Simulation of Electromagnetic Forming of a Cross-Shaped Cup by Means of a Viscoplasticity Model Coupled with Damage at Finite Strains

Abstract

In the field of sheet metal forming traditional forming processes are used. However, a quasi-static forming process combined with a high speed forming process can enhance the forming limits of a single one. In this paper, the investigation of the process chain quasi-static deep drawing – electromagnetic forming by means of a new coupled damage-viscoplasticity model for large deformations is performed. The finite strain constitutive model, used in the finite element simulation combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. The anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong–Frederick kinematic hardening. Hill-type plastic anisotropy is modelled by expressing the yield surface as a function of second-order structure tensors as additional tensor-valued arguments. The coupling of damage and plasticity is carried out in a constitutive manner according to the effective stress concept. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package of LS-Dyna with the electromagnetical modul. Aim of the work is to show the increasing formability of the sheet by combining quasi-static deep drawing processes with high speed electromagnetic forming process.