Numerical modeling of transformation superplasticity for an elastic, ideally-plastic material

A model for transformation superplasticity is presented using a finite-element formulation with coupled temperature and displacement. The evolution of temperature, stresses and strains during the ferrite-austenite phase transformation of iron is computed for different values of the applied stress. For low stresses, the numerical model predicts a linear relationship between the applied stress and the plastic strain increment accumulated after crossing the phase transformation range. For high stresses, the relationship becomes non-linear: the strain increments tend to infinity as the applied stress approaches the yield stress. Both these trends are in qualitative agreement with analytical solutions for transformation superplasticity. Furthermore, upon introducing plane-strain specific equivalent quantities for the transformation mismatch and the yield stress, the numerical model is in good quantitative agreement with the analytical predictions for iron.