Development of an Analytical Tool for Multilayer Stack Assemblies 2011-28-0083

The development of an analytical model for multilayer stack subjected to temperature change is demonstrated here. Thin continuous layers of materials bonded together deform as a plate due to their differing coefficients of thermal expansion upon subjecting the bonded materials to the change in temperature. Applications of such structures can be found in the electronics industry (the study of warpage issues in printed circuit boards) or in the aerospace industry as (the study of laminated thin sheets used as skin structures for load bearing members such as wings and fuselage). In automotive electronics, critical high-power packages (IGBT, Power FETs) include several layers of widely differing materials (aluminum, solder, copper, ceramics) subjected to wide temperature cyclic ranges. Modeling of such structures by using three-dimensional finite element methods is usually time consuming and may not exactly predict the inter-laminar strains. An attempt has been made here to obtain a closed form solution for such a multilayered stack using a set of recursive polynomial equations on subjecting the stack to temperature change under steady state conditions. Based on the closed form solution technique, a simple Excel®-based tool has been developed to predict the radius of curvature, to determine bending strains at both the bottom and the top layer of the stack and to compare the result with the numerical standard codes. Results show a close comparison for both the analytical and the finite element simulation. Analytical solutions are further extended to predict the interlayer displacements.