Superplasticity of ultrafine-grained Al–Mg–Sc–Zr alloy

Author’s Accepted Manuscript Superplasticity of ultrafine-grained Al-Mg-Sc-Zr alloy Diana Yuzbekova, Anna mogucheva, Rustam Kaibyshev www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(16)30983-2 http://dx.doi.org/10.1016/j.msea.2016.08.074 MSA34032

To appear in: Materials Science & Engineering A Received date: 18 May 2016 Revised date: 15 August 2016 Accepted date: 18 August 2016 Cite this article as: Diana Yuzbekova, Anna mogucheva and Rustam Kaibyshev, Superplasticity of ultrafine-grained Al-Mg-Sc-Zr alloy, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2016.08.074 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Superplasticity of ultrafine-grained Al-Mg-Sc-Zr alloy Diana Yuzbekova, Anna Mogucheva*, Rustam Kaibyshev Belgorod State University, Pobedy 85, Belgorod, Russia *

Corresponding author: [email protected]

Abstract The superplastic behavior of an Al–Mg–Sc–Zr alloy with a grain size of ~0.7 μm produced by equal channel angular pressing (ECAP) was examined in the temperature interval 150 – 500°C at strain rates ranging from 10–5 to 10–1 s–1. No significant grain coarsening occurs under static annealing up to 450°C because of the strong pinning effect of Al3(Sc,Zr) dispersoids. The alloy showed superior ductility of 365 pct at 175°C, 1200 pct at 275°C and ~3300 pct at 450°C and strain rates of 1.4×10–4 s–1, 5.6×10–3 s–1 and 5.6×10–1, with corresponding strain rate sensitivities of 0.3, 0.49 and 0.2, respectively. Analysis of the superplastic behavior in terms of threshold and surface observations showed that grain boundary sliding (GBS) controlled by grain boundary diffusion is the dominant deformation mechanism under all of the conditions. The strong pinning effect of coherent Al3(Sc,Zr) particles leads to a high dislocation density within grains after superplastic deformation that leads to initial strain hardening at low temperatures and high threshold stress. Analysis of the superplastic behavior showed that the strong temperature dependence of the threshold stress is most likely attributable to the interaction between dislocations and the coherent dispersoids, and the effect of temperature on the optimal strain rate of superplastic deformation associated with the highest values of elongation-to-failure is attributable to absorption of a lattice

dislocation by a grain boundary rather than the climb of this dislocation along the boundary. Keywords: aluminum alloy; equal-channel angular pressing; ultrafine-grained structure; superplasticity; deformation mechanism.

1. Introduction STRUCTURAL SUPERPLASTICITY is the ability of polycrystalline materials to exhibit very high tensile elongations without the formation of a neck prior to fracture because of a high value of the strain rate sensitivity values (m=dln σ/dln ε, where σ is the flow stress and  is the strain rate) [1-3]. Alloys with a grain size smaller than 10 m exhibit superplastic behavior at >0.5 Tm, where Tm is the absolute melting temperature of the material, and strain rates usually ranging from 10–5 to 10–3 s–1 [1-5]. The strain rate during superplastic deformation generally obeys the following relationship [1-3,6]: ̇

( ) ( )

(1)

where A is a dimensionless constant; b is the Burgers vector; d is the grain size;  is the applied stress; G is the shear modulus; k is Boltzmann's constant; T is the absolute temperature; and p is the exponent of the inverse grain size, which ranges from 2 to 3; the stress exponent, n, is defined as 1/m; and D (=Doexp(-Q/RT), where Dо is a frequency factor, Q is the activation energy, R is the gas constant, and T is the absolute temperature) is a diffusion coefficient. For the majority of superplastic materials, the rate-controlling process for superplastic deformation is grain boundary sliding (GBS) [1-5]. This mechanism defines the temperature dependence of the strain rate at constant

stress and structure through the activation energy of the grain boundary diffusion and the strain rate sensitivity of 0.5 [1-5]. Because the strain rate in superplasticity is inversely proportional to the square or cube of the grain size, a decrease in the grain size will lead to a displacement of the superplasticity regime to faster strain rates and/or lower temperatures [6-14]. Equal channel angular pressing (ECAP) and friction stir welding/processing (FSW/FSP) provide an attractive opportunity for extensive grain refinement in aluminum alloys containing a dispersion of nanoscale particles [6,8,10-17]. Merely producing a fine grain size is not in itself sufficient to achieve extraordinary superplastic ductility because the grain size needs to remain stable throughout the superplastic deformation [1,2,6]. Dispersoids exerting a high Zener drag pressure provide stability of the ultrafine-grain (UFG) structure under static and even dynamic annealing [18,19]. As a result, aluminum alloys containing Al3(Sc,Zr) dispersoids with ultrafine-grained (UFG) structure exhibit superior superplastic ductility (≥2000%) at strain rates  > 10–2 s–1 or moderate ductility (≥300%) below 0.5Tm [8,10-14,16,17,20-22]. Superplastic behaviors at these conditions were termed high-strain-rate superplasticity (HSRS) and low-temperature superplasticity (LTSP), respectively [4,6-14,23,24]. It is worth noting that the superplastic flow behaviors in the HSRS and LTSP regimes exhibit distinct features in comparison with conventional superplasticity. At low temperatures, the Q values are much higher than those for grain boundary diffusion in Al (84 kJmol-1), and the m values are usually less than 0.5 and tend to approach 0.33 [6,12,13], while in the HSRS regime, the Q values are close to that for the grain boundary diffusion and m0.5 [25]. Experimental data points of aluminum alloys with UFG structure plotted in the form of a temperature- and grain-size-compensated strain rate vs normalized stress

deviate from a straight line, presenting the theoretical prediction for superplastic flow in accordance with Eq. (1) [6], despite the fact that grain boundary sliding (GBS) is extensively operative in the HSRS and LTSP regimes [26,27]. It can be assumed that the superplastic behavior of aluminum alloys containing nanoscale dispersoids cannot be described by a single expression of the form given by Eq. (1) but is described more realistically by an equation accounting for the threshold stress [11,28]: ̇

( ) (

) ,

(2)

where th is the threshold stress resulting from the segregation of impurities at the grain boundaries and their interactions with grain boundary dislocations and/or the interaction between mobile lattice dislocations and dispersion particles. Introducing the threshold stress allows the fitting of experimental data with high accuracy to a single straight line with a slope of 2, representing a temperature- and grain-size-compensated strain rate dependence vs effective stress [12,28]. However, Eq. (2) was found to be applicable and results in reasonable data only in a relatively narrow temperature interval [12]. At present, limited experimental data exist for consideration of superplastic behavior of an aluminum alloy with UFG structure produced by ECAP or FSP in both HSRS and LTSP regimes [11,16,29]. Therefore, the main aims of the present study are (I) to examine the boundary characteristics and thermal stability of (II) to evaluate the superplastic behavior of an AA5024 alloy with UFG structure containing a dispersion of coherent Al3(Sc,Zr) particles [30] in a wide temperature-strain rate interval; and (III) to identify the deformation mechanism of superplasticity operating at high strain rates and/or low temperatures.

