domain: spi chim

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

Yousf Islem Bourezg

Abdel Yazid Khereddine

Thierry Baudin

Anne-Laure Helbert

Francois Brisset

Megumi Kawazaki

Djamel Bradai

Terence G Langdon

Yousf Islem Bourezg

François Brisset

An investigation of the stored energy and thermal stability in a Cu-Ni-Si alloy processed by high-pressure torsion

Keywords: copper alloy, DSC, hardness, recrystallization, severe plastic deformation, stored energy

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

Introduction

During the last decades, processing using severe plastic deformation (SPD), including equalchannel angular pressing (ECAP) and high-pressure torsion (HPT), has been successfully developed to produce bulk ultrafine-grained (UFG) materials [START_REF] Valiev | Principles of equal-channel angular pressing as a processing tool for grain refinement[END_REF][START_REF] Zhilyaev | Using high-pressure torsion for metal processing: Fundamentals and applications[END_REF]. The combination of a very small grain size and a defect structure introduced during processing leads to a high yield strength and additional excellent mechanical properties in the copper-based alloys [START_REF] Dalla Torre | Microstructures and properties of copper processed by equal channel angular extrusion for 1-16 passes[END_REF][START_REF] Lugo | Thermal stability of ultrafine grains size of pure copper obtained by equal-channel angular pressing[END_REF][START_REF] Khereddine | Microstructures and textures of a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF][START_REF] Hadj Larbi | Microstructure and texture evolution in a Cu-Ni-Si alloy processed by equal-channel angular pressing[END_REF][START_REF] Abib | On the microstructure and texture of Cu-Cr-Zr alloy after severe plastic deformation by ECAP[END_REF]. In practice, processing by ECAP is extensively used and well investigated due to the beneficial ability to process large bars and billets which have a high potential for subsequent structural applications in industry [START_REF] Valiev | Principles of equal-channel angular pressing as a processing tool for grain refinement[END_REF]. Nevertheless, processing by HPT is recognized to produce exceptional grain refinement and to produce a stabilized microstructure having a high fraction of high-angle grain boundaries (HAGBs) [START_REF] Khereddine | An examination of microstructural evolution in a Cu-Ni-Si alloy processed by HPT and ECAP[END_REF][START_REF] Alawadhi | Direct influence of recovery behaviour on mechanical properties in oxygen-free copper processed using different SPD techniques: HPT and ECAP[END_REF].

It is well known that the stored energy in deformed microstructures, mostly in the form of dislocation substructures and high concentrations of vacancies, plays a significant role in controlling the nucleation of recrystallization and this will affect the mechanical anisotropy of the materials [START_REF] Cao | Stored energy, vacancies and thermal stability of ultra-fine grained copper[END_REF][START_REF] Wang | Thermal behavior of copper processed by ECAP with and without back pressure[END_REF]. An estimate of the stored energy may be undertaken using several different techniques. For example, the total stored energy can be measured by differential scanning calorimetry (DSC) [START_REF] Gao | Using differential scanning calorimetry as an analytical tool for ultrafine grained metals processed by severe plastic deformation[END_REF] and the local stored energy can be estimated from microhardness measurements [START_REF] Hazra | Stored energy of a severely deformed interstitial free steel[END_REF], diffraction line broadening analysis by X-rays [START_REF] Schafler | Lattice defect investigation of ECAP-Cu by means of X-ray line profile analysis, calorimetry and electrical resistometry[END_REF] and neutron diffraction [START_REF] Etter | Stored energy evolution in both phases of a duplex steel as a function of cold rolling reduction[END_REF] or by electron back-scatter diffraction (EBSD) [START_REF] Fressengeas | On the evaluation of dislocation densities in pure tantalum from EBSD orientation data[END_REF].

Accordingly, numerous investigations were reported describing the stored energy and thermal stability of copper-based alloys processed by ECAP [START_REF] Lugo | Thermal stability of ultrafine grains size of pure copper obtained by equal-channel angular pressing[END_REF][START_REF] Cao | Stored energy, vacancies and thermal stability of ultra-fine grained copper[END_REF][START_REF] Wang | Thermal behavior of copper processed by ECAP with and without back pressure[END_REF][START_REF] Molodova | Thermal stability of ECAP processed pure copper[END_REF][START_REF] Hadj-Larbi | DSC analysis of an ecap-deformed Cu-Ni-Si alloy[END_REF][START_REF] Abib | DSC analysis of commercial Cu-Cr-Zr alloy processed by equal channel angular pressing[END_REF][START_REF] Abib | Thermal stability of Cu-Cr-Zr alloy processed by equal-channel angular pressing[END_REF] and it was found that the stored energy increases with increasing ECAP processing up to 12 passes (~50 J/mol) and thereafter decreases gradually between 16 and 24 passes [START_REF] Zhang | Stored energy and recrystallization temperature in high purity copper after equal channel angular pressing[END_REF]. Moreover, ECAP processing tends to show a higher stored energy and a lower activation energy in copper compared with the values obtained after cold rolling [START_REF] Cao | Stored energy, vacancies and thermal stability of ultra-fine grained copper[END_REF]. It was reported that annealing at low-temperature (100-300 °C) can improve the mechanical properties of HPT copper alloy by increasing the electro-conductivity and decreasing the wear rate [START_REF] Zhilyaev | Effect of annealing on wear resistance and electroconductivity of copper processed by highpressure torsion[END_REF]. However, the copper alloys processed by HPT suffer from low thermal stability [START_REF] Horita | Microstructures and microhardness of an aluminum alloy and pure copper after processing by high-pressure torsion[END_REF][START_REF] Schafler | Microstructural investigation of the annealing behaviour of high-pressure torsion (HPT) deformed copper[END_REF][START_REF] Vorhauer | In-Situ Annealing of Severe Plastic-Deformed OFHC Copper[END_REF][START_REF] Zhilyaev | Electron backscatter diffraction (EBSD) microstructure evolution in HPT copper annealed at a low temperature[END_REF]. The recrystallization peak was detected at 220 °C with an activation energy of 94.5 kJ/mol for the present purity of Cu (98.5%) after 1 HPT turn using DSC analysis [START_REF] Jiang | Microstructural evolution, microhardness and thermal stability of HPT-processed Cu[END_REF]. A similar recrystallization temperature (190 °C) was reported in highly pure Cu (99.99%) processed by HPT using positron lifetime annihilation spectroscopy measurements [START_REF] Čížek | Influence of ceramic nanoparticles on grain growth in ultra fine grained copper prepared by high pressure torsion[END_REF].

There are many reports on the self-annealing at room temperature in processed copper by HPT [START_REF] Huang | The significance of self-annealing at room temperature in high purity copper processed by high-pressure torsion[END_REF][START_REF] Huang | Comparisons of self-annealing behaviour of HPTprocessed high purity Cu and a Pb-Sn alloy[END_REF][START_REF] Almazrouee | Effect of Long-Term Storage on Microstructure and Microhardness Stability in OFHC Copper Processed by High-Pressure Torsion[END_REF]. Recently, it was shown that there was a very significant self-annealing effect after room temperature storage for 6 weeks in high purity Cu processed by HPT after N = ½ turn whereas the effect was absent after N = 5 and 10 turns [START_REF] Huang | The significance of self-annealing at room temperature in high purity copper processed by high-pressure torsion[END_REF]. Nevertheless, studies devoted to analyzing the stored energy and activation energy of recrystallization of HPT-processed copper alloys are limited. Thus, the aim of the present research was to evaluate the stored energy in a commercial Cu-Ni-Si alloy after HPT processing at room temperature through 10 turns. First, the evolution of the total stored energy was investigated by DSC measurements.

Second, the local stored energy was measured by microhardness testing and a kernel average misorientation (KAM) approach using an EBSD technique in order to quantify the contributions of the different defect sources to the total stored energy. The evolution of the activation energy of recrystallization was also examined in order to investigate the thermal stability of the Cu-Ni-Si alloy.

Experimental material and procedures

A commercial Cu-2.5Ni-0.6Si (wt.%) plate alloy with dimensions of 160 × 102 × 11 mm 3 was supplied by CLAL-MSX (Meru, FRANCE) as a supersaturated solid solution after hot rolling at 820 °C and quenching in water. Discs with a thickness of 0.8 mm and a diameter of 10 mm were machined from the plate and then processed by HPT for N = ½, 1, 5 and 10 revolutions at room temperature using an imposed pressure of 6.0 GPa and a rotational speed of 1 rpm.

The HPT processing was performed under quasi-constrained conditions where there is a small outflow of material around the edge of the disc between the two anvils [START_REF] Figueiredo | Using finite element modeling to examine the flow processes in quasi-constrained high-pressure torsion[END_REF].

It is well establish that the strain distribution within an HPT-processed disc is inhomogeneous and depends on the radial distance from the centre of the disc according to the expression [START_REF] Zhilyaev | Using high-pressure torsion for metal processing: Fundamentals and applications[END_REF]:

𝜀 𝑒𝑞 = 𝛾 √3 = 2𝜋𝑁𝑟 ℎ√3 (1)
where γ, N, r and h are the shear strain, the number of HPT turns, the radial distance from the centre of the disc and the thickness of the disc, respectively. It was reported that the final thickness of the sample depends slightly on the number of HPT turns [START_REF] Pereira | An examination of the elastic distortions of anvils in high-pressure torsion[END_REF]. However, in the absence of any thickness measurements, the present calculations assume a constant thickness of h = 0.85 mm.

Electron backscatter diffraction (EBSD)

The EBSD measurements were performed in the RD-SD plane of the processed discs where RD and SD denote the rotational and shear directions, respectively. The microstructures were investigated near the centre at r = 0.4 mm and near the edge at r = 4.5 mm of the deformed discs using a scanning electron microscope FEG-SEM SUPRA 55 VP operating at 20 kV.

The EBSD data acquisition and analysis were undertaken using TSL Orientation Imaging Microscopy, OIM TM software.

The scanned areas were 100×100 μm 2 with a step size of 0.1 μm for the disc processed through N = ½ turn and 25×25 μm 2 with a 25 nm step size for the remainder of the processed discs after N = 1, 5 and 10 turns. The grain size data were obtained using a grain tolerance angle of 5° and the minimum grain size was chosen as 2 pixels.

