An analysis of dynamic fracture in microcracking brittle solids

Abstract

Microcracks running dynamically in a brittle solid influence both the elastic moduli and the strength. If such a material contains a population of microcracks, the velocity of the microcracks and the conditions for microcrack coalescence in front of the macrocrack tip will determine the measured values of tensile fracture toughness. In this paper an analysis is presented which seeks to derive the ratio of dynamic to static fracture toughness values in microcracking brittle solids. A model is proposed which determines an estimate of the stiffness loss caused by a dilute population of microcracks aligned in a direction normal to the far-field tensile stress axis. This solution is then used to calculate the stiffness loss in brittle polycrystalline solids. On the assumption that microcrack coalescence and macrocrack initiation occur when the average opening displacement of the microcracks reaches a critical value, the ratio of dynamic to static fracture toughness is predicted as a function of microcrack velocity and elastic properties. The results of the analysis are compared with experimental results of quasi-static and dynamic fracture initiation roughness for polycrystalline ceramics. Experimentally measured ratios of dynamic to static fracture toughness in brittle ceramics fall within the bounds predicted by the analysis.