Applying hybrid equal channel angular pressing (HECAP) to pure copper using optimized Exp.-ECAP die

Equal channel angular pressing (ECAP), expansion equal channel angular pressing (Exp.-ECAP), and hybrid equal channel angular pressing (HECAP) or (Hybrid ECAP) processes were applied to pure copper specimens within this study. After the application of ECAP, the die used in the application of the Exp.-ECAP process was optimized considering the strain inhomogeneity in the specimen and the maximum load that occurred during the process. Finite element method (FEM), artificial neural network (ANN), and genetic algorithm (GA) were utilized together for the optimization process. The optimized die equally minimizes the pressing load and the strain inhomogeneity that occurred in the specimen. Using the optimized die, Exp.-ECAP and HECAP processes were applied to pure copper. The Exp.-ECAP process was previously applied only for aluminum alloys and magnesium alloys. With the application of the Exp.-ECAP process to pure copper, this gap in the literature was removed. In addition, with the application of the HECAP process, the effects of the Exp.-ECAP passes applied after ECAP were also examined which was not done earlier. The specimens, on which ECAP, Exp.-ECAP, and HECAP processes were applied, were subjected to microstructure analysis and mechanical tests, and the effects of these processes were examined. The results obtained showed that the Exp.-ECAP process gave better results in grain refinement and mechanical properties. The Exp.-ECAP passes applied after the ECAP process within the scope of the HECAP process provided a more homogeneous distribution for the microstructure and the hardness.


Introduction
Severe plastic deformation (SPD) is one of the important grain refinement processes preferred by researchers. Thanks to SPD processes, ultra-fine grained (UFG) materials can be obtained. The reason why SPD methods are preferred as grain refinement methods is that they do not cause any change in the external dimensions of the specimen during the process, and thus, the process can be continued repeatedly. There are many SPD processes such as high pressure torsion (HPT) [1], multi-directional forging (MDF) [2], twist extrusion (TE) [3], repetitive corrugation and straightening (RCS) [4], and accumulative roll-bonding (ARB) [5], but the equal channel angular pressing (ECAP) [6][7][8] is one of the most preferred SPD processes. This is because the ECAP method is a process that provides large effective strain and does not require a complex and expensive experimental setup. In recent years, studies proposing certain modifications to the process have been carried out to increase the efficiency of the ECAP process and to expand its application areas. As a result of these studies, many modified ECAP processes such as tubular channel angular pressing (TCAP) [9], incremental equal channel angular pressing (I-ECAP) [10], thin-walled open channel angular pressing (TWO-CAP) [11,12], and ECAP-Conform have been added to the literature. Expansion equal channel angular extrusion (Exp.-ECAE) [13] or expansion equal channel angular pressing (Exp.-ECAP) is one of the modified ECAP processes. The biggest difference in the die designed for this process compared to the classical ECAP die is that there is a spherical cavity which leads to pseudo-back pressure being exerted on the specimen during the process. In this way, a more homogeneous effective plastic strain distribution is obtained on the specimen, and higher strain values can be obtained thanks to the extrusion ratio between the spherical cavity and channels. Pure copper is a metal with high electrical conductivity and thermal conductivity properties, but it cannot be said to have high values in terms of mechanical properties. For this reason, it is a preferred metal in many SPD works [14][15][16][17][18][19][20]. Although the Exp.-ECAP process has been applied for some aluminum and magnesium alloys [13,21,22], it has not been applied before for pure copper.
In this study, pure copper was subjected to ECAP and Exp.-ECAP processes. In addition, a process called hybrid equal channel angular pressing (HECAP), which consists of the combination of ECAP and Exp.-ECAP process, was applied to pure copper. With this application, the effects of the Exp.-ECAP process applied to an ECAP applied specimen were investigated. In addition, the Exp.-ECAP die was optimized within the scope of this study and this optimized die was used in the Exp.-ECAP and HECAP processes.

