SEM/EBSD Analysis of Grain Refinement and Coarsening of Ultra-Fine-Grained Al during Simple Shear Deformation

Abstract

Although severe plastic deformation causes grain refinement of polycrystalline materials, saturation of grain refinement is known to be caused by simultaneous grain coarsening. In the present study, for ultra-fine-grained (UFG) pure Al prepared by equal-channel angular pressing, we studied the grain refinement and coarsening processes during large simple-shear deformation using scanning electron microscopy/electron backscatter diffraction. The changes of the crystal orientations in the grains as a function of position were analyzed using log angles as rotation angles around reference axes. This analysis enabled the evaluation of order of magnitude of the in-plane components of geometrically necessary dislocation (GND) density tensors. Detailed changes in the crystal orientations during shear deformation were measured for identical regions in UFG Al, and the changes in the components of the GND density tensors were discussed. Our findings indicate that the grain refinement and coarsening can be explained by the appearance and disappearance of grain boundaries composed of dislocation walls, respectively.

Fig. 7 IPF maps and log angle maps for grains “a” and “b” (“b1” and “b2” at γ = 0.39 and 0.61). The “X” mark in each IPF map represents the reference crystal orientation for log angle analysis at each deformation stage. The IPF maps at γ = 0.39 and 0.61 show that grains “b1” and “b2” were divided into three regions with respect to LAGBs. In the log angle maps, the LAGBs and boundaries of the regions are indicated by red and black lines, respectively. At γ = 0.61, the red dashed lines represent the position of the original LAGB between grains “a” and “b”. The double-headed arrows in the log angle maps show the typical value of the difference of the log angles between adjacent regions.

1. Introduction

Severe plastic deformation (SPD) methods can be used to produce fine-grained (FG) or ultra-fine-grained (UFG) materials.¹⁾ Equal-channel angular pressing (ECAP), which is a SPD method, can be repeated many times because the cross-sectional shape of the bulk material does not change before and after processing.^1–3) However, previous studies have shown that regardless of the number of processing steps, the grains can only be refined to a certain extent.^4–6) This saturation of grain refinement has been attributed to grain refinement and coarsening simultaneously occurring during plastic deformation.^7–12) The grain refinement is known to proceed via grain subdivision.^13–15) Although previous studies have suggested that the grain coarsening is caused by grain boundary migration^7–11) or the disappearance of grain boundaries,¹²⁾ the details of the microstructural evolution of the coarsening process have not yet been revealed.

To better understand this microstructural evolution process, it is necessary to evaluate the motion and arrangement of dislocations during plastic deformation. One method to evaluate the dislocation structure is to analyze the distribution of dislocations using the fact that the orientations of crystals change as a function of position when dislocation structures are formed in the crystals. This approach has been theoretically demonstrated in pioneering work by Nye.¹⁶⁾ In the recent few decades, the development of scanning electron microscopy/electron backscatter diffraction (SEM/EBSD) has enabled the measurement of crystal orientations over a wide area with high accuracy in a short time. Using this method, many studies have revealed grain refinement during plastic deformation caused by changes of dislocation structures. However, unlike for the grain refinement process, the details of the changes in dislocation structures for the grain coarsening process are not obvious. An analysis of these changes using the SEM/EBSD analysis is necessary and is the objective of the present study.

The theoretical study by Nye showed that the geometrically necessary dislocation (GND) density tensor in a crystal can be calculated from orientation changes in the crystal using the lattice curvature tensor κ.¹⁶⁾ κ is given by the changes in the rotation matrix R describing orientation changes of the crystal. The rotation matrix R is generally a 3 × 3 orthogonal matrix with respect to a reference orthogonal coordinate system. The logarithm ln R of the matrix R is also a 3 × 3 matrix but is a skew-symmetric matrix with three independent elements of real numbers.¹⁷⁾ The three elements of ln R are called the log angles ω_i, which are considered the characteristic angles of R.^17–21) Using the log angles ω_i, derivation of the components of the lattice curvature tensor κ from SEM/EBSD analysis is straightforward,^17–21) and such analysis is performed in the present study to discuss changes in the dislocation density tensor ρ_ij and dislocation structures during plastic deformation.

