materials and design - universidade de coimbra · the formability of the twbs, relative to the base...

Materials and Design xxx (2009) xxx–xxx

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Materials and Design

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A multi-step analysis for determining admissible blank-holder forces indeep-drawing operations

D.M. Rodrigues * , C. Leitão, L.F. MenezesCEMUC, Department of Mechanical Engineering, University of Coimbra, Coimbra, Portugal

a r t i c l e i n f o a b s t r a c t

Article history:Received 24 June 2009Accepted 16 August 2009Available online xxxx

Keywords:Finite elementsFormabilityAluminium alloys

0261-3069/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.matdes.2009.08.028

* Corresponding author. Tel.: +351 239 790 700; faE-mail addresses: [email protected] (D.M

dem.uc.pt (C. Leitão), [email protected] (L.F. M

Please cite this article in press as: Rodrigues DMJ Mater Design (2009), doi:10.1016/j.matdes.20

In present investigation a methodology to determine admissible blank-holder forces in deep-drawingoperations was established. According to this methodology, the deep-drawing operation is simulatedand the maximum blank-holder forces, for stamping friction stir welded tailored blanks, are establishedbased on the comparison of the numerical principal strains fields, obtained in the numerical simulations,with the limiting strains determined analytically for both base materials. Supporting experiments wereperformed and its results used to confirm the quality of the numerical predictions.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

In the last decades, various research works (e.g. [1–3]) showedthat the formability of the metallic materials strongly depends onthe deformation mode, loading history and on the plastic behav-iour and anisotropy of the rolled sheets. The formability limitsare usually established by determining the limiting strains at theonset of localized necking, from plastic instability analysis, andplotting Forming Limit Diagrams (FLDs). The experiments neces-sary to plot the FLDs are very laborious and time consuming.Therefore, the theoretical analysis of plastic instability become ofmajor importance in order to determine the forming limit strainsrapidly and economically [4–9].

The parameters involved in the forming operation can also sig-nificantly affect the formability of the material [1,10,11]. Fractureand wrinkling are usually considered the two major modes of fail-ure in sheet metal parts. By properly adjusting the blank-holderforce (BHF), and the way it is applied on the blank, it is possibleto expand the working window between the tearing and wrinklingboundaries. Other features that play an important role in the form-ability of the blanks are the drawing ratio, the lubrication condi-tions and the characteristics of the forming tool, such as the dieclearance, the die entry radius and the punch nose radius. Due tothe large amount of parameters to be considered, finite elementnumerical simulation become a precious tool that contributes to-wards the development and optimisation of the forming processes,leading to significant economic and technical gains [12,13]. In fact,

ll rights reserved.

x: +351 239 790 701.. Rodrigues), carlos.leitao@

enezes).

et al. A multi-step analysis fo09.08.028

a large range of forming parameters can be tested in finite elementnumerical simulations and the optimal values can be predicted atlow CPU cost, avoiding the expensive trial and error workshopapproach.

In present investigation the maximum admissible BHF for deep-drawing cylindrical cups from similar and dissimilar aluminiumtailor welded blanks (TWB) was established. It is well known thatthe formability of the TWBs, relative to the base materials, is highlyaffected by the weld characteristics, the strength and thicknessmismatch between the TWB components and the orientation ofthe blank sheets rolling direction relative to the weld line, whichmakes necessary additional cares in process design for TWBs form-ing [14–17]. The TWBs analysed in this work were obtained by fric-tion stir welding (FSW), in similar and dissimilar combinations,1 mm thick sheets of two aluminium alloys, the AA 5182-H111and the AA 6016-T4 alloys. According to the base materials, thewelds obtained had different mechanical and metallurgical charac-teristics and very large width relative to the sheets thickness,which makes its influence on the global behaviour of the TWBsnot negligible [15,18].

Admissible values of the BHF for deep-drawing cylindricalcups of 1.8 drawing ratio and 60 mm maximum draw depth, fromthe similar and dissimilar TWBs, were established by performinga multi-step analysis. In the first step, theoretical FLDs were plot-ted in order to establish the forming limits of the base materials.These FLDs were determined by using the stress based forminglimit criterion proposed by Alsos et al. [9]. In the second step,numerical simulations of the deep-drawing test were performed.Several values for the BHF were tested and the principal strainfields, at several stages of the stamping process, were plotted inthe FLDs. In the third step, the maximum admissible BHF values

r determining admissible blank-holder forces in deep-drawing operations.

