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Numerical and experimental analysis of twist channel angular pressing (TCAP) as a SPD process
Materials Science & Engineering A 563 (2013) 86–94
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Numerical and experimental analysis of twist channel angular pressing (TCAP) as a SPD process Radim Kocich a,b,n, Lenka Kuncˇicka´ a, Milan Mihola c, Kateˇrina Skotnicova´ b ˇ TU Ostrava 17.listopadu 15, Ostrava-Poruba 70833, Czech Republic Department of Material Forming, Faculty of Metallurgy and Materials Engineering, VSB ˇ TU Ostrava 17. listopadu 15, Ostrava-Poruba 70833, Czech Republic Regional Materials Science and Technology Centre, VSB c ˇ TU Ostrava 17. listopadu 15, Ostrava-Poruba 70833, Czech Republic Department of Robotics, Faculty of Mechanical Engineering, VSB a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 August 2012 Received in revised form 10 November 2012 Accepted 15 November 2012 Available online 21 November 2012
The article brings detailed information about the deformation behavior of copper during twist channel angular pressing (TCAP) obtained via 3D numerical analysis based on the finite element method (FEM). It was proved that the geometric parameters of the die, as well as the used deformation parameters, significantly affect the size and homogeneity of the effective strain, temperature or stability of the plastic flow of material. It may be stated that the largest effect on the size of the deformation was due to the twist rotation angle. The largest homogeneity of strain was detected at a higher friction coefficient. On the other hand, the distance between the twist and bend does not significantly affect the value of the strain. At higher extrusion speeds, the temperature of the extruded billet and the size of the dead zone both grow significantly. A comparison between the FEM and experimental results of the required loads and the homogeneity of the effective strain distribution showed good agreement. The homogeneity of the distribution of the deformation was confirmed by micro-hardness testing, whereas a relative growth of 80% was documented after the first pass. & 2012 Elsevier B.V. All rights reserved.
Keywords: Finite element method Bulk deformation TCAP Effective strain
1. Introduction Among the methods based on the application of severe plastic deformations (SPD), the ECAP process designed by Segal [1] continues to hold a significant place. For its relative simplicity, this procedure is used very frequently to increase, among others, the mechanical properties of metal materials. The main properties characterizing an ECAP process are the possibility of relatively keeping the original shape of the sample, as well as simple shear, as the main deformation mechanism at the point of intersection between both channel parts [2]. This process is currently under commercialization efforts. The goal is the possibility of the continuous processing of long products. Concrete results include dissimilar channel angular pressing (DCAP) [3], ECAP-Conform [4] or equal channel angular pressing with partial back pressure (ECAP–PBP) [5]. However, to obtain well-defined and stable microstructures, it is generally necessary to perform a large number of passes. Increasing process efficiency, in the sense of imposing larger strain during individual passes to reduce the number of passes, is thus one of the desired goals. The first solution variants was the application of a rotary die that allowed n Corresponding author at: Department of Material Forming, Faculty of Metalˇ TU Ostrava 17. listopadu 15, Ostrava-Poruba lurgy and Materials Engineering, VSB 70833, Czech Republic. Tel.: þ420 59694455; fax: þ 420 596994414. E-mail addresses: [email protected], [email protected] (R. Kocich).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.11.047
multiple extrusions without removing the sample from the die [6,7], or the use of ECAP with parallel channels [8]. Certain results can be seen, for example, in the manner of proposing more efficient deformation paths. A concrete example is, for example, the work [9] of using a newly designed deformation route (BcUdII) to obtain the desired state after a lower number of passes. Another method is based on non-equal channel angular pressing (NECAP) technology, where protrusion occurs through a die with differing channels [10]. This method can lead to an increase of shear deformation by 25%, at a 50% reduction of the cross-section of the output channel in one direction. The relatively promising solution variants also include the recently proposed twist channel angular pressing (TCAP) process [11,12]. The process is based on the assumption that the bend of the channel is preceded by a twist situated in the vertical part of the channel. As the first partial results documented, this method can lead to higher homogeneity, as well as higher values of the imposed strain for each pass. Numerical simulations based on the finite element method (FEM) have long been used to predict the deformation behavior of materials during plastic deformation for a long time now. A similar case also applies for SPD techniques. The large number of published results in this area confirms the applicability of this approach in various fields. Djavanroodi et al. [13] used 3D simulation to study the effects of channel angle, friction and backward pressure for the ECAP process when processing copper.
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Similarly, Kocich et al. carried out a 3D study of the ECAP process under temperature when considering Mg alloys based on Mg–Al– Zn [14]. Wang et al. used numerical analysis to evaluate geometric adjustments of the die to lower friction in the internal curving of the channel [15]. The purpose of this article is to provide a more detailed mapping of the TCAP process in the sense of ascertaining the influence of the variability of selected factors, especially the size of effective strain (ES). A more detailed description of this process with respect to the influences of geometry (die parameters, i.e., position of twist, angle of twist or angle between individual parts of channel) or deformation parameters (e.g., velocity of extrusion) has never been carried out. The subsequent experimental application of this process can then represent a partial verification of the predicted results (e.g., required pressing force).
2. Experimental The goal of the experiment was to provide a more detailed description of the TCAP technology with respect to various influences of die parameters and selected deformation parameters on the resulting temperature, ES, in-homogeneity of strain at the cross-section of the sample, or pressing force needed for extrusion. The other monitored characteristics also included material flow. The TCAP process principle is illustrated in Fig. 1a. The first part of the paper contains a numerical analysis of various variants of this process. The influence of the extrusion speed was monitored here, whereas the behavior of the material at extrusion speeds v¼3 mm/s and v¼6 mm/s were investigated. Other monitored factors included applied friction, which was
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represented in the simulation by two selected values of Coulomb friction (m ¼0.02, m ¼0.05). The discussed values of friction coefficient were chosen considering experiments carried out before, of which mutual comparison of values predicted with numerical simulations was successful with the help of measurement of punch loading. The influence of the geometry of the used die was also monitored. Specifically, this was carried out by simulating the influence of angle j (angle between individual parts of the channel), angle b (twist slope angle), and angle o (angle of the twist rotation) (Fig. 1a). The ECAP process was also analyzed to compare the efficiency of the TCAP process. The second part of the experiment was based on the practical realization of the TCAP process. This part was focused on verification of the model used in FEM. The selected material was commercially pure Cu (99.97%) with a chemical composition of 0.0074Ni, 0.0058Sn, 0.0031Fe, 0.0030Zn, 0.0023Si (in wt%). The extruded samples were defined to match the numerical simulation, i.e., they had a square 12 mm 12 mm 130 mm cross-section. The experiment itself followed the copper being annealed at 650 1C/h. To objectively evaluate the results of numerical prediction, the die used in the experiment was defined by j angle of 901, c angle (outer corner) of 201, b angle of 401, and o angle of 901. Extrusion was carried out at room temperature (25 1C) on a hydraulic press at a rate of extrusion of 3 mm/s and MoS2 was used as lubricant. During the practical experiment, the temperature of the extruded material was also monitored. This was done via two thermocouples located at a distance of 1 mm from both primary deformation areas (the twist and bend). Simultaneously, the force load of the extruder during TCAP was also monitored. These parameters were subsequently verified with the results obtained from the numerical
Fig. 1. Diagram of the TCAP process including monitoring points located on the ‘‘dividing’’ plane. 1, 2, 3—monitored places, o—angle of twist rotation, b—twist slope angle, l—distance between the end of twist part of the channel and the bend of channel, j—channel angle, c—angle associated with the arc of curvature where the two parts of the channel intersect, F—force (a) Stress–strain curves of Cu used in FEM (b).
