STIFFNESS EVALUATION FOR SOLIDS CONTAINING DILUTE DISTRIBUTIONS OF INCLUSIONS AND MICROCRACKS

Materials, such as ceramics, intermetallics, and rocks, contain varyin g amounts of inhomogeneities, and the matrix material is vulnerable to microcracking in the neighborhood around these inhomogeneities. In an attempt to model the micromechanical aspects of this type of material , a solid containing dilute inclusions surrounded by cracks is investi gated in this paper. The dilute-inclusion assumption neglects any inte ractions among different inclusion-crack clusters, but local inclusion -crack and crack-crack interactions are taken into account fully. It i s shown that additional strain due to microcracking in a solid contain ing inclusions can be represented by an integral of crack opening disp lacements weighted by a nonuniform stress field induced by inclusions alone (in the absence of microcracking). An effective numerical approa ch is then developed to evaluate the effective moduli and additional m acroscopic strain due to microcracking in composites. It is found that an increase in the number of hard inclusions may not always lead to e xpected strengthening of the materials, if the matrix material is vuln erable to microcracking around inclusions and a relatively large micro cracking zone develops. The limited calculations show that a quasi-sta tic crack-growing process can lead to an actively growing crack being arrested or to a stationary crack starting to grow. This suggests that self-similar crack growth may not be enough to describe the behavior of microcracked composites.