An incremental constitutive relationship incorporating phase transformation with the application to stress analysis for the quenching process

Abstract This paper deals with the constitutive relationships of thermoelastic–plastic bodies during heat processing/treatment when considering phase transformation. The material undergoing phase transformation due to the heat processing/treatment is assumed to be a mixture. A non-classical constitutive equation involving phase transformation is put forward based on irreversible thermodynamics with internal variables. Interaction between temperature and metallic structures is discussed to obtain the heat-conduction equation including latent heat due to phase transformation. The application of the theory to the cases of quenching is also presented. The structure and temperature distributions are calculated numerically by a finite element technique. The variations of stress are analyzed. Calculated results of the residual stress are compared with experimental data measured by X-ray diffraction and Sachs’ boring-out technique.