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A crystallographic orientation based model for describing the precipitation strengthening of stress-aged Al–Cu alloy
Materials Science & Engineering A 644 (2015) 358–364
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
A crystallographic orientation based model for describing the precipitation strengthening of stress-aged Al–Cu alloy Xiaobin Guo a, Yunlai Deng a,b,n, Jin Zhang b,c, Xinming Zhang a,b a
School of Materials Science and Engineering, Central South University, Changsha, China State Key Laboratory of High Performance and Complex Manufacturing, Central South University, Changsha, China c Light Alloy Research Institute, Central South University, Changsha, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 June 2015 Received in revised form 19 July 2015 Accepted 23 July 2015 Available online 29 July 2015
The effects of stress magnitude and crystallographic orientation on the mechanical properties of stress− aged Al–2Cu alloy single crystal specimens are investigated. The specimens with ( 1, 1, 6) plane orientation were stress-aged − and 60 MPa. Specimens with five different plane orientations − − − −under 0, 15,−40, ((1, 2, 6), (3, 1, 3), (1, 3, 3), (1, 1, 6), and (1, 4 , 6)) were stress-aged under stress with the same magnitude of 40 MPa. The results of mechanical properties and TEM microstructure show that the yield stress of stress-aged specimens depends on the crystallographic orientation as well as the stress magnitude. A model based on crystallographic orientation describes the precipitation strengthening of stress-aged Al– 2Cu alloy. The calculated yield stresses in the model fit well with the experimental observations. This model results not only provide important insight into solving the anisotropy problem attributed to precipitation strengthening, but also offer a benchmark for choosing the right range of stress in the manufacture of Al–Cu alloys. & 2015 Elsevier B.V. All rights reserved.
Keywords: Al–Cu alloys Single crystal Crystallographic orientation Stress-aging Model
1. Introduction Age forming is a combined age strengthening process with the forming of metals. This manufacture process has many applications in the aerospace industry [1–2]. In stress-aged aluminum alloys, fine precipitates disperse in the matrix and coarse precipitates form on the grain boundary, so the strength and corrosion resistance of alloys are improved compared with conventional cold-forming process [3–6]. But in some 2XXX series aluminum alloys, application of a stress during aging can significantly affect the orientation of precipitates, namely the stress-orienting effect, which leads to the anisotropy of strength properties [7–11]. This stress-orienting effect directly restricts the development of “ageforming” technique in manufacturing progress of 2XXX aircraft structures. Earlier investigations [7–9] on Al–Cu alloys indicated that the stress-orienting effect depends on the applied stress, temperature and alloy composition. Hosford and Agrawal [7] first studied the stress-orienting in Al–4Cu alloys single crystal. They found that θ’′ precipitates on habit planes perpendicular to the applied compressive stress were generated preferentially. But Eto et al. [8] n Corresponding author at: School of Materials Science and Engineering, Central South University, Changsha, China. E-mail address: [email protected] (Y. Deng).
http://dx.doi.org/10.1016/j.msea.2015.07.067 0921-5093/& 2015 Elsevier B.V. All rights reserved.
found the contrary results when Al–4Cu alloys single crystal were stress-aged under a lower temperature, where θ’′ precipitates were preferential orientation on habit planes parallel to the applied compressive stress. Based on the relationship between misfit inclusion and the applied stress they explained the stress-orienting effect. Later, Skrotzki et al. [10] found that there was a threshold value (16–19 MPa) of the applied stress that must be exceed to form the preferential oriented θ’′ precipitates in the 160 °C stress-aged Al–5Cu alloys samples. They explained the phenomenon with experiments and calculations, and they believed that stress induced the θ’′-plates nucleate preferentially on variants under compression as θ’′ precipitates have negative misfit with the Al matrix. In order to model the precipitation strengthening of stress-aged Al–Cu alloys, Zhu et al. [9] have studied the dependence of applied stress, temperature and alloy composition on stress-aged Al–Cu alloys single crystal systematically. They found that the stress-orienting effect of θ’′ precipitates increased with the increasing of applied stress, and the yield stresses of the stress-aged specimens were lower than those of stress-free aged specimens. However, they only investigated the Al–Cu alloys single crystal with {100} crystallographic orientation. Since the direction of applied stress depends on the crystallographic orientation, it is significant to study more single crystal specimens with various crystallographic orientations. In this study, we describe the results of our investigation on Al– Cu alloys single crystal with five different crystallographic
X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364
orientations. The resulting microstructure and mechanical properties were analyzed to study the influence of crystallographic orientation on stress-orienting effect. The purpose of this paper is to modeling the precipitation strengthening of stress-aged Al–Cu alloys based on crystallographic orientations.
359
Side
Single crystal Front 2cm
2. Experimental procedure Fig. 1. Macro-grains specimen of the Al–2Cu alloy.
Al–2Cu alloy single crystal specimens were prepared. The exact chemical composition is given in Table 1. Macro-grains specimens with grains up to 10 mm diameter were grown by pulling bars cut from the Al–2Cu alloy plate to 0.5–1.0 pct strain, followed by annealing in a forced-air furnace at 525 °C for 24 h, then repeating the strain-annealing cycle 8–10 times. One of the macro-grains specimens is shown in Fig. 1. Single crystal specimens were cut from the macro-grains bars by means of a spark–erosion–cutting machine. The orientations of the Al–2Cu alloy single crystal specimens were determined by Electron Backscattered Diffraction (EBSD) in the FEI Nova NanoSEM 230. IPF (inverse pole figure) maps of five single crystal specimens with various crystallographic orientations are shown in Fig. 2. After being solution treated at 525 °C for 2 h and quenched into water, specimens with various crystallographic orientations were aged at 180 °C for 66 h with applied compressive stresses. The aging condition and applied stress used for each specimen are given in Table 2. The aged specimens were then tested under compressive load to determine the yield stress. The yield stress was determined at 0.2% offset from the elastic response of compressive tests on specimens using a strain rate 10 2/s in a CSS44110 machine. The Vickers hardness of aged specimens was s measured from more than 10 indents in a huayin HV-5 microhardness tester. The precipitate structure of the specimens was characterized by means of transmission electron microscopy (TEM). Disks 3 mm in diameter were punched from the aged sheets, ground to a thickness of 0.1 mm, and twin-jet electro polished in a solution of HNO3 and methanol (1:3 in volume), at 25 °C and 20 V. TEM foils were examined using a JEM-2100F microscope operating at 200 kV. The features of the precipitate including the average radius, the average thickness and the distribution were determined by quantitative analysis of the TEM specimens.
