Microstructure-based modeling of the ageing effect on the deformation behavior of the eutectic micro-constituent in SnAgCu lead-free solder

The eutectic micro-constituent in SnAgCu solder governs the deformation behavior of the joint as it shows better deformation resistance than the Sn dendrites and occupies a high volume percentage of the whole solder. The main scope of this study is to develop a three-dimensional (3-D) homogenization model taking into account the microstructural evolution in the eutectic micro-constituent of SnAgCu solder in order to simulate the change in mechanical behavior of the joint caused by isothermal ageing. For this purpose, 3-D configurations of Ag3Sn and Cu6Sn5 intermetallic compounds (IMCs) in near-eutectic SnAgCu solder are visualized in the as-soldered condition and after ageing by focused ion beam/scanning electron microscopy tomography. The tomographic images are used to generate feature-preserving finite element meshes of the actual microstructures. The representative volume element size and constitutive behavior of the eutectic mixture in the two conditions are determined by a numerical homogenization procedure. The results show a considerable reduction in the yield stress level of the eutectic micro-constituent after ageing of the solder joint. It is shown that the increase in the inter-particle spacing and decrease in the aspect ratio of IMCs due to ageing cause a significant change in the strain distribution in the tin matrix, which leads to a lower contribution of IMCs in load-sharing and yield strength of aged solder. The elastic-plastic properties of as-soldered and aged eutectic mixtures are determined by nanoindentation. The results of homogenization are validated through comparison with experimental results and prediction of the dislocation detachment theory.