Influences of Different Die Bearing Geometries on the Wire-Drawing Process

metals

Article Inﬂuences of Diﬀerent Die Bearing Geometries on the Wire-Drawing Process

Gustavo Aristides Santana Martinez 1,*, Eduardo Ferro dos Santos 1 , Leonardo Kyo Kabayama 2 , Erick Siqueira Guidi 3 and Fernando de Azevedo Silva 3

1 Engineering School of Lorena, University of São Paulo-USP, Lorena 12602-810, Brazil; [email protected] 2 Institute of Mechanical Engineering, Federal University of Itajubá-UNIFEI, Itajubá 37500-903, Brazil; [email protected] 3 Guaratinguetá School of Engineering, Campus de Guaratinguetá,São Paulo State University-UNESP, 12516-410 Guaratinguetá, Brazil; [email protected] (E.S.G.); [email protected] (F.d.A.S.) * Correspondence: [email protected]; Tel.: +55-12-3159-5337

Received: 2 September 2019; Accepted: 8 October 2019; Published: 10 October 2019

Abstract: Metalworking is an essential process for the manufacture of machinery and equipment components. The design of the die geometry is an essential aspect of metalworking, and directly affects the resultant product’s quality and cost. As a matter of fact, a comprehensive understanding of the die bearing geometry plays a vital role in the die design process. For the specific case of wire drawing, however, few efforts have been dedicated to the study of the geometry of the bearing zone. In this regard, the present paper involves an attempt to investigate the effects of different geometries of the die bearing. For different forms of reduction as well as bearing zones, measurements are carried out for the wire-drawing process. Subsequently, by extracting the friction coefficients from the electrolytic tough pitch copper wire in cold-drawn essays, the numerical simulations are also implemented. We present the results on both the superficial and center radial tensions obtained by finite element methods. It is observed that the reduction of the friction coefficient leads to an increase in radial stress, while for a given friction coefficient, the substitution of the C-type die by the R-type one results in a decrease in the superficial radial stress of up to 93.27%, but an increase at the center of the material. Moreover, the die angle is found to play a less significant role in the resultant center radial stress, but it significantly affects the superficial radial stress. Lastly, R-type dies result in smaller superficial radial stress, with a change of up to 34.48%, but a slightly larger center radial stress up to 6.55% for different die angles. The implications of the present findings are discussed.

Keywords: wire drawing; ﬁnite element method; drawing die; die geometry; radial stress; friction

1. Introduction The influence of die drawing in the metalworking processes has attracted much attention. A vital feature of the process is that the resulting stress is applied indirectly by an external source, as in the cases of extrusion [1,2] and wire drawing [3]. Previous studies on wire drawing have reported the improvement of the drawing quality by selecting the appropriate die geometry (Figure1). The influence of the reduction zone as well as the bearing zone is known to significantly affect the drawing force, spatial profile of the radial stress, residual stress behavior, and properties of the resultant wire [4–12].

Metals 2019, 9, 1089; doi:10.3390/met9101089 www.mdpi.com/journal/metals Metals 2019, 9, x FOR PEER REVIEW 2 of 10

Metalsit has2019 been, 9, demonstrated 1089 in [18,19] that the radial stress due to specific die bearing contour geometry2 of 10 has a significant impact on the degree of residual stress.

FigureFigure 1. Schematic 1. Schematic illustration illustration of the of internal the internal longitudinal longitudinal section section structure structure of the of wire the wire die. die.

