Materials Science & Engineering A 563 (2013) 86–94

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Materials Science & Engineering A

0921-50

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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 Kuncicka a, Milan Mihola c, Katerina Skotnicova b

a Department of Material Forming, Faculty of Metallurgy and Materials Engineering, VSB TU Ostrava 17.listopadu 15, Ostrava-Poruba 70833, Czech Republicb Regional Materials Science and Technology Centre, VSB TU Ostrava 17. listopadu 15, Ostrava-Poruba 70833, Czech Republicc Department of Robotics, Faculty of Mechanical Engineering, VSB TU Ostrava 17. listopadu 15, Ostrava-Poruba 70833, Czech Republic

a r t i c l e i n f o

Article history:

Received 23 August 2012

Received in revised form

10 November 2012

Accepted 15 November 2012Available online 21 November 2012

Keywords:

Finite element method

Bulk deformation

TCAP

Effective strain

93/$ - see front matter & 2012 Elsevier B.V. A

x.doi.org/10.1016/j.msea.2012.11.047

esponding author at: Department of Materia

d Materials Engineering, VSB TU Ostrava 17.

Czech Republic. Tel.: þ420 59694455; fax: þ

ail addresses: r.kocich@seznam.cz, radim.koci

a b s t r a c t

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.

1. Introduction

Among the methods based on the application of severe plasticdeformations (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 propertiescharacterizing an ECAP process are the possibility of relativelykeeping the original shape of the sample, as well as simple shear,as the main deformation mechanism at the point of intersectionbetween both channel parts [2]. This process is currently undercommercialization efforts. The goal is the possibility of thecontinuous processing of long products. Concrete results includedissimilar 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 stablemicrostructures, it is generally necessary to perform a largenumber of passes. Increasing process efficiency, in the sense ofimposing larger strain during individual passes to reduce thenumber of passes, is thus one of the desired goals. The firstsolution variants was the application of a rotary die that allowed

ll rights reserved.

l Forming, Faculty of Metal-

listopadu 15, Ostrava-Poruba

420 596994414.

ch@vsb.cz (R. Kocich).

multiple extrusions without removing the sample from the die[6,7], or the use of ECAP with parallel channels [8]. Certain resultscan be seen, for example, in the manner of proposing moreefficient 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 ofpasses. Another method is based on non-equal channel angularpressing (NECAP) technology, where protrusion occurs through adie with differing channels [10]. This method can lead to anincrease of shear deformation by 25%, at a 50% reduction of thecross-section of the output channel in one direction. The rela-tively promising solution variants also include the recentlyproposed twist channel angular pressing (TCAP) process [11,12].The process is based on the assumption that the bend of thechannel is preceded by a twist situated in the vertical part of thechannel. As the first partial results documented, this method canlead to higher homogeneity, as well as higher values of theimposed strain for each pass.

Numerical simulations based on the finite element method(FEM) have long been used to predict the deformation behavior ofmaterials during plastic deformation for a long time now.A similar case also applies for SPD techniques. The large numberof published results in this area confirms the applicability of thisapproach in various fields. Djavanroodi et al. [13] used 3Dsimulation to study the effects of channel angle, friction andbackward pressure for the ECAP process when processing copper.

R. Kocich et al. / Materials Science & Engineering A 563 (2013) 86–94 87

Similarly, Kocich et al. carried out a 3D study of the ECAP processunder temperature when considering Mg alloys based on Mg–Al–Zn [14]. Wang et al. used numerical analysis to evaluate geo-metric adjustments of the die to lower friction in the internalcurving of the channel [15].

