Finite Element Analysis of the Thermomechanical Coupling in Quenching of Steel Cylinders Using a Constitutive Model with Diffusional Phase Transformations

Quenching is a heat treatment usually employed in industrial processes. It provides a mean to control mechanical properties of steels as toughness and hardness. Phenomenological aspects of quenching involve couplings among different physical processes and its description is unusually complex. Basically, three couplings are essential: thermal, phase transformation and mechanical phenomena. This article deals with the modeling and simulation of quenching in steel cylinders using a multiphase constitutive model with internal variables formulated within the framework of continuum mechanics and the thermodynamics of irreversible processes. The energy equation thermomechanical coupling terms are exploited, considering two different models. The first one is an uncoupled model where thermo-mechanical couplings are neglected, corresponding to the rigid body energy equation. The second model considers the latent heat associated with phase transformation in order to represent thermomechanical coupling. A numerical procedure is developed based on the operator split technique associated with an iterative numerical scheme in order to deal with non-linearities in the formulation. With this assumption, the coupled governing equations are solved to obtain the temperature, stress and phase fields from four uncoupled problems: thermal, phase transformation, thermo-elastic and elastoplastic. Finite element method is employed for spatial discretization. The proposed general formulation is applied to the through hardening of steel cylinders. Numerical simulations present a good agreement with experimental data for temperature and phase transformation distributions, indicating some situations where it is important to consider the thermomechanical coupling in the description of quenching process.