Hot Extrusion of Thin-Wall Multichannel Copper Profiles

Transcription

1 Frank F. Kraft 1 Associate Professor Mem. ASME kraftf@ohio.edu Jonathan Kochis kochisj@gmail.com Mechanical Engineering Department, Ohio University, Athens, OH Hot Extrusion of Thin-Wall Multichannel Copper Profiles This paper presents the development of a unique, net shape, hot-extrusion process to produce precision, thin-wall, multichannel copper profiles for high efficiency heatexchangers. This process is a departure from conventional copper extrusion, which is a nonisothermal process used primarily to produce simple semifinished products and hollow profiles requiring cold drawing after hot extrusion. A lab-scale apparatus was developed to simultaneously extrude multiple heated billets through a porthole type hollow die to form the multi-channel profiles. The process is performed at C, essentially at isothermal extrusion conditions. Temperature and tooling strength considerations necessitated the use of superalloys for the apparatus (which included dies, container, ram stems, and support tooling). A 250 kn computer controlled servo-hydraulic MTS VR machine was used to provide the extrusion ram force. Two part designs were extruded to demonstrate process feasibility and versatility. A two-channel design with 0.2 mm wall thicknesses and an 11-channel design with wall-thicknesses of 0.3 mm were extruded. The extrusion ratios for these profiles are 67 and 25, respectively. Experimental data and an approach to analytically model the process are presented. Because solid-state welds in the tube walls are necessitated by the use of hollow extrusion dies, the microstructure in these regions is also presented. [DOI: / ] 1 Introduction and Background Tubular copper profiles are generally hot extruded first into semifinished parts that are subsequently cold drawn to final dimensions. Simple seamless round tube for plumbing and refrigeration applications accounts for the vast amount produced in this manner, and processing has essentially been optimized for efficiency. The semifinished tube sections are hot extruded at billet temperatures up to 1000 C with special presses that pierce a solid billet to form the single internal passage [1,2]. To prevent overheating and softening of the tool steel, extrusion must take place at high speeds to minimize the contact time of the hot billet with the tooling. This also serves to minimize billet cooling which would increase flow stress and the ram pressure required. From a practical sense, this limits such extrusion processes to simple hollow profiles with low extrusion ratios and thick walls, hence, the need for finishing via cold drawing. Extrusion of thin walled hollow profiles was thought to be prohibitive because of the inherently higher extrusion ratios and slower extrusion speeds needed. Also, extrusion of copper at these temperatures precludes the typical use of porthole dies, such as that used to extrude aluminum tubes and hollow profiles. The high process temperatures and high stresses on the bridge of a hollow die present the main challenges that need to be overcome in extruding copper tubes to finished dimensions. The development of high-efficiency heat exchangers for automotive climate control systems and other cooling applications has seen the emergence and wide use of small, thin-walled, and multichannel aluminum tubes. These tubes are commercially produced, essentially net-shape, via direct hot extrusion from Aluminum Association (AA) 1000 and 3000 series alloys and with porthole type hollow dies. Only post extrusion straightening, sizing, and cutting of the tube are required. The development of a process to produce similar tube from copper is the subject of this paper. Early in the development of this process, a simple assessment of crucial parameters for aluminum and copper extrusion was performed. A comparison of these parameters for aluminum (AA3003 alloy assumed) and copper extrusion is presented in 1 Corresponding author. Manuscript received May 1, 2013; final manuscript received September 18, 2013; published online November 5, Assoc. Editor: Yung Shin. Table 1. Several conclusions were drawn from this assessment. To achieve a flow stress in copper somewhat similar to that for aluminum extrusion, the temperature should be over 700 C. Since thinwalled hollow sections require slower (ram) extrusion speeds and thus longer contact time between the work piece and tooling, the use of steel tooling (such as AISI H13) is precluded. This also means that the tooling temperature must be maintained at or near the extrusion temperature (as is done with aluminum extrusion), to prevent excessive work-piece cooling. Near-isothermal extrusion is thus an important goal. To achieve this, superalloys were used for the tooling. These alloys provide strengths at copper extrusion temperatures that are comparable to those of tool steels at aluminum extrusion temperatures. The basic approach and some of the initial successes (and challenges) in this endeavor have been previously reported in the literature [3,4]. The work presented herein specifically focuses on recent developments in the process, lab apparatus, and modeling. 