BOUNDARY ELEMENT ANALYSIS OF COMPLEX STRESS INTENSITY FACTORS OF BIMATERIAL INTERFACE CRACKS1)
Gu Yan,*,2), Zhang Yaoming†*School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China †School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, Shandong, China
Abstract The asymptotic crack-tip field for bimaterial interface cracks exhibits an oscillatory behavior which is quite different from that for cracks in homogeneous materials. Modeling such interface cracks by the conventional solution procedures designed for homogeneous materials is inadequate, and may not lead to accurate solutions. This paper introduces a new set of novel special crack-tip elements for analysis of interface cracks in linear elastic bimaterials by using the boundary element method (BEM). The method can properly describe the oscillatory displacement and stress fields in the vicinity of the interfacial crack-tip. Furthermore, the troublesome nearly-singular integrals, which are crucial in the application of the BEM for ultra-thin structural problems, are calculated accurately by using a nonlinear coordinate transformation. Accurate and reliable BEM results with only a small number of boundary elements can be obtained for interface crack analysis of ultra-thin composite bimaterials. Keywords:boundary element method;interface crack analysis;stress intensity factors;special crack-tip elements;nearly singular integrals
PDF (1712KB)元数据多维度评价相关文章导出EndNote|Ris|Bibtex收藏本文 本文引用格式 谷岩, 张耀明. 双材料界面裂纹复应力强度因子的正则化边界元法1). 力学学报[J], 2021, 53(4): 1049-1058 DOI:10.6052/0459-1879-20-440 Gu Yan, Zhang Yaoming. BOUNDARY ELEMENT ANALYSIS OF COMPLEX STRESS INTENSITY FACTORS OF BIMATERIAL INTERFACE CRACKS1). Chinese Journal of Theoretical and Applied Mechanics[J], 2021, 53(4): 1049-1058 DOI:10.6052/0459-1879-20-440
(ZhangMing, YaoZhenhan, DuQinghua, et al. Boundary element analysis of stress intensity factors of bimaterial interface crack Chinese Journal of Applied Mechanics, 1999,16(1):21-26 (in Chinese)) [本文引用: 1]
AntwerpenVAV, MulderWA, HermanGC. Finite-difference modeling of two-dimensional elastic wave propagation in cracked media Geophysical Journal International, 2002,149:169-178 [本文引用: 1]
MoesN, DolbowJ, BelytschkoT. A finite element method for crack growth without remeshing International Journal for Numerical Methods in Engineering, 1999,46(1):131-150 [本文引用: 1]
CruseTA. BIE fracture mechanics analysis: 25 years of developments Computational Mechanics, 1996,18(1):1-11 [本文引用: 1]
LeiJ, WangYS, GrossD. Two dimensional numerical simulation of crack kinking from an interface under dynamic loading by time domain boundary element method International Journal of Solids and Structures, 2007,44(3):996-1012
(GaoXiaowei, ZhengBaojing, LiuJian. Dynamic fracture analysis of functionally graded materials by radial integration BEM Chinese Journal of Theoretical and Applied Mechanics, 2015,47(5):868-873 (in Chinese))
(ChengYumin, JiXing, HePengfei. Infinite similar boundary element method for dynamic fracture mechanics Chinese Journal of Theoretical and Applied Mechanics, 2004,36(1):43-48 (in Chinese))
(NiuZhongrong, ChengChangzheng, HuZongjun, YeJianqiao. Boundary element analysis of the stress intensity factors for the v-notched structures Chinese Journal of Theoretical and Applied Mechanics, 2008,40(5):849-857 (in Chinese))
(QinTaiyan, TangRenji, ChenWeijiang. Hypersingular integral equations and boundary element method for planar crack problems in three-dimensional finite bodies Chinese Journal of Theoretical and Applied Mechanics, 1997,29(3):481-485 (in Chinese)) [本文引用: 1]
DuflotM. A meshless method with enriched weight functions for three-dimensional crack propagation International Journal for Numerical Methods in Engineering, 2006,65(12):1970-2006 [本文引用: 1]
(ChenShenshen, WangJuan. An element-free Galerkin scaled boundary method for anti-plane crack problem Chinese Journal of Computational Mechanics, 2017,34:57-61 (in Chinese)) [本文引用: 1]