The purpose of this article is to provide a more detailed mappingof the TCAP process in the sense of ascertaining the influence of thevariability of selected factors, especially the size of effective strain(ES). A more detailed description of this process with respect to theinfluences of geometry (die parameters, i.e., position of twist, angleof twist or angle between individual parts of channel) or deforma-tion parameters (e.g., velocity of extrusion) has never been carriedout. The subsequent experimental application of this process canthen 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 detaileddescription of the TCAP technology with respect to various influ-ences of die parameters and selected deformation parameters onthe resulting temperature, ES, in-homogeneity of strain at thecross-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 ofvarious variants of this process. The influence of the extrusionspeed was monitored here, whereas the behavior of the material atextrusion speeds v¼3 mm/s and v¼6 mm/s were investigated.Other monitored factors included applied friction, which was

Fig. 1. Diagram of the TCAP process including monitoring points located on the ‘‘divid

angle, l—distance between the end of twist part of the channel and the bend of channe

parts of the channel intersect, F—force (a) Stress–strain curves of Cu used in FEM (b).

represented in the simulation by two selected values of Coulombfriction (m¼0.02, m¼0.05). The discussed values of friction coeffi-cient were chosen considering experiments carried out before, ofwhich mutual comparison of values predicted with numericalsimulations was successful with the help of measurement of punchloading. The influence of the geometry of the used die was alsomonitored. Specifically, this was carried out by simulatingthe influence of angle j (angle between individual parts of thechannel), angle b (twist slope angle), and angle o (angle ofthe twist rotation) (Fig. 1a). The ECAP process was also analyzedto compare the efficiency of the TCAP process.

The second part of the experiment was based on the practicalrealization of the TCAP process. This part was focused onverification of the model used in FEM. The selected materialwas commercially pure Cu (99.97%) with a chemical compositionof 0.0074Ni, 0.0058Sn, 0.0031Fe, 0.0030Zn, 0.0023Si (in wt%).The extruded samples were defined to match the numericalsimulation, i.e., they had a square 12 mm�12 mm�130 mmcross-section. The experiment itself followed the copper beingannealed at 650 1C/h. To objectively evaluate the results ofnumerical prediction, the die used in the experiment was definedby j angle of 901, c angle (outer corner) of 201, b angle of 401, ando 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 andMoS2 was used as lubricant.

During the practical experiment, the temperature of the extrudedmaterial was also monitored. This was done via two thermocoupleslocated at a distance of 1 mm from both primary deformation areas(the twist and bend). Simultaneously, the force load of the extruderduring TCAP was also monitored. These parameters were subse-quently verified with the results obtained from the numerical

ing’’ plane. 1, 2, 3—monitored places, o—angle of twist rotation, b—twist slope

l, j—channel angle, c—angle associated with the arc of curvature where the two

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simulation. For these reasons, the micro-hardness was measured onthe transversal cross-section of the sample after the first pass.

3. Finite element analysis

The Forge 2009 commercial software was used to analyze thedeformation behavior of the extruded material. The simulationswere performed using a model in which the geometrical dimen-sions and mechanical properties of the billet in the simulationwere identical to those of the experiment. This allowed for thedirect comparison of simulation results with those obtainedexperimentally. The deformation behavior of copper after onepass was predicted. Elasto-plastic model with the Newton–Raphson convergent algorithm was utilized to determine simula-tion parameters. The billet was characterized by a mesh with48,675 nodes. Mesh with tetrahedral elements was employed tomodel the workpiece sections. The extruder, as well as the die,was considered to be rigid parts. Due to the expectation of largeshear deformations during the simulation, automatic re-meshingwas activated. The stress–strain curve (Fig. 1b) valid for theexperimentally used material was determined based on a torsiontest made at room temperature and with two strain rates(0.01 s�1 and 0.1 s�1) on SETARAM, a servo-hydraulic torsionplastometer.

These experimentally obtained data were entered into thematerial flow stress database of software. The Haensel–Spittelequation (Eq. (1)) was used to describe the behavior of thematerial during deformation.

sf ¼ Aem1T Tm9em2 em4=e 1þeð Þm5T em7e _em3 _em8T

ð1Þ

where e is the equivalent strain, _e is the equivalent strain rate, T isthe temperature and A, m1, m2, m3, m4, m5, m6, m7, m8, m9 are theregression coefficients. The values of individual coefficients are

Fig. 2. 3D sections and effective strain contours in the samples after the TCAP pro

homogeneity of distribution for appropriate places.

