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Experimental characterization of sheet metal deformation during electro-hydraulic forming
Journal of Materials Processing Technology 211 (2011) 1824–1833
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Experimental characterization of sheet metal deformation during electro-hydraulic forming夽 Aashish Rohatgi ∗ , Elizabeth V. Stephens, Ayoub Soulami, Richard W. Davies, Mark T. Smith Pacific Northwest National Laboratory (PNNL), 902 Battelle Boulevard, P.O. Box 999, Richland, WA 99352, USA
a r t i c l e
i n f o
Article history: Received 16 March 2011 Received in revised form 1 June 2011 Accepted 4 June 2011 Available online 12 June 2011 Keywords: Electro-hydraulic forming High strain-rate Formability Digital image correlation Light-weight Automotive
a b s t r a c t A novel experimental technique, that combines high-speed imaging and digital image correlation techniques, has been developed and applied to investigate the high-rate deformation behavior of aluminum sheet during electro-hydraulic forming (EHF). Aluminum alloy AA5182-O sheets (1 mm thick and ∼152 mm diameter) were EHF deformed by high-energy (up to ∼21 kJ) pressure-pulse and the timeevolution of sheet-displacement, velocity, strain and strain-rate quantified. The data shows that different locations on the sheet undergo unique deformation history that is not apparent from the conventional post-mortem strain measurement (using etched circle/grid pattern) approach. Under the experimental conditions used in this work, the sheets were formed into domes and the maximum strain-rate observed was ∼664/s. Further, this maximum strain-rate was observed at an off-apex location and was ∼2.5 times greater than the maximum strain-rate at the dome apex. The maximum velocity observed was ∼100 m/s and the velocity–time data showed evidence of pressure-wave reverberations during the forming process. We believe that knowledge of such time-evolution of sheet deformation is necessary for a better understanding and accurate modeling of sheet formability that has often been reported to exceed quasi-static forming limits under high-rate forming conditions. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Our group at the Pacific Northwest National Laboratory is involved in research with the overarching theme of automotive weight reduction in support of the US DOE and the FreedomCAR and Fuel Partnership (USCAR) efforts to reduce a car’s weight by 50%, as outlined in their Plan (USDOE, 2006). While the goal of automotive weight reduction through the use of low-density metals such as aluminum (Al) and magnesium (Mg) alloys has been pursued for many years, mild steel is still the predominant choice for body-in-white and automotive closure panels owing to its better room-temperature formability than Al or Mg sheets. The use of
夽 Disclaimer: This manuscript has been authored by Battelle Memorial Institute, Pacific Northwest Division, under Contract No. DE-AC05-76RL01830 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. ∗ Corresponding author. Tel.: +1 509 372 6047; fax: +1 509 375 4448. E-mail addresses: [email protected] (A. Rohatgi), [email protected] (E.V. Stephens), [email protected] (A. Soulami), [email protected] (R.W. Davies), [email protected] (M.T. Smith). 0924-0136/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2011.06.005
advanced high-strength steels (AHSS) such as dual-phase steels, and conventional high-strength steels (HSS) can also contribute to automotive lightweighting by enabling use of thinner gauge sheets that have equivalent strength as thicker gauge (thus, heavier) mild steel. However, AHSS too suffer from poor formability compared to mild steel thus, limiting their deployment for automotive lightweighting. For example, Golovashchenko et al. (2009) noted that the room-temperature formability of aluminum alloys and AHSS under plane-strain conditions typically does not exceed ∼25% and ∼30%, respectively, while the same figure for deep drawing quality (DDQ) steel exceeds 45%. Therefore, there is a need to develop techniques to successfully form materials such as Al, Mg, AHSS and HSS, preferably at room temperature, for cost-effective automotive lightweighting. High strain-rates have been shown to enhance the formability (relative to formability at quasi-static strain-rates) of sheet metal in many instances. High strain-rates for sheet forming are typically obtained by techniques such as explosive forming, electrohydraulic forming (EHF) and electro-magnetic forming (EMF). Such high-strain-rate forming techniques may also incur lower tooling costs due to the elimination of matching die which is, instead, replaced by the impulse force generated by an explosive (explosive forming), electromagnetic repulsion (EMF) or electrical discharge (EHF). Several authors, e.g. Balanethiram et al. (1994), Fenton and Daehn (1998) and Golovashchenko et al. (2003), also cite lower
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spring-back as an advantage of high-strain-rate forming. Hence, owing to their potential to successfully form low-formability metals at room temperature, such as Al, HSS and AHSS, with additional benefits of reduced tooling costs and minimal/no spring-back, high-strain-rate forming techniques are of great interest to the automotive industry. The reader is referred to a recent review by Daehn (2006) of various high-rate forming techniques. Although explosive forming is one of the earliest high-rate forming techniques, handling explosives for routine research is not feasible. Therefore, majority of recent formability-related research has employed EHF and EMF techniques. For example, Balanethiram and Daehn (1992) deformed interstitial free (IF) iron into a conical die (90◦ apex angle) using EHF technique and measured engineering plane-strains on the order of ∼160% near the fracture region and ∼120% away from the fracture; the corresponding quasi-static strains in IF iron are on the order of 30–40%. Using the same EHF procedure as before, the same authors in a subsequent publication (Balanethiram and Daehn, 1994) observed large plane-strains near failure in 6061-T4 aluminum (engineering strain ∼120–130% at high-rate vs. ∼20% at quasi-static rates) and in oxygen-free highconductivity copper (engineering strain ∼100% at high-rates vs. ∼30% at quasi-static rates). Seth et al. (2005) used EMF to impact steel sheets on axisymmetric and wedge-shaped dies and measured engineering plane-strains at failure to be ∼50–60% as compared to ∼10% under quasi-static deformation. Golovashchenko et al. (2003) compared the rate-dependence of formability of several materials (Al, Cu, steel and Ti alloys) and observed that EHF into an open die (free-forming) could increase the local deformation by 40–90%. Golovashchenko et al. (2003) also observed higher failure strains (∼60% strain at high-rates vs. ∼25% at quasi-static rates) in 6111T4 Al when using the EMF technique and forming the Al sheet into a V-shaped die. Imbert et al. (2005b) investigated EMF of AA5754 sheet into an open die (free-forming) and a conical die (112◦ apex angle) and observed maximum strains on the order of ∼35–45% at high rates as compared to quasi-static strains of 20–30%. In another study, Imbert et al. (2005a) measured maximum engineering strains of ∼65% for AA5754 formed by the EMF technique into a conical die (100◦ apex angle) as compared to quasi-static strains of ∼20–30%. Oliveira and Worswick (2003) measured maximum engineering strains of ∼40–50% when forming AA5754 by EMF into a rectangular die. Thus, the observation of increased formability at high strain-rates has been generally established in the literature. However, as will be described subsequently, the quantification of deformation history of the sheet metal, subjected to high-rate deformation, has not been clearly established and is the topic of this paper. The formability in high-rate deformed sheets is typically determined by measuring strains using the circle grid analysis, as outlined by Taylor (1988). While this strain-measuring technique determines the final strain distribution in the deformed sheet, it is unable to determine the strain and strain-rate history at different sheet locations. Consequently, there is lack of in-process deformation behavior in the literature, which, in authors’ opinion, has led to a lack of consensus on the mechanisms responsible for the enhanced-formability in sheet metals. For example, Balanethiram and Daehn (1992) estimated a sheet velocity of 300 m/s and a strain rate of ∼1050/s during EHF of IF steel sheet and attributed formability improvement to inertial stabilization on account of high velocity. In another publication, similar velocity and (some-what lower) strain rate estimates, as well as conclusions were reached by the same authors (Balanethiram and Daehn, 1994) for EHF tested 6061-T4 Al and OFHC Cu. Seth et al. (2005) experimentally measured the impact velocity of steel sheets on a steel punch (though strains were still measured by the etched-circle technique (Taylor, 1988) and attributed the enhanced formability to inertial stabilization and compressive stresses generated during impact. Other
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authors, such as Golovashchenko et al. (2003), Golovashchenko and Mamutov (2005) and Golovashchenko (2007), determined only the post-mortem strain (via the circle-etching technique) in EMF and EHF experiments and attributed improved sheet formability to high strain-rates and high-rate impact with the tooling even though the strain and strain-rate history of the deforming sheet were unknown. Imbert et al. (2005a) numerically modeled EMF of Al alloy sheet and concluded that high-strain rates (estimated to be on the order of 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 well as non-linear strain-paths were the responsible factors. However, Imbert et al. (2005a) noted that such conclusions about extremely high strainrates and strain-path need to be validated experimentally. Finally, modeling efforts, such as those by Oliveira and Worswick (2003) tend to validate their numerical models using final strain distribution as the key criterion but neglect the prior strain and strain-rate history owing to the lack of corresponding experimental data. Only recently has some progress been reported in obtaining deformation-history from high-rate forming experiments. Badelt et al. (2003) used contact-pins and laser-shadow methods to determine displacement–time history of individual locations on a sheet during electromagnetic forming. However, their method was unsuitable for direct measurement of strains and strain-rates and necessitated the use of mathematical modeling to estimate the same. Johnson et al. (2009) used Photon Doppler Velocimetry technique in electromagnetically expanding ring experiment to determine in-process velocity vs. time at four locations. However, Johnson et al. (2009) did not demonstrate the actual strain or strain-rate history for the expanding rings from this data. Mercier et al. (2010) used VISAR and Doppler Laser Fabry-Pérot Interferometry technique to measure velocity (at 3 locations) during explosive-driven expansion of tantalum and copper hemispheres, respectively. Again, experimental strain or strain-rates could not be determined by their (Mercier et al., 2010) method. Finally, Wielage and Vollertsen (2011) used high-speed imaging to determine velocity of laser shock formed metal foils (20–50 m thick). Owing to the simple bending geometry employed in this work, the authors (Wielage and Vollertsen, 2011) used geometrical arguments to estimate the total bending strain and the corresponding strain-rate. Thus, it is concluded that prior research has principally relied upon final strain measurements, estimated strain-rates and numerical models to postulate mechanisms responsible for enhanced formability. Further, the numerical models themselves are validated by the post-mortem strain measurements and neglect the prior strain and strain-rate history. Therefore, the primary objective of this work is to quantify the in-process strain and strain-rates and improve our understanding of high-strain-rate forming events. The technique selected for this work is EHF owing to its applicability (unlike EMF technique) to both high conductivity (e.g. Al) as well as low-conductivity (e.g. steel and magnesium) sheets. The work presented below describes the equipment, measurement techniques and results obtained for high-strain-rate forming of Al sheets. It is anticipated that this research will contribute to our understanding of the high-rate deformation behavior through experimental determination of strain and strain-rate history of deforming sheets and help elucidate the mechanisms responsible for enhanced formability while helping validate the numerical models.
