An improved estimate for thermal stresses in multi-layer assemblies

Electronic assemblies may often be approximated as layered structures during their analysis. Therefore, the thermal stresses that develop in bonded layers is of interest in the modeling of reliability of electronic assemblies. At the present time, analytical models of thermal stresses in multilayered assembly, inspired by the classical work of Timoshenko, exist in the literature. The current approaches to modeling bonded layers philosophically follow the derivations of Chenand Nelson (W.T. Chen, 1979) or Suhir (1986). The accuracy of these two modeling approaches depend on assumptions on the "softness or the relative "stiffness" of the bond layers. It is also difficult to extend Chen and Nelson's solution to assembly with more than three layers since the order of governing equation increases upon introduction of additional layers, and the resulting equation is very difficult to solve analytically. Suhir's model yields an accurate solution when the moduli and the thickness of each layer is comparable, as the different layers are assumed to possess the same radius of curvature at a position along the length. The purpose of current paper is to improve the analytical estimates of thermal stresses in multilayered structures that is provided by existing models. The improvement is aimed at providing accurate solutions when the layers are of significantly different thicknesses or moduli. The total thickness of the layers, however, is constrained to be small compared to the length of the structure.