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2 D.M. Rodrigues et al. / Materials and Design xxx (2009) xxx–xxx

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for deep-drawing the different types of blanks were establishedby comparing the numerical strain fields with the forming limitvalues established for the base materials. Finally, experimentaldeep-drawing tests were performed in order to test the numericalpredictions.

Table 1Strain paths under proportional loading.

Deformation mode b Stress relations

Uniaxial tension (UT) �0.5 r2 = r3 = 0Plane strain (PS) 0 r2 = r1/2; r3 = 0Equibiaxial tension (EBT) 1 r2 = r1, r3 = 0

2. Theoretical prediction of sheet metal instability

Many attempts have been made to predict forming limit dia-grams by taking into account the theory of plasticity, materialparameters and instability conditions. In this paper, the stressbased forming limit criterion proposed by Alsos et al. [9] wasused to predict the FLDs for the base materials in study. Thestress-based FLDs were found to be less strain path dependentthan the strain-based FLDs [6,9]. However, there are two draw-backs associated to the use of the stress-based FLDs: the difficultyin measuring the stress components during experiments and therelatively poor resolution of it as compared to the strain-basedcriteria.

The stress based forming limit approach proposed by Alsos et al.[9], called BWH model by the authors, combines the Hill [19] andthe Bressan and Williams [20] instability criteria to predict the un-set of necking and is valid for both the positive and negative quad-rants of the FLDs. Formulated in terms of the linear strain rate ratio,b ¼ _e2= _e1, the criterion reads

r1 ¼2Kffiffiffi

3p 1þ 1

2 bffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 þ bþ 1

q 2ffiffiffi3p e1

1þ b

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 þ bþ 1

q� �n

; b 6 0;

r1 ¼2Kffiffiffi

3p

2ffiffi3p e1

� �n

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� b

2þb

� �2r ; b > 0

ð1Þ

In these expressions, the maximum principal stress at the onset ofnecking (r1) is determined as a function of the material parametersK and n and the critical strain at the unset of necking e1. Theseparameters are determined assuming that the material stress–strain curves is represented by the Hollomon power law expression,

�r ¼ K�en ð2Þ

where �r is the equivalent flow stress and �e is the equivalent plasticstrain. According to this equation, e1 is equal to the power law expo-nent n (Considère criterion), although measured values can be used.Analytical and experimental validation of BWH model can be foundin [9].

In current work, despite the FLDs were determined using theBWH stress based approach, they were plotted in the principalstrain axes ðe1; e2Þ. To perform the stress–strain conversion, theHill’s quadratic anisotropic criteria was used as plastic potential.The Hill-48 plastic potential function as originally defined by Hillcan be written as

�r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiFðr1 � r3Þ2 þ Gðr3 � r1Þ2 þ Hðr1 � r2Þ2

qð3Þ

where r1;r2 and r3 are the components of the principal stress ten-sor r defined in the orthotropic frame and F, G and H are the coef-ficients that define the anisotropy.

The principal plastic strain increments dei are obtained from theassociated flow rule

dei ¼ dk@�r@ri

ð4Þ

where dk is the plastic multiplier. From previous equations, dk ¼ d�ein which d�e is the equivalent plastic strain increment. According toStoughton [6], assuming plastic anisotropy, the linear strain rate ra-tio b is given by

Please cite this article in press as: Rodrigues DM et al. A multi-step analysis foJ Mater Design (2009), doi:10.1016/j.matdes.2009.08.028

b ¼ ðF þ HÞa� H1� Ha

ð5Þ

where a = r1/r2. For uniaxial tension a = 0, for plane strain a = 0.5and for equibiaxial tension a = 1. For the linear strain paths, usuallyassumed when plotting the FLDs, and isotropic materials, b is con-stant and assume the values given in Table 1.

