pulsed electrohydraulic springback calibration of parts stamped from advanced high strength steel

Accepted Manuscript

Title: Pulsed Electrohydraulic Springback Calibration of PartsStamped from Advanced High Strength Steel

Author: Sergey F. Golovashchenko Alan J. Gillard AlexanderV. Mamutov Ramy Ibrahim

PII: S0924-0136(14)00026-0DOI: http://dx.doi.org/doi:10.1016/j.jmatprotec.2014.01.012Reference: PROTEC 13881

To appear in: Journal of Materials Processing Technology

Received date: 11-9-2013Revised date: 15-1-2014Accepted date: 18-1-2014

Please cite this article as: Golovashchenko, S.F., Gillard, A.J., Mamutov, A.V.,Ibrahim, R.,Pulsed Electrohydraulic Springback Calibration of Parts Stamped fromAdvanced High Strength Steel, Journal of Materials Processing Technology (2014),http://dx.doi.org/10.1016/j.jmatprotec.2014.01.012

This is a PDF file of an unedited manuscript that has been accepted for publication.As a service to our customers we are providing this early version of the manuscript.The manuscript will undergo copyediting, typesetting, and review of the resulting proofbefore it is published in its final form. Please note that during the production processerrors may be discovered which could affect the content, and all legal disclaimers thatapply to the journal pertain.

http://dx.doi.org/doi:10.1016/j.jmatprotec.2014.01.012

http://dx.doi.org/10.1016/j.jmatprotec.2014.01.012

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Pulsed Electrohydraulic Springback Calibration of Parts Stamped from Advanced

High Strength Steel

Corresponding author and first authorSergey F. GolovashchenkoEmail: [email protected]: (313) 337-3738Fax: (313) 390-0514Ford Motor CompanyFord Research and Innovation CenterP.O. Box 2053Mail Drop 3135 RICDearborn, MI 48121-2053 USA

Second authorAlan J. GillardEmail: [email protected]: (313) 805-7417Ford Motor CompanyFord Research and Innovation CenterP.O. Box 2053Mail Drop 3135 RICDearborn, MI 48121-2053 USA

Third authorAlexander V. MamutovEmail: [email protected]: (313) 248-2473Oakland UniversityRochester, MI 48309 USA

Fourth authorRamy IbrahimEmail: [email protected] UniversityRochester, MI 48309 USA

Note: We intend for the electronic version of the paper to have color Figures, and for the print version to have black and white Figures. Therefore, two versions of the Figures will be submitted.

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Highlights

! ! A novel method for removing springback from sheet metal panels has been developed.

! ! Several grades and gauges of steel were calibrated, including DP980 at 1.4 mm thick.

! ! Electrohydraulic calibration works by applying pressure through the sheet thickness.

! ! EH calibration does not require high velocity impact between the part and the die.

Abstract

Electrohydraulic calibration (EHC) of springback is a novel method of removing springback from stamped sheet metal panels and is based upon the electro-hydraulic effect: a complex phenomenon related to the discharge of high voltage electrical current through a liquid. The EHC process involves clamping a stamped panel against a female die with the desired part shape and then applying several pulses pressure onto and through the thickness of the sheet, in a process somewhat similar to conventional coining operations. However, in EHC the pressure is applied by a fluid and through the use of the electrohydraulic effect, and not with a matching hard tool as done in coining. In EHC, electrical energy is stored in a bank of capacitors and is converted into kinetic energy within the liquid by rapidly discharging the stored energy across a pair of electrodes submerged in a fluid. The objective of this paper is to describe the newly developed EHC process, to report the results of early proof-of-concept experiments, to present the results of more advanced experiments using a more industrial tool and actual part geometry, and to describe how numerical modeling techniques were used to optimize the design of the larger and more industrial tool. The developed concept of electrohydraulic stress relieving calibration is based upon clamping a stamped panel to the calibration die surface with the target shape and then applying pulses of pressure to eliminate internal stresses in the stamped panel. When a stamped blank is removed from a forming die, allowed to springback, and then clamped to a calibration die, the internal elastic stresses within the panel in such a configuration serve as a memory of the shape of the blank after springback, and it is these residual stresses that EH calibration is intended to remove from the panel. The developed concept of stress relieving calibration was initially validated by a simple experiment consisting of submerging a bent strip of aluminum into the fluid within an EH chamber, so that both the outer and inner surfaces of the strip (where the internal stresses from bending are located) were exposed to the fluid and the pressure pulse. This experiment served as an initial confirmation that impact with the tool is not necessary to achieve the calibration effect. The sheet metal materials used in this study, and for

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which springback was eliminated after forming, include DP 980 at 1.0 mm and 1.4 mm thick, and also DP600 at 1.0 mm thick.

KeywordsElectrohydraulicCalibrationSpringbackDual phase steelPulsed forming

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Pulsed Electrohydraulic Springback Calibration of Parts Stamped from Advanced High Strength Steel

S. Golovashchenko, A. Gillard, A. Mamutov and R. Ibrahim

1. Introduction

Recently legislated fuel economy standards require new passenger vehicles to substantially

reduce fuel consumption. The most common and effective method of achieving improved fuel

economy in passenger vehicles is reducing the weight of the vehicle. A technical study

conducted by Cheah and Heywood (2011) comparing a number of different scenarios indicated

that the maximum possible vehicle weight reduction achievable by material substitution and

vehicle redesign, using the average 2011 model year vehicle as the baseline, is 25% (947 lbs.)

by 2016, and 35% (1322 lbs.) by 2030. According to Brooke and Evans (2009), during the next

decade it is anticipated that unibody vehicles will not substantially reduce in size. Therefore,

implementation of lightweight materials and the technologies that enable their implementation in

high volume production is swiftly becoming a strategic pathway for achieving the fuel economy

goals. A number of strategic design concepts and manufacturing technologies for vehicle weight

reduction are outlined by Allwood and Cullen (2012). As mentioned by Davies (2003), broad

implementation of Advanced High Strength Steels (AHSS), Ultra High Strength Steels (UHSS)

and aluminum alloys is also a key pathway for accomplishing the weight reduction goals.

The primary high volume method for manufacturing automotive body panels and structural parts

in contemporary industry is stamping from sheet metal in a two-sided die installed in a single

transfer press or in a line of tandem presses. During the era of low oil prices, most automotive

parts were stamped from low carbon mild steel. However, the formability of AHSS and

especially UHSS is substantially lower than that of mild steel. Furthermore, due to the

significantly increased flow stress, the springback of these materials (defined as the elastic

relaxation of a stamped blank that occurs after release from the stamping die) is greatly

increased as compared to mild steels if the blank is stamped in cold forming conditions. Solving

the springback problem often requires expensive iterative solutions including multiple re-cuts of

the die face in order to compensate for the springback which, according to Roll et al. (2005),

often results in increased cost of the stamping dies.

