Materials and Design 32 (2011) 2650–2662

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Materials and Design

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Comparative investigations on numerical modeling for warm hydroformingof AA5754-O aluminum sheet alloy

Hasan Gedikli a,b, Ömer Necati Cora a, Muammer Koç a,c,⇑a NSF I/UCR Center for Precision Forming, Virginia Commonwealth University, Richmond, VA 23284, USAb Karadeniz Technical University, Department of Mechanical Engineering, Trabzon 61080, Turkeyc Department of Industrial Engineering, _Istanbul S�ehir University, _Istanbul, Turkey

a r t i c l e i n f o

Article history:Received 20 August 2010Accepted 13 January 2011Available online 18 January 2011

Keywords:A. Non-ferrous metal and alloysB. Film and sheetC. Forming

0261-3069/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.matdes.2011.01.025

⇑ Corresponding author at: NSF I/UCR Center forCommonwealth University, Richmond, VA, 23284, US

E-mail address: mkoc@vcu.edu (M. Koç).

a b s t r a c t

This study aimed to determine the proper combinations of numerical modeling conditions (e.g. solver,element type, material model) for warm hydroforming of AA5754-O aluminum alloy sheets. Assessmentof finite element analyses (FEA) is based on comparison of numerical results and experimental measure-ments obtained from closed-die forming, hydraulic bulge and tensile tests at different temperature (25–300 �C) and strain rate (0.0013–0.013 1/sec) levels. Thinning (% t) and cavity filling ratios (CFR) on theformed parts were taken as comparison parameters. Several numerical analyses employing different ele-ment types, solution methods and material models were performed using the commercially available FEApackage LS-Dyna to determine the best combination of modeling options to simulate the actual warmhydroforming operation as accurately as possible. Analyses showed that relatively better predictionswere obtained using isotropic material model, shell elements and implicit solution technique when com-pared with experimental results.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Lightweight materials, in particular, aluminum alloys have beenwidely used in automative and aircraft industry as the highstrength-to-weight ratio of aluminum results in significant weightand fuel savings [1–4]. In addition to weight reduction, utilizationof aluminum offers some other advantages such as better corrosionresistance, higher recyclability potential and increased energyabsorption during a crash situation. 5XXX alloys, in particular, havethe highest formability, and are used in automotive inner panels[5]. Automotive industry has a special interest in AA5754 becauseof its high ductility, lightweight, strength and weldabilityproperties [6]. However, because of their susceptibility to micro-structural damage, aluminum alloy sheets generally exhibits alower level of formability compared to typical sheet steels [7].Furthermore, utilization of aluminum alloys in the automotiveindustry has been far behind of steel because of cost and formabil-ity issues at room temperature [8]. On the other hand, this alloypresents some problems such as surface roughening duringdeformation, yield point phenomena, and the Portevin–LeChatelier (PLC) effect [9]. Therefore, innovations are imposed toachieve higher formability of aluminum including the attemptsof increased forming temperature [10–15], heat treating [16,17]

ll rights reserved.

Precision Forming, VirginiaA. Tel.: +1 804 827 7029.

or using new forming technologies such as hydroforming [10]. Itwas reported that limiting drawing ratio of AA5754 aluminum al-loy cup can be increased from 1.9 (at room temperature) to 2.7when the forming die is heated to 250 �C [5].

Quite a few studies investigating the proposed solutions for im-proved formability of AA 5754 are available in literature. Multiaxialas well as uniaxial tests were performed with AA5754-O byIadicola et al. to better predict the AA5754-O deformation behavior[18]. Similarly, Mahabunphachai et al. conducted a series of tensile(at strain rate of 0.0083/s) and hydraulic bulge tests (at strain ratesof 0.0013/s and 0.013/s) for AA5754-O sheet blanks at differenttemperatures ranging from 23 �C to 260 �C [19]. As a general obser-vation, significantly improved formability beyond 200 �C, and atlow strain rates were reported [17–19].