3. Results The Vickers hardness and yield stress of five Al–2Cu singlecrystal specimens, which have different crystallographic orientations and were aged at 180 °C for 66 h under 40 MPa are given in Fig. 3. The change of Vickers hardness and yield stress with or-
−
and 60 MPa. The yield stress of stress-aged specimens with (1, 1, 6) plane-orientation decreased with external stress during aging. As the compressive stress increasing from 15 MPa to 60 MPa, the yield stress decreased from 100 MPa to 86 MPa (Fig. 6). This phenomenon is due to the applied stress induced preferentially oriented θ’′ precipitates, thereby the mechanical properties and anisotropy of the Al–2Cu alloy were affected. It can be seen from the TEM-BF images that the stress-orienting effect of θ’′ precipitates increased with the applied stress (Fig. 5). The volume fraction of θ’′ precipitates was calculated using the lever rule in Al–Cu phase diagram, and the result is fv ¼ 0.00621. The volume fraction, mean diameter and mean thickness of the parallel and perpendicular θ’′-plates were quantitatively analyzed and summarized in Table 3. In Table 3, the fv// is the volume fraction of θ’ precipitates on [001]Al direction, and the fv⊥ is the volume fraction of θ’′ precipitates on [010]Al direction. The volume fractions of fv// and fv⊥ were calculated by counting the number of θ’′-plates on [001]Al and [010]Al direction, where fv// þ fv⊥¼fv. Zhu [9] introduced a parameter to describe the degree of alignment of the θ′-plates. However, the parameter in this study describes the stress-orienting effect on the decrease of mechanical properties. A parameter α is introduced as
α=
2 (fv //⋅fv ⊥)0.5 fv
(1)
When specimen was aged without stress, the θ’-plates on [001]Al and [010]Al direction are almost the same (Fig. 5a). As fv //¼ fv⊥¼0.5fv , the parameter α ¼ 1, there is no stress-orienting effect. When fv//≠fv⊥, the parameter α o1, there is stress-orienting effect on θ’′ precipitates. It is indicated that the difference between fv// and fv⊥ increases with the increase of the magnitude of applied compressive stress (Fig. 5b–d), and the value of fv⊥ is greater than fv//. Consequently, the parameter α decreases and the stressorienting effect on θ’′ precipitates increases with the increase of the magnitude of applied stress.
−
ientation are almost the same. Specimen with ( 1, 3, 3) plane-orientation has the lowest hardness and yield stress, and the values −
of specimen with ( 1, 1, 6) plane-orientation are the highest. In order to illustrate the effect of crystallographic orientation, the Vickers hardness of specimens with different orientations is shown in the (001) pole figure (Fig. 4). −
The grain of single crystal specimen with ( 1, 1, 6) plane-orientation was divided into four parts to be stress-aged at 0, 15, 40 Table 1 Composition of the Al–2Cu alloy in weight percent. Alloys
Cu
Mg
Si
Fe
Zn
Al
Al–2Cu
1.4472
0.00
0.01
0.01
0.005
Balance
4. Modeling the precipitation strengthening of stress-aged Al– Cu alloy 4.1. Effect of stress magnitude An investigation was conducted on the effect of stress magni−
tude using the Al–2Cu single-crystal specimens, which have ( 1, 1, 6) plane-orientation and were aged at 180 °C for 66 h. The applied stress was 0 MPa, 15 MPa, 40 MPa and 60 MPa, respectively. The quantitative TEM analysis results listed in Table 3 was used in Zhu's [12] theory, as shown in Eq. (2) to calculated the strengthening shear stress τp associated with {100}-θ′-plates.
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X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364
− −
Fig. 2. The orientations of the Al–2Cu alloys single crystal specimens were determined by EBSD, (a) Euler's angles of (175°, 21°,206°) or {hkl} − plane orientation of ( 1, 2 ,6); (b) Euler's angles of (267°, 44°,72°) or −{hkl} plane orientation of (3,1,3); (c) Euler's angles of (347°, 46°,343°) or − −{hkl} plane orientation of ( 1,3,3); (d) Euler's angles of (4°, 13°,326°) or {hkl} plane orientation of (1,1,6); (e) Euler's angles of (133°, 35°,192°) or {hkl} plane orientation of (1, 4 ,6); (f) Color coded map type of the [001] IPF in aluminum. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
-1,-1,0
Table 2 The applied stress during stress aging for specimen with various orientations. Orientations Applied stress
− −
( 1, 2 ,6) – – 40 MPa –
(3,1,3) – – 40 MPa –
−
−
− −
( 1,3,3)
( 11,1,6)
( 1, 4 ,6)
– – – –
0 MPa 15 MPa 40 MPa 60 MPa
– – 40 MPa –
67.51 61.13 (-1,-4,6) 68.21 (-1,-2,6) 001
100
120
Hardness Yield Strength
110
-1,1,0 55.84
90
(-1,3,3)
100 80 90 70
80 70
60
010
60 50 40
(-1,-2,6)
(3,1,3)
(-1,3,3)
(-1,1,6)
68.03
100
110 Hardness after Stress-aging at different orientation
50
40
1,-1,0
(-1,1,6)
(313)
Vickers Hardness
Yield Strength / MPa
0,-1,0
-1,0,0
Fig. 4. The Vickers hardness of specimens with different orientations in the (001) pole figure.
(-1,-4,6)
Crystal Orientation Fig. 3. The Vickers hardness and yield stress of five Al–2Cu single-crystal specimens with various crystallographic orientations after stress aging at 180 °C for 66 h under 40 MPa.
