Maximum entropy fracture model and its use for predicting cyclic hysteresis in solder alloys

Appropriate constitutive, damage accumulation and fracture models are critical to accurate life predictions. In our recent research we developed the maximum entropy fracture model, a thermodynamically consistent and information theory inspired (non-empirical) damage accumulation theory for ductile solids, validated on both area array and peripheral array packages. The model uses a single damage accumulation parameter to relate the probability of fracture to accumulated entropic dissipation. We demonstrate the ability of the Anand model and the above mentioned damage accumulation model to non-empirically predict the softening phenomena during cyclic fatigue testing of Sn3.0Ag0.5Cu solder alloy. A custom-built microscale mechanical tester capable of submicron displacement resolution was utilized to carryout isothermal cycling fatigue tests on specially designed assemblies. The resultant relationship between load drop and accumulated inelastic dissipation was used to extract the temperature and geometry-independent damage accumulation parameter of the maximum entropy fracture model for each alloy. The damage accumulation relationship is input into the Anand viscoplastic constitutive model, allowing prediction of the stress-strain hysteresis and cyclic load drop. This approach allows for a non-empirical prediction of both constitutive and fracture behavior of packages of different geometries under thermo-mechanical fatigue.