2 Process and Experimental Apparatus A lab scale apparatus was developed with a 250 kn (56,000 lb), computer-controlled, servo-hydraulic MTS VR machine, which provides extrusion force and velocity control. It was designed and fabricated to extrude two billets, simultaneously, to form multichannel, thin-wall hollow profiles that are typical of designs from aluminum alloys. The purpose of the dual billet configuration was to eliminate adverse (axial) stresses on the die bridge during high temperature extrusion of alloys with such high flow stresses. Nickel-based superalloys were used such that a requisite amount of strength in the tooling at C was achieved. This effectively allowed the tooling to be held in this temperature range for near-isothermal extrusion. The relatively slow extrusion speeds and thin tube walls necessitated heating to maintain the extrusion temperature. Thus, this approach overcomes the challenges of extruding high-ratio hollow copper profiles at the high temperatures required. A sketch and photo of the extrusion apparatus are presented in Fig. 1; portions have been previously described in the literature [4,5]. The apparatus uses a 250 kn (28 US ton) servo-hydraulic, PC controlled MTS VR machine to provide the ram pressure. The maximum (specific) ram pressure available for this configuration Journal of Manufacturing Science and Engineering DECEMBER 2013, Vol. 135 / Copyright VC 2013 by ASME

2 Table 1 Temperature and flow stress for copper and aluminum extrusion, and tooling strengths at these temperatures. Aluminum extrusion (AA3003) Copper extrusion Billet temperature C C Billet flow de/dt ¼ 0.5 s MPa MPa Tooling material Tool steel (H13) Superalloys Tooling strength at forming temp MPa MPa is 722 MPa (104.7 kpsi). Ram control is PC-based using MTS s object-oriented programming. Control can be via either force or ram speed, and both control schemes are used in this effort. The temperatures of the container and die holder are independently controlled via separate controllers. Eight cartridge heaters are used in the container and two are used in the die holder. K-type thermocouples provide the feedback to the temperature controllers, which provide the control signals to solid state relays. The thermocouples that provide feedback to the respective controllers are located directly adjacent to heaters in the container and in the die holder. The heaters have special grooves in their sheaths to accommodate the thermocouples. Temperature control in this manner ensures that no portion of the tooling will be exposed to excessively high or otherwise unknown temperatures. Figure 2 shows a front view of the apparatus just after an extrusion trial. The extruded copper tube is protruding from the nitrogen gas tube in the bottom center of the photo. The separate temperature controllers are shown at the bottom right in Fig. 2. The process is indeed direct extrusion, even though the stems are stationary (on the top crosshead) and the container is mounted to the bottom hydraulic ram of the machine. The billets are effectively pushed down, through the die and into the nitrogen-gas tube where cooling takes place while preventing oxidation of the hot tubing. A graphite block directs the tube from the die backer exit to the nitrogen tube. For experimental trials, the extrusion speeds were low enough for sufficient cooling to take place prior to the tube exiting the nitrogen atmosphere. Also, to isolate the Fig. 2 Photo of the extrusion apparatus just after an extrusion trial of copper tube. The insulation that surrounded the heated container has just been removed. temperature of the apparatus from the MTS machine, watercooled aluminum heat-exchangers were placed between the locations where the container and stems mount to the machine grips. During the process, the simultaneously extruded billets are deformed in the die to form the internal walls of the tube. Solid state joining of the two halves takes place in the die s weld chambers. This takes place just prior to formation of the tube walls final dimensions. Figure 3 illustrates the progression from the container to the final profile, for the 11-channel design with an extrusion ratio of 25. Similar to typical hollow-die extrusion, the two metal flow streams must converge in the weld chambers of the die. In this instance, the surface area of the billet increases by almost 2000% as it is deformed in the die, and this is deemed important to produce good clean solid-state welds in the internal walls of the tube. Figure 4 shows photos of a tube section with two billets that were similar to those used to produce it, and the extrusion die. Fig. 1 Experimental extrusion apparatus. Figure (a) shows an annotated sketch of the components for the extrusion tooling, from the US patent [4]. Figure (b) shows the apparatus after an extrusion trial (the copper tube exits the nitrogen-cooling tube, at the bottom right). Detached dummy blocks are used during extrusion / Vol. 135, DECEMBER 2013 Transactions of the ASME

