A dual-scale elasto-viscoplastic self-consistent model for the cyclic behavior of polycrystalline materials considering combined nonlinear kinematic hardening

Sn–Ag–Cu alloy, which is a solder widely used in the microelectronic industry, exhibits obvious viscoplasticity even at room temperature. Since its mechanical properties largely control the integrity of electronic packages and solder joints experience fatigue loads in most cases, the cyclic behaviors are investigated in the present work. Firstly, the experiments of Sn-3.0Ag-0.5Cu under three conditions, fully reversed loading, cyclic loading with hold time, and stress-controlled loading are conducted to characterize the rate- and temperature-dependent deformation and ratcheting behaviors. Then, a dual-scale elasto-viscoplastic constitutive model is developed based on the crystal plasticity and self-consistent method. A new hardening law is proposed to describe the features of cyclic deformation, such as the Bauschinger effect, hardening rate change in reversal loading, cyclic hardening, and so on. A combined nonlinear kinematic hardening model is adopted to simulate the ratcheting effect. Both the crystal elasto-viscoplastic model and the kinematic hardening model are embedded in the self-consistent scheme to characterize the macroscopic constitutive relationship of this polycrystalline material. Finally, the developed model is employed to simulate the experimental data. The calculated result shows that the model gives a good description of the cyclic behaviors of Sn-3.0Ag-0.5Cu alloy under various conditions.