A Mechanics-Based Phase-Field Model and Finite Element Simulations for Microstructure Evolution during Solidification of Ti-6Al-4V

In this paper, a mechanics-based phase-field model at the microscale is introduced for microstructure evolution during solidification. The couple phase-field model consists of Allen–Cahn equation for phase order parameter, Cahn–Hilliard equation for composition, heat conduction and elasticity equations. The introduced elastic energy allows for volumetric inelastic strains due to melting/solidification as well as a thermodynamically consistent solid-melt interface stress and consequently, residual stresses during solidification at the microscale and deformation can be captured. The computational microcell is considered at the melt-solid interface and the temperature as a time dependent function is used for its boundary conditions to solve the coupled phase-field model. Using COMSOL FE code, examples of columnar growth are studied. As result, the suppressive effect of elastic driving forces and the reduction in solidification rate, due to the volumetric inelastic strains, on solidification are revealed. The inelastic surface stress, concentrated inside the interface, can change the morphology of solidified structure but does not show a remarkable effect on the solidification rate. The thermal strain was included which reduced the effect of volumetric transformation strain and consequently, the internal stresses near constrained regions were decreased. The effect of undercooling was studied which showed that increasing the undercooling increased the temperature gradient in the vertical direction and near the interface and solidification rate and significantly changed the morphology of solidified structure, as a homogeneous growth was resolved for larger undercooling while a columnar growth was obtained for smaller undercooling. Solidification was studied under mechanical loading which showed external loading changes the stress distribution and magnitude and the morphology of solidified structure. Effect of an inclusion on solidification was also investigated. The inclusion represented a more homogeneous distribution of stress and temperature with different magnitudes compared to the rest of the sample, creating a directional solidification toward the inclusion.