A multiscale analytical framework for mode I crack in staggered composites

Abstract

Owing to the special arrangement of platelets, staggered composites can achieve superior fracture toughness. Nevertheless, a rigorous mathematical framework for the fracture analysis on them remains a challenge. Here, we show that by incorporating the mechanical behavior of individual unit cells, a multiscale analytical framework for a mode I crack propagation in staggered composites can be setup adopting the “fishnet” scheme proposed recently. The mathematical formulae for the mode I crack turn out to coincide with those for the mode III crack in homogenous ideal elastic-plastic media. Using red abalone nacre as a case study, we show that the inelastic zone in front of the crack and the R-curve given by our analysis agree remarkably well with the experiments. In the last, the design space for the damage-tolerant composites emerges from the crack sensitivity analysis, which could guide the advanced materials design.