A numerical model of transformation superplasticity for iron

A numerical model of transformation superplasticity for an elastic, ideally plastic material is presented using a two-dimensional plane-strain formulation considering both temperature and displacement. The evolution of temperature, stresses and strains during the α/γ 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 uniaxial applied stress and the uniaxial 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 of these trends are in qualitative agreement with existing analytical solutions for transformation superplasticity in an ideally plastic material. 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 both analytical predictions and experimental data for pure iron.