τp = 0.13G ⋅ ln
b ⎡ f 0.5 + 0.75 (D /t )0.5f + 0.14 (D /t ) f 1.5 ⎤ p p p p v ⎦ ⎣ v (Dp tp )0.5 v
0.87 (Dp /tp )0.5 r0
(2)
where G is the shear modulus, b the magnitude of the Burgers vector, r0 the interaction inner cut-off radius of the dislocation, and fv the volume fraction, Dp the mean diameter and tp the mean
X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364
020 000
361
020 000
002
002
020
020
000
000
002
002
−
Fig. 5. Bright-field TEM images and diffraction patterns of the specimen with ( 1,1,6) orientation that were compressive stress-aged at 180 °C for 66 h under (a) 0 MPa; (b) 15 MPa; (c) 40 MPa; (d) 60 MPa.
120
Table 3 The diameter and thickness data obtained by quantitative TEM and image analysis of the θ’ precipitates in the Al–2Cu alloy compressive stress-aged at 180 °C for 66 h under different stress. The volume fraction of θ’′ precipitates was calculated using the lever rule in Al–Cu phase diagram. D//
D⊥
t//
t⊥
fv//
fv ⊥
α
15 MPa 40 MPa 60 MPa
288 155 174
204 171 175
3.6 4.7 3.0
5.6 3.6 2.9
0.0029 0.0017 0.0007
0.0033 0.0045 0.0055
0.996 0.812 0.632
thickness of the θ′-plates. Using the results in Table 3, Dp ¼(D// þD⊥)/2, and tp ¼(t//þ t⊥)/2. The yield stress sy can be calculated from the strengthening shear stress τp according to Eq. (3)
σy =
α⋅τp + σ0 η
(3)
where η is the Schmid factor for the single-crystal specimens, s0 the contribution of Cu solid solution hardening. The value of s0 is set at 60 MPa for the aged Al–2Cu alloys [9]. The yield stress sy of our calculations results are compared with the experimental results (Fig. 6). The effect of applied stress on the yield stress of stress-aged specimens comes from two sides. The precipitates in stress-aged specimens are dispersed distribution. The θ’′ precipitates in stressaged specimens (Fig. 5b–d) disperse finer than in the stress-freeaged specimens (Fig. 5a). The data listed in Table 3 show that the diameter and thickness of θ′ precipitates decrease with the increasing of applied stress. So the strengthening stress is greater
Yield Strength/ MPa
Applied stress
Experiment Computer modeling
110 100 90 80 70 60 10
20
30
40
50
60
Applied Stress/ MPa Fig. 6. The calculated and experimental yield stresses of Al–2Cu single-crystal − specimens with ( 1,1,6) orientation after stress aging under different stress.
with finer precipitates according to Eq. (2). According to the quantitative data of θ′ precipitates in Table 3, the relationship between applied stress and size of θ′ precipitates could be built. The effect of stress on diameter and thickness of θ′ precipitates may be written as
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120
Experiment Calculated by the equation (6)
Yield Strength/ MPa
110 100 90 80
Vickers Hardness/HV
55
50
45
(-1,1,6) (3,1,3) (-1,3,3) (-1,-4,6) (-1,-2,6)
40
35
70 0
20
40
60
80
100
Aging Time t/h
60 10
20
30
40
50
Fig. 8. The Vickers hardness curves of the Al–2Cu alloy single crystal with different orientations during aging at 180 °C.
60
Applied Stress/ MPa Fig. 7. The calculated yield stresses by Eq. (6) compared with the experiment re− sults of Al–2Cu single-crystal specimens with ( 1,1,6) orientation after stress aging under different stress.
Dp = Dp 0
tp = tp0
Cm ln σc
Cm ln σc
(4)
(5)
δτp + σ0 η
(-1,-4,6) (-1,-2,6) -1,1,0
1,-1,0
001
(-1,1,6) (-1,3,3) (3,1,3) 100
010
110
(6)
where k is the constant of the composition and aging temperature, and the value of k is 7.8 for Al–2Cu alloy aged at 180 °C. When aging without stress, the value of δ is 1, so there is no stress-orienting effect. With the increasing of applied stress, the value of δ is less than 1 and decrease. The yield stresses sy of our calculations by Eq. (6) are compared with the experimental results (Fig. 7). It can be shown from Figs. 6 and 7 that the parameter δ is more appropriate than α. The parameter δ can well describe the stressorienting effect on the decrease of yield stress. So the parameter α can be replaced with δ, Eq. (3) can be written as
σy =
0,-1,0
-1,0,0
where Dp0 is the diameter of θ′ precipitates in stress-free aged specimen; tp0 is the thickness of θ′ precipitates in stress-free aged specimen; sc is the applied stress during stress aging; Cm is the constant of the matrix and the precipitates, and the value of Cm is 2.6 of θ’′ precipitates. However, when aging under stress, the stress-orienting effect of θ’′ precipitates occurs. So the yield stresses of stress-aged specimens decrease. A parameter δ that describes the stress-orienting degree can be written as −0.5 ⎛k σ ⎞ + 2 + c⎟ δ = 2⎜ ⎝ σc k⎠
-1,-1,0
Fig. 9. The position of different crystallographic orientation in a (001) pole figure.
Fig. 8. The hardness of aged specimens comes to the highest at 66 h, but the values are various for different crystallographic orientation, especially at the stage of peak-aging and over-aging. The −
peak hardness of aged-specimen with (1, 1, 6) plane-orientation is −
the highest, while the specimen with ( 1, 3, 3) orientation is the lowest. The position of different crystallographic orientation is shown in a (001) pole figure (Fig. 9). From Figs. 8 and 9, we found that the peak hardness of specimen with orientation near (001) is −
(7)
4.2. Effect of the crystallographic orientation The effect of crystallographic orientation on the yield stress of stress-aged specimens comes from two sides. With different crystallographic orientation, the yield stress of specimens after stress-free aging is different. Since the compressive yield stress were tested on the plane orientation of specimens, the difference of yield stress comes from the anisotropy of single crystal. Considering the effect of different compressive tests orientation, single crystal specimens with different orientation are aged without stress at 180 °C, and the hardness curves are shown in
higher. (1, 1, 6) orientation is the nearest of five pairs specimens, so −
the peak hardness is the highest. But ( 1, 3, 3) and (3, 1, 3) orientation are further from the (001), the peak hardness is lower. This phenomenon could be explained from the relationship between precipitation strengthening and habit plane. θ′ precipitates forms on {100} habit planes, so the precipitation Table 4 The values of parameter β between the crystallographic orientation and {100} habit planes of different plane orientations. Orientations
(001)
β
1
−
− −
− −
( 1,1,6)
( 1, 2 ,6)
( 1, 4 ,6)
0.973
0.937
0.824
(3,1,3) 0.688
−
( 1,3,3) 0.688
X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364
θ//
θĵ
θ//
θ//
θĵ
363
θ//
θĵ
θĵ
Fig. 10. Bright-field TEM images of single crystal specimens with different −crystallographic orientation that were compressive stress-aged at 180 °C for 66 h under 40 MPa; − − − − (a) (3,1,3) orientation; (b) ( 1, 4 ,6) orientation; (c) ( 1, 2,6) orientation; (d) ( 1,3,3) orientation.
