hahn 2016
TRANSCRIPT
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Journal of Materials Processing Technology 230 (2016) 131142
Contents lists available at ScienceDirect
Journal ofMaterials Processing Technology
journal homepage: www.elsevier .com/ locate / jmatprotec
Analytical approach for magnetic pulse welding ofsheet connections
Marlon Hahn , Christian Weddeling,Joern Lueg-Althoff, A. Erman TekkayaInstitute of Forming Technology and Lightweight Construction(IUL), TU Dortmund University, Baroper Str. 303, 44227 Dortmund, Germany
a r t i c l e i n f o
Article history:
Received 18 July 2015
Received in revised form
20 November 2015
Accepted 21 November 2015Available online 2 December 2015
Keywords:
Magnetic pulse welding (MPW)
Lightweight structures
Analytical model
Impact velocity
a b s t r a c t
An analytical model to calculate the acting forming pressure in magnetic pulse welding by determining
the magnetic field strength between the flyer sheet and a one-turn coil was presented. By neglecting
plastic deformation ofthe flyer, the model allows to calculate the transient velocity and displacement
behavior, too. The electromagnetic acceleration of5000-series aluminum alloy sheets was investigatedunder various experimental parameters. Utilizing Photon Doppler Velocimetry revealed that the ana-
lytical model appropriately describes the influence ofcurrent amplitude, coil geometry, and, especially,
discharge frequency on the velocity-displacement curve of the flyer and hence on the impact velocity.
The model introduced was applied to compute the impact velocity for the welding oflong lapjoints of
5000-series aluminum alloy sheets and 6000-series aluminum alloy hollow profiles. Through peel tests
it was shown that the weld strength at least complied with the strength ofthe weaker base material as
failure always happened in the flyer sheet. The wavy interface pattern typical for impact welding was
identified with the help ofmetallography.
2015 Elsevier B.V. All rights reserved.
1. Introduction
There is a risingdemand forlightweight structures in transport-related applications with the aim of reducing energyconsumption
to minimize costs as well as environmental pollution so that more
and more light metals are applied in the automotive industry. As a
consequence thereof, manufacturers face the challenge of joining
different grades of aluminum alloys. If welding is the joining pro-
cess of choice, conventional fusion-based techniques often reach
their limitsdue to theoccurrence of microstructural andmechani-
cal changesin theweldbead andheataffectedzone(HAZ)reducing
the strength of the joint and frequently causing hot cracks espe-
cially in welds between 5000- and 6000-series aluminum alloys
(PraveenandYarlagadda,2005). Theseproblemsmaybeavoidedby
utilizing high velocity impact welding processes such as magnetic
pulse welding (MPW). It is a solid-state welding process, which
also allowsto minimize or even eliminate the formationof contin-uous intermetallic phases when joining dissimilar metals (Zhang
et al., 2011). MPW is thereforewell suited for creating strongmet-
allurgical bondsbetween both similar anddissimilarmetalsand its
alloys.
Thegeneralworkingprincipleof impactweldingis illustratedin
Fig. 1. Besides MPW, further impact welding processes are (Zhang
Corresponding author.E-mail address:[email protected](M. Hahn).
et al., 2011): explosivewelding (EXW), laser impact welding (LIW),
andthe latelyby Viveketal.(2013) introducedvaporizing foilactu-
ator welding (VFAW).As outlined by Mori et al. (2013), thetwojoiningpartners, com-
monlynamedflyerand target,collideunder theangleatvelocitiesvimin therange of several hundred m/sproducing impactpressures
of the order of GPa. This process is accompanied by the so-called
jetting effect that leaves behind chemically pure surfaces allowing
a metallic bond to be formed. The atoms of the involved materi-
als are impacted to such an extent that they share and exchange
valence electrons. As a result, a wavy interface morphology is often
observable (see Fig. 1). A common explanation for the evolution
of these waves was given by Ben-Artzy et al. (2010). The authors
stated that reflected shock waves in the joining partners lead to a
KelvinHelmholtz instability.Fora given materialcombination,the
domainof thetwocrucialparameters (impactangle)andvc (colli-
sion velocity)necessary fora successful weld maybeplotted in theform of a weldingwindow, whichoriginates from EXW(Mousavi
and Sartangi, 2009). In contrast to EXW though, both and vc donot remain constant during MPW(Verstraete et al., 2011). A com-
pilation of welding windows as well as different bonding criteria
available in literature so far was presented by Kapil and Sharma
(2015).BymeansofX-raydiffractionanalysisandscanningelectron
microscopy,Koreet al. (2009) found that neither meltedzones nor
intermetallicphasesmaybepresent inmagneticpulsewelds,while
http://dx.doi.org/10.1016/j.jmatprotec.2015.11.021
0924-0136/ 2015 Elsevier B.V. All rightsreserved.
