2022 Volume 62 Issue 10 Pages 2069-2073
In this study, the strain distribution in grains with a preferred orientation in a cold-rolled steel plate was investigated. This was done by measuring the amount of strain in a region of the material using nanoscale fine markers applied by a focused ion beam (FIB). We obtained the crystal orientations and strain distributions in the same region using scanning electron microscopy-electron backscatter diffraction and the markers made by the FIB during rolling to a 60% to 70% thickness reduction. The method revealed the strain distributions in the grains with the major preferred orientations (cube:{100}<001>; α-fiber:{100}<011>, {211}<011>; γ-fiber:{111}<011>, {111}<211>). The average strains that accumulated in the grains with different major preferred orientations during cold-rolling were almost the same at thickness reduction in the range of 60%–70%. However, the strain distribution width of the γ-fiber grains was approximately twice that of grains with other orientations. These results suggest that the deformation inhomogeneity during rolling is more pronounced for γ-fiber-oriented grains than for grains with other preferred orientations.
The formation of a preferential crystallographic orientation distribution in thin steel plates significantly affects their formability and electrical properties. Therefore, it is imperative to elucidate the principles that controlling the distribution of preferential crystallographic orientations to better understand steel materials. The crystallographic orientation of steel plates is typically determined using diffraction methods such as X-ray diffraction and scanning electron microscopy-electron backscatter diffraction (SEM-EBSD). These methods have been used in conjunction with various techniques specifically developed for determining crystallographic orientation distributions. Thus, the conditions for obtaining the macroscopic and average orientation distributions of plates have already been determined. Dislocation substructures have often been observed to develop inhomogeneously with increasing strain in rolled plates,1,2,3,4,5) furthermore, their formation causes fluctuations in the local crystallographic orientation. The narrow regions in these microstructures have a relatively large misorientation with the surrounding regions and serve as the initial regions for recrystallization during heat treatment after rolling. To understand the formation mechanism of a preferential crystallographic orientation during the early stages of recrystallization,6,7) it is important to understand the features of inhomogeneous microstructures in the cold-rolled plates, especially in their initial state.
Efforts have also been devoted toward investigating the influence of a local plastic deformation on the macroscopic mechanical properties of materials, by measuring the strain distribution through tracking the displacement of specific points in the same region of the material surface. Among the employed methods, digital image correlation (DIC) has been used to capture macroscopic positional changes in bridges and other structures.8) Recently, DIC has also been used to analyze the microscopic strain in crystalline materials using the visualized microstructures as markers.9,10) Methods for measuring the displacement of microstructures by marking include the following: spraying nanoparticles onto the material surface and estimating changes in their random dispersion with deformation (used exclusively in DIC), and lithographically drawing specific geometric figures and capturing changes in their shape with deformation. These techniques are used to mark the entire observation surface, regardless of the location. However, if the strain distribution to be measured is extremely localized, there is no need to use such a method. In addition, the surface of samples with high aspect ratios, such as the longitudinal plane of a rolled plate, is difficult to mark uniformly using the above methods. As DIC considers the correspondence before and after deformation as a marker, it is useful for capturing small changes in the displacement. However, local displacement associated with large deformations is difficult to determine using DIC. Hence, in this study, precise nanoscale markers were regularly applied to a longitudinal surface using a focused ion beam (FIB) to capture the deformation state of the same area during rolling. FIB deposition enables the application of markings on surfaces with any shape. Therefore, the FIB method is the most effective for obtaining the strain distributions inside grains with a specific preferred orientation, as in this study. The displacement of the marker was measured by continuously observing the area to obtain the local strain distribution associated with the formation of the microstructures during rolling.
Ti-added ultra-low carbon steel was employed. It had an initial grain size of approximately 50 μm after heat treatment.11) The plate was cold-rolled without lubrication until its thickness was reduced by 60%, following which it was cut out. At this time, another specimen of the same shape was also cut out (Fig. 1(a)). The longitudinal plane was polished for observation. (the observed surface is shown in black in Fig. 1(b)). The deformation structure was observed using SEM, and the crystal orientation distribution was examined using SEM-EBSD. Some preferentially oriented grains were selected. The α-fiber is oriented along the rolling direction (RD) parallel to <110>; γ-fiber is oriented along the normal direction (ND) to the plate surface parallel to <111>; and cube orientation is RD, ND//<100>. Carbon dots with a diameter of 0.3 μm were used as markers, and were deposited on the grains using a FIB. The markers were arranged in a square array and were deposited at intervals of 0.7 μm. To re-examine the marked longitudinal plane after additional rolling, the specimen was inserted into a mold frame with the other specimen before being rolled again to protect the observation surface (Figs. 1(c) and 1(d)). Additional rolling was conducted to attain a 70% thickness reduction, and the plastic strain distributions were obtained by tracing the displacement of the markers and capturing the changes in the crystal orientation in the selected regions.
