3. Results and Discussion
3.1. Microstructure Characteristics
During two stage cold rolling, the variation of microstructure evolution with reduction distribution coefficient (n) was revealed in Fig. 2. Before cold rolling, some elongated grains were observed in the initial microstructure in addition to some equiaxed grains (Fig. 2(a)). The reason for this was that during hot-band annealing the partial recrystallization occurred. The grains elongated and in-grains shear bands developed after first stage cold rolling. As n decreased, more and more shear bands formed owing to an increase in cold rolling reduction in this stage (Figs. 2(b1)–2(b6)). At higher n, especially n=0.881, in addition to some elongated grains some approximately equiaxed grains were also observed because of relatively lower first stage cold rolling reduction, which resembled the initial microstructure (Fig. 2(a)). For this microstructure, distinct recovery, that is, recrystallization in situ, and weak grain growth tendency tended to occur during subsequent annealing. After intermediate annealing, the microstructure was made up of equiaxed grains, and some approximately equiaxed grains were also observed at higher n. With decreasing n, the microstructure became finer and its uniformity increased (Figs. 2(c1)–2(c6)). This was attributed to a finer and more uniform deformed microstructure, more shear bands and higher deformation energy storage, resulting from a larger cold rolling reduction prior to annealing.
Fig. 2. Changes in microstructure evolution with reduction distribution coefficient (n). (b1), (c1), (d1), (e1) n=0.095; (b2), (c2), (d2), (e2) n=0.214; (b3), (c3), (d3), (e3) n=0.405; (b4), (c4), (d4), (e4) n=0.524; (b5), (c5), (d5), (e5) n=0.762; (b6), (c6), (d6), (e6) n=0.881.
After second stage cold rolling, the coarser deformed grains developed at lower n (Figs. 2(d1)–2(d6)), because the second cold rolling reduction gradually decreased with the decrease of n. After final annealing, the recrystallized microstructures experienced a gradual refinement followed by a gradual coarsening with increasing n (Figs. 2(e1)–2(e6)), which indicated that during two stage cold rolling, larger or smaller n was not conducive to the microstructure refinement. At lower n, with increasing n, the number of in-grains shear band developed during second stage cold rolling and the nucleation site of recrystallization during final annealing gradually increased, leading to the recrystallized microstructure refinement. At larger n, with decreasing n, the intermediate annealed microstructure refined gradually, and this change was inherited to the final sheet, leading to the recrystallized microstructure refinement. However, the change in grain size with n was not significant because of same total reduction of 84% during two stage cold rolling.
3.2. Texture Characteristics
During two stage cold rolling, the variation of texture evolution with reduction distribution coefficient (n) was revealed in Fig. 3. The texture before cold rolling displayed prominent α-fiber and faint γ-fiber having a dominating component at approximately {111}<110>, and its peak intensity was at {001}<110> (Fig. 3(a)).
Fig. 3. Changes in texture evolution with reduction distribution coefficient (n). (b1), (c1), (d1), (e1) n=0.095; (b2), (c2), (d2), (e2) n=0.214; (b3), (c3), (d3), (e3) n=0.405; (b4), (c4), (d4), (e4) n=0.524; (b5), (c5), (d5), (e5) n=0.762; (b6), (c6), (d6), (e6) n=0.881. (Online version in color.)
After first stage cold rolling, all textures still exhibited strong α-fiber, together with faint γ-fiber possessing a dominant orientation of near {111}<110>, and their maximum components gradually rotated towards {112}<110>, {223}<110> and the corresponding intensity for most of textures increased as n decreased. After intermediate annealing, the prominent components for most of textures concentrated on γ-fiber, the corresponding peak intensity was near {111}<112> and increased with the decrease of n. Note that at higher n, feeble γ-fiber with a dominant orientation of near {111}<112> was found in intermediate annealing texture, while strong α-fiber was observed and the prominent components concentrated on α-fiber, which resembled the textures before intermediate annealing (such as at n=0.881, Figs. 3(c6) and 3(b6)), because distinct recovery (namely, recrystallization in situ) and weak grain growth tendency tended to occur during intermediate annealing. In addition to sharp α-fiber or γ-fiber, relatively very faint {110}<001> component also developed (Here, {110}<001> component was very weak compared to γ-fiber.), such as intermediate annealing texture in Fig. 3(c4), and it undergone a gradual strengthening followed by a gradual weakening as n decreased.
