Brittle fracture in disordered materials: A spring network model

Abstract

A model for investigating the influence of distributed disorder on the failure of brittle materials is introduced. The model assumes that microstructural features of a material can be represented by simple linear springs with a failure threshold, and that the entire material can be represented by a connected network of such springs. Distributed disorder is introduced by allowing spring-to-spring variations in spring characteristics such as the modulus and the failure strain. The conditions under which such a spring network model is valid for studying failure are discussed. The consequences of distributed residual stress disorder on macroscopic mechanical behavior are then studied using the network model, and a brittle to ductile-like transition in the stress-strain behavior is observed with increasing disorder. All the qualitative features of the network results can be described theoretically by a statistical analysis of this problem. Finally, notch tests are performed to evaluate the strength and toughness of the ductile-like materials as compared to the uniform (no disorder) material, and the ductile-like material is found to have (i) a larger work of fracture, (ii) comparable strength in the presence of processing flaws, and (iii) the possibility of larger toughness. Based on these results, the possibility of observing such ductile-like behavior in real composite materials is discussed.