Material and method
The methodology applied within the scope of the study consists of several steps. Firstly, the ECAP process was subjected to copper specimens. Secondly, a finite element (FE) model was generated for the ECAP process and validated by comparing load-displacement curves obtained from the experiment and finite element analysis (FEA). After validating the FE model generated for the ECAP process, another FE model was generated for the Exp.-ECAP process using the same boundary conditions used in the ECAP FE model. In the next step, the Exp.-ECAP die was optimized utilizing FEA, artificial neural network (ANN), and genetic algorithms (GA). After obtaining optimum geometry for the Exp.-ECAP die, Exp.-ECAP and HECAP processes were completed. At the last step, mechanical tests and microstructural examinations were carried out.
The flow chart of the methodology applied within the scope of the study can be seen in Figure 1. Although the study was carried out in the order shown in the flow chart, experimental and numerical studies of ECAP, Exp.-ECAP, and HECAP processes are given under the same titles.

Experimental study
Within the scope of the experimental study, firstly, pure copper specimens were prepared for ECAP and Exp.-ECAP processes. The channel diameter in the ECAP die is 20 mm, while the channel diameter in the Exp.-ECAP die is 16 mm. For this reason, the specimens prepared are not the same size. Since it has been shown in the study conducted by Frint et al. that the differences in specimen sizes do not affect the ECAP process [23], it is possible to say that there will be no inconsistency in the comparison of the results obtained. The prepared copper specimens were annealed at 600°C for 2 h. The ECAP process was carried out after annealing from one pass to four passes. Hexa-ECAP die designed by Kaya was utilized for the ECAP process [24,25]. The ECAP process was carried out at 200°C and the preferred pressing speed is 1 mm/s. Molybdenum disulfide (MoS 2 ) was used as a lubricant in order to minimize the friction between the specimen and the die during the process. During the ECAP processes, load and time graphs were obtained to be used in the verification of finite element analysis. The Hexa-ECAP die and the CAD geometry of the die are shown in Fig. 2a and b. Also, ECAPed copper is shown in Fig. 2b.
After the ECAP process, the Exp.-ECAP process was carried out from one pass to four passes as well as in the ECAP process. With the preferred operating temperature and pressing speed values for the Exp.-ECAP process, the lubricant is the same as those used in the ECAP process. The CAD Fig. 1 Flow chart of the methodology applied within the study geometry of the die and plunger used in the Exp.-ECAP process is shown in Fig. 2c, while the die itself and the Exp.-ECAPed specimen are shown in Fig. 2d. After the completion of the Exp.-ECAP process, the HECAP process was carried out. The HECAP process has been applied in two stages. First of all, copper specimens were subjected to 1-pass and 4-pass ECAP process. Later, the diameters of the ECAPed specimens were reduced to a diameter compatible with the Exp.-ECAP die. Subsequently, one passage Exp.-ECAP process was applied to ECAPed specimens with 1 pass and 4 passes.
Mechanical tests of processed specimens were carried out after ECAP, Exp.-ECAP, and HECAP processes. First of all, tensile test specimens and hardness test specimens were prepared. Secondly, the tensile tests were carried at room temperature and the preferred tension speed is 1 mm/s. The tensile tests were repeated three times for each pass and the average results were taken as the tensile test result. After the tensile tests were carried out, fracture surfaces were visualized by SEM. Information about the fracture mechanism was obtained by examining the fracture surface on the obtained images. Later, microhardness tests were carried out using the Vickers (HV) method. Hardness values were taken from five different points along the radius on the hardness specimen prepared for all cases. The average of these values was accepted as the hardness value. While the load used during the tests is 50 gf, the dwell time is 10 s.
Microstructure studies carried out within the scope of the study consist of four main steps. Before proceeding to these steps, the surfaces of the specimens used in hardness tests were subjected to grinding and polishing for microstructure studies. The copper specimens were then etched for OM imaging using an etchant composed of 1 g FeCl 3 , 10 ml HCl, and 100 ml distilled water. Etched specimens were visualized by OM. The grain sizes were measured from the OM images obtained by using NIS Element Basic Research software.

