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Journal of Materials Processing Technology 210 (2010) 429–436

Contents lists available at ScienceDirect

Journal of Materials Processing Technology

journa l homepage: www.e lsev ier .com/ locate / jmatprotec

etermination of the flow stress of five AHSS sheet materials (DP 600, DP 780, DP80-CR, DP 780-HY and TRIP 780) using the uniaxial tensile and the biaxialiscous Pressure Bulge (VPB) tests

. Nasser, A. Yadav, P. Pathak, T. Altan ∗

ngineering Research Center for Net Shape Manufacturing (ERC/NSM), The Ohio State University, Columbus, OH, USA1

r t i c l e i n f o

rticle history:eceived 23 April 2009eceived in revised form0 September 2009ccepted 6 October 2009

a b s t r a c t

Room temperature uniaxial tensile and biaxial Viscous Pressure Bulge (VPB) tests were conducted forfive Advanced High Strength Steels (AHSS) sheet materials, and the resulting flow stress curves werecompared. Strain ratios (R-values) were also determined in the tensile test and used to correct the biaxialflow stress curves for anisotropy. The pressure vs. dome height raw data in the VPB test was extrapolatedto the burst pressure to obtain the flow stress curve until fracture. Results of this work show that the flowstress data can be obtained to higher strain values under biaxial state of stress. Moreover, it was observed

eywords:HSSniaxial tensile testiaxial bulge testlow stressormability

that some materials behave differently if subjected to different state of stress. These two conclusions, andthe fact that the state of stress in actual stamping processes is almost always biaxial, suggest that thebulge test is a more suitable test for obtaining the flow stress of AHSS sheet materials for use as an inputto Finite Element (FE) simulation models.

© 2009 Elsevier B.V. All rights reserved.

ual Phase (DP)ransformation-Induced Plasticity (TRIP)

. Introduction

This study is concerned about two types of AHSS; Dual PhaseDP) steels and Transformation-Induced Plasticity (TRIP) steels. The

icrostructure of DP steels is composed of ferrite and marten-ite, while the microstructure of TRIP steels is a matrix of ferrite,n which martensite and/or bainite, and more than 5% retainedustenite exist. The increased formability of AHSS is the maindvantage over conventional HSS. DP steels, for example, haveigh initial strain hardening and a high tensile-to-yield strengthatio, which accounts for the relatively high ductility, compared toonventional HSS. This issue was pointed out (a) by ASTM (2007)hich discusses the standard test methods for obtaining the ten-

ile strain hardening components and (b) by ASTM (2006) that

xplains the test methods used for measuring the plastic strain ratio

r’ for sheet metals. Nevertheless, compared to Draw Quality SteelsDQS), AHSS steels have relatively low ductility. In the stampingndustry, running Finite Element (FE) simulations is an important

∗ Corresponding author at: Engineering Research Center for Net Shape Manufac-uring (ERC/NSM), The Ohio State University, 339 Baker Systems Building, 1971 Neilvenue, Columbus, OH 43210, USA. Tel.: +1 614 292 5063.

E-mail address: altan.1@osu.edu (T. Altan).1 www.ercnsm.org.

924-0136/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.jmatprotec.2009.10.003

step in the process/tool design. A critical input to FE models isthe mechanical properties (flow stress curve) of the sheet materialused. Usually, flow stress curves are obtained using the uniaxialtensile test. Although accurate and convenient, two main limita-tions exist for this test. First, values of strain attained in this testare generally less than the values observed in stamping processes.As a result, data obtained in a tensile test, is usually extrapolatedin conducting FE simulations. Second, the state of stress in actualstamping is usually biaxial, which raises questions on the suit-ability of using flow stress data obtained under a uniaxial loadingcondition. Based on these considerations, the biaxial bulge testwas used extensively in the Engineering Research Center for NetShape Manufacturing (ERC/NSM), for obtaining flow stress input toFE models. The ERC/NSM bulge test uses viscous material as thepressurizing medium. Therefore, it is called the “Viscous PressureBulge (VPB)” test. This test was originally developed by Gutscherand Altan (2004) and further developed to include anisotropy byPalaniswamy and Altan (2007).

