Quasi-brittle fracture as failure of hierarchical structure

Abstract

The paper proposes a quasi-brittle fracture model based on the kinetic approach and empirical regularities such as the concentration criterion and Zhurkov’s formula for a material in the form of a nested self-similar hierarchical structure. The concentration criterion is reformulated as a failure probability condition for structural levels. The hierarchy scheme takes into account critical values of the concentration parameter. The failure probabilities of hierarchy levels are calculated as functions of time, temperature, material parameters, and loading condition. Knowing the failure probabilities of hierarchy levels allows one to evaluate the stress dynamics in a material, average failure volume, elastic energy and inelastic strain release, etc. Experimental and calculated dependences are compared.