A multiscale damage accumulation theory for solder joint failure

In heterogeneous microstructures that include several grains, secondary phases and interfaces, cracks are known to initiate and grow through different mechanisms. The failure processes however are not well understood. Solder alloys in general, and Pb-free alloys in particular possess complex, heterogeneous microstructures that evolve in fracture in ways that are challenging to model. Often, underlying a fracture observed under a microscope is a hierarchy of fracture-related phenomenon from atomic to macro length-scales. In this paper we develop a failure model inspired by information theory and continuum thermodynamics to capture the multiscale fracture processes in solder joints. We systematically develop measures of dissipation from continuum thermodynamics for materials described by J2 plasticity theory. Crack growth is known to be dissipative and such measures are natural candidates for predicting failure within a mechanics framework. The dissipation estimates, multiple fracture mechanisms and the notions of continuity, monotonicity and composition borrowed from information theory suggest a single model as being capable of predicting both ductile and brittle types of failures.