WuZJ, WongLNY. Frictional crack initiation and propagation analysis using the numerical manifold method Computers and Geotechnics, 2012,39:38-53 [本文引用: 1]
(JiaoYu-yong, ZhangXiuli, LiuQuansheng, ChenWeizhong. Simulation of rock crack propagation using discontinuous deformation analysis method Chinese Journal of Rock Mechanics and Engineering, 2007,26:682-691 (in Chinese)) [本文引用: 1]
RountreeCL, KaliaRK, LidorikisE, et al. Atomistic aspects of crack propagation in brittle materials: Multimillion atom molecular dynamics simulations Annual Review of Materials Research, 2002,32:377-400 [本文引用: 1]
ErdoganF. Stress distribution in bonded dissimilar materials with cracks Journal of Applied Mechanics, 1965,32(2):403-410 [本文引用: 2]
WilliamsML. The stresses around a fault or crack in dissimilar media Bulletin of the Seismological Society of America, 1959,49(2):199-204 [本文引用: 2]
EnglandAH. A crack between dissimilar media Journal of Applied Mechanics, 1965,32(2):400-402 [本文引用: 2]
YuukiR, XuJQ. Boundary element analysis of dissimilar materials and interface crack Computational Mechanics, 1994,14(2):116-127 [本文引用: 1]
OrtizJE, CisilinoAP. Boundary element method for J-integral and stress intensity factor computations in three-dimensional interface cracks International Journal of Fracture, 2005,133(3):197-222 [本文引用: 1]
LiuY, FanH. Analysis of thin piezoelectric solids by the boundary element method Computer Methods in Applied Mechanics and Engineering, 2002,191(21-22):2297-2315 [本文引用: 1]
LuoJF, LiuYJ, BergerEJ. Analysis of two-dimensional thin structures (from micro- to nano-scales) using the boundary element method Computational Mechanics, 1998,22(5):404-412 [本文引用: 1]
ZhouHL, NiuZR, ChengCZ, et al. Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems Computers & Structures, 2008,86(15):1656-1671
SladekV, SladekJ, TanakaM. Nonsingular BEM formulations for thin-walled structures and elastostatic crack problems Acta Mechanica, 1993,99(1):173-190
XieG, ZhangJ, DongY, et al. An improved exponential transformation for nearly singular boundary element integrals in elasticity problems International Journal of Solids and Structures, 2014,51(6):1322-1329
NiuZ, ZhouH. The natural boundary integral equation in potential problems and regularization of the hypersingular integral Computers & Structures, 2004,82(2-3):315-323
MaH, KamiyaN. A general algorithm for the numerical evaluation of nearly singular boundary integrals of various orders for two- and three-dimensional elasticity Computational Mechanics, 2002,29(4):277-288
GaoXW. An effective method for numerical evaluation of general 2D and 3D high order singular boundary integrals Computer Methods in Applied Mechanics and Engineering, 2010,199(45-48):2856-2864 [本文引用: 1]
GuY, ZhangC. Novel special crack-tip elements for interface crack analysis by an efficient boundary element method Engineering Fracture Mechanics, 2020,239:107302 [本文引用: 7]
(ZhangYaoming, SunCuilian, GuYan. The evaluation of nearly singular integrals in the boundary integral equations with variables transformation Chinese Journal of Theoretical and Applied Mechanics, 2008,40(2):207-214 (in Chinese)) [本文引用: 1]
ZhangYM, GuY, ChenJT. Boundary element analysis of the thermal behaviour in thin-coated cutting tools Engineering Analysis with Boundary Elements, 2010,34(9):775-784 [本文引用: 1]
RiceJR. Elastic fracture mechanics concepts for interfacial cracks Journal of Applied Mechanics, 1988,55(1):98-103 [本文引用: 1]
(ZhangYaoming, GuYan, ChenJeng-Tzong. Boundary layer effect and thin body structure in BEM for potential problems Chinese Journal of Theoretical and Applied Mechanics, 2010,42(2):219-227 (in Chinese)) [本文引用: 2]
GuY, ChenW, ZhangC. Stress analysis for thin multilayered coating systems using a sinh transformed boundary element method International Journal of Solids and Structures, 2013,50(20-21):3460-3471 [本文引用: 1]