Experimental study and finite element modelling of pure copper tube fabrication via the Parallel Tubular Channel Angular Pressing (PTCAP) Process

The Parallel Tubular Channel Angular Pressing Process (PTCAP) has emerged as a promising method for refining the grain structure and enhancing the mechanical properties of metallic materials through severe plastic deformation. This study focuses on a comprehensive investigation of the PTCAP process, combining experimental and numerical analysis to gain insights into its underlying mechanisms. Experimental investigations involve processing a commercially pure copper tube using PTCAP under controlled conditions. In parallel, an explicit numerical analysis is developed using ABAQUS software to simulate the deformation behavior during PTCAP. The model incorporates material constitutive equations and accounts to describe the material response under high strain rates and large deformations. The research aims to investigate how multi-pass PTCAP affects hardness, strain homogeneity, and stress distribution. A comparison between the load punch from the experimental and FEM is conducted to validate the FEM results, and there is a good correlation between both. Hardness measurements are conducted at various stages to quantify the changes in material hardness resulting from the successive PTCAP passes. The hardness of the Cu tube increased by 63.45, 94.51, 103.98, and 105.64% after 1 to 4 passes, respectively.


Introduction
Recent advancements in technology have led to the production of firm and corrosion-resistant tubes through innovative methods.Severe plastic deformation (SPD) processes have emerged as a cost-effective way to generate high-strength metals with exceptional mechanical properties [1].By subjecting soft metals to high strain, SPD processes transform them into ultra-fine grain (UFG) materials, thereby improving their mechanical properties [1][2][3].Commonly used SPD processes such as equal channel angular pressing (ECAP) [4], tubular channel angular pressing (TCAP) [5], and parallel tubular channel angular pressing (PTCAP) [6,7].These processes play a pivot-al role in shaping the next generation of materials, offering a pathway to achieve enhanced strength and durability in metal tubes through controlled and innovative de-formation mechanisms [8].
The Finite Element Method (FEM) stands as a powerful and versatile tool for comprehending the intricate deformation behavior exhibited by materials undergoing the PTCAP process.Through the application of FEM, researchers can gain valuable in-sights into the complex mechanical responses of materials subjected to PTCAPinduced plastic deformation.Rajabi et al [9] conducted a comprehensive study on the PTCAP process using ABAQUS software their investigation study provides valuable insights into optimizing PTCAP parameters for enhanced material characteristics.Moreover, the study introduces the effect of ultrasonic vibration on the PTCAP, and the results indicate a significant change in forming force due to vibration.Javidikia and Hashemi [10].They presented a distinctive contribution by introducing a variant of the PTCAP process, deviating in key aspects such as materials and dimensions.The novelty of their work lies in utilizing aluminium alloy 5083 properties for the analysis and simulation of the PTCAP process, the results of the study provide valuable insights into the interplay between curvature angle, strain distribution, and channel angles in the processing of tubes, aiding in the optimization of the relevant parameters for desired outcomes.Akbari et al [11] the focused on investigating the energy ab-sorption capacity of UFG Al 5083 tubes produced through the PTCAP process across various passes.The study involved the experimental evaluation of mechanical proper-ties and microstructure after each PTCAP cycle.By delving into the energy absorption capacity of the processed Al 5083 tube, the researchers aimed to provide valuable in-sights into the performance of the material under different processing conditions.
