Statistical simulation of microcrack toughening in advanced ceramics

Abstract

A statistical distribution of microcracks is simulated as a damage process zone developed around the vicinity of a macro-crack in a brittle ceramic. Uniform distributions of microcrack location and orientation are assumed in a Monte Carlo process to represent isotropic damage. An alternating iteration numerical technique is employed to evaluate the main-crack and the damage zone microcracks interactions, and the behavior of the main-crack either in shielding or anti-shielding modes may then be assessed. With the assumption of dilute microcrack concentration, however, one can neglect the microcrack–microcrack interaction, and the interacting stress intensity factor (SIF) at the main-crack tip can then be superimposed for each microcrack. In this study, two general sources of loading are evaluated, one is for the main-crack microcrack interaction under an applied remote load, and the other is for the main-crack microcrack interaction accompanied by the relief of residual stresses on the microcrack surfaces. Nevertheless, the results show that these two conditions together with the isotropic damage assumption can always shield the main-crack tip, and therefore increase the ceramic toughness. In addition, it is found that microcracks behind the main-crack tip can make the most shielding whereas microcracks ahead of the main-crack tip play no role in shielding.