Schematic of the rolling procedure. (a) A specimen for observation is cut out from a pre-rolled plate together with another specimen of the same shape. (b) The observed surface is shown in black. (c–d) The specimen and the other specimen are inserted together into a mold frame to protect the observed surface.
Figures 2(a) and 2(b) show the orientation images for the grains with a nearly cube orientation obtained at thickness reductions of 60% and 70%, respectively; each orientation image shows the ND. During rolling, the red grains in the center of the Fig. 2(a) elongate along the RD. The color within the grains changes slightly, indicating the occurrence of a misorientation, however, no boundary with a large misorientation is formed. Figures 2(c) and 2(d) show the SEM images obtained at a thickness reduction of 70% and the equivalent plastic strain distribution obtained from the displacement of the markers, respectively. The grains extending along the RD (horizontal direction in the figure) in the center of Fig. 2(c) have a cube-orientation, and the markers are primarily applied to these grains when the plate undergoes at 60% reduction in thickness. The displacement of the markers at 70% reduction in thickness, shown in Fig. 2(c), is relatively uniform, and the rectangular area formed by the dot markers is slightly elongated along the RD. In Fig. 2(d), the strain distribution is relatively uniform, although there is a strain concentration area inclined toward the RD.
(a) Orientation image (OI) in the ND obtained from the longitudinal plane at a thickness reduction of 60%. (b) OI obtained from the same field of view as in (a) at a thickness reduction of 70%. (c) SEM image at 70% reduction in thickness. (d) Distribution map showing the equivalent plastic strain obtained by displacement of markers shown in (c). The color bar on the right side of the figure shows the color coding of equivalent plastic strain.
Figure 3 shows the orientation images obtained from the same area on the longitudinal plane. Figures 3(a) and 3(c) show images of the ND and RD, respectively, obtained at a 60% thickness reduction. The orientation of the grain extending along the RD at the center of Fig. 3(c) (grain boundaries above and below the grain are indicated by black lines) is typically ND//<100> and RD//<110>, indicating that this grain is an α-fiber, which possesses the typical preferred orientation due to rolling. Figures 3(b) and 3(d) show the ND and RD, respectively, corresponding to the same area as that in Fig. 3(a) at a 70% reduction in thickness. Figure 3(b) shows that the color of the central area of the α-fiber grain in the ND direction changes from red to vermilion in color, and that of the lower area near the grain boundary changes from red to almost purple. Both are divided into the orientations that are parallel to <301> and <112>, respectively.
(a) Orientation image (OI) in the ND obtained from the longitudinal plane at a thickness reduction of 60%. ND of a grain in the center of the figure (the area bounded by black lines) corresponds to <100>. (b) OI in the ND obtained from the same field of view as in (a) at a thickness reduction of 70%. (c) OI in the RD showing the same area as in (a). RD of the grain corresponds to <110>. (d) OI in the RD showing the same area as in (b).
Figure 4(a) shows the SEM image of the markers in the black frame in Fig. 3(a). Before additional rolling, carbon dots were deposited via FIB as markers onto a portion of the targeted grain surface, as shown in Fig. 3(a). The markers are considerably displaced after the additional rolling, indicating that the marker method is useful for capturing the non-uniform deformation inside the grain (Fig. 4(b)). The markers are typically displaced in an S-shape, and a zone of concentrated deformation is observed in the center of the field of view, which is inclined at approximately 30° from the RD from the upper right to the lower left. In this region, the position of the marker is sheared along the inclined band; it is considered that a slip with a large shear component parallel to the observed plane appears locally. Figure 4(c) shows the equivalent plastic strain (Green-Lagrange strain) inside the rectangle surrounded by the dotted markers, calculated based on the marker displacements shown in Fig. 4(b). 2400 dot markers were created, 40 in the horizontal direction and 60 in the vertical direction. By counting the numbers of these dots, their positions of the dots can be determined, and the displacement after additional rolling can be evaluated for the same area of the observed surface. Figure 4(c) shows the formation of a zone of strain concentration corresponding to the shear deformation shown in Fig. 4(b). These zones of strain concentration appear in a zigzag shape, indicating the formation of inhomogeneous slip bands within the grain.
(a) SEM image showing carbon dots markers created in the black frame in Fig. 3(a). (b) SEM image of the markers at a thickness reduction of 70%. (c) Distribution map showing the equivalent plastic strain obtained by displacement of markers shown in (c). The color bar on the right side of the figure shows the color coding of the equivalent plastic strain.
Figures 5(a) and 5(c) shows the orientation images along the ND and RD, respectively, obtained for the same area in the longitudinal plane. Here, the grains appear to have a preferred orientation different from that shown in Fig. 3. The orientation of the grain extending along the RD in the center of Fig. 5 is generally ND//<111> and RD//<110>, indicating that it is a γ-fiber. The grain boundaries above and below the grain are indicated by black lines. Band-shaped inhomogeneous deformation regions are observed in the grains of the sample at a 60% reduction in thickness (Fig. 5(a)). These bands extend from the upper left to the lower right in the upper part of the grain, whereas, the bands in the lower part of the grain extend from the upper right to the lower left. These results suggest that different slip systems were activated in the upper and lower regions of the grain during rolling. Figures 5(b) and 5(d) show the orientation images of the same grains shown in Figs. 5(a) and 5(c) at a 70% reduction in thickness. The grains shown at the center of Fig. 5 have a clear preferred orientation (ND//<111>, RD//<110>) at a reduction ratio of >60%; however, a small area with an orientation different from that of the surrounding area appears in the lower part of the grain. These small regions with a new orientations form band-like structures, representing the formation of shear bands.12)
(a) Orientation image (OI) in the ND obtained from the longitudinal plane at a thickness reduction of 60%. ND of a grain in the center of the figure (the area bounded by black lines) corresponds to <111>. (b) OI in the ND obtained from the same field of view as in (a) at a thickness reduction of 70%. (c) OI in the RD showing the same area as in (a). RD of the grain corresponds to <110>. (d) OI in the RD showing the same area as in (b).
Figure 6(a) shows the dotted markers deposited using the FIB inside the black frame in Fig. 5(a). The size, shape, and spacing of the markers are similar to those shown in Fig. 4(a). Figure 6(b) shows the SEM image of the same field of view as that of Fig. 6(a), representing the results of the observation conducted after rolling to achieve a 70% reduction in thickness. After the additional rolling, the markers are significantly displaced. In particular, in the lower part of the grain, there is also rough surface irregularity, and the deformation characteristics are very different from those in the upper part of the grain. Figure 6(c) shows the distribution of the equivalent plastic strain accompanying the displacement of the markers shown in Fig. 6(b). Compared with the strain distribution shown in Fig. 4(c), which was obtained for the α-fiber grains, that in Fig. 6(c) shows a more pronounced inhomogeneous deformation. In the upper part of the measurement range, the strain distribution is relatively uniform (except for some parts), whereas in the lower part of the range, several large strain concentration zones with strain values exceeding 2 appear as bands; furthermore, the deformation is small (<0.5) in the areas adjacent to these zones.
(a) SEM image showing carbon dots markers created in the black frame in Fig. 5(a). (b) SEM image of the markers at a thickness reduction of 70%. (c) Distribution map showing the equivalent plastic strain obtained by displacement of markers shown in (c). The color bar on the right side of the figure shows the color coding of equivalent plastic strain in the figure.
Figure 7 shows the mean values and distribution widths of the equivalent plastic strain within each grain at a 70% reduction in thickness (i.e., accumulated strain when the strain at a 60% reduction in thickness is considered as zero). The bars in Fig. 7 correspond to the widths of the maximum and minimum values, and the black squares represent the average values for each preferred orientation. The maximum and minimum strain values for the {100}<011> (α1) orientation are 1.1 and 0.15, respectively, while those for the {112}<110> (α2) orientations are 1.48, 0.07, respectively. This indicates that the dispersion of strain at α2 is slightly larger than that at α1. In contrast, the maximum and minimum strain values for the {111}<112> (γ1) orientations are 2.96, 0.064, respectively. While those for the {111}<011> (γ2) orientations are 2.78, 0.093, respectively. While the average strain values for all grain orientations are similar (α-fiber/γ-fiber = 0.46/0.48), the strain distribution in the γ-fiber grains is approximately twice as wide as that in grains with the other orientations. The deformation inhomogeneity in the grains with a γ-fiber orientation is more remarkable than that in grains with other orientations. As shown in Fig. 6, the γ-fiber grain exhibits a markedly non-uniform deformation microstructure, such as a shear bands, which corresponds to the strain distribution shown in Fig. 7. However, the strain distribution width of the cube-oriented grains is narrower than that of the grains with other orientations. This corresponds to the relatively uniform deformation after rolling as shown in Fig. 2.
Equivalent plastic strain distribution generated in grains with major preferential orientation by additional rolling from 60% to 70% reduction in thickness. The bars correspond to the maximum and minimum strain values, and the squares indicate the average values.
Figures 8(a) and 8(b) show the frequency distribution of the equivalent plastic strain for the α-fiber (α1 and α2) and γ-fiber (γ1 and γ2) grains, respectively, at 60% to 70% reductions in the thickness, and the accumulation of each strain value. In the α-fiber, a frequency peak is observed at approximately 0.5, and the strain values are distributed within a narrow range around this value, whereas in the γ-fiber, the frequency peak is reduced to approximately 0.3. However, in the γ-fiber, there are many regions with high strain values of>1, indicating that the broadening of the strain distribution. The variances in Figs. 7(a) and 7(b) are 0.44 and 0.94, respectively. As the frequency distribution in Fig. 8(a) is almost normal, the appearance of the strain distribution in grains with an α-fiber is most likely attributable to a combination of stochastic events. The activation of the slip system is responsible for plastic deformation, and the basic mechanism of slip deformation is the motion of dislocations on the slip plane. The motion of dislocations overcoming resistance on the slip plane owing to shear stress is a stochastic event based on an activation process that includes a frequency factor, although different degrees of slip activation locally cause strain distributions. Therefore, the occurrence of strain distribution based on the normal dislocation glide in a crystalline material is considered to follow a normal distribution.
Frequency distribution of equivalent plastic strain and accumulation of strain in the grains with α-fiber(a) and γ-fiber(b) due to additional rolling from 60% to 70% reduction in thickness.
On the other hand, the frequency distribution in Fig. 8(b) slightly deviates from the normal distribution. The deviations of distributions from the normal distribution are typically caused by nonlinear phenomena rather than the linear addition of stochastic events.12) The accumulation of plastic strain in the γ-fiber may involve some cooperative phenomena, including relaxation processes such as plastic instability, in addition to the normal plastic deformation of crystalline materials. Typically, work-hardening progresses faster in the grain with γ-fiber because the Taylor factor is larger.7) In significantly work-hardened work conditions, plastic instability may occur locally, and new plastic deformation mechanisms, such as the formation of shear bands, may appear. This plastic deformation mechanism may be associated with the development of plastic strain distribution in the γ-fiber oriented grains.
The inhomogeneous state of deformation inside the grain corresponds to the development of local strain gradients rather than to a simple accumulation of strain. This corresponds to an increase in geometrically necessary dislocations microscopically. The increase in local misorientation caused by inhomogeneous plastic deformation is closely related to the recrystallization behavior. Therefore, the stored energy accumulated in grains owing to plastic deformation has been previously estimated, and the relationship between the magnitude of stored energy and recrystallization behavior has been discussed.7) The degree of stored energy has been estimated based on the density of dislocations and grain boundaries as well as microstructure formation,13) etc.
In contrast, this study directly demonstrates the non-uniformity of deformation, that is, the distribution of strain gradients, through the actual measurement of marker displacements. Furthermore, we found that this distribution depends on the crystallographic orientation of the α- and γ-fibers. This corresponds to the difference in the stored energy for each preferred orientation, which obtained from the deformation microstructure.14,15) It is also known that the recrystallization rate of γ-fibers is higher than that of α-fibers.16,17) Thus, the results obtained in this study suggest that inhomogeneous deformation has a significant effect on the recrystallization behavior.
(1) The strain distribution inside the grains during rolling was obtained by tracing the displacement of precise markers deposited using an FIB.
(2) The average strains that accumulated in the grains with different major preferred orientations during cold-rolling (cube, α-fiber and γ-fiber grains) were almost the same at 60% to 70% reduction in the thickness. However, the strain distribution width of the γ-fiber grains was approximately twice that of the other orientations.
(3) Deformation inhomogeneity during rolling was more pronounced for γ-fiber- oriented grains than for grains with other preferential orientations.
