Microstructure evolution and deformation behavior of ultrafine-grained Al–Zn–Mg alloys with fine η′ precipitates

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Acta Materialia 58 (2010) 6695–6705 www.elsevier.com/locate/actamat

Microstructure evolution and deformation behavior of ultrafine-grained Al–Zn–Mg alloys with fine g0 precipitates S. Zhang 1, W. Hu ⇑, R. Berghammer, G. Gottstein Institute of Physical Metallurgy and Metal Physics, RWTH Aachen University, Aachen, Germany Received 27 May 2010; received in revised form 13 July 2010; accepted 25 August 2010 Available online 23 September 2010

Abstract An aged Al–5Zn–1.6Mg alloy with fine g0 precipitates was grain refined to 100 nm grain size by means of confined channel die pressing. Microstructure observations and mechanical tests were carried out to characterize the materials before and after various degrees of severe plastic deformation. Deformation processing enhanced the strength of the alloy, but limited its work hardenability. An analysis of deformation mechanisms revealed that plasticity proceeded by dislocation slip through ultrafine-grained cellular and subgrain arrangements. g0 precipitates strengthened the alloy by dispersion hardening, but retarded an increase in the strain rate sensitivity during grain refinement. The influence of g0 precipitates is discussed with respect to their effect on dislocation configurations and deformation mechanisms during processing of the alloy. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Aluminum alloy; Ultrafine grain; Precipitate; Strain rate sensitivity; Activation volume

1. Introduction There are various methods of strengthening metallic materials. If the chemistry is not to change, grain refinement is a successful means to raise the strength of a polycrystalline material. In fact, it is known that nanocrystalline (NC) and ultrafine-grained (UFG) metals and alloys possess high strength. However, their ductility is generally lower than their microcrystalline counterparts [1]. Poor ductility is often a problem in NC/UFG metals and alloys produced by severe plastic deformation (SPD). Failure at low levels of plastic strain is mostly due to the early occurrence of plastic instabilities, such as shear bands or necking, and can be attributed to insufficient strain hardening and strain rate hardening capability of these materials [2]. Accordingly, many attempts have been made to enhance the strain hardening and strain rate hardening capability of ⇑ Corresponding author. Tel.: +49 241 8026869; fax: +49 241 8022301.

E-mail address: [email protected] (W. Hu). Present address: Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK. 1

NC/UFG metals and alloys. Corresponding concepts include the introduction of a bimodal or multi-modal grain size distribution into NC and UFG metals and alloys [3], deformation of the material to an ultra-large strain [4], utilization of the interaction between dislocations and boundaries of nanoscale twins [5] or the implementation of second-phase particles or solute elements in grains and grain boundaries [6–9]. Investigations into the effect of precipitates and solute elements on microstructure and mechanical behavior of NC and UFG alloys demonstrate the complicated influence of second-phase particles. The impact of precipitates on microstructure evolution during SPD was investigated on different Al alloys [6–9] where, in particular, their role in grain refinement was addressed. However, the influence of fine precipitates on mechanical behavior, such as strain hardening and strain rate sensitivity (SRS), have only rarely been studied, but more detailed investigations are needed for a deeper understanding of the dominant mechanisms that control the microstructure evolution and mechanical behavior of NC/UFG alloys with dispersed second-phase particles.

1359-6454/$36.00 Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2010.08.034

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To explore the interaction of fine precipitates with the process of grain refinement during SPD, especially the concurrent effects of dispersion strengthening and grain refinement on the mechanical properties after SPD, this study investigated the microstructure evolution during SPD and the mechanical behavior of an UFG Al–Zn–Mg alloy in a fully precipitated state. 2. Experimental An Al alloy with 5 wt.% Zn and 1.6 wt.% Mg, each component with a purity of better than 99.99%, was prepared by melt processing. The cast ingot was solution annealed at 520 °C for 8 h, followed by a quench in ice water and subsequent aging at 200 °C for 2 h, again followed by a quench in ice water. The as-aged ingot is designated as F0. Its grain size was of the order of 1 mm. The ingot was then cut into 12  9  9 mm3 billets by electron discharge machining. The billets were subjected to SPD by confined channel die pressing (CCDP) [10] at room temperature (RT) with a strain rate of 103 s1. Each pressing proceeded to a pressure of 1000 MPa, at which point the billets would fill the die. After each pressing, the billet was rotated in the fashion shown in Fig. 1 prior to the next deformation so that it would be compressed in turn along all three axes. The initial billet geometry was retrieved at the end of each pressing, but rotated by 90° compared with the former shape (Fig. 1). Each compressionpffifficonveyed a mean von Mises equivalent strain of ffi ð2= 3Þ lnð12=9Þ ¼ 0:33 to the specimen. The strain distribution in the sample was not homogeneous, owing to friction effects [11]. A finite element method study showed that the central region (3.5  1.5  1.5 mm3) of each billet underwent the highest, but also a homogeneous, deformation with a von Mises strain of >0.7 [12]. The billets were subjected to 1, 3, 6, 9 and 18 passes and will be referred to as F1, F3, F6, F9 and F18, correspondingly. The samples for microstructure observations, tensile tests and SRS measurements were taken from the central homogeneously deformed region of the billets with a plastic strain of 0.7, 2.1, 4.2, 6.3 and 12.6 for F1, F3, F6, F9 and F18, respectively. To study the microstructure, transmission electron microscopy (TEM) with a JEM 2000 FX (for conventional analytical TEM) and an FEI Tecnai F20 (for high resolution analytical TEM (HRTEM)) was employed. Foils were thinned and polished with a TenuPol-5 twin jet electro-polisher using an electrolyte composed of 78 ml HClO4, 100 ml C6H14O2 and 700 ml C2H5OH at 5 °C. The pump

