Size effects in layered composites - Defect tolerance and strength optimization

Mixture of hard and soft phases in a smart way makes strong and tough materials - this approach, inspired by natural composites, has been widely adopted by scientists and engineers. Behind it exist many interesting fundamental mechanics. In this study, we solve analytically the stress intensity factor for a crack propagating from the hard to the soft phase in a layered composite starting with the postulation on the crack profile inspired by the shear-lag model. Our analysis shows that when a crack extends from the hard phase into the soft one, the stress intensity factor amplifies first at the hard-soft interface and then declines quickly to zero as it progresses toward the next hard phase. This crack arresting mechanism works until a secondary crack initiates in the next hard layer and then merges with the main crack. The efficiency of the defect tolerance, measured by the effective strength of the layered composite, is found to exhibit strong size effects. Overall, the smaller the dimensions of two phases are, the more efficiently of the layered composites tolerate defects. Furthermore, if the dimension of one phase is given, there always exists a critical dimension of the other phase that optimizes the efficiency (or the composite strength). A relationship between the defect tolerance efficiency with the nanostructures which is analogous to the famous “Hall-Petch” and “inverse Hall-Petch” relationships for polycrystalline metals is found. The analysis in this work can be used to guide the micro-to nano-structure design for synthesizing innovative defect-tolerant composites.