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Texture development in Fe–3.0 mass% Si during high-temperature deformation: Examination of the preferential dynamic grain growth mechanism
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Acta Materialia 61 (2013) 1294–1302 www.elsevier.com/locate/actamat
Texture development in Fe–3.0 mass% Si during high-temperature deformation: Examination of the preferential dynamic grain growth mechanism Yusuke Onuki a,⇑, Ryosuke Hongo a, Kazuto Okayasu b, Hiroshi Fukutomi b a
Graduate School of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa, Japan b Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa, Japan Received 1 August 2012; received in revised form 16 October 2012; accepted 5 November 2012 Available online 6 December 2012
Abstract A new mechanism of texture evolution, named “preferential dynamic grain growth mechanism”, is examined experimentally by hightemperature plane-strain compression deformation of Fe–3.0 mass% Si alloy. The proposed mechanism is based on preferential growth of the orientations having low Taylor factors and stability against deformation. According to the mechanism, the growing orientation is expected to be {0 0 1}h1 1 0i in the case of plane-strain compression deformation. In fact, the textures formed by deformations up to the desired strain of 1.0 have high orientation densities around {0 0 1}h1 1 0i in accordance with the proposed mechanism. With decreasing strain rate, the volume fraction of {0 0 1}h1 1 0i increases with the increase in the average intercept length of crystal grains along the transverse direction at both 1093 K and 1173 K, which implies the occurrence of dynamic grain growth during the deformation. The volume fraction of {0 0 1}h1 1 0i is higher at 1173 K than at 1093 K for the same strain rate. Electron backscatter diffraction measurements show that the density of small-angle grain boundaries decreases with increasing temperature and decreasing strain rate. The lower density of small-angle grain boundaries implies that distribution of dislocations in grains approaching homogeneity results in the enhancement of preferential dynamic grain growth at higher temperatures and lower strain rates. This suggests that high-temperature deformation might be applied as a new method for controlling texture. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Texture; High-temperature deformation; Microstructure formation mechanism; Solid solution; Preferential dynamic grain growth
1. Introduction The importance of textures for improving the performance of metallic materials has been widely recognized. Improving the formability of steel sheets by {1 1 1} texture [1], increasing the magnetic permeability of electric steels by Goss texture [2,3] and increasing the capacity of an electrolytic capacitor by cube texture in aluminum foils [4] are a few of the well-known examples. These textures are controlled by the combination of cold-working and annealing. There is ongoing research to develop new methods for
⇑ Corresponding author. Tel./fax: +81 45 339 4225.
E-mail address: [email protected] (Y. Onuki).
controlling texture in order to achieve high-performance materials without adding new alloying elements [5,6]. For industrial production of metallic materials in sheet form, the products were made by hot rolling followed by cold rolling. Hot rolling has been applied as a process to change the material thickness while overlooking its possibility as a method of controlling texture. Two of the authors previously observed the development of a sharp texture during high-temperature deformation achieved by extensive grain boundary migration for enlarging the specific orientations in Al–Mg and Al–Cu binary solid solution alloys [7,8]. By examining the results, a mechanism was proposed for developing textures achieved through high-temperature deformation. This mechanism is affected by two major factors that enhance the dynamic
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.11.007
Y. Onuki et al. / Acta Materialia 61 (2013) 1294–1302
growth of grains with specific orientations which have (1) stability against deformation and (2) low Taylor factors, causing them to form the dominant components of the texture. The mechanism is typically activated when the deformation is dominated by the motion of dislocation dragging the solute atmosphere [9]. Hereafter, we will refer to this mechanism as the preferential dynamic grain growth mechanism. This preferential dynamic grain growth mechanism should hold true independent of the crystal structure of an alloy. The mechanism was thus examined experimentally using body-centered cubic (bcc) Fe–3.0 mass% Si solid solution alloy [10,11]. The textures formed in those studies were in accordance with the predictions based on the hypothesis described above. However, the behavior could not be examined in detail, because the deformation was carried out in the uniaxial compression mode. Therefore, orientation characteristics as well as the characteristics of orientation distribution were not clear enough to discuss the mechanism of the formation of the texture. To understand whether the preferential dynamic grain growth mechanism drives the texture development in Fe–3.0 mass% Si, the microstructure, texture and spatial distribution of orientations were investigated by carrying out plane-strain compression deformation at high temperatures. 2. Experimental The as-received material was a hot-rolled plate of Fe– 3.0 mass% Si with a thickness of 20 mm. The chemical composition is shown in Table 1. The plate was cold-rolled up to a reduction of 40% in thickness with the same sample geometry as the prior hot rolling. Then rectangular specimens for plane-strain compression testing were machined to 10 mm in height (normal direction, ND), 20 mm in width (transverse direction, TD) and 40 mm in longitudinal length (rolling direction, RD). Plane-strain compression deformation is often conducted using an anvil called a “channel die” in laboratories, in which a specimen is compressed in a channel in order to restrict TD deformation along TD [12]. In this testing system, the friction between TD restriction wall and the specimen causes deformation inhomogeneity along TD. In order to reduce deformation inhomogeneity, an “openend channel die” was used in this study (Fig. 1). In this testing system, both RD ends are located out of the deformation zone. These zones that are not deformed keep an interface between the deformed and undeformed zones straight, resulting in the homogeneous elongation to RD. Before the test, BN lubricant was sprayed on the friction surfaces of the specimen and the anvil. Then the open-end
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Fig. 1. Schematic drawing of the open-end channel die used in this study.