The confidence index (CI) quantifies the reliability of the indexed Kikuchi pattern and only datum points with CI higher than 0.05 (indexing reliability is 95%) were taken into account to exclude poor quality pixels and to avoid possible errors introduced during the cleanup procedures [START_REF] Mikami | Effect of reference point selection on microscopic stress measurement using EBSD[END_REF]. The data taken from each sample included more than 2000 grains.

A quantification of the recrystallization processes for the HPT-deformed samples was estimated by applying the Grain Orientation Spread (GOS) criterion where GOS is 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], where the recrystallized grains are separated from the deformed grains with values of GOS <1° [START_REF] Cho | Determination of a mean orientation in electron backscatter diffraction measurements[END_REF].

Generally, KAM is used to quantify the average misorientation between a given point and its nearest neighbors which belong to the same grain [START_REF] Badji | Texture, misorientation and mechanical anisotropy in a deformed dual phase stainless steel weld joint[END_REF] where KAM reflects the distribution of strain and the dislocation density on individual measurement points [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]. The misorientation angle, θKAM , is connected directly with the plastic strain stored energy as well as the density of geometrically necessary dislocations, ρ [START_REF] Liu | Effect of grain orientation on deformation structure in cold-rolled polycrystalline aluminium[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]:

𝜌 = 𝛼𝜃 𝐾𝐴𝑀 𝑛𝑑𝑏 (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], b = 0.255 nm is the Burgers vector, n is for the nearest neighbor and d is the EBSD scan step size. The θKAM value was calculated from the mean misorientation angle between the point and its three neighbors excluding misorientations greater than 5°.

It is well known that the magnitude of the KAM value is affected by the scan step size [START_REF] Takayama | Analysis of Intragranular Misorientation Related to Deformation in an Al-Mg-Mn Alloy[END_REF][START_REF] Wright | Orientation Precision of Electron Backscatter Diffraction Measurements Near Grain Boundaries[END_REF][START_REF] Moussa | About quantitative EBSD analysis of deformation and recovery substructures in pure Tantalum[END_REF]. The difference of the chosen scan step size for the disc after N = ½ turn and the other processed discs was unintentional. Thus, it is reasonable to use the normalized KAM value (KAM /d) to directly compare the evolution of the KAM value as a function of the numbers of HPT turns.

It is known that the KAM value depends on the EBSD clean-up parameters (grain tolerance angle and minimum grain size). In this case, a measurement of KAM values was also performed using a grain tolerance angle of 3° and the minimum grain size of 2 pixels. The difference between the two clean-up procedure was found to be very small, ∆KAM = 0.05°. Subsequently, the stored energy from the estimated dislocation density was estimated using the following equation [START_REF] Liu | Effect of grain orientation on deformation structure in cold-rolled polycrystalline aluminium[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]:

𝐸 𝐾𝐴𝑀 = 1 2 𝜌𝜇𝑏 2 = 𝜇𝑏𝜃 𝐾𝐴𝑀 2𝑑 (3)
where  is the shear modulus having a value of µ = 48.3 GPa for copper.

Vickers microhardness

The Vickers microhardness, Hv, was measured using a Zwick 3212 microhardness tester near the centres (r = 0.4 mm) and edges (r = 4.5 mm) of the deformed samples with a load of 0.98 N maintained for 10 s. The average hardness at each position were estimated from four individual points recorded around the selected position and separated by distances of 0.15 mm. It is noted that using four points is a standard procedure for measuring Hv and the highest error for the Hv measurements was estimated to be about 5 %.

The dislocation density was estimated from the HV values using the Taylor equation [START_REF] Hazra | Stored energy of a severely deformed interstitial free steel[END_REF][START_REF] Taylor | The mechanism of plastic deformation of crystals. Part I.-Theoretical[END_REF]:

𝜌 = 1 13.5 ( 𝐻 𝑣 -𝐻 𝑣0 𝑀𝛼𝜇𝑏 ) 2 (4)
where HV0 = 82.12 is the microhardness of the initial sample prior to deformation [START_REF] Khereddine | An examination of microstructural evolution in a Cu-Ni-Si alloy processed by HPT and ECAP[END_REF], M is the Taylor factor of ~3.08 and α = 0.22 is a constant. Hence, the stored energy, EHv, may be obtained from the Hv values using the following equation [START_REF] Hazra | Stored energy of a severely deformed interstitial free steel[END_REF]:

𝐸 𝐻𝑣 = 1 2 𝜌𝜇𝑏 2 = 1 27𝜇 ( 𝐻 𝑣 -𝐻 𝑣0 𝑀𝛼 ) 2 (5)

Differential scanning calorimetry (DSC)

The total stored energy and activation energy for recrystallization of the deformed samples were calculated by DSC analysis. Samples with weights of 45-50 mg were cut near the centres of the discs and then inserted in an aluminum crucible having a diameter of 5 mm and subjected to DSC analysis using a 2920 MDSC calorimeter under a nitrogen atmosphere. Data obtained with an empty Al crucible was used as a reference. The DSC experiments were performed using four heating rates of 10, 20, 30 and 40 °C/min and with scanning temperature ranging from 80 to 500 °C. The total stored energy, EDSC, of the deformed samples was estimated based on the area of the heat release from the recrystallization peak [START_REF] Gao | Using differential scanning calorimetry as an analytical tool for ultrafine grained metals processed by severe plastic deformation[END_REF]. However, it is useful to mention that in future investigations it will be better to extend the temperature range even lower to room temperature especially with a high heating rate such as 40 °C/min in order to obtain more accurate measurements.

The activation energy for recrystallization was calculated using the dependence of the peak temperature on the heating rate (10, 20, 30 and 40 °C/min) given by the Boswell method [START_REF] Kissinger | Reaction Kinetics in Differential Thermal Analysis[END_REF][START_REF] Boswell | On the calculation of activation energies using a modified Kissinger method[END_REF]:

𝑙𝑛 ( 𝑉 𝑇 𝑝 ) = 𝐶 - 𝐸 𝑅𝑇 𝑝 (6)
where V is the heating rate, E is the activation energy, Tp is the maximum temperature at the peak, R is the universal gas constant and C is a constant. From a statistical viewpoint, it important to note that only one sample was used for each method to estimate the stored energy. HPT through N = ½, 1, 5 and 10 turns. It is worth noting that the DSC curves over the full range (80-500 °C) contain several exothermic and endothermic peaks belonging to a complex sequence of precipitation. For the purpose of this report, only the first exothermic peak corresponding to the recrystallization phenomenon is considered. It is reasonable to mention also that no recovery peak before the recrystallization peak was detected in the DSC curves.

Results

Stored energy estimates

Previously, it was shown that the no precipitation was detected in the Cu-Ni-Si alloy during HPT processing [START_REF] Azzeddine | An in situ synchrotron X-ray diffraction study of precipitation kinetics in a severely deformed Cu-Ni-Si alloy[END_REF]. Moreover, the quasi-binary section of the ternary Cu-Ni-Si phase diagram and recent results on the precipitation kinetics of the same Cu-Ni-Si alloy after HPT processing indicate that the precipitation of the δ-Ni2Si and γ-Ni5Si2 phases occur at high annealing temperatures ranging from 450 to 700 °C [START_REF] Azzeddine | An in situ synchrotron X-ray diffraction study of precipitation kinetics in a severely deformed Cu-Ni-Si alloy[END_REF]. It is apparent that the discs processed by higher numbers of HPT turns show peaks at lower recrystallization temperatures at each heating rate. Moreover, a significant peak shift towards a higher temperature is observed upon increasing the heating rate. Nevertheless, the DSC scans exhibit peaks extending more or less between 120 and 220 °C for all measurement conditions. For better visualization of Fig. 1, the results are re-plotted in Fig. 2 as the peak recrystallization temperature against the equivalent strain at each heating rate for the Cu-Ni-Si alloy. It is to be noted that the equivalent strain, εeq, for the DSC measurement was taken as the mean value between the centre and the edge of the HPT discs. This plot shows a trend that the temperature peak of recrystallization first decreases with increasing equivalent strain to εeq ~ 49.3 (N = 5 turns) and then tends to stabilize where the temperature peak of recrystallization remains unchanged with further straining.

Figure 3 presents the KAM maps corresponding to the 1 st neighbor with 5° threshold angle and GOS maps near the centres (left column) and edges (right column) of the discs processed by HPT for N = ½, 1, 5 and 10 turns, respectively. The estimated volume fractions of recrystallization, Fv, are specified in each GOS map. Significant microstructural refinement is apparent at the edges from the early stage of HPT from εeq = 8 (N = ½ turn) through εeq = 160 (N =10 turns) and there is a gradual refinement at the disc centres followed by a reasonable level of homogeneity along the disc diameter after εeq = 16 (N = 10 turns). More details on the evolution of microstructural parameters such as grain size, grain boundary distributions and crystallographic texture of the same Cu-Ni-Si alloy after HPT processing was reported earlier [START_REF] Khereddine | Microstructures and textures of a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF]. Figure 3 shows that after N = ½ and 1 turn, the disc centre showed severe grain refinement but with low Fv of ~1% but the Fv value increased to ~ 25% at the edge of the discs for both N = ½ (εeq = 8) and 1 turns (εeq =16). The microstructure after N = 5 turns (εeq = 80) maintains microstructural heterogeneity between these regions but it is apparent that the microstructure after N = 10 turns (εeq = 160) achieved reasonable homogeneity and contained about ~30-35% of recrystallized grains in both the disc centre and edge.

The evolution of the normalized KAM value (KAM /d) as a function of the numbers of HPT turns is shown in Figure 4a. The KAM values near the centres of the Cu-Ni-Si alloy discs increase from 5°/μm to 40°/μm with increasing HPT turns from N = ½ turn (εeq = 0.8) to N = 5 turns (εeq = 8) and this is followed by a decrease to 35.5°/μm after N = 10 turns (εeq = 16). A reasonable consistency in the KAM values at the centre and edge was achieved after HPT for N = 10 turns as shown in Fig. 4a. Moreover, as shown also in Fig. 4a, the normalized KAM value of the N = ½ turn sample increases from the centre (εeq = 0.8) to the edge (εeq = 8) of the disc.

