Journal of Materials Processing Technology 212 (2012) 1070–1079
Contents lists available at SciVerse ScienceDirect
Journal of Materials Processing Technology
journal homepage: www.elsevier.com/locate/jmatprotec
Electro-hydraulic forming of sheet metals: Free-forming vs. conical-die forming
Aashish Rohatgi a,∗ , Elizabeth V. Stephens a , Richard W. Davies a , Mark T. Smith a , Ayoub Soulami a ,
Said Ahzi b
a
b
Pacific Northwest National Laboratory (PNNL), 902 Battelle Boulevard, P.O. Box 999, Richland, WA 99352, USA
University of Strasbourg, Institut de Mecanique des Fluides et des Solides, 2 rue Boussingault, 67000 Strasbourg, France
a r t i c l e
i n f o
Article history:
Received 22 September 2011
Received in revised form
24 December 2011
Accepted 24 December 2011
Available online 3 January 2012
Keywords:
Electro-hydraulic forming
High strain-rate
Conical die
Formability
Digital image correlation
Light-weight
a b s t r a c t
This work builds upon our recent advances in quantifying high-rate deformation behavior of sheet metals,
during electro-hydraulic forming (EHF), using high-speed imaging and digital image correlation techniques. Aluminum alloy AA5182-O and DP600 steel sheets (1 mm thick, ∼152 mm diameter) were EHF
deformed by high-energy (up to ∼34 kJ) pressure-pulse in an open die (free-forming) and inside a conical die. The deformation history (velocity, strain, strain-rate, and strain-path) at the apex of the formed
domes was quantified and analyzed. The data shows that the use of a die in the EHF process resulted in
an amplification, relative to free-forming conditions, of the out-of-plane normal velocity and in-plane
strain-rate at the dome apex. This amplification is attributed to the focusing action of the die on account
of its conical geometry. Further, while the strain-path at the dome apex was generally linear and proportional, the use of a die resulted in greater strain at the apex relative to the strain during free-forming. The
sheet deformation profile in the EHF process was found to be different from that previously observed in
electromagnetic forming (EMF) and, thus, the two processes are expected to result in different strainpaths and formability. It is anticipated that quantitative information of the sheet deformation history,
made possible by the experimental technique developed in this work, will improve our understanding
of the roles of strain-rate and sheet–die interactions in enhancing the sheet metal formability during
high-rate forming.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
According to the U.S. National Highway Traffic Safety Administration (NHTSA, 2010), the U.S. corporate average fuel economy
(CAFE) standards for passenger cars have remained steady at 27.5
miles per gallon (mpg) since 1990. As Table 1 shows, these standards were recently raised to 30.4 mpg for the passenger car model
year 2011 and will increase in subsequent years, at an average
rate of ∼5% every year, to 37.8 mpg for model year 2016. While
the effort to reduce a vehicle’s weight is not a new phenomenon,
strong emphasis by the U.S. government on increased fuel economy and reduced greenhouse gas emissions (GHG) has renewed
the focus on vehicle weight-reduction as one of the means to
achieve the government mandated fuel economy and GHG emission targets. Therefore, one of the challenges for the auto industry
is to develop a low-cost light-weight alternative to conventionally used low-cost mild steel for sheet applications. In a recent
∗ Corresponding author. Tel.: +1 509 372 6047; fax: +1 509 375 4448.
E-mail addresses: aashish.rohatgi@pnnl.gov (A. Rohatgi),
elizabeth.stephens@pnnl.gov (E.V. Stephens), rich.davies@pnnl.gov (R.W. Davies),
mark.smith@pnnl.gov (M.T. Smith), ayoub.soulami@pnnl.gov (A. Soulami),
ahzi@imfs.u-strasbg.fr (S. Ahzi).
0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
doi:10.1016/j.jmatprotec.2011.12.014
review, Kleiner et al. (2003) have discussed issues related to integrating vehicle design, material selection, metal forming processes,
and costs for manufacturing light-weight automotive components.
Table 2 from Powers (2000) shows that mass reduction in an automobile is possible through material replacement (e.g., by replacing
heavier steel with lighter aluminum (Al) or magnesium (Mg), etc.)
but at a cost-penalty attributed to materials and manufacturing
costs. This cost-penalty is one of the key barriers to automotive
lightweighting in high-volume manufacturing since the consumers
are not always willing to pay a premium for a lighter car. Therefore, the goal of this work is to enable cost-effective deployment
of light-weight sheet materials, such as Al alloys, Mg alloys, and
high-strength and advanced high-strength steels (HSS and AHSS,
respectively), in body-in-white and closure panels. This research
represents efforts of our group at the Pacific Northwest National
Laboratory to assist the U.S. Department of Energy (DOE) and the
auto industry to reduce a car’s weight by 50% (USDOE, 2006) relative
to a comparable 2002 vehicle.
It is well known in the literature that Al alloys, Mg alloys, and
HSS/AHSS have lower room-temperature formability than mild
steels. Formability of these metals can be increased at higher temperatures, e.g. as shown by Li and Ghosh (2004) in Al alloys and
by Hsu et al. (2008) in Mg and Al alloys. Merklein and Geiger
(2002) have also discussed the use of laser heating to alter the
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
1071
Table 1
Average required fuel economy (mpg) under final CAFE standards issued by the U.S.
Environmental Protection Agency and NHTSA (EPA and DOT, 2010).
