Maximum-Entropy Principle for Modeling Damage and Fracture in Solder Joints: Enabling Life Predictions under Microstructural Uncertainty

A maximum-entropy fracture model (MEFM) is derived from concepts of information theory and statistical thermodynamics. Exploiting the maximum-entropy principle enables life predictions for a structure in the presence of microstructural uncertainty. This single-parameter model relates the probability of fracture to accumulated entropic dissipation at a given material point. Using J 2 plasticity and equilibrium thermodynamics, entropic dissipation is related to inelastic dissipation. We demonstrate the MEFM by extracting the single damage accumulation parameter for Sn-3.8Ag-0.7Cu solder through cyclical fatigue testing. We then apply the model with the single parameter to numerically predict, in three dimensions, crack initiation and growth in Sn-3.8Ag-0.7Cu solder joints of a wafer-level chip-scale package (WLCSP). The simulated crack fronts are validated against experimentally observed crack fronts obtained by testing 64 packages under conditions identical to those used in the simulations. The model is shown to accurately predict the geometrical profile of the observed crack fronts, and the number of cycles corresponding to the observed crack profile to within 10% of the measured number of cycles.