(8)
where θ is the minimum angle between the plane orientation of specimens and (001) orientation. The parameter β describes the effect of anisotropy of aged single crystal specimens. The values of β for different specimens are listed in Table 4, the value is 1 for −
Orientations β q Q
−
− −
− −
( 1,1,6)
( 1, 2,6)
( 1, 4 ,6)
0.973 0.749 0.73
0.937 0.812 0.76
0.824 0.872 0.72
(3,1,3) 0.688 0.927 0.64
−
( 1,3,3) 0.688 0.662 0.46
−
(001) orientation. The value of (1, 1, 6) orientation is higher than (1, 3, 3) and (3, 1, 3) orientation, which fit well with the peak hardness changes in Fig. 8. The definition of parameter β can extend to other precipitation strengthening alloys, where θ is the minimum angle between the crystallographic orientation and habit plane. The second side effect of the crystallographic orientation is the axi of the applied stress during stress aging. When single crystal specimen with (hkl) orientation is stress aged, the stress is applied on the (hkl) plane and the axi of the stress is [hkl]. There was a threshold value of the applied stress that must be exceed to form the preferential oriented θ′ precipitates [10]. So the criterion for stress orienting effect occurring is introduced as
⎧ h ⋅σ ≥ σm ⎪ 2 ⎪ h + k 2 + l2 ⎪ ⎪ k ⋅σ ≥ σm ⎨ or ⎪ h2 + k 2 + l2 ⎪ l ⎪ or ⋅σ ≥ σm ⎪ 2 ⎩ h + k 2 + l2
Table 5 The values of parameter β, q and parameter Q of different plane orientations.
100
1.0
Hardness Q Factor
0.9
90
0.8 0.7
80
0.6 0.5
70
0.4 60
0.3 0.2
Vickers Hardness
β = cos θ
β is
Q Factor
strengthening on (001) orientation is higher. A parameter introduced as
50
0.1 0.0
40
(-1,-2,6)
(3,1,3)
(-1,3,3)
(-1,1,6)
(-1,-4,6)
Crystal Orientation
(9)
Fig. 11. The values of parameter Q and hardness of five Al–2Cu single-crystal specimens with various crystallographic orientations.
where sm is the threshold value of the applied stress. TEM-BF images in Fig. 10 show that when Al–2Cu single crystals with different crystallographic orientations are stress aged at the same stress magnitude (40 MPa), the stress orienting effect of them is various. When the (hkl) plane is one of the {100}-planes, stress is applied on {100} habit plane for θ′ precipitates, so the stress orienting effect is serious. For the {101}-planes, the applied stress is decomposed on two {100} habit planes, so the stress orienting effect is weaken. For the {111}-planes, the applied stress is decomposed on three {100} habit planes and the stress on one single habit plane is the minimum. So the stress orienting effect of specimen with {111} orientation is minimal. According to Eq. (9), a parameter q is introduced as
crystallographic orientation and the weaken orientation of the stress orienting effect. Consequently, the effect of the crystallographic orientation on the yield stresses of stress-aged specimens can be described by parameters β and q. The impact factor is represented by a parameter Q, Q is introduced as
q = cos λ
σy =
(10)
where λ is the minimum angle between the plane orientation of specimens and (111) orientation. The parameter q describes the effect of the axi of the applied stress during stress aging. The definition of parameter q can extend to other precipitation strengthening alloys, where λ is the minimum angle between the
Q = β⋅q = cos θ cos λ
(11)
The values of Q for specimens with different crystallographic orientation are listed in Table 5. The values of Q are compared with the mechanical properties in Fig. 3, and depicted in Fig. 11, the changes of Q fit well with the mechanical properties changes. The yield stress of stress-aged specimens may be written as
δQτp + σ0 η
(12)
5. Conclusion The effects of stress magnitude and crystallographic orientation on the yield stress of stress-aged Al–2Cu alloy single crystal
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X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364 −
specimens are investigated. The specimen with (1, 1, 6) orientation was stress-aged under 0, 15, 40, and 60 MPa. Specimens with five − −
−
− −
−
different orientations ( (1, 2, 6), (3, 1, 3), (1, 3, 3), (1, 1, 6), and (1, 4 , 6) ) were stress-aged under stress with the same magnitude of 40 MPa. The results of mechanical properties and TEM microstructure show that the yield stress of stress-aged specimens depends on the crystallographic orientation as well as the stress −
magnitude. The specimen with ( 1, 1, 6) orientation is near the θ′ precipitates (001) habit plane and the weaken orientation (111)plane of the stress orienting effect, so the impact factor Q is maximal and the yield stress is highest. However, specimen with −
( 1, 3, 3) orientation is far away from (001) habit plane and the weaken orientation (111)-plane, so the yield stress is lower. Modeling the precipitation strengthening of stress-aged Al–2Cu alloys with different crystallographic orientations as follows σy =
δQτ p η
+ σ0
τp = 0.13G { Dp =
b [fv 0.5 (Dp tp )0.5
+ 0.75 (Dp/tp )0.5fv + 0.14 (Dp /tp ) fv1.5 ]⋅ ln
0.87 (Dp / tp )0.5 r0
C Dp0 lnmσ c C
tp = tp0 lnmσ
c
k
α = 2(σ + 2 + c
experimental observations.
σc −0.5 ) k
Q = cos θ cos λ
The calculated yield stresses are in agreement with the
Acknowledgments The authors gratefully acknowledge the support from the Chinese National Science Foundation (Project no. 51375503).