Model year
2011-base
2012
2013
2014
2015
2016
Passenger cars
Light trucks
Combined cars & trucks
30.4
24.4
27.6
33.3
25.4
29.7
34.2
26.0
30.5
34.9
26.6
31.3
36.2
27.5
32.6
37.8
28.8
34.1
Table 2
Weight saving and relative costs for lightweight materials (Powers, 2000).
Lightweight material
Material
replaced
Mass
reduction (%)
High strength steel
Aluminum
Mild steel
Steel, cast
iron
Steel or
cast iron
Aluminum
Steel
10
40–60
1
1.3–2
60–75
1.5–2.5
25–35
25–35
1–1.5
1–1.5
Magnesium
Magnesium
Glass fiber reinforced
polymers
Relative
cost/Parta
(Reprinted with permission from ASM International. All rights reserved.
www.asminternational.org.)
a
Includes both materials and manufacturing.
local strength/microstructure in sheet metals to improve the deepdrawability of hardenable Al alloys and bending and roll-forming of
high-strength steels. However, elevated temperature forming adds
additional expense owing to increased energy consumption, lubricant costs, die wear/tear, post-forming cleaning, etc. Moreover, the
post-formed strength of the parts may be low on account of exposure to elevated forming temperatures. Therefore, mild steel is still
the preferred choice for the majority of sheet metal applications
in the automotive industry. One of the strategies to overcome the
limited room-temperature formability of sheet metals is to conduct the forming process at high strain-rates, an approach that
has been shown in the literature to enhance sheet metal formability. For example, in a recent patent, Golovashchenko et al. (2009)
describe an EHF tool system as a means to form sheet metal at high
strain-rates and overcome the formability limitations in Al alloys
and AHSS. Rohatgi et al. (2011) have summarized prior literature
where enhanced formability in Al and steels, deformed via highrate forming processes such as electro-hydraulic forming (EHF) and
electro-magnetic forming (EMF), has been reported.
Majority of the prior literature report enhanced formability,
using either EHF or EMF, when the metal sheet is formed inside
a die. However, the mechanism(s) for enhanced formability at high
strain-rates and the role of a die are still not clear. A comparison of deformation history in sheets deformed by EHF or EMF
is also not adequately addressed in the literature. For example,
Balanethiram and Daehn used EHF process to form sheet metals into a conical die and attributed formability improvement in
interstitial-free (IF) iron (1992), and in 6061-T4 Al and oxygen free
high-conductivity copper (1994) to inertial stabilization on account
of high forming velocity. Seth et al. (2005) impacted steel sheets
on a steel punch and attributed the resulting enhanced formability to inertial stabilization and compressive stresses generated
during impact. Golovashchenko et al. (2003), Golovashchenko and
Mamutov (2005), and Golovashchenko (2007) used EMF and EHF
processes to form sheet metals into a die and attributed improved
sheet formability to high strain-rates and high-rate impact with
the tooling. Imbert et al. (2005a) numerically modeled EMF of
Al alloy sheet and concluded that high strain-rates (theoretically
estimated by the authors to be ∼30,000–69,000 /s in the locations where sheet impacts the die) and inertial stabilization alone
could not be responsible for enhanced formability; instead, high
through-thickness compressive and shear stresses and strains as
Fig. 1. A schematic of the EHF sheet specimen geometry.
well as non-linear strain-paths were the responsible factors. Needless to say, enhanced formability has generally been associated
with forming inside a die. However, researchers in this field have
typically relied upon post-mortem strain measurements to draw
conclusions about the possible causes for enhanced formability. Unfortunately, post-mortem strain measurements provide an
incomplete picture of the forming process with no guidance on the
deformation path or the role of the die. Hence, the lack of knowledge
of the deformation history of sheet metals (during EHF/EMF) has
prevented a clear understanding of the mechanism(s) responsible
for enhanced formability and in turn, has hindered broad implementation of EHF/EMF techniques in the automotive industry.
In this work, a recently developed experimental technique comprising high-speed imaging and digital image correlation (DIC)
(Rohatgi et al., 2010, 2011) was used to quantify the deformation history of 5182-O Al and DP600 sheets that were free-formed
or formed inside a conical die using the EHF technique. Although
enhanced formability was not observed in these experiments,
the differences in the sheet deformation history during conicaldie forming, relative to free forming, provide insights into why
enhanced formability has generally been associated with the
former. A comparison of EHF results is also made with existing
literature data on EMF to highlight differences in the deformation history associated with these processes. Such understanding is
expected to enable wider deployment of light-weight materials in
automotive applications and could not have been gained through
conventional post-mortem strain measurement techniques.
2. Experimental procedure
Rohatgi et al. (2011) have previously described the experimental technique for performing EHF and to quantify the deformation
history using high-speed imaging and digital image correlation.
Therefore, only the key aspects of the experimental procedure are
described here.
2.1. EHF test configuration
The sheet metals used in this work are 1 mm thick 5182-O Al
and DP600 steel. The specimen geometry is shown in Fig. 1. Fig. 2
shows a picture of the EHF chamber which is essentially a hemispherical steel vessel with a central opening of diameter 152.4 mm.
1072
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
Fig. 2. Schematic of PNNL’s EHF setup showing the initial (undeformed) and final
(deformed) positions of the sheet (a) under free-forming and (b) inside a conical die.
Two copper electrodes enter the EHF chamber from opposing sides.
