**1. Introduction**

During past three decades, numerous studies have been conducted on the structure and mechanical properties of bulk nanostructured (NS) and ultra-fine-grained (UFG) materials produced by severe plastic deformation (SPD) processing. In these studies, considerable effort has been devoted to high pressure torsion (HPT) [1,2] as well as equal channel angular pressing (ECAP) [3–5] since these two are the best-known SPD techniques for producing UFG metallic materials. UFG materials with unique combinations of mechanical properties such as high strength and plasticity [6] have generated intensive interest because the results of some studies have suggested the presence of new strengthening mechanisms.

NS metals, including those processed by HPT, generally exhibit very high strength but limited tensile ductility (with a uniform elongation, only reaching a few percent) with almost no work-hardening [7]. Low ductility is believed to be an intrinsic "Achilles heel" of NS metals because the conventional deformation mechanisms cease to operate at the nanoscale level such that: (i) the dislocation slip is substantially suppressed by the extremely small grains (which, however, account for the extreme strength values in NS metals); and (ii) grain boundary (GB) sliding or diffusional creep is not active enough to accommodate plastic straining at ambient temperature [8]. However, some experimental data have hinted to the possibility that the generally observed low plasticity in NS metals might be extrinsic rather than intrinsic to these materials. For instance, dimples have been observed on fracture surfaces of various NS metals, indicating substantial plastic deformation before failure [7]. In addition, large plastic strains were also obtained when using other deformation schemes such as compression and rolling [3,5]. Indeed, limited tensile ductility of NS metals has often been attributed to the absence of work hardening and to their nano-sized grains, so that strain localization and early necking occur immediately after the onset of yielding. On the other hand, intrinsic tensile plasticity of NS metals can be detected by effective suppression of strain localization.

There are several kinds of SPD techniques, which combine extrusion and shear, e.g., twist extrusion [9], extrusion compression [10] and cyclic expansion extrusion [11]. In this study, we used the high pressure torsion extrusion (HPTE) approach, with prevailing shear strain at the periphery of bulk rod samples and extrusion-like deformation near the center of the rods [12–14]. The strain conditions at the center and at the edge of the HPTE-processed rods depend on the processing parameters and they can vary by several orders of magnitude. Therefore, HPTE is the one of the SPD methods which is capable of producing rod samples with controlled gradient heterogeneous structures.

During the past decades, comprehensive analyses on the influence of the deformation mode on the structural evolution and the resulting physical properties of initially structurally homogeneous materials have been conducted. For example, refer to the study on the hardness and electrical conductivity of pure copper processed by ECAP and HPT [15]; the study on the structural evolution in a Siclanic alloy (Cu–Ni–Si) processed by ECAP and HPT [16]; and the studies on the effect of the SPD deformation mode on the microstructure of pure copper [17,18].

Recently, a few studies have been reported on the mechanical properties of structurally heterogeneous materials [7,19], consisting of hard and soft domains, which may demonstrate the combination of very attractive properties such as high strength and high tensile ductility values. Knowledge on the effects of fine–ultrafine and nano-grained structures on mechanical properties will make it possible to significantly extend our understanding of the deformation processes from the analysis of homogeneous materials to that of heterogeneous counterparts and, in particular, structurally gradient materials [20].

One of the clearest structural features of Cu after the HPTE processing is a strong grain refinement in the peripheral area, and a less pronounced grain refinement in the sample's core [12]. Such heterogeneous structure was the result of strain gradient along the sample radius. Tensile tests, carried out on the gradient Cu samples after a surface mechanical grinding treatment, have shown that the combination of NS to coarser grained microstructure provide an effective approach for enhancing the "strength–ductility" synergy of materials which offer a potential for using the gradient NS layers as an advanced coating of the bulk materials [7].

However, since HPTE it is a newly established SPD technique, data on the applicability of this method to produce structurally gradient materials are still not available. Consequently, results on the characterization of their mechanical properties are also limited. This study aims to bridge this gap by conducting a critical analysis of both the structure and the mechanical test results obtained on HPTE-processed Cu rod samples to reveal possible strengthening effects of varying grain refinement steps giving rise to gradient (heterogeneous) structures.