90°

A A A A C C

B B

B

C C

1st pass, pressing along A-axis

B B

90°

C C

B B

C C

A A

C C

C C

A A

2nd pass, pressing along B-axis

3. Results 3.1. Microstructure Bright field TEM micrographs (Fig. 2) revealed the microstructure evolution of the aged Al–5Zn–1.6Mg alloy during CCDP. The initial microstructure before CCDP consisted of coarse grains in which fine g0 precipitates were homogeneously distributed (Fig. 2a). During SPD, the microstructure transformed from initially coarse-grained to an elongated dislocation cell structure (Fig. 2b) and subgrain structure (Fig. 2c) to an eventually equiaxed cellular structure (Fig. 2d–f). The grain boundary misorientation monotonously increased with rising number of passes, as qualitatively demonstrated by the corresponding selected area diffraction (SAD) patterns (Fig. 2a–f), which changed from a single crystal type to a polycrystal type as CCDP progressed. From the sixth pass on, the deformation structure and grain refinement became homogeneous. The crosssectional area A of individual grains was measured from dark field TEM images and converted to equivalent circle diameters (grain size) by d ¼ ð4A=pÞ1=2

C C

B B

A

flow rate was set to 12, and the applied voltage ranged between 25 V and 30 V. Tensile tests were conducted on an electromechanical materials testing machine (DZM) at a constant true strain rate of 5  104 s1 at RT on dog-bone-shaped samples machined from the central part of the sample parallel to the long axis of each billet with a gauge volume of 3.5  1.5  1 mm3. To measure the SRS, two different methods were applied: stress relaxation after compressive loading and rate jump tests during nanoindentation, both at RT. For stress relaxation tests, cylindrical samples 1.5 mm in diameter and 3 mm long were machined from the center of the billet and subjected to compression tests on the DZM at a constant true strain rate of 1  104 s1 to a plastic strain of 0.8%. At this point, the cross-head of the test machine was arrested, and the stress would decrease with time, owing to inelastic deformation. After the stress relaxation tests, the slightly compressed cylinders (plastic strain e  0.8%) were polished on their longitudinal sections for nanoindentation. Indentation was conducted on a Hysitron TriboIndenter with a Berkovich tip. Four load rate jumps (from 0.1 to 0.03, 0.03 to 0.01, 0.01 to 0.03 and 0.03 to 0.1 mN s1) were applied during each indent, with a load between 5 mN and 8 mN. The hardness was evaluated after indentation from the load– depth curve by means of the Oliver–Pfarr method [13]. For each sample, six indentations were carried out.

ð1Þ

C C A A

B

B B

A A

A

B B

3rd pass, pressing along C-axis

Fig. 1. Schematics of CCDP strain path between consecutive pressings.

It is evident from Fig. 3 that the grain size distributions were of logarithmic normal type, with average diameters as listed in Table 1. After 18 passes CCDP, the grain size had been refined from initially 1 mm to 123 nm.

S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

a

200 nm

6697

b

500 nm

c

d

500 nm

200 nm

e

f

200 nm

200 nm

Fig. 2. Bright field TEM micrographs of microstructure evolution during CCDP: (a) before CCDP; (b) 1 pass; (c) 3 passes; (d) 6 passes; (e) 9 passes; (f) 18 passes.

