PNNL-13501 - Pacific Northwest National Laboratory

Modeling of High-Velocity Forming for Lightweight Materials Applications
Study Control Number: PN99047/1375
Mark R. Garnich, Anter A. El-Azab
Electromagnetic forming has the potential to overcome formability barriers that prevent more widespread use of
aluminum for lightweight energy-efficient vehicles. This project develops numerical modeling technology essential for
designing electromagnetic forming systems for general sheet metal applications.
Project Description
This project aims to develop theoretical and
computational models to simulate electromagnetic
forming electromagnetic forming of lightweight metal
sheets. Electromagnetic forming is a high velocity metal
working process that uses electromagnetic driving forces.
The work is multidisciplinary in nature, as it involves
simultanteous development and numerical treatment of
Maxwell’s equations, finite deformation elastoplasticity
and elasto-viscoplasticity, as well as heat generation. As
Maxwell’s equations are significantly affected by the
deformation field in the work piece, an incremental
formulation of the boundary-value problem of
electromagnetics is first developed. This, along with the
conventional metal plasticity models for finite
deformation, render the work computationally intensive.
The work is intended for use in simulation of high-speed
metal forming related to auto and aerospace industries and
in design and performance analyses of high-speed,
electromagnetic metal forming systems. The main benefit
of such advanced forming techniques lies in the improved
formability limits of materials at high speeds, as well as in
providing solutions for other issues related to spring-back
and material damage exhibited during conventional
forming processes.
Introduction
The basic electromagnetic forming process involves a low
inductance electrical circuit with large capacitance and
high speed switches to deliver a high frequency (~20 kHz)
current pulse to a working coil. Conducting work pieces,
such as the aluminum sheet, close to the coil are exposed
to an intense transient magnetic field that generates eddy
currents in the work piece. The currents interact with the
magnetic field to create force (Lorentz forces) that pushes
the work piece away from the coil. The forces can be
large and the work piece can achieve velocities on the
order of 100 m/s in less than 0.1 millisecond. The high
speed and associated impact with die surfaces result in
dynamics-related benefits to metal forming not seen with
quasi-static forming processes. The most important
benefits are increased ductility and reduced springback.
Electromagnetic forming is an old technology that has had
limited use due to the complexity in applications that go
beyond simple cylindrical geometry. The main issues are
the difficulty in designing a system that results in a
desired part shape and the durability of working coils for
high volume production. Both of these issues could be
effectively dealt with using advanced modeling
technology. Models could predict the time and space
distributions of forces and temperatures that affect
material behavior in both the coil and work piece. The
challenges in modeling are to accurately and efficiently
capture the physics of the interaction between the
electromagnetic, mechanical, and thermal fields.
Results and Accomplishments
We previously reviewed the state of technology for
modeling electromagnetic forming. We identified the
need for a general robust numerical capability for
simulating electromagnetics in deforming media. We
then developed a new form of the electromagnetic
constitutive laws based on a Lagrangian form of
Maxwell’s equations. In addition, we developed a
numerical algorithm, based on least-squares finite element
method (Bochev and Gunzburger 1998) to deal directly
with the first-order set of Maxwell’s equations. This
formulation avoids some of the numerical difficulties
associated with the “potential formulations” that have
seen widespread use (Jiang et al. 1996).
This year, we focused on developing software. A code
was written in FORTRAN 77 that solves the first-order
set of Maxwell’s equations in a least-squares finite
element method numerical framework. A preconditioned
conjugate gradient solver was applied for efficient
solution of the sparse system of equations stored in
optimized skyline form. A limited implementation that
Design and Manufacturing Engineering 189