Variational modeling of temperature induced and cooling-rate dependent phase transformations in polycrystalline steel

Abstract

Phase transformations in steel have a high impact on the material properties. The material is modified by a changed stiffness as well as residual stresses which are a result of transformation strains and plastic deformations during the phase transition. In the current work, we propose a variational material model which is able to display the phase transformations which occur during thermal processes like induction hardening and grinding. Depending on the cooling rate, the material model is able to show the transformation between austenite and martensite, austenite and ferrite as well as a mixture of both. The polycrystalline structure of the steel is taken into account by use of different oriented grains which are considered by a combined Voigt–Reuss bound for the energy of the phase and grain mixture. The material model is derived using the principle of the minimum of the dissipation potential for non-isothermal problems. Compared to classical approaches in material science, the model is thermomechanically coupled. Thus, the phase transformation is also influenced by the stress state and individual martensitic variants are favored during the transformation process, which is an important property for applications to process chains. The model’s ability to show the complex material behavior is proven by calculations on the material point level as well as by finite element simulations.