A binding scheme to minimize thinning of formed tailor welded blanks

Abstract

Weld line movements (WLM) and thinning in draw bending and deep drawing of Tailor Welded Blanks (TWBs)
constitute major defects in automotive applications. The present work aims at the development of a binding scheme
that improves sheet thinning and eliminates WLM. This is achieved by using controlled blank holding segmented
binders (blank holders) at the boundaries of the parent sheets of the TWB and counter pins at the weld lines.
Analytical models for the 2-D draw bending and 3-D deep drawing are developed to predict the required
blank-holder/counter-pin forces that insures identical elongation (deformation) on both sides of the TWB and thus
eliminates the WLM. The 2-D model is validated by a series of draw-bending laboratory experiments. The experimentation
of the proposed force scheme produced identical elongations on both parent sheets and consequently zero
weld line movement (WLM) as targeted by the analytical model and hence the feasibility of the proposed scheme is
proved in practice. Additional draw-bending/box-drawing experiments are conducted to compare the proposed scheme
with separate use of either segmented blank holders, weld line clamping pins or counter punch. The results showed
improved reduction in thinning and elimination of WLM when the binding forces of the process are controlled as
proposed by the developed model.

Full text

1 23
The International Journal of
Advanced Manufacturing Technology
ISSN 0268-3768
Int J Adv Manuf Technol
DOI 10.1007/s00170-018-1686-6
A binding scheme to minimize thinning of
formed tailor welded blanks
Mahmoud S.Seyam, Mostafa Shazly,
Alaa El-Mokadem & Abdalla S.Wifi