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
A crystallographic orientation based model for describing the precipitation strengthening of stress-aged Al–Cu alloy Xiaobin Guo a, Yunlai Deng a,b,n, Jin Zhang b,c, Xinming Zhang a,b a
School of Materials Science and Engineering, Central South University, Changsha, China State Key Laboratory of High Performance and Complex Manufacturing, Central South University, Changsha, China c Light Alloy Research Institute, Central South University, Changsha, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 June 2015 Received in revised form 19 July 2015 Accepted 23 July 2015 Available online 29 July 2015
The effects of stress magnitude and crystallographic orientation on the mechanical properties of stress− aged Al–2Cu alloy single crystal specimens are investigated. The specimens with ( 1, 1, 6) plane orientation were stress-aged − and 60 MPa. Specimens with five different plane orientations − − − −under 0, 15,−40, ((1, 2, 6), (3, 1, 3), (1, 3, 3), (1, 1, 6), and (1, 4 , 6)) were stress-aged under stress with the same magnitude of 40 MPa. The results of mechanical properties and TEM microstructure show that the yield stress of stress-aged specimens depends on the crystallographic orientation as well as the stress magnitude. A model based on crystallographic orientation describes the precipitation strengthening of stress-aged Al– 2Cu alloy. The calculated yield stresses in the model fit well with the experimental observations. This model results not only provide important insight into solving the anisotropy problem attributed to precipitation strengthening, but also offer a benchmark for choosing the right range of stress in the manufacture of Al–Cu alloys. & 2015 Elsevier B.V. All rights reserved.
Keywords: Al–Cu alloys Single crystal Crystallographic orientation Stress-aging Model
1. Introduction Age forming is a combined age strengthening process with the forming of metals. This manufacture process has many applications in the aerospace industry [1–2]. In stress-aged aluminum alloys, fine precipitates disperse in the matrix and coarse precipitates form on the grain boundary, so the strength and corrosion resistance of alloys are improved compared with conventional cold-forming process [3–6]. But in some 2XXX series aluminum alloys, application of a stress during aging can significantly affect the orientation of precipitates, namely the stress-orienting effect, which leads to the anisotropy of strength properties [7–11]. This stress-orienting effect directly restricts the development of “ageforming” technique in manufacturing progress of 2XXX aircraft structures. Earlier investigations [7–9] on Al–Cu alloys indicated that the stress-orienting effect depends on the applied stress, temperature and alloy composition. Hosford and Agrawal [7] first studied the stress-orienting in Al–4Cu alloys single crystal. They found that θ’′ precipitates on habit planes perpendicular to the applied compressive stress were generated preferentially. But Eto et al. [8] n Corresponding author at: School of Materials Science and Engineering, Central South University, Changsha, China. E-mail address: [email protected] (Y. Deng).
http://dx.doi.org/10.1016/j.msea.2015.07.067 0921-5093/& 2015 Elsevier B.V. All rights reserved.
found the contrary results when Al–4Cu alloys single crystal were stress-aged under a lower temperature, where θ’′ precipitates were preferential orientation on habit planes parallel to the applied compressive stress. Based on the relationship between misfit inclusion and the applied stress they explained the stress-orienting effect. Later, Skrotzki et al. [10] found that there was a threshold value (16–19 MPa) of the applied stress that must be exceed to form the preferential oriented θ’′ precipitates in the 160 °C stress-aged Al–5Cu alloys samples. They explained the phenomenon with experiments and calculations, and they believed that stress induced the θ’′-plates nucleate preferentially on variants under compression as θ’′ precipitates have negative misfit with the Al matrix. In order to model the precipitation strengthening of stress-aged Al–Cu alloys, Zhu et al. [9] have studied the dependence of applied stress, temperature and alloy composition on stress-aged Al–Cu alloys single crystal systematically. They found that the stress-orienting effect of θ’′ precipitates increased with the increasing of applied stress, and the yield stresses of the stress-aged specimens were lower than those of stress-free aged specimens. However, they only investigated the Al–Cu alloys single crystal with {100} crystallographic orientation. Since the direction of applied stress depends on the crystallographic orientation, it is significant to study more single crystal specimens with various crystallographic orientations. In this study, we describe the results of our investigation on Al– Cu alloys single crystal with five different crystallographic
X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364
orientations. The resulting microstructure and mechanical properties were analyzed to study the influence of crystallographic orientation on stress-orienting effect. The purpose of this paper is to modeling the precipitation strengthening of stress-aged Al–Cu alloys based on crystallographic orientations.
359
Side
Single crystal Front 2cm
2. Experimental procedure Fig. 1. Macro-grains specimen of the Al–2Cu alloy.
Al–2Cu alloy single crystal specimens were prepared. The exact chemical composition is given in Table 1. Macro-grains specimens with grains up to 10 mm diameter were grown by pulling bars cut from the Al–2Cu alloy plate to 0.5–1.0 pct strain, followed by annealing in a forced-air furnace at 525 °C for 24 h, then repeating the strain-annealing cycle 8–10 times. One of the macro-grains specimens is shown in Fig. 1. Single crystal specimens were cut from the macro-grains bars by means of a spark–erosion–cutting machine. The orientations of the Al–2Cu alloy single crystal specimens were determined by Electron Backscattered Diffraction (EBSD) in the FEI Nova NanoSEM 230. IPF (inverse pole figure) maps of five single crystal specimens with various crystallographic orientations are shown in Fig. 2. After being solution treated at 525 °C for 2 h and quenched into water, specimens with various crystallographic orientations were aged at 180 °C for 66 h with applied compressive stresses. The aging condition and applied stress used for each specimen are given in Table 2. The aged specimens were then tested under compressive load to determine the yield stress. The yield stress was determined at 0.2% offset from the elastic response of compressive tests on specimens using a strain rate 10 2/s in a CSS44110 machine. The Vickers hardness of aged specimens was s measured from more than 10 indents in a huayin HV-5 microhardness tester. The precipitate structure of the specimens was characterized by means of transmission electron microscopy (TEM). Disks 3 mm in diameter were punched from the aged sheets, ground to a thickness of 0.1 mm, and twin-jet electro polished in a solution of HNO3 and methanol (1:3 in volume), at 25 °C and 20 V. TEM foils were examined using a JEM-2100F microscope operating at 200 kV. The features of the precipitate including the average radius, the average thickness and the distribution were determined by quantitative analysis of the TEM specimens.