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simulation. For these reasons, the micro-hardness was measured on the transversal cross-section of the sample after the first pass.
3. Finite element analysis The Forge 2009 commercial software was used to analyze the deformation behavior of the extruded material. The simulations were performed using a model in which the geometrical dimensions and mechanical properties of the billet in the simulation were identical to those of the experiment. This allowed for the direct comparison of simulation results with those obtained experimentally. The deformation behavior of copper after one pass was predicted. Elasto-plastic model with the Newton– Raphson convergent algorithm was utilized to determine simulation parameters. The billet was characterized by a mesh with 48,675 nodes. Mesh with tetrahedral elements was employed to model the workpiece sections. The extruder, as well as the die, was considered to be rigid parts. Due to the expectation of large shear deformations during the simulation, automatic re-meshing was activated. The stress–strain curve (Fig. 1b) valid for the experimentally used material was determined based on a torsion test made at room temperature and with two strain rates (0.01 s 1 and 0.1 s 1) on SETARAM, a servo-hydraulic torsion plastometer. These experimentally obtained data were entered into the material flow stress database of software. The Haensel–Spittel equation (Eq. (1)) was used to describe the behavior of the material during deformation.
sf ¼ Aem1 T T m9 em2 em4 =e ð1 þ eÞm5 T em7 e e_ m3 e_ m8 T
ð1Þ
where e is the equivalent strain, e_ is the equivalent strain rate, T is the temperature and A, m1, m2, m3, m4, m5, m6, m7, m8, m9 are the regression coefficients. The values of individual coefficients are
410.08 MPa, 0.00121 MPa, 0.21554 MPa, 0.01472 MPa, and 0.00935 MPa, m5–m9 are 0. The boundary conditions of the simulation were defined by a temperature of 25 1C, values describing the temperature behavior of copper, the die, and the number of passes (one pass). Young’s modulus, Poisson’s ratio, thermal expansion, thermal conductivity, heat transfer coefficient, specific heat, emissivity and density were defined as the constant of 112 (GPa), 0.3, 1.7 10 5 (K 1), 394 (W/(m K)), 100,000 (W/m2 K), 398 (J/kg K), 0.7 (kg/m3) and 8960 (kg/m3). To better specify individual monitored parameters, the extruded material included a definition and the monitoring of three specific areas (points 1–3). These points were placed on a plane parallel to the longitudinal axis of the sample passing through its center (Fig. 1a). The purpose of this part was to study the influence of die parameters on the magnitude of effective strain, in-homogeneity of strain at the cross-section of the sample or pressing force needed for extrusion.
4. Results and discussion 4.1. Friction One of the monitored factors was the influence of friction during TCAP. As was detected for the modeled TCAP process, the growing value of friction increases the resulting value of the imposed strain. These findings are in good agreement with most published results valid for the ECAP process although most published works that model the ECAP process are based on the assumption of an absence of friction and the angle j ¼901 [16,17]. For lower friction coefficients (m ¼0.02), the average value of the imposed strain is 2.3. Higher applied friction (m ¼0.05) also meant an increase of the average ES value up to 3. However, it needs to be noted that this increase was also accompanied by the
Fig. 2. 3D sections and effective strain contours in the samples after the TCAP process for different friction coefficients (a) m ¼ 0.02 (b)¼ 0.05 with the curves of homogeneity of distribution for appropriate places.
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simultaneous growth of the strain homogeneity (Fig. 2a and b). It is also possible to simultaneously see a certain difference in the deformed ends of the sample with respect to the value of the inserted deformation. While lower friction leads to the end of the sample being defined by the lowest values of the inserted deformation, higher friction reverses this trend. As subsequently specified (in Section 4.7), the reasons for this may be found in the plastic flow of the material. For all subsequently simulated variants, only friction defined by m ¼0.02 was taken into account. 4.2. Velocity of extrusion Another modeled variable factor of the TCAP process was the speed of extrusion. Extrusion speeds of 3 mm/s and 6 mm/s were analyzed. This factor has also been studied by a relatively large number of works focusing on the ECAP process. Such works document a certain influence of the size of ES on the used velocity. During TCAP, detectable partial differences were confirmed not only in ES size, but also in ES distribution homogeneity. When using a lower extrusion speed, ES distribution was more homogeneous (Figs. 2a and 4b). The growth of the non-homogeneity of the strain is in accordance with the observed significant increase of the size of the dead zone, as documented in Fig. 7a. In this case (6 mm/s), the largest size of this area was documented for a simulated j angle of 901. As follows from very recently published work [18], a higher extrusion speed of the ECAP process can negatively affect billet cohesion. Due to the very unstable material flow, in conjunction with the occurrence of significant lateral gaps behind the inner radius of channel bend, it is very probable that similar behavior may also be observed for the TCAP process. However, the very negative influence of higher extrusion speeds was documented in the temperature of the extruded billet. As the channel detail documents (Fig. 3), the maximum temperatures were always located in the area of the intersection between both channel parts, i.e., the main deformation zone (MDZ). The resulting temperature curves thus capture the time dependency of the central areas (monitored point 2). While almost all modeled TCAP variants led to a temperature increase to a level comparable with ECAP ( 35 1C), this does not apply to higher extrusion speed. At an extrusion speed of 6 mm/s, the temperature increase was up to two times higher than in other variants. The extrusion speed will thus be a significant factor and needs to be thoroughly taken into account during TCAP. One of the reasons is also adherence to the process temperature in relation to the possible unintentional exceeding of the temperature necessary for the activation of restoration processes.
Fig. 3. Distribution of temperature in extruded sample (section) during TCAP and time dependence of the temperature for individual variants.
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The result on the temperature curve for higher friction is relatively unexpected (Fig. 2). It is clear that the maximum obtained temperature of the billet is lower than in the case of higher friction. This fact is very probably related to the faster heat transfer through the die due to better contact between the billet and channel walls. When comparing this to the results published in [11], it may be stated that higher extrusion speed has a much larger impact on temperature increase than higher simulated friction for the TCAP process. It should be stressed that the temperature curve for TCAP already becomes affected in the first stages of the pass. This is documented by the presence of the first peak on all curves, which did not occur in ECAP. This initial increase is caused by the sample passing through the twist. It is thus clear that a twist located in the vertical part of the channel participates in the temperature increase much less than the subsequent bend. This applies to all modeled TCAP variants, including higher extrusion speeds. An extrusion speed of v¼3 mm/s was assumed for all subsequent simulated variants. 4.3. Distance l The effects of the distance of the twist from the bend of channel were also monitored during numerical simulation. This distance, denoted by l, was examined with the goal of finding a possible dependency between the imposed strain and the position of the extruded sample with respect to deformation zones. The first model example was based on the assumption of a minimum (i.e., minimum required) transition area between the output part of the twist and the input part of the bend (l ¼2 mm). The second case then modeled a similar situation with l¼10 mm. Although relatively similar ES values were detected in both modeled cases, both variants were not equivalent (Figs. 4a,4b). The differences were based mostly in the obtained ES homogeneity. As was found, the existence of a transition zone between the individual deformation zones caused a significant difference between the upper and lower half of the sample. Due to different material flow, the ES values differed especially in corner areas. In the case of l¼2 mm, the effective strain is distributed in the cross section more or less symmetrically (Fig. 4c). The maximum ES values are located in the area of sample edges. For the l¼10 mm variant, it is clearly visible that the strain maxima are kept only in the corner areas next to the internal curve, i.e., in the upper half of the billet (Fig. 4c). Additionally, the higher peak values of ES in the corner areas also need to be noted. The reasons for the diverging material behavior stem from the area before the channel bend. The growing distance of the twist from the bend causes the ES gradient to grow in the area behind the twist after the cross section of the extruded material. This increases the value of ES, especially in the corner areas. A similar finding is known for example from the TE process [19]. The subsequent bend during the TCAP process can further increase ES in these corner areas. In other words, a certain similarity to the ECAP process can be mentioned based on the known finding that ES maxima are located in the upper half (of corner areas). As further commented, the characteristics of similarity between the TCAP variant (l¼10 mm) and ECAP may also be found in the material’s plastic flow. The differences between both variants are also confirmed by their mutual comparison with respect to strain rate (Figs. 4d, 4e). In the case of l¼2 mm, a much wider MDZ area is apparent than in the case of a larger l. In the twist area, the MDZ is extended both into the input as well as the output part of the channel. Additionally, the average value of strain rate in the case of a longer transition zone is only half (i.e., 0.08 s 1) that of the second variant. While in the case of l¼2 mm, the corners of the sample in the twist area are characterized by a higher strain rate, in the second case this is not so due to the influence of the transition zone. These conclusions also lead to a different material flow,
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Fig. 4. Effective strain contours and appropriate strain rate contours in longitudinal and transversal section of the sample after the TCAP process for different transition regions l ¼2 mm (a, d), l ¼ 10 mm (b, e) with the curves of homogeneity of distribution in diagonal direction (c).