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132 M.Hahn et al./ Journal of Materials Processing Technology 230 (2016) 131142
Nomenclature
Symbol/meaning/unit
a Length of the pressure lead of the tool coil in mmB Magnetic flux density (vector) in GBg Magnetic flux density in the gap between the flyer
and the tool coil in G
C Capacitance of the pulse generator in F
c1, c2 , c3 Constants in theanalytical modelD Flyer displacement in mm
d1, d2 Distances from a two-sided tool coil in mm
Dch Critical flyer displacement in the analytical model
in mm
E0 Initial chargingenergy in J
EL Total magnetic energy in J
f Frequency of the discharge circuit in HzFL Lorentz force (vector) in N/mm3f0, fd,fb Initial (0), Doppler-shifted (d), and beat (b) fre-
quency of the Photon Doppler Velocimeter in Hz
FPeel Test force during peel test (index max for the max-
imum) in N
FUTS Ultimate tensile strength for a specific specimen
geometry in Nh Height of the tool coil in mmH Magnetic field strength (vector) in A/mmh Effective height of the trapezoidal coil in mmHg Magnetic field strength in thegap between the flyer
and the tool coil in A/mm
Hh Magnetic field strength at the sidewall of the tool
coil in A/mm
Hh0, Hy0 Coefficient functions in the analytical model in
A/mm
HS Magnetic field strength due to the skin effect in
A/mm
I Coil current (indexa foramplitudeor peak value) in
A
Ih
Current at the sidewall of the tool coil in A
Ip Current due to the proximity effect in A
IS Current due to the skin effect in A
j Imaginary unitJ Current density (vector) in A/mm2k Complex propagation constant (indices F and T for
flyer and tool coil, respectively) in 1/mm
l Length in mm
L Total inductance of the discharge circuit in H
Li Inner inductance of the pulse generator in H
p Magnetic pressure (index hf for the high-frequency
limit) in MPa
pc Plastic collapse pressure in MPa
R Total resistance of the discharge circuit inRi Inner resistance of thepulse generator in
s Sheet thickness in mm
t Time ins
trise Current rise time in s
v Flyer velocity (index m for measured velocities) in
mm/s
vc Collision velocity in mm/s
vim Impact velocity in mm/s
w Width of the tool coil in mm
w Width of the bottom of the trapezoidal coil in mm Impact angle in
Skin depth in mm Electrical conductivity in 1/
0 Operating wavelength of the Photon DopplerVelocimeter in mm
Magnetic permeability (index 0 for air) in Vs/Amb Density of the flyer material in kg/mm
3
Y Flow stress of the flyer material in MPa
Goebelet al.(2010)similarlyshowedthatthesephenomena cannot
becompletely avoided forsomematerials. InMPWtheelectromag-
netic forming (EMF) technology isused to plastically accelerate theflyer plate.Jablonski and Winkler (1978) stated that the forming
pressure in EMF is generated by penetration of a pulsed magnetic
field into a conductive workpiece to be formed. Themagnetic field
in turn results from a rapid discharge of a capacitor through the
tool coil (see Fig.2a). Materialsof lowelectrical conductivitycan be
formed with the help of thin high-conductivity driver plates (Gies
et al., 2014). Such drivers are positioned between the workpiece
and the coil to provide the forming pressure.
Neglecting the nonlinearity of circuit parameters due
to workpiece deformation, Jablonski and Winkler (1978)
described the coil current I by a simple series RLC (equivalent
resistanceinductancecapacitance) circuit yielding an exponen-
tially damped sine wave with frequency f and initial charging
energy E0:
I(t) =
E02CfL
exp
R
2Lt
sin (2ft) (1)
where
f = 12
1
LC R
2
4L2 . (2)
In order to simplify the analysis, Buehler and Bauer (1968)
approximated the frequency based on the time triseuntil peak cur-
rent Ia as
f= 14trise
. (3)
The transient magnetic field in the vicinity of the workpiece
(flyer plate) induceseddy currents in it that opposethecoil current
implying the appearance of the Lorentz volume forceFL (Lorentz,1895):
FL= J B . (4)J andB are the vectors of current density and magnetic flux
density. FollowingAizawa (2003), thisvolume force can be mathe-
maticallytransformedintoapressurep, also referredto asmagnetic
pressure, acting on both the workpiece and the coil. It can be cal-
culated as
p = B2g
2
1 exp2s
. (5)
Here, s is the flyer thickness and Bg is the magnetic flux den-sity tangential to the flyer surface near the tool coil. The presence
of a transient magnetic field between flyer and coil leads to the
evolution of two related effects, the internally caused skin and
Fig. 1. Schematic of impact welding (Mori et al., 2013).