2. Experimental procedure A key contribution of this paper is the quantification of the inprocess deformation parameters (displacement, velocity, strain and
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Fig. 1. Schematic representation of PNNL’s EHF setup showing the initial (undeformed) and the final (deformed) positions of the sheet.
strain-rate) that have typically been unknown, or estimated at the best, in the literature. The quantification method, as well as the equipment and the test procedures employed in this research are described below; additional details are described in a prior publication (Rohatgi et al., 2010). 2.1. Quantification of sheet deformation behavior Overall, the approach comprised painting a speckle pattern on the undeformed metal sheet. The sheet was then deformed via EHF and the deformation process was imaged by a pair of highspeed cameras. The images of the deforming sheet were captured and post-processed by the digital image correlation (DIC) software to calculate the displacement, velocity, strain and strain-rate, as a function of time, at any given point on the sheet. Digital image correlation is an optical method to measure deformation on an object surface. This method uses white-light speckle correlation to measure deformation in each image of an image sequence where any two consecutive speckled images, captured by a video camera, represent the incremental stages during the deformation process. In this project, digital image correlation software (Vic-3d, Version 2009.1.0) from Correlated Solutions, Inc., in conjunction with the image sequence captured by the high-speed cameras, was used to quantify the in-process sheet displacement, velocity, strain and strain-rate, as a function of time. A software calibration was performed at the start of the experiments by imaging a pre-measured geometrical test-pattern using the cameras. This calibration essentially defines the cameras’ orientation in space, relative to each other. Following calibration, the cameras position was held fixed such that the sheet deformation was imaged without disturbing the camera’s relative orientation to each other. Thus, when the software analyzes the images of the sheet, captured during the EHF test and representing sequential stages of its deformation, the software is able to quantify the displacement of the speckles in the image sequence and the strain tensor can be determined at any point on the sheet surface. Knowing the inprocess displacement and image capture rate, the velocity, strain, and strain-rate at each point on the sheet 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.
Fig. 2. Photograph of PNNL’s EHF fixture.
inserted through the chamber walls. The electrodes were copper rods, 6.35 mm in diameter with a gap of ∼11.5 mm between the two ends. A thin copper wire was used to join the electrode ends, thus, creating an electrical “short” between the electrodes. External to the chamber, the copper electrodes were connected to a capacitor bank with ∼2.44 m (8 ft.) long cables and a program written in LabView software was used to control the charge–discharge process. For a given charge voltage V, the electrical energy input was calculated as 1/2CV2 where C is the capacitance (750 F) of the bank. The voltage at the positive electrode at the EHF chamber was measured using a single-ended high voltage probe (Tektronix P6015A with ∼7.62 m (25 ft.) cable and a 1000× attenuator) and Tektronix oscilloscope model TDS3034B. The discharge currents were measured by Rogowski coils and recorded by the data acquisition system. The chamber was filled with water prior to each test. 2.3. Specimen preparation and boundary conditions The sheet metal tested in this work was 1 mm thick 5182-O aluminum. Typical specimen geometry is shown in Fig. 3. One face
2.2. Electro-hydraulic forming apparatus and instrumentation A schematic of PNNL’s EHF setup is shown in Fig. 1 and a close-up photograph of the EHF fixture is shown in Fig. 2. The EHF fixture was machined out of steel and consisted of a hemispherical cavity (∼152 mm diameter) with two opposing electrodes
Fig. 3. A schematic of the EHF sheet specimen geometry.
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Fig. 6. A photograph of an EHF-deformed sheet. Some water has leaked out from the hemi-spherical chamber owing to fracture (not visible) in the sheet.
the final deformed shape of the sheet was in the form of a dome, as shown in Fig. 6. The center of the 152 mm circular portion of the undeformed sheet was marked and is referred to as the “apex” in subsequent discussion. Fig. 4. A top view of an undeformed speckle patterned sheet clamped in the EHF fixture.
of the sheet specimens was speckle-patterned by spray-painting it with white automotive paint and then creating a random pattern of spots with a black-color marker (Fig. 4). The sheet was bolted to the EHF chamber (Fig. 2) through a hold-down ring with the speckled face facing the cameras and illuminated by several highintensity lights (Fig. 5). This testing configuration is referred to as “free-forming” in that the sheet is constrained circumferentially by a ring and a central region (∼152 mm diameter) of the sheet is free to deform when subjected to the pulse-pressure wave originating from the underlying hemispherical EHF chamber. Consequently,
2.4. High-speed camera imaging A pair of Photron SA1 high-speed cameras was used to capture the sheet deformation at a frame rate of 67,500/s and at an image resolution of 256 × 256 pixels. The cameras were simultaneously triggered to capture the images when the capacitor banks were discharged to initiate the EHF process. At the end of the test, the image sequence corresponding to the sheet deformation was saved on the computer for subsequent image analysis. 2.5. Conducting the electro-hydraulic forming test The EHF chamber was filled with tap-water and the specklepatterned sheet clamped over it ensuring that there was no air gap between the water and the sheet bottom. The capacitor bank was charged to the desired voltage (energy) and discharged immediately upon reaching the set voltage level. The capacitor discharge results in large currents (10 s of KA) to flow through the copper wire that result in its rapid melting, vaporization and expansion, thus, leading to a pressure-pulse. Tests were conducted at voltages of 5000, 6500 and 7500 V corresponding to an energy (stored in the capacitor banks) of ∼9.4, 15.8 and 21.1 kJ. The entire deformation event for each test was captured by the high-speed cameras and the images were stored for subsequent analysis. Table 1 lists the experimental details for various tests. Table 1 also compares the physically measured dome height (measured relative to the top surface of the undeformed portion of the test sheet) and thickness strain at the apex relative to those calculated by the image analysis DIC software. 3. Results 3.1. Coordinate system and quantification of sheet deformation The displacements and velocity of any point on the sheet were calculated by the DIC software in the global coordinate system i.e. the x and y axes correspond to the horizontal and vertical direction in the 2-dimensional camera images while z-axis is normal to the plane of the image and corresponds to the normal to undeformed Al sheet. The strain and strain-rate at any point on the surface of the sheet are presented in local coordinate system which is constructed (by the software) as follows:
Fig. 5. An overview of PNNL’s EHF experimental arrangement.
- A tangent plane is drawn at the point of interest on the sheet. - The local z-axis is normal to the tangent plane. - The local x-axis is the projection of the global x-axis in the tangent plane.
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Table 1 Summary of EHF test results of 1 mm thick 5182-O Al sheet deformed under free- forming conditions. Test name
T-26 T-24 T-28 a
Voltage (V)
5000 6500 7500
Energy (kJ)
9.4 15.8 21.1
Dome height measurements (mm)
Thickness strain at apex (Engineering)a
Max. velocity (m/s)
Calipers
DIC
Calipers
DIC
Loc. 1
Loc. 2
Loc. 3
Loc. 1
Loc. 2
Loc. 3
37.9 40.7 47.5
37.1 40.0 49.0
0.13 0.19 0.22
0.13 0.19 0.23
65 70 94
62 70 83
58 64 100
207 237 271
166 283 383
196 435 664
Max. strain-rate (1/s)
Thickness strain at the apex, measured by the DIC technique, was converted from Lagrangian into engineering strain using Eq. (1).
- The local y-axis is perpendicular to the x-axis and also lies in the tangent plane. The DIC software calculates the strain in Lagrangian formulation and is presented as such in this paper unless indicated otherwise. Lagrangian strain is related to engineering strain by the following relation: Lagrangian exx = Engineering exx +
1 (Engineering exx )2 2
distance of ∼22.5 mm and ∼45 mm from the apex along the x-axis. Table 1 summarizes deformation parameters for various tests and the data from test done at 7500 V is analyzed in the subsequent sections as an example. It is noted that in Figs. 9–11, the electrodes are positioned along the x-axis in the images and each data point in the associated graph represents a camera frame captured during the EHF test.
