Experimental and Numerical Analyses of Magnetic Pulse Forming of A1050Aluminum Sheet

Takashi Kambe+1, Yasutaka Kedo+2, Shinji Muraishi and Shinji Kumai

Department of Materials Science and Engineering, Tokyo Institute of Technology, Tokyo 152-8552, Japan

An A1050 aluminum sheet was collided against a steel mold with a small V-shaped through-thickness groove by using magnetic pulseforming (MPF) at various charging energy conditions. Deformation behavior of the sheet was also reproduced by using a series of numericalanalyses. The groove was filled at high charging energy condition. Almost no change in grain morphology was observed at the mid-thicknessarea of the sheet, but extremely large intensive deformation occurred at the metal surface region along the slope of the mold. Deformation of theMPFed Al sheet was numerically analyzed by using ANSYS Emag-Mechanical. Electromagnetic force and deformation of the sheet wasreproduced, and the impact velocity of the sheet to the mold was obtained. Deformation behavior of Al under various impact velocity conditionswas analyzed by using Smoothed Particle Hydrodynamics (SPH) method of ANSYS AUTODYN. The groove was completely filled with Al atthe high impact velocity condition, and an extremely large plastic strain and strain rate were observed only at the sheet surface. These simulationresults corresponded very well to the final shape and the local microstructure change observed in the MPFed Al sheet.[doi:10.2320/matertrans.L-M2019862]

(Received September 12, 2019; Accepted October 17, 2019; Published January 10, 2020)

Keywords: magnetic pulse forming, numerical analysis, microstructure change, plastic strain distribution, strain rate distribution

1. Introduction

Magnetic pulse forming (MPF) is one of the high-speedforming processes using electromagnetic force. MPF hasseveral advantages over other conventional mechanicalforming techniques.1­3) The force application is contact-freeand no working medium is required. A high repeatabilitycan be achieved by adjusting the forming machine once. TheMPF process uses only one mold, hence the tool costscan be decreased significantly. Springback is significantlyreduced in comparison to conventional quasi-static formingoperations.4) Fine and sharp details of the product can beobtained.

The principle of MPF is briefly described below. A metalsheet is placed over the coil in the discharge circuit. Thedischarge current runs through the coil, and a magnetic fieldis produced around the coil. An eddy current is induced inthe metal sheet. The interaction between the magnetic fieldand the eddy current creates an electromagnetic force. Themetal sheet accelerated by the electromagnetic force collidesonto the mold. Forming is completed in a few tens of micro-seconds. MPF is suitable for metals with a high electricalconductivity like Al and Cu.

The MPFed metal may have a characteristic microstructurebecause of the high strain rate deformation. There are severalreports which examined the microstructure of MPFed metals.For example, Liu et al. reported that the electromagneticformed A5052 Al alloy sheet had high dislocation density.5)

Jiang et al. reported the dislocation slip mechanism ofelectromagnetic bulged pure Cu based on microstructureobservation.6,7) Ferreira et al. deformed a 304 stainless steelusing electromagnetic forming (EMF) and found that theplastic deformation in this case was dominated by twinning

due to the easy nucleation of partial dislocations at high strainrate.8)

It is hard to understand the deformation mechanism onlyby microstructure observation of the deformed metal. This isbecause the resultant microstructure of MPFed metal includesa series of local and overall strain, strain rate and temperaturechanges during the deformation process. It is difficult toexamine these changes only by experimental measurements.Therefore, a numerical analysis is required to deal with thepresent subject.

Fenton and Daehn demonstrated that a two-dimensionalArbitrary Lagrangian Eulerian (ALE) finite difference codecan accurately predict the dynamics of the EMF process.9)

Oliveira et al. adopted a “two-way, loose coupling” approachto predict the EMF process, which contains a double spiralcoil.10) Cui et al. investigated a bulging behavior of theMPFed metal sheet by using ANSYS Emag and ANSYSMechanical.11) The shape of the specimen experimentallyobtained and that obtained by numerical analysis werecompared in these studies. However, local microstructurechange of the metal during MPF was not examined.