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 atemperature of 25 1C, values describing the temperature behaviorof copper, the die, and the number of passes (one pass). Young’smodulus, Poisson’s ratio, thermal expansion, thermal conductiv-ity, heat transfer coefficient, specific heat, emissivity and densitywere 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) and8960 (kg/m3).

To better specify individual monitored parameters, theextruded material included a definition and the monitoring ofthree specific areas (points 1–3). These points were placed on aplane parallel to the longitudinal axis of the sample passingthrough its center (Fig. 1a). The purpose of this part was to studythe influence of die parameters on the magnitude of effectivestrain, in-homogeneity of strain at the cross-section of the sampleor pressing force needed for extrusion.

4. Results and discussion

4.1. Friction

One of the monitored factors was the influence of frictionduring TCAP. As was detected for the modeled TCAP process, thegrowing value of friction increases the resulting value of theimposed strain. These findings are in good agreement with mostpublished results valid for the ECAP process although mostpublished works that model the ECAP process are based on theassumption of an absence of friction and the angle j¼901 [16,17].For lower friction coefficients (m¼0.02), the average value of theimposed strain is �2.3. Higher applied friction (m¼0.05) alsomeant an increase of the average ES value up to �3. However, itneeds to be noted that this increase was also accompanied by the

cess for different friction coefficients (a) m¼0.02 (b)¼0.05 with the curves of

R. Kocich et al. / Materials Science & Engineering A 563 (2013) 86–94 89

simultaneous growth of the strain homogeneity (Fig. 2a and b).It is also possible to simultaneously see a certain difference inthe deformed ends of the sample with respect to the value of theinserted deformation. While lower friction leads to the end ofthe sample being defined by the lowest values of the inserteddeformation, higher friction reverses this trend. As subsequentlyspecified (in Section 4.7), the reasons for this may be found in theplastic flow of the material.

For all subsequently simulated variants, only friction definedby m¼0.02 was taken into account.

4.2. Velocity of extrusion

Another modeled variable factor of the TCAP process was thespeed of extrusion. Extrusion speeds of 3 mm/s and 6 mm/s wereanalyzed. This factor has also been studied by a relatively largenumber of works focusing on the ECAP process. Such worksdocument a certain influence of the size of ES on the used velocity.During TCAP, detectable partial differences were confirmed not onlyin ES size, but also in ES distribution homogeneity. When using alower extrusion speed, ES distribution was more homogeneous(Figs. 2a and 4b). The growth of the non-homogeneity of the strainis in accordance with the observed significant increase of the size ofthe dead zone, as documented in Fig. 7a. In this case (6 mm/s), thelargest size of this area was documented for a simulated j angle of901. As follows from very recently published work [18], a higherextrusion speed of the ECAP process can negatively affect billetcohesion. Due to the very unstable material flow, in conjunctionwith the occurrence of significant lateral gaps behind the innerradius of channel bend, it is very probable that similar behavior mayalso be observed for the TCAP process.

However, the very negative influence of higher extrusion speedswas documented in the temperature of the extruded billet. As thechannel detail documents (Fig. 3), the maximum temperatureswere always located in the area of the intersection between bothchannel parts, i.e., the main deformation zone (MDZ). The resultingtemperature curves thus capture the time dependency of thecentral areas (monitored point 2). While almost all modeled TCAPvariants led to a temperature increase to a level comparable withECAP (�35 1C), this does not apply to higher extrusion speed. At anextrusion speed of 6 mm/s, the temperature increase was up totwo times higher than in other variants. The extrusion speed willthus be a significant factor and needs to be thoroughly taken intoaccount during TCAP. One of the reasons is also adherence to theprocess temperature in relation to the possible unintentionalexceeding of the temperature necessary for the activation ofrestoration processes.

Fig. 3. Distribution of temperature in extruded sample (section) during TCAP and

time dependence of the temperature for individual variants.

The result on the temperature curve for higher friction is relativelyunexpected (Fig. 2). It is clear that the maximum obtained tempera-ture of the billet is lower than in the case of higher friction. This fact isvery probably related to the faster heat transfer through the die dueto better contact between the billet and channel walls. Whencomparing this to the results published in [11], it may be stated thathigher extrusion speed has a much larger impact on temperatureincrease than higher simulated friction for the TCAP process.