3. Experimental deep-drawing tests

The formability tests were performed by drawing cylindricalcups with the tool shown in Fig. 1. This testing device, that com-prises a 100 mm punch, a 110 mm diameter die and a blank-holder(Fig. 1a), was developed to be operated in a classical electrome-chanical tensile test machine. To apply and maintain the chosenBHF, 10 calibrated springs were used (Fig. 1b). One of these springswas equipped with a 10 kN force sensor in order to verify if the BHFremained stable during the tests. The stamping operation was al-ways performed on lubricated blanks. The lubricant used was thedeep-drawing QUAKER N6130 oil. It was applied 1.4 g/m2 of oilper blank face using a pre-impregnated paper weighted beforeand after the application. In this work, cylindrical cups 60 mmdeep were obtained from 180 mm round sheet TWBs obtained byfriction stir welding the AA 5182-H111 and AA 6016-T4 aluminiumalloys, in similar and dissimilar combinations (Fig. 2). Three typesof TWBs were tested: S55 (similar: AA5182–AA5182), S66 (similar:AA6016–AA6016) and D56 (dissimilar: AA5182/AA6016). In all thetests performed, the punch speed was 100 mm/min. Several BHFs,between 8 and 32 kN, were tested in order to validate the numer-ical results. Punch speed was 100 mm/min.

4. Numerical simulation of the deep-drawing process

An in-house three-dimensional implicit finite element code(DD3IMP) was used for the numerical simulation of the deep-drawing test. The mechanical model of the program takes into ac-count the large elastoplastic strains and rotations that occur in thedeep-drawing process. Details of this framework can be found in[12,21–24].

In this work, the Hill-48 orthotropic yield criteria Eq. (2) com-bined with isotropic hardening, described by the saturation law

�r ¼ r0 þ Rsatð1� expð�nv�eÞÞ; ð6Þ

were used to describe the mechanical behaviour of the materials. Inprevious equation, r0 is the initial yield stress, Rsat is the saturationstress and nv is a constant. Coulomb’s classical law was used tomodel the frictional contact problem treated with an augmentedLagrangian approach.

The numerical simulations were performed using a finite ele-ment model that reproduces the forming tool used in the experi-mental work (Fig. 1) and the round blanks represented in Fig. 2.The forming tools were modelled as rigid bodies using Bézier sur-faces (Fig. 3a). Three-dimensional isoparametric finite elementsassociated with a selective reduced integration scheme were usedfor the spatial discretization of the blanks. Considering the geomet-ric and material symmetry, 1=4 of the blank was used in the simula-tions of the similar TWBs (Fig. 3b), and ½ of the blank was used inthe simulations of the dissimilar TWBs (Fig. 3c). Two layers of finiteelements were used through thickness in order to allow a better



Fig. 1. Stamping tool: sketch (a) and global view of the experimental device (b).

S55 D56 S66

A5182 A5182 A5182 A6016 A6016 A6016

Fig. 2. Tailor welded blanks.

Fig. 3. (a) Tools used in the numerical simulation and FE model of the similar (b)and dissimilar TWBs (c).

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 15 30 45 60 75 90

αº

r

AA 5182-H111AA 6016-T4

σα/σ

0

Fig. 4. Variation of the normalized yield stress and anisotropy coefficients in thesheet plane.

200

300

400

g St

ress

(MPa

)

AA 5182S55

D56

AA 6016

D.M. Rodrigues et al. / Materials and Design xxx (2009) xxx–xxx 3

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calculation of the through thickness stress and strain gradients aswell as the thickness evolution over the entire deep-drawing sim-ulation. In the TWBs finite element meshes, the weld seam wasmodelled with the same width and mechanical properties of thewelds obtained in the experimental work. The weld seam wasmodelled by assigning, to the finite elements located in this zone(see fig. 3b and 3c), the mechanical properties determined experi-mentally for each weld type. In the numerical simulations severalBHF were tested, varying from 8 to 40 kN, in order to determine themaximum BHF for each type of TWB.

0

100

0 0.05 0.1 0.15 0.2 0.25 0.3Engineering Strain

Engi

neer

in S66

weld

Longitudinal Sample

Fig. 5. Engineering stress strain curves for the base materials AA 5182 and AA 6016and for the S55, S66 and D56 welds.

