Using a phase-field approach with the heat conduction equation, we predict the grain growth behaviors in tungsten (W) and their effects on the effective thermal conductivity. Results show that the simulated grain growth kinetics is basically consistent with the experimental observations. An empirical correlation describing the averaged grain area as a function of the temperature and time is derived. Further, we study the effect of the grain growth, columnar crystal structure, and the recrystallization on the effective thermal conductivity of W. It is found that the effective thermal conductivity non-linearly increases with increasing the grain size, and a simple correlation of converting two-dimension into three-dimension effective thermal conductivity is obtained. Interestingly, the effective thermal conductivity of the columnar crystal is relatively high along the elongated direction and higher than that of the isometric crystal. Nevertheless, the effective thermal conductivity decreases with the occurrence of the recrystallization due to the increased grain boundary density. Our results reveal that grain growth and grain structure can affect the capacity of the heat transfer at high temperatures, which could be considered in the transient event of the long-time service of W materials in fusion devices.
In this work, we propose an efficient numerical method to study the effects of microstructures on the effective diffusion coefficient of the diffusion component in materials. We take the diffusion of hydrogen (H) atoms in porous polycrystalline tungsten (W) as an example. The grain structures and irradiated void microstructures are generated by using the phase-field model. The effective diffusion coefficients of H in these microstructures are obtained by solving the steady-state diffusion equation, using a spectral iterative algorithm. We first validate our simulation code for calculating the effective diffusion coefficient by using three simple examples. We then investigate the effects of the grain morphology and porosity on the effective diffusion coefficient of H in W. Regardless of whether the grain boundary is beneficial to the diffusion of H or not, it is found that the effective diffusion coefficient of H along the elongated grain direction in columnar crystals is always greater than that in isometric crystals. The increase of the porosity can significantly decrease the effective diffusion coefficient of H from the simulations of the porous W. A correlation of converting the two-dimensional (2D) effective diffusion coefficient into three-dimensional (3D) in the porous and polycrystalline W is fitted by using our simulation data, respectively. Two fitted correlations can be used to predict the synergistic effect of the porosity and grain boundary on the effective diffusion coefficient of H in W. Consequently, our simulation results provide a good reference for understanding the influence of the complex microstructures on H diffusion, and may help to design W-based materials for the fusion reactor.
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