Phase Field Modelling of microstructure evolution and non-equilibrium alloy solidification

In metal additive manufacturing, which involves melting and diffusing metal powder or wires, layer by layer, the solidification process at the melt pool plays the most critical role in underlying microstructure and its properties. This process fundamentally shapes the microstructure and dictates the mechanical properties of the finished parts. Complementing experimental techniques, computational models have proven to be a powerful tool to predict the microstructure of the build components. Among various computational techniques, the Phase Field (PF) method excels in simulating microstructure by using a continuously varying order parameter to diffuse interface descriptions, eliminating explicit interface tracking. In the present research we implemented the PF method in OpenFOAM leveraging its opensource nature and customizable modelling capabilities. Initially, a model using the Kobayashi Phase Field approach was developed to simulate dendritic growth in pure materials, investigating the effects of latent heat and interfacial energy anisotropy. The simulation results align closely with Kobayashi's findings. Additionally, a custom solver was implemented and verified against benchmarks from the NIST repository, showing excellent agreement in terms of system free energy, solid fraction, and dendrite tip positioning. Using Warren and Boettinger’s phase field methodology, a binary alloy solidification model was developed to simulate dendritic growth under both isothermal and non-isothermal conditions, the latter achieved by applying a thermal gradient. An antitrapping flux term was integrated to mitigate solute trapping due to non-equilibrium solute partitioning. Simulations for equiaxed dendrites in an undercooled melt considered factors like interface thickness, crystal anisotropy strength, stochastic noise amplitude, and initial computational grid orientation, revealing that morphology is sensitive to anisotropy and noise levels but independent of initial orientation, ensuring no mesh dependency. Thermal gradients notably impacted solute distribution and dendritic growth patterns. A cellular automaton-like approach was developed to simulate multiple grain orientations in polycrystalline solidification, successfully predicting realistic structures and microstructures post-solidification. Adapting the thin interface phase field model from Echebarria et al., a framework for directional solidification was developed. Simulations were performed for Al-3wt.%Cu alloy and IN718 alloy within a 2D computational domain in a Bridgman set-up, to explore the influence of thermal gradients and solidification (or pulling) velocities. Results showed that lower gradients facilitate smoother solute redistribution and more pronounced dendritic side branches. Increased pulling velocities led to reduced primary dendritic arm spacing and deviations from equilibrium in solute partition coefficients, indicating non-equilibrium conditions. Additionally, simulations under a frozen temperature approximation demonstrated that a planar interface in IN718 alloy transitioned into a cellular pattern over time. The primary dendritic arm spacing (PDAS) decreased with higher cooling rates, following an inverse empirical relationship. While at low cooling rate PDAS values aligned well with Hunt’s and Kurz-Fisher analytical models, at higher colling rates resulted in deviations from analytical model. This can be attributed to the analytical model’s reliance on geometric assumptions, which fail to capture the dynamic conditions of actual solidification processes. The developed computational models are beneficial in unfolding the complex solidification process through opensource tools to enable reproducibility and customization suited for diverse manufacturing industries.