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Fig. 2. Schematic of MPW: (a) one-sidedaccessibility as illustrated in Weddeling et al. (2014), (b) two-sided accessibility.
the externally caused proximity effect, inducing current crowd-
ing mainly to the surfaces opposite each other in case of reverse
current flow. Leastwise the skin effect can be characterized by an
equivalent conductor thickness, theskindepth (Heaviside, 1951):
=
(f)1/2 . (6)
The parameters f, , and stand for frequency, electri-
cal conductivity, and magnetic permeability. Low inductances
and capacitances facilitate high discharge frequencies, which are
required for attaining an appropriate magnetic field and thus
high forming pressure (Daehn, 2010). Generally, tool coils can be
dividedintothree basiccategoriesafterHarvey andBrower (1958):
compression coils, expansion coils, and flat coils for sheet metal
forming. Certainly hybrids exist, also for welding tasks. Weddeling
etal.(2014), for instance,useda modifiedexpansioncoilintroduced
by Kamal (2005) (called uniform pressure electromagnetic actua-
tor) to manufacture flat lap joints. A tool coil for such weld types
frequently resemblesa single rectangular conductor thepressure
lead having a wider return path away from the weld area (see
Fig. 2a). As can be seen in Fig. 2b, the return path can serve as asecond pressure lead if it is narrow enough and properly placed
below the targetplate so that both joining partners areaccelerated
against one another (Aizawa, 2003). The mathematical description
of the magnetic flux density in Eq. (5) strongly depends on the
coilgeometry, amongother factors.Formulaerelatingthe magnetic
fieldto thedischargecurrentwerereviewedby Psyketal.(2011)for
rotationally symmetric geometries. For a double-sided conductor
configuration with two sheets as shown in Fig. 2b, Aizawa (2003)
provided the followingequation:
Bg= Iw
tan1 w
2d1
+ tan1
w
2d2
. (7)
In this, w is the width of the two pressure leads, d1 and d2 ineach case represent the distance between the coil surface facing
the sheet and the point where magnetic flux density is observed.
All else being equal, Eq. (7) does not consider the variation of the
magnetic field with frequency and workpiece conductivity, mean-
ing it always yields the same magnetic flux density for a given
current value independent of the chosen frequency and conduc-
tivity. Moreover, Eq. (7) is only valid fora symmetric configuration
consisting of two one-turn coils and thus not applicable for the
welding with one-sided accessibility (e.g., welding of sheets onto
larger profiles). Since an analytical approach that overcomes the
disadvantages mentioned above has not yet been found in litera-
ture, an approach which eventually allows to calculate the impact
velocity when one-sidedly using one-turn coils is proposed and
verified in thepresent paper.
Fig. 3. Flyer segment interpreted as fully clamped beam.
Fig. 4. Visualization of magnetic field and current distribution in rectangular coil
and flyer plate with respect to proximity and skin effect.
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134 M.Hahn et al./ Journal of Materials Processing Technology 230 (2016) 131142
2. Analyticalmodel
First, a setup as depicted in Fig. 2 is considered, particularly the
forming or weld area. There, the flyer plate is fixed between two
spacers. It is a reasonable simplification to treat a cross-section of
this flyer segment as a fully clamped beam of density b, length l,andthicknesss under partial, uniformloadingp over thecoil width
w (see Fig. 3).
With flow stress Y, the corresponding static plastic collapse
pressurepcof the beam as known from rigid-plastic theory can be
written as (Jones, 1989)
pc= 2s2Ywl
. (8)
It is assumed that this collapse pressure is much smaller than
the acting magnetic pressure (pcp) so that the influence ofpcon theflyer acceleration is ignored. Here, a one-dimensional rigid-
body motion accordingto Newtons second lawis taken todescribe
the velocity vof the flyer plate and its displacementD :
v= 1bs
pdt , (9)
D = vdt. (10)Once the temporal evolution of the magnetic flux density Bg is
determined, magnetic pressure, flyer velocity, and displacement
may be computed according to Eqs. (5), (9), and (10). For that rea-
son, the electrical part of the model is established in what follows.
If an harmonic magnetic field strengthHas well as good conduc-tors(J= H) areassumed,Maxwellsequations (Maxwell,1865)may be put in the form of the second-order partial differential
equation below:
2 H= k2n H (11)where
kn= 1n +j 1n , n = F, T . (12)
It is noted thatj is the imaginary unit, Fand Trepresent the skindepth in the flyer and the tool coil, respectively. Furthermore, the
total current can be expressed by Ampres circuital law as
I=r
H dr . (13)
Now, solutions of Eq. (11) and boundary conditions that ade-
quately relate to the current distribution indicated in Fig. 4 must
be found. For the determination of the magnetic field strength in
tube compression or expansion, it is a common simplification to
neglect the workpiece movement (Psyk et al., 2011). As the dis-
placements inMPWaregenerally lowin comparison tosheetmetalforming tasks in EMF, thesame simplification is made here as well.