### **2. Materials and Methods**

CP copper samples containing 99.0 wt% of Cu and 1.0 wt% of Al were first machined, annealed for two hours at 600 ◦C, and then water quenched to obtain a coarse-grained (CG) microstructure. A typical orientation imaging microscopy (OIM) map of the initial structure is shown in Figure 1a. The OIM map was obtained from the electron backscatter diffraction (EBSD) data and it demonstrates, random grain orientations. The initial structure is characterized by near-ellipsoid-shaped grains (the aspect ratio was ~1.3) with numerous annealing twins (Figure 1a) and an average grain size of ~30 μm. As shown by the back-scattered electron (BSE) image in Figure 1b, the microstructure also contains second-phase particles. The BSE image shows that the second phases are nearly spherical

with an average diameter of ~1–5 μm. Usually, these particles are Cu-rich AlCu3, Al4Cu9 and AlCu2 intermetallic phases [21,22]. According to the technical specifications of CP copper [22], the particles have a metallurgic origin and they can also include oxides, hydrides, and flux-income impurities.

**Figure 1.** (**a**) Typical orientation imaging microscopy (OIM) map and (**b**) back-scattered electron (BSE) image of the annealed Cu rod (longitude section).

The HPTE apparatus (Karlsruhe Institute of Technology, Institute of Nanotechnology, Eggenstein-Leopoldshafen, Germany), with a specially designed die, is shown in Figure 2a. The material processing was performed at 100 ◦C with an extruding velocity (υ) of 1 mm/min and a rotational velocity (ω) of 1 rpm. According to [12], HPTE-processed copper with v1w1 regime at room temperature led to the formation of a UFG structure. In our study, cylindrical shaped (rod) samples with an initial diameter of 11.8 mm and a length of 35 mm were processed using molybdenum disulfide (MoS2) as a lubricant to facilitate the extrusion process. The HPTE apparatus was described in detail in [12]. During the processing, the Cu rod samples were exposed to expansion and extrusion as well as torsion.

**Figure 2.** HPTE die with (**a**) holding elements and (**b**) a schematic drawing of the tensile test sample. Dimensions are given in millimeters.

Additional details regarding the development of the die design and the compressive strength the material samples are subjected to during the HPTE processing have been described in an earlier study [23]. The resulting equivalent strain depends on the ratio of the channel diameters (D1/D0 and D1/D2), the extruding velocity (υ), and the angular velocity of the die (ω), and it can be calculated as follows [12]:

$$\mathbf{e} = 2\text{lnD1/D0} + 2\text{lnD1/D2} + (\mathbf{w}^\* \mathbf{R}^\* \mathbf{D1}) (\sqrt{3}^\* \mathbf{v}^\* \mathbf{D2}) \tag{1}$$

where D0, D1, and D2 are fixed and equal to 12, 14, and 10.6 mm, respectively, and R is the distance from the center in the sample's cross section.

Under the above-mentioned parameters, Table 1 contains the strain values calculated using Equation (1). The equivalent strain is in the range between 5.2 and 22.4, depending on the distance from the center, which ensures the formation of a gradient structure.

**Table 1.** Structure parameters of CP Cu rod after the HPTE treatment, based on the SEM–EBSD and BSE imaging \*.


\* All microstructure parameters are given for the transverse/longitudinal sections. \*\* Here the grain size values for two maxima of the grain size distribution by the specific area are given.

The HPTE-processed samples were afterwards sectioned both in the transverse (normal) and longitude directions, thinned to the foil thickness, grinded, and mechanically polished. The polished samples were subsequently examined by EBSD technique, using a ZeissAuriga60 scanning electron microscope (SEM), equipped with an EDAX-TSL EBSD system, and operated at 20 kV. The samples for SEM observations were prepared by conventional electro-polishing procedure with a Tenupol-5 twinjet polisher, using standard Struers solution for copper. Final polishing on GATAN PIPS system was performed to remove the surface oxide layer.

TSL OIM EDAX v.7 (EDAX Inc., Draper, UT, USA) software was used for indexing the EBSD patterns. The dimension of the scan areas was 20 × 20 μm. OIM maps were collected from transverse (shear plane) and longitudinal sections of the samples. They were collected at the sample's center (~0.5 mm from the sample axis), at the middle-radius (~2.7 mm from the sample axis), and at the sample's edge (~4.5 mm from the sample axis). Scan step was 0.1 μm for the initial state and at the central area of the deformed samples, and 0.05 μm at the mid-radius and edge of the HPTE samples.