which can also be viewed in the different shapes of sample ends. The transition zone between the twist and bend thus leads to the relative suppression of the influence of the vortex-like flow of material. This holds especially in areas next to the external channel curve. This finding, together with the shape and size of MDZ, will thus have a different influence on the above-listed situation in the twist area for both variants. A longer transition region between the individual deformation zones leads to a more homogeneous distribution of the strain after the sample cross section. This finding corresponds very well with the study conclusions [20] in the case of the ECAP process with parallel channels. A growing distance between the individual deformation zones increases the homogeneity of the strain. Although these are not identical processes, an analogy may be drawn between both deformation zones in this respect.
with respect to ES size. There thus exists a certain analogy to the ECAP process. However, the average ES value during TCAP (j ¼1101) is 1.38, which is comparable to the ECAP process for j ¼901. The relatively lower homogeneity in the ES distribution along the extruded billet (Fig. 5) also needs to be mentioned. A growing j, similarly to the ECAP process, leads to a larger dead zone creation—this is often considered as one of the negative reasons leading to non-homogeneous strain distribution [21,22]. As subsequently discussed, this angle has led to the largest dead zone, as well as lateral gaps (Fig. 7a). On the other hand, the application of this die has led to a significant reduction of extrusion load in comparison to an angle of j ¼901 (Fig. 7b). The force requirement of this variant is comparable to the requirements for a conventional ECAP process. 4.5. Angle b
4.4. Angle j As documented by Fig. 2a, the use of a die with an angle of j ¼901 leads to a relatively homogeneous distribution of the imposed strain along the sample length. When applying a die with a larger angle (j ¼1101), it becomes clear that the value of ES at TCAP drops for higher angles. When compared to the die with an angle of 901, a significant difference appears, especially
As listed for example in [23] regarding a fundamentally similar process—twist extrusion (TE), the optimum of the twist slope angle (b) lies in the interval of up to 201. The main reason for this is especially a significant change of the geometry of the cross section of the extruded material in the case of higher angles. On the other hand, a lower b means a lower size of the imposed strain. A possible way of crossing this ‘‘limit’’ value in the case of
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Fig. 5. 3D shape and effective strain contours in the sample after the TCAP process (j ¼1101) with the histogram of homogeneity of distribution.
Fig. 6. 3D shape and effective strain contours in the sample after the TCAP process b ¼401 (a) o ¼ 1801 (b) with the time dependence of effective strain for all modeled variants (c).
TE is the use of backward pressure, which however significantly complicates realization. Additionally, not even the application of backward pressure can generally guarantee a homogeneous distribution of the deformation. On the other hand, the construction of the TCAP process allows the deformation to be applied even with a significantly higher b without the use of backward pressure. This is especially due to the subsequent bend in the channel, which ensures that the original dimensions of the extruded billet are kept intact. The friction, together with a sudden change of the material flow (channel bend) provide sufficient resistance against material flow, and thus prevent the cross section of the channel from being filled at least in the twist area. This also allows the elimination of unwanted geometry changes of the sample caused during the process with higher twist slope angles. For these reasons, the experiment analyzes a TCAP process with a twist defined by an angle of b ¼401. This means that the total height of the twist in this case was only half that of the
previously modeled variants. The minimum required transition area of l ¼2 mm was considered between the twist and bend. As confirmed by the carried out numerical simulation, the value of b significantly affects both the ES value as well as its homogeneity after the cross section of the extruded billet. It is clear that higher values of b mean a larger ES size (Fig. 6c). The majority cause of this is the lower helix slope. The positive influence of a higher b may thus be seen in a deeper penetration of the strain in the twist area in the direction of the diagonals (Fig. 6a). This is caused by a lower sloping of the helix, which forces the material into a more intense vortex-like flow. 4.6. Angle o To define the influence of the angle o during the TCAP process, the case of its size being given by a 1801 rotation around the axis was simulated. The twist slope was considered to be constant for the whole height of the twist, and defined by an angle of b ¼401.
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This kept the total height of the twist intact. Similarly to the previous case, a transition zone of l¼2 mm was also considered here. The comparison of individual modeled variants with respect to ES value (Fig. 6b) lists individual time courses monitored in their central areas (point 2). This dependency documents that for the variant of o ¼ 1801 there was a significant increase of the size of imposed strain. The average value of ES after the first pass in this case ranged in the area of 3.27. This is almost three times larger than in the classic ECAP process, and an approximate 50% increase compared to TCAP with o ¼901. However, regarding the homogeneity of the imposed strain, it may be said that this is much lower than in the previous cases. As follows from Fig. 6b, the ES distribution on the surface as well as below the surface of the sample is relatively uneven. The minimum ES values are detected at the ends of the sample. In comparison to the previous cases, it is necessary however to state that the volume of the sample defined by the ES minimum is much lower than in the previous variants. In the case of TCAP with a larger rotation angle, the minimum ES is even higher than for ECAP. As is clearly visible in Fig. 6b, the largest sizes of the ES are obtained in the case of dies with a rotation angle of o ¼1801. Additionally, it is necessary to mention the influence of angle b, where a lower twist slope leads to higher strain values. These findings thus confirm the significant role of the twist on the total imposed strain during the TCAP process. On the other hand, the effect of the distance of the twist from the channel bend seems to be less relevant than other factors with respect to the value of the imposed strain.
4.7. Plastic flow Both processes, TCAP and ECAP, were also studied with respect to plastic flow. Superimposed grids were used to evaluate material flow during plastic deformation. Grids were superimposed in parallel with the longitudinal axis of the sample to allow the assessment of individual modeled variants. To allow exact evaluation, the designed grids were defined by very small (0.5 mm 0.5 mm) square cells. These grids then allowed the monitoring of the influence of die geometry, as well as other parameters of material flow. One of the often discussed factors is the size of the dead zone. As previously mentioned, most published studies assume its negative influence on the value and homogeneity of the imposed strain [24,25]. As is clear from Fig. 7a, differences exist between individual simulated variants of TCAP. In all modeled cases of the TCAP process, there is a significant reduction of the size of the dead zone in comparison to the ECAP process. This is caused by a different method of material entry into the place of bend in the die. During TCAP, the extruded material better fills the channel volume due to the vortex-like flow than in the case of ECAP. It is clear that higher extrusion speed and higher values of j increase the size of the dead zone, similarly to the ECAP process [14,26,27]. However, the resulting size of the dead zone for TCAP in these cases is still lower than in comparable cases of ECAP. The vortex-like flow of course also affects the shape and size, specifically the shape of output ends. While in the case of the ECAP process the MDZ is located especially in the direction of the diagonal between both channel radiuses, in the case of TCAP this is significantly extended both in the output and especially the input part of the channel. Other differences include the absence of lateral gaps in the area behind the inner radius of the output part of the channel during the TCAP process. It is known that this factor negatively affects the state of stress in the extruded billet during ECAP, where unwanted tensile stress concentrates in these
Fig. 7. Plastic flow pattern for individual variants (a) dependence of punch load for individual variants (b).