VariationsA reduction in zone radial determines stress aff ectthe theprimary mechanical deformation properties, during and the plastic subsequently, metal forming the quality process of, theindicated drawn by product, the ∆ parameter which might defined lead in toEq disqualification.uations (1–2). To be Such more defects specific, include it gives shape the relation distortion,ship crackbetween propagation, the geometrical inferior measures surface and finish the semi quality, die angle and β, reduced which consequently dimensional affects accuracy the drawing [13–17]. Forforce instance, and friction it has [20 been–22]. demonstrated in [18,19] that the radial stress due to specific die bearing contour geometry has a significant impact on the degree of residual stress. β 2 A reduction zone determines the primaryΔ = deformation[1 + √1 − r during] the plastic metal forming process,(1) r a indicated by the ∆ parameter defined in Equationsa (1) and (2). To be more specific, it gives the Af relationship between the geometrical measuresra = 1 and− the, semi die angle β, which consequently affects(2) Ai the drawing force and friction [20–22]. where ra is the reduction in area and β is the semi-angle of the die in radians. In [7], Kraft et al. reported the process ofβ hdrawingp a commerciali2 electrolytic tough pitch copper ∆ = 1 + 1 ra (1) (Cu-ETP) wire in an annealed condition at lowra speed with− a drawing block. The authors showed that different die angles result in significant differences in the parameter ∆, strain rate, and total Af deformation strain (due to redundant strain).ra Atkins= 1 [22,] observed that the deformations in the cases (2) − Ai ∆  1 can be better explained by the redundant work factor (Φ). The factor Φ is defined by the ratio of β wherethe total ra isdeformation the reduction work in areato that and due isto thedimension semi-angle change. of the In die other in radians.words, it carries the information on theIn [additional7], Kraft et plastic al. reported deformation the process besides of drawingthose owing a commercial to the cross electrolytic-sectional tougharea reduction. pitch copper The (Cu-ETP)corresponding wire invalue an annealedfor Cu-ETP condition is found at to low be speed with a drawing block. The authors showed that different die angles result in significant differences in the parameter ∆, strain rate, and total deformation strain (due to redundant strain).Φ Atkins ≈ 1 + 0.27∆ [22]. observed that the deformations in the cases(3) ∆ 1 can be better explained by the redundant work factor (Φ). The factor Φ is defined by the ≥ Other studies by Nakagiri [8], Coser [17], and Godfrey [23] focused on the effects of the wire/die ratiocontact of thelength total to deformationdiameter ratio work (L/Di to). thatHere due the tolength dimension of L is defined change. as In the other sum words, of the frustum it carries slant the informationlength at 2β ondie theangle additional and the length plastic of deformation the bearing besideszone Hc those indicated owing in Figure to the cross-sectional1. It was shown area that reduction.both the L/Di The ratio corresponding and residual value stress for were Cu-ETP small. is found to be Nonetheless, for the specific case of wire drawing die, to the best of our knowledge, few efforts Φ 1 + 0.27∆. (3) have been dedicated to the geometry of the ≈bearing zone. Therefore, the main object of the present Otherpaper studies is to evaluat by Nakagirie the [8 effects], Coser of [ 17 die], and contours. Godfrey To [23 be] focused specific, on we the study effects different of the wire forms/die contact of die lengthgeometry to diameter and its ratioimpact (L /Di).on reducing Here the the length radial of L stress is defined during as theand sum after of the frustumwire-drawing slant length process. at 2Therefore,β die angle the and present the length study of thewill bearing potentially zone improve Hc indicated the organizational in Figure1. It was process shown in that terms both of the the Lreduction/Di ratio andof shape residual distortion, stress were crack small. propagation, surface finish quality, and dimensional accuracy of the partsNonetheless,. for the specific case of wire drawing die, to the best of our knowledge, few efforts have been dedicated to the geometry of the bearing zone. Therefore, the main object of the present paper 2. Materials and Methods is to evaluate the effects of die contours. To be specific, we study different forms of die geometry and its impactA onbetter reducing understanding the radial stressof the duringeffects andof the after die the geometry wire-drawing in the process.process of Therefore, plastic deformation the present studyprovid willes valuablepotentially information improve the and organizational potential for process further in terms development of the reduction in practice. of shape In the distortion, present crackstudy, propagation, we focus on surface the influences finish quality, of the andreduction dimensional and bearing accuracy zones of the of parts.the wire drawing die. The work is divided into three stages. In the first part of the study, tensile testing in commercial Cu-ETP 2.(99.94% Materials Cu) andwith Methods Ø 0.5 mm and a length of 200 mm in the annealed condition was performed using a tensileA better test understanding machine. The of object the e ffwasects ofto the obtain die geometry the mechanical in the process properties ofplastic of specimens. deformation The provides valuable information and potential for further development in practice. In the present study, Metals 2019, 9, 1089 3 of 10 we focus on the influences of the reduction and bearing zones of the wire drawing die. The work is Metals 2019, 9, x FOR PEER REVIEW 3 of 10 divided into three stages. In the first part of the study, tensile testing in commercial Cu-ETP (99.94% Cu)experimental with Ø 0.5 data mm collected and a length from ofthe 200 wire mm-drawing in the annealed process at condition different was speeds performed were used using to calculate a tensile testthe friction machine. coefficient The object (µ). was At tothis obtain stage, the cold mechanical wire drawing properties with a ofsingle specimens. block drawing The experimental was used. dataThe first collected type of from die thewas wire-drawing made of crystal process poly diamond at different (PCD) speeds with were 2β = used 10° and to