Strain path dependence of microstructure and annealing behavior in high purity tantalum

Author’s Accepted Manuscript Strain path dependence of microstructure and annealing behavior in high purity tantalum Y.H. Liu, S.F. Liu, J.L. Zhu, C. Deng, H.Y. Fan, L.F. Cao, Q. Liu www.elsevier.com/locate/msea

PII: DOI: Reference:

S0921-5093(17)31265-0 http://dx.doi.org/10.1016/j.msea.2017.09.097 MSA35564

To appear in: Materials Science & Engineering A Received date: 11 June 2017 Revised date: 29 August 2017 Accepted date: 20 September 2017 Cite this article as: Y.H. Liu, S.F. Liu, J.L. Zhu, C. Deng, H.Y. Fan, L.F. Cao and Q. Liu, Strain path dependence of microstructure and annealing behavior in high purity tantalum, Materials Science & Engineering A, http://dx.doi.org/10.1016/j.msea.2017.09.097 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Strain path dependence of microstructure and annealing behavior in high purity tantalum Y.H. Liua, S.F. Liua,*, J.L. Zhua, C. Denga, H.Y. Fanb, L.F. Caoa, Q. Liua a

College of Materials Science and Engineering, Chongqing University, No. 174 Shazheng Street, Shapingba District, Chongqing

400044, China b

Department of Materials Engineering (MTM), KU Leuven, Kasteelpark Arenberg 44, Box 2450, B-3001, Heverlee, Belgium

Abstract Unidirectional rolled (UR) and clock rolled (CR) high purity tantalum sheets were analyzed with an emphasis on the microstructural difference in surface layers. Misorientation characteristics of deformed grains with different orientations are analyzed in detail by visualizing the misorientation angle based on an electron backscatter diffraction dataset. {100}(<100>// normal direction (ND)) grains were found to associate with long-range cumulative orientation changes in CR sample while {111} (<111>// ND) grains were found to contain many micro-shear bands and microbands in UR sample. Then, micro-shear bands and micro-bands were detailedly characterized by transmission electron microscope, and the analysis based on Schmid factor suggested that the primary slip system activated in {111} grains leads to the formation of micro-bands during UR process. Band contrast values were used to evaluate the energy stored in {100} and {111} grains and results showed that the gap of energy between them was narrowed by CR process. Additionally, significant dispersion degree of hardness values indicates the inhomogeneous deformation in UR sample, while different degree in annealed stage indicates the different recrystallization kinetic for UR and CR samples. Upon annealing, nucleation prefers to occur along {111} deformed matrices or {111}-{100} boundaries in UR sample and recrystallization grains are large in size. While nucleation tend to take place in intersected regions in CR sample and recrystallization grains are small, which contributes to the appearance of fine grains in fully recrystallized CR sample.

Keywords: clock rolling;

strain path;

micro-band;

nucleation;

recrystallization

1. Introduction Rolling is a common deformation technique in sheet manufacturing [1, 2]. During rolling, the downward pressure and the forward fraction would create a resultant force in the sheet, which is termed as shear force. The shear force, especially meeting with the large rolling reduction, would lead to the formation of special microstructure and texture, such as ultrafine grains, shear banding or through-thickness texture when happened to meet materials with high stacking fault energy [3-5]. During rolling, 1 / 21 *

Corresponding author. Tel.: +86 23 65106024; fax: +86 23 65106407.

Email address: [email protected] (S.F. Liu)

gradients of shear force in the process zone result in gradients of structure and properties, and the surface layer of the sheet is subjected to the intense stress field and responsible for passing it to the center layer [6]. Although the above phenomenon caused by shear force would significantly affect the microstructure and texture of the surface layer, few studies have focused on the detailed characterization to investigate the effects. The change of strain path, which are usually encountered during manufacturing, has significant influence on grain size, texture, annealing behavior, and even the mechanical properties of a material [7]. For this reason, a clock rolling (CR) in which the sample is rotated by 135o around the normal direction between consecutive passes is presented below. Further, large rolling reduction results in more serious subdivision of grains and the division behavior depends heavily on the orientations of grains [8-10]. But, what the microstructure of grains with different orientations (e.g., {111} and {100} orientations) would be if they encounter the change of strain path? Therefore, characterization of the surface layer is essential to overcome the current lack of scientific knowledge regarding the deformation behavior. The investigated metal is tantalum (Ta) in this work. Ta has been widely used in varied fields including microelectronics, biomedicine, and high-temperature structural materials due to its outstanding ductility, high hardness and remarkable corrosion resistance [11].The aim of the current work is to develop a basic understanding of the role of strain path in the microstructural evolution in the surface layer of the sample upon rolling and subsequent annealing process.

