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IDDRG 2013 Conference June 2 – 5, 2013, Zurich, Switzerland
* Corresponding author: Patrick Larour, voestalpine Stahl GmbH, R&D Forming Technologies, 4020 Linz,Austria. tel: +435030415-74150; fax: +435030455-74024; email: patrick.larour@voestalpine.com
SENSITIVITY ANALYSIS ON THE CALCULATED BENDINGANGLE IN THE INSTRUMENTED BENDING TEST
Patrick Larour1*, Benjamin Hackl1, Franz Leomann1
1voestalpine Stahl GmbH, Forming Technologies, voestalpine Str. 3, A-4020 Linz, Austria
ABSTRACT: The VDA238 instrumented 3 point free bending test is increasingly used for AHSS sheetsteels. A sensitivity analysis on bending angle has been performed. On the one side the bending formulagenerally overestimates the real bending angle due to the elastic deformation of the vertical machine frame(which is implicitly considered) as well as the transverse shift of the rolls (which is ignored), respectively.On the other side the experimental sheet bending radius is significantly higher than the punch radius. This isignored in the bending formula, which then underestimates the real bending legs angle. Considering alleffects together leads to an overall under evaluation of up to 5° of the real bending angle at low bendingangle below 100°, where the sheet radius effect predominates. At high bending angle over about 120° thecalculated bending angle overestimates the real bending angle, mainly due to the dominating effect of trans-verse stiffness, especially at high load level. Additionally, edge cracks decrease the bending angle at maxi-mum load up to 5°. The initial curvature of bending samples out of warped industrial components alsobrings around 5° scattering in bending angle, as well as uncertainties in the initial setting of the bendingrolls distance. Optical bending angle measurement from bending legs is therefore recommended, due to thecomplexity of all mentioned experimental artifacts on bending angle calculation.
KEYWORDS: Instrumented 3-point bending test, bending angle, sensitivity analysis, machine stiffness.
1 INTRODUCTIONThe instrumented 3-point free bending test is in-creasingly used in the steel and automotive indus-try. The bending angle at maximum load is a goodindicator of the axial crash folding ability for highstrength steels [1]-[7]. Some bending test standardsalready exist according to ISO 7438 [8] or arebeing developed as for the VDA 238-100 [9].Some discrepancies however still exist betweentest laboratories. There is therefore some need tounderstand any experimental artifacts and approx-imations in the bending angle. Some work has beenperformed to assess the accuracy of such calculatedbending angles and test set-up influence parametersin [2],[6],[7],[10]-[12]. Any mathematical bendingformula using the punch displacement can onlydeliver an approximate bending angle value. Thisinvestigation focuses therefore on various influenceparameters on calculated bending angle.
2 EXPERIMENTAL PROCEDURES3-point bending tests are conducted at voestalpineStahl (VAS) according to VDA238-100 [9] testspecification (Fig. 1). The 60×60 mm test piece isbent in the bending device without lubricant and on
free rotating bending rolls (15mm roll radius) witha very sharp punch radius of 0.4mm and a narrowrolls distance of 2a+0.5mm (a: sheet thickness)[3],[5],[9]. Such an instrument-monitored bendingtest provides a load-displacement curve from thebending punch stroke S. Sample failure is assumedto occur in the maximum load range (Fig. 1).
Bending sample60 x 60mm
Bending rollersRoller distance: 2xthickness+0.5mm
Rolls radius: 15mm
Bending punchPunch radius: 0.4mm
Bending angle
Fig. 1 Instrumented 3-point bending test set-up
Punch stroke S is converted into a bending angleas defined in Fig. 1 and Fig. 2 in accordance withan alternative bending formula in Eq. (1) recentlydeveloped [10],[11]. This bending formula isequivalent to ISO 7438, but differs substantiallyfrom the VDA238-100 formula, since it considers
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IDDRG 2013 Conference June 2 – 5, 2013, Zurich, Switzerland
the punch bending radius (the VDA not) and isexpressed in a much simpler analytical way [10]:
180.2
arctan2
arcsin222 LR
arRS
LRarRS
arR (1)
R: rolls radius, r: punch radius, L: rolls distance, S:(relative) punch stroke, a: sheet thickness (Fig. 2).
a
S
2/L
2rollsd
R
2
aSS '
2punchd
r
rolls)theoftop(from strokepunchabsolute:S' sheet) sampletheoftop(from strokepunchrelative:S
Fig. 2 Bending angle parameters.