It should be stressed that the temperature curve for TCAP alreadybecomes affected in the first stages of the pass. This is documentedby the presence of the first peak on all curves, which did not occur inECAP. This initial increase is caused by the sample passing throughthe twist. It is thus clear that a twist located in the vertical part ofthe channel participates in the temperature increase much less thanthe subsequent bend. This applies to all modeled TCAP variants,including higher extrusion speeds. An extrusion speed of v¼3 mm/swas assumed for all subsequent simulated variants.

4.3. Distance l

The effects of the distance of the twist from the bend ofchannel were also monitored during numerical simulation. Thisdistance, denoted by l, was examined with the goal of finding apossible dependency between the imposed strain and the positionof the extruded sample with respect to deformation zones. Thefirst model example was based on the assumption of a minimum(i.e., minimum required) transition area between the output partof the twist and the input part of the bend (l¼2 mm). The secondcase then modeled a similar situation with l¼10 mm.

Although relatively similar ES values were detected in bothmodeled cases, both variants were not equivalent (Figs. 4a,4b). Thedifferences were based mostly in the obtained ES homogeneity.As was found, the existence of a transition zone between theindividual deformation zones caused a significant difference betweenthe upper and lower half of the sample. Due to different materialflow, the ES values differed especially in corner areas. In the case ofl¼2 mm, the effective strain is distributed in the cross section moreor less symmetrically (Fig. 4c). The maximum ES values are located inthe area of sample edges. For the l¼10 mm variant, it is clearly visiblethat the strain maxima are kept only in the corner areas next to theinternal 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 thearea before the channel bend. The growing distance of the twistfrom the bend causes the ES gradient to grow in the area behindthe twist after the cross section of the extruded material. Thisincreases the value of ES, especially in the corner areas. A similarfinding is known for example from the TE process [19]. Thesubsequent bend during the TCAP process can further increase ESin these corner areas. In other words, a certain similarity to theECAP process can be mentioned based on the known finding thatES maxima are located in the upper half (of corner areas). Asfurther commented, the characteristics of similarity between theTCAP variant (l¼10 mm) and ECAP may also be found in thematerial’s plastic flow.

The differences between both variants are also confirmed bytheir mutual comparison with respect to strain rate (Figs. 4d, 4e).In the case of l¼2 mm, a much wider MDZ area is apparent than inthe case of a larger l. In the twist area, the MDZ is extended bothinto the input as well as the output part of the channel. Addition-ally, the average value of strain rate in the case of a longertransition zone is only half (i.e., �0.08 s�1) that of the secondvariant. While in the case of l¼2 mm, the corners of the sample inthe twist area are characterized by a higher strain rate, in thesecond case this is not so due to the influence of the transitionzone. These conclusions also lead to a different material flow,

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 l¼2 mm (a, d), l¼10 mm (b, e) with the curves of homogeneity of distribution in diagonal direction (c).

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which can also be viewed in the different shapes of sample ends.The transition zone between the twist and bend thus leads to therelative suppression of the influence of the vortex-like flow ofmaterial. This holds especially in areas next to the external channelcurve. This finding, together with the shape and size of MDZ, willthus have a different influence on the above-listed situation in thetwist area for both variants.

A longer transition region between the individual deformationzones leads to a more homogeneous distribution of the strainafter the sample cross section. This finding corresponds very wellwith the study conclusions [20] in the case of the ECAP processwith parallel channels. A growing distance between the individualdeformation zones increases the homogeneity of the strain.Although these are not identical processes, an analogy may bedrawn between both deformation zones in this respect.