The purpose of the present work is to reproduce thedeformation behavior of the Al sheet during MPF by usinga numerical analysis method, and to elucidate the formationmanner of microstructure of MPFed Al sheet by comparingthe experimental results.

To achieve this task, an appropriate mold shape selectionwhich is suitable for both experimental and numericalanalysis is important. In a preliminary examination, a steelblock mold with a straight rectangular through-thicknessgroove was tested. A 0.8mm-thick pure Al sheet was MPFedagainst the mold. The groove was almost filled with Alsuccessfully. Numerical analysis of MPF for this situation waschallenged by using SPH method of ANSYS AUTODYN.However, it was difficult to reproduce the MPF behavior ofthe Al sheet. In a trial-and-error approach, we tried to findthe ideal groove shape, and finally, found that the mold with aV-shaped groove was suitable to satisfy the requirements.

+1Graduate Student, Tokyo Institute of Technology. Corresponding author,E-mail: kambe.t.ab@m.titech.ac.jp

+2Graduate Student, Tokyo Institute of Technology. Present address:Research and Development Group, Hitachi, Ltd., Yokohama 244-0817,Japan

Materials Transactions, Vol. 61, No. 2 (2020) pp. 346 to 354©2020 The Japan Institute of Light Metals

In the present study, the deformation behavior of the Alsheet by MPF was examined by using a series of numericalanalyses, and the overall and local high-speed deformationmanner of the sheet were reproduced. The characteristicmicrostructure change of the MPFed Al sheet was examinedbased on the strain and strain rate changes reproduced bynumerical analysis.

2. Experimental Procedure

The MPF was performed by using a magnetic pulsegenerator (Bmax MP 12.5/25) with capacitance of 40 µF.Figure 1(a) shows a schematic diagram of the experimentalsetup. CD, GD and VD in the figure are the longitudinaldirection of the coil, the longitudinal direction of the groove,and the direction perpendicular to them, respectively. Thematerial used was a pure Al sheet (A1050, 200 © 70 ©0.8mm3). The Al sheet was also annealed at 773K for 2 h.The grain morphology was equiaxed, and the average grainsize was about 30 µm in diameter. A tool steel block (SKD11(JIS G4404), 50 © 25 © 10mm3) with a V-shaped through-thickness groove was used as the mold. The size of thegroove is 500 µm in depth and 1000 µm in width and thebottom of the groove has a right angle. The Al sheet wasplaced over the middle part of one-turn coil and the moldwas fixed above the Al sheet with a distance. The Al sheetwas arranged as shown in Fig. 1(b) and (c). The projectedlength of the sheet including the upper-width of the coilwas set to 8mm. The distance between the upper surface ofAl sheet and the bottom surface of mold was set to 1.2mm.Three charging energy conditions (2, 4, 6 kJ) were selected.

A Rogowski coil was used in order to obtain the coil currentfor every single discharging.

Microstructure observation of the MPFed Al sheet wasconducted by using an optical microscope. The cross sectionnormal to the GD was polished and chemically etched bysolution: HF:H2O = 1:50 in volume.

3. Numerical Analysis Methods

3.1 Construction of Model 1 and Model 2 and theirtasks

In order to reproduce the MPF behavior of the Al sheet, theprocess of MPF was divided into two stages, and each stagewas analyzed by using Model 1 and Model 2. In Model 1,ANSYS Emag-Mechanical using finite element method(FEM) was used. A discharge current through the coil, agenerated magnetic field around the coil, and an inducedelectromagnetic force were calculated, and the deformationbehavior of the metal sheet by the electromagnetic forcewas reproduced. Impact velocity of the Al sheet to the moldwas obtained by using Model 1.