2. Background on the VPB test

Fig. 1 is a schematic of the tooling used in the VPB test. The upperdie is connected to the slide and the cushion pins support the lowerdie (the blank holder) to provide the required clamping force. The

430 A. Nasser et al. / Journal of Materials Processing Technology 210 (2010) 429–436

re Bul

psmturcpThttsuafs

3s

3

s(

�

Tbas

Fig. 1. Viscous Pressu

unch in the lower die is fixed to the press table and thereforetationary. At the beginning, the tooling is open and the viscousaterial is filled into the area on the top of the punch. When the

ooling closes, the sheet is totally clamped [Fig. 1(a)] between thepper and the lower dies using a lockbead to prevent any mate-ial draw-in in order to maintain the sheet in a pure stretchingondition throughout the test. The clamping force (the selectedress cushion force) depends on the material and thickness tested.he slide then moves down together with the upper die and blankolder. Consequently, the viscous medium is pressurized by the sta-ionary punch and the sheet is bulged into the upper die. Since theools are axisymmetric, the sheet is bulged under balanced biaxialtress. Continuously during the test, the dome height is measuredsing a potentiometer, and the bulging pressure is measured usingpressure transducer. Fig. 2 shows the details of the geometrical

eatures of the VPB test tooling. All symbols used in this paper areummarized in the nomenclature, given at the end of the paper.

. Inverse analysis methodology for determining the flowtress curve

.1. Isotropic materials

The methodology used for determining the flow stress of theheet assumes that the material follows the Hollomon power lawEq. (1)).

¯ = Kε̄n (1)

he effective stress and strain equations from the classical mem-rane plasticity theory are used (Eqs. (2) and (3)). These equationsre derived under the assumptions that the bulge (dome) shape ispherical and that the sheet thickness is small compared to the sur-

Fig. 2. Geometrical features of the VPB test.

ge (VPB) test tooling.

face area so that the bending stresses can be neglected as discussedby (Gutscher and Altan (2004) in detail.

�̄ = �r = p

2

[Rd

td+ 1

](2)

ε̄ = −εt = − lntd

to(3)

In addition to the bulging pressure and dome height which canbe easily measured in the test, Eqs. (2) and (3) above contain twoother unknowns; the thickness and radius of curvature at the domeapex. To determine these unknowns, a series of FE simulationswith different material properties (different n-value) were con-ducted using the commercial FE software PAMSTAMP to generatea database. This database shows how the thickness and radius ofcurvature at the dome apex change with the dome height. The Von-Mises yield criterion and the constitutive modeling of plasticity,outlined by (Hill, 1990) were used in the simulations.

An excel macro was then developed to iteratively determine theflow stress curve of the material using both the database and theexperimental pressure vs. dome height curve. A flow chart describ-ing the FE-based inverse analysis methodology is shown in Fig. 3.An initial guess of the n-value is made. Using the measured domeheight and the database, the radius of curvature and thickness atthe dome apex are calculated. Now that all the information neededare available, the membrane theory equations can be used to cal-culate the effective stress and strain. The power law is then used torepresent the resulting curve. Another iteration is performed witha different n-value, and the process continues until the difference inthe n-value between two subsequent iterations becomes less thanor equal to 0.001. At this moment, the iterations are stopped, andthe flow stress curve is extracted and reported.

3.2. Anisotropic materials

Since sheet materials are usually anisotropic (i.e. mechanicalproperties vary from one direction to another), the flow stress curveobtained in the bulge test may not be accurate if the material isassumed to be isotropic. Therefore in this study, the calculated flowstress curve using the methodology described in Section 3.1 wascorrected for anisotropy. While Von-Mises yield criterion is usedin the methodology described above, Hill (1990)’s anisotropic yieldcriteria is used in this section. Following is the correction factor

used to correct for anisotropy:

�̄anis =√

R90 + R0

R90(R0 + 1)�̄iso (4)

A. Nasser et al. / Journal of Materials Processing Technology 210 (2010) 429–436 431

d to d

i

�

4

cH

(

(

(

5

5

op7prtFftrp

twwotl0t

considerable effect on the R-values and therefore the total strainvalues were used in the calculations.

The engineering stress, S, was calculated by dividing the mea-sured load by the original cross sectional area (12.7 mm × 1 mm).The following formulas were used to calculate the true stress–true

Table 1The test matrix used for the tensile and VPB tests.

