Numerical Analysis of Thermo-Mechanical Phenomena of the Progressive Hardening Elements Made of Tool Steel for Cold Work

The numerical algorithm of thermal phenomena is based on the solution of the heat conduction equations in Petrov-Galerkin’s formula using the finite element method. In the modeling of phase transformation in the solid state, the models based on the diagrams of continuous heating and continuous cooling (CHT and CCT). In the modeling of mechanical phenomena, equations of equilibrium and constitutive relationships were adopted in the rate form. It was assumed that the hardened material is elastic-plastic, and the plasticizing can be characterized by isotropic, kinematic or mixed strengthening. In the model of mechanical phenomena besides thermal, plastic and structural strains, the transformations plasticity was taken into account. Thermo-physical size occurring in the constitutive relationship, such as Young’s modulus and tangential modulus, while yield point depend on temperature and phase composition of the material. The modified Leblond model was used to determine transformation plasticity. This model was supplemented by an algorithm of modified plane strain state, advantageous in application to the modeling of mechanical phenomena in slender objects. The problem of thermoelasticity and plasticity was solved by the FEM. In order to evaluate the quality and usefulness of the presented numerical models, numerical analysis of temperature fields, phase fractions, stresses and strains was performed, i.e. the basic phenomena accompanying surface layer of progressive-hardening with a movable heat source of slender elements made of tool steel for cold work.