Numerical analysis, especially the finite element method (FEM),has been extensively used in automotive design and forming pro-cesses to accurately predict deformation mechanics. It is vitallyimportant for understanding, and forecasting the complex defor-mation behaviors that take place during sheet forming processes.For example, Ahmed and Hashmi modeled the hydraulic bulgingprocess with combined pressure and in-plane compressive loadson the sheet-plate by finite element method. They used elastic, lin-early plastic (bi-linear) isotropic material models with 2D 4-nodequadrilateral elements that allow large-deformation and large-strain analysis [20]. Wowk investigated strain rate sensitivity ofAA5754 sheets experimentally employing very wide range of strainrates (0.001/s–1500/s), and then numerically implemented these

Table 1Test types and conditions for determination of mechanical properties of AA5754-O[19].

Materialtesting

Temperature(�C)

Materialmodel

Constitutive equations Lankford’scoefficients

Tensiletest(TT)

Room Power law r ¼ 482:74 � e0:3215

150 Power law r ¼ 346:33 � e0:2355 r�

0 = 0.656260 Power law r ¼ 174:76 � e0:1209 r

�

45 = 0.644Bulge

test(BT)

150 Strain ratepower law

r ¼ 435:59 � e0:3127 � _e0:0422 r�

90 = 0.752

260 Strain ratepower law

r ¼ 474:71 � e0:1844 � _e0:1766

Table 2Barlat YLD2000 material model anisotropy coefficients for AA5754 [15].

Anisotropic coefficients for YLD2000-2d Temperature

150 �C 260 �C

a1 0.9471 0.9814a2 1.0863 1.0423a3 0.9085 0.9321a4 0.9955 0.9813a5 1.0009 0.9933a6 0.9826 0.9759a7 1.2016 2.4780a8 1.1459 1.0181

H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662 2651

data into rate-sensitive Voce material model available in Ls-Dyna[6]. Likewise, Smerd experimentally studied the deformationbehavior of aluminum alloy sheets at high strain rates (between600/s and 1500/s), and temperature levels of 25–300 �C using atensile split Hopkinson bar apparatus [21]. He used the Johnson–Cook and Zerilli–Armstrong constitutive material models fornumerical simulations of different aluminum alloys. The Zerilli–Armstrong model was noted to be suitable for a wide range ofFCC materials, but it underestimates the strength of BCC materials,and is only valid for high strain rates (104/s–106/s) and relativelylow temperatures [6].

Reliability of finite element analyses for forming processes ishighly affected by variety of factors including accuracy of geometricand material models, reasonability of assumptions and simplifica-tions, element type and size, solution algorithm. Anisotropicmaterial models, which include temperature variation effects, havebeen widely used for more realistic modeling of warm formingprocesses of lightweight alloys. Barlat et al. developed a series ofconstitutive equations for anisotropy, and implemented those inpast 20 years such as 3-parameter Barlat Yld89 [22], Yld91 [23],Yld96 [24], YLD2000-2d [25], Yld2004 models [26]. After him,several researchers implemented these models in their numericalmodeling studies. Abedrabbo et al. used Barlat’s Yld96 temperature-dependant anisotropic material model for thermo-mechanicalcoupled FEA of AA3003-H111 aluminum alloy sheet forming[13,14]. Similarly, in another work by the same authors, Barlat’sYld2000-2d was used to simulate forming of AA5754-O and

B

B

AA

B

B

AA SECTION B-B

SECTION A-A

(a)

(b)Fig. 1. (a) Shape and dimensions of non-axisymmetric die used in closed-die warm hydro-forming experiments (dimensions in mm), and (b) sample part with thickness andCFR measurement profiles and locations.

2652 H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662

AA5182-O aluminum alloys [27–29]. Korkolis used Yld2000-2d Bar-lat model in FEA analysis of forming of aluminum tubes [30]. How-ever, thus far, effects of material models, element types andsolution methods on the numerical analysis for the warm hydro-forming of aluminum alloy AA5754 have not been investigated indetail.

In this study, first, a series of closed-die warm hydroformingexperiments were performed to determine the effect of processparameters, such as temperature, pressure, and pressure rate onthe forming limits of the AA 5754-O alloy. Then, a set of finite ele-ment analyses were performed using different combinations of ele-ment types (solid vs. shell elements), solution procedures (explicit vs.implicit), and material models (isotropic strain rate power law, aniso-tropic 3-parameter Barlat, and anisotropic Yld2000-2d). Comparisonof FEA predictions with experimental measurements (such as cav-ity filling ratio-CFR and thinning-% t) were used to verify the accu-racy of the numerical models and to reveal the best combination ofmodeling variables. Next section introduces the experimental

Fig. 2. (a) Finite element model of closed-die warm hydroforming, and (b) FE meshof blank at the final stage of process.

