A multiple‐crack model of brittle fracture: 2. Time‐dependent simulations

Abstract

A numerical multiple‐crack interaction model is developed to simulate the failure process in brittle solids containing significant populations of flaws. The model, which is two dimensional, allows for the growth of microcracks on a regular array of potential crack sites. Individual cracks may be oriented vertically, horizontally, or at 45° to the sample axes. Quasi‐static equilibrium equations are expressed in terms of finite difference approximations and are solved by applying a renormalization group theory approach. In this paper the results presented in the companion paper are extended to include time‐dependent processes. In particular, both subcritical mode I crack growth and stress‐sensitive stable slip on existing crack surfaces are included. Crack growth rate and shear slip rate are defined by the local stress conditions. By including these two simple rules in the crack model, constant stress creep simulations are performed which reproduce the classic creep response, including all three modes of creep. In addition, the model predicts the proper stress sensitivity of creep rate. This result supports the interpretation that room temperature creep in crystalline rock in compression is dominated by the same stress corrosion process that occurs during subcritical crack growth observed in tension experiments. The process of crack localization, characteristic of the tertiary creep phase and culminating in failure, is discussed. The relation between inelastic strain and acoustic emission is also examined.