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The springback compensation techniques reviewed by Wagoner (2002) comprise the major

tools which industry is using today. Further development is still ongoing and is directed toward

improving the accuracy and efficiency of springback prediction algorithms, and the work of

Chung et al (2011) is one example. Besides numerical prediction and correction, other methods

of addressing springback include using considerable blankholder pressure during forming, as

indicated by Liu et al. (2002), or to include a coining step at the end of forming, as discussed by

Mori et al. (2007). For these methods to be successful in practical applications, the overall

formability of the material would in many cases need to be increased over its usual limits in

order to meet the demands of the target geometry and the advanced process.

However, there are still several sources of variability which can lead to undesirable variation in

the springback performance of a forming process, such as variability in the mechanical

properties of the sheet from one coil to another, variation in the friction conditions in the tool due

to changes in temperature or changes in lubricant coverage, slight changes in the die face

geometry due to wear over time, and variation in the initial positioning of the blank before

forming. These issues can be eliminated by addressing the root cause of the springback

phenomenon – the presence of residual stresses in the stamped blank. These stresses can be

eliminated if an additional manufacturing operation is introduced: electrohydraulic calibration of

the stamped part.

It should be noted that the calibration process in sheet metal forming is hereby being defined

much more broadly than merely the elimination of springback distortions. In a number of

publications reviewed by Psyk et al. (2011), the calibration process is understood as a restrike

operation where sharper corners and local features are filled with relatively small displacements

of the already formed blank. In reality, further filling of sharp corners would most likely reduce

the overall springback by applying additional stretching to the sheet and as a result make the

stress distribution through the thickness more uniform, reducing the springback that results from

bending moments in the sheet.

2. Review of methods of springback calibration

The efforts to eliminate residual stresses and the distortions associated with them in welded

structures have a long history of development. One of the earliest methods broadly used in low

volume production is elimination of residual stresses by a stress relieving heat treatment, as

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described by Van Horn (1967). The fundamental mechanism of thermal stress relieving

involves placing the metal in a plastic state temporarily. In this state, the initial differential strains

that created the high residual stresses in the elastic condition can be relaxed to much lower

stress levels by yielding. The plastic condition is usually attained by heating to a temperature

high enough to greatly reduce the yield and creep strengths. This allows residual stresses to

relax. This method is used for sizing of parts in low volume production, for example in the

aerospace industry or the gas turbine industry. The part is usually clamped in a contour-

restraining fixture and heated to a target temperature at which stress relief is expected to

happen and then kept at this temperature for a number of hours, allowing creep to transform

elastic strains into plastic strains. This well-known industrial method is rather slow, however,

and requires a protective atmosphere in the furnace while stress relieving steel blanks. Also,

this method would not be acceptable for most heat treatable materials, for example materials

that exhibit precipitation hardening.

In contrast to thermal calibration methods, pulsed calibration methods are: (1) intended to

achieve a much faster cycle time than thermal stress relieving, (2) are applicable to all kinds of

metallic alloys since heating of the blank is not required, and (3) are based on dynamic loading

of the calibrated blank by a high-intensity pressure pulse supplied by either electromagnetic or

electrohydraulic forming processes. Two different concepts of pulsed calibration can be found in

the literature. In the first concept, the calibration effect is accomplished by high velocity impact

and mutual deformation of the calibrated part with the die surface. This concept is well known in

the literature and is often associated with pulsed forming processes as one of their essential

advantages. However, elimination of springback is not automatically accomplished by

employing one of the pulsed forming processes. Usually it requires a certain impact velocity

between the blank and the die to lower springback substantially. Therefore, even if a high

velocity forming technique was used to form a part, if the die cavity is simply filled by the part

but with minimal or no impact velocity then this type of process would not be sufficient for

eliminating springback as an advantage of the forming process itself. An additional pulse of

energy within for forming tool or an additional process step with more energy in a secondary tool

would be required.

An example of this effect was reported by Baron and Henn (1964), who used explosive forming

to form plates into spherical dies and found that an increase of the deployed explosive charge

leads to a decrease in springback. Yamada et al. (1981) employed a high-speed plastic

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projectile in water, which transmitted a shock wave onto a sheet metal blank to form it into a

hemispherical shape. Yamada et al. (1981) also found an optimal collision speed at which the

springback is very close to zero. Impact speeds below the optimum resulted in a part radius that

was larger than the die radius, while higher collision speeds generated a part radius that was

smaller than the die radius. Golovashchenko (1999) discussed calibration of tubular parts made

from high strength aluminum alloys and steel by applying internal pulsed pressure to the

cylindrical part while it was positioned inside a calibration die. A complex process of mutual

deformation was simulated, involving the propagation of stress waves, bounce-back of the part

from the die and multiple impacts during mutual oscillations between the part and the die.

Numerical results were compared with experimental data which confirmed that the dimensional

accuracy of parts can be improved if the velocity of impact is increased. Similar experimental

results were described by Minors and Zhang (2002) for forming of sheet metal parts by

explosive forming, where an improvement in the dimensional accuracy of the explosively formed

parts was attributed to the elastic deformation of the die and additional deformation of the

workpiece together with the die as a result of the high speed impact.

A similar mechanism of calibration was described by Iriondo et al. (2011) where the calibration

mechanism was attributed to the high contact pressure during the impact between the blank and

the die. The average blank velocity during the calibration process reported by Iriondo (2007)

was in the range of 35 to 50 m/s for AHSS. The contact stress that occurs when a steel blank is

calibrated into a steel die at such an impact velocity range can be estimated according to the

method highlighted by Iriondo (2011) to be in the range of 682 to 975 MPa. This estimation is

done under the assumption of two identical bars impacting each other, with one bar traveling at

the impact speed and the other bar being stationary. The solution can then be found by applying

the one-dimensional stress wave equation in each bar, as provided by Johnson (1972) in the

following formula:

[1]

where ! represents density and C represents longitudinal wave speed.

Unfortunately, no simulation was performed to analyze the stress evolution by Iriondo et al

(2011) during the described electromagnetic calibration process. Iriondo et al. (2013) studied

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the EM shape calibration and correction of springback (sidewall curl) of U-channels deep drawn

from DP600 and TRIP700 high strength steels. Woodward et al. (2011) conducted an

experimental study on electromagnetic calibration of a stamped component that exhibited

unwanted curvature in a critical area and direction in the part. The springback was reduced by

up to 87% using a disposable electromagnetic actuator.

At the current state of the art, no analysis explaining the mechanics of springback

reduction/elimination can be found in the literature. Such an analysis would probably require

development of a more complex model of the material than is commonly used for sheet metal

forming simulation. With an integrated model of the entire calibration process, the necessary

discharge energies could be predicted and the pulsed pressure requirements could be defined

for a given part geometry with a known distribution of residual stresses causing a defined level

of springback.