calculate Hc = 35%Df, the friction which µ coewillffi becient denoted ( ). At as this C- stage,type. Here, cold wire water drawing-soluble with oil aand single mineral block lubricants drawing was were used. implemented. The first type The of β diedrawing was made stress of was crystal determined poly diamond by measuring (PCD) with the 2drawing= 10◦ andload Hc using= 35%Df, a load whichcell system will be mounted denoted on as C-type.the die. Here,The object water-soluble of the second oil and stage mineral was lubricantsto simulate were the process implemented. by employing The drawing a finite stress-element was determinedsolver. Calculations by measuring were thecarried drawing out for load the using radial a loadstress cell both system at the mounted center and on theon the die. surface The object of the of thematerial. second For stage the waspurpose to simulates of comparison, the process four by different employing values a finite-element of µ were selected, solver. obtained Calculations from were the carriedfirst stage, out to for perform the radial the stress numerical both atsimulations. the center andBesides on the the surface C-type ofdies, the a material. different For type the of purposesdrawing µ ofdie comparison, was introduced, four where differentby the values straight of cylindricalwere selected, bearing obtained zone of from length the Hc first is stage,substituted to perform by an theinwardly numerical curved simulations. bearing zone Besides with the (contour) C-type length dies, a diR,ff whicherent typewill ofbe drawingreferred dieto as was an introduced,R-type die wherebyhereafter. the straight cylindrical bearing zone of length Hc is substituted by an inwardly curved bearing zoneThe with Ansys (contour) workbench length R, 15,which a finite will be element referred program to as an R-type based die on hereafter. quasi-static formulation, is employedThe Ansys for the workbench numerical 15, simulations. a finite element Due program to the existing based on symmetry quasi-static presented formulation, in the is employedproblem, foronly the one numerical-quarter simulations.of the real Due die geometryto the existing is implemented symmetry presented numerically in the problem,in the three only-dimensional one-quarter ofmodel the (Figure real die 2 geometry). In practice, is implementedwe consider the numerically die as a rigid in body, the three-dimensional whereas the behavior model of the (Figure material2). Inis practice,modeled we by consider a multilinear the die isotropic as a rigid hardening body, whereas curve. the To behavior generate of the the finitematerial element is modeled meshes, by aelements multilinear such isotropicas SOLID186, hardening MASS21, curve. TARGE170, To generate and theCONTA174 finite element are made meshes, use of. elements The real suchcontact as SOLID186,between the MASS21, die and TARGE170,the thread andis the CONTA174 frictional type, are made namely, use of. solid The to real solid contact friction between is im theplemented die and theby using thread different is the frictional values type,for the namely, friction solid coefficient to solid, friction as discussed is implemented above. Moreover, by using diadaptivefferent values mesh forrefinement the friction is carried coeffi cient,out regarding as discussed the accuracy above. Moreover,of the calculations. adaptive The mesh process refinement is invoked is carried until outthe regardingvariations theof the accuracy surface of and the center calculations. radial stresses The process become is invoked less than until 10% the with variations respect of to the the surface latest one. and centerBy using radial the stressesstatic implicit become method, less than the 10% resultant with respect mesh contains, to the latest on one.average, By using 23,000 the nodes static and implicit 5000 method,elements. the Also, resultant substeps mesh have contains, been utilized on average, to accelerate 23,000 nodes the convergence, and 5000 elements. as well Also, as to substeps facilitate have the beensubsequent utilized interpolation to accelerate for the spatial convergence, profiles of as the well stress. as to The facilitate size of thesubstep subsequent varies from interpolation 0.005 to 0.02 for spatials, while profiles the total of increment the stress. of The one size step of is substep 1 s. For varies the third from and 0.005 last to stage, 0.02 s, additional while the simulations total increment are ofcarried one step out with is 1 s. the For aim the of third analyz anding last the stage, radial additional stress resulting simulations from the are C carried-type and out R with-type the dies. aim It ofis analyzingdone by choosing the radial different stress resulting die angles from 2β thewith C-type 14 and and 18 R-type degrees dies., together It is done with by the choosing smallest di ffµerent that β µ dieoccurs angles in the 2 experimentalwith 14 and 18wire degrees,-drawing together process with at different the smallest speeds.that Last occurs but no int theleast, experimental in order to wire-drawingvalidate the finite process element at diff erentmodel, speeds. the resultant Last but drawingnot least, forcesin order extracted to validate from the the finite numerical element model,simulations the resultant are compared drawing against forces those extracted obtained from the empirically, numerical as simulations shown below are compared in Figure against4. The thosediscrepancies obtained between empirically, the experimental as shown below and in theore Figuretical 4. Theones discrepancies are found to betweenbe around the 10%. experimental These are andattributed, theoretical by and ones large, are found to the todifferences be around in 10%. the model These areimplementations attributed, by andregarding large, tothe the specific differences type inof lubricant the model used implementations in practice as well regarding as other the uncertainty, specific type presented of lubricant experimentally. used in practice We understand, as well as othertherefore, uncertainty, that our presentedpresent finite experimentally. element approach We understand, is reasonable, therefore, and the that main our features present finitederived element from approachthe numerical is reasonable, simulations and are the meaningful. main features derived from the numerical simulations are meaningful.