Fig. 4 reveals the fine precipitates in the as-aged Al–5Zn– 1.6Mg alloy subjected to CCDP for 0, 9 and 18 passes. After 18 passes, fine precipitates still existed in the matrix. The pre-

cipitate size evolution with progressing deformation was measured from bright field TEM images. The equivalent precipitate diameter was determined from Eq. (1) by measuring

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S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

cipitate in the Al matrix. The local dislocation density next to the precipitates reached 1016 m2 according to HRTEM images shown in Fig. 6c and d.

(a) F6: 537 counted grains

100

Count

80 60 40

3.2. Mechanical properties

20 0 46

56

68

83 102 124 152 185 226 276 337 412 503 614

Count

Grain Diameter (nm)

(b) F9: 873 counted grains

160 140 120 100 80 60 40 20 0 46

56

68

83 102 124 152 185 226 276 337 412 503 614 Grain Diameter (nm)

(c) F18: 517 counted grains 120

Count

100 80 60 40 20 0 46

56

68

83 102 124 152 185 226 276 337 412 503 614 Grain Diameter (nm)

Fig. 3. Grain (cell, subgrain and grain) size distribution after CCDP of samples F6, F9 and F18.

Table 1 Grain size statistics of F6, F9 and F18.

No. of studied grains Mean grain area (nm2) Mean grain diameter (nm)

F6

F9

F18

537 2.03  104 178

873 1.31  104 147

517 9.3  103 123

the projected particle area A. As shown in Fig. 5, the particle size followed a logarithmic normal distribution, and their mean values decreased slightly with the number of CCDP passes, as summarized in Table 2. Moreover, no indication of dislocation cutting through the precipitates was observed, as further corroborated by HRTEM imaging (Fig. 6). No indication of cutting is seen even after 18 passes CCDP (Fig. 6a). The precipitate was identified as hexagonal MgZn2 g0 phase with an orientation relationship to the Al matrix of ½2  1 10g0 ==½001Al and ð01  14Þg0 ==ð200ÞAl (Fig. 6b). The interface between particle and matrix was semi-coherent with a plane spacing mismatch of 4.3% (d ð0114Þg0 = 0.1937 nm calculated from a = 0.496 nm, c = 0.868 nm [14], d(200)Al = 0.2025 nm). Inverse fast Fourier transformation (FFT) images in Fig. 6c and d, which were obtained from the ð200ÞAl  ð 200ÞAl and ð020ÞAl  ð0  20ÞAl diffraction patterns, respectively, reveal the positions of dislocations at the g0 pre-

3.2.1. Tensile test The true stress–strain curves of an aged Al–5Zn–1.6Mg alloy subjected to different CCDP (Fig. 7a) render the yield strength (r0.2) and the ultimate tensile strength (UTS) (rUTS) (Fig. 7c). The curves reveal a single peak type behavior, which means that strain softening occurred at large strains. This is typical for SPD processed materials [15,16] and is most likely due to microstructural rearrangements resulting from the strain pass change from CCDP to uniaxial deformation. These microstructural changes are, however, not the subject of this study. The uniform elongation e1 and the initial strain softening e0 were determined from H  e plots (Fig. 7b) for Þ is the norH = 1 and H = 0, respectively, where H ¼ r1 ð@r @e e malized strain hardening rate. The strength of the samples improved monotonically with increasing number of CCDP passes (Fig. 7c), while e1 and e0 passed through minima (Fig. 7d). Both e1 and e0 dropped remarkably up to the sixth pass: e1 decreased from initially 9% for F0 to 3.2% for F6, and e0 was reduced from 12% for F0 to 4.4% for F6. Upon further CCDP deformation for 18 passes, e1 increased only slightly to 3.6%, while e0 rose to 8.6%. Interestingly, beyond six CCDP passes, the onset of strain softening was remarkably delayed to higher strains, although the uniform elongation hardly changed at all. 3.2.2. Strain rate sensitivity 3.2.2.1. Stress relaxation tests. The stress relaxation of an aged Al–5Zn–1.6Mg alloy subjected to different passes of CCDP was analyzed in compression tests to determine the SRS m of the material. An example of the stress relaxation analysis for a sample subjected to 18 passes CCDP is given in Fig. 8. The strain rate sensitivity (SRS) is defined as m¼

@ ln r @ ln e_

ð2Þ

where r is the flow stress and e_ the strain rate. Making use of the fact that the strain rate is proportional to the stress decrease rate during stress relaxation [17–19], the m value of the sample is obtained from m¼

@ ln r @ ln r ¼ _ @ ln e_ @ lnðrÞ

ð3Þ

_ is the stress decrease rate during stress relaxawhere ðrÞ tion. The determined values of m are listed in Table 3. The SRS was found to increase with progressing CCDP. 3.2.2.2. Nanoindentation tests with load rate jump. The SRS was also determined by load rate jump tests with a nano-

S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

a

6699

c

b

50 nm

50 nm

50 nm

Fig. 4. Bright field TEM micrographs of an aged Al–5Zn–1.6Mg alloy: (a) before CCDP; (b) after 9 passes; (c) after 18 passes.