2. Material and Experimental Procedure The AA5024 alloy with a chemical composition of Al–4.57Mg–0.35Mn–0.2Sc– 0.09Zr (wt pct) was produced by continuous casting [30]. Ingots with initial dimensions of 620 mm were subjected to homogenization annealing at 370°C for 12 h. Next, the ingot was extruded at a temperature of 380°C into a billet with a rectangular cross section and dimensions of 155×255 mm2 [30]. The billets, having a plate-like shape (180 mm ×180 mm ×40 mm), were machined from the extruded ingot and pressed 12 times through the ECAP die at a temperature of 300°C using route BCZ with a back pressure of approximately 100 MPa, where the billet is rotated by 90° in the same sense around the normal direction (Z-axis) of the horizontal plate after each pass [15,17,31]. Other details of the processing were reported in previous works [17,30]. Tensile specimens with a 6-mm gauge length and a cross-section of 1.5×3 mm2 were cut parallel to the last extrusion axis of the pressed billets. Tensile tests were conducted in the temperature interval 150–500°C and at strain rates between 10–5 and 10–1 s–1 using an Instron 5882 testing machine operating at a constant cross-head velocity and equipped with an Instron 3119-408 chamber providing almost no temperature gradient along the gauge lengths. Each sample was held at the testing temperature for approximately 10 min to reach thermal equilibrium. Strain rate change tests were used to measure the coefficient of strain rate sensitivity, m [1,2]. In addition, samples cut from the central part of the billet were annealed at different temperatures ranging from 150 to 500°C for 20 min each. Microstructural characterization and analysis of the 5024 alloy were carried out using a Jeol–2100 (JEOL Ltd., Tokyo, Japan) transmission electron microscope (TEM) and a Quanta 600FEG (FEI Corporation, Hillsboro, OR) scanning electron microscope (SEM)

incorporating an orientation imaging microscopy (OIM) system. These techniques were described in previous work in detail [30]. The average grain size was measured by the mean linear intercept method using the OIM software. The boundary misorientation distributions were calculated using pixel-to-pixel measurements. For structural characterization, samples were cut from the grip and gauge sections of the tested tensile specimens. In the latter case, the areas located 5 mm apart from the fracture surface were observed. Cavitation was measured on the as-polished samples, using the standard point-counting technique described in work [32] in detail. An Olympus GX70 (Olympus Ltd., Shinjuku, Tokyo, Japan) optical microscope (OM) was used to observe cross-sectional views of samples strained to failure.

3. Experimental Results 3.1. Microstructure after ECAP ECAP at 300°C with a total strain of ~12 led to the formation of a fully recrystallized structure with a high population of high-angle grain boundaries (HAGBs) of ~0.85 and an average misorientation of 35.5° (Fig. 1) [30]. These values are high for ECAP processing and could be achieved by friction stir processing, mainly [12,25]. The recrystallized grains exhibit an equiaxial shape with an average size of 0.7 m; their area fraction composes ~0.9 (Fig. 1(a)). The frequency distribution of misorientations is shown in Fig. 1(b). For comparison, the theoretical distribution of misorientations predicted by Mackenzie for a random polycrystal of cubic structure [33] is also shown in Fig. 1(b) as the dashed line. It is seen that the misorientation distribution for the 5024 alloy subjected to ECAP approaches Mackenzie’s distribution. Therefore, ECAP of a plate in a horizontal configuration [15,17] is more effective in producing UFG structure

with a high portion of HABs and increased average misorientation than conventional ECAP with bars [30]. TEM observations (Fig. 1(c)) revealed as high a density of lattice dislocations (~2×1014 m−2) within the interiors of recrystallized grains as after conventional ECAP [30]. A dispersion of particles with sizes ranging from approximately 5 to 20 nm and having a round shape was found within the grain interiors (Fig. 1(d)). These dispersoids are distributed homogeneously in the Al matrix; a minor portion of them exhibits a well-known “coffee-bean”-like contrast, which can be attributed to the coherent dispersoids [34]. Typical {100} and {110} super-lattice reflections of the L12 structure are distinguished in the diffraction pattern taken from these dispersoids (Fig. 1(d)). In addition, these dispersoids exhibit the cube-on-cube orientation relationship, i.e., (100)Al3Sc//(100)Al and [010]Al3Sc//[010]Al, supporting the coherent origin of their interfaces. 3.2. Thermal stability of ultrafine grains Figure 2 shows the variation with increasing temperature of the average grain size of static annealing from 150 to 500°C for the grip sections of specimens. The 5024 alloy exhibits excellent thermal stability, and the UFG structure is retained up to an annealing temperature of 450°C. This stability is superior in comparison with Al-3Mg-0.2Sc alloy processed by ECAP at room temperature [35] because of the lower driving forces for static recrystallization provided by stored dislocations and boundary energy per unit area [18,19,36]. ECAP at 300°C produced lower dislocation density and higher grain size in comparison with this processing at room temperature. In addition, Zr additives provide increased density Al3(Sc,Zr) particles, and therefore, the high Zener drag pressure exerted by these particles promotes stability of the UFG structure [19,37-41].