3. Results The Vickers hardness and yield stress of five Al–2Cu singlecrystal specimens, which have different crystallographic orientations and were aged at 180 °C for 66 h under 40 MPa are given in Fig. 3. The change of Vickers hardness and yield stress with or-
−
and 60 MPa. The yield stress of stress-aged specimens with (1, 1, 6) plane-orientation decreased with external stress during aging. As the compressive stress increasing from 15 MPa to 60 MPa, the yield stress decreased from 100 MPa to 86 MPa (Fig. 6). This phenomenon is due to the applied stress induced preferentially oriented θ’′ precipitates, thereby the mechanical properties and anisotropy of the Al–2Cu alloy were affected. It can be seen from the TEM-BF images that the stress-orienting effect of θ’′ precipitates increased with the applied stress (Fig. 5). The volume fraction of θ’′ precipitates was calculated using the lever rule in Al–Cu phase diagram, and the result is fv ¼ 0.00621. The volume fraction, mean diameter and mean thickness of the parallel and perpendicular θ’′-plates were quantitatively analyzed and summarized in Table 3. In Table 3, the fv// is the volume fraction of θ’ precipitates on [001]Al direction, and the fv⊥ is the volume fraction of θ’′ precipitates on [010]Al direction. The volume fractions of fv// and fv⊥ were calculated by counting the number of θ’′-plates on [001]Al and [010]Al direction, where fv// þ fv⊥¼fv. Zhu [9] introduced a parameter to describe the degree of alignment of the θ′-plates. However, the parameter in this study describes the stress-orienting effect on the decrease of mechanical properties. A parameter α is introduced as
α=
2 (fv //⋅fv ⊥)0.5 fv
(1)
When specimen was aged without stress, the θ’-plates on [001]Al and [010]Al direction are almost the same (Fig. 5a). As fv //¼ fv⊥¼0.5fv , the parameter α ¼ 1, there is no stress-orienting effect. When fv//≠fv⊥, the parameter α o1, there is stress-orienting effect on θ’′ precipitates. It is indicated that the difference between fv// and fv⊥ increases with the increase of the magnitude of applied compressive stress (Fig. 5b–d), and the value of fv⊥ is greater than fv//. Consequently, the parameter α decreases and the stressorienting effect on θ’′ precipitates increases with the increase of the magnitude of applied stress.
−
ientation are almost the same. Specimen with ( 1, 3, 3) plane-orientation has the lowest hardness and yield stress, and the values −
of specimen with ( 1, 1, 6) plane-orientation are the highest. In order to illustrate the effect of crystallographic orientation, the Vickers hardness of specimens with different orientations is shown in the (001) pole figure (Fig. 4). −
The grain of single crystal specimen with ( 1, 1, 6) plane-orientation was divided into four parts to be stress-aged at 0, 15, 40 Table 1 Composition of the Al–2Cu alloy in weight percent. Alloys
Cu
Mg
Si
Fe
Zn
Al
Al–2Cu
1.4472
0.00
0.01
0.01
0.005
Balance
4. Modeling the precipitation strengthening of stress-aged Al– Cu alloy 4.1. Effect of stress magnitude An investigation was conducted on the effect of stress magni−
tude using the Al–2Cu single-crystal specimens, which have ( 1, 1, 6) plane-orientation and were aged at 180 °C for 66 h. The applied stress was 0 MPa, 15 MPa, 40 MPa and 60 MPa, respectively. The quantitative TEM analysis results listed in Table 3 was used in Zhu's [12] theory, as shown in Eq. (2) to calculated the strengthening shear stress τp associated with {100}-θ′-plates.
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− −
Fig. 2. The orientations of the Al–2Cu alloys single crystal specimens were determined by EBSD, (a) Euler's angles of (175°, 21°,206°) or {hkl} − plane orientation of ( 1, 2 ,6); (b) Euler's angles of (267°, 44°,72°) or −{hkl} plane orientation of (3,1,3); (c) Euler's angles of (347°, 46°,343°) or − −{hkl} plane orientation of ( 1,3,3); (d) Euler's angles of (4°, 13°,326°) or {hkl} plane orientation of (1,1,6); (e) Euler's angles of (133°, 35°,192°) or {hkl} plane orientation of (1, 4 ,6); (f) Color coded map type of the [001] IPF in aluminum. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
-1,-1,0
Table 2 The applied stress during stress aging for specimen with various orientations. Orientations Applied stress
− −
( 1, 2 ,6) – – 40 MPa –
(3,1,3) – – 40 MPa –
−
−
− −
( 1,3,3)
( 11,1,6)
( 1, 4 ,6)
– – – –
0 MPa 15 MPa 40 MPa 60 MPa
– – 40 MPa –
67.51 61.13 (-1,-4,6) 68.21 (-1,-2,6) 001
100
120
Hardness Yield Strength
110
-1,1,0 55.84
90
(-1,3,3)
100 80 90 70
80 70
60
010
60 50 40
(-1,-2,6)
(3,1,3)
(-1,3,3)
(-1,1,6)
68.03
100
110 Hardness after Stress-aging at different orientation
50
40
1,-1,0
(-1,1,6)
(313)
Vickers Hardness
Yield Strength / MPa
0,-1,0
-1,0,0
Fig. 4. The Vickers hardness of specimens with different orientations in the (001) pole figure.
(-1,-4,6)
Crystal Orientation Fig. 3. The Vickers hardness and yield stress of five Al–2Cu single-crystal specimens with various crystallographic orientations after stress aging at 180 °C for 66 h under 40 MPa.
τp = 0.13G ⋅ ln
b ⎡ f 0.5 + 0.75 (D /t )0.5f + 0.14 (D /t ) f 1.5 ⎤ p p p p v ⎦ ⎣ v (Dp tp )0.5 v
0.87 (Dp /tp )0.5 r0
(2)
where G is the shear modulus, b the magnitude of the Burgers vector, r0 the interaction inner cut-off radius of the dislocation, and fv the volume fraction, Dp the mean diameter and tp the mean
X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364
020 000
361
020 000
002
002
020
020
000
000
002
002
−
Fig. 5. Bright-field TEM images and diffraction patterns of the specimen with ( 1,1,6) orientation that were compressive stress-aged at 180 °C for 66 h under (a) 0 MPa; (b) 15 MPa; (c) 40 MPa; (d) 60 MPa.