areas. Such stress may then initiate the creation of cracks on the deformed sample [18,26]. After a comparison between individual modeled variants of the TCAP process, a large dependence of material flow on the extrusion speed and friction ratios between the die and billet is apparent. It is clear that higher friction coefficients lead to an almost full suppression of the dead zone. Simultaneously, it is possible to monitor a relatively steady material flow in the output part of the channel. The oscillation of horizontal lines of the superimposed grid is detected only in isolated regions, which contrasts with the situation of higher extrusion speed, where the plastic material flow is significantly unstable and very uneven after the cross section. These findings are evidently related to the known fact that the influence of friction drops with increasing speed. It is clear that the maximum speed-up of central layers of the material during TCAP occurs in the case of the use of a die with o ¼ 1801. This is confirmed especially by the significantly deformed vertical lines. In the case of a higher angle b, a similar trend as in the case of higher friction coefficients may be observed. 4.8. Punch load Punch load is an important factor due to the verification of simulated results, as well as with respect to the assessment of parameters such as friction coefficient. All the modeled variants
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were thus also evaluated with respect to their force requirements. The individual analyzed variants were processed in the form of time courses. As documented by Fig. 7b, the load on punch is relatively higher during TCAP than during the classic ECAP process. The difference between both technologies is, however, not large. It may be said that in the case of using a die with a twist angle of j ¼1101, the force requirements for punch in the case of TCAP are comparable to ECAP applied using a die at an angle of j ¼901. The above-listed dependence clearly documents that friction has a much larger impact on punch load than the geometry of the vertical part of the channel. The dependency demonstrates that during increased friction, the load of the punch increases to twice the values obtained in other variants. It is also necessary to take into account the factor of very large pressure oscillation during the above-mentioned higher friction coefficient. Such a serrated curve is very frequently linked to the instability of plastic flow of the deformed material during the process [18,26]. However, in the case of TCAP, these may be detected mostly in the areas next to the upper surface of the output part of the channel. In the case of a larger angle o in the vertical part of the channel, the pressure increases only by 26%. This leads to the possibility of increasing the value of the imposed strain during the given pass without the potential risk of destroying the tools. The predicted values of pressure of the punch were subsequently verified by an experiment carried out using a die with an angle of j ¼ 901. Differences in the course of the predicted and experimentally tested curve (Fig. 7b) may be caused by several factors. These include for example the accuracy of sensors, friction variability, material properties, simplifications, or the used mathematical model. The results of the comparison however imply that the experimentally obtained data correlated relatively well with the dependence on pressure predicted for friction defined by a coefficient of 0.02. 4.9. Micro-hardness After the pass, the micro-hardness after sample cross section was measured. To obtain a more exact evaluation, the values of both diagonals were determined (Fig. 8a). As is clear from the attached graphical dependency, the highest values were not located in the corner areas of the sample. However, it is necessary to mention that there was only a small difference between the maximum and minimum measured hardness (in comparison with central areas). On the other hand, it needs to be said that the external measured indentations were located very close to the ends of the sample diagonals, hence the high possibility of influencing, the measured values. Despite this fact, only soft drops of hardness were detected. It means a relatively good correlation between the micro-hardness with the predicted ES distribution in the extruded sample. One pass increased microhardness to an average value of 108 HV, which represents an increase of 80% against the undeformed state. On the basis of achieved results, the TCAP process defined with lower extrusion rate applied in the die, where the distance between twist and bending is longer, can be considered to be optimal from the achieved strain homogeneity point of view. Those factors coupled with assumption of low friction coefficient appear to be suitable conditions for high homogeneity of imposed strain achievement. Rotation of twist angle (o) is of the largest influence on strain values, then the channel bend angle (j) and the twist slope angle (b). It has been proved, that the extrusion rate must be chosen very carefully (increasing value of the rate influences greatly growth of the dead zone and, above all, the deformed material temperature). Similar influence on dead zone size has higher channel bend angle.
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Fig. 8. Micro-hardness of processed copper: measured places (a) obtained dependence (b).
5. Conclusions The work contains a numerical simulation of the TCAP process, whereas various variants of die geometry and deformation parameters were modeled. The article focuses especially on determining the efficiency of the process in relation to the size of the imposed strain. The subsequent experiment was then aimed at verifying the predicted results. The main results may be defined as follows: Maximum values of the effective strain occurred for higher rotation angles. The average ES size in this case reached 3.27. The construction of TCAP allows the use of higher angles b to obtain higher values of the imposed strain without an undesired change of the cross section of the extruded billet than in several other processes utilizing twist. Higher twist slope angle and lower angle between the individual channel parts stand for the higher value of imposed strain. It is recommended to use dies with angle of twist rotation up to 901 because larger angle signifies larger values of imposed strain but also higher strain inhomogeneity within the crosssection. The punch load during TCAP with respect to the value of imposed strain is comparable to the punch load during ECAP. As the one of necessary presumptions is good lubrication of samples (friction coefficient minimization). Higher friction coefficient causes significant increasing of punch load as well as. The distance between the twist and bend of the channel does not significantly affect the value of the imposed strain, but relatively significantly affects its distribution. The size of the dead zone during TCAP is significantly lower than during conventional ECAP. This finding is also related to
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the resulting homogeneity of the ES for both types of processes. The experimentally obtained micro-hardness after the cross section of the deformed sample correlated relatively well with the predicted values of the imposed strain.
Acknowledgements This paper was created in the project no. CZ.1.05/2.1.00/ 01.0040 ‘‘Regional Materials Science and Technology Centre’’ within the frame of the operation program ‘‘Research and Development for Innovations’’, financed by the Structural Funds and from the state budget of the Czech Republic.
