Plastic anisotropy calculation of severely-deformed Al-Mg-Si alloy considering texture changes in electron backscatter diffraction

1. Introduction

Commercial Al and its alloys with several shapes, such as bar, rod, and plate, were used in various fields of modern automotive industries owing to suitable strength and ductility [1,2]. The industrial shortcoming of Al-Mg-Si alloy was originated from the limited drawability to fabricate the complicated forms after plastic deformation at room and high temperatures [3,4]. This drawability of crystalline metals represented as Lankford value (r) was related closely to texture variants, depending upon deformation and heat treatment [[5], [6], [7], [8]]. Irrespective of deformation mode applied, plastic anisotropy took place inevitably during plastic deformation as deformation characteristics and resultant deformed microstructure in three dimensions might be different along with major deformation flow [9]. Moreover, the subsequent annealing of the deformed sample gave rise to a certain change in r values with respect to 0°, 45°, and 90° directions from deformation flow [10].

The use of asymmetrical rolling (AR) as one of the severe plastic deformation methods would allow most of the grains to be refined even down to micrometer scale in sheet metals [11]. According to the recent work reported by the present authors [12], a good combination of strength and ductility was attained successfully by the concept of cross-shear where two macro-shear plane were conjugated by rotating the sample along the longitudinal axis between adjacent passages of AR. This finding was attributed mainly to weakening (or softening) behavior of pre-existing texture components. As aforementioned, it is also anticipated that the effect of cross-shear deformation on the change in texture components formed during annealing would be significant. Up to date, a correlation between the texture evolution and plastic anisotropy of severely-deformed Al-Mg-Si alloy subjected to AR followed by annealing was explored rarely. Therefore, the plastic anisotropy of the present sample is investigated by calculating both average Lankford value ($\bar{r}$) and in-plane anisotropy (Δr) on the basis of texture components during static annealing at 598 K where microstructure and texture are changed fairly by recrystallization phenomenon [13]. For this purpose, electron backscatter diffraction (EBSD) analysis is used to figure out a variety of texture components found in fcc metals, such as plane-strain, shear, and recrystallization textures before and after annealing treatment.

2. Experimental procedures

The as-received sample used in this study was an Al-Mg-Si alloy sample with the chemical composition of 0.91Mg-0.72Si-0.52Fe-0.21Cu-0.19Cr, and balance Al (in wt%). A series of AR were performed at room temperature by using two identical rolls whose speed ratio was fixed to 1:4 for the lower and upper rolls, respectively under the conditions that the speed of the lower roll was fixed at $\widetilde{5}$0 mm/s. The thickness reduction was maintained to be 50% for each pass so that the total reduction of 75% was achieved after two-pass AR. The samples were rotated 180° around their rolling axis (so-called cross-shear) between passes since this method was beneficial to controlling materials with fine grains. This severely-deformed sample was designated as CS sample hereafter. A detail of experimental set-up and conditions were available elsewhere [14]. After AR, CS sample was subjected to annealing step at 598 K for 1 h, which was designated as CSA. To analyze the various texture components, both inverse pole figure (IPF) and orientation distribution function (ODF) were obtained from EBSD observations at a step size of 20 nm. The ODF maps were generated by utilizing the harmonic series expansion method using the non-orthonormal sample symmetry. The fraction of texture was determined from the well-known orientation in Euler space and the data were averaged from at least five maps with $\widetilde{2}$00 grains. For plastic anisotropy in conjunction with EBSD, the values of $\bar{r}$ and Δr were calculated using Eqs. (1) and (2) from r₀, r₄₅, and r₉₀ corresponding to r values along three directions of 0°, 45°, and 90° away from AR direction in the sample.

$\bar{r}=\frac{r_{0}+2r_{45}+r_{90}}{4}$ (1)

$Δr=\frac{r_{0}+r_{90}-2r_{45}}{2}$ (2)

High $\bar{r}$ and low Δr values indicated low thickness reduction ratio during plastic deformation, which would be desirable for deep drawing with good plastic isotropy.

3. Results and discussion

Fig. 1 shows both IPF and ODF results in CS sample with various colors representing the individual orientation of every single grain. The black line indicated the high-angle grain boundaries (≥15°). Some fine-grains appeared in the vicinity of the lamellar-like band structures that were developed along RD whereas the misorientation angles of most of the grains inside the deformed bands were as low as 15° (Fig. 1(a)). This was typical for the deformed structure via intense straining as reported earlier [15].