The electrode ends (within the EHF chamber) are connected by a
thin copper wire while the electrodes are connected externally to a
capacitor bank. The charge voltage V in the present work ranged
from 5000 V to 9500 V with the corresponding stored electrical
energy of ∼9.4–33.8 kJ, calculated as 1/2CV2 where C is the capacitance (750 ␮F) of the capacitor bank. A program written in LabView
software was used to control the charge–discharge process. Prior to
the test, the sheet specimen was “speckle” patterned in the form of
a random pattern of black colored dots on a white background. The
EHF chamber was filled with water and the speckle patterned sheet
clamped in the fixture with/without the conical die depending upon
if the deformation process was carried out under “free-forming”
conditions (Fig. 2a) or inside the conical die (Fig. 2b), respectively.
The conical die subtends an angle of 84◦ at the apex and is truncated below the apex to yield a ∼38 mm opening to allow cameras
to view the sheet. In the results presented subsequently, the xdirection in the plane of the test sheet is along the electrodes while
the z-direction corresponds to the out-of-plane normal to the test
sheet.
2.2. Quantification of deformation history
A pair of Photron high-speed cameras was used to capture the
sheet deformation at a frame rate of up to 67,500 /s and at an image
resolution of 256 × 256 pixels (see Table 3 for test details). The cameras were simultaneously triggered to capture the images when the
capacitor banks were discharged to initiate the EHF process. The
images of the deforming sheet were captured and post-processed
by the DIC software (Vic-3d, Version 2009.1.0, from Correlated
Solutions, Inc.). Under free-forming test configuration (Fig. 2a), the
entire 152.4 mm deforming area of the sheet was visible to the cameras whereas when the sheets were deformed into the conical die
(Fig. 2b), the effective viewing area was limited to ∼25 mm central
portion of the sheet. Fig. 3a shows the conical die clamped on the
EHF chamber and the inset shows the interior of the die. Fig. 3b
Fig. 3. (a) Photograph of PNNL’s conical die with the inset showing the same die
inverted. (b) Camera point-of-view looking down into the conical die on the specklepatterned sheet that is lit-up by multiple light sources.
shows a picture of the cameras’ view through the conical die and
looking at the speckle-patterned sheet. The DIC software analyzes
the speckle pattern in the image sequence from the EHF test and
determines the displacement and strain tensor at a given location
on the viewable area of the sheet. Knowing the in-process displacement and image capture rate, the velocity, strain, and strain-rate
can be plotted as a function of time. A quick check of the software’s
analysis was performed by comparing the final dome heights determined by the DIC software with those measured physically on the
deformed sheet.
3. Results
Irrespective of the test configuration, free-form or inside the
conical die, the DIC software calculates the displacements and
velocity of any point on the sheet in the global coordinate system.
Thus, the x and y axes correspond to the horizontal and vertical
directions in the 2-dimensional camera images while the z-axis is
normal to the plane of the image and corresponds to the normal
to the undeformed sheet. The in-plane strain and strain-rate at any
point on the surface of the sheet are presented in Lagrangian formulation and are related to the respective engineering quantities
by the following relations:
εxx = exx +
1 2
e
2 xx
dεxx
dexx
= (1 + exx )
dt
dt
(1)
(2)
where εxx and dεxx /dt are the strain and strain-rate, respectively, in
Lagrangian formulation and exx and dexx /dt are the corresponding
quantities in the conventional engineering units.
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
1073
Table 3
Summary of EHF tests.
Material
Die
Test name
Voltage (V)
Energy (kJ)
Calipers
DIC
5182-O Al (1 mm)
Free-forming
Free-forming
Free-forming
Conical-die
Conical-die
T-26
T-24
T-28
T-30
T-34
5000
6500
7500
6500
7500
9.4
15.8
21.1
15.8
21.1
37.9
40.7
47.5
44.9
51
37.1
40
49
44.1
46.1a
67,500
67,500
67,500
45,000
45,000
DP600 Steel (1 mm)
Free-forming
Conical-die
DP6-4
DP6-6
9500
9500
33.8
33.8
33.8
34.2
37.1
33.6
67,500
45,000
a
Dome height (mm)
Camera frames
per second
Height from the last analyzable image frame; subsequent images of still deforming sheet could not be analyzed because of the delamination of paint/speckle pattern.
The velocity, strain and strain-rate history are now described
to highlight the differences between the free-form deformation
and forming inside the conical die, as well as differences in sheet
deformation history in EHF and EMF techniques.
3.1. Overall deformation
Table 3 summarizes deformation parameters and dome heights
achieved for various tests. The data in Table 3 show that with the
Fig. 4. Images of free-formed (a, c, e) and conical-die formed (b, d, f) domes using Al (a–d) and steel (e–f) sheets.
1074
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
Fig. 6. Velocity (z-direction) at the apex of the free-formed Al dome at different
charging voltages.
broad maxima, between ∼207–237 microseconds and between
∼459–548 microseconds, with small undulations (e.g. at 60 and
160 microseconds) superimposed upon the overall curve. In the
present work, the maximum velocities observed at the first maxima
were ∼65 m/s, ∼70 m/s, and ∼94 m/s at 5.0 kV, 6.5 kV, and 7.5 kV,
respectively. At ∼650 microseconds, the sheet velocity is observed
to swing from positive to negative values implying sheet’s displacement away from the cameras and indicative of reverberations in the
sheet at the end of the forming process.
