Constitutive behavior and Anand model of novel lead-free solder Sn-Zn-Bi-In-P

The Anand constitutive model has emerged as a popular method to describe the inelastic deformation behavior of Sn-Pb solders and, more recently, to describe the behavior of lead-free solders in electronic assemblies, mainly due to its effective description of constitutive behavior and high compatibility with finite element modes. Heretofore, although plenty of experimental and theoretical works have been conducted on building constitutive models for lead-free solders, e.g. Sn-Ag, Sn-Ag-Cu, Sn-Cu based solders, insufficient works have been conducted on modeling Sn-Zn based lead-free solder alloys. In this paper, a series of compression tests were conducted for a novel lead-free solder Sn-9Zn-2.5Bi-0.5In-0.05P and Sn-8Zn-3Bi solder at three constant strain rates (10^-3/s, 10^-2/s, 10^-1/s) and different temperatures (20°C, 60°C, 100°C). Anand constitutive model was applied to describe the inelastic behavior as well as saturation stress of both solder alloys. Comparison of the experimental results and Anand model predictions were evaluated with the material parameters extracted from compression tests and non-linear least squares fitting of the constitutive relation. The results reveal that, for both two solder alloys, the Anand model predictions are in good agreement with experimental data of stress-strain responses at various strain rates and temperatures applied in the present work. In addition, the stress-strain responses of both solder alloys are also discussed on the basis of experimental data.