Experimental determination and finite element model validation of the Anand viscoplasticity model constants for SnAgCu

The major focus of this work was the experimental determination of the nine constants required for Anand´s viscoplastic constitutive model for a lead-free solder alloy, 95.5Sn3.8AgO.7Cu. A series of tensile experiments were carried out: constant displacement rate tests with strain rates ranging from 6.0E-5/s to 1.0E-3/s at temperatures of 20°C, 75°C, and 125°C; constant load tests at a range of loads from 8MPa to 64MPa for the same temperature range. The test specimen was a cast dog bone shape based on the ASTM E 8M-01 standard, with a diameter of 4mm and a gauge length of 20mm. Nonlinear least-squares fitting was used to determine the model constants. Comparisons were then made with experimental measurements of the stress-inelastic strain curves: excellent agreement was found. A finite element model of the test was also constructed using ANSYS 8.1 software. This software includes the Anand model as an option for its range of viscoplastic elements, requiring that the nine constants be input. In this case, an 8-noded axisymmetric element (VISCO108) was used to model the test specimen under constant displacement rate loading. The model was then used to predict the stress-inelastic strain curve under constant displacement rate conditions and this was compared to both the experimental measurements and the fitted Anand model. It was found that the Anand model and finite element predictions matched the experimental stress-inelastic strain curves for small strain rates, but that at higher strain rates the strain hardening behaviour of the solder was not captured accurately. The benchmarking of the ANSYS software showed that the Anand model was being implemented as expected. Using the fitted parameters in an FE model of an electronic component undergoing thermal cycling is likely to give acceptable results as the strain rates in this case are comparatively small.