Physically based constitutive analysis and microstructural evolution of AA7050 aluminum alloy during hot compression

Materials and Design 107 (2016) 277–289

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Physically based constitutive analysis and microstructural evolution of AA7050 aluminum alloy during hot compression S. Wang a, J.R. Luo a, L.G. Hou a,⁎, J.S. Zhang a, L.Z. Zhuang a,b,⁎⁎ a b

State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing 100083, PR China Tata Steel, 1970 CA IJmuiden, Netherlands

a r t i c l e

i n f o

Article history: Received 20 April 2016 Received in revised form 29 May 2016 Accepted 7 June 2016 Available online 08 June 2016 Keywords: 7050 aluminum alloy Constitutive model Dynamic recrystallization Grain boundary sliding Dislocation creep

a b s t r a c t The hot compression tests of AA7050 aluminum alloy were conducted under conditions of 603–693 K and 0.001– 10 s−1, and the related microstructures were observed. Physically based constitutive analysis was conducted to describe the flow behaviors, which can relate the microstructural evolution with flow behaviors for high stacking fault energy (SFE) and/or precipitation-strengthened alloys. A revised model considering the coupling effects of lattice diffusion and grain boundary diffusion was proposed to characterize the transition of diffusion mechanisms under different deformation conditions. The main diffusion mechanism is determined as lattice diffusion at 633–693 K and grain boundary diffusion at 603 K. The microstructural evolution can be reflected by the deviation of creep exponent n' from the theoretical value (n'=5). The reasons for the creep exponent n' N 5 could be related to the change of internal stress and creep rate by dynamic precipitates at lower temperatures. At higher strain rates, it could be related to the impediment of dislocations motion by defects and the change of rate controlling mechanism. The operation of grain boundary sliding (GBS) may lead to n' b 5 at higher temperatures and lower strain rates. Moreover, the mechanisms of dynamic recrystallization under wide conditions and highstrain-rate superplasticity were discussed. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction The Al-Zn-Mg-Cu aluminum alloys have been widely used for structural applications in automobile and aerospace industries due to their high strength-to-density ratio, high toughness and good corrosion resistance. The good mechanical properties and desired microstructural characteristics can be resulted from appropriate deformation conditions, such as temperature, strain rate and degree of deformation. The influence of these deformation parameters on microstructural evolution can be characterized by relating the dynamic recrystallization (DRX) with flow behaviors in the form of constitutive analyses for low stacking fault energy (SFE) materials [1] or by relating power dissipation and flow instability with flow behaviors in the form of processing maps [2]. Therefore, a deeper understanding of flow behaviors can play an important role in optimizing the design of metal-forming processes and controlling the microstructural evolution during hot working. As summarized in Table 1, two types of constitutive models are often used to describe the flow behaviors [3]: (1) phenomenological constitutive models; (2) physically based constitutive models. The Arrhenius⁎ Corresponding author. ⁎⁎ Correspondence to: L.Z. Zhuang, Tata Steel, 1970 CA IJmuiden, Netherlands. E-mail addresses: [email protected] (L.G. Hou), [email protected] (L.Z. Zhuang).

http://dx.doi.org/10.1016/j.matdes.2016.06.023 0264-1275/© 2016 Elsevier Ltd. All rights reserved.

type model [4] and Johnson-Cook model [5], as two widely used phenomenological models, have been successfully applied to predict the flow behaviors of many materials [6,7]. However, the materials constants in these models have less metallurgical meaning and cannot reflect the microstructural evolution. As a physically based model, the Zerilli-Armstrong model [8] has been widely employed to describe the dislocation mechanism for BCC and FCC metals. In this type model, the coupling effects of strain-hardening, strain-rate hardening and thermal softening on the flow behaviors are considered [9], however less information on microstructural evolution can be obtained. For the Estrin and €m [11] model, another widely-used and physMecking [10] and Bergstro ically-based model, its greatest advantage is to relate the flow stress with the volume fraction of DRX. Essentially, this model considering the influence of the work-hardening and dynamic softening on flow stress is based on the variation of dislocation density [12]. However, the hypothesis that the flow stress is only influenced by the work-hardening and dynamic restoration (i.e. dynamic recovery (DRV) and/or DRX) limits its application in some alloys, such as precipitationstrengthened alloys. In addition, the DRX volume fraction equation used in this model is based on the Avrami equation which is suitable for discontinuous DRX (DDRX, in the form of nucleation and growth). For high SFE metals/alloys (e.g. aluminum alloys), the main DRX mechanism during hot deformation is continuous DRX (CDRX), which occurs by progressive subgrain rotation without grain boundary migration

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Table 1 The advantages and disadvantages of four widely-used constitutive models. Model types Arrhenius-type [6] Johnson-Cook [7] Zerilli-Armstrong [9] Estrin and Mecking and Bergström [12]

Model descriptions

Advantages and/or disadvantages 1=n

2=n

0:5

_ =ARTÞ þ ½ðεQ _ =ARTÞ þ 1 g σ ¼ α1 ; ln fðεQ _ ε_ r ÞÞ½1−ðT−T r Þ=ðT m −T r Þ σ ¼ ðA þ Bε n Þð1 þ Clnðε= _ for FCC σ ¼ C 0 þ C 2 ε0:5 ; expð−C 3 T þ C 4 T ; ln εÞ _ þ C 5 εn for BCC σ ¼ C 0 þ C 1 ; expð−C 3 T þ C 4 T ; ln εÞ −Ωε 0.5 2 2 2 ] ε ≤ εc σ = σrec = [σsat + (σ0 − σsat)e σ = σrec − (σsat − σss)Xdrx ε ≥εcXdrx = 1 − exp [−kd((ε − εc)/εp)nd]

These three models can be applied for many materials successfully with simple forms, but they cannot reflect the microstructural evolution during deformation. It can be used to relate the DRX with flow behaviors for low SFE metals/alloys, but it may be unsuitable for high SFE and/or precipitation-strengthened metals/alloys.

(The definition of materials constants in these models can be referred to the corresponding references.)