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[9] W. Liang, L. Bian, G. Xie, W. Zhang, H. Wang, S. Wang, Mater. Sci. Eng., A 527 (2010) 5557–5564. [10] L.S. To´th, R. Lapovok, A. Hasani, Ch. Gu, Scr. Mater. 61 (2009) 1121–1124. [11] R. Kocich, M. Greger, M. Kursa, I. Szurman, A. Macha´cˇkova´, Mater. Sci. Eng., A 527 (2010) 6386–6392. [12] R. Kocich, J. Fiala, I. Szurman, A. Macha´cˇkova´, M. Mihola, J. Mater. Sci. 46 (2011) 7865–7876. [13] F. Djavanroodi, M. Ebrahimi, Mater. Sci. Eng., A 527 (2010) 1230–1235. [14] R. Kocich, M. Greger, A. Macha´cˇkova´, Finite element investigation of influence of selected factors on ECAP process, in: Proceedings of the Conference Metal, TANGER, Ostrava, 2010, pp. 166–172. [15] S. Wang, W. Liang, Y. Wang, L. Bian, K. Chen, J. Mater. Process. Technol. 209 (2009) 3182–3186. [16] H.S. Kim, Mater. Sci. Eng., A 328 (2002) 317–323. [17] R.B. Figueiredo, I.P. Pinheiro, M.T. Paulino Aguilar, P.J. Modenesi, P.R. Cetlin, J. Mater. Process. Technol. 180 (2006) 30–36. [18] R.B. Figueiredo, P.R. Cetlin, T.G. Langdon, Metall. Mater. Trans. 41A (2010) 778–786. [19] S.A.A. Akbari Mousavi, S.R. Bahadori, A.R. Shahab, Mater. Sci. Eng., A 527 (2010) 3967–3974. [20] F. Djavanroodi, M. Ebrahimi, Mater. Sci. Eng., A 527 (2010) 7593–7599. [21] H.S. Kim, S.I. Hong, M.H. Seo, J. Mater. Res. 16 (2001) 856–864. ¨ Mater. Sci. Eng., A 503 (2009) 148–151. [22] P. Karpuz, C. Simsir, C.Hakan Gur, [23] Y.Y. Beygelzimer, D.V. Orlov, V.N. Varyukhin, in: Y.T. Zhu, T.G. Langdon, R.S. Mishra, S.L. Semiatin, M.J. Saran, T.C. Lowe (Eds.), Proceeding of the Second International Symposium on Ultrafine Grained Materials II, Seattle, Washington, USA, 2002. pp. 297–304. [24] H.S. Kim, M.H. Seo, S.I. Hong, Mater. Sci. Eng., A 291 (2000) 86–90. [25] T.R. Milind, P.P. Date, Int. J. Mech. Sci. 56 (2012) 26–34. [26] R. Kocich, M. Kursa, A. Macha´cˇkova´, Acta Phys. Pol. A 122 (2012) 581–587. [27] P.R. Cetlin, M.T.P. Aguilar, R.B. Figueiredo, T.G. Langdon, J. Mater. Sci. 45 (2010) 4561–4570.
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Materials Science & Engineering A journal homepage: www.elsevier.com/locate/msea
Numerical and experimental analysis of twist channel angular pressing (TCAP) as a SPD process Radim Kocich a,b,n, Lenka Kuncˇicka´ a, Milan Mihola c, Kateˇrina Skotnicova´ b ˇ TU Ostrava 17.listopadu 15, Ostrava-Poruba 70833, Czech Republic Department of Material Forming, Faculty of Metallurgy and Materials Engineering, VSB ˇ TU Ostrava 17. listopadu 15, Ostrava-Poruba 70833, Czech Republic Regional Materials Science and Technology Centre, VSB c ˇ TU Ostrava 17. listopadu 15, Ostrava-Poruba 70833, Czech Republic Department of Robotics, Faculty of Mechanical Engineering, VSB a
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 August 2012 Received in revised form 10 November 2012 Accepted 15 November 2012 Available online 21 November 2012
The article brings detailed information about the deformation behavior of copper during twist channel angular pressing (TCAP) obtained via 3D numerical analysis based on the finite element method (FEM). It was proved that the geometric parameters of the die, as well as the used deformation parameters, significantly affect the size and homogeneity of the effective strain, temperature or stability of the plastic flow of material. It may be stated that the largest effect on the size of the deformation was due to the twist rotation angle. The largest homogeneity of strain was detected at a higher friction coefficient. On the other hand, the distance between the twist and bend does not significantly affect the value of the strain. At higher extrusion speeds, the temperature of the extruded billet and the size of the dead zone both grow significantly. A comparison between the FEM and experimental results of the required loads and the homogeneity of the effective strain distribution showed good agreement. The homogeneity of the distribution of the deformation was confirmed by micro-hardness testing, whereas a relative growth of 80% was documented after the first pass. & 2012 Elsevier B.V. All rights reserved.
Keywords: Finite element method Bulk deformation TCAP Effective strain
1. Introduction Among the methods based on the application of severe plastic deformations (SPD), the ECAP process designed by Segal [1] continues to hold a significant place. For its relative simplicity, this procedure is used very frequently to increase, among others, the mechanical properties of metal materials. The main properties characterizing an ECAP process are the possibility of relatively keeping the original shape of the sample, as well as simple shear, as the main deformation mechanism at the point of intersection between both channel parts [2]. This process is currently under commercialization efforts. The goal is the possibility of the continuous processing of long products. Concrete results include dissimilar channel angular pressing (DCAP) [3], ECAP-Conform [4] or equal channel angular pressing with partial back pressure (ECAP–PBP) [5]. However, to obtain well-defined and stable microstructures, it is generally necessary to perform a large number of passes. Increasing process efficiency, in the sense of imposing larger strain during individual passes to reduce the number of passes, is thus one of the desired goals. The first solution variants was the application of a rotary die that allowed n Corresponding author at: Department of Material Forming, Faculty of Metalˇ TU Ostrava 17. listopadu 15, Ostrava-Poruba lurgy and Materials Engineering, VSB 70833, Czech Republic. Tel.: þ420 59694455; fax: þ 420 596994414. E-mail addresses: [email protected], [email protected] (R. Kocich).
0921-5093/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.msea.2012.11.047
multiple extrusions without removing the sample from the die [6,7], or the use of ECAP with parallel channels [8]. Certain results can be seen, for example, in the manner of proposing more efficient deformation paths. A concrete example is, for example, the work [9] of using a newly designed deformation route (BcUdII) to obtain the desired state after a lower number of passes. Another method is based on non-equal channel angular pressing (NECAP) technology, where protrusion occurs through a die with differing channels [10]. This method can lead to an increase of shear deformation by 25%, at a 50% reduction of the cross-section of the output channel in one direction. The relatively promising solution variants also include the recently proposed twist channel angular pressing (TCAP) process [11,12]. The process is based on the assumption that the bend of the channel is preceded by a twist situated in the vertical part of the channel. As the first partial results documented, this method can lead to higher homogeneity, as well as higher values of the imposed strain for each pass. Numerical simulations based on the finite element method (FEM) have long been used to predict the deformation behavior of materials during plastic deformation for a long time now. A similar case also applies for SPD techniques. The large number of published results in this area confirms the applicability of this approach in various fields. Djavanroodi et al. [13] used 3D simulation to study the effects of channel angle, friction and backward pressure for the ECAP process when processing copper.
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Similarly, Kocich et al. carried out a 3D study of the ECAP process under temperature when considering Mg alloys based on Mg–Al– Zn [14]. Wang et al. used numerical analysis to evaluate geometric adjustments of the die to lower friction in the internal curving of the channel [15]. The purpose of this article is to provide a more detailed mapping of the TCAP process in the sense of ascertaining the influence of the variability of selected factors, especially the size of effective strain (ES). A more detailed description of this process with respect to the influences of geometry (die parameters, i.e., position of twist, angle of twist or angle between individual parts of channel) or deformation parameters (e.g., velocity of extrusion) has never been carried out. The subsequent experimental application of this process can then represent a partial verification of the predicted results (e.g., required pressing force).
