Numerical modeling and simulation of a diffusion-controlled liquid–solid phase change in polycrystalline solids

A fully implicit two-dimensional moving-mesh finite element simulation model was developed to study the influence of grain boundaries in polycrystalline solids on diffusion-controlled liquid–solid transition during transient liquid phase (TLP) bonding. The new model, which was developed without the non-trivial symmetry assumption in existing numerical models for the process, was found to conserve solute and its calculated solutions were unconditionally stable and in good agreement with experimental results. Contrary to the assumption that increased grain boundary diffusion coefficient would significantly accelerate the rate of liquid–solid interface migration, numerical calculations and experimental verification showed that enhanced intergranular diffusivity had a minimal effect on the time required to achieve complete diffusion-induced solidification in cast superalloys. The results indicate that reducing the number of grain boundaries in structural alloys through directional solidification casting techniques did not constitute a disincentive to efficient application of TLP bonding to this class of materials.