Constitutive Modeling of Sintered Nano-silver Particles: A Variable-order Fractional Model versus an Anand Model

In high-power electronics packaging, nano-silver sintering technology has been widely applied due to its excellent electrical and thermal conductivity and its low-temperature packaging and high-temperature operation. In this study, 50-nm nano-silver particles are sintered at 275°C for 50 min and placed under a dynamic thermomechanical analyzer (DMA Q800) with three strain rates (0.001%s-1, 0.01%s-1, and 0.1%s-1) and seven ambient temperatures (-40°C, 0°C, 25°C, 60°C, 120°C, 150°C, and 185°C). Both the variable-order fractional constitutive model and Anand model are adopted to characterize the tensile behaviors of sintered nano-silver particles. The results show that (1) the tensile strength of sintered nano-silver particle samples declines under the lower strain rate and higher temperature; and (2) both the variable-order fractional model and Anand model can well represent the tensile mechanical properties of sintered nano-silver. According to the root mean square error (RMSE) calculation, the fitting accuracy of the variable-order fractional model is slightly better than that of the Anand model. Furthermore, the variable-order fractional model involves fewer parameters, which makes it easier to fit than the Anand model.