A unified model for deformation instability based on energy inflection

The critical state of plastic instability preceding the fracture of metals, such as necking under tension and shear banding under torsion, was carefully analyzed from thermodynamics considerations. A unified criterion based on energy inflection (EI criterion) was established which takes stress states and loading rates into account. Different from many other criteria that are based on a specified energy, the proposed criterion assumes deformation instability would occur at the point of energy inflection. Through calibrating the parameters that governed the entropy evolution, the EI criterion was shown to exhibit significant efficacy in predicting the critical strain at which instability occurred for Ti-6Al-4V, aluminum alloy, and pure copper under various loading conditions. Furthermore, a comparison of the proposed EI criterion was made with other criteria in the literature.