A Continuum Damage Mechanics Approach for the Reliability of Lead-Free Solders Subjected to Cyclic Loading

Cyclic loading of solder joints in electronic assemblies often leads to damage accumulation and fatigue failure. One cause of such loading is exposure to cyclic temperatures when coefficient of thermal expansion mismatches exist in the assembly. In addition, exposure to high vibration environments can lead to mechanical cycling. In our previous papers at ECTC 2021 [1] and ECTC 2022 [2], we investigated the accumulation of damage in several lead-free solder materials during mechanical cycling. Various levels of damage were first introduced in a set of reflowed lead free solder uniaxial specimens by isothermal mechanical cycling. After damage accumulation, the mechanical responses of the preconditioned specimens were measured via stress-strain testing, and the changes in mechanical properties due to the damage were characterized. In addition, changes in the microstructure and growth of micro-cracks during cycling have been characterized. In our more recent study [3], an initial set of creep experiments were performed on similarly damaged samples. In the current investigation, we have extended our work in this area to perform creep testing on damaged samples with additional levels of applied stress and additional levels of prior damage. The degradations of the creep strain rate with room temperature mechanical cycling were evaluated and plotted versus the duration of cycling for various applied levels of damage per cycle. In addition, we have utilized a formulation based on damage mechanics to model the accumulation of damage in the solder samples, as well as the effects of the damage on the creep behavior of the material. The damage levels induced in the mechanically cycled specimens were specified in terms of the energy dissipation per cycle (ΔW = hysteresis loop area), as well as the number of applied mechanical cycles. The total energy dissipation that had occurred in the sample (ΣΔ W = sum of ΔW for all cycles) was found to be an appropriate metric for characterizing the amount of damage. This was found to be true regardless of the damage level applied during each cycle. A single damage parameter D = D(ΣΔ W) was then identified, and fit with an empirical model for use in a damage mechanics analytical formulation. The level of D (0 ≤ D ≤1) could be used to accurately predict the degradations in the creep response of the lead free solder due to prior damage induced by mechanical cycling.