The evolution of normalized KAM values as a function of equivalent strain is shown in Figure 4b for the centres and edges of the Cu-Ni-Si alloy discs after HPT through 10 turns. It is expected that the KAM value continuously increases with increasing strain but instead there is a consistent trend, at both the centres and edges of the Cu-Ni-Si alloy, that the KAM value initially increases dramatically to an equivalent strain of εeq ~ 8 (N = ½ turn) and then it saturates thereafter to a strain of εeq ~160 (N = 10 turns). In practice, the KAM value near the edge is lower than the centre after N = 1 and N = 5 turns but there are similar values after N =10 turns. This indicates that the edges of the processed discs have a smaller internal strain than near the centres of the processed discs.

Figure 4c and4d show the evolution of microhardness as a function of the numbers of HPT turns and the equivalent strain near the centres and edges of the Cu-Ni-Si alloy discs processed by HPT through N = ½, 1, 5 and 10 turns, respectively. It is apparent that the microhardness values at the edges of the processed discs are always much higher than near the centres of the discs, thereby implying an inhomogeneity in the grain size across the disc after HPT for N = 10 turns. Moreover, it is expected that the presence of the impurities and the Ni and Si alloying elements in the Cu-Ni-Si alloy contributed to the strain hardening as solidsolution hardening. Actually, it was demonstrated that 15% of the total hardening is due to solid-solution hardening in single-phase alloys processed by HPT [START_REF] Edalati | Influence of dislocation-solute atom interactions and stacking fault energy on grain size of single-phase alloys after severe plastic deformation using high-pressure torsion[END_REF]. In practice, the microhardness shows saturation around Hv  260 and reaches a steady-state at the disc edge after N = ½ turn (εeq = 8) while the saturation of Hv  220 was achieved at the disc centres after N = 5 turns (εeq = 8).

Nevertheless, when the hardness evolution is plotted against equivalent strain as in Fig. 4d the hardness development at both the centres and the edges of the Cu-Ni-Si alloy tend to show reasonable agreement with the general model for hardening without any microstructural recovery [START_REF] Kawasaki | Different models of hardness evolution in ultrafine-grained materials processed by high-pressure torsion[END_REF]. A large hardness variation without achieving a hardness homogeneity was already reported in pure Cu (99.95 wt.%) and in a Cu-Ag alloy after HPT processing at room temperature for N = 20-25 turns [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][START_REF] Čížek | Evolution of defects in copper deformed by high-pressure torsion[END_REF].

Figure 5 presents the evolution of the mean hardness values taken from the Hv values at the disc centre and at the edge for each HPT-processed disc and re-plotted as a function of the inverse of the square root of the mean grain size reported previously [START_REF] Khereddine | Microstructures and textures of a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF]. In addition, the data of the same Cu-Ni-Si alloy processed by ECAP at 150 °C through N = 2, 8 and 12 passes using route A [START_REF] Hadj Larbi | Microstructure and texture evolution in a Cu-Ni-Si alloy processed by equal-channel angular pressing[END_REF] are also plotted to verify the validity of the Hall-Petch relationship over the range of grain sizes produced by HPT and ECAP processing. These data were fitted using a Hall-Petch equation in the following form in order to examine the contribution of the grain boundary strengthening mechanism to the increase of microhardness as shown in Figure 5 [START_REF] Armstrong | Engineering science aspects of the Hall-Petch relation[END_REF]:

𝐻 𝑣 = 𝐻 𝑣0 + 𝐾 𝐻 𝑑 -1/2 (7)
where Hv0 is the friction hardness which represents the resistance of the crystal lattice to the movement of dislocations and KH is a locking parameter which indicates the contribution of the grain boundaries to the hardening.

It is evident from Figure 5 that there is no linear relationship between the microhardness Hv The difference between the ECAP and HPT processing is a consequence of the much higher strains that can be attained by HPT and this means the grain sizes are generally smaller as may be seen in Figure 5. The present results demonstrate that the Hall-Petch relationship is valid for the Cu-Ni-Si alloy over the range of grain sizes produced by both HPT and ECAP processing.

Figure 6 presents the evolution of stored energy at the disc centres and edges estimated from the DSC method, KAM using eq. ( 3) and microhardness using eq. ( 5) plotted as a function of It can be recognized from Fig. 6 that EKAM at both positions of the disc after N = ½ HPT turn were close or even higher than the EHv at the disc centre after N = ½ HPT turn. This is attributed in part to the difference in the step size during the EBSD measurement of the ½ turn disc compared to the other samples as mentioned earlier in the experimental section.

By contrast, the stored energy, EDSC, obtained by the DSC measurements shows a different tendency from these other two approaches where the EDSC value decreases rapidly from ~100 J/mol after N = ½ turn (εeq ~ 4.5) to ~71 J/mol after N = 1 turn (εeq ~ 9) and then exhibits a reasonable saturation at ~67-70 J/mol through N = 10 turns (εeq ~ 86).

It is important to note that the stored energy varies in the following order: EDSC >EHv > EKAM for all sample conditions. The difference in the estimated stored energy values is attributed directly to the different types of measurements. It is well known that the DSC analysis is used to calculate the energy stored in the vacancies and the different types of dislocations such as geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs) [START_REF] Gao | Using differential scanning calorimetry as an analytical tool for ultrafine grained metals processed by severe plastic deformation[END_REF].

The stored energy estimated via microhardness tests incorporates the contributions of both the GNDs and the SSDs simultaneously [START_REF] Hazra | Stored energy of a severely deformed interstitial free steel[END_REF]. By contrast, the KAM approach is used only to evaluate the stored energy from the GNDs [START_REF] Pantleon | Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction[END_REF][START_REF] Field | Quantification of dislocation structure heterogeneity in deformed polycrystals by EBSD[END_REF].

Activation energy for recrystallization

Considering eq. ( 6), the plot of ln(V/Tp) versus (1000/Tp) was constructed as shown in Fig. 7a by applying the recrystallization peaks measured by the DSC scans at the four heating rates of 10, 20, 30 and 40 °C/min. It is evident that this Boswell plot shows relative straight lines and the activation energy may be determined directly from the slope of the lines. energy is in good agreement with the variation of the total stored energy (Figure 6). It is interesting to note that the present range of activation energy (89.7-92.2 kJ/mol) is smaller than the reported activation enthalpy of boundary migration in Cu (106.1 kJ/mol) [START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF].

Discussion

Significance of the stored energy

The plastic deformation of polycrystalline materials leads to the introduction of different lattice defects such as vacancies and dislocations. These dislocations are classified into GNDs and SSDs. The GNDs accommodate the lattice curvature from the deformation gradient to ensure compatibility requirements which will create orientation gradients in the crystal lattice.

The SSDs accumulate due to statistical entanglements and they are formed due to the trapping process of dipoles and/or multipole dislocations [START_REF] Ashby | The deformation of plastically non-homogeneous materials[END_REF][START_REF] Jiang | Evolution of dislocation density distributions in copper during tensile deformation[END_REF][START_REF] Konijnenberg | Assessment of geometrically necessary dislocation levels derived by 3D EBSD[END_REF].

A significant amount of the accumulated energy during plastic deformation is dissipated as heat and the remainder is stored in SSDs, GNDs and vacancies [START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF]. It is expected that the stored energy will increase with increasing strain. However, the total stored energy estimated by DSC analysis, as shown in Figure 6, decreases in the very early stage of HPT from N = ½ to 1 turn (εeq ~ 4.5) and this implies that the density of defects decreases due to the occurrence of recovery or dynamic recrystallization during processing [START_REF] Vorhauer | In-Situ Annealing of Severe Plastic-Deformed OFHC Copper[END_REF]. The present result shows a saturation of the stored energy and this agrees with several earlier reports on ultrafine-grained oxygen-free high conductivity (OFHC) copper and single phase Cu-Ni-Si and Cu-Cr-Cr alloys [START_REF] Cao | Stored energy, vacancies and thermal stability of ultra-fine grained copper[END_REF][START_REF] Hadj-Larbi | DSC analysis of an ecap-deformed Cu-Ni-Si alloy[END_REF][START_REF] Abib | DSC analysis of commercial Cu-Cr-Zr alloy processed by equal channel angular pressing[END_REF] while a decrease in the stored energy was also reported in various FCC alloys after SPD processing [START_REF] Alawadhi | Direct influence of recovery behaviour on mechanical properties in oxygen-free copper processed using different SPD techniques: HPT and ECAP[END_REF][START_REF] Zhang | Stored energy and recrystallization temperature in high purity copper after equal channel angular pressing[END_REF][START_REF] Murata | Assessment of Strain Energy by Measuring Dislocation Density in Copper and Aluminium Prepared by ECAP and ARB[END_REF]. Furthermore, the recovery rate is faster for HPT copper deformed samples than for ECAP samples [START_REF] Alawadhi | Direct influence of recovery behaviour on mechanical properties in oxygen-free copper processed using different SPD techniques: HPT and ECAP[END_REF]. Nevertheless, the stored energy values estimated in the present experiments after HPT processing are even higher than those reported in pure copper processed by ECAP [START_REF] Zhang | Stored energy and recrystallization temperature in high purity copper after equal channel angular pressing[END_REF].

