In many polycrystalline materials, second phase particles and solute atoms impose a drag pressure on the motion of grain boundaries. The drag effect occurs on a scale comparable to the particle diameter and interface thickness. However, to simulate grain growth with numerical efficiency one requires a model that captures the drag pressure on the interfaces but does not resolve the fine particles or solute segregation spike. In this paper, a multiphase-field model is proposed to simulate the evolution of microstructure under constant and velocity dependent drag pressures. The accuracy of the model is confirmed in comparison with analytical expressions for a shrinking circular grain. Application of the model is presented for grain growth in two dimensions under particle pinning. Measuring curvature of grain-boundary segments reveals that in the completely pinned structure, the average driving pressure is not equal to but lower than the pinning pressure. Considering this effect, the predicted limiting grain size is about three times larger than that assumed in conventional mean-field theories. Based on this observation, a correction factor is introduced for these mean-field models. The proposed phase-field formulation is also applied to simulate grain growth in the presence of solute drag. The grain growth kinetics follows a phenomenological relationship that can be described with a power law with a time exponent in the range 0.35–0.50. The deviation of the time exponent from 0.5, associated with ideal grain growth, and its correlation with the solute drag parameters is discussed.

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The kinetics of static recrystallization in cold rolled ferritic stainless steel sheet tends to slow drastically over the last 10-20% of recrystallization. This has its origins in both the microstructure (deformed grain shape, precipitates) and in the local deformation texture. In this work we have sought to provide a physical explanation for the slow last stages of recrystallization through a texture dependent JMAK model which is informed by the microstructure of the partially recrystallized microstructure. The geometrical assumptions made in developing this JMAK model have been compared to phase field simulations using experimental observations as the source of their starting configuration.

A new analytic method based on the microstructural path method with nucleation rate and growth rate as descriptors is proposed, which provides a link between the nonhomogeneous distribution of stored energy in plastically deformed materials and the recrystallization rate. The proposed approach uses easily measured recrystallization rates to provide information about the deformation history and the inhomogeneity of stored energy. The theory was evaluated by comparing direct differential scanning calorimetry measurements of inhomogeneity factor, m, on deformed samples of pure Cu at 498 K (225°C), to those extracted from hardness measurements. Excellent agreement between the model and the experiment was found. In addition, it is shown how any given probability function describing the initial distribution of stored energy can be used to predict the evolution of the residual stored energy as recrystallization proceeds.