(GBM) [13,14]. Thus, this model can reflect microstructural evolution during deformation for low SFE materials, but it may be unsuitable for metals/alloys with high SFE such as aluminum alloys. In recent years, the hot deformation behaviors of Al-Zn-Mg-Cu alloys have been extensively studied, including constitutive analysis [15], hot workability [16], dynamic precipitates [17] and DRX mechanisms [18], etc. However, less researches were focused on relating the microstructural evolution with constitutive analysis for such high SFE metals/alloys and/or precipitation-strengthened alloys. So it is useful and necessary to construct a physically constitutive model which can reflect the microstructural evolution for metals/alloys such as Al-Zn-Mg-Cu alloys. Cabrera et al. [19–22] proposed a physically based constitutive model with a creep exponent (n = 5) to describe the flow behaviors successfully as long as the deformation mechanism is controlled by dislocation glide and climb. In this model, the Young's modulus (E) and the self-diffusion coefficient (D) are taken as function of temperatures (T), and the relationship can be expressed as: _ ðT Þ ¼ B½ sinhðασ =EðT ÞÞ5 ε=D

ð1Þ

where ε_ and σ are the strain rate ( s−1 ) and flow stress (MPa), respectively. B and α are materials constants, and 5 represents the theoretical value of the creep exponent n. In this study, a revised model based on Eq. (1) was constructed in an attempt to determine the main diffusion mechanisms (grain boundary diffusion or lattice diffusion) under different deformation temperatures. Simultaneously, the microstructural evolution during hot deformation of AA7050 aluminum alloy was characterized and related with the variation of the creep exponent. 2. Experimental materials and procedures The compression specimens with 10 mm in diameter and 15 mm in height were machined from commercial AA7050 aluminum alloy plate according to ASTM: E209. Before compression tests, all samples were treated at 748 K for 2 h, and then quenched into room-temperature water immediately. Hot compression tests were conducted on a Gleeble-3500 thermo-simulator at temperature range of 633–693 K and strain rate range of 0.001–10 s−1. Before compression, each specimen was heated to the preset temperature with a heating rate of 2 K/s and held at that temperature for 5 min to minimize thermal gradients. Thin graphite sheets were used to reduce frictions, and all the deformed specimens after compression were quenched into room-temperature water immediately for microstructural observation. The microstructures of some samples were observed on the center of the axial section by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and electron backscattered diffraction (EBSD) technique. The SEM samples were firstly mechanical-polished and then etched with the Keller solution. TEM samples were prepared by twin-jet electro-polishing using the solution of HNO3 and methanol (1:3 in volume) and conducted on a Tecnai G2 F30 S-TWIN TEM. The EBSD samples were electro-polished in a solution of 5% perchloric acid and 95% ethanol at 30 V for 20 s. The EBSD data were analyzed through HKL Channel 5 software. The low angle grain boundaries (LAGBs, grain

boundary orientation angle: 2°–15°) were marked by thin red lines for 2°–5° and thin fuchsia lines for 5°–15°, and the high angle grain boundaries (HAGBs, grain boundary orientation angle N15°) were marked by thick black lines in all the EBSD restructured maps. The Kernel average misorientation (KAM) maps represent the local misorientation which means an average misorientation of a point with all of its neighboring points in a grain. The average misorientation of a point was calculated with a provision that misorientation exceeding some tolerance value (5°) are excluded. 3. Results and discussion 3.1. Flow behaviors The flow stress curves of AA7050 aluminum alloy under the temperature range of 603–693 K and the strain rate range of 0.001–10 s−1 are gained from Ref. [13] and displayed in Fig. 1. Generally, the flow stresses increase with increasing strain rates or decreasing deformation temperatures. The flow stress curves of aluminum alloy show an obvious difference to that of low SFE materials such as austenitic steel [13]. At lower deformation temperature (603 K and 0.001 s−1 in Fig. 1(a)), the DRV may be the main softening mechanism. However, the flow stresses increase to peak stress and then decrease to a steady stress continuously, which is similar to the flow curves of low SFE materials undergoing DRX. In the case of DRX (e.g. 693 K and 0.001 s−1 in Fig. 1(a)), the flow stress curve keeps constant after reaching peak stress, which is the typical feature of low SFE materials under condition of DRV. With microstructural observation, the DRX is easy to occur at higher temperatures and low strain rates due to higher rate and more times for dislocation motion. In addition, at higher strain rates (N 1 s−1), the deformation heating can be produced and promote the occurrence of DRV and/or DRX [23]. So the flow curves show dynamic softening at lower and higher strain rates. At intermediate strain rates (e.g. 0.1 s−1 in Fig. 1(c) and 1 s−1 in Fig. 1(d)), the flow stresses increase with increasing strains (from 0.35 to 0.65 for 0.1 s−1 and from 0.1 to 0.65 for 1 s−1), which may be related to the combined effects of less DRV and/or DRX and the Orowan strengthening mechanisms caused by dynamic precipitates [13]. 3.2. Original physically based model with considering lattice diffusion The activation energy represents the level of an energy barrier to be surmounted in some atomistic mechanisms such as diffusion, deformation, microstructures and so on [24]. Based on the result of Arrhenius model analysis [13], the apparent hot working activation energy, which assumed that the microstructure remained constant and ignored the underlying atomic mechanisms during hot deformation, was calculated as 200 KJ mol−1 for AA7050 aluminum alloy. This value is higher than the self-diffusion activation energy of aluminum, no matter the activation energy of lattice diffusion (142 KJ mol−1) or grain boundary diffusion (84 KJ mol−1) [25]. Some researchers have pointed out that the variation of Young's modulus with temperatures may be one of the reasons caused the deviation of activation energy from self-diffusion activation energy and the creep exponent n from the theoretical value

S. Wang et al. / Materials and Design 107 (2016) 277–289

279

Then the unified equation can be expressed as: _ ðT Þ ¼ B½ sinhðασ =EðT ÞÞn ε=D

ð2Þ

And the relationships between temperature and self-diffusion coefficient (D) [20–22,27] and the Young's modulus (E) [22] can be expressed as: DðT Þ ¼ D0 expð−Q sd =RT Þ

ð3Þ


 T M dμ ðT−300Þ EðT Þ ¼ 2ð1 þ vÞμ ¼ 2ð1 þ vÞμ 0 1 þ μ 0 dT TM

ð4Þ

where D(T) is the self-diffusion coefficient of aluminum and supposed to be the coefficient of lattice diffusion [19–22,27]. D0 is the pre-exponential coefficient of lattice diffusion in aluminum and equals to 1.7 × 10−4 according to the Frost and Ashby tables [25]. Qsd is the activation energy for self-diffusion and equals to 142 KJ mol−1 for lattice diffusion in aluminum [25]. R is the universal gas constant (8.314 J mol−1 K−1). T is the deformation temperature. v is the Poisson's coefficient (0.33), and μ is the shear modulus, μ0 is the shear modulus at 300 K (2.54×104 MPa for aluminum) [25]. TM is the melting temperature (933 K for aluminum). The term TμM dμ equals to −0.5 [25]. dT 0