3 EXPERIMENTAL ERRORSA sensitivity analysis has been performed on thebending angle according to Eq. (1). Changes to thebending angle are determined through variationsin punch stroke S, rolls distance L, punch diameterdpunch and sheet thickness a. Negligible deviationsin rolls diameter within manufacture tolerances arenot considered in this investigation.
3.1 PUNCH STROKEFig. 3 illustrates an increase in bending anglewith increasing punch stroke.
a
S‘
S‘
Fig. 3 Influence of (absolute) punch stroke
Errors in the punch stroke S can come from thevertical set-up stiffness, from the initial sheet cur-vature (pre-bending) as well as from sample lift offat high bending angle as described hereafter.
Vertical machine stiffness: Fig. 4 shows the proce-dure of vertical calibration of the bending machineby means of a massive and rigid steel block andload-stroke hysteresis without sample but withdifferent bending punch geometries. Elastic verti-cal deformation S of the VAS 100kN test set-upreaches up to 0.25mm and depends solely on theabsolute bending load for a given punch geometry
(Fig. 5). The higher the maximum load Fmax, thehigher is the effect on the measured bending angleas described analytically in Fig. 5.
Steelblock
Bendingrolls
Bendingpunch
VDA2
38,R
0.4m
m
vAS,
R0,4
mm
VAS,
R0,2
mm
VAS,
R1.
0mm
Fig. 4 Vertical test set-up stiffness measurement
0.00
0.05
0.10
0.15
0.20
0.25
0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000
Elas
ticpu
nch
stro
keS
[mm
]
Punch load [N]
VAS-R0.2mm
VAS-R0.4mm
VAS-R1.0mmVDA238-R0.4mm
R0.2, VAS R0.4, VAS R1.0, VAS R0.4, VDA238-100A0 0 0 0 0A1 5.80E-05 3.74E-05 4.54E-05 4.08E-05A2 -1.58E-08 -5.13E-09 -1.35E-08 -5.64E-09A3 3.00E-12 4.80E-13 3.48E-12 5.38E-13A4 -2.90E-16 -2.21E-17 -5.44E-16 -2.54E-17A5 1.10E-20 3.95E-22 4.48E-20 4.75E-22A0 7.41E-02 5.94E-02 5.53E-02 6.27E-02A1 1.03E-05 9.96E-06 9.72E-06 1.12E-05Fpunch 8000N
punch geometryparameterpunch load
Fpunch < 8000N
0A.FA.FA.FA.FA.FAS punch1punch2
2punch3
3punch4
4punch5
5
Fig. 5 Vertical punch elastic stiffness calibration
The bending angle Fmax is therefore systematicallyoverestimated by 2° to 4° especially for thick andhigh strength steels with high bending load level(Fig. 6). Punch displacement should be thereforemeasured locally or corrected with such calibrationdata prior to bending angle calculation.
0
2000
4000
6000
8000
10000
12000
0 20 40 60 80 100 120 140 160
Ben
ding
load
[N]
Bending angle [°]
without vertical stiffness correction
with vertical stiffness correction
= 2,0°
= 1,8°
Fig. 6 Vertical punch elastic stiffness correction
Sheet curvature: Perfect flatness of the test piece isnever completely achievable in coil specimens andeven less in bending samples out of components.The initial punch stroke value is influenced by pre-bending and may not be simply set to zero (zero-point shift), because this would result in a mathe-matically incorrect calculation of the bending angleand artificial enhanced scattering in Fmax bendingangle values (Fig. 7). Fig. 8 shows the initial de-flection statistics ( 2000 tests at VAS) for bendingsamples out of coils and components. It most oftenreaches 20% of the sheet thickness. This results in
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IDDRG 2013 Conference June 2 – 5, 2013, Zurich, Switzerland
a non-negligible error of 0.3mm in the punchstroke or about 5° in the bending angle for a 1.5mm thick sheet. This source of error is howevereliminated if the absolute method of punch strokemeasurement is applied (punch stroke S’= 0 on theupper roll side).
S2
2
S1
1
S3
3
1 = 2 = 3 but S1 > S2 > S3 !!
Case 1: curvature upward (>0)
Case 2: no curvature (=0)
Case 3: curvature downward (<0)
curvature>0
curvature<0
Scurvature
Load
Angle
Load
Angle
O-Point shift
scattering in Fmax
=0 at the beginning
wrong method!