In Model 2, ANSYS AUTODYN using smoothed particlehydrodynamics (SPH) method was used. The SPH methodis a mesh-free analysis and superior to analyzing heavydeformation. The impact velocity obtained by the Model 1was used as an initial condition. The deformation behavior ofAl sheet, in particular, flowing manner of the Al sheet into thegroove and local strain and strain rate change in the deformedsheet were analyzed by using the Model 2.

3.2 Model 1: Estimation of impact velocity3.2.1 Electromagnetic analysis

The governing equations of electromagnetic field arededuced by Maxwell’s equations (eqs. (1)­(4)).

r �H ¼ J ð1Þ

r �K ¼ � @B

@tð2Þ

r � B ¼ 0 ð3Þr � J ¼ 0 ð4Þ

where, H: magnetic field intensity, B: magnetic flux density,J: electric current density, K: electric field, and r: nablaoperator. To these differential relations, the constitutiverelations are included from eqs. (5) and (6).

B ¼ ®H ð5ÞJ ¼ ·K ð6Þ

where, ®: permeability and ·: conductivity. It is oftenconvenient to choose the magnetic vector potential A as asystem variable in the electromagnetic model such that

K ¼ � @A

@tð7Þ

B ¼ r � A ð8Þr � A ¼ 0 ð9Þ

Substitution of eqs. (7)­(9) into the Maxwell’s equation gives

r � 1

®r � A

� �¼ J � £

@A

@tð10Þ

Fig. 1 (a) Schematic diagram of experimental setup, (b) view from CDdirection, (c) view from the GD direction.

Experimental and Numerical Analyses of Magnetic Pulse Forming of A1050 Aluminum Sheet 347

where, J: current density in coil, ¹£(@A/@t): induced currentdensity in metal sheet, and £: conductance of medium.According to Maxwell’s equations, the magnetic forcedensity f is expressed as the following equation:

f ¼ J � B ð11ÞThe magnetic force can be obtained by substitutingeqs. (8) and (10) into eq. (11) and used as the input load inmechanical model.12)

3.2.2 Modelling of the Al sheet deformation andestimating of the impact velocity

The electromagnetic field and deformation behavior of theAl sheet were analyzed by using ANSYS Emag-Mechanical.The schematic illustration of Model 1 is shown in Fig. 2.Model 1 consists of the FEM circuit and the FEM model.The FEM circuit consists of inductance, capacitor, resistanceand coil. The values of circuit component were determinedby fitting between the experimental and analytical currentwaveforms. The FEM model consists of the Al sheet, mold,coil, air and infinite boundary. The properties of the Al sheet,Cu coil and steel mold are shown in Table 1. The coil in theFEM circuit and FEM model were coupled. For modellingthe constitutive law of the Al sheet, the true stress-straincurve obtained at a high strain rate condition was used.13)

Discharge current, magnetic flux and electromagnetic forcewere analyzed by using Emag, and the deformation behaviorof the Al sheet was analyzed by Mechanical, respectively.The impact velocity was obtained according to the procedureshown below. In the first step, the discharging currentthrough the coil was calculated by FEM circuit. In the second

step, the magnetic flux around the coil was calculated, andthe eddy current produced in the Al sheet was analyzed byEmag FEM model. The electromagnetic force was calculatedand used as input to the mechanical model. In the third step,the deformation behavior of the Al sheet by electromagneticforce was reproduced by Mechanical FEM model. Thesesteps were repeated until the Al sheet collided with the mold,and the velocity at the moment of the collision was defined asthe impact velocity (Vi).

