热机载荷作用下三维界面裂纹问题的权函数法分析

ANALYSIS OF WEIGHT FUNCTION METHOD FOR THREE DIMENSIONAL INTERFACE CRACK UNDER MECHANICAL AND THERMAL LOADING

热机载荷共同作用下双材料和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.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,因此在求解复杂冲击载荷下界面裂纹应力强度因子随时间的变化过程时,避免了反复的应力分析,计算效率得到提高.根据Betti互易原理,论文推导出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.通过与实例计算比较,表明此方法得到的结果可以达到满意的工程应用精度.

Crack propagation in bimaterials and composites tends to occur at the interface when the materials are applied to mechanical and thermal loadings. Most cracks presented in engineering practice are three dimensional. The universal weight function （UWF） is only dependent on the crack configuration and body geometry, and independent of temperature fields and time, which avoids the repeated determinations of stress field for individual time instants and has an enhanced efficiency when determining the variation of transient stress intensity factors of an interface cracked body subjected to complex impact loads. 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 are given in this paper based on the Betti＇s reciprocal theorem. Numerical results show that the UWF＂ method is of good accuracy and suitable for the engineering application.