(d) F6: 631 counted particles 100

120

80 Count

Count

(a) F0: 822 counted particles 150

90 60 30

60 40 20 0

0 4.81

5.88

7.18

8.77

10.7

13.1

16

4.81

19.5

5.88

7.18

8.77

10.7

13.1

16

19.5

16

19.5

Particle Diameter (nm)

Particle Diameter (nm)

(b) F1: 732 counted particles

(e) F9: 575 counted particles

120

80 60

80

Count

Count

100 60 40

40 20

20 0

0

4.81

5.88

7.18

8.77

10.7

13.1

16

4.81

19.5

5.88

7.18

(c) F3: 345 counted particles

10.7

13.1

(f) F18: 1032 counted particles

60

120

50

100

40

80

Count

Count

8.77

Particle Diameter (nm)

Particle Diameter (nm)

30 20 10

60 40 20 0

0 4.81

5.88

7.18

8.77

10.7

13.1

16

3.94

19.5

4.81

5.88

7.18

8.77

10.7

13.1

16

19.5

Particle Diameter (nm)

Particle Diameter (nm)

Fig. 5. Size distributions of g0 precipitates with increasing pass number of CCDP.

Table 2 Precipitate statistics of the samples. Precipitate

F0

F1

F3

F6

F9

F18

Studied no Mean particle area (nm2) Mean particle diameter (nm) Mean particle volume (nm3) Volume fraction (%) Spacing s (nm)

822 82.7 10.6 751 3.2 34.2

732 79.8 10.4 719 3.1 34.5

345 84.8 10.8 783 3.3 34.0

631 70.1 9.8 600 2.6 36.3

575 70.1 9.8 631 2.7 35.2

1032 50.9 8.6 471 2.0 36.9

indenter. An example of such tests for a sample subjected to 18 passes of CCDP is shown in Fig. 9, in which the arrows point out the moments of load rate jumps from 0.1 to 0.03, 0.03 to 0.01, 0.01 to 0.03 and 0.03 to 0.1 mN s1. The m values were determined from the hardness jumps (arrows in Fig. 9a) by m¼

ln H 1  ln H 2 ln e_ 1  ln e_ 2

ð4Þ

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S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

a

b

(200)Al // (01-14) ' [001]Al // [2-1-10] ' c

d

Fig. 6. HRTEM analysis of a precipitate. (a) HRTEM image: the direction vertical to the page is [0 0 1] of Al. (b) Reciprocal lattice from Al and fine precipitates obtained by FFT. (c and d) Inverse FFT image obtained using ð2 0 0ÞAl =ð2 0 0ÞAl (in Fig. 6c) and ð0 2 0ÞAl =ð0 2 0ÞAl (in Fig. 6d) diffraction patterns show the dislocation positions surrounding the g0 precipitate.

where the subscripts 1, 2 denote the hardness and load rate values before and after each rate jump. The hardness differences were derived from the hardness H (Fig. 9a) and the strain rate de/dt (Fig. 9b) vs. the indentation depth h. The relationships H–P/h2 and de/dt–d(ln h)/dt were used to convert the measured load P and indentation depth h to hardness and strain rate [20]. Although these relationships did not yield the absolute values of hardness and strain rate, they were sufficient for the analysis, as only the ratios of hardness and strain rate were of interest, as indicated by Eq. (4). The calculated m values from load rate jump tests during nanoindentation are listed in Table 3 and shown in Fig. 10a together with the m values measured by stress relaxation tests. The indicated scatter of nanoindentation tests indicates the statistical variance from six indentations. Evidently, the m values obtained from stress relaxation and nanoindentation tests compare well. The absolute hardness values H were determined according to the Oliver–Pharr method [13] from the unloading curve after a peak load of 8 mN. These values divided by a factor three are shown in Fig. 10b together with the yield strength measured from tensile and compression (stress relaxation) tests. The yield strength derived

from indentation tests according to the Tabor relation of ryield = H/3 [21] is obviously larger than the yield strengths obtained in tensile or compression tests [22], but shows the same trend with increasing CCDP deformation. The yield strength measured in tensile and compression tests was essentially the same. 4. Discussion 4.1. Behavior of g0 precipitates during CCDP The average size of g0 (MgZn2) precipitates was found to decrease slightly during CCDP. This may be due to (1) disintegration of precipitates during deformation, (2) formation of new small precipitates, and (3) dissolution of preexisting large precipitates. TEM and HRTEM observations revealed that the particles remained intact, and no dislocation slip steps were observed on the particle surface, which is evidence of dislocation cutting. Hence, disintegration of particles from option (1) can be ruled out. Also, no new precipitates were found to form upon CCDP from the GP zones in a naturally aged Al–5Zn–1.6Mg alloy [12], which rules out the second option. However, precipitate

