A multi-scale constitutive model of porous sintered nano-silver

Sintered nano-silver has become an ideal solder for advanced packaging due to its low-temperature process and excellent thermodynamic properties. However, since nano-silver is a polycrystalline material with abundant voids inside, under the trend of miniaturization of advanced packaging, the traditional macroscopic constitutive model has failed to precisely characterize the intricate deformation response of the nano-silver solder at the microscopic scale. Aiming at the problem of mechanical reliability of the nano-silver particles in advanced packaging, this paper describes the local mechanical behavior of silver nanoparticles via the lens of crystal plasticity theory, and a mean-field model is proposed to characterize the deformation behavior of the nano-silver particles. The mean-field model assumes that the representative volume element (RVE) compises two components: the void phase and the polycrystalline matrix which consists of grains that have different orientations. For the elastic-viscoplastic deformation of the polycrystalline matrix and RVE, an extended self-consistent model and Mori-Tanaka model are used to describe them respectively. The mean-field model was employed to simulate the tensile characteristics of nano-silver materials with a grain number of 50 and a porosity of 10%. The acquired stress-strain curve closely aligned with the actual experimental results, so validating the developed model’s predictive accuracy regarding the deformation response of the sintered nano-silver solder. The developed mean-field model has a wide range of applicability. Besides porous polycrystalline materials, the elastic-viscoplastic deformation of multiphase alloys, and other complex structural materials can be accurately characterized by modifying the model parameters.