The stored energy in GNDs measured by the KAM approach in Fig. 6b achieves a saturation at an equivalent strain of εeq ~ 20. Such evolution involving the density of GNDs can be explained by the mechanism responsible for grain refinement during HPT processing which has a correlation with the continuous dynamic recrystallization [START_REF] Vorhauer | In-Situ Annealing of Severe Plastic-Deformed OFHC Copper[END_REF]. During the early stage of plastic deformation, dislocation slip systems are activated in different regions of the grains leading to the formation of GNDs to maintain a strain compatibility [START_REF] Kuhlmann-Wilsdorf | Geometrically necessary, incidental and subgrain boundaries[END_REF] and this causes a rapid increase in the value of the stored energy. Such rearrangements contribute to the formation of low-angle substructures of cells and sub-grains [START_REF] Kuhlmann-Wilsdorf | Geometrically necessary, incidental and subgrain boundaries[END_REF][START_REF] Belyakov | Grain refinement in copper under large strain deformation[END_REF] and it is also possible that the heat generated during the deformation contributes to the re-arrangement of dislocations into low-angle grain boundaries (LAGBs) with misorientations lower than 15°. A further increase in deformation straining causes the increase of the misorientation between the cells which leads to the transformation of LAGBs into high-angle grain boundaries (HAGBs, with misorientations higher than 15°) [START_REF] Renk | Generation of extreme grain aspect ratios in severely deformed tantalum at elevated temperatures[END_REF] and this leads to the formation of new ultrafine equiaxed grains accompanied by a saturation in the GND density. The GOS maps shown in Fig. 3 demonstrate clearly that dynamic recrystallization took place rapidly at an equivalent strain of εeq ~ 8. Previously, it was shown that the fractions of HAGBs for the present HPTprocessed Cu-Ni-Si alloy increase with increasing strain to reach steady state around 65 % at an equivalent strain of εeq ~ 80 [START_REF] Khereddine | Microstructures and textures of a Cu-Ni-Si alloy processed by high-pressure torsion[END_REF]. A higher fraction of HAGBs (80%) was found in pure OFHC copper processed by HPT at an equivalent strain of εeq ~ 32 [START_REF] Vorhauer | In-Situ Annealing of Severe Plastic-Deformed OFHC Copper[END_REF]. This difference is attributed to the delaying effect of the solute atoms (Ni and Si) on the dislocation motion by increasing the localized stress needed for dislocation motion and thereby reducing the amount of LAGBs transformed to HAGBs [START_REF] Edalati | Influence of dislocation-solute atom interactions and stacking fault energy on grain size of single-phase alloys after severe plastic deformation using high-pressure torsion[END_REF].

It should be noted that the heat generated during HPT processing is in practice very limited and a recent report showed a very small increase in temperature for several different metals in the very early stages of HPT after processing for <1 turn [START_REF] Edalati | Effect of temperature rise on microstructural evolution during high-pressure torsion[END_REF]. Using the general relationship for the prediction of the temperature rise, ΔT, in the sample during HPT processing [START_REF] Pereira | Modeling the temperature rise in high-pressure torsion[END_REF]:

∆𝑇 = 0.22𝜎𝜔[1 + 1.28(1 -𝑒 -(𝑡 482 ⁄ ) )] ( 8
)
where σ is the stress level, ω is the rotating speed and t is the time for the experimental HPT processing, it was estimated that there was a temperature rise of about ΔT = 12 K after 1 turn and about ΔT = 30 K after 10 turns in the present alloy. A similar value for the temperature rise (~40 K) was reported in pure Cu after N = 10 turns using the same experimental conditions [START_REF] Edalati | Significance of temperature increase in processing by high-pressure torsion[END_REF].

Furthermore, the stored energy in the GNDs is lower at the disc edges by comparison with the centres of the processed discs (Figures 3 and7) and this is contrary to the distribution of the equivalent strain across the disc radius given in Eq. ( 1). It was demonstrated by scanning electron microscopy that the strain occurs initially at the edge of the discs and with increasing numbers of HPT turns the deformation spreads towards the centre [START_REF] Tian | Direct observations of microstructural evolution in a two-phase Cu-Ag alloy processed by high-pressure torsion[END_REF]. The high accumulated strain in the edge region leads to the rapid occurrence of dynamic recrystallization and fast softening by comparison with the centre zone where there is a low imposed strain [START_REF] Xu | The evolution of homogeneity in processing by high-pressure torsion[END_REF][START_REF] Hanna | Evaluating the textural and mechanical properties of an Mg-Dy alloy processed by high-pressure torsion[END_REF].

This result is in good agreement with the estimated fraction of recrystallized grains in the present alloy as shown in Figure 3. The dynamic recrystallization is more pronounced at the edges of the discs during the early stage of deformation (εeq ~ 8-16). With increasing strain in the range of εeq ~ 80-160 the dynamic recrystallization increases and appears to be more homogenous along the radial distances from the centres of the discs.

The stored energy in SSDs at the centres and edges of the processed discs was estimated from the difference between the stored energy calculated using the microhardness values and the KAM approach and these data are presented in Table 1. The density of SSDs near the centres of the processed discs acts differently to the GNDs where the SSDs increase gradually to ~16.7 J/mol with increasing strain up to N = 5 turns (εeq = 8) and decreases slightly to ~15.4

J/mol after N = 10 turns (εeq = 16). By contrast, the magnitude of the stored energy in SSDs near the edge of the processed discs is high after N = ½ turn (εeq = 8) and then decreases to ~24.2 J/mol after N = 1 turn (εeq = 16) and appears to stabilize with increasing numbers of HPT turns up to N = 10 turns (εeq = 160).

It was reported that the GND density was 3 times higher than the SSD density in HPTprocessed copper annealed at a low temperature of 100 °C [START_REF] Zhilyaev | Electron backscatter diffraction (EBSD) microstructure evolution in HPT copper annealed at a low temperature[END_REF]. Studies found that only 3.5 % of the total stored energy was from the SSD and 44 % from the contribution of GND in OFHC copper processed by ECAP through 8 passes using route Bc [START_REF] Cao | Stored energy, vacancies and thermal stability of ultra-fine grained copper[END_REF]. In addition, it was reported that 10 % from the stored energy estimated by neutron diffraction (taking into account both SSD and GND) is attributed to the SSD in strongly cold rolled Fe-48Ni (wt.%) alloy [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]. In the present study, the GND density exceeds the SSD density only near the centre of the processed discs and in the early stage of deformation εeq ~ 0.8-1.6 (N = ½ and 1 turn) but with a further increase of strain to εeq ~ 16 (N = 5 turns) the contribution to the stored energy was similar. It is reasonable to conclude that this similarity is due to a balance between the rates of dislocation nucleation and recovery.

The stored energy of the vacancies is summarized in Table 1 which was estimated from the difference between the stored energy of DSC and the Hv measurements. It should be noted that the mean value corresponding to the centre and the edge of the discs was used to obtain the mean stored energy from the Hv measurements. As can be seen from these data, an increase in numbers of HPT turns leads to a decrease in their concentration. Since the dislocation density decreases with increasing strain near the edges of the discs, it is reasonable to assume a similar decrease for vacancies. However, it can be observed that the stored energy of vacancies (58.6 J/mol) exceeds that for dislocation (EHv ~ 41.3 J/mol) in the early stage of deformation (N = ½ HPT turn). In fact, several studies demonstrated that SPD processing leads to the development of a very high concentration of vacancies [START_REF] Schafler | Lattice defect investigation of ECAP-Cu by means of X-ray line profile analysis, calorimetry and electrical resistometry[END_REF][START_REF] Čížek | Evolution of defects in copper deformed by high-pressure torsion[END_REF].

For comparison, the dislocation density estimated previously for the same Cu-Ni-Si samples by an X-ray diffraction line profile analysis (XRDLPA) [START_REF] Khereddine | An examination of microstructural evolution in a Cu-Ni-Si alloy processed by HPT and ECAP[END_REF] was used to calculate their stored energy using the following equation based on DSC measurements [START_REF] Bever | The stored energy of cold work[END_REF]:

𝐸 𝑋𝑅𝐷 = 𝜇𝑏 2 𝜌 𝑋𝑅𝐷 4𝜋𝜖 𝑙𝑛 ( 1 𝑏√𝜌 𝑋𝑅𝐷 ) (9)
where XRD is the dislocation density, ε is the arithmetic average of 1 and (1-υ) and υ is the Poisson ratio (υ = 0.355) for copper.

It is reasonably assumed that the dislocation density estimated by XRDLPA represents the true dislocation density [START_REF] Ungár | Vacancy production during plastic deformation in copper determined by in situ X-ray diffraction[END_REF] present in the deformed materials since XRDLPA is able to quantify the lattice distortions caused by defects that are larger than 5 nm [START_REF] Ungar | X-ray line-broadening study of the dislocation cell structure in deformed [001]-orientated copper single crystals[END_REF]. Therefore, it can be considered that the dislocation density estimation from XRDLPA involved both SSD and GND [START_REF] Gubicza | The effect of severe plastic deformation on precipitation in supersaturated Al-Zn-Mg alloys[END_REF].

In this case, the stored energy from the vacancies Evac' was calculated from the difference between EDSC and EXRD. In fact, the correlation between the DSC analysis and the XRDLPA approach is a procedure often used to estimate the concentration of vacancies in severely deformed materials [START_REF] Schafler | Lattice defect investigation of ECAP-Cu by means of X-ray line profile analysis, calorimetry and electrical resistometry[END_REF][START_REF] Ungár | Vacancy production during plastic deformation in copper determined by in situ X-ray diffraction[END_REF][START_REF] Setman | The presence and nature of vacancy type defects in nanometals detained by severe plastic deformation[END_REF][START_REF] El-Tahawy | Stored energy in ultrafine-grained 316L stainless steel processed by high-pressure torsion[END_REF][START_REF] Kapoor | Stored energy in nanocrystalline Ni-Mo films processed by electrodeposition[END_REF]. The evolution of XRD , EXRD and Evac' as a function of the number of HPT turns are summarized in Table 1. It can be clearly seen that the values of the stored energy of the vacancies (Evac'= EDSC -EXRD) are very close to those calculated from the difference (Evac = EDSC -EHv). It may be concluded that the use of the Hv procedure gives a good estimation of the sorted energy of both dislocation types (SSD and GND).

The concentration of vacancies may be estimated based on the stored energy using the following equation:

𝐶 𝑣 = 𝐸 𝑣𝑎𝑐 86.84.10 3 (10)
where 86.84  10 3 J/mol ≈ 0.9eV is the vacancy formation energy in copper [START_REF] Meechan | Formation energies of vacancies in copper and gold[END_REF].