Finite element analysis
The simulation procedure of this study consists of two parts. In the first part, a FE model was generated to simulate the ECAP process. For this purpose, Deform 3D software, which is frequently preferred in SPD studies, was preferred. CAD geometries of the die and specimen shown in Figure 2a are used in the FE model. The channel and the pin diameters of the ECAP die are 20 mm. Likewise, the workpiece diameter is 20 mm while the length is 55 mm. While the die and pins are modeled as rigid, the specimen is modeled as a plastic material. Subsequently, a mesh structure consisting of 50000 tetrahedral elements was generated for the workpiece. The initially created mesh structure changes during FEA due to its remeshing feature. Thus, high strains occurring in the specimen could be calculated. During the process, the relative Fig. 2 a ECAP die CAD geometry, b ECAP die and processed specimen, c Exp.-ECAP die CAD geometry, d Exp.-ECAPed die and processed specimen interference depth criterion used for remeshing was taken as 0.7. Boundary conditions such as process temperature and pressing speed in the ECAP process as explained in "Section 2.1" were taken to be the same for the FE model. Finally, the friction coefficient between the specimen and the die was taken as 0.08 because this is the coefficient friction value provided by the solid lubricant during the pressing operation. After the FE model was created, the simulation was started and FEA was performed. Then, the load-stroke curves obtained from the experimental and numerical analyses are compared for the validation of the FE model.
In the second part, the FE model has been generated for the Exp.-ECAP process. The plunger diameter and the channel diameter are 16 mm. Likewise, the workpiece diameter is 16 mm while its length is 70 mm. While generating the FE model for the Exp.-ECAP process, all the boundary conditions used in the FE model of the ECAP process. Element type, element number, and relative interference depth values are the same with those used in ECAP simulation. Since the only significant differences between the two processes are the die geometry and dimensions, the FE model generated for the Exp.-ECAP process is assumed as also validated. In the following part of the study, the validity of this assumption has been proven by comparing numerical and experimental studies. An example of the FE models generated for ECAP and Exp.-ECAP processes can be seen in Fig. 3.

Optimization of Exp.-ECAP die
Optimization of an Exp.-ECAP die was previously done by Fereshteh-Saniee et al. [22]. However, in the mentioned study, optimization was done separately for two different objective functions. However, dies were not produced for the optimum geometries obtained and the Exp.-ECAP process was not applied for any specimen. In this study, optimization has been performed by using an objective function in which two different objectives are equally effective and a die has been produced for the obtained optimum geometry. In addition, one of the two objectives used was determined as the maximum load that occurred on the die during the process, unlike the reference optimization study. The Exp.-ECAP process was applied to pure copper specimens by using the optimum die produced at the end of the study. The optimization process carried out in this study consists of four main stages: design of experiments, objective function, artificial neural network, and genetic algorithm.

Design of experiments
The geometric parameters taken into account in the optimization process are as shown in Fig. 4. These geometric parameters are the channel diameter (D 0 ), the diameter of the spherical cavity (D 1 ), the fillet radius (r), and eccentricity of the cavity center with respect to the intersect of the centerlines of the channels (e). These parameters were nondimensionalized as in the reference study as follows [22]: After that, the design of the experiment was carried out by adhering to the limit values obtained for dimensionless parameters in the reference study [22]. A total of 30 experiments were determined to be simulated using the finite element method and were shown in Table 1.