5. Base materials and friction stir welds characterization

The two base materials used in this work were the AA 5182-H111 and AA 6016-T4 aluminium alloys. The AA 5182-H111 alu-minium–magnesium alloy suffers from stretcher lines, which givesan uneven surface after deformation, restricting its application inthe production of inner automobile panels. On the other hand,the AA 6016-T4 aluminium–magnesium–silicon alloy is often used


for obtaining outer panels. These features make the joining of thesetwo alloys interesting for automotive applications.

Both base materials were extensively characterized by perform-ing monotonic tensile tests at several angles a with the rollingdirection (RD), namely, 0�, 15�, 30�, 45�, 60�, 75� and 90�. In orderto account for the anisotropic properties of the materials the yieldstresses (ra) and r-values (ra) for each tensile direction were deter-mined. In Fig. 4, the normalized yield stresses (ra/r0) and the ravalues, registered from the tensile tests, are plotted as a function



Table 2Material parameters used in the numerical simulations.

Eq. (2) Eq. (3) Eq. (6)

K n Y0 Cy Ysat F G H L M N

AA5182 528.48 0.31 110.5 11.1 270.8 0.54 0.60 0.42 1.50 1.50 1.45AA6016 391.5 0.23 107.9 10.2 251.2 0.66 0.63 0.45 1.50 1.50 1.27S55 welds – – 195.0 9.9 397.1 0.50 0.50 0.50 1.50 1.50 1.50S66 welds – – 127.9 14.6 228.3 0.50 0.50 0.50 1.50 1.50 1.50D56 welds – – 139.6 18.0 269.0 0.50 0.50 0.50 1.50 1.50 1.50

0.40

0.50UT

PS


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of the angle of the tensile axis with the rolling direction. The ra val-ues were calculated from the fitting of the width (ew) versus thick-ness (et) plastic deformation curves from 0.2% to 20% of equivalentplastic deformation. As it can be seen in the figure, the AA 6016 al-loy displays stronger anisotropy in r than the AA 5182 alloy. Bothalloys exhibit small anisotropy in yield stress.

The FSW process was used for joining the two base materials insimilar (S55 and S66) and dissimilar (D56) TWBs. The125 � 250 � 1 mm base material plates were welded parallel tothe rolling direction. Before the formability tests, visual andX-ray examination of the welds was performed, in order to identifypossible defects in the TWBs. The mechanical properties of thewelds were evaluated by performing tensile tests. The engineeringstress–strain curves obtained for the base materials and longitudi-nal weld samples extracted from the S55, S66 and D56 blanks areshown in Fig. 5. According to the results plotted in the figure it ispossible to conclude that the welds of the S55 blanks were in over-match relative to AA 5182 base material mechanical properties andalso had good ductility. On the other hand, the welds of the S66blanks displayed undermatched mechanical properties relative tothe AA 6016 base material and also lower ductility. The welds ofthe D56 dissimilar blanks were in overmatch relative to yield stressand in evenmatch relative to the tensile strength of the weakestbase material, the AA 6016 alloy. The ductility of the D56 sampleswas much lower than that of both base materials. It is also impor-tant to enhance that no substantial changes were observed in themicrostructure and mechanical properties of the HAZ relative tothe base materials, neither in the advancing nor in the retreatingsides of the similar and dissimilar welds. A detailed mechanicaland metallurgical characterization of the welds can be found in Lei-tao et al. [25] and Leal et al. [26].

Material parameters identification according to Eqs. (2), (3), and(6) was performed from the tensile experimental results by usingthe in-house code DD3MAT [27]. The results are shown in Table 2.Since the microstructure of all the welds was characterized by veryfine and equiaxed grains, the materials of the welds were consid-ered isotropic: F = G = H = 0.5 and L = M = N = 1.5. The value forthe friction coefficient used in the numerical simulations was0.280 for all the blanks. This value was determined experimentallyfor both base material blanks by Wouters et al. [28].

0.00

0.10

0.20

0.30

-0.25 -0.15 -0.05 0.05 0.15 0.25 0.35

ε 2

ε1

AA 5182

AA 6016

EBT

Fig. 6. Forming limit diagrams resulting from the BHW model for the AA 5182-H111 and AA 6016-T4 alloys.

