Glenn S. Daehn

Department of Materials Science and Engineering

The Ohio State University

614/292-6779

e-mail: Daehn.1@osu.edu

Vincent J. Vohnout

Department of Industrial Systems and Welding Engineering

The Ohio State University

Larry DuBois

Project Manager, Electromagnetic Forming Demonstration Project,

United States Automotive Materials Partnership (Chrysler, Ford and General Motors)

Engineering and Development Center

MidLux Division of General Motors, Flint, MI

Abstract: The basic attributes of high velocity metal forming are discussed. These include improved formability and inhibition of wrinkling. Also, methods for the practical use of high velocity metal forming are demonstrated. Both stand-alone electromagnetic forming and a hybrid technique based on stamping with electromagnetic forming are demonstrated. It is concluded that with further development, this may be an important sheet metal forming technology.

Introduction: High velocity metal forming has always been regarded as a technique that could enable the fabrication of many complex components and/or enabling sheet forming of low-ductility materials. It was this aspect that drove much of the development of this technology in the 1960’s. In fact between 1961 and 1972 the Engineering Index shows that between 20 and 40 papers per year were published on some aspect of high velocity metal forming including such techniques as explosive forming, electromagnetic forming, electrohydraulic forming and closely related techniques. Between 1973 and present the Engineering Index reports the publication of fewer than five papers per year in these areas combined [1]. While it may be interesting to speculate on the reasons for this abrupt fall off in activity some 25 years ago, the purpose of this paper is to argue that some aspects of high velocity forming offer elegant and robust solutions to problems associated with forming of sheet metals with limited formability, and that while much is known about these forming techniques, further research is needed to exploit them fully.

As a direct result of the work in the 60’s there is significant manufacturing activity that is ongoing in a rather unpublicized way involving high velocity forming. For example, Dynamic Materials in Lafayette, Colorado is a business that has been employing explosive forming for the past 25 years. They specialize in components that cannot be formed by traditional means either because the components are too large or the shapes are not amenable to traditional tooling. They regularly supply components to advanced systems companies such as Boeing and Rocketdyne. They have not yet had to turn away business because they could not form the component, nor do they modify part shapes to make the component manufacturable, as is common practice in traditional stamping [2]. This is a testimony to the robustness of this explosive forming process. Also, electromagnetic forming has been actively used over the past 30 years. Maxwell-Magneform has produced several hundred capacitor banks which are used in electromagnetic forming. The vast majority of the operations carried out with this equipment are related to the electromagnetic expansion or compression of tubes to develop assemblies using a high velocity variant of crimping that does not involve springback. Often these operations are carried out in mass production such as in crimping retaining rings on rubber shock absorber boots. In possibly the most advanced application of this technique, steel yokes are crimped on the end of tubular aluminum torque tubes for use in the Boeing 777 aircraft. This technique was developed by Grumman Aerospace and is carried out at Boeing Georgia. These examples demonstrate that high velocity forming in general and electromagnetic forming specifically are compatible with the conventional manufacturing environment.

It is presently proposed that with modest additional development, high-velocity electromagnetic forming can address significant problems that now exist in forming aluminum and other materials with limited formability (see [3] for a discussion of the prioritized technology needs in the auto industry). Work carried out over the last several years at Ohio State University has demonstrated that high velocity metal forming can stretch material to much higher strains than are expected based upon the conventional forming limit diagram. Also, in collaboration with industrial partners, we have developed a number of strategies that can be used to form aluminum components in a robust and cost-effective manner. The purpose of this note is to argue that extensions of conventional electromagnetic forming can improve forming limits in metals such as aluminum and implementation of this in forming systems offers elegant approaches to forming complex components.