1 23
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ORIGINAL ARTICLE
A binding scheme to minimize thinning of formed tailor welded blanks
Mahmoud S. Seyam
1
&Mostafa Shazly
2
&Alaa El-Mokadem
1
&Abdalla S. Wifi
1
Received: 3 January 2017 /Accepted: 30 January 2018
#Springer-Verlag London Ltd., part of Springer Nature 2018
Abstract
Weld line movements (WLM) and thinning in draw bending and deep drawing of Tailor Welded Blanks (TWBs)
constitute major defects in automotive applications. The present work aims at the development of a binding scheme
that improves sheet thinning and eliminates WLM. This is achieved by using controlled blank holding segmented
binders (blank holders) at the boundaries of the parent sheets of the TWB and counter pins at the weld lines.
Analytical models for the 2-D draw bending and 3-D deep drawing are developed to predict the required
blank-holder/counter-pin forces that insures identical elongation (deformation) on both sides of the TWB and thus
eliminates the WLM. The 2-D model is validated by a series of draw-bending laboratory experiments. The experi-
mentation of the proposed force scheme produced identical elongations on both parent sheets and consequently zero
weld line movement (WLM) as targeted by the analytical model and hence the feasibility of the proposed scheme is
proved in practice. Additional draw-bending/box-drawing experiments are conducted to compare the proposed scheme
with separate use of either segmented blank holders, weld line clamping pins or counter punch. The results showed
improved reduction in thinning and elimination of WLM when the binding forces of the process are controlled as
proposed by the developed model.
Keywords Tailor welded blanks .Formability .Segmented binders .Draw-bending .Box deep drawing .Weld line movement .
Finite element analysis
Nomenclatures
fTensile force along the deformed profile (normal to the sheet
thickness)
BHF
s
Blank holding force on the stronger side
BHF
w
Blank holding force on the weaker side
F
pin
Clamping force along the weld line
μ
p
Friction coefficient at the weld line
μ
s
Friction coefficient at the stronger side
μ
w
Friction coefficient at the weaker side
KStrength coefficient (in the maximum principal direction)
nStrain hardening exponent
L
o
Original length (for each parent sheet s and w)
t
o
Original thickness (for each parent sheet s and w)
LCurrent length (for each parent sheet s and w)
tCurrent thickness (for each parent sheet s and w)
ΔLstot Total increase in the original length (the total elongation) of
the stronger parent sheet
ΔLwtot Total increase in the original length (the total elongation) of
the weaker parent sheet
cDie/punch clearance
R
d
Die corner radius
R
p
Punch corner radius
YPunch current vertical position
θWrap Angle
MInternal bending moment (for each parent sheet s and w)
X
w
Initial weld line position
σMaximum principal stress
ϵMaximum principal strain
αStress ratio σ2
σ1
βStrain ratio ϵ2
ϵ1
*Mostafa Shazly
mostafa.shazly@bue.edu.eg
1
Department of Mechanical Design and Production, Faculty of
Engineering, Cairo University, Giza, Egypt
2
Mechanical Engineering Department, Faculty of Engineering, The
British University in Egypt, Al-Shorouk City, Cairo 11873, Egypt
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https://doi.org/10.1007/s00170-018-1686-6
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1 Introduction
Innovative solutions to reduce vehicle’sweighttoim-
prove fuel consumption are crucial to automotive indus-
try. Currently, body panels in modern vehicles are con-
structed using Tailor Welded Blanks (TWBs) to achieve
improved performance while minimizing total weight. A
TWB consists of several flat metallic sheets with differ-
ent characteristics (parent sheets) joined together prior to
stamping to final shapes. The major success of the pro-
cess, however, comes with detrimental reduction in form-
ability as a result of the geometrical/material discontinu-
ity [1]. The blank heterogeneity also causes diversity in
the developed strains when uniform loads are applied,
leading to accidental relocation of the parent sheets
which is also known as Weld Line Movement (WLM).
Several attempts were made to enhance the formability of
TWBs by eliminating the WLM. Ahmetoglu et al. [2]man-
aged to control the weld line movement in deep drawn cups
made of AKDQ TWB with a thickness ratio of 1.8/0.8 using
segmented binders with different levels of blank holding
force on each parent sheet. The blank holding force (BHF)
at the thinner side was increased by 100% while simulta-
neously decreased at the thicker side by 80%. Kinsey and
Cao [3] applied additional constrains to the weld line direct-
ly using clamping pins to prevent WLM and enhance form-
ability. Similarly, Morishita et al. [4] used a counter punch
instead of the pins. They experimentally proved that a half
counter punch causes the same result of a full counterpunch
if applied to the stronger side of the cup bottom, while
causes early failure if applied to the weaker side. Other
techniques including the adjustment of initial under
binder-blank shape [4] and draw beads [5]werealsocapable
of reducing the WLM. Chen et al. [6] studied the effect of
using both stepped and flat binders during the box drawing
of a 1.2/0.8 mm thick TWB. In the case of stepped binders,
full contact with the thinner flange was achieved unlike the
case with a flat binder where the gap between the binder and
theflangepromptedwrinkling.Theyalsoshowedthatthe
application of clamping pins and stepped binder together
gave better results in terms of WLM/wrinkling prevention
and thinning reduction.
It should be noted that the predictions of BHFs com-
binations are crucial for a successful application of the
segmented binder technique. Such predictions can be
achieved through analytical or numerical models. For
example, He et al. [7] developed a 2-D analytical model
to estimate the required BHFs difference for zero weld
line movement in a plane strain U-draw-bending process.
Kinsey and Cao [8] developed another model to predict
WLM given the BHF on both sides which was also ex-
tended to predict the required BHF combination required
for zero WLM. FE simulations based on reaction forces
measured at weld line bonded to the punch were used to
estimate the required BHF [9]. Shazly et al. [10]used
numerical experiments to study the effect of several var-
iable blank holding force (VBHF) schemes on WLM for
a plane strain draw-bending process. Based on the evo-
lution pattern of weld line movements during the draw-
ing process, they suggested applying a higher BHF on
the weaker side with its peak value at the beginning of
the process. More reduction of the weld line movement
was achieved by increasing the peak BHF, however, con-
siderable thinning occurred at the weaker side’s wall be-
fore complete elimination of the WLM. The same au-
thors [11]alsousedthereactionforcesattheweldline
(following Kinsey and Cao [3] and Kinsey et al. [9]) to
improve the VBHF scheme.
As shown above, previous analyses are based on the
assumption that WLM elimination and thinning reduction
Fig. 1 Draw bending of U-shaped part. aMaterial flow pattern. bProfile segmentation for each side
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are connected. The previous attempts to reduce thinning
were done through the elimination of WLM. However,
the success of such assumptions depends on the tech-
nique used to eliminate WLM. Previous attempts to con-
trol the weld line via segmented blank holders only
showed significant increase in thinning as a result of
increased binding force on the weaker side of the TWB
[2,10]. Alternatively, the clamping pin and counter
punch techniques were able to eliminate the WLM with-
out increasing thinning. However, the weaker side
showed larger thickness reduction as compared to the
stronger side when both are subjected to same BHF. In
case of high difference ratio (i.e., thickness and/or
strength) between the parent sheets, applying identical
BHF may cause tearing at the weaker side and/or wrin-
kling at the stronger side. In such a case, controlling the
weld line by any of the discussed techniques separately
will not prevent failure.
In the present work, a 2-D analytical model is devel-
oped for a new scheme that combines the segmented
blank holder and the clamping pin techniques to control
the stretching forces acting on each parent sheet separate-
ly such that the tearing limit for each sheet is not
exceeded. The scheme is developed and applied on
U-shapeddrawnpartsandextendedtobox-shapeddrawn
parts. Given the tool/blank geometry, materials properties,
and the BHF on one side, the model provides the required
BHF on the other side to produce equal elongation in both
sides and calculates the required counter pin force at the
weld line to achieve force equilibrium and produce zero
WLM. The suggested approach is verified experimentally
by a series of laboratory tests under different conditions.
Additional experiments on box-shaped parts and finite
element tests based on published experimental work from
literature are used to demonstrate the advantage of the
combined segmented blank holder/counter pin technique
over other techniques. The work methodology and model
development are presented in the subsequent sections
followed by results and discussions.
2Methodology
2.1 Model development
Considering the schematic drawing in Fig. 1a, if the forces
BHF
s
,BHF
w
,andF
pin
are to cause identical elongation in both
sides, the boundary line between both sides remains fixed
horizontally and the flow pattern will be as shown in
Fig. 1a. In the present analysis, the friction model f
′
=fe
μθ
is
used to describe sliding over the punch/die corners [12], where
fis the tensile force normal to the cross section. Side walls are
assumed straight and the maximum principal direction is as-
sumed along the deformed shape. The profile of the blank
Fig. 3 Biaxial condition at the bottom section—one side of the TWB is
illustrated
Fig. 2 Blank holding configurations. aCase 1: The flange is completely under binder with decreasing blank holding area. bCase 2: The flange is
partially constrained with a constant blank holding area
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during the process is divided into ten segments; five segments
at each side as shown in Fig. 1b. BHF
s
,BHF
w
,andF
pin
are the
blank holding force on the stronger side, the weaker side, and
the total counter pin force, respectively. The subscripts
′
s
′
and
′
w
′
indicate the strong and weak sides. In this model, the clamping
pins only contacts the lower face of the blank pushing it against
the punch bottom face (i.e. counter pins) [6]. In order to identify
the weak and strong sides for a given—initial—thickness/
length and material combinations, the elongations for both
sides are calculated for a given tensile force Fand the side with
lower strain and hence elongation will be considered the stron-
ger side. Hence
∴ΔLs<ΔLw;ΔL¼LoeF
toK
ðÞ
1
n−1
 ð1Þ
The tensile forces at the boundaries between segments are
obtained from force equilibrium in terms of the blank holding
forces as follows:
fa¼2μwBHFw
ðÞ;fA¼2μsBH Fs
ðÞ ð2Þ
fb¼2μwBHFw
ðÞeμwθw¼fc;fB¼2μsBHFs
ðÞeμsθs¼fCð3Þ
fd¼2μwBHFw
ðÞ;fD¼2μsBHFs
ðÞ ð4Þ
The clamping force required to produce frictional forces
that eliminate the net horizontal forces and achieve equilibri-
um at the weld line (not the total clamping force F
pin
)isgiven
by:
F¼2μsBHFs
ðÞ−μwBH Fw
ðÞ
μp
!ð5Þ
where μ
p
,μ
s
,andμ
w
are the friction coefficients at the weld
line, the strong side and the weak side, respectively. The log-
arithmic strains along segments 1, 3, and 5 are assumed con-
stant for each segment and are obtained by solving Eq. (6):
f¼σt¼KϵðÞ
ntoe−ϵð6Þ
where Kis the strength coefficient (in the maximum principal
direction). The logarithmic strain at the curved segments are
averaged as shown in Eqs. (7)and(8):
ϵ2w ¼ϵ1w þϵ3w
2;ϵ2s ¼ϵ1s þϵ3s
2ð7Þ
ϵ4w ¼ϵ3w þϵ5w
2;ϵ4s ¼ϵ3s þϵ5s
2ð8Þ
The elongation in each segment is calculated from the log-
arithmic strain in terms of the current length as shown in Eq.
(9):
ϵ¼ln L
Lo