# Material Thickness Number of samples tested

Tensile testa VPB test

0◦ 45◦ 90◦ Total Burst

1 DP 600 1 mm 3 3 4 6 12 DP 780 1 mm 3 2 4 10 43 DP 780-CR 1 mm 4 3 4 7 1

Fig. 3. A flow chart describing the FE-based inverse analysis methodology use

If the material does not have any planar anisotropy (i.e. R-values the same in all directions), then Eq. (4) simplifies to Eq. (5):

¯ anis =√

2

R̄ + 1)�̄iso (5)

. Objectives of the study

The main objective of the study is to determine the flow stressurves of five AHSS materials: DP 600, DP 780, DP 780-CR, DP 780-Y, and TRIP 780.

The detailed objectives are to:

1) Compare the flow stress curves obtained under balanced biax-ial state of stress with those obtained under uniaxial condition(tensile test) for the materials tested.

2) Study the effect of anisotropy correction on the flow stresscurves obtained by the VPB test.

3) Investigate the strain hardening characteristic and formabilityof the materials tested.

. Experimental procedure

.1. Tensile tests

To eliminate edge effect problems associated with shearingperations, tensile test specimens were prepared by wire EDMrocess. For each of the five AHSS materials (DP 600, DP 780, DP80-CR, TRIP 780, and DP 780-HY), at least three samples wererepared at each of the three orientations (0◦, 45◦, and 90◦) withespect to the rolling direction. Specimen dimensions specified inhe International Standard ASTM E 646-07 were used. MTS 810lexTest Material Testing Machine, 100 KN in capacity, was usedor testing. A hydraulic wedge grips and a 2-in. Epsilon extensome-er were used in all the tests. Samples were loaded at a strainate of 0.1 min−1 (1.67 × 10−3 s−1) which is also according to thereviously mentioned standard.

Before starting the test, the specimen was properly aligned withhe loading axis and gripped carefully to avoid twisting. Samplesere loaded to an engineering strain of 8% (±0.5%) where the testas stopped and the sample width was measured for the purpose

f determining the Strain Ratio (only for DP 780-HY at 90◦, theest was stopped at about 7% since this grade at this direction hasess uniform elongation). A micrometer with a minimum division of.01 mm (±0.005 mm) was used to measure the width at three loca-ions within the gauge length (as recommended by the standard

etermine the flow stress curve of sheet materials (Gutscher and Altan, 2004).

ASTM E 646) and the average width was calculated. After measur-ing and recording the width, the sample is loaded again until failure.Throughout the test, both the load and the measured engineeringstrain were recorded to be used in calculating the true stress andstrain. The test matrix is summarized in Table 1.

The width true strain was calculated from the measured width.Using the axial true strain at which loading stops and the calculatedwidth true strain, the thickness true strain was calculated from theprinciple of volume constancy (Eq. (6)).

εax + εw + εt = 0 (6)

For each material, the strain ratio (R-value) in each directionwas calculated, and then the average normal anisotropy and planaranisotropy were calculated. Formulas 7 through 9 were used inthe calculations and the International Standard ASTM E 517-00,described in ASTM (2007) was followed.

R = εw

εt(7)

R̄ = R0 + 2R45 + R90

4(8)

�R = R0 + R90 − 2R45

2(9)

Note: the ASTM standard E517 states that the plastic componentof the total strain should be used in calculating the strain ratio.Subtracting the elastic strain from the total strain will not have a

4 DP 780-HY 1 mm 3 3 2 7 25 TRIP 780 1 mm 3 3 3 7 2

a It was originally planned to test at least three samples for each condition. How-ever, some samples were lost during the initial trials and therefore not included inthis table.

432 A. Nasser et al. / Journal of Materials Processing Technology 210 (2010) 429–436

Fig. 4. Comparison of engineering stress–engineering strain curves of various AHSSgrades obtained by the tensile test.

Fig. 5. Comparison of true stress–true strain curves of various AHSS grades obtainedby tensile test.

Ft

su

ε

�

TC

Fig. 7. Uniform and total elongation of various AHSS grades (gauge length: 2 in.)(average values are shown).

Fig. 8. UTS and 0.2% offset yield strength of various AHSS grades (average UTS valuesare shown).

