Anisotropic grain growth with pore drag under applied loads

In the final stage of sintering of ceramics, residual pores co-evolve with grain boundaries because of incomplete densification. Their interactions coupled with external loads are critical to the microstructural evolution of structural ceramics. A modified two-dimensional (2D) diffuse-interface phase field model, which differs from the boundary-tracking methods, is utilized to investigate the effects of stochastically distributed pore drag on grain growth kinetics and morphological evolution process of ceramics under applied loads. Contributions from both the boundary energy and elastic strain energy caused by pore drag forces and applied loading are incorporated in the modified phase field model to describe the isotropic or cubically anisotropic behaviors of polycrystalline materials. The temporal evolution of the spatially dependent grain orientation variables is determined by numerically solving non-linear Ginzburg-Landau equations using a semi-implicit Fourier-spectral method. Numerical results show that the anisotropic strain energy dominates the non-self-similar growth manner, leads to ordered grain morphologies and changes the growth rate.