Motivation and Background: Electromagnetic forming is arguably the most flexible and cost effective method of implementing high velocity sheet metal forming. In principle, electromagnetic forming is very simply accomplisehed by connecting a conductive actuator (usually a solinoid coil fabricated from copper windings) in series with a large capacitor bank with a high voltage charging circuit and fast-action switching. When the capicators are charged and switched the large current transient in the work coil, or actuator, produces a transient magnetic field which induces eddy currents in any nearby conductive material. The fields of the actuator and the eddy currents are always repulsive in such experiments. The resultant electromagnetic pressure can become quite high. The eddy currents effectively exclude the magnetic field up to a distance known as the magnetic skin depth, d:

where s is the electrical conductivity of the workpiece, w is the ringing frequency of the circuit and µ_o is the magnetic permeability of free space. The circuit frequency is determined by the same considerations that govern simple LRC circuits (but L changes due to workpiece motion). Provided the material conductivity and ringing frequency are such that skin depth is less than material thickness, the local magnetic pressure that acts between the actuator and workpiece can be estimated as:

where B is the magnetic flux density, which is generally proportional to the current and the density of the windings in the solinoid. Pressures that exceed those required for plastic yielding of metal sheets can be easily obtained, possibly providing material acceleration to high velocity. Key points are that this technique works for any sufficiently conductive metal and some simple engineering calculations are possible. Detailed calculations are more complex as many aspects are coupled and flux density and pressure distributions may take on complex three-dimensional configurations with advanced actuator designs. The electromechanical fundamentals [4,5] and application to conventional electromagnetic forming systems [6-9] is covered in detail elsewhere.

One of the observations that motivates the proposed work is that the material forming limits of common metals can be dramatically increased far beyond those available in quasi-static forming. One of our earliest examples of this is shown in Figure 1. Here 6061-T4 aluminum was formed into a conical die with a 90o apex angle in two sets of conditions. In the case on the left, quasi-static hydraulic pressure was applied beneath an aluminum sheet that drove it into the die. In the second case an intense electrical discharge was used to set up a shock wave (electrohydraulic forming [6]) that drove it into the die at a velocity estimated near 150 m/s. With quasi-static pressure the material failed in near accord with the traditional forming limit diagram. While in the discharge case extensions in excess of 100% were observed with minor strains near zero (near plane strain). This increases by a factor of near 4 the extension available in 6061-T4 aluminum. Very similar results were seen in companion experiments in iron and copper [10-12].

This demonstrates that under appropriate conditions forming at high velocity can improve material formability relative to conventional forming methods. What is still needed however is a quantitative description of the conditions under which the material will form at high velocity as opposed to those in which it will tear or wrinkle. Methods to design electromagnetic actuators that are effective in producing velocity profiles that maximize formability are also presently unavailable.

High Velocity Formability: The examples shown in Figure 1 demonstrate that extremely large improvements in formability are possible in high rate forming. There are a large number of issues that can affect high-velocity formability including both inertial effects and changes in material behavior with strain rate. Some of the important issues related to formability in high velocity formability are briefly discussed in the following.

Inertial stabilization of necks One of the most straightforward ways to explain the observed improvement in high-velocity ductility is by considering the effect of inertia on a neck that is forming in a tensile sample being extended in one dimension. Several researchers have shown failure in a tensile sample is delayed when inertial forces are relatively large [11, 13-15]. The essence of the argument follows [16]. Either at high or low velocity, at relatively low strains, the sample may deform in a uniform manner. During uniform deformation, the local velocity of any location of the sample will vary linearly with its position along the sample. After the Consideré instability point (i.e., load maximum), if necking is to ensue, a sharp velocity gradient will be developed in the sample. This velocity gradient is accommodated over the region of the neck. In going from the stable state to the localized state, there must be a change in the velocity profile of the sample. This change in velocity over time (acceleration) produces non-uniform inertial forces in the sample. The inertial forces tend to produce additional tensile stresses outside the neck. These produce additional extension in the uniform part of the sample. This is similar to how increasing flow stress with strain rate inside a neck produces additional sample extension in superplasticity.

