Thermodynamically consistent phase-field modeling for polycrystalline multi-phase continua

Abstract

The macroscopic material properties of steels are affected by microstructure evolution during hot-forming. Phase transformations, carbide precipitation, and recrystallization are examples of the relevant phenomena. Most engineering components require high strength and sufficient residual ductility to withstand mechanical loads and to provide favorable manufacturing conditions. One way to achieve this state is a microstructure composed of bimodal grains. The key contribution of the present manuscript is the proposition of a prototype model for an existing thermodynamic framework, combining two phase-field approaches for the numerical investigation of recrystallization effects. The developed prototype model captures phase transformations, carbon diffusion, and carbide precipitation during static recrystallization. A combined phase-field approach models the microstructure evolution driven by temperature, curvature effects and stored energy effects. The corresponding order parameters are fractions of ferrite, martensite, and carbide phases as well as grain orientation and microstructure crystallinity describing grain boundary movement. The grain boundary evolution is captured by a Kobayashi–Warren–Carter approach. The prototype model builds upon a generalized framework on thermodynamics and captures grain boundary motion in multi-phase continua. This yields a novel constitutive framework capable of describing the complex material behavior of metals during recrystallization annealing. To demonstrate the evolution of phase fractions and carbide precipitation, conclusive two-dimensional phase-field simulations are solved with the finite-element method.