Critical hardening rate model for predicting path-dependent ductile fracture

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.