Comparison of Fully Coupled Modeling and Experiments for Electromagnetic Forming Processes in Finitely Strained Solids
Résumé
In fracture and fragmentation research the technique of electromagnetic forming, which uses electromagnetic (Lorentz) body forces to shape metallic parts, is finding significant use due to the high velocity, high strain rate loading it can impart without contact on workpieces. The same process is also becoming increasingly relevant formanufacturing processes in sheet metal forming, where this technique offers several advantages: speed, repeatability, non-contact loading, reduced springback and considerable ductility increase in several metals. Current modeling techniques for these coupled electromagnetic and thermomechanical processes are not based on coupled variational principles that can simultaneously account for electromagnetic and mechanical effects. Typically, separate solutions to the electromagnetic (Maxwell) and motion (Newton) equations are combined in staggered or lock-step methods, sequentially solving the mechanical and electromagnetic problems. To address this issue, Thomas and Triantafyllidis (J Mech Phys Solids 57:1391-1416, 2009) have recently introduced a fully coupled Lagrangian (reference configuration) variational principle, involving the magnetic field potential and the displacement field as independent variables. The corresponding Euler-Lagrange equations areMaxwell's and Newton's equations in the reference configuration under the eddy current approximation. This novel approach is used here to simulate free expansion experiments of AA6063-T6 aluminum tubes. A viscoplastic constitutive model, developed independently by the authors (Thomas et al. Acta Mater 55:2863-2873, 2007) for necking experiments in tubes of the same aluminum alloy, is used in the simulations. The measured electric currents and tube deformation--the latter obtained by Photon Doppler Velocimetry--show reasonably good agreement with the corresponding simulations, which are obtained using a variational integration numerical scheme that results in an efficient staggered solution algorithm.