Acta Metall. Sin.(Engl. Lett.)Vol.21 No.6 pp451-458 Dec. 2008

DEFORMATION BEHAVIOR OF AA6063 ALUMINIUM ALLOYAFTER REMOVING FRICTION EFFECT UNDER HOTWORKING CONDITIONS

Z.Y. Chen1), S.Q. Xu2) and X.H. Dong1)1) National Die & Mold CAD Engineering Research Center, Shanghai Jiaotong University, Shanghai 200030,China

2) College of Materials Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, ChinaManuscript received 16 October 2007; in revised form 18 January 2008

The hot deformation behavior of AA6063 aluminium alloy has been investigated bymeans of compression tests at temperatures between 400 and 520C, and strain ratesranging from 2.5 to 10 s1. Owing to the barreling, the theoretical model on thebasis of Hills general method is used to calculate the flow stress of a cylindrical spec-imen under uniaxial simple compression so as to consider the friction effect at thedie-specimen interface. A method of evaluating the friction coefficient by combiningcompression tests with the finite element method is presented. The real flow behaviorof AA6063 aluminium alloy can be described with sinh-Arrhenius equation. The hotdeformation activation energy Q derived from the corrected stress and strain data is232.350 kJ/mol.KEY WORDS Barreling; Compression test; Friction; Flow stress; Aluminium

alloy; Activation energy

1. Introduction

Because of their lightweight, easy extrudability and high strength, pure aluminum andaluminium alloys are widely used in automobile, architecture, and other areas[1].

The alloys of the Al-Mg-Si system are mostly used in the extrusion processing[2,3].AA6063 aluminum alloy has better ductility at elevated temperatures than at room tem-perature. In order to simulate and optimize a tube porthole die extrusion process, there isa need to investigate the flow stress behavior of the material at elevated temperatures. Thecylinder compression test is a commonly used method for the determination of materialstress-strain curves. But even under the suitable lubricated condition, the friction can notbe eliminated completely[4]. Thus, the homogeneous deformation can not be ensured, andthe friction at the interface between the two flat dies and the cylindrical specimen inevitablycauses barreling, which sequentially affects the precision of the flow curve. Therefore, theconventional method used to calculate the flow stress and the effective strain assuminguniformly deformed specimen is not applicable.

There are various studies on barreling in the simple compression test. Narayanasamyet al.[5,6] found a power relationship between the barrel radius and the shape factor.

Corresponding author. Tel.: +86 21 62813435.E-mail address: chenzhying@gmail.com (Z.Y. Chen)

452

Ebrahimi and Najafizadeh[4] proposed a new useful method for calculating friction factorin cold or hot bulk metal formation by measuring the degree of barreling in compressiontest. Chen et al.[7] developed a theoretical model for the calculation of flow stress underaxial compression considering the barreling effect.

Although the above-mentioned works have taken the effect of friction into considera-tion, the efforts are mainly focused on developing the mathematical models. No attemptis made to relate the specimen barreling with the friction coefficient and further, to cor-rect the experimental flow stress. Several studies on AA6063 aluminium alloy have beencarried out[810], but there is little information about the flow stress behavior at elevatedtemperatures and high strain rates, especially considering the friction effect.

In the present work, the flow behavior of AA6063 aluminium alloy is investigated bya series of hot compression tests under hot-working conditions, which is relevant to thepractical porthole die extrusion process. The friction coefficients are evaluated through anew method combining compression tests with the finite element method. The flow stressof the material is corrected after removing friction effect, and it is sensitive to strain, strainrate, and deformation temperature. The hyperbolic-sine relationship is applicable for thedescription of the temperature and strain rate dependence of steady state flow stress.

2. Experimental Procedures

2.1 Thermo-mechanical experimentMaterial used in the experiments was AA6063 aluminium alloy ingot for profile extru-

sion process in an aluminum manufacturer. The compositions (wt pct) are Mg 0.52, Si0.42, Fe 0.35, and balanced with Al. Cylindrical specimens of 10.0 mm in diameter and15.0 mm in height were machined. The ratio of height to diameter is 1.5. To determinethe stress-strain behavior of the alloy, uniaxial hot compression tests were carried out witha Gleeble-1500 thermo-mechanical simulator at strain rates of 2.5, 4, 6.4, and 10 s1 attemperatures of 400, 440, 480 and 520C. To minimize the friction effect, both ends of thespecimens were recessed to a depth of 0.2 mm to hold lubricant. As a suitable lubricant,the mixture of molybdenum disulphide, black lead, and alcohol was filled to the two endsof the specimen. But the barreling still took place after compression.