120
Table 3 The diameter and thickness data obtained by quantitative TEM and image analysis of the θ’ precipitates in the Al–2Cu alloy compressive stress-aged at 180 °C for 66 h under different stress. The volume fraction of θ’′ precipitates was calculated using the lever rule in Al–Cu phase diagram. D//
D⊥
t//
t⊥
fv//
fv ⊥
α
15 MPa 40 MPa 60 MPa
288 155 174
204 171 175
3.6 4.7 3.0
5.6 3.6 2.9
0.0029 0.0017 0.0007
0.0033 0.0045 0.0055
0.996 0.812 0.632
thickness of the θ′-plates. Using the results in Table 3, Dp ¼(D// þD⊥)/2, and tp ¼(t//þ t⊥)/2. The yield stress sy can be calculated from the strengthening shear stress τp according to Eq. (3)
σy =
α⋅τp + σ0 η
(3)
where η is the Schmid factor for the single-crystal specimens, s0 the contribution of Cu solid solution hardening. The value of s0 is set at 60 MPa for the aged Al–2Cu alloys [9]. The yield stress sy of our calculations results are compared with the experimental results (Fig. 6). The effect of applied stress on the yield stress of stress-aged specimens comes from two sides. The precipitates in stress-aged specimens are dispersed distribution. The θ’′ precipitates in stressaged specimens (Fig. 5b–d) disperse finer than in the stress-freeaged specimens (Fig. 5a). The data listed in Table 3 show that the diameter and thickness of θ′ precipitates decrease with the increasing of applied stress. So the strengthening stress is greater
Yield Strength/ MPa
Applied stress
Experiment Computer modeling
110 100 90 80 70 60 10
20
30
40
50
60
Applied Stress/ MPa Fig. 6. The calculated and experimental yield stresses of Al–2Cu single-crystal − specimens with ( 1,1,6) orientation after stress aging under different stress.
with finer precipitates according to Eq. (2). According to the quantitative data of θ′ precipitates in Table 3, the relationship between applied stress and size of θ′ precipitates could be built. The effect of stress on diameter and thickness of θ′ precipitates may be written as
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120
Experiment Calculated by the equation (6)
Yield Strength/ MPa
110 100 90 80
Vickers Hardness/HV
55
50
45
(-1,1,6) (3,1,3) (-1,3,3) (-1,-4,6) (-1,-2,6)
40
35
70 0
20
40
60
80
100
Aging Time t/h
60 10
20
30
40
50
Fig. 8. The Vickers hardness curves of the Al–2Cu alloy single crystal with different orientations during aging at 180 °C.
60
Applied Stress/ MPa Fig. 7. The calculated yield stresses by Eq. (6) compared with the experiment re− sults of Al–2Cu single-crystal specimens with ( 1,1,6) orientation after stress aging under different stress.
Dp = Dp 0
tp = tp0
Cm ln σc
Cm ln σc
(4)
(5)
δτp + σ0 η
(-1,-4,6) (-1,-2,6) -1,1,0
1,-1,0
001
(-1,1,6) (-1,3,3) (3,1,3) 100
010
110
(6)
where k is the constant of the composition and aging temperature, and the value of k is 7.8 for Al–2Cu alloy aged at 180 °C. When aging without stress, the value of δ is 1, so there is no stress-orienting effect. With the increasing of applied stress, the value of δ is less than 1 and decrease. The yield stresses sy of our calculations by Eq. (6) are compared with the experimental results (Fig. 7). It can be shown from Figs. 6 and 7 that the parameter δ is more appropriate than α. The parameter δ can well describe the stressorienting effect on the decrease of yield stress. So the parameter α can be replaced with δ, Eq. (3) can be written as
σy =
0,-1,0
-1,0,0
where Dp0 is the diameter of θ′ precipitates in stress-free aged specimen; tp0 is the thickness of θ′ precipitates in stress-free aged specimen; sc is the applied stress during stress aging; Cm is the constant of the matrix and the precipitates, and the value of Cm is 2.6 of θ’′ precipitates. However, when aging under stress, the stress-orienting effect of θ’′ precipitates occurs. So the yield stresses of stress-aged specimens decrease. A parameter δ that describes the stress-orienting degree can be written as −0.5 ⎛k σ ⎞ + 2 + c⎟ δ = 2⎜ ⎝ σc k⎠
-1,-1,0
Fig. 9. The position of different crystallographic orientation in a (001) pole figure.
Fig. 8. The hardness of aged specimens comes to the highest at 66 h, but the values are various for different crystallographic orientation, especially at the stage of peak-aging and over-aging. The −
peak hardness of aged-specimen with (1, 1, 6) plane-orientation is −
the highest, while the specimen with ( 1, 3, 3) orientation is the lowest. The position of different crystallographic orientation is shown in a (001) pole figure (Fig. 9). From Figs. 8 and 9, we found that the peak hardness of specimen with orientation near (001) is −
(7)
4.2. Effect of the crystallographic orientation The effect of crystallographic orientation on the yield stress of stress-aged specimens comes from two sides. With different crystallographic orientation, the yield stress of specimens after stress-free aging is different. Since the compressive yield stress were tested on the plane orientation of specimens, the difference of yield stress comes from the anisotropy of single crystal. Considering the effect of different compressive tests orientation, single crystal specimens with different orientation are aged without stress at 180 °C, and the hardness curves are shown in
higher. (1, 1, 6) orientation is the nearest of five pairs specimens, so −
the peak hardness is the highest. But ( 1, 3, 3) and (3, 1, 3) orientation are further from the (001), the peak hardness is lower. This phenomenon could be explained from the relationship between precipitation strengthening and habit plane. θ′ precipitates forms on {100} habit planes, so the precipitation Table 4 The values of parameter β between the crystallographic orientation and {100} habit planes of different plane orientations. Orientations
(001)
β
1
−
− −
− −
( 1,1,6)
( 1, 2 ,6)
( 1, 4 ,6)
0.973
0.937
0.824
(3,1,3) 0.688
−
( 1,3,3) 0.688
X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364
θ//
θĵ
θ//
θ//
θĵ
363
θ//
θĵ
θĵ
Fig. 10. Bright-field TEM images of single crystal specimens with different −crystallographic orientation that were compressive stress-aged at 180 °C for 66 h under 40 MPa; − − − − (a) (3,1,3) orientation; (b) ( 1, 4 ,6) orientation; (c) ( 1, 2,6) orientation; (d) ( 1,3,3) orientation.
