应用半权函数法计算界面裂纹的应力强度因子

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

应用半权函数法求解双材料界面裂纹的应力强度因子 ,得到以半权函数对参考位移与应力加权积分的形式表示的应力强度因子。针对特征值为复数λ的双材料界面裂纹裂尖应力和位移场 ,设置与之对应特征值为 -λ的位移函数 ,即半权函数。半权函数的应力函数满足平衡方程 ,应力应变关系 ,界面的连续条件以及在裂纹面上面力为 0 ;半权函数与裂纹体的几何尺寸无关 ,对边界条件没有要求。由功的互等定理得到应力强度因子KⅠ 和KⅡ 的积分形式表达式。本文计算了多种情况下界面裂纹应力强度因子的算例 ,与文献结果符合得很好。由于裂尖应力的振荡奇异性已经在积分中避免 ,只需考虑绕裂尖远场的任意路径上位移和应力 。

Semi-weight function method is used and developed in this paper to solve the problem of two bonded dissimilar materials containing a crack along the bond. Expressions of stress and displacement fields are obtained. Strain component ε x is naturally continuous throughout the entire plate. Two sets of analytical expression of semi-weight functions, which satisfy conditions of continuity across interface, equilibrium equation, stress and strain relationship, u i～r -λ near the crack tip and the traction free on the crack surface, are obtained. Integral expression of fracture parameters, K I and K II, are 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 among high precision calculation methods, compared with the weight function method, this method provides applicable analytical expressions of semi-weight functions and in less restrict conditions. Compared with finite element method, it needs fewer amounts of calculation and simple and convenient FEA model.