6. Results and discussion

6.1. Forming limit diagrams

The BWH criterion (Eq. (1)) was used to generate the FLDs forthe AA5182 and AA6016 base materials. The values calculated forthe material parameters K and n are shown in Table 2. e1 was setequal to n for both base materials. The limiting principal stress val-ues (r1, r2) were determined by considering the proportionalstrain paths of Table 1 and the corresponding principal strain val-ues (e1, e2) were calculated. The FLDs obtained for both base mate-rials are plotted in Fig. 6. In the same graph are also plotted theuniaxial tension (UT), equibiaxial tension (EBT) and plane strain


(PS) paths. These linear strain paths (e2 = be1) were plotted consid-ering b calculated from Eq. (5). The forming limits for the AA 5182alloy are higher than for the AA 6016 alloy.

6.2. Numerical principal strain fields

In order to determine the forming limits of both alloys, based ina necking analysis, the principal strains (e1, e2) registered in all thenodes of the finite element meshes, at several stages of the punchstroke (Dz), between 0 and 60 mm, were plotted in the FLDs deter-mined for each base material. In this analysis were used the resultsof several numerical simulations, performed considering differentvalues of BHF.

The principal strain (e1, e2) values registered for all the nodes ofthe finite element meshes in the numerical simulations of the S55blanks, for BHF = 39 kN and Dz = 60 mm and for BHF = 40 kN andDz = 40 mm, are plotted in the FLD of Fig. 7. Analysing the resultsof Fig. 7 it is possible to conclude that, for BHF = 40 kN, the princi-pal strains for several nodes are above the FLD of the base materialwhich indicates the occurrence of necking for a punch displace-ment of 40 mm. For BHF = 39 kN, the principal strain values fallall in the safe zone under the FLD. In the graph of Fig. 7 it is alsoshown a figure illustrating the thickness variation in the cup walls,corresponding to the BHF = 40 kN situation. The location, in thecup walls, of some of the finite element nodes in which criticalprincipal strain values were registered is identified in this figure.Analysing the figure it is possible to conclude that the strains inzone 1 of the FLD, correspond to nodes of the finite element meshin a region of the cup wall where no significant thickness reductionoccur. On the other hand, nodes in zone 2 of the FLD, for whichprincipal strain values are above the FLD limits, are located in azone of the cup wall where thinning is extreme. The thickness dis-tribution in the cup also indicates that necking is more probable inthe base material, for which lower thickness values can be ob-served, than in the weld.



Fig. 7. FLD and principal strain fields for S55 blanks.


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In Fig. 8 are plotted the same type of results, but obtained in thenumerical simulation of the S66 blanks, for BHF = 16 kN andDz = 60 mm and for BHF = 20 kN and Dz = 35 mm. For these TWBs,the weld was in undermatch relatively to the AA 6016 base mate-rial mechanical properties, which could affect its formability. Ana-lysing the results in Fig. 8 it is possible to conclude that forBHF = 20 kN, the principal strains registered for several nodes ofthe mesh are above the FLD, and for BHF = 16 kN, the principalstrains for all the nodes fall in the safe region under the FLD, whichindicates that this is the maximum BHF allowed for deep-drawingthe S66 blanks. Like in the previous analysis, a figure illustratingthe thickness distribution in the cup walls was added in the graphof Fig. 9. Analysing the figure it is possible to conclude that, despitethe S66 weld had undermatched mechanical properties, the lowestthickness values (indicative of necking) were registered in the basematerial, which indicates that the formability of TWB is mainlycontrolled by the characteristics of the base material. In fact, theprincipal strains registered for the nodes located in the zone whereextreme thinning can be seen, correspond to the principal strainvalues above the FLD (zone 2).

Finally, the results obtained in the numerical simulation of theD56 blanks, for BHF = 16 kN and Dz = 60 mm and for BHF = 20 kN

Fig. 8. FLD and principal stra


and Dz = 35 mm, are shown in Fig. 9. Performing the same typeof analysis, as for the previous figures, it is possible to concludethat the maximum blank-holder force admissible for these TWBsis 16 kN, as for the S66 blanks. Analysing the thickness distribu-tion in the cup, it is also possible to observe that the maximumthinning region is localized in the AA 6016 side of the TWB. Theprincipal strains registered in this region of the cup correspondto the values plotted above the FLD (zone 2). Again, no extremethickness reduction was registered in the weld, which indicatesthat failure will be determined by the formability behaviour ofthe base materials.

