A Simplified Model for Interconnect Stresses Induced by Bending of Printed Wiring Boards

Abstract

A simplified model is developed for analysis of interconnect stresses induced by changes in the curvature of printed wiring boards. The model utilizes the Rayleigh-Ritz variational approach and can be used for rapid assessment and is well-suited for parametric studies because it does not need any numerical meshing. This simplified model represents the component as an equivalent shell and the interconnects as deformable beams. As a simplification, any initial warpage of the component has been neglected in this study. Finite element models are used to verify the simplified model: a simplified FEA model that utilizes the same shell idealization as the proposed Rayleigh-Ritz model and a more detailed 3D solid model. The proposed simplified model provides a faster, more versatile alternative to FEA and can be used to estimate the interconnect stresses caused by PWB warpage under a variety of thermomechanical, vibration, and shock/drop loading conditions.

This thesis focuses on demonstrating the use of this simplified modeling approach for area array surface mount components (e.g. stud-grid array, land-grid array, column grid array, and ball grid array). In particular, the example problem addressed in this thesis is the pre-stress induced in surface mount area-array interconnects during the solder reflow process used for attaching surface mount packages to printed wiring boards (PWBs). The possibility exists for the PWB and component to warp during the reflow process and therefore exhibit some concave or convex curvature once the process has been completed. If the PWB is then straightened during the assembly process, the act of straightening the PWB can cause pre-stresses to develop in the interconnects between the PWB and the component package. It is important to understand these pre-stresses because unaccounted for interconnect pre-stresses can result in premature wear-out failures or unexpected overstress failures of the assembly.