The Phase Field Model of the Insoluble Particle–Interface Interaction During Solidification

In this work, the phase field model was developed to understand the redistribution behavior of insoluble particles during metal solidification. This was achieved by modifying the pure solidification model to incorporate the insoluble particle using an interaction term for phase change interactions and the Lagrange multiplier for particle conservation. The novelty of this work involves the use of the phase field model for solidification and the use of the Lagrange multiplier as a simple diffuse interface approach to simulate particle capture or pushing with changes in solidification variables compared to complicated interface tracking approaches where particle capture and pushing are difficult to simulate. The developed model was applied to investigate the influence of materials properties and processing conditions on particle behavior at the solidification interface. The effect of parameters like particle diameter, solidification velocity, particle thermal conductivity, particle–solid interfacial energies and melt viscosities were investigated. The developed model can predict the influence of different parameters on particle behavior during both planar and dendritic solidification. Comparison of results shows that particles are easily engulfed during planar solidification whilst particle engulfment during dendritic solidification is difficult. In both cases, the critical velocities for particle incorporation increase with an increase in particle–solid surface energy and a decrease in particle to melt thermal conductivity ratios and melt viscosities.