The Al3(Sc,Zr) dispersoids did not exhibit noticeable coarsening after static annealing even at 450°C for 20 min because of the Zr additives [42] (Fig. 3). These precipitates retain their coherence, spherical shape, dimension and extremely homogeneous distribution throughout the matrix (Fig. 3). As a result, no continuous coarsening takes place up to 450°C [43,44]. At T≥400°C, continuous grain coarsening [18,19,43,44] occurs. It is worth noting that only the Al-4Mg-1Zr alloy containing a very high density of coherent Al3Zr dispersoids with dimensions ranging from 3 to 20 nm is not susceptible to continuous grain coarsening up to 500°C [12]. In this study the grain aspect ratio (AR), defined as the ratio of the grain dimension in the longitudinal direction to that in the transverse direction, does not exceed 1.4 up to 450°C, and therefore, grains retain their nearly round shape. No evidence for discontinuous grain coarsening [18,19,43,44] was found. 3.3. Superplastic behavior True flow stress at the offset strain, p, at which peak strain is attained, the coefficient of strain rate sensitivity, m, and elongation-to-failure, , are plotted on a double- and semi-logarithmic scale, respectively, as functions of strain rate in two temperature ranges of 150–275 and 300–500°C in Fig. 4. Characteristics of superplastic behavior as the highest elongation-to-failure with corresponding m values and the highest coefficient of strain rate sensitivity with corresponding ductility at various temperatures and corresponding strain rates are summarized in Table 1. In the temperature range 150-500°C, the strain rate dependencies of flow stress exhibit a sigmoidal shape (Fig. 4(a,a’)); three well-known regions of superplastic deformation can be identified [1-3,5]. At 150°C, limited experimental data did not allow

demonstrating a sigmoidal shape of the -  curve (Fig. 4(a)). Flow stress in the optimal strain interval of superplasticity associated with the highest values of elongation-tofailure and the coefficient of strain rate sensitivity tend to decrease with increasing temperature up to 450°C (Fig. 4(a’)). At 500°C, this tendency becomes reversed. In the temperature interval 150–275°C, an increase in temperature leads to a shift of the optimum strain rate interval of superplastic deformation to higher strain rates. In the  m LTSP regime, the opt values are almost equal to the opt value (Table 1). The

superplastic ductility of more than 300 pct. was obtained at T≥175°C, while at 150°C, elongation-to-failure did not exceed 200 pct., which is related to m≤0.3 (Fig. 4(b,c)). In the temperature interval 300–450°C, the strain interval attributed to the highest m values is nearly independent of temperature and shifts to lower strain rates with a further  temperature increase to 500°C (Fig. 4(b’)). The opt magnitude tends to increase with m increasing temperature from 300 to 450°C and becomes higher than opt (Table 1). At

300°C (~0.52Tm) and 350°C (~0.6Tm), the highest values of elongation-to-failure of ~1350 pct. and ~1830 pct. appear at 5.6×10–2 and 1.4×10–1 s–1, respectively, while the highest m values were found at a strain rate of 1.4×10–2 s–1 (Fig. 4(c’), Table 1). At 450°C, the highest m value of 0.55 is observed at ε= 1.4×10–2 s–1, while the highest elongation-to-failure of 3300 pct. appeared at ε= 5.6×10–1 s–1, corresponding to an  m unreasonably low value of m~0.2; opt 40× opt (Fig. 4(b’,c’), Table 1).

Typical true stress–strain curves for the AA5024 alloy at 175, 275 and 450°C and initial strain rates ranging from 1.4×10–4 to 6.9×10–1 s–1 are shown in Fig. 5. In the HSRS regime, the extensive strain hardening takes place initially. After reaching a maximum stress, the flow stress continuously decreases until fracture. A peak in flow

stress can be observed, and no steady-state flow occurs, which is typical for Al 3÷4.7Mg-Sc alloys [16,22,35]. The highest offset strain is observed at opt and

decreases on either side of this strain rate. In the LTSP regime, the short stage of strain hardening can be distinguished. An apparent steady state flow appears, as in an Al4Mg-1Zr alloy in the LTSP regime [45]. Therefore, the transition from the LTSP to HSRS conditions leads to a strong decrease in the extension of initial strain hardening and the appearance of steady state flow. Figure 6 shows variations of the coefficient of strain rate sensitivity with true strain. In the HSRS and LTSP regimes, the m value remains nearly unchanged and tends to slightly decrease with strain, respectively (Fig. 6). At 450°C, the combination of m≥0.4 with strong strain hardening before offset strain and small strain softening after offset strain can result in high resistance to neck development, thus providing high tensile elongations. A very uniform deformation is visible in gauge lengths, and no evidence for unstable plastic flow was found (Fig. 7). Pseudo-brittle fracture by cavitation is observed (Fig. 7). At 175°C, the material is pulled out to a fine point to failure, as the low m value could confer a resistance to neck development and fracture occurs by unstable plastic flow because of necking over the gauge lengths after high strain (Fig. 7) [2]. This fracture type corresponds to rapid strain softening after a stress peak and decreasing m value with strain (Figs. 5-7). At 275°C, a mixed type of fracture is observed. Uniform elongation appears in the gauge length, but fracture occurs because of unstable plastic flow within a narrow area. The combination of a high m value and strong hardening provides uniform elongation up to the offset strain. However, the decreased m value (Fig. 6) could not compensate for extensive strain softening at >p, and the necking starts to occur.

3.4. Microstructure of deformed specimens and fracture The microstructural evolution of the 5024 alloy was studied under dynamic (gauge section) annealing (Fig. 8) in the specimens strained up to offset strain and up to failure at 175°C (365 pct.), 275°C (1200 pct.) and at 450°C (3300 pct.). At 175°C, the dimensions of the initial grains remain unchanged up to the offset strain, and further superplastic deformation leads to grain refinement up to ~0.5 m (Fig. 8(a)). Therefore, dynamic recrystallization (DRX) [46] is an important component of LTSP. At 275°C, no effect of superplastic deformation on grain dimensions was found; the elongation of initial grains occurs toward the tension direction, and ARd is 1.7 in (Fig. 8(a’)). At T=450°C, the ARd reaches ~2.3 and the average grain size is 2 and 4 μm after offset strain and failure, respectively (Fig. 8(a’’)), indicating that strain-induced grain growth provides an increased contribution of dislocation glide to the total elongation [2,8,47,48]. The population of HAGBs and average misorientation remain nearly unchanged during superplastic deformation (Fig. 8(b-b’’)). The main feature of the microstructure after superplastic deformation to the offset strain, εp, (Fig. 9(a,b,c)) is relatively high dislocation density of ~1.5×1014, ~4×1014 and ~3×1014 m-2 at 450, 275 and 175oC, respectively. Commonly, such high values of dislocation density are observed after cold working [18,46]. It should also be noted that the lattice dislocation density is almost the same before and after superplastic deformation. The high dislocation density within grains after superplastic deformation of the AA5024 alloy is associated with coherent Al3(Sc,Zr) particles, which are highly effective in dislocation pinning and strengthening [37,38]. Therefore, superplastic deformation of the aluminum alloy containing a dispersion of coherent dispersoids leads to a high lattice dislocation density that is in contrast with conventional superplastic