Statements given in the following explicitly refer to Fig. 4, whereH
g =Bg/ applies with0 = 4107 N/A2 in air.The magnetic field strength Hg in the small gap gbetween the
flyer and the tool coil is assumed spatially constant as the flyer
remains in close proximity to the coil until the impact. Regarding
the flyer plate, a one-dimensional field with an exponential decay
from Hg to Hgexps/F
at the side facing the target is already
implicated in Eq. (5). In the flyer, only the proximity effect plays a
rolesinceonlythe inducededdy current Ip emergesthere(no forced
current as in the coil). This differs from the two-dimensional dis-
tributionin thecurrent-carryingcoil, where thetotal current Imay
be split abstractly as follows. On the surface close to the flyer, the
proximityeffect, as an antimirror-image ofIp, aswell as IS, which is
caused by the skineffect, is present. For the bottom side of the coil,
it is supposed that only the skin effect and thus ISremainsbecause
the flyer is too far away to have an influence on the magnetic field
HS there. The magnetic field and the current density in the inner
area of thecoil areassumed to be negligibly small. Locally employ-
ing Ampres law at the bottom of the coil may then simply result
in
IS= |
HS|
w
2
. (14)
Accordingly, the transition from the topto thebottom along the
outer vertical surface of thecoil (heighth) may be expressedby the
residual current Ih as
Ih=h0
Hhdy . (15)
The function Hh is discussed in more detail later in this sec-
tion. Applying Ampres law globally around both the coil and the
corresponding flyer segment, such that Ipcancels out, yields
2 (2IS + Ih) = Hgexp s
Fw + |HS|w + 2
h
0Hhdy , (16)
which, after inserting Eqs. (14) and (15), eventually leads to
|HS| = Hgexp sF
. (17)
For thetwo-dimensional magneticfielddistributionH= [HxHy]in the coil as described above, the following functions, that satisfy
Eq. (11), are proposed here:
Hx(y, t)= Hx1 exp(kTy)+Hx2 exp (kTy) with Hx(0, t)= Hg,Hx(h, t) = HS (18)
Hy (x, y, t) = Hy0 sinhkTc1x
exp
kTc2y
with
1
c21+ 1
c22= 1.
(19)
With a time-dependent function Hh0 and the constant c2, the
real part ofHy at the vertical coil surface (x=w/2) may be written
as
ReHyw
2,y, t
= Hh0exp
yTc2
cos
yTc2
0 for 0 y h (20)
Concerning boundaryconditions, it is assumed that the vertical
magnetic field strengths at the edges of the coil (points P1 and P2)
are specified by:
Re
Hy
w
2, 0, t
= Hg Hh0= Hg , (21)
Re
Hy
w
2,h,t
= |HS| . (22)
As Eq. (22) hasno closed-form solution when solving for c2, the
function Hh with constant c3 is taken to roughly approximate the
regarded real part in the form
Hh= Hgexp yTc3
Re
Hy
w
2,y,t
for 0 y h . (23)
Taking this into account in Eq. (22) ultimately results in
Hh
=Hgexp
sy
Fh . (24)
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It can be shown that this simplification in the end leads to
slightly higher values ofHg compared to using a numerical solu-
tion for c2 in Eq. (22). In this way, Eq. (23) indirectly even takes
account of edge-effects (current concentration at sharp edges of a
conductor). Again utilizing Ampres law, but with an integration
path just around the coil now gives
I= Hgw+ Hgexp sFw + 2h
0
Hhdy , (25)
which, after solving the integral and rearranging, can be rewritten
as
Hg= Iw
1+ exp
s/F
+ 2Fh
1 exp
s/F
/s
. (26)
Eq. (26) is put into Eq. (5) to complete the model providing
p =0I
2 1 exp
2s/F
2w 1+ exps/F+ 2Fh 1 exps/F /s
2 (27)
for the transient pressures based on a measured or calculated coil
current I if its decaying time course is interpreted as a sequence
of harmonic half-waves. Thecharacteristics of the proposed model
are plotted exemplarily in Fig. 5 for an arbitrary point in time.
It can be seen that the pressure theoretically increases till infin-
ity for an infinitely large current and that it decreases to zero for a
verywidecoil. Themostconspicuouspoint, though, is theexistence
ofa high-frequencylimit,which isphf =p (f) =0.5 (I/w)2 andequivalent to the hypothesis that the current entirely flows on the
coil surface near the flyer plate. Naturally, the pressure becomes
zero for a frequency of zero. The physical explanation for that is
given by the fact that eddy currents are only induced in the flyer
in case of a temporally varying magnetic field. A higher flyer con-
ductivitymathematically equals a higher frequency with regard tomagnetic pressure since both parameters similarly affectp via the
skin depth of the flyer. It is further noted that the assumed mag-
netic field distribution is only valid for flyers situated close to the
pressure lead of the coil. This assertion will be further discussed
later.
Fig. 5. Exemplary analytically calculated pressures for rectangular one-turn coils
and a flyer conductivity of 30.16MS/m according to Eq.(27).
3. Experimental procedure
TheMPWexperiments conducted withinthe scope of this workcan be divided into two major parts: velocity measurements (part
I) and welding experiments (part II). Firstly, data obtained from
part I was used to verify the analytical model introduced above
and, secondly, to identify suitable parametersettings for theactual
welding part. Every experiment was repeated three times for rea-
sons of statistical certainty. The basic setup of both experimental
partsis schematically shown inFig.6. Theproposedmodel assumes
a two-dimensional field distribution in the tool coil, which theo-
retically implies an infinite coil lengthalong the axis of the current
flow. That is why relatively long coils (effective length300mm)were used for the experimental part of the work reported here.