2. Experimental The goal of the experiment was to provide a more detailed description of the TCAP technology with respect to various influences of die parameters and selected deformation parameters on the resulting temperature, ES, in-homogeneity of strain at the cross-section of the sample, or pressing force needed for extrusion. The other monitored characteristics also included material flow. The TCAP process principle is illustrated in Fig. 1a. The first part of the paper contains a numerical analysis of various variants of this process. The influence of the extrusion speed was monitored here, whereas the behavior of the material at extrusion speeds v¼3 mm/s and v¼6 mm/s were investigated. Other monitored factors included applied friction, which was
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represented in the simulation by two selected values of Coulomb friction (m ¼0.02, m ¼0.05). The discussed values of friction coefficient were chosen considering experiments carried out before, of which mutual comparison of values predicted with numerical simulations was successful with the help of measurement of punch loading. The influence of the geometry of the used die was also monitored. Specifically, this was carried out by simulating the influence of angle j (angle between individual parts of the channel), angle b (twist slope angle), and angle o (angle of the twist rotation) (Fig. 1a). The ECAP process was also analyzed to compare the efficiency of the TCAP process. The second part of the experiment was based on the practical realization of the TCAP process. This part was focused on verification of the model used in FEM. The selected material was commercially pure Cu (99.97%) with a chemical composition of 0.0074Ni, 0.0058Sn, 0.0031Fe, 0.0030Zn, 0.0023Si (in wt%). The extruded samples were defined to match the numerical simulation, i.e., they had a square 12 mm 12 mm 130 mm cross-section. The experiment itself followed the copper being annealed at 650 1C/h. To objectively evaluate the results of numerical prediction, the die used in the experiment was defined by j angle of 901, c angle (outer corner) of 201, b angle of 401, and o angle of 901. Extrusion was carried out at room temperature (25 1C) on a hydraulic press at a rate of extrusion of 3 mm/s and MoS2 was used as lubricant. During the practical experiment, the temperature of the extruded material was also monitored. This was done via two thermocouples located at a distance of 1 mm from both primary deformation areas (the twist and bend). Simultaneously, the force load of the extruder during TCAP was also monitored. These parameters were subsequently verified with the results obtained from the numerical
Fig. 1. Diagram of the TCAP process including monitoring points located on the ‘‘dividing’’ plane. 1, 2, 3—monitored places, o—angle of twist rotation, b—twist slope angle, l—distance between the end of twist part of the channel and the bend of channel, j—channel angle, c—angle associated with the arc of curvature where the two parts of the channel intersect, F—force (a) Stress–strain curves of Cu used in FEM (b).
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simulation. For these reasons, the micro-hardness was measured on the transversal cross-section of the sample after the first pass.
3. Finite element analysis The Forge 2009 commercial software was used to analyze the deformation behavior of the extruded material. The simulations were performed using a model in which the geometrical dimensions and mechanical properties of the billet in the simulation were identical to those of the experiment. This allowed for the direct comparison of simulation results with those obtained experimentally. The deformation behavior of copper after one pass was predicted. Elasto-plastic model with the Newton– Raphson convergent algorithm was utilized to determine simulation parameters. The billet was characterized by a mesh with 48,675 nodes. Mesh with tetrahedral elements was employed to model the workpiece sections. The extruder, as well as the die, was considered to be rigid parts. Due to the expectation of large shear deformations during the simulation, automatic re-meshing was activated. The stress–strain curve (Fig. 1b) valid for the experimentally used material was determined based on a torsion test made at room temperature and with two strain rates (0.01 s 1 and 0.1 s 1) on SETARAM, a servo-hydraulic torsion plastometer. These experimentally obtained data were entered into the material flow stress database of software. The Haensel–Spittel equation (Eq. (1)) was used to describe the behavior of the material during deformation.
sf ¼ Aem1 T T m9 em2 em4 =e ð1 þ eÞm5 T em7 e e_ m3 e_ m8 T
ð1Þ
where e is the equivalent strain, e_ is the equivalent strain rate, T is the temperature and A, m1, m2, m3, m4, m5, m6, m7, m8, m9 are the regression coefficients. The values of individual coefficients are
410.08 MPa, 0.00121 MPa, 0.21554 MPa, 0.01472 MPa, and 0.00935 MPa, m5–m9 are 0. The boundary conditions of the simulation were defined by a temperature of 25 1C, values describing the temperature behavior of copper, the die, and the number of passes (one pass). Young’s modulus, Poisson’s ratio, thermal expansion, thermal conductivity, heat transfer coefficient, specific heat, emissivity and density were defined as the constant of 112 (GPa), 0.3, 1.7 10 5 (K 1), 394 (W/(m K)), 100,000 (W/m2 K), 398 (J/kg K), 0.7 (kg/m3) and 8960 (kg/m3). To better specify individual monitored parameters, the extruded material included a definition and the monitoring of three specific areas (points 1–3). These points were placed on a plane parallel to the longitudinal axis of the sample passing through its center (Fig. 1a). The purpose of this part was to study the influence of die parameters on the magnitude of effective strain, in-homogeneity of strain at the cross-section of the sample or pressing force needed for extrusion.
4. Results and discussion 4.1. Friction One of the monitored factors was the influence of friction during TCAP. As was detected for the modeled TCAP process, the growing value of friction increases the resulting value of the imposed strain. These findings are in good agreement with most published results valid for the ECAP process although most published works that model the ECAP process are based on the assumption of an absence of friction and the angle j ¼901 [16,17]. For lower friction coefficients (m ¼0.02), the average value of the imposed strain is 2.3. Higher applied friction (m ¼0.05) also meant an increase of the average ES value up to 3. However, it needs to be noted that this increase was also accompanied by the
Fig. 2. 3D sections and effective strain contours in the samples after the TCAP process for different friction coefficients (a) m ¼ 0.02 (b)¼ 0.05 with the curves of homogeneity of distribution for appropriate places.
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simultaneous growth of the strain homogeneity (Fig. 2a and b). It is also possible to simultaneously see a certain difference in the deformed ends of the sample with respect to the value of the inserted deformation. While lower friction leads to the end of the sample being defined by the lowest values of the inserted deformation, higher friction reverses this trend. As subsequently specified (in Section 4.7), the reasons for this may be found in the plastic flow of the material. For all subsequently simulated variants, only friction defined by m ¼0.02 was taken into account. 4.2. Velocity of extrusion Another modeled variable factor of the TCAP process was the speed of extrusion. Extrusion speeds of 3 mm/s and 6 mm/s were analyzed. This factor has also been studied by a relatively large number of works focusing on the ECAP process. Such works document a certain influence of the size of ES on the used velocity. During TCAP, detectable partial differences were confirmed not only in ES size, but also in ES distribution homogeneity. When using a lower extrusion speed, ES distribution was more homogeneous (Figs. 2a and 4b). The growth of the non-homogeneity of the strain is in accordance with the observed significant increase of the size of the dead zone, as documented in Fig. 7a. In this case (6 mm/s), the largest size of this area was documented for a simulated j angle of 901. As follows from very recently published work [18], a higher extrusion speed of the ECAP process can negatively affect billet cohesion. Due to the very unstable material flow, in conjunction with the occurrence of significant lateral gaps behind the inner radius of channel bend, it is very probable that similar behavior may also be observed for the TCAP process. However, the very negative influence of higher extrusion speeds was documented in the temperature of the extruded billet. As the channel detail documents (Fig. 3), the maximum temperatures were always located in the area of the intersection between both channel parts, i.e., the main deformation zone (MDZ). The resulting temperature curves thus capture the time dependency of the central areas (monitored point 2). While almost all modeled TCAP variants led to a temperature increase to a level comparable with ECAP ( 35 1C), this does not apply to higher extrusion speed. At an extrusion speed of 6 mm/s, the temperature increase was up to two times higher than in other variants. The extrusion speed will thus be a significant factor and needs to be thoroughly taken into account during TCAP. One of the reasons is also adherence to the process temperature in relation to the possible unintentional exceeding of the temperature necessary for the activation of restoration processes.
Fig. 3. Distribution of temperature in extruded sample (section) during TCAP and time dependence of the temperature for individual variants.