Objective function
As stated before, the optimization process is carried out as multi-objective optimization. Optimization is carried out by creating an objective function in which two different objectives are combined.
There are studies showing that there is a relationship between the changes in the mechanical properties of the specimen in excessive plastic deformation applications and the effective plastic strain in the specimen during the process [26]. In specimens subjected to the SPD process, homogeneity is important as well as the magnitude of the strain values. It is seen that more homogeneous hardness values are obtained with a more homogeneous strain distribution. For this reason, strain homogeneity calculations have been made in SPD studies in recent years [27,28]. The coefficient of variance (CV) is a statistical formula used to calculate the distribution around the mean of any data set. This formula was used to calculate strain inhomogeneity by Patil Basavaraj et al. and called the coefficient of variance for effective plastic strain (CVε p ) [28]. This formula was chosen as the first objective to be used in the optimization study.
where Stdevε p is the standard deviation of effective plastic strain and Avε p is the average of effective plastic strain. Effective plastic strain values were extracted from 50 points from the transverse plane of the Exp.-ECAPed specimen as shown in Fig. 5.
Dies used in ECAP and similar studies are exposed to high loads during the process. In some cases, dies are damaged due to improper design. In order to eliminate this situation, larger sizes are generally preferred in dies; thus, both the die costs increase and the application of the process becomes more difficult as a result of the increase in size. Since the increased extrusion rate in the Exp.-ECAP die will increase the resulting load, it would be reasonable to use an objective that will minimize the load by controlling the extrusion rate. For this reason, the second objective to be used in the multi-objective  Fig. 5 The pattern of the points used to extract effective strain values optimization process has been determined as the maximum load (ML) to which the die is exposed.
The objectives mentioned above are considered as equally effective in the literature, so these objectives are combined in this study whose form is given in equation (4). This objective function is used to obtain the optimum die geometry. Thus, a single optimum geometry could be obtained.
Objective function ¼ 0:5*Objective 1 þ 0:5*Objective 2 ð4Þ Since there are no theoretical or empirical equations that give the values in the first and second objectives, network files were generated at the next step by using the ANN method to obtain the determined objectives.

Artificial neural network
Artificial neural network (ANN) is a tool preferred to use instead of making hard-to-repeat experiments and time-consuming simulations. It is also a tool used in optimization operations when it is not possible to specify objective functions mathematically. Within the scope of this study, since the objectives cannot be obtained mathematically, the ANN method was used. The generated network files receive alpha, beta, and gamma as input and predict CVε p and ML. The network files have a back-propagation algorithm and consist of four layers, namely, the input layer, two hidden layers, and the output layer. While the preferred training function in the network file was Levenberg-Marquardt, the number of neurons used in hidden layers was determined as 15. While deciding on these parameters, many trials have been made and those with the best performance have been chosen. Neural network files were generated using the inputs and outputs of 30 FE analyzes. Since CVε p and ML results obtained from 30 FE analyses have different ranges, before using these data in ANN, they were normalized between 0.1 and 0.9 in order to make them have equal effect on the objective function. Data of 20 of these analyzes were used for training, while 10 of them were used for testing.
After the network files generated for CVε p and ML were put into the objective function, the optimization process was carried out using the genetic algorithm.

Results and discussion
The results obtained within the scope of the study are given under four main titles. First, the results obtained from the FE analysis of the ECAP process and the results obtained from the 30 FE analyses performed for the Exp.-ECAP process are given. Secondly, optimization results are given. FE analysis results of the Exp.-ECAP process are also given with the optimization results. Subsequently, the mechanical properties of the specimens subjected to ECAP, Exp.-ECAP, and HECAP processes were given. Finally, the microstructure results of these specimens are given.

Results for finite element analysis
ECAPed specimen shapes obtained from experiment and FE analysis are compared in Fig. 6a and b. In addition, the curves showing the load applied to the die during the ECAP process and stroke values were obtained both experimentally and numerically and shown in Fig. 6c. Considering the results given in Fig. 6a-c, it can be concluded that the FE analysis performed for the ECAP process is validated. The effective strain distribution of the ECAPed specimen is shown in Fig. 6d. The average strain value of the specimen was obtained by taking the average of the values extracted from 50 points on the transverse section. Also, the CVε p given in equation (2) is also calculated by taking the values extracted from these 50 points. The average strain value obtained is 1.25 and this value is very close to 1.15 which is the theoretical value that should be in the ECAP process. CVε p value was also calculated as 0.434.
In addition to the results of the ECAP FE analysis, the results obtained from the 30 Exp.-ECAP FE analyses were given in Table 1.

