Numerical Modeling of Continuous Dynamic Recrystallization in Sn-Based Solder Connection Under Cyclic Loading

The reoccurring cyclic load imposed onto soldered electronic components during their operation time leads to accumulation of inelastic strains in the structure. On a microscale level, the degree of plastic deformation is determined by the formation and annihilation of dislocations, leading to continuous refinement by creation of new grain boundaries, precipitates relocation and growth. This microstructure rearrangement, triggered by an increasing amount of inelastic deformation, is defined as dynamic recrystallization. This work presents a macroscale modelling approach for the description of continuous dynamic recrystallization observed in Sn-based solder connections. The model used in this work describes kinetics of macroscopic gradual evolution of equivalent grain size, where the initial grain size is continuously refined with increasing accumulated inelastic strain until a saturation grain size is reached. The rate and distribution of dynamic recrystallization is further numerically modelled dependent on the effective accumulated inelastic strain and governing stress multiaxiality. A parameter study of the presented model and its employment in finite element (FE) simulation is further described. Finally, FE simulation of the grain size evolution is demonstrated on an example of a bulky sample under isothermal cyclic mechanical loading, as well as a BGA-like structure under tensile, shear and mixed mode cyclic load.