Analytical estimate for curing‐induced stress and warpage in coating layers

A thermoset coating that is applied to an elastic substrate will develop residual stresses during curing because of polymerization shrinkage of the resin. This shrinkage only partly contributes to the residual stresses because, before gelation, the stresses relax completely. In this study, we developed explicit analytical expressions for the curing efficiency factor, the residual stresses, and the resulting warpage. We did this by assuming that after gelation, the material was in its rubbery state and that viscoelastic effects were absent. A difference between the free and constrained warpages during curing was made. The analytical warpage models were shown to give results comparable to those of the numerical calculations with a fully curing‐dependent viscoelastic material model. Furthermore, for the first time, accurate analytical expressions for the stress‐free temperature and stress‐free strain were obtained. With these expressions, the effect of curing shrinkage on the residual stresses could easily be incorporated into existing (numerical) stress analysis without the need for extensive curing‐dependent viscoelastic material models. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2012