Second stage cold rolling texture featured pointed α-fiber or intense γ-fiber, and as n decreased, α-fiber gradually abated and γ-fiber gradually fortified. At lower n (n≤0.405, lower cold rolling reduction during this stage), prominent γ-fiber still existed and still exhibited the dominating orientation near {111}<112>. At higher n (n≥0.524, higher cold rolling reduction during this stage) faint γ-fiber having a dominating component at approximately {111}<110> was found, and intense α-fiber formed, owning dominating orientation near {223}<110>. The prominent γ-fiber appeared in final annealing texture, and as n decreased, the corresponding peak intensity decreased and the distribution consistency for intensity along γ-fiber gradually enhanced. Moreover, there were visibly lower distribution consistency for intensity along γ-fiber and higher intensity of recrystallized texture for final sheet under n≥0.524 than that under n≤0.405. In addition to prominent γ-fiber, relatively very weak {110}<001> component was also observed, such as the texture in Fig. 3(e4), and its intensity also exhibited a gradual increase and followed by a gradual reduce as n decreased.
During cold rolling, texture components for steel possessing bcc structure tended to rotate towards some more stable components (for instance, {223}<110>, {112}<110>, {111}<110>) along two following paths:27)
(1) {110}<001>→{554}<225>→{111}<112>→{111}<110>→{223}<110>
(2) {001}<110>→{112}<110>→{223}<110>
Increasing cold rolling reduction undoubtedly accelerated the above crystal rotation. As n decreased, cold rolling reduction during first stage gradually increased, while as n increased, cold rolling reduction during second stage gradually increased. Hence, in the presence of conspicuous α-fiber owning a dominant component at {001}<110> and faint γ-fiber having a dominating orientation of {111}<110> prior to first stage cold rolling, as n decreased, the dominant components in the texture after first stage cold rolling gradually shifted towards {112}<110> and {223}<110> and their intensity gradually increased, and the {111}<110> component consistently predominated in the weak cold rolling γ-fiber texture. Under the condition that the texture before second stage cold rolling was mainly made of γ-fiber and its intensity gradually reduced with increasing n, γ-fiber gradually abated and its main component transitioned from {111}<112> to {111}<110>, and α-fiber gradually reinforced and its dominating orientation transitioned to {223}<110> as n increased during second stage cold rolling (Figs. 3(d1)–3(d6)). At lower n, the texture still exhibited well-marked γ-fiber having dominating component near {111}<112>, while at higher n, sharp α-fiber with dominating orientation near {223}<110> was developed, along with faint γ-fiber having the main component at {111}<110>.
For figuring out the change of annealing texture, the microstructures after first stage cold rolling and during subsequent intermediate annealing under different n were researched using EBSD in this study, such as n=0.095, 0.214, 0.405, or even n=0 (traditional single cold rolling). These microstructures under different n possessed some similar features, and these similar features were expressed through first stage cold rolled microstructure and partially recrystallized microstructure under n=0.214, as shown in Figs. 4 and 5. During annealing, for recrystallized grains the growth rate was computed based on the literature.28)
Fig. 4. EBSD (a–d2) and TEM analyses (e) of microstructure after the first stage cold rolling under reduction distribution coefficient (n) of 0.214. (a) IPF maps for cold rolled microstructure; (b) IPF maps for crystallites; (c) Texture for crystallites; (d1) IPF maps for crystallite A in (a); (d2) Distribution map of {110}<001> and {111}<112> orientations in crystallite A in (a). (The scattered data pointed by the arrows in (c) represent the orientation near {111}<110>. The crystallites pointed by the arrows in (b) have orientation near {111}<110>.) (Online version in color.)