Fig. 9. Experimental pressure vs. time curve for sample 1 of TRIP 780 steel sheetmaterial.

ig. 6. True stress–true strain curves of DP 780-HY at 0◦ , 45◦ , and 90◦ with respecto rolling direction obtained by tensile test.

train data from the engineering data: (these formulas were used

p to the instability/necking point)

= ln(1 + e) (10)

= S × (1 + e) (11)

able 2omparison of anisotropy ratios of various AHSS grades.

0◦ 45◦ 90◦ R̄ �R

DP 600 0.942 1.01 1.08 1.0105 0.001DP 780 0.802 0.9 0.874 0.869 −0.062DP 780-CR 0.925 0.811 1.064 0.90275 0.1835TRIP 780 0.498 0.872 0.583 0.70625 −0.3315DP 780-HY 0.843 1.108 0.931 0.9975 −0.221

Fig. 10. Example tested specimens for TRIP 780 sheet material (a) sample burst and(b) sample not burst.

A. Nasser et al. / Journal of Materials Processing Technology 210 (2010) 429–436 433

Fig. 11. Experimental pressure vs. dome height curves obtained from the VPB testfor the five AHSS sheets materials tested (these curves are the measured curveswithout any extrapolation).

Fig. 12. Comparison of the flow stress curves of the five AHSS materials tested usingthe VPB test (these curves are neither corrected for anisotropy nor extrapolated).

Fig. 13. Pressure vs. dome height curve (for TRIP 780, sample 6) extrapolated fromlast measured datapoint (212 bars) up to burst pressure (226 bars) using higher orderpolynomial approximation.

Fig. 14. The flow stress curve of TRIP 780 (sample 6) obtained from both experi-mentally measured and extrapolated pressure vs. dome height curves.

Fig. 15. Comparison of true stress–strain curves of DP 600 determined by the tensiletest and VPB test (curves are not extrapolated).

Fig. 16. Comparison of true stress–strain curves of DP 780 determined by the tensiletest and VPB test (curves are not extrapolated).

Fig. 17. Comparison of true stress–strain curves of DP 780-CR determined by thetensile test and VPB test (curves are not extrapolated).

5.2. VPB tests

For each of the five AHSS materials, at least six 10 in. × 10 in.square samples were sheared. All samples are 1 mm thick andwere prepared from the same sheets from which tensile testing

Fig. 18. Comparison of true stress–strain curves of TRIP 780 determined by thetensile test and VPB test (curves are not extrapolated).

434 A. Nasser et al. / Journal of Materials Proces

Ft

cp(thStttdt0

smktp

rScbumeamsbsbos

6

6

scsattfisv

ig. 19. Comparison of true stress–strain curves of DP 780-HY determined by theensile test and VPB test (curves are not extrapolated).

oupons were prepared. Minster Tranemo DPA-160-10 hydraulicress, 160 metric tons in capacity, was used for the test. HoneywellS-model) pressure transducer and ETI (LCP 12 S-100 mm) poten-iometer were used to measure the bulging pressure and domeeight, respectively. National Instrument (SCXI) Data Acquisitionystem (hardware: SCXI-1000 and software SCXI-1520) was usedo collect the data. Measuring devices were calibrated before theest to ensure accurate measurements. The clamping force was seto 100 metric tons to ensure no draw-in of the sheet material in theie cavity. The die cavity diameter of bulge test tools available athe ERC/NSM is 4.161 in (105.7 mm) and the die corner radius is.25 in. (6.35 mm).

The potentiometer used is a delicate device and cannot with-tand impact loading at the burst of the specimen. Thus, for eachaterial, at least one sample was burst without a potentiometer to

now the bursting pressure. To avoid bursting the other samples,hey were pressurized to 90–95% of the burst pressure while theotentiometer was used to measure the bulge height.

Pressure vs. dome height raw data, sheet thickness, and strainatios at 0◦ and 90◦ were used as inputs to the excel macro (seeection 3) to calculate the flow stress curve. To obtain the flow stressurve assuming the material is isotropic, value of one was used foroth R0 and R90. Since it is not possible to obtain experimental datap to the burst pressure, and in order to get a rough estimate of theaterial formability under balanced biaxial condition, the data was

xtrapolated to the burst pressure using a higher order polynomialpproximation. The extrapolated curve was then used in the excelacro to obtain the flow stress curve. The dome height of the burst

amples can be used as a measure of material formability underalanced biaxial condition. However, since the main objective of thetudy was not to evaluate the formability, the number of samplesurst and measured was not sufficient from the repeatability pointf view. Thus, these results are not presented in this paper. Table 1ummarizes the test matrix for both the tensile and the VPB tests.

