Computer Simulations of R-Curve Behavior in Microcracking Materials

Abstract

A computer program has been developed which simulates the process of microcracking in two-phase ceramic materials. This simulation provides a method of examining the complex interactions which occur between a propagating crack and the residually stressed particles around it. As the residual stresses near second-phase inclusions are relieved by microcrack formation, a process zone forms around the main crack, partially shielding it. The resulting crack resistance curves, or R curves, associated with crack shielding mechanisms are generated by the program. Three variables— the microcrack density (f_s), the dilatant strain associated with each microcracked particle (θ), and the orientation of the microcracks (Ψ)— were used to determine their influence on fracture toughness. The steady-state toughness was found to increase with second-phase particle additions, increased dilatant strain, and the formation of microcracks parallel to the direction of applied stress. However, the magnitude of toughening increase attained in these-simulations was generally lower than that predicted by continuum models. This discrepancy is attributed to the fact that interactions between microcracks produce frontal zones which result in a positive Δk, and hence, a lower steady-state toughness. This behavior is enhanced when microcracks link with the main crack to promote further extension.