Figure 2. An illustration of the geometrical layout and the mesh of finite elements used in numerical Figure 2. An illustration of the geometrical layout and the mesh of ﬁnite elements used in numerical simulations. The red arrow indicates the drawing direction. simulations. The red arrow indicates the drawing direction. 3. Results As discussed before, we first determine the mechanical properties by carrying out a tension test of the samples used in the wire drawing process, which will be utilized later for numerical simulations. The relevant measurements include elastic modulus (E = 14 GPa), yield strength (σe,0.2% = 130 MPa), tensile stress limit (σr = 349 MPa), and Poisson’s ratio (0.34). In Figure 3 we show the

Metals 2019, 9, 1089 4 of 10

3. Results As discussed before, we ﬁrst determine the mechanical properties by carrying out a tension test of the samples used in the wire drawing process, which will be utilized later for numerical simulations. The relevant measurements include elastic modulus (E = 14 GPa), yield strength (σe,0.2% = 130 MPa), tensile stress limit (σr = 349 MPa), and Poisson’s ratio (0.34). In Figure3 we show the experimental results of Cu-ETP wire drawing of Ø0.5 (Di) to Ø 0.45 mm (Df), performed with C-type die with 2β = 10◦ and Hc = 35%Df. The total strain in one pass was 19% (ra) for varied speeds from 0 to 25 m/s. The increase in speed causes a speciﬁc variation in the drawing force for each type of lubricant, as shown in Figure3. This is understood to be due to the lubricant listed in Table1 and its ease of entering the metal/die interface. It was not possible to measure the dynamic viscosity of the water-soluble lubricant, which contains 93% water in its composition.

Figure 3. Experimental results obtained in C-type copper wire drawing process with mineral and soluble lubricants for diﬀerent speeds.

Table 1. Dynamic viscosity at diﬀerent temperatures.