Resuming, from previous analysis it is possible to conclude thatmaximum BHFs for drawing the TWBs studied in this work, are:39 kN for the S55 blanks and 16 kN for the S66 and D56 blanks.

7. Experimental validation

Experimental tests were carried out using the testing deviceand procedures previously described. The main outputs from thesetests were the punch force–displacement record and the thicknessvariation along the cup walls. In Fig. 10 are plotted the maximumpunch forces (MPFs) registered in the experimental tests for the

in fields for S66 blanks.



Fig. 9. FLD and principal strain fields for D56 blanks.

50

52

54

56

58

60

62

64

66

68

70

Fzm

áx [k

N]

S55 S66 D56

8 kN 16 kN 20 kN 32 kN

S66

D56S55

Fig. 10. Maximum punch force registered in the experimental deep-drawing tests.


ARTICLE IN PRESS

various types of blanks (S55, S66 and D56) and different BHF val-ues, varying from 8 kN to 32 kN. It is important to enhance that,in all the tests realized, fracture of the cups was only registeredfor the D56 blanks tested under BHF = 8 kN. The weld inspectionresults revealed that these D56 blanks had defective welds, andtherefore, failure could not be related with the forming conditions.In all the other tests, no defects were observed in the TWBs and nofailure was registered in all the tests realized. The main aspect ofthe cups obtained, from the different TWBs, is illustrated by thepictures added in the graph of Fig. 10. As it can be seen in the fig-ure, the final shape of the cups is very different, for the differentTWBs. In fact, meanwhile a deep material bending over the weldcan be observed at the flange area in the S55 cups, in the S66 cups,which had the most anisotropic base material (Fig. 4), it is possibleto observe strong earing, especially, near the weld line. In fact,since the S66 weld material is softer than the base material, itundergoes stronger plastic deformation under the same BHF. Final-ly, comparing the shape of the dissimilar cups with that of the sim-ilar ones, it is possible to conclude that the D56 blanks conjugatethe forming characteristics of the S55 and S66 blanks. In fact, atthe cup flange, near the weld line, it is possible to see strong bend-ing, in the A5182 side of the TWB, and earing at the A6016 side ofthe TWB. Finally, it is important to enhance that for each type ofTWB, the shape of the cups was very similar, independently ofthe blank-holder force used in the tests.


Analysing now the MPF values presented in the graph of Fig. 10,it is possible to see that the higher values of MPF were registeredfor the S55 blanks, which had the base material and the weld withhigher tensile strength. According to the graph, for these TWBs, theMPF increases with increasing BHF. This is normal since underincreasing BHF, the normal pressure between the sheet flangeand the blank-holder increases, increasing the friction and makingmore difficult the flow of the material into the die, and thus, mak-ing necessary increasing punch forces to perform the forming oper-ation. On the other hand, for the S66 blanks, that had the softerbase material and undermatched welds, the MPF registered inthe experimental forming tests are much lower than that regis-tered for the S55 blanks. It is also evident that the MPF values reg-istered in the tests realized with BHF of 16, 20 and 32 kN are verysimilar, for the S66 blanks. The maintenance of the MPF underincreasing BHF values can be considered indicative of the occur-rence of necking for BHF higher than 16 kN, which is in accordancewith the numerical previsions. In fact, when necking occurs, thepunch force is controlled by the plastic instability of the drawmaterial, and similar values of MPF can be attained under differentBHFs. The MPFs registered in the D56 formability tests, realizedwith 16, 20 and 32 kN, are also very similar, which also indicatesnecking for BHFs higher than 16 kN. These results confirm thevalidity of the numerical predictions that indicate that the maxi-mum BHF for deep-drawing the dissimilar blanks is 16 kN, as forthe similar S66 blanks.