Table 3Details of numerical simulations performed.

Sim. Gr. No Test conditions Material models used

Anisotropic Isotrop

3-Parameter Barlat Barlat’s YLD2000 Strain

1 (a) 150 �C & 20 MPa U

2 U

3 U

4 (b) 150 �C & 30 MPa U

5 U

6 U

7 (c) 260 �C & 20 MPa U

8 U

9 U

10 (d) 260 �C & 30 MPa U

11 U

12 U

conditions while the third section presents the FEA results ofAA5754 warm hydroforming process. Results and discussions arefollowed by conclusions in section four and five, respectively.

2. Closed-die warm hydroforming experiments

This study was intended to investigate the limits of warmhydroforming process and its proper simulation methods that willfurther help determination of the optimal process conditions andunderstanding of the forming behavior for different materials ofinterest under this forming process. To this goal, a set of closed-die hydroforming experiments were conducted in order to studythe effects of pressure and temperature on the forming limits ofthe AA5754-O. The pressure and temperature levels were selectedas 20–30 MPa and 150 �C, and 260 �C, respectively. The pressurerate was fixed to be 0.22 MPa/s for all tests. Each condition wastested at least three times to address the repeatability. The die/partgeometry of warm hydroforming experiments is shown in Fig. 1.

After the tests performed, a 3D optical photogrammetric sys-tem, ARAMIS was employed to capture the final profiles/shapesof the hydroformed parts to obtain the coordinate information onthe part surface. Cavity filling ratio (CFR) was calculated usingthe coordinate information distribution along different contourson the part (Profile A–A, short side and Profile B–B, long side asshown in Fig. 1a). These profiles were selected along and acrossthe rolling direction so that effect of anisotropy can be revealed.Along the same contours, thickness (t) measurements were per-formed on 10 different locations. At each location, at least six thick-ness measurements were performed (Fig. 1b).

3. Numerical analyses

Numerical analyses were performed using the commercial ex-plicit and implicit finite element code Ls-Dyna. Necessary mechan-ical properties for modeling of AA5754-O sheet metals wereobtained from authors’ previous study as well as from literatureas given in Table 1, and Table 2 based on the well agreement ofthe flow curves obtained for current study and the others availablein literature [12,19].

To take advantage the symmetry of the part, a quarter-model ofthe closed-die warm hydroforming setup, as shown in Fig. 2a, wasconsidered in the FEA model to reduce the simulation time and in-crease the model accuracy using relatively higher number of ele-ments. The sheet blank with an initial thickness of 1 mm wasmodeled as an elasto-plastic material while the upper and lowerdies were defined as rigid bodies using 3D shell elements. Twodifferent element types, namely 3D shell and 3D solid elements,

Element type Solution procedure Flow curve data

ic

rate power law Shell Solid Explicit Implicit Tensile test Bulge test

U U U

U U U

U U U

U U U

U U U

U U U

U U U

U U U

U U U

U U U

U U U

U U U

Fig. 3. Hydroformed specimens at temperature 150 �C and pressure of 20 MPa: (a) experimental, and (b) FEA.

Fig. 4. Hydroformed specimens at temperature 150 �C and pressure of 30 MPa: (a) experimental, and (b) FEA.

Fig. 5. Hydroformed specimens at temperature 260 �C and pressure of 20 MPa: (a) experimental, and (b) FEA.

H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662 2653

were used in simulations. In the simulations where shell elementsemployed, shell element type 16 with four nodes, and full integra-tion feature was utilized. On the other hand, simulations per-formed using 3D solid elements utilized type 2 elements witheight nodes which had full integration and selective-reduced capa-bility. Sheet blank was modeled with 225 shell element at the

beginning of the simulation whereas, with adaptive meshing fea-ture, the number of elements went up to as high as 5000 elementsas the forming progressed which can be seen in Fig. 2b. For thesimulations in which 3D hexagonal solid elements were used, con-stant number of 3600 elements were used since adaptive reme-shing feature was not available with this element type. Adaptive

Fig. 6. Hydroformed specimens at temperature 260 �C and pressure of 30 MPa: (a) experimental, and (b) FEA result.