4.4. Angle j

As documented by Fig. 2a, the use of a die with an angle ofj¼901 leads to a relatively homogeneous distribution of theimposed strain along the sample length. When applying a diewith a larger angle (j¼1101), it becomes clear that the value ofES at TCAP drops for higher angles. When compared to the diewith an angle of 901, a significant difference appears, especially

with respect to ES size. There thus exists a certain analogy to theECAP process. However, the average ES value during TCAP(j¼1101) is �1.38, which is comparable to the ECAP processfor j¼901. The relatively lower homogeneity in the ES distribu-tion along the extruded billet (Fig. 5) also needs to be mentioned.A growing j, similarly to the ECAP process, leads to a larger deadzone creation—this is often considered as one of the negativereasons leading to non-homogeneous strain distribution [21,22].As subsequently discussed, this angle has led to the largest deadzone, as well as lateral gaps (Fig. 7a). On the other hand, theapplication of this die has led to a significant reduction ofextrusion load in comparison to an angle of j¼901 (Fig. 7b).The force requirement of this variant is comparable to therequirements for a conventional ECAP process.

4.5. Angle b

As listed for example in [23] regarding a fundamentally similarprocess—twist extrusion (TE), the optimum of the twist slopeangle (b) lies in the interval of up to 201. The main reason for thisis especially a significant change of the geometry of the crosssection of the extruded material in the case of higher angles. Onthe other hand, a lower b means a lower size of the imposedstrain. A possible way of crossing this ‘‘limit’’ value in the case of

Fig. 5. 3D shape and effective strain contours in the sample after the TCAP process (j¼1101) with the histogram of homogeneity of distribution.

Fig. 6. 3D shape and effective strain contours in the sample after the TCAP process b¼401 (a) o¼1801 (b) with the time dependence of effective strain for all modeled

variants (c).

R. Kocich et al. / Materials Science & Engineering A 563 (2013) 86–94 91

TE is the use of backward pressure, which however significantlycomplicates realization. Additionally, not even the application ofbackward pressure can generally guarantee a homogeneous dis-tribution of the deformation. On the other hand, the constructionof the TCAP process allows the deformation to be applied evenwith a significantly higher b without the use of backwardpressure. This is especially due to the subsequent bend in thechannel, which ensures that the original dimensions of theextruded billet are kept intact. The friction, together with asudden change of the material flow (channel bend) providesufficient resistance against material flow, and thus prevent thecross section of the channel from being filled at least in the twistarea. This also allows the elimination of unwanted geometrychanges of the sample caused during the process with highertwist slope angles.

For these reasons, the experiment analyzes a TCAP processwith a twist defined by an angle of b¼401. This means that thetotal height of the twist in this case was only half that of the

previously modeled variants. The minimum required transitionarea of l¼2 mm was considered between the twist and bend.

As confirmed by the carried out numerical simulation, thevalue of b significantly affects both the ES value as well as itshomogeneity after the cross section of the extruded billet. It isclear that higher values of b mean a larger ES size (Fig. 6c). Themajority cause of this is the lower helix slope. The positiveinfluence of a higher b may thus be seen in a deeper penetrationof the strain in the twist area in the direction of the diagonals(Fig. 6a). This is caused by a lower sloping of the helix, whichforces 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 theaxis was simulated. The twist slope was considered to be constantfor the whole height of the twist, and defined by an angle of b¼401.

R. Kocich et al. / Materials Science & Engineering A 563 (2013) 86–9492

This kept the total height of the twist intact. Similarly to theprevious case, a transition zone of l¼2 mm was alsoconsidered here.

The comparison of individual modeled variants with respect toES value (Fig. 6b) lists individual time courses monitored in theircentral areas (point 2). This dependency documents that for thevariant of o¼1801 there was a significant increase of the size ofimposed strain. The average value of ES after the first pass in thiscase ranged in the area of �3.27. This is almost three times largerthan in the classic ECAP process, and an approximate 50% increasecompared to TCAP with o¼901. However, regarding the homo-geneity of the imposed strain, it may be said that this is muchlower than in the previous cases. As follows from Fig. 6b, the ESdistribution on the surface as well as below the surface of thesample is relatively uneven. The minimum ES values are detectedat the ends of the sample. In comparison to the previous cases,it is necessary however to state that the volume of the sampledefined by the ES minimum is much lower than in the previousvariants. In the case of TCAP with a larger rotation angle, theminimum ES is even higher than for ECAP.

