非对称Ⅲ型界面裂纹受变载荷作用下的解析解  

Analytical solutions of mode Ⅲ asymmetrical interface crack under variable loads

作　　者：吕念春[1,2] 程云虹[3] 程靳[2] 

机构地区：[1]沈阳理工大学材料科学与工程学院,辽宁沈阳110168 [2]哈尔滨工业大学航天工程与力学系,黑龙江哈尔滨150001 [3]东北大学土木工程系,辽宁沈阳110006

出　　处：《辽宁工程技术大学学报（自然科学版）》2009年第3期386-388,共3页Journal of Liaoning Technical University (Natural Science)

基　　金：中国博士后基金资助项目(2005038199);黑龙江省自然科学基金重点资助项目(ZJG04-08)

摘　　要：采用复变函数论的方法,对非对称Ⅲ型界面裂纹的动态扩展问题进行了研究。通过自相似方法,并根据任意自相似指数的非对称动态扩展问题进行自相似求解,导出解析解的一般表达式。采用自相似函数的方法可以轻易地将所论问题转化为Riemann—Hilbert问题,并求得了扩展裂纹表面分别受到运动变载荷Px2/t2、Px作用下的位移、应力和动态应力强度因子的解析解。利用这些解并采用叠加原理,就可以求得任意复杂问题的解。这些解在断裂动力学以及弹性动力学、静力学问题当中具有重要的应用价值和理论意义。Dynamic propagation of mode Ⅲ asymmetrical interface crack was investigated using the theory of complex functions. A formulation of analytical solution was derived based on self-similar functions and asymmetrical dynamic propagation with arbitrary index of self-similarity. The problems investigated can be easily translated into Riemann-Hilbert problem using self-similar functions. Therefore, the analytical solutions for displacements, stresses and dynamic stress intensity factors of propagation crack under variable loads Px^2/t^2 and Px were obtained. Furthermore, using the solutions and superposition theorem, the solutions for discretionally complex problems can be found. These solutions can be applied in fracture dynamics, elastodynamics and elastostatics.

关 键 词：复变函数 Ⅲ型非对称界面裂纹 动态扩展 自相似函数 解析解 

分 类 号：O346.1[理学—固体力学]