三维横观各向同性介质界面裂纹的边界积分方程方法

赵明皡; 李冬霞; 沈亚鹏

三维横观各向同性介质界面裂纹的边界积分方程方法

1.
郑州大学工程力学系,郑州 450002;2.中原工学院基础部,郑州 450007;3.西安交通大学工程力学系,西安 710049

基金项目: 河南省高校新世纪优秀人才支持计划资助项目

详细信息

中图分类号: O346.11
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出版历程
- 收稿日期: 2004-05-17
- 修回日期: 2005-08-17
- 刊出日期: 2005-12-15

Interfacial Crack Analysis in Three-Dimensional Transversely Isotropic Bi-Materials by Boundary Integral Equation Method

1.
Department of Engineering Mechanics, Zhengzhou University, Zhengzhou 450002, P. R. China;

摘要

摘要: 基于两相三维横观各向同性介质的基本解和Somigliana恒等式，对三维横观各向同性介质中的任意形状的平片界面裂纹，以裂纹面上的不连续位移为待求参量建立了超奇异积分-微分方程，界面平行于横观各向同性面．根据发散积分的有限部积分理论，应用积分方程方法研究得到裂纹前沿的位移和应力场的表达式、奇性指数以及应力强度因子的不连续位移表达式．在非震荡情形下，超奇异积分-微分方程退化为超奇异积分方程，与均匀介质的超奇异积分方程形式完全相同．
- 三维两相介质 /
- 横观各向同性 /
- 界面裂纹 /
- 应力强度因子 /
- 积分-微分方程
Abstract: 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.
- three-dimensional bi-material /
- transversely isotropic /
- inter facial crack /
- stress inte nsity factor /
- integral-differential equation

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参考文献(10)

[1]	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
[5]	汤任基，陈梦成，乐金朝.三维界面裂纹的理论分析[J].中国科学，1998,28（2）:177—182.
[6]	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