3.3 Model 2: Analysis of deformation behavior of Alsheet

3.3.1 SPH methodThe deformation behavior of the Al sheet flowing into the

groove was reproduced by ANSYS AUTODYN using thesmoothed particle hydrodynamics (SPH) method. The SPHmethod is a mesh-free analysis method which is superior forthe analysis of the heavy and rapid deformation. In theSPH method, particles are defined as interpolated points fromwhich values of functions and their derivatives can beestimated at discrete points in the continuum. The functionvalues and their derivatives are found by a kernelapproximation instead of being constructed from a grid.The diameter of the particle is defined as smoothing length(h). The physical quantity of the particle is calculated inreference to neighboring particles inside a circle of radius2h.14)

3.3.2 Equation of state (EOS) and constitutive modelThe Mie-Grüneisen EOS based on the shock Hugoniot

was applied for the Al sheet and the steel mold. TheseEOSs use the base relationship of particle velocity to shockvelocity, which are of the form (eqs. (12)­(14)):

p ¼ pH þ �µðe� eH Þ ð12Þ

pH ¼ c20µ0µðµ � µ0Þ½µ0 � ðs� 1Þðµ � µ0Þ�2

ð13Þ

eH ¼ 1

2

pH

µ0

µ � µ0

µ

� �ð14Þ

where, p: pressure, ! : Grüneisen parameter, µ: currentdensity, µ0: initial density, e: specific internal energy, c0: bulksound speed, and s: material-specific constant.

The constitutive model should be used to represent themechanical behavior of metals, which are subjected to largestrains, high strain rate and high temperature. The Steinberg-Guinan constitutive model (eqs. (15)­(17))15) was applied forthe Al sheets, and the Johnson-Cook constitutive model(eq. (18))16) was applied for the mold.

G ¼ G0 1þ G0p

G0

� �p

©13

þ G0T

G0

� �ðT � 300Þ

� �ð15Þ

Y ¼ Y0 1þ Y 0p

Y0

� �p

©13

þ G0T

G0

� �ðT � 300Þ

� �½1þ ¢¾�n ð16Þ

Y0½1þ ¢¾p�n � Ymax ð17Þ

Y ¼ ½Y0 þ ¢¾pn�½1þ C ln ¾�P� 1� T � Troom

Tmelt � Troom

� �m� �ð18Þ

where, ©: compression, defined as the initial specific volumeV0 divided by the specific volume V, ¾p: effective plasticstrain, ¾�P: normalized effective plastic strain rate. Parameters

Fig. 2 Schematic illustration of Model 1 by using ANSYS Emag-Mechanical.

Table 1 Properties used in Model 1 for each material.

T. Kambe, Y. Kedo, S. Muraishi and S. Kumai348

used in EOS and constitutive models for Al and the steelmold are listed in Table 2.3.3.3 Setup of Model 2

Figure 3 shows the SPH model setup. The Vi obtained byEmag-Mechanical was given to the Al sheet as the initialcondition. The upper part of the mold was fixed. Thediameter of the SPH particle was defined as smoothing length

(h). In this study, in order to reproduce the detaileddeformation behavior of the metal sheet, the appropriatesmoothing length (h) was selected according to the impactvelocity. The h of the Al sheet was set to 3 µm for thelow impact velocity condition (Fig. 3(b)). For the highimpact velocity conditions, h was 1.5 µm from the surface to120 µm, and the h of the remaining area was 3 µm (Fig. 3(c)).The h near the mold surface was set to 3 µm and 1.5 µm forhigh and low impact velocity conditions, respectively. The hwas stepwisely selected to be larger in a direction away fromthe mold surface. The symmetric system of the SPH modelwas a two-dimensional planar system that is assumed tocontinue infinitely in the CD direction. The deformationbehavior of the Al sheet flowing into the groove wasreproduced, and the local strain and strain rate change duringdeformation were analyzed by calculating the physicalquantity of each SPH particle.

4. Results and Discussion

4.1 Deformation and local microstructure change of theMPFed Al sheet

Figure 4 shows the as-polished cross-sectional view of theMPFed Al sheet. For the condition of 2 kJ, the Al sheet didnot fill up the groove perfectly (Fig. 4(a)). On the other hand,the groove was almost completely filled with the deformed Alat the conditions of 4 kJ and 6 kJ (Fig. 4(b) and (c)). This isprobably due to the increased impact velocity of Al to themold as increasing the charging energy. Figure 4(d)­(f )shows the enlarged view at the front area of the deformedsheet for each condition. The front area was flat for theconditions of 2 kJ and 4 kJ (Fig. 4(d) and (e)). On the otherhand, the characteristic protruded wave-like shape wasobserved for 6 kJ condition (Fig. 4(f )).

