A micromechanical analysis to the elasto-viscoplastic behavior of solder alloys

A small strain multi-scale elasto-plastic self-consistent constitutive model is developed to describe the rate and temperature dependent behavior of solder alloys. In the extended model, a modified Voce hardening law is proposed to describe the change of hardening rate as a function of accumulated shear strain. The developed model has been incorporated into finite element analysis to obtain the macroscopic behavior of polycrystalline materials. The stress updating algorithms of both microscopic and macroscopic scales are presented. The effect of grain shape on macroscopic behavior is investigated. The proposed model is verified with the Taylor factor and the experimental data of Sn-3.0Ag-0.5Cu and Sn-0.7Cu solder alloys at different temperatures and strain rates. In general, the numerical results can fit the experimental data with reasonable accuracy.