¼ln L
L−ΔL

→ΔL¼L1−e−ϵ
ðÞ ð9Þ
where Land L
0
are the current deformed and original lengths of
the segment, respectively. Regardless of the difference in the
initial lengths, the target of the model is to provide the BHFs
that produce identical elongation for both sides such that:
ΔLstot ¼ΔLwtot ð10Þ
where ΔLstot and ΔLwtot are the total increase of the original
length (the total elongation) of the strong and weak sides of
the TWB, respectively. Knowing that the total elongation is
the summation of the segments’elongations in each side, Eq.
Fig. 4 Assembly and dimensions of the die set used in the experimental work
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(10)becomes:
∑
5
i¼1
ΔLis−∑
5
i¼1
ΔLiw¼0ð11Þ
Substituting Eq. (9) in Eq. (11)yields
∴∑
5
i¼1
Lis1−e−ϵis
ðÞ−∑
5
i¼1
Liw1−e−ϵiw
ðÞ¼0ð12Þ
The current length of segment 1 is obtained in terms of the
other segments’lengths for two cases depending on the blank
holding area. The first case is illustrated in Fig. 2a, where the
flange is completely constrained by the blank holder and the
binding area is gradually decreasing with the condition
(L
BH
≥L
1
) satisfied. The current length of segment 1 in this
case is calculated as follows:
Ltot ¼Lotot þΔLtot
∑
5
i¼2
LiþL1¼Lotot þ∑
5
i¼2
Li1−e−ϵi
ðÞþL11−e−ϵ1
ðÞ
∴L1¼eϵ1Lotot −∑
5
i¼2
Lie−ϵi
 ð13Þ
Substituting Eq. (13) in Eq. (12)yields:
∴Lostot eϵ1s−1ðÞþ∑
5
i¼2
Lis1−eϵ1s−ϵis
ðÞ


