A closed-form analytical solution for residual stresses due to the bending of bilayer sheets

Bending is a conventional manufacturing process of sheet forming. This process induces reasonable residual stress through the thickness. Prediction of this residual stress profile is more difficult in bilayer sheet bending due to different material properties and thickness of layers. In this article, the residual stress distribution will be derived analytically for a bilayer sheet. The induced stress profile due to loading and released stress after unloading has been derived by integration along with the thickness. Also, the neutral axis movement due to non-uniform plastic deformation has been involved in the solution. The stress distribution has been derived analytically for elastic-perfect plastic, elastic-linear plastic and elastic-power law hardening material behavior. The results obtained from the proposed equation are compared by a finite element analysis. The finite element analysis contains bending a bilayer sheet to a specified curvature radius by a three-roll bending process. Comparing the results of the analytical solution and finite element analysis shows good agreement. The location of the neutral axis and the maximum of residual stresses in the thickness have been predicted very well with the proposed equation.