Theoretical Formulation and Numerical Implementation of Electromagnetic and Thermomechanical Loading Processes in Solids.

Abstract

The electromagnetic-thermal-mechanical process of electromagnetic forming (EMF) is a high velocity manufacturing technique that uses electromagnetic (Lorentz) body forces to shape sheet metal parts. One of the several advantages of this technique is the considerable ductility increase observed in several metals, particularly aluminum. In this research two important aspects of this process are addressed: the influence of the sheet metal’s constitutive response on ductility and the consistent formulation of the fully coupled electromagnetic-mechanical problem.

The first part of the work addresses the necking localization of a metal sheet during an electromagnetic process. A “weak band” model is used to predict the onset of necking of a thin sheet under plane stress and in-plane electric currents, an idealization of the local conditions in unconstrained electromagnetic loading. This work finds that EMF increases ductility over quasistatic techniques, due to the material’s strain-rate sensitivity, and details how the material constitutive response and process characteristics affect ductility.

The general theory is subsequently applied to freely expanding electromagnetically loaded aluminum tubes. Necking strains are measured in tubes of various geometries that are loaded by different forming coils and electric currents. The experimental results show reasonable agreement with the corresponding theoretical forming limit predictions, which indicate a two to three fold increase in the forming limits with respect to the quasistatic case.

The second part of the work pertains to predictive modeling of EMF processes. Recent works do not consistently account for the coupling between electromagnetic fields and finite deformations. Typically, separate solutions to the electromagnetic and finite strain mechanical problems are combined in lock-step. The present work employs a fully coupled Lagrangian (reference configuration) least-action variational principle. This principle forms the basis of the proposed variational integration numerical scheme that provides a consistent staggered solution algorithm.

Application of the general theory is considered for axisymmetric problems. Results from this simulation compare well with known analytical ring expansion solutions. Finally, this work simulates a range of realistic tube expansion processes, including the novel problem of electromagnetic expansion of tubes with non-conducting outer coatings.