−Lowtot eϵ1w−1ðÞþ∑
5
i¼2
Liw1−eϵ1w−ϵiw
ðÞ


¼0ð14Þ
The second case is illustrated in Fig. 2b, where the binding
area is kept constant by constraining a specific domain in the
flange. In this case, the flange is divided into two segments;
one is under the binder segment (L
1
= blank holder contact
length) and the other is the unconstrained segment (L
1′
≥0)
which gradually decreases with the punch movement. When
the length of segment L
1′
becomes zero, case 1 is then
Distance along TWB (mm)
Vickers Hardness, Hv
-30 -20 -10 0 10 20 30
100
200
300
400
500
600
Weld
Line
Center
Thick Side
Thin Side
Fig. 5 Vickers hardiness test—HAZ width = 17 mm
Table 1 Characteristics of the TWB used in the present work
Material Mild steel Galvanized steel
Thickness (mm) 1.75 0.7
Length (mm) 150 150
Width (mm) 55 55
Yield strength (MPa) 262 233
Tensile strength (MPa) 309 295
n0.09 0.12
K(MPa) 462 420
Fig. 6 Dimensions of die set and initial blank used for rectangular box
studies in the present analysis. All dimensions in mm
Fig. 7 Half the die set for the proposed approach
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retrieved. The length of segment L
1′
is calculated as follows:
Ltot ¼Lotot þΔLtot
∑
5
i¼1
LiþL10¼Lotot þ∑
5
i¼1
Li1−e−ϵi
ðÞ
∴L10¼Lotot −∑
5
i¼1
Lie−ϵi
ð15Þ
The current lengths of segments 2, 3, 4, and 5 are calculated
using the geometrical model (see Appendix Afor details) with
respect to the current position of the punch such that:
L2w ¼θwRdw;L2s ¼θsRds ð16Þ
L4w ¼θwRpw;L4s ¼θsRps ð17Þ
L3w ¼Y−Tw1−cosθw
ðÞ
sinθw
;L3s ¼Y−Ts1−cosθs
ðÞ
sinθsð18Þ
The wrap angle is related to the punch vertical displace-
ment as follows:
θ¼2tan−1
C−ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C2þY2−2TY
p2T−Y
!
;Y≠2T
C¼cþRpþRd;T¼tþRpþRd
ð19Þ
In order to eliminate the effect of internal bending moments
M
s
and M
w
at segments 4
s
and 4
w,
which contribute to the
vertical WLM and reduce the resultant counter pin force
(F
pin
), additional amount of force F
′
must be applied by the
counter pin such that:
F0¼Ms
L5s þMw
L5w
;where M
¼2∫r¼0:5t
r¼0rK ln 1 þr
Rþ0:5t

n
dr ;
R¼Rp
ð20Þ
The bending moment is calculated assuming the neutral
line at the mid-plane of the sheet and neglecting the effect of
stretching (see Appendix A). Moment integration is done nu-
merically and the total minimum counter pin force is then
calculated as:
Fpin ¼FþF0ð21Þ
Fig. 8 Schematics for each of the
compared WLM controlling
schemes
Fig. 9 FEA model for plane strain draw-bending process based on refs.
[13,14]
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In box-shaped drawing, the straight sides can be approxi-
mated by 2-D plane strain sections, while the bottom section at
the punch face is subjected to biaxial stretching forces as
shown in Fig. 3.
Assuming the weld line is along direction “y,”the elonga-
tion in direction “x”at the bottom in each side is:
ΔLx¼L1−e−ϵx
ðÞ
Equation (6)thenbecomes:
Fx¼
ϵxffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4
31þβþβ2

