A variable-order fractional model of tensile and shear behaviors for sintered nano-silver paste used in high power electronics

Next generation power electronics demand not only miniaturization and integration, but also higher power and harsher operation conditions. However, the conventional lead-free solders can't meet these requirements. Sintering of nano-silver paste has already become one of popular substitutes, as it can achieve low temperature packaging and high temperature operation. The mechanical performance of sintered nano-silver paste is of great importance for its applications in high power electronics. In this study, a variable-order fractional constitutive model is adopted to characterize tensile behaviors of sintered nano-silver paste at different strain rates and ambient temperatures. A comparative study with the well-known Anand model is conducted to present the advantages of the proposed model with simpler formulation, higher accuracy and fewer parameters. The fractional order is also found to well indicate the evolution of mechanical properties along with varying strain rates or temperatures. Furthermore, the model is firstly extended to describe shear experimental data at different temperatures, especially those with strain softening stages. All simulation results reveal that the variable-order fractional model is an effective tool in characterizing both tensile and shear behaviors and demonstrating the evolution of mechanical properties.