In order to obtain the value of three unknown parameters (α, n and B), following equations were introduced and a linear regression method was applied [21,27]: _ ðT Þ ¼ B1 ½σ =EðT Þn1 ε=D

ð5Þ

_ ðT Þ ¼ B2 expðβσ=EðT ÞÞ ε=D

ð6Þ

in which, B1 , B2 , n1 , β are material constants, α = β/n1. ε_ and σ are the strain rate ( s−1 ) and the flow stress (MPa), respectively. Taking the logarithm of both sides of Eqs. (5) and (6), and the following equation can be given:

Fig. 1. Flow stress curves of AA7050 aluminum alloy under different conditions: (a) 0.001 s−1, (b) 0.01 s−1, (c) 0.1 s−1, (d) 1 s−1, (e) 10 s−1.

[19–22,25]. As mentioned in Section 1, a physically based model with a creep exponent n = 5 can be used to describe the flow behaviors in terms of atomic mechanisms when the dependence of Young's modulus (E) and self-diffusion coefficient (D) on temperature are taken into account [19–22,26,27]. However, n = 5 is true in the case that the deformation mechanism is only controlled by the glide and climb of dislocations. The microstructural evolution such as dynamic precipitates and DDRX can lead to the change of the creep exponent n from the theoretical value [20,21], and thus the creep exponent n should be reasonably treated as a variable rather than a constant [20–22,27].

_ lnðε=DðTÞ Þ ¼ ln B1 þ n1 lnðσ=EðTÞÞ

ð7Þ

_ ðT ÞÞ ¼ ln B2 þ βσ=EðT Þ ln ðε=D

ð8Þ

Taking the flow stress data at the strain of 0.1 as an example, the values of material constants n1 and β can be obtained from the slopes of _ _ the fitting lines ln(ε=DðTÞ) − ln(σ/E(T)) in Fig. 2 (a) and ln(ε=DðTÞ) − σ/E(T) in Fig. 2(b), respectively. Then the parameter α is calculated as 672.39412. Then, taking the logarithm of both sides of Eq. (2), the remaining two material constants n and B can be obtained from the slopes _ and intercepts of lines ln( ε=DðTÞ) − ln[sinh(ασ/E(T))] in Fig. 2(c), respectively. Then the mean values of n and lnB are calculated as 5.690518439 and 31.6212175. With repeating above solution procedure, the parameters of α, n and lnB under strains from 0.1 to 0.65 with an interval of 0.05 can be obtained. Then the relationships between material constants (α, n and lnB) and strains can be expressed by a 5th order polynomial by polynomial fitting in Fig. 3. Then the resultant constitutive equations can be written as: α ε ¼ 650:7202 þ 307:0895ε  1175:1484ε 2 þ 2259:4464ε3  2472:7593ε4 þ 797:9873ε5

ð9Þ

nε ¼ 6:6090−15:6675ε þ 83:2105ε 2 −217:0850ε3 þ 266:7537ε4 −124:4603ε5

ð10Þ

ln Bε ¼ 31:7864−1:8489ε þ 2:1216ε2 þ 3:8350ε3 −14:5327ε4 þ 11:1891ε5

ð11Þ

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_ _ _ Fig. 2. Relationships among different parameters: (a) ln(ε=DðTÞ) − ln(σ/E(T)), (b) lnðε=DðTÞÞ − σ/E(T), (c) ln(ε=DðTÞ) − ln[sinh(ασ/E(T))].

Fig. 3. Relationships between true strain (ε) and α (a), n (b) and lnB (c) by polynomial fitting.

S. Wang et al. / Materials and Design 107 (2016) 277–289

σ¼


  _ ðT Þ− lnBε EðT Þ ln ½ε=D arcsinh exp nε αε

281

0

ð12Þ

ε_ ¼ Deff ðT ÞB2 expðβ0 σ=EðT ÞÞ

ð21Þ

Substituting Eq. (16) into Eq. (19), then: With Eqs. (9)–(12), the flow stresses can be calculated under different conditions and the predictability of this model will be discussed later. 3.3. Revised physically based model with considering lattice diffusion and grain boundary diffusion For the particle or precipitation-strengthened alloys, the particle/ precipitate-matrix interfaces are the preferential sites for voids nucleation, and precipitate/particle can also hinder the dislocation motion. As a result, the stress concentrations would be formed at the particle/ precipitate-matrix interfaces since the particle and incoherent precipitate cannot accommodate sliding strain by slip, and it should be relaxed by diffusional flow for homogeneous deformation [28]. In order to study the relaxation theory of stress produced at the particle/precipitate-matrix interfaces during deformation, Humphreys and Kalu [29] pointed out that the main thermal diffusion mechanism would be changed from surface diffusion (i.e. grain boundary diffusion) at low deformation temperatures to bulk diffusion (i.e. lattice diffusion) at high deformation temperatures in a two-phase aluminum alloy. However, the physically based model in Section 3.2 is constructed on the mechanism of lattice diffusion, in which the transition of diffusion mechanism from high to low deformation temperatures cannot be reflected. From the metallurgical standpoint, to identify the main diffusion mechanism under different deformation temperatures by constitutive analysis can provide an approach to understand the intrinsic atomic mechanisms. Therefore, a revised physically model based on Eqs. (2)–(4) was proposed as follows. In Eq. (2), the term D(T) represents that the self-diffusion mechanism is controlled by lattice diffusion, however, the effective self-diffusion mechanism should be the coupling effects of lattice diffusion and grain boundary diffusion. Therefore, the revised model can be written as: 0