In part I, a flyer plate was accelerated over a distance of
5 mm by a one-turn coil without a real target, but with a hole
drilled into the opposing clamping fixture to allow for recordingthe transient flyer velocity at the central point between the two
5 mm-spacers by means of a Photon Doppler Velocimetry (PDV)
system, which is addressed later in this section. On the basis of
a copper-chrome-zirconiumcoil designed by PoyntingGmbH(coil
type:F-VWB-300-10), twodifferentpressureleadgeometries were
Table 1
Experimental design of part I.
Velocitymeasurements (PDV, 5mm travel)
Each experiment: 3 repetitions Approx. frequency
CMaxwell =504F: 20kHz CSMU= 80F:55 kHz CSMU= 40F: 65kHz
Charging
energy
3.25kJ ,
4.09kJ
5.75kJ
6.68kJ
8.25kJ
Experiments were conducted for both coils (RE, TR) with 1mm thick EN AW 5005A flyers
Energy variation: , frequency variation (with Ia
207kA):
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Fig. 6. Schematic of experimental setup for part I and II ofMPW experiments.
Table 2
Experimental design of part II.
Weldingexperiments
Each experiment:
3 repetitions
Standoffdistance
1mm 2mm
Charging
energy
5.75kJ , ,
8.25kJ , ,
9 kJ
TRcoil onSMUcapacitor bank at approx. 55kHz
Target: EN AW 6060 hollow profile, flyer: 1mm thick EN AW 5005A sheet
Withmandrel in profile: , withoutmandrel:
tested (seeFig.6). Strictlyspeaking,the cross-sectionof thetoolcoil
with the chamfers was a hexagon consisting of a trapezoid and an
adjacentrectangle. To emphasize thegeometryof thepressure lead
in close proximity to the flyer, this coil is called trapezoid (TR) in
Fig.6 andhereafter; thecompletelyrectangular one iscalled REcoil
from now on. In part II, flyer plates were accelerated onto a rect-angular hollow profile to create magnetic pulse welds in the form
of a lap joint havinga predetermined standoff distance,whichwas
ensured by two insulating spacers. In some cases a massive steel
mandrel wasput into the hollow profile to prevent deformation of
the profile upon flyer plate impact. In both experimental parts the
horizontal distance between the two insulating spacers amounted
to50 mm. Theparameters variedarelisted in theensuingtables for
each part.
The experimental design of part I is summarized in Table 1 and
may be further divided into the two subparts frequency variation
and energy variation. When changing the discharge frequency of
the circuit, it is useful to keep the peak current Iaconstant in order
toretaincomparability. Therefore,dependingon thecapacitorbank
configuration, various charging energies needed to be employed
Fig.7. Schematicof thePDVsystemusedfor experimentalpartI (Lueg-Althoff et al.,
2014).
(RLC analysis). Regarding the two coil types, however, the same
charging energies were applied for the frequency variation yield-
ing peak currents that were not perfectly identical but in the same
range (approx. 207 kA, seeTable 1). Two different pulsegenerators
(9kJ Poynting SMU 0612 FS and 32kJ Maxwell Magneform 7000
series)wereused tocovera frequency rangefrom20 kHztill65kHz.
The second subpart, the variation of the charging energy, comes
along with a variation of the peak current; in this case, at a rela-
tivelyconstant frequency of about 55kHz. 1mm thicksheetsmadefrom the aluminum alloy ENAW5005A were chosen asflyer mate-
rial. The rolling direction was always perpendicular to the length
of the pressure lead of the coil. Density and electrical conductiv-
ity of the flyer plates were taken to be 2.70g/cm3 and 30.16MS/m,
respectively (N.N., 2015).
The experimental design of part II is compiled in Table 2. With-
outanticipating results, it canbe seen that only onecapacitorbank
configuration (55 kHz: SMU pulse generator with a capacitance of
80F) and only the TR coil were utilized for the magnetic pulsewelding of the EN AW 5005A flyer plates onto extruded rectangu-
lar EN AW 6060 profiles with a wall thickness of 5mm. Moreover,
chargingenergies ranging from5.75kJ to9 kJas well asstandoffdis-
tances of 1mm and 2mm were deployed with the aim to provide
different impact velocities and angles.
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Fig. 8. IUL peel test setup integrated in Zwick/Roell tensile testing machine.
During every experiment, the coil current was measured with
the help of a Rogowski coil (type: PEM CWT2500B with 500kA
peak current rating in case of the SMU pulse generator and PEMCWT1500R with 300kA peak current rating in case of the Maxwell
pulse generator) placed at the terminals of the capacitor bank. As
mentioned above, a PDV system was used to record velocity-time
graphs. Such an optical measurement systemis illustrated in Fig. 7.
It is based onthe idea thata laser beam of a known initial wave
length 0 (1550 nm here) is reflected from a moving workpiece the flyer plate with a Doppler-shifted frequency so that a com-
binedtime-dependent beatfrequency, which is proportional to the
wanted workpiece velocity, can be detected (see Fig. 7). The func-
tioning of a PDV system is treated in more detail by Strand et al.(2004). Besides theRIO Grande LaserModulewithanoutputpower
of 1W used here, theotherPDV componentsconformedwiththose
described in Daehn et al. (2008). A LeCroy Waverunner 104MXi
oscilloscope having a maximum sampling rate of 10GS/s ensured
the recording of both the PDV data and the coil currents. Further
dataprocessingwas performedwiththeproprietarysoftwareMAT-
LAB.