Figure 5 shows the grain morphology of the MPFed Alsheet for 2 kJ and 6 kJ conditions. The white spots in the Al

Table 2 Parameters used for EOSs and constitutive models for eachmaterial.

Fig. 3 (a) SPH model setup of Model 2 by using ANSYS AUTODYN, (b) size of h for low impact velocity condition, (c) size of h forhigh impact velocity condition.

Experimental and Numerical Analyses of Magnetic Pulse Forming of A1050 Aluminum Sheet 349

matrix are artifacts by etching. The grains at the slope areawere deformed along the groove surface for both conditions.The degree of elongation of the grain was greater for the 6 kJcondition (Fig. 5(d)) than for the low energy conditions(Fig. 5(c)). Figure 5(d) shows the change in grain morphol-ogy from the surface to the interior for the 6 kJ condition.Grain morphology at the mid-thickness area of the Al sheetdid not change and was almost the same as the original one.In contrast, heavy deformation occurred in the vicinity ofthe sheet surface. The grain morphology changed drasticallyin the range of about 30 µm from the surface and the grainswere elongated along the slope of the groove. The degreeof elongation decreased with an increased distance from thesurface.

4.2 Deformation manner of the Al sheet and impactvelocity analyzed by Model 1

Magnetic flux density and electromagnetic force werecalculated, and the deformation of the Al sheet wasreproduced by Model 1. For the circuit analysis, the valuesof the circuit components are required. In this study, theirvalues were determined by fitting the current waveforms

obtained from the experiment with those of analytical results.Figure 6 shows the comparison of the current waveformsobtained from the experiments and the results of thenumerical analysis. The analysis was conducted from theonset of discharging to the instant of the collision of the metalsheet to the mold surface.

As we increased the charging energy, the maximum currentamplitude increased. The current amplitude obtained by thenumerical analysis shows a very good agreement with theexperimental result.

Figure 7 shows the change in magnetic flux density aroundthe coil and deformation behavior of the Al sheet reproducedby Model 1. The analytical result for the 6 kJ condition isshown here as an example. A large magnetic flux density wasgenerated between the Al sheet and the coil. This means thata large electromagnetic force was applied to the Al sheet. Thelocal area of the Al sheet located above the coil deformedradially and hit the mold. The elapsed time from the onset ofdischarge current introduction to the collision was 9.5 µs inthis case. Such a deformation behavior of the Al sheet wascommon in the other conditions. The location where the sheethit the mold surface at first was defined as the first impact

Fig. 4 As-polished cross-section of MPFed Al sheet for (a) 2 kJ, (b) 4 kJ and (c) 6 kJ conditions. Enlarged view at the top area of theMPFed Al sheet for (d) 2 kJ, (e) 4 kJ and (f ) 6 kJ conditions.

Fig. 5 Overall microstructure change of the MPFed Al sheet for (a) 2 kJ and (b) 6 kJ conditions. (c) Enlarged view of the area in the whitecolumn in (a). (d) Enlarged view of the area in the white column in (b).

T. Kambe, Y. Kedo, S. Muraishi and S. Kumai350

point. The velocity profiles of VD direction at the first impactpoint are shown in Fig. 8. The velocity immediately before asudden drop was defined as the impact velocity. The impactvelocity increased with the increase of charging energy.This is because the magnetic force applied to the Al sheet

increased with increasing charging energy, or as the currentthrough the coil was increased. The obtained impact velocityvalues were used as the initial conditions of the followinganalysis by using Model 2.