Since necking in plastically deformed parts occurs by localizedthinning, the thickness variation along the cup walls was measuredin samples sectioned perpendicular to the weld. The results ob-tained for the S55 and S66 cups, formed with 32 kN blank-holderforce, are shown in Fig. 11. As it can be seen in the figure, minimumthicknesses values were registered at the cups bottom radius andvertical side walls and thickening at the flange area. Blank thicken-ing near the top of the cup sections occurs due to the friction at thedie/blank interface and due to the circumferential forces. Compar-ing the thickness profile near the cups bottom, where thinning oc-curs, it is possible to conclude that it is different for the two typesof blanks. In fact, while for the S55 cup the thickness reduction oc-curs gradually along the cup radius, for the S66 cup, lower thick-ness values were registered in a very localized region (seenumbers in bold in both figures), indicating the beginning of neck-ing in this area. However, it is important to enhance that, despitenecking was previewed in the numerical study and registered inthe experimental work, for BHFs higher than 16 kN, for the similar



0.95 0.94 0.92

0.90

0.92

0.93

0.93

1.10

0.88

0.940.940.940.93

0.92

0.88

0.93

0.97

1.08

1.171.16

1.20

0.900.88

1.16

0.90

0.87

0.920.88

0.870.90

0

10

20

30

40

50

60

-70 -35 0 35 70x (mm)

z (m

m)

S55 - 32 kN

0.91 0.93 0.89 0.92

0.92

0.92

0.98

1.07

0.88

0.90

0.94

1.19

0.83

0.960.950.910.910.87

0.830.84

0.87

0.91

0.91

0.99

1.141.21

1.201.250

10

20

30

40

50

60

-70 -35 0 35 70x (mm)

z (m

m)

S66 - 32 kN

a

b

Fig. 11. Thickness variation along the cup walls measured in the S66 and S55 cups(BHF = 32 kN).


ARTICLE IN PRESS

S66 and dissimilar D56 blanks, no rupture was registered in theexperimental tests when using BHFs higher than that value. In fact,for all the TWBs studied in this work (S55, S66 and D56), the mac-roscopic aspect of the cups remained unchanged when increasingthe BHF from 8 kN to 32 kN.

8. Conclusions

In this paper, a multi-step analysis was used to preview theformability behaviour of TWBs obtained by joining two aluminiumalloys, the AA 5182-H111 and the AA 6016-T4 alloys, in similar anddissimilar combinations. Analytical FLDs were plotted, for bothbase materials, by using a theoretical stress based criteria. Theprincipal strains in the cup walls, obtained in the numerical simu-lation of deep-drawing tests performed with different BHF values,were compared with the formability limits established by the FLDs.This procedure enabled to determine the maximum BHF for deep-drawing the different TWBs. Supporting experiments were per-formed and the results obtained enable to confirm the adequacyof the numerical previsions.

Acknowledgements

The authors are indebted to the Portuguese Foundation for theScience and Technology (FCT) and FEDER for the financial supportthrough the POCI 2010 program and to Novelis Switzerland SA forsupplying the aluminium sheets.


References

[1] Obermeyer EJ, Majlessi SA. A review of recent advances in the application ofblank-holder force towards improving the forming limits of sheet metal parts. JMater Process Tech 1998;75:222–34.

[2] Laukonis JV, Ghosh AK. Effects of strain path changes on the formability ofsheet metals. Metall Mater Trans A 1978;9:1849–56.

[3] Graf AF, Hosford WF. Calculations of forming limit diagrams for changingstrain paths. Metall Mater Trans A 1993;24(11):2497–501.

[4] Marciniak Z, Kuczyski K. Limit strains in the processes of stretch-forming sheetmetal. Int J Mech Sci 1967;9(9):609–12.

[5] Lian J, Baudelet B. Forming limit diagram of sheet metal in the negative minorstrain region. Mat Sci Eng A 1987;86:137–44.

[6] Stoughton TB. A general forming limit criterion for sheet metal forming. Int JMech Sci 2000;42:1–27.

[7] Ito K, Satoh K, Goya M, Yoshida T. Prediction of limit strain in sheet metal-forming processes by 3D analysis of localized necking. Int J Mech Sci2000;42:2233–48.