3 Fig. 3 Progression of dual-billet extrusion from container/billets to final profile. The metal forming the internal walls flows together in the weld chambers of the mandrel. Fig. 4 (a) Photos of the 11-channel copper tube with two billets that are similar to the ones used during the extrusion process. (b) Extrusion die, showing the billet entrance and the exit (inset). The extrusion tooling was fabricated from nickel based superalloys: Inconel 718, Rene 41, and ATI 720. Extrusion tooling temperatures were generally in the C range, and these superalloys provided the strength required, and which was not achievable with hot work tool steels. Figure 5 compares the strength of these alloys to H13 steel, at temperatures up to 750 C. The properties of these alloys allow the apparatus to be operated for extended periods of time at these extrusion temperatures. The process is essentially isothermal extrusion, being governed by the temperature of the tooling. Although heat is generated during extrusion, the relatively large thermal mass of the apparatus and the slow speeds readily allow the heat to dissipate. 3 Extrusion Modeling An approach was developed to analytically characterize the process from some basic principles. The desire is to use such an analysis to scale-up the process for future prototype production. The model is based on extrusion ram pressure (P e ), which is equivalent to the total work per unit volume of metal being extruded [9 11]. Per Eq. (1), the ram pressure can be equated to the sum of the work required in the die (w d ) and in the container (w c ). P e ¼ w d þ w c (1) The work expended in the die can be expressed by Eq. (2) as a function of ideal deformation and an efficiency term (g), which accounts for nonuniform deformation and friction work [10]. Fig. 5 Tooling material strength as a function as a function of temperature. The data are from Uddeholm, ATI Allvac, and High Temp Metals [6 8]. Y w d ¼ ln R (2) g where Y is the mean flow stress and R is the extrusion ratio, the ratio of the areas of the die inlet opening to the extruded profile in Journal of Manufacturing Science and Engineering DECEMBER 2013, Vol. 135 /

4 where C is a constant (0.571 MPa), m is strain rate sensitivity (0.16), Z is the Zener-Hollomon parameter, _e is strain rate, Q is activation energy (234 kj/mol), R is the gas constant (8.314 J/mol- K), and T is the absolute temperature. These values were determined by Rogers [12] for oxygen free high conductivity (OFHC) (UNS C10100) copper with hot compression testing. For this analysis, the extrusion strain rate is estimated by the time average mean strain rate (_e), according to Eqs. (6) and (7) [11]. _e ¼ ln R t (6) t ¼ V v r A c (7) Fig. 6 Ram pressure is graphed as a function of ram displacement. The temperature at the entrance of the die was 727 C and the ram velocity was constant at 9 mm/min (0.006 in/s). The extruded profile was the 16 mm mm 3 11 channel design. this instance. Note that the die opening and the container bores are the same size in this experimental work. The work in the container is due to friction. A constant interfacial shear stress between the billets and container is assumed and modeled using below equation. w c ¼ m f Yp c b pffiffi (3) 3 Ac where m f is the friction factor, p c is the perimeter of the container bore, b is the length of the billet in contact with the container, p and A c is the cross sectional area of the container bore. The Y= ffiffiffi 3 value in Eq. (3) represents the von Mises shear flow stress of the billet material. The mean flow stress Y is a function of strain rate and temperature and is modeled with the Zener-Hollomon model, Eqs. (4) and (5). Y ¼ CZ m (4) Z ¼ _e exp Q RT (5) where t is the time that the billet is being deformed and is a function of the volume in the deformation zone (V), the ram velocity v r and A c. Combining Eqs. (1) (7) leads to a general equation for the extrusion pressure as a function of basic process and material parameters. For the dual billet process, the total extrusion ram force (F) is equal to 2A c P e. P e ¼ C v ra c ln R exp Q m ln R V RT g þ m f p c b pffiffiffi 3 Ac For a constant ram pressure (or related force), the billets will deform at a strain rate given in below. (8) _e ¼ exp Q C ln R RT P e g þ m f p c 1 m b pffiffi (9) 3 Ac Using Eqs. (6) and (7), the ram velocity can be calculated for a constant extrusion pressure using Eq. (10). This equation is used to determine the die efficiency, and it effectively validates the extrusion model over a wide range of velocities during a constant force test. In applying this equation to extrusion data for which a constant extrusion pressure was applied, all other parameters would be known except g. v r ¼ V Q C ln R exp A c ln R RT P e g þ m f p c 1 m b pffiffi (10) 3 Ac Fig. 7 These graphs show ram velocity and temperature data for a constant force extrusion trial. The billet temperature at the entrance of the die was 720 C and the force was constant at 200 kn (45,000 lbs). The extrusion profile was the 16 mm mm 3 11 channel design / Vol. 135, DECEMBER 2013 Transactions of the ASME

5 Fig. 8 Ram force and velocity is shown as a function of time and ram displacement. The temperature at the entrance of the die was 727 C and the ram velocity was constant at 9 mm/min (0.006 in/s). The profile was the 16 mm mm 3 11 channel design. Maximum pressure is predicted within about 2%. 4 Experimentation A series of extrusion trials was performed to develop the process beyond the initial feasibility work performed by Vaitkus [3]. A more robust apparatus was developed, as previously described herein, and two different dies and profiles were used and tested under varying process conditions (constant force and constant velocity). In the new apparatus, more attention was given to temperature measurement and control. Cartridge heaters with a special groove to accommodate a thermocouple were chosen, and it was from these specific thermocouples in the container and the die holder that temperature was controlled. Temperature was also monitored at the die inlet and in the container adjacent to its liner. For these tests, the desired temperature at the inlet to the die was in the range of C. Initial trials with the 11-channel tube were at 727 C. The billet material in this research was OFHC copper, designated UNS C10100 (99.99% Cu minimum). Billets were 95 mm in length and machined from commercially available bar-stock, to readily fit within the container (see Figs. 3 and 4). In a commercial application, UNS C12200 copper (phosphorous deoxidized) may be substituted since this is what is typically used in refrigeration applications. Constant force tests were performed to determine the speeds at which the process can be performed, and to determine a reasonable estimate for the die deformation efficiency (using Eq. (10) with the data). With prior determination of the other parameters in this equation, the efficiency value (g) that provides the best fit of the equation to the data are taken as the die efficiency. This approach is unique in that the efficiency is evaluated for a wide range of speeds and related strain rates and flow stresses, with only a single extrusion trial. Force, and thus ram pressure, is held constant and the velocity is allowed to increase during extrusion as container friction decreases. For the 11-channel tube, a constant force of 200 kn was programmed and for the 2-channel tube, a constant force of 220 kn was used. Subsequent constant velocity tests were performed at ram speeds of 9 mm/min in order to ensure that the entirety of the extrusion trials would be performed at a constant velocity, and not subject to the force limitation of the MTS machine. Data from these trials were used to determine friction factor in the container and validate ram pressure model. 5 Results The results of two initial extrusion trials, using the die for the 11-channel tube, are presented first. This is to demonstrate how the efficiency term (g) and friction factor (m f ) are determined from experimental data. These trials were also performed at slightly lower temperatures than later experimentation. Although the constant force trial was performed first, the data analysis will begin here with the constant velocity test data presented in Fig. 6. It is from these data that the friction factor was determined. The force data are divided by the container bore area to determine ram pressure as a function of ram displacement, and only for the portion of constant velocity extrusion. The decrease in ram pressure is attributed to the decrease in container friction from decreasing surface contact of the shortening billet. The slope of the linear fit to these data (related to the decrease in friction work/ volume) is used to determine the friction p factor. From Eq. (3), the slope of these data is equal to m f Yp c = ffiffiffi 3 Ac, and the friction factor was determined to be 0.6. Y was determined from Eqs. (4) (7) as MPa (3966 psi). p c is mm (1.959 in.), and A c is mm 2 ( in 2 ). Fig. 9 Graphs show ram velocity, ram force, and temperature data for two constant force extrusion trials. Temperature at the entrance of the die was 740 C and the force was constant at 200 kn (45,000 lbs). The extrusion profile was the 16 mm mm 3 11 channel design. Journal of Manufacturing Science and Engineering DECEMBER 2013, Vol. 135 /

