Modeling of bending characteristics of symmetric tri-layer laminated Sheet materials

Abstract

Bending of sheet materials is widely applied to shaping many automotive, aerospace and other industrial components. Tailored laminate sheet materials are desirable in bending applications where monolithic sheets do not meet the design requirements or manufacturing demands. An accurate analytical model can be effectively utilized for rapid design of components for laminated sheet materials for a given application. Many analytical models based on advanced theory of bending have been proposed in the literature to predict plane strain bending characteristics of monolithic sheet materials. However, there are very few such models for laminated sheet materials. In this study, an analytical model for tri-layer laminated sheet material is developed based on advanced theory of bending. The model considers Mises yielding and Ludwik non-linear plastic hardening with Bauschinger effect for various laminate thickness ratios. Also, a 3D FE model based on Marciniak-Kuczynski (MK) bend test design is developed to assess pure bending characteristics of a symmetric tri-layer aluminum sheet laminate with softer and thinner clad layers on both surfaces and a harder thicker core in the middle. The through-thickness tangential stresses from the analytical model are compared with those from FE model for different clad to matrix thickness ratios. The tangential stresses decrease in magnitude with increasing aluminum clad thickness ratios in the analytical model. This behavior is in good general agreement with the results from the mid-width section for the FE model. The analytical and FE models also yield similar order trend in relative thickness change with increasing clad thickness ratios and with increasing specimen radius of curvature. The 3D FE model exhibited anticlastic curvature at the edges as a result of strain inhomogeneity across the width. Unlike the tangential stress distribution, the tangential strain is maximum at the specimen edges than at the mid-width. The inhomogeneity in stress and strain across the bend line shows that plane strain condition is not consistent across the width of the sheet.