Finite Element Method for Predicting Equilibrium Shapes of Solder Joints

[+] Author and Article Information
N. J. Nigro, A. F. Elkouh, X. Zou, R. Fournelle

Mechanical Engineering Department, Marquette University, Milwaukee, WI 53233

S. M. Heinrich

Department of Civil and Environmental Engineering, Marquette University, Milwaukee, WI 53233

Ping S. Lee

Allen-Bradley Company, A Rockwell International Company, Milwaukee, MI 53204

J. Electron. Packag 115(2), 141-146 (Jun 01, 1993) (6 pages) doi:10.1115/1.2909309 History: Received February 20, 1992; Revised March 20, 1993; Online April 28, 2008


This paper discusses the development and application of a finite element method for determining the equilibrium shapes of solder joints which are formed during a surface mount reflow process. The potential energy governing the joint formation problem is developed in the form of integrals over the joint surface, which is discretized with the use of finite elements. The spatial variables which define the shape of the surface are expressed in a parametric form involving products of interpolation (blending) functions and element nodal coordinates. The nodal coordinates are determined by employing the minimum potential energy theorem. The method described in this paper is very general and can be employed for those problems involving the formation of three dimensional joints with complex shapes. It is well suited for problems in which the boundary region is not known a priori (e.g., “infinite tinning” problems). Moreover, it enables the user to determine the shape of the joint in parametric form which facilitates meshing for subsequent finite element stress and thermal analyses.

Copyright © 1993 by The American Society of Mechanical Engineers
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