Thus, the concentration of vacancies is estimated as in the range of ~1.0 -6.7  10 -4 where these values are in the same range as those reported in copper processed by ECAP [START_REF] Schafler | Lattice defect investigation of ECAP-Cu by means of X-ray line profile analysis, calorimetry and electrical resistometry[END_REF] and they are much higher than in copper deformed by conventional deformation such as cold rolling [START_REF] Schafler | Lattice defect investigation of ECAP-Cu by means of X-ray line profile analysis, calorimetry and electrical resistometry[END_REF][START_REF] Setman | The presence and nature of vacancy type defects in nanometals detained by severe plastic deformation[END_REF]. In practice, it was demonstrated that the variation of the vacancy concentration is more sensitive to the extent of hydrostatic pressure than the dislocation density [START_REF] Schafler | Lattice defect investigation of ECAP-Cu by means of X-ray line profile analysis, calorimetry and electrical resistometry[END_REF]. This is consistent with the present results where a high concentration of vacancies is produced after N = ½ turn and the significant decrease in the vacancy concentration after N = 5 turns is attributed to the role of vacancies in the climb of dislocations during processing [START_REF] Setman | The presence and nature of vacancy type defects in nanometals detained by severe plastic deformation[END_REF]. In severely deformed copper the vacancies are generated as agglomerates and no single or double vacancies were observed due to the medium value of the stacking fault energy [START_REF] Setman | The presence and nature of vacancy type defects in nanometals detained by severe plastic deformation[END_REF].

The creation and annihilation of vacancies play an important role in the hardening of materials during deformation [START_REF] Zehetbauer | Deformation Induced Vacancies with Severe Plastic Deformation: Measurements and Modelling[END_REF]. Thus, the presence of a high concentration of vacancies can retard the movement of dislocations leading to an increase in the strength of the material.

It may be concluded that, in the initial stage of deformation at εeq ~ 0.8-1.6 (N = ½-1 turn), the high densities of dislocations are mostly of the GND type and vacancies are produced in order to accommodate grain rotation and the formation of an ultrafine microstructure. With further increase in the numbers of HPT turns, and after the formation of the fine microstructure, the dislocations are in SDD type and play an important role in accommodating the deformation process. This conclusion is consistent with the TEM observations which demonstrate that a high dislocation density is present at sub-grain boundaries during the early stage of the HPT process and these dislocations were not visible within each sub-grain [START_REF] Belyakov | Grain refinement in copper under large strain deformation[END_REF][START_REF] Wang | Mechanism of grain growth during severe plastic deformation of a nanocrystalline Ni-Fe alloy[END_REF]. By contrast, at high deformation strains the dislocations are observed within the grains and this corresponds to the SSD dislocations [START_REF] Wang | Mechanism of grain growth during severe plastic deformation of a nanocrystalline Ni-Fe alloy[END_REF].

Significance of the activation energy

The activation energy of recrystallization calculated in the present Cu-Ni-Si alloy was in the range of ¬89.7-92.2 kJ/mol, depending on the imposed strain. It was found that the activation energy increases rapidly at low equivalent strain (εeq ~ 10) and more slowly at higher equivalent stain (εeq ~ 50). However, some studies demonstrated that the activation energy of recrystallization decreases with increasing strain in severely deformed copper-based alloys [START_REF] Cao | Stored energy, vacancies and thermal stability of ultra-fine grained copper[END_REF][START_REF] Abib | DSC analysis of commercial Cu-Cr-Zr alloy processed by equal channel angular pressing[END_REF][START_REF] Setman | Activation Enthalpies of Deformation-Induced Lattice Defects in Severe Plastic Deformation Nanometals Measured by Differential Scanning Calorimetry[END_REF]. Such evolution was explained by the excessive formation of vacancy agglomerates with increasing strain [START_REF] Cao | Stored energy, vacancies and thermal stability of ultra-fine grained copper[END_REF]. Table 1 shows that the vacancy concentration decreases drastically soon after N = ½ turn due to the dynamic recrystallization which probably explains the increase of the activation energy of recrystallization with further strain increases. Moreover, the annihilation of the dislocations needs more activation enthalpy due to their rearrangement at high strains [START_REF] Setman | Activation Enthalpies of Deformation-Induced Lattice Defects in Severe Plastic Deformation Nanometals Measured by Differential Scanning Calorimetry[END_REF].

A compilation of different values for the activation energy of variously deformed copperbased alloys is listed in Table 2. The present values of the activation energy are somewhat lower than those found for the same alloy processed by ECAP via route A up to 12 passes at 150 °C [START_REF] Hadj-Larbi | DSC analysis of an ecap-deformed Cu-Ni-Si alloy[END_REF]. This may be explained by the higher strain introduced in the material by HPT relative to processing by ECAP. Table 2 shows that copper-based alloys processed by ECAP have a high activation energy compared to HPT processing. These results demonstrate that the HPT processing exhibits poor thermal stability compared to ECAP processing. However, a lower activation energy of ~65 kJ/mol was calculated from hardness tests of a copper alloy after 12 ECAP passes [START_REF] Molodova | Thermal stability of ECAP processed pure copper[END_REF]. Moreover, it appears that the activation energy varies significantly with the elemental additions in the alloys. For example, the addition of only 0.0068 at.% of copper to pure aluminum raised the activation energy for recrystallization from ~60 to ~120 kJ/mol [START_REF] Humphreys | Chapter 7 -Recrystallization of Single-Phase Alloys[END_REF].

It was assumed that the activation energy of recrystallization is independent of the stored energy in ECAP-processed high purity copper and at high strains the recrystallization kinetics are more dependent on structural factors such as the grain size rather than on the stored energy [START_REF] Zhang | Stored energy and recrystallization temperature in high purity copper after equal channel angular pressing[END_REF]. However, the evolution of activation energy of recrystallization in the present Cu-Ni-Si alloy demonstrates a net dependency on the stored energy. As expected, the activation energy of the recrystallization increases with decreasing stored energy in the alloy.

In fact, the decrease in the stored energy due to the occurrence of dynamic recrystallization causes a decrease of the driving force for recrystallization and thereby an increase in the activation energy.

Thus, the evolution of the total stored energy and local stored energy in GNDs, SSDs and vacancies was estimated during increasing strain in the HPT processing and as a function of the radial distances from the centres of the discs. Further, the evolution activation energy of the recrystallization was also calculated as a function of number of HPT turns. The present results contribute towards our understanding of the recrystallization mechanism in severely deformed materials.

Figure 1

 1 Figure 1 presents a compilation of the DSC scans at four different heating rates of 10, 20, 30 and 40 °C/min demonstrating the recrystallization peaks for the Cu-Ni-Si alloy processed by

and d - 1 / 2

 12 for both the HPT and ECAP-processed Cu-Ni-Si alloy. In this case, the data were treated separately from each type of SPD processing. The linear fit of the datum points gives estimates of Hv0 = 172 ± 5.2 Hv and KH = 32 ± 3.1 Hv μm 1/2 with a residual sum R 2 =0.991 for samples processed by HPT and Hv0 = 155 ± 0.8 Hv, KH = 45 ± 1.2 Hv μm 1/2 and R 2 =0.999 for samples processed by ECAP.

  (a) the numbers of HPT turns and (b) the equivalent strain for the Cu-Ni-Si alloy after HPT processing. It is readily apparent from these plots that the stored energy EKAM estimated from KAM increases with increasing numbers of HPT turns to N = 1 turn (εeq ~ 16) and then tends to saturate at ~38 J/mol for both the centres and edges of the processed discs at higher numbers of HPT turns up to N = 10 turns (εeq ~ 160). The stored energy estimated by Hv measurements near the edges is much higher than near the centres of the discs, especially in the early stages of deformation for N = ½ (εeq ~ 8) and N = 1 turn (εeq ~ 16). The increase of the stored energy, EHv, with increasing numbers of HPT turns is more pronounced near the disc centre where EHv increases from ~30 J/mol after N = ½ turn (εeq ~ 0.8) to ~ 61 J/mol after N =5 turns (εeq ~ 8) and then decreases to ~55 J/mol after N = 10 turns (εeq ~ 16). In addition, EHv at the disc edge after N = 10 HPT turns (εeq ~ 160) reaches EHv  60 J/mol immediately after N = ½ turn (εeq ~ 8) and then slowly increases to ~64 J/mol through N =10 turns (εeq ~ 160).

Figure 7b shows the

  Figure 7b shows the variation of the estimated activation energy for recrystallization as a function of the equivalent strain for the Cu-Ni-Si alloy. The activation energy increases from 89.7 kJ/mol at εeq ~ 4.5 (N = ½ turn) to 91.8 kJ/mol at εeq ~ 9 (N = 1 turn) and then it slightly increases to ~92.2 kJ/mol through N = 10 turns (εeq ~ 100). The evolution of the activation

Conclusions 1 . 2 . 5 . 6 .

 1256 A commercial Cu-Ni-Si alloy was subjected to HPT processing at room temperature up to 10 turns and the stored energy and activation energy for recrystallization were estimated using differential scanning calorimetry, electron backscatter diffraction and Vickers microhardness. The fraction of recrystallized grain increases rapidly to 25 % at the edge of the N = ½ turn disc (εeq = 8). The microstructure was more homogenized along the radial distance of the disc processed through N = 10 turns (εeq = 160) and contained about 30-35% of recrystallized grains in both the disc centre and edge.3. The Hall-Petch relationship is valid for the Cu-Ni-Si alloy over the range of grain sizes produced by HPT and ECAP processing.4. The total stored energy calculated from DSC measurements decreases rapidly after εeq = 16 (N = 1 turn) but then stabilizes at ~70 J/mol for processing up to εeq = 86 (N = 10 HPT turns). This decrease is attributed to the rapid occurrence of dynamic recrystallization during the earlier stage of HPT processing. The local stored energy estimated from the KAM approach (GNDs) and Hv (GNDs + SSDs) measurements was shown to be inhomogeneous along the radial distance from the centre of the HPT-processed disc and increased with increasing equivalent strain at εeq ~ 16 and saturated with further strain increases. GNDs and vacancies are responsible for the high stored energy in the initial stage of deformation at εeq =8.6-16 (N = ½-1 turn). The contribution of the SSDs is similar to that of the GNDs only in high strain deformation as at εeq = 49.3 (N = 5 turns) when dynamic recrystallization is occurring. The recrystallization temperature was in the range of 157-194 °C. It increases with increasing heating rate and decreases with increasing numbers of HPT turns. A low value in the range of ~ 89.7-98.7 kJ/mol was measured for the activation energy of recrystallization, thereby suggesting a poor thermal stability.

