Prediction of flatness defects and of the stable configuration of thin multilayer assemblies due to chemical shrinkage

Abstract

The manufacturing process of multimaterial and multilayer assemblies involving pre-impregnated laminates consist of heating the composite structure at high temperature, typically of the order of 200 °C, at which polymerization occurs. During the curing, a permanent deformation, called chemical shrinkage strain, is generated and may strongly influence the future flatness of the assembly. Moreover, the cooling generates additional thermal deformations, which also participate into the manifestation of flatness defects at room temperature. To predict warpage or flatness defects, the chemical shrinkage strain needs to be precisely determined.This work proposes an analytical approach dedicated to flatness prediction of multilayer composites taking into account shrinkage strain generated during processing. Our contribution also aims at predicting and analyzing stable and unstable solutions of flatness defects. The proposed analytical model, developed for any multilayer composite, is obtained from an extension of the classical laminate theory (CLT). Geometrical nonlinearities are also accounted for. The analytical approach relies on trial fields for strain and displacements, and on total potential energy minimization. The theory is applied to a bilayer laminate consisting of a cured layer made of epoxy/glass fiber composite and of a pre-impregnated one of the same material. Results obtained from the analytical modeling are validated by numerical simulations. Influence of material parameters is also analyzed for this configuration. Finally, from experimental measurements of curvatures on bilayer composite samples, an inverse method and a minimization procedure, the proposed analytical development provides an estimate of the effective shrinkage strain, which is responsible for the flatness defect. Illustration of this strategy is exemplified by considering a bilayer composite manufactured for this work.