Lazarus V, Leblond J B.Three-dimensional crack-face weight functions for the semi-infinite interface crack—Ⅱ integrodifferential equations on the weight functions and resolution[J].J Mech Phys Solids,1998,46(3):513—536. doi: 10.1016/S0022-5096(97)00074-4
[7]
Pavlou D G.Green's function for the bimaterial elastic solid containing interface annular crack[J].Engineering Analysis With Boundary Elements,2002,26(10):845—853. doi: 10.1016/S0955-7997(02)00052-8
[8]
QU Jian-min, XUE Yi-bin.Three-dimensional interface cracks in anisotropic bimaterials: the non-oscillatory case[J].ASME J Appl Mech,1998,65(4):1048—1055. doi: 10.1115/1.2791899
[9]
ZHAO Ming-hao,SHEN Ya-peng,LIU Yuan-jie,et al.Method of analysis of cracks in three-dimensional transversely isotropic media: boundary integral equation approach[J].Engineering Analysis With Boundary Elements,1998,21(2):169—178. doi: 10.1016/S0955-7997(98)00033-2
[10]
Pan Y C,Chou T W.Green's functions for two-phase transversely isotropic materials[J].ASME J Appl Mech,1979,46(3):551—556. doi: 10.1115/1.3424604
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