Liquid- solid interface migration at grain boundary regions during transient liquid phase brazing

A two-dimensional (2-D) finite difference model has been used to analyze the effect of grain boundary regions on the migration of the liquid-solid interface during transient liquid phase (TLP) brazing of Ni with Ni-11 wt pct P filler metal. This work has been carried out to explain the differences observed between actual and calculated completion times for isothermal solid- ification during TLP brazing and the faster isothermal solidification rates when brazing fine- grained nickel-base material. Modeling considers the situation where the grain boundary intersects the liquid-solid interface at right angles. Four factors are considered in addition to solute diffusion in solid and liquid phases,viz., (1) high diffusivity at the grain boundary region, (2) the balance between the grain boundary energy and the liquid-solid interfacial energy, (3) the interfacial energy due to the curvature of the liquid-solid interface, and (4) diffusional flow along the liquid-solid interface (produced by the gradient of solute chemical potential resulting from factors (2) and (3)). Increased solute diffusivity at the grain boundary region has a neg- ligible effect on migration of the liquid-solid interface in the bulk region and shifts the interface at the grain boundary region in a direction opposite that observed in actual brazed samples. On the other hand, when factors (2) through (4) above are taken into account, the liquid-solid interface in the region of the grain boundary is displaced in the same direction as in the ex- perimental results and liquid penetration comparable with the experimental results occurs at the grain boundary region. Factors (2) through (4) accelerate the isothermal solidification process in the bulk region in accordance with actual experimental test results.