A model of Crack Nucleation in layered electronic assemblies under thermal cycling

A model for crack nuclealion in layered electronic assemblies under thermal cycling isdeveloped in this paper. The present model includes three scales: (i) at the microscale orthe mechanism level, the damage mechanisms such as diffusive void growth or fatiguecracks, determine the damage growth rale; (2) at an intermediate mesoscaie, the localized damage bands are modeled as variable stiffness springs connecting undamaged materi-als; and (iii) at the macroscale or the continuum level, the localized damage band grow-ing in an otherwise undamaged material is modeled as an array of dislocations. The threescales are then combined together to incorporate damage mechanisms into continuumanalysis. Traditional fracture mechanics provides a crack propagation model based onpre-existing cracks. The present work provides an approach for predicting crack nucle-ation. The proposed model is then utilized to investigate crack nucieations in three-layered electronic assemblies under thermal cycling. The damage is observed to accumu-late rapidly in the weakest regions of the band. Estimates are obtainedfor critical time orcritical number of cycles at which a macroscopic crack will nucleate in these assemblies under thermal cycling. This critical number of cycles is found to be insensitive to the sizeof the damage cluster, but decreases rapidly as the local excess damage increases.