(1)
Fig. 7 shows photographs of EHF domes, free-formed at 5000, 6500 and 7500 V charging voltages. The dome formed at 6500 V is shown with the speckle pattern cleaned-off around the apex as well as sectioned across the middle (to machine out a specimen from the apex for microstructural examination). Fig. 8 shows the software reconstruction of dome profiles, corresponding to the end of the test and at the indicated time (from the beginning of deformation). The DIC technique allows the deformation history to be obtained for any point on the dome. As an example, the deformation parameters were determined at specific locations identified as locations 1–3. Location 1 refers to the dome apex while locations 2 and 3 lie at a
3.2. Sheet displacement Fig. 9 shows the out-of-plane displacement contours at selected times during the sheet deformation under free forming conditions and at a charging voltage of 7500 V. The contours are generally symmetrical in nature. The graph in Fig. 9 shows the zdisplacement–time history for three locations on the sheet. The data shows that the vertical displacement of the sheet at the end of the test (∼600–650 s from start), as calculated by the DIC software, was ∼50 mm at the dome apex. Similar contours and plots can be obtained for displacements in the x and y directions as well as for tests done at any charging voltage.
Fig. 7. Post-test photographs of the domes that were EHF free-formed at (a) 5000 V, (b) 6500 V and (c) 7500 V.
Fig. 8. Dome profiles reconstructed by the DIC software for the test at (a) 5000 V, (b) 6500 V and (c) 7500 V.
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Fig. 9. z-Displacement (global coordinate system) contours of EHF formed sheet (7500 V) at selected instances during the test with the graph showing the entire displacement–time history for three locations (identified as 1, 2 and 3) on the sheet.
3.3. Sheet velocity Fig. 10 shows the out-of-plane velocity contours at selected times corresponding to the displacement data (7500 V) shown in Fig. 9. The velocity contours are generally symmetrical in nature upto ∼400 s following which (e.g. at t = 503 s) the right half of the sheet undergoes deceleration that is not observed in the remainder of the sheet. The graph in Fig. 10 shows the entire velocity–time history for three locations on the sheet. At these locations, the velocity rises to a maximum by 200–300 s from the start, followed by a decrease. The velocity–time profile at the apex (location 1) shows a double-peak behavior with velocity peaks of ∼94 m/s at ∼207 s and of ∼76 m/s at ∼503 s. On the other hand, location 2 has a broad maximum of 80–90 m/s between 200 and 300 s and location 3 has a single velocity peak of ∼100 m/s at ∼267 s. Similar contours and plots can be obtained for velocity components in the x and y directions as well as for tests done at any charging voltage. The data also shows some velocity oscillations superimposed on the overall velocity–time curve of any given location. As described subsequently, these velocity oscillations are likely due to the pressure-wave reverberations within the EHF chamber. 3.4. Sheet strain (Lagrangian) Fig. 11 shows the strain (exx ) contours at selected times corresponding to the displacement data (7500 V) shown in Fig. 9. Fig. 12 compares the time evolution of exx and eyy strains. Unlike the symmetrical nature of displacement and velocity contours in Figs. 9 and 10, respectively, the exx strain contours (Fig. 11,
t ≥ 400 s) are not symmetrical and show strain concentration that subsequently moves from the right side of the sheet to the apex and to the left of the sheet. The strain–time graph shows that locations 1 and 2 have a similar strain–time history for the duration of the test whereas location 3 deviates from the trend at ∼267 s and accumulates strain at a higher rate than locations 1 or 2. Maximum strain was accumulated at location 2 and was ∼0.15 while location 3 accumulated a total strain of ∼0.09. The rate of strain accumulation is indicated by the maximum strain rate, over the entire test duration, observed at each of the three locations in this test. 3.5. Sheet strain-rate (local coordinate system) Fig. 13 plots the strain-rate (dexx /dt) as a function of strain (exx ) at three locations in the sheet at three different voltages. The data shows that the maximum strain-rates achieved were ∼207, ∼435 and ∼664/s at 5000, 6500 and 7500 V charging voltage, respectively. At any given charging voltage, the maximum was observed at location 3 (except at 5000 V) while location 1 (apex) showed lower strain-rate. The strain-rate vs. strain data in Fig. 13 is characterized by “jumps” in the strain-rate. For example, at 7500 V and location 3, the strain rate rapidly increases to ∼213/s and after a brief interval, rapidly increases to ∼664/s followed by a decrease to ∼524/s and a final decrease at a faster rate. The data in Fig. 13 also shows the strain-rate swings to negative values towards the end of deformation. The minimum strain-rate (i.e. most negative value), though somewhat lower in absolute magnitude, was of similar order of magnitude (∼423/s) as the maximum positive strain-rate (∼664/s).
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Fig. 10. Velocity contours (z-direction in global coordinate system) of EHF formed sheet (7500 V) at selected instances during the test with the graph showing the entire velocity–time history for three locations (identified as 1, 2, 3) on the sheet.
4. Discussion The main goal of this work is to quantify the deformation evolution of sheet metal during EHF. Therefore, unlike the majority of the published literature that relies principally upon post-mortem strain measurements to characterize high-rate forming processes but lacks direct knowledge of deformation history, this work aims to fill-in the information gap by quantifying the in-process deformation parameters. The results obtained in this work are discussed below. 4.1. Overall deformation The DIC technique is a well-known technique in the literature to quantify deformation. However, its use for quantification of 3-d forming and at high strain-rates (such as EHF) has not been reported previously. Therefore, it is important to validate the deformation parameters (e.g. displacement and strain) calculated by the DIC technique against an independent measurement method. The data in Table 1 shows that the dome height and thickness strain at the dome apex are within a few percent of the physically measured (using calipers) values thus, providing a good check of the accuracy of the DIC technique employed in this work. Since DIC is an image-based technique, “good” quality images (sharp, in-focus, and brightly lit) are essential for analysis. Considering that the EHF process results in large (10 s of mm) out-of-plane deformation, it is essential to adjust the optics (focal length, aperture and sheet-tocamera distance) to achieve a large depth-of-field which ensures that the speckle pattern stays in focus during the entire forming event. Further, the high strain-rates and large sample size involved in the EHF process necessitates capturing images at a fast enough
rate and with sufficient pixels to obtain good spatial and time resolution of the process. In the present work, an image size of 256 × 256 pixels and a frame rate of 67,500/s was deemed suitable to represent the EHF process with good fidelity. 4.2. Sheet displacement As expected, the dome height (Table 1) increases with increasing voltage (i.e. increasing energy). The symmetrical nature of displacement contours in Fig. 9 indicates a symmetrical incident pressure-pulse and uniform clamping around the circumference. A rapid increase in displacement–time curves (Fig. 9) can be associated with initial pressure rise upon initiation of the electrical discharge. At the end of the electrical discharge, the amplitude of the pressure-pulse decays resulting in a plateau in the displacement–time curve. However, the slope of the displacement–time curve (i.e. velocity) and the time at which the displacement reaches a plateau, vary with location on the sheet. Hence, the spatial and temporal profiles of the displacement are an indication of the corresponding profiles of the incident pressurepulse. Post-mortem displacement measurements alone cannot be used to determine displacement evolution shown in Fig. 9 nor can they be used to accurately determine the incident pressure profile. 4.3. Sheet velocity Fig. 10 shows the spatial and temporal variations in the velocity. The velocity–time plot for apex shows an interesting double-peak behavior that is not seen at other locations. Further, low-amplitude oscillations are superimposed on overall velocity–time behavior for all the locations. The double-peak behavior (at apex) and the
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Fig. 11. Lagrangian strain contours, exx (local coordinate system), of EHF formed sheet (7500 V) at selected instances during the test with the graph showing the entire strain–time history for three locations (identified as 1, 2, 3) on the sheet.
low-amplitude oscillations arise presumably due to the pressure wave reflections occurring within the EHF chamber. Thus, the position and magnitude of the double-peaks/oscillations are influenced by the boundary conditions i.e. the EHF chamber geometry and the moving sheet. The maximum velocity measured in the EHF experiments in this work is ∼100 m/s (7500 V/∼21 kJ). In the literature, Balanethiram and Daehn (1992) estimated a sheet velocity of ∼300 m/s for IF steel in EHF experiment, Seth et al. (2005) measured velocities in the range of 50–220 m/s for electromagnetically launched steel sheets, Johnson et al. (2009) measured velocities in the range of 50–300 m/s for electromagnetically launched copper and aluminum sheets, and Mercier et al. (2010) measured sheet
Lagrangian Strain
0.2
Test T-28 5182-O Al, 1 mm 7500 V Open symbols: exx Filled symbols: eyy
0.15
4.4. Sheet strain
0.1
0.05
Location 1 (apex) Location 2 Location 3
0 0
200
velocities of ∼300 m/s for explosively driven copper and tantalum spheres. It is not possible to directly compare the absolute magnitudes of the velocities obtained in this work with those reported in the literature owing to differences in test configurations, input energy for deformation, materials tested, specimen geometry and different equipment. Nevertheless, a key contribution of the present work is the ability to determine velocity evolution over the entire viewable area of the specimen whereas the prior work in literature is limited to velocity determination at only a limited number of locations. The ability to determine velocity evolution over an entire large sized specimen is crucial to understand the forming processes that are typically characterized by a spatially varying pressure-pulse and the corresponding deformation field.
400
600
800
Time (µs) Fig. 12. Time evolution of Lagrangian strains (exx and eyy ) at different locations on the EHF formed Al sheet (7500 V).
