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Change in mechanical properties of fine copper wire manufactured by continuous rotary draw bending process
Journal of Materials Processing Technology 212 (2012) 2505–2513
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Review
Change in mechanical properties of fine copper wire manufactured by continuous rotary draw bending process Junichiro Tokutomi a,c,∗ , Kenichi Hanazaki a,b , Nobuhiro Tsuji b , Jun Yanagimoto c a b c
Yazaki Corporation, Yazaki Research and Technology Center, Shizuoka, Japan Kyoto University, Graduate School of Engineering, Department of Material Science and Engineering, Kyoto, Japan The University of Tokyo, Institute of Industrial Science, Tokyo, Japan
a r t i c l e
i n f o
Article history: Received 11 March 2012 Received in revised form 13 June 2012 Accepted 15 June 2012 Available online 29 June 2012 Keywords: Bending Mechanical properties Vickers hardness Microstructure Fine copper wire
a b s t r a c t The mechanical behaviors of Cu–Sn alloy wire specimens processed by the newly proposed method of rotary draw bending are systematically investigated, mainly by considering the relationship between the Vickers hardness (HV) on the cross section and the compressive residual energy during draw bending. It was found that during draw bending, the HV was lower than that of the specimen subjected to wire drawing, particularly on the inside of the bend, and it was confirmed that the softening induced by plastic deformation is promoted by increasing the compressive residual energy. The changes in HV and compressive residual energy were closely related. Consequently, there was a large difference in the hardness distributions on the inside and outside of the bend, and the mechanical properties of the wire specimen changed greatly during draw bending. Additionally, the change in the texture resulting from draw bending obtained by the finite element method (FEM) analysis of stress and the measured change in the texture showed good qualitative agreement. © 2012 Elsevier B.V. All rights reserved.
Contents 1. 2.
3.
4.
5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 2.1. CBD process and materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 2.2. Draw bending in CBD process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 2.3. Evaluation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2507 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2508 3.1. Changes in drawing tension and mechanical properties during rotary draw bending. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2508 3.2. Hardness distributions in cross sections of the wire specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2508 3.3. FEM analysis of rotary draw bending at various angular velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2509 3.4. Change in texture during draw bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2509 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2511 4.1. Relationship between elastic energy of dislocations and plastic strain energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2511 4.2. Relationship between HV and plastic strain energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2512 4.3. Change in formation of texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2512 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513
∗ Corresponding author at: Yazaki Research and Technology Center, Yazaki Corporation, Mishuku 1500, Susono, Shizuoka 410-1194, Japan. Tel.: +81 55 9653207; fax: +81 55 9650479. E-mail address: [email protected] (J. Tokutomi). 0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.06.008
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Nomenclature b Burgers vector radius of wire specimen after bending da db radius of wire specimen before bending plastic strain energy EP E0e elastic energy of edge dislocations E0s elastic energy of screw dislocations total self-energy per dislocation ET E residual energy (=compressive residual energy) L grain diameter n number of dislocations in a grain R radius of die B R1 and R2 directions of rotation mean distance between dislocations Rd Rn curvature radius in neutral plane of wire specimen V drawing speed plastic work increment WP Greek letters εbending bending strain εPij strain tensor of plastic range plastic strain in longitudinal direction εx diameter of shaft 0 radius of dislocation cores Lame’s constant dislocation density ij stress tensor ω angular velocity of shaft
1. Introduction Fine electrical wires are required to have good mechanical properties and high electrical conductivity for use in applications such as automobiles, home electronics and industrial robots. However, there is a risk of breakage during the manufacture and use of fine wires, since their cross-sectional areas are extremely small. Consequently, high strength and ductility are required for fine wires. There are several methods of strengthening metallic materials. The authors have focused on ultrafine-grain (UFG) metallic materials formed by severe plastic deformation (SPD), which markedly suppresses electrical conductivity. Various SPD processes have been developed for manufacturing UFG metallic materials with grain sizes smaller than 1 m. They can be summarized into three types of processes as reviewed by Azushima et al. (2008): accumulative roll bonding (ARB), equal channel-angular pressing (ECAP) and high-pressure torsion (HPT). In the ARB process, the stacking of sheets and conventional roll bonding with a 50% reduction per cycle are repeated, meaning that a very large plastic strain can be applied to the material. Saito et al. (1999) conducted a basic study of texture formation and tensile strength for ARB using aluminum (1100), Al–Mg alloy (5083) and Ti-added interstitial free steel. In ECAP, pure shear deformation can be repeatedly imposed on a material so that an intense plastic strain is produced without any change in the cross-sectional dimensions of the workpiece. Segal (1995) investigated structure formation, mechanical properties and physical properties in ECAP by applying various equivalent strains and shear directions. In the HPT process, a very thin disk is compressed in a closed die by a very high pressure, and then torque is provided by a punch with contact friction at the interface between the punch and disk. Valiev et al. (1993) applied the HPT process at various temperatures to investigate the change in mechanical properties and microstructural evolution.
