On the formulation of the kinematics and thermodynamics for polycrystalline materials undergoing phase transformation

Commonly implemented material processing routines not limited to quenching, welding or heat treatment requires exposure of a part to complex thermal and mechanical loading histories that manifest as residual stress and distortion. Of interest to material designers and fabricators is modeling and simulating the evolutionary process a part undergoes for the sake of capturing this observable residual stress states and geometric distortion accumulated after processing. To move toward an overall consistent modeling approach, we premise this investigation with a consistent thermodynamic framework for a generalized multiphase material. Following this, we extend the single phase Evolving Microstructural Model of Inelasticity (EMMI) internal state variable model to multiphase affirming that the interaction between phases is through an interfacial stress. We then use a self-consistent polycrystalline model to partition each individual phase's strain field ensuring a hybrid between compatibility and equilibrium. With a synthesis of the aforementioned ideas, the additional transformation plasticity (TRIP) is accounted for by changing each phase's flow rule to accommodate an interfacial stress. Following this, we couple the mechanical multiphase model equations with a previously developed non-diffusional phase transformation kinetics model. Contrary to the classical modeling approach, our material model is based on mixture theory wherein we track the behavior of each individual phase. A numerical evaluation of the coupled model is performed and applied to a simplified quenching boundary value problem.