q

n
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1−αþα2
pKt
oe−1þβðÞϵxð22Þ
where α¼
Fy
Lx
Fx
Ly
;β¼2αþ1
2þα
Table 2 Input values the selected case studies
Case
Configuration
Case1
Case2
Case3
Case4
Case5
Case6
Case7
Thickness
ratio tow/tos
0.25
0.25
0.25
0.25
0.25
0.25
1/12
Original
Sheet Length
(Lw/Ls)
1
1
1
1
5/9
9/5
1
Punch
Corner
Radius (Rp)
10tow
Die Corner
Radius (Rd)
Punch Die
Clearance (c)
Punch Face
Width (P)
100tow
100tow
100tow
280tow
280tow
280tow
100tow
Initial Weld
Line Position
(Xw)
0
0
0
0
-100tow
+100tow
0
BHFs
Minimum value to prevent the sheet from departing the die
10tow
10tow
2tow 6tow 2tow 6tow 2tow 6tow 2tow 6tow 2tow 6tow
10tow 40tow 40tow 40tow 40tow
40tow 40tow
40tow 40tow 40tow 40tow 40tow 40tow 20tow 20tow
20tow 20tow
20tow 20tow 20tow 20tow 20tow 20tow 20tow 20tow 20tow 20tow 20tow 20tow
Fig. 10 Draw-bending process
for all cases with process and
geometrical input parameters
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2.2 Model verification
2.2.1 U-draw-bending model
Laboratory experiments are conducted to verify the devel-
oped analytical model and prove its feasibility in practice.
The die set assembly shown in Fig. 4is used to conduct
U-draw-bending experiments on TWBs. In the present
work, a TWB consisting of a mild and galvanized steel par-
ent sheets are TIG welded prior to drawing. The geometrical
and material properties of the parent sheets are measured
and given in Table 1. The width of the heat affected zone
(HAZ) is obtained via HV-50A Vickers hardness tester as
showninFig.5. The HAZ width is found to be approximate-
ly 17 mm, with 8 mm on the thicker side and 9 mm on the
thinner side. A strength coefficient and hardening exponent
of 355 MPa and 0.173, respectively, are obtained from a
tension test specimen of the HAZ.
The BHF and the counter-pin force are applied using two
coil compression springs with identical stiffness of 70 N/mm on
each side. Six different experiments with different conditions
are used to verify the analytical model. In the first three exper-
iments namely cases A, B, and C, the weld line is initially
shifted from the center of the punch toward the thicker side
by 0, 10, and 20 mm, respectively. Both sides are subjected to
identical BHF of 3080 N and no direct constrain at the weld
line. The value of this force is the minimum required for suc-
cessful drawing and was determined by FE simulations. The
friction coefficients for the parent sheets are taken initially as
0.2forthemildsteeland0.17forgalvanized steel and are used
to simulate one of the cases (e.g., case C) using ABAQUS/
Explicit. These values are then adjusted such that the total elon-
gation, WLM, and the final deformed shape for simulation and
experiment are identical. The adjusted friction coefficient
values are then used in the analytical model to generate the
required BHF and counter punch force that will be applied to
cases D, E, and F to achieve identical elongation in both sides
and zero WLM. Cases D, E, and F share the same initial weld
line position as cases A, B, and C, respectively, while the weld
line is constrained by a counter pin. The experimental results of
these six cases are presented in “Section 3.”
2.2.2 Box-shaped drawn model
The extended analytical model for box shape is used to
apply the combined segmented binder/counter-pin
Fig. 11 Experimental comparisons between free weld line and new
scheme. aCases A and D. bCases B and E. cCases C and F
Table 3 Experimental and FE results for model verification
Case no. Weld line position (mm) BHFw/BHFs Fpin/BHFs Lw/Ls HWLM (mm) VWLM (mm)
A (experiment) 0 1.00 0.0 1.013 7.4 5.1
B (experiment) 10 1.00 0.0 1.020 13.8 5.6
C (experiment) 20 1.00 0.0 1.020 20.0 11.2
C (simulation with HAZ) 20 1.00 0.0 1.014 19.2 11.3
C (simulation without HAZ) 20 1.00 0.0 1.019 19.4 11.4
D (experiment) 0 0.13 1.1 1.001 0.0 0.0
E (experiment) 10 0.13 1.2 1.000 0.0 0.0
F (experiment) 20 0.13 1.5 1.007 0.0 0.0
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technique to the TWB of rectangular box-shaped parts pro-
duced by the die set shown in Fig. 6. The experimental
setupshowninFig.4is upgraded to accommodate the
dimensions of the rectangular box shown in Fig. 6with
segmented binder/counter pin as schematically shown in
Fig. 7. The TWB used in the rectangular box-shaped parts
consists of a 2-mm low carbon steel sheet with a strength
coefficient and a hardening exponent of K= 436 MPa and
n= 0.38, respectively, and a 1-mm low carbon steel sheet
with a strength coefficient and a hardening exponent of K
=509 MPa and n= 0.22, respectively. Three different ex-
periments are conducted to test different conditions. In the
first experiment, a base line experiment, the TWB is sub-
jected to identical BHF and the weld line is unconstrained.
The objective of this experiment is to determine the limit-
ing drawing height. The second experiment (only
counter-pin case) is the same as the first experiment except
for the additional clamping of the weld line provided by
the counter pin to prevent its movement. In the third ex-
periment (new scheme), the weld line is clamped and the
BHF on the weaker and stronger sides and the counter-pin
force are determined using the procedure detailed in
Appendix B. Finally, a finite element model is constructed
and validated following the data of the experimental work
reported by Morishita et al. [4] to compare the proposed
scheme against the counter punch technique. The devel-
oped analytical model in the present work is applied to
(a)
(b)
Punch Displacement (mm)
Displacement (mm)
0 102030405060
-30
-20
-10
0
10
20
30
40
50
60
70
80
Line sigments forModels with no HAZ
Symbols for Models with HAZ
Thin Flange
Displacement
WLM
Thick Flange
Displacement
Fig. 12 Comparisons between FE
models with and without HAZ for
case 3. aFlange displacement and
WLM. bOverlay plot of the
drawn parts—line model for FE
model with HAZ
Fig. 13 Forces predicted by the developed analytical model in each case
and used in the FE simulations
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the validated FE model to test its merit in drawing square