Analogous to the displacement and velocity data in Figs. 9 and 10, respectively, Fig. 11 shows the temporal and spatial distribution of strain (exx ) during EHF. However, unlike displacement and velocity contours, the strain evolution (t ≥ 400 s) does not seem to occur in a symmetrical manner. Further, while locations 1 and 2 seem to continue accumulating the strain, location 3 appears to undergo reverse straining at ∼489 s. It is interesting to note that maximum strain accumulation occurs at a location (#2) that is not necessarily the location experiencing maximum strain-rate (i.e. location #3). The reasons for the observed non-symmetrical strain distribution are not clear at the moment and are hypothesized to be related to the non-symmetrical nature of the discharge process and/or non-uniformity in the clamping force around the sheet circumference. Fig. 12 compares the time evolution of exx and eyy strains and essentially demonstrates the
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Fig. 13. Strain vs. strain-rate data (local coordinate system) at the three locations on a sheet deformed at the charging voltages shown.
ability to determine the strain tensor (shear strain can also be determined but is not shown) that may be subsequently used to validate numerical models. It is noted that the maximum strains obtained in this work are lower than the strains achieved in prior literature that also used EHF or EMF, as described in the Introduction section. The lower strains in this work are ascribed to differences in capacitor bank response, design of the EHF chamber, discharge process within the EHF chamber and the sheet material properties. Nevertheless, it is emphasized that the goal of the present work is not so much to achieve the high-strains but to characterize the deformation history associated with high-rate forming processes. Such time-evolution of strain and its spatial variations has not been shown in prior literature and could not have been determined by post-mortem strain measurements from the conventional strain gridding technique. Using the strain data from the DIC technique, the equivalent plastic strain at apex was calculated to be ∼0.143, ∼0.213 and ∼0.268 for tests at 5000, 6500 and 7500 V, respectively. Using stress-strain data of 5182 Al by Smerd et al. (2005), the strain energy density (area under the stress-strain curve) for above mentioned equivalent plastic strains is ∼36, 61 and 82 MJ/m3 , respectively. Relative to the test at 5000 V, the strain energy density increases by ∼69% and ∼128% for 6500 and 7500 V tests. Increasing the test voltage from 5000 V to 6500 and 7500 V increases the electrical energy (1/2CV2 ) by 69% and 125%, respectively. Thus, it is interesting to note that the increase in plastic strain at the apex (described by the plastic strain energy at equivalent plastic strain) is almost proportional to the % increase in electrical energy. In other words, the proportion of input electrical energy converted to plastic deformation of the sheet appears to remain constant within the range of energy employed in this work. 4.5. Sheet strain-rate Plotting the sheet deformation data in terms of strain-rate vs. strain, as shown in Fig. 13, provides valuable information on the strain-rates associated with plastic deformation at any given location on the deforming sheet. Such strain-rate information is specially critical in modeling the deformation behavior of strain-rate sensitive materials. Further, such quantitative strainrate data is also critical in addressing the possible causes of extended ductility during sheet metal forming that has typically been attributed to (among other factors) “high” strain-rates by prior researchers, such as Balanethiram and Daehn (1992), Balanethiram and Daehn (1994), Golovashchenko et al. (2003), Golovashchenko and Mamutov (2005), Golovashchenko (2007) and Imbert et al. (2005a) despite the lack of actual strain-rate information. In fact, the data in Fig. 13 demonstrates that ascribing one particular strainrate to the entire sheet and for the entire forming event, as it has been generally done in the existing literature, may not be
correct. Instead, different locations in the sheet may undergo plastic deformation at vastly different strain rates, specially at higher voltages. For example, Fig. 13 shows that while locations 1–3 experienced a majority of deformation at a similar maximum strain rate of ∼200/s at 5000 V, increasing the discharge voltage to 7500 V moved the location of overall maximum strain rate to location 3 where the strain-rate magnitude (∼664/s) was ∼2.5 times that observed at location 1 (∼271/s). Fig. 13 also shows that plastic deformation at locations 2 and 3 (6500 and 7500 V) was associated with non-monotonic variations in strain-rate during the entire test. Therefore, Fig. 13 shows the wealth of information that can be obtained from the data measurement/analysis technique presented here. We believe that such detailed spatial and time dependence of strain-rate is necessary for accurate modeling of sheet deformation during the EHF process as well as an important step towards understanding the mechanisms underlying enhanced formability in sheet metals during high-rate forming processes. 4.6. Applicability to industrial EHF Irrespective of the unique configuration of each EHF setup, the key message of this work is the need to consider spatial and temporal variation of sheet deformation (strain, strain-path, strain-rate) when designing the EHF process. Such consideration of deformation history is necessary to formulate accurate models of the EHF process that should be validated against strain-rates and strainpath in addition to the conventional post-deformation strain. Knowing that formability can be enhanced via strain-rates and strain-path, such appropriately validated models can be invaluable in designing complex parts using appropriately designed tooling and EHF process. Since the characterization technique used in this work is imaging-based, its applicability when forming inside a closed die is quite limited and requires some ingenuity. For example, Rohatgi et al. (2010) have demonstrated the applicability of this technique through the use of a conical die where a hole at the apex (of the conical die) enabled the cameras to image (and quantify) the sheet deformation inside the die. Although the portion of the sheet metal in contact with the die cannot be imaged, deformation history of the non-contacted and visible sheet can still be used to validate mathematical models and subsequently predict the strain, strain-rate and strain-path at the un-imaged locations. Finally, the EHF setup in this work discharged the electrical energy through a copper wire (electrical “short”) bridging the electrodes. Use of a bridge wire helps to amplify the EHF pressure by increasing the conversion efficiency of electrical energy to mechanical (pressure-pulse) energy. However, the test can be conducted with/without the electrical “short” using the same experimental procedure in either case. It is noted that extra time involved in placing a new wire bridge for each sample may not be cost-effective in
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industrial settings and therefore, the EHF process is more likely to be performed by discharging through water/working fluid itself.
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Work is in progress to use the quantitative data, such as that presented in this work, to develop validated models for sheet deformation during the EHF process. Work is also in progress to ascertain the incident pressure-profile that may then be used as an input to the models and predict the deformation behavior as a function of discharge voltage (energy). Finally, experiments are in progress that investigate sheet deformation inside a die and understand the influence of stress-state, strain-path and strain-rates on sheet formability associated with sheet-impact with the die.
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 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.
5. Conclusion
References
4.7. Future work
A combination of high-speed imaging and digital image correlation technique was used to quantify the deformation (displacement, velocity, strain and strain-rate) of 1 mm thick 5182-O Al alloy sheets, deformed under free-forming conditions using the EHF technique. The experimental capability developed in this work provides time and spatial evolution of the deformation over the entire sheet and is a significant improvement over the conventional strain-gridding technique that only provides the post-mortem strain distribution on the sheet. To the authors’ knowledge, such detailed information on sheet deformation evolution in a high-rate forming process, such as EHF, has not been reported before. Based on the experimental conditions of this work, the following conclusions can be drawn pertaining to free-forming deformation of 5182-O Al sheet: A. The Al sheet experienced different strain-rate magnitude and history depending upon the location on the sheet. The maximum strain-rate was ∼207, ∼435 and ∼664/s at discharge voltages of 5000, 6500 and 7500 V, respectively. This maximum strain-rate was observed at a location away from the dome apex (except for 5000 V test). B. With a voltage increase from 5000 V to 7500 V, the maximum strain-rate at the apex showed only a modest increase from 207/s to 271/s. On the other hand, the maximum strain-rate at nonapex location increased by ∼2.4× for the same voltage increase. C. At 5000 V, locations 1–3 experienced similar maximum strainrate. On the other hand, the maximum strain-rate at 6500 and 7500 V was observed at location 3 and not at the apex. Further, the maximum strain-rate at location 3 was found to be ∼1.8× and ∼2.5× greater, relative to the strain-rate at apex, respectively. D. The maximum velocity of the sheet (7500 V) was ∼100 m/s and was observed at a location away from the apex. The velocity–time curves showed repeated oscillations that are attributed to pressure-wave reflections between the sheet and the EHF chamber. Further, the velocity–time curve for apex location showed a double-peak behavior that is likely related to the duration of discharge process and the EHF test geometry. E. The strain-rate vs. strain data shows that the strain accumulation at any given location on the sheet occurs over a range of strain-rates. Further, different locations undergo their own unique strain and strain-rate histories. Such information is specially valuable to model deformation behavior of strain-rate sensitive materials. Acknowledgments The Pacific Northwest National Laboratory is operated by Battelle Memorial Institute for the U.S. Department of Energy under
Badelt, M., Beerwald, C., Brosius, A., Kleiner, M., 2003. Process analysis of electromagnetic sheet metal forming by online-measurement and finite element simulation. In: ESAFORM 2003-6th International Conference on Material Forming , Salerno, Italy, pp. 123–126. 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. Balanethiram, V.S., Hu, X.Y., Altynova, M., Daehn, G.S., 1994. Hyperplasticity— enhanced formability at high-rates. J. Mater. Process. Technol. 45, 595– 600. Daehn, G.S., 2006. High-velocity metal forming. In: Semiatin, S.L. (Ed.), ASM Handbook, Metalworking: Sheet Forming. ASM International, Materials Park, Ohio, pp. 405–418. Fenton, G.K., Daehn, G.S., 1998. Modeling of electromagnetically formed sheet metal. J. Mater. Process. Technol. 75, 6–16. Golovashchenko, S.F., 2007. Material formability and coil design in electromagnetic forming. J. Mater. Eng. Perform. 16, 314–320. Golovashchenko, S.F., Gillard, A.J., Cedar, D.A., Illnich, A.M., 2009. Electrohydraulic forming tool. United States Patent 7516634 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 2003. 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. TMS, Warrendale, PA, pp. 65–70. Imbert, J., Worswick, M., Winkler, S., Golovashchenko, S., Dmitriev, V., 2005a. Analysis of the increased formability of aluminum alloy sheet formed using electromagnetic forming, 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. Johnson, J.R., Taber, G., Vivek, A., Zhang, Y., Golowin, S., Banik, K., Fenton, G.K., Daehn, G.S., 2009. Coupling experiment and simulation in electromagnetic forming using photon doppler velocimetry. Steel Res. Int. 80, 359–365. Mercier, S., Granier, N., Molinari, A., Llorca, F., Buy, F., 2010. Multiple necking during the dynamic expansion of hemispherical metallic shells, from experiments to modelling. J. Mech. Phys. Solids 58, 955–982. Oliveira, D.A, Worswick, M., 2003. Electromagnetic forming of aluminium alloy sheet. J. Phys. IV 110, 293–298. 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. Seth, M., Vohnout, V.J., Daehn, G.S., 2005. Formability of steel sheet in high velocity impact. J. Mater. Process. Technol. 168, 390–400. Smerd, R., Winkler, S., Salisbury, C., Worswick, M., Lloyd, D., Finn, M., 2005. High strain rate tensile testing of automotive aluminum alloy sheet. Int. J. Impact Eng. 32, 541–560. Taylor, B., 1988. Formability testing of sheet metals. In: Metals Handbook—Forming and Forging, 9 ed. ASM International, Metals Park, Ohio, pp. 877–879. USCAR, http://www.uscar.org/guest/partnership/1/freedomcar-fuel-partnership (accessed on 19th September 2010). USDOE, 2006. FreedomCAR and Fuel Partnership Plan, downloaded on: 17th September 2010 from http://www1.eere.energy.gov/vehiclesandfuels/about/ partnerships/freedomcar/index.html. Wielage, H., Vollertsen, F., 2011. Classification of laser shock forming within the field of high speed forming processes. J. Mater. Process. Technol. 211, 953– 957.