Fig. 7a and b compares the apex velocity of the free-formed and
conical-die formed Al and DP600 steel domes, respectively. The
curves in Fig. 7 show that the velocity–time profile for both the
materials is similar and is characterized by the presence of double
Fig. 5. Time history of the test sheet profile under (a) free-forming (T-24) and (b)
conical-die forming (T-30). Note that the die was not used in test T-24 and is overlaid
on the sheet profiles only as a reference.
exception of test DP6-4, there is a good correspondence between
the physically measured dome height and that determined by the
DIC software. Further, for a given charging voltage, the conical-die
formed Al domes were ∼10% taller than their free-formed counterparts while the heights were similar in the case of steel domes. Fig. 4
shows the post-test photographs of the EHF domes. Under the conditions employed in this work, none of the domes were strained to
failure. The images also show that the free-formed domes possess
a “rounder” profile relative to the conical-die formed domes. The
displacement history of the domes was determined by the DIC software and is shown as a time history of profile of the test sheet for
samples T-24 and T-30 in Fig. 5a and b, respectively, as an example.
The location of the inner surface of the conical die is also marked
in Fig. 5 to show its relative position with respect to the deforming sheet. Unlike the full-field (∼152 mm) view of the sheet during
free-forming (Fig. 5a), the sheet profile in Fig. 5b corresponds to
only ∼25 mm analyzable area in the center of the sheet owing to
the cameras’ limited view inside the die.
3.2. Velocity at the dome apex
Fig. 6 shows the velocity–time history at the apex of the EHF
formed Al sheets at different charging voltages. The velocity–time
curves for all the voltages display a similar trend with the
magnitude of the sheet velocity increasing with increasing voltage. The curves are characterized by the presence of two
Fig. 7. Comparison of velocity (z-direction) at the apex of free-formed and conicaldie formed (a) Al domes and (b) DP600 steel domes.
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
1075
Fig. 8. In-plane strain-rate (x-direction) at the apex of the free-formed Al dome at
different charging voltages.
maxima irrespective of the charging voltage or boundary conditions (i.e. free-forming or conical-die forming). However, while
the general shape (double maxima) is similar for free-forming or
conical-die forming, the magnitude of the velocity is greater in
the latter case for any given voltage. Specifically, for the case of Al
(Fig. 7a), at the first maximum in the velocity–time curve, the peak
apex velocity in conical-die forming is ∼34% and 21% greater relative to the peak apex velocity in free-forming at 6.5 kV and 7.5 kV,
respectively. Further, at the second maximum (Fig. 7a), the increase
in conical-die forming velocity relative to free-forming velocity
is 72% and 28% for 6.5 kV and 7.5 kV, respectively. In the case of
forming of DP600 steel at 9.5 kV (Fig. 7b), the first and second velocity peaks in conical-die forming are ∼26% and ∼16%, respectively,
greater than the corresponding peaks under free-forming.
While the general characteristics of the velocity–time curves
for Al and steel are similar, the deformation duration in
Al is ∼600–700 microseconds while that for steel is shorter
(∼500 microseconds). It is noted that the data for conical-die
formed DP600 steel (Fig. 7b) looks sparse relative to free-formed
case since the camera frame-rate was lower in the former case, i.e.
45,000 frames per second (fps) as opposed to 67,500 fps for freeformed DP600.
3.3. Strain-rate at the dome apex
Fig. 8 shows the in-plane strain-rate at the apex of the
free-formed Al dome at three different charging voltages. The
strain-rate–time curves have a similar trend at all the voltages with
the strain-rate magnitude increasing with increasing voltage. The
curves are characterized by the presence of two broad maxima
between ∼178–193 microseconds and ∼415–548 microseconds,
respectively. In the present work, the maximum strain-rates
recorded were, respectively, ∼207 /s, ∼237 /s, and 271 /s, at 5.0 kV,
6.5 kV, and 7.5 kV. The negative values of the strain-rate at
∼650 microseconds indicate elastic unloading of the sheet at the
end of deformation.
Fig. 9a and b compares the in-plane strain-rate at the apex of
free-formed and conical-die formed Al and DP600 steel domes,
respectively. The curves in Fig. 9 show that for both the materials,
the strain-rate during conical-die forming is greater than during
free-forming for the same voltage. However, unlike the case of
velocity–time profiles in Fig. 7a and b, the strain-rate-time profile
for free-forming is quite different from that of conical-die forming. Specifically, the strain-rate curves in Al during free-forming
(Fig. 9a) show gradual rise and fall while the conical-die forming
curves show many large oscillations in the strain-rate, leading up
to a rapid increase (or amplification) shortly before the end of the
Fig. 9. Comparison of in-plane strain-rate (x-direction) at the apex of free-formed
and conical-die formed (a) Al domes and (b) DP600 steel domes.
deformation. The maximum strain-rates during conical-die forming of Al are ∼846 /s and ∼1213 /s at 6.5 kV and 7.5 kV, respectively.
These strain-rates represent an amplification of ∼3.5× and ∼4.5×
relative to the maximum strain-rate under free-forming (∼237 /s
and ∼271 /s at 6.5 kV and 7.5 kV, respectively). In the case of DP600
steel (Fig. 9b), the strain-rate during free-forming shows a smooth
rise and fall analogous to free-forming Al. However, the strainrate during conical-die forming of DP600 steel shows two peaks
that exceed the free-forming strain-rate curve. Thus, the maximum
strain-rate during conical-die forming of DP600 steel is ∼583 /s
that represents an amplification of ∼2.6× relative to the maximum
strain-rate (∼224 /s) during free-forming.
