Analysis and prediction of bending-torsion coupled stress in BGA stacked solder joints considering interaction effects

Abstract

A finite element model of BGA stacked solder joints was established, and finite element simulation analysis of bending-torsion coupled stress and strain was conducted. A testing platform for measuring bending-torsion coupled strain was constructed to validate the accuracy of the simulation. The solder joint diameter, pad diameter, and solder joint height were selected as influencing factors, and an orthogonal table considering the interactions between these factors was designed and established. The maximum bending-torsion coupled stress for 18 different combinations of structural parameter levels in BGA stacked solder joints was obtained, and range and variance analyses of the stress were performed. A multiple nonlinear regression prediction model for the bending-torsion coupled stress of BGA stacked solder joints was established. The results indicate that the order of influence of the factors and their interactions on the bending-torsion coupled stress of BGA stacked solder joints is as follows: solder joint diameter $>$ pad diameter $>$ solder joint height $>$ interaction between pad diameter and solder joint height $>$ interaction between solder joint diameter and solder joint height $>$ interaction between solder joint diameter and pad diameter. At a confidence level of 99%, the solder joint diameter, pad diameter, and solder joint height have a significant effect on the bending-torsion coupled stress of BGA stacked solder joints, while the interactions among these three structural parameters have an insignificant effect on the bending-torsion coupled stress. The established multiple nonlinear regression prediction model can accurately predict the bending-torsion coupled stress of BGA stacked solder joints, with a maximum error of 2.47% and an average error of 0.95% for the mathematical model.