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Journal of Materials Processing Technology journal homepage: www.elsevier.com/locate/jmatprotec
Experimental characterization of sheet metal deformation during electro-hydraulic forming夽 Aashish Rohatgi ∗ , Elizabeth V. Stephens, Ayoub Soulami, Richard W. Davies, Mark T. Smith Pacific Northwest National Laboratory (PNNL), 902 Battelle Boulevard, P.O. Box 999, Richland, WA 99352, USA
a r t i c l e
i n f o
Article history: Received 16 March 2011 Received in revised form 1 June 2011 Accepted 4 June 2011 Available online 12 June 2011 Keywords: Electro-hydraulic forming High strain-rate Formability Digital image correlation Light-weight Automotive
a b s t r a c t A novel experimental technique, that combines high-speed imaging and digital image correlation techniques, has been developed and applied to investigate the high-rate deformation behavior of aluminum sheet during electro-hydraulic forming (EHF). Aluminum alloy AA5182-O sheets (1 mm thick and ∼152 mm diameter) were EHF deformed by high-energy (up to ∼21 kJ) pressure-pulse and the timeevolution of sheet-displacement, velocity, strain and strain-rate quantified. The data shows that different locations on the sheet undergo unique deformation history that is not apparent from the conventional post-mortem strain measurement (using etched circle/grid pattern) approach. Under the experimental conditions used in this work, the sheets were formed into domes and the maximum strain-rate observed was ∼664/s. Further, this maximum strain-rate was observed at an off-apex location and was ∼2.5 times greater than the maximum strain-rate at the dome apex. The maximum velocity observed was ∼100 m/s and the velocity–time data showed evidence of pressure-wave reverberations during the forming process. We believe that knowledge of such time-evolution of sheet deformation is necessary for a better understanding and accurate modeling of sheet formability that has often been reported to exceed quasi-static forming limits under high-rate forming conditions. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Our group at the Pacific Northwest National Laboratory is involved in research with the overarching theme of automotive weight reduction in support of the US DOE and the FreedomCAR and Fuel Partnership (USCAR) efforts to reduce a car’s weight by 50%, as outlined in their Plan (USDOE, 2006). While the goal of automotive weight reduction through the use of low-density metals such as aluminum (Al) and magnesium (Mg) alloys has been pursued for many years, mild steel is still the predominant choice for body-in-white and automotive closure panels owing to its better room-temperature formability than Al or Mg sheets. The use of
夽 Disclaimer: This manuscript has been authored by Battelle Memorial Institute, Pacific Northwest Division, under Contract No. DE-AC05-76RL01830 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. ∗ Corresponding author. Tel.: +1 509 372 6047; fax: +1 509 375 4448. E-mail addresses: [email protected] (A. Rohatgi), [email protected] (E.V. Stephens), [email protected] (A. Soulami), [email protected] (R.W. Davies), [email protected] (M.T. Smith). 0924-0136/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2011.06.005
advanced high-strength steels (AHSS) such as dual-phase steels, and conventional high-strength steels (HSS) can also contribute to automotive lightweighting by enabling use of thinner gauge sheets that have equivalent strength as thicker gauge (thus, heavier) mild steel. However, AHSS too suffer from poor formability compared to mild steel thus, limiting their deployment for automotive lightweighting. For example, Golovashchenko et al. (2009) noted that the room-temperature formability of aluminum alloys and AHSS under plane-strain conditions typically does not exceed ∼25% and ∼30%, respectively, while the same figure for deep drawing quality (DDQ) steel exceeds 45%. Therefore, there is a need to develop techniques to successfully form materials such as Al, Mg, AHSS and HSS, preferably at room temperature, for cost-effective automotive lightweighting. High strain-rates have been shown to enhance the formability (relative to formability at quasi-static strain-rates) of sheet metal in many instances. High strain-rates for sheet forming are typically obtained by techniques such as explosive forming, electrohydraulic forming (EHF) and electro-magnetic forming (EMF). Such high-strain-rate forming techniques may also incur lower tooling costs due to the elimination of matching die which is, instead, replaced by the impulse force generated by an explosive (explosive forming), electromagnetic repulsion (EMF) or electrical discharge (EHF). Several authors, e.g. Balanethiram et al. (1994), Fenton and Daehn (1998) and Golovashchenko et al. (2003), also cite lower
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spring-back as an advantage of high-strain-rate forming. Hence, owing to their potential to successfully form low-formability metals at room temperature, such as Al, HSS and AHSS, with additional benefits of reduced tooling costs and minimal/no spring-back, high-strain-rate forming techniques are of great interest to the automotive industry. The reader is referred to a recent review by Daehn (2006) of various high-rate forming techniques. Although explosive forming is one of the earliest high-rate forming techniques, handling explosives for routine research is not feasible. Therefore, majority of recent formability-related research has employed EHF and EMF techniques. For example, Balanethiram and Daehn (1992) deformed interstitial free (IF) iron into a conical die (90◦ apex angle) using EHF technique and measured engineering plane-strains on the order of ∼160% near the fracture region and ∼120% away from the fracture; the corresponding quasi-static strains in IF iron are on the order of 30–40%. Using the same EHF procedure as before, the same authors in a subsequent publication (Balanethiram and Daehn, 1994) observed large plane-strains near failure in 6061-T4 aluminum (engineering strain ∼120–130% at high-rate vs. ∼20% at quasi-static rates) and in oxygen-free highconductivity copper (engineering strain ∼100% at high-rates vs. ∼30% at quasi-static rates). Seth et al. (2005) used EMF to impact steel sheets on axisymmetric and wedge-shaped dies and measured engineering plane-strains at failure to be ∼50–60% as compared to ∼10% under quasi-static deformation. Golovashchenko et al. (2003) compared the rate-dependence of formability of several materials (Al, Cu, steel and Ti alloys) and observed that EHF into an open die (free-forming) could increase the local deformation by 40–90%. Golovashchenko et al. (2003) also observed higher failure strains (∼60% strain at high-rates vs. ∼25% at quasi-static rates) in 6111T4 Al when using the EMF technique and forming the Al sheet into a V-shaped die. Imbert et al. (2005b) investigated EMF of AA5754 sheet into an open die (free-forming) and a conical die (112◦ apex angle) and observed maximum strains on the order of ∼35–45% at high rates as compared to quasi-static strains of 20–30%. In another study, Imbert et al. (2005a) measured maximum engineering strains of ∼65% for AA5754 formed by the EMF technique into a conical die (100◦ apex angle) as compared to quasi-static strains of ∼20–30%. Oliveira and Worswick (2003) measured maximum engineering strains of ∼40–50% when forming AA5754 by EMF into a rectangular die. Thus, the observation of increased formability at high strain-rates has been generally established in the literature. However, as will be described subsequently, the quantification of deformation history of the sheet metal, subjected to high-rate deformation, has not been clearly established and is the topic of this paper. The formability in high-rate deformed sheets is typically determined by measuring strains using the circle grid analysis, as outlined by Taylor (1988). While this strain-measuring technique determines the final strain distribution in the deformed sheet, it is unable to determine the strain and strain-rate history at different sheet locations. Consequently, there is lack of in-process deformation behavior in the literature, which, in authors’ opinion, has led to a lack of consensus on the mechanisms responsible for the enhanced-formability in sheet metals. For example, Balanethiram and Daehn (1992) estimated a sheet velocity of 300 m/s and a strain rate of ∼1050/s during EHF of IF steel sheet and attributed formability improvement to inertial stabilization on account of high velocity. In another publication, similar velocity and (some-what lower) strain rate estimates, as well as conclusions were reached by the same authors (Balanethiram and Daehn, 1994) for EHF tested 6061-T4 Al and OFHC Cu. Seth et al. (2005) experimentally measured the impact velocity of steel sheets on a steel punch (though strains were still measured by the etched-circle technique (Taylor, 1988) and attributed the enhanced formability to inertial stabilization and compressive stresses generated during impact. Other
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authors, such as Golovashchenko et al. (2003), Golovashchenko and Mamutov (2005) and Golovashchenko (2007), determined only the post-mortem strain (via the circle-etching technique) in EMF and EHF experiments and attributed improved sheet formability to high strain-rates and high-rate impact with the tooling even though the strain and strain-rate history of the deforming sheet were unknown. Imbert et al. (2005a) numerically modeled EMF of Al alloy sheet and concluded that high-strain rates (estimated to be on the order of 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 well as non-linear strain-paths were the responsible factors. However, Imbert et al. (2005a) noted that such conclusions about extremely high strainrates and strain-path need to be validated experimentally. Finally, modeling efforts, such as those by Oliveira and Worswick (2003) tend to validate their numerical models using final strain distribution as the key criterion but neglect the prior strain and strain-rate history owing to the lack of corresponding experimental data. Only recently has some progress been reported in obtaining deformation-history from high-rate forming experiments. Badelt et al. (2003) used contact-pins and laser-shadow methods to determine displacement–time history of individual locations on a sheet during electromagnetic forming. However, their method was unsuitable for direct measurement of strains and strain-rates and necessitated the use of mathematical modeling to estimate the same. Johnson et al. (2009) used Photon Doppler Velocimetry technique in electromagnetically expanding ring experiment to determine in-process velocity vs. time at four locations. However, Johnson et al. (2009) did not demonstrate the actual strain or strain-rate history for the expanding rings from this data. Mercier et al. (2010) used VISAR and Doppler Laser Fabry-Pérot Interferometry technique to measure velocity (at 3 locations) during explosive-driven expansion of tantalum and copper hemispheres, respectively. Again, experimental strain or strain-rates could not be determined by their (Mercier et al., 2010) method. Finally, Wielage and Vollertsen (2011) used high-speed imaging to determine velocity of laser shock formed metal foils (20–50 m thick). Owing to the simple bending geometry employed in this work, the authors (Wielage and Vollertsen, 2011) used geometrical arguments to estimate the total bending strain and the corresponding strain-rate. Thus, it is concluded that prior research has principally relied upon final strain measurements, estimated strain-rates and numerical models to postulate mechanisms responsible for enhanced formability. Further, the numerical models themselves are validated by the post-mortem strain measurements and neglect the prior strain and strain-rate history. Therefore, the primary objective of this work is to quantify the in-process strain and strain-rates and improve our understanding of high-strain-rate forming events. The technique selected for this work is EHF owing to its applicability (unlike EMF technique) to both high conductivity (e.g. Al) as well as low-conductivity (e.g. steel and magnesium) sheets. The work presented below describes the equipment, measurement techniques and results obtained for high-strain-rate forming of Al sheets. It is anticipated that this research will contribute to our understanding of the high-rate deformation behavior through experimental determination of strain and strain-rate history of deforming sheets and help elucidate the mechanisms responsible for enhanced formability while helping validate the numerical models.