0

_ eff ðT Þ ¼ B ½ sinhðα 0 σ=EðT ÞÞn ε=D 0

_ eff ðT Þ ¼ B1 ½σ =EðT Þ ε=D

0 n1

_ eff ðT Þ ¼ B2 expðβ0 σ =EðT ÞÞ ε=D

ð15Þ

Deff ðT Þ ¼ k1 DL ðT Þ þ k2 DGB ðT Þ

ð16Þ

DL ðT Þ ¼ D0;L expð−Q L =RT Þ

ð17Þ

DGB ðT Þ ¼ D0;GB expð−Q GB =RT Þ

ð18Þ

ð22Þ

where k'1 and k'2 are the material constant (k'1 = B 'k1 and k'2 = B ' k2). Similar to the solution procedures in Section 3.2, taking the flow stress data at the strain of 0.1 as an example, n'1 and β' can be obtained from the slopes of the plots of ln ε_ − ln(σ/E(T)) in Fig. 4(a) and ln ε_ − σ/ E(T) in Fig. 4(b), respectively. Then, substituting the calculated result of α' into Eq. (22) and taking the logarithm of both sides of it, the values of n' and k'1DL(T) + k'2DGB(T) can be obtained from the slopes and intercepts of plots of ln ε_ − ln[sinh(α'σ/E(T))] in Fig. 4(c). Then, the values of k'1 and k'2 at a specific strain can be obtained by the binary linear regression analysis (z(x, y) =ax+ by + 0). Similarly, the values of α', n', k'1 and k'2 were obtained at the strain range from 0.1 to 0.65 with an interval of 0.05 and listed in Table 2. By conducting polynomial fitting in Fig. 5, all these constants can be treated as function of strain (ε) and expressed in the form of the 5th order polynomial (Eqs. (23)–(27)). Then the resultant equations can be summarized as: 0

α ε ¼ 650:7202 þ 307:0895ε−1175:1484ε2 þ 2259:4464ε3 −2472:7593ε 4 þ 797:9873ε 5

ð23Þ

n0ε ¼ 6:6090−15:6675ε þ 83:2105ε 2 −217:0850ε3 þ 266:7537ε4 −124:4603ε5

ð24Þ

0

k1;ε ¼ 1:1588  1014 −8:4992  1014 ε þ 4:1335  1015 ε2 −1:0386 ð25Þ  1016 ε3 þ 1:2656  1016 ε4 −5:9093  1015 ε5 0

k2;ε ¼ 1:0541  1018 þ 2:0274  1019 ε−1:4416  1020 ε2 þ 4:3060 ð26Þ  1020 ε3 −5:8131  1020 ε4 þ 2:8878  1020 ε5

ð13Þ ð14Þ

0

  n0 ε_ ¼ B0 k1 DL ðT Þ þ B0 k2 DGB ðT Þ ½ sinhðα 0 σ =EðT ÞÞ  0  0 n 0 ¼ k1 DL ðT Þ þ k2 DGB ðT Þ ½ sinhðα 0 σ =EðT ÞÞ

σ¼

" EðT Þ arcsinh exp α 0ε

 0 !# 0 ln ðε_ Þ− ln k1 DL ðT Þ þ k2 DGB ðT Þ n0ε

ð27Þ

Thus, the flow stresses under different deformation conditions can be predicted by equations listed above. In order to compare the predictability of these two physically based models, a comparison between experimental and predicted data was conducted by measuring the average absolute relative error (AARE) and the correlation coefficient (R) [27]. The equations for calculating R and AARE values are expressed as: N

where, α' =β'/n'1, Deff(T) represents the effective diffusion coefficient of aluminum, which depends on temperature. DL(T) and DGB(T) are coefficients of the lattice diffusion and grain boundary diffusion, respectively. D0 , L is the pre-exponential coefficient of lattice diffusion (1.7 × 10−4) and QL is the activation energy for lattice diffusion (142 KJ mol− 1) [25]. D0 , GB and QGB are the pre-exponential coefficient (5.0 × 10− 14) and activation energy (84 KJ mol−1) of grain boundary diffusion, respectively [25]. k1, k2, B'and α' are material constants. The value of the creep exponent n' equals that of n. In this model, Deff(T) is taken as a constant at a specific deformation temperature, so Eqs. (13)–(15) can be rewritten as: 0

n ε_ ¼ Deff ðT ÞB0 ½ sinhðα 0 σ =EðT ÞÞ 0

0

ε_ ¼ Deff ðT ÞB1 ½σ =EðT Þn1

ð19Þ ð20Þ

∑i¼1 ðEi −EÞðP i −P Þ R ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N N ∑i¼1 ðEi −EÞ2 ∑i¼1 ðP i −P Þ2 AAREð% Þ ¼

  1 N Ei −P i   100% ∑ N i¼1 Ei 

ð28Þ

ð29Þ

where, Ei is the experimental value and Pi is the predicted value. E and P are the mean values of E and P, respectively. N is the total number of data used. As seen from Fig. 6, the correlation between experimental and predicted data by two models has been performed. Most data points lie closely to the best fitting line, and the R values for the original model and revised model are 0.987 and 0.959, respectively. Meanwhile, the AARE values are calculated as 7.97% for the original model and 8.23% for the revised model. In summary, the two models can describe the flow stress well, and the original model considering only lattice

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S. Wang et al. / Materials and Design 107 (2016) 277–289

0

_ ln½ sinhðα σ =EðTÞÞ. Fig. 4. Relationships among different parameters: (a) ln ε_ − ln(σ/E(T)), (b) ln ε_ − σ/E(T), (c) ln ε−

diffusion gives higher prediction accuracy, while the revised model with more constants and relatively higher regression error leads to slight decline of the prediction accuracy. However, the revised model can provide more information about the transition of diffusion mechanisms under different deformation temperatures: if k'1DL(T) N k'2DGB(T), the main diffusion mechanism during deformation is lattice diffusion; while the main diffusion mechanism will be changed to grain boundary diffusion with deformation temperatures when k'1DL(T) b k'2DGB(T). With the data in Table 2 and diffusion coefficients (DL(T) and DGB(T)) at different temperatures, it can be seen that the main diffusion mechanism at the deformation temperatures range of 633–693 K is lattice diffusion, while it changes to grain boundary diffusion at 603 K in AA7050 aluminum alloy. This result is consistent with the study of Humphreys and Kalu on a similar precipitation-strengthened aluminum alloy [25,29].

determined as 603–633 K and 1–10 s−1 under the strains of 0.1–0.65; 603–633 K at 0.1 s−1 under the strains of 0.3–0.65, and 663 K and 1– 10 s−1 under the strains of 0.1–0.25. For the deformation conditions where n' b 5, it can be determined as 693 K and 0.001–0.01 s−1 under the strains of 0.1–0.65, 663 K and 0.001–0.01 s−1 under the strains of 0.25–0.65, and 693 K and 0.1 s−1 under the strains of 0.1–0.3. 3.4.1. The case of the creep exponent n' N 5 In the case of n' N 5, the higher creep exponent n' could be caused by the lower deformation temperatures and higher strain rates. For the temperature effect, this reason may be attributed to the internal stress (or terms as threshold stress) caused by the Orowan strengthening effects of the fine dynamic precipitates [20,22,30–32]. The Ashby-Orowan equation for incoherent particles gives a better correlation between the particles volume/size and the stress increment [33]. The expression is written as:

3.4. Influence of microstructural evolution on the creep exponent n' It is widely recognized that the value of the creep exponent n' equals 5 as long as the deformation mechanism is controlled by the glide and climb of dislocations for different materials [19–21], which is commonly referred as “five-power-law” creep [26]. As shown in Fig. 7, the values of n' increase with increasing strain rates and decreasing deformation temperatures, and the deformation conditions where n' N 5 can be

Δσ y ¼

0:538μbf X

0:5

!

 ln

 X 2b

ð30Þ

where Δσy is the increment of yield stress due to the particles, μ is the shear modulus of the matrix, b is the Burgers vector of the dislocation. f is the volume fraction of particles, and X is the real spatial diameter

Table 2 The values of α', n', k'1 and k'2. Strains

k'1(×1013) k'2(×1018) n' α'

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

6.2876 2.0183 5.6905 672.3941

5.3032 2.0095 5.5011 676.4378

4.5362 2.0087 5.4637 682.9264

4.3657 1.7921 5.4431 686.1827

4.0786 1.7973 5.3875 686.8027

3.8882 1.7051 5.3503 690.8143

3.4516 1.8688 5.3013 694.5929

3.5186 1.5796 5.2808 697.537

3.2280 1.6833 5.2391 700.9162

3.1031 1.6320 5.1880 704.0044

3.1659 1.4120 5.1563 705.9592

3.1014 1.3234 5.1456 708.0504

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283

Fig. 5. Relationships between true strain (ε) and α' (a), n' (b), k'1 (c) and k'2 (d) by polynomial fitting.

of particles. So it can be summarized that the yield strength will be increased with higher volume fraction and smaller particle size. As shown in Fig. 8, the size of precipitates (MgZn2, η and/or η ') increases with increasing temperatures. It is about 100 nm at the condition of 603 K and 0.001 s−1 (Fig. 8(a)) and 50 nm at the condition of 603 K and 1 s− 1 (Fig. 8(c)), then the average precipitates size increases to 500 nm at 693 K and 0.001 s− 1 (Fig. 8(b)) and 200 nm at 663 K and 1 s−1 (Fig. 8(d)). The higher volume fraction and smaller size of precipitates lead to higher strengthening effects and n' N 5 under lower deformation temperatures, which can be attributed to the pinning and inhibiting effects of precipitates on dislocation motion. However, the volume fraction of precipitates decreases and the precipitates size increases under higher deformation temperatures, which would weaken the strengthening effects and pinning effects of precipitates and reduce the values of n'. Moreover, the fine precipitates can influence the creep

Fig. 6. Correlation between the measured and predicted flow stresses of the original and revised physically based models.

rate and may lead to the deviation of rate controlling mechanism from climb-controlled creep and thus the increase of creep exponent n' [34]. On the other hand, higher strain rates could also lead to the increase of the flow stress and thus the creep exponent n'. It may be due to the higher strain rates which lead to less time for DRV and/or DRX (shown in Fig. 9(a)–(c)), then dislocation tanglement is aggravated and the dislocation movement becomes difficult [13,26]. Moreover, the rate controlling mechanism switches to dislocation glide at moderate/high strain rates while it is mainly controlled by dislocation climb at lower strain rates. Under higher strain rates, deformation mechanism is more sensitive to the defects such as (sub)grain boundaries and voids formed by particle/precipitate cracking or debonding (Fig. 9(d)), which can also hinder the dislocation motion and then increase the internal stress as well as the creep exponent n' [20]. 3.4.2. The case of the creep exponent n' b 5 As mentioned in Section 3.2, the theoretical value of creep exponent n' = 5 is obtained if the dislocations glide and climb are the only deformation mechanism, which means that DRV is the only deformation mechanism and the rate controlling mechanism is climb-controlled creep [21,25]. However, some deformation mechanisms such as DDRX and superplastic flow may happen under different deformation conditions and thus can also lead to the variation of the creep exponent n' [21,25,35,36]. As well documented, the superplasticity behavior can be related to the operation of grain boundary sliding (GBS) during deformation at higher temperatures and lower strain rates. Another advantage for occurrence of the GBS is the fine grained structure with grain size b 10 μm and well-formed HAGBs [37–39]. Thus it is helpful to study the DRX behaviors such as the nucleation mechanisms and grain size for identifying the reason of n' b 5. Even though some efforts have been devoted to study the DRX behaviors under certain deformation conditions in AA7050 aluminum alloy [13,40], the DRX behaviors in wide deformation temperatures and strain rates are less documented systematically.

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Fig. 7. The influence of deformation temperature (a) and strain rate (b) on the creep exponent n'.

Fig. 10(a) shows a typical DRV microstructure under condition of 603 K and 0.001 s− 1 with 50% height reduction, however, a few fine grains have been formed at the mantle of original HAGBs (marked with box and shown in Fig. 10(b)). After 70% height reduction, the fraction of new fine grains with HAGBs increase at 603 K and 0.001 s−1 in Fig. 10(c) and (d). At the condition of 693 K and 0.001 s−1, a higher fraction of DRX is gained with 50% (Fig. 10(e)) and 30% (Fig. 10(f)) height reduction. As shown in Fig. 10(g), DRX can also happen in local area under the condition of 693 K and 10 s− 1 with 50% height reduction due to the deformation heating at higher strain rates. For high SFE metals/alloys, the main DRX mechanism is proved to occur in terms of CDRX rather than DDRX [13,14]. And new grains are formed by progressive subgrain rotation, in which the LAGBs are transformed to HAGBs gradually by absorbing dislocations. It can be seen that some nuclei marked with white circles in Fig. 10(b), (d) and (f) have formed HAGBs but still with partial LAGBs, which proves that the new grains may be formed by CDRX rather than a

nucleation-growth process (i.e. DDRX). Moreover, the KAM distribution can be used to describe the dislocation density or strain in grains, and the new DRX grains formed by nucleation and growth have lower dislocation density [41]. As marked in Fig. 10(b), (d) and (f), there are still many dislocations in the incompletely formed new grains, and it also validates the DRX mechanism in aluminum alloy is mainly conducted by CDRX. Some researchers pointed out that DDRX may decrease the creep exponent n' in some low SFE metals/alloys such as austenite steel [21]. The CDRX, as an extended recovery process, is only related to the dislocation glide and climb and has no relation to the GBM of HAGBs. Theoretically, the CDRX in aluminum alloy cannot decrease the creep exponent n'. Although the fine new grains with HAGBs can grow by GBM at deformation condition such as 693 K and 0.001 s − 1 , the contribution of grain growth to the decrease of n' may be neglected due to higher DRV rate for high SFE metals/alloys during deformation and less stored energy/ driving force (as shown in Fig. 8(b)) for GBM.