Fig. 7. Effect of pressure on thickness change for elements S7444 and S7728 as indicated in the figure (for TT-Shell-Implicit-30 MPa condition).

Fig. 8. Effect of temperature on thickness distribution along Profile A (for TT-Shell-Implicit-30 MPa condition).

ºC)

Fig. 9. Effect of temperature on cavity filling ratio along Profile A (numericalsolution was obtained for TT-Shell-Implicit-30 MPa condition).

2654 H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662

mesh parameters were based on multiple criteria and the timeinterval between adaptive refinements was set to 0.01 s. Adaptiveerror tolerance for total angle change in degrees relative to the sur-rounding element for each element to be refined was selected as

2�. The other adaptive remeshing criterion selected was the abso-lute minimum shell thickness, and pre-defined as 0.9 mm.

(a)

(b)Fig. 10. Effects of solver, material and element type on cavity filling for profile A at 150 �C and 30 MPa forming conditions: (a) die shape based filling comparisons, and (b)cavity filling ratio comparisons.

H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662 2655

Mechanical properties for AA 5754 sheet blank such as Young’smodulus, Poisson’s ratio and density were entered into model as68 GPa, 0.33 and 2.66 g/cm3, respectively.

The contact conditions in both upper die-blank and lower die-blank pairs were imposed as ‘‘forming one way surface to surface’’contact. Coulomb friction model with a coefficient of friction of0.1 was employed for all contacting surfaces after testing the effectdifferent of friction coefficients varying between 0.01 and 0.5. Sym-metrical boundary conditions were imposed to perpendicularedges at the periphery of the model. To simulate the blank holderforce, the sheet blank was subjected to clamping force of 1000 kN

in between lower and upper dies. The sheet blank was also ex-posed to maximum hydroforming pressure of 30 MPa with a0.22 MPa/s pressure rate.

Since the element type, material model and solution method af-fect several response factors such as accuracy, solution time, con-vergence of the numerical approximation; different combinationmodeling variables need to be tested to have a well-establishedmodel [31–34]. Numerical simulations were conducted using 3Dshell and 3D solid elements; explicit and implicit solution tech-niques; isotropic strain rate power law material model, and aniso-tropic material models such as three-parameter Barlat (3P-Barlat),

(a)

(b)Fig. 11. Effects of solver, material and element type on cavity filling for profile B at 150 �C and 30 MPa forming conditions: (a) die shape based filling comparisons, and (b)cavity filling ratio comparisons.

2656 H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662

and Barlat Yld2000-2d (YLD2000) at different four test conditions:(a) 150 �C/20 MPa, (b) 150 �C/30 MPa, (c) 260 �C/20 MPa, and (d)260 �C/30 MPa. A total number of 48 simulations, as presented inTable 3, were performed using an Intel Core i7 2.8 GHz CPU with8 GB of RAM. Prior to these simulations, a non-isothermal FEAwas carried out to find out the temperature variation on the sheetblank and found that sheet blanks can be modeled as equallyheated (isothermal condition), and hence, structural-only type offinite element analyses were conducted.

4. Results and discussion

The experimental and numerical results of formed parts fromthe closed-die hydroforming tests are presented in Figs. 3–6 for

150 �C/20 MPa, 150 �C/30 MPa, 260 �C/20 MPa, 260 �C/30 MPa con-ditions, respectively.

4.1. Effects of forming pressure and temperature on sheethydroformability

Effects of pressure and temperature on the formability charac-teristics of AA 5754-O sheet blanks were investigated experimen-tally and numerically using two different responses: (a)distribution of thinning in the A-A (Profile A) and B–B (Profile B)sections (as described in Fig. 1), and (b) cavity filling ratio (CFR).In addition, strain distribution and the highest strain levels weredetermined from the finite element analyses as can be seen fromFigs. 3–6. It was noted that both pressure and temperature havesignificant effect on the strain levels experienced. Maximum strain

Die Profile AExperimentalBT-Shell-Imp-No SpringbackBT-Shell-Imp-Springback

Fig. 12. Cavity filling for Profile A after springback analysis (for 150 �C and 30 MPa conditions).

