Generalized multi-domain method for fatigue analysis of interconnect structures

Abstract

This paper describes a generalized multi-domain finite element stress analysis method to obtain the stress and strain fields for a variety of packaging styles under cyclic thermal environments. The elastic–plastic analysis was demonstrated on ceramic chip component, gull-wing, plated-through hole, and plastic ball grid array solder joints. The solder joints were modeled by colonies of sub-domains at stress risers identified in advance by finite element analysis. In this approach, the physical domain was mapped into isoparametric regions, which were divided into nested sub-domains according to projected high-stress gradients. The previous multi-domain method, based on Rayleigh-Ritz energy principle, utilized polynomials to interpolate the displacement within sub-domains. On the other hand, the displacements in the main and sub-domains, for the improved method used in this paper, are represented by the nodal displacements through isoparametric interpolation, which is similar to the finite element method. The solution at each domain was formed as the superposition of the results corresponding to their sub-domains. The Broyden-Fletcher-Goldfarb-Shanno (BFGS), a quasi-Newton method with line search, was used for fast convergence. All results were compared with finite element analyses (FEA) for the same loading conditions. The demonstration concluded that the proposed multi-domain method decreases the presented (example) problem's solution time by a factor ranging from 3.4 to 4.5 compared to finite element model (FEM) at a comparable accuracy.