Prediction of rate-independent constitutive behavior of Pb-free solders based on first principles

This paper presents a methodology for the theoretical estimation of rate-independent plastic constitutive properties of Pb-free solders using three approaches. The first approach is based on a nonlinear effective medium theory (NEMT) that is scale independent. The second approach is based on the micromechanics and physics of plastic slip in heterogeneous alloys (henceforth called the physical model). This approach explicitly includes microstructural features such as grain size, particle size etc. The third approach is a combination of NEMT and the physical model. Our estimates involve no adjustable calibration parameters and are based on first principles and constituent properties. Parametric studies are conducted to show that the physical model is more effective for small particles sizes (nanoscale <100 nm), small particle spacing (~ nm range) and low volume fractions (<2.5%); while NEMT performs well for large volume fractions (>5%), large particle sizes (micron size) and large particle spacing (micron scale). The proposed hybrid approach, however, appears to be valid for a wider range of particle sizes and volume fractions. Limited comparison with experimental data is also made and implications of our work in the economical design of novel Pb-free solders is discussed.