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Modelling of carbon diffusion and ferritic phase transformations in an unalloyed hypoeutectoid steel
Arch. Mech. 59 (4-5), 435-466, 2007
Keywords: mathematical modelling; steel; case hardening; carbon diffusion; phase transformations; system of PDEs and ODEs
Abstract
During the important industrial process of case hardening, phase transformations in a steel workpiece are essentially influenced by the (non-homogeneous) carbon distribution (near the surface). Moreover, the temperature course is of great importance. We develop a mathematical model of case hardening which takes diffusion of carbon in austenite, heat conduction and possible phase transformations into account. In this work, mechanical behaviour (thermo-elasticity, classical plasticity and transformation-induced plasticity) is not included in the model. As a result we obtain an initial-boundary-value problem for a coupled system of two parabolic partial and several ordinary differential equations. Finally, we present some numerical simulations.