Critical hardening rate model for predicting path-dependent ductile fracture

Abstract

A new phenomenological framework for predicting ductile fracture after non-proportional loading paths is proposed, implemented into FE software and validated experimentally for a limited set of monotonic and reverse loading conditions. Assuming that ductile fracture initiation is imminent with the formation of a shear band, a shear localization criterion in terms of the elastoplastic tangent matrix is sufficient from a theoretical point of view to predict ductile fracture after proportional and non-proportional loading. As a computationally efficient alternative to analyzing the acoustic tensor, a phenomenological criterion is proposed which expresses the equivalent hardening rate at the onset of fracture as a function of the stress triaxiality and the Lode angle parameter. The mathematical form of the criterion is chosen such that it reduces to the Hosford–Coulomb criterion for proportional loading. The proposed framework implies that the plasticity model is responsible for the effect of loading history on ductile fracture. Important non-isotropic hardening features such as the Bauschinger effect, transient softening and hardening stagnation must be taken into account by the plasticity model formulation to obtain reasonable fracture predictions after non-proportional loading histories. A new comprehensive plasticity model taking the above effects into account is thus an important byproduct of this work. In addition, compression–tension and reverse-shear experiments are performed on specimens extracted from dual-phase steel sheets to validate the proposed plasticity and fracture model.