A mathematical model for case hardening of steel

Abstract

A mathematical model for the gas carburizing of steel is presented. Carbon is dissolved in the surface layer of a low-carbon steel part at a temperature sufficient to render the steel austenitic, followed by quenching to form a martensitic microstructure. The model consists of a nonlinear evolution equation for the temperature, coupled with a nonlinear evolution equation for the carbon concentration, both coupled with two ordinary differential equations to describe the phase fractions. We prove existence and uniqueness of a solution and finally present some numerical simulations.