As is clearly visible in Fig. 6b, the largest sizes of the ES areobtained in the case of dies with a rotation angle of o¼1801.Additionally, it is necessary to mention the influence of angle b,where a lower twist slope leads to higher strain values. Thesefindings thus confirm the significant role of the twist on the totalimposed strain during the TCAP process. On the other hand, theeffect of the distance of the twist from the channel bend seems tobe less relevant than other factors with respect to the value of theimposed strain.

Fig. 7. Plastic flow pattern for individual variants (a) dependence of punch load

for individual variants (b).

4.7. Plastic flow

Both processes, TCAP and ECAP, were also studied with respectto plastic flow. Superimposed grids were used to evaluatematerial flow during plastic deformation. Grids were superim-posed in parallel with the longitudinal axis of the sample to allowthe assessment of individual modeled variants. To allow exactevaluation, the designed grids were defined by very small(0.5 mm �0.5 mm) square cells. These grids then allowed themonitoring of the influence of die geometry, as well as otherparameters of material flow.

One of the often discussed factors is the size of the dead zone.As previously mentioned, most published studies assume itsnegative influence on the value and homogeneity of the imposedstrain [24,25]. As is clear from Fig. 7a, differences exist betweenindividual simulated variants of TCAP. In all modeled cases of theTCAP process, there is a significant reduction of the size of thedead zone in comparison to the ECAP process. This is caused by adifferent method of material entry into the place of bend in thedie. During TCAP, the extruded material better fills the channelvolume due to the vortex-like flow than in the case of ECAP. It isclear that higher extrusion speed and higher values of j increasethe size of the dead zone, similarly to the ECAP process [14,26,27].However, the resulting size of the dead zone for TCAP in thesecases 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 theECAP process the MDZ is located especially in the direction of thediagonal between both channel radiuses, in the case of TCAP thisis significantly extended both in the output and especially theinput part of the channel. Other differences include the absence oflateral gaps in the area behind the inner radius of the output partof the channel during the TCAP process. It is known that thisfactor negatively affects the state of stress in the extruded billetduring ECAP, where unwanted tensile stress concentrates in these

areas. Such stress may then initiate the creation of cracks on thedeformed sample [18,26].

After a comparison between individual modeled variants of theTCAP process, a large dependence of material flow on the extrusionspeed and friction ratios between the die and billet is apparent. It isclear that higher friction coefficients lead to an almost full suppres-sion of the dead zone. Simultaneously, it is possible to monitor arelatively steady material flow in the output part of the channel.The oscillation of horizontal lines of the superimposed grid isdetected only in isolated regions, which contrasts with the situationof higher extrusion speed, where the plastic material flow issignificantly unstable and very uneven after the cross section. Thesefindings are evidently related to the known fact that the influence offriction drops with increasing speed.

It is clear that the maximum speed-up of central layers of thematerial during TCAP occurs in the case of the use of a die witho¼1801. This is confirmed especially by the significantlydeformed vertical lines. In the case of a higher angle b, a similartrend 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 ofsimulated results, as well as with respect to the assessment ofparameters such as friction coefficient. All the modeled variants

Fig. 8. Micro-hardness of processed copper: measured places (a) obtained

dependence (b).

R. Kocich et al. / Materials Science & Engineering A 563 (2013) 86–94 93

were thus also evaluated with respect to their force requirements.The individual analyzed variants were processed in the form oftime courses. As documented by Fig. 7b, the load on punch isrelatively higher during TCAP than during the classic ECAPprocess. The difference between both technologies is, however,not large. It may be said that in the case of using a die with a twistangle of j¼1101, the force requirements for punch in the case ofTCAP are comparable to ECAP applied using a die at an angle ofj¼901.

