A scaled model describing the rate-dependent compressive failure of brittle materials

Abstract

A universal relationship is developed that describes the rate-dependent compressive strength of brittle solids based on the micromechanics of the growth of brittle cracks from populations of initial flaws. Real-time observations of crack growth provide insight to the model which captures the dynamics of interacting and rapidly growing cracks. Fundamental time and length scales involved in the problem are used to develop expressions for a characteristic stress and a characteristic strain rate in terms of material and microstructural properties. Scaling simulation results by the characteristic stress and strain rate collapses the data to a single curve in failure stress-strain rate space. This curve represents the universal response, which captures both the relatively constant failure stress at low rates as well as the dramatic increase in strength observed in experiments as the applied strain rate increases above the transition rate. The resulting model for the universal response compares well with experimental data for ceramics and geologic materials, indicating that the model has adequately captured the physics of compressive failure for a wide range of materials.