Thermomechanical multi-domain stress modeling for fatigue analysis of electronic packaging

This paper describes a generalized multi-domain Rayleigh-Ritz 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, ceramic ball grid array, and plated-through hole 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. In each sub-domain, the displacements were expressed in polynomials with unknown coefficients. The Rayleigh-Ritz energy method was then used to determine those coefficients. The solution at each domain was formed as the superposition of the results corresponding to their sub-domains. All results were compared with finite element analyses (FEA) for the same loading conditions. The Broyden-Fletcher-Goldfarb-Shanno (BFGS), a quasi-Newton method with line search, was used for fast convergence. The demonstration concluded that the proposed multi-domain method decreases the presented (example) problem's solution time by a factor ranging from 4.2 to 7.6 compared to finite element model (FEM) at a comparable accuracy.