Thermodynamic framework for coupling of elasto-viscoplasticity and nonlocal anisotropic damage for microelectronics solder alloys

The microstructure of soldered materials is known to have a strong influence on damage initiation and propagation and being localised. Moreover, it is well-established in the literature that the final failure of a solder joint is preceded by inhomogeneities in the deformation of the joint at relatively early stages, and that predicting the non-uniform micro-damage distribution during thermo-mechanical loading allows one to ultimately predict the failure location and time and then in turn improve the performance and reliability of microelectronic solder alloys. This study develops a general consistent and systematic framework for the analysis of microelectronic solder alloys that assesses a strong coupling between rate-dependent plasticity and rate-dependent damage within the framework of thermodynamic laws and nonlocal gradient-dependent theory. The model presented in this paper can be considered as a feasible thermodynamic approach for microelectronic solder alloys that enables one to derive various coupled thermo-viscoplasticity-viscodamage theories by introducing simplifying assumptions.