Figure caption Figure 1 :

 caption1 Figure captionFigure 1: DSC scans at a heating rate of 10, 20, 30 and 40 °C/min corresponding to the recrystallization phenomena in Cu-Ni-Si alloy processed by HPT for N = ½, 1, 5 and 10 turns respectively.

Figure 2 :

 2 Figure 2: Evolution of the recrystallization temperature peak of Cu-Ni-Si alloy as function of equivalent strain.

Figure 3 :

 3 Figure 3: KAM and GOS maps near the centre (left column) and near the edge (right column) of Cu-Ni-Si discs processed by HPT for N = ½, 1, 5 and 10 turns, respectively.

Figure 4 :

 4 Figure 4: (a, b) Evolution of averaged KAM values as function of number of HPT turns and equivalent strain and (b, c) evolution of mean value of microhardness as function of number of HPT turns and equivalent strain for Cu-Ni-Si alloy processed by HPT for N = ½, 1, 5 and 10 turns, respectively.

Figure 5 :

 5 Figure 5: Evolution of microhardness for Cu-Ni-Si alloy processed by HPT for N = ½, 1, 5 and 10 turns as function of inverse of the square root of the mean grain size representing the Hall-Petch relationship. Data from the same Cu-Ni-Si alloy processed by ECAP at 150 °C through N = 2, 8 and 12 passes using route A [6] are also presented.

Figure 6 :

 6 Figure 6: Evolution of stored energy estimated by KAM, Hv and DSC analysis for Cu-Ni-Si alloy processed by HPT for N = ½, 1, 5 and 10 turns as function of: a) number of HPT turns and b) equivalent strain.

Figure 7 :

 7 Figure 7: (a) Boswell plots for recrystallization peak in Cu-Ni-Si alloy processed by HPT for N = ½, 1, 5 and 10 turns and (b) Evolution of activation energy of recrystallization as function of equivalent strain.

Figure 1 Figure 2 Figure 4 Figure 5

 1245 Figure 1

Figure 6 Figure 7

 67 Figure 6

Table caption Table 1 .

 caption1 Estimation of stored energy of SSDs dislocations (EHv -EKAM) and vacancies (EDSC -EHv) as function of the number of HPT turns. True dislocation density (XRD) estimated using XRDLPA[START_REF] Khereddine | An examination of microstructural evolution in a Cu-Ni-Si alloy processed by HPT and ECAP[END_REF], corresponding stored energy (EXRD) and stored energy of vacancies (Evac' = EDSC -EXRD).

	 XRD	E XRD

N E SSD (J/mol) (E DSC -E Hv ) E vac (J/mol) (E DSC -E Hv ) (J/mol) E vac' (J/mol) (E DSC -E XRD )

Acknowledgements

The authors wish to thank Mr. Hacen Hadj Larbi from CLAL-FRANCE for kindly providing the Cu-Ni-Si alloy. One of the authors (YIB) wishes to heartily thank Prof. Jose Maria Cabrera from Polytecnia ETSEIB, Universidad Politécnica de Cataluña (UPC), for an invitation to UPC and for help during the scientific research and to the staff of the Biomaterials research group of UPC for their support in the DSC analysis. This study was supported in part by the National Science Foundation of the United States under Grant No. DMR-1810343 (MK) and in part by the European Research Council under ERC Grant Agreement No. 267464-SPDMETALS (TGL).


Saliha Gachi
email: s_gachi@yahoo.fr

Mouloud Aissani

Thierry Baudin

Anne Laure Helbert

François Brisset

Sébastien Gautrot

Marie-Hélène Mathon

Djamel Bradai

Fouad Boubenider

Keywords: friction stir welded aluminum alloy Aluminum alloy, FSW, Microstructure, Texture, Microhardness, Young modulus

Microstructure, texture and mechanical properties of

Introduction

One of the main materials used for aeronautical applications is the heat treatable 7075 aluminum alloy. It fulfills the main requirements of weight, availability, formability, cost, reliability and maintainability. Due to its excellent strength/weight ratio, this alloy is widely used for the fuselage, the wings and the supporting structure. Unfortunately, fusion welding of this alloy is difficult by conventional techniques due to its copper content which leads to a solidification and liquation cracking in the heat affected zone with a great reduction in mechanical properties within the joint [1, 2].

Friction stir welding (FSW) has been proved as a powerful joining method and has matured over the last two decades for various metals and alloys. The main advantages of this processing are that it produces materials free of distortion, cracks, porosity, oxidation, and other defects that result after conventional fusion welding to improve the mechanical properties of the weld [1,2].

In this process, a cylindrical tool composed essentially of a shoulder and profiled pin is rotated and inserted into the adjacent edges of the clamped work pieces to be welded.

Frictional heat between the wear resistant tool and the workpieces causes the softening of material without reaching melting phase allowing the tool to move along the joint line. As a result, a weld joint is produced in solid state. Near the center of the weld, is located the nugget zone (NZ), also called dynamically recrystallized zone. This region consists of fine equiaxed grains that are formed by dynamic recrystallization due to the severe plastic deformation and high temperature. An extra zone is created between the nugget zone and the base metal (BM), namely the thermo-mechanically affected zone (TMAZ). The reason for the formation of this area is that the workpiece is subject to both temperature and deformation during the welding process. This is the different point from the other general welding methods. TMAZ is characterized by a highly deformed structure. It is followed by the heat affected zone (HAZ) which experiences a thermal cycle but did undergo any plastic deformation [START_REF] Fonda | Texture variations in an aluminum friction stir weld[END_REF].

The FSW process is not symmetric with respect to the weld line. The advancing side (AS) is the zone where the rotational and welding speed have the same direction whereas in the retreating side (RS), the two velocities have opposite directions.

Numerous published reports [START_REF] Diwahar | A review on friction stir welding of similar and dissimilar aluminium alloys[END_REF][START_REF] Huang | Atypical grain coarsening of friction stir welded AA6082-T6: Characterization and modeling[END_REF][START_REF] Xu | Microstructural Investigation of Friction-Stir-Welded 7005 Aluminum Alloy[END_REF][START_REF] Fonda | Microstructural evolution ahead of the tool in aluminum friction stir welds[END_REF][START_REF] Gachi | Residual stress, microstructure and microhardness measurements in AA7075-T6 FSW welded sheets[END_REF][START_REF] Wang | EBSD study on microstructure and texture of friction stir welded AA5052-O and AA6061-T6 dissimilar joint[END_REF][START_REF] Imam | Microstructure-property relation and evolution in friction stir welding of naturally aged 6063 aluminium alloy[END_REF][START_REF] Peel | Microstructure, mechanical properties and residual stresses as a function of welding speed in aluminium AA5083 friction stir welds[END_REF][START_REF] Prangnell | Grain structure formation during friction stir welding observed by the stop action technique[END_REF][START_REF] Cho | Texture and microstructure evolution and mechanical properties during friction stir welding of extruded aluminum billets[END_REF] indicate that there is strong microstructural and textural evolution in similar and dissimilar heat treatable aluminum joints that are characterized by the thermal and deformation histories. These authors evidenced the occurrence of a recrystallization concomitant with the texture change and both contributed to the grain refinement of a stirred zone down to the sub-micrometer level.

properties, microstructure evolution, failure super-plasticity, peening effects and temperature distribution, as well as post weld heat treatment effects [14˗20]. As part of the optimization of processing parameters and following a previous investigation [START_REF] Boukraa | Friction stir welding process improvement through coupling an optimization procedure and three-dimensional transient heat transfer numerical analysis[END_REF][START_REF] Aissani | Design and Optimization of Friction Stir Welding Tool: Materials and Manufacturing Processes[END_REF], an optimal weld obtained during this process requires more knowledge of the microstructural-textural as well as the mechanical properties evolutions. In the current study, a microstructural and textural characterization of 7075˗T6 after FSW has been undertaken. The texture evolution was measured using local electron backScatter diffraction (EBSD) and global neutron diffraction (ND) techniques. Special experimental measurement allowed drawing 2D and 3D plots of the microhardness.

Moreover, the evolution of the Young's modulus (E) in different zones through the weld was treated too using two different methods. The first one, destructive, was the nanoindentation technic which use the inverse method of calculations [START_REF] Ambriz | Local mechanical properties of the 6061-T6 aluminium weld using micro-traction and instrumented indentation[END_REF]. The second one was the ultrasonic method which has the advantageous to be nondestructive, easy, inexpensive and fast to use in situ. Very few works have used ultrasound techniques to measure E in FSW process except Caroline et al. [START_REF] Carlone | Longitudinal Residual Stress Analysis in AA2024-T3 Friction Stir Welding[END_REF] published data on 2024-T3 aluminum alloy. In the present work, the invest igations concerned only the 7075-T6 alloy. The obtained results were compared to those derived from instrumented indentation tests and discussed.

Experimental procedure

The material used in this investigation was a 7075 alloy with dimensions of 200 mm × 250 mm × 3 mm. The chemical composition of this alloy is presented in Table 1.

The considered material has been subjected to a T6 heat treatment, which comprises solubilisation, a quench in water and artificial ageing. The used FSW tool is made from a 42CD4 treated steel "a low alloyed" (EN 10027˗1). The main elements of FSW tool are the shoulder and pin. The shoulder diameter is 20 mm associated with a conical threaded pin having 6 and 5 mm as upper and lower diameters, respectively, and 2.7 mm length (Fig. 1a).

However the pin was made from AISI H11, owing to its very good mechanical resistance at high temperatures and good toughness. The used 42CD4 steel has the following mechanical properties: tensile strength Rm = 860 MPa, yield strength Rp0.2 = 730 MPa, density ρ= 7850 kg/m 3 and elongation A=14 %. Its chemical composition is listed in Table 2.