Viscosity (Pa.s) Temp. (◦C) Soluble Mineral 25 0.2940 50Out of range 0.0704 70 0.0448

By using the mineral lubricant, the drawing force is found to attain the minimum value (11.60 N) at a relatively low speed (11.99 m/s) compared to that for the soluble lubricant (24.20 m/s) due to its larger viscosity. On the other hand, an increase in the drawing force is observed for the former as the speed exceeds 11.99 m/s. This probably occurs owing to the excess of lubricant in the metal/die interface. The results indicate that the optimized conditions of the process, namely, the lowest drawing force, are presented at different speeds, depending on the specific type of lubricant. The second stage starts with the calculation of friction coefficients, determined by the experimental data on drawing force at different speeds, whereby Equations (4) and (5) were derived [24]. Metals 2019, 9, 1089 5 of 10

The corresponding results are presented in Figure3. The results show that the smallest µ (0.026) occurs in the drawing with water-soluble oil at a drawing speed of 24.20 m/s. The speciﬁc values of the friction coeﬃcient employed in the simulations (Figure3) with Ansys-15 are 0.136 (soluble), 0.046 (soluble), 0.090 (mineral), and 0.026 (soluble), respectively, in accordance with standard practice. σxb ri 2 β σ0 + 2 f(β) ln + 2 cot gβ σxf · σ0 · · rf √3 · sin β − − µ = n h io (4) Hc σxb ri ri Hc 2 σxf σ0 (cot gβ) 1 ln ln + · rf · − · · − σ0 − rf · rf rf  q   q 1+ 11   11 2 1 12  1 (cos β) 1 12 sin β + ln q q   − · − · √11 12 · 11 β+ 11 2 β   · 12 cos 1 12 sin  f(β) = · − , (5) sen2β

where σ0 stands for the yield stress, σxb is the backward stress, and σxf is the wire-drawing stress, while ri and rf indicate the initial and final radii of the wire, respectively. In order to study the effect of the internal die geometry, both the C-type die with a cylindrical bearing zone of length Hc and the R-type die with the radius R at its narrowest region are utilized. Metals 2019, 9, x FOR PEER REVIEW 5 of 10 Metals 2019, 9, x FOR PEER REVIEW 5 of 10 To be specific, the following measures are utilized for the C-type (2β = 10◦; Hc = 35%Df) and R-type 11 1+√ dies (2β = 10◦;R = 1, 2 mm). The values of the radius11 √11 R1 of R-type12 dies are chosen in such a way to 11 {1−1(cosβ)⋅√1−1+⋅si12n2β+ ⋅ln } {1−(cosβ)⋅√1− ⋅sin2β+ ⋅ln 12 √11⋅}12 11 11 12 11⋅12 √ ⋅cos +√1− sin2 (5) maintain the contact length L, identical√ to that√11 of the√ 11 C-type2 dies.12 β The12 purposeβ of(5) the above setup is f(β) = 12⋅cosβ+ 1−12sin β , f(β) = sen2β, that the ratio L/Di should not influence thesen2 stressβ [8]. The values of L shown in Table2 are evaluated by where σ0 stands for the yield stress, σxb is the backward stress, and σxf is the wire-drawing stress, wherethe sum σ0 sta ofnds the fo contactr the yield length, stress, namely,σxb is the theback sumward of stres thes, length and σxf ofis reductionthe wire-drawin zoneg andstress, Hc (R) for C-type while ri and rf indicate the initial and final radii of the wire, respectively. while(R-type) ri and dies. rf indicate the initial and final radii of the wire, respectively.

Table 2. Dimension of die geometry used in numerical simulation.

C-Type R-Type

L Hc 2β RL L/Di. L/Di (mm) (%) ( ) ◦ (mm) 0.889 0.4443 35 1.0 0.4443 0.889 10 —– —– —– 0.4442 0.888 0.726 0.3631 142.0 0.3629 0.726 35 C-type R-type 0.636 0.3182C-type 18R-type 0.3176 0.635 R—curve bearing zone with (contour) length R.

