SENSITIVITY ANALYSIS ON THE CALCULATED BENDING ANGLE … · rolls distance. Optical bending angle measurement from bending legs is therefore recommended, due to the complexity of

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: [email protected]

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

317


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

318


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).

319


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°



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


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 [°]


< 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


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 [°]


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 [°]


< 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


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


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.

REFERENCES[1] Walp M.S.: Impact Dependent Properties of

Advanced and Ultra High Strength Steels.SAE 2007-01-0342, 2007

[2] Boul I. et al.: Bending test and bendability ofultra high strength steels. IDDRG 2007,Gy r, Hungary, 21-23 May, 2007

[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

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SENSITIVITY ANALYSIS ON THE CALCULATED BENDING ANGLE … · rolls distance. Optical bending angle measurement from bending legs is therefore recommended, due to the complexity of