The second approach of pulsed calibration is based upon the concept of stress relief. However,

instead of using either a heat treatment or a high velocity impact, a pulsed load is applied to the

surface of the blank. In this case, no impact between the blank and the die is required.

Furthermore, this process takes place at room temperature. This concept is relatively new, and

therefore a very limited number of publications can be found on this concept in the literature.

The concept of clamping and stress relieving at room temperature using a pulsed

electromagnetic field was first described by Golovashchenko (2009d). Golovashchenko (2005)

introduced a very simple test in the form of flattening a previously bent strip. After initially

bending the strip over a cylindrical mandrel, an attempt was made to flatten the strip by

clamping it between two flat plates using a press with a clamping force of 1.5 MN. However, the

press clamping step did not remove all of the residual stresses, because after removal from the

press the strip still had some curvature to it. The strip was then clamped to a multi-turn

electromagnetic coil, with insulation between the coil and the strip, and a high voltage discharge

was sent through the coil. As a result, the vast majority of the springback was eliminated from

the strip. This effect was demonstrated for aluminum alloys and advanced high strength steels.

Traditionally, AHSS would not be considered good candidates for electromagnetic forming

because of their high mechanical strength. However, in the case of calibration the technology

worked well. The mechanism of this process was not fully clarified. It can be partially attributed

to the pulsed pressure generating compressive stresses in the direction perpendicular to the

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sheet metal surface. On the other hand, this effect may be related to the pulsed electric current

induced in the blank during the electromagnetic pulse.

The effect of pulsed electric current on the stresses inside a sheet metal blank subjected to a

tensile load was described by Golovashchenko et al. (2009c). A substantial drop in the flow

stress was observed when electric current was passed through a sheet metal sample during a

quasistatic tensile test. The reduction in stress was proportional to the amplitude of the DC

current. Even though the amplitude of the current in this experiment was at least order of

magnitude smaller than what is present in pulsed electromagnetic forming, the duration of the

DC current was much longer. Therefore, the results of the experiments involving tensile testing

and DC current can be considered as a qualitative confirmation of the pulsed current effect on

the internal stresses during pulsed calibration.

A similar process of electromagnetic calibration was illustrated by Golovashchenko et al. (2006)

for springback calibration of conventionally stamped U-channels. To return the stamped panel to

the target shape, the U-channel was clamped by two C-clamps on the straight sides of the

channel and positioned inside the single-turn flat concentrator. In this configuration, the only

portions of the U-channel that were exposed to the concentrator were the bend radii from the

horizontal to vertical surfaces. After the electric discharge, internal stresses created by the C-

clamps were relieved, and the shape of the U-channel was very close to the target shape. In

this case, no die was inserted inside the U channel; therefore, the calibration observed could be

attributed only to the effect of the induced current and the surface pressure on the blank.

The advantage of the stress relief mechanism of calibration as compared to the impact

calibration mechanism in our opinion is twofold. Firstly, the stress relief mechanism eliminates

any possible bounce-back of the blank away from the die surface. Secondly, the stress relief

mechanism also results in a very substantial reduction of dynamic loads on the die surface.

Even though the electromagnetic calibration process described thus far looks rather attractive,

the challenge of creating a coil design applicable to the complex shapes found in automotive

panels motivated the development of other pulsed calibration techniques. As stated previously,

a numerical model of the stress-relieving calibration process has not yet been development, and

the same is true for the impact-based calibration process. More comments on this subject are

provided in Section 5: Future Work.

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3. Electrohydraulic Processes

3.1 Electrohydraulic forming

Electrohydraulic forming is based upon the electro-hydraulic effect: a complex phenomenon

related to high voltage electrical discharge through a liquid. The first observations of strong

mechanical forces generated during electric discharge in a liquid were reported by Lane (1767)

and Priestly (1769). Additional historical perspectives as well as early laboratory experiments on

electrohydraulic forming (EHF) were described by Bruno (1968). Davies and Austin (1970)

discussed the initial low volume industrial applications of EHF. According to Chachin (1978),

during a high voltage discharge of capacitors through a pair of electrodes submerged in a liquid-

filled chamber, a high pressure, high temperature plasma channel is created between the tips of

the electrodes. The shockwave in the liquid, initiated by the expansion of the plasma channel, is

propagated toward the blank at high speed, and the mass and momentum of the water in the

shock wave forms the sheet metal blank into the die. At the beginning of the discharge process,

the electrical resistance of the plasma channel between the electrodes drops by several orders

of magnitude, and the electric current grows sharply, quickly depositing electrical energy into the

discharge channel. Such intensive energy deposition results in rapid growth in pressure and

increased temperature, leading to quick expansion of the plasma channel and generation of a

shock wave in the liquid. As shown schematically in Figure 1, the plasma channel forms

between the two electrodes with shock waves emanating outward. The energized electrode

must be insulated from the steel chamber by materials such as polyurethane, polyethylene or

other insulation materials with high insulation capability and good mechanical resiliency to

withstand intensive dynamic loading within the chamber. Depending on the electrical

characteristics of the pulsed current generator being used in EHF, as well as the design of the

tooling and the electrode system, sometimes a consumable bridge wire is used to connect the

two electrodes in order to initiate or to improve the stability and efficiency of the discharge.

When the inter-electrode gap is about 15 mm or less, then a bridge wire is usually not

necessary. With electrode gaps larger than 15 mm, a bridge wire is usually used to improve the

efficiency of the discharge or simply to ensure that a discharge is able to occur. Even with

smaller electrode gaps of around 10 mm, sometimes a bridge wire is still used for improvements

in electrical efficiency and energy efficiency. The trade-off which must be considered with such

a strategy is that the wire must be added between the electrodes with each new discharge,

which would lead to higher costs and likely a slower process cycle time.

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Chamber

Die

Electrodes

Blank

Water Chamber

Die

Electrodes

Blank

Water

Figure 1. Cross-sectional diagram of tooling used for EHF, depicting schematically the moment

of high-voltage discharge.

Further analysis of EHF capabilities indicated that it offers substantially better manufacturing

flexibility compared to EMF and Explosive forming (EF). Sandford (1970) described a hybrid

technology where static hydroforming was used to bulge sheet metal into the die cavity,

followed by a pulse of EHF which provided a higher pressure level and filled the details of the

die cavity. In addition to the hybrid hydroforming-EHF process, several EHF discharges can be

employed sequentially to form the blank into the die cavity and calibrate springback without

opening the EHF chamber. This is possible because of the presence of water as a pressure-

transmitting medium filling the volume between the electrodes and the blank. In EMF, the

efficiency of the process diminishes proportionally to the clearance between the coil and the

blank. Since it is not possible to form a part with complex geometry using only one pulse, EMF

would require several coils and additional clamping presses to form such a shape. In EF, the

use of sequential explosions is possible only if each individual batch of fuel material is

introduced into the explosive chamber after the previous explosion has already occurred.

