Mathematical model of phase transformations and elastoplastic stress in the water spray quenching of steel bars

A mathematical model, based on the finite-element technique and incorporating thermo-elasto-plastic behavior during the water spray quenching of steel, has been developed. In the model, the kinetics of diffusion-dependent phase transformation and martensitic transformation have been coupled with the transient heat flow to predict the microstructural evolution of the steel. Furthermore, an elasto-plastic constitutive relation has been applied to calculate internal stresses resulting from phase changes as well as temperature variation. The computer code has been verified for internal consistency with previously published results for pure iron bars. The model has been applied to the water spray quenching of two grades of steel bars, 1035 carbon and nickel-chromium alloyed steel; the calculated temperature, hardness, distortion, and residual stresses in the bars agreed well with experimental measurements. The results show that the phase changes occurring during this process affect the internal stresses significantly and must be included in the thermomechanical model.