2. Experimental method A high purity Ta was divided into two groups to be rolled in unidirectional rolling (UR) and CR with a reduction of 87% (16 passes in total), and rolling schedules are shown in Fig. 1. Details about chemical components and the microstructure of the original sample are given in Ref. [12, 19]. Samples (10L×8W×3T mm3) were cut from as-rolled Ta plates. Subsequent annealing treatments were executed under an inert atmosphere at 1050 oC for 7 min, 60min, 120 min and 150 min, respectively.

Fig. 1. Schematic diagrams of the unidirectional and 135o clock rolling employed in this study. The sample was 2 / 21

rolled without changing its rolling directions in UR rolling while the sample was counterclockwise rotated by 135o around ND direction between consecutive passes in CR rolling.

X-ray diffraction (XRD) technique was applied to investigate the macroscopic texture near the surface layer as described in Fig. 2, where δt1/δ0=0.9 (δt: the distance from testing layer to the central layer, δ0: half of the thickness of the sample). Four pole figures (110), (200), (211) and (222) were measured to a maximum tilt angle of 70o. The Arbitrarily Defined Cells (ADC) method was used to calculate orientation distribution functions (ODFs). Electron backscatter diffraction (EBSD) technique was applied to characterize the microstructure in the zone of the surface layer to the adjacent layer (δt2/δ0=0.95 to 0.85) of the samples in the normal direction (ND). EBSD measurements were conducted at an accelerating voltage of 20 kV using a JEOL JSM-7800F scanning electron microscope. For EBSD analysis, specimens were prepared by fine mechanical polishing followed by electro-polishing using a mixture of hydrofluoric acid and sulphuric acid (1:9 by volume) at ambient temperature. The TEM observation was conducted with a JEOL JEM-2100 transmission electron microscope. The operated accelerating voltage is 200 kV. The specimens were jet polished in a mixture of HF, H2SO4 and CH3OH (1:5:94) at 0 oC. Vickers harness (HV) of as-rolled and annealed plates were measured by an MH-5L model hardness tester with a load of 300g and dwell time of 10 s, 15 measurements were made for each condition in the normal direction (δt/δ0=0.9).

Fig. 2. Testing positions for XRD, EBSD, TEM and Vickers hardness measurements in a sample, where δt is the distance from testing layer to the central layer and δ0 is half of the thickness of the sample.

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3. Results 3.1. Deformed microstructure Fig. 3a is the merged map of orientation imaging map (OIM) and the grain boundary map for UR sample. UR deformation results in a straight ribbon-like microstructure consisting of highly elongated original grains along the rolling direction (RD). {111}(<111>//ND) grains exhibit pronounced micro shear bands (MSBs) in zone indicating by yellow oblique arrows. The grain boundaries, including the high-angle grain boundaries (HAGBs) (>10o) and the low-angle grain boundaries (LAGBs) (2-10o), distributed more locally and more densely in {111} oriented grains than that in {100}(<001>//ND) oriented grains. Fig. 3b and 3c show the misorientation angle distribution along the line ‘L1’ and ‘L2’, respectively. The red line is the ‘point to point’ (PTP) misorientation which reveals the orientation difference between neighboring points. The blue line represents the ‘point to origin’ (PTO) misorientation which indicates the orientation difference referred to the origin. Many sharp peaks in the PTP plot (Fig. 3b) indicate the existence of well-defined band boundaries [1, 13] in {111} deformed matrices. Especially, peaks with higher angle, ranging from 30o to 50o, were classified as MSBs in this study, while the others were termed as micro-bands (MBs) in a mathematics way. The boundaries of these bands are straight and sharp, which can be illustrated by the abrupt change in PTP misorientation along the line [14]. While peaks of PTP profile are in general lower than 2o and few peaks appeared in the PTO plot in grain with {100} orientation. Instead, orientation gradients occurred in this grain, as illustrated by the gentle arch in PTO plot (Fig. 3c) [14, 15]. As shown in Fig. 4a, MBs are more or less parallel to each other and appear as regions about 10o inclined to RD direction. These bands are bounded by straight and sharp dislocation walls and about 0.1-0.3 µm in width. At this point, the dislocations, appeared as long and aligned dislocation walls, is strongly heterogeneous distributed in {111} grains. MSBs, do not arrange regular as MBs, appear as narrow regions about 20-27o inclined to RD direction and about 30-37o to the direction of MBs. Fig. 4c and 4d are TEM observations of {100} grains. MB or MSB are not found in these regions. Instead, dislocations are densely distributed in these regions.