To minimize misindexing error, nine Kikuchi-bands were used for indexing. To ensure reliability of the EBSD data, all grains comprising of three or fewer pixels were automatically removed from the maps using the grain-dilation and neighbor orientation correlation options of the TSL software (minimal grain tolerance angle was 5◦). The camera settings and the Hough parameters allowed us to collect data without significant decrease in pattern quality with the angular resolution ~0.5◦. For noise reduction, a lower limit boundary misorientation cut-off value of 2◦ was applied. A 15◦ criterion was used to differentiate between low—(LABs) and high—(HABs) angle GBs. The grain size (D) was computed using the equal diameter method. Two misorientation threshold values, of 3◦ and 15◦, were used to define the grain area. The respective mean grain sizes are labeled as D3 and D15. Specific grain area (S/S*i*) distributions by the grain equivalent diameter were plotted for more than 500 grains in each state, where S is the map area and S*<sup>i</sup>* is the area of the grains within the *i*-th interval.

Grain shape was characterized by the N*x*/N*y*, the aspect ratio parameter corresponding to the ratio between the number of HAB intersections with vertical (N*x*) and horizontal (N*y*) secant lines in the transverse and longitude sample sections, respectively. The dislocation density was measured by means of two methods, i.e., EBSD and X-ray diffraction (XRD). The EBSD technique allows to define only geometrically necessary dislocation (GND) density [24], whereas XRD measured total dislocation density, including GNDs and statistically stored dislocations (SSDs). As a first-order estimate, the

kernel average misorientation (KAM), which is retrieved directly from EBSD data, was chosen as a measure for the local misorientations. KAM gives the average misorientation around a measurement point with respect to a defined set of nearest and second-nearest neighbor points. The GND density was calculated from the local misorientations, using the option of the OIM software for the angles smaller than 2◦. Standard preset for fcc crystal-type slip systems was used in the software set-up. For the calculation of KAM, we considered the slip in (111) crystallographic planes and four possible slip systems along four close-packed <110> directions. We computed the GND density, using the experimental data on the misorientation angle. Additional details regarding GND density calculation can be found elsewhere [25]. The calculation was done for each map pixel, taking into account the data for five nearest neighbors. Orientation gradient was determined as the misorientation between two points over the corresponding length [26].

XRD spectra were collected with a Philips X'Pert powder diffractometer (Malvern Panalytical Ltd., Almelo, The Netherlands), operating in the Bragg–Brentano geometry with the Cu-Kα emission line. The background pattern was calculated by the X'pert HighScore software (Malvern Panalytical Ltd., Malvern, UK). The irradiation area had the dimensions of 5 mm in width and 1 mm in length. This made it possible to obtain XRD spectra from three different locations of the sample along the shear direction (SD) in the longitudinal rod section.

Parameters of the XRD peak profiles, i.e., peak intensity and full width at half maximum, were fitted by the Pseudo-Voigt function. The mean diameter of the crystallites (size of coherently scattering domains) and micro-strain have been estimated from the diffraction peak broadening, including reflections up to (420), in a modified Williamson–Hall method [27]. It is known that in the case of the random distribution of dislocations, the total dislocation density ρ can be defined as [28,29]:

$$\rho = \frac{2\sqrt{3}\left\langle \varepsilon\_{hkl}^2 \right\rangle^{1/2}}{D\_{hkl}b},\tag{2}$$

where D*hkl* is crystallite size, < ε<sup>2</sup> *hkl* <sup>&</sup>gt;1/<sup>2</sup> is the mean squared micro-strain value, and *<sup>b</sup>* is the absolute value of the Burgers vector.

SEM Zeiss LEO1530 at the acceleration voltage of 20 kV coupled with energy-dispersion spectrometry (EDS) was used for the elemental analysis of the samples.

To enhance the spatial and angular resolution of the OIM analysis we carried out the investigations using the FEI Tecnai F20 transmission electron microscope (200 kV) with field emission gun, equipped with the system for automated crystal orientation mapping in the TEM (ACOM-TEM) [30]. For the mapping we used the μ-probe set-up with a beam diameter of ~1–1.5 nm and step size of 5 nm.

A Buehler Micromet-5104 tester was used for the Vickers hardness measurements. A load of 0.2 kg with a dwell time of 15 s was applied to all samples during the hardness measurements. Five indentations spaced 1 mm apart were made along two mutually perpendicular diameters of the specimens. The average value of each measurement was computed from 10 indentations.

Tensile tests were carried out at ambient temperature at a strain rate of 1 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>s</sup><sup>−</sup>1, using a Zwick Z100 screw-driven testing machine on cylinder-shaped samples with twist holders (Figure 2b). The tensile samples were machined from the three HPTE-processed billets along the extrusion direction in accordance with ASTM E 8/E 8M-08 requirements.
