A nonlocal diffuse interface model for microstructure evolution of tin–lead solder

Abstract

Microstructural length scales are relatively large in typical soldered connections. A microstructure which is continuously evolving is known to have a strong influence on damage initiation and propagation in solder materials. In order to make accurate lifetime predictions by numerical simulations, it is therefore necessary to take the microstructural evolution into account. In this work this is accomplished by using a diffuse interface model incorporating a strongly nonlocal variable. It is presented as an extension of the Cahn–Hilliard model, which is weakly nonlocal since it depends on higher order gradients which are by definition confined to the infinitesimal neighbourhood of the considered material point. Next to introducing a truly nonlocal measure in the free energy, this nonlocal formulation has the advantage that it is numerically more efficient. Additionally, the model is extended to include the elastically stored energy as a driving force for diffusion after which the entire system is solved using the finite element approach. The model results in a computational efficient algorithm which is capable of simulating the phase separation and coarsening of a solder material caused by combined thermal and mechanical loading.