Fig. 8. The dynamic precipitates under conditions of: (a) 603 K and 0.001 s−1, (b) 693 K and 0.001 s−1, (c) 603 K and 1 s−1, (d) 663 K and 1 s−1.

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285

Fig. 9. The deformed microstructures under conditions of: (a) EBSD map of 633 K and 1 s−1, (b) TEM map of 603 K and 10 s−1, (c) EBSD map of 633 K and 10 s−1, (d) SEM map of 633 K and 1 s−1.

In addition, the strain induced boundary migration (SIBM), one kind of DDRX, may occur at higher deformation temperatures and strain rates [23,42]. In order to identify this DRX mechanism, the orientation relationship between some nuclei and their surrounding grains are displayed in Table 3 and marked in Fig. 11(a). And three types of nuclei are found and orientation relationships of three typical nuclei are shown on {111} pole figures (Fig. 11(b)). The SIBM can occur easily at the grain boundaries misoriented by 40° about 〈111〉 axes within ±10°, which is proved to be with high boundary migration rate for aluminum alloy [43]. Among 17 selected nuclei, only the nucleus N4 (Type II) gives a 33.3° 〈111〉 with respect to one of the deformed grains at the triple junctions. Most nuclei (Type I) have similar orientations with related deformed matrix, which means the main DRX mechanism is CDRX. In addition, the nuclei in Type III have new orientations but far away from 40°〈111〉 misorientation relationship. These nuclei with completely formed HAGBs may be the protrusion of other oriented grains, the grown grains of new DRX nuclei or the new grains formed by other nucleation mechanisms. Due to the lack of misorientation relationship between the nuclei and deformed grains before and during deformation, the specific nucleation mechanism cannot be identified in this study. In summary, it can be concluded that the SIBM may occur at 693 K and 0.1 s−1 to some extent, however, the main DRX mechanism is CDRX and gives little influence on the variation of creep exponent n'. As discussed above, the main DRX mechanism in aluminum alloy is CDRX, which is considered to retain the rolling texture [43]. However, as shown in Fig. 10(h), the IPF map of 693 K and 0.001 s−1 shows a random texture with the maximum intensity value of 2.31, while there are strong texture with the maximum intensity value of 9.04 and 10.34 under the condition of 603 K and 0.001 s− 1 (70% height reduction) and 693 K and 10 s−1 (50% height reduction), respectively. This can be attributed to the operation of GBS during deformation by multiple random grain rotations at 693 K and 0.001 s− 1 [35,37,39], while the GBS cannot be activated at lower temperature (603 K and 0.001 s−1)

and higher strain rate (693 K and 10 s−1). In addition, the wedge cracking at the triple grain junction can also indicate the occurrence of the GBS, which is the result of the considerable stress concentration caused by the GBS between neighboring grains [44]. As shown in Fig. 12, it can be seen that the wedge cracking occurs heavily at an intermediate strain rate (Fig. 12(a)) and no wedge cracking at 693 K and 0.001 s−1 in Fig. 12(b). It can be interpreted that the relief of stress concentration by dislocation creep and diffusional flow is a thermal activation process and occurs easily at higher temperature. Moreover, lower strain rates provide enough times to remove the stress concentration at the triple grain junction. For higher strain rates, the GBS can be neglected due to the faster rate of matrix deformation (Fig. 12(c)) [44]. Due to few fine DRX grains at intermediate strain rates and lower temperatures, the GBS is also difficult to operate at condition such as 603 K and 1 s− 1 (Fig. 12(d)). In summary, at the condition of the creep exponent n' b 5, the reason may be related to the operation of GBS rather than the DDRX in low SFE metals/alloys. The value of n' corresponding to superplasticity behavior is always reported as about 2 [36,39], however, the values of n' with the operation of GBS are between 2 and 5 in this study. This phenomenon can be interpreted as the symbiosis mechanism of dislocation creep in coarse grains and GBS among fine grains [37,39]. As schematically shown in Fig. 13, at the early stage of deformation, the dislocations slip and climb (i.e. dislocation creep) are the main deformation mechanism, and GBS may happen at some local regions of the rugged HAGBs, then subgrains besides HAGBs will rotate progressively with increasing misorientation. Subsequently, new fine grains are formed and the GBS occurs within these fine grains simultaneously. Finally, full evolution of the fine-grained structure with HAGBs and good superplasticity can be obtained by operating above process repeatedly at high strains. Although the elongation to failure by GBS accompanied dislocation creep is lower than that deforming by complete GBS, this mechanism is regarded as a potential way to obtain high-strain-rate superplasticity

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Fig. 10. The EBSD micrographs (a, c, e, g) and the KAM maps (b, d, f) under conditions of: (a) and (b) 603 K and 0.001 s−1 with 50% height reduction, (c) and (d) 603 K and 0.001 s−1 with 70% height reduction, (e) 693 K and 0.001 s−1 with 50% height reduction, (f) 693 K and 0.001 s−1 with 30% height reduction, (g) 693 K and 10 s−1 with 50% height reduction; (h) inverse pole figure (IPF) maps corresponding to microstructures in (c), (e) and (g). (The color bar of KAM represents the extent of dislocation density or strain in grains: blue color means the lowest dislocation density/strain areas; the green color means the higher dislocation density/stain areas; and the red color means the highest dislocation density/strain areas.) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

at a strain rate of 0.1 s−1 in the sheet forming process of a well recovered metals/alloys [37,39]. And the operation of GBS and the accompanied dislocation creep are response for the good superplasticity and higher forming rate, respectively.

4. Conclusions In this study, a revised physically constitutive model considering the coupling effects of lattice diffusion and grain boundary diffusion was

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Table 3 Misorientations of the 17 nuclei with their surrounding grains. Type

No.