[8] Banabic D, Dannenmann E. Prediction of the influence of yield locus on thelimit strains in sheet metals. J Mater Process Tech 2001;109:9–12.

[9] Alsos HS, Hopperstad OS, Tornqvist R, Amdahl J. Analytical and numericalanalysis of sheet metal instability using a stress based criterion. Int J SolidsStruct 2008;45:2042–55.

[10] Padmanabhan R, Oliveira MC, Alves JL, Menezes LF. Influence of processparameters on the deep drawing of stainless steel. Finite Elem Anal Des2007;43:1062–7.

[11] Padmanabhan R, Oliveira MC, Alves JL, Menezes LF. Numerical simulation andanalysis on the deep drawing of LPG bottles. J Mater Process Tech 2008;200:416–23.

[12] Menezes LF, Teodosiu C. Three-dimensional numerical simulation of the deep-drawing process using solid finite elements. J Mater Process Tech 2000;97:100–6.

[13] Santos AD, Duarte JF, Reis A, da Rocha B, Neto R, Paiva R. The use of finiteelement simulation for optimization of metal forming and tool design. J MaterProcess Tech 2001;119:152–7.

[14] Reis A, Teixeira P, Duarte JF, Santos A, Barata da Rocha A, FernandesAA. Tailored welded blanks – an experimental and numerical study insheet metal forming on the effect of welding. Comput Struct 2004;82:1435–42.

[15] Baptista AJ, Rodrigues DM, Menezes LF. Influence of the weld on themechanical behaviour of tailor welded blanks. Mater Sci Forum 2006;514–516:1493–7.

[16] Zadpoor AA, Sinke J, Benedictus R. Mechanics of tailor welded blanks: anoverview. Key Eng Mater 2007;344:373–82.

[17] Padmanabhan R, Baptista AJ, Oliveira MC, Menezes LF. Effect of anisotropy onthe deep-drawing of mild steel and dual-phase steel tailor-welded blanks. JMater Process Tech 2007;184:288–93.

[18] Rodrigues DM, Menezes LF, Loureiro A, Fernandes JV. Numerical study on theplastic behaviour in tension of welds in high strength steel. Int J Plasticity2004;20:1–18.

[19] Hill R. On discontinuous plastic states with special reference to localizednecking in thin sheets. J Mech Phys Solids 1952;1:19–30.

[20] Bressan JD, Williams JA. The use of a shear instability criterion to predict localnecking in sheet metal deformation. Int J Mech Sci 1983;25:155–68.

[21] Oliveira MC, Alves JL, Menezes LF. Improvement of a frictional contactalgorithm for strongly curved contact problems. Int J Numer Meth Eng2003;58(14):2083–101.

[22] Oliveira MC, Menezes LF. Automatic correction of the time step in implicitsimulations of the stamping process. Finite Elem Anal Des 2004;40:1995–2010.

[23] Oliveira MC, Alves JL, Chaparro BM, Menezes LF. Study on the influence ofwork-hardening modeling in springback prediction. Int J Plasticity 2007;23:516–43.

[24] Oliveira MC, Alves JL, Menezes LF. Algorithms and strategies for treatment oflarge deformation functional contact in the numerical simulation of deep-drawing process. Arch Comput Meth Eng 2008;15:113–62.

[25] Leitao C, Leal RM, Rodrigues DM, Loureiro A, Vilaça P. Tensile behaviour ofsimilar and dissimilar AA5182-H111 and AA6016-T4 thin friction stir welds.Mater Des 2009;30:101–8.

[26] Leal RM, Leitão C, Loureiro A, Rodrigues DM, Vilaça P. Material flow inheterogeneous friction stir welding of thin aluminium sheets: effect ofshoulder geometry. Mater Sci Eng A 2008;498:384–91.

[27] Chaparro BM, Thuillier S, Menezes LF, Manach PY, Fernandes JV. Materialparameters identification: gradient-based, genetic and hybrid optimizationalgorithms. Comp Mater Sci 2008;44(2):339–46.

[28] Wouters P, Daniel D, Magny C. Selection and identification of friction modelsfor the 3DS materials – determination of the friction behaviour. Work Package3, Digital Die Design System (3DS), IMS 1999 000051, Work Package 3, Task 1;2002.



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