The mathematical modeling of phase transformation of steel during quenching

In the heat treatment of steel, uneven cooling in variably introduces residual stresses in the workpiece. These residual stresses can combine with the thermomechanical stresses encountered in operation to cause premature fatigue failure of the material. A prediction of the residual and thermoelastoplastic stresses developed during heat treatment would be beneficial for component design. In this article a numerical model is developed to predict the thermoelastoplastic and residual stresses during rapid cooling of a long solid cylinder. The total strains developed during cooling of the cylinder comprise elastic, thermal, and plastic strains and strains due to phase transformation. For plastic deformation an extension of Jiang’s constitutive equations developed by Jahanian is adopted. The properties of the material are assumed to be temperature dependent and characterized by nonlinear strain hardening. For phase transformation two parts are considered: nucleation according to Scheil’s method and phase growth according to Johnson and Mehl’s law. For martensitic transformation, a law established by Koisteinin and Marburger is used. Non-additivity of pearlitic and bainitic nucleation suggested by Manning and Lorig is taken into account by means of a correction factor to Scheil’s summation of the transition from pearlitic to bainitic. The effect of phase transformation and temperature dependence of material properties is investigated. It is shown that by neglecting the temperature dependency and phase transformation in numerical calculations, the results are underestimated. The numerical results are compared with the available experimental data in the literature, and good agreement is observed.