However, it is difficult to apply these SPD processes to existing practical and mass production techniques for bulky metals. On the other hand, Negroni et al. (1986) used copper as a test material and investigated the change in various mechanical properties in deep wire drawing (WD) at a large strain with up to 99% reduction in area. It was clarified by Hanazaki et al. (2010) that WD is a type of SPD process, in which the metallic substructure of a wire specimen formed by WD consists of UFGs with a dislocation substructure existing inside the grains. These studies indicate that WD processes can be applied to practical use and mass production. Although the mechanism of strength improvement in UFG materials has been clarified, that of ductility improvement is still unclear. In one of our previous studies, the continuous bending-drawing (CBD) method was proposed to improve the ductility of WD specimens (Yanagimoto et al. (2011)). It was confirmed that draw bending in the final stage was able to produce fine wires with excellent mechanical properties. Additionally, Tokutomi et al. (2012) confirmed that a wire specimen subjected to the CBD process had dislocation substructures inside the UFGs. However, the crosssectional shapes of wire specimens are irregular when the shaft in the bending area is fixed. Moreover, the risk of breakage is greatly increased because the tension increases during drawing and almost reaches the breaking force. In this study, a new CBD method using a rotary draw bending die is proposed. The die is designed to decrease the drawing tension and prevent the formation of an irregular cross-sectional shape by constraining the rotation of the shaft. We investigate the change in mechanical properties of a wire processed using the rotary draw bending process. After that, the total processing energy required by the rotating draw bending process is determined by finite element method (FEM) analysis, and the relation between this energy and the change in the mechanical characteristics is discussed. 2. Experimental 2.1. CBD process and materials A dilute Cu–Sn alloy is used in this investigation. The chemical composition of the alloy is shown in Table 1. As shown in table, the alloy contains only a small amount of Sn as the alloying element. This alloy was the same as that used by Tokutomi et al. (2012). Fig. 1(a) shows the total CBD process in this investigation. A rod of the alloy was first prepared by groove-rolling and annealing. Then the internal strain was eliminated by annealing. The grooverolled specimen was annealed at 673 K for 60 min under a nitrogen atmosphere before the WD process, resulting in a recrystallized structure. The rod was elongated by WD with multiple passes. It was then subjected to WD at room temperature with lubrication. The diameter of the initial rod was 7.7 mm, whereas the diameter of the fine wire after 23 passes of WD was 210 m; thus, the maximum total area reduction was 99.93%, which corresponded to a total equivalent strain of 7.2. The WD specimen had a lamellar microstructure elongated in the drawing direction, and dislocation substructures were formed within the lamellar microstructure. The grain boundary spacing in the WD specimen was approximately 150 nm. Draw bending was imposed in the final step of the CBD process. This was performed to induce plastic deformation in different loading directions to control the strength and elongation of the fine wire. 2.2. Draw bending in CBD process Fig. 1(b) shows details of the draw bending die. The position of draw bending die D is fixed, whereas the positions of dies A–C can be changed to control the bending radius. Another feature of the
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Table 1 Chemical composition of the Cu–0.3 mass% Sn alloy (mass%).
Cu–0.3 mass% Sn
O
As
Sn
Fe
P
Pb
Cu
0.014
<0.001
0.266
<0.001
0.001
<0.001
Bal.
Fig. 1. Schematic diagram showing sample setup during CBD. (a) Total process of CBD and (b) dimensions of the rotational draw bending die.
rotary draw bending die is that the rotational direction and angular velocity of the shaft can be controlled. The draw bending conditions are shown in Table 2. The wire was drawn in the Y-direction at a relatively low speed of 1.66 mm/s. The cases in which the shaft rotates in the same direction and in the reverse direction relative to the drawing direction are denoted by positive and negative signs, respectively. Note that at an angular velocity of 11.12 rad/s and a drawing speed of 1.66 mm/s, the velocity ratio is 1:1. Hence, when the angular velocity of the shaft exceeds 11.12 rad/s, the wire is driven by the rotating shaft. The bending strain (εbending ) of draw bending was estimated by Yanagimoto et al. (2011) using the equation
εbending = ln 1 +
da Rn
1+
db Rn
(1)
here Rn is the curvature radius in the neutral plane of the wire specimen, and da and db are the radii of the wire specimen after and before bending, respectively. Draw bending was executed with a curvature radius of 0.84 mm, corresponding to an equivalent Table 2 Drawing bending conditions used in present study. Angular velocity [rad/s]
−11.12 0.0 11.12, 22.24, 33.36
Drawing speed [mm/s] Process temperature [K]
1.66 298
(Direction of rotation: R1) (Fixed) (Direction of rotation: R2)
bending strain of 0.23, which was selected to realize the optimal strength-ductility balance according to the experimental results in our previous study. 2.3. Evaluation method A tensile test on the wire specimens after draw bending was carried out at a nominal strain rate of 3 × 10−3 s−1 at room temperature. The strength of the wire specimens was measured using an Instron-type testing machine with cord and yarn grips, which prevented jaw breaks of the wire specimens. The elongation of wires was measured using a video extensometer with two foam polystyrene spheres containing slits as markers. The initial gauge length was 50 mm. The microstructural and crystallographic features of the wire specimens after the WD and draw bending processes were characterized by electron backscatter diffraction (EBSD) measurement using a field-emission-type scanning electron microscope (FE-SEM) operated at 25 kV and equipped with a TSL orientation imaging microscopy system. Fig. 2 shows the measurement area on the cross section of a wire specimen. The microstructures of the specimens subjected to WD and draw bending were measured 90 m from their center using mapping areas of 15 m × 15 m. The cross sections of the wire specimens were subjected to ion-beam polishing at 4.5 kV for 8 h in an argon gas atmosphere. Experimental hardness tests on the cross sections of specimens were performed with a Vickers microhardness tester. The
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Fig. 2. Schematic diagram showing the EBSD measurement area on the cross section of a wire specimen: (a) WD specimen and (b) drawing specimen.
compressive load and holding time of the indenter were 0.01 gf and 10 s, respectively. The hardness on the cross sections of wire specimens were measured at various distances from their centers with intervals of 10 m. The surface of each wire was electropolished by mechanical polishing to remove the processing history.