2. Experimental procedure A key contribution of this paper is the quantification of the inprocess deformation parameters (displacement, velocity, strain and
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Fig. 1. Schematic representation of PNNL’s EHF setup showing the initial (undeformed) and the final (deformed) positions of the sheet.
strain-rate) that have typically been unknown, or estimated at the best, in the literature. The quantification method, as well as the equipment and the test procedures employed in this research are described below; additional details are described in a prior publication (Rohatgi et al., 2010). 2.1. Quantification of sheet deformation behavior Overall, the approach comprised painting a speckle pattern on the undeformed metal sheet. The sheet was then deformed via EHF and the deformation process was imaged by a pair of highspeed cameras. The images of the deforming sheet were captured and post-processed by the digital image correlation (DIC) software to calculate the displacement, velocity, strain and strain-rate, as a function of time, at any given point on the sheet. Digital image correlation is an optical method to measure deformation on an object surface. This method uses white-light speckle correlation to measure deformation in each image of an image sequence where any two consecutive speckled images, captured by a video camera, represent the incremental stages during the deformation process. In this project, digital image correlation software (Vic-3d, Version 2009.1.0) from Correlated Solutions, Inc., in conjunction with the image sequence captured by the high-speed cameras, was used to quantify the in-process sheet displacement, velocity, strain and strain-rate, as a function of time. A software calibration was performed at the start of the experiments by imaging a pre-measured geometrical test-pattern using the cameras. This calibration essentially defines the cameras’ orientation in space, relative to each other. Following calibration, the cameras position was held fixed such that the sheet deformation was imaged without disturbing the camera’s relative orientation to each other. Thus, when the software analyzes the images of the sheet, captured during the EHF test and representing sequential stages of its deformation, the software is able to quantify the displacement of the speckles in the image sequence and the strain tensor can be determined at any point on the sheet surface. Knowing the inprocess displacement and image capture rate, the velocity, strain, and strain-rate at each point on the sheet 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.
Fig. 2. Photograph of PNNL’s EHF fixture.
inserted through the chamber walls. The electrodes were copper rods, 6.35 mm in diameter with a gap of ∼11.5 mm between the two ends. A thin copper wire was used to join the electrode ends, thus, creating an electrical “short” between the electrodes. External to the chamber, the copper electrodes were connected to a capacitor bank with ∼2.44 m (8 ft.) long cables and a program written in LabView software was used to control the charge–discharge process. For a given charge voltage V, the electrical energy input was calculated as 1/2CV2 where C is the capacitance (750 F) of the bank. The voltage at the positive electrode at the EHF chamber was measured using a single-ended high voltage probe (Tektronix P6015A with ∼7.62 m (25 ft.) cable and a 1000× attenuator) and Tektronix oscilloscope model TDS3034B. The discharge currents were measured by Rogowski coils and recorded by the data acquisition system. The chamber was filled with water prior to each test. 2.3. Specimen preparation and boundary conditions The sheet metal tested in this work was 1 mm thick 5182-O aluminum. Typical specimen geometry is shown in Fig. 3. One face
2.2. Electro-hydraulic forming apparatus and instrumentation A schematic of PNNL’s EHF setup is shown in Fig. 1 and a close-up photograph of the EHF fixture is shown in Fig. 2. The EHF fixture was machined out of steel and consisted of a hemispherical cavity (∼152 mm diameter) with two opposing electrodes
Fig. 3. A schematic of the EHF sheet specimen geometry.
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Fig. 6. A photograph of an EHF-deformed sheet. Some water has leaked out from the hemi-spherical chamber owing to fracture (not visible) in the sheet.
the final deformed shape of the sheet was in the form of a dome, as shown in Fig. 6. The center of the 152 mm circular portion of the undeformed sheet was marked and is referred to as the “apex” in subsequent discussion. Fig. 4. A top view of an undeformed speckle patterned sheet clamped in the EHF fixture.
of the sheet specimens was speckle-patterned by spray-painting it with white automotive paint and then creating a random pattern of spots with a black-color marker (Fig. 4). The sheet was bolted to the EHF chamber (Fig. 2) through a hold-down ring with the speckled face facing the cameras and illuminated by several highintensity lights (Fig. 5). This testing configuration is referred to as “free-forming” in that the sheet is constrained circumferentially by a ring and a central region (∼152 mm diameter) of the sheet is free to deform when subjected to the pulse-pressure wave originating from the underlying hemispherical EHF chamber. Consequently,
2.4. High-speed camera imaging A pair of Photron SA1 high-speed cameras was used to capture the sheet deformation at a frame rate of 67,500/s and at an image resolution of 256 × 256 pixels. The cameras were simultaneously triggered to capture the images when the capacitor banks were discharged to initiate the EHF process. At the end of the test, the image sequence corresponding to the sheet deformation was saved on the computer for subsequent image analysis. 2.5. Conducting the electro-hydraulic forming test The EHF chamber was filled with tap-water and the specklepatterned sheet clamped over it ensuring that there was no air gap between the water and the sheet bottom. The capacitor bank was charged to the desired voltage (energy) and discharged immediately upon reaching the set voltage level. The capacitor discharge results in large currents (10 s of KA) to flow through the copper wire that result in its rapid melting, vaporization and expansion, thus, leading to a pressure-pulse. Tests were conducted at voltages of 5000, 6500 and 7500 V corresponding to an energy (stored in the capacitor banks) of ∼9.4, 15.8 and 21.1 kJ. The entire deformation event for each test was captured by the high-speed cameras and the images were stored for subsequent analysis. Table 1 lists the experimental details for various tests. Table 1 also compares the physically measured dome height (measured relative to the top surface of the undeformed portion of the test sheet) and thickness strain at the apex relative to those calculated by the image analysis DIC software. 3. Results 3.1. Coordinate system and quantification of sheet deformation The displacements and velocity of any point on the sheet were calculated by the DIC software in the global coordinate system i.e. the x and y axes correspond to the horizontal and vertical direction in the 2-dimensional camera images while z-axis is normal to the plane of the image and corresponds to the normal to undeformed Al sheet. The strain and strain-rate at any point on the surface of the sheet are presented in local coordinate system which is constructed (by the software) as follows:
Fig. 5. An overview of PNNL’s EHF experimental arrangement.
- A tangent plane is drawn at the point of interest on the sheet. - The local z-axis is normal to the tangent plane. - The local x-axis is the projection of the global x-axis in the tangent plane.
