ISSN 00360295, Russian Metallurgy (Metally), Vol. 2010, No. 7, pp. 648–657. © Pleiades Publishing, Ltd., 2010. Original Russian Text © V.N. Serebryany, T.M. Ivanova, V.I. Kopylov, S.V. Dobatkin, N.N. Pozdnyakova, V.A. Pimenov, T.I. Savelova, 2010, published in Metally, 2010, No. 4, pp. 82–92.
Effect of EqualChannel Angular Pressing and Annealing Conditions on the Texture, Microstructure, and Deformability of an MA21 Alloy V. N. Serebryanya, T. M. Ivanovab, V. I. Kopylovc, S. V. Dobatkina, N. N. Pozdnyakovaa, V. A. Pimenovd, and T. I. Savelovab a
Baikov Institute of Metallurgy and Materials Science, Russian Academy of Sciences, Leninskii pr. 49, Moscow, 119991 Russia email:
[email protected] b Moscow Institute of Engineering Physics (State University MIFI), Kashirskoe sh. 31, Moscow, 115409 Russia c Physicotechnical Institute, Belarussian Academy of Sciences, ul. Tskhodinskaya 4, Minsk, 220730 Belarus dBardin Central Research Institute for the Iron and Steel Industry, Vtoraya Baumanskaya ul. 9/23, Moscow, 107005 Russia Received December 29, 2009
Abstract—Equalchannel angular pressing (ECAP) of am MA21 alloy according to routes A and Bc is used to study the possibility of increasing the lowtemperature deformability of the alloy due to grain refinement and a change in its texture. To separate the grain refinement effect from the effect of texture on the deform ability of the alloy, samples after ECAP are subjected to recrystallization annealing that provides grain growth to the grain size characteristic of the initial state (IS) of the alloy. Upon ECAP, the average grain size is found to decrease to 2–2.4 μm and the initial sharp axial texture changes substantially (it decomposes into several scattered orientations). The type of orientations and the degree of their scattering depend on the type of ECAP routes. The detected change in the texture is accompanied by an increase in the deformability param eters (normal plastic anisotropy coefficient R, strainhardening exponent n, relative uniform elongation δu) determined upon tensile tests at 20°C for the states of the alloy formed in the IS–4A–4Bc and IS–4Ao–4BcO sequences. The experimental values of R agree with the values calculated in terms of the Taylor model of plas tic deformation in the Bishop–Hill approximation using quantitative texture data in the form of orientation distribution function coefficients with allowance for the activation of prismatic slip, especially for ECAP routes 4Bc and 4BcO. When the simulation results, the Hall–Petch relation, and the generalized Schmid fac tors are taken into account, a correlation is detected between the deformability parameter, the Hall–Petch coefficient, and the ratio of the critical shear stresses on prismatic and basal planes. DOI: 10.1134/S0036029510070128
INTRODUCTION Deformable magnesium alloys of the Mg–Al–Zn– Mn system, which include an MA21 alloy, has low deformability at a testing temperature below 250°C because of a limited number of operating deformation systems. As a rule, basal slip is predominant in magne sium alloys during lowtemperature deformation; it favors the formation of a sharp basal texture, which then retards this basal slip. The situation can be improved if a finegrained structure is formed in a material in order to stimulate additional slip systems, such as prismatic slip (especially in nearboundary regions in grains) and a scattered nonbasal texture (which activates prismatic and basal slip) [1–3]. Equalchannel angular pressing (ECAP) is one of the methods of severe plastic deformation that can provide such changes in the microstructure and texture of the alloy [4–14]. The purpose of this work is to study the effect of various ECAP and ECAP + annealing conditions on
the texture, microstructure, deformability parame ters, and mechanical properties of a magnesium MA21 alloy. EXPERIMENTAL We studied an MA21 alloy rod 30 mm in diameter that was pressed, annealed at 345°C for 1 h, and air cooled; its chemical composition was (wt %) 4.5 Al, 1.3 Zn, 0.5 Mn, 0.025 Cu, 0.002 Ni, 0.05 Si, 0.001 Be, 0.02 Fe, and Mg for balance. ECAP was performed on 20 × 20 × 150mm sam ples according to routes A and Bc at an angle of chan nel intersection of 90° (Fig. 1). Route A Consists in Repeated Pressing of a Sample without Rotation Pressing in this route is carried out in one pass at a temperature of 260°C (true strain is ε ≈ 1.13); in two
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passes at a pressing temperature of 260°C in the first pass and 240°C in the second pass (true strain is ε ≈ 2.26); and in four passes at a pressing temperature of 260°C in the first pass, 240°C in the second and third passes, and 220°C in the fourth pass (true strain is ε ≈ 4.52).
