Microstructure dependent viscoplastic damage modelling of tin–lead solder

A theoretical framework describing the nonlinear mechanical behaviour of multiphase solders is introduced, along with its numerical implementation. Next to viscoplasticity, damage has been included in the model using a gradient-enhanced nonlocal damage description. Microstructural data are accounted for in the model by means of a phase field. In here, the methodology followed is generic and can be readily extended to numerous multi-phase materials. The model is applied to the eutectic Sn–Pb system whose mechanical properties are known to be heavily dependent on the underlying microstructure. The results indicate that coarser microstructures exhibit a more pronounced localisation behaviour compared to finer ones leading to higher local values for the stresses and viscoplastic strains. Furthermore, different damage evolution behaviour is observed for the investigated microstructures, with a coarser microstructure leading to earlier microstructural failure.