Results of optimization
The performances of the ANN files used in the optimization process and used to calculate CVε p and ML for any parameter set (α, β, and γ) are given in Fig. 7 and Table 2. Training and testing performance of maximum load (ML) neural network can be seen in Fig. 7a and b. Correlation coefficients of training and test data sets for ML neural network are given in Table 2 as 1 and 0.999, respectively. These correlation coefficient values are quite satisfactory. Also, the average absolute error values calculated for training and test data of ML neural network are 3.37 e−09 % and 0.177 %. On the other hand, Fig. 7c and d are displaying the performance of training and test data for the coefficient of variance for plastic strain (CVε p ) neural network. Calculated correlation coefficients for training and test data are given in Table 2 as 0.999 and 0.890. Although the correlation coefficient value of the test data of CVε p is lower than that of ML, it is at an acceptably good level. Finally, the average absolute error values calculated for training and test data of CVε p neural network are 0.022 % and 2.655 %.
The values obtained for the nondimensional α, β, and γ parameters as a result of the optimization and the values obtained for the D 1 , r, and e parameters in return for these values, together with the CVε p and ML values expected to be obtained as a result of the optimum design are given in Table 3.
When the results are examined, it is seen that the α is 0.766, which is a value close to the upper limit. This shows that the α, also expressed as inverse extrusion rate, is more effective on ML than CVε p . In addition, the ML value constantly decreases with the decrease of the extrusion rate. On the other hand, although the CVε p decreases with the increase of the extrusion rate, this situation changes after a certain value. The biggest reason for this is that the increasing extrusion rate is not reflected in the strain value as it should be in the theoretical equation which is shown in Eqn (5). This has been explained in detail by Fereshteh-Saniee et al. [22]. After a certain extrusion ratio, some part of the specimen remains constant in the spherical cavity and the extrusion rate takes a smaller value than it is. Thus, the average strain value does not increase and the CVε p cannot sustain its decrease. A similar situation can be seen in this study. Fig. 8 is comparing the total velocity distribution across the spherical cavity for different extrusion ratios.
The velocity values in the spherical cavity part are very close to the channel part for the lowest extrusion ratio (α = 0.8071) in Fig. 8a. However, the total velocity of the circled area is close to zero for the highest extrusion ratio (α = 0.45) as shown in Fig 8b. The circled area is nearly motionless and acts as a wall. This situation leads to a decrease in strain gained from the first term of Eqn (5).
After the optimum die geometry was manufactured, the experimental and numerical images of the specimen pressed  in this die were compared in Fig. 9a and b. In addition, the load-stroke curves of the Exp.-ECAP process carried out in the optimum die were obtained experimentally and numerically and compared in Fig. 9c. As a result of these comparisons, the earlier assumption made that the Exp.-ECAP finite element analysis was validated was proven. It is also seen that the maximum load (ML) values for both curves in the graph are very close to the ML value in Table 3. While the maximum load value (ML) obtained as a result of the optimization is 11.5 tons, the experimental maximum load during the ECAP process carried out in the produced optimum die is 11.4 tons and the maximum load in the FE analysis for the optimum die is 11.65 tons. On the other hand, the CVε p value calculated for the strain values shown in Fig. 9d obtained from the FE analysis performed for the optimum die is 0.245. This value, is very close to 0.232 which is obtained as a result of optimization. These results confirm the validity of the finite element model produced for the Exp.-ECAP process and indicate that the neural networks (ML and CVε p ) have sufficient performance to predict the maximum load and coefficient of variance for effective plastic strain. In addition, the CVε p value obtained from the FE analysis for the optimum Exp.-ECAP die and the CVε p value obtained from the FE analysis for the ECAP process are 0.434 and 0.245, respectively. This shows that the strain distribution of the specimen as a result of the Exp.-ECAP process is more homogeneous.

