Unified Creep Plasticity Damage (UCPD) Model for Solder

A unified creep plasticity damage (UCPD) model for Sn-Pb and Pb-free solders was developed and implemented into finite element analysis codes. The new model will be described along with the relationship between the model’s damage evolution equation and an empirical Coffin-Manson relationship for solder fatigue. Next, two significant developments were needed to model crack initiation and growth in solder joints. First, an ability to accelerate the simulations such that the effects of hundreds or thousands of thermal cycles could be modeled in a reasonable amount of time was needed. This was accomplished by applying a user prescribed acceleration factor to the damage evolution; then, damage generated by an acceleration factor of cycles could be captured by the numerical simulation of a single thermal cycle. Second, an ability to capture the geometric effects of crack initiation and growth was needed. This was accomplished by replacing material in finite elements that had met the cracking failure criterion with very flexible elastic material. This diffuse crack modeling approach with local finite elements is known to generate mesh dependent solutions. However, introduction of an element size dependent term into the damage evolution equation was found to be effective in controlling mesh dependency. Finally, experimentally observed cracks in a typical solder joint subjected to thermal mechanical fatigue are compared with model predictions.