3. Results 3.1. Changes in drawing tension and mechanical properties during rotary draw bending Fig. 3 shows the change in drawing tension during draw bending at various angular velocities. When the shaft rotated in the opposite direction to the drawing direction, such as for velocities of −11.12 rad/s and 0.00 rad/s, the drawing tension was approximately 8 N. However, when the shaft rotated in the drawing direction, such as for velocities of 11.12 rad/s, 22.24 rad/s and 33.36 rad/s, the drawing tension was approximately 6.5 N. The drawing tension decreased with increasing angular velocity when the shaft was rotated in the opposite direction to the drawing
Fig. 3. Change in drawing tension of wire specimens during draw bending.
direction. However, when the rotating speed was increased in the drawing direction, the drawing tension remained unchanged. Fig. 4 shows the nominal stress-strain curves of the wire specimens processed at various angular velocities. The ultimate tensile strength (UTS) and 0.1% proof stress were the same for all wire specimens processed by rotary draw bending, and reached approximately 750 MPa and 530 MPa, respectively. The UTS and 0.1% proof stress of the rotary draw bending specimens were almost 40 MPa and 150 MPa lower than those of the WD specimen, respectively. The total elongations of the wire specimens were 3.1% and 3.6%, respectively, when the shaft rotated at angular velocities of −11.12 rad/s and 33.36 rad/s. The total elongation increases as the drawing tension decreases as shown in Fig. 4. 3.2. Hardness distributions in cross sections of the wire specimens The hardness distributions on the cross sections of the wire specimens processed by rotary draw bending were measured since a change in the mechanical properties was confirmed. Fig. 5 shows the change in the Vickers hardness (HV) on the cross sections of
Fig. 4. Nominal stress-strain curves of the Cu−0.3 mass% Sn alloy specimens processed at various angular velocities.
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flexural center of the wire was about 10 HV lower than that of the WD specimen. In contrast, the hardness on the inside of the wire after draw bending was 30 HV lower than that at the flexural center. This result indicated that considerable deformation-induced softening occurred on the inside of the bend during draw bending. Moreover, when the directions of shaft rotation and drawing were the same and the angular velocity of the shaft was increased, the amount of softening increased.
3.3. FEM analysis of rotary draw bending at various angular velocities
Fig. 5. Change in HV of wire specimens processed at various angular velocities.
wire specimens processed at various angular velocities, where each value of HV is the average of five measurements. The values of HV from the center to the inside of the wire were less than those of the WD specimen. However, the values of HV from the center to the outside of the wire were almost identical to those of the WD specimen. This meant that deformation-induced softening occurred on the inside of the bend. The change in the hardness distribution of various parts of the wire specimen processed at an angular velocity of 11.12 rad/s is shown in Fig. 6. The hardness distribution was measured on cross sections of the wire specimen at the flexural center and after draw bending. The hardness distribution of the wire from the center to the outside at the flexural center was similar to that of the WD specimen. However, the hardness from the center to the inside at the
The plastic strain in a wire specimen during draw bending was estimated by FEM analysis. The wire specimen was constructed from 3D solid elements, and a simulation was carried out using ANSYS Mechanical software. The wire model was assumed to have a continuous strain distribution, and precise material properties were inputted. Drawing displacement was applied in the longitudinal direction of the wire specimen, and the radial direction was not constrained. The mass density, Young’s modulus, Poisson’s ratio and the friction coefficient between the die and the wire specimen used in the FEM simulation were 8.9 × 103 kg/m3 , 130 GPa, 0.33 and 0.12, respectively. The true stress-strain curve of the WD specimen obtained from the tensile test shown in Fig. 4 was used as the mechanical property. Fig. 7 shows contour figures of the equivalent true stress and equivalent true plastic strain during draw bending with an angular velocity of 11.12 rad/s. Fig. 8 shows the FEM simulation result of the true plastic strain in the longitudinal direction of the wire specimen for various angular velocities. The principal stress and strain were in the longitudinal direction of the wire specimen, and the other strain values were considerably lower than the principal stress and strain. Therefore, only the plastic strain in the longitudinal direction is shown in Fig. 8. In the case of inward bending, a compressive plastic strain of approximately εx = 0.30 was applied in the bending range, and then a tensile plastic strain was applied in the rebending range. Additionally, the tensile plastic strain in the rebending range decreased with the inverse rotation of the shaft and an increase in the angular velocity. This means that the movement of the shaft had a decisive effect on the plastic strain in the rebending range. This phenomenon was caused by the increase in the shearing plastic strain on the XY plane. In particular, a distinctive change occurred in the processing history in the case of inward bending. In the case of outward bending, it was confirmed that the same tensile plastic strain was continuously applied in the bending and rebending ranges at various velocities.
3.4. Change in texture during draw bending
Fig. 6. Change in hardness distribution of wire specimen in flexural center and after draw bending processed at angular velocity of 11.12 rad/s.
