Steel heat treating: mathematical modelling and numerical simulation of a problem arising in the automotive industry

We describe a mathematical model for the industrial heating and cooling processes of a steel workpiece representing the steering rack of an automobile.The goal of steel heat treating is to provide a hardened surface on critical parts of the workpiece while keeping the rest soft and ductile in order to reduce fatigue.The high hardness is due to the phase transformation of steel accompanying the rapid cooling.This work takes into account both heating-cooling stage and viscoplastic model.Once the general mathematical formulation is derived, we can perform some numerical simulations.