box-shaped part. The selected case consists of a TWB
made of two mild steel sheets with thickness ratio of 0.6/
1.16 mm. Detailed die design and process parameters can
be found in ref. [4]. The blank is simulated using four node
reduced integration shell elements with five integration
points through thickness and a dynamic explicit step of
0.01 s to model the forming stage of the TWB. All other
parts are modeled as rigid bodies. As reported during the
physical experiments, lubrication was used at the flange
zone to facilitate the metal flow into the die opening.
Therefore, a coulomb friction model with 0.2 and 0.25
friction coefficients are applied to the flange and punch
area, respectively. Due to symmetry of the experiment,
only half model is considered as shown in Fig. 7.
2.3 Applications of the combined segmented
binder/counter-pin developed scheme
to the U-draw-bending process
For the draw-bending process, a comparison between the
four schemes shown in Fig. 8including the proposed
scheme is applied using the ABAQUS 6.14 finite element
software. A series of 24 (six for each technique in Fig. 8)
simulationsbasedontheplanestraindraw-bendingbench-
mark test of a homogenous blank reported by Taylor et al.
[13] are carried out in this section. The original benchmark
test is used for verification in “ABAQUS Documentations”
[14]. Considering the homogenous blank as a special case
of TWBs with neglected weld line and identical parent
sheets, the FE model is reproduced for the comparison as
showninFig.9. The insignificance of the weld line in
TWBs forming simulation is discussed by Zhao et al.
[15]andtestedin“Section 3.”All model data such as
geometry, materials’properties, and friction conditions
can be found in ref. [14].Thesameelementsizeasthe
benchmark problem [14] is adopted here and has been ver-
ified by comparisons with other sizes. The recorded spring
back angle between the flange and the horizontal line in the
produced model is 0.22 rad and the experimental measure-
mentsrangefrom0.16to0.4rad(avg.=0.28rad).
All model parameters in the FE model are kept con-
stant except for the necessary tooling parameters and the
applied force schemes. The BHF at the strong side is kept
as applied in the benchmark test as well as the other side
except for the schemes where different force schemes ap-
plies. A mild steel blank shown in Fig. 9with thicknesses
ratio (t
ow
/t
os
)of0.25isusedforallcasesinTable2expect
(a) (b)
Relative Punch Position
VWLM / Weak side sheet thickness
00.250.50.751
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
Case 1
Case 2
Case 3
Case 4
Relative Punch Position
HWLM / Weak side sheet thickness
00.250.50.751
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Case 1
Case 2
Case 3
Case 4
Fig. 14 Weld line movement relative to punch position. aVe r t ic a l (V W L M ) . bHorizontal (HWLM)
Fig. 15 BHF inputs for the segmented binders technique
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for case 7. Cases 1, 2, and 3 have the same blank geom-
etry but different tool geometrical parameters and cases 4,
5, and 6 share the same tool geometry but different blank
geometry. Figure 10 shows schematically the blank, TWB
holder, and die assembly with the geometrical and process
parameters assigned to each part. For each of the first six
cases, the blank/tool geometry, the material properties, the
friction coefficients, and a selected value of the BHF on
the strong side are inserted to the analytical model. The
resulting BHF on the weak side and the counter-pin force
(clamping force) at the weld line are inserted to the FE
model.
In case 7, the comparison is extended to extreme limits
where a 1/12 thickness ratio and 0.4 friction coefficient are
selected to present a case in which, applying identical BHF on
both sides will cause tearing at the weaker side and incomplete
bending (or wrinkling) at the stronger side. In such case, in-
creasing the BHF on the weaker flange or reducing the BHF
on the stronger side is not justified; thus, the segmented
binders technique is excluded from the comparison in case 7.
3 Results and discussions
3.1 Draw-bending process
Figure 11 shows the parts produced under U-draw-bending
process for cases A to F. These figures are used to extract
the total elongation of each side for all cases. As shown in
Tab le 3and Fig. 11, the elongation ratio is close to unity and
the WLM is eliminated in cases D, E, and F as targeted by the
analytical model.
Theexperimentalworkisalsousedtoinvestigatethe
significance of incorporating HAZ properties into the FE
model. As shown in Table 3, the final elongation and
WLM for case C for two FE models; with and without
HAZ, agree well with the measured experimental results.
The flange draw-in and WLM for both FE models are
showninFig.12a while an overlay plot for the two
modelsisshowninFig.12b. The simulation results show
good agreements between the FE models developed with
and without considering modeling HAZ. This indicates
that modeling HAZ has no impact on TWB drawn parts
as also suggested by Zhao et al. [15].
The same analytical model is solved to apply the proposed
scheme to each of the cases listed in Table 2.Figure13shows
the calculated BHF
w
and the counter pin forces (F
pin
)re-
quired for cases 1 to 6. Figure 14 shows the vertical WLM
and horizontal WLM resulted from applying the new scheme
for these cases.
The blank in cases 1 to 4 has the same original di-
mensions and thus the predicted values of BHF
w
and
F
pin
are close to each other except for case 4. In case
4, the length of segments L
5s
and L
5w
at the punch face
are much larger than cases 1, 2, and 3, such that less
forces are required to overcome the internal bending mo-
ment at segments L
4s
and L
4w
.Incase5,thethickerside
is extended by 28.5% more than the thicker side of case
4.Atthesametime,thethinnersideisshortenedby
28.5% less than the thinner side of case 4 such that the
BHF
w
applied in case 4 will produce less elongation in
the thinner side of case 5. Consequently, the calculated
BHF
w
in case 5 is higher than case 4 in order to over-
