Determination of the Anand Viscoplasticity Model Constants for SnAgCu

The major focus of this work was the determination of the nine constants required for Anand’s viscoplastic constitutive model for a lead-free solder alloy, 95.5Sn3.8Ag0.7Cu and to compare them with those for SnPb. The test specimen was a cast dog bone shape based on ASTM E 8M-01, with a diameter of 4mm and a gauge length of 20mm. A series of tensile experiments were carried out: constant displacement tests ranging from 6.5 × 10⁻⁵/s to 1.0 × 10⁻³/s at temperatures of 20°C, 75°C, and 125°C; constant load tests at a range of loads from 10MPa to 65MPa, also at temperatures of 20°C, 75°C, and 125°C. A series of non-linear fitting processes was used to determine the model constants. Comparisons were then made with experimental measurements of the stress-plastic strain curves from constant displacement rate tests: it was found that the model matched the experimental data at low strain rates but did not capture the strain hardening effect, especially at high strain rates. A finite element model of the test was also constructed using ANSYS 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-plastic strain curve and this was compared to both the experimental measurements and the fitted Anand model. Reasonable agreement was found between the Anand model and the FE predictions at small strain rates. Finally, a BGA device was simulated under accelerated temperature cycling conditions using ANSYS with the fitted Anand for the SnAgCu solder joints. A Morrow-type fatigue life model was applied using empirical constants from two published sources and good agreement was found between experiment and predicted fatigue life.