In the present study, for UFG pure Al during simple shear deformation, we measured changes in the crystal orientations for identical regions using SEM/EBSD analysis. The changes in the crystal orientations were analyzed using the log angle method, and the in-plane components of κ were obtained. The changes in the dislocation distributions with grain refinement and coarsening were discussed based on the changes of the GND density tensor given by κ. The grain refinement and coarsening are discussed by considering the appearance and disappearance of grain boundaries composed of dislocation walls.

2. Experimental Procedure

A pure Al (A1070) rod (10 mm diameter, 60 mm in-length) was washed with dilute nitric acid and annealed at 673 K for 3.6 ks to produce homogeneously recrystallized microstructures. The rod was then processed by eight ECAP passes using route B_C,²²⁾ and the microstructure was refined to contain many grains with sizes of less than 1 µm.

During tensile tests, shear bands appear along the shear direction of the final ECAP processing step in as-ECAPed plate specimens.^23,24) Using this characteristic, shear bands can be intentionally concentrated in certain regions by processing notches on the side surface of as-ECAP plate-specimens.¹²⁾ Thus, in the present study, to intentionally produce shear bands in certain regions, we used notched specimens, as shown in Fig. 1(a). Figure 1(b) presents an enlarged view of the notches. The notched specimen resulted in simple shear deformation between the notches and caused the appearance of shear bands in that area.¹²⁾ That is, because these shear bands were caused by simple shear deformation in narrow regions, their deformation was similar to shear deformation by ECAP.^3,25) Next, to confirm the occurrence of such simple shear deformation between the notches and identify the same region before and after deformation, the specimen surface was inscribed with square grid using the focused ion beam (FIB) technique (JIB-4500, JEOL), as shown in Fig. 1(c). The position of these inscribed grids is shown in Fig. 1(a). The FIB equipment was operated with an approximately 100-nm-diameter beam at an intensity of 0.7 nC/µm².

Fig. 1

(a) Schematic illustration showing notched specimen shape. The specimen thickness was 0.7 mm. The coordinate axes of ECAP (TD: transverse direction, ND: normal direction, ED: extrusion direction, SD: shear direction of final ECAP) are also shown. The small black square shows the region where grids were inscribed using FIB. (b) Enlarged view of the notches. (c) The white dashed lines show the schematic shape of the FIB-scribed grids.

Tensile tests were performed using a tensile testing machine (Minebea NMB TG-50 kN) with a crosshead speed of 0.5 mm/min (the initial strain rate was 8.3 × 10⁻⁴ s⁻¹) under atmospheric pressure at room temperature. During the tensile test, the specimen was unloaded three times under local deformation. The microstructure before the tensile tests and after each unloading stage were observed using field-emission SEM (FE-SEM, JSM-7001F, JEOL) and EBSD. SEM analysis was performed at 15 kV, and the step size of the EBSD measurements was 0.05 µm. In addition, the same region before and after deformation was observed using SEM/EBSD analysis within the FIB-scribed grid at each deformation stage, and microstructural evolution during deformation was evaluated.

3. Results

3.1 Mechanical properties

In the current study, evaluation of the mechanical properties of the notched specimen using nominal stress–nominal strain curves would not be accurate because the cross-sectional area of the specimen was uneven because of the addition of notches and unloading after UTS. Thus, we instead evaluated the mechanical properties using the apparent stress σ_ap and strain ε_ap. The apparent stress σ_ap is described by   

\begin{equation} \sigma_{\text{ap}} = F/S, \end{equation} (1)

where F is the tensile testing load and S is the cross-sectional area without the effect of notches.¹²⁾ In addition, the apparent strain ε_ap is described by   

\begin{equation} \varepsilon_{\text{ap}} = u_{\text{c}}/l_{0}, \end{equation} (2)

where u_c is the crosshead displacement and l₀ is the initial gauge length of the specimen.¹²⁾ Figure 2 presents the σ_ap–ε_ap curve for the tensile test of the notched specimen. During the tensile test, a shear band appeared between the notches under local deformation, indicating that the notches could be used to control the regions of concentrated deformation under local deformation. As shown in Fig. 2, to observe the microstructural changes and evaluate shear deformation inside the shear bands, we unloaded the specimen at ε_ap = 0.03, 0.05, and 0.07 during the tensile test. However, we could not observe the microstructure using the SEM/EBSD analysis above ε_ap = 0.07.

Fig. 2

σ_ap–ε_ap curve for tensile test of notched specimen. The specimen was unloaded at ε_ap = 0.03, 0.05, and 0.07.

3.2 Evaluation of shear amount inside shear band

To verify the occurrence of simple shear deformation in the FIB-scribed grids, we evaluated the amount of deformation at ε_ap = 0.03, 0.05, and 0.07 using SEM. Figures 3(a) and (b) present SEM images of the FIB-scribed grids before the tensile test and at ε_ap = 0.07, respectively. Comparison of Fig. 3(a) and (b) indicates that the grids were deformed by the appearance of shear bands during the tensile test. Therefore, the displacement gradient tensor u_i,j were calculated, assuming that the deformation is uniform within the grids. Moreover, u_i,j was transformed by coordinates to evaluate the deformation caused between notches. When u_i,j was transformed with the counterclockwise rotation of θ = 45° by the coordinate as shown in Fig. 3(c), among the transformed gradient tensor u′_i,j (u′_2,2, u′_2,3, u′_3,2, and u′_3,3), u′_3,2 of all the grids were approximately 10 times larger than the other components; similar results were observed in our previous work on UFG pure Cu.¹⁴⁾ These results for the notched specimens of UFG pure Al indicate the occurrence of simple shear deformation between the notches. Likewise, we consider only u′_3,2 as the amount of deformation and define the shear amount γ as γ = u′_3,2. Table 1 presents the γ values of each grid at ε_ap = 0.03, 0.05, and 0.07. There were no significant differences in the grids at the different deformation stages, and γ of each grid at ε_ap = 0.07 was approximately 0.6. Increasing rates of γ during deformation can be calculated using experimental conditions and results, and these are about 10⁻² s⁻¹. The amount of simple shear deformation by 1-pass ECAP processing is known to be about 2,^3,26) which implies that simple shear deformation as much as γ = 0.6 in the shear band of a notched specimen at ε_ap = 0.07 corresponds to 30% of simple shear deformation per pass of ECAP.

Fig. 3

SEM images of the FIB-scribed grids inside a shear band (a) after ECAP and (b) after unloading at ε_ap = 0.07. (c) Relationship between the sample coordinate system and orthogonal coordinate system (x₁–x₂–x₃). The x₁–x′₂–x′₃ coordinate system was transformed with a counterclockwise rotation of 45° around the TD axis.

Table 1 Shear amount γ of each grid at various ε_ap.

3.3 SEM/EBSD analysis

Before the tensile test and at ε_ap = 0.03, 0.05, and 0.07, we examined the same regions, as identified by the FIB-scribed grids, using the SEM/EBSD analysis and investigated the changes in the crystal orientation of grains. Figure 4 presents EBSD-obtained inverse-pole-figure (IPF) maps at each deformation stage. The IPF maps consisted of high-angle and low-angle grain boundaries (HAGBs and LAGBs), which are defined as grain boundaries having misorientation angles greater than 15° and between 2° and 15°, respectively. The FIB-scribed grids are shown in these IPF maps as black lines. Figure 4 shows that the appearance of shear bands between the notches during the tensile tests caused the changes in the shape and crystal orientation of the grains. However, although these changes in the grains were caused by deformation, the average grain size in the grids changes between 0.9 and 1.1 µm, as shown in Fig. 5. In the case of the samples processed to 16 ECAP passes,²⁷⁾ the grain refinement was saturated at around 0.85 µm, so the change shown in Fig. 5 indicates the saturation of grain refinement.

Fig. 4

IPF maps showing crystal orientations with HAGBs and LAGBs (a) before the tensile test and at (b) ε_ap = 0.03, (c) ε_ap = 0.05, and (d) ε_ap = 0.07. The black lines represent the FIB-scribed grids. The sample coordinate system and color code of the IPF maps are also shown.

Fig. 5

Average grain size at each deformation stage. Points show the average grain size in all the grids. The error bars show the maximum and minimum values for each grid.

To clarify the grain refinement and grain coarsening processes, it was necessary to trace the change of each grain. Therefore, we compared the same grain or grains in each deformation stage. In grid “D”, we observed the occurrence of grain coarsening and refinement in the same group of grains, as illustrated in Fig. 6. As shown in Fig. 6(a), grains “a” and “b” were divided from each other by the LAGB with misorientation of approximately 5° before the tensile tests. As the deformation progressed in the grids, the misorientation of this LAGB gradually decreased, as shown in Figs. 6(b) and (c). Eventually, this misorientation decreased to less than 2°, such that grains “a” and “b” were coarsened by the dissipation of the LAGB at γ = 0.61. However, inside grain “b”, the misorientation slightly increased in the central region of grain “b”. At γ = 0.39, as shown in Fig. 6(c), grain “b” was refined into grains “b1” and “b2” with the generation of a LAGB. However, phenomena such as dynamic recrystallization^28,29) and grain boundary migration,^7–11) which have been suggested as causes of grain coarsening for UFG materials, could not be clearly identified within the observed grid regions in the present study.

Fig. 6

IPF maps for grains “a” and “b” (a) before the tensile test and at (b) γ = 0.10, (c) γ = 0.39, and (d) γ = 0.61. These grains are in grid “D” in Fig. 1(c).

4. Discussion

4.1 Log angle analysis of the grains

We used log angle analysis to investigate the changes of the crystal orientation of individual grains due to simple shear deformation. The log angles ω_i are the characteristic angles of the rotation matrix R, a 3 × 3 orthogonal matrix, with respect to a reference orthogonal coordinate system, composed of the three elements of the logarithm ln R. The log angles ω_i are described as follows. For a real number x, the relationship between x and the exponential function exp x is¹⁷⁾   

\begin{equation} \exp x = 1 + x + \frac{x^{2}}{2!} + \frac{x^{3}}{3!} + \frac{x^{4}}{4!} + \ldots = \lim_{p \to \infty}\left(1+\frac{x}{p} \right)^{p}. \end{equation} (3)

Using y = exp x (y > 0), (3) is rewritten by the logarithmic function as   

\begin{equation} y = \lim_{p \to \infty}\left(1 + \frac{\ln y}{p} \right)^{p}. \end{equation} (4)

In addition, by expanding the concept of numbers to matrices and using (4), the relationship between R and ln R is written as¹⁷⁾   

\begin{equation} \mathbf{R} = \lim_{p \to \infty}\left(\mathbf{E} + \frac{\ln \mathbf{R}}{p} \right)^{p}, \end{equation} (5)

where E is the 3 × 3 unit matrix. The log angles ω_i of R are elements of ln R and are written as^17,18)   

\begin{equation} \ln \mathbf{R} = \begin{pmatrix} 0 & - \omega_{3} & \omega_{2}\\ \omega_{3} & 0 & - \omega_{1}\\ - \omega_{2} & \omega_{1} & 0 \end{pmatrix} . \end{equation} (6)

In the present study, we discuss the changes of crystal orientation using the log angles of ω₁, ω₂, and ω₃ on the orthogonal sample coordinate system for ECAP, as shown in Fig. 3(c).

To evaluate the change in crystal orientation before and after deformation in the same region using log angle analysis, the reference coordinate system before and after deformation must not change as the log angles are based on the rotation matrix R with respect to a reference orthogonal coordinate system. However, in the present study, this reference coordinate system at each deformation stage may have changed due to misalignment of the specimen by attachment and detachment of the specimen from the SEM holder at each deformation stage. Thus, it was not possible to simply compare the crystal orientation before and after deformation. Therefore, a reference point was set at each deformation stage, and misorientation between this point and other points was described using log angles. This method reveals crystal orientation changes within a grain or grains at the same deformation stage, thus eliminating the need to consider the deviation of the reference coordinate system. Thus, the changes of crystal orientation of the same grain(s) before and after deformation can be evaluated through changes in the log angles Δω_i depending on their positions. Furthermore, selecting the same reference point before and after the deformation can more clearly reveal crystal orientation changes caused by deformation.

Figure 7 shows the misorientation within grains “a” and “b” using Δω_i calculated using this method. Because it is very difficult to identify the same position before and after deformation, for convenience, the center of a figure of grain “a” on the IPF map at each deformation stage was considered to be the same position and was used as the reference crystal orientation. The center of a figure of grain “a” was used as a reference point because grain “a” showed comparatively little change in shape and crystal orientation at each deformation stage.

Fig. 7

IPF maps and log angle maps for grains “a” and “b” (“b1” and “b2” at γ = 0.39 and 0.61). The “X” mark in each IPF map represents the reference crystal orientation for log angle analysis at each deformation stage. The IPF maps at γ = 0.39 and 0.61 show that grains “b1” and “b2” were divided into three regions with respect to LAGBs. In the log angle maps, the LAGBs and boundaries of the regions are indicated by red and black lines, respectively. At γ = 0.61, the red dashed lines represent the position of the original LAGB between grains “a” and “b”. The double-headed arrows in the log angle maps show the typical value of the difference of the log angles between adjacent regions.

By comparing Δω_i between adjacent regions at each deformation stage in Fig. 7, the appearance and disappearance of grain boundaries in grain “a” and “b” could be discussed more detail. Therefore, as shown in Fig. 7, we divided grain “b” (“b1” and “b2” at γ = 0.39 and 0.61) into three regions based on the grain boundaries and compared Δω_i between these adjacent regions. This comparison revealed that the appearance of the grain boundary in grain “b” resulted from the increasing Δω₁ and Δω₂ between the center and right region at γ = 0.39. Moreover, the disappearance of the grain boundary between grain “a” and “b” was shown to result from the decrease of Δω₁ between grain “a” and the left region at γ = 0.61. These results indicate that the changes of ω₁ have a significant on both the appearance and disappearance of the grain boundaries. ω₁ had a significant effect on the microstructural evolution because in-plate simple shear deformation on the x₂–x₃ plane caused by the notches tended to induce large crystal orientation changes around the x₁ axis, as illustrated in Fig. 7.

4.2 Dislocation density tensor

Figure 7 shows the log angles changes with the change in positions, such that grain “b” could be evaluated using Nye’s lattice curvature tensor κ. κ describes the orientation change δϕ_i around the x_i axis with the change in the position δx_j within a crystal as κ_ij = δϕ_i/δx_j on the orthogonal system (x₁–x₂–x₃). Our previous study¹⁷⁾ showed that when a crystal orientation changes, as described by ΔR, with the change of a position from x_i to x_i + Δx_i and the log angles of ΔR described by Δω_i, the average lattice curvature tensor κ for the region is given by   

\begin{equation} \kappa_{ij} = \Delta \omega_{i}/\Delta x_{j}, \end{equation} (7)

which can be rewritten as   

\begin{equation} \kappa = \begin{pmatrix} \Delta \omega_{1}/\Delta x_{1} & \Delta \omega_{1}/\Delta x_{2} & \Delta \omega_{1}/\Delta x_{3}\\ \Delta \omega_{2}/\Delta x_{1} & \Delta \omega_{2}/\Delta x_{2} & \Delta \omega_{2}/\Delta x_{3}\\ \Delta \omega_{3}/\Delta x_{1} & \Delta \omega_{3}/\Delta x_{2} & \Delta \omega_{3}/\Delta x_{3} \end{pmatrix} . \end{equation} (8)

Moreover, using the lattice curvature tensor κ_ij, Nye’s dislocation density tensor α_ij is given by¹⁶⁾   

\begin{equation} \alpha_{ij} = \kappa_{ji} - \delta_{ij}\kappa_{ij}, \end{equation} (9)

where δ_ij is the Kronecker delta. The non-diagonal components in α_ij give the edge GND density. Figure 8 schematically illustrates that the presence of edge dislocations between positions x_i and x_i + Δx_i cause crystal orientation changes around the x_j axis. That is, using the value of the difference in log angle Δω_i between two positions, the average edge GND density tensor ρ_ij is given by¹⁶⁾   

\begin{equation} \rho_{ij} = \alpha_{ij}/b, \end{equation} (10)

where b is the magnitude of the Burgers vector. From eqs. (8) to (10), non-diagonal components of ρ_ij with j ≠ i are given by   

\begin{equation} \rho_{ji} = \frac{\Delta \omega_{i}}{\Delta x_{j}}\frac{1}{b}(i \neq j). \end{equation} (11)

Note that the order of the subscripts i and j in the right-hand-side of eq. (11) is different from that of eq. (10). These non-diagonal components of ρ_ji show the densities of edge dislocations having the dislocation-line parallel to the x_i axis and the Burgers vector parallel to the x_j axis.¹⁶⁾ Although the components of ρ_ji do not correspond directly to the Burgers vectors of the {111} ⟨110⟩ actual slip systems in FCC metals, we can distinguish dislocations with different Burgers vectors and directions by different components of ρ_ji. The order of magnitude of dislocation density in the actual metals can also be evaluated by considering ρ_ji.

Fig. 8

Schematic illustration showing the change in crystal orientation with the change in position from (x₁, x₂, x₃) to (x₁, x₂ + Δx₂, x₃). The dislocations between two measurement points cause a crystal orientation change around the x₁ axis.

In the present study, the observation of surface (x₂–x₃ plane) crystal orientation enables analysis of ρ₁₂, ρ₁₃, ρ₂₃, and ρ₃₂ in the non-diagonal components of the dislocation density. Thus, assuming that the Burgers vector of edge dislocations in the measurement point interval Δx_i is constantly parallel to the coordinate axis x_i, ρ₁₂, ρ₁₃, ρ₂₃, and ρ₃₂ were analyzed using the following method:

1. (i)    The distributions of Δω_i in grain “b” shown in Fig. 7 were approximated by the polynomial surface of 5th degree.
2. (ii)    Each component of the lattice curvature tensor was calculated by partial differentiation of this obtained equation.
3. (iii)    We gave ρ₁₂, ρ₁₃, ρ₂₃, and ρ₃₂ from eq. (10) as the Burgers vector b = 0.286 nm.

For grain “b” at γ = 0.39, calculations to obtain ρ_ij were performed in each region separated by the grain boundaries that are shown in Fig. 7. This is because it is difficult to approximate orientation changes across the boundaries by the present polynomial function. Values of ρ_ij at γ = 0.61 were not obtained since the central region between boundaries was too small to calculate the values.

The dislocation densities ρ₁₂, ρ₁₃, ρ₂₃, and ρ₃₂ at γ = 0.10 and γ = 0.39 calculated using this method are presented in Fig. 9 and 10, respectively. Before the tensile test, the dislocation densities were less than 1 × 10¹⁴ m⁻² inside grain “b”. In addition, after the tensile test, the dislocation densities shown in Fig. 9 and 10 were within the range of 10¹⁴–10¹⁵ m⁻². These results corresponded well with the measurement of dislocation density using transmission electron microscopy³⁰⁾ and X-ray diffraction measurements³¹⁾ for UFG materials, indicating that this method provides reasonable results.

Fig. 9

Maps of IPF and dislocation density tensor ρ₁₂, ρ₁₃, ρ₂₃, and ρ₃₂ for grain “b” at γ = 0.10.

Fig. 10

Maps of IPF and dislocation density ρ₁₂, ρ₁₃, ρ₂₃, and ρ₃₂ for grains “b1” and “b2” at γ = 0.39. The dashed black lines in the maps of the dislocation density indicate the position of LAGBs.

Figure 9 and 10 show that the dislocation density increased within grain “b” during deformation and that some components of the dislocation density tensors in the vicinity of the grain boundary reached 10¹⁵ m⁻² at γ = 0.39. Furthermore, Fig. 10 shows that the values of each component of the dislocation density tensor and their distribution differed significantly between the left- and right-hand sides of the two grain boundaries formed in grain “b”. These distributions of dislocations in grain “b” show the distribution of GNDs to compensate for misorientation caused by the activation of different slip systems within grain “b” during plastic deformation. Previous studies have shown that such the activity of the slip system is related to the grain refinement process;^32,33) thus, Fig. 10 suggests the dislocation density for the GNDs constituting the dislocation wall formed by plastic deformation during the grain refinement process of grain “b”.

4.3 Process of grain refinement and coarsening

Figure 11 presents schematic illustrations of the grain refinement and coarsening processes of grain “a” and “b” and the dislocation distributions within them. Before the tensile test, as shown in Fig. 11(a), grains “a” and “b” were separated by sub-grain boundaries because of the effect of grain subdivision during ECAP, and the dislocation densities within them were low. During the tensile test, different slip systems were activated within grain “b”, and the formation of GNDs with different Burgers vectors was induced to accommodate for the incompatibility of the different active-slip-system regions, as illustrated in Fig. 11(b). As a result, these GNDs formed a dislocation wall within grain “b”, and grain “b” was subdivided into grains “b1” and “b2”. This grain refinement is due to grain subdivision, which has been reported in many studies.

Fig. 11

Schematic illustration of microstructural evolution for grains “a”, “b”, “b1”, and “b2”: (a) before the tensile test (γ = 0) and at (b) γ = 0.39 and (c) γ = 0.61. The red lines represent LAGBs. The dashed red line represents the position of the original LAGB.

On the other hand, as mentioned in section 4.1, few studies reported on the phenomenon of grain boundary disappearance during deformation such as the LAGB between grain “a” and “b”. The disappearance of this LAGB is partly due to the detachment of some dislocations from there by large in-plane simple shear deformation, as shown in Fig. 11(c). During deformation, the constraint effect of each grain may cause activation of different slip systems that varies from region to region as shown in Figs. 9 and 10. GNDs are formed by such motion of dislocations which are not relaxed by local dynamic recovery. GNDs increase the misorientation between the region and certain adjacent regions; however, these could also cause a decrease in the misorientation between that region and other regions. That is, the in-plane simple shear deformation in grains “a” and “b” induced the formation of GNDs that were strongly affected by the crystal rotation around the x₁ axis; as a result, the induced GNDs not only formed the grain boundaries in the adjacent region but also caused the disappearance of another grain boundary. This is the explanation of disappearance of grain boundaries observed in the present experiments.

5. Conclusions

In this study, we observed the microstructural evolution of UFG pure Al during simple shear deformation using SEM/EBSD analysis. Our findings are summarized as follows:

1. (1)    In the same grain(s) before and after deformation, we observed grain refinement and coarsening due to the appearance and disappearance of grain boundaries, respectively.
2. (2)    The changes in crystal orientation during simple shear deformation were studied using SEM/EBSD analysis. Log angle analysis of these orientation changes revealed that the changes in orientation within the grain(s) were greatly affected by the in-plane simple shear deformation.
3. (3)    We have evaluated the order of magnitude of in-plane components of GND density tensor by the log angle analysis. This analysis suggested the activation of different slip systems and that they formed dislocation walls within the grain.
4. (4)    The log angle analysis suggested that the crystal rotation around the normal direction of the specimen surface by simple shear deformation not only formed the grain boundaries through the generation of GNDs but also decreased the misorientation between adjacent regions. This decrease in the misorientation may have led to the disappearance of grain boundaries.

Acknowledgment

Funding: This work was supported by JSPS KAKENHI [grant number 19K04985].

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