Numerical modelling of 2D and 3D migrations of non-planar liquid-solid interface during transient liquid phase (TLP) bonding
Afolabi, Oluwadara Caleb
Transient liquid phase (TLP) bonding has emerged attractive for joining difficult-to-weld advanced materials in a variety of industrial applications. Despite its many advantages, TLP bonding requires relatively long processing time to produce good-quality bonds. In-depth understanding of the underlying mechanisms of TLP bonding is crucial for its optimization. Existing TLP bonding modelling work, for simplicity, mostly consider one-dimensional (1D) migration of the liquid-solid interface. However, the liquid-solid interfaces can practically undergo two-dimensional (2D) or three-dimensional (3D) migration. This work aims to use numerical modelling to study the behavior and kinetics of isothermal solidification during TLP bonding that involve 2D and 3D liquid-solid interface migration. In addition to addressing the complexity of multi-dimensional liquid-solid interface migration, the theoretical model developed in this work conserves solute and does not require the assumption of a concentration-independent solid-state diffusivity by applying a self-adaptive spatial discretization based on the Murray-Landis-Space-Transformation in an explicit-implicit-fusion finite difference modelling approach. Furthermore, in contrast to existing models in the literature, the TLP bonding model for dissimilar materials developed in this work incorporates the occurrence of liquid-state diffusion (LSD) by using a unique adaptation of the upwind/downwind estimation scheme in addition to the simultaneous treatment of the diffusion problems in the single liquid and the solid phases during isothermal solidification. This research shows that aside from the factors that are generally known to determine TLP bonding kinetics, a new factor – the type and degree of curvature of the migrating interfaces – is involved when the interfaces undergo 2D or 3D migration. Additionally, contrary to the general notion based on the Arrhenius relation, it is possible for the concentration-averaged diffusion coefficient to reduce with an increase in temperature, and this can cause an anomalous increase in processing time with an increase in bonding temperature. Furthermore, this work shows that contrary to general expectations, it is possible for the processing time to be longer during dissimilar bonding compared to similar bonding, despite an increase in the rate of solidification. The key theoretical findings from the research work are experimentally validated and are crucial to the application of TLP bonding for joining non-planar interfaces.
transient liquid phase bonding, TLP bonding, diffusion brazing, numerical modelling, multi-dimensional interface migration, non-planar interface, joining of dissimilar materials