channel die and the sample were set on the screw-driven testing machine, Shimadzu AG-X 50 kN, and heated up to 1173 K and kept for 30 min in an infrared furnace. This annealing process resulted in a fully recrystallized equiaxed structure with an average grain size of 426 lm. The deformation temperature was 1093 K and 1173 K, and the strain rates were 5.0 105 s1, 5.0 104 s1 and 5.0 103 s1. During deformation, the cross-head speed was changed at every strain increment of 0.01 to keep the strain rate constant. The specimens were quenched in water immediately after the test. In this paper, the strains of the deformed samples are given by the actual strains but the strain rates are indicated by the desired strain rates. For X-ray texture measurements, the deformed specimens were cut parallel to ND mid-plane and the sections were ground by emery papers. Rigaku Ultima-IV was used to perform the Schulz reflection method with Cu-Ka radiation filtered by a monochromator. Then on the basis of measured {1 1 0}, {2 0 0}, {2 1 1} and {3 1 0} pole figures, the orientation distribution function (ODF) was calculated using Resmat TexTools (ADC method [13]). Before the calculation, the pole figures were normalized and approximated by considering the sample orthogonal symmetry. Therefore, the calculated ODF is defined by 0 6 u1 6 90 ; 0 6 U 6 90 ; 0 6 u2 6 90 . For the quantitative texture analysis, the volume fractions of the regions aligned within 15° from specific orientations were calculated by the volume fraction calculation function included in TexTools. A volume fraction occupied by the regions having an orientation around g(u1, U, u2), DV/V can be calculated as [14] Z DV ¼ f ðgÞdg ð1Þ V where f(g) is the orientation density at the orientation g. The volume element in Euler space dg is defined as
Table 1 Chemical composition of the as-received material (mass%). C
Si
Mn
P
S
Al
N
0.0014
3.00
<0.01
<0.01
<0.0001
0.036
0.001
dg ¼
sin U du1 dUdu2 8p2
ð2Þ
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Eq. (2) means that the size of dg is dependent on the focused orientation, g. Therefore, when one compares the amount of a certain texture component with the other component, the volume fractions defined in Eq. (1) must be used rather than values of f(g). In order to clarify the relationship between the texture and the crystal grain structure, electron backscatter diffraction (EBSD) measurement was conducted on the ND midplane using a scanning electron microscope JEOL JSM5600. The measured surface was electrolytically polished in 10% perchloric acid + 90% ethanol solution. The orientation measurement and analysis were conducted by TSL OIM Data Collection ver. 4.6. The step size for the measurement was 4 lm. Optical microscopy was conducted on the ND midplane to obtain the information about the grain structure in an area (5 mm (TD) 4 mm (RD)) larger than for the EBSD measurement. The samples electrolytically polished in the above condition were dipped into 5% nital solution for 1 min to observe grain boundaries. In order to evaluate the grain size along TD, ten lines were drawn on the photomicrographs parallel to TD and the lengths of line segments divided by high-angle grain boundaries were measured. Then, the average value and the standard deviation of intercept lengths along TD were calculated. 3. Predictions based on the preferential dynamic grain growth theory As stated in Section 1, the authors expected that orientations having low Taylor factors and stability against the crystal rotation caused by slip deformation would be the dominant components of the texture formed by hightemperature deformation. Taking into account texture development in Al solid solution alloys, it can be inferred that the preferential dynamic grain growth is enhanced when the dislocations are homogeneously distributed in the grains [7–9,15]. Plane-strain compression deformation usually generates a texture consisting of a-fiber (h1 1 0i || RD) and c-fiber ({1 1 1} \ ND) in ferritic steels, at room temperature [16]. The orientations belonging to these fibers can be regarded as stable orientations. Therefore, it is expected that the orientations having lower Taylor factors in these fiber textures become the growing orientations as long as the primary slip systems do not change. The dependence of the Taylor factor on the crystal orientation is shown by the u2 = 45° section of Euler space in Fig. 2. Values of several orientations are also given in Table 2. For the calculation of the Taylor factor, 48 slip systems with {0 1 1}, {1 1 2} and {1 2 3} slip planes are considered [17]. The minimum value of the Taylor factor in a and cfibers is 2.121 at the top left corner of Fig. 2, namely at the rotated cube orientation ({0 0 1}h1 1 0i). The minimum value of the Taylor factor among all orientations exists around {1 1 8}h4 4 1i. This orientation is only 10° from
Fig. 2. Taylor factor distribution given by u2 = 45° section of Euler space. The orientations shown in Table 1 are also indicated.
the rotated cube orientation. With increasing U along the a-fiber, the Taylor factor gradually increases and reaches a maximum value of 3.719 in the a-fiber at {1 1 1}h1 1 0i. In the c-fiber, the lowest value is 3.565 at {1 1 1}h2 1 1i. Therefore, it can be said that all of the orientations in the c-fiber have high Taylor factors in comparison with the rotated cube orientation. From the above considerations, it can be predicted that the growing orientations in high-temperature plane-strain compression deformation are around the rotated cube, {0 0 1}h1 1 0i. The theory described above is based on the assumption that the driving force of the preferential dynamic grain growth is the difference of the deformation-induced stored energies between the growing and the consumed grains. This implies that the preferential dynamic grain growth is extensively activated after a certain amount of deformation. 4. Results 4.1. X-ray texture measurements {1 1 0} recalculated pole figures obtained by X-ray texture measurement and the subsequent ODF calculation are shown in Fig. 3. High pole densities are seen around RD in both Fig. 3a and b, suggesting the formation of afiber. At the same time, the development of the rotated cube component, {0 0 1}h1 1 0i, is seen in both Fig. 3a and b. The effect of deformation conditions on the textures can be examined by u2 = 45° sections of ODFs shown in Fig. 4. All of the textures obtained in this study have high orientation densities belonging to the a-fiber. Slightly higher orientation densities are seen along the c-fiber for the deformation at a strain rate of 5.0 103 s1, but the densities decrease with decreasing strain rate at both temperatures. It is also seen that the densities along the c-fiber are
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Table 2 Taylor factors for the plane-strain compression deformation at various orientations. Euler angles (u1, U, u2) a-Fiber
(0°, 0°, 45°) (0°, 35.26°, 45°)
Miller index ð0 0 1Þ½1 1 0 (Rotated cube) ð1 1 2Þ½1 1 0
Taylor factor
c-Fiber
(0°, 54.74°, 45°) (30°, 54.74°, 45°)
ð1 1 1Þ½1 1 0 ð1 1 1Þ½1 2 1
3.719 3.565
Other orientations
(45°, 0°, 45°) (90°, 9.73°, 45°) (0°, 90°, 45°)
ð0 0 1Þ½0 1 0 (Cube) ð1 1 8Þ½4 4 1 ð1 1 0Þ½1 1 0
2.449 2.000 (min.) 4.243 (max.)
2.121 3.156
Fig. 3. Recalculated {1 1 0} pole figures of the specimens compressed with a strain rate of 5.0 104 s1 at (a) 1093 K up to a strain of 0.85 and (b) 1173 K up to a strain of 0.86.
lower at the higher temperature, 1173 K, when the textures formed by the same strain rate are compared. In contrast, the peak intensity around the rotated cube orientation increases under high temperature and low strain rate condition. This agrees with the expectation based on the preferential dynamic grain growth mechanism described in Section 3. The orientations for the maximum values of orientation density slightly deviate from the exact rotated cube orientation, e.g. (u1, U, u2) = (0°, 0°, 45°) in all the cases except 1093 K, 5.0 104 s1. The deviation from the rotated cube is 5° at 1093 K and 5–11° at 1173 K and the orientations corresponding to the maximum values differ even at the same temperature. Hereafter, the samples deformed up to a desired strain of 1.0 are referred to by the characters in Fig. 4. For example, the sample deformed at 1093 K with a strain rate of 5.0 103 s1 is called the sample (a). 4.2. Microstructural observations The inverse pole figure (hereafter denoted as IPF) maps obtained by the EBSD measurements on the sample (a) are shown in Fig. 5. In Fig. 5a, it is seen that most regions of the measured area have h1 1 0i aligned parallel to RD. In Fig. 5b, h0 0 1i and h1 1 1i aligned to ND are frequently seen. These results correspond to the formation of high orientation density around the rotated cube, {0 0 1}h1 1 0i and c-fiber, {1 1 1}hu v wi, which coincides with the result of Xray texture measurement.
As for the microstructural aspect, it is observed that most of the grains are elongated along RD and surrounded by serrated high-angle grain boundaries. Small-angle grain boundaries (SAGBs) are also seen, suggesting dynamic recovery [18]. The serration of high-angle grain boundaries and the formation of SAGBs are features in common with the result of uniaxial compression deformation [11]. In Fig. 5, fine grains smaller than 100 lm are frequently observed. Since major portions of grain boundaries are serrated, such isolated grains might be parts of serrated grain boundaries appearing through surface polishing for EBSD observation. When the strain rate is reduced to 5.0 105 s1, grains elongated to RD are hardly observed, as shown in Fig. 6. Grains significantly larger than the initial average grain size of 426 lm are observed at both temperatures, 1093 K (Fig. 6a, the sample (e)) and 1173 K (Fig. 6b, the sample (f)). It seems that h1 1 1i || ND aligned grains are smaller than the grains aligned to h0 0 1i || ND. It is noteworthy that the number of SAGBs indicated by gray lines in Fig. 6a and b is less than in Fig. 5. Further discussion of the relationship between the number of SAGBs and the deformation condition will be made in Section 5. In plane-strain compression deformation, elongation of grains induced by deformation is expected to occur only along RD and not along TD. Thus, the degree of the preferential dynamic grain growth can be estimated by
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5. Discussion 5.1. The effect of deformation on texture development
Fig. 4. u2 = 45° sections of ODFs showing the textures on the mid-planes of specimens compressed up to the aimed strain of 1.0 under various conditions.
measuring grain size along TD in the deformed specimen. From this viewpoint, the average linear intercept lengths along TD were measured in the deformed samples. The results are shown in Fig. 7. It is seen that the intercept length increases with decreasing strain rate at both temperatures. Because crystal orientations of grains are not taken into account in this measurement, the TD intercept length does not directly correspond to the sharpness of texture. However, it can be said from Fig. 7 that the grain boundary migration occurs extensively during the hightemperature deformation.
Fig. 8 shows the volume fractions of several texture components with increasing strain under two conditions. It is seen in Fig. 8a that both {0 0 1} \ ND and {1 1 1} \ ND increase until a strain of 0.4 with strain rates of 5.0 103 s1 and 5.0 104 s1, which indicates the formation of deformation texture achieved by crystal slip deformation. However, in the latter half of the deformation, {0 0 1} \ ND continues to increase while {1 1 1} \ ND decreases. The decrease of the stable component, cfiber, indicates that the grains within c-fiber orientations were consumed by the others. The fact that the consumption is enhanced after a certain amount of straining supports the authors’ presupposition that the driving force of preferential growth originates from the in-grain stored strain energy. The difference of textures formed under the two conditions becomes obvious in the latter half of the deformation. At the strain rate of 5.0 103 s1, {0 0 1} \ ND increases with increasing strain, but no obvious change is seen in h1 1 0i || RD (Fig. 8b). This means that the change of the fraction of h1 1 0i || RD due to the development of {0 0 1}h1 1 0i is almost nullified by the decrease of {1 1 1}h1 1 0i. In the case of the strain rate of 5.0 104 s1, h1 1 0i || RD rapidly increases after the strain of 0.4 and the rate of increase is higher than that of the rotated cube. This indicates that the growing orientations exist even out of the defined range of rotated cube in which the tolerance angle is 15° at a maximum. As stated in Section 3, orientations belonging to the a-fiber are stable for the slip deformation and the change of Taylor factor in the a-fiber with increasing U is gradual. Therefore, orientations far from the rotated cube orientation but belonging to the afiber may grow up. For an instance, at g (u1, U, u2) = (0°, 10°, 45°), the value of The Taylor factor is 2.28, which is lower than the values in the c-fiber. This can also explain why the orientations with maximum orientation density deviate from the exact rotated cube orientation in most conditions. When the strain rate is reduced to 5.0 105 s1, the texture development is different from the others, even in the former half of the deformation. The volume fraction of {1 1 1} \ ND at the strain of 0.43 is lower than that in the as-annealed state. This implies that the preferential growth started earlier in this condition. Correspondingly, high volume fraction of {0 0 1} \ ND is seen at the strain of 0.43. However, the volume fraction of the rotated cube at this strain is almost the same as those formed with the higher strain rates. The volume fraction of h1 1 0i || RD is rather lower than the others. The above characteristics seen at strain of 0.43 with the strain rate of 5.0 105 s1 indicates that the growth of {0 0 1}hu v wi other than {0 0 1}h1 1 0i was also active during
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Fig. 5. IPF maps for ND mid-plane of the specimen compressed up to a strain of 0.85 at 1093 K with the strain rate of 5.0 103 s1 under plane-strain condition. The longitudinal direction of the maps is RD. The colors correspond to the crystal orientations of (a) RD and (b) ND. Black and gray lines are high-angle grain boundaries (>15°) and small-angle grain boundaries (2–15°), respectively.
Fig. 6. IPF maps for ND mid-plane of the specimen compressed up to a strain of 0.85 at (a) 1093 K and (b) 1173 K with the strain rate of 5.0 105 s1 under plane-strain condition. The colors correspond to the crystal orientations of ND. The definition of boundaries is the same as in Fig. 5. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7. Average intercept lengths along TD in the deformed specimens. The error bars show their standard deviations.
the former half of the deformation. Because these orientations have sufficiently low Taylor factors, it is possible for them to grow up before large crystal rotation is induced. Stojakovic et al. calculated the crystal rotation paths during plane-strain compression deformation of bcc crystal and showed that orientations around {0 0 1}hu v wi rotate toward the rotated cube [19]. Therefore, it can be considered that the sharp increase of the volume fraction of h1 1 0i || RD in the latter half of the deformation was derived by both the growth of {0 0 1}h1 1 0i and the crystal rotation of {0 0 1}hu v wi toward {0 0 1}h1 1 0i. The existence of such “rotating and growing” orientations may result in broad variation of orientation densities along u1 from rotated cube as shown in Fig. 4f. 5.2. The effect of dislocation distribution The results of EBSD measurements (Figs. 5 and 6) indicate that the deformed grains have subgrain structures. As stated in Section 3, the distribution of in-grain dislocations is considered to have an effect on preferential dynamic grain growth. Thus, the characteristic of the distribution of dislocations is examined from the viewpoint of subgrain boundary density.
In many cases, the degree of subgrain formation is characterized by subgrain size [20]. However, if the lower limit of misorientation of small-angle grain boundary is set as 2° in EBSD analysis, some parts of subgrain walls are not detected. Furthermore, in the present observation, subgrains completely enclosed by SAGB are hardly seen. On the other hand, if the lower limit of SAGB is set too low, the amount of SAGB and the size of subgrains may contain noise and become very sensitive to the quality of the measurement. Therefore, SAGB density, which was defined by the authors [11], is used to evaluate the degree of subgrain formation instead of subgrain size. SAGB density qSAGB is defined as qSAGB ¼
LSAGB A
ð3Þ
where A is the scanned area in EBSD measurement and LSAGB is the whole length of detected SAGB (2°-15°). In the case of uniaxial compression deformation of Fe–3.0 mass% Si, a linear relationship was found between flow stress and SAGB density in double-logarithmic plot [11]. In this study, flow stresses could not be accurately determined due to the friction between specimens and the constraints tools. Therefore, the relationship between SAGB density and the Zener–Hollomon (Z) parameter was examined. The Z parameter is defined as Z ¼ e_ expðQ=RT Þ. Here, e_ is the strain rate, T is the temperature, Q is the activation energy of deformation (310 kJ mol1 [21]) and R is the gas constant. The result is shown in Fig. 9. It is seen that SAGB density can be given as a function of Z: SAGB density decreases with decreasing Z, i.e. increasing temperature and decreasing strain rate. High-angle grain boundary (HAGB) density was also calculated and plotted in Fig. 9 in the same manner as SAGB density. When the grain boundary network is composed of straight boundaries such as seen in the annealed material, HAGB density corresponds to the reciprocal of the average grain size. However, because HAGBs in the deformed structures in this study are serrated, HAGB densities are not easily related to grain sizes in the deformed
Fig. 8. Development of texture with increasing strain at 1173 K with the strain rates of 5.0 103 s1 and 5.0 104 s1. The tolerance angle is 15°.
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Fig. 9. Relationship between low-/high-angle grain boundary density and Zener–Holomon parameter. The dotted line indicates HAGB density in as-annealed sample.
samples. Under high Z conditions, HAGB densities in the deformed samples are slightly higher than that in asannealed sample, although the apparent grain sizes on ND mid-planes should become larger than that in material that is not deformed. This is because of the serration of HAGBs. On the other hand, under low Z conditions where SAGB densities are lower than the HAGB density in the as-annealed sample, HAGB density decreases along the approximation line for SAGB density. This reflects the coarsening of grain size attributable to the preferential dynamic grain growth. In the situation wherein the SAGB density is lower than the initial HAGB density means that multiple subgrains can hardly be formed in a grain at the beginning of the deformation. Preventing subgrain formation is considered beneficial for increasing the driving force of grain boundary migration. The formation of SAGBs is a kind of dynamic recovery process, which reduces the energy stored in grains. This reduces the difference of stored energies between grains having different orientations, and hence the preferential grain growth contributing to texture development. This might be one of the reasons for the experimental fact that the texture formation attributable to the preferential grain growth is enhanced at low Z conditions, i.e. high temperatures and low strain rates. One may note that the dependences of HAGB density on the deformation condition are somewhat different from that of average TD intercept length shown in Fig. 7. Both are basically functions of grain size. However, the former shows the dependence both on temperature and strain rate and is determined by Z while the latter does not show clear dependence on temperature. As mentioned in Section 4.2, average intercept length along TD does not represent the shape of grains. In contrast, HAGB density is very sensitive to the shape of grains because it is defined as the length of HAGB per unit area as explained above. In order for average intercept length along TD to increase, the consumed grains existing between two growing grains must disappear. Hence, when the preferential
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dynamic grain growth is limited, the average TD intercept length does not change as seen in the case of the sample (a). However, because HAGBs in this sample is severely serrated as shown in Fig. 5, the HAGB density is higher than that in the as-annealed sample. On the other hand, in the sample (b), where the preferential dynamic grain growth is supposed to be more active than in the sample (a), disappearance of some grains or parts of them may occur. Therefore, the average TD intercept length in the sample (b) increases as shown in Fig. 7. However, the serration of HAGBs became more complex due to the grain boundary migration, the HAGB density also increases. Therefore, the value of HAGB density in the sample (b) is as high as in the sample (a). In the samples (b)-(f), temperature dependence of average intercept lengths along TD is not seen. However, as shown in Fig. 6, the sample deformed at 1093 K have more severely serrated HAGBs than one deformed at 1173 K when the strain rate is the same. Therefore, the HAGB densities in the samples deformed at 1093 K tend to be higher than those in the samples deformed at 1173 K. This resulted in the Z dependence of HAGB density observed in Fig. 9. However, both HAGB density and average TD intercept length do not include any information about crystal orientation of each grain. Therefore, the increase of average TD intercept length or the decrease of HAGB density does not directly express the growth of low-Taylor-factor grains. Hence, both of them do not simply relate to the texture development. However, the preferential growth does bring grain coarsening. The effect of the preferential growth is therefore reflected in both parameters. 5.3. Validity of the dynamic grain growth theory As described above, the results of the present study agree with the authors’ prediction based on the preferential dynamic grain growth mechanism given in Section 3. Therefore, it can be concluded that the proposed mechanism is valid in the present case. In addition, the dependence of texture formation in the case of uniaxial compression deformation seen in the previous study [11] is quite similar to the case of plane-strain compression deformation. From these results, it can be said that the preferential dynamic grain growth mechanism works in high-temperature deformation of Fe–3.0 mass% Si regardless of the deformation modes. In this study, it is pointed out that the growing orientation is not only exactly the rotated cube, {0 0 1}h1 1 0i. Some orientations that deviate from the rotated cube orientation with relatively low Taylor factors can be observed. Therefore, widely spread orientation densities with {0 0 1}h1 1 0i in the center, are formed under medium to high Z conditions. The others can be categorized as “growing and rotating” orientations such as {0 0 1}hu v wi, which are not stable but rotate toward {0 0 1}h1 1 0i. Therefore, they also contribute to the enhancement of rotated cube texture.
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6. Conclusions In order to verify the preferential dynamic grain growth mechanism proposed by the authors, high-temperature plane-strain compression deformation was carried out on Fe–3.0 mass% Si. The results are summarized as follows. (1) Textures develop in all the deformation conditions in this study. The sharpness of the texture varies depending on the deformation conditions. (2) The major texture components of texture approximate rotated cube, {0 0 1}h1 1 0i independent of the deformation conditions, which are predicted by the preferential dynamic grain growth mechanism. The development of rotated cube orientation was enhanced at higher temperature and lower strain rate, accompanying the decrease of the c-fiber, {1 1 1}hu v wi. (3) The average intercept lengths along TD grew with decreasing strain rate. The change was attributable to the dynamic grain growth. (4) The microstructures after the deformation consisted of serrated high-angle grain boundaries (HAGBs) and networks of small-angle grain boundaries (SAGBs). SAGB density decreased with decreasing Z, i.e. decreasing strain rate and increasing temperature. (5) The preferential dynamic grain growth of the rotatedcube-oriented grains is enhanced when the formation of SAGB is suppressed. This fact supports the consideration that the preferential dynamic grain growth becomes obvious when the distribution of dislocations is homogeneous. (6) The preferential dynamic grain growth mechanism can reasonably explain the formation of the rotated cube texture in high-temperature plane-strain compression deformation of Fe–3.0 mass% Si. This
implies that high-temperature deformation may be applied as a new method of texture control not only for fcc alloys but also for bcc alloys. Acknowledgement The authors would like to express their appreciation to the Amada foundation for their financial support. References [1] Samajdar I, Verlinden B, Van Houtte P, Vanderschueren D. Mater Sci Eng A 1997;238:343–50. [2] Goss NP. Trans Am Soc Met 1935;23:511–76. [3] Suzuki S, Ushigami Y, Homma H, Takebayashi S, Kubota T. Mater Trans 2001;42:994–1006. [4] Engler O, Huh MY. Mater Sci Eng A 1999;271:371–81. [5] Kim J, Okayasu K, Fukutomi H. Netsu Shori (J Jpn Heat Treat) 2012;52:4–10. [6] Druker A, Sobrero C, Brokmeier HG, Malarria J, Bolmaro R. Mater Sci Eng A 2008;481–482:578–81. [7] Okayasu K, Takekoshi H, Fukutomi H. Mater Trans 2007;48:2002–7. [8] Okayasu K, Takahata S, Fukutomi H. Mater Sci Forum 2012;702– 703:336–9. [9] Jeong HM, Okayasu K, Fukutomi H. Mater Trans 2010;51:2162–7. [10] Onuki Y, Okayasu K, Fukutomi H. ISIJ Int 2011;51:564–1565. [11] Onuki Y, Okayasu K, Fukutomi H. Tetsu-to-Hagane´ 2001;98:177– 83. [12] Gehrmann R, Frommert MM, Gottstein G. Mater Sci Eng A 2005;395:338–49. [13] Pawlik K, Pospiech J, Lu¨cke K. Text Micrstruct 1991;14–18:25–30. [14] Dahms M, Bunge HJ. J Appl Cryst 1989;22:439–47. [15] Horiuchi R, Otsuka M. Trans JIM 1972;13:284–93. [16] Ho¨lscher M, Raabe D, Lu¨cke K. Steel Res 1991;62:567–75. [17] Barrett CS, Ansel G, Mehl RF. Trans Am Soc Met 1937;25:702–36. [18] Oudin A, Hodgson PD, Barnett MR. Mater Sci Eng A 2008;486:72–9. [19] Stojakovic D, Doherty RD, Kalidindi SR, Landgraf FJG. Metall Mater Trans A 2008;39:1738–46. [20] Glover G, Sellars CM. Metall Trans 1973;4:765–75. [21] Inoue E, Sakai T. J Jpn Inst Met 1991;55:286–93.
Acta Materialia 61 (2013) 1294–1302 www.elsevier.com/locate/actamat
Texture development in Fe–3.0 mass% Si during high-temperature deformation: Examination of the preferential dynamic grain growth mechanism Yusuke Onuki a,⇑, Ryosuke Hongo a, Kazuto Okayasu b, Hiroshi Fukutomi b a
Graduate School of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa, Japan b Faculty of Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya-ku, Yokohama, Kanagawa, Japan Received 1 August 2012; received in revised form 16 October 2012; accepted 5 November 2012 Available online 6 December 2012
Abstract A new mechanism of texture evolution, named “preferential dynamic grain growth mechanism”, is examined experimentally by hightemperature plane-strain compression deformation of Fe–3.0 mass% Si alloy. The proposed mechanism is based on preferential growth of the orientations having low Taylor factors and stability against deformation. According to the mechanism, the growing orientation is expected to be {0 0 1}h1 1 0i in the case of plane-strain compression deformation. In fact, the textures formed by deformations up to the desired strain of 1.0 have high orientation densities around {0 0 1}h1 1 0i in accordance with the proposed mechanism. With decreasing strain rate, the volume fraction of {0 0 1}h1 1 0i increases with the increase in the average intercept length of crystal grains along the transverse direction at both 1093 K and 1173 K, which implies the occurrence of dynamic grain growth during the deformation. The volume fraction of {0 0 1}h1 1 0i is higher at 1173 K than at 1093 K for the same strain rate. Electron backscatter diffraction measurements show that the density of small-angle grain boundaries decreases with increasing temperature and decreasing strain rate. The lower density of small-angle grain boundaries implies that distribution of dislocations in grains approaching homogeneity results in the enhancement of preferential dynamic grain growth at higher temperatures and lower strain rates. This suggests that high-temperature deformation might be applied as a new method for controlling texture. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Texture; High-temperature deformation; Microstructure formation mechanism; Solid solution; Preferential dynamic grain growth
1. Introduction The importance of textures for improving the performance of metallic materials has been widely recognized. Improving the formability of steel sheets by {1 1 1} texture [1], increasing the magnetic permeability of electric steels by Goss texture [2,3] and increasing the capacity of an electrolytic capacitor by cube texture in aluminum foils [4] are a few of the well-known examples. These textures are controlled by the combination of cold-working and annealing. There is ongoing research to develop new methods for
⇑ Corresponding author. Tel./fax: +81 45 339 4225.
E-mail address: [email protected] (Y. Onuki).
controlling texture in order to achieve high-performance materials without adding new alloying elements [5,6]. For industrial production of metallic materials in sheet form, the products were made by hot rolling followed by cold rolling. Hot rolling has been applied as a process to change the material thickness while overlooking its possibility as a method of controlling texture. Two of the authors previously observed the development of a sharp texture during high-temperature deformation achieved by extensive grain boundary migration for enlarging the specific orientations in Al–Mg and Al–Cu binary solid solution alloys [7,8]. By examining the results, a mechanism was proposed for developing textures achieved through high-temperature deformation. This mechanism is affected by two major factors that enhance the dynamic
1359-6454/$36.00 Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actamat.2012.11.007
Y. Onuki et al. / Acta Materialia 61 (2013) 1294–1302
growth of grains with specific orientations which have (1) stability against deformation and (2) low Taylor factors, causing them to form the dominant components of the texture. The mechanism is typically activated when the deformation is dominated by the motion of dislocation dragging the solute atmosphere [9]. Hereafter, we will refer to this mechanism as the preferential dynamic grain growth mechanism. This preferential dynamic grain growth mechanism should hold true independent of the crystal structure of an alloy. The mechanism was thus examined experimentally using body-centered cubic (bcc) Fe–3.0 mass% Si solid solution alloy [10,11]. The textures formed in those studies were in accordance with the predictions based on the hypothesis described above. However, the behavior could not be examined in detail, because the deformation was carried out in the uniaxial compression mode. Therefore, orientation characteristics as well as the characteristics of orientation distribution were not clear enough to discuss the mechanism of the formation of the texture. To understand whether the preferential dynamic grain growth mechanism drives the texture development in Fe–3.0 mass% Si, the microstructure, texture and spatial distribution of orientations were investigated by carrying out plane-strain compression deformation at high temperatures. 2. Experimental The as-received material was a hot-rolled plate of Fe– 3.0 mass% Si with a thickness of 20 mm. The chemical composition is shown in Table 1. The plate was cold-rolled up to a reduction of 40% in thickness with the same sample geometry as the prior hot rolling. Then rectangular specimens for plane-strain compression testing were machined to 10 mm in height (normal direction, ND), 20 mm in width (transverse direction, TD) and 40 mm in longitudinal length (rolling direction, RD). Plane-strain compression deformation is often conducted using an anvil called a “channel die” in laboratories, in which a specimen is compressed in a channel in order to restrict TD deformation along TD [12]. In this testing system, the friction between TD restriction wall and the specimen causes deformation inhomogeneity along TD. In order to reduce deformation inhomogeneity, an “openend channel die” was used in this study (Fig. 1). In this testing system, both RD ends are located out of the deformation zone. These zones that are not deformed keep an interface between the deformed and undeformed zones straight, resulting in the homogeneous elongation to RD. Before the test, BN lubricant was sprayed on the friction surfaces of the specimen and the anvil. Then the open-end
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Fig. 1. Schematic drawing of the open-end channel die used in this study.
channel die and the sample were set on the screw-driven testing machine, Shimadzu AG-X 50 kN, and heated up to 1173 K and kept for 30 min in an infrared furnace. This annealing process resulted in a fully recrystallized equiaxed structure with an average grain size of 426 lm. The deformation temperature was 1093 K and 1173 K, and the strain rates were 5.0 105 s1, 5.0 104 s1 and 5.0 103 s1. During deformation, the cross-head speed was changed at every strain increment of 0.01 to keep the strain rate constant. The specimens were quenched in water immediately after the test. In this paper, the strains of the deformed samples are given by the actual strains but the strain rates are indicated by the desired strain rates. For X-ray texture measurements, the deformed specimens were cut parallel to ND mid-plane and the sections were ground by emery papers. Rigaku Ultima-IV was used to perform the Schulz reflection method with Cu-Ka radiation filtered by a monochromator. Then on the basis of measured {1 1 0}, {2 0 0}, {2 1 1} and {3 1 0} pole figures, the orientation distribution function (ODF) was calculated using Resmat TexTools (ADC method [13]). Before the calculation, the pole figures were normalized and approximated by considering the sample orthogonal symmetry. Therefore, the calculated ODF is defined by 0 6 u1 6 90 ; 0 6 U 6 90 ; 0 6 u2 6 90 . For the quantitative texture analysis, the volume fractions of the regions aligned within 15° from specific orientations were calculated by the volume fraction calculation function included in TexTools. A volume fraction occupied by the regions having an orientation around g(u1, U, u2), DV/V can be calculated as [14] Z DV ¼ f ðgÞdg ð1Þ V where f(g) is the orientation density at the orientation g. The volume element in Euler space dg is defined as
Table 1 Chemical composition of the as-received material (mass%). C
Si
Mn
P
S
Al
N
0.0014
3.00
<0.01
<0.01
<0.0001
0.036
0.001
dg ¼
sin U du1 dUdu2 8p2
ð2Þ
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Eq. (2) means that the size of dg is dependent on the focused orientation, g. Therefore, when one compares the amount of a certain texture component with the other component, the volume fractions defined in Eq. (1) must be used rather than values of f(g). In order to clarify the relationship between the texture and the crystal grain structure, electron backscatter diffraction (EBSD) measurement was conducted on the ND midplane using a scanning electron microscope JEOL JSM5600. The measured surface was electrolytically polished in 10% perchloric acid + 90% ethanol solution. The orientation measurement and analysis were conducted by TSL OIM Data Collection ver. 4.6. The step size for the measurement was 4 lm. Optical microscopy was conducted on the ND midplane to obtain the information about the grain structure in an area (5 mm (TD) 4 mm (RD)) larger than for the EBSD measurement. The samples electrolytically polished in the above condition were dipped into 5% nital solution for 1 min to observe grain boundaries. In order to evaluate the grain size along TD, ten lines were drawn on the photomicrographs parallel to TD and the lengths of line segments divided by high-angle grain boundaries were measured. Then, the average value and the standard deviation of intercept lengths along TD were calculated. 3. Predictions based on the preferential dynamic grain growth theory As stated in Section 1, the authors expected that orientations having low Taylor factors and stability against the crystal rotation caused by slip deformation would be the dominant components of the texture formed by hightemperature deformation. Taking into account texture development in Al solid solution alloys, it can be inferred that the preferential dynamic grain growth is enhanced when the dislocations are homogeneously distributed in the grains [7–9,15]. Plane-strain compression deformation usually generates a texture consisting of a-fiber (h1 1 0i || RD) and c-fiber ({1 1 1} \ ND) in ferritic steels, at room temperature [16]. The orientations belonging to these fibers can be regarded as stable orientations. Therefore, it is expected that the orientations having lower Taylor factors in these fiber textures become the growing orientations as long as the primary slip systems do not change. The dependence of the Taylor factor on the crystal orientation is shown by the u2 = 45° section of Euler space in Fig. 2. Values of several orientations are also given in Table 2. For the calculation of the Taylor factor, 48 slip systems with {0 1 1}, {1 1 2} and {1 2 3} slip planes are considered [17]. The minimum value of the Taylor factor in a and cfibers is 2.121 at the top left corner of Fig. 2, namely at the rotated cube orientation ({0 0 1}h1 1 0i). The minimum value of the Taylor factor among all orientations exists around {1 1 8}h4 4 1i. This orientation is only 10° from
Fig. 2. Taylor factor distribution given by u2 = 45° section of Euler space. The orientations shown in Table 1 are also indicated.
the rotated cube orientation. With increasing U along the a-fiber, the Taylor factor gradually increases and reaches a maximum value of 3.719 in the a-fiber at {1 1 1}h1 1 0i. In the c-fiber, the lowest value is 3.565 at {1 1 1}h2 1 1i. Therefore, it can be said that all of the orientations in the c-fiber have high Taylor factors in comparison with the rotated cube orientation. From the above considerations, it can be predicted that the growing orientations in high-temperature plane-strain compression deformation are around the rotated cube, {0 0 1}h1 1 0i. The theory described above is based on the assumption that the driving force of the preferential dynamic grain growth is the difference of the deformation-induced stored energies between the growing and the consumed grains. This implies that the preferential dynamic grain growth is extensively activated after a certain amount of deformation. 4. Results 4.1. X-ray texture measurements {1 1 0} recalculated pole figures obtained by X-ray texture measurement and the subsequent ODF calculation are shown in Fig. 3. High pole densities are seen around RD in both Fig. 3a and b, suggesting the formation of afiber. At the same time, the development of the rotated cube component, {0 0 1}h1 1 0i, is seen in both Fig. 3a and b. The effect of deformation conditions on the textures can be examined by u2 = 45° sections of ODFs shown in Fig. 4. All of the textures obtained in this study have high orientation densities belonging to the a-fiber. Slightly higher orientation densities are seen along the c-fiber for the deformation at a strain rate of 5.0 103 s1, but the densities decrease with decreasing strain rate at both temperatures. It is also seen that the densities along the c-fiber are
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Table 2 Taylor factors for the plane-strain compression deformation at various orientations. Euler angles (u1, U, u2) a-Fiber
(0°, 0°, 45°) (0°, 35.26°, 45°)
Miller index ð0 0 1Þ½1 1 0 (Rotated cube) ð1 1 2Þ½1 1 0
Taylor factor
c-Fiber
(0°, 54.74°, 45°) (30°, 54.74°, 45°)
ð1 1 1Þ½1 1 0 ð1 1 1Þ½1 2 1
3.719 3.565
Other orientations
(45°, 0°, 45°) (90°, 9.73°, 45°) (0°, 90°, 45°)
ð0 0 1Þ½0 1 0 (Cube) ð1 1 8Þ½4 4 1 ð1 1 0Þ½1 1 0
2.449 2.000 (min.) 4.243 (max.)
2.121 3.156
Fig. 3. Recalculated {1 1 0} pole figures of the specimens compressed with a strain rate of 5.0 104 s1 at (a) 1093 K up to a strain of 0.85 and (b) 1173 K up to a strain of 0.86.
lower at the higher temperature, 1173 K, when the textures formed by the same strain rate are compared. In contrast, the peak intensity around the rotated cube orientation increases under high temperature and low strain rate condition. This agrees with the expectation based on the preferential dynamic grain growth mechanism described in Section 3. The orientations for the maximum values of orientation density slightly deviate from the exact rotated cube orientation, e.g. (u1, U, u2) = (0°, 0°, 45°) in all the cases except 1093 K, 5.0 104 s1. The deviation from the rotated cube is 5° at 1093 K and 5–11° at 1173 K and the orientations corresponding to the maximum values differ even at the same temperature. Hereafter, the samples deformed up to a desired strain of 1.0 are referred to by the characters in Fig. 4. For example, the sample deformed at 1093 K with a strain rate of 5.0 103 s1 is called the sample (a). 4.2. Microstructural observations The inverse pole figure (hereafter denoted as IPF) maps obtained by the EBSD measurements on the sample (a) are shown in Fig. 5. In Fig. 5a, it is seen that most regions of the measured area have h1 1 0i aligned parallel to RD. In Fig. 5b, h0 0 1i and h1 1 1i aligned to ND are frequently seen. These results correspond to the formation of high orientation density around the rotated cube, {0 0 1}h1 1 0i and c-fiber, {1 1 1}hu v wi, which coincides with the result of Xray texture measurement.
As for the microstructural aspect, it is observed that most of the grains are elongated along RD and surrounded by serrated high-angle grain boundaries. Small-angle grain boundaries (SAGBs) are also seen, suggesting dynamic recovery [18]. The serration of high-angle grain boundaries and the formation of SAGBs are features in common with the result of uniaxial compression deformation [11]. In Fig. 5, fine grains smaller than 100 lm are frequently observed. Since major portions of grain boundaries are serrated, such isolated grains might be parts of serrated grain boundaries appearing through surface polishing for EBSD observation. When the strain rate is reduced to 5.0 105 s1, grains elongated to RD are hardly observed, as shown in Fig. 6. Grains significantly larger than the initial average grain size of 426 lm are observed at both temperatures, 1093 K (Fig. 6a, the sample (e)) and 1173 K (Fig. 6b, the sample (f)). It seems that h1 1 1i || ND aligned grains are smaller than the grains aligned to h0 0 1i || ND. It is noteworthy that the number of SAGBs indicated by gray lines in Fig. 6a and b is less than in Fig. 5. Further discussion of the relationship between the number of SAGBs and the deformation condition will be made in Section 5. In plane-strain compression deformation, elongation of grains induced by deformation is expected to occur only along RD and not along TD. Thus, the degree of the preferential dynamic grain growth can be estimated by
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5. Discussion 5.1. The effect of deformation on texture development
Fig. 4. u2 = 45° sections of ODFs showing the textures on the mid-planes of specimens compressed up to the aimed strain of 1.0 under various conditions.
measuring grain size along TD in the deformed specimen. From this viewpoint, the average linear intercept lengths along TD were measured in the deformed samples. The results are shown in Fig. 7. It is seen that the intercept length increases with decreasing strain rate at both temperatures. Because crystal orientations of grains are not taken into account in this measurement, the TD intercept length does not directly correspond to the sharpness of texture. However, it can be said from Fig. 7 that the grain boundary migration occurs extensively during the hightemperature deformation.
Fig. 8 shows the volume fractions of several texture components with increasing strain under two conditions. It is seen in Fig. 8a that both {0 0 1} \ ND and {1 1 1} \ ND increase until a strain of 0.4 with strain rates of 5.0 103 s1 and 5.0 104 s1, which indicates the formation of deformation texture achieved by crystal slip deformation. However, in the latter half of the deformation, {0 0 1} \ ND continues to increase while {1 1 1} \ ND decreases. The decrease of the stable component, cfiber, indicates that the grains within c-fiber orientations were consumed by the others. The fact that the consumption is enhanced after a certain amount of straining supports the authors’ presupposition that the driving force of preferential growth originates from the in-grain stored strain energy. The difference of textures formed under the two conditions becomes obvious in the latter half of the deformation. At the strain rate of 5.0 103 s1, {0 0 1} \ ND increases with increasing strain, but no obvious change is seen in h1 1 0i || RD (Fig. 8b). This means that the change of the fraction of h1 1 0i || RD due to the development of {0 0 1}h1 1 0i is almost nullified by the decrease of {1 1 1}h1 1 0i. In the case of the strain rate of 5.0 104 s1, h1 1 0i || RD rapidly increases after the strain of 0.4 and the rate of increase is higher than that of the rotated cube. This indicates that the growing orientations exist even out of the defined range of rotated cube in which the tolerance angle is 15° at a maximum. As stated in Section 3, orientations belonging to the a-fiber are stable for the slip deformation and the change of Taylor factor in the a-fiber with increasing U is gradual. Therefore, orientations far from the rotated cube orientation but belonging to the afiber may grow up. For an instance, at g (u1, U, u2) = (0°, 10°, 45°), the value of The Taylor factor is 2.28, which is lower than the values in the c-fiber. This can also explain why the orientations with maximum orientation density deviate from the exact rotated cube orientation in most conditions. When the strain rate is reduced to 5.0 105 s1, the texture development is different from the others, even in the former half of the deformation. The volume fraction of {1 1 1} \ ND at the strain of 0.43 is lower than that in the as-annealed state. This implies that the preferential growth started earlier in this condition. Correspondingly, high volume fraction of {0 0 1} \ ND is seen at the strain of 0.43. However, the volume fraction of the rotated cube at this strain is almost the same as those formed with the higher strain rates. The volume fraction of h1 1 0i || RD is rather lower than the others. The above characteristics seen at strain of 0.43 with the strain rate of 5.0 105 s1 indicates that the growth of {0 0 1}hu v wi other than {0 0 1}h1 1 0i was also active during
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Fig. 5. IPF maps for ND mid-plane of the specimen compressed up to a strain of 0.85 at 1093 K with the strain rate of 5.0 103 s1 under plane-strain condition. The longitudinal direction of the maps is RD. The colors correspond to the crystal orientations of (a) RD and (b) ND. Black and gray lines are high-angle grain boundaries (>15°) and small-angle grain boundaries (2–15°), respectively.
Fig. 6. IPF maps for ND mid-plane of the specimen compressed up to a strain of 0.85 at (a) 1093 K and (b) 1173 K with the strain rate of 5.0 105 s1 under plane-strain condition. The colors correspond to the crystal orientations of ND. The definition of boundaries is the same as in Fig. 5. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 7. Average intercept lengths along TD in the deformed specimens. The error bars show their standard deviations.
the former half of the deformation. Because these orientations have sufficiently low Taylor factors, it is possible for them to grow up before large crystal rotation is induced. Stojakovic et al. calculated the crystal rotation paths during plane-strain compression deformation of bcc crystal and showed that orientations around {0 0 1}hu v wi rotate toward the rotated cube [19]. Therefore, it can be considered that the sharp increase of the volume fraction of h1 1 0i || RD in the latter half of the deformation was derived by both the growth of {0 0 1}h1 1 0i and the crystal rotation of {0 0 1}hu v wi toward {0 0 1}h1 1 0i. The existence of such “rotating and growing” orientations may result in broad variation of orientation densities along u1 from rotated cube as shown in Fig. 4f. 5.2. The effect of dislocation distribution The results of EBSD measurements (Figs. 5 and 6) indicate that the deformed grains have subgrain structures. As stated in Section 3, the distribution of in-grain dislocations is considered to have an effect on preferential dynamic grain growth. Thus, the characteristic of the distribution of dislocations is examined from the viewpoint of subgrain boundary density.
In many cases, the degree of subgrain formation is characterized by subgrain size [20]. However, if the lower limit of misorientation of small-angle grain boundary is set as 2° in EBSD analysis, some parts of subgrain walls are not detected. Furthermore, in the present observation, subgrains completely enclosed by SAGB are hardly seen. On the other hand, if the lower limit of SAGB is set too low, the amount of SAGB and the size of subgrains may contain noise and become very sensitive to the quality of the measurement. Therefore, SAGB density, which was defined by the authors [11], is used to evaluate the degree of subgrain formation instead of subgrain size. SAGB density qSAGB is defined as qSAGB ¼
LSAGB A
ð3Þ
where A is the scanned area in EBSD measurement and LSAGB is the whole length of detected SAGB (2°-15°). In the case of uniaxial compression deformation of Fe–3.0 mass% Si, a linear relationship was found between flow stress and SAGB density in double-logarithmic plot [11]. In this study, flow stresses could not be accurately determined due to the friction between specimens and the constraints tools. Therefore, the relationship between SAGB density and the Zener–Hollomon (Z) parameter was examined. The Z parameter is defined as Z ¼ e_ expðQ=RT Þ. Here, e_ is the strain rate, T is the temperature, Q is the activation energy of deformation (310 kJ mol1 [21]) and R is the gas constant. The result is shown in Fig. 9. It is seen that SAGB density can be given as a function of Z: SAGB density decreases with decreasing Z, i.e. increasing temperature and decreasing strain rate. High-angle grain boundary (HAGB) density was also calculated and plotted in Fig. 9 in the same manner as SAGB density. When the grain boundary network is composed of straight boundaries such as seen in the annealed material, HAGB density corresponds to the reciprocal of the average grain size. However, because HAGBs in the deformed structures in this study are serrated, HAGB densities are not easily related to grain sizes in the deformed
Fig. 8. Development of texture with increasing strain at 1173 K with the strain rates of 5.0 103 s1 and 5.0 104 s1. The tolerance angle is 15°.
Y. Onuki et al. / Acta Materialia 61 (2013) 1294–1302
Fig. 9. Relationship between low-/high-angle grain boundary density and Zener–Holomon parameter. The dotted line indicates HAGB density in as-annealed sample.
samples. Under high Z conditions, HAGB densities in the deformed samples are slightly higher than that in asannealed sample, although the apparent grain sizes on ND mid-planes should become larger than that in material that is not deformed. This is because of the serration of HAGBs. On the other hand, under low Z conditions where SAGB densities are lower than the HAGB density in the as-annealed sample, HAGB density decreases along the approximation line for SAGB density. This reflects the coarsening of grain size attributable to the preferential dynamic grain growth. In the situation wherein the SAGB density is lower than the initial HAGB density means that multiple subgrains can hardly be formed in a grain at the beginning of the deformation. Preventing subgrain formation is considered beneficial for increasing the driving force of grain boundary migration. The formation of SAGBs is a kind of dynamic recovery process, which reduces the energy stored in grains. This reduces the difference of stored energies between grains having different orientations, and hence the preferential grain growth contributing to texture development. This might be one of the reasons for the experimental fact that the texture formation attributable to the preferential grain growth is enhanced at low Z conditions, i.e. high temperatures and low strain rates. One may note that the dependences of HAGB density on the deformation condition are somewhat different from that of average TD intercept length shown in Fig. 7. Both are basically functions of grain size. However, the former shows the dependence both on temperature and strain rate and is determined by Z while the latter does not show clear dependence on temperature. As mentioned in Section 4.2, average intercept length along TD does not represent the shape of grains. In contrast, HAGB density is very sensitive to the shape of grains because it is defined as the length of HAGB per unit area as explained above. In order for average intercept length along TD to increase, the consumed grains existing between two growing grains must disappear. Hence, when the preferential
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dynamic grain growth is limited, the average TD intercept length does not change as seen in the case of the sample (a). However, because HAGBs in this sample is severely serrated as shown in Fig. 5, the HAGB density is higher than that in the as-annealed sample. On the other hand, in the sample (b), where the preferential dynamic grain growth is supposed to be more active than in the sample (a), disappearance of some grains or parts of them may occur. Therefore, the average TD intercept length in the sample (b) increases as shown in Fig. 7. However, the serration of HAGBs became more complex due to the grain boundary migration, the HAGB density also increases. Therefore, the value of HAGB density in the sample (b) is as high as in the sample (a). In the samples (b)-(f), temperature dependence of average intercept lengths along TD is not seen. However, as shown in Fig. 6, the sample deformed at 1093 K have more severely serrated HAGBs than one deformed at 1173 K when the strain rate is the same. Therefore, the HAGB densities in the samples deformed at 1093 K tend to be higher than those in the samples deformed at 1173 K. This resulted in the Z dependence of HAGB density observed in Fig. 9. However, both HAGB density and average TD intercept length do not include any information about crystal orientation of each grain. Therefore, the increase of average TD intercept length or the decrease of HAGB density does not directly express the growth of low-Taylor-factor grains. Hence, both of them do not simply relate to the texture development. However, the preferential growth does bring grain coarsening. The effect of the preferential growth is therefore reflected in both parameters. 5.3. Validity of the dynamic grain growth theory As described above, the results of the present study agree with the authors’ prediction based on the preferential dynamic grain growth mechanism given in Section 3. Therefore, it can be concluded that the proposed mechanism is valid in the present case. In addition, the dependence of texture formation in the case of uniaxial compression deformation seen in the previous study [11] is quite similar to the case of plane-strain compression deformation. From these results, it can be said that the preferential dynamic grain growth mechanism works in high-temperature deformation of Fe–3.0 mass% Si regardless of the deformation modes. In this study, it is pointed out that the growing orientation is not only exactly the rotated cube, {0 0 1}h1 1 0i. Some orientations that deviate from the rotated cube orientation with relatively low Taylor factors can be observed. Therefore, widely spread orientation densities with {0 0 1}h1 1 0i in the center, are formed under medium to high Z conditions. The others can be categorized as “growing and rotating” orientations such as {0 0 1}hu v wi, which are not stable but rotate toward {0 0 1}h1 1 0i. Therefore, they also contribute to the enhancement of rotated cube texture.
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6. Conclusions In order to verify the preferential dynamic grain growth mechanism proposed by the authors, high-temperature plane-strain compression deformation was carried out on Fe–3.0 mass% Si. The results are summarized as follows. (1) Textures develop in all the deformation conditions in this study. The sharpness of the texture varies depending on the deformation conditions. (2) The major texture components of texture approximate rotated cube, {0 0 1}h1 1 0i independent of the deformation conditions, which are predicted by the preferential dynamic grain growth mechanism. The development of rotated cube orientation was enhanced at higher temperature and lower strain rate, accompanying the decrease of the c-fiber, {1 1 1}hu v wi. (3) The average intercept lengths along TD grew with decreasing strain rate. The change was attributable to the dynamic grain growth. (4) The microstructures after the deformation consisted of serrated high-angle grain boundaries (HAGBs) and networks of small-angle grain boundaries (SAGBs). SAGB density decreased with decreasing Z, i.e. decreasing strain rate and increasing temperature. (5) The preferential dynamic grain growth of the rotatedcube-oriented grains is enhanced when the formation of SAGB is suppressed. This fact supports the consideration that the preferential dynamic grain growth becomes obvious when the distribution of dislocations is homogeneous. (6) The preferential dynamic grain growth mechanism can reasonably explain the formation of the rotated cube texture in high-temperature plane-strain compression deformation of Fe–3.0 mass% Si. This
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