come the shortage at the thinner side and the additional
elongation at the thicker side while the F
pin
is decreased
to maintain force equilibrium along the blank profile.
The modifications applied in case 6 are the opposite of
those applied to case 5, thus the analytical model pre-
dicts less BHF
w
and higher F
pin
in case 6 as compared
to case 4.
The six cases are used for comparisons between the four
schemes shown in Fig. 8. The proper BHF combination for the
segmented binder technique that leads to zero WLM is obtain-
ed by a matching procedure (see Appendix B) and shown in
Fig. 15. For the weld line clamping technique, displacement
Fig. 16 Normalized overall thinning strain. aWeaker side. bStronger
side
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constrains are applied to the weld line such that no WLM
occurs. For each case, the final deformed lengths (L)atthe
top and bottom surfaces are extracted from FE models to cal-
culate an average total (overall) tensile strain in each side as
follows:
ϵtotal ¼ln L
Lo
;L¼Ltop surface þLbottom surface
2ð23Þ
Recalling the plane strain condition, the average tensile
strain can be used as an indication of the overall thinning in
each side of the deformed blank. For the sake of compar-
ison, the overall thinning strain value for each of the three
schemes b, c, and d shown in Fig. 8isdividedbythestrain
value of scheme a for the same case. A value higher than
one indicates that the applied technique causes more thin-
ning compared to the uncontrolled condition and vice
versa.
Relative Punch Position
Thickness Strain (L33)
00.20.40.60.81
0
0.25
0.5
0.75
1
1.25
1.5
No Control
Weld Line Clamping T echnique
New Scheme
Tearing
Tearing
Fig. 19 Maximum absolute thickness strain at the weaker side at different
punch positions
Relative Position along the Part Length
Thickness Strain (L
33
)
-0.75 -0.5 -0.25 0 0.25 0.5 0.75
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
59% Punch Stro ke
70% Punch Stro ke
Weak Side Strong Side
Weld Line
Fig. 18 Thickness strain along the blank top surface at different punch
depths—Weld line clamping technique Fig. 20 Rectangular drawn box with no counter pin and equal BHF
Relative Position along the Part Length
Thickness Strain (L
33
)
-0.5 -0.25 0 0.25 0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
20% PunchStroke
26% PunchStroke
Wea k Side S trong Side
WeldLine
Fig. 17 Thickness strain along the blank top surface at different punch
depths—uncontrolled condition
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As shown in Fig. 16a, the segmented binder technique
causes significant thinning (81 to 274% increase) in the
weaker side and consequently decreases the sheet form-
ability. On contrary, the new technique shows considerable
reduction in thinning (81.5 to 94.4% decrease) at the weak-
er side as well as the weld line clamping technique which
shows less thinning reduction (21.5 to 57%). Furthermore,
the stronger side is hardly affected by any of the discussed
techniques in all cases except case 3 as shown in Fig. 16b.
In case 3, large punch/die clearance facilitates the sliding
of the stronger segment at the punch face to the side walls,
resulting in less overall stretching compared to the other
three conditions where the stronger side is forced to stretch
over the punch corner.
In case 7, the uncontrolled condition is modeled first
and the recorded maximum WLM before failure are
13Tw and 30Tw in the horizontal and vertical directions
(relative to the punch displacement), respectively. The
BHF at the stronger side shows insufficient constraining
while the weaker side suffers from early failure near the
weld line. Localized necking is observed at 26% punch
travel as shown by the thickness strains distribution along
the top surface of the blank in Fig. 17. Likewise, applica-
tion of the weld line clamping technique with identical
BHF causes insufficient constraining at the strong side
and tearing at the weaker side where localization of neck-
ing in the side walls is observed at 70% punch travel as
shown in thickness strain distribution in Fig. 18.
On the other hand, when the BHF is decreased on the
weaker flange and increased on the stronger flange as the
new scheme suggests, a complete punch stroke with no
failure is obtained as shown in Fig. 19 where a compari-
son of the maximum thinning strain (absolute value) at
different punch positions is presented for the three
models. The new scheme (combined segmented binder/
counter pin—BHFw/BHFs = 0.085) shows considerable
reduction in thinning at the weaker side. In contrast, thin-
ning is considerably high at the two other cases namely
the weld line clamping technique (horizontally fixed weld
line—BHFw/BHFs = 1) and the uncontrolled condition
(free weld line—BHFw/BHFs = 1).
3.2 Rectangular box-shaped drawn parts
Figure 20 shows the drawn rectangular box for the first case
with no counter pin and equal BHF. The thinner side frac-
turedatacupheightof30mm.Figure21 shows the drawn
rectangular box at cup height of 35 mm for counter-pin
case and new scheme. In both cases, the rectangular box
is drawn successfully. The drawn parts are then sectioned
and the part thicknesses close to the paths shown in Fig. 22
are measured. Figure 23 shows a comparison between the
thickness distributions for the counter pin scheme and new
scheme. The new scheme showed an improvement in the
thickness reduction, especially along 90 and 45 degree
paths.
Figure 24 shows a comparison between experimental
measurements by Morishita et al. [4], and the FE model
developed for the same case. The logarithmic thickness
Fig. 21 Rectangular drawn box
using a counter pin and equal
BHF and the new scheme
Fig. 22 Path directions for thickness comparisons
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strains along the deformed paths show good agreement
to the experimental result and hence validates the FE
model. The FE model results of the proposed scheme
areshowninFig.25. The applied BHFw/BHFs and
Fpin/BHFs ratios from the analytical model are 1/2
and 20, respectively. The measured WLM and the final
(a)
(b)
(c)
Distance Along Path (mm)
Sheet Thickness (mm)
-100 -80 -60 -40 -20 0 20 40 60 80 100
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Counter Pin
New Scheme
Thick Side
Thin Side
Weld Line
Distance Along Path (mm)
Sheet Thickness (mm)
-100-80-60-40-20 0 20406080100
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Counter Pin
New Scheme
Thick Side
Thin Side
Weld Line
Distance Along Path (mm)
Sheet Thickness (mm)
-100 -80 -60 -40 -20 0 20 40 60 80 100
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Counter Pin
New Scheme
Thick Side
Thin Side
Weld Line
Fig. 23 Thickness distribution for experimental work on rectangular box-
shaped drawn parts. a0degreepath.b45 degree path. c90 degree path
(a)
(b)
(c)
Distance along Path (mm)
Thickness Strain (mm/mm)
-160 -120 -80 -40 0 40 80 120 160
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
FE Results
Experimental Results [4]
Distance along Path (mm)
Thickness Strain (mm/mm)
-200 -160 -120 -80 -40 0 40 80 120 160 200
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
FE Results
Experimental Results [4]
Distance along Path (mm)
Thickness Strain (mm/mm)
-160 -120 -80 -40 0 40 80 120 160
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
FE Results
Experimental Results [4]
Fig. 24 Thickness strain distribution for experimental work by Morishita
et al. [4] and FE simulation along. a0 degree path. b45 degree path. c90
degree path. The thick side is located on the positive x-axis
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length ratio Lw/Ls from the FE model are 1.19 mm and
1.02 between both sides, respectively. Such slight devi-
ation from the analytical model is affordable considering
the considerable thinning reduction (17 to 28% at the
corner zone Fig. 24) when the simplified approach is
adopted [12]. All attempts to eliminate the WLM or
increase the drawing limit using the conventional seg-
mented binder scheme alone in which higher binding
force is applied to the stronger side and lower force to
the weaker side had failed. Although the application of
the conventional segmented binder scheme alone seems
to be easier in practical terms, it increases the sheet
thinning and reduces the cup drawing limit. The com-
bined segmented binder/counter-pin technique proves to
be advantageous over other techniques and show signif-
icant reduction in drawn parts.
4 Conclusions
The present work suggested a new binding scheme to
reduce the thinning of TWBs. This scheme combined
weld line constraining via counter pins while applying
a lower BHF on the weaker side as compared to the
stronger side via segmented binders to achieve minimum
thinning in the final product. Adopting this scheme, an
analytical model was developed for the plane strain 2-D
draw-bending process to determine the required BHF and
counter-pin force values. Laboratory and numerical ex-
periments were conducted to examine the developed an-
alytical model and compare the proposed controlling
scheme with other schemes. The experimental results
showed that the new scheme was physically applicable
and was capable of providing accurate force values that
sufficiently eliminate the weld line movement and en-
hance formability (substantial reduction in thinning).
The present study showed the merit of implementing
the proposed scheme in cases where large thickness and/
or strength ratio of the sheets comprising the TWB exist.
In such cases, conventional segmented binders alone or
weld line clamping technique without any variation in
the applied BHF at each side cannot prevent failure.
Adopting the simplified approach presented in ref. [12],
the study proposed a 3-D binding scheme for the TWB
box-shaped parts. Experimental work conducted in deep
drawing of rectangular box-shaped parts showed that the
new scheme resulted in improvement in thickness reduc-
tion in the final product. Furthermore, a comparison with
published experimental work using counter punch tech-
nique validated the feasibility of applying the proposed
binding scheme. Finite element investigations showed a
clear improvement in the formability of the considered
case study. These results showed the merit of the devel-
oped scheme in improving the quality of the drawn
box-shaped parts made from TWBs.
(a)
(b)
(c)
Distance along Path (mm)
Thickness Strain (mm/mm)
-160 -120 -80 -40 0 40 80 120 160
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Counter Punch Scheme
New Scheme
Distance along Path (mm)
Thickness Strain (mm/mm)
-200 -160 -120 -80 -40 0 40 80 120 160 200
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Counter Punch Scheme
New Scheme
Distance along Path (mm)
Thickness Strain (mm/mm)
-160 -120 -80 -40 0 40 80 120 160
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Counter Punch Scheme
New Scheme
Fig. 25 Thickness strain distribution for FE model based Morishita et al.
[4] approach and present scheme. a0degreepath.b45 degree path. c90
degree path. The thick side is located on the positive x-axis
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Appendix A: Geometrical Model
Rd0¼Rd þt
21½
Rp ¼punch radius;Rp0¼Rp þt
22½
Y¼yp þyd þh
Let c
’
=c−t[3]
xp ¼Rp01−sinθ
ðÞ
;
xd ¼Rd01−sinθðÞ;
yp ¼Rp01−cosθðÞ;
yd =Rd
′
(1 −cos θ),
h¼c’þxp þxd

tanθ
∴Y¼R’p1−cosθðÞþR’d1−cosθðÞ
þc’þR’p1−sinθðÞþR’d1−sinθðÞ

tanθ
Substituting with [1], [2], [3] and rearranging
Y¼cþRp þRdðÞtan θ−tþRp þRdðÞsecθ−1ðÞ
Using MATLAB built-in solver
θ¼2tan−1
C−ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C2þY2−2TY
p2T−Y
!
;Y≠2T
C¼cþRpþRd;T¼tþRpþRd
Bending Moment Equation
ϵ¼ln l
lo¼ln θRpþ0:5tþr

θRpþ0:5t

¼ln 1þr
Rpþ0:5t

M¼2∫r¼0:5t
r¼0rdf ¼2∫r¼0:5t
r¼0rσdr ¼2∫r¼0:5t
r¼0rKϵndr
¼2∫r¼0:5t
r¼0rK ln 1þr
Rþ0:5t

n
dr
r:distance from the neutral axis
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Appendix B: MATLAB Code Flow Chart
The MATLAB code divides the punch stroke to a number of
increments (user selected) and for each increment the wrap
angle is calculated from the punch position using Eq. 19.
And the BHF
w
is calculated as shown in the following chart:
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