A study was conducted by Daryadel, Al-Mufadi, and Nagasekhar et al in 2020, 2015, and 2006 on the ECAP process to investigate the formation of Cu and Al tubes [4,12,13].The results indicated an increase in both UTS and σ y .Another experiment was carried out by Ghadimi et al on the Cu-Al bimetallic tube.They inserted the Cu tube into the Al tube with stripe number one and filled it with a lead mandrel.The hardness of the Cu and Al tubes increased by 157.13% and 129.25%, respectively [14].
The TCP (Tube Channel Pressing) process was successfully executed on the Al tube, resulting in a doubling of σ y , UTS, and HV of the tubes after up to 5 passes, when compared to the annealed tube.The initial grain size of the annealed sample measured approximately 1000 microns, after undergoing 3 passes, the grain size decreased to 400 microns and was further reduced to 200 microns after 5 passes [15].In 2012, Faraji and his colleagues introduced the TCAP (Tube Channel Angular Pressing) process to produce UFG tubes.The meth-od mainly relies on the application of shear stresses, which play a critical role in achieving UFG metals [16].The process under consideration bears resemblance to the TCP process, with a notable distinction lying in the protrusion of the mandrel and the mold [17].While the force exerted in the TCP process may be marginally lower, the overall strain experienced in the TCAP process is more substantial.In TCP, shear strain tends to be lower compared to compressive and tensile strains.Conversely, in TCAP, the tube undergoes higher shear stresses and experiences lower tensile and compressive stresses.In 2015, Pardis et al and their colleagues conducted research that demonstrated the effectiveness of the CEE method in increasing the UTS and σ y of commercially pure Cu rod or tube.Through 4 passes of the CEE process, the rod UTS, σ y , and HV are increased to ∼453 MPa, 386 MPa, and 149 HV after the number 4 passes, as compared to the annealed state ∼229 MPa, 45 MPa, and 66 HV, respectively [18].Faraji et al introduced the PTCAP process to tackle the load limitation issue in the TCAP process.Through FEM analysis, it was evident that the PTCAP process resulted in a more homogeneous strain distribution on the tube, leading to a more consistent mechanical property distribution, including hardness (HV).After a single pass, the HV remained consistent along the tube's thickness, Furthermore, the PTCAP process required 57.5% less force compared to the TCAP process to induce deformation [19,20].Abd El Aal and Gadallah et al examined the mechanical properties of UFG tubes after the PTCAP process using Cu-Zn-Al alloy and compared them to annealed tube state.They observed severe anisotropy in different directions of the tube, leading to increased strength and hard-ness after 2 passes of the PTCAP processing [6].
A process combining PTCAP and TBE was introduced by Abdolvand et al to create UFG, high-strength thinwalled tubes using AZ31 Mn alloy.Firstly, the PTCAP process produced a UFG thick-walled tube, and then the TBE process reduced its thickness [21].Eftekhari et al researched the hot deformation behavior of AZ31 Mn alloy, thin walls under the combined process of PTCAP and TBE [22].The bulge test was utilized to assess the bursting pressure of tubes post-PTCAP process.The outcomes indicated that the bursting pressure of tubes increased by 114, 103, and 87% respectively, after 1, 2, and 3 passes of the process as compared to annealed tubes state [23].The superplastic behavior of Mn alloys like cast AZ31 [24] and extruded AZ31 [25] were analyzed after the PTCAP process.Observations revealed that the mechanical and microstructural properties of the samples post-PTCAP process exhibited superior characteristics at room temperature (RT) compared to the annealed samples.Additionally, at elevated temperatures, they demonstrated remarkable superplastic properties in contrast to the annealed state samples.
The research introduces novelty by addressing the limited of numerical studies on multi-pass PTCAP processing.In response to this gap, the present investigation utilizes an Axisymmetric FEM simulation to explore the deformation behavior, stress distribution, and strain homogeneity evolution during multi-pass PTCAP processing, extending up to four passes.Notably, the study incorporates experimental verification.

