A mathematical model for case hardening of steel
- Fasano, Antonio
- Hömberg, Dietmar
- Panizzi, Lucia
2010 Mathematics Subject Classification
- 35K60 35R05 82B26
- Heat treatment, phase transitions, coupled PDE, case hardening
A mathematical model for the case hardening 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 evolution of phase fractions. We investigate questions of existence and uniqueness of a solution and finally present some numerical simulations.
- Math. Models Methods Appl. Sci., 19 (2009) pp. 2101--2126.