6 Fig. 10 Ram force and temperature data are shown for three extrusion tests. The temperature at the entrance of the die was 740 C and the ram velocity was constant at 9 mm/min (0.006 in/s). The profile was the 16 mm mm 3 11 channel design. Maximum pressure was predicted within about 4%. Fig. 11 Graphs show ram velocity, ram force, and temperature data for a constant force extrusion trial. Temperature at the entrance of the die was 748 C and the force was constant at 220 kn (50,000 lbs). The extrusion profile was the 7.9 mm mm 3 2 channel tube. The deformation efficiency term (g) was determined with test data from a constant force extrusion trial and Eq. (10). The results of this trial are presented in Fig. 7. An efficiency, g ¼ 0.215, was determined to provide the best fit of the model (Eq. (10)) to the data. To reproduce these results, it is important to suitably determine the billet length in contact with the container. The billet length is mm (3.75 in.), the cross sectional area of the billet is mm 2, the cross sectional area of the container bore is mm 2, and the die volume is 6500 mm 3. The maximum force is expected at the instant the billets are fully deformed in the container and die, and extrusion commences. For this analysis, the initial billet length at maximum force was calculated to be mm (2.985 in.). Complete ram force and velocity data for the extrusion trial partially presented in Fig. 6 is completely shown in Fig. 8 (noting that ram force is equal to 2 A c P e ). Figure 8 also shows a comparison of the model (Eq. (8)) in terms of extrusion force to the experimental data. The model predicts a ram force within 2.4% of the experimental data. The results of additional constant force and velocity extrusion trials for the 11-channel tube die are presented in Figs. 9 and 10. The temperature data show the variability in the container during extrusion and from extrusion trial to trial. As expected, the Die Holder Heater Temp. and Container Temp. data are extremely constant during extrusion since they are from the thermocouples located directly at the heat source, namely at the heaters. The decrease in container temperature is most likely related to the billet being extruded past the point of the thermocouple location. The temperature at the inlet to the die generally remains constant to within 3 C. For these trials, which were at a slightly higher temperature, the values g ¼ and m f ¼ 0.6 are still valid. Figures 11 and 12 show the data for the 2-channel tube die, which has an extrusion ratio of 67. These data indicate that the container friction was essentially what was previously determined, namely m f ¼ 0.6. However, the die efficiency increased slightly to g ¼ Although this is not considered to be a large increase, it may be related to the fewer internal walls that need to be formed for this design. Photos of the tubes that were extruded for this study are presented in Figure 13. Metallography was performed to verify that good solid state welds were formed, and two such photomicrographs for an 11-channel tube are shown in Fig. 14. The areas / Vol. 135, DECEMBER 2013 Transactions of the ASME

7 Fig. 12 Ram force and temperature data are shown for three extrusion tests. The temperature at the entrance of the die was 745 C and the ram velocity was constant at 9 mm/min (0.006 in/s). The profile was the 7.9 mm mm 3 2 channel design. Maximum pressure is predicted within 5%. Fig. 13 Photos of the 11-channel and 2-channel copper tubes produced in this research Fig. 14 Photomicrographs from a section of 11-channel tube, showing the solid state weld regions. The tube section was taken 152 mm (6 in.) from the start of extrusion. Figure (a) shows an internal wall and Figure (b) shows an external end-wall. indicated on these photos are where the two billet streams flowed together and formed solid state welds. The grain structure appears normal and continuous through these regions and this is a positive indication. Pressure testing, which is beyond the scope of this paper, further verified that proper joining had taken place. Average grain size appears to be less than 100 lm. Journal of Manufacturing Science and Engineering 6 Discussion The overall objective of this effort was to develop an extrusion process to produce net-shape, thin-wall, copper, and copper alloy multichannel tubing for high efficiency heat exchangers. However, a departure from typical hot copper extrusion processes was DECEMBER 2013, Vol. 135 /

8 necessary. This was partly due to the extended contact time of the hot billet with the tooling and this effectively excludes the use of typical hot work tool steels. The use of porthole extrusion dies was also necessary because of the multiple channels in the tube, and the inherent nature of the designs. Because the use of superalloy tooling still has temperature limitations which is probably C for this application, the flow stress of copper is still relatively high for isothermal extrusion, particularly if extrusion is at a high speed (or deformation rate). This is a concern for the die bridge in typical hollow die extrusion, where a single billet is pushed directly onto and into the die. To eliminate or minimize the stresses in the bridge of the porthole die, a dualbillet approach was chosen that effectively eliminates the adverse axial stresses on the die bridge. Two heated billets are separately, yet simultaneously, extruded through the hollow die to fully form the net-shape tube. This does result in higher container friction compared to a single billet configuration. An improvement to the current process would include die and tooling materials that could withstand even higher temperatures