Fig. 9. Analytical and measured flyer velocities at certain displacements for varied energies: (a)for therectangular coil, (b) forthe trapezoidal coil.
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138 M.Hahn et al./ Journal of Materials Processing Technology 230 (2016) 131142
For the purpose of assessing the static strength of sheet-to-
profile welds (and similar joints), a device for peel tests was
developed and integrated in a Zwick/Roell Z250 tensile testing
machine. With this test rig, which is pictured in Fig. 8, peel tests
can be conducted under different angles.
Theprincipal structure largely resembledthatof a conventional
tensile test, except that the upper clamping assembly (holds pro-
file) additionally featured one degree of freedom in the horizontal
direction, accomplished by a runner on a rail. The runner was con-
nectedto the lower clampingassembly(holdsbent sheet)by a wire
guidedovera pulley so that the vertical force lines of the lower and
upper clamping assembly steadily coincided when peeling off the
sheet fromthe profile. A plotof test force FPeelversus displacement
was made during every experiment.
4. Verification of the analyticalmodel
In case of MPW, the velocity versus displacement graph v(D) of
a flyer is an importanttoolwith regardto determiningstandoffdis-
tances and machine parameters for specific lap joints. Such graphs
constitute the focus of the verification of the analytical approach
developedin Section2. Fortoolcoilshavingageometryonlyslightly
differing from that of a rectangular one (e.g., TR coil in Fig. 6), Eq.
(27) may be modified as
p =0I
21 exp
2s/F
2w +w exp
s/F
+ 2Fh
1 exp
s/F
/s2 (28)
where w is still the width of the surface parallel and close to the
flyer plate(3mm;see Fig.6) whereaswis the widthof theoppositesurface (6mm, also see Fig. 6). In cross-section, h now representsthe lengthof the open polygonal path along the lines connectingw
andw(h = 15.6mm incaseof the TRcoil).Analyticalvelocities (Eq.(9))and displacements(Eq. (10)) generatedfrompressures accord-
ing to Eqs. (27) or (28) were based on measured coil currents in
this work. In the analytical model, dv/dt0 applies, while there isnaturally also a deceleration phase in reality. It is therefore useful
to compare the analytics with experimental results until or at thedisplacement where the measured flyer velocity vm achieved its
maximum, D(vm,max). Such comparisons areshown in Fig. 9a and b
in terms of varying the charging energy for a given capacitor bank
configuration and, thus, a constant discharge frequency (approx.
55kHz).
Maximum velocities ranged from less than 200m/s at a charg-
ing energyof 3.25kJ to 420m/s at 8kJ. The TR coil provided higher
velocities than the RE coil and these higher velocities already
occured at shorter distances compared to the RE coil, which can
be traced back to higher magnetic pressures due to the smaller
pressure lead. Calculated velocities at D(vm,max) were in accept-
able agreement with measured ones for both coil geometries. The
average deviation between model and experiment amounted to
9% for the variation of charging energy, the largest deviation was20% at 8kJ and a comparatively largeflyer displacementof 3.4mm.
In case of the TR coil, the charging energies corresponded to peak
currents ranging from 200kA at 4.8kJ to 303kA at 8kJ. A larger
cross-sectional area comes along with a lower resistance, which
is why higher peak currents were recorded when using the RE coil
(between214kA at3.25kJ and 338kAat8 kJ).Maximum measured
flyervelocitiesandassociatedanalyticalonesresulting fromchang-
ing the frequency while keeping the current amplitude almost
constant (approximately 207 kA) are depicted in Fig. 10a and b for
both coils used.
Here, the deviationbetween model and experiment also varied
from 0% to not more than 20%, again with an average deviation of
about 9%. It is noticeable that most of the measured and calculated
velocities lay in the same area (ca. 200m/s), only the correspond-
ingdisplacements partlydiffered to a greater extent. So, fora given
peak current and impact velocity, the discharge frequency might
serve as a parameter to adjust the desired standoff distance. Fast
capacitor banks can improve the process efficiency because higher
frequencies allow for achieving the same flyer velocity as with
slowercapacitorsbutwithless energy input(seeFig. 10). Certainly,
this isnota general statementdue to the fact that all circuit param-
eters are of interest when choosing the charging energy. In case of
the 65kHz experiments, for example, a lower capacitance facili-
tated the frequency increase, but, at the same time, an inductance
slightlyhigher than that forthe 55kHz experiments ledto the need
of a higher charging energy to reach the same peak current. The
latter two figures just refer to a specific flyer displacement. Rep-
resentative curves of velocity versus time and displacement are
displayed in Fig. 11a and b for the REcoilas well as in Fig. 12a and
b for the TR coil.
