Constitutive Models for Intermediate- and High-Strain Rate Flow Behavior of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu Solder Alloys

In much of the existing research, SnAgCu solder alloys are characterized at low strain rates, typically in the 10
^-6
to 1 s
^-1
range. In this paper, we report experimental results and constitutive models for two popular SnAgCu solder alloys at intermediate and high strain rates, ranging from 10
^-2
to 10
³
s
^-1
at room temperature. These experiments were performed using two different experimental setups: a MTS 810 uniaxial compression tester, and a split-Hopkinson pressure bar. In conjunction with our previous work at lower strain rates (10
^-6
to 10
^-3
s
^-1
), these results yield the plastic flow response of these solders over nine decades of strain rate, and demonstrate a remarkably consistent relationship between the yield stress and the strain rate over the entire nine decades. We also develop the Anand viscoplastic constitutive model, and demonstrate that fit parameters for the low-strain rate regime can be extrapolated to accurately predict the experimental response at high strain rates. Thus, the model presented here proffers the capability of modeling solder deformation under a wide range of loading conditions using most commercially available finite element (FE) programs. To illustrate the validity of the model parameters, we develop idealized FE models together with cohesive zone failure descriptions at the interface between the solder and the intermetallic compound. We demonstrate that when used in conjunction with appropriate failure models, the constitutive model developed here accurately captures the empirically observed shift in failure modes from bulk failure to interfacial failure under tensile loading at higher strain rates.