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Phase field modelling of grain growth with particle pinning and solute drag Shahandeh, Sina

Abstract

Second phase particles and solute atoms have been used as an important constituent in the design of materials and processes due to their ability to restrain 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 particles or solute segregation spike. In this work, a multi-scale modelling scheme is proposed to simulate grain growth with particle pinning and solute drag. The interaction of a grain boundary with an ensemble of particles is simulated to obtain the pinning pressure. A phase field model is then developed that incorporates the drag pressure in the meso-scale and simulates grain growth. The accuracy of the model is confirmed in comparison with analytical expressions. The application of the model is then presented for grain growth in two- and three-dimensional systems under the influence of particle pinning. Measuring the curvature of the grain boundary network reveals that in the completely pinned structure, the average driving pressure is not equal to but lower than the pinning pressure. The results of the nano-scale simulations for pinning pressure is combined with the results from the meso-scale to produce a limiting grain size that coincides with the experiments. This curvature analysis provides a kinetic model that describes the evolution of the structure more accurately than that of the mean field theories. 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 is described using a power law, with a time exponent in the range of 0.35 to 0.50. The deviation from ideal grain growth, associated with a time exponent lower than 0.50, and its correlation with the solute drag parameters is investigated.

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