During the last several years, EHF was taken into consideration as a potential technology for

automotive applications. Substantial effort was directed toward developing key enablers which

would bring EHF closer to potential high volume applications. These developments include a

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durable electrode system, a durable sealing system, an efficient water-air management system,

and a numerical modeling technique, as reported by Golovashchenko et al. (2011). Another

important capability which is currently under development is a process design methodology

which would enable the proper selection of parts and lightweight materials for future EHF

applications. A number of recent studies indicated improved formability in EHF conditions for

both aluminum and high strength steels. Balanethiram and Daehn (1994) demonstrated a

substantial increase of maximum strains while forming 6061-T4 aluminum sheet into a conical

die. Rohatgi et al. (2011) developed an experimental methodology to study the strain rate

history of sheet metal forming in EHF conditions and applied this technique to experiments with

5182 aluminum sheet. Rohatgi et al. (2012) compared the strain rate history of die forming and

free forming for AA5182 and DP600 steel, indicating substantially higher strain rates in die

forming conditions. Golovashchenko et al. (2013) quantified the formability improvement in EHF

for the advanced high strength steels DP500, DP600, DP780 and DP980. Gillard et al. (2013)

demonstrated that the benefits of improved formability in EHF conditions for dual phase steels

can be retained in a hybrid process where the blank is first pre-formed by quasistatic

hydroforming pressure and then fully formed using EHF.

In this paper we suggest a different vision of the electrohydraulic forming technology as a

separate tool to address the springback of sheet metal parts. When working with complex part

geometries, a separate springback calibration process may help to avoid costly die face recuts.

Furthermore, having a separate EH calibration step would enable production facilities to work

with different material suppliers without any concerns that the manufacturing variability may

result in an excessive number of rejected parts. The objective of this paper is to demonstrate

the electrohydraulic stress relieving calibration process, first on simple geometry coupons, and

then to illustrate how this process can be used to calibrate springback in an automotive

stamping formed from dual phase steel with complex geometry.

3.2 Concept of stress relieving electrohydraulic calibration

The concept of stress relieving through EH calibration was recently introduced by

Golovashchenko (2010). It follows the same general concept discussed earlier for both stress

relieving through heat treatment and stress relieving through electromagnetic springback

calibration. The blank needs to be deformed into a target shape, and then clamped by an

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auxiliary tool which holds the blank in the appropriate shape, thus creating the internal stresses

which are balanced by the external forces applied through the clamping tool. The internal

stresses created by the clamping process correspond to the same elastic stresses which were

present in the part at the end of the forming process. The clamped blank is then subjected to the

stress relieving process in the form of a rapid pulse of intense pressure generated through the

electrohydraulic effect.

As discussed in the previous sections and also in the previously mentioned literature on

calibration methods, calibration can be accomplished by impact-based methods and also by

stress relief through the application of pulsed pressure, and both methods are feasible. The

overall similarity between them is that both processes can be viewed as applying a normal,

through-thickness stress which eliminates in-plane stresses. In impact-based calibration

methods, the duration over which the normal stress is applied is determined by the amount of

time required for the stress wave to propagate through the thickness of the blank. For a 1 mm

thick steel blank, this duration would be 0.2 ! s. Assuming that the impact velocity during a

calibration process was 50 m/s, as was used by Iriondo (2007), and assuming that both the

calibrated sheet material as well as the die material is steel, then the contact stress can be

estimated to be 975 MPa. This level of stress would require a high quality tool steel to be

employed in the calibration die in order to have the proper tool life for production conditions.

Contact stresses for the stress relieving mechanism were estimated based upon numerical

simulation of an electrohydraulic discharge in the flattening test, assuming that the

electrohydraulic chamber represents a closed volume and that the blank is rigid. A detailed

description of this numerical model is provided in section 4.3 of this paper. According to this

estimation, the normal stress is on the order of 20 to 50 MPa, but applied over a duration of

approximately 100 ! s. In this paper, attention will be focused on the stress relieving method EH

calibration through application of pulsed pressure, which in our opinion is more advantageous

from the perspective of die durability. It also eliminates the issue of bounce-back of the blank

from the die as a result of impact, which obviously has the potential to negatively affect the

dimensional accuracy of parts calibrated with such a method.

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4. Experimental demonstrations of electrohydraulic calibration

4.1 Qualitative demonstration of the stress relieving EH calibration process

An initial demonstration of the EH stress relieving effect was done in a closed chamber in an

attempt to isolate the effect of stress relieving from the effects of impact-based calibration

methods. To accomplish this, a strip of 6111-T4 aluminum, 20 mm wide and 0.9 mm thick, was

bent around a cylindrical mandrel with a diameter of 25.4 mm to the point where the strip had a

u-shape. The ends of the strip were then clamped with a c-clamp, as shown in Figure 2a. The

bent strip and the c-clamp were then submerged in water within an EH chamber, with the bent

strip and clamp attached as one solid assembly in the clamped configuration. The electrodes

were positioned above the clamp assembly at a distance of 50 mm. A 15 kJ discharge was used

to generate the EH pressure pulse which applied the normal stress to the clamped strip. The

strip and clamp assembly was then removed from the chamber, and the strip was released from

the clamp. A comparison of the samples before and after the EH stress relieving process is

shown in Figure 2b. Since no impact occurred in this experiment, the effect of substantially

reducing springback can be attributed to the pressure-induced stress relieving mechanism. This

early, simple experiment was targeting only a qualitative demonstration of the effect of pressure-

induced stress relief.

(a) (b)

Figure 2. (a) A 6111-T4 aluminum strip bent into a U channel with its ends clamped by a C-

clamp prior to EH calibration; (b) strips of 6111-T4 aluminum before and after EH calibration.

Before EH Calibration

After EH Calibration

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The next step was to demonstrate the process on larger, straighter U-channels, which is a

geometry more representative of automotive stampings. The straight U-channel samples were

formed in a traditional channel forming tool, which consisted of a punch and a flat binder with a

rectangular opening for drawing the blank. The straight channels were formed from the same

6111-T4 aluminum sheet employed in the previous experiment. After completing the drawing

operation, and after removing the channels from the tool, not surprisingly the samples had

springback. To demonstrate the stress relieving effect, the samples were then clamped in the

tool shown schematically in Figure 3. The actual tooling is shown in Figure 4. It illustrates one

possible embodiment for clamping the blank and exposing most of its surface to the pressure

pulse generated inside the EH chamber. Only the ends of the blank were clamped between the

two surfaces of the steel tool, allowing the rest of the blank to have one surface in contact with

the water inside the chamber, while its other surface was in contact with the steel punch and the

upper portion of the chamber. A comparison of the shapes of the drawn U-channel samples

before and after EH calibration is shown in Figure 5.