I

N1

Misorientations with their surrounding grains 9.4° 〈101〉

21.8°〈412〉

N2

15.1°〈433〉

4.9°〈441〉

36.4° 〈342〉

N3

13.0°〈213〉

N5

9.4°〈412〉

51.5°〈234〉 28.0°〈411〉

44.7°〈131〉

N8 N9

4.1°〈141〉 4.6°〈121〉

42.8°〈133〉

N10

18.2°〈013〉

5.8°〈334〉

N13

41.0°〈121〉

44.6°〈231〉

N14

10.4°〈144〉 19.7°〈021〉

24.4°〈124〉

N15

25.6°〈414〉

10.6°〈401〉 11.3°〈120〉

N16 N17

57.4°〈221〉 9.4°〈110〉

II

N4

III

N6 N7

31.3°〈324〉

23.7°〈214〉

N11

38.2°〈112〉

45.5°〈214〉

N12

33.0°〈441〉

30.3°〈043〉

49.3°〈443〉

11.8°〈421〉

59.2°〈110〉

15.6°〈321〉

29.7°〈321〉

28.5°〈230〉 22.8°〈101〉

4.9°〈143〉

50.8°〈144〉

33.3°〈111〉

19.5°〈124〉

24.3°〈114〉

proposed to describe the flow behavior of AA7050 aluminum alloy well. And the revised model can relate microstructural evolution with flow behaviors by the variation of the creep exponent n'. Then following conclusions can be drawn:

32.9°〈342〉

16.0°〈110〉

(1) The revised physically based model can describe the flow behaviors well and reflect the transition of diffusion mechanism under different deformation conditions. The main diffusion mechanism is determined as lattice diffusion at the deformation

Fig. 11. (a) EBSD map marked with 17 recrystallized nuclei in the sample deformed at 693 K and 0.1 s−1, (b) The orientations relationship on {111} pole figures of three typical nuclei (N4, N6 and N10) with their surrounding grains.

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Fig. 12. SEM micrographs of samples with 50% height reduction at the conditions of: (a) 693 K and 1 s−1, (b) 693 K and 0.001 s−1, (c) 693 K and 10 s−1, (d) 603 K and 1 s−1.

temperature range of 633–693 K and grain boundary diffusion at 603 K. (2) The microstructural evolution during deformation under different conditions can lead to the deviation of the creep exponent n' from its theoretical value 5. The reasons for the higher value of the creep exponent n' may be related to the change of internal stress and creep rate by dynamic precipitates at lower temperatures. At higher strain rates, the dislocation motion is sensitive to impediment effects of defects and the rate controlling mechanism switches to dislocation glide, which can also lead to the increase of n'. The reason of the creep exponent n' b 5 at higher temperatures and lower strain rates could be attributed to the operation of GBS. (3) The main DRX mechanism for AA7050 aluminum alloy is proved to be CDRX, which is a process of dislocation creep and occurs readily at higher temperatures and lower strain rates. The simultaneous operation of CDRX in coarse grains and GBS among fine grains could attain high-strain-rate superplasticity.

Fig. 13. The schematic illustration of the symbiosis mechanism of CDRX by dislocation creep and GBS for achieving high-strain-rate superplasticity.

Acknowledgments The authors appreciate the financial supports from National Natural Science Foundation of China (No. 51401016) and State Key Laboratory for Advanced Metals and Materials of China and the Constructed Project for Key Laboratory of Beijing. And the funds from National High Technology Research and Development Program of China (863 Program, No. 2013AA032403) also should be acknowledged.

References [1] X.M. Chen, Y.C. Lin, D.X. Wen, J.L. Zhang, M. He, Dynamic recrystallization behavior of a typical nickel-based superalloy during hot deformation, Mater. Des. 57 (2014) 568–577. [2] K. Yue, Z.Y. Chen, J.R. Liu, Q.J. Wang, B. Fang, L.J. Dou, Hot compression of TC8M-1: constitutive equations, processing map, and microstructure evolution, Metall. Mater. Trans. A 47 (6) (2016) 1–15. [3] Y.C. Lin, X.M. Chen, A critical review of experimental results and constitutive descriptions for metals and alloys in hot working, Mater. Des. 32 (4) (2011) 1733–1759. [4] C.M. Sellars, W.J. McTegart, On the mechanism of hot deformation, Acta Metall. 14 (1966) 1136–1138. [5] G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech. 21 (1985) 31–48. [6] L. Chen, G.Q. Zhao, J.Q. Yu, W.D. Zhang, Constitutive analysis of homogenized 7005 aluminum alloy at evaluated temperature for extrusion process, Mater. Des. 66 (2015) 129–136. [7] Z. Akbari, H. Mirzadeh, J.M. Cabrera, A simple constitutive model for predicting flow stress of medium carbon microalloyed steel during hot deformation, Mater. Des. 77 (2015) 126–131. [8] F. Zerilli, R. Armstrong, Dislocation-mechanics-based constitutive relations for material dynamics calculation, J. Appl. Phys. 5 (1987) 1816–1825. [9] A. He, G.L. Xie, H.L. Zhang, X.T. Wang, A modified Zerilli-Armstrong constitutive model to predict hot deformation behavior of 20CrMo alloy steel, Mater. Des. 56 (2014) 122–127. [10] Y. Estrin, H. Mecking, A unified phenomenological description of work hardening and creep based on one-parameter models, Acta Metall. 32 (1) (1984) 57–70. [11] Y. Bergström, A dislocation model for the stress-strain behaviour of polycrystalline α-Fe with special emphasis on the variation of the densities of mobile and immobile dislocations, Mater. Sci. Eng. 5 (4) (1970) 193–200.