The values of the radial stresses are extracted from the simulations both at the center and the surface of the materials. In particular, as indicated in Table2, a point on the surface and another at the R L center of the material are chosenLto beHc monitored 2β LR dueHc toL their 2β distinctive roles during the wire-drawing process. The stress on the surface of the material is primarily applied by the die, and the stress at the center of the material is mostly identical to the external force exerted by the capstan. In Figure4, we present the results on radial stress as a function of displacement. It can be inferred that the reduction of fraction coefficient µ implies an increase in the radial stress, both on the surface and at the center of the material for both types of dies (C-type and R-type). Moreover, for a given R—curve bearing zoneR— withcurve (contour) bearing zone length with R. (contour) length R. µ, the R-type dies result in less radial stress on the surface than do C-type dies. On the other hand, theIn radial Figure stress 4, we present isI observedn Figure the results 4, towe increase present on radial the in stress results the as center ona function radial of thestress of displacement. material. as a function This It of can happens displacement. be inferred due It to can the be decrease inferred thatof redundantthe reduction workthat of fraction the and, reduction coefficient consequently, of fraction µ implies coefficient the an increase increase µ implies in of the the anradial material increase stress in flow., both the radialon As the a stress result,surface, both the on radial the surface stress and at the center of the material for both types of dies (C-type and R-type). Moreover, for a given µ, andbetween at the center the centerof the material and surface for both becomes types of dies closer, (C-type which and inR-type). turn Moreover, increases for the a homogeneitygiven µ, in plastic the R-type dies resultthe Rin-type less diesradial result stress in on less the radial surface stress than on do the C -surfacetype dies. than On do the C- othertype dies. hand, On the the other hand, the radial stress is observedradial strto essincrease is observed in the centerto increase of the in material. the center This of thehappens material. due Thisto the happens decrease due of to the decrease of redundant work and,redundant consequently, work and, the consequently,increase of the the material increase flow. of the As materiala result, flow.the radial As a stressresult, the radial stress between the centerbetween and surface the center become ands closer,surface which become in sturn closer, increase whichs thein turn homogeneity increases inthe plastic homogeneity in plastic deformation. The deformation.above feature The is observed above feature to be moreis observed prominent to be as more the valueprominent of R increases as the value from of R R increases from R = 1 mm to R = 2 mm.= 1 mmThese to resultsR = 2 mm. are inThese accordance results arewith in Vega’saccordance findings with [2 Vega’s5]. In other findings words, [25 ].the In other words, the bearing length hasbearing a significant length impact has a significant on the drawing impact process on the of drawing copper. process of copper. Metals 2019, 9, 1089 6 of 10 deformation. The above feature is observed to be more prominent as the value of R increases from R = 1 mm to R = 2 mm. These results are in accordance with Vega’s findings [25]. In other words, theMetals bearing 2019, 9, lengthx FOR PEER has REVIEW a significant impact on the drawing process of copper. 6 of 10

(a) µ = 0.136 (b) µ = 0.090

Figure 4.4. The calculated radial stress as a function of displacement, obtained by the finitefinite element methods with didifferentfferent coecoefficientsfficients ofof friction.friction.

ForFor the third and last last stage, stage, different different die die angles angles (2β) (2β )together together with with given given μ µ= =0.0260.026 are are utilized utilized in innumerical numerical simulations simulations in order in order to investigate to investigate the theeffect eff ofect the of thereduction reduction region region on radial on radial stress. stress. We Wechoose choose two twoangles angles with with2β = 214β° =and14 ◦18and°, which 18◦, whichare commonly are commonly adopted adopted in industry in industry practice. practice. Also, R Also,= 2 mm R is= chosen2 mm is to chosen reduce to the reduce surface the as surface well as asthe well center as radial the center stress radial and, stressconsequently, and, consequently, to increase tothe increase homogeneity the homogeneity in the plastic in deformation the plastic deformation of the material. of the The material. numerical The resu numericallts are presented results are in presentedFigure 5. For in a Figure clear 5understanding. For a clear understandingof the different ofregions the di offf theerent drawing regions die of in the question, drawing we die have in question,chosen three we haveevaluation chosen points three evaluation with different points displacements, with different displacements,namely 0.4 (start namely of the 0.4 deformation (start of the deformationzone), 0.6 (start zone), of be 0.6arin (startg zone of bearing), and 0.8 zone), (final and region 0.8 (finalof the region die), a ofs indicated the die), asin indicatedFigure 5a. in The Figure values5a. Theof radial values stress of radial of the stress mentioned of the mentioned points were points evaluated were evaluated and presented and presented in Figures in 5 Figureb for 5theb for center the centerradial stress radial and stress 5c andfor the Figure superficial5c for the radial superficial stress. radial stress.