alloys [1,2]. At the same time, the density of grain boundary dislocations is low (Fig. 9(a’,b’,c’)) that is much similar to other studies on conventional superplastic deformation [1,2,47]. It is worth noting that the discrepancy in lattice dislocation densities between different grains does not exceed 4 times for any superplastic condition, which is in contrast with superplastic alloys produced by powder metallurgy techniques and containing nanoscale oxides [28]. At 450°C, the grain boundaries are almost free of any extrinsic dislocations (Fig. 9(c’)), while individual extrinsic dislocations are clearly seen in grain boundaries at T≤275°C (Fig. 9(a’,b’)). Probably, the grain boundaries rapidly absorb all trapped dislocations at 450°C because no dislocation pile-ups were found near boundaries. Distinctive evidence of GBS was revealed on the surface of the pre-polished specimens, which looks like puffing out the grain and/or grain groups (Fig. 8(c-c’’)) [1,8,12,26,49]. It is worth noting that GBS occurs in a cooperative manner through the shift of grain groups as a unit relative to each other along common grain boundary surfaces [49,50]. These grain groups exhibit band-like shapes; their average sizes range from 3 to 6 units of the average matrix grain size. GBS of individual grains plays the role of an accommodation process for cooperative GBS [48,51]. Decreasing temperature leads to the appearance of distinct GBS of individual grains. At 175°C, the shift of grain groups as a unit is poorly defined, as in the Al-4Mg-1Zr alloy [12,26]. Superior elongation-to-failure is attributed to a strong suppress of cavitation, as could be seen in cross-sectional views of near-fracture-surface regions (Fig. 8(d-d’’)). Obviously, the low pore density is attributed to the low number of coarse particles playing a role as the sites for void initiation. Limited strain-induced cavitation is indicative of easy accommodation of GBS by dislocation slip with micron-scale grains

[1-3]. Two types of fracture are distinctly distinguished in the HSRS and LTSP regimes (Fig. 8(d-d’’)). At 175 and 275°C and initial strain rates of 1.4×10–4 and 5.6×10–3 s–1, respectively, the AA5024 alloy is not susceptible to cavitation, and localized necking induces the formation of coarse cracks (Fig. 8(d, d’)). At 450°C and ε=5.6×10–1 s–1, fracture occurs through crack propagation between coarse cavities at an angle of ~ 45° to the tension axis without strain localization (Fig. 8(d’’)). The formation of a coarse pore with irregular shape having strain-induced origin [2] initiates wedge cracks. Then, these cracks propagate under the highest shear stress.

4. Discussion 4.1. Thermal stability The AA5024 alloy exhibits superior stability of the UFG structure under static and dynamic superplastic conditions up to 450°C, despite a high stored energy because of the high dislocation density and the large surface area of grain boundaries [18,36,43]. The ability of the grain boundaries to migrate may be evaluated from the balance between the driving forces for recrystallization because of stored dislocations (Pd) and the boundary energy (Pb) and the Zener drag force (PZ) [18,43]. If the following ratio PZ ≥ Pd + Pb

(3)

is fulfilled, no continuous grain growth occurs [18,36]. A driving pressure provided by the accumulated dislocation density is given by [18]: Pd=0.5Gb2ρ

(4),

where G is the shear modulus (∼25.4 GPa), b is the Burgers vector (0.286 nm), and ρ is the dislocation density. For UFG material, Pd is 0.21 MPa.

The driving pressure related to the grain-boundary energy is given approximately by [18,43]: Pb = 3γb/D

(5),

where D is the mean grain size and γb ∼0.32 Jm–2 is the grain boundary energy for HABs in aluminum alloys [52]. For the mean grain size of 0.7 μm, the driving pressure is ∼1.4 MPa and tends to decrease with increasing grain size. The Zener pinning pressure exerted by uniformly distributed incoherent particles having spherical shape is given as [18]: Pz = 1.5fvγb/r

(6),

where fv is the volume fraction of dispersoids and r is the mean particle radius. The Zener pinning pressure exerted by coherent Al3(Sc,Zr) dispersoids is four-fold greater and is expressed as follows [43,53]: P*z = 6fvγb/r,

(7),

where fv is taken as 0.5 (in wt.%) from Thermo-Calc calculations and r ∼5.5 nm. For simplicity, γb was taken as the grain boundary energy instead of the interfacial free energy between the Al matrix and Al3(Sc,Zr) dispersoids, as was suggested by R.D. Doherty [53], because there is a great discrepancy in the reported energy of this interface measured by different indirect methods [38,41,54]. The Zener pinning pressure was calculated as ∼1.7 MPa. Thus the Zener drag pressure of the initial material is nearly equal to the sum (Pd + Pb), providing a high resistance of the UFG structure against continuous coarsening under static annealing. Moreover, this structure does not undergo discontinuous grain coarsening because of the extremely high portion of HABs and a uniform distribution of grain dimensions [19,37,43,55]. The strain-induced grain coarsening, generally, occurs

during superplastic deformation, in which GBS plays a key role [41,47]. During superplastic deformation at T>450°C, the partial loss of coherency by Al3(Sc,Zr)/Al interphases and coarsening of these dispersoids highly reduce the Zener drag pressure, and strain-induced grain coarsening may occur [41]. Moreover, the deformation enhancement of grain grows maybe caused by the damage created at triple junctions by GBS [47] and/or the shear – coupled grain boundary motion [56]. Thus, in contrast with aluminum alloys free of such strong pinning agents as Al3(Sc,Zr) [57,58], the Al-Mg-Sc alloy may exhibit superplasticity with extraordinarily high ductility in the HRSR regime and moderate ductility in the LTSP regime because of the combination of high Zener drag pressure, high portion of HABs and uniform grain structure [25,59]. Conventional aluminum alloys could be processed in the UFG condition [57,58]. However, under static annealing, this structure is stable in a limited temperature domain, and as a result, the superplastic response of these alloys subjected to severe plastic deformation or thermomechanical processing is nearly the same [13,57,58]. 4.2 Effect of temperature on superplastic behavior  The variation with temperature of the optimal strain rate, opt , at which the highest

ductility appears (Fig. 10(a)) can be described as:  log opt =0.0137T – 9.7

(8)

In the temperature interval 150–400°C the data points are fitted to linear dependence with a high accuracy (Fig. 10(a)) because no significant grain growth takes place under static and dynamic superplastic conditions [12]. At T≥450°C, the onset of continuous grain coarsening corresponds to a slight deviation from the linear dependence (Fig.