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Fig. 3. (a) Merged map of orientation imaging map (OIM) and grain boundary map for UR sample after 87% reduction. LAGB: low angle grain boundary (2-10o); HAGB: high angle grain boundary (>10o). (b) and (c) show the lines corresponding to ‘L1’ and ‘L2’ in the merged map. The yellow box reveals the detailed scan in Fig. 12.

Fig. 4. TEM observations for UR sample. (a) and (b) in {111} grains, while (c) and (d) in {100} grains.

In CR sample, the original grains showed a certain degree of bending and fluctuation along the RD direction. In contrast to the straight grain boundaries in UR sample, some grain boundaries in CR sample split, then grains on both sides came to 5 / 21

infiltrate and intertwine with each other. The region consisting of these intersected boundaries is defined as ‘intersected region’ (IR), as marked in Fig. 5a. Additionally, the distribution of boundaries is more uniform when compared with that in UR sample. Few peaks occurred in PTP plot in Fig. 5b. Instead, orientation gradients appeared in {111} oriented grains. In particular, smooth misorientation plot indicates the strong orientation gradients evolved in {100} oriented grains. As shown in Fig. 6a, regularly arranged MBs are scarcely founded in CR sample. Instead, the change of slip systems leads to subdivision and rotation of established blocks, which are bounded by dislocation walls. These walls are about 0-30o inclined to RD direction, namely, are unregularly distributed in {111} grains. More accurately, we can find many blocks with a great diversity of shapes existing in a {111} grain (Fig. 6b). While in {100} grains, similar to that of {100} grains in UR sample, dislocations with various morphology exist in these grains. Some dislocations walls are found and marked by dotted lines.

Fig. 5. (a) Merged map of OIM and grain boundary map for CR sample after 87% reduction. (b) and (c) show the lines corresponding to ‘L3’ and ‘L4’ in the merged map, respectively. The yellow box reveals the detailed scan in Fig. 13.

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Fig. 6. TEM observations for CR sample. (a) and (b) in {111} grains, while (c) and (d) in {100} grains.

3.2. Vicker hardness Vickers hardness measurement is an effective method to investigate the mechanical properties, even the degree of recrystallization, of a metal [16, 17]. In Fig. 7, the scattering points act as the hardness values from the test, and the mean value points in different annealing conditions are linked into a polyline. Apparently, large dispersion degree relative to the mean hardness value appeared in deformed UR sample, whereas the degree is quite slight in CR sample. Even so, the mean value for deformed UR sample is a little higher than that of CR sample. To disclose the relationship between the microhardness value and the microstructure more accurately, OIMs for all microhardness testing points of deformed samples were characterized by EBSD and some maps of interesting points were stacked in Fig. 8. For UR sample, the microhardness value for {111} grain is higher than that of {100} grain, and the great gap between them reaches 45.1 HV. As known to all, the more dislocations the region contains, the higher the hardness value is in this region. The large dispersion degree reveals the deformation at different level existing in {111} and {100} grains. Also, we can confirm this point according to the plenty of MBs formed in {111} grains (Fig. 4a). Raabe’s review reported that the {111}-oriented grains prefer to accommodate highly localized deformation due to the constraint imposed by the neighboring grains in body-centered cubic steel [18]. While in CR sample, the 7 / 21

annihilation of dislocations reduced the density of the dislocation, and a more homogeneous distribution of dislocations formed. Thereby the dispersion degree for CR sample is less than that for UR sample in deformation stage. After annealing for 7 min, {111} oriented grains in UR sample are consumed by the growing nuclei while the {100} grains are not obviously recrystallized yet, which causes the large dispersion degree for UR sample in the nucleation stage. In fact, {100} grains would be consumed by the nuclei formed in {111} grain or boundaries at last. It is obvious that recrystallization is faster for UR sample than that for CR sample. The hardness values decrease successively with the annealing time for both UR and CR samples. After 150 min, both UR and CR samples are almost completely recrystallized and the mean values for them tend towards an equalization. The dispersion degree for UR sample remarkably reduced in this stage as well as the CR sample.

Fig. 7. Hardness value of UR and CR samples for different annealing conditions.

Fig. 8. OIMs of vicker microhardness test points for UR and CR samples. 8 / 21

3.3. Texture The texture in the surface layer of the UR and CR samples mainly comprised typical deformation orientations of body-centered-cubic (BCC) metals and alloys. In such textures, most orientations are assembled along the γ-fiber, which runs through the Euler space from (0o, 54.7o, 45o) to (90o, 54.7o, 45o), and the θ-fiber, which are distributed at (φ1, 0o, 45o) in the Euler space. All the orientations along these two fibers can be revealed in the φ2 = 45o section in the Euler space. Rest grains which cannot be identified within them were classified as the ‘random’. Close to the surface, a strong θ-fiber texture was found in CR sample while the UR sample revealed weak texture. γ-fiber occupies about 16.57 pct in UR sample while 6.1 pct in CR sample, and the θ-fiber account for about 13.51 pct and 34.45 pct in UR and CR samples, respectively.

Fig. 9. Texture and volume fraction of samples after UR and CR processes, respectively. (a) texture of UR sample; (b) texture of CR sample; (c) volume fraction of texture for samples.

It is important to note that the original microstructure of Ta sheet used in this work was not uniform but revealed strong θ-fiber texture in the surface layer [19]. During UR rolling, grains subjected more seriously split and rotation compared with that of grains in CR sample. The fragments rotated to other orientations from pass to pass, thus the fraction of random orientations accounts a large portion in UR sample. As to CR sample, the change of strain path weakens the cumulative shear force, weakening the split of original grains to a certain extent. Especially, θ-fiber texture mainly retains to the as-rolled sample due to the decrease of stress concentration during the CR process. Similar result had been reported by Abhishck, in which the θ-fiber is stable during cross-rolling [20]. In addition, the texture distributed on the surface may affect the dispersion degree of hardness values. As demonstrated above, the hardness value is higher for {111} grain than that for {100} grain in both UR and CR samples, even though the gap was narrowed by CR process. Thus, large amount of θ-fiber texture in CR sample does a favor for the small dispersion degree of hardness values in it. 9 / 21

3.4. Annealed microstructure Fig. 10 shows the microstructure after annealing at 1050 oC for 7 min. Nucleation prefers to occur along {111} deformed matrices or {111}-{100} boundaries. Most of recrystallization grains are elongated along RD direction in UR sample. Recrystallization grains are mainly observed in triple junctions or IRs in CR sample, and these grains are small in size. It is clear that CR sample shows a less recrystallized fraction than that of UR sample, and the recrystallization is faster for UR sample than that for CR sample, which is in a good agreement with that of microhardness measurement. Furthermore, many sub-grains formed in both UR and CR samples. To be more specific, sub-grains are mostly presented in {111} grains in UR sample or IRs in CR sample. Over annealing time, both UR and CR samples are almost completely recrystallized (Fig. 11). Average grain size is 30.1 µm in UR sample and 22.9 µm in CR sample.

Fig. 10. OIMs and grain boundary maps for UR and CR samples after annealing at 1050 oC for 7 min: (a) OIM and (b) grain boundary map for UR sample; (c) OIM and (d) grain boundary map for CR sample. (b) and (d) show the microstructure in detail corresponding to ‘A3’ and ‘B3’ in (a) and (c) maps, respectively.

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Fig. 11. OIMs for UR and CR samples after annealing at 1050 oC for 150 min: (a) UR sample. (b) CR sample.

4. Discussion 4.1. The formation of various substructures The results demonstrate the difference of microstructure in surface layers of samples with different rolling paths. To the author’s knowledge, such a study has not been carried out in the past. The microstructure is characterized with an emphasis on the difference of misorientation distribution to investigate the response of grains to the applied stress. Nucleation and recrystallization behavior are summarized and classified as a function of strain path. In this study, the UR sample has been accumulatively rolled for 16 passes with a total thickness reduction of 87%. Repeatedly applying stress with the same direction leads to a strong cumulative shear strain among the surface layer. The strain would activate slip systems during deformation, and different combinations of slip systems give rise to the splitting of the original grain into separate blocks [21]. Among all the active slip systems, the one more active than others would lead to a region appears more like a spatially isolated single-slip domain. This slip system can be considered as the primary slip system [4, 14]. These primary slip system, which means a large shear localized on one slip plane upon rolling, make a contribution to the formation of MBs in {111} grains [22]. MBs result from the deformation introduced by intense glide on just one slip plane within a grain during the rolling processes and the evolution of them depends on the second strain path in the further deformation [22]. The glide on the only one slip plane lead to the formation of straight boundaries from the intricate arrangement of the dislocations, and the parallel boundaries would take place when a region experienced the primary slip system. The detailed analysis on slip systems activated for different oriented grains in UR and CR samples is in the following part. Upon large strain, the aligned MBs are often intersected by thin shear bands within the grains, which have been termed as MSBs [21, 22]. MSBs can accumulate large shear strains during deformation and leads to a concentration of stress in local regions. 11 / 21

The slip activated in {111} results in the splitting of grains accompanying with the formation of various kinds of mobile dislocations. These dislocations will pile up along the grain boundary when they encounter the boundary, which results in a local stress field along the boundary. The larger the misorientation, the more difficult dislocations can penetrate through the boundaries, which result in stress concentration in certain regions along the boundaries. These concentrations then would lead to the split of {100} grains, as illustrated in PTP plot (Fig. 3c). Due to the limitation of the view of TEM, the supposed bands may be missed during the characterization, in turn the peaks in PTP plot for {100} grain may be regard as the occurrence of MBs. It should be mentioned that these peaks cannot be termed as MBs because of the following two reasons. One is the lower height of peaks in PTP plot compared with that in {111} grain, and the peaks are not abrupt as in PTP plot in {111}. The abrupt changes indicate that the boundaries of MBs are straight and sharp. The other reason is that there are obvious orientation gradients on both sides of the peaks in PTO plot in {100}. The MBs are substructures with narrow sheets shape (0.1-0.3 µm in width) which cannot cause such obvious orientation gradients [1, 23]. Thus the peaks in PTP plot only mean the splits in certain regions of {100} grains but not the MBs structures, as shown in Fig. 4c and 4d. In Fig. 12b, we could find more MSBs existing in a {111} grain, as prioritized by yellow arrows. Further, we cited kernel average misorientation (KAM) and grain reference orientation deviation – hyper (GROD-Hyper) to explain the deformation behavior in differently oriented grains. In which, KAM is the average misorientation between a point on the measurement grid and its neighbors, and the closer to red the color be, the higher the local misorientation becomes. While GROD-Hyper represents the deviation between the point and the average misorientation of a grain, and the closer to the color in circumference of the circle the color be, the higher the deviation becomes. Fig. 12c showed the extremely uneven deformation in UR sample, {111} grain composed of large amount of dislocations while {100} grain seemed to be very ‘clean’. While in CR sample, as shown in Fig. 13c, the dislocations dispersed more uniform after rolling. For GROD-Hyper, the color close to brown in {111} grain while the color close to green in {100} grain, which means that the dispersion is larger in {100} grains, which is in a good agreement with the occurrence of orientation gradient in {100} grain in UR sample. For CR sample, more colorful substructures appeared in Fig. 13d, which means that orientation gradients occurred in both {111} and {100} grains.

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Fig. 12. OIM, grain boundary map, kernel average misorientation (KAM) and grain reference orientation deviation – hyper (GROD-Hyper) for UR sample. (a) reveals region ‘A1’ in Fig. 3a. (b), (c) and (d) reveal region ‘A2’ in Fig. 12a. Step size 0.3 μm for (a) while 0.15 μm for (b).

For CR sample, as strain path changed by 135o, the component of the strain parallel to the last strain path would active different slip systems, which may lead to the rearrangement and annihilation of dislocations in the deformed matrices. Multiple slip systems can be active to accommodate grain deformation during the change of strain path, which would perturb the morphology of sub-structure developed during the preceding process. Thus, the MBs are scarcely formed due to the multiple slip and homogeneous deformation. Instead, slip systems lead to subdivision and rotation of established blocks [24] , and sequential change of strain paths from pass to pass alters the orientations of the blocks continuously, which results in the orientation gradients in both {111} and {100} grains. Even so, the subdivision is more serious in {111} grain than that in {100} grain. When compared with that of UR, the change of strain path leads to more homogeneous deformation in CR sample, and the strain concentration is seldom occurred. Namely, the split of {100} grains is less frequently observed in CR sample. Thus, strong orientation gradients take place upon long-range orientation testing along a line. It must be kept in mind, however, that the original microstructures, the number rolling passes (16 passes in total) or the rolling reductions (87%) are the same for both UR and CR samples. The strain paths is the main factor impacting the microstructures, more specifically, the grain orientations, e.g., {111} and {100}, is a factor controlling the interior microstructures for these grains themselves.

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Fig. 13. OIM, grain boundary map, KAM and GROD-Hyper for CR sample. (a) reveals region ‘B1’ in Fig. 5a. (b), (c) and (d) reveal region ‘B2’ in Fig. 13a. Step size 0.3 μm for (a) while 0.15 μm for (b), (c) and (d).

4.2. Analysis based on slip systems MBs result from the deformation introduced by intense glide on just one slip within the {111} grain in UR sample, while strong orientation gradients in {100} grain arise from the activation of multiple slip systems upon CR process. To investigate this point more detailed, we selected 62 points randomly (248 points in total) along each line, L5, L6, L7, L8, as drown in {111} and {100} grains in Fig. 12 and Fig. 13, respectively. Then the Schmid factors of each slip system for them were computed based on the following equation [25]: SFrolling = 0.5×(cosφRD×cosλRD – cosφND×cosλND) In which φ(RD,ND) and λ(RD,ND) are the angles between the slip plane normal and the slip direction and the rolling and normal directions. To elucidate how a slip is chosen to be the primary slip systems, the Euler angles (φ1,Φ,φ2)，the maximum (SM) and secondary (SS) Schmid factor, the Schmid factor difference ratio (SFDR) between SM and SS, (SM-SS)×SM-1, of the 248 points were computed and some of them were listed in Table 1.

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Table 1. Euler angles, the maximum and secondary Schmid factors and the Schmid factor difference ratio of some points.

Type

Point

Eulars(φ1,Φ,φ2)

Maximum

Secondary

(SM-SS)×SM-1

(SM)

(SS)

（%）

{111}

P1

(340.2,36.9,72.7)

0.4788

0.4202

12.24

(UR)

P2

(346.6,35,62.9)

0.4701

0.4208

10.49

P3

(348.1,33.3,62.4)

0.473

0.4256

10.02

P4

(353.6,31.9,57.6)

0.4659

0.4232

9.17

P5

(346.7,39.5,75.5)

0.4821

0.4568

5.25

{100}

P1

(76.4,44.8,17.1)

0.2507

0.248

1.08

(UR)

P2

(77.6,44.8,16.9)

0.2519

0.2455

2.54

P3

(77.8,45.3,15.7)

0.2466

0.2428

1.54

P4

(78,45.1,15.6)

0.2459

0.2441

0.73

P5

(93.9,32.1,84.4)

0.2839

0.2748

3.21

{111}

P1

(178.7,32.9,39.4)

0.4445

0.4033

9.27

(CR)

P2

(178.8,33.9,38.9)

0.4447

0.3999

10.07

P3

(178.2,34.1,39.2)

0.4434

0.3975

10.35

P4

(177.8,33.7,40.6)

0.4381

0.3978

9.2

P5

(176.5,32.6,41.4)

0.4378

0.3998

8.68

{100}

P1

(123.4,15.2,63.8)

0.4089

0.3923

4.06

(CR)

P2

(123.8,15.3,63.2)

0.4091

0.391

4.42

P3

(123.4,14.9,64)

0.4102

0.3937

4.02

P4

(125.9,14.7,62.4)

0.4154

0.3972

4.38

P5

(130.2,15.6,59.1)

0.4199

0.3986

5.07

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The Schmid factor was computed using the {110}<111> and {112}<111> slip systems of BCC lattice. The SFDR value for a point was used to probe the possibility to activate one or more (two) slip systems in this point. In other words, a large value of SFDR means to have only one (the maximum) slip system activated for this point, while the point may experience both the maximum and the secondary slip systems during rolling when the SFDR value is very small. Then all the SFDR values were linked into polylines (Fig. 14). It appears that most of points in {111} grains in UR sample have comparatively large SFDR values, which implies that it is possible to active only one slip system during rolling. This has a good agreement with the fact that many MBs appeared in {111} grains in UR sample. While {100} grains having small values appear to activate multiple slip system, which indirectly explained the occurrence of orientation gradients in {100} grains in UR sample. For CR sample, remarkable fluctuation was found along the lines in both {111} and {100} grains. The low values and similar variation trend for {111} and {100} grains implies that their deformation behavior came to be similar during rolling, and this also explained the appearance of orientation gradients in both {111} and {100} grains. From this point of view, the situation that only one slip system operates in a certain region leads to the piling up of more and more dislocations on a certain slip plane, leading to the straight boundaries separating the submicron bands, therefore forming the microbands. Further, the misorientation between adjacent microbands increases with the increases of stress. Multiple slip may lead to the rearrangement and annihilation of dislocations introduced by the change of strain path, leading to the decrease in dislocation density. Additionally, straight boundaries are hard to form during multiple slip, therefore microbands are hard to form in CR sample.

Fig. 14. Schmid factor difference ratio (SFDR) values for 248 points selected in L5, L6, L7, L8 lines, respectively. (a) for the points in UR sample. (b) for the points in CR sample.

4.3. Nucleation sites and driving force The influence of strain path on the subsequent recrystallization behavior is mainly associated with the nucleation sites and driving force for grains. For UR sample, dense 16 / 21

boundaries (HAGBs and LAGBs included) indicate the high density of dislocations distributed in {111} grains [16]. Additionally, the distribution of these dislocations is strongly uneven, even formed MBs or MSBs, in {111} grains. For CR sample, the change of the strain path results in the annihilation of dislocations and subsequently reduced the amount of stored energy distributed in the matrices. More interesting finding is the gap of energy stored in {111} and {100} grains, and this can be evaluated by band contrast (BC) values collected in EBSD [26]. The BC value can reflect the state of deformation of different orientations grains, by detecting the grey levels corresponding to the minimum and the maximum in the Hough transform [27-29]. Fig. 15a showed low BC values of {111} grains in compared with the {100} grains collected from Fig. 12a, which indicates the higher stored energy in {111} grains. The values shown in Fig. 15b calculated from Fig. 13a, results showed that the gap of BC value for {111} and {100} grain is largely narrowed in CR sample. The energy Si is proportion to the pattern quality index Hi as shown in the following relation [29]: 𝑆𝑖 ∝ 𝐻𝑖 = 10 [1 −

𝑄𝑖 (𝑔𝑖 ) − 𝑄𝑚𝑖𝑛 ] 𝑄𝑚𝑎𝑥 − 𝑄𝑚𝑖𝑛

Where Si is stored energy for orientation ‘i’, Hi is pattern index, gi, Qmin and Qmax are the minimum and maximum pattern quality of the aggregate, respectively. Accordingly, the pattern quality index has a spectrum be 5 and 10 after being normalized by the equation. Thus, the pattern quality index is calculated to be 6.839 for {111} orientation and 6.082 for {100} in UR sample, while 6.203 for {111} and 6.029 for {100} in CR sample. The index value in {111} grains is much higher than that in {100} grains in UR sample, while the gap was narrowed by CR process. Compared to UR process, CR process can diminish the stored energy difference between {111} and {100} grains in the surface layer. It should be mentioned that the gap for these grains in center layer is larger than in surface in UR sample [26]. The strong cumulative shear strain among the surface layer may promote the subdivision of {100} grains in the UR process, to a certain extent. Additionally, it should be stressed that the shear strain among the surface also contribute to the more serious subdivision of {100} grains in the CR process when compared with {100} grains in the center layer. This fact also indirectly explains the small index gap between {111} and {100} grains, indicating the more homogeneous deformation in CR sample. On this point, we try to use BC values to evaluate energy stored in different regions in a plane, to quantitatively investigate the extent to which the energy unevenly distributed in the plane. Specifically, BC data for UR (Fig. 12a) and CR (Fig. 13a) sample was subdivided into 20 blocks, respectively, as shown in Fig. 16. Energy value for each block was evaluated and connected into a line. Energy values fluctuate significantly through the thickness of testing plane in UR sample, indicating the strongly heterogeneous deformation in UR sample. While the fluctuation is relatively weak in CR sample, which means that the sample had experienced homogeneous 17 / 21

deformation during CR process. It should be stressed that the large fluctuation in UR sample is mainly raised by the large energy gap between {111} and {100} grains. More specifically, region 10 and region 19 are both in {100} grains which contains lower stored energy when compared with that in {111} grains, e.g., region 5 or region 7. The energy may serve as driving force for the growth of newly formed grains during annealing.

Fig. 15. Band contrast distribution of {111} and {100} grains in (a) the UR sample and (b) the CR sample.

Fig. 16. Values of stored energy for different blocks in UR and CR sample. BC maps are on the left while energy value map is on the right.

As regarding to nucleation sites, MSBs in {111} grains in UR sample are preferential place for nucleation upon annealing, and driving force for the growth of nuclei is intensively distributed in {111} grains. Thus nuclei preferentially occur in {111} deformed matrices and most of recrystallized grains are elongated in UR sample. In CR sample, the IRs containing many HAGBs would serve as nucleation sites during annealing. As shown in Fig. 10, subgrains mainly formed in {111} grains in UR sample, while most of subgrains distributed uniformly in CR sample. These subgrains may transform to effective nuclei in the subsequent annealing. Obviously, recrystallization grains have a strong advantage of size in UR sample and an advantage of grains number in CR sample, so that recrystallized grains in CR sample are small in size. 18 / 21

5. Conclusions Ta polycrystal was respectively subjected to unidirectional (UR) and clock (CR) rolled without lubrication in this study. The microstructure, especially the microstructural difference for different grains in surface layers, was detailed characterized and analyzed in this paper. The principal results can be summarized as follows: 1. Line scans reveal essential information about the subdivision of grains with different orientations. Strong cumulative shear strain applied to the surface layer lead to the occurrence of micro-shear bands, which are about 20-27o inclined to RD direction and about 30-37o to the direction of micro-bands, and micro-bands implied the existing of primary slip system in {111} grains in UR sample. While the activation of multiple slip systems lead to the occurrence of orientation gradients in {100} grains in CR sample. 2. Analysis of Schmid factor and Schmid factor difference ratio values suggested that {111} grains are possible to active primary slip system during UR rolling, while {100} grains appear to activate multiple slip system. For CR sample, the low values and similar variation trend for {111} and {100} grains implies that their deformation behavior came to be similar during rolling. 3. Uneven deformation causes large deviation of hardness values for deformed UR sample, whereas small deviation occurred in CR sample due to its homogeneous deformation. The large deviation in UR sample did not weaken during nucleation due to the different recrystallization kinetics of {111} and {100} grains. 4. The energy stored in {111} and {100} grains were evaluated by bond contrast values collected from EBSD. The change of strain path diminishes the gap of stored energy between {111} and {100} grains, which promotes the uniform distribution of energy in the surface layer. Nucleation prefers to occur along {111} deformed matrices or {111}-{100} boundaries in UR sample and recrystallization grains are large in size. Interactive regions serve as primary nucleation places for CR sample and grains are small in size, which contributes to the appearance of fine grains in fully recrystallized CR sample.

Acknowledgement The present work was co-supported by the National Natural Science Foundation of China (Grants 51421001 and 51701032), the Major National Science and Technology Projects of China (no. 2011ZX02705), and the Chongqing Science and Technology Commission in China (CSTC, 2017jcyjAX0094). 19 / 21

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