1
Modified Route Bc Consists in Rotation of a Sample through 90° about Its Axis between the Second and Third Passes and a Change in the Pressing Direction after Every Pass In this route, pressing is carried out in four passes at a pressing temperature of 260, 240, 240, and 220°C in the first, second, third, and fourth pass, respectively (true strain is ε ≈ 4.52). After ECAP according to routes A and Bc, samples were subjected to annealing at 345°C for 1 h and air cooling. After ECAP and annealing, specimens (of AO or BcO type) were cut parallel to plane y to study the texture, microstructure, and mechanical properties of the alloy (see Fig. 1). The microstructure of the alloy was examined on a megavolt JEM1000 (JEOL) elec tron microscope at an accelerating voltage of 750 kV after ECAP and on a Neophot optical microscope in the initial state and after final annealing. The tensile tests were performed according to GOST (State Stan dard) 1170184 at a temperature of 20°C on a univer sal electromechanical Instron1185 testing machine at a strain rate of 2 × 10–3 s–1. A gage length of 30 mm was marked on tensile specimens with a vernier caliper and used to measure the thickness and the initial width at three points. Longitudinal deformation tensometers (the gage length was 4.35 mm, and the scale was 25%) were then put on the specimens, and they were ten sioned until necking (which was detected from a decrease in the load after its maximum). The speci mens were then removed from the tensile testing machine; the thickness was measured at three points; and the elongation was measured on the gage length preliminarily marked with a vernier caliper. The test ing results were used to determine yield strength σy, ultimate tensile strength σu, and uniform elongation δu. The deformability indices, namely, normal anisot ropy coefficient (NAC) R, strainhardening exponent (SHE) n, and deformability parameter (DP) K were calculated by the formulas [15] ε ln ( b d /b ) R = b = , εs ln ( s d /s ) where b and s are the specimen width and thickness before deformation, respectively; bd and sd are the specimen width and thickness after deformation, respectively; n = ln(1 + δu), K = Rn. RUSSIAN METALLURGY (METALLY)
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2 3 4 z x
y
Fig. 1. Schematic diagram for ECAP of an MA21 alloy sample: (1) plunger, (2) sample, (3) die, and (4) pressed sample. x, y, and z are the sample planes.