Despite a small difference in the time domain in Fig. 11a, the
related velocity-displacement curve in Fig. 11b shows how accu-
rate the model represented the experiment until the deceleration
phase of the flyer began. The same basically applies to the graphs
in Fig. 12a and b except that there was no differencebetween both
graphs at the beginningof theflyer acceleration, plus a slight over-
estimation at the maximum velocity wasobserved.
Theanalytical model providedsatisfying results until the actualflyer displacement D(vm,max) was reached. As can be seen in
Figs. 11 and 12, the model might also still be helpful in the
early decelerationphase just after vm,max. Moreover, velocity mea-
surements are always necessary to detect D(vm,max). An adequate
domain of definitionshall bedefined independentof specificveloc-
ity measurements. The magnetic field distribution as described in
Section 2 implies that the workpiece movement is ignored and
without specifying a distance that the flyer is located near the
pressure lead of the coil. A characteristic distance Dch between
tool coil and flyer plate, which can be set as maximum admissi-
ble flyer displacement in the analytical model, can be obtained by
considering the total magnetic energy EL :
EL= 12LI2 = 0
2
| H|2dV. (29)For long coils, EL may be assumed to be completely stored in
the gap between the coil and the flyer. To simplify matters, the
high-frequency limitwithHg= I/w is used so thatELcan be written
as
EL=1
2LI 0
2
H2gdV=
02 H2gwaDch=
0aDch2w
I2 (30)
wherea is the lengthof the pressure lead in the directionof current
flow (295mm here). Neglecting the resistance in Eq. (2), the total
inductance L can be expressed in the form
L 1
42f2C . (31)
After substituting Eq. (31) into Eq. (30), solving forDch yields
Dch= w
4a02f2C . (32)
Dch represents a criterion for the maximum flyer displacement at
which the analytical field distribution remains valid. For a given
current, and under the assumptions made above, a higher value of
Dch would lead to a magnetic energy larger than the initial charg-
ingenergy. Nevertheless, theactual maximumflyervelocityvm,maxmightoccurbefore, at,or afterDch. Measuredvelocitiesvm(Dch)and
analytically calculated ones v(Dch) for both the variation of energy
(or peak current Ia) and frequency are collected in Fig. 13a and b
for the respective coil geometry.
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M.Hahn et al. / Journal of Materials Processing Technology 230 (2016) 131142 139
Fig. 10. Analytical andmeasured flyer velocities at certain displacements forvaried frequencies:(a) forthe RE coil, (b) forthe TR coil.
Fig. 11. Example comparison between the analytical model and an experiment performed on the Maxwell pulse generator with the rectangular coil: (a) velocity-time and
current-time graph, (b) velocity-displacement graph.
Fig. 12. Example comparison between the analytical model and an experiment performed on the SMU pulse generator with the trapezoidal coil: (a) velocity-time and
current-time graph, b) velocity-displacement graph.
Thevelocities vm(Dch) usually lay inthesamerangeas the actual
maximum velocities vm,max(compare with Figs. 9 and 10. What is
more, the analytical velocities at Dch were mostly in good agree-
ment with the corresponding experimental velocities (see Fig. 13).
Deviations between them now ranged from perfect agreement to
55%. The largest deviations, though, were outliers in that they per-
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140 M.Hahn et al./ Journal of Materials Processing Technology 230 (2016) 131142
Fig. 13. Experimental and analytically calculated velocities at distanceDch: (a) trapezoidal coil, (b) rectangular coil.
tained to displacements of almost 4mm, which equals four times
the initial thickness of theflyer plate. At such large displacements,
the occurrence of considerable tensional membrane forces make
the assumption of a rigid-body motion (see Eq. (9)) seem inadmis-
sible. Consequently, the model clearly overestimated velocities at
large displacements(several timestheflyer thickness) where plas-
tic work became significant, meaning that the flyer was already in
the decelerationphase fora long time. Another reasonfor the inap-
plicabilityof themodelathighdisplacements is thatthemodel (Eqs.
(27) and(28), respectively)as wellas thecriteriongiventhroughEq.
(32)presumea spatiallyconstant magneticfield in thegapbetween
the flyer plate and the tool coil (see Fig. 4). This simplification con-
notes that the size of the gap and thus the flyer movement do not
influence the magnitude of magnetic pressure. If the gap becomes
too large in reality, though, the electromagnetic coupling and, as a
consequence thereof, the magnetic pressure diminish so that the
field distribution illustrated in Fig. 4 ultimately becomes invalid
at high displacements. It is therefore noted that both the analytical
modelaswell asthe displacementcriterionareonlyfeasibleas long
as a good coupling is ensured. Since maximum standoff distances
are typically only of the order of a very few millimeters or less in
MPW, theformulas introduced herecansupport theprocessdesign
of lap joints without the need of costly velocity measurements.
5. Evaluation ofweld quality
As the previous section showed, theanalytical model proposed
in this article couldbe used to approximate the impactvelocity vim
Fig.14. MPW strengthevaluation forpeel tests:maximum testforceversus impact velocity fordifferent standoffdistances(withand without putting a massive steel mandrel
in theEN AW 6060 hollowprofileduring magnetic pulse welding).