Figure 3. Schematic of the EH calibration tool employed for the straight channel calibration

experiments: (1) electrodes connected to the pulse generator; (2) water-filled chamber; (3) steel

punch to which the aluminum channel is clamped (workpiece not shown).

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2

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(a) (b)

Figure 4. (a) the steel punch mounted in the upper die of the EH calibration tool, and (b) the EH

chamber, the lower half of the tool, in the open position revealing the electrodes.

(a) (b)

Figure 5. Illustration of the amount springback present in 6111-T4 aluminum U-channel

samples: (a) formed channel before EH calibration, and (b) after EH calibration.

4.2 Measurement of springback after the EH flattening test

The EH flattening test described in this paper is similar to the EM flattening test described by

Golovashchenko (2005). The authors employed the EH flattening test because it is a simple and

straightforward test which can be used to estimate the calibration energy for a wide range of

bending radii and material gauges as well as various blank materials. This test does not require

fabrication of any special tooling: the sheet metal can be bent to a variety of radii using a very

inexpensive bending brake. Using other sample configurations would lead to the development of

Upper half of EH calibration tool Lower half of EH calibration tool

Electrodes Fluid cavitySteel die against which workpiece is clamped

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an individual dedicated tool for each sample geometry and each thickness of the material. If one

wanted to vary the thickness of the sheet metal blank, one half of the tool would need to be

fabricated for each thickness value in order to efficiently clamp the blank being calibrated.

Historically, the authors experienced this problem a number of years ago while first discovering

the electromagnetic calibration process by comparing the stress relieving concept and the

impact concept. With electromagnetic calibration, each radius of the U-channel would require a

new coil and a new calibrating die. Even changing the thickness of the blank from 1 mm to 1.5

mm or 2 mm would require a new coil and a new clamping portion of the tool. The flattening test

is free of these problems and requires minimal expenses to do a comparative analysis of

calibration for different radii of bending.

In order to highlight the effectiveness and the capabilities of the EH calibration process, the

initial flat samples were made of the dual phase steel DP980, which represents the highest

strength dual phase steel being used in industry today. The initial strips were fabricated from 1

mm and 1.4 mm thick DP980 sheet, and were 304.8 mm (12 inches) long and 50.8 mm (2

inches) wide. The experiment was conducted in three steps. Firstly, the sample was bent on a

sheet metal brake where the sheet was clamped against tool with a radius of either 25.4mm (1”)

or 12.7 mm (1/2”), and then bent to 90 degrees, as shown in Figure 6.

Figure 6. Bending of a flat strip on a sheet metal brake where the sample is clamped against a

tool with a 1” or ½” radius, bent to 90°, then released from the tool and allowed to springback.

Flat Blank

1” radius, 90°bending tool

½” radius, 90°bending tool

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Secondly, the strip was compressed between two flat steel plates using a 1 MN hydraulic press.

The difference between manual flattening with flat plate and flattening on a press was rather

small. Nevertheless, press flattening was selected to ensure repeatability of the process. As

expected, the press flattening operation did remove some of the springback but not all, and the

effect of the press flattening step is shown in Figure 7, along with the a flat strip that was

calibrated by the EH calibration process (for comparison). Thirdly, the strip was then placed on

the EH chamber shown in Figure 8 with the convex surface facing downward, toward the water-

filled cavity in the chamber. The strip was then clamped flat between the EH chamber and a flat

steel plate which in this case was acting as the calibration die. Also, as seen in Figure 8, an

aluminum bridge wire was installed across the two electrodes before each pulse, in order to

extend the length of the discharge channel beyond the capabilities of the electric breakdown

length in the water. The length of the wire was 100 mm, enabling more uniform pressure

distribution along the surface of the blank compared to a typical breakdown distance of 10 mm.

The entire experimental setup is shown in Figure 9, including the upper flat plate, the lower EHF

chamber, the sample placed in the tooling, and the busbars which connect the tooling to the

pulsed current generator. The chamber was connected to a pulse generator with a capacitance

of 200 ! F, a maximum stored energy of 22.5 kJ and an internal inductance of 230 nH (according

to the pulse generator specifications). A discharge at 6.3 kV and 4 kJ was found to be the most

effective for removing springback from the DP980 sheets of both 1.0 mm and 1.4 mm thickness.

After the EH calibration pulse was applied, the springback was eliminated, and the strip was flat.

An additional comparison of an EH calibrated strip to a non-calibrated strip is shown in Figure

10.

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Figure 7. Comparison of samples of DP980, 1 mm thick, after the following operations: (1) after

bending over a 1” radius in a brake, (2) after flattening in a 1 MN press, and (3) after one pulse

at 6.3 kV and 4 kJ in the EH calibration process.

Figure 8. EH calibration chamber with electrodes connected by an aluminum bridge wire.

49°

18°

#1

#2

#3

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Figure 9. The experimental setup used for the EH flattening test.

Figure 10. Comparison of a strip of DP980, 1 mm thick, bent over a 1” radius and then flattened

by a 1 MN clamping press, to a strip then calibrated by one EH pulse at 6.3 kV and 4 kJ.

Before EH Calibration

After EH Calibration

Upper flat plate

Workpiece

EH chamber

Busbars

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Quantitative experimental results are presented in Figures 11 through 13, where the springback

angle was measured for DP980 strips of both 1 mm and 1.4 mm thickness as a function of

discharge energy and bending radius. Based on the experimental results, the following

observations can be made. Lower thicknesses and larger bending radii result in a higher

springback angle for a given blank geometry, after the bending and flattening steps described

above. This effect can be seen by comparing the data points at the 0 kJ energy level in Figures

11 and 12, or in other words, the data points corresponding to initial bending and press

flattening but without any EH calibration. For the data points corresponding to EH calibration,

the general trend is that the springback is getting lower with the increase of the discharge

energy. It was observed with all combinations of sheet thickness and bending radius that most

of the springback was eliminated using a relatively low discharge energy of 4 kJ. For all

combinations of bending radii and sheet thickness studied in this experimental work, a 7.8 kJ

discharge resulted in a slight amount of “springforward,” which can be thought of as the

introduction of new residual stresses into the surface layer of the sheet, in a manner similar to

shot peening. However, the magnitude of this distortion was rather minimal compared to the

initial springback value. This effect can be minimized by limiting the amount of the discharge

energy. Also, all of the trend lines in Figures 11 and 12 are polynomial approximations of the

trend in the data points. For the 1 mm DP980 data points in Figure 11, the trend line is a 2nd

order polynomial, whereas all of the other trend lines are a 3rd order polynomial. Furthermore, all

of the data points in Figures 11 and 12 represent the average value of the springback angle

resulting from three samples calibrated at each energy level. Figure 13 shows the combined

results of all the springback measurements for all of the samples calibrated in this study, and

the error bars for each data set represent plus/minus one standard of deviation for the

springback angles at each condition.