1
1
2
2
3
3
No 0-Point shift
No scattering in Fmax
<>0 at the beginning
right method!
Fig. 7 Influence of sheet curvature on relativepunch stroke S and bending curves
0%
5%
10%
15%
20%
25%
30%
0-4 5-9 10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69
Occ
uren
cepr
obab
ility
[%]
Initial bending deflection/thickness [%]
Fig. 8 Relative initial sheet curvature statistics
Punch lift off: A lift off between punch and sheetusually occurs at high bending angles, the punchtip loses contact with the sheet sample (Fig. 9).
rsheet<rpunch(DP600)
Fig. 9 Punch lift off at high bending angle [10]
The local sheet radius is then lower than the punchradius. This leads to an additional punch stroke,which is not considered in the bending formula.
Edge cracks: Edge cracks can occur in bending ofsheet steels, especially in the shear-cut conditioneven with burr on the punch side (Fig. 10). Thisleads to a premature load drop without bulk mate-rial failure in the middle of the bending sample andinvalid test results. Additional scattering and un-derestimation up to 5° of the bending angle at fail-ure occurs. Edge cracks can be minimized withshear-cut & deburred, drilled or EDM-cut edgesdepending on edge crack sensitivity (Fig. 10).
0
1000
2000
3000
4000
5000
6000
7000
8000
0 20 40 60 80 100 120 140
Ben
ding
load
[N]
Bending angle [°]
polished
Shear-cut withdeburring
EDM-cut
drilled
Shear cut withoutdeburring
5°
Fig. 10 Influence of sample manufacturing method
3.2 ROLLS DISTANCEFig. 11 shows a decrease in bending angle withincreasing rolls distance L.
a
L
L
Fig. 11 Influence of rolls distance L
The roll distance is affected by the elastic stiffnessof the rolls set-up as well as the method used foradjusting the initial roll distance.
Horizontal transverse machine stiffness: The elas-tic transverse rolls shift L has been measuredonline during bend tests by means of a CTOD(crack-tip opening displacement) measuring devicethat is usually used for fracture mechanics testing.The transverse load component increases dramati-cally especially at high bending angle (Fig. 12). Atsmall bending angles, the clamps are pulled togeth-er and not apart by approximately 0.1mm (Fig. 13).Above roughly 80°, the transverse loads result inan elastic outward shift L up to 0.6mm of thebending rolls in the horizontal direction. The bend-ing punch acts hereby like a wedge (Fig. 13).
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IDDRG 2013 Conference June 2 – 5, 2013, Zurich, Switzerland
F
F/2F
Fn
transverse
2tan
2FFtransverse
CTOD
L
Ftrans verse/Fpunch
° - Fpunch=5kN Fpunch=10kN Fpunch=15kN Fpunch=20kN0 0 0 0 0 0
40 0.18 0.9 1.8 2.7 3.680 0.42 2.1 4.2 6.3 8.4
120 0.87 4.3 8.7 13.0 17.3160 2.84 14.2 28.4 42.5 56.7165 3.80 19.0 38.0 57.0 76.0
Ftransverse on each roll [kN]
Fig. 12 Transverse set-up stiffness measurement
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0 20 40 60 80 100 120 140 160 180
Tran
sver
sero
llssh
iftL
[mm
]
Bending angle [°]
TRIP700_2.0mm
HX340LAD_1.75mm
TRIP800_0.8mm
CP1200_1.3mmDP600_2.0mm
L0 K A B r2
-0.05449 4.1947E-11 0.68759 3.38565 97.60%
L: elastic transverse rolls shift (in mm),Fpunch: punch load (in N), : bending angle (in °)
r2: correlation coefficient (in %)
BApunchFKLL **0
Fig. 13 Rolls transverse shift vs. bending angle
Calculated bending angles can be therefore overes-timated by up to 3-4° at maximum load and bymore than 10° at high bending angle, since thebending formula neglects the additional lateral shiftof bending rolls L in such cases (Fig. 14).