4.3 Deformation behavior and final shape of the Al sheetreproduced by Model 2

The deformation behavior of the Al sheet was reproducedby Model 2. We could investigate how the part of the Alsheet was flowing into the groove and filled it. Thedeformation behavior of the 2 kJ and 6 kJ conditions isshown in Fig. 9. Here, 0 µs means the time at the momentthat the Al sheet collided with the mold surface. The impactvelocity obtained from Model 1 was given to the Al sheet asthe initial condition of velocity of each SPH particle. In thecase of the 2 kJ condition, the front line of the metal sheetflew into the groove remaining the flat surface as indicatedby the white arrow. The groove was not filled with Al, asshown in Fig. 9(a)­(d).

In contrast, for the 6 kJ condition, as shown in Fig. 9(e)­(h), a pair of metal fronts along the groove surface flew intothe groove faster than the metal front of the middle area asindicated by a pair of black arrows. Figure 9(i) and ( j) showsthe enlarged views of the area indicated by black arrows inFig. 9(f ) and (g), respectively. The SPH particles on theslope side preceded those in the central area. The movingfront of the particles along the slope reached the bottom ofthe groove prior to the central area. The groove was filledwith Al completely in about 1.1 µs as shown in Fig. 9(h). Itshould be mentioned that the deformation behavior of the Alsheet reproduced by Model 2 was reasonable to explain thecharacteristic cross-sectional morphology of the deformedsheet observed in Fig. 4. The amount of Al flowing intothe groove increased with increasing impact velocity. Thefinal shape of the MPFed Al sheet reproduced by Model 2showed a good agreement with the experimental results asshown in Fig. 4.

4.4 Change in effective plastic strain and strain rateduring deformation of the Al sheet analyzed byModel 2

It is difficult to measure experimentally the local strain andstrain rate change during the inflow of Al sheet into the

Fig. 7 Magnetic flux around the coil and deformation behavior of Al sheetfor 6 kJ condition reproduced by Emag-Mechanical. The color barrepresents the magnitude of magnetic flux density. (a) and (b) Initialconditions. (c) and (d) Magnetic flux density and deformation behaviorof the Al sheet after 3 µs, (e) and (f ) 6 µs and (g) and (h) 9.5 µs from theonset of the discharge current introduction.

Fig. 6 Comparison of the current waveform obtained by experiment andthe result of numerical analysis.

Fig. 8 Velocity profile and the estimated impact velocity (Vi) at the firstimpact point for each condition.

Experimental and Numerical Analyses of Magnetic Pulse Forming of A1050 Aluminum Sheet 351

groove. However, the effective plastic strain and strain ratecan be investigated with the help of numerical analysis bythe SPH method. Figure 10 shows the distribution of theeffective plastic strain reproduced by Model 2 for eachcondition. The increased effective plastic strain was observedat the surface along the slope for the low impact energycondition (Fig. 10(a)). On the other hand, for the highimpact energy condition, a large effective plastic strain wasobserved in the wide area of the deformed sheet located in the

groove. The plastic strain was extremely high at the surface(Fig. 10(b)).

Figure 10(c) shows the enlarged view of the slope area forthe low energy condition. The plastic strain at the surfaceof the low impact velocity condition was smaller than that ofthe high impact velocity condition. No localized plastic strainof the slope area was observed at the sheet surface for thelow impact velocity condition, and the plastic strain did notexceed 1. In contrast, for the high energy condition, a plastic

Fig. 9 Deformation behavior of the Al sheet reproduced by Model 2 by using SPH method. For 2 kJ condition, (a) the moment ofcollision, (b) 0.5 µs from collision, (c) 1.0 µs and (d) 1.4 µs. For 6 kJ condition, (e) the moment of the collision, (f ) 0.4 µs from collision,(g) 0.8 µs and (h) 1.1 µs. (i) and ( j) Enlarged views of the area indicated by black arrows in (f ) and (g).

Fig. 10 Effective plastic strain distribution in the Al sheet analyzed by Model 2 for (a) 2 kJ and (b) 6 kJ conditions. (c) Enlarged view ofthe area in the white column in (a). (d) Enlarged view of the area in the white column in (b). The color bar at the bottom indicates thelevel of effective plastic strain.