Hu and Daehn developed a one-dimensional finite element model to study this problem quantitatively [17]. In this model a simple rate-dependent Holomon flow law is assumed and the stress at any location in the sample is due both to inertial forces and material resistance. Figure 2 shows uniform sample extensions as a function of velocity as experimentally measured, and developed from the model for both conventional tensile testing [18] and axisymmetric electromagnetic ring expansion [19]. There are a few features of this analysis that are quite noteworthy. First, there is very good agreement between the relatively simple model and experimental observation. This suggests that, although other effects may also be at work, this inertial stabilization of necking is a first-order effect in high velocity ductility. Second, notice that ductility decreases rapidly in uniaxial tension beyond a critical velocity. This is known as the vonKarman velocity [20] and it represents the point at which a plastic wave cannot propagate through the fast enough to accommodate the motion of the sample end point. Beyond this velocity, tensile samples fail at the driven end. In ring expansion there is no driven end. The high symmetry dictates that the sample accelerates uniformly. This comparison between rings and tensile bars shows how important boundary conditions are in the forming of samples. Lastly note that the cones shown in Figure 1 demonstrate plane strain forming in excess of 4 times the usual forming limit. The analysis of high velocity ring expansion suggests at most about a factor of 2 in extension is possible at accessible ring velocities. Certainly, other factors must also be important in explaining the high velocity ductility of the samples shown in Figure 1.

Sample size and apparent anisotropy Sample size or shape has a significant effect on strain to failure in ring expansion. While the section above showed that a numerical model could satisfactorily predict strain to failure^* values for slender rings 30mm in diameter with a 1mm x 1 mm cross section, very different results were obtained when we studied taller rings of the same tube [21]. The studies were carried out with 6061-T4 aluminum and annealed OFHC copper. In either case rings 30mm in diameter with a 1mm thick wall and varied heights were studied (1mm to 16 mm tall) with the same driver coil. Figure 3 shows the maximum strain without failure as a function of ring height for a both the 6061-T4 and the OFHC Copper. It should be noted that the initial 'launch' velocity here is constrained to be a value that is sufficiently low that it does not cause failure of the sample. If the sample is expanded into a die such that it will stop before tearing, even higher strains are possible before failure. Despite this, very high extensions are available simply by changing the geometry of the component being formed. In the case of the 6061T4 aluminum, 70% extension is available from a material that only exhibits 26% in static uniaxial extension.

There is also a variation in the measured strain-ratio in these experiments which should favor increased major strain, but the change is far too small to explain the increases observed. The manner in which discharge energy and sample geometry affects the strain-ratios produced has been studied at Ohio State by Fenton [36], but a full understanding of how materials properties and boundary conditions affect anisotropy has not yet been developed.

Inertial ironing Traditional ironing between a tool and mandrel has been used to generate very large deformation in items such as beverage cans. In this, large through-thickness stresses are generated between tools that extend the sheet material by squeezing it in the through-thickness direction. Much the same effect can be produced by what is presently termed inertial ironing. In this, when a sheet of metal that is moving at high velocity is stopped by a fixed massive die it quickly decelerates to a stop. This produces a large through-thickness compressive stress that can also produce lateral extension of the material. The magnitude of the compressive stress produced when two elastic bodies collide with an initial velocity, Vo, is easily calculated as [22]:

where r is density and c is the propagation velocity of compressive waves generated upon impact. This is equal to (E/r)^.5 for longitudinal waves in a bar. The subscripts 1 and 2 represent the two materials being brought into contact.

When one or both of the bodies deform plastically upon collision, the situation is more complicated. But experiments in our laboratory have shown that very simple tooling can give coining-like effects (i.e., detailed patterns can be embossed into the face of the sheet metal, or the finish can be changed from matte to reflective by using rough or polished tools). Both models and experiments show that on impact the through thickness pressure can easily become on the order of the material flow stress in electromagnetic forming. This squeezing force should be able to affect the measured formability.