Die Profile BExperimentalBT-Shell-Imp-No SpringbackBT-Shell-Imp-Springback

Fig. 13. Cavity filling for Profile B after springback analysis (for 150 �C and 30 MPa conditions).

-4 1 6 11 16 21 26 31 36 41 46 51 56Profile B - Distance from Center (mm)

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental BT-Solid-Explicit BT-Solid-Implicit TT-Solid-Explicit TT-Solid-Implicit

32

4

6 8

10

1

Fig. 14. Thinning distribution obtained using solid elements for the profile B at 260 �C and 30 MPa.

H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662 2657

level was acquired as 0.29 for 150 �C/20 MPa case while this valuewent up to 0.33 for 150 �C/30 MPa case. Similarly, strain levels of0.37 and 0.40 were obtained for 260 �C/20 MPa and 260 �C/

30 MPa forming conditions, correspondingly. Thinning variationswith respect to pressure were presented for two elements thatattained the maximum thinning values on the Profile A (S7444)

Profile A - Distance from Center (mm)

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental BT-Shell-Explicit TT-Shell-Explicit YLD2000-Shell-Explicit 3P-Barlat-Shell-Explicit

-4 1 6 11 16 21 26 31 36 41 46 51 56

-4 1 6 11 16 21 26 31 36 41 46 51 56

Profile B - Distance from Center (mm)

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental BT-Shell-Explicit TT-Shell-Explicit YLD2000-Shell-Explicit 3P-Barlat-Shell-Explicit

(a)

(b)Fig. 15. Thinning distribution obtained with shell elements using explicit solver for: (a) Profile A at 260 �C–30 MPa, (b) Profile B at 260 �C–30 MPa conditions.

2658 H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662

and Profile B (S7728) contours as presented in Fig. 7. Numericalsimulations were conducted using implicit solver and isotropicmaterial model based on tensile test data (Profile A, TT150 and Pro-file B, TT150) and bulge test data (Profile A, BT260 and Profile B,BT260). Results showed that thickness values of the elementsS7444 and S7728 rapidly decreased with the increasing pressureup to 20 MPa, and then it was stabilized. In both temperature lev-els, the thickness along the Profile A declined relatively faster thanthat of along Profile B up to 5 MPa. After 5 MPa level, the thicknessalong Profile B decreased faster than that for along Profile A.

Fig. 8 shows the thickness distribution of the formed parts atdifferent temperature levels (for TT-Shell-Implicit-30 MPa condi-tion). As expected and observed from the experimental results,the CFR of AA 5754-O sheet alloy is increased with increasing tem-perature as shown in Fig. 9.

4.2. Effects of solver type, element type and material data source inFEA predictions

To analyze the effect of solver, element, and material datasource (tensile or bulge test) on the prediction accuracy of simula-tions, both cavity filling ratios (CFR) and part thickness values fromexperimental measurements and FE analyses were compared.

Experimental cavity filling ratio (CFR) (cavity filling area/dieprofile area) for the Profile A and Profile B were measured as 90%and 93%, respectively for the warm hydroforming condition of30 MPa/150 �C. Figs. 10 and 11 illustrate these comparisons. Max-imum differences between numerical and experimental resultswere obtained as around 9% on the Profile A, and 6% on the ProfileB. Comparisons were based on the 2D (filled area) measurementsand grouped for explicit and implicit analyses. Figs. 10 and 11

Profile A - Distance from Center (mm)

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental BT-Shell-Implicit TT-Shell-Implicit YLD2000-Shell-Implicit 3P-Barlat-Shell-Implicit

-4 1 6 11 16 21 26 31 36 41 46 51 56

-4 1 6 11 16 21 26 31 36 41 46 51 56Profile B - Distance from Center (mm)

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental BT-Shell-Implicit TT-Shell-Implicit YLD2000-Shell-Implicit 3P-Barlat-Shell-Implicit

(a)

(b)Fig. 16. Thinning distribution obtained with shell elements using implicit solver for: (a) Profile A at 150 �C/30 MPa, (b) Profile B at 150 �C/30 MPa, (c) Profile A at 260 �C/30 MPa, (d) Profile B at 260 �C/30 MPa conditions.