-0.1
0
0.1
0.2
0.3
0.4
0.5
0
1000
2000
3000
4000
5000
6000
7000
8000
0 20 40 60 80 100 120 140 160 180
Tran
sver
sero
llssh
iftL
[mm
]
Ben
ding
load
[N]
Bending angle [°]
without rolls stiffness correction
with rolls stiffness correction
transverse rolls shift
Fmax, with/without rollsstiffness correction: 71°/71°
Fmax, with/without rollsstiffness correction: 119°/122°
Fmax, with/without rollsstiffness correction: 138°/142°
Fig. 14 Bending curve vs. transverse rolls shift
The lateral cross-rigidity affects strongly the bend-ing curve shape beyond maximum load in the post-uniform area (Fig. 14). It has some overlappingeffects with the vertical machine rigidity, whichhas its largest effect at maximum load. The trans-verse rigidity matters therefore mostly for ductilethick steels. It can be minimized with an optimisedstiff bending grip design.
Adjusting the initial rolls distance: The rolls dis-tance (L=2a+0.5) is manually adjusted prior to thetest at VAS by inserting two sheet strips (at thick-ness a) and an additional 0.5 mm thick sheet stripbetween rolls (Fig. 15).
a0.5a
2a+0.5, cambered sample
a0.5a
L=2a+0.5 flat sample
Fig. 15 Influence of sheet cambering on manually-adjusted distance between bending rolls
Sample thickness fluctuations of 0.01mm have anegligible effect on rolls distance and bendingangle. This simple manual method is howeverespecially inaccurate with bending samples out ofindustrial warped component (Fig. 15) with up to
50% pre-bending relative to thickness (Fig. 8).The original distance should be therefore adjustedwith more precise mechanical and digital devices.
3.3 PUNCH DIAMETERFig. 16 shows an increase in bending angle withincreasing punch diameter dpunch.
a
dpunch
dpunch
Fig. 16 Influence of punch diameter dpunch
The punch radius should not be neglected in thebending formula as in the current VDA238 bendingtest formula [10]. This leads to an unnecessaryunderestimation of up to 16° of the calculatedbending angle at high punch stroke level (Fig. 17).
0
2
4
6
8
10
12
14
16
18
0
20
40
60
80
100
120
140
160
0 2 4 6 8 10 12 14 16
Off
set
VAS
-TK
SE
-V
DA
238-
100
[°]
Cal
cula
ted
bend
ing
angl
e[°
]
Punch stroke [mm]
a=1.0mm, L=2a+0.5, R=15, r=0.4
VAS-TKSEISO 7438VDA238-100Offset VAS-TKSE/VDA238-100
Fig. 17 Bending angle ISO7438 vs. VDA238 [10]
As shown in Fig. 18, the ISO 7438 assumption of aclose contact of the steel sheet sample along thepunch radius in Eq. (1) is however only fulfilled athigh bending angle [10],[13]. Taking into accountthe experimental average sheet curvature instead of
IDDRG 2013 Conference June 2 – 5, 2013, Zurich, Switzerland
0.4mm punch radius in Eq. (1) improves the agree-ment between calculated and measured bendingangle. An increasing punch radius also reducesdiscrepancies between calculated and measuredbending angle [10].
0
1
2
3
4
5
6
7
8
40 60 80 100 120 140 160 180
Onl
ine
load
edav
erag
ebe
ndin
gra
dius
[mm
]
Bending angle [°]
DX54D_0.7mmHX340LAD_1.0mmDP600_1.5mmCP800_1.35mmDP800_1.6mmCP1000_1.25mmDP1000_1.0mm22MnB5_1.0mm
rpunch = 0.4mm
A B C r2
880.6085 -1.30873 -0.90995 89.7%
CAR Baveragesheet *
Fig. 18 Average sheet radius vs. bending angle [10]
3.4 SHEET THICKNESSAn (engineering) thinning up to 15-20% usuallyoccurs directly below bending punch, due to theinner shift of neutral bending line (Fig. 19). Anabnormal flattening on the outer bending side withup to 30% sheet thinning is also seen for CP- andpress-hardened steels with low n-value (Fig. 20).This effect is enhanced with decreasing punchradius, increasing bending angle and decreasingwork hardening ability. The assumption of a roundsheet shape and constant thickness at the punch tipis not realistic. However a thickness decrease di-rectly below punch is not relevant for bendingangle calculation in Eq. (1). Almost no thinningoccurs indeed tangential on punch sides (Fig. 19)and the bending angle calculation is therefore notaffected. Material thinning rather matters whendetermining maximum bending strain at failure andcorrelating it with bending angle [4]. Materialthickness scattering of 0.01mm has almost noinfluence on bending angle ( 0.5°).
0%
5%
10%
15%
20%
25%
30%
0 20 40 60 80 100 120 140 160 180
Load
edsh
eett
hinn
ing
belo
wpu
nch
[%]
Bending angle [°]
DX54D_0.7mmHX340LAD_1.0mmDP600_1.5mmCP800_1.35mmDP800_1.6mmCP1000_1.25mmDP1000_1.0mm22MnB5_1.0mm
< t0
Fig. 19 Relative sheet thinning vs. bending angle
CP1200CP1000DX54D DP1000
No flattening Flattening
22MnB5 hardened
Fig. 20 Sample flattening below punch [10]
4 DISCUSSIONA sensitivity analysis of changes to the bendingangle that result from a deviation in the inputparameters is performed hereafter. Only errors inpunch stroke, rolls distance and punch diameter areinvestigated. Errors in initial sheet thickness, rollsdiameter, pre-bending curvature (flat coil samplesassumed) or edge cracks effects are not considered.Table 1 and Fig. 21 show the total deviation ofbending angle (real correct value-calculated bend-ing angle) with changes in punch stroke S, rollsdistance L, and punch diameter dpunch based onthe bending formula in Eq. (1). dpunch describeshereby the average bending diameter of the sheet,which is either the physical punch diameter in thebending formula or a fictive punch diameter corre-sponding to the real average bending sheet diame-ter. The variation ranges have been chosen fromexperimental results. S, L and dpunch are calcu-lated from Fig. 5, Fig. 13 and Fig. 18 respectively.
Thicknessa, mm
Fmax
N
Fmax
formula, °Spunchmm
dpunch
mmLrolls
mm °
1.19 5076 52 -0.12 7.48 -0.05 3.91.20 5607 78 -0.12 3.24 -0.01 5.01.02 5131 102 -0.12 1.50 0.04 4.81.00 5229 128 -0.12 0.45 0.15 0.21.20 6618 138 -0.14 0.16 0.26 -4.80.89 5343 158 -0.12 -0.29 0.37 -17.81.53 10174 47 -0.18 8.73 -0.04 2.71.60 10647 75 -0.18 3.58 0.00 3.81.52 10049 99 -0.18 1.68 0.08 3.41.48 10023 119 -0.17 0.77 0.20 0.51.47 10034 142 -0.18 0.06 0.41 -9.21.21 10019 158 -0.17 -0.29 0.60 -21.32.05 16794 52 -0.25 7.40 -0.03 2.02.00 16082 76 -0.24 3.42 0.02 2.82.05 14869 99 -0.23 1.69 0.12 2.22.00 16113 119 -0.24 0.75 0.30 -1.82.00 15660 140 -0.24 0.12 0.54 -10.31.49 15845 158 -0.24 -0.28 0.85 -24.7
dpunch = dsheet real - dpunch bending formula (0.8mm)
real - bending formula
Lrolls Lrolls,real - L rolls bending formula (2a+0.5mm)
spunch = Spunch real - Spunch bending fomula (punch stroke)
Table 1: Bending angle vs. parameter variations(L=2a+0.5mm, dpunch=0.8mm)
-28-26
-24-22
-20-18
-16-14
-12
-10-8
-6-4
-20
24
6
40 60 80 100 120 140 160
real
-fo
rmul
a[°
]
Bending angle [°]
5kN10kN15kN
Fig. 21 Bending angle deviation vs. bending angleand bending force
320
IDDRG 2013 Conference June 2 – 5, 2013, Zurich, Switzerland
0.4mm punch radius in Eq. (1) improves the agree-ment between calculated and measured bendingangle. An increasing punch radius also reducesdiscrepancies between calculated and measuredbending angle [10].
0
1
2
3
4
5
6
7
8
40 60 80 100 120 140 160 180
Onl
ine
load
edav
erag
ebe
ndin
gra
dius
[mm
]
Bending angle [°]
DX54D_0.7mmHX340LAD_1.0mmDP600_1.5mmCP800_1.35mmDP800_1.6mmCP1000_1.25mmDP1000_1.0mm22MnB5_1.0mm
rpunch = 0.4mm
A B C r2
880.6085 -1.30873 -0.90995 89.7%
CAR Baveragesheet *
Fig. 18 Average sheet radius vs. bending angle [10]
3.4 SHEET THICKNESSAn (engineering) thinning up to 15-20% usuallyoccurs directly below bending punch, due to theinner shift of neutral bending line (Fig. 19). Anabnormal flattening on the outer bending side withup to 30% sheet thinning is also seen for CP- andpress-hardened steels with low n-value (Fig. 20).This effect is enhanced with decreasing punchradius, increasing bending angle and decreasingwork hardening ability. The assumption of a roundsheet shape and constant thickness at the punch tipis not realistic. However a thickness decrease di-rectly below punch is not relevant for bendingangle calculation in Eq. (1). Almost no thinningoccurs indeed tangential on punch sides (Fig. 19)and the bending angle calculation is therefore notaffected. Material thinning rather matters whendetermining maximum bending strain at failure andcorrelating it with bending angle [4]. Materialthickness scattering of 0.01mm has almost noinfluence on bending angle ( 0.5°).
0%
5%
10%
15%
20%
25%
30%
0 20 40 60 80 100 120 140 160 180
Load
edsh
eett
hinn
ing
belo
wpu
nch
[%]
Bending angle [°]
DX54D_0.7mmHX340LAD_1.0mmDP600_1.5mmCP800_1.35mmDP800_1.6mmCP1000_1.25mmDP1000_1.0mm22MnB5_1.0mm
< t0
Fig. 19 Relative sheet thinning vs. bending angle
CP1200CP1000DX54D DP1000
No flattening Flattening
22MnB5 hardened
Fig. 20 Sample flattening below punch [10]
4 DISCUSSIONA sensitivity analysis of changes to the bendingangle that result from a deviation in the inputparameters is performed hereafter. Only errors inpunch stroke, rolls distance and punch diameter areinvestigated. Errors in initial sheet thickness, rollsdiameter, pre-bending curvature (flat coil samplesassumed) or edge cracks effects are not considered.Table 1 and Fig. 21 show the total deviation ofbending angle (real correct value-calculated bend-ing angle) with changes in punch stroke S, rollsdistance L, and punch diameter dpunch based onthe bending formula in Eq. (1). dpunch describeshereby the average bending diameter of the sheet,which is either the physical punch diameter in thebending formula or a fictive punch diameter corre-sponding to the real average bending sheet diame-ter. The variation ranges have been chosen fromexperimental results. S, L and dpunch are calcu-lated from Fig. 5, Fig. 13 and Fig. 18 respectively.
Thicknessa, mm
Fmax
N
Fmax
formula, °Spunchmm
dpunch
mmLrolls
mm °
1.19 5076 52 -0.12 7.48 -0.05 3.91.20 5607 78 -0.12 3.24 -0.01 5.01.02 5131 102 -0.12 1.50 0.04 4.81.00 5229 128 -0.12 0.45 0.15 0.21.20 6618 138 -0.14 0.16 0.26 -4.80.89 5343 158 -0.12 -0.29 0.37 -17.81.53 10174 47 -0.18 8.73 -0.04 2.71.60 10647 75 -0.18 3.58 0.00 3.81.52 10049 99 -0.18 1.68 0.08 3.41.48 10023 119 -0.17 0.77 0.20 0.51.47 10034 142 -0.18 0.06 0.41 -9.21.21 10019 158 -0.17 -0.29 0.60 -21.32.05 16794 52 -0.25 7.40 -0.03 2.02.00 16082 76 -0.24 3.42 0.02 2.82.05 14869 99 -0.23 1.69 0.12 2.22.00 16113 119 -0.24 0.75 0.30 -1.82.00 15660 140 -0.24 0.12 0.54 -10.31.49 15845 158 -0.24 -0.28 0.85 -24.7
dpunch = dsheet real - dpunch bending formula (0.8mm)
real - bending formula
Lrolls Lrolls,real - L rolls bending formula (2a+0.5mm)
spunch = Spunch real - Spunch bending fomula (punch stroke)
Table 1: Bending angle vs. parameter variations(L=2a+0.5mm, dpunch=0.8mm)
-28-26
-24-22
-20-18
-16-14
-12
-10-8
-6-4
-20
24
6
40 60 80 100 120 140 160
real
-fo
rmul
a[°
]
Bending angle [°]
5kN10kN15kN
Fig. 21 Bending angle deviation vs. bending angleand bending force
321
IDDRG 2013 Conference June 2 – 5, 2013, Zurich, Switzerland
On the one side the bending formula generallyoverestimates the real bending angle due to theelastic deformation of vertical machine frame(which is implicitly considered) as well as thetransverse shift of the rolls (which is ignored). Onthe other side the experimental sheet bending radi-us is significantly higher than the punch radius.This is ignored in the bending formula, which thenunderestimates the real bending legs angle. Con-sidering all effects together leads to an overallunder evaluation of up to 5° of the real bendingangle at low bending angle below 100°, where thesheet radius effect predominates. At high bendingangle over 110-130° the calculated bending angleoverestimates the real bending angle, mainly due tothe dominating effect of transverse stiffness, espe-cially at high load level (Fig. 22).
0
20
40
60
80
100
120
140
160
180
0 20 40 60 80 100 120 140 160 180
Expe
rimen
talb
endi
ngle
gsan
gle
[°]
Calculated bending angle [°]
punch radius: 0.4mm
DX54D_0.7mmHX340LAD_1.0mmDP600_1.5mmCP800_1.35mmDP800_1.6mmCP1000_1.25mmDP1000_1.0mm22MnB5_1.0mm
Fig. 22 Measured vs. calculated bending angle [10]
5 CONCLUSIONSA sensitivity analysis of parameters such as punchstroke, rolls distance and punch diameter on bend-ing angle calculation has been performed.While vertical punch stroke S and rolls distanceerror L both lead to an overestimation of bendingangle (mostly at high bending angle and high forcelevel for thick high strength ductile steels), theeffect of bending sheet diameter dpunch leads to anopposite underestimation of bending angle. At lowbending angle the bending angle is underestimatedof 4-5° mainly due to sheet curvature. At highbending angle, the transverse stiffness effect pre-dominates, while the sheet radius is forced tomatch with the physical punch radius.Bending angle deviations become dramaticallylarger above 140° where any bending formulabecomes numerically instable. Neglecting thepunch diameter for example as actually done in theVDA238 test standard leads to an underestimationof the bending angle up to 16° at 160° [10]!Additionally, edge cracks decrease the bendingangle at maximum load up to 5°. The initial curva-ture of bending samples out of warped industrialcomponents also brings around 5° scattering inbending angle, as well as uncertainties in the initialsetting of the bending rolls distance. Not all exper-imental artifacts can be corrected analytically.
Due to the complexity of all possible errors inbending angle calculation, direct online opticalbending angle measurement from bending legs, asperformed in [10]-[15], is therefore recommended.A still open (but essential) question also ariseswhether bending angle at maximum load alwaysmatch with the onset of material failure in the outerbulk material [2],[4]. This is obviously not the casefor ductile HSLA steels and in the case of prema-ture edge cracks.
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[3] Larour P. et al.: Influence of post uniformtensile and bending properties on the crashbehaviour of AHSS and press-hardening steelgrades. IDDRG, Graz, Austria, 2010
[4] Atzema E.: Different aspects of formability inAHSS. Forming in Car Body Engineering,Bad Nauheim, 26-27.09, 2012
[5] Walch C. et al.: High Ductility AHSS. Form-ing in Car Body Engineering, Bad Nauheim,26-27.09, 2012.
[6] Schäffner C. et al.: Warmblechumformung -Große Variantenvielfalt durch Kombinationsmöglichkeiten von Stahlwerkstoff und Pro-zessführung. 30. EFB-Kolloquium Blechver-arbeitung, Bad Boll, 231-248, 2010
[7] Laumann T.: Qualitative und quantitativeBewertung der Crashtauglichkeit von höchst-festen Stählen. Meisenbach-Edition, 2009,ISBN 978-3-87525-299-6
[8] ISO7438(2005):Metallic materials-Bend test.[9] VDA 238-100 test specification draft: Plate
bending test for metallic materials. 12/2010[10] Larour P. et al.: Bending angle calculation in
the instrumented three-point bending test.IDDRG Mumbai, India, 203-215, 2012
[11] Neuhaus R., Borsutzki M.: Plättchen-Biegeversuch nach VDA238-100. Werkstoff-prüfung Bad Neuenahr, 45-50, 2012
[12] Maclean S.H. et al.: Bending Properties ofBoron Sheet Steel Processed with VariableCooling Rates. ICTP, 110-115, 2008
[13] Garcia-Romeu et al.: Determining curvatureof air bended parts by digital image pro-cessing. ESAFORM, Brescia, Italy, 2010
[14] Väisänen, A. et al.: Bendability of ultra-high-strength steel. Key Engineering Materials,410/411, 611-620, 2009
[15] Hezler C. et al.: Characterisation of the tran-sition area at partial hot stamped car bodycomponents by the 3-point bending test.SCT 2011, Salzburg, 280-287, 2011
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