双材料界面裂纹平面问题的半权函数法  

Semi-Weight Function Method on Computation of Stress Intensity Factors in Dissimilar Materials

作　　者：马开平[1] 柳春图[1] 

机构地区：[1]中国科学院力学研究所,北京100080

出　　处：《应用数学和力学》2004年第11期1135-1142,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(19872066)

摘　　要：　应用半权函数法求解双材料界面裂纹的平面问题·　由平衡方程、应力应变关系、界面的连续条件以及裂纹面零应力条件推导出裂尖的位移和应力场,其特征值为lambda及其共轭·　设置特征值为lambda的虚拟位移和应力场,即界面裂纹的半权函数·　由功的互等定理得到应力强度因子KⅠ和KⅡ以半权函数与绕裂尖围道上参考位移和应力积分关系的表达式·　数值算例体现了半权函数法精度可靠。Semi-weight function method is developed to solve the plane problem of two bonded dissimilar materials containing a crack along the bond. From equilibrium equation, stress and strain relationship, conditions of continuity across interface and free crack surface, the stress and displacement fields were obtained. The eigenvalue of these fields is lambda. Semi-weight functions were obtained as virtual displacement and stress fields with eigenvalue -lambda. Integral expression of fracture parameters, K_Ⅰ and K_Ⅱ, were obtained from reciprocal work theorem with semi-weight functions and approximate displacement and stress values on any integral path around crack tip. The calculation results of applications show that the semi-weight function method is a simple, convenient and high precision calculation method.

关 键 词：双材料 界面裂纹 应力强度因子 半权函数法 平面问题 

分 类 号：O346.1[理学—固体力学]