 10(a)). This linear dependence indicates a real effect of the temperature on the opt

value [12] up to 450°C. For the purpose of comparison, the superplastic data from other studies [8,10,29] are also included in this plot, and it distinctly departs from the linear relationship at higher temperatures because of extensive coarsening at high temperatures. The HSRS and LTSP regimes with superior ductility could be observed concurrently in an aluminum alloy with a uniform UFG structure retaining stability under superplastic conditions up to 450°C because of the lack of discontinuous grain coarsening attributed to remnants of unrecrystallized grains [16,19,26,27,30,35]. In the AA5024 alloy, the onset of extensive continuous grain coarsening was found at 500°C, at which the regularities of superplastic behavior become distinctly different from those at lower temperatures (Figs. 4 and 9(a)). In the present work, the consideration of superplastic response will be limited by the temperature domain at T≤450°C in which the UFG structure produced by ECAP remains nearly unchanged under superplastic deformation. The temperature dependence of the optimum strain rate for the highest m value, m opt , is presented in Fig. 10(b). It is observed that the difference between the LTSP m and HSRS regimes consists of the temperature dependence of the opt value.

4.3 Mechanical aspects of superplastic behavior It is known [2,60] that plastic stability in tension can be provided by strain hardening and/or strain rate hardening, defined by

  K m n

(9)

where K is a constant, m is the coefficient of strain rate sensitivity, and n is the strain hardening coefficient. Numerous works [1-3] have demonstrated that if (n+m)>0.5,

fracture does not occur because of unstable plastic. As was shown in Section 3.3, in the AA5024 alloy, the m magnitude of 0.35 confers stable plastic flow, and therefore, the condition for stable plastic flow of (n+m)0.5 was overestimated. In conventional superplastic materials, there is no strain hardening [1-3]. In contrast, the AA5024 alloy exhibits extensive initial strain hardening up to the offset strain, εp, as in other aluminum alloys with UFG structure [57]. The strain hardening makes a significant contribution to the total ductility, especially in regimes where m≤0.35. The origin of this strain hardening is different in the LTSP and HSRS regimes. In the LTSP regime, a weak strain hardening is attributed to the increasing density of lattice dislocations. The dislocation strengthening is described by the Taylor relationship:

 d  MGb 1/ 2 ,

(10)

where  is the dislocation forest density, α is a constant (0.24), and M is the orientation factor calculated from EBSD data. In the LTSTP regime, the strain hardening stage is relatively short (Fig. 11(a)), and the strengthening is two-fold higher than that predicted by Eq. (10). Therefore, the other work-hardening mechanisms may contribute to the overall strain hardening. At elevated temperatures, the strengthening can be associated with grain coarsening during superplastic deformation. Eq. (1) with p=3 and n=2 can be re-written in the following form to express flow stress as a function of grain size:

 

GkT d 3 / 2 1 / 2  ADGB b 2

(11)

At 450°C and ε= 5.6×10–1 s–1, Eq. (11) predicts with high accuracy a 58 pct increase in flow stress attributed to a 150 pct increase in grain size at the offset strain rate,  p , which is lower than the initial one by a factor of 4 at p=1.24. Therefore, in the HSRS regime, the dislocation density remains unchanged and strong strain hardening is attributed to increasing grain size. Thus, the transition from the LTSP to the HSRS regime is accompanied by the change in the work-hardening mechanism that leads to expanding the initial strain hardening stage by a factor of 6 and decreasing the workhardening rate, d/d by a factor of 2 (Figs. 5 and 11). It is known that plastic stability in tension attributed to strain hardening occurs up to a point of tensile instability leading to localized deformation defined by the Considère condition [60,61]: = d/d

(12)

Inspection of Fig. 11(a) shows that at all superplastic conditions, the tensile instability appears at d/d<. The work-hardening initially decreases linearly with the strain, as in Al-Mg alloys at ambient and cryogenic temperatures [61]. However, no typical rapid drop of hardening rate is observed below the Considère condition, and moreover, the d/dvalue tends to approach zero gradually because of the strain rate hardening expressed by the m value. Therefore, strain rate hardening is the most important mechanism providing stable plastic flow. Pure strain hardening may confer stable plastic flow at  p. However, superposition of the strain hardening and strain rate  sensitivity at opt confers stable plastic flow up to the offset strain, p, for any

superplastic condition. At the offset strain, p, the work-hardening is replaced by

apparent strain softening and the stability of plastic flow is conferred solely by the strain rate hardening associated with m≥0.4 [2,57]. In the LTSP regime, the highest work-hardening level is close to that observed in dilute Al-3.5÷4.5%Mg alloys at cryogenic and room temperatures [61] but decreases with a very high rate of strain. Therefore, stability of plastic flow may be provided mostly by strain rate hardening in a wide strain rate interval that yields the unified  m optimal strain rate ( opt  opt ). At >p, the m value is <0.4, which is not sufficient

to prevent instability of plastic flow that results in the material pulling out to a fine point or distinct necking prior to failure at 175 or 275°C, respectively (Fig. 5).  At 450°C and opt =5.6×10–1 s–1, m≤0.3 at the strain hardening stage (Table 1a).

These m values are not sufficient to stop unstable plastic flow because of pure strain rate hardening [2,57]. However, the offset strains for the HSRS regime are relatively high (Table 1a), and strain hardening attributed to grain coarsening provides stability of plastic flow up to p. A four-fold decrease in the true strain rate occurs at p. Because m the true strain rate decreases with strain and tends to approach opt , the m values

approaching ≥0.4 provide a very uniform deformation visible within the gauge length up to failure at the strain-softening stage (Fig. 7). Therefore, the expansion of the workhardening stage because of strain-induced coarsening to higher strains leads to  m increasing discrepancies in the opt and opt values (Fig. 10). The initial strain

hardening in the HSRS regime provides stability of plastic flow at the initial stage of plastic flow despite low m values.