Experimental procedures
In this study, a commercial copper (Cu) tube was used with compositions listed in table 1.The PTCAP process is performed at room temperature (RT).To reduce friction between the tube, mandrel, and die walls during each run of PTCAP, all parts were thoroughly lubricated with Molybdenum disulfide (Mo S 2 ) [6].
The pure Cu of the inner and outer tube (core and shell).The inner and outer diameter of the copper tube are 15 mm, and 20 mm and its thickness is 2.5 mm, respectively.The length of the tube is 80 mm.H13 steel is employed for crafting both the die and mandrel, with the die being hardened to 55 RC.The punches, also made of H13 steel, exhibit a hardness of 56 RC.The inner and outer diameter of the first punch is 15 mm and 20 mm, and the second punch is 20 and 25 mm respectively, as shown in figure 1(a).The copper tube alloy underwent annealing at 700 °C in a vacuum furnace with argon gas for a duration of one hour to accomplish a homogeneous microstructure, followed by furnace cooling to RT.All components, including the tube die, mandrel, and punches (refer to figure 1(b)), as well as the hydraulic press and experimental setup, are depicted in figure 2.
The Vickers hardness test stands as one of the most prevalent methods for assessing the hardness of thin parts.In this experiment, the tubes were initially cut and transformed into rings.Subsequently, the hardness of the specimens following the PTCAP process, extending up to four passes, was determined using a Vickers hardness tester Model HV Qness 250 MS (Austria).The test was conducted under a 500-gf load with a loading time of 15 s, as depicted in figure 3. The hardness of specimens was assessed by calculating the average hardness across all points on the samples.A comparison was conducted between the hardness of rings after one, two, three, and four passes of the PTCAP process, and rings in the annealed state.Figure 3 displays the surface of the copper ring under the hardness testing device.

Finite element modelling (FEM)
The procedural sequence of the PTCAP process involves two replicable half-passes.In the initial simulation phase, the tube was positioned between the mandrel and the die for the first pass.Utilizing a cylindrical punch mirroring the tube's dimensions, the tube underwent extrusion, transitioning from a smaller to a larger    diameter, as depicted in figure 4(a).Subsequently, the second pass commenced with the die's inversion, facilitating the re-extrusion of the tube within the channel using a second punch with a larger diameter.This process resulted in the restoration of the tube diameter to its original size, as illustrated in figure 4(b).The completion of this first cycle allows for the repetition of the same technique, leading to a cumulative total of four passes.The imperative nature of numerical analysis in comprehending the deformation behavior of the PTCAP process necessitates meticulous modelling and analysis.In this study, the influence of various passes in the PTCAP process on equivalent plastic strain (PEEQ), stress distribution, and forming force has been thoroughly investigated.The simulation of multi-passes in the PTCAP process was executed using ABAQUS/Explicit, chosen specifically for its superior capabilities in solving dynamic problems.To validate the precision of the simulation results, an experimental test was conducted to empirically determine the forming force.

Description of FE model
A full-scale, axisymmetric model for PTCAPed tubes of commercially pure copper alloy.The tubes were subjected to dynamic explicit numerical analysis.This modelling choice, based on axisymmetric, allows for an efficient and accurate representation of the complex deformation behavior during the PTCAP process across various passes.The PTCAP analysis is structured into five distinct components, as illustrated in figure 5.In this modelling framework, the die, mandrel, upper punch, and lower punch are discretely represented as rigid parts, emphasizing their fixed geometries and limited deformation.In contrast, the forming tube is treated as a  deformable element, acknowledging its susceptibility to plastic deformation during the process.This differential modelling approach enables a comprehensive examination of the interaction dynamics between the rigid components and the deformable forming tube throughout the PTCAP analysis [6,26].
The material characteristics of copper alloy employed in this analysis encompass a density of 8.1 g cm −3 , Poisson's ratio of 0.33, and a modulus of elasticity of 110 GPa [6].Furthermore, the friction coefficient value is assumed to be 0.025.Additionally, the plastic properties of the material, crucial for capturing its anisotropic behavior as per Hill's 48 criteria, are derived from uniaxial tensile tests.The true stress/strain curve, depicted in figure 5, serves as a pivotal reference for modelling the material's behavior during plastic deformation.The current analysis adopts PTCAP die parameters, including die angles of curvature ψ 1 = ψ 2 of 0°, Channel angles j 1 = j 2 of 135°, and K ratio 0.6  t .The maximum equivalent plastic strain of PTCAP was 2.5 per pass approximately, based on equation (1) [6].The PTCAP process was implemented at 25 °C with a lower punch speed of 2 mm min −1 to reduce heat generation at the PTCAP process.
where N, j , 1,2 y 1,2, and R 1,2 parameters are the numbers of passes, die channel angle, die angle of curvature, and tube outer, and inner radius, respectively.

Mesh design
For the explicit numerical analysis of large deformation problems, the Arbitrary Lagrangian Eulerian (ALE) approach has emerged as the predominant methodology for mitigating element distortion during the analysis.The general strategy in the ALE solution step is to carry out three sequential sub-steps namely, the Lagrangian step, the remapping step, and the advection step [27].The mesh deforms in tandem with the material during the Lagrangian step, the mesh undergoes deformation in synchronization with the material.Subsequently, the remapping phase is employed to interpolate the mesh, generating a redesigned mesh that offers improved localization for the de-formed configuration.In the advection step, the material has the potential to flow onto the updated mesh.To facilitate this process, the material state variables from the pre-ceding stage are meticulously transferred to the newly updated mesh [28].This trans-fer of material state variables ensures the continuity of information and enables a seamless transition between mesh configurations, contributing to the overall accuracy of the large deformation analysis.
In this study, the PTCAP tools (die, punches, and mandrel) are modelled as a rigid body, since the deformations of the tools should be elastic and free of plastic deformation.The tools are meshed using shell elements, with an element edge length set at 0.5 mm.The mesh design for the axisymmetric PTCAP tube and its 360-revolved development is illustrated in figures 6(a), (b).Several models with varying element sizes were generated to assess the dependency of outcomes on mesh size.Upon scrutiny of the mesh sensitivity diagram depicted in figure 6(c), the results stabled at an optimal mesh size is 0.4 mm, incorporating enhanced hourglass control.The free, Quad-dominated medial axis (CAX4R) is used for deformable parts, however, and (RAX2) elements are used for rigid parts.

Load and boundary conditions
The loading and boundary conditions in this simulation are detailed in figure 7. The punch uniformly advances at a rate of 2 mm min −1 towards the inner diameter of the tube.The loading is characterized by a smooth load defined as an amplitude function.In this context, the die and mandrel exhibit fixed displacements in all directions, as depicted in figure 7.This assumption is made based on the rigid nature attributed to the die and mandrel components in the simulation.
In the explicit analysis, a mass scaling factor of 100 was employed to expedite computational processes and reduce simulation time.It is noted in ABAQUS literature [29], that the mass scaling factor serves as a beneficial tool for this purpose, although its application requires careful consideration to prevent the model's kinetic energy from surpassing 5% of the total energy.Ensuring that the forming force and contact stresses remain unaffected by the mass scaling factor was a priority to maintain the accuracy of simulation outcomes [29].This approach allows for a balance between computational efficiency and the preservation of key mechanical characteristics during the explicit analysis of the forming process.The analysis is conducted through four distinct simulations, each corresponding to an individual pass of the PTCAP process.To accurately represent material work hardening, the pertinent result variables are also transferred accordingly, as outlined in the study [30].To accurately implement contact constraints, which govern the interaction between surfaces (surface-tosurface contact) definition is essential.A penalty contact algorithm is selected, offering flexibility in enforcing constraints and accommodating various types of contact.The friction coefficient between surfaces is assumed to be 0.05 influencing the contact behavior during the simulation [9].This comprehensive approach ensures the incorporation of material properties, work hardening effects, and appropriate contact constraints in the iterative simulations of each PTCAP pass.

Results and discussion
In the PTCAP process, PEEQ serves as a critical metric to quantify the deformation undergone by a material during the forming operation.As the copper tube is subjected to constrained angular positioning within the parallel tabular channels of the die and mandrel, the PEEQ provides a measure of the accumulated plastic deformation in the material.Notably, the distribution of PEEQ across the processed material reveals insights into the varying levels of deformation experienced at different locations.Figure 8 presents contours depicting the distribution of PEEQ on the longitudinal section during the first pass of PTCAP.In figure 8(a), the PEEQ in the first pass is approximately 2.1 which is in agreement with equation (1).It is evident that the strain values at the inner surface interacting with the mandrel are higher than those at the outer surface inter-acting with the die.However, despite these variations, the strain distribution along the longitudinal direction appears reasonably uniform.In practical terms, the reduced PEEQ values observed at the outer surface of the tube in figure 8(a) can be attributed to the creation of a corner gap between the die and the tube, as depicted in figure 8(b).The formation of this corner gap during the pressing operation results in a scenario where the tube is no longer in direct contact with the die wall.Consequently, this gap leads to a diminished level of deformation, subsequently causing a lower applied strain on the material in that specific region.The plastic strain experienced by the material in the PTCAP process is significantly influenced by the number of passes.Through successive passes in the parallel tubular channels, the cumulative plastic strain increases, profoundly impacting de-formation characteristics.Equation (1) estimates a PEEQ of approximately 2.5 for each PTCAP pass, resulting in an expected maximum cumulative PEEQ of 10 after four passes.Figure 9 visually validates this estimation, demonstrating agreement between the observed maximum PEEQ values and equation (1) predictions, reinforcing its accuracy in forecasting cumulative plastic strain in multi-pass PTCAP processes.Figures 9(a)-(d) illustrates the effective strain distribution during the multi-stage PTCAP approach on a deformed copper tube.With each pass, the effective strain experiences a significant increase, indicating a cumulative influence on the material's deformation.Furthermore, as the pass number rises, there is a notable reduction in the variation of PEEQ distribution through the material thickness.This trend suggests a progressive development towards a more uniform distribution of deformation, reflecting an enhanced level of deformation homogeneity with successive passes in the PTCAP process.
Figure 10 presents the stress distribution observed in the multi-pass PTCAP process.The initial increase in stress during the first pass can be attributed to the combined effects of friction and the material's coarse grain with a non-homogeneous microstructure experiencing its first deformation phase, see in figure 10(a).In the second pass, there is a minor decrease in the maximum shear stress due to the attainment of a microstructure with reduced non-homogeneity, as shown in figure 10(b).Moving to the third pass as shown in figure 10(c), a slight increase in stress is noted, reflecting an improvement in material strength, thereby rendering subsequent deformations more challenging.In the final pass, the stress reaches its maximum value compared to earlier passes, indicative of the compression punch process encountering failure [31,32].Notably, the material exhibits increased brittleness after undergoing the PTCAP technique three times, as evident in the simulations shown in figure 10(d).
Figure 11 presents a comprehensive comparison between experimental and numerical results for the punch load versus ram displacement diagrams.The depicted results exhibit a commendable concordance between the experimental and Finite Element (FE) outcomes.Specifically, the maximum disparity in punch load between the experimental and FE results for Pass 1 is indicated to be 4.2%, as shown in figure 11(a).Subsequently, for passes 2, 3, and 4, the disparities are reported to be 7%, 4.3%, and 6.5%, respectively, as elucidated in figures 11(b)-(d).This observation underscores the reliability of the numerical simulations in accurately predicting the punch load throughout various passes, with the differences falling within acceptable limits between the experimental and numerical data sets.
The examination of Vickers hardness (HV) distribution serves as a crucial aspect in validating the mechanical properties attained through the (PTCAP) process.To substantiate this, experimental results for a copper tube were measured and are visually presented in figure 12.The color-coded hardness maps in the figure provide a clear depiction of the hardness evolution across various PTCAP passes in the X-Z plane.The annealed tube sample has a homogeneous hardness distribution in the X-Z plane with an average hardness of 61.86 HV and an inhomogeneity index of 0.61, as shown in figures 12(a) and 13.The hardness distribution becomes nonhomogeneous after the PTCAP for 1 pass, where the hardness increases from the top to bottom with a low hardness area at the top and occupies 13% of the sample, as shown in figure 12(b).With a further increase in the number of PTCAP passes, the hardness distribution becomes more homogeneous, as shown in figures 12(c), (d) and 13.The increase in hardness homogeneity is because of the backpressure that decreases the changes that occur during the PTCAP process.Also, the variation of hardness is related to both the dominant mechanisms in the PTCAP process such as grain refinement and work hardening [33][34][35][36][37]

