Abstract
A model for crack nucleation in layered electronic assemblies under thermal cycling is developed in this paper. The present model includes three scales: (i) at the microscale or the mechanism level, the damage mechanisms such as diffusive void growth or fatigue cracks, determine the damage growth rate; (2) at an intermediate mesoscale, the localized damage bands are modeled as variable stiffness springs connecting undamaged materials; and (iii) at the macroscale or the continuum level, the localized damage band growing in an otherwise undamaged material is modeled as an array of dislocations. The three scales are then combined together to incorporate damage mechanisms into continuum analysis. Traditional fracture mechanics provides a crack propagation model based on pre-existing cracks. The present work provides an approach for predicting crack nucleation. The proposed model is then utilized to investigate crack nucleations in three-layered electronic assemblies under thermal cycling. The damage is observed to accumulate rapidly in the weakest regions of the band. Estimates are obtained for critical time or critical 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 size of the damage cluster, but decreases rapidly as the local excess damage increases.
