Energy Approach to Fracture Prediction under Developed Irreversible Deformation

This paper presents an energy-based approach for predicting elastoplastic fracture, formulated through the concept of a critical strain energy threshold. The method combines a newly introduced energy fracture criterion with a modified relaxation model of plasticity belonging to the structural-temporal class of theories. This combination enables the accurate description of materials exhibiting complex deformation behavior, including non-monotonic stress–strain curves and the yield point phenomenon, which are particularly relevant for metallic materials deformed at relatively low strain rates. A key advantage of the approach lies in its compactness and physical interpretability: the model parameters are directly related to the material’s initial defect structure and remain independent of the loading history. This allows for predictive capability across different grain sizes and material states without introducing damage accumulation functions or additional fitting parameters. The model is validated against experimental data for magnesium alloys Mg–0.3Ca (wt %) and Mg–1.0Al–1.0Ca–0.4Mn (wt %) with varying grain sizes. The predicted deformation curves (up to fracture) show good agreement with the experiments, even under conditions of developed plastic deformation. In one case, a single critical energy value proved sufficient, while in the other, a Hall–Petch-type grain size dependence was incorporated. The proposed framework shows strong potential for extension to more complex loading paths and other classes of metallic alloys.