Conclusions
An axisymmetric simulation was successfully used to investigate the deformation behavior of commercial copper tubes during multiple-stages of PTCAP processing.Utilizing ABAQUS software, a process simulation was executed to assess the influence of the number of passes on both equivalent plastic strain and the ensuing stress distribution within the tube.Experimental validation was carried out to confirm the impact of multiple passes on forming force.Additionally, hardness was measured on the tubes to study the effect of passes on the hardness of the material, and the main findings are presented below: 1.The results indicate the existence of strain inhomogeneity during the initial phases of PTCAP processing.In these early stages, there is a notable reduction in PEEQ observed on the outer surface of the tube, attributed to the development of a corner gap in a representative strain-hardening material.Nevertheless, as the number of passes increases, this strain inhomogeneity diminishes and a more uniform distribution is achieved.
2. During the first pass, the highest shear stress is found, as it represents the initial deformation applied to a material featuring coarse grains and a non-homogeneous microstructure.Consequently, the stress diminishes in the second pass, attributed to the achievement of reducing the microstructure inhomogeneity.With an increase in the number of passes, the stress on the material rises progressively, culminating in its peak during the fourth pass.This escalation in stress corresponds to an increased brittleness in the material.
4. The observed improvement in hardness values correlates with an increase in the number of passes after the PTCAP process, from one to four passes the hardness of the Cu tube increased by 63.45%, 94.51%, 103.98%, and 105.64%, respectively.

Figure 1 .
Figure 1.(a) Photo of the copper tube and (b) Die, mandrel and punches used.

Figure 3 .
Figure 3.The Cu ring tube is under the Vickers hardness testing device.

Figure 4 .
Figure 4.A sliced PTCAP set-up displaying the die, mandrel, upper and lower punch; (a) first pass and (b) a second pass.

Figure 5 .
Figure 5. True stress-strain curve of pure copper tube.

Figure 8 .
Figure 8. Equivalent plastic strain distribution at pass one; (a) inner surface interacting with the mandrel is higher than those at the outer surface interacting with the die, and (b) corner gap.

Figure 12 .
Figure 12.Hardness distribution contours maps through the X/Z plane of the Cu tube; (a) annealed and processed by PTCAP up to (b) pass 1, (c) pass 2, (d) pass 3 and (e) pass 4.

.
The average hardness of the PTCAP samples increases from 61.86 HV to 101.11 HV after 1 pass, then to 120.32 HV, 126.18 HV, and 127.21HV after 2, 3, and 4 passes, as shown in figures 12(b)-(d).On the side, the hardness percentage increased by about 63.45, 94.51, 103.98 and 105.64% after the PTCAP pass respectively, relative to the unprocessed PTCAP tubes.The hardness values of PTCAPed samples in the present work were higher or near those of 62-142 HV of the PTCAP, TCEC, CEE, and ECAPed pure Cu and Cu processed up to 4 passes [6, 18, 19, 38-41].

Figure 13 .
Figure 13.The experimental hardness inhomogeneity index of the Cu tube before and after the PTCAP passes specimens in the X/Z plane.

Table 1 .
Chemical composition of the copper tubes alloy (in wt%).