H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662 2659

revealed that, in all simulations, the explicit analyses yielded high-er cavity filling ratios compared to the implicit analyses. This canbe explained by the fact that explicit analysis results deviate fromthe exact solutions as the certain critical time step size is surpassed[31].

It was also noticed from Figs. 10 and 11 that the numerical anal-yses yielded higher cavity filling ratios when compared to theexperimental values, in general. This was assumed to be resultedfrom negligence of springback in the analyses that commonlyexperienced in sheet metal forming. It was reported that elevatedspringback related issues are experienced in aluminum sheet usecompared to steels [35,36], and these issues are diminished or lessexperienced with increasing forming temperature, advanced form-ing techniques techniques such as hydroforming and superplasticforming [37].

Therefore, a set of simulations in which springback effect in-cluded were performed for some of the simulation cases (with flowcurves obtained from bulge tests using shell elements and implicitsolution techniques) as presented in Figs. 12 and 13. It was ob-served that simulations taking springback into account yieldedslightly lower cavity filling ratios and were considered more reli-able than non-springback type analyses. It was also concluded thatshell elements led to higher filling ratios than solid elements owingto their higher number of elements and stiffness matrixdifferences.

In order to analyze the effects of element type and solution pro-cedures on simulation results and accuracy, thinning of the actualhydroformed parts were compared with the simulation results.Numerical and experimental thinning comparisons are shown inFigs. 14–16 at different test conditions for Profile A or B.

Profile A - Distance from Center (mm)

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental BT-Shell-Implicit TT-Shell-Implicit YLD2000-Shell-Implicit 3P-Barlat-Shell-Implicit

-4 1 6 11 16 21 26 31 36 41 46 51 56

-4 1 6 11 16 21 26 31 36 41 46 51 56Profile B - Distance from Center (mm)

-5

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental BT-Shell-Implicit TT-Shell-Implicit YLD2000-Shell-Implicit 3P-Barlat-Shell-Implicit

(c)

(d)Fig. 16 (continued)

2660 H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662

Fig. 14 shows the simulation results obtained with using solidelements and with both implicit and explicit solution proceduresfor 260 �C and 30 MPa conditions along profile B direction.Although there is no significant difference between the simulationresults wherein solid elements used, FE analyses that utilized: (a)flow curves obtained from bulge tests and (b) explicit procedureprovided better approximation for thinning predictions, in general.However, in terms of predicting the thinning in the critical regionswhere the highest thinning occurred, the FE model that was basedon flow curves from tensile tests with solid elements and implicitsolution procedure (TT-Solid-Implicit) yielded closer results toexperimental part measurements as can be seen from Fig. 14. Itcan be concluded that finite element analyses resulted in reason-ably acceptable predictions for thinning within the deviation rangeof 5–15%.

Figs. 15 and 16 illustrate thinning for hydroformed parts ob-tained from simulations that performed with shell elements, and

using explicit (Exp) and implicit (Imp) solvers at different formingconditions. FE analyses facilitated TT-Shell-Exp, BT-Shell-Exp,3P_Barlat-Shell-Exp and YLD2000-Shell-Exp combinations pro-vided conforming approximations to experimental results for pro-file A, up to the contour length of 20 mm. In the maximumthinning location, the analysis employed YLD2000-Shell-Exp fea-tures resulted in higher accuracy and it was followed by TT-Shell-Exp, 3P_Barlat-Shell-Exp and BT-Shell-Exp, respectively. Forprofile B, on the other hand, analyses with different numericalpreferences yielded very close results to each other up to thecontour length of 35 mm. All numerical results except YLD2000-Shell-Exp were in close proximity, however; beyond 35 mmTT-Shell-Exp and 3P_Barlat-Shell-Exp were closer to experimentalvalues. TT-Shell-Exp was determined to yield best results. The totalcomputational time was 15 h, approximately.

In the analyses in which implicit solver were exploited, the FEmodels with TT-Shell-Imp, BT-Shell-Imp, YLD2000-Shell-Imp, and

-4 1 6 11 16 21 26 31 36 41 46 51 56Profile A - Distance from Center (mm)

0

5

10

15

20

25

30

35

Thin

ning

(%)

Experimental TT-Solid-Implicit TT-Shell-Implicit TT-Shell-Explicit

Fig. 17. Thinning distribution obtained with shell and solid elements at 150 �C and 30 MPa for profile A.

