Characterization of microstructure in Nb rods processed by rolling: Effect of grooved rolling die geometry on texture uniformity

Characterization of microstructure in Nb rods processed by rolling: Effect of grooved rolling die geometry on texture uniformity

Accepted Manuscript Characterization of microstructure in Nb rods processed by rolling: Effect of grooved rolling die geometry on texture uniformity ...

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Accepted Manuscript Characterization of microstructure in Nb rods processed by rolling: Effect of grooved rolling die geometry on texture uniformity

Marko Knezevic, Abhishek Bhattacharyya PII: DOI: Reference:

S0263-4368(16)30708-9 doi: 10.1016/j.ijrmhm.2017.02.007 RMHM 4418

To appear in:

International Journal of Refractory Metals and Hard Materials

Received date: Revised date: Accepted date:

31 October 2016 7 January 2017 16 February 2017

Please cite this article as: Marko Knezevic, Abhishek Bhattacharyya , Characterization of microstructure in Nb rods processed by rolling: Effect of grooved rolling die geometry on texture uniformity. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Rmhm(2017), doi: 10.1016/j.ijrmhm.2017.02.007

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ACCEPTED MANUSCRIPT Characterization of microstructure in Nb rods processed by rolling: Effect of grooved rolling die geometry on texture uniformity

Marko Knezevica, * and Abhishek Bhattacharyyab Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA b H.C. Starck, Newton, MA 02465, USA

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Abstract

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Uniformity of crystallographic texture in rods of niobium (Nb) is one of the most important microstructural parameter determining the quality of rods. In this work, we perform a

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quantitative texture uniformity study in rods of high purity Nb, which were manufactured by rolling using square-to-round shaped rolling die assembly and oval-to-round shaped rolling die

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assembly. After rolling, the rods were annealed under the same condition. Texture characterization was carried out using electron backscatter diffraction (EBSD). We observe that

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the oval-to-round die assembly produced a more uniform <110> fiber texture in the rod crosssection compared to the square-to-round die assembly. To confirm the observation, texture in the

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rods processed in the two different dies were quantitatively compared through the calculations of two suitably defined metrics: texture difference index (TDI) and pole figure difference (PFD).

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The calculations verify that rolling of Nb in the oval-to-round shaped die assembly produces rods of superior texture uniformity. Strain fields developed in the rods during the two processes were

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predicted using finite element (FE) analysis. The strain distribution in the rod made using the oval-to-round shaped dies was determined to be more uniform than in the rod made using the

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square-to-round shaped dies. In particular, the simulations reveal that the square-to-round rolling dies create highly localized strains that are detrimental towards achieving uniform final microstructure in the rods.

Keywords: Niobium; Rods; Rolling; Texture; Texture difference index, Pole figure difference

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Corresponding author at: University of New Hampshire, Department of Mechanical Engineering, 33 Academic Way, Kingsbury Hall, W119, Durham, New Hampshire 03824, United States. Tel.: 603 862 5179; fax: 603 862 1865. E-mail address: [email protected] (M. Knezevic).

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ACCEPTED MANUSCRIPT 1. Introduction Niobium (Nb) exhibits a range of desirable properties such as high melting temperature, ductility, strength, fracture toughness, and conductivity. As such, Nb is an excellent candidate for components that operate under mechanical and thermal extremes. Examples of applications include capacitors, aircraft engine and rocket motor parts and nuclear reactor parts [1, 2]. It is heavily used as an alloying element, in particular in steels to increase strength. The deformation

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behavior of Nb, like other body-centered cubic (BCC) metals such as Ta and Mo, is markedly

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influenced by crystallographic texture as well as alloying additions and is sensitive to

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temperature and strain-rate [3-7]. The controlling mechanisms giving rise to these sensitivities in deformation behavior have been related to Peierls stresses, dislocation substructure formation

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due to a low degree of thermally-activated dynamic recovery of screw dislocations, and dislocation interactions [3, 8-13].

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Crystallographic texture (the Orientation Distribution Function or the ODF) is an important microstructural feature governing anisotropy of various material properties in polycrystalline

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metals [14-26]. When subject to bulk metal forming processes, such as rolling, polycrystalline metals develop texture [14, 16, 27-30]. Texture affects both mechanical [31-37] and functional

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properties [17, 38]. As such, control of texture evolution during processing is an approach often used to help attain target properties and eventual performance [39-41]. Furthermore, gradients in

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texture introduce gradients in material properties that often lead to undesirable stress-strain localizations in the microstructure [42]. In contrast, gradients in microstructure can be

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specifically designed to enhance certain material properties [43-45]. One of the main processing of Nb involve rod-rolling, where the manufactured Nb rods are

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used in semiconductor industries, jewelry, and superconductivity products [46]. Especially in the case achieving the superior functional property of Nb3Sn superconductors, it is important that the Nb rods remain circular during further drawing since the superconductivity performance is affected by the eccentricity of the final Nb wires [47]. To keep the rods as circular as possible while being drawn into wires, their starting microstructure must be as uniform as possible in cross-section. Thus, only uniform grain size and crystallographic texture in the rod cross-section leads to circular diameter of the final wires. The present study is concerned with characterization of microstructure and texture in Nb rods and, in particular, quantitative assessment of the microstructural uniformity in the Nb rods, 2

ACCEPTED MANUSCRIPT which are drawn into wires. The high purity Nb rods were manufactured using two rolling die assemblies with: (1) square-to-round and (2) oval-to-round grooves. Microstructure analysis of grain size and texture was done using Oxford HKL Channel 5 electron backscatter- diffraction (EBSD) that was attached to a Leo Evo 60 Scanning Electron Microscope with a tungsten filament electron source. Beam energy of 20 keV with a spot size of 50 nm and a spatial resolution of 1 µm was used. Qualitatively, we observe that the oval-to-round die assembly

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produced a more uniform <110> fiber texture in the rod cross-section compared to the square-to-

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round die assembly. To further asses texture difference between the two types of Nb rods

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quantitatively, we calculate two parameters: texture difference index (TDI) and pole figure difference (PFD). We find that rolling of Nb in the oval-to-round shaped die assembly produces

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rods of superior texture uniformity. Strain fields developed in the rods during the two processes were predicted using finite element (FE) analysis. The results show that square-to-round dies

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create localized strains that are detrimental towards achieving uniform final microstructure in the rods, which is not the case when the oval-to-round dies are used instead.

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2. Die geometry

Here, we use two differently grooved rolling dies for manufacturing Nb rods to evaluate their

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advantages in terms of producing rods having uniform texture. The dies are shown in Fig. 1. Figure 1a shows a square-to-round rolling die assembly, where the rolling dies at one end (on the

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right) form a diamond shape (with its mating dies) that progressively changes to a circular shape (on the left). The rod rolling process starts with a rod being rolled from right to left. On the other

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hand, Fig. 1b shows an oval-to-round rolling die assembly where the rod is rolled using the widest oval dies (in the middle) initially and is gradually rolled using the circular shaped dies.

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The most distinguishing design difference between the two die assemblies is shown schematically in Figure 2. Both of these manufacturing processes produce circular rods (in crosssection) of 17 mm in diameter in three passes starting from a 38 mm diameter rod-like product created during ingot conversion i.e. open dies forging process followed by the GFM process.

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(b) Fig. 1. (a) Square-to-round rolling die assembly and (b) oval-to-round rolling die assembly used for making Nb rods. The longer lines on the ruler show cm scale from 0 to 30. The manufacturing was conducted at H.C. Starck, Newton, MA 02465.

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(b)

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(a)

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Fig. 2. Schematic showing the starting cross-sectional die opening: (a) square (with rounded end radius of 5.25 mm) and (b) oval used for rolling rods. 3. Material and experiments

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Two high purity Nb rods (99.999 % purity) with the same final diameter of 17 mm were produced though open die forging ingot conversion followed by rod rolling process from an

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ingot. The diameter of the cast ingot, produced through vacuum arc remelting (VAR), was 200 mm. The ingot grain size was very large (> cm). It was forged to a diameter of 38 mm and,

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successively, annealed. The average grain size of the annealed material was 70 µm. The length of ingots varies with the desired length of rods. This study is focused on the rod rolling part of

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the process. The main distinguishing processing steps between the two rods are: one was rolled using a square-to-round rolling die assembly (referred as process 1), whereas, the other one was

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rolled using an oval-to-round rolling die assembly (referred as process 2) (see, Figure 1). The rods undergo through an intermediate annealing step every time upon being deformed to

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approximately 80 % strain. The final rods were in the annealed state. The intermediate as well as the final annealing was done at a fixed temperature of 1339 K for an hour in vacuum. The two final annealed rods are designated as rods 1 and 2 for processes 1 and 2, respectively. Both rods exhibited hardness of 70 HV (measured with 25 gf load). Metallographic cross-sectional samples were made out of rods 1 and 2 by waterjet cutting perpendicular to the rod length. The two samples were mounted, ground and mechanically polished progressively using 400 and 800 grit SiC abrasive papers, and 9 and 3 µm diamond paste. Final polish was done using colloidal silica for a mirror-like surface finish. Primary texture characterization using HKL EBSD was performed in the central section of the rods. The 5

ACCEPTED MANUSCRIPT locations will be designated as location (1). Additional measurements were also made around the perimeter of the rods. These will be designated as locations (2) - (5). Figure 3 shows a schematic of the final 17 mm diameter Nb rod cross-section with rectangular areas highlighting where the EBSD scans were taken. Each scan covered an area of 1.5 mm by 1.5 mm. The corresponding

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co-ordinate axes are also indicated for two particular scans.

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Fig. 3. Schematic of the 17 mm diameter Nb rod showing the five rectangular areas where the EBSD scans were performed.

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4. Results

Figure 4a shows the inverse pole figure (IPF) maps of the annealed 17 mm Nb rod

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manufactured using the square-to-round rolling die assembly. The scan was taken near the center of the rod over an area, which is much smaller than the area of the scans taken for the texture

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evaluation. The rod axis is perpendicular to the scan while the two axis within the rod crosssectional area were arbitrary. A step size of 1 µm was used to create the IPF map. The raw map

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was cleaned using standard noise reduction described in section 11.39 of HKL Channel 5 user manual (Release date: June 2007). The average grain size was found to be approximately 9 µm, and the grain structure was nearly equiaxed. All other scans showed nearly identical grain structure. Therefore they are not shown. The map displays low angle grain boundary (light gray color) for misorientation less than 5° and high angle grain boundary (dark black color) for misorientation greater than 5°. Clearly, the rod was not fully recrystallized after annealing at 1339 K for an hour due to the presence of numerous sub-grain boundaries. The rod manufactured using oval-to-round process, underwent

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ACCEPTED MANUSCRIPT same intermediate and final annealing conditions exhibited very similar microstructure to the one shown in Figure 4a and, is therefore, not provided. Figure 4b shows

,

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pole figures of the central portion of Nb rods 1 and

2 (rod 1 on the left and rod 2 on the right). The axes x and y in the figure refer to two perpendicular axes (arbitrary) on the rod cross-sectional surface. These pole figures as well as all the other pole figures presented later in the paper were created using discrete binning with half

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width of 10° and cluster size of 5°. Both the rods exhibit a strong <110> along the rod length i.e.,

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perpendicular to the x-y axes. However, rod 2 (processed using the oval-to-round dies, i.e.,

pole intensity around

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process 2) show a better defined <110> fiber texture, due to the presence of the ring of uniform , compared to rod 1 (processed using the square-to-round dies, i.e.,

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process 1). Such differences in texture may be tied directly to the different rolling die grooves used for processing such rods, since it was the only variable between the two Nb rods. Also, the

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more uniform for rod 2 than that for rod 1.

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cross-sectional texture, comprising of all the five individual sets of pole figures, appeared to be

(a)

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Fig. 4. (a) 17 mm Nb rod axial direction inverse pole figure (IPF) map for a rod manufactured using the square-to-round roll assembly. Grains with <110> along the rod axial direction are colored green. A 1 µm step size was used showing low angle grain boundaries (< 5°, colored gray) and high angle grain boundaries (> 5°, colored black). The micron bar is of 100 µm in length. (b) Pole figures of the central portion of the 17 mm Nb rods rolled using the square-toround die assembly (on the left) and oval-to-round die assembly (on the right). The accompanying legend shows intensity values expressed as multiples of random distribution.

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In addition to qualitative texture comparison analysis, quantitative texture comparison was carried out. However, in order to compare various textures quantitatively, it was first realized that appropriate co-ordinate axes needed to be chosen for each EBSD map. Figure 5 shows an

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example of a case where, depending on the orientation of the pole figures, the texture difference can be low or high. The figure also shows the axes used for creating different pole figures. The

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location of high intensity

poles (shown by an arrow) may be used as a benchmark for

gauging the texture difference between regions 3 and 5. It can be seen that the difference in pole

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intensities is smaller between poles figures (3) and (5’), compared to (3) and (5). Therefore, instead of Cartesian coordinate system, a cylindrical coordinate system was pertinently chosen for such a study. Fresh set of EBSD measurements were made at four locations around the perimeter of the rod spaced by 90º by considering radial (r) and cross-radial () axes as sample in-plane axes. Similar to the Fig. 1, Fig. 6 shows the new coordinate axes. Note that the center EBSD map (i.e. Map 1, already shown in Figure 4) was left intact. The new measured pole figures (except the central pole figures of rods 1 and 2) are shown in Fig. 7 and denoted by (2) to (5). Again, as expected, the textures showed a strong <110> along the rod direction. Evidently, 8

ACCEPTED MANUSCRIPT pole figures plotted in Fig. 7a referring to rod 1 rolled using the square-to-round die assembly are more symmetric and display a stronger <110> fiber texture than those plotted in Fig. 7b referring to rod 2 obtained using the oval-to-round die assembly. These observations suggest qualitatively that the oval-to-round rod rolling process produces more uniform texture in the material. With these new measured Euler angles from different locations for the two rods, texture difference metrics TDI and PFD were calculated by choosing 2000 measured values having the

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highest area fraction.

Fig. 5. Rod 2 pole figures of regions 3 and 5 with different sets of axes. (5’) refers to 180° rotated pole figures of (5) using the dotted X0-Y0 axes.

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Fig. 6. Schematic of the Nb rod with cylindrical co-ordinate system.

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Fig. 7. Pole figures of Nb annealed rods using cylindrical coordinate system (see, Figure 6): (a) rod 1 and (b) rod 2. The EBSD measurements (2) – (5) are taken from around the perimeter of the rod with approximately 90º spacing in between scans.

5. Quantitative comparison of texture in Nb rods processed with different die assemblies

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We perform the comparison using two measures specifically defined to facilitate texture comparison: (texture difference index (TDI) and pole figure difference (PFD). The former has

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been recently introduced [48, 49] and is more accurate than the latter since it operates on the entire ODF while the later compares individual pole figures. The former relies on the spectral

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representation of an ODF function, which requires the calculation of Fourier coefficients using generalized spherical harmonics (GSH) basis. The importance of this series representation is that

textures representing their difference.

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the linearity of the basis can be exploited to calculate the normalized distance between two

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ODF, f(g), is the normalized probability density associated with the occurrence of the crystallographic orientation, g, in the sample. It can be mathematically expressed as:

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 f g dg  1 ,

(1)

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dV  f g  dg , V

where V denotes the total sample volume and dV is the sum of all sub-volume elements in the

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sample associated with a lattice orientation lying within an incremental invariant volume, dg, of a given orientation, g. The OS refers to an orientation space. Here, it is the Bunge-Euler space [14, 50]. The crystal orientation is an ordered set of three rotation angles that transform the crystal local frame to the sample reference frame, i.e.,

. The main advantage of

the Bunge–Euler space is that the rotation angles are inherently periodic. Any ODF can be expressed efficiently in a Fourier series using GSH functions [14] as: 

f g    l 0

M(l) N(l)

F μ 1 ν 1

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μν

Tl μν g  ,

(2)

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ACCEPTED MANUSCRIPT where Tl μν g  denotes the GSH functions and Fl μν are Fourier coefficients uniquely representing the ODF. The limits M(l) and N(l) respectively depend on selected crystal and sample symmetry [14]. These limits define the number of dimensions considered for the representation of an ODF in an infinite dimensional Fourier space. We perform the calculations using l values of 16 since this is a default value in plotting the pole figures. The Fourier coefficients beyond this value are

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small and insignificant. Eq. (2) allows representation of ODF as a single point in an infinite

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dimensional Fourier space with coordinates given by Fl μν . If we define k Fl   as the Fourier

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coefficients of a single crystal, k, it is then possible to define a convex and compact texture hull representing the complete set of all physically realizable ODFs [51], M, as:

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  M  Fl   Fl      k k Fl   , k Fl    M k , αk  0 , αk  1 , k k  

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where:

  ' 1 M k   k Fl   k Fl    Tl   g k , g k  FZ  . 2l  1  

 

(3)

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(4)

The prime symbol (') in superscript of the GSH function in eq. (4) denotes the complex

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conjugate. The bar on top of the Fourier coefficients in eq. (3) indicates an averaged value of the Fourier coefficients based on the weights of crystal orientations,

, in a given ODF. In order to

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quantify the difference between two textures in the spectral representation, we take the advantage of an appropriate normalized error metric called TDI expressed as [48]:

  f g   f g  dg

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*

TDI 

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

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2 ~ f g   f g  dg *



F   

*  l

 Fl  

*  l

~  Fl  

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F   

 

2

2

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(5)

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In Eq. (5), f * g  denotes a given ODF (the average ODF in our case) and f g  represents another ODF (the ODF at a specific location in our case). The Fourier coefficients are calculated using Eq. (3). The normalization factor has been selected to represent the largest distance in the hull from f * g  . The furthest ODF and the corresponding Fourier coefficient are denoted as 12

ACCEPTED MANUSCRIPT ~ ~ f g  and Fl   , respectively. This ODF is typically a single crystal. Note also that

~  f g dg   f g dg   f g dg 1 . '

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To quantify the degree of the texture difference, we also calculate the pole figure difference † (PFD) between textures at two different positions, which is given by [52]:

  I     I    sin dd   ref ,



 I

ref  , 

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PFD

0 0 2  / 2

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 I  ,  sin dd

(2)

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hkl

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2  / 2

 0  0

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where  and  are the longitude and latitude positions in a h k l pole figures and I ref  ,  (corresponding to a reference taken to be average and random) and another pole figure I  , 

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(corresponding to five different locations) intensities.

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TDI and PFDs were calculated between the individual edge textures and an average computed texture for the two rods. The results are shown in Table 1. The PFD values are

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reported as the average values over (100), (110) and (111) pole figures. Rod 2 has lower average TDI and PFD values than Rod 1. A lower TDI and PFD number indicates a better correlation

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between the two textures. These calculations further support the claim that process 2, involving

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the oval-to-round rod rolling process, produces more uniform texture around the rod perimeter. The textures produced through such rod processing techniques were also compared against a numerically ideal <110> fiber texture (BCC metals develop <110> fiber texture under uniaxial

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tension). The ideal <110> texture used for the computation is the simulated <110> ideal texture, obtained by running VPSC code of 2000 random initial orientations under simple tension to 80% strain (approximately the same strain levels as the experimentally drawn Nb rods). Table 2 shows the TDI and PFD calculations for the central part of the rods (Figures 6a(1) and 6b(1)). Process 2 shows a better agreement with the ideal texture, as well.



The pole figure difference indices were calculated using POLE ver. 8c, code developed by C.N. Tomé.

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ACCEPTED MANUSCRIPT Table 1. TDI and average PFD calculated between the four edge texture measurements and the overall average texture for the two processes.

(a) Process 1 w.r.t.

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PFD

Edge 1

0.0966186

0.2138

Edge 2

0.0822868

0.1971

Edge 3

0.0902259

0.2120

Edge 4

0.0926472

0.2114

Mean

0.090445

0.208575

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Average

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(b) Process 2 w.r.t.

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Average

PFD

0.0756119

Edge 2

0.0729937

0.1790

Edge 3

0.0802318

0.1912

0.1706

0.0929714

0.2068

0.080452

0.1869

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Mean

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Edge 4

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Edge 1

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Table 2. TDI and average PFD between measure texture at the central portion of the rods and an ideal <110> fiber texture obtained by simple tension.

w.r.t.

TDI

PFD

0.13513

0.32651

<110> Ideal Texture Process 1

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0.0921244

0.22416

6. Discussion A numerical analysis was conducted to better understand the effect of initial die geometry on deformation of the Nb rods. A 2D cross-sectional deformation simulation was performed using

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ABAQUS/Explicit 6.14-1 to get a strain distribution within the rod due to square and oval dies.

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Figure 8a shows the strain map (in terms of equivalent plastic strain, PEEQ) in the Nb rod cross-

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section after being deformed by two sets of perpendicular square dies. Similarly, Figure 8b shows the strain distribution in the Nb rod cross-section after being deformed by two sets of

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perpendicular oval dies. As the rod is deformed further (and made circular in the process), the final strain distribution in the rod is a superposition of such strain distributions around its center.

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Since the rod is rolled a finite number of times using the square dies, the region of high localized strain of 0.5 (shown by an arrow in Figure 8a) may not get uniformly “smeared” around the rod

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center. The end result is a non-uniform strain distribution in the rod cross-section due to the presence of finite number of such highly localized strain regions. When oval dies are used

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instead, there are no such regions of highly localized strain. It leads to a relatively uniform strain distribution in the final rod cross-section. Texture uniformity in rod 2 is a consequence of such

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strain uniformity produced during the oval-to-round rolling process. Hence, the innovative ovalshaped dies are preferred over the square-corner dies for producing axially symmetric

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microstructure.

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Fig. 8. Equivalent plastic strain distribution in Nb rod cross-section after being deformed using two sets of perpendicular (a) square dies and (b) oval dies during the initial stages of the rod rolling process.

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7. Conclusion

The study here pertains to understanding texture evolution in Nb rods and the effect of die

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geometry on the uniformity of microstructure in rods during manufacturing. The manufactured Nb rods had <110> fiber texture. It is found that oval-shaped rolling dies used in oval-to-round

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rolling process produces a more uniform cross-sectional texture than the square-corner rolling dies used in square-corner-round rolling process. Furthermore, quantitative texture uniformity assessment was carried out using two metrics, TDI and PFD. These calculations quantitatively confirmed the qualitative assessment that the rods produced using oval rolling dies generated a more uniform texture than the square rolling dies. Finally, through numerical simulations it was shown that square-to-round rolling dies create highly localized strains that may be detrimental towards achieving uniform final microstructure in the rods, which is not the case when oval-toround rolling dies are used instead.

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ACCEPTED MANUSCRIPT Acknowledgements Support for this research was provided by H.C. Starck, Newton, MA, 02461, USA.

References

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ACCEPTED MANUSCRIPT Highlights fiber texture develops during rolling of high purity Nb into rods. Effect of rolling die geometry for making Nb rods on texture uniformity is studied. Oval-to-round rolls produce rods of higher texture uniformity than square-to-round rolls.

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Quantitative measures of TDI and PFD confirm the qualitative observations.

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FE simulations reveal more uniform strain in rods made in oval than in square grooved rolls.

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