A high density of lattice dislocations within micron-scale grain interiors promotes accommodation of GBS [1-3], and cavitation plays an unimportant role in fracture at any conditions. 4.4 Threshold stress The validity of Eq. (2) for description of the superplastic behavior of Al-Mg-Sc(Zr) alloys was recently confirmed in works [12,25]. Therefore, to calculate the true activation energy, Qt, and the true stress exponent, n, in Eq. (2), the deformation behavior of the AA5024 alloy has to be analyzed in terms of threshold stress. In region I, the low m values do not represent a genuine change in the rate-controlling mechanism but rather originate from the existence of a threshold stress because of the segregation of impurity atoms on the grain boundaries or interfaces of dispersoids [28,62,63]. A standard procedure was used to determine the threshold stress, taking into account that regions II and I are controlled by the same deformation process [12,25,28,62-64]. The experimental data in regions II and I at a single temperature and offset strain were plotted as ε1/n (n=1, 2, 3 and 5) against peak stress or steady state flow stress, σ, on a double-linear scale (Fig. 4(a, a’)). The stress exponent of n = 2 provided the best linear fit among the assumed stress exponents at all temperatures, and therefore, this magnitude is the true stress exponent [28,64]. Threshold stresses estimated by an extrapolation of the data to zero strain rates with a linear regression, as illustrated in Fig. 12, are summarized in Table 2. The threshold stress decreases, decreasing from a very high value of 123 to 1.6 MPa with increasing temperature from 150 to 450°C. At T=175°C and ε=1.4×10–4 s–1, the threshold stress approaches the yield stress (Fig. 5(a) and Table 2). At 450°C, the threshold stress is low (Table 2). The same magnitude of threshold stress was reported for Al-4Mg-1Zr alloy [12] and a dispersion-bearing grade

of Zn-22Al alloy [28], Al-5Mg-0.2Sc alloy with a partially recrystallized structure [28]. Dispersion-free Zn-22Al and Pb-62Sn alloys produced by ingot metallurgy [62,63] and Al-5Mg-0.2Sc alloy with fully recrystallized structure [25] exhibit lower threshold stress. Therefore, the data of the present work support the conclusion of F. Mohamed et al. [28] that the superplastic deformation process incorporates a threshold stress originating from the interaction between dislocations and dispersion particles. However, at present, there is no model predicting strong temperature dependence of the threshold stress [28,64]. The temperature dependence of the normalized threshold stress can be expressed by a relationship of the form [28,62-64]: ( ),

(13)

where Bo is a constant and Qo is an energy term representing the activation energy for a dislocation to overcome an obstacle. The temperature dependence of the shear modulus was taken for pure Al (in MPa) as [62]: G = (3.022 × 104) − 16T

(14)

The Qo value inferred from the slope of this plot in the temperature range 150–450°C is ~32 kJ/mol (Fig. 13). The unified temperature dependence of the threshold stress is an indication that the mechanism of interaction between a dislocation and an Al3(Sc,Zr) dispersoid is the same at any temperature. The Qo value is higher than that for superplastic deformation of dispersion-bearing and dispersion-free Zn-22Al alloy grades produced by cryomilling and ingot metallurgy, respectively, (21 ÷ 23 kJ/mol), and Pb-62Sn alloy (17 kJ/mol) [28,62,63].

Superplastic deformation up to the offset strain is driven by an effective stress, not by  m the applied stress [4,28,65]. The discrepancy in effective stress between opt and opt

conditions is attributed to the role of strain hardening in attaining the highest ductility in the HSRS regime (Section 4.3). 4.5 True activation energy and the normalized creep data To determine the true activation energy, the normalized effective stresses (σ – σth)/G for regions I and II were plotted as a function of 1/T at fixed strain rates (Fig. 14), where the slope is equivalent to Qt/nR (n is the true stress exponent and R is the gas constant) [62]. The average Qt value is approximately 83 and 70 kJ/mol in the LTSP and HSRS regimes, respectively, that is, similar and close to the activation energy for boundary self-diffusion of pure Al (84 kJ/mol) [66]. Thus, the incorporation of the threshold stress in the activation energy analysis provides realistic values of the true activation energy and the true stress exponent, and there is no doubt that GBS is the dominant superplastic deformation mechanism, as was shown by surface observations in the present study and by F.C. Liu et al. [26]. These parameters are nearly similar for the LTSP and HSRS regimes, and therefore, the controlling mechanism of superplastic deformation at low temperatures and high strain rates is the same and attributed to dislocation climb along a boundary controlled by grain boundary diffusion. Figure 15 represents a double logarithmic plot of the normalized strain rate, ̇kT/(DGb), against the normalized effective stress, (σ–σth)/G. The Burgers vector and the boundary self-diffusion, D, for pure aluminum were taken [3,64]. The AA5024 alloy exhibits a well-defined superplastic behavior with the stress exponent n2. There

is a deviation of the experimental data points from a straight line in the range of low temperatures that is typical for the transition to ̇exp() dependence [62]. 4.6 Superplastic deformation mechanism in the LTSP and HSRS regimes Inspection of experimental results shows that there are no fundamental differences between the regularities and mechanisms of superplasticity in the present aluminum alloy with UFG structure containing a dispersion of coherent dispersoids and microcrystalline aluminum alloys containing incoherent particles under superplastic conditions [1-3,12,25], although the present alloy is characterized by a high density of lattice dislocations. Analysis of constitutive Eq. (2) suggests that the mechanism of superplastic deformation in the AA5024 alloy in the HSRS and LTSP regimes is similar to conventional superplasticity [1-3,63,65]. The difference in the superplastic mechanism between dispersion-free and dispersion-bearing aluminum alloys consists of the presence of strong obstacles within the micron-scale grains. The role of these coherent dispersoids in superplastic deformation is three-fold. These particles provide high stability of the UFG structure under static and dynamic superplastic conditions and extraordinary accumulation of lattice dislocations, which exert high threshold stress. However, these particles do not modify the mechanism of superplastic deformation, which appears to be consistent with the modified model of Ball and Hutchison (Fig. 16(a-c)) [2,65,67]. The sliding of a group of grains as a unit is accommodated by dislocation motion within the grain interiors. Dislocations emitted by grain boundary sources from a grain-side glide need to traverse the interior of the blocking grain and then pile up at the opposite grain boundary. The leading dislocation enters in a boundary as mobile extrinsic and climbs along it. Two sequential processes occur during the superplastic deformation: fast dislocation glide in the interiors of the

grains and slow dislocation climb along the boundaries [1-3]. The last process controls superplastic deformation [1-3]. The rate of GBS is controlled by the rate at which the dislocations are removed by climb from the head of the pile-up and next are adsorbed by a grain boundary [1-3] (Fig. 16). In the Ball and Hutchison mechanism, the climb of a lattice dislocation trapped (TLD) by a grain boundary along this boundary is considered as a process controlled by the strain [2-4,67]. In the modified mechanism [1,65], the absorption of this dislocation by the boundary is considered to be a ratecontrolled process. We will consider two mechanisms in sequence to give an  unambiguous interpretation of the temperature dependence of opt described by Eq. 8.