Fig. 9 shows the change in texture during draw bending with an angular velocity of 11.12 rad/s. The texture was measured by EBSP in the area shown in Fig. 2. The 0 0 1 and 1 1 1 textures were the main textures in the cross section of the WD specimen. On the inside of the bend at the flexural center, the textures were dispersed as shown in Fig. 9(b). On the other hand, after draw bending, the 0 0 1 and 1 1 1 textures increased in concentration (Fig. 9(d)), whereas on the outside of the bend the concentrations of the 0 0 1 and 1 1 1 textures were hardly changed as shown in Fig. 9(c). However, on the outside of the bend after draw bending, the textures were dispersed slightly. When the change behavior of the texture was compared at each measurement point, markedly different behavior was found on the inside and outside of the bend.
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Fig. 7. Results of the FEM simulation during draw bending at angular velocity of 11.12 rad/s: (a) equivalent true stress distribution and (b) equivalent true plastic strain distribution.
Fig. 8. Results of FEM simulation showing applied plastic strain in longitudinal direction: (a) definition of the range of deformation, (b) angular velocity of 33.36 rad/s, (c) angular velocity of 11.12 rad/s and (d) angular velocity of −11.12 rad/s.
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Fig. 9. Change in texture during draw bending: (a) WD specimen, (b) and (c) correspond to the specimen on the inside of the bend, (d) and (e) correspond to the specimen on the outside of the bend. (b) and (d) were obtained at the flexural center, (c) and (e) were obtained after draw bending.
4. Discussion
relationship between the mean distance between the dislocations and the dislocation density is
4.1. Relationship between elastic energy of dislocations and plastic strain energy
1 Rd = √
In this section, the plastic strain energy obtained from FEM analysis and the elastic energy obtained from the theory of elasticity of dislocations are compared, and the validity of the energy calculated by FEM analysis is discussed. Compressive deformation and tensile deformation occurred in the longitudinal direction of the wire specimen during draw bending, particularly on the inside of the wire (shown in Fig. 8). It was reported by Hasegawa et al. (1975) that the movement of dislocations in a grain is changed significantly by the reversal of stress. When the elastic energy of the dislocation motion and the plastic strain energy calculated from FEM analysis are predicted quantitatively, the correlation between them can be determined. First, the plastic strain energy on the inside of the bend during draw bending was calculated by FEM analysis. This value was used in our quantitative evaluation, and a value of 2.29 × 1010 J was obtained using the following equation:
EP =
ıW P =
ij · dεPij
(2)
On the other hand, to estimate the motion of dislocations, it is necessary to consider the energy required to move the dislocations inside a grain. The total elastic energy required to move the dislocations was considered in the following quantitative evaluation by Kato (2007) and is equal to the sum of the elastic energies of the screw dislocations and edge dislocations as follows. E T = E0s + E0e = =
b2 ln 4
R
1 B2 ln 2
d
r0
+
R
B2 ln 4 (1 − )
R d
r0
(3)
d
r0
here ET is the total self-energy per dislocation, E0s is the elastic energy of the screw dislocations, E0e is the elastic energy of the edge dislocations, is Lame’s constant (=41.4 GPa), b is the Burgers vector (=0.256 nm), Rd is the mean distance between dislocations, and r0 is the radius of the dislocation cores (=0.0224 nm). The
(4)
where is the dislocation density (=4.8 × 1014 m−2 ) of the WD specimen. This value was empirically estimated by Tokutomi et al. (2012) by removing a thin cross-sectional sample from a WD specimen using a focused ion beam (FIB) then observing the dislocations in a grain using a transmission electron microscope (TEM). The number of dislocations in each grain was derived from the relationship between the mean distance between dislocations and the spacing between neighboring agglomerations of dislocations. Additionally, if the spacing between agglomerations of dislocations is assumed to be half of the grain diameter, the number of dislocations can be shown to be L 2R √ L = 2
n=
(5)
here n is the number of dislocations in a grain and L is the grain diameter (=0.145 m). Therefore, from the product of Eqs. (3) and (5), the total elastic energy of all dislocations in a grain is ET =
1 nb2 ln 2
R r0
(6)
The total elastic energy of all the dislocations in a grain was estimated to be 7.87 × 1010 J using Eq. (6). The total elastic energy of all the dislocations in a grain required for their motion and the plastic strain energy determined by FEM analysis were compared. The generation and annihilation of dislocations during draw bending cannot be estimated using Eq. (6). Therefore, it is very difficult to precisely estimate the plastic strain energy. However, we consider that a rough estimate of the plastic strain energy is possible, because the elastic energy of all the dislocations inside a grain and the plastic strain energy determined by FEM analysis have the same order of magnitude. Changes in the hardness and mechanical properties are closely related to the metallographic structure. In particular, the change in hardness may be strongly affected by the dislocation substructure. Therefore, the plastic strain energy obtained by FEM analysis can explain the decrease in hardness during draw bending.
