Internal-state-variable based self-consistent constitutive modeling for hot working of two-phase titanium alloys coupling microstructure evolution

An internal-state-variable based self-consistent constitutive model was proposed for unified prediction of flow stress and microstructure evolution during hot working of wrought two-phase titanium alloys in both single-beta region and two-phase region. For each constituent phase of titanium alloys, a set of constitutive equations incorporating solution strengthening, Hall–Petch effect, dislocation interaction, and dynamic recrystallization were developed using internal state variable method. The effect of second phase on recystallization was modeled by considering particle stimulated nucleation and exerting drag force on boundary migration. The constitutive equations of constituent phases were implemented into a viscoplastic self-consistent scheme to predict the overall response of the aggregate. Predictions of the model are in good agreement with experimental results of the Ti–6Al–4V alloy and IMI834 alloy. The model can reproduce many features of the hot working of two-phase titanium alloys, including the dependence of flow stress on temperature, strain rate and alloying elements; the increase of strain rate sensitivity with temperature; the stress and strain partitionings between alpha and beta phases; the relatively high apparent activation energy in two-phase region, the decrease of recrystallization kinetics with temperature in two-phase region; and the decrease of recrystallized grain size with Zener–Hollomon parameter in beta working.