Phase field modeling of grain growth in porous polycrystalline solids
The concurrent evolution of grain size and porosity in porous polycrystalline solids is a technically important problem. All the physical properties of such materials depend strongly on pore fraction and pore and grain sizes and distributions. Theoretical models for the pore-grain boundary interactions during grain growth usually employ restrictive, unrealistic assumptions on the pore and grain shapes and motions to render the problem tractable. However, these assumptions limit the models to be only of qualitative nature and hence cannot be used for predictions. This has motivated us to develop a novel phase field model to investigate the process of grain growth in porous polycrystalline solids. Based on a dynamical system of coupled Cahn-Hilliard and All en-Cahn equations, the model couples the curvature-driven grain boundary motion and the migration of pores via surface diffusion. As such, the model accounts for all possible interactions between the pore and grain boundary, which highly influence the grain growth kinetics. Through a formal asymptotic analysis, the current work demonstrates that the phase field model recovers the corresponding sharp-interface dynamics of the co-evolution of grain boundaries and pores; this analysis also fixes the model kinetic parameters in terms of real materials properties. The model was used to investigate the effect of porosity on the kinetics of grain growth in UO2 and CeO2 in 2D and 3D. It is shown that the model captures the phenomenon of pore breakaway often observed in experiments. Pores on three- and four- grain junctions were found to transform to edge pores (pores on two-grain junction) before complete separation. The simulations demonstrated that inhomogeneous distribution of pores and pore breakaway lead to abnormal grain growth. The simulations also showed that grain growth kinetics in these materials changes from boundary-controlled to pore-controlled as the amount of porosity increases. The kinetic growth parameters such as the growth exponent and the rate constant (or equivalently the activation energy) were found to depend strongly on the precise amount and distribution of porosity, which reconciles the different experimental results reported for grain growth in such materials.
El-Azab, Purdue University.
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