Grain Growth Simulations Including Particle Pinning Using the Multiphase-field Concept

In this paper, the effect of particle pinning on grain boundary motion is investigated by phase-field modeling. In general, the kinetics of grain growth in multicrystalline materials is determined by the interplay of curvature driven grain boundary motion and the balance of interfacial tension at the vertices of a grain boundary network. A comprehensive way to treat both effects in one model is given by the phase-field approach. The specific feature of the multiphase-field model used for this investigation is its ability to treat each grain or phase boundary with its individual characteristics, together with a thermodynamic coupling which allows a sound treatment of phase transformation, e.g. the formation of precipitates of a second phase.The pinning effect itself is simulated on the nanometer scale resolving the interaction of individual inert or reactive precipitates with a curved grain boundary. From these simulations an effective pinning force is deduced, and a model for a driving force dependent grain boundary mobility is formulated accounting for the pinning effect in the grain growth simulation on the mesoscopic scale. These simulations demonstrate how particle pinning leads to much slower growth kinetics and a different grain morphology with higher boundary curvatures in the stationary state. Finally, an increase of the pinning force due to a changing particle density, e.g. during heat treatment, is shown to result in a transition between normal and abnormal grain growth before grain coarsening is inhibited completely.