We introduced parameter K for an integral estima tion of deformability due to the effect of a texture (R) and microstructure (n). Specimens for texture measurements were cut from the specimens exhibiting the maximum values of δu. Texture in the form of incomplete six pole figures (PFs) {00.4}, {20.0}, {10.1}, {10.2}, {10.3}, and {11.0} were studied in reflection geometry on a DRON7 Xray diffractometer using CuKα radiation. We used the angle of inclination α range 0°–70° and the rota tion angle β range 0°–360° at an α or β step of 5°. The defocusinginduced decrease in the intensity at the periphery of a PF was corrected using coefficients cal culated for PF recording conditions. The texture was studied in the initial pressed state (IS) of the alloy, after ECAP, and after ECAP + annealing. The PFs were characterized by the presence of triclinic symmetry even after tensile deformation in the presence of sev eral rather sharp maxima. The main specific features of texture can be described by a small number of parameters using tex ture components and the approximation of orienta tion distribution functions (ODFs) by central normal distributions (CNDs) [16]. As model components, we chose a circular normal distribution for group SO(3). The centers of the components and the initial values of the scattering parameters were obtained by a graphical method in a dialog mode. When choosing the initial positions of the components, we used all six PFs. To
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refine the positions of the components and scattering parameters and to determine the volume fraction and a background component, we used a nonlinear opti mization method based on the Levenberg–Marquardt algorithm and orthogonal expansions (SVD algo rithm). The nonlinear optimization was performed using {00.4}, {10.2}, and {10.1} PFs, and the adequacy of the model was estimated with parameter RP(Δ). PROCEDURE OF CALCULATING THE NORMAL ANISOTROPY COEFFICIENT FROM THE TEXTURE OF HEXAGONAL SHEETS The procedure of calculating NAC from texture for the case of orthorhombic and monoclinic symmetry of a sample was described in [17–19]. Here, we apply this procedure for the case of triclinic symmetry of a sam ple. Our method is based on calculating the external deformation work and related Taylor factor M(q, g), where q is the parameter determining the strain tensor and g is the grain orientation, for every grain. The Tay lor factor is then averaged over all orientations using ODF f(g) M(q) =
∫ M ( q, g )f ( g ).
If f(g) and M(q, g) are expanded into a series in μν spherical harmonics T λ ( g ) of triclinic symmetry and the last function is also expanded into a power series in q, the integral takes the form L
M(q) =
λ
λ
r
∑∑ ∑∑
λ = 0 μ = –λ ν = –λ ρ = 0
p
μν μν q m λρ C λ . 2λ + 1
The coefficients of ODF expansion are determined by analyzing experimental PFs using the component method [16], and the coefficients of expansion of the Taylor factor in spherical harmonics are calculated by the formula μν mλ ( q )
∫
= ( 2λ + 1 ) M ( q,
μν g )T λ ( g ) dg.
the entire sample. For this approximation to be applied, we should find all possible states of stress that can simultaneously activate at least five independent deformation systems. If such states of stress are known for multiple slip, the state of stress that activates the introduction of the corresponding state of strain is chosen from the maximum work principle. We assumed that plastic deformation during uniax ial tension of the magnesium alloy under study at a temperature of 20°C is provided by {0001} basal and {1010} prismatic slip of dislocations along the 〈1120〉 direction and {1012}〈1011〉 twinning (hereafter, sub scripts “bas,” “prism,” and “tw.ten” of shear stress τ, respectively). In the equal strain approximation, we applied the Bishop–Hill principle of the maximum work and calculated all possible states of stress that can simultaneously activate at least five independent deformation systems by the Thornburg–Piehler tech nique [19, 20]. For a given value of q, M(q, g) was determined as the ratio of the maximum deformation work for a given grain orientation normalized to unit deformation to the critical shear stress for the pris matic slip system. A similar procedure was repeated for various orientations g = {ϕ1, Φ, ϕ2} (where ϕ1, Φ, ϕ2 are the Eulerian angles) in the triclinic symmetry approximation. These angles changed in the ranges 0° < ϕ1 < 360°, 0° < Φ < 90°, and 0° < ϕ2 < 60° at a step of 3° for each angle and 0.1 for q (0 < q < 1). As a result, we obtained normalized orientation functions M(q, g). With this procedure, we then determined the NAC for the magnesium MA21 alloy, and ODF coefficients μν C λ were calculated from a PF to Lmax = 25 using the technique from [16]. We modified this algorithm of calculating the normal plastic anisotropy coefficient of magnesium alloy samples with triclinic symmetry. These algorithms were used to write computer pro grams. RESULTS AND DISCUSSION Microstructure
Experimental parameter q takes a value qmin and, thus, optimizes an averaged Taylor factor. Then, R is determined by the formula R = qmin/(1 – qmin). To calculate NAC R using this algorithm, we have to construct an orientation function for the Taylor fac tor M(q, g). This function is constructed for any mate rial with allowance for its plastic deformation on cer tain crystallographic deformation systems. To con struct this function, we used the Taylor plastic deformation model in the Bishop–Hill approxima tion. The main assumption of this model consists in the fact that each grain in a polycrystalline sample is deformed by analogy with the macrodeformation of
Figures 2 and 3 show the typical microstructures of the MA21 alloy in the initial state (Fig. 2a), after ECAP according to route 4A (Figs. 3a, 3b), after ECAP according to route 4A plus annealing (Fig. 2b), ECAP according to route 4Bc (Figs. 3c, 3d), and ECAP according to route 4Bc plus annealing (Fig. 2c). The microstructure of the magnesium alloy in the initial state is characterized by recrystallized grains slightly elongated in the pressing direction. After ECAP by routes 4A and 4Bc, the average grain size decreases and recrystallized grains are equiaxed and have the same size for both regimes. Annealing after ECAP leads to grain growth to the size characteristic of the IS.
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(а)
20 μm
(c)
20 μm
(b)
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20 μm
Fig. 2. Macrostructure of the MA21 alloy (a) in the initial state and after ECAP according to routes (b) 4A + annealing and (c) 4Bc + annealing.
(а)
1 μm
(b)
1 μm
(c)
1 μm
(d)
1 μm
Fig. 3. Microstructures of the MA21 alloy ((a, c) brightfield images, (b, d) darkfield images) after ECAP according to routes (a, b) 4A and (c, d) 4Bc. RUSSIAN METALLURGY (METALLY)
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SEREBRYANY et al. (a)
Thus, the effect of the average grain size on the change in the mechanical properties and deformabil ity of the alloy after ECAP by various regimes and after ECAP + annealing may be neglected.
(b)
Texture P 0.80 1.51 2.22 2.94 3.65 4.36 5.08
(c)
Figure 4 shows the experimental and calculated {00.4} PFs for the MA21 alloy after tensile deforma tion at 20°C and after ECAP and ECAP + annealing under various conditions. The PFs are seen to have tri clinic symmetry except for the initial state.
P 0.80 1.51 2.22 2.94 3.65 4.36 5.08
(d)
P 0.80 1.39 1.98 2.58 3.17
Using the technique in [16], we approximated the experimental PFs by a set of CND orientations. Table 1 gives the sets of such orientations and their volume fractions fi for various ECAP and ECAP + annealing regimes for the MA21 alloy. As is seen from Fig. 4, the calculated PFs mainly repeat the principal specific features of the experimental PFs. The existing differ ences are related to the errors in measuring PFs.
P 0.80 1.39 1.98 2.58 3.17
(e)
(f)
P 0.48 0.84 1.56 1.92 2.28 2.64
As a result of ECAP by routes 4A and 4Bc, radical changes in the texture of the MA21 alloy take place: the initial onecomponent sharp axial texture decom poses into several axial and peak components with dif fuse maxima. Both subsequent annealing and tensile deformation change the positions of the maxima and their pole densities, and triclinic symmetry remains unchanged. In contrast to the microstructure, the alloy texture differs substantially after both ECAP according to various regimes and ECAP + annealing. Therefore, we assume that the mechanisms of plastic deformation of the alloy are different for different treatment regimes. The detected radical change in the texture is caused by intense ECAPinduced shear strains in the material and by dynamic recrystalliza tion in the severely deformed material [21]. We will use these results of texture evolution to estimate the NAC and to calculate the generalized Schmid factors.
P 0.48 0.84 1.20 1.56 1.92 2.28 2.64
(g)
(h)
P 0.88 1.69 2.49 3.30 4.10 4.91 5.71
(i)
P 0.88 1.69 2.49 3.30 4.10 4.91 5.71
(j)
P 0.83 1.47 2.10 2.74 3.37 4.01 4.64
Deformability Parameters
P 0.83 1.47 2.10 2.74 3.37 4.01 4.64
Fig. 4. (a, c, e, g, i) Experimental and (b, d, f, h, j) cal culated (00.4) PFs for the MA21 alloy (a, b) in the ini tial state and after ECAP according to routes (c, d) 4A, (e, f) 4A + annealing, (g, h) 4Bc, and (i, j) 4Bc + annealing.
The average grain sizes in the MA21 alloy sub jected to ECAP according to various routes and subse quent annealing are as follows: IS
4A
4AO
4Bc
4BcO
9.8
2.0
9.75
2.4
9.5
Figure 5 shows the effect of the treatment condi tions on the deformability parameters of the alloy. In the IS–4A–4Bc sequence, NAC increases and SHE and DP first decrease and then increase sharply. Sub sequent annealing slightly decreases NAC and increases SHE and DP. The deformability parameters are maximal after ECAP treatment by routes 4Bc and 4Bc + annealing. The high deformability parameters of the alloy under these treatment conditions correlate with the high values of uniform relative elongation. The authors of [4–6] also detected an increase in the ductility of AZ31 and AZ61 magnesium alloys after ECAP according to route Bc. We now try to relate the high values of the deformability and ductility parame
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EFFECT OF EQUALCHANNEL ANGULAR PRESSING AND ANNEALING Table 1. Orientations and their volume fractions for various ECAP and ECAP + annealing regimes of treatment of an MA21 alloy Sam Compo ple nent1 IS
1a
Eulerian angles2 ϕ1/Φ/ϕ2, deg
Polar/azimuthal angles3, deg
fj
–/–/–
90.6/86.5
0.830
tl 4A
–/–/–
28.3/1.6
0.375
2a
–/–/–
28.4/103.5
0.188
Sample τprism/τbas τtw.ten/τbas
3a
–/–/–
28.6/82.7
1p
259.2/8.9/30
2p
calculation
experiment
IS
2.90
2
0.90
0.89
0.086
4A
1.80
3
1.19
1.19
–/–
0.022
4AO
2.80
3
1.15
1.15
259.2/27.2/30
–/–
0.016
3p
261.0/48.8/30
–/–
0.042
4Bc
1.15
3
2.58
2.54
4p
444.6/8.5/30
–/–
0.017
4BcO
1.35
3
1.96
1.96
5p
439.2/24.2/30
–/–
0.010
6p
439.2/39.3/30
–/–
0.042 0.202
1a
–/–/–
90/162.9
0.239
2a
–/–/–
90/207.5
0.217
1p
90/0/30
–/–
0.017
2p
90/15/30
–/–
0.018
3p
90/35.8/30
–/–
0.051
4p
270/14.3/30
–/–
0.019
5p
270/37/30
–/–
0.047
6p
445.5/89.5/30
–/–
0.268 0.125
1a
–/–/–
90/302.2
0.232
2a
–/–/–
90/245.5
0.242
3a
–/–/–
83.6/32.9
0.354
4a
–/–/–
–41.6/32.9
0.112
tl 4BcO
Value of R0
1a
tl 4Bc
Table 2. Ratio of CHSs for ECAP deformation systems and experimental and calculated NACs for various regimes of treatment of an MA21 alloy
0.170
tl 4AO
653
0.060
1p
127.1/10.2/58.1
–/–
0.114
2p
188.8/17.8/47.9
–/–
0.001
3p
258.7/23.8/36.5
–/–
0.171
4p
417.2/82.7/33.7
–/–
0.162
5p
415.9/64.9/16.4
–/–
0.067
6p
239.0/73.0/52.2
–/–
0.067
7p
103.4/44.1/15.9
–/–
0.086
8p
285.6/81.0/24.6
–/–
0.133
tl
Estimation of the Normal Anisotropy Coefficient from Texture We applied the algorithm of estimating NAC described above to simulate the tensile deformation of the magnesium alloy at a temperature of 20°C on the assumption that tensile plastic strains are provided by the operation of the basal and prismatic slip and {1012}〈1011〉 twinning. The critical shear stresses (CHSs) for these deformation systems were chosen from the coincidence of the calculated and experi mental values given in Table 2. The results presented in Table 2 demonstrate the dependence of NAC on the CHS ratio τprism/τbas. A decrease in this ratio to