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4.2. Relationship between HV and plastic strain energy We next discuss the correlation between the change in HV on the inside of the bend and the plastic strain energy obtained from FEM analysis. Then, the change in the metallographic structure is considered on the basis of this discussion. As shown in Fig. 7, the principal stress and principal strain were in the longitudinal direction of the wire specimen. The plastic strain energy was calculated using Eq. (2) for various angular velocities and both rotational directions of the shaft, particularly on the inside of the bend. The residual energy on the inside of the bend during draw bending is denoted by E and is given by E = Ebending − Erebending
(7)
here Ebending is the plastic strain energy in the bending range and Erebending is the plastic strain energy in the rebending range. Ebending and Erebending were both obtained from Eq. (6). It was confirmed that the main types of plastic strain energy in the bending range and rebending range were compression and tension, respectively, in the longitudinal direction of the wire specimen. In Eq. (7), E is the mean compressive residual energy during draw bending, namely, a large amount of compression energy remained after draw bending and rebending. Fig. 10 shows the relationship between the compressive residual energy and HV on the inside of the bend. The HV was measured at the position of the node used to calculate the plastic strain energy. The HV decreased substantially as the compressive residual energy was increased. The relationship between the change in HV and the compressive residual energy was closely related to the microstructural evolution. It is assumed that the dislocations were in a stable state owing to the tensile energy during WD, since the energy in the compression direction maintained the state of the dislocations. Since the compression energy was loaded on the inside of the bend during draw bending, it can be considered that the compression energy also induced the piling up of dislocations in the opposite direction. Consequently, a difference in hardness occurred since
Fig. 10. Change in HV of wire specimens during drawing as a function of compressive residual energy.
the dislocation substructures were changed. Note that the angular velocity and rotational direction of the shaft may be used to control the compressive energy. 4.3. Change in formation of texture In this section, the relationship between the changes in the principal stress during draw bending and the texture is discussed. We clarified that tension and compression on the inside and
Fig. 11. Comparison of the measured and the texture predicted change in texture during draw bending with an angular velocity of 11.12 rad/s: (a) inverse pole figure map for various cross sections, (b) stress distribution in longitudinal direction and measurement cross sections and (c) rotations in a fcc metal under tension and compression (Calnan and Clews, 1950).
J. Tokutomi et al. / Journal of Materials Processing Technology 212 (2012) 2505–2513
outside of the bend were applied to the wire specimen (shown in Fig. 8). Moreover, a change in texture during draw bending was confirmed (shown in Fig. 9). The general behavior of rotations in a face-centered cubic (fcc) metal, such as pure copper or copper alloy, under tension and compression was reported by Calnan and Clews (1950) and Calnan (1954). When their theory is applied to the calculation of stress by FEM, the results of which are shown in Fig. 8, the change in texture can be predicted. Fig. 11 shows a comparison of the measured and predicted change in texture during draw bending with an angular velocity of 11.12 rad/s. The measured changes in the texture showed good qualitative agreement with the change in texture calculated by FEM analysis. Namely, the deformation-induced texture formation of a copper polycrystal is affected by the applied stress during draw bending. Additionally, the direction of the principal stress obtained by FEM analysis may qualitatively indicate the change in orientation. 5. Conclusions The mechanical behaviors of Cu–Sn alloy wire specimens processed by rotational draw bending and the relationship between the HV on the cross section and the compressive residual energy during draw bending were systematically investigated. During draw bending, particularly on the inside of the bend, the WD specimen was subjected to compressive/tensile strain in the longitudinal direction, and the softening induced by plastic deformation was promoted by increasing the compressive residual energy. Additionally, it is considered that the increase in the compressive residual energy is related to the change in mechanical properties. Consequently, there was a large difference in the hardness distributions on the inside and outside of the bend, namely, the mechanical properties of the wire specimen were changed greatly during draw bending. The change in the texture obtained by FEM analysis of the stress and the measured change in the texture showed good qualitative agreement.
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Acknowledgments This study was financially supported by a grant-in-aid for Scientific Research on Innovative Areas, “Bulk Nanostructured Metals”, through MEXT, Japan (Contract No. 22102005), which is gratefully appreciated. Yazaki Parts Company is also acknowledged for supplying the copper rods used in this study. References Azushima, A., Kopp, R., Korhonen, A., Yang, D.Y., Micari, F., Lahoti, G.D., Groche, P., Yanagimoto, J., Tsuji, N., Rosochowski, A., Yanagida, A., 2008. Severe plastic deformation (SPD) processes for metals. CIRP Annals–Manufacturing Technology 57, 716–735. Calnan, E.A., Clews, C.J.B., 1950. Deformation textures in face-centered cubic metals. Philosophical Magazine 41, 1085–1100. Calnan, E.A., 1954. Deformation textures of face-centred cubic metals. Acta Metallurgica 2, 865–873. Hanazaki, K., Shigeiri, N., Tsuji, N., 2010. Change in microstructures and mechanical properties during deep wire drawing of copper. Materials Science and Engineering A 527, 5699–5707. Hasegawa, T., Yakou, T., Karashima, S., 1975. Deformation behaviour and dislocation structures upon stress reversal in polycrystalline aluminium. Materials Science and Engineering 20, 267–276. Kato, M., 2007. Introduction to the Theory of Dislocations, Sixth ed. Shokabo, Tokyo, pp. 42–48. Negroni, F.D., Thomsen, E.G., Kobayashi, S., 1986. A drawing modulus for multi-pass drawing. CIRP Annals–Manufacturing Technology 35, 181–183. Saito, Y., Utsunomiya, H., Tsuji, N., Sakai, T., 1999. Novel ultra-high straining process for bulk materials-development of the accumulative roll-bonding (ARB) process. Acta Materialia 47, 579–583. Segal, V.M., 1995. Materials processing by simple shear. Materials Science and Engineering A 197, 157–164. Tokutomi, J., Hanazaki, K., Tsuji, N., Yanagimoto, J., 2012. Changes in mechanical characteristics of pre-annealed wires of Cu–Sn alloy manufactured by continuous draw bending. Materials Transactions 53, 116–122. Valiev, R.Z., Korznikov, A.V., Mulyukov, R.R., 1993. Structure and properties of ultrafine-grained materials produced by severe plastic deformation. Materials Science and Engineering A 168, 141–148. Yanagimoto, J., Tokutomi, J., Hanazaki, K., Tsuji, N., 2011. Continuous bendingdrawing process to manufacture the ultrafine copper wire with excellent electrical and mechanical properties. CIRP Annals–Manufacturing Technology 60, 279–282.