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M.Hahn et al. / Journal of Materials Processing Technology 230 (2016) 131142 141
Fig. 15. Exemplary photograph and micrograph of MPW sheet-to-profile lap joint.
(first impact onto the profile in this case) for the welding experi-
ments mentionedin Section3 (experimentalpartII). Themaximum
test force Fmax recorded during the peel test also explained in Sec-
tion 3 was taken as a representative value for the weld strength.
Expressing the strength in terms of stress would not be feasible
here due to the fact that the area truly welded was not accessible
nondestructively. Hence,adiagramwhereFmax isplottedversus vimfor various experimental configurations is shown in Fig. 14. Even
though the impact angles were not known here (not reliably mea-
surable in situ), it canbe statedthat higher standoff distanceswere
accompanied by higher impact angles.
Data points lying around Fmax =0 symbolize that no weld was
achieved in those cases. From vim =400m/s on, it seems that the
maximum load the joint was able to bear was reached (approx.
3kN), independent of impact angle (or standoff distance) and
impact velocity. Certainly, this maximum force indicated a min-
imum peel strength of the joint because all welded specimens
failed in the base metal of the flyer plate near the weld seam while
the weld seam itself remained free of failure (see photograph in
Fig. 14). It can also be seen from Fig. 14 that the force FUTS, whichcorresponds to the ultimate tensile strength of the flyer material,
was a little higher than Fmax of the joints. This observation may
be explained by the stress state of a flyer segment in the region
wherefailure occured duringpeeling (see sketch in Fig. 14): On the
one hand, the test load FPeel acted as a tensional membrane force
within the flyer. On the other hand, the test force also caused a
bending moment in a flyer cross-section close to the weld seam.
This moment was characterized by tensional stresses near the tar-
get (profile here) and compressive stresses near theopposing flyer
surface. Consequently, the superposition of tensional stresses gen-
erated by FPeel and its associated bending moment led to a lower
maximum test force than in pure tension. Furthermore, it can be
concludedfrom Fig. 14that the usageof a mandrel topreventdefor-
mationof theprofile didnot affectthe weld strength. Naturally, the
experimentalsetup is less complex andmoreflexible ifa mandrel is
not required. When no mandrel was used, the deflection resulting
from theflyer impactreduced the innerheight of thehollow profile
from 50mm to approximately 49mm (1/5 of the wall thickness).
With mandrel, no deflection of the profile could be detected. Yet,
Psyk et al. (2014) showed that the target deformation can signifi-
cantlyinfluence thejointquality if the flyer and thetarget aremore
similar in thickness than in the present study.
Finally, in Fig. 15, a welded specimen, representative of thesuc-
cessful welding experiments, was regarded on the macro as well
as on the micro scale to further evaluate the quality of the MPW
joints. In the etched microsection, it can be seen that there were
twosmall symmetric regions, where the flyer wasactually welded
to theprofile (bigger grains in the profiledue to extrusionprocess),
while noweld could be created in the center. Since a small fraction
of the flyer surface was parallel to the targetsurfaceat theveryfirst
impact, the impactanglewas too low for the formation of a weld in
this central region. Within theweldedregion, however, the typical
wavy interface could be observed. Microscopically, neither inter-layers nor local melt zones are visible (see Fig. 15). Raoelison et al.
(2013) found waves of about the same amplitude (ca. 20m) intubular MPWjoints of aluminum alloy 6060 and claimed that such
continuous interfacial waves without voids imply a good and per-
manentbonding, whichagainendorses thepeel test results shown
in Fig. 14.
6. Conclusions
Forthemagneticpulsewelding(MPW)offlat sheetsusinga one-
turn coil, the following conclusions can be drawn from the work
presented:
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142 M.Hahn et al./ Journal of Materials Processing Technology 230 (2016) 131142
A simplified analytical model that allows to compute the mag-neticpressureaswellas thevelocity-timeanddisplacement-time
history of the flyer plate until the first impact onto the target
was introduced. It takes into account the geometry, the current
amplitude, and the discharge frequency. The model was verified experimentally by utilizing Photon
Doppler Velocimetry (PDV) to record the transient flyer veloci-
ties for various charging energies (3.258.25kJ) and frequencies
(approx. 20kHz to approx. 70kHz). Average deviations between
the model and the experiments amounted to 9%. Further insight into the impact welding process was gained with
the help of the modelbyshowing that an impactvelocity ofabout
400m/s isnecessary forthemagneticpulseweldingof 1mmthick
EN AW 5005A sheet onto an EN AW 6060 hollow profile. Etchedmicrosections made clear that a wavy interfacemorphol-
ogy is present in the welded regions in which no interlayers,
voids, or melt zones could be found.
Acknowledgements
This paper is based on investigations of the Collaborative
Research Center SFB/TR 10, subproject A10 Joining by forming,
which is kindly supported by the German Research Foundation
(DFG). The peel test used for this work has been developed within
the scope of subproject A1 of thepriority program SPP1640 (join-
ingby plastic deformation) also funded by theDFG.
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