Metals 2019 9 Metals 2019,, 9,, 1089x FOR PEER REVIEW 77 of of 10

(a) Evaluation Points

(b) Center (c) Surface

Figure 5.5. ((a)) EvaluationEvaluation points.points. (b(b)) The The center center radial radial stress stress as as a functiona function of displacement,of displacement, evaluated evaluated for thefor the evaluation evaluation points. points. (c) The(c) The superﬁcial superficial radial radial stress stress as a as function a function of displacement, of displacement, evaluated evaluated for thefor evaluationthe evaluation points. points.

For a given frictionfriction coecoefficientfficient µ == 0.026,0.026, the variation of the die angle 22ββ has a less significantsignificant impact on on the the radial radial stress stress in thein the center center of the of material, the material, compared compared to that to on that the surface on the of surface the material, of the asmaterial, shown as in Figureshown5 inb,c. Figure Subsequently, 5b,c. Subsequently, as the redundant as the workredundant decreases, work it decreases, enables one it toenables increase one the to materialincrease flow,the material which is flow, accompanied which is accompanied by a slight increase by a slight in the increase radial stress in the at radial the center stress of at the the material. center Thisof the result material. can be This intuitively result can understood be intuitively as the understood surface of as the the material surface that of the suff materialers heavily that from suffe thers deformationheavily from process.the deformation The observed process. variation The observed in radial variation stress takes in radial place stress as a reaction takes place to the as increase a reaction in theto the parameter increase∆ inand the the parameter subsequent ∆ and impact the subsequent on the redundant impact work on the factor redundantΦ, as shown work in factor Table 3Φ. , as shown in Table 3. Table3. The calculated redundant work factor Φ as a function of ∆ and 2β used in numerical simulations. Table 3. The calculated redundant work factor Φ as a function of Δ and 2β used in numerical 2β ∆ Φ simulations. 14 2.32 1.62 182β Δ 2.98 Φ 1.8 14 2.32 1.62 On the other hand, the superficial radial18 stress2.98 is significantly1.8 influenced by the increase of the die angle 2β. Consequently, the most substantial flow of material also occurs for the die angle of 2β On the other hand, the superficial radial stress is significantly influenced by the increase of the = 14 . At the entrance region (point 0.4) the superficial radial stress is slightly more significant for die angle◦ 2β. Consequently, the most substantial flow of material also occurs for the die angle of 2β = 14°. At the entrance region (point 0.4) the superficial radial stress is slightly more significant for the