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Table 1 Summary of EHF test results of 1 mm thick 5182-O Al sheet deformed under free- forming conditions. Test name
T-26 T-24 T-28 a
Voltage (V)
5000 6500 7500
Energy (kJ)
9.4 15.8 21.1
Dome height measurements (mm)
Thickness strain at apex (Engineering)a
Max. velocity (m/s)
Calipers
DIC
Calipers
DIC
Loc. 1
Loc. 2
Loc. 3
Loc. 1
Loc. 2
Loc. 3
37.9 40.7 47.5
37.1 40.0 49.0
0.13 0.19 0.22
0.13 0.19 0.23
65 70 94
62 70 83
58 64 100
207 237 271
166 283 383
196 435 664
Max. strain-rate (1/s)
Thickness strain at the apex, measured by the DIC technique, was converted from Lagrangian into engineering strain using Eq. (1).
- The local y-axis is perpendicular to the x-axis and also lies in the tangent plane. The DIC software calculates the strain in Lagrangian formulation and is presented as such in this paper unless indicated otherwise. Lagrangian strain is related to engineering strain by the following relation: Lagrangian exx = Engineering exx +
1 (Engineering exx )2 2
distance of ∼22.5 mm and ∼45 mm from the apex along the x-axis. Table 1 summarizes deformation parameters for various tests and the data from test done at 7500 V is analyzed in the subsequent sections as an example. It is noted that in Figs. 9–11, the electrodes are positioned along the x-axis in the images and each data point in the associated graph represents a camera frame captured during the EHF test.
(1)
Fig. 7 shows photographs of EHF domes, free-formed at 5000, 6500 and 7500 V charging voltages. The dome formed at 6500 V is shown with the speckle pattern cleaned-off around the apex as well as sectioned across the middle (to machine out a specimen from the apex for microstructural examination). Fig. 8 shows the software reconstruction of dome profiles, corresponding to the end of the test and at the indicated time (from the beginning of deformation). The DIC technique allows the deformation history to be obtained for any point on the dome. As an example, the deformation parameters were determined at specific locations identified as locations 1–3. Location 1 refers to the dome apex while locations 2 and 3 lie at a
3.2. Sheet displacement Fig. 9 shows the out-of-plane displacement contours at selected times during the sheet deformation under free forming conditions and at a charging voltage of 7500 V. The contours are generally symmetrical in nature. The graph in Fig. 9 shows the zdisplacement–time history for three locations on the sheet. The data shows that the vertical displacement of the sheet at the end of the test (∼600–650 s from start), as calculated by the DIC software, was ∼50 mm at the dome apex. Similar contours and plots can be obtained for displacements in the x and y directions as well as for tests done at any charging voltage.
Fig. 7. Post-test photographs of the domes that were EHF free-formed at (a) 5000 V, (b) 6500 V and (c) 7500 V.
Fig. 8. Dome profiles reconstructed by the DIC software for the test at (a) 5000 V, (b) 6500 V and (c) 7500 V.
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Fig. 9. z-Displacement (global coordinate system) contours of EHF formed sheet (7500 V) at selected instances during the test with the graph showing the entire displacement–time history for three locations (identified as 1, 2 and 3) on the sheet.
3.3. Sheet velocity Fig. 10 shows the out-of-plane velocity contours at selected times corresponding to the displacement data (7500 V) shown in Fig. 9. The velocity contours are generally symmetrical in nature upto ∼400 s following which (e.g. at t = 503 s) the right half of the sheet undergoes deceleration that is not observed in the remainder of the sheet. The graph in Fig. 10 shows the entire velocity–time history for three locations on the sheet. At these locations, the velocity rises to a maximum by 200–300 s from the start, followed by a decrease. The velocity–time profile at the apex (location 1) shows a double-peak behavior with velocity peaks of ∼94 m/s at ∼207 s and of ∼76 m/s at ∼503 s. On the other hand, location 2 has a broad maximum of 80–90 m/s between 200 and 300 s and location 3 has a single velocity peak of ∼100 m/s at ∼267 s. Similar contours and plots can be obtained for velocity components in the x and y directions as well as for tests done at any charging voltage. The data also shows some velocity oscillations superimposed on the overall velocity–time curve of any given location. As described subsequently, these velocity oscillations are likely due to the pressure-wave reverberations within the EHF chamber. 3.4. Sheet strain (Lagrangian) Fig. 11 shows the strain (exx ) contours at selected times corresponding to the displacement data (7500 V) shown in Fig. 9. Fig. 12 compares the time evolution of exx and eyy strains. Unlike the symmetrical nature of displacement and velocity contours in Figs. 9 and 10, respectively, the exx strain contours (Fig. 11,
t ≥ 400 s) are not symmetrical and show strain concentration that subsequently moves from the right side of the sheet to the apex and to the left of the sheet. The strain–time graph shows that locations 1 and 2 have a similar strain–time history for the duration of the test whereas location 3 deviates from the trend at ∼267 s and accumulates strain at a higher rate than locations 1 or 2. Maximum strain was accumulated at location 2 and was ∼0.15 while location 3 accumulated a total strain of ∼0.09. The rate of strain accumulation is indicated by the maximum strain rate, over the entire test duration, observed at each of the three locations in this test. 3.5. Sheet strain-rate (local coordinate system) Fig. 13 plots the strain-rate (dexx /dt) as a function of strain (exx ) at three locations in the sheet at three different voltages. The data shows that the maximum strain-rates achieved were ∼207, ∼435 and ∼664/s at 5000, 6500 and 7500 V charging voltage, respectively. At any given charging voltage, the maximum was observed at location 3 (except at 5000 V) while location 1 (apex) showed lower strain-rate. The strain-rate vs. strain data in Fig. 13 is characterized by “jumps” in the strain-rate. For example, at 7500 V and location 3, the strain rate rapidly increases to ∼213/s and after a brief interval, rapidly increases to ∼664/s followed by a decrease to ∼524/s and a final decrease at a faster rate. The data in Fig. 13 also shows the strain-rate swings to negative values towards the end of deformation. The minimum strain-rate (i.e. most negative value), though somewhat lower in absolute magnitude, was of similar order of magnitude (∼423/s) as the maximum positive strain-rate (∼664/s).
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Fig. 10. Velocity contours (z-direction in global coordinate system) of EHF formed sheet (7500 V) at selected instances during the test with the graph showing the entire velocity–time history for three locations (identified as 1, 2, 3) on the sheet.
4. Discussion The main goal of this work is to quantify the deformation evolution of sheet metal during EHF. Therefore, unlike the majority of the published literature that relies principally upon post-mortem strain measurements to characterize high-rate forming processes but lacks direct knowledge of deformation history, this work aims to fill-in the information gap by quantifying the in-process deformation parameters. The results obtained in this work are discussed below. 4.1. Overall deformation The DIC technique is a well-known technique in the literature to quantify deformation. However, its use for quantification of 3-d forming and at high strain-rates (such as EHF) has not been reported previously. Therefore, it is important to validate the deformation parameters (e.g. displacement and strain) calculated by the DIC technique against an independent measurement method. The data in Table 1 shows that the dome height and thickness strain at the dome apex are within a few percent of the physically measured (using calipers) values thus, providing a good check of the accuracy of the DIC technique employed in this work. Since DIC is an image-based technique, “good” quality images (sharp, in-focus, and brightly lit) are essential for analysis. Considering that the EHF process results in large (10 s of mm) out-of-plane deformation, it is essential to adjust the optics (focal length, aperture and sheet-tocamera distance) to achieve a large depth-of-field which ensures that the speckle pattern stays in focus during the entire forming event. Further, the high strain-rates and large sample size involved in the EHF process necessitates capturing images at a fast enough
rate and with sufficient pixels to obtain good spatial and time resolution of the process. In the present work, an image size of 256 × 256 pixels and a frame rate of 67,500/s was deemed suitable to represent the EHF process with good fidelity. 4.2. Sheet displacement As expected, the dome height (Table 1) increases with increasing voltage (i.e. increasing energy). The symmetrical nature of displacement contours in Fig. 9 indicates a symmetrical incident pressure-pulse and uniform clamping around the circumference. A rapid increase in displacement–time curves (Fig. 9) can be associated with initial pressure rise upon initiation of the electrical discharge. At the end of the electrical discharge, the amplitude of the pressure-pulse decays resulting in a plateau in the displacement–time curve. However, the slope of the displacement–time curve (i.e. velocity) and the time at which the displacement reaches a plateau, vary with location on the sheet. Hence, the spatial and temporal profiles of the displacement are an indication of the corresponding profiles of the incident pressurepulse. Post-mortem displacement measurements alone cannot be used to determine displacement evolution shown in Fig. 9 nor can they be used to accurately determine the incident pressure profile. 4.3. Sheet velocity Fig. 10 shows the spatial and temporal variations in the velocity. The velocity–time plot for apex shows an interesting double-peak behavior that is not seen at other locations. Further, low-amplitude oscillations are superimposed on overall velocity–time behavior for all the locations. The double-peak behavior (at apex) and the
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Fig. 11. Lagrangian strain contours, exx (local coordinate system), of EHF formed sheet (7500 V) at selected instances during the test with the graph showing the entire strain–time history for three locations (identified as 1, 2, 3) on the sheet.
low-amplitude oscillations arise presumably due to the pressure wave reflections occurring within the EHF chamber. Thus, the position and magnitude of the double-peaks/oscillations are influenced by the boundary conditions i.e. the EHF chamber geometry and the moving sheet. The maximum velocity measured in the EHF experiments in this work is ∼100 m/s (7500 V/∼21 kJ). In the literature, Balanethiram and Daehn (1992) estimated a sheet velocity of ∼300 m/s for IF steel in EHF experiment, Seth et al. (2005) measured velocities in the range of 50–220 m/s for electromagnetically launched steel sheets, Johnson et al. (2009) measured velocities in the range of 50–300 m/s for electromagnetically launched copper and aluminum sheets, and Mercier et al. (2010) measured sheet
Lagrangian Strain
0.2
Test T-28 5182-O Al, 1 mm 7500 V Open symbols: exx Filled symbols: eyy
0.15
4.4. Sheet strain
0.1
0.05
Location 1 (apex) Location 2 Location 3
0 0
200
velocities of ∼300 m/s for explosively driven copper and tantalum spheres. It is not possible to directly compare the absolute magnitudes of the velocities obtained in this work with those reported in the literature owing to differences in test configurations, input energy for deformation, materials tested, specimen geometry and different equipment. Nevertheless, a key contribution of the present work is the ability to determine velocity evolution over the entire viewable area of the specimen whereas the prior work in literature is limited to velocity determination at only a limited number of locations. The ability to determine velocity evolution over an entire large sized specimen is crucial to understand the forming processes that are typically characterized by a spatially varying pressure-pulse and the corresponding deformation field.