Considering the bulge profile as a circular arc, the radius of the barreled curvature Ris obtained from an empirical formula as follows[7]

R =(2H)2 + (d2 d1)2

4(d2 d1) =(H)2 + (r2 r1)2

4(r2 r1) (1)

where d1 is the minimum diameter of the barreled specimen, d2 is the maximum diameterof the barreled specimen, 2H0 is the original height of the specimen, and 2H is the instan-taneous height of the specimen. r1 and r2 are the minimum and maximum radius of thebarreled specimen, respectively.

A simple sketch of barrel-shaped specimen during the cylindrical compression test isshown in Fig.1. After each test, the following final dimensions could be measured easily: (1)height of the compressed deformed specimen (2H); (2) minimum and maximum diametersof the deformed specimen (d1 and d2).

2.2 Experiment on the basis of finite element methodIn an actual compression test, it is very difficult to determine and change the exact

453 friction condition at the interfaces betweendies and specimen. But using the finite el-ement simulation, it is more convenient toset frictional condition and calculate the cor-responding barreled curvature for the speci-men. Here, the upsetting test in Section 2.1was simulated to find the relationship be-tween the barreling and the friction coeffi-cient. Because of symmetry, only a quarterof the model was analyzed. The 4-node ax-isymmetric elements were used for the billet.The top die was considered as a rigid sur-face. Fig.2 shows the undeformed configura-tion and the deformed finite element mesh.

Following the idea that the friction coef-ficient depends on the lubrication conditionand not on the specimen material[11], DIN-AlMgSi1 alloy in DEFORM-2D material li-brary, which has the similar properties withAA6063 aluminium alloy, was taken as thebillet material in a series of simulation tests.The constant shear friction coefficient m wasgiven as 0.1, 0.2, 0.3, and 0.4, respectively.

Chen et al.[7] provides the theoretical jus-tification and indicates that the mean effec-tive strain for a barreled specimen is the

Fig.1 Configuration of barrel-shaped speci-men during the non-uniform compres-sion.

Fig.2 Sketch of undeformed configurationand deformed finite element mesh.

same as in the case of compression without barreling to a first order of approximation.So, for every constant punch stroke Hi, the mean effective strain is obtained from thefollowing equation

i = ln2H02Hi

= lnH0Hi

= lnH0

H0 iHi (2)

where H0 is the initial half height of the undeformed billet, and Hi is the instantaneoushalf height of the billet after each step. The total displacement of the punch was departedinto 10 steps. At each end of the step, the mean effective strain was calculated usingEq.(2), and the minimum radius r1, the maximum radius r2, and the instantaneous halfheight Hi were all measured and recorded. Then, the barreled curvature R was obtainedusing Eq.(1). The relationship between mean effective strain and barreled curvature R isestablished for each shear friction coefficient m.

3. Results and Discussion

3.1 Correlation of friction coefficient and barreled curvatureThrough the approach in Section 2.2, the relationship curves of the mean effective

strain, constant shear friction coefficient, and barreled curvature R are shown in Fig.3.It is seen in Fig.3 that the barreled curvature R decreases almost exponentially with

the increase of strain, and the specimen with higher friction coefficients has smaller radius

454 of curvature. The result in Fig.3 agrees withthe findings of Chen et al.[7].

The dimensions of cylinders, such asmaximum and minimum diameters, weremeasured after each experimental compres-sion test. According to Eqs.(1) and (2), thelogarithm strain and barreled curvature Rwere calculated. The R value points of thepractical compression tests are illustrated inFig.3.

The experimental friction coefficientswere estimated according to the position ofthese test points at the relation curves ofstrain, friction coefficient, and R in Fig.3.The experimental barreled curvature R andthe estimated friction coefficients for all spec-imens are listed in Table 1.

0.3 0.4 0.5 0.6 0.7 0.8 0.9

0

5

10

15

20

25

30

35

Strain

m=0.1

m=0.2

m=0.3

m=0.4

Test points

R / mm

Fig.3 Relationship of strain, friction coef-ficient and barreled curvature, andexperimental R distribution points(2H0/d0=1.5).

Table 1 Experimental R value, estimated friction coefficient m and corrected peak stress of AA6063

400C 440C 480C 520Cs1 R/mm m p/MPa R/mm m p/MPa R/mm m p/MPa R/mm m p/MPa2.5 4.331 0.17 63.99 4.564 0.16 51.84 5.144 0.145 42.89 5.036 0.15 34.844.0 5.052 0.15 67.63 4.720 0.16 54.09 4.521 0.162 43.36 4.540 0.16 36.536.4 5.515 0.14 70.88 4.713 0.15 55.55 5.560 0.12 46.79 6.097 0.18 38.8210.0 5.054 0.15 71.30 6.312 0.15 58.78 4.676 0.16 47.10 4.374 0.16 41.11

3.2 Flow stress behaviorHill[12] proposed a theoretical model to calculate the true flow stress considering the

friction effect of the die-specimen interfaces under cylindrical specimen axial compression

S = (1 +

3 d2H

)(3)

where S is unit average pressure, and it is the ratio of the instantaneous force and averagecross sectional area. is the true stress without friction effect, and is the Coulombfriction factor. The transient true stress can be written as

=S(

1 + m33 d2H

) (4)where m is the shear friction coefficient, =m/

3.

The series of friction coefficient values in Table 1 were substituted into Eq.(4). Theexperimental flow stress data were corrected through releasing the friction effect. Thecorresponding true peak stresses are listed in the Table 1, and the true stress-strain curvesobtained at various temperatures and strain rates are shown in Fig.4.

It can be seen that the flow stress curves of AA6063 aluminium alloy are of dynamicrecovery form. During the hot deformation process, work hardening and dynamic recoverysoftening happen simultaneously. At the beginning of deformation, work hardening is do-

455

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10

20

30

40

50

60

70

80

Strain

Stress / MPa

520

o

C

480

o

C

440

o

C

400

o

C

Experimental

Corrected

(a)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10

20

30

40

50

60

70

80

Experimental

Corrected

520

o

C

480

o

C

440

o

C

400

o

C

(b)

Strain

Stress / MPa

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10

20

30

40

50

60

70

80

Experimental

Corrected

520

o

C

480

o

C

440

o

C

400

o

C

(c)

Strain

Stress / MPa

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

10

20

30

40

50

60

70

80

Experimental

Corrected

(d)

520

o

C

480

o

C

440

o

C

400

o

C

Strain

Stress / MPa

Fig.4 Experimental and corrected stress-strain curves of AA6063 under different deformationconditions: (a) =2.5 s1, (b) =4.0 s1, (c) =6.4 s1, (d) =10.0 s1.

minant, so the curves are characterized by a sharp increase. Along with the increase instrain, stress is not increased obviously. The flow stress increases steadily with strain to astable state owing to work hardening and dynamic recovery softening reaching a balance.Dynamic recovery is found to be the major softening mechanism in high temperaturedeformation, which has been described by McQueen et al.[13].

Fig.4 shows, with the increase in temperature and decrease in strain rate, the flowstress of the material decreases. The temperature and strain rate have a significant effecton flow stress. Because of the friction effect, the experimental stresses are higher than thecorrected true ones. Taking the test of 520C in Fig.4c for example, the maximum relativeerror between the experimental stress and true stress is about 6.07%, which means thefriction correction is essential.

3.2 Constitutive analysisIn hot working, the temperature and strain rate dependence of the stress can be ex-

pressed by the following constitutive equations[1417]

exp(Q/RT ) = Z = An

(5)

exp(Q/RT ) = Z = Aexp() (6)

exp(Q/RT ) = Z = A(sinh)n (7)

456

where represents the strain rate, and A, A, A, n, n, , and are material constants.The Zener-Hollomon parameter Z is temperature compensated strain rate[18,19]. Both thepower law Eq.(5) suitable at lower stresses and the exponential law Eq.(6) fit for higherstresses are limited[14]. However, across the entire range of hot working, the temperatureand strain rate dependence of the peak stress is generally described by the sinh-ArrheniusEq.(7).

The calculation of Q can be performed according to the following formula

Q = R [ ln ln sinh()

]T[ ln sinh()

(1/T )

]

(8)

where Q, R, and T refer to deformation activation energy, universal gas constant8.314 J/(molK), and absolute temperature, respectively.

The peak stress variations as a function of strain rate in the temperature range of 400520C are illustrated in Fig.5. The slope of p vs. ln linear relation ranged from 0.169to 0.253, with an average value of =0.211. The average value of the stress exponent n

is equal to 10.581 according to the lnp vs. ln relation plot. /n=0.0199 MPa1.On the basis of this approximate value, the appropriate stress multiplier was obtainedby an optimization procedure keeping the ln vs. lnsinh(p) plots linear and parallel.=0.0168 MPa1.

ln is plotted vs. lnsinh(p) as shown in Fig.6a, and lnsinh(p) is plotted vs. 1000/T

30 40 50 60 70 80

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

(a)

400

o

C

440

o

C

480

o

C

520

o

C

p

ln

3.5 3.6 3.7 3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

(b)

400

o

C

440

o

C

480

o

C

520

o

C

ln

p

ln

Fig.5 Effect of the strain rate on the corrected peak stress of AA6063 aluminium alloy: (a) ln vs.p; (b) ln vs. lnp.

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

(a)

lnsinh(

p

)

400

o

C

440

o

C

480

o

C

520

o

C

ln

1.25 1.30 1.35 1.40 1.45 1.50

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

(b)

lnsinh(

p

)

(1000/T) / K

-1

2.5 s

-1

4.0 s

-1

6.4 s

-1

10.0 s

-1

Fig.6 Variation of peak stress with strain rate and deformation temperature: (a) ln vs.lnsinh(p); (b) lnsinh(p) vs. T

1.

457

as shown in Fig.6b. It is shown that the peak stress increases with raising strain rate at afixed temperature and with decreasing temperature when the strain rate is fixed. Values ofthe second term of the right hand side of Eq.(8) are determined from the ln vs. lnsinh(p)relation. The slope of the relation for AA6063 aluminium alloy in the temperature rangeof 400520C is changed in a very narrow range from 7.318 to 9.610, and the average valueis equal to 8.484. Meanwhile, the average slope of the relation of lnsinh(p) vs. 1000/Tis 3294.203. The deformation activation energy for the peak stress is determined to be232.350 kJ/mol.

Zener-Hollomon parameter Z, embrac-ing the relative influences of strain rate andtemperature in the hot working process hasbeen plotted vs. lnsinh(p) in Fig.7. Theplot brings all the corrected peak stress datainto a single line, and the linear relationshipis satisfied between lnsinh(p) and Zener-Hollomon parameter. The correlation coeffi-cient of the fit is 0.998. In conclusion, thehyperbolic-sine relationship Eq.(7) can beused to describe the elevated flow behavior ofAA6063 aluminum alloy. The value of stressexponent n identified by using linear regres-sion analysis is 8.467. A=2.96817 s1.

-0.4 -0.2 0.0 0.2 0.4

36

37

38

39

40

41

42

43

44

lnsinh

p

)

lnZ

Fig.7 Linear relation between lnZ andlnsinh(p).

4. Conclusions

Isothermal uniaxial compression tests are performed on AA6063 aluminium alloy atstrain rates of 2.5 to 10 s1 over a temperature range of 400 to 520C and are summarizedas follows:

(1) A method of evaluating the friction coefficient by combining compression testswith the FEM analysis is presented, and it can be extended to other materials and underdifferent friction conditions;

(2) The experimental stress-strain curves of AA6063 aluminium alloy are corrected bytaking into account the effect of friction using Hills general method;

(3) Within the ranges of temperature and strain rate, the sinh-Arrhenius equationis established to describe the true flow behavior of AA6063 aluminium alloy. The hotdeformation activation energy Q is 232.350 kJ/mol.

AcknowledgementsThis study was supported by the Scientific Research Foundation for the ReturnedOverseas Chinese Scholars of Shanxi Province of China (No.9835).

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