There were some crystallites along shear band in the deformed grain with γ-fiber orientations, even including brand-new grains, Figs. 4(a) and 4(b). The grain boundary between crystallite and its surrounding deformed matrix was completely composed of high angle grain boundaries (>15°, HAGBs) or partially composed of HAGBs. Its formation was because of sequential starting of multislip systems in the shear band formation zone during deformation (namely, shear band-induced crystallite).29) The γ-fiber orientations possessed higher Taylor factor compared with other orientations, so during deformation compared with other grains, a larger amount of slip occurred within the grains with γ-fiber orientations. Hence, the crystallite was primarily distributed in γ-fiber deformed grains. These crystallites displayed prominent {111}<112> and {110}<001> orientations (Fig. 4(c)) and relatively very faint {111}<110> orientation which corresponded to the scattered data pointed by the arrows in Fig. 4(c) and the crystallites pointed by the arrows in Fig. 4(b). This was because of the following reasons: (1) the prominent shear strain at the shear bands. Owing to this intense shear strain, the shear band-induced crystallites usually could display typical shear texture component ({110}<001>) in the initial stage of formation; (2) {110}<001> component rotating towards stable texture components (such as {111}<112>, {111}<110>) along path 1 stated above. After crystallite induction, the orientation of some crystallites began to become more stable {111}<112> orientation, even {111}<110> as cold rolling continued. This could be confirmed by the fact that orientations close to {111}<112> and near {110}<001> occasionally coexisted in one crystallite, such as crystallite A in Fig. 4(a) (Figs. 4(d1) and 4(d2)). The shear band-induced crystallite in this study was in agreement with the research results of the heterogeneity of cold-rolled structures in ferritic steel by Ushioda et al.30) and Nakanishi et al.31) They found that the fine grain structure formed within the shear bands in ferritic steel and some fine grain structures imbedded in the shear band displayed {110}<001> orientation.
Within crystallite induction area, there were numerous dislocations and dislocation tangles owing to the starting of multislip systems, which can be demonstrated by the fact that more dislocations were observed in the shear band formation zone than in its surrounding area, Fig. 4(e). This resulted in the high deformation stored energy and thereby promoted recrystallized nuclei development. On the other hand, the crystallite owned high misorientation with surrounding matrix, facilitating boundary migration and recrystallized nuclei development. Hence, in the initial phase of recrystallization, recrystallized nuclei development was prioritized through the crystallite. The texture of recrystallized grains possessed similar characteristics to that of crystallites (Figs. 4(c) and 5(b)), exhibiting prominent {111}<112> and {110}<001> and relatively very faint {111}<110> texture components.
As described above, the shear band-induced crystallites, preferentially developing into recrystallized grains, were mainly distributed in γ-fiber deformed grains. The main component of the γ-fiber deformed grains was {111}<110> or {111}<112> during cold rolling (Figs. 3(b1)–3(b6) and 3(d1)–3(d6)). E.g. their main component was {111}<110> during first stage cold rolling, Fig. 3(b2). Whereas, the recrystallized grain in the initial phase of recrystallization possessed prominent {111}<112> and {110}<001> components and relatively very faint {111}<110> components, Fig. 5(b). Considering that 30°<111> misorientation between {111}<112> and {111}<110>, the grain boundary having a special 30°<111> orientation relationship, which represented high migration rate during annealing, was easily formed between the γ-fiber recrystallized grain and deformed matrix. E.g. the ~30°<111> orientation relationship of recrystallized grains having ~{111}<112> with some surrounding matrixes was observed at initial stage of recrystallization (the area A in Fig. 5(a), Figs. 5(c1) and 5(c2)). Therefore, the recrystallized grain with γ-fiber orientations possessed greater grow tendency than that with {110}<001> orientation during recrystallization (Fig. 5(d)), promoting γ-fiber recrystallization texture development. Raabe et al.32) and Park et al.33) also suggested that the special orientation relationship between the cold rolling texture component and the orientation of recrystallized grains resulted in the development of recrystallization texture. Eventually, sharp γ-fiber recrystallization texture developed, accompanied by weak {110}<001> component after annealing. A model of crystallite-assisted recrystallization texture formation was presented to illustrate the experimental results above. For this proposed development model for recrystallization texture, the mechanism of shear band nucleation and its role in the recrystallization texture formation were elucidated, and the role of oriented grain growth was also illustrated during recrystallization texture formation in this study. Note that when a strong {111}<110> cold rolling texture existed, after subsequent annealing the experimental steel possessed sharp γ-fiber texture having a dominant orientation of near {111}<112> (such as, in Figs. 3(b2) and 3(c2)). In contrast, the presence of the cold rolling γ-fiber having dominant orientation of {111}<112> contributed to heightening grow tendency of {111}<110> recrystallized grain during subsequent annealing and finally enlarging intensity of {111}<110> component (such as, in Figs. 3(d2) and 3(e2)), as per the above recrystallization texture development model.
High cold rolling reduction promoted the shear band formation (Figs. 2(b1)–2(b6) and 2(d1)–2(d6)) and thus increased the number of shear band-induced crystallites (exhibiting strong {111}<112> component) in the deformed microstructure.29) Hence, high reduction contributed to raising recrystallized nuclei having {111}<112> orientation during annealing and thereby reinforcing γ-fiber texture. Moreover, large size deformed microstructure was developed at low cold rolling reduction. Its size was highly likely to be larger than the critical size achievable by γ-fiber recrystallized grain nuclei during annealing,34) so it was difficult to consume deformed grains around these large size grains through γ-fiber recrystallized grain growth. Subsequently, the probability of recrystallized grains with other orientations developed within these surrounding deformed grains heightened significantly during annealing, weakening the γ-fiber texture. Hence, the γ-fiber texture gradually reinforced and impaired with decreasing n after intermediate annealing and final annealing, respectively.
Besides the intensity, the distribution consistency for intensity along γ-fiber during two stage cold rolling was also correlated with n. As per the above recrystallization texture development model, the crystallite, primarily formed in γ-fiber deformed grains, preferentially became recrystallized nuclei during initial stage of recrystallization. These recrystallized nuclei had similar texture characteristics to these crystallites, featuring sharp {111}<112> and {110}<001> orientations, along with faint {111}<110> orientation. The recrystallized nuclei with different orientations demonstrated varying growth tendencies during the subsequent stage of recrystallization owing to the alteration in the primary component for deformed γ-fiber texture:
(1) In the first stage cold rolled sheet, {111}<110> orientation dominated the deformed γ-fiber texture, Figs. 3(b1)–3(b6). Consequently, strong {111}<112> recrystallized nuclei grew preferentially during subsequent intermediate annealing due to the 30°<111> orientation relationship between {111}<112> and {111}<110>. Ultimately, this resulted in a γ-fiber texture with a dominant orientation of approximately {111}<112>, Figs. 3(c1)–3(c6).
(2) After second stage cold rolling, major components transitioning from {111}<110> to {111}<112> for deformed γ-fiber texture were observed at decreasing n, Figs. 3(d1)–3(d6). At higher n (n≥0.524), the {111}<110> component dominated. A γ-fiber texture with a dominating orientation of approximately {111}<112> formed during subsequent final annealing, resulting in a higher recrystallization texture intensity and lower consistency for distribution of intensity along γ-fiber, Figs. 3(e4)–3(e6), considering the recrystallized nuclei exhibiting sharp {111}<112> and faint {111}<110> components. At lower n (n≤0.405), in contrast, the primary component of deformed γ-fiber was {111}<112>. As a result, weak {111}<110> recrystallized nuclei exhibited high growth tendency during final annealing. This, in turn, induced lower recrystallization texture intensity and enhanced the consistency for distribution of intensity along γ-fiber, Figs. 3(e1)–3(e3). Eventually, with decreasing n, the distribution consistency for intensity along γ-fiber enhanced, and there were visibly lower distribution consistency for intensity along γ-fiber and higher intensity of recrystallized texture under n≥0.524 than those under n≤0.405.
In addition, the crystallites induced by shear band usually exhibited strong {110}<001> component and their acquisition was undoubtedly enhanced through heightening cold rolling reduction. Thus, the amount of recrystallized grain nuclei with {110}<001> orientation increased during annealing with increasing cold rolling reduction, increasing the intensity of {110}<001> component in annealing texture, even though these grain nuclei possessed lower grow tendency during recrystallization, Fig. 5(d). However, as cold rolling reduction continued to increase, the rotation of some crystallites with {110}<001> towards some stable orientations began to occur, eventually resulting in a reduce in {110}<001> component after annealing. This demonstrated that higher and lower reductions can be adverse to the increase in intensity of {110}<001> component in annealing texture. Therefore, as n decreased, the {110}<001> component experienced a step-by-step rise in intensity followed by a step-by-step reduce after intermediate annealing (Figs. 3(b1)–3(b6)) and after final annealing (Figs. 3(e1)–3(e6)).
3.3. Grain Cluster Characteristics
According to the study on the relationship of ridging and texture for FSSs,35,36,37,38) grain clusters (along RD) exhibiting difference in deformation behavior was considered the main cause inducing ridging during drawing: (1) grain clusters with different strains in ND (namely, having different ε33) during deformation (this giving rise to different average r-value). During deformation, undoubtedly, numerous such grain clusters in the matrix led to a sequence of difference in strain along ND, finally generating step-like ridging, Fig. 6(a). (2) grain clusters exhibiting difference in shear strain during deformation (namely, having same orientation but corresponding variants having ε23 of different sign). This shear strain was exerted on cross section normal to RD. Undoubtedly, during deformation, in the matrix having numerous such grain clusters, a sequence of this difference in shear strain was formed, developing wavy-like ridging, Fig. 6(b) (TD: Transverse Direction). The change in the characteristics of grain cluster brought about ridging change. The change in grain cluster with n should first be analyzed for studying the variation of ridging under different n.
Fig. 6. Schematic diagram illustrating the occurrence of ridging. (Online version in color.)
The change of grain clusters in the final annealed sheet with n was analyzed using EBSD, as revealed in Fig. 7. From Fig. 7, the fractions of LAGBs (low angle grain boundaries, <15°) were 12.8% and 16.7% at n=0.095 and n=0.405, respectively, while the fractions of LAGBs were 35.6% at n=0.762, 32% and n=0.881, respectively. The formation of a prominent oriented grain clusters was usually accompanied by a large proportion of LAGBs, while a small proportion was observed in the microstructure exhibiting random orientation.18) This indicated that the characteristic of grain cluster changed with increasing n.
Fig. 7. EBSD observation for microstructures in final sheets under different reduction distribution coefficients (n). (a1), (b1), (c1) n=0.095; (a2), (b2), (c2) n=0.405; (a3), (b3), (c3) n=0.524; (a4), (b4), (c4) n=0.762; (a5), (b5), (c5) n=0.881. (Online version in color.)
In regard to grain cluster with different strains along the ND (i.e., difference in ε33), to investigate its change with n, typical orientations possessing high r-value ({111}<110>, {111}<112>) and low r-value ({001}<110>, {001}<140>, {225}<110>, {225}<492>) were chosen based on final annealing texture (Figs. 3(e1)–3(e6)). In this study, except {111}<110> and {111}<112> orientations, {001}<110>, {001}<140>, {225}<110>, {225}<492> orientations were also observed in the final annealing texture (Figs. 3(e1)–3(e6)). Among these typical orientations mentioned above, the r-value of {001}<110> and {001}<140> orientations were similar and lowest, the {225}<492> and {225}<110> orientations exhibited approximate r-value and relatively higher r-value, and the {111}<110> and {111}<112> orientations possessed higher r-value than the above typical orientations according to the calculation of r-value by relaxed constraint models.39,40) Moreover, Huh et al.12) suggested that very low r-value was received for the {001}<110> orientation, the α-fiber orientations deviating less than 40° from {001}<110> displayed low r-values (<1), and the γ-fiber orientations possessed the very high r-value, which was obtained through the calculation based on minimum deformation work principle. Chung et al.41) and Kodukula et al.42) calculated r-value by using simplified roping model simulation and considering 24 slip systems, respectively, and both obtained r-value contours for orientations in the φ2=45° section of the ODF. According to the calculation results of Chung et al.41) and Kodukula et al.,42) {001}<110>, {001}<140>, {225}<110>, {225}<492> orientations possessed much lower r-value (<1) than {111}<110> and {111}<112> orientations. Although the calculation methods of r-value mentioned above were different, similar results were obtained, that is, {001}<110>, {001}<140>, {225}<110>, and {225}<492> orientations had low r-value and high r-value was obtained for {111}<110> and {111}<112> orientations. Eventually, in the final annealing texture, {001}<110>, {001}<140>, {225}<110>, and {225}<492> typical orientations were selected as the orientations possessing low r-value, while typical orientations possessing high r-value were {111}<110> and {111}<112> orientations. The distribution of these typical orientations in the microstructure was exhibited in Figs. 7(b1)–7(b5). When n≤0.405, the uniformity of distribution for grain having alike r-value increased gradually with the increase of n, but when n>0.405, the change was opposite to the above. Moreover, to quantitatively express the distribution of grain having alike r-value, along TD each map gained using EBSD in the Fig. 7 was divided into 90 sections. The content of grains with similar r-value in each section can be obtained using AZtecCrystal software, and the change in this content along TD was showed in Fig. 8. The difference between the highest and lowest contents of grain with similar r-value along TD was employed for illustrating the fluctuation, Fig. 8(f). Clearly, the fluctuation displayed a gradual decrease followed by a gradual increase then as n increased.
Fig. 8. Distribution of volume fraction (a–e) for orientation having high and low r-value components under different reduction distribution coefficients (n) and the relationship between the fluctuation of content of grains with similar r-value along TD and reduction distribution coefficient (f). (a) n=0.095; (b) n=0.405; (c) n=0.524; (d) n=0.762; (e) n=0.881. (Online version in color.)
In regard to grain cluster with same orientation but variants having difference in ε23 signs (±ε23), to investigate its change with n, the {225}<492> and {111}<112> typical orientations were selected. This was because after deformation the variants with different sign of ε23 of {225}<492> and {111}<112> typical orientations displayed different spatial morphologies, and this different spatial morphologies were symmetrical with respect to the longitudinal section, contributing to developing wavy-like ridging (Fig. 6(b)), while after deformation the variants with different sign of ε23 of other typical orientations (such as {001}<110>, {001}<140>) displayed alike spatial morphology.40) The distribution of variants with different sign of ε23 for the {225}<492> and {111}<112> typical orientations was displayed in Figs. 7(c1)–7(c5). Clearly, as n increased, the distribution of the grain with same orientation and the corresponding variant having same sign of ε23 experienced a gradual uniform distribution followed by a gradual inhomogeneous distribution.
For analyzing significant change of grain cluster distribution with n, the initial experimental steel was cold rolled with diverse reductions using traditional approach and annealed, and corresponding microstructures were detected using EBSD and grain clusters in these microstructures were analyzed by the method using in Fig. 7 (Fig. 9). Clearly, with increasing reduction during traditional cold rolling, uniformity of distribution for grain having alike r-value and that for grain owning identical orientation and corresponding variant with identical sign in ε23 initially improved and then worsened. Moderate reduction during single cold rolling was conducive to improving the distribution uniformity of oriented grain.
Fig. 9. EBSD analyses of microstructures under different single cold rolling reductions. (a1), (b1), (c1) 76%, (a2), (b2), (c2) 50%, (a3), (b3), (c3) 40%, (a4), (b4), (c4) 20%, (a5), (b5), (c5) 10%. (Online version in color.)
In this study, many larger elongated grains were found in initial experimental steel. During cold rolling, there was a very distinct possibility of the transformation of elongated grain into extremely elongated band having approximated orientation, and this band was highly likely to lead to the formation of grain cluster having approximated orientation through recrystallization during subsequent annealing and the decrease of the distribution uniformity of oriented grains. When cold rolling reduction was lower, it was difficult to obtain effective fragmentation of larger elongated grains. Moreover, during subsequent annealing the deformed grains tended to occur recovery due to lower cold rolling reduction and deformation storage energy,43,44) promoting the formation of grains with similar orientation in some local regions. When cold rolling reduction was higher, the nucleation and growth of some typical orientations (such as {111}<112>) were facilitated in some local regions that contained a large number of shear bands during subsequent annealing. That is to say, in some local regions, the volume fraction of some typical orientations significantly increased. Meanwhile, this meant a decrease in fraction of other typical orientations (such as {001}<110>) in these local regions and a relative increase in surrounding regions. Therefore, in the present work, during conventional single cold rolling, higher or lower reduction accelerated the inhomogeneous distribution for grain with similar orientations (including grain having approximated r-value and grain with identical orientation and its variant having same sign of ε23).
During two stage cold rolling with different n, the change in distribution uniformity of oriented grains can be explained by this change during single cold rolling with different reduction. As n decreased, cold rolling reduction for first stage raised, so after intermediate annealing distribution uniformity for oriented grains displayed a step-by-step rise followed by a step-by-step reduce as n increased, that is, lower distribution uniformity was displayed at lower and higher n. This trend would be inherited into the final sheet. Furthermore, as n decreased, cold rolling reduction for second stage decreased, so distribution uniformity for oriented grains after final annealing after second stage cold rolling further lowered under higher and lower n. Finally, the distribution uniformity for grains possessing approximated r-value and that for grain with identical orientation and its variant having same sign of ε23 displayed a step-by-step rise followed by a step-by-step reduce as n increased.
3.4. Ridging and Formability
The variation trend of formability for final sheet with n increased was revealed in Fig. 10. As n increased, the r-value displayed a step-by-step rise followed by a step-by-step reduce and as n was 0.762, r-value reached maximum, but its change was unobvious.
Fig. 10. Effect of reduction distribution coefficient (n) on formability. (Online version in color.)
The r-value corresponded strongly to recrystallization texture characteristics. Enhancing the intensity, heightening the distribution consistency for intensity along γ-fiber and weakening the texture gradient along ND were conducive to raise r-value.44,45) As n increased, the intensity of recrystallized texture in the final sheet increased, Figs. 3(e1)–3(e6). However, the r-value was not monotonically increasing with the increase of n for experimental steel. The r-value exhibited a step-by-step rise followed by a step-by-step reduce, and as n was 0.762, r-value reached maximum. This could be attributed to the obvious difference in texture gradient between the final sheet with n=0.762 and n=0.881. For delving deeper into the correlation of r-value with n, the surface layer textures were detected for the final sheet with n=0.762 (highest r-value) and 0.881 (lower r-value), as shown in Fig. 11. Obviously, the final sheet with n=0.881 exhibited a significant texture gradient compared to that with n=0.762 according to Figs. 3(e5) and 3(e6) and 11. Moreover, the combined effect of changes in the intensity and the texture gradient along ND leads to relatively small difference in r-value between n=0.762 and n=0.881. In addition, the corresponding difference in r-value was also relatively small or unobvious despite of the increase of intensity with n at n≤0.762. This could be explained by the decrease of distribution consistency for intensity along γ-fiber with increasing n. For example, although there was a significantly higher intensity of recrystallized texture for final sheet under n≥0.524 than that under n≤0.405, the final sheets under n≤0.405 possessed higher distribution consistency for intensity along γ-fiber compared with those under n≥0.524 (Figs. 3(e1)–3(e6)).
Fig. 11. Textures in the surface layer of final sheets with reduction distribution coefficient of 0.762 (a) and 0.881 (b). (Online version in color.)
In addition, the r-value of typical orientation changed with the change of angle between tensile direction and RD, and different orientations displayed different variation tendencies. As n changed, the final sheets exhibited different textures and thus contained different fractions of typical orientations. Hence, as n changed, the r-value in direction at a different angle to RD for final sheet displayed different variation tendencies, Fig. 10(a). In order to illustrate this change, further work needs to be implemented for systematically investigating the relationship of deformation behavior of orientation with deformation direction and the contribution of orientation to the r-value.
As n increased, the Δr-value displayed a step-by-step rise followed by a step-by-step reduce, Fig. 10(b), which can be explained as follows. Based on the anisotropy prediction model,39,40) the Δr-value of {111}<112> and {110}<001> typical orientations were the lowest and very close to 0, the {225}<492>, {225}<110>, {001}<140>, and {001}<110> typical orientations exhibited relatively high anisotropy and the {110}<001> orientation possessed higher anisotropy than the above typical orientations. Moreover, according to the study on texture development in Section 3.2, as n increased, the intensity of {110}<001> orientation exhibited a step-by-step rise followed by a step-by-step reduce.
The surface morphologies after 15% tensile deformation of final sheets with different n were displayed in Fig. 12. Obviously, the ridging resistance was compactly connected with n during two stage cold rolling. After 15% deformation, the surface of final sheets was relatively rough at lower and higher n, while that was relatively smooth at moderate n. Figure 13 exhibited roughness curves and average ridging heights at different n. As n increased, the fluctuation in roughness curve experienced a gradual decrease followed by a gradual increase, and the variation of average ridging height with n also showed the same trend and lowest average ridging height was observed at n=0.405.
Fig. 12. Macroscopic morphologies under different reduction distribution coefficients (n). (a) n=0.095, (b) n=0.214, (c) n=0.405, (d) n=0.524, (e) n=0.762, (f) n=0.881. (Online version in color.)
Fig. 13. Roughness curves (a–f) under different reduction distribution coefficients (n) and the relationship between average ridging height and n (g). (a) n=0.095, (b) n=0.214, (c) n=0.405, (d) n=0.524, (e) n=0.762, (f) n=0.881.
The ridging for FSSs was closely related with the grain clusters possessing difference in deformation behavior (Fig. 6). Based on the above research, as n increased, the grain having approximated r-value and the grain with identical orientation and corresponding variant having identical sign in ε23 exhibited a gradual uniform distribution followed by a gradual inhomogeneous distribution. The uniform distribution of oriented grains was conducive to improving deformation uniformity of experimental steels through weakening the deformation difference in different regions and strengthening the compensation obtained from the surrounding regions, relieving the ridging. Thus, the ridging resistance displayed a step-by-step rise followed by a step-by-step reduce with the increase of n. According to the above study, the final sheet possessed lowest average ridging height and highest ridging resistance at n=0.405. Moreover, at n≤0.762, the r-value increased with n, but this change was unobvious. This is to say, at moderate n (such as n=0.405), the final sheet still exhibited excellent r-value. Thus, the n of 0.405 contributed to the implementation of optimal performance.
