On the impact of inhomogeneities on vacancy diffusion controlled void and crack formation in SAC305 solder joints

At elevated temperatures, crack formation and propagation in metals are tied to thermodynamic processes like vacancy generation, diffusion, and condensation. This study develops a comprehensive thermodynamic framework to model these phenomena at mesoscopic scales using non-equilibrium thermodynamics principles. A generalized Lagrangian formulation captures the coupling between mechanical loading and vacancy diffusion, yielding partial differential equations (PDEs) that govern their interactions. Under specific conditions, these PDEs can be reduced to ordinary differential equations (ODEs), facilitating analysis of damage initiation and evolution at inhomogeneities like grain boundaries. The results highlight the role of strain energy density gradients, jog density, and vacancy generation dynamics in determining fatigue evolution. As a first step towards validating our model, we compare its predicted damage evolution with experimental data given in terms of a Weibull distribution. Using literature values for known parameters and a parameter study for the unknown dislocation density, our preliminary results appear promising. However, further experimental validation is necessary to confirm our model and the underlying mechanism it explores.