Three-dimensional thermo-elastic–plastic finite element modeling of quenching process of plain-carbon steel in couple with phase transformation

The Numerical Analysis of the Phenomena of Superficial Hardening of the Hot-Work Tool Steel Elements / Analiza Numeryczna Zjawisk Przypowierzchniowego Hartowania Elementów Ze Stali Narzędziowej Do Pracy Na Gorąco

“…heat transfer equation (1) with completed initial (2) and boundary conditions (3), (4), the finite element method in Galerkin formulation was used [3,22].…”

“…As a result of the complexity of phenomenon of heat treatment process, there are many mathematical and numerical difficulties in its modelling. For this reason there hasn't a model which includes phenomenon accompanying heat treatment and hardening of hot-work tool steel [1][2][3][4][5][6].…”

“…The phenomena occurring during the heat treatment are very complex and still incompletely described. The model of the hardening process should contain at least with three coupling elements: thermal, structural and mechanical [3,4,[7][8][9][10][11]. Determination of the composition of each phases, their kinetics and obtained structures during the cooling process of iron alloys is necessary to calculate the stresses for the hardening process.…”

“…Therefore, in the modeling of mechanical phenomena the use of the models of elastic-plastic materials is required. Additionally, to ensure the reliability of the results of numerical simulations of mechanical phenomena, except thermal, structural and plastic strains the transformation induced plasticity should be taken into account [3,[12][13][14][15][16][17][18].…”

“…Therefore, in the paper paid attention to this problem by comparing the results from numerical simulation for the two rate of cooling, although both are relatively small. To implement this type of algorithms one usually applies the FEM, which makes it possible to take into account both nonlinearities and inhomogeneity of thermally processed material [1,3,10,13,19,20]. …”