Microstructural effects in finite multilayers with aligned cracks

A study of microstructural effects in finite layered media containing single and periodically distributed cracks is carried out based on an exact elasticity solution. First, the effect of microstructural refinement of a multilayer comprised of alternating hard and soft layer pairs on the stress intensity factors and crack-opening displacements of a single crack embedded in the middle of the layered structure is studied. The results indicate that the crack-opening displacements converge to the corresponding ones in the fully homogenized configuration with increasing microstructural refinement. In contrast, the stress intensity factors asymptotically converge to values that depend on the layer stiffness. For configurations with many layers, partial homogenization efficiently captures these microstructural effects and preserves the homogenization’s efficiency. Then the exact elasticity solution is employed to study the response of a homogeneous solid with elastic properties degraded by periodically aligned cracks. The effective properties obtained from a homogenization scheme are used to quantify the convergence behavior of the stress intensity factors of cracks far and near the bounding surface of the periodically cracked solid as a function of different levels of partial homogenization.