3.4. Strain-path at the dome apex
Fig. 10 shows the strain-path, in terms of the strain in two
principal in-plane directions, at the apex of free-formed domes.
The data shows that the dome apex undergoes proportional and
almost equi-biaxial straining for the duration of the test with the
maximum strain increasing with increasing voltage. The maximum
strain obtained in free-formed Al in this work was ∼0.14–0.17
Lagrangian (or ∼0.13–0.16 engineering, using Eq. (1)).
Fig. 11a and b compares the strain-path at the apex of Al and
DP600 steel domes, respectively, under free-forming and conicaldie forming conditions. The data for both the materials show that
for a given voltage, the final strain achieved at the apex is greater
under conical-die forming relative to free-forming conditions. For
example, Fig. 11a shows that the final strain (x-direction) in Al
deformed at 6.5 kV is ∼0.18 under conical-die forming as compared to ∼0.11 under free-forming conditions. In the case of DP600
steel, Fig. 11b shows that the final strains in either direction are
1076
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
Fig. 12. Time profile of an aluminum disk-shaped sheet during EMF (Takatsu et al.,
1988).
Fig. 10. Strain-path at the apex of the free-formed Al dome at different charging
voltages.
∼0.10 under conical-die forming as compared to ∼0.07 under freeforming conditions.
4. Discussion
The deformation behavior of 5182-O Al and DP600 steel during electro-hydraulic forming under free-forming and conical-die
forming conditions was quantified using a novel combination of
high-speed imaging and DIC techniques. The results of this work
are discussed below. A comparison is also made with the published
(Adapted and reproduced with permission from The Japan Society of Mechanical
Engineers (JSME).)
results on EMF technique to highlight the differences in the sheet
deformation history during these two forming techniques.
4.1. Dome shape and height
As observed from the post-test images of the domes in Fig. 4,
the conical-die formed domes have a distinctive profile on account
of the constraining effect of the conical die on the sheet deformation. Thus, the free-formed domes possess a “rounder” profile
as the sheet is able to deform in an unconstrained manner. The
height of the conical-die formed Al domes is somewhat greater
than the free-formed domes (Table 3) at the same charging voltage
on account of the velocity amplification in the former case. In the
case of steel domes, the height difference between the free-formed
and conical-die formed domes is within the measurement error
and although velocity amplification was observed during conicaldie forming (Fig. 7b), the amplification was insufficient to increase
the dome height significantly. The representative time history of
the profile of a free-formed test sheet shown in Fig. 5a is similar to
that observed by Tobe et al. (1984) although the absolute magnitudes of the displacement and time-scale are different on account
of differences in the overall system performance.
One important difference between EHF and EMF can be seen by
comparing the time history of free-formed sheet profiles (e.g. EHF
data in Fig. 5a and EMF data in Fig. 12, (Takatsu et al., 1988)). Fig. 12
shows that the EMF technique, using a circular coil placed in the
center of the sheet, produces a marked depression in the center of
the sheet during initial stages of deformation. This central depression in the sheet is due to the magnetic pressure being minimal
at this location, as has been shown by, for example, Takatsu et al.
(1988), Imbert et al. (2005a), and Kleiner et al. (2005). On the other
hand, with the electrical discharge during EHF occurring below the
sheet center (as is the case in the present work), the pressure at the
center of the sheet is most likely maximum. Hence, the sheet profile
during EHF is generally convex during the entire process (Fig. 5a)
unlike the concave–convex sheet profile during EMF (Fig. 12). As a
consequence, EHF and EMF are likely to result in different strainpaths which, in turn, may lead to different formabilities.
4.2. Velocity–time history at the dome apex
Fig. 11. Strain-path at the apex of the free-formed and conical-die formed (a) Al and
(b) DP600 steel domes.
Fig. 6 shows that the use of higher voltage, and hence, greater
input energy for deformation, leads to a greater velocity. Fig. 7b
shows that the DP600 steel, being stronger than 5182-O Al, required
a higher voltage (9500 V) than Al (6500–7500 V) to achieve similar
velocity magnitudes as Al. However, other than the difference in
velocity magnitude or the voltage necessary to achieve a certain
velocity, all the velocity–time curves are similar in shape which
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
Fig. 13. Measured vertical displacement at the center of EHF free-formed rectangular Al sheet (Tobe et al., 1984).
(Adapted and reproduced with permission from The Japan Society of Mechanical
Engineers (JSME).)
suggests a corresponding similarity in the spatial and temporal profile of the incident pressure-pulses generated by the EHF process.
However, two features of the velocity–time curves in Figs. 6 and 7
stand out and are discussed below.
1. Double-peaks in velocity–time curves: The double-peak behavior
is observed for both Al (Figs. 6 and 7a) and steel (Fig. 7b). Considering that these two materials have vastly different strengths and
constitutive behaviors, the double-peak behavior is attributed
to the pressure-pulse profile during the EHF process. It is generally known that under-water electric discharge generates an
expanding, high-pressure plasma/gas-bubble within the water
that eventually collapses towards the end of the discharge process. It is this expansion and collapse of the bubble that results in
a pressure-pulse whose interactions with the deformable sheet
and rigid chamber walls result in a double-peak velocity–time
curve of the sheet. This description of the EHF process is supported by high-speed imaging results and analysis of Tobe et al.