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Review
Change in mechanical properties of fine copper wire manufactured by continuous rotary draw bending process Junichiro Tokutomi a,c,∗ , Kenichi Hanazaki a,b , Nobuhiro Tsuji b , Jun Yanagimoto c a b c
Yazaki Corporation, Yazaki Research and Technology Center, Shizuoka, Japan Kyoto University, Graduate School of Engineering, Department of Material Science and Engineering, Kyoto, Japan The University of Tokyo, Institute of Industrial Science, Tokyo, Japan
a r t i c l e
i n f o
Article history: Received 11 March 2012 Received in revised form 13 June 2012 Accepted 15 June 2012 Available online 29 June 2012 Keywords: Bending Mechanical properties Vickers hardness Microstructure Fine copper wire
a b s t r a c t The mechanical behaviors of Cu–Sn alloy wire specimens processed by the newly proposed method of rotary draw bending are systematically investigated, mainly by considering the relationship between the Vickers hardness (HV) on the cross section and the compressive residual energy during draw bending. It was found that during draw bending, the HV was lower than that of the specimen subjected to wire drawing, particularly on the inside of the bend, and it was confirmed that the softening induced by plastic deformation is promoted by increasing the compressive residual energy. The changes in HV and compressive residual energy were closely related. Consequently, there was a large difference in the hardness distributions on the inside and outside of the bend, and the mechanical properties of the wire specimen changed greatly during draw bending. Additionally, the change in the texture resulting from draw bending obtained by the finite element method (FEM) analysis of stress and the measured change in the texture showed good qualitative agreement. © 2012 Elsevier B.V. All rights reserved.
Contents 1. 2.
3.
4.
5.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 2.1. CBD process and materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 2.2. Draw bending in CBD process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2506 2.3. Evaluation method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2507 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2508 3.1. Changes in drawing tension and mechanical properties during rotary draw bending. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2508 3.2. Hardness distributions in cross sections of the wire specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2508 3.3. FEM analysis of rotary draw bending at various angular velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2509 3.4. Change in texture during draw bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2509 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2511 4.1. Relationship between elastic energy of dislocations and plastic strain energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2511 4.2. Relationship between HV and plastic strain energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2512 4.3. Change in formation of texture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2512 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2513
∗ Corresponding author at: Yazaki Research and Technology Center, Yazaki Corporation, Mishuku 1500, Susono, Shizuoka 410-1194, Japan. Tel.: +81 55 9653207; fax: +81 55 9650479. E-mail address: [email protected] (J. Tokutomi). 0924-0136/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmatprotec.2012.06.008
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Nomenclature b Burgers vector radius of wire specimen after bending da db radius of wire specimen before bending plastic strain energy EP E0e elastic energy of edge dislocations E0s elastic energy of screw dislocations total self-energy per dislocation ET E residual energy (=compressive residual energy) L grain diameter n number of dislocations in a grain R radius of die B R1 and R2 directions of rotation mean distance between dislocations Rd Rn curvature radius in neutral plane of wire specimen V drawing speed plastic work increment WP Greek letters εbending bending strain εPij strain tensor of plastic range plastic strain in longitudinal direction εx diameter of shaft 0 radius of dislocation cores Lame’s constant dislocation density ij stress tensor ω angular velocity of shaft
1. Introduction Fine electrical wires are required to have good mechanical properties and high electrical conductivity for use in applications such as automobiles, home electronics and industrial robots. However, there is a risk of breakage during the manufacture and use of fine wires, since their cross-sectional areas are extremely small. Consequently, high strength and ductility are required for fine wires. There are several methods of strengthening metallic materials. The authors have focused on ultrafine-grain (UFG) metallic materials formed by severe plastic deformation (SPD), which markedly suppresses electrical conductivity. Various SPD processes have been developed for manufacturing UFG metallic materials with grain sizes smaller than 1 m. They can be summarized into three types of processes as reviewed by Azushima et al. (2008): accumulative roll bonding (ARB), equal channel-angular pressing (ECAP) and high-pressure torsion (HPT). In the ARB process, the stacking of sheets and conventional roll bonding with a 50% reduction per cycle are repeated, meaning that a very large plastic strain can be applied to the material. Saito et al. (1999) conducted a basic study of texture formation and tensile strength for ARB using aluminum (1100), Al–Mg alloy (5083) and Ti-added interstitial free steel. In ECAP, pure shear deformation can be repeatedly imposed on a material so that an intense plastic strain is produced without any change in the cross-sectional dimensions of the workpiece. Segal (1995) investigated structure formation, mechanical properties and physical properties in ECAP by applying various equivalent strains and shear directions. In the HPT process, a very thin disk is compressed in a closed die by a very high pressure, and then torque is provided by a punch with contact friction at the interface between the punch and disk. Valiev et al. (1993) applied the HPT process at various temperatures to investigate the change in mechanical properties and microstructural evolution.
