Numerical Investigation of the Evolving Inelastic Deformation Path of a Solder Ball Joint under Various Loading Conditions

Solder joints of ball grid arrays (BGA) have been widely used to connect electronic components to printed circuit boards (PCBs) and are often subjected to mechanical stress. Several studies have been conducted on the mechanical reliability of solder joints. While these studies have been useful in the industry, detailed studies on how the inelastic deformation path of the solder ball joints evolves under specific loading conditions have not been sufficiently reported. This study aims to understand how the inelastic deformation path evolves when a solder joint is subjected to a constant external force by utilizing the theory of mechanics. It has also been found that the mechanical failure is strongly influenced by the evolution history of the deformation modes in materials. For this study, an elastoplastic constitutive model and a ductile fracture criterion were implemented into the vectorized user-defined material (VUMAT) subroutine of the ABAQUS program for finite element (FE) analysis. With the model, the evolution of the inelastic deformation path of a single solder ball under different loading conditions was numerically analyzed. Three loadings (shear, compression, and bending) were chosen as the basic loading conditions. In addition, combinations of the basic loadings resulted in three dual loadings and one complex loading. The simulation results showed that the shear and bending caused the fracture for both single and dual loadings, but when combined with compression, the fracture was suppressed. The results indicate that fracture is not solely determined by the magnitude of equivalent plastic strain but also by the evolution of inelastic deformation mode. This research offers an improved understanding of the significance of the inelastic deformation path and fracture.