Results for mechanical properties
In this study, the first of the mechanical tests applied to processed specimens is the tensile test. Fig. 10a shows a tensile test specimen produced in accordance with the ASTM-E8 standard, and Fig. 10c shows the dimensions of this specimen. Fig. 10b shows a specimen subjected to the tensile test.
Tensile tests were carried out in 3 repetitions for each pass of ECAP, Exp.-ECAP, and HECAP processes. The stress-strain curves obtained by averaging the three tests performed for each pass are shown in Fig. 11. Also, the yield strength and tensile strength values of each pass of each SPD method are given in Table 4.  When the values are examined, it is seen that the yield strength and ultimate tensile strength values increase in both ECAP and Exp.-ECAP processes with the increasing number of passes. Especially, while the strength increases in the first passes were dramatic, elongation values decreased up to 50 % in the first passes. It is seen in Table 4 that the toughness values are lower than the values of the annealed copper specimen, despite the increase in the strength values with the increasing number of passes and the improvement in the elongation values in the progressive passes. When the effects of ECAP and Exp.-ECAP processes on the strength values are compared, it is seen that Exp.-ECAP specimens have higher yield and tensile strength than ECAPed specimens at the same number of passes. This can be attributed to the fact that the specimen is subjected to more strain than the ECAP specimen in the Exp.-ECAP process. In addition, in ECAP and Exp.-ECAP processes, it is seen that elongation values show a dramatic decrease in the first passes and then increase slightly with increasing passes. While these increases occur in the second pass in the Exp.-ECAP process, they occur in the third pass in the ECAP process. This situation can be attributed to the fact that these two different processes cause different plastic deformation processes in the materials and thus create differences in the recovery processes of the materials. In the After the tensile tests were completed, fracture surface investigation was carried out for these specimens. In Fig. 10e, the area where the fracture surface examination of a specimen was performed is shown closely. Fig. 10f is an example showing where and how the fracture surface images were taken. Fracture surface images taken from all specimens are given in Fig. 12. When the broken surfaces are examined, it is seen that    Table 4. When the hardness values were examined, it was seen that the hardness values increased by 65% and 79%, respectively, with the first passes of the ECAP and Exp.-ECAP processes. With the increasing number of passes in both processes, the hardness values increase, but the rate of increase decreases. When the two processes are compared, it is seen that Exp.-ECAP causes more increase in hardness values compared to ECAP. It is seen that the Exp.-ECAP passes applied after ECAP continues to increase the hardness values.
In recent studies, the distribution of hardness values is also examined, as well as the average hardness values [29]. In addition to having high average hardness values, it is also very important to have a homogeneous distribution. For this reason, the hardness distributions of the specimens were also examined in this study. The coefficient of variance (CV) factor used to examine the strain inhomogeneity is adapted as in Eqn. (6) to examine the hardness inhomogeneity: where StdevHV is the standard deviation of hardness values and AvHV is the average of hardness values. The values obtained using Equation (6) are shown in Fig. 13.
When the values are examined, it is seen that CVHV values decrease with the increasing number of passes in ECAP and Exp.-ECAP processes, in other words, the hardness