. Results

.1. Tensile test

Figs. 4 and 5 show a comparison of the engineering and truetress–strain curves obtained by the tensile test, respectively. Noonsiderable variation of the flow stress curves between differentamples orientations was observed. Thus the flow stress curves forll materials and orientations are not presented. As an example, the

rue stress–true strain curves of DP 780-HY for the three orienta-ions are shown in Fig. 6. Table 2 summarizes the strain ratios of theve AHSS materials in the three orientations, as well as, the averagetrain ratio and planar anisotropy. Figs. 7 and 8 compare the averagealues (0◦, 45◦, and 90◦) for the uniform elongation, total elonga-

sing Technology 210 (2010) 429–436

tion, UTS, and 0.2% offset yield strength of the five AHSS tested bythe tensile test.

6.2. VPB test

Fig. 9 shows a sample pressure vs. time curve for TRIP 780 fromwhich the burst pressure was obtained. The burst pressure wasabout 225 bars for sample 1 and 226 bars for sample 2. Fig. 10 showsa picture of a burst sample (a) and a sample bulged but not burst(b) for TRIP 780. Since a large clamping force (100 metric tons) wasused, no material draw-in was observed in all tests. Fig. 11 shows acomparison of the experimental pressure vs. dome height curves ofthe five AHSS materials obtained by the VPB test. The correspond-ing flow stress curves are compared in Fig. 12. The curves of bothDP 600 and DP 780-HY were obtained up to bursting since a sampleaccidently burst during the test. As an example of experimental dataextrapolation to the burst pressure, Fig. 13 shows the pressure vs.dome height curve of TRIP 780 (sample 6) with and without extrap-olation. Fig. 14 shows the flow stress curve of TRIP 780 (sample6) obtained from both experimentally measured and extrapolatedpressure vs. dome height curves.

6.3. Comparison of tensile and VPB tests

Figs. 15–19 show the comparison of the flow stress curves deter-mined by the tensile and VPB tests for the five AHSS materialstested. Table 3 shows the comparison of the K and n-values obtainedfrom the two tests.

7. Discussion and conclusions

7.1. Tensile tests

Fig. 4 shows that the engineering stress–strain curves of the fiveAHSS grades tested become almost flat around the UTS for a widestrain range, making it difficult to visually identify the instabilitypoint (the UTS and uniform elongation). Thus, these values thatare clearly identified for low carbon steels are difficult to deter-mine for AHSS. As seen in Figs. 7 and 8, DP 600 has the highestpost-uniform elongation (about 10%). Although DP 780-HY has thelowest uniform elongation, it has the second highest post-uniformelongation of about 9.5%. As seen in Table 2, DP 600 has the highestaverage anisotropy ratio (strain ratio) of about 1.01, while TRIP 780has the lowest value (about 0.7). TRIP 780 has the highest planaranisotropy (�R) of about 0.33, while DP 600 has the lowest value(about 0.001). Thus, non-uniform flow in the flange region (earing)when forming TRIP 780 sheet can be an issue.

One of the problems faced during tensile testing is that neck-ing and failure for some materials at certain orientations occurredoutside the gauge length. This was the case for some samples ofDP 780 at 45◦ and 90◦, TRIP 780 at 45◦, and both DP 780-CR andDP 780-HY in all orientations. Since deformation is uniform beforethe instability point and since the presented true stress–true straincurves are plotted up to this point, the data obtained from thesesamples was not discarded.