(8)
where θ is the minimum angle between the plane orientation of specimens and (001) orientation. The parameter β describes the effect of anisotropy of aged single crystal specimens. The values of β for different specimens are listed in Table 4, the value is 1 for −
Orientations β q Q
−
− −
− −
( 1,1,6)
( 1, 2,6)
( 1, 4 ,6)
0.973 0.749 0.73
0.937 0.812 0.76
0.824 0.872 0.72
(3,1,3) 0.688 0.927 0.64
−
( 1,3,3) 0.688 0.662 0.46
−
(001) orientation. The value of (1, 1, 6) orientation is higher than (1, 3, 3) and (3, 1, 3) orientation, which fit well with the peak hardness changes in Fig. 8. The definition of parameter β can extend to other precipitation strengthening alloys, where θ is the minimum angle between the crystallographic orientation and habit plane. The second side effect of the crystallographic orientation is the axi of the applied stress during stress aging. When single crystal specimen with (hkl) orientation is stress aged, the stress is applied on the (hkl) plane and the axi of the stress is [hkl]. There was a threshold value of the applied stress that must be exceed to form the preferential oriented θ′ precipitates [10]. So the criterion for stress orienting effect occurring is introduced as
⎧ h ⋅σ ≥ σm ⎪ 2 ⎪ h + k 2 + l2 ⎪ ⎪ k ⋅σ ≥ σm ⎨ or ⎪ h2 + k 2 + l2 ⎪ l ⎪ or ⋅σ ≥ σm ⎪ 2 ⎩ h + k 2 + l2
Table 5 The values of parameter β, q and parameter Q of different plane orientations.
100
1.0
Hardness Q Factor
0.9
90
0.8 0.7
80
0.6 0.5
70
0.4 60
0.3 0.2
Vickers Hardness
β = cos θ
β is
Q Factor
strengthening on (001) orientation is higher. A parameter introduced as
50
0.1 0.0
40
(-1,-2,6)
(3,1,3)
(-1,3,3)
(-1,1,6)
(-1,-4,6)
Crystal Orientation
(9)
Fig. 11. The values of parameter Q and hardness of five Al–2Cu single-crystal specimens with various crystallographic orientations.
where sm is the threshold value of the applied stress. TEM-BF images in Fig. 10 show that when Al–2Cu single crystals with different crystallographic orientations are stress aged at the same stress magnitude (40 MPa), the stress orienting effect of them is various. When the (hkl) plane is one of the {100}-planes, stress is applied on {100} habit plane for θ′ precipitates, so the stress orienting effect is serious. For the {101}-planes, the applied stress is decomposed on two {100} habit planes, so the stress orienting effect is weaken. For the {111}-planes, the applied stress is decomposed on three {100} habit planes and the stress on one single habit plane is the minimum. So the stress orienting effect of specimen with {111} orientation is minimal. According to Eq. (9), a parameter q is introduced as
crystallographic orientation and the weaken orientation of the stress orienting effect. Consequently, the effect of the crystallographic orientation on the yield stresses of stress-aged specimens can be described by parameters β and q. The impact factor is represented by a parameter Q, Q is introduced as
q = cos λ
σy =
(10)
where λ is the minimum angle between the plane orientation of specimens and (111) orientation. The parameter q describes the effect of the axi of the applied stress during stress aging. The definition of parameter q can extend to other precipitation strengthening alloys, where λ is the minimum angle between the
Q = β⋅q = cos θ cos λ
(11)
The values of Q for specimens with different crystallographic orientation are listed in Table 5. The values of Q are compared with the mechanical properties in Fig. 3, and depicted in Fig. 11, the changes of Q fit well with the mechanical properties changes. The yield stress of stress-aged specimens may be written as
δQτp + σ0 η
(12)
5. Conclusion The effects of stress magnitude and crystallographic orientation on the yield stress of stress-aged Al–2Cu alloy single crystal
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X. Guo et al. / Materials Science & Engineering A 644 (2015) 358–364 −
specimens are investigated. The specimen with (1, 1, 6) orientation was stress-aged under 0, 15, 40, and 60 MPa. Specimens with five − −
−
− −
−
different orientations ( (1, 2, 6), (3, 1, 3), (1, 3, 3), (1, 1, 6), and (1, 4 , 6) ) were stress-aged under stress with the same magnitude of 40 MPa. The results of mechanical properties and TEM microstructure show that the yield stress of stress-aged specimens depends on the crystallographic orientation as well as the stress −
magnitude. The specimen with ( 1, 1, 6) orientation is near the θ′ precipitates (001) habit plane and the weaken orientation (111)plane of the stress orienting effect, so the impact factor Q is maximal and the yield stress is highest. However, specimen with −
( 1, 3, 3) orientation is far away from (001) habit plane and the weaken orientation (111)-plane, so the yield stress is lower. Modeling the precipitation strengthening of stress-aged Al–2Cu alloys with different crystallographic orientations as follows σy =
δQτ p η
+ σ0
τp = 0.13G { Dp =
b [fv 0.5 (Dp tp )0.5
+ 0.75 (Dp/tp )0.5fv + 0.14 (Dp /tp ) fv1.5 ]⋅ ln
0.87 (Dp / tp )0.5 r0
C Dp0 lnmσ c C
tp = tp0 lnmσ
c
k
α = 2(σ + 2 + c
experimental observations.
σc −0.5 ) k
Q = cos θ cos λ
The calculated yield stresses are in agreement with the
Acknowledgments The authors gratefully acknowledge the support from the Chinese National Science Foundation (Project no. 51375503).
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