(1984) who used EHF to deform Al sheets and concluded that
the non-monotonic displacement–time profile of the sheet center is due to pressure wave reflection off of the moving sheet
and collapse of bubbles under the sheet (see Fig. 13). Similarities between the displacement–time profiles in the data of Tobe
et al. (1984) (Fig. 13) and that obtained in this work (Fig. 14) can
be easily seen where inflexion points are labeled (a–c) to show
similarities in the two sets of data.
The double-peak behavior in EHF velocity–time curves is contrary to the single-peak behavior observed by Vivek et al. (2011)
during electromagnetic compression of steel tubes. In another
work, Kleiner et al. (2005) used EMF to free-form AA6016 sheet
and their measured displacement–time data did not show any
indications of multiple slope changes similar to those shown in
1077
Fig. 13 or Fig. 14. Thus, had Kleiner et al. (2005) explicitly plotted their data as velocity vs. time, it would have shown a single
peak in the curve, similar to the results of Vivek et al. (2011) but
different from the EHF results in this work or that of Tobe et al.
(1984). Considering that the double-peaks in the velocity–time
data in EHF can be attributed to pressure wave reflections and
bubble collapse, the absence of these phenomena during EMF on
account of the absence of a medium to transmit the magnetic
pressure, results in a single peak in the EMF velocity–time data.
It should be pointed out that the double peak behavior
was obtained at the center of the sheet/dome apex. However,
since the pressure-pulse profile is likely to vary laterally, the
velocity–time behavior at off-center/non-apex locations may be
different from that at the center/apex. Indeed, Rohatgi et al.
(2011) showed that the double-peak behavior was not observed
in non-apex locations in EHF deformed Al. Further, unlike a single
electrode-pair used in the present work and by Tobe et al. (1984),
an EHF chamber may be designed with multiple electrodes
(Golovashchenko et al., 2011) which may result in velocity–time
profiles different than those shown in Figs. 13 and 14. In summary, the quantitative results shown in this work highlight the
complex deformation history in EHF that cannot be ascertained
by direct analogy with existing results of EMF or from postdeformation measurements of strain distribution.
2. Velocity amplification in conical-die forming: Fig. 7a and b shows
that for any given voltage, the apex velocity is greater in conicaldie forming than in free-forming conditions. Although the
incident EHF pressure-pulse profiles are not known at present,
the incident pulse magnitude at any given voltage and during the
initial stages of the deformation is expected to be independent
of the presence/absence of the conical die since the test sheet
has not yet impacted the die. Moreover, the velocity amplification is seen both in Al and steel. Therefore, the greater velocity
during conical-die forming cannot be attributed to differences
in the incident pressure-pulse or material behavior. Instead, the
authors believe that conical shape of the die results in a “focusing” action wherein as the pressure-pulse moves from the EHF
chamber towards the die apex, the rigid die (a) constrains the
sheet upon impact with the die and forces the deformation to
occur in a gradually decreasing area and (b) reduces the areal
spread of the energy contained within the pressure pulse. Based
on the above arguments, the focusing effect is expected to be a
function of the die angle, all other conditions staying the same.
In this work, a die angle (apex) of 84◦ was used. Although EHF
with additional dies of different angles was not attempted in this
work, initial results (unpublished) from numerical modeling in
this work, assuming an exponentially decaying pressure-pulse,
have confirmed the dependence of maximum apex velocity on
the die angle.
4.3. Strain-rate–time history at the dome apex
Fig. 14. Vertical displacement and corresponding velocity at the center of EHF freeformed circular Al sheet in this work.
Figs. 8 and 9 show a compilation of the strain-rate–time histories
at the dome apex for Al and steel, at different charging voltages and
different boundary conditions (free-forming and conical-die forming). Fig. 8 shows that the use of higher voltage, and hence, greater
input energy for deformation, leads to a gradual increase in the freeform strain-rate while the overall profile of the curve is unchanged.
Similar to the free-forming velocity–time curves shown in Fig. 6, the
free-forming strain-rate–time curves also show two broad maxima although the strain-rate maxima in Fig. 8 occur at a time that
is somewhat earlier than the velocity maxima in Fig. 6. However,
the reason for the differences in the time-window over which the
maxima occur and the variations in the width of these peaks are
not clear and require additional analysis.
1078
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
Fig. 9 shows the differences in the strain-rate–time histories
between conical-die forming and free-forming conditions. Specifically, Fig. 9a and b, respectively, shows that conical-die forming
of Al and DP600 steel exhibits strain-rate amplification relative to
free-forming strain-rates. Such strain-rate amplification in conicaldie, akin to previously described velocity amplification, is also
attributed to the focusing action of the conical die. Interestingly,
Fig. 9a shows that the focusing action of the conical die was more
effective in enhancing the strain-rate than increase in voltage alone.
In the prior literature, EMF inside conical die has been shown to
result in larger regions with enhanced formability (Imbert et al.,
2005b) or greater formability (Golovashchenko et al., 2003) as
compared to under free-forming conditions. However, the reasons
behind improved formability, when forming inside a conical die,
were not clear. While early work by Balanethiram and Daehn (1992,
1994) used a conical die and attributed enhanced formability to
“high” strain-rates, the strain-rates were estimated at best and no
attempt was made to clarify the role of conical die in comparison with free-forming conditions. Using numerical modeling and
experimental analysis of post-mortem strain distribution on EMF
formed parts, Imbert et al. (2005a) concluded that a combination
of high strain-rates and sheet–die interactions (through-thickness
and shear stresses and strain-path changes) was responsible for
enhanced formability when forming inside a die. However, to the
authors’ knowledge, this work is the first to provide experimentally
measured strain-rates as well as to quantify the differences in the
deformation history under free-forming and conical-die forming
conditions.
