Stiffness Evaluation for Solids Containing Dilute Distributions of Inclusions and Microcracks

Materials, such as ceramics, intermetallics, and rocks, contain varying 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 investigated in this paper. The dilute-inclusion assumption neglects any interactions among different inclusion-crack clusters, but local inclusion-crack and crack-crack interactions are taken into account fully. It is shown that additional strain due to microcracking in a solid containing inclusions can be represented by an integral of crack opening displacements weighted by a nonuniform stress field induced by inclusions alone (in the absence of microcracking). An effective numerical approach is then developed to evaluate the effective moduli and additional macroscopic strain due to microcracking in composites. It is found that an increase in the number of hard inclusions may not always lead to expected strengthening of the materials, if the matrix material is vulnerable to microcracking around inclusions and a relatively large microcracking zone develops. The limited calculations show that a quasi-static 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.