计算微裂纹损伤材料有效模量的一种简单方法

A SIMPLIFIED CALCULATION METHOD FOR EFFECTIVE MODULI OF MICSOCRACKED SOLIDS

给出了一种基于Ｔａｙｌｏｒ模型的有效介质方法，用以计算微裂纹相互作用对有效本构关 系的影响．该方法假设每一个微裂纹位于一种有效介质之中，该有效介质的弹性模量由不考虑 微裂纹相互作用的 Ｔａｙｌｏｒ模型计算．和自洽方法相比，这种方法计算简单，而且结果更准确．

To estimate the effects of microcrack interaction on the effective moduli of inho- mogeneous solids,some approximate methods based on the concept of effective medium (e.g., self-consistent method, generalized self-consistent method and differential method) may be consid- ered.Howerver,these conventional schemes do not ensure a satisfactory accuracy of the results, at least in some cases, although cumbersome numerical computations or theoretical derivations are often needed. Therefore, it is of importance to develop some methods appropriate for engineers who want to account for the effects of microcrack interaction in simpler ways. An effective medium method based on the Taylor model, which is also refered to the noninteractiong approximation, is suggested to determine the effects of microcrack interaction on the overall constitutive relations of brittle materials weakened by distributed microcracks. Each microcrark is assumed to be embed- ded in an effective medium with a compliance without accounting for interaction. Such a scheme has two advantages. First, it does not requires no numerical iteration to determine the effective moduli. Second, it can account for the effects of microcrack interaction with hotter accuracy than the self-consistent method, which generally overestimates the effects of microcrack interaction. This approximate scheme have been used to analyze some important two-or three-dimensional, isotropic or anisotropic problems,and implemented into a three-dimentional micromechanical damage model based on the concept of domain of microcrack growth. The discussion in this paper can be extended to other heterogeneous materials, such as composites containing inclusions and solids with frictionally sliding or fluid-saturated microcracks or with inclusions.