Fracture Criteria and Duality of Critical Damage-Failure Transitions

Abstract

Duality of criticality of damage-failure transitions, caused by two intermediate self-similar singular solutions for the stress field at the crack tip (the stress intensity factor criteria) and the blow-up damage localization kinetics, is used for the interpretation of two-parameters fracture criteria. Two additional parameters (cohesive strength and cohesive length) are associated with parameters of the blow-up damage localization kinetics initiated by critical (cohesive) stress at the crack process zone. The presence of two self-similar solutions provides the variety of crack advance depending on the load intensity or the notch type. Two parameters criteria was introduced as the measure of the average stress at the damage localization area (the so-called, process zone). The idea of averaging a sharply increasing stress in front of a notch (crack) over a characteristic length with the subsequent comparison of the obtained averaged stress with the ultimate strength of the material was introduced by Novozhilov as stress averaging criterion and modified as the two-parameters criteria. The two stress criteria in the presence of two characteristic lengths allow the interpretation of the Critical Distance approach in terms of mentioned two intermediate self-similar singular solutions. Realization of experimental program analyzing the DIC pattern in the stretched notch sample revealed the presence of two attractors (corresponding to two self-similar solutions) responsible for two mechanisms of damage-failure transition related to two-parameters fracture criteria.