The Connection between Microstructural Damage Modeling and Continuum Damage Modeling for Eutectic Sn-Pb Solder Alloys

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Abstract
Researchers resort to a wide range of simplified representations at the continuum scale, to model creep-fatigue damage in viscoplastic heterogeneous materials, such as Sn-Pb eutectic solders, caused by thermomechanical and mechanical cyclic loading (e.g., due to power cycling, environmental temperature cycling, vibration, etc.). Typically, in macroscale phenomenological damage models, the cyclic damage is assumed to depend on some loading parameter, such as cyclic strain range, work dissipation per cycle, partitioned strain range, partitioned work dissipation per cycle, cyclic entropy changes, cyclic stress range, integrated matrix creep, etc. In many instances, some of these variables are weighted with a factor to account for rate-dependent effects. The task of finding the best damage metric is difficult because of complex microstructural interactions between cyclic creep and cyclic plasticity due to the high homologous temperature under operating conditions. In this study, we use insights obtained from microstructural and more mechanistic modeling to identify the most appropriate macroscale damage metrics. The microstructural models are based on such phenomena as grain boundary sliding, blocking of grain boundary sliding by second-phase particles, volumetric and grain boundary surface diffusion, void nucleation, void growth, and plastic collapse of cavitating grain boundaries. As has been demonstrated in the literature, micro-structural models suggest that fatigue damage caused by cyclic plasticity should correlate well with either of the two most commonly used damage indicators: cyclic strain range and plastic work dissipation per cycle. This study, however, demonstrates that in the case of damage dominated by cyclic creep, microstructural models developed by the authors indicate closer correlation of fatigue damage with creep work dissipation per cycle, than with cyclic creep strain range.