400
600
800
Time (µs) Fig. 12. Time evolution of Lagrangian strains (exx and eyy ) at different locations on the EHF formed Al sheet (7500 V).
Analogous to the displacement and velocity data in Figs. 9 and 10, respectively, Fig. 11 shows the temporal and spatial distribution of strain (exx ) during EHF. However, unlike displacement and velocity contours, the strain evolution (t ≥ 400 s) does not seem to occur in a symmetrical manner. Further, while locations 1 and 2 seem to continue accumulating the strain, location 3 appears to undergo reverse straining at ∼489 s. It is interesting to note that maximum strain accumulation occurs at a location (#2) that is not necessarily the location experiencing maximum strain-rate (i.e. location #3). The reasons for the observed non-symmetrical strain distribution are not clear at the moment and are hypothesized to be related to the non-symmetrical nature of the discharge process and/or non-uniformity in the clamping force around the sheet circumference. Fig. 12 compares the time evolution of exx and eyy strains and essentially demonstrates the
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Fig. 13. Strain vs. strain-rate data (local coordinate system) at the three locations on a sheet deformed at the charging voltages shown.
ability to determine the strain tensor (shear strain can also be determined but is not shown) that may be subsequently used to validate numerical models. It is noted that the maximum strains obtained in this work are lower than the strains achieved in prior literature that also used EHF or EMF, as described in the Introduction section. The lower strains in this work are ascribed to differences in capacitor bank response, design of the EHF chamber, discharge process within the EHF chamber and the sheet material properties. Nevertheless, it is emphasized that the goal of the present work is not so much to achieve the high-strains but to characterize the deformation history associated with high-rate forming processes. Such time-evolution of strain and its spatial variations has not been shown in prior literature and could not have been determined by post-mortem strain measurements from the conventional strain gridding technique. Using the strain data from the DIC technique, the equivalent plastic strain at apex was calculated to be ∼0.143, ∼0.213 and ∼0.268 for tests at 5000, 6500 and 7500 V, respectively. Using stress-strain data of 5182 Al by Smerd et al. (2005), the strain energy density (area under the stress-strain curve) for above mentioned equivalent plastic strains is ∼36, 61 and 82 MJ/m3 , respectively. Relative to the test at 5000 V, the strain energy density increases by ∼69% and ∼128% for 6500 and 7500 V tests. Increasing the test voltage from 5000 V to 6500 and 7500 V increases the electrical energy (1/2CV2 ) by 69% and 125%, respectively. Thus, it is interesting to note that the increase in plastic strain at the apex (described by the plastic strain energy at equivalent plastic strain) is almost proportional to the % increase in electrical energy. In other words, the proportion of input electrical energy converted to plastic deformation of the sheet appears to remain constant within the range of energy employed in this work. 4.5. Sheet strain-rate Plotting the sheet deformation data in terms of strain-rate vs. strain, as shown in Fig. 13, provides valuable information on the strain-rates associated with plastic deformation at any given location on the deforming sheet. Such strain-rate information is specially critical in modeling the deformation behavior of strain-rate sensitive materials. Further, such quantitative strainrate data is also critical in addressing the possible causes of extended ductility during sheet metal forming that has typically been attributed to (among other factors) “high” strain-rates by prior researchers, such as Balanethiram and Daehn (1992), Balanethiram and Daehn (1994), Golovashchenko et al. (2003), Golovashchenko and Mamutov (2005), Golovashchenko (2007) and Imbert et al. (2005a) despite the lack of actual strain-rate information. In fact, the data in Fig. 13 demonstrates that ascribing one particular strainrate to the entire sheet and for the entire forming event, as it has been generally done in the existing literature, may not be
correct. Instead, different locations in the sheet may undergo plastic deformation at vastly different strain rates, specially at higher voltages. For example, Fig. 13 shows that while locations 1–3 experienced a majority of deformation at a similar maximum strain rate of ∼200/s at 5000 V, increasing the discharge voltage to 7500 V moved the location of overall maximum strain rate to location 3 where the strain-rate magnitude (∼664/s) was ∼2.5 times that observed at location 1 (∼271/s). Fig. 13 also shows that plastic deformation at locations 2 and 3 (6500 and 7500 V) was associated with non-monotonic variations in strain-rate during the entire test. Therefore, Fig. 13 shows the wealth of information that can be obtained from the data measurement/analysis technique presented here. We believe that such detailed spatial and time dependence of strain-rate is necessary for accurate modeling of sheet deformation during the EHF process as well as an important step towards understanding the mechanisms underlying enhanced formability in sheet metals during high-rate forming processes. 4.6. Applicability to industrial EHF Irrespective of the unique configuration of each EHF setup, the key message of this work is the need to consider spatial and temporal variation of sheet deformation (strain, strain-path, strain-rate) when designing the EHF process. Such consideration of deformation history is necessary to formulate accurate models of the EHF process that should be validated against strain-rates and strainpath in addition to the conventional post-deformation strain. Knowing that formability can be enhanced via strain-rates and strain-path, such appropriately validated models can be invaluable in designing complex parts using appropriately designed tooling and EHF process. Since the characterization technique used in this work is imaging-based, its applicability when forming inside a closed die is quite limited and requires some ingenuity. For example, Rohatgi et al. (2010) have demonstrated the applicability of this technique through the use of a conical die where a hole at the apex (of the conical die) enabled the cameras to image (and quantify) the sheet deformation inside the die. Although the portion of the sheet metal in contact with the die cannot be imaged, deformation history of the non-contacted and visible sheet can still be used to validate mathematical models and subsequently predict the strain, strain-rate and strain-path at the un-imaged locations. Finally, the EHF setup in this work discharged the electrical energy through a copper wire (electrical “short”) bridging the electrodes. Use of a bridge wire helps to amplify the EHF pressure by increasing the conversion efficiency of electrical energy to mechanical (pressure-pulse) energy. However, the test can be conducted with/without the electrical “short” using the same experimental procedure in either case. It is noted that extra time involved in placing a new wire bridge for each sample may not be cost-effective in
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industrial settings and therefore, the EHF process is more likely to be performed by discharging through water/working fluid itself.
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Work is in progress to use the quantitative data, such as that presented in this work, to develop validated models for sheet deformation during the EHF process. Work is also in progress to ascertain the incident pressure-profile that may then be used as an input to the models and predict the deformation behavior as a function of discharge voltage (energy). Finally, experiments are in progress that investigate sheet deformation inside a die and understand the influence of stress-state, strain-path and strain-rates on sheet formability associated with sheet-impact with the die.
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 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.
5. Conclusion
References
4.7. Future work
A combination of high-speed imaging and digital image correlation technique was used to quantify the deformation (displacement, velocity, strain and strain-rate) of 1 mm thick 5182-O Al alloy sheets, deformed under free-forming conditions using the EHF technique. The experimental capability developed in this work provides time and spatial evolution of the deformation over the entire sheet and is a significant improvement over the conventional strain-gridding technique that only provides the post-mortem strain distribution on the sheet. To the authors’ knowledge, such detailed information on sheet deformation evolution in a high-rate forming process, such as EHF, has not been reported before. Based on the experimental conditions of this work, the following conclusions can be drawn pertaining to free-forming deformation of 5182-O Al sheet: A. The Al sheet experienced different strain-rate magnitude and history depending upon the location on the sheet. The maximum strain-rate was ∼207, ∼435 and ∼664/s at discharge voltages of 5000, 6500 and 7500 V, respectively. This maximum strain-rate was observed at a location away from the dome apex (except for 5000 V test). B. With a voltage increase from 5000 V to 7500 V, the maximum strain-rate at the apex showed only a modest increase from 207/s to 271/s. On the other hand, the maximum strain-rate at nonapex location increased by ∼2.4× for the same voltage increase. C. At 5000 V, locations 1–3 experienced similar maximum strainrate. On the other hand, the maximum strain-rate at 6500 and 7500 V was observed at location 3 and not at the apex. Further, the maximum strain-rate at location 3 was found to be ∼1.8× and ∼2.5× greater, relative to the strain-rate at apex, respectively. D. The maximum velocity of the sheet (7500 V) was ∼100 m/s and was observed at a location away from the apex. The velocity–time curves showed repeated oscillations that are attributed to pressure-wave reflections between the sheet and the EHF chamber. Further, the velocity–time curve for apex location showed a double-peak behavior that is likely related to the duration of discharge process and the EHF test geometry. E. The strain-rate vs. strain data shows that the strain accumulation at any given location on the sheet occurs over a range of strain-rates. Further, different locations undergo their own unique strain and strain-rate histories. Such information is specially valuable to model deformation behavior of strain-rate sensitive materials. Acknowledgments The Pacific Northwest National Laboratory is operated by Battelle Memorial Institute for the U.S. Department of Energy under
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