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Fig. 1.   (a) EBSD-IPF map taken from the center of the normal direction (ND)-rolling direction (RD) plane of CS sample. Rolling direction is left to right. (b) EBSD-ODF in the reduced Euler space (ϕ₁:0-90°, Φ:0-90°) for ϕ₂=0°, ϕ₂=45°, and ϕ₂=65°.

As shown in Fig. 1(b), ODFs obtained at φ₂ = 0°, 45° and 65° were chosen to reveal the micro-texture of the deformed grains. In general, the textures in fcc metals were three different types which were classified into (i) plane-strain texture consisting of Brass ({011}〈112〉), Copper ({112}〈111〉), and S ({123}〈634〉), (ii) shear texture consisting of E ({111}〈110〉) and F ({111}〈112〉), and (iii) recrystallization texture consisting of Cube ({001}〈100〉) and Goss ({110}〈001〉) [[16], [17], [18], [19], [20]]. From Fig. 1(b and c) with maximum intensity of ≈8.9, most of the grains possessed either plane-strain or shear textures, depending upon the thickness of the deformed bands. It is seen that shear texture was governed relatively as the thickness of the deformed bands decreased. This was due to the fact that shear strain induced by AR caused the thin thickness of ≈0.3 μm in the deformed bands. Per the recent results on the cold-deformation of 5052 Al alloy via differential speed rolling, the thickness of the band structures became thinner with increasing amount of shear strain. A similar result was also found in the previous study [14]. On the other hand, some fine-grains with recrystallization texture formed as a necklace structure. Considering the total amount of strain (ε≈1.6) imparting the sample, the reduction in the grain size below 1 μm shown in Fig. 1(a) was expected to occur through continuous dynamic recrystallization (CDRX).

In addition, some peaks in ODFs were shifted from their ideal positions. For instance, E and Cube showed a slight shift of ≈10° at φ₂ = 45° while S exhibited a pronounced orientation shifting of ≈20° along φ₁ and Φ direction at φ₂ = 65°. The large shifting was confirmed to be that of S by the grain morphology from IPF maps although recent studies about textural behavior of rolled-Al during annealing by Shuai et al. applied a maximum of 15° deviation from the exact orientation to determine the texture component [21]. The large deviation was attributed mainly to the change of deformation mode generated by the change in the deformation direction between deformation passes [22]. In the present study, due to the sample rotation 180° around their rolling axis, the macro-shear band formed by first AR was crossed (cross-shear) evidently by the second macro-shear band, giving rise to the stress-triaxiality in the sample after two-pass ARs. Thus, some shifting behavior was detected more or less. It is concluded based on the different values of intensity in texture components that the intensity of plane-strain texture was much higher than the others, implying that plane-strain texture would be major texture components after AR deformation. Both IPF and ODF results in CSA sample are displayed in Fig. 2. Unlike CS sample, the overall microstructure comprised the nearly equiaxed grains decorated by high-angle grain boundaries due to the occurrence of static recrystallization. From Fig. 2(b), it is interesting that the intensity of Cube component reaching ≈9.8 was observed to be higher than those of any plane-strain components. This finding was in contrast to typical Cube whose intensity was almost twice higher than those of plane-strain texture during heat treatment of 1050 Al alloy deformed by differential friction rolling [23]. Thus, the transition mechanism from plane-strain to Cube components, which happened during recrystallization, would be considered in order to figure out the present propensity in ODF components. The annealed grains with Cube would tend to form on the basis of 40°<111> relationship with plane-strain oriented grains, so that Cube started to appear at the expense of plane-strain texture [24,25]. Such relationship was unlikely to be satisfied if Copper, S, and Brass were not positioned at their ideal places in the Euler space due to the orientation shifting. In CS sample, 40°<111> relationship between S and Cube was seldom made because the principal pole of S was clearly shifted ≈20° in the Euler domain at φ₂ = 65°. This was reinforced by the nearly same values in the texture intensity of S components found between Figs. 1(b) and 2 (b). A clear evidence of reduced growth capacity of cube texture due to the loss of 40°<111> relationship was reported previously [22]. On the other hand, the orientation shifting would also allow E and F components to retain their intensities despite poor thermal stability at ≈0.65 T/T_m (T_m: melting temperature). Since the use of conjugated shearing imposed by AR would give rise to the orientation shifting, the annealing behavior of some grains with S, E, and F components was altered significantly at 598 K.

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Fig. 2.   (a) EBSD-IPF map taken from the center of the normal direction (ND)-rolling direction (RD) plane of CSA sample. (b) EBSD-ODF in the reduced Euler space (ϕ₁:0-90°, Φ:0-90°) for ϕ₂=0°, ϕ₂=45°, and ϕ₂=65°.

As for mechanical reliability, the plastic anisotropy response of both CS and CSA samples was analyzed in this study. The calculation of r value was performed by taking the changes in EBSD texture into account on the assumption that all slip systems contributed to plastic deformation in proportion to their Schmid factors (S). Eqs. ((3), (4), (5)) reappraised by Lee and Oh [26] was used to calculate r value.

$S=|(l·p)(l·d)|$ (4)

where ε_w and ε_t are the strain values along the width and thickness directions of the sheet sample and Σ is the mathematical summation of slip systems operated during AR and annealing. Fig. 3 showed the schematic illustration depicting the above unit vectors which necessary for calculating the r values. Vectors of b and t are unit vectors along the width and thickness directions. Vectors of d and p are unit vector along slip direction and the direction normal to slip plane. l is the unit vector along the tension direction. The unit vectors of l, t, and b were derived below,

where α is the angle between rolling direction and tensile direction l, such as 0°, 45°, and 90°. The unit vectors along the normal to the plane (R₁ R₂ R₃) and the direction [A₁ A₂ A₃] were expressed as r = [R₁/R R₂/R R₃/R] and a = [A₁/A A₂/A A₃/A]. Vector of n is the unit vector normal to both a and r.

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Fig. 3.   Schematic illustration showing the bulk polycrystalline sample and its FCC unit cells with one of its slip systems. The unit vectors necessary to calculate the r values were shown.

Fig. 4(a) shows the intensity values of texture components in CS and CSA samples taken from five different ODF images. Although the size and morphologies of grains would affect plastic anisotropy as primary source, the effect of preferred orientation needed to be considered in this study since a significant change in the texture components was attained as seen clearly from ODF images in Figs. 1(b) and 2 (b). After AR, the present EBSD calculation of r₀, r₄₅, and r₉₀ in CS sample agreed well with those measured mechanically by Engler group, where their r values before recrystallization showed a concave shape while after recrystallization showed an almost linear shape [18]. These values with appreciable deviations revealed as shown in Fig. 4(b) that plane-strain textures became more predominant than the others due to the fact that most grains would be prone to be aligned toward flow direction of AR where plane-strain condition was mainly applied. The values of $\bar{r}$ and Δr were measured to be ≈0.76 and ≈0.36, typical of deformed metals with strong anisotropy.

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Fig. 4.   (a) Intensity values of texture components in CS and CSA samples. An inset indicates the principle to calculate the anisotropy from the texture components. (b) Change in r values in CS and CSA samples.

After annealing at 598 K, the r values became stabilized with negligible fluctuation. This was attributed mainly to the relative rise in intensity value of Cube component through orientation shifting based on 40°<111> relationship (Fig. 4(b)). Thus, the active formation of Cube as recrystallization texture played an important role in lowering the Δr value. In addition, the survival of red-short E and F components even with small fraction would be responsible for high $\bar{r}$ value. Thus, the values of $\bar{r}$ and Δr were measured to be ≈0.90 and ≈0.04. As a result, the Al-Mg-Si alloy sample subjected to AR with cross-shear followed by annealing at 598 K exhibited a significant improvement in the values of $\bar{r}$ and Δr, which would be beneficial for enhancing drawability of the sheet sample.

4. Conclusion

The present work investigated the plastic anisotropy of the Al-Mg-Si alloy sample deformed by two-pass ARs under cross-shear with a focus on significant changes in texture components. After AR, texture components relating to plane-strain governed with formations of the lamellar-like band structures which were parallel to RD. After annealing at 598 K, these hard textures were transformed markedly into Cube ({001}〈100〉) component while both E ({111}〈110〉) and F ({111}〈112〉) survived. Accordingly, the values of $\bar{r}$ and Δr of CSA sample were estimated to be ≈0.90 and ≈0.04, which exhibited better plastic isotropy and, thereby, drawability than those of CS sample.

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (MOE), Republic of Korea (No. NRF-2017R1D1A1A09000921).

The authors have declared that no competing interests exist.