However, it is difficult to apply these SPD processes to existing practical and mass production techniques for bulky metals. On the other hand, Negroni et al. (1986) used copper as a test material and investigated the change in various mechanical properties in deep wire drawing (WD) at a large strain with up to 99% reduction in area. It was clarified by Hanazaki et al. (2010) that WD is a type of SPD process, in which the metallic substructure of a wire specimen formed by WD consists of UFGs with a dislocation substructure existing inside the grains. These studies indicate that WD processes can be applied to practical use and mass production. Although the mechanism of strength improvement in UFG materials has been clarified, that of ductility improvement is still unclear. In one of our previous studies, the continuous bending-drawing (CBD) method was proposed to improve the ductility of WD specimens (Yanagimoto et al. (2011)). It was confirmed that draw bending in the final stage was able to produce fine wires with excellent mechanical properties. Additionally, Tokutomi et al. (2012) confirmed that a wire specimen subjected to the CBD process had dislocation substructures inside the UFGs. However, the crosssectional shapes of wire specimens are irregular when the shaft in the bending area is fixed. Moreover, the risk of breakage is greatly increased because the tension increases during drawing and almost reaches the breaking force. In this study, a new CBD method using a rotary draw bending die is proposed. The die is designed to decrease the drawing tension and prevent the formation of an irregular cross-sectional shape by constraining the rotation of the shaft. We investigate the change in mechanical properties of a wire processed using the rotary draw bending process. After that, the total processing energy required by the rotating draw bending process is determined by finite element method (FEM) analysis, and the relation between this energy and the change in the mechanical characteristics is discussed. 2. Experimental 2.1. CBD process and materials A dilute Cu–Sn alloy is used in this investigation. The chemical composition of the alloy is shown in Table 1. As shown in table, the alloy contains only a small amount of Sn as the alloying element. This alloy was the same as that used by Tokutomi et al. (2012). Fig. 1(a) shows the total CBD process in this investigation. A rod of the alloy was first prepared by groove-rolling and annealing. Then the internal strain was eliminated by annealing. The grooverolled specimen was annealed at 673 K for 60 min under a nitrogen atmosphere before the WD process, resulting in a recrystallized structure. The rod was elongated by WD with multiple passes. It was then subjected to WD at room temperature with lubrication. The diameter of the initial rod was 7.7 mm, whereas the diameter of the fine wire after 23 passes of WD was 210 m; thus, the maximum total area reduction was 99.93%, which corresponded to a total equivalent strain of 7.2. The WD specimen had a lamellar microstructure elongated in the drawing direction, and dislocation substructures were formed within the lamellar microstructure. The grain boundary spacing in the WD specimen was approximately 150 nm. Draw bending was imposed in the final step of the CBD process. This was performed to induce plastic deformation in different loading directions to control the strength and elongation of the fine wire. 2.2. Draw bending in CBD process Fig. 1(b) shows details of the draw bending die. The position of draw bending die D is fixed, whereas the positions of dies A–C can be changed to control the bending radius. Another feature of the
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Table 1 Chemical composition of the Cu–0.3 mass% Sn alloy (mass%).
Cu–0.3 mass% Sn
O
As
Sn
Fe
P
Pb
Cu
0.014
<0.001
0.266
<0.001
0.001
<0.001
Bal.
Fig. 1. Schematic diagram showing sample setup during CBD. (a) Total process of CBD and (b) dimensions of the rotational draw bending die.
rotary draw bending die is that the rotational direction and angular velocity of the shaft can be controlled. The draw bending conditions are shown in Table 2. The wire was drawn in the Y-direction at a relatively low speed of 1.66 mm/s. The cases in which the shaft rotates in the same direction and in the reverse direction relative to the drawing direction are denoted by positive and negative signs, respectively. Note that at an angular velocity of 11.12 rad/s and a drawing speed of 1.66 mm/s, the velocity ratio is 1:1. Hence, when the angular velocity of the shaft exceeds 11.12 rad/s, the wire is driven by the rotating shaft. The bending strain (εbending ) of draw bending was estimated by Yanagimoto et al. (2011) using the equation
εbending = ln 1 +
da Rn
1+
db Rn
(1)
here Rn is the curvature radius in the neutral plane of the wire specimen, and da and db are the radii of the wire specimen after and before bending, respectively. Draw bending was executed with a curvature radius of 0.84 mm, corresponding to an equivalent Table 2 Drawing bending conditions used in present study. Angular velocity [rad/s]
−11.12 0.0 11.12, 22.24, 33.36
Drawing speed [mm/s] Process temperature [K]
1.66 298
(Direction of rotation: R1) (Fixed) (Direction of rotation: R2)
bending strain of 0.23, which was selected to realize the optimal strength-ductility balance according to the experimental results in our previous study. 2.3. Evaluation method A tensile test on the wire specimens after draw bending was carried out at a nominal strain rate of 3 × 10−3 s−1 at room temperature. The strength of the wire specimens was measured using an Instron-type testing machine with cord and yarn grips, which prevented jaw breaks of the wire specimens. The elongation of wires was measured using a video extensometer with two foam polystyrene spheres containing slits as markers. The initial gauge length was 50 mm. The microstructural and crystallographic features of the wire specimens after the WD and draw bending processes were characterized by electron backscatter diffraction (EBSD) measurement using a field-emission-type scanning electron microscope (FE-SEM) operated at 25 kV and equipped with a TSL orientation imaging microscopy system. Fig. 2 shows the measurement area on the cross section of a wire specimen. The microstructures of the specimens subjected to WD and draw bending were measured 90 m from their center using mapping areas of 15 m × 15 m. The cross sections of the wire specimens were subjected to ion-beam polishing at 4.5 kV for 8 h in an argon gas atmosphere. Experimental hardness tests on the cross sections of specimens were performed with a Vickers microhardness tester. The
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Fig. 2. Schematic diagram showing the EBSD measurement area on the cross section of a wire specimen: (a) WD specimen and (b) drawing specimen.