The above-listed dependence clearly documents that frictionhas a much larger impact on punch load than the geometry of thevertical part of the channel. The dependency demonstrates thatduring increased friction, the load of the punch increases to twicethe values obtained in other variants. It is also necessary to takeinto account the factor of very large pressure oscillation duringthe above-mentioned higher friction coefficient. Such a serratedcurve is very frequently linked to the instability of plastic flow ofthe deformed material during the process [18,26]. However, inthe case of TCAP, these may be detected mostly in the areas nextto the upper surface of the output part of the channel. In the caseof a larger angle o in the vertical part of the channel, the pressureincreases only by 26%. This leads to the possibility of increasingthe value of the imposed strain during the given pass without thepotential risk of destroying the tools.

The predicted values of pressure of the punch were subse-quently verified by an experiment carried out using a die with anangle of j¼901. Differences in the course of the predicted andexperimentally tested curve (Fig. 7b) may be caused by severalfactors. These include for example the accuracy of sensors, frictionvariability, material properties, simplifications, or the used math-ematical model. The results of the comparison however implythat the experimentally obtained data correlated relatively wellwith the dependence on pressure predicted for friction defined bya coefficient of 0.02.

4.9. Micro-hardness

After the pass, the micro-hardness after sample cross sectionwas measured. To obtain a more exact evaluation, the values ofboth diagonals were determined (Fig. 8a). As is clear from theattached graphical dependency, the highest values were notlocated in the corner areas of the sample. However, it is necessaryto mention that there was only a small difference between themaximum and minimum measured hardness (in comparison withcentral areas). On the other hand, it needs to be said that theexternal measured indentations were located very close to theends of the sample diagonals, hence the high possibility ofinfluencing, the measured values. Despite this fact, only softdrops of hardness were detected. It means a relatively goodcorrelation between the micro-hardness with the predicted ESdistribution in the extruded sample. One pass increased micro-hardness to an average value of 108 HV, which represents anincrease of 80% against the undeformed state.

On the basis of achieved results, the TCAP process defined withlower extrusion rate applied in the die, where the distancebetween twist and bending is longer, can be considered to beoptimal from the achieved strain homogeneity point of view.Those factors coupled with assumption of low friction coefficientappear to be suitable conditions for high homogeneity of imposedstrain achievement. Rotation of twist angle (o) is of the largestinfluence on strain values, then the channel bend angle (j) andthe twist slope angle (b). It has been proved, that the extrusionrate must be chosen very carefully (increasing value of the rateinfluences greatly growth of the dead zone and, above all, thedeformed material temperature). Similar influence on dead zonesize has higher channel bend angle.

5. Conclusions

The work contains a numerical simulation of the TCAP process,whereas various variants of die geometry and deformation para-meters were modeled. The article focuses especially on determin-ing the efficiency of the process in relation to the size of theimposed strain. The subsequent experiment was then aimed atverifying the predicted results. The main results may be definedas follows:

�

Maximum values of the effective strain occurred for higherrotation angles. The average ES size in this case reached �3.27.

�

The construction of TCAP allows the use of higher angles b toobtain higher values of the imposed strain without an unde-sired change of the cross section of the extruded billet than inseveral other processes utilizing twist. Higher twist slopeangle and lower angle between the individual channel partsstand for the higher value of imposed strain.

�

It is recommended to use dies with angle of twist rotation upto 901 because larger angle signifies larger values of imposedstrain but also higher strain inhomogeneity within the cross-section.

�

The punch load during TCAP with respect to the value ofimposed strain is comparable to the punch load during ECAP.As the one of necessary presumptions is good lubrication ofsamples (friction coefficient minimization). Higher frictioncoefficient causes significant increasing of punch load aswell as.

�

The distance between the twist and bend of the channel doesnot significantly affect the value of the imposed strain, butrelatively significantly affects its distribution.

�

The size of the dead zone during TCAP is significantly lowerthan during conventional ECAP. This finding is also related to

R. Kocich et al. / Materials Science & Engineering A 563 (2013) 86–9494

the resulting homogeneity of the ES for both types ofprocesses.

�

The experimentally obtained micro-hardness after the crosssection of the deformed sample correlated relatively well withthe 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 Devel-opment for Innovations’’, financed by the Structural Funds andfrom the state budget of the Czech Republic.

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