Elastoplastic Analysis of the Erichsen Cupping Test Using Comsol Multiphysics FEM Code

One of the standard procedures to test the formability of sheet material is the Erichsen cupping test, in which the metal sheet blank is held in its place over a circular space and depressed by a semi-spherical punch. The depth of depression that can be reached is the measure of the formability. In this work the elastoplastic deformation of the sheet is analyzed by multipurpose Finite Element Method software Comsol Multiphysics. The Comsol package is not specifically developed or focused on the analysis of solid mechanical problems with elastoplastic model behavior and contact problems, and still limited literature is available in which sheet forming processes are analyzed with Comsol. In this work, the development and testing of a simulation model in Comsol is reported and comparison is made with results reported with other FEM software.The development and testing is realized in successive steps of increasing complexity. First a uniaxial stretching is simulated in order to evaluate the implementation of the elastoplastic material behavior. Next, the bending of a plate over a straight line is analyzed, adding the contact boundary condition between tool and sheet surface into the model. Finally, the axisymmetric model of the Erichsen cupping test is implemented.It is found that the default Von Mises yield function results in incorrect stresses, and needs to be replaced by a yield function in which the Von Mises stress is calculated based on the Cauchy tensor. The non-linear contact condition is a source of oscillations in the local stresses near the zone where contact is established. The simulation results obtained with the final model are compared with punch forces, stresses and strains obtained in literature, showing an adequate comparison.Copyright © 2014 by ASME