The FSW process was carried out with a rotational and a welding speed of 1400 rpm and 60 mm/min respectively, a tilt angle of 1° and applied load of 1375 N. The welding direction (WD) was parallel to the rolling direction (RD). The transverse direction (TD) of the welded joint was denoted as cross welding direction (CWD) (Fig. 1). After the welding process, specimens for different analysis were cut from the welding zones: nugget zone (NZ), thermo˗mechanically affected zone/heat affected zone (TMAZ / HAZ) and base metal (BM) as indicated in Fig. 2. The texture of the samples was determined from neutron diffraction measurements on the 6T1 goniometer in the rolling plane of the sheet at the Léon Brillouin laboratory (CEA, Saclay, France). Sheet packets (1 cm 3 ) were prepared from the FSW processed sheets near the BM, HAZ and the nugget zones (as shown in Fig. 2). A set of three {111}, {200}, and {220} pole figures using a 5°*5° grid was used to calculate the orientation distribution function (ODF)

using Bunge series˗expansion method, with an expansion order of lmax = 22, using LABOTEX software [www.labosoft.com.pl].

Vickers microhardness was measured on weld cross surface mechanically polished using Wilson micro˗hardness tester. The measurements were made on five levels in the transverse direction (TD) through the thickness. A hundred of indentations per level were used to obtain the microhardness values with a load of 100 g (Hv100) and indentation time of about 10 s.

Local elastic modulus (E) has been determinate firstly by means of nondestructive method.

This one is based on ultrasonic time of flight (TOF) measurements to assess the experimental longitudinal (VL) and shear (Vs) bulk wave velocities. The velocity is given by the following fundamental equation:

𝑉 = 2𝑒 𝑇𝑂𝐹 (1)
Where "e" is the sheet thickness.

The TOF was calculated assuming a homogenous and isotropic sample, using ultrasonic transducers (OLYMPUS) with 5 MHz frequency and diameter of 15 mm, working on pulse echo mode. An ultrasound gel is spread between transducer and specimen. The ultrasonic signals are visualized on a digital GwINSTEK GDS˗2102 oscilloscope piloted by a computer, with a band wide of 100 MHz (Fig. 3). The Poisson ratio 𝜐 and local Young's modulus E (elastic modulus) are calculated using the following relations:

𝜐 = 𝑉 𝐿 2 -2𝑉 𝑆 2 2𝑉 𝐿 2 -2𝑉 𝑆 2
(2)

𝐸 = 2𝜌(1 + 𝜐)𝑉 𝑆 2 ( 3
)
where  is the sheet density. The measurements have been taken in the different weld zones.

Ultrasonic method has the advantageous to be nondestructive, easy, inexpensive and fast but unfortunately, we cannot make measurements only in the TMAZ only because of its narrow width (2mm) comparing to transducer diameter (15mm). So, another measurement technique such as the nanoindentation method can be taken on to verify the ultrasonic Young modulus measurement results. Although this method is destructive, it allows us to precisely localize the four zones.

Nanoindentation experiments were carried out on an Anton˗Paar nano˗hardness tester equipped with a Pyramidal Berkovich tip. The loads were between 1 and 500 mN, six tests were performed at each zone. The Young modulus was calculated using the model developed by Oliver and Pharr [START_REF] Oliver | An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments[END_REF].

Results and discussion

3.1. Macrostructure, microstructure and texture evolution

The overall macrograph of the 7075˗T6 welded sheet exhibits quite good surface appearance with some minor and marginal defects (Fig. 2). The macrostructure consists of four distinct regions including base metal (BM), heat affected zone (HAZ), thermo˗mechanically affected zone (TMAZ) and nugget zone (NZ) as shown in Fig. 4. This classification follows the adopted nomenclature on the American Welding Society Standard D17.3M as defined by Threadgill et al. [START_REF]Specification for friction stir welding of aluminum alloys for aerospace applications[END_REF][START_REF] Threadgill | Friction stir welding of aluminium alloys[END_REF].

The orientation imaging micrographs (OIM) in inverse pole figure (IPF) maps in ˂001˃ direction of the weld are presented in Fig. 5a˗c. These IPF maps were collected in the zones corresponding to BM, HAZ, TMAZ and NZ, respectively. The corresponding SEM images are shown in Fig. 5d˗f. The microstructure of BM (Fig. 5a) is characterized by coarse grains morphology, a large number of high angle grain boundaries (HAGBs) and lot of precipitates (indicated by black non index zones and that appear in the grain interior and at the grain boundaries) that should probably be MgZn2 type precipitates [START_REF] Mishra | Friction Stir Welding and Processing[END_REF]. However, Fig. 5b-c reveals that the NZ shows a fine equiaxed grain morphology that exhibits a high fraction of HAGBs. This indicates that a dynamic recrystallization (DRX) process occurred owing to the severe plastic deformation at high temperature during the friction stir welding.

Manifestly, the sharp microstructural (size, morphology, aspect ratio) difference between the NZ and TMAZ zones is materialized by a net interface as shown in Fig. 5b-e.

In the medium of the sheet thickness, the nugget zone has been located approximately in the weld center line at a width of 4 mm on both sides of this center line, while the TMAZ which is considered as a transition zone between the HAZ and the NZ, is extended approximately to 1 mm. It worth noting that just near the NZ/TMAZ interface, the grains exhibit strongly sheared and elongated morphology with a shearing direction being fairly opposite to that of tool rotation indicated by curved arrows. This zone belongs to the TMAZ and extends approximately to 200˗250 μm (Fig. 5b). respectively, near the BM and the NZ zones. Since all the pole figures manifested triclinic symmetry rather than orthotropic, the ODF was calculated accordingly.

The intensities of texture components are expressed in multiple of random density (mrd) units. The locations of ideal texture components after recrystallization and simple shear for FCC materials are presented in Fig. 10 and in Table 3. As obviously seen in Fig. 8, the main texture components of the 7075˗T6 base metal are {001}˂100˃ Cube and {011}˂100> Goss. In the NZ, it can be clearly seen that the texture is dominated by simple shear texture components A1*, A2*, A, Ā, B and B ̅ . The B and B ̅ components largely dominates (with intensity ~ 4.2 mrd) over C orientation. In general, shear deformation occurs by glide on {111} planes in ˂110˃ type direction. This results in the formation of two partial fibers called A and B and denoted {111}˂uvw˃ and {hkl}˂110˃, respectively. Along the A fiber, the most intense are the A, Ā, A1*and A2* components, while the B fiber contains the A, Ā, B, B ̅ and C ideal orientations [33].

From Fig. 9, it is obvious that neutron diffraction measurements enabled to evidence the same texture components of the BM with approximately close maximum intensities (~5.2 mrd). It is worth noting that the Cube component is still visible in the NZ zone but with very weak intensity. The Cube texture component is known to be metastable in the FSW process at ambient temperature [START_REF] Chen | Texture evolution and deformation mechanism in friction stir welding of 2219Al[END_REF]. Surprisingly, the texture measured and calculated near the NZ is almost different of that obtained through EBSD experiments and consists mainly of weak Cube and Goss recrystallization components with intensities that did not exceed 2.1 mrd.

Two main causes should explain why these shear components are not evidenced by neutron diffraction in the present study. The first is inherently associated with the well˗known under˗estimation of volume fraction (Fv) and intensity by neutron diffraction˗based technique [START_REF] Bolmaro | X-ray and neutron diffraction measurement of texture of two phase-materials[END_REF] and hence the minority A1*, A2*, A, Ā, B, B ̅ and C shear components should be « invisible », i.e. their expected volume fraction would be less than a cut off value (~ 2˗3 %).

However, evident shear texture components are seen in Fig. 9b and correspond to B and B ̅ orientations. Similar extinction of shear components during the measurement of texture via neutron diffraction have been reported by Azzeddine et al. [START_REF] Azzeddine | Neutron diffraction versus EBSD analysis of the texture in Fe-36%Ni alloy after accumulative roll bonding[END_REF] in a Fe˗Ni alloy processed by accumulative roll bonding and subsequent ageing.

The second cause arose from the fact the samples for neutron diffraction (stacked sheet packet) must have specific dimensions of 1×1×1 cm 3 . They were cut, as shown in Fig. 2, in an area which encompasses the BM and the TMAZ/ NZ zones. These latter extend beyond 2 mm over the limit of the nugget zone. Consequently, the almost and global texture obtained by neutron diffraction should be influenced by that of TMAZ/HAZ zones. HAZ zone is known to exhibit a texture that is often close to BM one [START_REF] Cho | Texture and microstructure evolution and mechanical properties during friction stir welding of extruded aluminum billets[END_REF]. As stated in [START_REF] Gan | Evolution of microstructure and hardness of aluminum after friction stir processing[END_REF], although the TMAZ undergoes plastic deformation, recrystallization does not occur entirely in this zone due to insufficient deformation strain. Beyond the TMAZ, in the HAZ, there is no plastic deformation, only a thermal cycle experiences in this zone. It has been evidenced that the HAZ retained the same grain structure (morphology) as the base material.

Quite similar results of texture evolution have been reported by Ahmed et al. [START_REF] Ahmed | Microstructure, crystallographic texture and mechanical properties of friction stir welded AA2017A[END_REF] on AA2017A FSW processed alloy. However, no such evolution of texture was evidenced in AA2024 [40]. These authors claimed that the recrystallization occurred in the FSW joined samples and this phenomenon led to the decrease in the initial orientation that was characterized by the α fiber (that containes Goss and Brass components) and τ˗fibrer (that goes from Copper to Goss orientations) while the Copper and Goss orientations remarkably increased.

Texture of the friction stir welded Al˗based alloys has been intensively analyzed [40][START_REF] Prangnell | Grain structure formation during friction stir welding observed by the 'stop action technique[END_REF][START_REF] Jin | Characterisation of microstructure and texture in friction stir welded joints of 5754 and 5182 aluminium alloy sheets[END_REF][START_REF] Sato | Microtexture in the Friction-Stir Weld of an Aluminum Alloy[END_REF][START_REF] Su | Microstructural investigation of friction stir welded 7050-T651 aluminium[END_REF].

This texture near the NZ was found as shear deformation process type and follows the torsion texture or simple shear texture of FCC materials [START_REF] Azzeddine | Neutron diffraction versus EBSD analysis of the texture in Fe-36%Ni alloy after accumulative roll bonding[END_REF]40]. The texture of the NZ exhibited mainly simple shear B (11˗2)[1˗10]/B ̅ (112)[1˗10] and C{001}˂110˃ components and B/B ̅ components dominated. Such a texture has also been evidenced in an ultrafine˗grained (UFG) Al-0.2 Wt.% Sc sheet, fabricated by accumulative roll bonding and subsequently welded by applying FSW process [45].

The occurrence of recovery during FSW is indubitable owing to the high stacking fault energy of 7075˗T6 alloy (γSFE˃ 170 mJm -2 ). The texture evolution is associated with the deviator stress states. FSW process needs the forward motion of the rotating tool toward the welding direction. This introduces several stresses in the material. The texture in the NZ is mainly related to the stresses at the backside of the tool that are generated by the rotation of the tool shoulder and the cylindrical pin an "over aging" because of the high temperature reached during welding that caused a certain growth of the grains and precipitate particles in this zone compared to BM as assumed by Ambriz et al. [START_REF] Ambriz | Local mechanical properties of the 6061-T6 aluminium weld using micro-traction and instrumented indentation[END_REF]. The increase of the microhardness in the nugget zone might be due to smaller grain size in this region and the re˗precipitation of the hardening phase and the existence of grain boundary precipitate as stated in [START_REF] Gan | Evolution of microstructure and hardness of aluminum after friction stir processing[END_REF].

To better characterize the microhardness distribution and localize the soft zone highlighted by Vickers microhardness low isovalues, a two dimensional microhardness map was plotted accordingly (Fig. 11b). It can be clearly seen that near blue color corresponds to the TMAZ (purple in Fig. 11a) where the minimum microhardness is reached (103Hv). The overall evolution of the microhardness seems to be corroborated by Fig. 11. represented. From Fig. 12, no important TOF differences was observed in the HAZ (or TMAZ) and NZ with respect to BM. The calculated Poisson ratio and elastic modulus are presented in Table 4. Regarding to the Young's modulus, the results show a small difference between the values calculated in each zone. In the NZ, the Young's modulus is equal to 70.3 GPa, it experiences an increase of 2.8 GPa (~ 4.2 %) relatively to the BM one. This variation can be expected from the microstructural observation where the fine grains are obtained in the NZ. The same conclusions were drawn by Carlone et al. [START_REF] Carlone | Longitudinal Residual Stress Analysis in AA2024-T3 Friction Stir Welding[END_REF] who noted an increase of 4.6 % in NZ with respect to the base metal modulus. However, a slight decrease of 1.3 GPa (~ 1.9 %) is measured in the HAZ/TMAZ compared to BM. This softening may be associated with a decrease of the microhardeness in this zone.

In order to validate the previously results by local investigation, nanoindentation measurements were also carried out. Fig. 13 shows the mean Young's modulus resulting from six indentations in each zone as a function of the different zones. The Young modulus value in the BM zone is quite close to that in NZ however, it slightly decreases in the softened HAZ and TMAZ zones.

Table 5 summarises the elastic modulus obtained by ultrasonic (US) and nanoindentation techniques. The difference (in %) between the values obtained via both techniques is also given. The Young modulus in both methods decreases in the HAZ and TMAZ with respect to the BM. It increases in the NZ. Furthermore, it can be observed that the difference between the two methods results is negligeable which indubitably indicates an acceptable agreement between the achieved techniques.

Conclusions

The microstructure, crystallographic texture and mechanical properties of FSWed aluminium alloys 7075˗T6 have been investigated and the most important results are:

• The NZ contained fine equiaxed and fully recrystallized grains while BM consisted of coarse grains. The average grain size in the MB and NZ were 52.9 and 1.82 μm.

• The NZ showed a high fraction (~ 57 %) of HAGBs. This indicated that a dynamic recrystallization (DRX) process occurred owing to the severe plastic deformation at high temperature during the friction stir welding.

• The texture of the BM mainly consisted of recrystallization Cube and Goss components.

In the stir zone, the dominant texture components were B and 𝐵 ̅ component among faint other shear orientations. • EBSD and neutron diffraction techniques resulted in identical texture in the BM zone.

While totally, different textures were measured near the stirred zone.

• The drop of microhardness in the HAZ might probably be caused by an over aging and a re˗precipitation of the hardening phase and the existence of grain boundary precipitates.

• An evident correlation has been found between the ultrasonic measurements of Young modulus and nanoindentation method.

References:

[

Figure 1 :

 1 Figure 1: (a) FSW process, (b) Shoulder and pin.

Figure 2 : 3 imaging

 23 Figure 2: Macrography of the FSW 7075-T6 alloy.

Figure 3 :

 3 Figure 3: Experimental used set up for the determination of the ultrasonic velocities.

Figure 4 :

 4 Figure 4: Macrostructure of weld zones in cross section.

Figure 5 :

 5 Figure 5: OIM in IPF map and corresponding SEM images obtained from the FSW 7075-T6 alloy in: a-d) BM, b-e) interface between NZ and TMAZ and c-f) NZ, respectively.

Figure 6 :

 6 Figure 6: Grain size distribution of the base metal and nugget zones.

Figure 7 :

 7 Figure 7: Grain boundary character distribution (GBCD) in the BM and NZ zones. The texture change during recrystallization and grain growth was analyzed by plotting the orientation distribution function (ODF) sections. Fig. 8 and 9 show the ODF sections at 2 = 0 and 45° obtained from the EBSD measurements and neutron diffraction (ND)

  Since the NZ zone exhibits recrystallized fine grains with shear texture accompagnied by minor Cube component let's enforces the possibility that the weld zone was dynamically recrystallized during plastic flow. It could experience a statical recrystallization after the rotating pin passes. Many authors stated that the dynamic recrystallization was responsible of the fine recrystallized microstructure [47˗50]. However, very few is known about the effective role fo static recrystallization.

Figure 8 :

 8 Figure 8: ODF sections at 2 = 0° and 45° obtained from the EBSD measurements near (a) BM zone and (b) NZ, respectively.

Figure 9 :

 9 Figure 9: ODF sections at 2 = 0° and 45° obtained from the neutron diffraction measurements near (a) BM and (b) NZ, respectively.

Figure 10 :

 10 Figure 10: The locations of the ideal (a) recrystallization components in FCC materials components and (b) simple shear texture components.

Figure 11 :

 11 Figure 11: Vickers microhardness evolution through the weld on cross setion ( x and y coordinates): (a) 3D view and (b) 2D isovalue map.3.3 Young's modulus measurements Fig. 12 shows the utrasonic signals for shear and longitudinal bulk waves in BM, HAZ and NZ. The width of the TMAZ is very small compared to transducers diameter so the signals obtained in the HAZ and TMAZ are superimposed. For this reason, only one signal has been

Figure 12 :

 12 Figure 12: Utrasonic signals for: (a) shear and (b) longitudinal bulk waves in the BM, HAZ and NZ.

Figure 13 :

 13 Figure 13: Evolution of the mean elastic modulus obtained in the four zones over AS and RS.

Table 1

 1

	: Chemical composition in Wt% of 7075˗T6
		Al	Si	Fe	Cu	Mn	Mg	Zn	Cr
	Wt.%	89.6	0.120	0.188	1.65	0.0202	2.47	5.66	0.208
	Table 2: Chemical composition in Wt% of 42CD4
		C	Si	Mn	P	S	Cr	Mo
	Wt.%	0.45	0.40	0.9	0.025	0.035	1.2	0.3

Table 3 :

 3 Ideal positions of main shear and recrystallization texture components in FCC

	materials taken from [30]
	Texture	Miller indices		Euler angles (°)
	components	(hkl) [uvw]	1		2
	A 1 *	(111)[1 ̅ 1 ̅ 2]	35.26	45	0
	A 2 *	(111)[112] ̅	54.74	90	45
	A	(11 ̅ 1)[110]	0	35.26	45
	Ā	(1 ̅ 11)[1 ̅ 1 ̅ 0]	180	35.26	45
	B	(11 ̅ 2) [110]	0	35	45
	B ̅	(1 ̅ 12 ̅ )[1 ̅ 1 ̅ 0]	60	54.74	45
	C	(001)[110]	90	45	0
	Cube	(001)[100]	0/90	0	0
	Copper(Cu)	(112)[111]	90	35	45
	Goss	(011)[100]	0	45	0

Table 4 :

 4 Experimental values of the mechanical properties of 7075˗T6 alloy. The Poisson ratio is an intrinsic property of the material that often changes very slightly during thermomechanical processing. The experimental values obtained are the same in the different zones and very close to the theoretical one (0.33) for pure Al and its alloys [51].

		BM	HAZ	NZ
	𝝊	0.34 ± 0.01	0.34 ± 0.01	0.34 ± 0.01
	E (GPa)	67.5 ± 0.8	66.2 ± 0.8	70.3 ± 0.8

Table 5

 5

	: Comparison of ultrasonic elastic modulus measurement by the nanoidentation
	method.
	E(GPa)	BM	HAZ	TMAZ	NZ
	EUS	69	66.2	66.2	70.3
	Enano	72.0	65.7	65.1	70.8
	Diff (%)	4.1	0.76	1.68	0.70

  1] Hidalgo˗Manrique, P., Cepeda˗Jimenez, C.M., Ruano, O.A., and Carreno, F., Effect of warm accumulative roll bonding on the evolution of microstructure, texture and creep properties in the 7075 aluminium alloy, Mat. Sci. Eng. A, 2012, vol. 556, pp. 287-294. [2] Mao, Y., Ke, L., Liu, F., Liu, Q., Huang, C., and Xing, L., Effect of tool pin eccentricity on microstructure and mechanical properties in friction stir welded 7075 aluminum alloy thick plate, Mater. Des, 2014, vol. 62, pp. 334˗343.