Grain boundary curvature and grain growth kinetics with particle pinning

Second-phase particles are used extensively in design of polycrystalline materials to control the grain size. According to Zener’s theory, a distribution of particles creates a pinning pressure on a moving grain boundary. As a result, a limiting grain size is observed, but the effect of pinning on the detail of grain growth kinetics is less known. The influence of the particles on the microstructure occurs in multiple length scales, established by particle radius and the grain size. In this article, we use a meso-scale phase-field model that simulates grain growth in the presence of a uniform pinning pressure. The curvature of the grain boundary network is measured to determine the driving pressure of grain growth in 2D and 3D systems. It was observed that the grain growth continues, even under conditions where the average driving pressure is smaller than the pinning pressure. The limiting grain size is reached when the maximum of driving pressure distribution in the structure is equal to the pinning pressure. This results in a limiting grain size, larger than the one predicted by conventional models, and further analysis shows consistency with experimental observations. A physical model is proposed for the kinetics of grain growth using parameters based on the curvature analysis of the grain boundaries. This model can describe the simulated grain growth kinetics.