4.4. Strain-path at the dome apex
Figs. 10 and 11 show a compilation of the strain-path at the
dome apex for Al and steel, at different charging voltages and different boundary conditions (free-forming and conical-die forming).
Under the conditions employed in this work, the apex undergoes
proportional and almost equi-biaxial straining, especially in the
case of free-forming while the strain-path deviates somewhat from
equi-biaxial nature during conical-die forming. While the reason
for this deviation is not clear at present and requires further investigation, it is hypothesized that interaction of the pressure-pulse
with the die and/or presence of non-symmetrical friction conditions at the sheet/die interface may play a part. Fig. 11a and b shows
that the final strain (x-direction) in conical-die forming can be up
to ∼64% more than in free-forming (Al 6.5 kV). Although the absolute magnitude of these strains are significantly lower than the
strains characterized as “enhanced formability” in the literature,
the relative difference in strains between free-forming and conicaldie forming is in agreement with the observations of Imbert et al.
(2005b) and Golovashchenko et al. (2003).
Numerical modeling of EMF of AA 5754 sheet inside a conical die
(Imbert et al., 2005a) has shown that the sheet location that impacts
the die shows significantly non-proportional loading following
impact. Imbert et al. (2005a) also noted that non-proportional
strain-path makes direct comparisons of formability with conventional forming limit diagrams difficult since the latter were
developed with the assumption of a linear and proportional strainpath. Hence, a priori assumption of a proportional and linear
strain-path during EHF or EMF can lead to incorrect analysis and
conclusions. Although the experimental technique developed in
this work can be utilized to verify the strain-path under freeforming, it is somewhat limited when forming inside a die since the
technique is image-based and the die blocks the cameras’ access to
the speckle pattern on the sheet. Nevertheless, in an experimental
setup, it may be possible to machine openings inside the die and
allow cameras to view the sheet deformation, as demonstrated in
this work. Quantitative information from such visible regions can
be used to validate models which can then be used, with a greater
degree of confidence, to model the sheet locations that are hidden
from the camera.
5. Conclusions
A combination of high-speed imaging and digital image correlation technique was used to compare and contrast the free-forming
and conical-die forming behavior of 1 mm thick 5182-O Al and
DP600 steel sheets using the EHF technique. Deformation behavior at the dome apex of the EHF formed sheets was quantified and
discussed in relation to the often-reported enhanced formability at
high strain-rates, and deformation history during EMF technique.
The following conclusions can be drawn:
A. EHF domes of 5182-O Al and DP600 steel show similar deformation history at the dome apex irrespective of the input energy or
boundary conditions (free-forming or conical-die forming). The
primary difference in the response of Al and DP600 steel is that
the steel experiences lower velocity, strains, and strain-rates
than Al on account of its greater strength than Al.
B. Use of a conical die during EHF was found to result in an amplification of the apex velocity, strain-rate, and strain, relative to
free-forming conditions. The amplification is attributed to the
focusing action of the die on account of its conical geometry and
the relative amplification is likely to vary with the cone angle.
C. The general shape of the velocity–time curves is similar under
free-forming and conical-die forming conditions with the curves
shifted to greater magnitude in the latter case. However, the
strain-rate–time curves under free-forming and conical-die
forming are quite different from each other: the former show
smooth rise and fall while the latter are characterized by sharp
peak(s) indicative of the strain-rate amplification attributed to
the focusing action of the die.
D. The use of conical die was found to be more effective than an
increase in capacitor bank voltage (i.e. input discharge energy) in
achieving higher strain-rates. However, the conical-die induced
strain-rate amplification occurs over short time intervals during
the test instead of an overall general increase over the entire test
duration.
E. The strain-path at the apex is generally linear and proportional
for both free-forming and conical-die forming conditions. The
strain in one of the principal directions is, however, greater during conical-die forming.
F. Enhanced formability of metals during EHF and EMF has traditionally been attributed collectively to variables such as high
velocity, high strain-rates, strain-path changes, and throughthickness stresses. It is expected that the ability to quantify the
sheet deformation history, using the technique developed in
this work, will help elucidate the relative importance of these
variables.
G. The experimental technique developed in this work can help
validate and develop accurate numerical models that will enable
the automotive (and other industries) to fabricate light-weight
and low-cost components by taking advantage of enhanced
formability of sheet metals at high-strain rates.
Acknowledgments
The Pacific Northwest National Laboratory is operated by Battelle Memorial Institute for the U.S. Department of Energy under
contract DE-AC05-76RL01830. This work was sponsored by Drs.
Joseph Carpenter and Carol Schutte in association with the U.S.
Department of Energy, Office of Vehicle Technologies, as part of
the Lightweight Materials program. The authors are thankful to
A. Rohatgi et al. / Journal of Materials Processing Technology 212 (2012) 1070–1079
S.F. Golovashchenko (Ford), J.F. Quinn and J.R. Bradley (General
Motors), and A. Desai and D.J. Zhou (Chrysler) for their suggestions.
Capacitor banks’ operational guidance provided by J. Johnson (Bonneville Power Administration), and technical support provided by
G.L. Vanarsdale (Science Applications International Corporation)
and PNNL staff (M.E. Dahl, K.F. Mattlin, P.A. Boyd, and C.A. Bonebrake) is gratefully acknowledged. Technical support, to operate
the cameras and image analysis using DIC software, provided by
Alistair Tofts and Hubert Schreier at Correlated Solutions is also
acknowledged.
