A Two-Body Formulation for Solder Joint Shape Prediction

Abstract

Solder shape prediction is essential for accurate fatigue life determination and joint design optimization. In the present paper, a new solution approach using the surface tension theory is developed to simultaneously predict standoff height, wetted surface area, contact angles, and solder shape by including energy effects between a molten solder body and an arbitrarily shaped solid body. Existing models for solder shape prediction do not appear to determine all characteristics including joint standoff height, wetted surface area, and contact angles simultaneously. A general two-body axisymmetric finite element code is developed and coupled with a constrained optimizer to solve four illustrative examples. These examples include the shape of a sessile droplet on a fixed pad, a flip-chip joint, a sessile droplet on a free surface, and a typical ceramic ball grid array solder joint. In all four examples, the results predicted by the present approach compare favorably with available experimental and numerical results.

jNURBS: An object-oriented, symbolic framework for integrated, meshless analysis and optimal design

“…The standoff height predicted by the program is 43 mm, which is identical to the value obtained through finite element analysis in the earlier study [34]. The initial and the final shapes of the droplet are shown in Fig.…”

“…The finite element method is a common choice for determining the total potential for a given shape [34,33]. Since the droplet profile, area of the surface over which external forces act (the wetted area), and the joint height (standoff) are often unknown, the equilibrium shape is determined by an iterative optimization process.…”