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Figure 11. Experimental results of EH calibration of DP980 strips, in terms of springback angle as a function of discharge energy, using an initial bending radius of 1”.

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Figure 12. Experimental results of EH calibration of DP980 strips, in terms of springback angle as a function of discharge energy, using an initial bending radius of 0.5”.

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Figure 13. Combined experimental results of EH calibration of DP980 strips, in terms of springback angle as a function of discharge energy, for all thicknesses and all energies.

4.3 Validation of stress relieving EH calibration technology for an automotive structural panel

Further validation of the EH stress relieving technology required demonstrating the process on a

real automotive panel with complex springback modes. After reviewing a number of possible

applications, a current production panel serving as a part of front rail structure was selected.

The decision was made based upon the knowledge of the prior history of this particular panel,

which required several tooling recuts to achieve the required dimensional accuracy in the

formed panels. Since this study represented one of the tasks in a larger project funded by US

Department of Energy, the decision was made to fabricate a dedicated draw die to form the

selected panel at 50% scale, and then to conduct EH trimming of the drawn panels followed by

EH calibration of the trimmed panels. The selected panel was formed out of 1 mm thick DP590,

a dual phase steel. The EH trimming study will be the subject of a separate publication.

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The chamber which was used in the EH calibration process was designed based upon the

methodology of numerical simulation described by Golovashchenko et al. (2013). Since the

blank is clamped to the die surface in EH stress relieving calibration, the displacements of the

blank and the elasticity of the die surface were neglected in our simulation of the EH calibration

process. Therefore, the EH discharge was simulated as occurring in a closed volume with no

displacement of any fluid or sheet metal. Based on the assumption that no major distortion of

the mesh occurs in a closed volume, a Lagrangian formulation of the problem was considered

more appropriate. In order to create a numerical model of the EH calibration process, the

following models were developed and later on coupled: (1) an electrical model of the discharge

channel; (2) a model of the plasma channel; and (3) a model of the liquid as a pressure

transmitting medium. Models 2 and 3 were developed using the capabilities of the LS-DYNA

commercial code. Model 1 was developed based on basic electrical circuit analysis as well as

experimental measurements of current waveforms. More details about the construction of the

numerical model are provided in the following paragraphs, and these details are very similar to

the description provided in Golovashchenko et al. (2013). The key difference in this modeling

effort was the design of the EH chamber being modeled, which consisted of multiple sub-

chambers as part of one overall chamber. The objective of the modeling effort was to optimize

the geometry of the sub-chambers so as to maximize the pressure pulse that reaches the

surface of the sheet metal panel. In order to minimize the time necessary for model construction

and computation, the initial discharge was simulated as a small diameter sphere positioned

between two electrodes.

Electrical model of the discharge channel

The parameters which govern the current i(t) in the circuit in Figure 14 include the variable

resistance of the discharge channel Rv, the cumulative resistance of the pulsed forming

machine and the connecting cables R0, and the inductance of the discharge circuit L.

Figure 14. Schematic of the electrical circuit used in EHF (C – capacitance of the pulse

generator, L – total inductance of the system, R0 – resistance of the circuit external to the

discharge channel, Rv – variable resistance of the discharge channel).

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The differential equation for current i(t) in the circuit in Figure 14 can be written in the following

form:

! !0

1, 02

2

!!!!

! iLCdt

di

L

RtiR

dt

id v

[2]

The following initial conditions were employed:

L

U

dt

dii

t

0

0

,0)0( !!!! [3]

where U0 is initial voltage of the capacitor battery.

The electric power being pumped through the discharge channel can be defined by the following

equation:

),( tiRiN v2! [4]

Integrating equation 4 by time produces a function for the energy deposition in the discharge

channel Ech(t) during the discharge process:

dttiRtiE v

t

ch ),()(0

2!![5]

Plasma channel

The plasma channel is modelled in LS DYNA as an adiabatically expanding volume of gas. The

electric energy is assumed to be introduced uniformly through the channel volume based upon

equation 5. The pressure in each finite element of the plasma channel can be calculated as:

pch = (! - 1)(! /! 0)E [6]

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where

pch – pressure at a given point of the discharge channel

! - current mass density at a given point

! 0 – initial mass density at a given point

E – portion of the energy produced inside the channel inside a given finite element

! - adiabatic coefficient for plasma produced from tap water inside the channel;

Model of the liquid

The liquid was modelled within LS DYNA as an ideal compressible liquid with the specific

cavitation threshold. The list of necessary parameters includes the initial mass density,

compression modulus and negative pressure threshold corresponding to the beginning of

cavitation, which in this case was modelled as -0.1 MPa. Heat transfer between the plasma

channel and the liquid was not taken into account in this version of the model.

Results of the numerical simulation

Since the selected part represented a channel of variable cross-section where springback

occurs in every cross-section, it was considered necessary to apply stress relieving pressure

over the entire surface of the trimmed panel. Since there is no analytical model available which

would predict the stress relieving effect based on applied pressure parameters, the design of

the chamber was developed through relying on the concept that the distribution of stress-

relieving pressure can be adjusted during the experimental tryout if the chamber has multiple

electrodes which can apply pressure to different areas of the blank independently. The concept

of multichannel EH chamber design was described by Golovashchenko et al. (2009a), whereas

details about the multi-electrode approach within a single chamber can be found in another work

by Golovashchenko et al. (2009b). Initially, the multi-electrode approach in a single fluid cavity

was given a preference in order to have a smooth distribution of pulsed pressure across the

whole surface of the blank. The design of the chamber corresponding to this single-cavity

concept is shown in Figure 15a.

A number of other chamber designs were developed based upon the concept of subdividing the

single fluid cavity into several sub-chambers separated by internal walls. Based on prior

experience with electrohydraulic processes this approach was pursued, because it was

expected to produce a higher pressure amplitude on the blank surface as a result of the

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concentrating effect of the dividing walls. After multiple iterations of design and simulation, the

design of the chamber shown in Figure 15b was selected. The new design had three sub-

chambers, an overall reduction in height, and a more smooth shape in comparison with the

single-cavity configuration of the initial design.

(a) (b)

Figure 15. Geometry of the chamber for the single-cavity chamber concept (a) and for the multiple sub-chamber concept (b).

A comparison of the two configurations was made based upon the magnitude of the pressure

pulse reaching the blank surface. Four points of observation, A, B, C, and D, were chosen on

the surface of the blank as shown in Figure 16, and pressure values were compared for both

chamber designs throughout the whole calibration process. The simulations for both

configurations were conducted at the same level of discharge energy. The results of the

simulation, in terms of the pressure history at points A, B, C, and D, are shown in Figure 17 for

the single-cavity chamber design (see Figure 15a for geometry), and are shown in Figure 18 for

the multi-cavity chamber design (see Figure 15b for geometry).