H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662 2661

3P_Barlat-Shell-Imp arrangements resulted in very close approxi-mations (�5% difference) to experimental data in Profile A, up toa contour distance of 25 mm (i.e., measurement location #6). Afterthis critical region where maximum thinning is usually observedat, the difference between experimental and numerical analyseswent up to �10% levels, which is still in acceptable range. Similarobservations were made for Profile B. As a general conclusion,the locations where maximum thinning occurred were estimatedmoderately better with the recently developed material models(3P_Barlat, YLD 2000). These material models were proven to yieldaccurate results, especially where anisotropy is present [12,29]. Asoverall evaluation, FE models that utilized TT-Shell-Imp combina-tions showed more consistent predictions. The corresponding com-putational time was recorded as short as 13 min.

Thinning comparison given in Figs. 14–16 showed that, the dif-ferent numerical solution attempts were able to approximate thecritical thinning regions with varying degree of deviations fromexperimental values, limited up to 15%, at most. For flat sectionsof the hydroformed parts, the numerical results were highly accu-rate (less than 1% difference between experimental measurementsand numerical predictions in some cases) while in curved parts ofsheet blanks, deviation were usually in 5–15% range, which is stillin admissable margin of prediction error. Uncertainties andapproximations in temperature distribution, friction and materialmodeling may have contributed to these deviations. It should alsobe noted that there are also several other factors that cause dis-crepancies such as manual measurement errors, inability to obtainthe numerical results from exact corresponding location wheremanual measurements were obtained (element size related is-sues). Based on the previous knowledge available in the literature,anisotropy of AA 5754-O can be assumed insignificant and it is notresponsible from the deviation of FEA results from experimentalobservations [38].

Solid elements, in general, resulted in better predictions, partic-ularly for the flat region of the parts (i.e., up to �30 mm distancefrom center point, Fig. 15) especially with the strain rate powerlaw material model. Nevertheless, for the curved regions of theformed part (i.e. after 30 mm contour distance in Fig. 17), the re-sults obtained with shell elements were closer to measured thick-ness values than the results obtained with solid elements. In

contrast, finite element analyses that use solid elements are re-garded as more realistic compared to analyses in which shell ele-ments utilized [39]. This can be explained with the adaptiveremeshing feature that was used in conjunction with the shell ele-ments. Different from the shell elements, the analyses in which so-lid elements (3D, hexagonal) were employed performed withoutadaptive remeshing feature. Another factor for the difference be-tween the analyses is the fact that the response to bending andstraining are obtained with different stiffness matrices in solidand shell elements formulations.

5. Conclusions

Forming characteristics of AA5754-O aluminum alloy underwarm hydroforming process conditions were numerically investi-gated and were compared with the experimental findings obtainedat different elevated temperature and pressure values. Thinningdistribution and the cavity filling ratio (CFR) values of the formedpart were taken as measures to compare and assess the effect ofthe temperature and pressure as well as the accuracy of numericalmodels.

As expected, increasing temperature and pressure values re-sulted in an increased cavity filling ratio and thinning. For theclosed-die hydroforming problem discussed in this study, no sig-nificant advantage was observed by using the anisotropic materialmodels (3-parameter Barlat, and YLD2000) over isotropic materialmodels (strain rate power law). Nevertheless, the locations on thepart that underwent excessive thinning were predicted slightlybetter with the recently developed material models that takeanisotropy into consideration. It is believed that these modelswould result in better predictions for the materials exhibit higherdegree of anisotropy. In terms of the effect of material test type(bulge vs. tensile test), the numerical models that were built onthe flow stress curves obtained from tensile tests resulted in closerprediction to the experimental results. In comparison to solid ele-ments, shell elements were found to be more appropriate to pre-dict the thinning in the part. From overall observations, the bestcombination for the FEA parameters is found to be ‘‘TT-Shell-Imp’’ with isotropic material model based on tensile tests, shell

2662 H. Gedikli et al. / Materials and Design 32 (2011) 2650–2662

elements and implicit solver, which offered better predictions anda significant savings in simulation time.

Acknowledgments

The authors are thankful to National Science Foundation (NSF)for the partial support on this project through NSF ENG/CMMIGrants 0703912; and NSF IIP IUCRC Grant 0638588.

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