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Metals 2019, 9, x FOR PEER REVIEW 8 of 10 the die angle 2β = 14◦, as shown in Figure5c. The central region (point 0.6) clearly demonstrates the mostdie angle substantial 2β = 14 influence°, as shown between in Figure different 5–c. The types central of dies. region The radial(point stress 0.6) clearly in the finaldemonstrate region ofs the diemost (point substantial 0.8) is influencedinfluence between by a flow different facility types permitted of dies. by The the radial smaller stress angle in of the 2β final. With region the aimof the of comparingdie (point 0.8) the is behaviors influenced of dibyff erenta flow types facility of dies,permitted the higher by the radial smaller stresses angle at of the 2β. center With andthe aim on the of surfacecompar ofing the the material behaviors are of chosen different and types presented of dies, in Figurethe higher6. From radial Figure stresses6, it canat the be center inferred and that on the the modificationsurface of the of material the die are geometry chosen fromand presented C-type to R-typein Figure reduces 6. From the Figure radial 6 stress, it can on be the inferred surface that of the materialmodification (between of the die23.10% geometry and 34.48%)from C-type but increases to R-type that reduces at the the center radial (from stress+2.16 on the to + s6.55%)urface forof the all − − simulatedmaterial (between die angles. −23. The10% proposedand −34.48%) modification but increases of die that geometry at the center decreases (from the+2.16 di fftoerence +6.55%) by for up all to 93.27%.simulated The die R-type angles. die The with proposed R = 2 mm modification has less of anof impactdie geometry on the surfacedecreases and the center difference of radial by stress,up to 93.27%. The R-type die with R = 2 mm has less of an impact on the surface and center of radial stress, especially for the die angles 2β = 10◦ and 14◦, and a slightly more considerable variation is observed especially for the die angles 2β = 10° and 14°, and a slightly more considerable variation is observed for 2β = 18◦. In this case, the superficial radial stress increases, while the stress at the center decreases. for 2β = 18°. In this case, the superficial radial stress increases, while the stress at the center decreases.

Figure 6. RRadialadial stress in the center and surface of the material for several 22ββ.

4. Conclusions The eeffectffect of die geometrygeometry is a relevant research topic for the metalworkingmetalworking industry, owing to its direct association to productivity and cost cost-benefit‒benefit eefficiency.fficiency. TheThe problemproblem isis ratherrather complex since it is alsoalso aaffectedffected byby variousvarious otherother sensitive factors such as the working conditions,conditions, properties of the specimens, etc.etc. Nonetheless,Nonetheless, thethe wire wire drawing drawing branch, branch, specifically, specifically, deserves deserves more more attention attention due due to the to apparentthe apparent lack of lack insightful of insightful investigations. investigations. The results The obtained results obtained in the present in the study present may study potentially may contributepotentially tocontribute the ongoing to the eff ongoingorts to exploreefforts to this explore area. this For area. different For different die angles die as angles well asas bearingwell as zones,bearing investigations zones, investigations are carried are carried out for out the for wire-drawing the wire-drawing process. process. In particular, In particular, by extracting by extracting the frictionthe friction coe fficoefficientscients from from the Cu-ETPthe Cu-ETP wire wire in cold-drawn in cold-drawn essays, essays, the numericalthe numerical simulations simulations are also are performed.also performed. We present We present the results the resultsfor both for the both superficial the superficial and center and radial center tensions radial by tensions employing by finiteemploying element finite methods. element It methods. is found It that is found the reduction that the reduction of the friction of the coe frictionfficient coefficient leads to anleads increase to an inincrease radial in stress. radial For stress. a given For frictiona given coe frictionfficient, coefficient, the substitution the substitution of the C-type of the die C- withtype die an R-typewith an one R- resultstype one in results a decrease in a decrease in the superficial in the superf radialicial stress, radial accompanied stress, accompanied by an increase by an increase at the centerat the center of the material.of the material. Moreover, Moreover the die, the angle die isangle found is found to play to a play less significanta less significant role in role the resultantin the resultant center center radial stress,radial stress, but it significantly but it significantly affects theaffects superficial the superficial radial stress. radial Last stress. but Last not least,but not R-type least, dies R-type result dies in smallerresult in superficial smaller superficial radial stress radial but stress slightly but more slightly significant more significant center radial center stress radial for di stressfferent for die different angles. Thedie angles. findings The of finding the presents of the study present are meaningfulstudy are meaningful regarding regarding better die better geometry die geometry designs aimed designs at reducingaimed at the reducing radial stress the radial during stress and duringafter the and wire-drawing after the wire process-drawing and consequently process and increasing consequently the productionincreasing the capability production of an capability organization. of an We organization. plan to continue We our plan study to continue in future our works. study in future works.

Metals 2019, 9, 1089 9 of 10

Author Contributions: G.A.S.M. was responsible for the general conceptualization and experimental approach; E.F.d.S. and L.K.K. were responsible for the interpretation of the results; E.S.G. and F.d.A.S. were responsible for simulations with the finite element solver Ansys. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

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