The Poisson's Ratio of Lead Free Solder - The Often Forgotten But Important Material Property

The Poisson's ratio (PR) is a basic mechanical property of a material that relates the transverse contraction strain to the axial extension strain in a uniaxial tension stress-strain test. It is a required input parameter in almost all material constitutive models (e.g. elastic, elastic-plastic-creep, Anand model, etc.) used for solder in finite element simulations. Since it is more difficult to measure relative to standard stress-strain and creep curves, it is often guessed or assumed to be a fixed value (e.g. PR = 0.3), independent of temperature, strain rate, and material composition. Using finite element simulations of several PBGA configurations subjected to thermal cycling, we have shown that the plastic strain and energy dissipation results predicted by the FEA calculations are strongly dependent on the specified value of the solder Poisson's ratio. Several sizes (5, 10, 15 mm) of PBGA components with SAC305 solder joints with 0.4 and 0.8 mm spacing were modeled, and the package assemblies were subjected to a time dependent cyclic temperature distribution from -40 to 125 oC. Our simulation results have demonstrated that for specified values of 0.15 < PR < 0.40, the solder plastic work varied over 20% and the predicted reliability varied over 50% when using a Morrow-Darveaux energy-based fatigue model. Thus, the FEA results are highly sensitive to the specified value of the solder Poisson's ratio, so that it is important to carefully characterize the Poisson's effect in lead free solders. In this work, we have conducted an experimental investigation to characterize the Poisson's ratio of several SAC and SAC+X lead free solders. Uniaxial tensile stress-strain tests were carried out on SAC305 (96.5Sn3.0Ag0.5Cu), SAC405 (95.5Sn4.0Ag0.5Cu), and SAC_Q (SAC+3.3Bi) specimens using a micro tension/torsion testing machine with two strain rates (0.0001, and 0.00001 (sec-1)) and four testing temperatures (T = 25, 50, 75, 100 oC). Deformations and strains in the axial and transverse directions were measured using miniature strain gages with automatic data acquisition from LabVIEW software. The recorded transverse strain vs. axial strain data for each test were then fit with a linear regression analysis to determine the Poisson's ratio value. A large test matrix of experiments was developed to study the effects of temperature, strain rate, alloy composition, solidification cooling profile, and isothermal aging exposure on the value of solder Poisson's ratio; and to create a material property database for finite element simulations. The Poisson's ratio was found to increase with increasing temperature, and decrease with increasing strain rate, alloy silver content, and cooling rate after solidification. Finally, the microstructural coarsening that occurs during isothermal aging led to an increase in the Poisson's ratio (up to 15% increase with one day of aging). Considering all of the possible branches of the test matrix (temperatures, strain rates, prior aging conditions, and microstructure), the value of the Poisson's ratio of SAC305 ranged from 0.31 < PR < 0.44. Analogous results were found for the other solder alloys.