In the Ball and Hutchinson mechanism, the leading dislocations climb the short distance, which is equivalent to 10b or even less [2,65,67]. If dislocations move across a grain and pile up at a boundary, the stress at the head of the pile-up, pile-up, is given by [65,68]

 pileup 

2 L 2 , Gb

(15)

where L is the length of the pile-up, being equivalent to the linear intercept size, and  =

/3 is the shear stress acting on the slip plane on the direction of the Burgers vector. We calculated p=148 MPa, p=55 MPa and p=37 MPa at 175, 275 and 450C, m respectively, at the offset strain and opt condition.

We assume that the climb velocity, vc-ld, at the head of the pile-up is controlled by the rate of grain boundary diffusion given by [68]:

vc  ld

  pile  up b3 DGB   exp( )  1  ,   kT 

(16)

whereis a distance at which the vacancies conservation varies near the dislocation. We assume λ = 30b  10 nm for the sake of simplicity. DGB is the diffusion coefficient calculated as [65]

 - 84  10 3 DGB=1.7110–4exp   RT

  , 

(17)

where Do was taken for pure aluminum as 1.7110–4 m2/s-1 and Q is the activation energy for boundary self-diffusion of pure Al (84 kJ/mol). In physical models of superplasticity [68], Eq. (16) is simplified to

vC  LD

3 DGB  pileup b  ,      kT 

(18)

taking the condition of pile-upb3«kT. However, our calculation using simplified Eq. (18) for 275 and 450C showed that kT is more than pile-upb3 by a factor of 1.4 and 3.5, and the simplification is appropriate for T≥275C only. The difference in climb velocity between the values obtained through Eq. (16) and Eq. (18) for 450°C (15 pct.) is considered to be insignificant, while it is 30 pct. for 275°C. In contrast, at 175°C, pile-upb3 is higher than kT by a factor of 5.9, and only the complete Eq. (16) can be used to appropriately describe superplastic behavior in the LTSP regime. In this case, the strain rate of superplastic deformation is dependent upon stress through a relationship of the form:

  A1  exp( 2 )

(19)

where A1 and  are constants. The transition from the power-law (Eq. (2)) to a type of exponential superplasticity at low temperatures is observed in Fig. 15.

 Finally, the variation with temperature of the climb velocity, υC-LD, at opt

conditions calculated by Eq (18) in the HSRS and LTSP regimes, respectively, is presented in Fig. 17 and described by linear dependence as: log υC-LD =0.009T – 9.

(20)

 This temperature dependence is weaker than the temperature dependence of opt (Eq.

2). Most existing models consider only the first process [2-4]. However, the absorption of lattice dislocation is a necessary process, providing low density of grain boundary dislocation. It is known [51] that a high dislocation density blocks the occurrence of GBS, and no superplastic behavior is observed. In the superplastic mechanism suggested by Kaibyshev, Valiev and Emaletdinov, [1,69], the absorption of a lattice dislocation by a boundary occurs in three sequential steps [70-75]: the trapping of a lattice dislocation by a grain boundary; the dissociation/splitting of a lattice dislocation into sessile and glissile extrinsic grain boundary dislocations (EGBD) with smaller Burgers vectors; and spreading of the dissociation products in mutually opposite directions to minimize energy. The ratelimiting process is the spreading of grain boundary dislocations along the boundary. Because the grain boundary dislocations are also extrinsic ones, this process occurs by climb and is controlled by grain boundary diffusion [70-75] as the climb of lattice dislocation along a boundary in the Ball and Hutchison mechanism [2,65,67]. It is worth noting that the role of dislocation spreading in superplasticity is the unlocking of a boundary dislocation source that would allow another dislocation to be emitted and enable further GBS (Fig. 16(a-c)). Therefore, the climb of grain boundary dislocation through the grain boundary is not only a mechanism for absorption of a primary lattice

dislocation by boundary but also contributes to the elementary process of GBS (Fig. 16(d)) [65]. There are several models of the lattice dislocation absorption, but they estimate approximately the same spreading rate. The spreading rate of grain boundary  dislocations, SR-GBD, at opt conditions is assumed to be equal to the spreading rate

defined as the time derivative of the distance between the dissociation products, d/dt, as in [70,75-77]:

vSR GBD 

DGB Gb , CkT2

(21)

where C = constant dependent on the assumed model, 1 ≤ C ≤ 10 [77], in this study C=1, =b3 is the atomic volume. The temperature dependence of the dislocation spreading is described by linear dependence as: log SR-GBD =0.0131T – 11.

(22)

This temperature dependence (Fig. 17) matches with high accuracy the temperature   dependence of opt described by Eq. (2). Therefore, the increase in opt with

increasing temperature is attributed to promoting the grain boundary dislocation spreading rather than increased velocity of lattice dislocation climb along a boundary. It is worth noting that temperature dependencies of both processes are attributed to increasing the grain boundary diffusion rate. In addition, we evaluated the spreading rate using the simplified approach of R.A. Varin et al. [78] and A.P. Zhilyaev [72] and obtained a similar value. At high temperatures, the climb and absorption of grain boundary dislocations occur  at a very high rate (Fig. 17). The opt value is restricted by the velocity of the

dislocation climb along a boundary and the stability of the UFG structure at high

temperatures. At low temperature, the disappearance of superplasticity with decreasing temperature could be attributed to a critical decrease in the climb rate. It is known that the energy of a boundary trapped lattice dislocation is strongly dependent on the distance of the products of their dissociation [71,72,75]. If this distance is low, no effective spreading of the lattice dislocation occurs and the back stress locks boundary dislocation sources (Fig. 16(a-c)). As a result, extensive accumulation of dislocations in grain boundaries occurs. Materials with boundaries containing high dislocation density exhibit no superplastic behavior at any grain size [51].

5. Conclusions 1.

The ultrafine grain structure of the 5024 alloy with an average size of ~0.7 m is

stable after static annealing at elevated temperatures up to 450°C because of the strong pinning effect of fine Al3(Sc,Zr) particles. A high portion of high-angle boundaries and a uniform grain size distribution provide no susceptibility to discontinuous grain coarsening. 2.

At low temperature of 175°C (~0.3Tm) and ε=1.4×10–4 s–1, the tensile elongation

is ~365 pct with corresponding strain rate sensitivity coefficient m~0.3. The highest superplasticity of ~1200 pct. in the low-temperature region was obtained at a temperature of 275°C (~0.47Tm) and ε=5.6×10–3 s–1 with corresponding strain rate sensitivity coefficient m~0.49. At a temperature of 450°C (~0.78Tm) and a high strain rate of 5.6×10–1 s–1, the highest ductility of ~3300 pct was attained. 3.

