Improved predictions of cyclic stress-strain curves for lead free solders using the Anand viscoplastic constitutive model

Solder materials in electronic packages are often subjected to thermal cycling, either during their application in products or during accelerated life qualification testing. Cyclic temperatures cause the solder joints to be subjected to cyclic mechanical stresses and strains due to the mismatches in the thermal expansion coefficients of the assembly materials. Such loads lead to thermo-mechanical fatigue including damage accumulation, crack initiation and propagation, and eventual failure. Prior studies have revealed that the predictions of cyclic stress-strain curves using the standard Anand viscoplastic constitutive model yield hysteresis loops that are different in shape and loop area when compared with the experimental results. In this investigation, the evolution equation of the Anand constitutive model has been modified for the lead free solders by adding a static recovery term. This modification results in the reduction of value of the internal variable (resistance to plastic deformation) of the model during the unloading/reloading steps. Software has been written to implement the modified relationship for the change of the internal variable during the cyclic stress-strain experiments of non-aged SAC305 solder material. The cyclic stress-strain data have also been measured for the same solder material and the hysteresis loop has been plotted. From the results, it has been observed that the modified equation of the Anand constitutive model gives much better correlation between the experimental and predicted cyclic stress-strain curves. Simulations have also been performed for aged SAC305 solder (0-180 days of aging of SAC305 solder material at 100 oC), and the effects of aging on the cyclic stress-strain curves have been determined. For all aging conditions, better correlations with experimental data were obtained when the modified Anand model approach was used. With aging, the area of the hysteresis loop is reduced with increasing aging time for strain controlled cyclic stress-strain tests.