T. Kambe, Y. Kedo, S. Muraishi and S. Kumai352

strain exceeding 2 was observed at the surface for the highenergy condition. Figure 10(d) shows the distribution ofthe effective plastic strain from the surface to the interior ofhigh impact energy condition. A very large effective plasticstrain was observed near the surface, and the width of thelarge plastic strain region was about 20 µm from the sheetsurface. The amount of plastic strain gradually decreasedfrom the surface toward the interior of the material, and it wasnegligibly small at the mid-thickness area.

Figure 11 shows the plastic strain rate distribution of thehigh energy condition when the moving front of Al reachedthe halfway-up of the groove slope. The strain rate of thecenter area was small (Fig. 11(b)); on the other hand, a largestrain rate was observed at the sheet surface of the slope area(Fig. 11(c)). The strain rate on the sheet surface exceeded1 © 107 s¹1. The strain rate gradually decreased toward theinterior of the material. The strain rate of the center area wasless than 1 © 105 s¹1. There was a large difference betweenthe strain rate of the center area and that of the sheet surface.Grain morphology heavily deformed in the vicinity of thesheet surface; however, the grain morphology at the mid-thickness area did not change and was almost the same as theoriginal one shown in Fig. 5(d). The strain and strain ratewere large in the region of about 20 µm from the surface,which corresponds very well with the 30 µm width wherethe grain morphology changed drastically. These simulationresults showed a good correspondence to the local micro-structure change observed in the MPFed Al.

Temperature increase was also analyzed by using Model 2.A large temperature increase occurred only in the vicinity ofthe sheet surface because of the large deformation in a veryshort time. The temperature of the slope surface was about1000K, and might have exceeded the melting point. Finegrains were observed in the slope surface by using TEM. It isconsidered that the microstructure of this region was affectedby heat. On the other hand, temperature increase in the mid-thickness area of the sheet is considered to be negligiblysmall. The details on the relationship between the temper-ature and microstructure change during deformation will bereported in another report.

5. Conclusions

Impact deformation behavior of MPFed pure Al sheet wasinvestigated by both experimental and numerical analysis

methods. The sheets were collided to the steel mold with aV-shaped through-thickness groove at various chargingenergy conditions, and morphological and microstructurechanges of the sheet were examined. The progress of metaldeformation was also reproduced by using a series ofnumerical analyses. The following findings were obtained:

The groove was completely filled with Al under the highenergy conditions. In this case, an extremely large change inthe grain morphology was observed only at the surface ofthe sheet along the slope of the groove. Almost no changewas observed in the interior of the sheet.

Deformation of the Al sheet by electromagnetic force wasreproduced by ANSYS Emag-Mechanical, and the impactvelocity of the Al sheet to the mold was obtained. Theimpact velocity increased with an increasing charging energy.Detailed deformation behavior of the Al sheet wasreproduced by using the SPH method of ANSYSAUTODYN for various impact velocity conditions. Thecross-sectional shape obtained from the simulation showeda good quantitative agreement with the experimental result.The flowing behavior of the Al into the groove and progressin effective plastic strain were reproduced by SPH analysis.The intensive large plastic strain was observed only at thesurface of the sheet, and almost no plastic strain wasobserved in the interior of the sheet for the high impactvelocity condition. An extremely large strain rate wasobserved at the sheet surface, but the strain rate of the centerarea was very small compared to that of the sheet surface. Itwas found that the local microstructure change observed inthe MPFed Al sheet can be explained reasonably well basedon the simulation results. This confirms the validity of thepresent numerical analysis.

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Fig. 11 (a) Effective plastic strain rate during deformation analyzed by Model 2 for 6 kJ condition. (b) Enlarged view of the center area.(c) Enlarged view of the slope area. The color bar at the bottom indicates the level of effective plastic strain rate.

Experimental and Numerical Analyses of Magnetic Pulse Forming of A1050 Aluminum Sheet 353

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