Analysis in terms of threshold stress showed that superplastic behavior of the

material is described by the true stress exponent of 2, and the activation energy is close to the activation energy for boundary self-diffusion of pure Al (84 kJ/mol) in a wide

temperature range. Distinct direct evidence of grain boundary sliding was obtained by surface observations. The superplastic mechanisms of aluminum alloy containing coherent Al3(Sc,Zr) particles and conventional aluminum alloys are nearly the same. The mechanism of LTSP and HSRS in the 5024 alloy is the grain boundary sliding controlled by boundary self-diffusion. 4.

Coherent Al3(Sc,Zr) particles provide a very high dislocation density (≥1014 m-2)

in grains during superplastic deformation. At low temperatures, strong initial strain hardening is attributed to accumulation of lattice dislocations. At high temperatures, extended strain hardening is attributed to strain-induced grain growth. The latter is  responsible for the discrepancy between the optimal rate, opt , and the strain rate m corresponding to the highest the value of m, opt . The strain hardening makes a

significant contribution to attaining high ductility.

Acknowledgments The financial support received from the Ministry of Education and Science, Russia, under Project No. 11.1533.2014/K is gratefully acknowledged. The main results were obtained by using equipment of Joint Research Center, Belgorod State University. The authors are grateful to Andrey Belyakov for discussion of results.

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Fig. 1. Microstructures of the 5024 alloy subjected to ECAP. Fig. 2. Grain size as a function of annealing temperature for the 5024 alloy subjected to ECAP. Fig. 3. Typical micrographs showing Al3(Sc,Zr) precipitate distributions for 5024 alloy processed by ECAP after static annealing at 450°C. Fig. 4. The variation of true stress (a, a’), the coefficient of strain rate sensitivity (b, b’), elongation-to failure (c, c’) with strain rate for testing temperatures (a, b, c) of 150– 275°C and (a’, b’, c’) of 300–500°C. Fig. 5. True stress–true strain curves of the 5024 alloy tested at 175°C (a), 275°C (b) and 450°C (c).

Fig. 6. The variation of the strain rate sensitivity with true strain at 175°C and initial strain rate of 1.4×10-4 s-1, 275°C and initial strain rate of 5.6×10-3 s-1, 450°C and initial strain rate of 5.6×10-1 s-1. Fig. 7. Appearance of specimens that exhibited a maximum elongation-to-failure at LTSP and at HSRS. Fig. 8. EBSD map (a, a’, a’’), misorientation distribution (b, b’, b’’), SEM micrograph showing surface morphology (c, c’, c’’) and cross-sectional view (d, d’, d’’) of ECAP sample superplastically deformed to failure at 175°C and ε=1.4×10–4 s–1 (a-d) at 275°C and ε=5.6×10–3 s–1 (a’-d’) and 450°C and ε=5.6×10–1 s–1 (a’’-d’’). Fig. 9. TEM micrographs showing the microstructure of the samples after superplastic deformation up to offset strain at various temperature. Fig. 10. Variation of optimum strain rate for maximum superplasticity (a) and optimum strain rate for the highest value of strain rate sensitivity (b) with temperatures for ECAP Al–Mg–Sc–Zr and other UFG aluminum alloys. Fig. 11. Work hardening as a function of true strain at different temperatures for the present material (a). The dashed lines indicate the Considere criterion. Relationship between peak strain and peak stress at constant strain rate (b) and constant temperature (c). Fig. 12. Variation of flow stress as a function of ε1/2 for the 5024 alloy subjected to ECAP. Fig. 13. Plot of the logarithm of the normalized threshold stresses vs reciprocal absolute temperature. Fig. 14. Variation of ln(σ–σth) as a function of reciprocal temperature for the 5024 alloy subjected to ECAP.

Fig. 15. Normalized strain rate vs. normalized effective stress for the 5024 alloy. Fig. 16. a) TLDs in high-angle GBs; b) the structure resulting from TLD dissociation; c) equilibrium EGBD array in GB; (d) deformation model of fine-grained superplasticity. Fig. 17. Variation of climb velocity of lattice dislocations, vC-LD, and spreading rate of EGBD, vSR-GBD, as a function of reciprocal temperature for the UFG 5024 alloy.

Table 1. A summary of the superplastic properties at various temperatures of the 5024 alloy subjected to ECAP. For highest (a) δ and (b) m. (a) SP

T, °C

150 175 200 LTSP 225 250 275 300 350 HSRS 400 450 500

Initial strain rate, s-1 1.4×10-4 1.4×10-4 2.8×10-4 1.4×10-3 2.8×10-3 5.6×10-3 5.6×10-2 1.4×10-1 2.8×10-1 5.6×10-1 5.6×10-3

δ, pct

Corresponding m value

160 365 500 1000 880 1200 1350 1830 2190 3300 1810

0.21 0.30 0.26 0.33 0.43 0.49 0.25 0.25 0.31 0.19 0.63

p

p

0.36 233 0.38 148 0.35 93 0.48 88 0.75 62 0.89 55 0.85 82 1.0 55 1.0 35 1.3 37 1.5 9

(b) SP

T, °C

150 175 200 LTSP 225 250 275 300 350 HSRS 400 450 500

Initial strain rate, s-1 1.4×10-4 1.4×10-4 1.4×10-4 5.6×10-4 1.4×10-3 5.6×10-3 5.6×10-3 1.4×10-2 1.4×10-2 1.4×10-2 5.6×10-3

m

Corresponding δ value, pct

0.21 0.30 0.31 0.39 0.44 0.49 0.42 0.45 0.46 0.57 0.64

160 365 490 690 720 1200 590 720 1040 1360 1570

p

p

0.36 233 0.38 148 0.28 81 0.51 62 0.95 50 0.89 55 0.86 36 1.1 22 1.4 11.5 1.6 9.5 1.5 9

Table 2. Threshold stress at various temperatures of the 5024 alloy subjected to ECAP. Temperature, °C

Threshold stress, MPa

150 175 200 225 250 275 300 350 400 450

123.4 65.7 62.3 13.3 12.4 9.6 9.1 7.1 3.7 1.6

Effective stress, MPa at strain rate for highest δ 109.6 82.3 30.7 74.7 49.6 45.4 72.9 47.9 31.3 35.4

Effective stress, MPa at strain rate for highest m 109.6 82.3 18.7 48.7 37.6 45.4 26.9 14.9 7.8 7.9