Results for microstructural analysis
Fig. 14 shows optical microscope (OM) and scanning electron microscope (SEM) images of specimens subjected to ECAP, Exp.-ECAP, and HECAP processes. When OM and SEM images are examined, it is seen that particle sizes decrease with the increase in the number of passes applied in ECAP and Exp.-ECAP processes. Also, with the increasing number of passes, orientation is observed in the grains and these orientations are shown with arrows on the OM images. When the average grain sizes given in Table 5 are examined, it is seen that the Exp.-ECAP process reduces the grain sizes more than the ECAP process in the same number of passes. It can be understood from the values in Table 5 that the Exp.-ECAP passes applied after ECAP within the scope of the HECAP process continue to reduce the grain sizes. In addition to the average particle sizes, the standard error (SE) values calculated using the data obtained from the particle size measurements are also shown in Table 5. SE values were calculated for each specimen to give an idea about the grain size distributions of the microstructure. When SE values are examined, it is seen that ECAP and Exp.-ECAP processes provide a more homogeneous grain distribution with the increasing number of passes. The Exp.-ECAP process enabled the formation of a more homogeneous microstructure compared to the ECAP process. As a result, it can be said that the findings related to grain sizes and distributions are in parallel with the results obtained from hardness and tensile tests. TEM images and SAED patterns of 4-pass ECAPed, 4-pass Exp.-ECAPed, and 4-pass ECAPed + 1-pass Exp.-ECAPed specimens are shown in Figure 15. When the TEM images are examined, it is seen that the crystal sizes of 4-pass Exp.-ECAPed and 4-pass ECAPed + 1-pass Exp.-ECAPed specimens are smaller than the 4-pass ECAPed specimens. Besides, when the SAED patterns are examined, it is seen that the electron scattering is the highest in the 4-pass Exp.-ECAPed specimen, while the scattering in the 4-pass ECAPed specimen is less than the other two specimens. Using the relationship between the electron scattering and misorientation [30], it is possible to say that, between these three specimens, the specimen with the highest misorientation is the 4-pass Exp.-ECAPed specimen, while the specimen with the lowest misorientation is the 4-pass ECAPed specimen.
The XRD patterns obtained from the XRD study are shown in Figure 16. The crystal size calculation was made for each specimen using the Scherrer and Wilson method [31] on the XRD graphs obtained, and the crystal sizes are given in Table 5. During the calculations, each peak in the XRD graphs was calculated and the average of the obtained crystal sizes was taken as the crystal size for the corresponding specimen. When the results are examined, it is observed that the crystal size values obtained in the first passes in ECAP and Exp.-ECAP processes are quite low compared to the annealed specimen. Also, the decrease in crystal sizes continued with the increasing number of passes. It is observed that the Exp.-ECAP passes applied after ECAP within the scope of the HECAP process continue to decrease in crystal sizes. When compared, it is also seen that the Exp.-ECAP process causes a greater reduction in crystal size than the ECAP process. The specimen with the smallest crystal size is the 4-pass Exp.-ECAPed specimen with 30.8 nm, while the 4-pass ECAPed + 1-pass Exp.-ECAPed specimen is the second specimen with 31.2 nm.
The dislocation density of the specimens was calculated with the Williamson-Smallman formula and shown in Table 5. The opposite of the effects of the ECAP and Exp.-ECAP processes on the crystal size is true for the dislocation density, as there is an inverse proportion between the dislocation density and the crystal size according to this formula. Therefore, the 4-pass Exp.-ECAPed and the 4-pass ECAPed + 1-pass Exp.-ECAPed specimens with the smallest crystal size have the highest dislocation density.

Conclusions
In this study, ECAP, Exp.-ECAP, and HECAP processes were applied to pure copper specimens. The die used in Exp.-ECAP and HECAP processes has been optimized in a way that CVε p and maximum load objectives are equally effective. The effects of these three processes on the mechanical properties and microstructures of the specimens were investigated. Also, the strain formed during the process in the specimens and the homogeneity of the hardness values obtained as a result of the process were examined. The results obtained are as follows: Considering all the results, it is seen that the Exp.-ECAP process, which is applied by using the optimum die, offers higher mechanical properties than the ECAP process and also provides a more homogeneous distribution in the average grain size, hardness values, and strain values obtained in FE analysis. It is also observed that Exp.-ECAP passes applied after ECAP make the grain size and hardness distributions more homogeneous.