Materials Letters 62 (2008) 4085–4087

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Materials Letters

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Strain hardening and orientation hardening/softening in cold rolled AA 5052aluminum alloy

H. Yuan, J. Li, X.Y. Kong, C.C. Yu, Q.X. Yang, W.C. Liu ⁎Key Laboratory of Metastable Materials Science and Technology, College of Materials Science and Engineering, Yanshan University, Qinhuangdao 066004, PR China

⁎ Corresponding author. Tel.: +1 859 9678946; fax: +8E-mail address: wcliu@engr.uky.edu (W.C. Liu).

0167-577X/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.matlet.2008.05.067

A B S T R A C T

A R T I C L E I N F O

Article history:

The tensile properties of co Received 4 December 2007Accepted 22 May 2008Available online 4 June 2008

Keywords:AluminumCold rollingStrain hardeningOrientation hardening/softening

ld rolled sheets were measured for the hot band and annealed hot band of AA5052 aluminum alloy. The variation in yield strength with rolling true strain was used to represent thehardening rate of cold rolled sheets. The Taylor factor (M

―) of cold rolled sheets in tension along the rolling

direction was calculated based on the measured orientation distribution functions. The strain hardening andorientation hardening/softening produced by cold deformation were analyzed. The results show that thecontribution to the hardening rate of cold rolled sheets comes largely from the deformed microstructure andpartly from the texture change. For the annealed hot band the orientation softening occurs at strains below0.5, while the orientation hardening occurs at strains over 0.5. For the hot band the dM

―/dε value is always

positive, indicating that orientation softening does not occur.© 2008 Elsevier B.V. All rights reserved.

1. Introduction

The evolution of microstructure and texture during deformation aswell as the flow stress has been studied extensively. During deformationthe grains are separatedbydislocationboundaries into dislocation cells orcell blocks, leading to an increase in the flow stress [1–4]. At the sametime initial grain orientations are rotated to stable end orientations. Thechange in texture during deformation affects the Taylor factor (M

―) of

deformed samples and hence the flow stress [5–7]. Wen and Lee [7]studied the orientation hardening of AA 3003 aluminum alloy under in-plane strain stretching. The value of (1/M

―)(dM

―/dε) varied in the range of 0

to 0.15 when the true strain was less than 0.25. For larger straindeformations the orientation hardening/softening may have a strongereffect on the flow stress. In the present work strain hardening andorientation hardening/softening produced by cold deformation wereanalyzed based on the variation in the yield strength and Taylor factor ofcold rolled aluminum sheets with cold rolling strain.

2. Experimental

2.1. Sample preparation

The material used in the present investigationwas continuous cast(CC) AA 5052 aluminum alloy. The chemical composition of the alloy is(in wt.%): 96.9 Al, 0.115 Si, 0.372 Fe, 0.055 Mn, 2.363 Mg, and 0.191 Cr.The as-received material was commercially produced CC hot band

6 335 8074545.

l rights reserved.

with a thickness of 2.1 mm. The CC hot band possessed a typicaldeformed microstructure and a strong β fiber rolling texture. The hotbandwas annealed at 371 °C for 3 h to obtain a recrystallized structurewith the cube texture [8]. The hot band and annealed hot band werethen cold rolled to different reductions ranging from 0 to 90%. Tensilespecimens of 25 mm in length and 6.5 mm in width were machinedfrom the cold rolled sheets along the rolling direction. The thickness ofthe tensile samples was equal to that of the cold rolled samples. Thetensile tests were performed on an Instron testing machine. The yieldstrength was determined at 0.2% offset strain.

2.2. Texture measurements and calculation of Taylor factors

Texture measurements were performed at one fourth-thickness ofthe cold rolled sheets. The (111), (200), and (220) pole figures weremeasured up to a maximum tilt angle of 75° by the Schulz back-reflection method using CuKα radiation. The orientation distributionfunctions (ODFs) were calculated from the incomplete pole figuresusing the series expansion method (lmax=16) [9].

In order to estimate the contribution of orientation distributionfunctions to the yield strength of cold rolled sheets, the ODFs wereused to calculate the Taylor factor for the tensile loading along therolling direction. By using Roe and Bunge's series expansion method,the orientation distribution function ω can be expressed as [9,10]

ω φ; θ;ϕð Þ ¼ ∑∞

l¼0∑l

m¼−l∑l

n¼−lWlmnZlmn cos θð Þe−imφe−inϕ ð1Þ

where φ, θ, ϕ are the Euler angles which describe the rotation from thesample frame to the crystal coordinate,Wlmn is the texture coefficients,and Zlmn(cosθ) is the generalized Jacobi polynomial. The Taylor modelhas been applied to calculate the Taylor factorM(φ, θ, ϕ) in tension for a

Fig. 1. Tensile properties of cold rolled sheets as a function of cold rolling reduction for (a) the annealed hot band and (b) hot band of AA 5052 alloy.

Fig. 2. Yield strength and hardening rate vs. rolling true strain for (a) the annealed hot band and (b) hot band of AA 5052 alloy.

4086 H. Yuan et al. / Materials Letters 62 (2008) 4085–4087

given crystallographic orientation [11]. The average Taylor factor (M―) of

cold rolled sheets in tension can be given by

M ¼ iEulerM φ; θ;ϕð Þω φ; θ;ϕð Þsinθdφdθdϕ ð2Þ

3. Results and discussion

3.1. Tensile properties of cold rolled sheets

Fig. 1 shows the tensile properties of cold rolled sheets as a function of cold rollingreduction for the hot band and annealed hot band of AA 5052 aluminum alloy. As thecold rolling reduction increased, yield strength (σ0.2) and ultimate tensile strength (σb)of cold rolled sheets increased, whereas elongation (δk) decreased for the hot band andannealed hot band. Comparing Fig. 1(a) with Fig. 1(b), it is seen that at a given reductionthe strength of sheets directly cold rolledwas higher than that of sheets cold rolled afterannealing at 371 °C. The yield strength of cold rolled sheets depends on theirmicrostructure and texture. The variation in the yield strength with true strain cantherefore be used to represent the hardening of cold rolled sheets. Fig. 2 shows the yieldstrength and the hardening rate of cold rolled sheets as a function of rolling true strain. It

Fig. 3. Variation in the Taylor factor and the value of dM―/dε with rolling true

is seen that the hardening rate decreased rapidly with rolling true strain at the earlystages of deformation (εb0.07). As the true strain further increased, the decrease in thehardening rate becamemore gradual and then tended to be a stable value. At a given truestrain the hardening rate of the annealed hot band was larger than that of the hot band.

3.2. Orientation hardening and orientation softening

The yield strength of cold rolled sheets depends on their deformed microstructureand texture. It can be expressed as

σ0:2 ¼ Mτc ð3Þ

whereM―

is the average Taylor factor of all oriented grains of cold rolled sheets, and τc isthe critical resolved shear stress. During cold rolling the change in yield strength of coldrolled sheets can be expressed as

1σ0:2

dσ0:2

de¼ 1

τcdτcde

þ 1M

dMde

ð4Þ

The term (1/σ0.2)(dσ0.2/dε) is composed of two parts, one (1/τc)(dτc/dε) which isrelated to the deformedmicrostructure, the other (1/M

―)(dM

―/dε) which is dependent on

strain for (a) the annealed hot band and (b) hot band of AA 5052 alloy.

Fig. 4. (1/σ0.2)(dσ0.2/dε), (1/τc)(dτc/dε) and (1/M―)(dM

―/dε) vs. rolling true strain for (a) the annealed hot band and (b) hot band of AA 5052 alloy.

4087H. Yuan et al. / Materials Letters 62 (2008) 4085–4087

the deformation texture. The term (1/M―

)(dM―

/dε), which reflects the effect oforientation distribution function on the yield strength of cold rolled sheets, can bereferred as orientation hardening/softening rate during deformation based on thepositive/negative sign [6,7].

The Taylor factor of cold rolled sheets can be calculated based on the orientationdistribution functions of cold rolled sheets. Fig. 3 shows the relationship between theTaylor factor of cold rolling sheets and rolling true strain for the hot band and annealedhot band. The value of dM

―/dε, which was derived from the curve of the Taylor factor and

rolling true strain, is also depicted in Fig. 3 as a function of rolling true strain. The Taylorfactor of the annealed hot band in tension along the rolling direction was calculated tobe 2.91. During cold rolling the cube recrystallization texture was gradually convertedinto the β fiber rolling texture, leading to the change in the Taylor factor of cold rolledsheets. It is seen from Fig. 3 that as the rolling true strain increased, the Taylor factor ofcold rolled sheets first decreased to a minimum of 2.84 at a true strain of 0.5, and thenincreased to 2.96 at a true strain of 2.3. The hot band of AA 5052 aluminum alloypossessed a strong β fiber rolling texture. Further cold rolling continued to increase thestrength of the β fiber rolling texture [8]. Therefore, the Taylor factor increased withincreasing rolling true strain. After a true strain of 0.6, the Taylor factor approached astable value of 3.15.

For the annealed hot band, the dM―

/dε value was negative at strains below 0.5,indicating that orientation softening occurs in this deformation range. At strains above0.5 the change in texture resulted in the orientation hardening. For the hot band, thedM―/dε value was always positive, indicating that orientation softening does not occur

during rolling of the hot band.

3.3. Comparison of strain hardening and orientation hardening/softening

The contribution of strain hardness and orientation hardness/softening to the yieldstrength of cold rolled sheets is shown in Fig. 4, where the values of (1/σ0.2)(dσ0.2/dε),(1/τc)(dτc/dε) and (1/M

―)(dM

―/dε) were plotted as a function of rolling true strain. For the

annealed hot band, the effect of orientation hardening/softening on (1/σ0.2)(dσ0.2/dε)was very small when the true strain was less than 0.2. Therefore, the effect oforientation hardening/softening may be neglected. When the true strainwasmore than0.2, the crystallographic texture of cold rolled sheets affected the value of (1/σ0.2)(dσ0.2/dε) although the term (1/τc)(dτc/dε) was the major part of (1/σ0.2)(dσ0.2/dε). For the hotband, the crystallographic texture had a strong effect on the hardening of cold rolledsheets when the true strainwas in the range of 0.2 to 0.7. In addition, it is noted that the

value of (1/τc)(dτc/dε) decreased with increasing rolling true strain, and then increasedslightly and stayed roughly constant. The initial state of materials before cold rollingaffected the critical strain where there was a minimum value of (1/τc)(dτc/dε). Thecritical strain was 0.9 for the annealed hot band, while it was 0.5 for the hot band.

4. Conclusions

(1) For the hot band and annealed hot band of AA 5052 aluminumalloy, yield strength and tensile strength increase with increasing coldrolling reduction. The variation in yield strength with true strain canbe used to represent the hardening rate of cold rolled sheets.

(2) The contribution to the hardening rate of cold rolled sheetscomes largely from the deformed microstructure and partly from thetexture change.

(3) For the annealed hot band the orientation softening occurs atstrains below 0.5, while the orientation hardening occurs at strainsover 0.5. For the hot band the dM

―/dε value is always positive,

indicating that orientation softening does not occur.

References

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