and still provide the strength necessary. Thermal management is a term used in hot metal-forming industries to signify the importance of effective temperature control throughout the process. Extrusion temperatures can directly affect extrudate microstructure and mechanical properties, surface finish, part dimensions and the ability to meet tolerances, and tooling and die life. Thermal management is particularly important in this process because the required tooling temperatures are rather high for hot extrusion. These types of profiles most likely cannot be extruded fast enough to minimize overheating of tool steels and even superalloys (especially not with the limited capabilities of this lab apparatus). Furthermore, the thin sections of these profiles would also be subject to faster cooling and higher work-piece flow stress. The high temperatures also increase the gradients within the tooling, such as the container and die holder. For this small lab apparatus, these gradients were as high as 75 C. Thus, the physical limitations of tooling materials, billet size, and tube design must be carefully considered with respect to extrusion speed and temperature and the flow stress of copper at these conditions. To this end, the data and model presented in this paper will be paramount to scaling-up the process to a larger, prototype production scenario. 7 Conclusions Hot extrusion of net-shape, thin-wall, multichannel copper profiles has been demonstrated with a unique lab scale process that uses superalloy tooling, porthole dies and a configuration in which two billets are simultaneously extruded through a two-chamber container. The following conclusions are made with respect to the work presented herein. Numerous extrusion trials were performed with the apparatus to produce tubes of sufficient quality for the development of prototype heat-exchangers (by others). The process has been successfully demonstrated with two thin-wall profiles (dies) containing multiple channels, having extrusion ratios of 25 and 67. The data suggest the process is repeatable, and the current tooling has withstood numerous extrusion trials. Sufficient extrusion data were gathered, and an analytical model was developed to predict ram pressure with respect to process and material parameters. An approach is presented where the deformation efficiency in the die is evaluated over a wide range of extrusion speeds within a single extrusion trial, performed at a constant ram force. Maximum extrusion force is predicted to within 5% with the analytical model and data. The data suggest a friction factor in the container of about 0.6, which is less than that for a sticking friction condition. It is inferred from the data and process parameters that extrusion is essentially isothermal, even though significant thermal gradients exist in the heated tooling. The importance of temperature control is very evident from this work. High temperatures are required at the heaters to provide the required temperature for the deforming billet. From the samples inspected, solid state welds fully and satisfactorily form in the tube within 152 mm from the start of extrusion. Acknowledgment The authors would like to thank the International Copper Association (ICA) and Ohio University for providing financial support for this work. Thanks to Mr. Randy Mulford and Jared Rich for helping with the experiments. Thanks also to T.C.E. References [1] Laue, K., and Stenger, H., 1981, Extrusion: Processes, Machinery, Tooling, American Society for Metals, Metals Park, OH, pp ,162. [2] Bauer, M., Sauer, G., and Siegert, K., eds., 2006, Extrusion, 2nd ed., ASM International, Materials Park, OH, pp. 49, , 245, 247, [3] Vaitkus, V., 2008, A Process for the Direct Hot Extrusion of Hollow Copper Profiles, M.S. thesis, Ohio University, Athens, OH. [4] Kraft, F. F., 2012, Micro-Channel Tubes and Apparatus and Method for Forming Micro-Channel Tubes, U.S. Patent No [5] Kraft, F. F., 2012, Extrusion of Hard-Alloy, Thin-Wall Hollow Profiles, Proceedings of the Tenth International Aluminum Extrusion Technology Seminar ET 12, ET (Extrusion Technology) Foundation Wauconda, IL. [6] ATI Allvac, ATI 720 Alloy Technical Data Sheet, accessed on Jan. 20, 2011, (accessed on Dec. 31, 2011), pages/pdf/tech/ni-826%20720.pdf [7] High Temp Metals, Data Library, 2011, accessed on Dec. 31, 2011, [8] Uddeholm, ORVAR 2 Microdized Hot Work Tool Steel, accessed on Jan. 3, 2006 (accessed on Dec. 31, 2011, [9] Kraft, F. F., and Gunasekera, J. S., 2005, Conventional Hot Extrusion, ASM Handbook Volume 14A, Metalworking: Bulk Forming, S. L. Semiatin, ed., ASM International, Materials Park, OH, pp [10] Hosford, W. F., and Caddell, R. M., 1993, Metal Forming, Mechanics and Metallurgy, 2nd ed., PTR Prentice Hall, Upper Saddle River, NJ, p [11] Dieter, G. E., 1986, Mechanical Metallurgy, McGraw-Hill, New York, p [12] Rogers, S., 2009, Flow Stress Analysis of Copper at Elevated Temperatures, Senior Engineering Project, Ohio University, Athens, OH / Vol. 135, DECEMBER 2013 Transactions of the ASME