S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705 F0

a

F0

F9

F6

F3

F1

b

F18

F1

6701 F9

F6

F3

F18

7 6 5 4

300

Θ

True Stress (MPa)

400

200

3 2 1

100

0 0

-1 0

2

4

8 10 12 14 16 18 20 22

6

0

2

c

4

6

d 14

450

Strain (%)

Stress (MPa)

350 σ0.2

250

10

12

ε1 ε0

12

400

300

8

True Strain (%)

True Strain (%)

UTS

10 8 6 4 2 0

200 0

3

6

12

9

15

0

18

CCDP Passes

3

6

9

12

15

18

CCDP Passes

Fig. 7. (a) True stress–strain curves of aged Al–5Zn–1.6Mg alloy subjected to different passes of CCDP. (b) Normalized strain hardening rate H ¼ r1 @r je_ @e as evaluated from tensile tests in Fig. 7a. (c) Yield strength r0.2 and UTS. (d) Uniform elongation (e1) and strain of starting strain softening (e0) as obtained from H(e) in (b).

Table 3 Strain rate sensitivity (m) derived from stress relaxation and nanoindentation tests.

6,07

ln σ (lnMPa)

Stress relaxation test

F18: m = 0.0095

6,06

F0 F1 F3 F6 F9 F18

6,05

6,04

6,03 -4

-3

-2

-1

0

ln σ ( ln MPa s)

Fig. 8. Evaluation of the stress relaxation tests with respect to the SRS according to Eq. (3).

dissolution during SPD was reported for Al–Cu alloys [6] (complete dissolution of h0 platelets) and for Al–Mg–Si alloys [8] (complete dissolution of b00 and b0 needles) at RT and in an Al–Zn–Mg alloy [9] (dissolution and aging of the g phase) at 473 K. Hence, it is concluded that the slight decrease in the average particle size with progressing CCDP has to be attributed to occasional precipitate dissolution. From the mean size and volume of the particles, their volume fraction in the aluminum matrix can be estimated. Prior to CCDP, the precipitate volume fraction was estimated from the equilibrium phase diagram on the basis of the alloy composition. If all Zn in solid solution had pre-

0.0058 0.0058 0.0062 0.0095

Nanoindentation test 0.0065 ± 0.0006 0.0064 ± 0.0007 0.0061 ± 0.0008 0.0074 ± 0.0010 0.0072 ± 0.0010 0.0092 ± 0.0008

cipitated out as MgZn2 during aging, it would form 5.93 wt.% MgZn2 and leave 0.66 wt.% Mg in solid solution. Hence, the initial precipitate volume fraction amounted to f0 = 3.2% in view of the densities qAl = 2.7 g cm3 and qMgZn2 = 5.16 g cm3. In the course of precipitate dissolution during CCDP their volume fraction decreased to f ¼ f0 V =V 0 ; where V0 and V are the average precipitate volumes prior and subsequent to CCDP. The calculated volume fractions are listed in Table 2 and show a gradual decrease during CCDP with increasing number of passes from F0 to F18. Because the particle size distribution did not shift, whereas the peak size decreased slightly during CCDP (Fig. 5), the dissolution apparently affected particles of all sizes to the same extent. Therefore, the majority of the particles only shrank a little. From the size and volume fraction of the particles, the mean inter-particle spacing s can be derived according to [23] pffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffi s¼r 2p=3f  8=3 ð5Þ

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S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

b

0.037 0.036

0.1 Strain rate (/s)

Hardness (10E12 Pa)

a

0.035 0.034 0.033

0.01

0.001

0.032 0.031 350

400 450 Indentation Depth (nm)

500

0.0001 350

400 450 Indentation depth (nm)

500

Fig. 9. Analysis of nanoindentation test of F18.

a

The strengthening effects of solutes in Al–Zn–Mg alloys can represented according to Ref. [23] as

0.01

2=3

Strain rate sensitivity, m

0.008

0.006

0.004

Indentation Stress Relaxation

0.002

0 0

b

3

6

9 CCDP Passes

12

15

18

450

400

Stress (MPa)

2=3

rSS ¼ MAZn cZn þ MAMg cMg

350

300

Compressive yield Indentation

200 0

3

6

9 CCDP Passes

12

where M  3 is the Taylor factor for tensile deformation and AZn = 3.1, AMg = 20.5 are the strengthening coefficients of Zn and Mg in Al, respectively. The concentrations cZn and cMg are given in weight per cent [23]. As mentioned in Section 4.1, the solute concentrations in the aged alloy matrix before CCDP are supposed to be cZn = 0 and cMg = 0.66. As a result, according to Eq. (7), solid solution strengthening led to an increase in strength of 47 MPa. This strength contribution may have increased mildly during CCDP, as precipitates of limited amount were dissolved, yielding a higher solute content. The calculated changes in rSS with progressing CCDP are given in Table 4. Because the precipitates were found non-sheared by dislocations, they must have been bypassed by the Orowan mechanism, which requires a stress [24] rP ¼ bGb=s

Tensile yield 250

ð7Þ

15

18

Fig. 10. Comparison of SRS values obtained by stress relaxation tests and nanoindentation tests (a), and yield strength measured by tensile, compression and nanoindentation tests (b).

It is evident from Table 2 that the particle spacing did not vary much with progressing SPD (sF0 = 34.2 nm = 120b, sF18 = 36.9 nm = 129b, where b = 0.286 nm is the Burgers vector of Al).

ð8Þ

where b is a constant of the order of 1, G = 26 GPa [23] is the shear modulus of Al, and s is the mean spacing of the precipitates in the glide plane. To evaluate b, the undeformed and coarse-grained sample F0, whose strengthening from dislocations and grain boundaries is negligible, was considered. Eq. (6) renders rP-F0 = rF0  rSSF0 = 22447 MPa = 177 MPa, and thus from Eq. (8), b = rP-F0 sF0/Gb = 0.81, where sF0 = 34.2 nm. It is evident from Table 2 that the particle spacing did not increase much during CCDP. Therefore, the Orowan stress rP decreased only slightly with progressing CCDP (Table 4). The grain size contribution to the flow stress is related to the grain size after SPD. To identify the relevant mechanisms of the grain size effect, the yield stress r of the aged

4.2. Strengthening mechanisms To analyze the effect of processing and constitution on the strength of the material, the simplifying assumption is made that the various contributions to the strength of the material from solutes (rSS), precipitates (rP), dislocations (rDisl) and grain boundaries (rGB) can be simply linearly superimposed: r ¼ rSS þ rP þ rGB þ rDisl

ð6Þ

Table 4 Strength contributions to the flow stress.

r0.2 (MPa) Zn solute (wt.%) Mg solute (wt.%) rSS (MPa) rP (MPa) rDisl/rGB (MPa)

F0

F1

F3

F6

F9

F18

224 0 0.66 46.5 177.7 0

298 0.21 0.69 51.5 175.5 70.9

321 0 0.62 44.6 179.7 96.7

340 0.98 0.84 63.9 167.6 108.5

350 0.78 0.80 60.9 171.5 117.6

406 1.83 1.00 75.3 165.0 165.8

S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

UFG Al–Zn–Mg alloy was measured by tensile tests and plotted as function of grain size (Fig. 11). Grain size strengthening follows a Hall–Petch type relationship pffiffiffi rGB ¼ r0 þ k H–P = d ð9Þ where kH–P is the Hall–Petch constant, and r0 is the yield strength of a single crystal. However, the microstructure after SPD is still a deformed structure, and the majority of the boundaries are low angle boundaries. For cellular dislocation arrangement it is reported [25] that rGB ¼ k

Gb d

ð10Þ

where k is a constant of the order of 10. Indeed, the results show that a plot of rGB vs. 1/d gives apmuch better fit ffiffiffi (r2 = 0.9844, Fig. 11a) than rGB vs. 1= d (r2 = 0.9363, Fig. 11b). From the slope of the line rGB vs. 1/d, kGb = 2.02  105 MPa m = 20.2 N m1 (Fig. 11a), one obtains k = 2.7. The flow stress contribution from single dislocations— which still exist inside the cell and subgrain interior with a high density—and from subgrain respectively cell boundaries is difficult to distinguish, since they are related by a rule of similarity [25,26] which states that subgrain size d and dislocation spacing ‘ are proportional to each other: ‘ = v0 d

a

b

6703

rGB ¼ kG db pffiffiffi rDisl ¼ aGb q ¼ aGb ‘

ð11Þ

k ¼ va0 where a is the dislocation interaction factor with a value of a  0.5 [24], q is the dislocation density. In contrast to rSS and rP, the strengthening from cells/subgrains (rGB) or forest dislocations (rDisl) increased monotonically with imposed strain, owing to the reduced cell or subgrain size, respectively an increased dislocation density, with progressing deformation (Table 4). 4.3. Deformation mechanisms In order to identify the major deformation mechanisms, the activation volume V of the aged Al–Zn–Mg alloy was investigated, which can be related to the SRS of the material m by [18] pffiffiffi 3k B T  V ¼ ð12Þ mr where kB is the Boltzmann constant, T the absolute temperature, m the SRS of the material, and r the stress component which accounts for the strain rate and temperature dependence of the applied stress. The latter is related to the deformation free activation energy (DG) as well as activation volume (V) by V = DG(T, s)/s, where p ffiffi ffi s ¼ r = 3 is the effective von Mises shear stress. The Orowan stress rP is an athermal stress and varies only slightly with temperature through the temperature dependence of the shear modulus G. Thus, rP does not affect the activation volume. Solid solute strengthening rSS is also thermally activated, but the glide resistance of solute atoms is small compared with dislocation–dislocation interaction. Moreover, if the solid solution hardening were to control thermally activated dislocation glide, the activation volume ought to be of the order of 1–2 nm or 3–7b (the mean spacing of solute atoms that was estimated according to the calculated solute element content shown in Table 4), which is dramatically smaller than several hundred b3 as measured on coarse-grained and UFG material (Table 5). This indicates that the activation volume, respectively the activation length, associated with solute atoms can be neglected. Hence, only the non-chemical contribution to the flow stress, i.e., rapplrPrSS, was considered for a thermal activation analysis.

Table 5 Calculated activation volume V, activation length L, mean forest spacing ‘ and ratio L/d of F6, F9 and F18.

Fig. 11. Grain size contribution to the flow stress (rGB). (a) rGB vs. d1 and (b) rGB vs. d1/2.

V (b3) L (nm) ‘ (nm) d (nm) L/d

F6

F9

F18

Average

373 107 103 178 0.599

353 101 95 147 0.687

196 56 67 123 0.456

0.58

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S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

The activation volume with progressing CCDP was calculated according to Eq. (12) from the m values measured by load rate jumps during nanoindentation (Table 5). The activation volume of the aged Al–Zn–Mg alloy decreased from about several thousand b3 for coarse-grained and undeformed material to 200–300b3 (373b3 for F6 and 196b3 for F18) for the alloy subjected to SPD (Table 5). These values are larger by far than 1b3, the expected activation volume for grain boundary mediated deformation mechanisms (e.g., grain boundary sliding, grain rotation, Coble creep) [1]. Therefore, the calculated activation volume is associated with thermally activated dislocation movement in the interior of cells or subgrains. Hence, dislocation glide remained the dominant deformation mechanism during grain refinement, even if the grain size had already decreased to 100–200 nm, whereas the contribution of grain boundary plasticity to strain was negligible. This is in contrast to other investigations which reported grain boundary plasticity in UFG aluminum [29]. It is noted, however, that the material in the current investigation contained finely dispersed particles. Apparently, the dispersed g0 precipitates prevented grain boundary sliding and were effective in impeding dynamic recovery and thus beneficial for the development of a more uniform dislocation configuration. The activation volume can be factorized as [27,28] V  ¼ Lbw  Lb2

ð13Þ

where w  b is the obstacle width, and L is the activation length that characterizes the free length of the thermally activated dislocation segment. The calculated activation length L of samples F6–F18 (Table 5) was L  107 nm for F6, L  101 nm for F9 and L  56 nm for F18. This dislocation segment length compares well with the mean dislocation spacing according to Eq. (11). The calculated dislocation spacing ‘ for F6, F9 and F18 is listed in Table 5 and amounts to ‘  103 nm for F6, ‘  95 nm for F9, and ‘  67 nm for F18, respectively, corresponding to a dislocation density of the order of 1014 m2, which is reasonable for the dislocation density in Al alloys at large strain. The result L  ‘ supports the hypothesis that dislocation glide controls large strain deformation and that dislocation forest cutting contributes the thermally activated component of the flow stress. The ratio of dislocation segment length L and subgrain size d (v = L/d) for F6, F9 and F18 was also determined (Table 5). According to this analysis, the dislocation segment length L and thus, the mean dislocation spacing ‘ was about half the subgrain size. Consequently, the dislocation interaction occurred mainly in the interior even of UFG cells or subgrains.

[29] and m  0.014 at d  400 nm [30] were reported, i.e., considerably larger than the m values 0.007–0.009 for the aged Al–Zn–Mg alloys with fine g0 precipitates in the current study. Although an increase in m with increasing strain was also observed, the total increment from the undeformed coarse-grained alloy to the UFG alloy was just from m  0.006 to m  0.009 (Table 3), i.e., much smaller than for pure Al, where m increased from m  0.005 for coarse-grained material to m  0.03–0.04 for UFG samples [18,29]. Zhao et al. also reported that the SRS was not enhanced by the introduction of precipitates to an oversaturated Al7075 alloy with d = 100 nm and s = 25 nm [31]. This insensitivity of the SRS to plastic deformation and grain refinement of an aged UFG Al–Zn–Mg alloy can be rationalized in terms of competition between grain size d and activation length L during SPD. Eq. (12) can be rewritten as pffiffiffi pffiffiffi pffiffiffi pffiffiffi 3k B T 3k B T 3k B T 3k B T A m ¼   ¼  2 ¼ kGb ð14Þ ¼ ¼ 2 3 L rV  Lb r Lb kGb  d v d pffiffiffi where A ¼ 3k B T =kGb3 = 0.0044 is a dimensionless constant and v = L/d, as given in Table 5. It is seen from Eq. (14) that the change in the SRS depends not only on grain refinement and dislocation multiplication during deformation, but also on the ratio of these structural parameters. A weak increase in the SRS during progressing CCDP therefore reflects a small decrease in v (Tables 3 and 5). In essence, the authors contend that the insensitivity of the SRS to strain and grain refinement in aged and UFG Al–Zn–Mg alloy can be attributed to the influence of dispersed g0 precipitates. The values of V and SRS of aged, UFG Al–Zn–Mg alloys are mainly related to the thermal stress component r of the flow stress, i.e., rDisl in the present study. In the current case r (or rDisl) = rappl–rP–rSS, where rP is athermal Orowan stress, and rSS the friction stress arising from solute atoms. It is obvious from Table 4 that rP contributes 80% to the total yield strength in coarse-grained and undeformed samples (F0) but still 40–50% after microstructure refinement to 100– 200 nm (F6–F18). Owing to the dominance of rP, the relatively small thermal component of the flow stress remained insignificant at large strains, in contrast to pure Al, where the flow stress is essentially controlled by the thermally activated dislocation glide. 5. Conclusions

4.4. Strain rate sensitivity

The microstructure evolution and mechanical behavior of an aged Al–Zn–Mg alloy with finely dispersed g0 MgZn2 precipitates during CCDP was studied. The results allow the following conclusions to be drawn.

The ultrafine grained, aged Al–Zn–Mg is quite small compared with pure UFG aluminum. For pure UFG aluminum at RT values of m  0.03–0.05 at d = 100–200 nm

1. The microstructure of the aged Al–Zn–Mg alloy can be effectively refined by CCDP. The refined structure consists mainly of cellular dislocation arrangements such

S. Zhang et al. / Acta Materialia 58 (2010) 6695–6705

as cells and subgrains with mainly low angle boundaries. The average cell diameter decreased to d  100–200 nm after 6–18 passes of CCDP. 2. The strength of the grain refined alloys is determined by dislocation density, grain size, solute content and g0 precipitates. Insufficient strain hardening capability after CCDP led to a poor uniform elongation (3%) of the UFG alloy. 3. The activation volume of UFG alloy was in the range 200–300b3 and could be attributed to dislocation interactions. The major deformation mechanism remained unaffected by SPD even at a grain size of d  100– 200 nm. 4. The finely dispersed g0 precipitates prevented a substantial increase in the SRS during grain refinement with progressing CCDP, in contrast to pure aluminum. This can be attributed to the relatively small contribution of thermally activated glide to the overall flow stress.

Acknowledgments The authors are grateful to the Deutsche Forschungsgemeinschaft (DFG) for the financial support to the DFG Project “HU 821–1”. The authors thank Dr. Emmerlich and MSc. Jiang from the Materials Chemistry of RWTH Aachen University for their help with the nanoindentation tests. The assistance of Mr. Dorn and Mrs. Herwartz from the Central Facility for Electron Microscopy of RWTH Aachen University during the HRTEM observations is appreciated. References [1] Dao M, Lu L, Asaro R, Hosson J, Ma E. Acta Mater 2007;55:4041. [2] Wang YM, Ma E. Acta Mater 2004;52:1699. [3] Wang YM, Chen MW, Zhou FH, Ma E. Nature 2002;419:912.

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