应用通用权函数法计算热机载荷作用下三维界面裂纹的应力强度因子

热机载荷共同作用下双材料、复合材料中的裂纹扩展往往发生在界面处，并且工程中实际遇到的裂纹大多数是三维裂纹，传统的求解热冲击及机械载荷共同作用下界面裂纹应力强度因子的数值方法如有限元、边界元法计算量大，计算效率低。由于通用权函数仅仅与裂纹体的几何形状有关，与载荷、时间无关，求解应力强度因子时避免了反复的应力分析，计算效率大大提高, 通用权函数法非常适合计算复杂冲击载荷下应力强度因子分布的过渡过程。根据Betti互易原理，本文推导出了三维界面裂纹问题通用权函数法的普遍表达式，并给出了热机载荷共同作用下三维界面I型、Ⅱ型和Ⅲ型裂纹问题通用权函数法的有限元格式. 通过实例计算比较，表明此方法得到的结果可以达到满意的工程应用精度。

Calculation of the Stress Intensity Factors of Three Dimensional Interface Crack Under Mechanical and Thermal Loading Using Universal Weight Function Method

Crack propogation in bimaterials and composites tends to occur at the interface when they withstand mechanical and thermal loadings, most cracks in engineering practice are three dimensional cracks, the traditional numerical methods such as finite element method and boundary element method for determination of transient stress intensity factor of interface crack under mechanical and thermal loadings are inefficient due to large amount of calculation. The universal weight function (UWF) is only dependent on the crack configuration and body geometry, and is independent of temperature fields and time, which avoids the repeated determinations of stress field for individual time instants and has an enhanced efficiency. The UWF method is especially suitable for determining the variation of transient stress intensity factors of an interface cracked body subjected to thermal and mechanical shock. The basic equation and finite element implementation of the UWF method for three dimensional Mode I, Mode II and Mode III interface cracks subjected to thermal and mechanical loadings is given in this paper based on Betti’s reciprocal theorem. Numerical results show that the UWF method is of good accuracy and satisfies the engineering application demand.