Changes in constitutive behavior It appears likely that the dominant effects responsible for the improvement in material formability at high sample velocities arise from inertial effects that are very general and independent of the details of a given material system. The main arguments for this are that similar effects have been seen in several materials and that inertially-based analyses can explain many of the phenomena seen to date (e.g., Fig. 2). It is not suggested that changes in constitutive behavior are always unimportant. There are always temperature rises (due to resistive and deformation heating in electromagnetic forming and only deformation heating in electrohydraulic forming), but temperature rises are usually modest (<200o C). Also it is well known that at a given strain, material flow stress rises with strain rate. The rate of flow stress rise commonly increases beyond strain rate of 103 s-1 [23,24]. It seems that an increasing strain-rate-sensitivity with strain rate could also be partly responsible for improved formability [25,26].

Wrinkling and springback in high velocity forming Inertial effects have been shown to have an important influence on buckling instabilities as well as necking [27-29]. Our recent experiments on ring compression and sheet forming show this to be the case. Figures 4 and 5 from the recent thesis of Padmanabhan [1] show this clearly. Both show situations where compression is required along one direction. At sufficiently high velocity, wrinkling can be eliminated. This is another manner in which high velocity forming can address problems that are of practical concern to the metal forming community. These examples also demonstrate that the equipment used in electromagnetic forming can be extremely simple.

It also appears that springback problems are minimized in high velocity deformation. It has been previously reported that springback is reduced in high velocity forming [30] and it has been proposed is that the high through-sheet compressive stresses that act at impact with a die are responsible [31]. Further examination of the experimental results shown in Figure 5 support this contention. Coordinate measurements were taken off of the impacted die as well as the inner surface of the formed Al sheet. At very low energies, the sample does not meet the die at all locations and at energies that are far too high some flaring of the shape takes place at the extreme edges. However over a wide range of energies, there is nearly perfect correspondence between the shapes (within the resolution of our procedure) [1].

An Example of Aggressive Electromagnetic Sheet Metal Forming: Several studies and demonstrations have shown that by substituting aluminum for steel in automobile bodies can reduce the mass of the automotive body-in-white by 40-60% [3]. This, of course, translates into many other benefits in automobile performance and fuel economy [32]. The improved fuel economy has further obvious societal benefits. Forming aluminum represents significant technical challenges. Although a few vehicles featuring aluminum body panels are available, the manufacturing processes that must be used are expensive. For example presently aluminum panels are fabricated by superplastic forming or door assembled from at least three separate aluminum sheets. Such assemblies are expensive and would not generally be acceptable in high volume vehicles. A strategy for using electromagnetic forming to permit the robust fabrication of aluminum door-inners has recently been developed.

Recently two electromagnetic forming demonstration projects were sponsored directly by Chrysler, Ford and General Motors under their United States Council for Automotive Research’s (USCAR) materials research. One of these projects was related to demonstrating the feasibility of fabricating aluminum door inners using a hybrid technique of conventional stamping augmented with electromagnetic forming. The GM J-car (Cavalier, Sunfire) door inner was chosen as the subject part as the die try-out tools were available. In one experiment forming was attempted with 6111 T4 aluminum sheets with the same tools that are used with steel sheets (but altering the binders to increase draw-in, and reduce the tendency to tear). The results of these experiments are shown in Figure 6. These basically show that even when binder configuration and loads are varied over a wide range wrinkling and/or tearing cannot be prevented and usually both occur. This experiment supported the commonly-held belief that a one-piece aluminum door inner cannot be fabricated using conventional stamping.

A strategy for strategically using electromagnetic forming to augment conventional stamping was developed in consort with the USCAR Aluminum Forming Committee. The approach involved dramatically softening the corner shape on the entire hinge face of the door. When this and other important shapes were significantly softened, the panel was formable with conventional stamping technology. As something close to the original product shape is required for sealing and to eliminate wind noise, etc., a secondary electromagnetic operation was carried out with an elongated doubly-curved electromagnetic forming actuator. The actuator was designed for this purpose and the electromagnetic forming was carried out at The Ohio State University. The experiment is schematically depicted in Figure 7, along with the results. Here the softened section is re-formed into a die that has the desired product shape using a 40 kJ electromagnetic impulse. A rough vacuum was provided between the sheet and die.

