Mathematical model coupling phase transformation and temperature evolution during quenching of steels

AbstractTo calculate the internal stresses in steels during quenching it is necessary to be able to predict accurately the evolution of phase transformations during the cooling process. After a review of published papers, a mathematical model coupling phase transformations with temperature field predictions at each instant during the cooling process is proposed. Incubation and growth periods are treated separately, using Scheil's method and the Johnson–Mehl–Avrami formulation, respectively. Martensitic growth is considered separately using the Koistinen and Marburger law. The temperature field calculation is carried out by the resolution of the heat equation using an implicit finite–difference method. An internal heat source term has been included in the heat equation to take into account the heat generated by the phase transformation. The results of the theoretical calculations are compared with those obtained by experiment, and the validity of the model and the effect of internal stresses on the theoret...