For TRIP steels, strain hardening at the beginning takes placeby the interaction of dislocations with second phases existingin the matrix as discussed by (Shaw and Zuidema, 2001). Later,when the material starts to loose its hardening characteristics, theretained austenite transforms to martensite (the strain at whichphase transformation takes place depends mainly on the amount

of carbon in the alloy). As a result, the alloy retains it harden-ing characteristic, which explains the delayed necking of TRIP 780in uniaxial tensile test as compared to other DP steels with thesame UTS (see Figs. 5 and 7). It can be seen from Figs. 4 and 5that the flow stress curves of TRIP 780 have relatively low slope

A. Nasser et al. / Journal of Materials Processing Technology 210 (2010) 429–436 435

Table 3Comparison of the K and n-values obtained using both the tensile and VPB tests for the five AHSS materials.

Material Tensile test Bulge test (w/o correcting for anisotropy)

K (MPa) na R2b K (MPa) nc R2b

DP 600 952 0.175 0.9975 1056 0.167 0.9816DP 780 1541 0.188 0.9877 1382 0.116 0.9613DP 780-CR 1436 0.187 0.9736 1437 0.155 0.9701DP 780-HY 1332 0.142 0.9882 1220 0.097 0.9544TRIP 780 1444 0.208 0.9934 1454 0.183 0.9755

e from the 0.2% offset yield point to the instability point.

ange from about 0.04 to the last datapoint available without extrapolation (note that ther

atgamtcts

7

escsTaaHhcnrm

7

i

TC

TC

a The n-value in the tensile test was obtained by fitting the power law in the rangb R2 is the square of the correlation coefficient.c The n-value in the VPB test was obtained by fitting the power law in the strain r

ange in which the curve is fit affects the fit parameters).

t lower strains compared to other grades with the same UTS. Still,his alloy has the largest values of both uniform and total elon-ation. This maybe attributed to the transformation mentionedbove. Shaw and Zuidema (2001) reported that the austenite-to-artensite transformation of TRIP steels is easier under biaxial

ension than under compression. Thus, if used in drawing appli-ations, TRIP steels shows relatively good performance since theransformation strengthens the side wall, while the flange regiontays soft and easy to draw.

.2. Bulge tests

Figs. 13 and 14 show how much flow stress data is lost whennding the test at a pressure value slightly below the burst pres-ure. Moreover, these figures illustrate the high strain values whichan be attained under balanced biaxial condition. The burst pres-ures in the VPB test for the five AHSS materials are shown in Fig. 20.he dome height at fracture (bursting) in the VPB test can be used asmeasure of formability and therefore used as a quick and reliablecceptance test of incoming raw material in the stamping plant.owever, not many samples were burst in this study so that bursteight cannot be considered to be reliable in describing and/oromparing the formability of the different AHSS grades tested. Theegligible variation in the dome height vs. pressure curves, and cor-esponding flow stress curves, among different samples of the sameaterial, indicate the consistency in their deformation behavior.

.3. Comparison of tensile and VPB tests

For all materials, the stress levels obtained from the tensile tests lower than the levels obtained from the VPB test. Depending on R0

able 4omparison between the stress levels in the tensile and VPB tests at a strain values equal

DP 600 DP 780

True strain at instability (in the tensiletest)

0.154 0.84

Maximum true stress level obtained inthe tensile test (MPa)

681 946

True stress level in VPB test (MPa) (at astrain value equals to the instabilitystrain in the tensile test)

747 1062

Maximum percent difference betweentensile test and bulge test

9.7% 12.3%

able 5omparison between the maximum true strain that can be obtained in the tensile test an

DP 600 DP

Maximum true strain that can be obtained intensile test (at instability point)

0.154

Maximum true strain obtained in the bulgetest (without extrapolation)

0.545

Percent difference 254% 32

Fig. 20. Burst pressure of the five AHSS materials tested.

and R90, the corrected flow stress may increase, decrease, or stay thesame. It can be seen from Figs. 15–19 that there is almost no differ-ence between the anisotropy-corrected and uncorrected flow stresscurves for both DP 780 and DP 780-HY, while the biggest differenceis for TRIP 780. This illustrates how correcting for anisotropy maybe important for some materials. Table 4 compares the stress lev-els in the tensile test and the bulge test at a true strain value whichcorresponds to the instability point in the tensile test. This partic-ular point was selected for comparison because the difference inthe stress level between the two tests reaches it maximum at thispoint. It can be seen that the percentage difference in stress level

between the VPB and the tensile tests can be as high as 17% as isthe case for TRIP 780.

Theoretically speaking, the effective strain at instability underbalanced biaxial loading is twice the instability strain under uniax-

to the true strain at the onset of necking in the tensile test.