This series of experiments demonstrated that electromagnetic augmentation of conventional forming may enable the cost-effective fabrication of many aluminum panels that are at best quite difficult to form presently. In the present example plane-strain values in excess of 25% are observed on the re-formed panel (outside the safe region of the conventional FLD). More important than the change in forming limit in this case is the ability a hybrid system holds in modifying the strain distribution to one that cannot be obtained in stamping alone. In an actual production scenario, it is anticipated that the electromagnetic actuator would be part of the forming tool and it would be energized at the bottom of the press stroke. There is nothing inherently difficult about such a process and the demonstration also showed that sheet forming actuators can be relatively robust. This demonstrates that this forming technology can offer many of the same benefits provided by superplastic forming (one-sided dies, ability to improve forming limits) without the important restrictions (high temperatures, controlled strain rates and specially processed materials). The hybrid system should yield low production costs and it can be implemented largely with existing stamping presses.

In addition to demonstrating the essential viability of EM augmentation of stamping, this project pointed out areas in which our basic understanding is still very weak. First, the entire system had to be designed by ‘gut-feel’; the degree to which the sheet would fill the die and the energies needed had to be relatively crudely estimated. Also, the strains available, while somewhat larger than available >from static forming, are lower than those seen in many of the other observations of formability at high velocity. If forming procedures like this are to be used, an improved understanding of formability at high velocity must be attained. The literature on high rate forming developed in the 60’s offers little insight. For example, the concept of the forming limit diagram was introduced by Goodwin in 1968 [33], standard test methods were not available until the mid 70’s [34]. By this time research in high velocity forming had effectively stopped. With today’s improved understanding of formability and available numerical techniques, we may expect significant progress.

Tools: The forgoing discussion points out a number of areas in which our understanding of electromagnetic forming may be improved. In order to do so rapidly, both experimental and analytical techniques must be brought to bear upon the problem.

In analogy with recent progress in the analysis of conventional sheet metal stamping, it would be very desirable to model the electromagnetic forming process with finite element codes. Unfortunately it appears that presently there are no codes that incorporate Maxwell’s equations of electromagnetics and induction along with the usual elements for plasticity and inertia. Applied Research Associates [35] is presently developing a smooth particle hydrocode tool that includes all of the necessary ingredients. Preliminary modeling with the code appears quite promising.

In terms of verifying models, the usual approaches of measuring strain distributions after forming work well. In addition it is useful to measure the current-time profile during forming. This allows estimation of the pressure-time profile applied to the sheet. Furthermore, high speed photography is another useful tool for verifying predictions. This is especially important as the shapes that components take on after launch are often not what would be predicted intuitively. Figure 8 shows an example of a high speed series of photographs of a plate of aluminum being launched off a simple actuator.

A Concluding Remark: High velocity metal forming can offer many useful features to the field of sheet metal fabrication. Most importantly tearing and wrinkling instabilities are mitigated and simple tooling systems, often including one-sided dies, are used. With modest additional development it is anticipated that this technology will play an important role in the fabrication of advanced aluminum components.

Acknowledgments: The general portion of this paper represents a summary of work done over several years, by several students (see references). This work was carried out under the support of: NSF (through young investigator award DMR 9258172), United States Automotive Materials Partnership (USAMP) in conjunction with the Partnership for a New Generation of Vehicles (PNGV) and the Center for Advanced Materials and Manufacturing of Automotive Components (CAMMAC) at Ohio State. Most recently this area is supported by the NSF Division of Design Manufacture and Industrial Innovation, Delcie Durham, Program manager.