Near‐Tip Mechanics of Stress‐Induced Microcracking in Brittle Materials

A continuum‐mechanics description of stress‐induced microcracking was developed. Modulus‐reduction effects due to microcracking are taken into account through the model of Budiansky and O'Connell. This is used in conjunction with a modified microcracking criterion that stems from the work of Evans and Fu. The resulting constitutive law for a microcracking material was used in finite‐element calculations to study the near‐tip stress and strain fields and the size and shape of a small‐scale damaged zone for a stationary mode I crack in an elastic body. The finite‐element results for the stationary crack are used to predict asymptotic toughening values which correspond to a fully developed wake of microcracked material for a propagating crack. Substantial toughening can result. In contrast, the microcracking zone for a stationary crack is thought to make little or no contribution to material toughening. The theoretical results are discussed in the context of experimental observations for zirconiatoughened alumina.