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The result on the temperature curve for higher friction is relatively unexpected (Fig. 2). It is clear that the maximum obtained temperature of the billet is lower than in the case of higher friction. This fact is very probably related to the faster heat transfer through the die due to better contact between the billet and channel walls. When comparing this to the results published in [11], it may be stated that higher extrusion speed has a much larger impact on temperature increase than higher simulated friction for the TCAP process. It should be stressed that the temperature curve for TCAP already becomes affected in the first stages of the pass. This is documented by the presence of the first peak on all curves, which did not occur in ECAP. This initial increase is caused by the sample passing through the twist. It is thus clear that a twist located in the vertical part of the channel participates in the temperature increase much less than the subsequent bend. This applies to all modeled TCAP variants, including higher extrusion speeds. An extrusion speed of v¼3 mm/s was assumed for all subsequent simulated variants. 4.3. Distance l The effects of the distance of the twist from the bend of channel were also monitored during numerical simulation. This distance, denoted by l, was examined with the goal of finding a possible dependency between the imposed strain and the position of the extruded sample with respect to deformation zones. The first model example was based on the assumption of a minimum (i.e., minimum required) transition area between the output part of the twist and the input part of the bend (l ¼2 mm). The second case then modeled a similar situation with l¼10 mm. Although relatively similar ES values were detected in both modeled cases, both variants were not equivalent (Figs. 4a,4b). The differences were based mostly in the obtained ES homogeneity. As was found, the existence of a transition zone between the individual deformation zones caused a significant difference between the upper and lower half of the sample. Due to different material flow, the ES values differed especially in corner areas. In the case of l¼2 mm, the effective strain is distributed in the cross section more or less symmetrically (Fig. 4c). The maximum ES values are located in the area of sample edges. For the l¼10 mm variant, it is clearly visible that the strain maxima are kept only in the corner areas next to the internal curve, i.e., in the upper half of the billet (Fig. 4c). Additionally, the higher peak values of ES in the corner areas also need to be noted. The reasons for the diverging material behavior stem from the area before the channel bend. The growing distance of the twist from the bend causes the ES gradient to grow in the area behind the twist after the cross section of the extruded material. This increases the value of ES, especially in the corner areas. A similar finding is known for example from the TE process [19]. The subsequent bend during the TCAP process can further increase ES in these corner areas. In other words, a certain similarity to the ECAP process can be mentioned based on the known finding that ES maxima are located in the upper half (of corner areas). As further commented, the characteristics of similarity between the TCAP variant (l¼10 mm) and ECAP may also be found in the material’s plastic flow. The differences between both variants are also confirmed by their mutual comparison with respect to strain rate (Figs. 4d, 4e). In the case of l¼2 mm, a much wider MDZ area is apparent than in the case of a larger l. In the twist area, the MDZ is extended both into the input as well as the output part of the channel. Additionally, the average value of strain rate in the case of a longer transition zone is only half (i.e., 0.08 s 1) that of the second variant. While in the case of l¼2 mm, the corners of the sample in the twist area are characterized by a higher strain rate, in the second case this is not so due to the influence of the transition zone. These conclusions also lead to a different material flow,
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Fig. 4. Effective strain contours and appropriate strain rate contours in longitudinal and transversal section of the sample after the TCAP process for different transition regions l ¼2 mm (a, d), l ¼ 10 mm (b, e) with the curves of homogeneity of distribution in diagonal direction (c).
which can also be viewed in the different shapes of sample ends. The transition zone between the twist and bend thus leads to the relative suppression of the influence of the vortex-like flow of material. This holds especially in areas next to the external channel curve. This finding, together with the shape and size of MDZ, will thus have a different influence on the above-listed situation in the twist area for both variants. A longer transition region between the individual deformation zones leads to a more homogeneous distribution of the strain after the sample cross section. This finding corresponds very well with the study conclusions [20] in the case of the ECAP process with parallel channels. A growing distance between the individual deformation zones increases the homogeneity of the strain. Although these are not identical processes, an analogy may be drawn between both deformation zones in this respect.
with respect to ES size. There thus exists a certain analogy to the ECAP process. However, the average ES value during TCAP (j ¼1101) is 1.38, which is comparable to the ECAP process for j ¼901. The relatively lower homogeneity in the ES distribution along the extruded billet (Fig. 5) also needs to be mentioned. A growing j, similarly to the ECAP process, leads to a larger dead zone creation—this is often considered as one of the negative reasons leading to non-homogeneous strain distribution [21,22]. As subsequently discussed, this angle has led to the largest dead zone, as well as lateral gaps (Fig. 7a). On the other hand, the application of this die has led to a significant reduction of extrusion load in comparison to an angle of j ¼901 (Fig. 7b). The force requirement of this variant is comparable to the requirements for a conventional ECAP process. 4.5. Angle b
4.4. Angle j As documented by Fig. 2a, the use of a die with an angle of j ¼901 leads to a relatively homogeneous distribution of the imposed strain along the sample length. When applying a die with a larger angle (j ¼1101), it becomes clear that the value of ES at TCAP drops for higher angles. When compared to the die with an angle of 901, a significant difference appears, especially
As listed for example in [23] regarding a fundamentally similar process—twist extrusion (TE), the optimum of the twist slope angle (b) lies in the interval of up to 201. The main reason for this is especially a significant change of the geometry of the cross section of the extruded material in the case of higher angles. On the other hand, a lower b means a lower size of the imposed strain. A possible way of crossing this ‘‘limit’’ value in the case of
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Fig. 5. 3D shape and effective strain contours in the sample after the TCAP process (j ¼1101) with the histogram of homogeneity of distribution.
Fig. 6. 3D shape and effective strain contours in the sample after the TCAP process b ¼401 (a) o ¼ 1801 (b) with the time dependence of effective strain for all modeled variants (c).
TE is the use of backward pressure, which however significantly complicates realization. Additionally, not even the application of backward pressure can generally guarantee a homogeneous distribution of the deformation. On the other hand, the construction of the TCAP process allows the deformation to be applied even with a significantly higher b without the use of backward pressure. This is especially due to the subsequent bend in the channel, which ensures that the original dimensions of the extruded billet are kept intact. The friction, together with a sudden change of the material flow (channel bend) provide sufficient resistance against material flow, and thus prevent the cross section of the channel from being filled at least in the twist area. This also allows the elimination of unwanted geometry changes of the sample caused during the process with higher twist slope angles. For these reasons, the experiment analyzes a TCAP process with a twist defined by an angle of b ¼401. This means that the total height of the twist in this case was only half that of the
previously modeled variants. The minimum required transition area of l ¼2 mm was considered between the twist and bend. As confirmed by the carried out numerical simulation, the value of b significantly affects both the ES value as well as its homogeneity after the cross section of the extruded billet. It is clear that higher values of b mean a larger ES size (Fig. 6c). The majority cause of this is the lower helix slope. The positive influence of a higher b may thus be seen in a deeper penetration of the strain in the twist area in the direction of the diagonals (Fig. 6a). This is caused by a lower sloping of the helix, which forces the material into a more intense vortex-like flow. 4.6. Angle o To define the influence of the angle o during the TCAP process, the case of its size being given by a 1801 rotation around the axis was simulated. The twist slope was considered to be constant for the whole height of the twist, and defined by an angle of b ¼401.
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This kept the total height of the twist intact. Similarly to the previous case, a transition zone of l¼2 mm was also considered here. The comparison of individual modeled variants with respect to ES value (Fig. 6b) lists individual time courses monitored in their central areas (point 2). This dependency documents that for the variant of o ¼ 1801 there was a significant increase of the size of imposed strain. The average value of ES after the first pass in this case ranged in the area of 3.27. This is almost three times larger than in the classic ECAP process, and an approximate 50% increase compared to TCAP with o ¼901. However, regarding the homogeneity of the imposed strain, it may be said that this is much lower than in the previous cases. As follows from Fig. 6b, the ES distribution on the surface as well as below the surface of the sample is relatively uneven. The minimum ES values are detected at the ends of the sample. In comparison to the previous cases, it is necessary however to state that the volume of the sample defined by the ES minimum is much lower than in the previous variants. In the case of TCAP with a larger rotation angle, the minimum ES is even higher than for ECAP. As is clearly visible in Fig. 6b, the largest sizes of the ES are obtained in the case of dies with a rotation angle of o ¼1801. Additionally, it is necessary to mention the influence of angle b, where a lower twist slope leads to higher strain values. These findings thus confirm the significant role of the twist on the total imposed strain during the TCAP process. On the other hand, the effect of the distance of the twist from the channel bend seems to be less relevant than other factors with respect to the value of the imposed strain.
