A new numerical model for simulating transient liquid phase (TLP) bonding of dissimilar materials involving 1D, 2D and 3D solid–liquid interface migration

ABSTRACT

A new numerical model which incorporates the occurrence of liquid-state diffusion (LSD) during isothermal solidification is developed to simulate transient liquid phase (TLP) bonding of dissimilar materials in contrast to previous dissimilar TLP bonding models where LSD during isothermal solidification is ignored. The new model which conserves solute and avoids the assumption of concentration-independent solid-state diffusivity applies Murray–Landis–Space-Transformation-based self-adaptive spatial discretisation with a unique adaptation of up/down-wind estimation scheme in a hybrid explicit-implicit finite difference approach. It is found that although LSD can increase isothermal solidification rate during dissimilar-bonding, yet, it is possible for the isothermal solidification completion time, $t_f$ to be longer during dissimilar bonding compared to similar bonding, notwithstanding the higher solidification rate of the dissimilar bonding. Moreover, contrary to general notion, numerical analyses show that solid-state diffusion exerts significant influence on $t_f$ during TLP bonding that involves LSD and so should be adequately considered.

KEYWORDS:

• Transient liquid phase bonding
• joining of dissimilar materials
• solid–liquid inter-diffusion bonding
• 2D and 3D migration
• liquid-state diffusion

Acknowledgement

The authors gratefully acknowledge financial support by the NSERC of Canada.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada.