domain: spi chim

text:
Dr Hiba Azzeddine
email: hiba.azzeddine@univ-msila.dz

Thierry Baudin

Anne-Laure Helbert

François Brisset

Yi Huang

Megumi Kawasaki

Djamel Bradai

Terence G Langdon

A stored energy analysis of grains with shear texture orientations in Cu-Ni-Si and Fe-Ni alloys processed by high-pressure torsion

Keywords: Cu-Ni-Si alloy, Fe-Ni alloy, High-pressure torsion, Shear texture, Stacking fault energy, Stored energy

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

It is well known that crystallographic texture significantly controls the anisotropy of mechanical properties and the formability during the thermo-mechanical processing of metallic alloys [START_REF] Kocks | Texture and Anisotropy. Preferred Orientations in Polycrystals and Their Effect on Material Properties[END_REF]. Generally, the orientations of the deformed grains depend on the specific deformation processing such as rolling, extrusion or torsion. In practice, a rolling texture, including the Copper {112}<111 ̅ >, S {123}<634>, Brass {110}<11 ̅ 2>, Goss {110}<001> and Cube {100}<001> components, was widely reported in face-centered cubic (FCC) alloys processed by conventional rolling and severe plastic deformation by accumulative rollbonding (ARB) [START_REF] Kestens | Texture formation in metal alloys with cubic crystal structures[END_REF][START_REF] Tirsatine | Texture and microstructure evolution of Fe-Ni alloy after accumulative roll bonding[END_REF]. By contrast, shear textures composed of

𝐴 1 * {111}<1 ̅ 1 ̅ 2>, 𝐴 2 * {111}<12 ̅ 1>, A {111}<11 ̅ 0>, 𝐴 ̅ {111}<01 ̅ 1>, B {112}<11 ̅ 0>, 𝐵 ̅ {112}<11 ̅ 0> and C
{100}<110> were formed during equal-channel angular pressing (ECAP) and high-pressure torsion (HPT) processing of several FCC alloys [START_REF] Beyerlein | Texture evolution in equal-channel angular extrusion[END_REF][START_REF] Khereddine | Microstructures and textures of a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF][START_REF] Tirsatine | An EBSD analysis of Fe-36%Ni alloy processed by HPT at ambient and a warm temperature[END_REF].

The development of a deformation texture in rolled FCC alloys depends strongly on the stacking fault energy (γSFE) of the processed alloys. The deformation texture after conventional rolling is classified into three categories depending on the value of γSFE. First, the deformation texture of alloys with low γSFE, such as a Cu-30Zn alloy (γSFE = 14 mJ/m 2 ), is characterized by a dominant Brass {110}<11 ̅ 2> component known as a Brass-type texture.

Second, for alloys with high γSFE, such as aluminum (γSFE = 160 mJ/m 2 ), the Copper {112}<111 ̅ > and S {123}<634> components are often dominant and this is known as a

Copper-type texture. Third, it is generally assumed that the texture of alloys with medium γSFE, such as copper (γSFE = 78 mJ/m 2 ) and an Fe-Ni alloy (γSFE ~ 122 mJ/m 2 ), contains

Copper, S and Brass components in fairly equal fractions.

Nevertheless, the evolution of a deformation texture in alloys with medium γSFE is complicated and no definitive trends exist in texture evolution. For example, while cold rolling of Fe-36Ni alloy samples leads to the formation of a typical copper texture with the presence of Copper, S and weak Brass components [START_REF] Gervas'eva | Formation of texture in thin tapes of Fe-Ni alloys during cold rolling and recrystallization[END_REF], the deformation textures of coldrolled Cu-2.7Ni-0.6Si (wt.%) and Cu-15Ni-8Sn (wt.%) alloys, having medium γSFE (~50 mJ/mol for the Cu-15Ni-8Sn alloy), show dominant Brass components which are typical for alloys with low γSFE [START_REF] Wei | Study on Texture Evolution and Deformation Mechanism of the Cu-Ni-Si Alloy during Cold-rolling Treatment[END_REF][START_REF] Alili | On the rolling and annealing texture in a Cu-15Ni-8Sn (wt.%) alloy[END_REF]. It has been also shown that the Brass component might strengthen with increasing deformation strain due to the presence of twins that produces a re-orientation of the Copper component to a Brass component [START_REF] Wei | Study on Texture Evolution and Deformation Mechanism of the Cu-Ni-Si Alloy during Cold-rolling Treatment[END_REF]. Moreover, it is reasonable to expect that the recrystallization texture of medium to high γSFE alloys may be characterized by the formation of a Cube {100}<001> texture but many experiments have shown the deformation texture is retained after annealing of the cold-rolled Cu-15Ni-8Sn alloy [START_REF] Alili | On the rolling and annealing texture in a Cu-15Ni-8Sn (wt.%) alloy[END_REF]. Accordingly, it was concluded that the deformation and recrystallization textures of alloys with medium γSFE strongly depend on the nature of the deformation processing and the chemical composition of the alloy.

In investigations of the deformation textures, it was demonstrated that the numbers of dislocations stored within the grains was dependent upon the local crystallographic orientation [START_REF] Wauthier-Monnin | The evolution with strain of the stored energy in different texture components of cold-rolled IF steel revealed by high resolution X-ray diffraction[END_REF][START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF][START_REF] Etter | Influence of the cold rolled reduction on the stored energy and the recrystallization texture in a Fe-53%Ni alloy[END_REF]. In practice, the stored energy in deformed grains of different orientations plays a significant role in controlling the onset of recrystallization and the corresponding texture development [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF].

Generally, the total dislocation density is composed of two types: geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF]. The stored energy related to the Brass {110}<11 ̅ 2>, Copper {112}<111 ̅ >, S {231}<346> and Cube {001}<100> texture components of several FCC alloys was investigated after conventional rolling and ARB [10-12, 14, 15]. A hierarchy was found in several processed alloys whereby the stored energy, E, of the texture components varied as ECopper > ES > EBrass > ECube [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF][START_REF] Etter | Influence of the cold rolled reduction on the stored energy and the recrystallization texture in a Fe-53%Ni alloy[END_REF][START_REF] Betanda | Measurement of stored energy in Fe-48%Ni alloys strongly cold-rolled using three approaches: Neutron diffraction, Dillamore and KAM approaches[END_REF]. It was suggested that the orientated grains with high energy were rapidly replaced by Cube grains (with low energy) during annealing treatments [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF][START_REF] Etter | Influence of the cold rolled reduction on the stored energy and the recrystallization texture in a Fe-53%Ni alloy[END_REF]. The stored energy in the oriented grains in an ARB-processed Fe-36Ni alloy was found to fluctuate (specifically, to decrease and subsequently to increase) upon increasing the numbers of ARB processing passes due to the occurrence of dynamic recrystallization (DRX), the formation of fine grains and the production of new dislocations [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF]. In addition, it was demonstrated that the GNDs in the cells/sub-grains walls are responsible for the increase in the stored energy during ARB processing [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF]. The GNDs also contributed significantly to the bulk stored energy of the HPT-processed Cu-2.5Ni-0.6Si alloy at equivalent strains in the range of ~8.6-16 and afterwards this contribution slightly decreased due to the occurrence of DRX and the formation of fine grains [START_REF] Azzeddine | An investigation of the stored energy and thermal stability in a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF]. The evolution of the shear texture components by HPT processing as a function of the γSFE of alloys is rarely documented in published reports and no systematic investigation has been undertaken to evaluate the stored energy in the shear texture oriented grains.

In fact, it is only known that the Taylor factor in the different shear texture components increases in the following order: A/𝐴 ̅ < 𝐴 1 * /𝐴 2 * < B/𝐵 ̅ < C [START_REF] Jonas | Modelling oriented nucleation and selective growth during dynamic recrystallization[END_REF][START_REF] Naghdy | Evolution of microstructure and texture in commercial pure aluminum subjected to high pressure torsion processing[END_REF]. The Taylor factor is defined as the total slip amplitude corresponding to a unit macroscopic strain increase [START_REF] Jonas | Modelling oriented nucleation and selective growth during dynamic recrystallization[END_REF][START_REF] Beladi | Texture and substructure characteristics of dynamic recrystallization in a Ni-30%Fe austenitic model alloy[END_REF]. Consequently, it may be suggested that a grain with high Taylor factor has higher dislocation density and hence high stored energy [START_REF] Beladi | Dynamic Recrystallization of Austenite in Ni-30 Pct Fe Model Alloy: Microstructure and Texture Evolution[END_REF][START_REF] Takayama | Stored Energy and Taylor Factor Relation in an Al-Mg-Mn Alloy Sheet Worked by Continuous Cyclic Bending[END_REF]. However, a direct correlation between the Taylor factor and the stored energy is not yet established.

Based on the limited data available to date, the present study was initiated in order to quantify the stored energy and thereby to clarify its relationship with the shear texture components for Cu-2.5Ni-0.6Si and Fe-36Ni alloys after HPT processing at room temperature for ½, 1 and 10 turns using a Kernel Average Misorientation (KAM) approach. The effect of γSFE on the stored energy is also examined. It must be noted that the stored energy estimated in the present study arose from the GND dislocations since the KAM approach allows only an estimation of this type of dislocation [START_REF] Azzeddine | An investigation of the stored energy and thermal stability in a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF][START_REF] Fressengeas | On the evaluation of dislocation densities in pure tantalum from EBSD orientation data[END_REF]. Full details on the evolution of the texture and the microstructural parameters, such as grain size and grain boundary orientation distributions, of the HPT-processed Cu-2.5Ni-0.6Si and Fe-36Ni alloys were given in earlier reports [START_REF] Khereddine | Microstructures and textures of a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF][START_REF] Tirsatine | An EBSD analysis of Fe-36%Ni alloy processed by HPT at ambient and a warm temperature[END_REF] and therefore the present investigation was undertaken to provide a special emphasis on the stored energy and the shear texture component correlations.

Experimental materials and procedures

The Cu-2.3Ni-0.5Si (wt. %) and Fe-36Ni (wt. %) alloys were supplied by CLAL-MSX (Meru, France) and APERAM Alloys Imphy Society, France, respectively.

Accordingly, the Cu-2.3Ni-0.5Si alloy was provided in supersaturated solid-solution condition after casting and hot rolling at 830 °C whereas, the Fe-36Ni sheet alloy was provided in a fully recrystallization state. Both alloys were machined into disks having diameters of 10 mm and thicknesses of ~0.85 mm. The HPT processing was performed at ambient temperature through totals, N, of 1/2, 1, 5 and 10 turns using an imposed pressure of 6.0 GPa and a rotational speed of 1 rpm under quasi-constrained conditions [START_REF] Figueiredo | Using finite element modeling to examine the flow processes in quasi-constrained high-pressure torsion[END_REF].

The microstructure and microtexture were analysed using a scanning electron microscope FEG-SEM SUPRA 55 VP operating at 20 kV with TSL Orientation Imaging Microscopy, OIM TM software. The electron backscatter diffraction (EBSD) measurements were performed in the RD-SD plane of the processed discs where RD and SD denote the rotational and shear directions, respectively, after mechanical and electrolytic polishing at ambient temperature using an A2 Struers electrolyte at 24 V for 20 sec (for Cu-2.5Ni-0.6Si alloy) and at 30 V for 12 sec (for Fe-36Ni alloy). The presentation of the axis system and the EBSD position measurement on the disk is illustrated in Figure 1. The EBSD maps were collected at the mid-radius (r = 2.5 mm, as shown in Figure 1) of each disk on a 25 × 25 μm 2 area using a step size of 25 nm for the Cu-2.5Ni-0.6Si alloy and a 50 ×50 μm 2 area with a step size of 50 nm for the Fe-36Ni alloy. An area of 100 × 100 μm 2 was used with step sizes of 1 and 0.1μm for the initial states of the Cu-2.5Ni-0.6Si and Fe-36Ni alloys, respectively. A grain tolerance angle of 5° and a minimum grain size of 2 pixels were chosen to obtain the grain size data. All datum points with a confidence index (CI) lower than 0.05 were excluded from the analysis where CI quantifies the reliabilities of the indexed patterns [START_REF] Mikami | Effect of reference point selection on microscopic stress measurement using EBSD[END_REF].

A quantitative texture analysis was carried out by calculating the Orientation Distribution Function (ODF) using MTex software [START_REF] Bachmann | Texture Analysis with MTEX -Free and Open Source Software Toolbox[END_REF]. The recalculated {111} pole figures were determined using the harmonic method (L = 22) with each orientation modeled with a Gaussian function having a half-width of 5°. Usually, the KAM approach allows quantifying the dislocation density belonging to the GNDs type and the corresponding stored energy in the microstructure by the following equations [START_REF] Betanda | Measurement of stored energy in Fe-48%Ni alloys strongly cold-rolled using three approaches: Neutron diffraction, Dillamore and KAM approaches[END_REF][START_REF] Badji | Texture, misorientation and mechanical anisotropy in a deformed dual phase stainless steel weld joint[END_REF]:

𝜌 = 𝛼𝜃 𝐾𝐴𝑀 𝑛𝑑𝑏 (1)
𝐸 𝐾𝐴𝑀 = 1 2 𝜌𝜇𝑏 2 = 𝜇𝑏𝜃 𝐾𝐴𝑀 2𝑑 ( 2
)
where α is a parameter which depends on the grain boundary type with values of 2 and 4 for pure tilt and twist boundaries, respectively [START_REF] Takayama | Analysis of Intragranular Misorientation Related to Deformation in an Al-Mg-Mn Alloy[END_REF], θKAM is the misorientation angle, b the magnitude of the Burgers vector (b = 0.255 and 0.253 nm for Cu-2.5Ni-0.6Si and Fe-36Ni, respectively), n = 3 for the nearest neighbor, d the EBSD scan step size, and μ the shear modulus having values of 48.3 and 57 GPa for copper and iron, respectively. The θKAM value was calculated from the mean misorientation angle between the point and its third neighbor excluding misorientations greater than 5°. It may be preferable to increase the CI to 0.1 since the samples undergo SPD processing and to ensure the reliability of the EBSD scans.

However, the difference between the two clean-up procedures was very small and ∆θKAM = 0.01°. In practice, it is better for comparison to use the normalized KAM (KAMnor = KAM/nd) parameter since the EBSD step sizes for both alloys are not the same [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF].

The grain orientation spread (GOS) approach implemented in the OIM TM software is used to separate the recrystallized grains from the deformed grains where GOS is defined as the average deviation between the orientation of each point in the grain and the average orientation of the grain [START_REF] Cho | Determination of a mean orientation in electron backscatter diffraction measurements[END_REF]. In this research, grains were considered recrystallized if the value of GOS was lower than 1° [START_REF] Cho | Determination of a mean orientation in electron backscatter diffraction measurements[END_REF].

Experimental results

Figure 2 shows (a) and (b) the KAM maps and (c) and (d) the recalculated {111} pole figures for the as-received Cu-2.5Ni-0.6Si and Fe-36Ni alloys, respectively. The positions of the main ideal rolling texture components for FCC alloys are listed in

A {111}<11 ̅ 0> 0° 54.74° 45° A {111}<01 ̅ 1> 60° 54.74° 45° B {112}<11 ̅ 0> 0° 35.26° 45° B {112}<1 ̅ 10> 180° 35.26° 45° C {001}<110> 45° 0° 0°
Figures 3 and4 show a series of KAM and GOS maps and the recalculated {111} pole figures of the HPT-processed Cu-2.5Ni-0.6Si and Fe-36Ni alloys after, from top, N = ½, 1, 5 and 10 turns, respectively. The KAMnor values and the fractions of the recrystallized grains (FDRX) for each sample are presented in the KAM and GOS maps. After N = ½ turn, the normalized KAM value increases rapidly from 1.3°/μm to 16.2°/μm for the Cu-2.5Ni-0.6Si alloy and from 0.8°/μm to 9.2°/μm for the Fe-36Ni alloy due to the generation and accumulation of dislocations. For the Cu-2.5Ni-0.6Si alloy the normalized KAM value continues to increase to 16.6°/μm after N = 1 turn and then decreases to 15.2°/μm after N = 10 turns whereas for the Fe-36Ni alloy the normalized KAM value appears to saturate at 9°/μm after N = 1 turn and then continuously decreases to 6.9°/μm through N = 10 turns. The decrease in the normalized KAM values is accompanied by an increase in the fraction of recrystallized grains, thereby indicating the occurrence of a dynamic recrystallization process.

This trend is especially evident between 1 and 5 turns for the Fe-Ni alloy. It is also noted that the fraction of DRX of 37 % is higher for Fe-36Ni after N = 5 turns than the fraction of 26%

for Cu-2.5Ni-0.6Si.

The evolution of the texture by means of the {111} recalculated pole figures as a function of the numbers of HPT turns is shown in Figures 3 and4 for Cu-2.5Ni-0.6Si and Fe-36Ni, respectively. The main ideal shear texture components of FCC alloys are summarized in Thereafter, the stored energy decreased rapidly in all shear components after N = 5 turns. The stored energy decreased continuously to N = 10 turns except for a stabilization at 16.9  0.8 mJ/mol and 17.1  0.7 mJ/mol for the 𝐴 1 * and 𝐴 ̅ components, respectively.

Generally, the amount of the stored energy was similar in the different shear texture components for both alloys and no hierarchy was formed as reported previously in an ARBprocessed Fe-36Ni alloy [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF]. However, close inspection shows that the C and 𝐴 2 * components exhibit the lower stored energy among all shear components for the Cu-2.5Ni-0.6Si alloy after high strains for N = 5 and 10 turns while the B, 𝐵 ̅ and C components have the highest values for the Fe-36Ni alloy. Such high values of stored energy in grains with B, 𝐵 ̅ and C components imply a relatively faster recrystallization during an annealing treatment after HPT processing.

Discussion

The results from this investigation demonstrate that the Cu-2.5Ni-0.6Si and Fe-36Ni alloys exhibit different microstructural evolutions after HPT processing. First, the dislocation density increases in Cu-2.5Ni-0.6Si with increasing numbers of HPT turns at N =1 turn and then decreases up to N = 10 turns. By contrast, the dislocation density continuously decreases with increasing HPT turns through N= 10 turns for Fe-36Ni. Moreover, these alloys show inconsistent trends in the evolution of stored energy in the shear components as demonstrated in Figure 5. Second, it is anticipated from the behavior of the stored energy in the different shear texture components that DRX is restricted in Cu-2.5Ni-0.6Si compared to Fe-36Ni and this is apparent especially after N = 5 turns. Third, a typical shear texture was formed in Cu-2.5Ni-0.6Si as early as N = 1/2 turn and then stabilized whereas the shear component continuously developed with increasing numbers of HPT turns for Fe-36Ni. However, both alloys share a common behavior where the texture does not sharpen with increasing strain as usually observed in rolled or ARB-processed alloys [START_REF] Tirsatine | Texture and microstructure evolution of Fe-Ni alloy after accumulative roll bonding[END_REF][START_REF] Alili | On the rolling and annealing texture in a Cu-15Ni-8Sn (wt.%) alloy[END_REF]. This difference is attributed to the nature of the simple shear strain mode and the established occurrence of a strong grain subdivision during HPT processing [START_REF] Naghdy | Evolution of microstructure and texture in commercial pure aluminum subjected to high pressure torsion processing[END_REF].

The inconsistency in the microstructural and texture evolution between the two alloys is due to the difference in the values of their stacking fault energy, γSFE. The γSFE of the Fe-36Ni alloy was estimated from X-ray diffraction line profile analysis as ~122 mJ/m 2 [START_REF] Schramm | Stacking fault energies of fcc fe-Ni alloys by x-ray diffraction line profile analysis[END_REF]. The γSFE of the Cu-2.5Ni-0.6Si alloy is not at present available but it may be estimated from the relationship [START_REF] Gallagher | The influence of alloying, temperature, and related effects on the stacking fault energy[END_REF]:

𝛾 𝑆𝐹𝐸 = 𝜇𝑎 3 𝜌 24√3𝜋𝛼 ( 3
)
where a is the lattice spacing and α is the net stacking fault probability. In a previously reported X-ray diffraction analysis of results of the same Cu-2.5Ni-0.6Si alloy after coldrolling followed by annealing [START_REF] Khereddine | X-ray diffraction analysis of cold-worked Cu-Ni-Si and Cu-Ni-Si-Cr alloys by Rietveld method[END_REF], the value of γSFE was estimated as ~64.2 mJ/m 2 . It is recognized therefore that, based on the available data, the γSFE values for both Cu-2.5Ni-0.6Si

and Fe-36Ni are in the medium range but the γSFE of Cu-2.5Ni-0.6Si is lower by a factor of ~2 than Fe-36Ni (thus, γSFE (CuNiSi) ≈ γSFE (FeNi)/2).

Considering these differences, it is well known that a low γSFE promotes deformation twinning due to an insufficient dislocation system for accommodating the plastic deformation.

No twins were observed in the EBSD maps for Cu-2.5Ni-0.6Si in the early stage of HPT processing for N =1/2 turn although it is recognized that this may depend at least in part on limitations in the EBSD facility. In an earlier study, transmission electron microscopy (TEM) revealed the presence of twins in the same Cu-2.5Ni-0.6Si alloy after ECAP processing up to 12 passes but not after HPT processing of this alloy [START_REF] Khereddine | An examination of microstructural evolution in a Cu-Ni-Si alloy processed by HPT and ECAP[END_REF] where the absence of twins after HPT was attributed to the very small size of the twins and the limitation of conventional TEM. Twins were observed by TEM in pure copper (γSFE = 78 mJ/m 2 ), Cu-10 wt.% Zn (γSFE = 35 mJ/m 2 ) and Cu-30 wt.% Zn (γSFE = 14 mJ/m 2 ) after HPT processing for N = 5 turns at room temperature but it was found that the density of twins was significantly lower in pure copper compared with the Cu-Zn alloys [START_REF] Zhao | Influence of stacking fault energy on nanostructure formation under high pressure torsion[END_REF]. Therefore, it is reasonable to conclude that twins are found only occasionally after the SPD processing of copper-based alloys [START_REF] An | Significance of stacking fault energy in bulk nanostructured materials: Insights from Cu and its binary alloys as model systems[END_REF].

Twinning may lead to the formation of new orientations since it causes re-orientations of the parent grains. However, the evolution of texture in the Cu-2.5Ni-0.6Si alloy was stable and no new orientations were detected with increasing numbers of HPT turns, thereby indicating the occurrence of twinning only in the very early stage of HPT processing through ½ turn. In practice, the continuous texture transformation observed for the HPT-processed Fe-36Ni alloy indicates that twinning is not the only responsible mechanism for texture modification since twining is usually hardly activated during room temperature deformation of Fe-36Ni because of the relatively high γSFE. It was suggested earlier that dislocation generation may be hindered by grain boundaries that produce changes in the slip activity due to anisotropic hardening and hence texture modification [START_REF] Beyerlein | Texture evolution in equal-channel angular extrusion[END_REF]. The formation of all shear components in Cu-2.5Ni-0.6Si immediately after N = ½ turn retains the texture upon increasing numbers of HPT turns leading to a repetition of the deformation path. By contrast, texture stabilization was not evident in Fe-36Ni where the shear components gradually developed with increasing numbers of HPT turns and became relatively stable after 10 turns since all shear components developed during HPT processing for N = 5 turns.

It should be noted that the initial texture may also influence the difference in the texture evolution for both alloys especially in the early stage of deformation through N = ½ and 1 turn. Figure 2 shows that the initial textures of the alloys were different and, in order to examine the effect of the initial texture, a visco-plastic self-consistent (VPSC) model was used to simulate the deformed texture after torsional deformation. Details of the VPSC theory, the general formulation and the relevant algorithms are given elsewhere [START_REF] Tome | The relation between macroscopic and microscopic strain hardening in F.C.C. polycrystals[END_REF][START_REF] Molinari | A self consistent approach of the large deformation polycrystal viscoplasticity[END_REF].

In the present study, an equivalent strain of εeq = 5.52 at a mid-radius of 2.5 mm in the disk sample after HPT for N = ½ turn was simulated by imposing successive deformation increments under a velocity gradient tensor as follows:

𝛾̇= [ 0 0 1 0 0 0 0 0 0 ] (4)
The equivalent stain introduced by HPT processing for N = ½ turn was calculated using the conventional relationship for |HPT processing [START_REF] Valiev | Structure and deformaton behaviour of Armco iron subjected to severe plastic deformation[END_REF]:

𝜀 𝑒𝑞 = 2𝜋𝑁𝑟 ℎ√3 (5)
where r is the radial distance from the centre of the disk and h is the disk thickness equal to 0.85 mm.

The simulated texture is presented in Figure 6 for the initial texture (upper) and the deformed texture after N = ½ turn (lower) for the Cu-2.5Ni-0.6Si (on left) and Fe-36Ni (on right) alloys, respectively. For comparison purposes, the textures measured in the experiments as shown in Figures 3 and4 for N = ½ turn are also given (middle). The starting texture used in the simulation was represented by 1000 orientations obtained from the initial textures of the alloys shown in Figure 2. It was assumed that the plastic deformation was accommodated by {111}<110> slip systems with constant critical resolved shear stress. Inspection shows that the VPSC model provides a reasonably good representation of the main features of the experimental texture for both alloys after HPT processing for 1/2 turn and this demonstrates that the initial texture is responsible for the differences in the textures developed through HPT processing between the Cu-2.5Ni-0.6Si and Fe-36Ni alloys.

In practice, the presently studied alloys fail to exhibit a stored energy evolution that follows any systematic hierarchy depending on the texture components as found earlier in the rolling textures of an ARB-processed Fe-36Ni alloy [START_REF] Azzeddine | On the stored energy evolution after accumulative roll-bonding of invar alloy[END_REF]. As shown in Figure 5, all shear components in both alloys stored similar densities of dislocations at any numbers of HPT turns. This may be due to the very large strain introduced by HPT processing that activates all populations of the {111}<110> slip systems in all deformed grains having various orientations. However, in practice the values of the stored energy in the Cu-2.5Ni-0.6Si alloy are higher than in the Fe-36Ni alloy for all shear texture components and this indicates that Cu-2.5Ni-0.6Si contains a higher dislocation density than Fe-36Ni. This is expected since the SPD processing of alloys with low γSFE produces a high degree of dislocation dissociation that subsequently hinders their annihilation and consequently leads to very large dislocation densities [START_REF] Hegedűs | Microstructure of low stacking fault energy silver processed by different routes of severe plastic deformation[END_REF]. In addition, the stored energy in all shear components continuously decreases with increasing numbers of HPT turns for the Fe-36Ni alloy whereas the reduction starts only after 5 turns for the Cu-2.5Ni-0.6Si alloy. This indicates that the rate of dislocation annihilation in the Cu-2.5Ni-0.6Si alloy is relatively low compared to the Fe-36Ni alloy.

The low value of the γSFE means that the recombination and cross-slip of dissociated dislocations is difficult, thereby delaying the recovery and dynamic recrystallization processes [START_REF] Zhao | Influence of stacking fault energy on nanostructure formation under high pressure torsion[END_REF]. This is in good agreement with the evolution of the DRX fraction shown in Figures 3 and4 where the fraction of DRX was relatively high in the Fe-36Ni alloy compared to the Cu-2.5Ni-0.6Si alloy, especially after N = 5 and 10 turns. Thus, the recovery and DRX processes take place after N = 5 turns (εeq = 53.3) for the Cu-2.5Ni-0.6Si alloy but this occurs as early as after N = 1 turn (εeq = 10.6) for the Fe-36Ni alloy.

The rapid softening observed in the Fe-36Ni alloy is explained by the grain refinement mechanism in alloys with high γSFE. During the initial stage of HPT processing, the dislocation density increases and the dislocations accumulate to form dislocation cells and/or low-angle grain boundaries (LAGBs) and then they gradually transform to high-angle grain boundaries (HAGBs) through dislocation rearrangement with increasing numbers of HPT turns. This is in good agreement with the microstructural evolution presented in Figures 3 and4 where the fraction of DRX in both alloys increases with increasing numbers of HPT turns.

By contrast, the Cu-2.5Ni-0.6Si alloy shows a general strain hardening behavior and the slow annihilation of dislocations during deformation processing produces a smaller grain size as reported for low γSFE alloys [START_REF] Zhao | Influence of stacking fault energy on nanostructure formation under high pressure torsion[END_REF]. It should be noted that a smaller grain size was reported in Cu-2.5Ni-0.6Si (~0.2 μm after N = 10 turns) [START_REF] Khereddine | Microstructures and textures of a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF] compared with Fe-36Ni (~0.37 μm after N = 10 turns) [START_REF] Tirsatine | An EBSD analysis of Fe-36%Ni alloy processed by HPT at ambient and a warm temperature[END_REF]. It is worth noting also that such softening behavior, due to the advent of rapid microstructural recovery, was first reported in an HPT-processed high purity Al with high γSFE [START_REF] Xu | The evolution of homogeneity in processing by highpressure torsion[END_REF] while most metals and alloys including Cu alloys [START_REF] Jiang | Microstructural evolution, microhardness and thermal stability of HPT-processed Cu[END_REF][START_REF] Tian | Microstructural evolution and mechanical properties of a two-phase Cu-Ag alloy processed by high-pressure torsion to ultrahigh strains[END_REF] demonstrate a hardness model of strain hardening without microstructural recovery with increasing numbers of HPT turns. These separate hardness models were more recently summarized and categorized for a variety of metals and alloys processed by HPT [START_REF] Kawasaki | Different models of hardness evolution in ultrafine-grained materials processed by high-pressure torsion[END_REF].

The grain refinement mechanism is often accompanied by a variation in grain boundary misorientation. Accordingly, Table 3 summarizes the evolution of the fraction of sub-grain boundaries (2-5°), LAGBs (5-15°) and HAGBs (>15°) in the shear components for the Cu-2.5Ni-0.6Si and Fe-36Ni alloys after HPT processing at N = 10 turns. A detailed inspection shows that all shear components contain high fractions of sub-grain boundaries ranging from ~69-75% for both alloys after 10 turns. It is expected that the new fine grains will further deform and accumulate dislocations due to the continuous HPT processing.

However, both alloys show a difference in the fractions of LAGBs and HAGBs. Specifically, the shear components of the Cu-2.5Ni-0.6Si alloy contain high fractions of LAGBs of ~23-26% while the shear components of the Fe-36Ni alloy exhibit higher fractions of HAGBs of ~13-18% compared with ~2.6-4.6% of HAGBs in the Cu-2.5Ni-0.6Si alloy. This confirms the rapid formation of new fine grains with HAGBs in the Fe-36Ni alloy while the LAGBs require longer times for transformation to HAGBs in the Cu-2.5Ni-0.6Si alloy.

Summary and conclusions

 The correlation between the stored energy and the shear texture components of Cu-2.5Ni-0.6Si and Fe-36Ni alloys was investigated after HPT processing up to 10 turns at ambient temperature using the KAM approach.

 A typical stable shear texture developed for the Cu-2.5Ni-0.6Si alloy after 1 turn while a continuous transformation of the texture was observed in the Fe-36Ni alloy up to 10 turns. The texture difference between these two alloys is associated with differences in the γSFE and in the initial textures.

 HPT processing produced approximately the same amount of stored energy in the different shear texture components (~35 J/mol) for the Cu-2.5Ni-0.6Si alloy and lower values (~24 J/mol) for the Fe-36Ni alloy. There was no apparent hierarchy between these components.

 The stored energy in all shear components for the Cu-2.5Ni-0.6Si alloy increased with increasing processing to N = 1 turn and then slightly decreased up to N = 10 turns whereas the stored energy of the Fe-36Ni alloy continuously decreased with increasing numbers of HPT turns. These differences are related to the grain refinement mechanism during HPT processing. Table 3. Evolution of fraction (as a percentage) of different grain boundary misorientations in the shear components for Cu-2.5Ni-0.6Si and Fe-36Ni alloys after HPT processing for N = 10 turns.

Figure caption

Table 1 .Figure 5

 15 Figure5as a function of the numbers of HPT turns for (a) Cu-2.5Ni-0.6Si and (b) Fe-36Ni alloys. In addition, the values of the dislocation density calculated from the KAM approach and used to estimate the stored energy and summarized in Table2. After N = ½ turn, the 𝐴 1 *

Figure 1 :

 1 Figure 1: Illustration of axis system of the processed disc for the EBSD measurement. SD, RD and CD correspond to the shear, rotation and compression directions, respectively.

Figure 2 :

 2 Figure 2: KAM maps and the recalculated {111} pole figure of the as-received: (a, c) Cu-2.5Ni-0.6Si and (b, d) Fe-36Ni alloys.

Figure 3 :

 3 Figure 3: KAM, GOS maps and the recalculated {111} pole figure of the HPT processed Cu-2.5Ni-0.6Si alloy after N = ½, 1, 5 and 10 turns.

Figure 4 :

 4 Figure 4: KAM, GOS maps and the recalculated {111} pole figure of the HPT processed Fe-36Ni alloy after N = ½, 1, 5 and 10 turns.

Figure 5 :

 5 Figure 5: Evolution of the stored energy in the shear texture components as a function of number of HPT turns of the: (a) Cu-2.5Ni-0.6Si and (b) Fe-36Ni alloy.

Figure 6 :

 6 Figure 6: Experimental and VPSC simulated texture after HPT processing for N =1/2 turn showing the effect of the initial texture.

Figure 6

 6 Figure 6

Table 1 .

 1 The normalized KAM value of 1.3°/μm for Cu-2.5Ni-0.6Si is relatively higher than 0.8 °/μm for Fe-36Ni as shown in the upper regions of the KAM maps indicating high dislocation densities. Both alloys exhibit microstructures with equiaxed grains containing high fractions of twins (Σ3 60°<111>) as can be seen by the arrows. The mean grain sizes were determined

	without considering twins and the results gave ~20 μm for Cu-2.5Ni-0.6Si and ~10 μm for Fe-
	36Ni, respectively. The Copper, S and Brass components were equally present for the as-
	received Cu-2.5Ni-0.6Si alloy where it is a typical texture for rolled FCC alloys having
	medium values of γSFE. By contrast, a typical recrystallization texture with a dominant Cube
	component was observed for the as-received Fe-36Ni alloy while a weak Brass component is
	evident in the {111} pole figure for this alloy. The variations in the initial microstructures and
	textures between these two alloys is due to differences in their manufacturing processing
	histories.

Table 1 .

 1 Main ideal rolling and shear texture components of FCC alloys.

	Component	{hkl}<uvw>	Euler Angle
			1		2
	Brass	{110}<11 ̅ 2>	54.7°	90°	45°
	Cube	{001}<100>	0°	0°	0°
	Copper	{112}<111 ̅ >	270°	35°	45°
	S	{123}<634>	59°	36.7° 63.4°
	* A 1	{111}<1 ̅ 1 ̅ 2>	90° 54.74° 45°
	* A 2	{111}<12 ̅ 1>	30° 54.74° 45°

Table 2 .

 2 Evolution of the dislocation density in grains with different shear texture components as a function of number of HPT turns for Cu-2.5Ni-0.6Si and Fe-36Ni alloys.

				Dislocation density (×10 15 m 2 )
	Alloy	N	𝐴 1 *	𝐴 2 *	A	𝐴 ̅	B	𝐵 ̅	C
	Cu-2.5Ni-0.6Si ½ 3.35 3.03 3.11 3.14 3.27 3.16 3.11
		1 3.35 3.33 3.19 3.30 3.38 3.35 3.14
		5 3.22 3.11 3.22 3.30 3.16 3.16 3.08
		10 3.06 2.98 3.16 3.11 3.06 3.06 3.00
	Fe-36Ni	½ 1.91 1.76 1.91 1.91 1.84 1.90 1.88
		1 1.84 1.80 1.80 1.86 1.81 1.83 1.88
		5 1.33 1.42 1.40 1.34 1.49 1.49 1.45
		10 1.34 1.33 1.27 1.34 1.44 1.40 1.34
	For the Fe-36Ni alloy, the 𝐴 2

* component exhibits the lowest stored energy of ~22.6  0.7 mJ/mol compared to any other shear components after N = 1/2 turn. The stored energy of the 𝐴 2 * and C components was unchanged at ~22.5  1.2 mJ/mol and ~24.0  0.5 mJ/mol, respectively, after N = 1 turn while it decreased slightly for the remaining shear components.

Table 3 .

 3 Evolution of fraction (as a percentage) of different grain boundary misorientations in the shear components for Cu-2.5Ni-0.6Si and Fe-36Ni alloys after HPT processing for N = 10 turns.

		𝑨 𝟏 *	𝑨 𝟐 *	A	𝑨 ̅	B	𝑩 ̅	C
	Cu-2.5Ni-0.6Si
	2-5° (%)	71.0 69.0 71.2 73.9 71.2 74.0 72.7
	5-15°(%)	24.8 26.4 25.2 23 24.7 23.4 24.4
	>15°(%)	4.2 4.6 3.7 3.2 4.1 2.6 2.9
	Fe-36Ni
	2-5°(%)	69.9 75.3 72.1 74.8 63.8 63.8 68.6
	5-15°(%)	15.1 11.6 13.2 12.2 18.5 18.1 17.0
	>15°(%)	15.0 13.1 14.7 13.0 17.7 18.0 14.4

Table caption Table 1 .

 caption1 Main ideal rolling and shear texture components of FCC alloys.

Table 2 .

 2 Evolution of the dislocation density in grains with different shear texture components as a function of number of HPT turns for Cu-2.5Ni-0.6Si and Fe-36Ni alloys.

Acknowledgements

The authors wish to thank Mr. Hacen Hadj-Larbi from CLAL-FRANCE and Pierre-Louis REYDET from APERAM-alloys Imphy Society for kindly providing the Cu-2.5Ni-0.6Si and Fe-36%Ni alloys. This work was supported in part by the National Science Foundation of the United States under Grant No. DMR-1810343 (M.K.) and in part by the European Research Council under ERC Grant Agreement No. 267464-SPDMETALS (T.G.L.).


Anatoliy Zavdoveev
email: avzavdoveev@gmail.com

Thierry Baudin
email: thierry.baudin@universite-paris-saclay.fr

Elena Pashinska

Hyoung Seop Kim
email: hskim@postech.ac.kr

Francois Brisset

Mark Heaton
email: mark.heaton@antsltd.com

Valeriy Poznyakov

Massimo Rogante

Viktor Tkachenko

Ilya Klochkov

M Skoryk

Paton Electric

A A Galkin

G V Kurdyumov

Continuous Severe Plastic Deformation of Low-Carbon Steel: Physical-Mechanical Properties and Multi-Scale Structure Analysis

Keywords: continuous severe plastic deformation, drawing, low-carbon steel, structure, properties

published or not. The documents may come

L'archive ouverte

Introduction

Drawing is one of the most widespread methods of metal forming processes [START_REF] Wei | Microstructure and mechanical properties of cold drawn pearlitic steel wires: Effects of drawing-induced heating[END_REF][START_REF] Lee | Process design of multi-stage wet wire drawing for improving the drawing speed for 0.72 wt% C steel wire[END_REF][START_REF] Bargujer | Thermoprocessing and wire drawing behaviour of ultra high strength steel wires[END_REF], and welding wire is used in lots of construction and production processes. Thus, the technology of wire manufacturing is very important. Notably, partial reduction [START_REF] Zavdoveev | Drawing of the wire of low-carbon steel: plasticity resource, optimal reduction, structure, properties[END_REF] during wire drawing, in the mean of exhausting of plasticity resources, is essential. Good optimal reduction choice is a very important step in developing the effective manufacturing technology of drawing. When the plasticity resource is exhausted during the drawing process [START_REF] Zavdoveev | Drawing of the wire of low-carbon steel: plasticity resource, optimal reduction, structure, properties[END_REF], the wire starts breaking and the whole process is stopped. Then additional softening annealing is needed. The main aim of this procedure is to heal microvoids and eliminate strain hardening. However, this is a very expensive procedure. In addition, there is a need to enhance the performance characteristics of drawn steel for a minimum number of intermediate softening annealing steps [START_REF] Pashinska | Formation of structure and properties of low-carbon steel under rolling with shear and cold drawing[END_REF]. Severe plastic deformation (SPD) methods are able to solve these tasks.

Today, SPD enables the obtaining ultrafine-grained (UFG) structure in almost any material [START_REF] Rosochowski | Severe Plastic Deformation Technology[END_REF][START_REF] Vinogradov | Mechanical Properties of Ultrafine-Grained Metals: New Challenges and Perspectives[END_REF][START_REF] Lee | Single-roll angular-rolling: A new continuous severe plastic deformation process for metal sheets[END_REF][START_REF] Kim | Plastic deformation behaviour of fine-grained materials[END_REF]. These materials possess unique and complex mechanical properties, such as a combination of high strength and plasticity [START_REF] Vinogradov | Mechanical Properties of Ultrafine-Grained Metals: New Challenges and Perspectives[END_REF][START_REF] Song | Mechanical properties of an ultrafine grained C-Mn steel processed by warm deformation and annealing[END_REF][START_REF] Song | Overview of processing, microstructure and mechanical properties of ultrafine grained bcc steels[END_REF]. The main features of the SPD [START_REF] Estrin | Extreme grain refinement by severe plastic deformation: A wealth of challenging science[END_REF] is an accumulation of a high degree of strain. This is possible, due to the shape of the billet that remains unchanged from pass to pass (i.e., Brigman anvils, equal channel angular pressing, twist extrusion). During these metal forming processes, the dominant deformation scheme is simple shear. This peculiarity of SPD methods was at the basis of the continuous process design [START_REF] Pashinska | Formation of structure and properties of low-carbon under rolling with shear and cold drawing[END_REF]. While manufacturing wire with SPD methods, one of the limitations is that it occurs in a continuous drawing scheme. A typical volume of manufacturing is calculated in terms of tens of thousands of kilometers and in tons.

Therefore, when incorporating SPD into the drawing process, special dies should be used without decreasing the process efficiency.

There is much research aimed at SPD methods of application in drawing [START_REF] Kireev | Influence of final alternating flexure on the mechanical properties of cold-drawn reinforcement[END_REF][START_REF] Raab | Tailoring the gradient ultrafine-grained structure in low-carbon steel during drawing with shear[END_REF][START_REF] Muszka | The effects of deformation and microstructure inhomogeneities in the Accumulative Angular Drawing (AAD)[END_REF][START_REF] Hwang | The effect of microstructure and texture evolution on mechanical properties of low-carbon steel processed by the continuous hybrid process[END_REF][START_REF] Lee | The effect of the multi-pass non-circular drawing sequence on mechanical properties and microstructure evolution of low-carbon steel[END_REF].

The simplest in terms of implementation is the method described in [START_REF] Kireev | Influence of final alternating flexure on the mechanical properties of cold-drawn reinforcement[END_REF]. Authors consider the use of reverse bending on cold drawn fittings without additional heating. The main advantages of this method are its continuity and its ability to be used to produce long products with enhanced mechanical properties. Another SPD method for producing long products combined with drawing is described in [START_REF] Raab | Tailoring the gradient ultrafine-grained structure in low-carbon steel during drawing with shear[END_REF]. Its main advantage is the continuity Accepted Article technology of wire manufacturing is very important. Notably, partial reduction Accepted Article technology of wire manufacturing is very important. Notably, partial reduction wire drawing, in the Accepted Article wire drawing, in the reduction choice is a very important step in developing the effective manufactur Accepted Article reduction choice is a very important step in developing the effective manufactur technology of drawing. When the plasticity resource is exhausted during Accepted Article technology of drawing. When the plasticity resource is exhausted during [START_REF] Zavdoveev | Drawing of the wire of low-carbon steel: plasticity resource, optimal reduction, structure, properties[END_REF] Accepted Article [START_REF] Zavdoveev | Drawing of the wire of low-carbon steel: plasticity resource, optimal reduction, structure, properties[END_REF], the wire star Accepted Article , the wire star softening annealing is needed. The main aim of this procedure is to heal microvoids and Accepted Article softening annealing is needed. The main aim of this procedure is to heal microvoids and eliminate strain hardening. However, this is a very expensive procedure. In addition, there Accepted Article eliminate strain hardening. However, this is a very expensive procedure. In addition, there Accepted Article methods are able to solve these tasks.

Today, SPD enables the obtaining ultrafine This article is protected by copyright. All rights reserved of the process and the possibility to apply it for drawing mass production. The disadvantage of this method is the process complexity during drawing as it uses a complex technical assembly, which needs to be dismantled and reassembled when changing the dies. In Ref. [START_REF] Muszka | The effects of deformation and microstructure inhomogeneities in the Accumulative Angular Drawing (AAD)[END_REF], it is shown that the most effective SPD technique is to bend the wire during the drawing. This can be achieved, for example, by changing the location of dies relative to the drawing axis. The main disadvantages of such to this scheme are low speed (0.05 m/s), the difficulty of filling wire into the die before each new drawing, and the complex system of the die unit, which can significantly reduce the drawing efficiency if it breaks. These methods show that the change of metal flow is relative to the axis during drawing and leads to positive effects on the structure and properties. However, some of them showed conflicting information about the change in the mechanical properties of obtained wire [START_REF] Kireev | Influence of final alternating flexure on the mechanical properties of cold-drawn reinforcement[END_REF].

It is of great importance to consider the factors that affect the efficiency of drawing while developing a technology based on the SPD process (continuous SPD). These include the speed of wire passage through the die, the required number of passes, and the manner of dies combination. Optimization of these parameters will allow creating a steel wire drawing technology with a particular required efficiency and manufacturability.

Significant improvements in efficiency could be reached with the elimination of intermediate annealing. For this, the enhanced plasticity resource (PR) is needed.

Measuring damage to the physical density includes a lot of constituents. These features should be studied from microstructure to properties at each stage. Thus, the purposes of this article are 1) to study the effect of drawing with shear both on the microstructure and on the mechanical properties, of low-carbon steel with various combinations of standard round dies and dies with shear and 2) to create a new technology of drawing with the shear of low-carbon wire, which will eliminate intermediate annealing.

Methodology

The studied material is a commercial low-carbon steel (0.08 C, 1.87 Mn, 0.82 Si, 0.02 S, 0.022 P wt% -grade G3Si1, most widespread welding wire).

Deformation scheme

The drawing with shear (DSh) was carried out by using a specially designed set of dies which promoted the "twist" character of the material flow. A schematic sketch of the twist die channel is shown in Figure 1. To estimate the equivalent true strain during drawing with shear, a simplified relation in the form of the equation below was used as in [START_REF] Pashinskaya | Effect of drawing with shear on structure and properties of low-carbon steel[END_REF]:

Accepted Article where d 0 and d are the wire diameters before and after drawing, respectively, and tan() is the tangent of the angle of the twist line slope (25 or 0.44 rad), as defined in Figure 1 a. In this equation, the first term is the normal drawing strain and the second represents the "twist" component of strain [START_REF] Orlov | Comparative Analysis of Plastic Flow and Grain Refinement in Pure Aluminium Subjected to Simple Shear-Based Severe Plastic Deformation Processing[END_REF]. Based on the above equation, the material underwent  0.25 of "twist" strain in each drawing pass. However, it should be emphasized that these To show the effect of such die geometry finite element method simulations of deformation during DSh were conducted with the aid of Deform-3D software permitting three-dimensional analysis. Design model of DSh die is shown in Figure 1. The die was modeled with rigid elements, while 50,000 tetrahedral elements were employed for the samples and the adaptive meshing was used to accommodate large strains during simulations [START_REF] Markov | Development of forging processes using intermediate workpiece profiling before drawing: research into strained state[END_REF][START_REF] Perig | Effects of material rheology and die walls translational motions on the dynamics of viscous flow during equal channel angular extrusion through a segal 2θ-Die: CFD 2D solution of a curl transfer equation[END_REF]. Friction between the samples and the matrix walls was expressed according to the Zibel's law [START_REF] Kulagin | Modelling of High Pressure Torsion using FEM[END_REF]: τ = μ·σ y , where σ y -yield stress, μfriction coefficient (μ = 0.1). Equivalent strain distribution for a cross-section for drawing and DSh die is shown in Figure 1. d and e, respectively. The isostrain contours form closed loops around the Centre of the cross-section.

Optimal reduction for drawing

Considering the problem of choosing optimal reduction, we should take into account that during plastic deformation, all kinds of damage occur and accumulate in the material.

Damaging is a quantitative measure of the microfracture of material during deformation.

The latter immediately precedes macro-destruction. In accordance with the principle of macroscopic definability, it is believed that the value of damage is uniquely determined by the loading process and is presented as a certain function from this process. The criterion of macroscopic destruction is written as a condition when a measure of damage reaches a critical value.

It is accepted that the increment of damage is proportional to the increment of the degree of shear strain  d [START_REF] Zavdoveev | Drawing of the wire of low-carbon steel: plasticity resource, optimal reduction, structure, properties[END_REF] :

𝑑𝜀 = 𝛼 * 𝑑𝛬 , (2.2.1)
where  is a proportionality factor determining the intensity of accumulation and development of microcracks.

Moreover, it is assumed [START_REF] Zavdoveev | Drawing of the wire of low-carbon steel: plasticity resource, optimal reduction, structure, properties[END_REF] that the formation of a macroscopic crack occurs when the damage reaches a critical value   кр . The degree of shear deformation that the representative volume of the metal has undergone by the time it reaches the ultimate damage is called ductility and denote  р . Assuming that the  parameter is constant for a Accepted Article samples and the adaptive meshing was used to accommodate large strains during Accepted Article samples and the adaptive meshing was used to accommodate large strains during simulations Accepted Article simulations [START_REF] Markov | Development of forging processes using intermediate workpiece profiling before drawing: research into strained state[END_REF][START_REF] Perig | Effects of material rheology and die walls translational motions on the dynamics of viscous flow during equal channel angular extrusion through a segal 2θ-Die: CFD 2D solution of a curl transfer equation[END_REF] Accepted Article [START_REF] Markov | Development of forging processes using intermediate workpiece profiling before drawing: research into strained state[END_REF][START_REF] Perig | Effects of material rheology and die walls translational motions on the dynamics of viscous flow during equal channel angular extrusion through a segal 2θ-Die: CFD 2D solution of a curl transfer equation[END_REF]. Friction between the samples and the matrix walls was expressed Accepted Article

. Friction between the samples and the matrix walls was expressed according to the Zibel's law Then, the condition of deformation without fracture becomes:

1 0     t p Hdt  , (2.2.4)
with the condition of destruction:

1 0     t p Hdt  . (2.2.5)
The results of the study of plasticity under proportional loading with sufficient accuracy for practice can be represented by parametric dependences reflecting the relationship of the ultimate degree of shear strain  р with stress indicator  T ( is the hydrostatic stress and  the tensile stress intensity).

The most important application of the theory of deformability is not the prediction of the fracture moment according to criterion (2.2.5), but the assessment of metal damage by determining the value  . This allows us to predict the quality indicators of workpieces and products associated with damage, and to correctly set up the modes of recovery annealing. To this end, the theory of deformability has developed ideas about the effect of annealing on the value of exhaustion of the plasticity resource [START_REF] Kolmogorov | Model of metal fracture in cold deformation and restoration by annealing[END_REF].

Accepted Article

The most important application of the theory of deformability is not the prediction of Accepted Article which there is a sharp decrease in the recovery of plasticity resource. When   is reached untreated micropores begin to appear, then after    (0.5-0.7) [4] untreated microcracks appear.

The simplest version of the deformability theory for calculating the exhaustion of the plasticity resource is the drawing of steel wire. The dependence approximating the experimental curve is:

) 11 . 1 exp( T p     (2.2.7)
Were "-1.11" is experimental constant, and when drawing, indicator T  varies along the deformation zone and is a first approximation, it can be expressed by the following equation:

15 . 1 ln ) 1 ( 73 . 1 0      f f ctg m T   (2.2.8)
where m is the friction coefficient,  the half-angle of the die cone, f 0 the wire area before drawing, and f is the current sectional area of the deformation zone.

Equation (2.2.8) shows that value

T  during drawing is changed along deformation zone from   15 . 1 0   T  at the entrance ( 0 f f  ), to   15 . 1 ln ) 1 ( 73 . 1 1 0 1      f f ctg m T   at the exit from the deformation zone ( 1 f f  , where 1
f is the sectional area of the wire after drawing).

The magnitude of the increment of shear deformation during drawing in a first approximation can be specified by the following relation: Accepted Article drawing). This article is protected by copyright. All rights reserved Substituting relations (2.2.7) -(2.2.9) into expression (2.2.3), the following expression is obtained for the value of the exhaustion of the plasticity resource when passing through the draw:

f df d    (2.2.9)
Accepted Article   Accepted Article  1 Accepted Article 1 0 Accepted Article 0  0  Accepted Article  0   Accepted Article   Accepted Article  T Accepted Article T  Accepted Article     Accepted Article    Accepted Article
    ctg m ctg m       1 1 252 . 0 ) 1 ( 92 . 1 , ( 2
    1
1 , the exhaustion of plasticity resource can be calculated with the next formula:

    ctg m ctg m                1 1 1 1 252 . 0 ) 1 ( 92 . 1 (2.2.11)
This equation (2.2.11) can also be used to determine the exhaustion of the plasticity resource in multi-pass drawing.

Using this formula, one can estimate the value of single area reduction, after which it is still possible to restore the damaged metal structure by annealing, and it becomes possible to prescribe annealing rationally. The simple model we developed allows us to study the effect of deformation fractionality on the depletion of the plasticity resource.

Suppose you need to get some total reduction   in two passes. The dependence of the total exhaustion of the plasticity resource   is independence from partial reduction. The value   is estimated by the formula valid for monotonic deformation:

2 1       (2.2.12)
where 1  and 2  are the exhaustion of the plasticity resource for the first and second transitions, respectively. It is easy to show that:

1 1 1 2         (2.2.13)
where 1

 and 2  are the reductions for the first and second pass, respectively.

Accepted Article

where Accepted Article where Accepted Article Figure 2 shows that redistributing the strain along the transitions can significantly reduce the value of exhaustion of the plasticity resource. Based on the results in (Figure 2) and eq. 2.2.13., at   = 0.4 the most preferred reduction redistribution is: 1  = 0.23 and 2  = 0.22 (according to eq. 2.2.13). In this case, almost all the damage accumulated by the metal can be healed by means of regenerative annealing (

1 Accepted Article 1 0 Accepted Article 0 f Accepted Article f 1 f 1 Accepted Article 1 f 1 f Accepted Article f 0 f 0 Accepted Article 0 f 0  Accepted Article   Accepted Article
      35 . 0
), while with a single reduction of 40% this cannot be done (

      52 . 0 = 0..35).
Thus, during the first reduction, it is more grounded to use 23% of area reduction in the case of conventional drawing. Based on these results, the following scheme of the experiment was chosen (Figure 3). The 1 st step is drawing from the round die (5.57mm) to shear die (23% area reduction), while the 2 nd step was subdivided into 3 different substeps of classical drawing after shear drawing: idrawing die to 9.3% reduction iidrawing die to 16.6% reduction iii-drawing die to 23.2% reduction Accepted Article Fig.

Accepted Article

Physical-mechanical properties

The mechanical properties, namely the ultimate tensile strength (UTS) and plasticity (, for the investigated steels were determined from the static tensile test (3 for each measurement) at ambient temperature. To characterize the metal's structural imperfection, the material density, that is a physical property of the material was measured by hydrostatic weighing using the weighing scales AX-200 by Shimadzu. 10 mm-long samples of each diameter were measured six times each. The relative error using this method is 0.003g/cm 3 . Such accuracy allows us to detect micro-imperfections. The maximum change in density, by increasing dislocation and vacancy densities is 0.1% (0.007g/cm 3 ) [START_REF] Pashinska | Formation of structure and properties of low-carbon under rolling with shear and cold drawing[END_REF]. To establish the effect of drawing strain on material strength a Vickers microhardness test was done by applying a load of 200g for 10s. At least 10 measurements were made to obtain an average value.

Residual stress estimation with SANS

The assessment of the residual stress (RS) state is fundamental to adequately improve knowledge of the effect of intense plastic deformation on metal. Despite the significant amount of data available concerning the constitutive steels of wires, such as those relating to resistance and plasticity, further investigations at an advanced level are necessary for deeper knowledge. Accepted Article [START_REF] Pashinska | Formation of structure and properties of low-carbon under rolling with shear and cold drawing[END_REF] Accepted Article [START_REF] Pashinska | Formation of structure and properties of low-carbon under rolling with shear and cold drawing[END_REF]. To establish the effect of drawing strain on material strength a Vickers Accepted Article

. To establish the effect of drawing strain on material strength a Vickers

Accepted Article

Residual stress estimation with

The assessment of the residual stress (RS) state is fundamental to adequately improve

Accepted Article

The assessment of the residual stress (RS) state is fundamental to adequately improve This article is protected by copyright. All rights reserved appropriate in-depth investigation aimed at their improvement is essential [START_REF] Rogante | Caratterizzazione avanzata di fili d'acciaio mediante tecniche neutroniche[END_REF][START_REF] Rogante | Residual stress determination by neutron diffraction in low-carbon steel wires with accumulated shear deformation[END_REF]. TKSN-400 facility of CANAM NPL infrastructure was used by the Rogante Engineering Office (REO) to analyze the considered wire samples, carrying out RS measurement by neutron diffraction (ND) [START_REF] Rogante | Residual stress determination by neutron diffraction in lowcarbon steel wires with accumulated shear deformation[END_REF]. The samples were positioned for measurement of the axial and radial components of the strain. Due to the size of the samples, the measurement was carried out only in the center of the wires. The peak positions and their widths were determined by fitting a Gaussian curve to the measured (310) peak of each sample. From the 2θ peak positions, the strains were calculated by using Eq. 2.4.1:

𝜀 ��� = � ��� �� �,��� � �,��� = ∆� ��� � �,��� = -𝑐𝑜𝑡𝜃 ��� ∆𝜃 ��� (2.4.1)
obtained by differentiating d in Eq. 2.4.2 (Bragg law) with respect to θ:

2𝑑𝑠𝑖𝑛𝜃 = 𝜆 (2.4.2)
RS was evaluated from the measured strains by using Eq. 2.4.3.

𝜎 � = � � (����)(���) [(1 -𝜈)𝐸 � + 𝜈(𝐸 � + 𝐸 � )] (2.4.3)
For stress calculation from the measured strains, it was supposed that in the wire's center the hoop strain is equal to the radial strain. Using this assumption, the radial and axial stresses were calculated using the procedure described in [START_REF] Hutchings | Introduction to the Characterization of Residual Stress by Neutron Diffraction[END_REF].

Microstructural observations

Microstructural observations were performed using optical microscopy and electron backscatter diffraction (EBSD). As regards to optical microscopy, specimens were mechanically polished following convention (SiC and diamond) and finally chemically etched with a 4% Nital solution. The quantitative estimation of the grain size and its fragments was made in both transversal and longitudinal directions and 100 measurements were made on every micrograph.

For EBSD, the final surface was prepared by electro-polishing in a 65% orthophosphoric acid + 15% sulphuric acid + 6% chromic anhydride + 14% water solution Accepted Article evaluated from the measured strains by using Eq. 2.4.3.

𝜎

Accepted Article

𝜎 � Accepted Article � 𝜎 � 𝜎

Accepted Article

𝜎 � 𝜎

For stress calculation from the measured strains, it was supposed that in the wire's center

Accepted Article

For stress calculation from the measured strains, it was supposed that in the wire's center the hoop strain is equal to the radial strain. Using this assumption, the radial and axial

Accepted Article

the hoop strain is equal to the radial strain. Using this assumption, the radial and axial stresses were calculated using the procedure described in Accepted Article stresses were calculated using the procedure described in

Microstructural observations

Accepted Article

Microstructural observations

Microstructural observations were performed using optical microscopy and electron

Accepted Article

Microstructural observations were performed using optical microscopy and electron backscatter diffraction (EBSD). As regards to optical microscopy, specimens were

Accepted Article

current density 1 А/cm This article is protected by copyright. All rights reserved dilation/one step and Grain CI standardization). In addition, all points with a confidence index (CI) lower than 0.1 were excluded from the analysis (where CI quantifies the reliability of the indexed pattern). Moreover, to eliminate spurious boundaries caused by orientation noise, a lower-limit boundary-misorientation cut-off of 2 o was used. Finally, a 15 criterion was chosen to differentiate low-angle boundaries (LABs) and high-angle boundaries (HABs).

X-Ray thin structure characterization

To analyze the atomic structures of long-range and mesoscopic orders, diffraction graphs of the samples were captured using the Cr-Kα-emission. A V-filtering photographic technique, sensitive to diffusive coherent and incoherent scattering of X-ray beams, was used. This allows analyzing details of structural changes on the atomic order when working with SPD metals [START_REF] Samoilenko | Multiscale structural changes of atomic order in severely deformed industrial aluminum[END_REF].

Results and discussion

Physical-mechanical properties of low-carbon steel after drawing with

shear.

The first step in the development of continuous severe plastic deformation (CSPD)

technique, was the implementation of shear die in the conventional drawing process. As was shown above, the first area reduction was chosen equal to 23%. Such partial reduction provides less accumulation of damage. The present study has shown that at this reduction of die with shear, the strength of wire (UTS) increases from 1210 (initial state) to 1280 MPa (Figure 4). In other words, the die with shear at high reduction degree (23%) results in less strain hardening of the wire, compared to conventional drawing. This is unusual, because often the increase in the reduction degree (compression) must lead to a greater increase in strength [START_REF] Mayo | On the characterization procedure to quantify the contribution of microstructure on mechanical properties in intercritically deformed low carbon HSLA steels[END_REF].

Results

Accepted Article

Results and discussion

Accepted Article Furthermore, the plastic properties are increasing in-line with the increase of reduction degree. This is a phenomenon which is not typical in traditional drawing. Indeed, ductility  increases significantly with increasing the reduction degree of shear die (Figure 4). This is beneficial for the development of continuous SPD technology, because ductility is the most important item of the manufacturability.

With the aim to demonstrate the behavior of the low-carbon steel properties data for conventional drawing (Figure 4) is shown. Here in conventional drawing the traditional curve evolution of UTS (increase) and density (decrease) is observed and the total EPR is equal to 2.92 if the area reduction at one time is equal to 62.4%. However, using partial reduction with 4 passes it is only accumulated 0.749 total EPR.

Next to shear die, the conventional round die is applied. And here with the purpose of showing an effect of partial area reduction, a set of round dies was used (Figure 3). In this case, a set of the EPR measurements varies from 0.43 (9.3% area reduction on the 2 nd pass) to 0.35 (23.2% area reduction on the 2 nd pass). It is evidential that based on section 2.2, calculating for the last case is preferable from the point of damage accumulation. The further behavior of the mechanical properties while drawing with shear is shown in Figure

Accepted Article

Furthermore, the plastic properties are increasing in degree. This is a phenomenon which is not typical in traditional drawing. Indeed, ductility Accepted Article degree. This is a phenomenon which is not typical in traditional drawing. Indeed, ductility increases significantly with increasing the reduction degree of shear die (Fig

Accepted Article

Next to shear die, the conventional round die is applied. And here with the purpose

Accepted Article

Next to shear die, the conventional round die is applied. And here with the purpose Accepted Article This article is protected by copyright. All rights reserved 5. As can be seen, with the increase of the reduction degree, the strength properties tend to decrease. Such behavior can be described with the Bauschinger effect and reversed Investigations on density measurements showed that while drawing through the die with shear, the density changes in the range of error limits (Figure 5b). In the subsequent reduction, with a round die of 9.3%, wire density increases compared to the density after drawing with shear. Further increase in the reduction when using round dies does not lead to the classical picture of the density decreasing with the increase in the partial reduction.

The wire density is also in the range of error limits. An exception is the change of the density after shear dies with a reduction degree of 23%. This means that changing the shear die to the round leads to the healing of the pores [START_REF] Zavdoveev | Small Angle Neutron Scattering study of nanoscale structure of low-carbon steel after rolling with shear followed by cold drawing[END_REF] by changing the direction of the metal flow. Healing pores improves damage measures and thus increases the plasticity resource. This phenomenon is an additional favorable factor for increasing technological plasticity while drawing with shear. Based on the data density and strength properties, it can be concluded that the combination of the dies with a reduction in 23% yields to the optimal combination of technological properties.

Accepted Article The microhardness behavior also has certain features as well as at first step of DSh and on the second step of conventional drawing (Figure 6). From the homogeneity point, the drawing with shear has less explicit anisotropy of microhardness (Figure 6a). The difference of microhardness between longitudinal and transversal sections is equal to 160

MPa (drawing with shear) versus 204 MPa (initial state). After the first "shear" stage at the cross-section of the wire, the shape of the microhardness distribution looks like a "boatshape" (Figure 6b). Further conventional drawing leads to flattening this profile. This is also unusual for a pure drawing scheme, as it is commonly known that "V" like distribution of microhardness is attributed to twisting/revolution deformation scheme [START_REF] Beygelzimer | Twist Extrusion as a Potent Tool for Obtaining Advanced Engineering Materials: A Review[END_REF]. The "boatshaped" microhardness distribution could an additional proof of the twist-like flow of the metal.

Effect of drawing with shear on residual stress in low-carbon steel wire

In some preliminary ND tests carried out, each wire sample was placed with its longitudinal axis in a vertical position, and a 2 mm wide slit and a hole having a diameter of 3 mm were used respectively for the incident and the diffracted beam [START_REF] Rogante | Residual stress determination by neutron diffraction in lowcarbon steel wires with accumulated shear deformation[END_REF]. Concerning the successive full ND measurements, figure 8 shows, e.g., the measured (310) peaks for the radial direction, related to two wire samples. This analysis qualitatively assessed the evolution of these imperfections with subsequent deformation steps. FWHM increases, as expected, with the intensity of deformation, as shown in Figure 7 e,f. The largest growth occurs during the shear deformation, and the subsequent drawing further gradually adds a number of imperfections (dislocations and/or amount of grain boundaries, due to the grain refinement). ND results have provided substantial data helping to evaluate the effect of shear deformation on RS of low-carbon steels, as well as additional support to complement the information already achieved by using the other characterization methodologies. Knowledge of the RS status can help developing a low-carbon wire drawing technology with needed manufacturability and efficiency, and can play a decisive role also in the debugging of material selection and engineering design requirements [START_REF] Rogante | Residual stress determination by neutron diffraction in lowcarbon steel wires with accumulated shear deformation[END_REF].

Effect of drawing with shear on microstructure of low-carbon steel wire

The changes in the grain structure under different schemes of deformation are observed in the wire cross-sections with optical microscopy. Figure 8 shows that when drawing with shear, the microstructure becomes finer: the ferrite grain size decreases and the pearlite colonies are 1.5 times smaller in size. This modification of the microstructure is normal as a large partial area reduction of the DSh must lead to grain refinement. The finest and the most uniform microstructure arises when the DSh is followed with a conventional drawing at 23% area reduction (Figure 8) and both grain refinement and large density of subboundaries are observed (Figure 9) by EBSD.

These previous observations are important proof for the following: DSh leads to an intensification in grain growth and then to the sequential grain refinement after the subsequent drawing. Peculiarities of such behavior during DSh with a decrease of strength and an increase in plasticity, is explained by the development of dynamic polygonization.

In this case, it yields grain growth due to grain boundary movement and annihilation of micro-voids. In addition, considering grain orientations, a predominance of directions <110> (// normal direction to the drawing plane) is clearly seen, as indicated by the EBSD orientation distribution maps (Figure 9).

Accepted Article

The amorphized fraction is in the form of a diffusive halo maximum at the base of the line

Accepted Article

The amorphized fraction is in the form of a diffusive halo maximum at the base of the line During shear deformation in metal, special structures are formed. Owing to "twist" character of the metal flow it becomes possible during further elongation deformation to change the deformation direction. This is very similar to Bauschinger's effect when the This article is protected by copyright. All rights reserved sign of the load was changed and when the metal flowed in the direction normal to the last deformation step. An additional observed effect of the application of shear deformation is deformation softening [START_REF] Kolmogorov | Model of metal fracture in cold deformation and restoration by annealing[END_REF][START_REF] Huang | Hardening by annealing and softening by deformation in nanostructured metals[END_REF]. Such behavior of metal gives the possibility to continue conventional drawing without any additional treatment. The density of metal influenced by Bauschinger's effect is also increased. This could be indirect evidence of micro voids healing and as a result, increasing plasticity resource. That opens the way to further accumulation of deformation without fracture.

Conclusion.

In this work, we demonstrate that the application of the SPD principles generates an effective effect on the low-carbon steel structure. The structural features were considered at several scales, using a wide range of methods. Combining shear deformation with the conventional scheme, the grain growth (reverse grain refinement) process is reached as well as the effect of dislocation annihilation. As a result, the plasticity is enhanced.

Residual stress also has a positive influence on manufacturability through the existence of compression stress after shear deformation. These peculiarities of the structure affect the behavior of both mechanical and physical properties (density). The application of the DSh technology leads to a softening effect as well as the healing of micro voids.

These positive effects give the opportunity to increase the effectiveness of drawing technology through controlling plasticity (ductility). It has been shown that in the case of a two-step deformation, there is a parabolic dependence of the EPR measure, and a minimum damage level is reached in a special combination of partial reductions. These results open the way to develop manufacturable continuous technology for steel wire drawing, in particular for welding purposes.

Highlights:

 Shear deformation incorporation into conventional drawing is the advantage.

Changing deformation direction in the drawing process gives an opportunity to obtain a higher level of manufacturability.

 For partial reduction in the case of two passes, the first one should be 23%, as that provides an optimum plasticity resource exhausting.

Accepted Article accumulation of deformation without fracture.

Accepted Article accumulation of deformation without fracture.

onclusion.

Accepted Article onclusion.

In this work, we demonstrate that the application of the SPD principles generates an

Accepted Article

In this work, we demonstrate that the application of the SPD principles generates an effective effect on the low Accepted Article effective effect on the low at several scales, using a wide range of methods. Combining shear deformation w Accepted Article at several scales, using a wide range of methods. Combining shear deformation w conventional scheme, the grain growth (reverse grain refinement) process is reached as Accepted Article conventional scheme, the grain growth (reverse grain refinement) process is reached as well as the effect of dislocation annihilation. As a result, the plasticity is enhanced.

Accepted Article

well as the effect of dislocation annihilation. As a result, the plasticity is enhanced.

Residual stress also has a positive influence on manufacturability throu

Accepted Article

Residual stress also has a positive influence on manufacturability throu compression stress after shear deformation. These peculiarities of the structure affect the

  is a need to e Accepted Article is a need to enhance the performance characteristics of drawn steel for a minimum Accepted Article nhance the performance characteristics of drawn steel for a minimum number of intermediate softening annealing steps Accepted Article number of intermediate softening annealing steps methods are able to solve these tasks.

( 0 .Fig. 1 .

 01 Fig.1. Schematic illustration of the shear dies channel (a) -sketch, (b, c) -3D model. Equivalent strain distribution (Finite Element Method (FEM) modeling) for a cross-section for drawing (d) and DSh (e)

  the wire diameters before and after drawing, respectively Accepted Article and d are the wire diameters before and after drawing, This article is protected by copyright. All rights reserved two strain components have completely different natures and thus Eq. (2.1.1) is oversimplified.

  This article is protected by copyright. All rights reserved circumstance leads to the fact that there are some critical values of   , above which the annealing efficiency changes. At    through annealing, it is possible to completely heal micro-discontinuities and restore the intact metal structure. At    only partial repair of the damage is possible. The value   depends on the metal deformability, its characteristic range of change is

  Passing to the single reduction  and taking into account that

  this formula, one can estimate the value of single Accepted Article Using this formula, one can estimate the value of single Accepted Article is still possible to restore the damaged metal structure by annealing Accepted Article is still possible to restore the damaged metal structure by annealing possible to prescribe annealing rationally. Accepted Article possible to prescribe annealing rationally. study the effect of deformation fractionality on the depletion of the plasticity resource. Accepted Article study the effect of deformation fractionality on the depletion of the plasticity resource. Suppose you need to get some total reduction Accepted Article Suppose you need to get some total reduction total exhaustion of the plasticity resource This article is protected by copyright. All rights reserved

Fig. 2 -

 2 Fig. 2 -Dependence of the total exhaustion of the plasticity resource (EPR) [4] on compression during the first pass (   =0.4, =8 0 , m=0.05), calculated by the formula (2.2.11).

-Fig. 3 -

 3 Fig. 2 Accepted Article 2 -Accepted Article -Dependence of the total exhaustion of the plasticity resource Accepted Article Dependence of the total exhaustion of the plasticity resource compression during the first pass ( Accepted Article compression during the first pass (

  microhardness test was done by applying a load of 200g for 10s. At least 10 Accepted Article microhardness test was done by applying a load of 200g for 10s. At least 10 measurements were made to obtain an average value Accepted Article measurements were made to obtain an average value Residual stress estimation with

[ 29 ]

 29 . The important electro-polishing parameters were: temperature 70-90 o C, anodic current density 1 А/cm 2 , voltage 23 V and exposure 19s.EBSD analysis was conducted using a Zeiss SUPRA 55 VP scanning-electron microscope (FEG-SEM) operating at 20 kV. The EBSD data acquisition and analysis were undertaken using the EDAX-TSL Orientation Imaging Microscopy, OIM TM software. The scanned areas were of 100 × 100 μm 2 with a 0.1 μm step size. To improve the readability of the EBSD data, maps were "cleaned" using standard clean-up options (Grain Accepted Article fitting a Gaussian curve to the measured (310) peak of each sample. From the Accepted Article fitting a Gaussian curve to the measured (310) peak of each sample. From the positions, the strains were calculated by using Eq. 2.4.1: Accepted Article positions, the strains were calculated by using Eq. 2.4.1: obtained by differentiating Accepted Article obtained by differentiating evaluated from the measured strains by using Eq. 2.4.3.

Fig. 4 -

 4 Fig. 4 -Mechanical properties of the wire at the initial state (1) and after a reduction of 23% during the transition from a circle (1) to a shear die (2): left scaleultimate tensile strength (UTS), right scaleductility 

  plastic properties are increasing in

Fig. 5

 5 Fig. 5 Diagrams of property changes in the wire at different degrees of reduction using die with shear (ø4.65 sh -shear die) and round dies: а -UTS; b -Density; 1-initial state, 2shear die, 3 -DSh+9.3% reduction, 4 -DSh+16.6% reduction, 5 -23.3% reduction

5 Accepted Article 5

 55 Diagrams of property changes in the wire at different degrees of reduction using Accepted Article Diagrams of property changes in the wire at different degrees of reduction using die with shear (ø4.measurements showed that while drawing through the die Accepted Article Investigations on density measurements showed that while drawing through the die with shearof 9.3%, wire density increases compared to the density after Accepted Article round die of 9.3%, wire density increases compared to the density after drawing with shear. Further increase Accepted Article drawing with shear. Further increase classical picture of the density decreasing with the increas Accepted Article classical picture of the density decreasing with the increas The wire density is also in the range of error limits. An exception is the change of the Accepted Article The wire density is also in the range of error limits. An exception is the change of the density after shear dies with a reduction degree of 23%. This means that chang Accepted Article density after shear dies with a reduction degree of 23%. This means that chang shear die to the round leads to the healing of the pores Accepted Article shear die to the round leads to the healing of the pores the metal flow. Healing pores improves damage measures and thus increases the Accepted Article the metal flow. Healing pores improves damage measures and thus increases the Accepted Article This article is protected by copyright. All rights reserved

Fig. 6

 6 Fig. 6 Microhardness distribution of studied samples: anisotropy of microhardness at shear drawing (a), distribution of microhardness in cross-section (b,c).

Figure 7 aFig. 7 .

 77 Fig Accepted Article igure Accepted Article ure 6Accepted Article 6b). Further conventional drawing leads to flattening this profile. This is Accepted Article b). Further conventional drawing leads to flattening this profile. This is also unusual for a pure drawing scheme, as it is commonly known that "V" like distribution Accepted Article also unusual for a pure drawing scheme, as it is commonly known that "V" like distribution of microhardness Accepted Article of microhardness is Accepted Article is shaped" microhardness distribution could be an additional proof of the twist Accepted Article shaped" microhardness distribution could be an additional proof of the twist Accepted ArticleFig.Accepted ArticleFig. 6 Accepted Article 6 Microhardness distribution of studied samples Accepted Article Microhardness distribution of studied samples at shear drawing (a), distribution of Accepted Article at shear drawing (a), distribution of

Fig. 8

 8 Fig. 8 Optical microstructure of the low-carbon steel wires a,cinitial; b,d -DSh 23%; e,h -DSh+conventional drawing 9.3%; f,I -DSh+conventional drawing 16.6%; j,g -DSh+conventional drawing 23.2%; a,b,e,f,jcross section; c,d,h,I,gtransverse section.

Fig 9 . 3 . 4 . 3 . 4 . 3 . 4 .-

 9343434 Fig 9. EBSD characterization of low-carbon steel wires, cross-section. orientation maps a,b,c,d,e,f,j,h; grain boundary misorientation -I,g,k,l,m,n,o,p; center -a,b,c,d,I,g,k,l; periphery -e,f,j,h,m,n,o,p; initial -a,e,I,m; DSh+conventional drawing 9.3% -b,f,g,n; DSh+conventional drawing 16.6% -c,j,k,o; DSh+conventional drawing 23.2% -d,h,l,p. IPF, crystallographic direction // DD (Drawing direction)

(

  211). The Debye line from the family of planes (211) is asymmetric, is split from the side Accepted Article (211). The Debye line from the family of planes (211) is asymmetric, is split from the side at the base (Fig diffusive halo band with the maximum corresponding to the angular position of the Accepted Article diffusive halo band with the maximum corresponding to the angular position of the maximum of the line (211) and pulled in by a decrea Accepted Article maximum of the line (211) and pulled in by a decrea flat apex indicates the formation of identical (200) type planes in this group, but with a wide Accepted Article flat apex indicates the formation of identical (200) type planes in this group, but with a wide set of interplanar spacings. Accepted Article set of interplanar spacings. The main changes in the diffraction graphs of the sample after DSh combined with Accepted Article The main changes in the diffraction graphs of the sample after DSh combined with conventional drawing 23.2% supplement the described effects for previous samples. Accepted Article conventional drawing 23.2% supplement the described effects for previous samples. the (211) and (200) Accepted Article the (211) and (200) of atomic order with a phase transition (PT) of the second kind of order Accepted Article of atomic order with a phase transition (PT) of the second kind of order which is clearly manifested in the form of generating the amorphous fraction in the Accepted Article which is clearly manifested in the form of generating the amorphous fraction in the polycrystalline main structure. This PT led to partial relaxation of elastic Accepted Article polycrystalline main structure. This PT led to partial relaxation of elastic Accepted Article deformed structure, which is confirmed by the weak intensity of Accepted Article deformed structure, which is confirmed by the weak intensity of diffusive coherent scattering Accepted Article diffusive coherent scattering phase over the background line (Fig Accepted Article phase over the background line (Fig It is revealed Accepted Article It is revealed that the effect of spatial delamination of crystallographic planes (211) Accepted Article that the effect of spatial delamination of crystallographic planes (211) has on cluster groups differing by a value of interplanar spacing in the range 1.156 < d Accepted Article has on cluster groups differing by a value of interplanar spacing in the range 1.156 < d 1.178 Å. The linear size of groups D = 100 Accepted Article 1.178 Å. The linear size of groups D = 100 the character of position of the generated groups relative to the Accepted Article 1000, and the character of position of the generated groups relative to the unstressed relaxed state (initial): d0 = 1.172 Å, D = 450 Å, and n = 396. Here, the Accepted Article unstressed relaxed state (initial): d0 = 1.172 Å, D = 450 Å, and n = 396. Here, the Accepted Article sion of the planes by the value of interplanar spacings was realized in samples Accepted Article sion of the planes by the value of interplanar spacings was realized in samples This article is protected by copyright. All rights reserved Calculating with X-Ray data, the dislocation density ( 𝜌 ���� = 𝜋 • ( � ��� �) � , were b -Burgers vector)[START_REF] Malykhin | An X-ray method of analysis of dislocation structure in HCP metals[END_REF] for hkl (211) after DSh is  disl =13.7*10 13 cm -2 and after conventional drawing (DSh+Drawing) dislocation density is  disl =6.8*10 13 cm -2 that means two times lower. Thus, softening by deformation is very positive for the development of cost-effective continuous metal forming technologies.

Fig. 10 X

 10 Fig.10 X-Ray spectra for investigated samples of low-carbon steel wires.

5 .

 5 figures. A.Z., T.B, F.B. and M.S. manufactured the samples and characterized them with EBSD and SEM. T.B., M.R., M.H., I.K. aided in interpreting the results and worked on the manuscript. A.Z developed theory for partial reduction prediction. A.Z. and H.K. performed FEM modelling with Deform 3D. All authors discussed the results and commented on the manuscript.

Acknowledgements

Financial supports through MŠMT project No. LM2015056 and infrastructural

Acknowledgements

Accepted Article

Acknowledgements

Financial supports through MŠMT project No. LM2015056 and infrastructural

Conflict of interest:

Accepted Article

Conflict of interest: