A Modified Constitutive Model With Grain Rotation for Superplastic Forming of Ti-6Al-4V Alloy

A physically based constitutive model with internal state variables (ISVs) is established, it is used to describe the flow stress and microstructure evolution of Ti-6Al-4V alloy in the superplastic forming (SPF). The ISVs in the constitutive model includes the dislocation density, grain size, and the volume fraction of dynamic recrystallization. The flow stress consists of sigma(fd), sigma(ta), and sigma(GB), which are related to forest dislocation, thermal activation, and grain boundary sliding (GBS), respectively. The material constants of the constitutive model are determined, and the genetic algorithm (GA) optimization. A modeling method path to optimize the flow stress model is established, which is on the basis of the errors between the predicted and experimental flow stresses. In the modified flow stress constitutive model, the grain rotation (GR) is applied as a hardening mechanism, and the void is treated as a softening mechanism. A new GR model is proposed to describe the flow stress which is related to the GR. The modified constitutive model can accurately predict the evolution of yield stress, grain size and flow stress in SPF. With the calculation results of the multi-scales constitutive model, the mechanism of Ti-6Al-4V in SPF is discussed, and a new deformation map with dominant mechanisms for Ti-6Al-4V is obtained.