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Figure 16. Points of observation on the surface of the blank.

Figure 17. Pressure history after the discharge in the single-cavity EH calibration chamber.

A B C D

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Figure 18. Pressure history during the EH discharge in the multi chamber design.

A comparison of the two graphs clearly shows the difference in pressure. With the same total

energy, the multi-chamber design produces much higher pressure peaks, which leads to the

conclusion that less energy would be required in this chamber in order to produce the same

calibration effect. Another added benefit of the sub-chamber concept in the multi chamber

design is the presence of multiple pressure peaks, which occur due to reflection of the pressure

waves off of the sub-chamber walls. Multiple pressure peaks also may reduce the number of

discharges needed for calibration, and therefore have the potential to reduce the overall cycle

time of the calibration process. The history of the pressure distribution on the surface of the

blank within the first sub-chamber is shown in Figure 19. It can be observed that the pressure

initially builds up in the area close to the electrode and then propagates toward the edges of the

sub-chamber. The location of the electrode in each sub-chamber was determined based upon

the goal of providing a more uniform maximum pressure through the whole area of the blank

within each sub-chamber. In a very small volume chamber, multiple reflections from the

chamber walls play a very critical role, and higher levels of pressure can be accomplished within

a smaller volume chamber. Also, bringing the electrodes closer to the surface of the blank

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usually increases the pulsed pressure amplitude in the shock wave coming directly from the

discharge channel, prior to reflecting from the walls of the chamber. However, reducing the

volume of each individual sub-chamber leads to the necessity of having more discharges and

dedicating more modules of capacitors in order to serve each individual pair of electrodes with a

single block of capacitors managed individually by a dedicated switch. Another limitation which

needs to be taken into account is that the chamber should be able to accommodate an

electrode with the appropriate insulation, preventing a short circuit discharge within the wall of

the chamber. More details about the design of the electrodes can be found in a recently

published study by Bonnen et al. (2013). Also, increasing the number of sub-chambers would

shade a larger area of the blank due to the presence of the walls separating individual sub-

chambers. Based on these considerations, the three-chamber design shown in Figure 20 was

chosen to be fabricated for further experimental study.

t = 0 µs t = 55 µs

t = 80 µs t = 105 µs

t = 135 µs t = 160 µs

t = 185 µs t = 210 µs

Figure.19. Propagation of pressure inside the first sub-chamber during the EH calibration

process.

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Figure 20. Design of the chamber which was selected for fabrication.

Figure 21 shows photographs of the finished EH calibration tool in a 1.5 MN hydraulic press

during the initial tryout process. Figure 21a provides an overall view of the lower tool, showing

the three sub-chambers and the electrodes. Figure 21b provides a close-up view of the two sub-

chambers near the back end of the part, showing the position of the energized electrodes with

polyurethane insulation and the ground (non-energized) electrodes. The polarity of the

energized electrodes can be either positive or negative, and this process parameter is dictated

by the internal design of the pulsed current generator. However, no matter whether the

energized electrode is charged positive or negative, it is necessary that the energized electrode

be disconnected from the ground by an insulation block of sufficient thickness and mechanical

strength. The force applied to the energized electrode is directed along the axis of the electrode

and away from the chamber, driven by the internal pulsed pressure during the discharge. The

energized electrodes are mounted on steel brackets connected by bolts to a spacer block made

out of high voltage insulation material. Figure 21c provides an overall view of the upper tool,

which consists of a female die surface cut to the desired part geometry.

Energized electrode

Non-energized electrode

Electrode #1

Electrode #2

Electrode #3

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(a)

(b)

Energized electrode



Energized electrode

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(c)

Figure 21. (a) The lower half of the EH calibration tool, showing three sub-chambers and three

electrodes; (b) close-up view of the two sub-chambers near the back end of the EH calibration

tool, showing the position of the energized electrodes and the ground electrodes; (c) overall

view of the upper half of the EH calibration tool, which consists of a female die surface cut to the

desired part geometry.

After a series of preliminary experiments, an appropriate sequence of pulses and pulse energies

was defined which was able to remove virtually all of the springback from the experimental

panels. The sequence of pulses consisted of one pulse in each sub-chamber, with each pulse

done at 13 kV. This voltage level corresponds to an energy of 27 kJ when using a capacitor

bank of 320 ! F capacitance. The sequence of calibration discharges was done in numerical

order from electrode 1 to electrode 3, as shown in Figure 20. Figure 22 shows a summary of the

results of the calibration process in terms of removal of springback from the stamped panels.

Figure 22a shows the panel resting on the lower tool before the calibration process was applied.

The lower left flange can be seen deviating from the desired part geometry by a full 25 mm, due

to various modes of springback throughout the panel, such as bending modes and twisting

modes. Figure 22b shows the panel again resting on the lower tool, but after the calibration

process has been applied, and the panel is now virtually in complete contact with the lower tool.

In Figure 22b, the deviation of the part from the desired geometry of the tool is less than 1 mm

in all locations, which is an acceptable level of dimensional accuracy for interior automotive

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panels. Figures 22c and 22d show the same EH calibration results as Figure 22a and 22b, but

from a different viewing angle.

(a)

(b)

(c)

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(d)

Figure 22. The stamped panel before (a) and after (b) the EH calibration process was applied;

(c) and (d) also show the stamped panel before and after the EH calibration process,

respectively, but from a different viewing angle.

Even though the presented study does not provide a complete mathematical model of the suggested calibration process, the following trends still can be derived from the knowledge gained during the experimental work.

! ! In general the amount of geometrical deviation from the targeted shape decreases as the discharge energy is increased. However, some “over-calibration” is possible when the discharge energy is too high. A very simple flattening test was demonstrated and this test may serve as a preliminary rough estimate of the pulsed pressure necessary for calibration. Even though the authors have a simulation technique which can predict the pressure in the EHF chamber, the distribution of residual stresses in the workpiece can be highly variable from one area of the blank to another. Furthermore, an even wider range of residual stress values can be possible when one considers the introduction of new part geometries, new materials and other thicknesses into the process.

! ! A more intense pressure pulse can be obtained from smaller volume chambers and also when the discharge channel is located closer to the surface of the sheet metal blank being calibrated. These considerations are supported by early analytical studies of shock wave propagation from local explosive charges described by Cole (1948) for cylindrical and spherical symmetry. For a cylindrical model, the pressure amplitude decays proportionally to the value (a0/R)0.6, while for a spherical case the pressure amplitude

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decays proportionally to (a0/R)1.15, where a0 is the initial radius of the explosive channel.This analysis supports the argument that an EHF chamber with a discharge initiated by a long bridge wire is more energy efficient than an EHF chamber with a discharge initiated over a much shorter length through a breakdown mechanism.