S. Wang et al. / Materials and Design 107 (2016) 277–289 [12] Y.C. Lin, X.M. Chen, D.X. Wen, M.S. Chen, A physically-based constitutive model for a typical nickel-based superalloy, Comput. Mater. Sci. 83 (2014) 282–289. [13] S. Wang, L.G. Hou, J.R. Luo, J.S. Zhang, L.Z. Zhuang, Characterization of hot workability in AA 7050 aluminum alloy using activation energy and 3-D processing map, J. Mater. Process. Technol. 225 (2015) 110–121. [14] X.H. Fan, M. Li, D.Y. Li, Y.C. Shao, S.R. Zhang, Y.H. Peng, Dynamic recrystallisation and dynamic precipitation in AA6061 aluminium alloy during hot deformation, Mater. Sci. Technol. 30 (11) (2014) 1263–1272. [15] C.J. Shi, X.G. Chen, Evolution of activation energies for hot deformation of 7150 aluminum alloys with various Zr and V additions, Mater. Sci. Eng. A 650 (2016) 197–209. [16] C.J. Shi, X.G. Chen, Hot workability and processing maps of 7150 aluminum alloys with Zr and V additions, J. Mater. Eng. Perform. 24 (5) (2015) 2126–2139. [17] Y.J. Lang, G.X. Zhou, L.G. Hou, J.S. Zhang, L.Z. Zhuang, Significantly enhanced the ductility of the fine-grained Al-Zn-Mg-Cu alloy by strain-induced precipitation, Mater. Des. 88 (2015) 625–631. [18] Z.C. Sun, L.S. Zheng, H. Yang, Softening mechanism and microstructure evolution of as-extruded 7075 aluminum alloy during hot deformation, Mater. Charact. 90 (2014) 71–80. [19] J.M. Cabrera, A. Al Omar, J.M. Prado, J.J. Jonas, Modeling the flow behavior of a medium carbon microalloyed steel under hot working conditions, Metall. Mater. Trans. A 28 (11) (1997) 2233–2244. [20] J.M. Cabrera, J.J. Jonas, J.M. Prado, Flow behaviour of medium carbon microalloyed steel under hot working conditions, Mater. Sci. Technol. 12 (7) (1996) 579–585. [21] H. Mirzadeh, J.M. Cabrera, A. Najafizadeh, Constitutive relationships for hot deformation of austenite, Acta Mater. 59 (16) (2011) 6441–6448. [22] A. Thomas, M. El-Wahabi, J.M. Cabrera, J.M. Prado, High temperature deformation of Inconel 718, J. Mater. Process. Technol. 177 (1) (2006) 469–472. [23] Q.Y. Yang, Z.H. Deng, Z.Q. Zhang, Q. Liu, Z.H. Jia, G.J. Huang, Effects of strain rate on flow stress behavior and dynamic recrystallization mechanism of Al-Zn-Mg-Cu aluminum alloy during hot deformation, Mater. Sci. Eng. A 662 (2016) 204–213. [24] F. Reyes-Calderón, I. Mejía, J.M. Cabrera, Hot deformation activation energy (QHW) of austenitic Fe-22Mn-1.5Al-1.5Si-0.4C TWIP steels microalloyed with Nb, V, and Ti, Mater. Sci. Eng. A 562 (2013) 46–52. [25] H.J. Frost, M.F. Ashby, Deformation-Mechanism Maps: The Plasticity and Creep of Metals and Ceramics, Pergamon Press, Oxford, 1982. [26] S.F. Harnish, H.A. Padilla, J.A. Dantzig, A.J. Beaudoin, B.E. Gore, I.M. Robertson, et al., High-temperature mechanical behavior and hot rolling of AA705X, Metall. Mater. Trans. A 36 (2) (2005) 357–369. [27] H.L. Wei, G.Q. Liu, M.H. Zhang, Physically based constitutive analysis to predict flow stress of medium carbon and vanadium microalloyed steels, Mater. Sci. Eng. A 602 (2014) 127–133.

289

[28] H. Watanabe, T. Mukai, M. Mabuchi, K. Higashi, Superplastic deformation mechanism in powder metallurgy magnesium alloys and composites, Acta Mater. 49 (11) (2001) 2027–2037. [29] F.J. Humphreys, P.N. Kalu, Dislocation-particle interactions during high temperature deformation of two-phase aluminium alloys, Acta Metall. 35 (12) (1987) 2815–2829. [30] Z.Y. Ma, S.C. Tjong, Creep deformation characteristics of discontinuously reinforced aluminium-matrix composites, Compos. Sci. Technol. 61 (5) (2001) 771–786. [31] K.T. Park, F.A. Mohamed, Creep strengthening in a discontinuous SiC-Al composite, Metall. Mater. Trans. A 26 (1995) 3119–3129. [32] L. Kloc, S. Spigarelli, E. Cerri, E. Evangelista, Creep behaviour of an aluminium 2024 alloy produced by powder metallurgy, Acta Mater. 45 (1995) 529–540. [33] T. Gladman, Precipitation hardening in metals, Mater. Sci. Technol. 15 (1) (1999) 30–36. [34] M. Malu, J.K. Tien, The elastic modulus correction term in creep activation energies: applied to oxide dispersion strengthened superalloy, Scr. Metall. 9 (10) (1975) 1117–1120. [35] M.T. Pérez-Prado, G. González-Doncel, O.A. Ruano, T.R. McNelley, Texture analysis of the transition from slip to grain boundary sliding in a discontinuously recrystallized superplastic aluminum alloy, Acta Mater. 49 (12) (2001) 2259–2268. [36] O.A. Ruano, J. Wadsworth, O.D. Sherby, Deformation of fine-grained alumina by grain boundary sliding accommodated by slip, Acta Mater. 51 (12) (2003) 3617–3634. [37] T. Sakai, X. Yang, H. Miura, Dynamic evolution of fine grained structure and superplasticity of 7075 aluminum alloy, Mater. Sci. Eng. A 234 (1997) 857–860. [38] F.C. Liu, Z.Y. Ma, Contribution of grain boundary sliding in low-temperature superplasticity of ultrafine-grained aluminum alloys, Scr. Mater. 62 (3) (2010) 125–128. [39] J.A. del Valle, M.T. Pérez-Prado, O.A. Ruano, Symbiosis between grain boundary sliding and slip creep to obtain high-strain-rate superplasticity in aluminum alloys, J. Eur. Ceram. Soc. 27 (11) (2007) 3385–3390. [40] M.H. Wang, W.H. Wang, J. Zhou, X.G. Dong, Y.J. Jia, Strain effects on microstructure behavior of 7050-H112 aluminum alloy during hot compression, J. Mater. Sci. 47 (7) (2012) 3131–3139. [41] H.L. Li, E. Hsu, J. Szpunar, H. Utsunomiya, T. Sakai, Deformation mechanism and texture and microstructural evolution during high-speed rolling of AZ31B Mg sheets, J. Mater. Sci. 43 (22) (2008) 7148–7156. [42] G.L. Wu, D.J. Jensen, Orientations of recrystallization nuclei developed in columnargrained Ni at triple junctions and a high-angle grain boundary, Acta Mater. 55 (15) (2007) 4955–4964. [43] O. Engler, Nucleation and growth during recrystallisation of aluminium alloys investigated by local texture analysis, Mater. Sci. Technol. 12 (10) (1996) 859–872. [44] R. Raj, Development of a processing map for use in warm-forming and hot-forming processes, Metall. Mater. Trans. A 12 (6) (1981) 1089–1097.