For the extreme pressure and temperature arising in the hot rolling process, thermomechanical (TM) models are used to predict the residual stresses on the surface of the die because a quantification of the TM stresses allows a prediction of the life span of the rolling die. As the accuracy and consistency of models developed in this area show a large variation due to the considered parameters, conditions, and assumptions, the capability of the developed models needs to be verified for a particular set of circumstances. In this study, new constitutive equations are proposed and a model consisting of five sub-models that computes temperature distribution, thermal stresses, mechanical stresses, and thermomechanical stress for the rolling die under continuous casting application has been developed and presented in this paper. The first sub-model describes the temperature distribution on the rolling die surface by accounting for the effects of different process parameters such as the initial temperature of the slab, reduction ratio, and the rolling speed, while the second and the third sub-models describe the thermal cyclic stress and the elasticity deformation of mechanical stress, respectively. Furthermore, the fourth sub-model describes the TM stress generation through inheriting numerical approaches, and the last sub-model is developed for the H13 tool material response at a high temperature. To verify the developed analytical models, a finite element simulation and the experimental data are considered. The analytical models are computed using Python, and the ABAQUS software has been used for the finite element simulations. The results show a good agreement with the finite element simulation and experimental data.
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