! ! In a small volume chamber, multiple reflections of the shock wave from the walls of the chamber take place. It was observed that for a channel type of chamber geometry, the pressure wave propagates through the channel like a roller and applies approximately the same level of pressure at all points on the surface of the blank. The results of a numerical simulation of pressure distribution in a channel chamber were recentlyreported by Golovashchenko et al. (2013). Therefore, the surface of the blank should be subdivided into zones such that an approximately uniform calibration pressure within each individual zone would be sufficient to relieve the residual stresses in that area of the part.

! ! In a very small volume chamber multiple reflections from the chamber walls play a very critical role in the calibration process, and higher levels of pressure can be achieved in such a configuration. However, reducing the volume of each individual sub-chamber leads to the necessity of having more discharges and dedicating more modules of capacitors in order to serve each individual pair of electrodes with a single block of capacitors managed individually by a dedicated switch. Another limitation which needs to be taken into account during tool design is that the chamber should be able to accommodate an electrode with the appropriate insulation in order to prevent a short-circuit discharge within the wall of the chamber.

5. Future work

At the current stage of development of the EH stress relieving calibration process, the chamber

was designed based on the assumption that it is necessary to apply the pulsed pressure over

the entire surface of the part, since springback is expected to happen at virtually every cross-

section of a channel-type structural panel. Future development should be directed toward

numerical simulation of the stress relieving process. Ideally, this model should correlate the

applied pressure pulse with the amount of stress relief that will occur at each given element of

the part. However, in order to develop such a model, a more complex material model should be

introduced which would be able to predict the conversion of elastic strains into plastic strains

under pulsed loading conditions, possibly by adding a viscoplasticity term. Such a prediction

would require a detailed material study which would define the parameters of this model in order

to make it practical. The development of this model as well as its experimental validation should

be the subject of future research.

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6. Conclusions

1. The developed concept of electrohydraulic stress relieving calibration is based upon

clamping a stamped panel to the calibration die surface with the target shape and then

applying pulses of pressure to eliminate internal stresses in the stamped panel. When a

stamped blank is removed from a forming die, allowed to springback, and then clamped

to a calibration die, the internal elastic stresses within the panel in such a configuration

serve as a memory of the shape of the blank after springback, and it is these residual

stresses that EH calibration is intended to remove from the panel.

2. The developed concept of stress relieving calibration was initially validated by a simple

experiment consisting of submerging a bent strip of aluminum into the fluid within an EH

chamber, so that both the outer and inner surfaces of the strip (where the internal

stresses from bending are located) were exposed to the fluid and the pressure pulse.

This experiment served as an initial confirmation that impact with the tool is not

necessary to achieve the calibration effect.

3. The stress relieving EH calibration process applies substantially lower stresses to the

calibration die as compared to the impact calibration process described in earlier

publications, and this difference is expected to substantially extend the life of the

calibration die. Furthermore, the effect of sheet bounce-back from the die surface, which

is a common occurrence in impact calibration processes, is not present in the EH stress

relieving calibration process.

Acknowledgement

This material is based upon work supported by the Advanced Manufacturing Office of the United States Department of Energy under Award Number DE-FG36-08GO18128.

Disclaimer

This report is prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warrantee, express or implied any legal liability or responsibility for the

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accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use wouldn't infringe any privately owned rights. Reference herein to any specific commercial product, process or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement or recommendation or favouring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

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Captions for Figures

Figure 1. Cross-sectional diagram of tooling used for EHF, depicting schematically the moment of high-voltage discharge.

Figure 2. (a) A 6111-T4 aluminum strip bent into a U channel with its ends clamped by a C-clamp prior to EH calibration; (b) strips of 6111-T4 aluminum before and after EH calibration.

Figure 3. Schematic of the EH calibration tool employed for the straight channel calibration experiments: (1) electrodes connected to the pulse generator; (2) water-filled chamber; (3) steel punch to which the aluminum channel is clamped (workpiece not shown).

Figure 4. (a) the steel punch mounted in the upper die of the EH calibration tool, and (b) the EH chamber, the lower half of the tool, in the open position revealing the electrodes.

Figure 5. Illustration of the amount springback present in 6111-T4 aluminum U-channel samples: (a) formed channel before EH calibration, and (b) after EH calibration.

Figure 6. Bending of a flat strip on a sheet metal brake where the sample is clamped against a tool with a 1” or ½” radius, bent to 90°, then released from the tool and allowed to springback.

Figure 7. Comparison of samples of DP980, 1 mm thick, after the following operations: (1) after bending over a 1” radius in a brake, (2) after flattening in a 1 MN press, and (3) after one pulse at 6.3 kV and 4 kJ in the EH calibration process.

Figure 8. EH calibration chamber with electrodes connected by an aluminum bridge wire.

Figure 9. The experimental setup used for the EH flattening test.

Figure 10. Comparison of a strip of DP980, 1 mm thick, bent over a 1” radius and then flattened by a 1 MN clamping press, to a strip then calibrated by one EH pulse at 6.3 kV and 4 kJ.

Figure 11. Experimental results of EH calibration of DP980 strips, in terms of springback angle as a function of discharge energy, using an initial bending radius of 1”.

Figure 12. Experimental results of EH calibration of DP980 strips, in terms of springback angle as a function of discharge energy, using an initial bending radius of 0.5”.

Figure 13. Combined experimental results of EH calibration of DP980 strips, in terms of springback angle as a function of discharge energy, for all thicknesses and all energies.

Figure 14. Schematic of the electrical circuit used in EHF (C – capacitance of the pulse generator, L – total inductance of the system, R0 – resistance of the circuit external to the discharge channel, Rv – variable resistance of the discharge channel).

Figure 15. Geometry of the chamber for the single-cavity chamber concept (a) and for the multiple sub-chamber concept (b).Figure 16. Points of observation on the surface of the blank.

Figure 17. Pressure history after the discharge in the single-cavity EH calibration chamber.

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Figure 18. Pressure history during the EH discharge in the multi chamber design.

Figure.19. Propagation of pressure inside the first sub-chamber during the EH calibration process.

Figure 20. Design of the chamber which was selected for fabrication.

Figure 21. (a) The lower half of the EH calibration tool, showing three sub-chambers and three electrodes; (b) close-up view of the two sub-chambers near the back end of the EH calibration tool, showing the position of the energized electrodes and the ground electrodes; (c) overall view of the upper half of the EH calibration tool, which consists of a female die surface cut to the desired part geometry.

Figure 22. The stamped panel before (a) and after (b) the EH calibration process was applied; (c) and (d) also show the stamped panel before and after the EH calibration process, respectively, but from a different viewing angle.

pulsed electrohydraulic springback calibration of parts stamped from advanced high strength steel

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