References
Balanethiram, V.S., Daehn, G.S., 1992. Enhanced formability of interstitial free iron
at high-strain rates. Scripta Metall. Mater. 27, 1783–1788.
Balanethiram, V.S., Daehn, G.S., 1994. Hyperplasticity – Increased forming limits at
high workpiece velocity. Scripta Metall. Mater. 30, 515–520.
EPA and DOT, 2010. Light-Duty Vehicle Greenhouse Gas Emission Standards and Corporate Average Fuel Economy Standards; Final Rule, http://
www.nhtsa.gov/Laws+&+Regulations/CAFE+-+Fuel+Economy/Model+Years+
2012-2016:+Final+Rule (downloaded 30.08.11).
Golovashchenko, S.F., 2007. Material formability and coil design in electromagnetic
forming. J. Mater. Eng. Perform. 16, 314–320.
Golovashchenko, S.F., Bessonov, N.M., Ilinich, A.M., 2011. Two-step method of forming complex shapes from sheet metal. J. Mater. Process. Technol. 211, 875–885.
Golovashchenko, S.F., Gillard, A.J., Cedar, D.A., Illnich, A.M., 2009. Electrohydraulic
forming tool. United States Patent 7,516,634 B1, 1–11.
Golovashchenko, S.F., Mamutov, V., Dmitriev, V.V., Sherman, A.M., 2003. Formability
of sheet metal with pulsed electromagnetic and electrohydraulic technologies.
In: Das, S.K. (Ed.), Aluminum. TMS, Warrendale, PA, pp. 99–110.
Golovashchenko, S.F., Mamutov, V.S., 2005. Electrohydraulic forming of automotive panels. In: Bieler, T.R., Carsley, J.E., Fraser, H.L., Sears, J.W., Smurgeresky, J.E.
(Eds.), Trends in Materials and Manufacturing Technologies for Transportation
Industries and Powder Metallurgy Research and Development in the Transportation Industry. , pp. 65–70.
Hsu, E., Carsley, J.E., Verma, R., 2008. Development of forming limit diagrams of
aluminum and magnesium sheet alloys at elevated temperatures. J. Mater. Eng.
Perform. 17, 288–296.
1079
Imbert, J., Worswick, M., Winkler, S., Golovashchenko, S., Dmitriev, V., 2005a.
Analysis of the increased formability of aluminum alloy sheet formed using
electromagnetic forming. In: SAE World Congress, Paper 2005-01-0082. SAE
International, Detroit, Michigan, USA.
Imbert, J.M., Winkler, S.L., Worswick, M.J., Oliveira, D.A., Golovashchenko, S., 2005b.
The effect of tool-sheet interaction on damage evolution in electromagnetic
forming of aluminum alloy sheet. J. Eng. Mater. Technol. Trans. ASME 127,
145–153.
Kleiner, M., Beerwald, C., Homberg, W., 2005. Analysis of process parameters and
forming mechanisms within the electromagnetic forming process. CIRP Ann.
Manuf. Technol. 54, 225–228.
Kleiner, M., Geiger, M., Klaus, A., 2003. Manufacturing of lightweight components
by metal forming. CIRP Ann. Manuf. Technol. 52, 521–542.
Li, D.M., Ghosh, A.K., 2004. Biaxial warm forming behavior of aluminum sheet alloys.
J. Mater. Process. Technol. 145, 281–293.
Merklein, M., Geiger, M., 2002. New materials and production technologies for innovative lightweight constructions. J. Mater. Process. Technol. 125, 532–536.
NHTSA, 2010. Summary of Fuel Economy Performance, http://www.nhtsa.gov/fueleconomy (accessed 24.03.11).
Powers, W.F., 2000. Automotive materials in the 21st century. Adv. Mater. Process.,
38–41.
Rohatgi, A., Stephens, E.V., Soulami, A., Davies, R.W., Smith, M.T., 2010. High-strainrate forming of aluminum and steel sheets for automotive applications. In:
Kolleck, R. (Ed.), International Deep Drawing Group (IDDRG). Graz, Austria, pp.
441–450.
Rohatgi, A., Stephens, E.V., Soulami, A., Davies, R.W., Smith, M.T., 2011. Experimental
characterization of sheet metal deformation during electro-hydraulic forming.
J. Mater. Process. Technol. 211, 1824–1833.
Seth, M., Vohnout, V.J., Daehn, G.S., 2005. Formability of steel sheet in high velocity
impact. J. Mater. Process. Technol. 168, 390–400.
Takatsu, N., Kato, M., Sato, K., Tobe, T., 1988. High-speed forming of metal sheets by
electromagnetic force. JSME Int. J. Series III – Vibration Control Eng. Industry 31,
142–148.
Tobe, T., Kato, M., Obara, H., 1984. Metal-forming by underwater wire explosions. 2:
Experiments on bulging of circular aluminum sheets by copper wire explosions.
Bull. JSME 27, 130–135.
USDOE, 2006. FreedomCAR and Fuel Partnership Plan, http://www1.eere.energy.
gov/vehiclesandfuels/about/partnerships/freedomcar/index.html (downloaded
17.09.10).
Vivek, A., Kim, K.H., Daehn, G.S., 2011. Simulation and instrumentation of electromagnetic compression of steel tubes. J. Mater. Process. Technol. 211, 840–850.