Phase Structure and Cyclic Deformation in Eutectic Tin-Lead Alloy: A Numerical Analysis

Abstract

This study is devoted to providing a mechanistic rationale of coarsening induced failure in solder alloys during thermomechanical fatigue. Micromechanical modeling of cyclic deformation of eutectic tin-lead alloy was undertaken using the finite element method. The models consist of regularly arranged tin-rich and lead-rich phases, simulating the lamellar array and colony structure in a typical eutectic system. A fine structure and a coarse structure, bearing the same phase fraction but different in the aspect ratio of each lead-rich layer and in the number of lead-rich layers in each colony, are utilized for representing the microstructure before and after coarsening, respectively. Both phases are treated as elastic–plastic solids with their respective properties. For simplicity the creep effect is ignored without compromising the main objective of this study. Cyclic loading under pure shear and uniaxial conditions is modeled. It is found that both the fine and coarse structures exhibit essentially the same macroscopic stress–strain response. The coarse structure, however, shows a greater maximum effective plastic strain on a local scale throughout the deformation. The numerical result implies that, in a solder joint, a locally coarsened region may not be mechanically weaker than its surrounding, but it is subject to early damage initiation due to accumulated plasticity. Other implications regarding solder alloy failure and micromechanical modeling of two-phase materials are discussed.