4.7. Plastic flow Both processes, TCAP and ECAP, were also studied with respect to plastic flow. Superimposed grids were used to evaluate material flow during plastic deformation. Grids were superimposed in parallel with the longitudinal axis of the sample to allow the assessment of individual modeled variants. To allow exact evaluation, the designed grids were defined by very small (0.5 mm 0.5 mm) square cells. These grids then allowed the monitoring of the influence of die geometry, as well as other parameters of material flow. One of the often discussed factors is the size of the dead zone. As previously mentioned, most published studies assume its negative influence on the value and homogeneity of the imposed strain [24,25]. As is clear from Fig. 7a, differences exist between individual simulated variants of TCAP. In all modeled cases of the TCAP process, there is a significant reduction of the size of the dead zone in comparison to the ECAP process. This is caused by a different method of material entry into the place of bend in the die. During TCAP, the extruded material better fills the channel volume due to the vortex-like flow than in the case of ECAP. It is clear that higher extrusion speed and higher values of j increase the size of the dead zone, similarly to the ECAP process [14,26,27]. However, the resulting size of the dead zone for TCAP in these cases is still lower than in comparable cases of ECAP. The vortex-like flow of course also affects the shape and size, specifically the shape of output ends. While in the case of the ECAP process the MDZ is located especially in the direction of the diagonal between both channel radiuses, in the case of TCAP this is significantly extended both in the output and especially the input part of the channel. Other differences include the absence of lateral gaps in the area behind the inner radius of the output part of the channel during the TCAP process. It is known that this factor negatively affects the state of stress in the extruded billet during ECAP, where unwanted tensile stress concentrates in these
Fig. 7. Plastic flow pattern for individual variants (a) dependence of punch load for individual variants (b).
areas. Such stress may then initiate the creation of cracks on the deformed sample [18,26]. After a comparison between individual modeled variants of the TCAP process, a large dependence of material flow on the extrusion speed and friction ratios between the die and billet is apparent. It is clear that higher friction coefficients lead to an almost full suppression of the dead zone. Simultaneously, it is possible to monitor a relatively steady material flow in the output part of the channel. The oscillation of horizontal lines of the superimposed grid is detected only in isolated regions, which contrasts with the situation of higher extrusion speed, where the plastic material flow is significantly unstable and very uneven after the cross section. These findings are evidently related to the known fact that the influence of friction drops with increasing speed. It is clear that the maximum speed-up of central layers of the material during TCAP occurs in the case of the use of a die with o ¼ 1801. This is confirmed especially by the significantly deformed vertical lines. In the case of a higher angle b, a similar trend as in the case of higher friction coefficients may be observed. 4.8. Punch load Punch load is an important factor due to the verification of simulated results, as well as with respect to the assessment of parameters such as friction coefficient. All the modeled variants
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were thus also evaluated with respect to their force requirements. The individual analyzed variants were processed in the form of time courses. As documented by Fig. 7b, the load on punch is relatively higher during TCAP than during the classic ECAP process. The difference between both technologies is, however, not large. It may be said that in the case of using a die with a twist angle of j ¼1101, the force requirements for punch in the case of TCAP are comparable to ECAP applied using a die at an angle of j ¼901. The above-listed dependence clearly documents that friction has a much larger impact on punch load than the geometry of the vertical part of the channel. The dependency demonstrates that during increased friction, the load of the punch increases to twice the values obtained in other variants. It is also necessary to take into account the factor of very large pressure oscillation during the above-mentioned higher friction coefficient. Such a serrated curve is very frequently linked to the instability of plastic flow of the deformed material during the process [18,26]. However, in the case of TCAP, these may be detected mostly in the areas next to the upper surface of the output part of the channel. In the case of a larger angle o in the vertical part of the channel, the pressure increases only by 26%. This leads to the possibility of increasing the value of the imposed strain during the given pass without the potential risk of destroying the tools. The predicted values of pressure of the punch were subsequently verified by an experiment carried out using a die with an angle of j ¼ 901. Differences in the course of the predicted and experimentally tested curve (Fig. 7b) may be caused by several factors. These include for example the accuracy of sensors, friction variability, material properties, simplifications, or the used mathematical model. The results of the comparison however imply that the experimentally obtained data correlated relatively well with the dependence on pressure predicted for friction defined by a coefficient of 0.02. 4.9. Micro-hardness After the pass, the micro-hardness after sample cross section was measured. To obtain a more exact evaluation, the values of both diagonals were determined (Fig. 8a). As is clear from the attached graphical dependency, the highest values were not located in the corner areas of the sample. However, it is necessary to mention that there was only a small difference between the maximum and minimum measured hardness (in comparison with central areas). On the other hand, it needs to be said that the external measured indentations were located very close to the ends of the sample diagonals, hence the high possibility of influencing, the measured values. Despite this fact, only soft drops of hardness were detected. It means a relatively good correlation between the micro-hardness with the predicted ES distribution in the extruded sample. One pass increased microhardness to an average value of 108 HV, which represents an increase of 80% against the undeformed state. On the basis of achieved results, the TCAP process defined with lower extrusion rate applied in the die, where the distance between twist and bending is longer, can be considered to be optimal from the achieved strain homogeneity point of view. Those factors coupled with assumption of low friction coefficient appear to be suitable conditions for high homogeneity of imposed strain achievement. Rotation of twist angle (o) is of the largest influence on strain values, then the channel bend angle (j) and the twist slope angle (b). It has been proved, that the extrusion rate must be chosen very carefully (increasing value of the rate influences greatly growth of the dead zone and, above all, the deformed material temperature). Similar influence on dead zone size has higher channel bend angle.
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Fig. 8. Micro-hardness of processed copper: measured places (a) obtained dependence (b).
5. Conclusions The work contains a numerical simulation of the TCAP process, whereas various variants of die geometry and deformation parameters were modeled. The article focuses especially on determining the efficiency of the process in relation to the size of the imposed strain. The subsequent experiment was then aimed at verifying the predicted results. The main results may be defined as follows: Maximum values of the effective strain occurred for higher rotation angles. The average ES size in this case reached 3.27. The construction of TCAP allows the use of higher angles b to obtain higher values of the imposed strain without an undesired change of the cross section of the extruded billet than in several other processes utilizing twist. Higher twist slope angle and lower angle between the individual channel parts stand for the higher value of imposed strain. It is recommended to use dies with angle of twist rotation up to 901 because larger angle signifies larger values of imposed strain but also higher strain inhomogeneity within the crosssection. The punch load during TCAP with respect to the value of imposed strain is comparable to the punch load during ECAP. As the one of necessary presumptions is good lubrication of samples (friction coefficient minimization). Higher friction coefficient causes significant increasing of punch load as well as. The distance between the twist and bend of the channel does not significantly affect the value of the imposed strain, but relatively significantly affects its distribution. The size of the dead zone during TCAP is significantly lower than during conventional ECAP. This finding is also related to
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the resulting homogeneity of the ES for both types of processes. The experimentally obtained micro-hardness after the cross section of the deformed sample correlated relatively well with the predicted values of the imposed strain.
Acknowledgements This paper was created in the project no. CZ.1.05/2.1.00/ 01.0040 ‘‘Regional Materials Science and Technology Centre’’ within the frame of the operation program ‘‘Research and Development for Innovations’’, financed by the Structural Funds and from the state budget of the Czech Republic.
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