DP780-CR TRIP 780 DP 780-HY

0.10 0.138 0.765

904 935 911

979 1094 956

8.3% 17% 4.9%

d that obtained in the VPB test.

780 DP780-CR TRIP 780 DP 780-HY

0.84 0.10 0.138 0.765

0.356 0.237 0.258 0.508

4% 137% 88% 564%

4 roces

ictfltew5tsmpo

7

pstasttottdwm

N

deFhKnpSR

36 A. Nasser et al. / Journal of Materials P

al loading. It can be seen from Table 5 that data in the bulge testan be collected up to a very high strain values compared to theensile test. This is an advantage of the bulge test, especially if theow stress data is to be used for FE simulation, since no extrapola-ions is needed as is the case when using tensile data. Although wexpect the percent difference to be about 200% (should be 100%),e can see that it can be as low as 88% (for TRIP 780) and as high as

64% (for DP 780-HY). This emphasizes the importance of the bulgeest because of its capability to provide data for a bigger range oftrain compared to the traditional tensile test. In addition, someaterials may behave differently (especially from the formability

oint of view) under different loading conditions. DP 780-HY is anbvious example.

.4. Future work

In addition to the inverse analysis methodology used in thisaper, a new optimization methodology to determine the flowtress of sheet materials, tested by the bulge test, was developed athe ERC/NSM. The new methodology uses the commercially avail-ble FE software LS-DYNA, and the optimization tool LS-OPT, and istill based on the idea of inverse analysis. However, the membraneheory equations used in the current methodology which assumeshe bulge shape to be spherical are not used in the new method-logy. In addition, the need to have the FE-based database prioro the analysis is eliminated. This new methodology was proveno work well for room temperature bulge test, and it is still underevelopment for elevated temperature to provide reliable data forarm sheet forming of light-weight materials such aluminum andagnesium alloys.

omenclature

c diameter of die cavityengineering strain in axial direction (tensile test)

c clamping forced dome height

strength coefficientstrain hardening exponentbulging pressureengineering stress in axial direction (tensile test)strain ratio (plastic anisotropy or normal anisotropy)

sing Technology 210 (2010) 429–436

R̄ average strain ratio�R planer anisotropyR0 strain ratio in the rolling directionR90 strain ratio in the transverse directionRc die corner radiusRd radius of curvature at dome apexto initial sheet thicknesstd thickness at dome apex

Greek lettersε̄ effective strainεax or ε true strain in axial direction (tensile test)εt true strain in thickness direction (tensile test)εw true strain in width direction (tensile test)� true stress in axial direction (tensile test)�̄ effective stress�1 and �2 principal stresses in the sheet surface�̄anis effective stress corrected for anisotropy�̄iso effective stress not corrected for anisotropy�r stress in the radial direction

Acknowledgements

The Engineering Research Center for Net ShapeManufacturing—ERC/NSM (www.ercnsm.org) gratefully acknowl-edges the Auto-Steel Partnership (A/S P) for sponsoring this studyand United States Steels for providing the AHSS test materials.Special thanks to Mike Bzdok of A/S P and Ming Chen of USS fortheir support and valuable feedback.

References

ASTM Committee E28/Subcommittee E28.02, 2007. Standard Test Method for Ten-sile Strain-Hardening Exponents (n-Values) of Metallic Sheet Materials, ASTME646-07.

ASTM Committee E28/Subcommittee E28.02, 2006. Standard Test Method for PlasticStrain Ratio r for Sheet Metal, ASTM E517-00.

Gutscher, G., Altan, T., 2004. Flow stress determination using viscous pressure bulge(VPB) test. Journal of Materials Processing Technology 146 (1), 116–123.

Hill, R., 1990. Constitutive modeling of orthotropic plasticity in sheet metals. Journalof Mechanical Physics of Solids 38, 405–417.

Palaniswamy, H., Altan, T., 2007. Process simulation and optimization in metalforming—selected examples and challenges. Steel Research International 78,733.

Shaw, J., Zuidema, B., 2001. New High Strength Steels Help Automakers Reach FutureGoals for Safety, Affordability, Fuel Efficiency and Environmental Responsibility,SAE 2001-01-3041.