Constitutive model for high temperature deformation of titanium alloys using internal state variables

Abstract

The internal state variable approach nowadays is more and more used to describe the deformation behavior in all of the metallic materials. In this paper, firstly the dislocation density rate and the grain growth rate varying with the processing parameters (deformation temperature, strain rate and strain) are established using the dislocation density rate as an internal state variable. Secondly the flow stress model in high temperature deformation process is analyzed for each phase of titanium alloys, in which the flow stress contains a thermal stress and an athermal stress. A Kock–Mecking model is adopted to describe the thermally activated stress, and an athermal stress model is established using two-parameter internal state variables. Finally, a constitutive model coupling the grain size, volume fraction and dislocation density is developed based on the microstructure and crystal plasticity models. And, the material constants in present model may be identified by a genetic algorithm (GA)-based objective optimization technique. Applying the constitutive model to the isothermal compression of Ti–6Al–4V titanium alloy in the deformation temperature ranging from 1093 to1303 K and the strain rate ranging from 0.001 to 10.0 s −1, the 20 material constants in those models are identified with the help of experimental flow stress and grain size of prior α phase in the isothermal compression of Ti–6Al–4V titanium alloy. The relative difference between the predicted and experimental flow stress is 6.13%, and those of the sampled and the non-sampled grain size are 6.19% and 7.94%, respectively. It can be concluded that the constitutive model with high prediction precision can be used to describe the high temperature deformation behavior of titanium alloys.