compressive load and holding time of the indenter were 0.01 gf and 10 s, respectively. The hardness on the cross sections of wire specimens were measured at various distances from their centers with intervals of 10 m. The surface of each wire was electropolished by mechanical polishing to remove the processing history.
3. Results 3.1. Changes in drawing tension and mechanical properties during rotary draw bending Fig. 3 shows the change in drawing tension during draw bending at various angular velocities. When the shaft rotated in the opposite direction to the drawing direction, such as for velocities of −11.12 rad/s and 0.00 rad/s, the drawing tension was approximately 8 N. However, when the shaft rotated in the drawing direction, such as for velocities of 11.12 rad/s, 22.24 rad/s and 33.36 rad/s, the drawing tension was approximately 6.5 N. The drawing tension decreased with increasing angular velocity when the shaft was rotated in the opposite direction to the drawing
Fig. 3. Change in drawing tension of wire specimens during draw bending.
direction. However, when the rotating speed was increased in the drawing direction, the drawing tension remained unchanged. Fig. 4 shows the nominal stress-strain curves of the wire specimens processed at various angular velocities. The ultimate tensile strength (UTS) and 0.1% proof stress were the same for all wire specimens processed by rotary draw bending, and reached approximately 750 MPa and 530 MPa, respectively. The UTS and 0.1% proof stress of the rotary draw bending specimens were almost 40 MPa and 150 MPa lower than those of the WD specimen, respectively. The total elongations of the wire specimens were 3.1% and 3.6%, respectively, when the shaft rotated at angular velocities of −11.12 rad/s and 33.36 rad/s. The total elongation increases as the drawing tension decreases as shown in Fig. 4. 3.2. Hardness distributions in cross sections of the wire specimens The hardness distributions on the cross sections of the wire specimens processed by rotary draw bending were measured since a change in the mechanical properties was confirmed. Fig. 5 shows the change in the Vickers hardness (HV) on the cross sections of
Fig. 4. Nominal stress-strain curves of the Cu−0.3 mass% Sn alloy specimens processed at various angular velocities.
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flexural center of the wire was about 10 HV lower than that of the WD specimen. In contrast, the hardness on the inside of the wire after draw bending was 30 HV lower than that at the flexural center. This result indicated that considerable deformation-induced softening occurred on the inside of the bend during draw bending. Moreover, when the directions of shaft rotation and drawing were the same and the angular velocity of the shaft was increased, the amount of softening increased.
3.3. FEM analysis of rotary draw bending at various angular velocities
Fig. 5. Change in HV of wire specimens processed at various angular velocities.
wire specimens processed at various angular velocities, where each value of HV is the average of five measurements. The values of HV from the center to the inside of the wire were less than those of the WD specimen. However, the values of HV from the center to the outside of the wire were almost identical to those of the WD specimen. This meant that deformation-induced softening occurred on the inside of the bend. The change in the hardness distribution of various parts of the wire specimen processed at an angular velocity of 11.12 rad/s is shown in Fig. 6. The hardness distribution was measured on cross sections of the wire specimen at the flexural center and after draw bending. The hardness distribution of the wire from the center to the outside at the flexural center was similar to that of the WD specimen. However, the hardness from the center to the inside at the
The plastic strain in a wire specimen during draw bending was estimated by FEM analysis. The wire specimen was constructed from 3D solid elements, and a simulation was carried out using ANSYS Mechanical software. The wire model was assumed to have a continuous strain distribution, and precise material properties were inputted. Drawing displacement was applied in the longitudinal direction of the wire specimen, and the radial direction was not constrained. The mass density, Young’s modulus, Poisson’s ratio and the friction coefficient between the die and the wire specimen used in the FEM simulation were 8.9 × 103 kg/m3 , 130 GPa, 0.33 and 0.12, respectively. The true stress-strain curve of the WD specimen obtained from the tensile test shown in Fig. 4 was used as the mechanical property. Fig. 7 shows contour figures of the equivalent true stress and equivalent true plastic strain during draw bending with an angular velocity of 11.12 rad/s. Fig. 8 shows the FEM simulation result of the true plastic strain in the longitudinal direction of the wire specimen for various angular velocities. The principal stress and strain were in the longitudinal direction of the wire specimen, and the other strain values were considerably lower than the principal stress and strain. Therefore, only the plastic strain in the longitudinal direction is shown in Fig. 8. In the case of inward bending, a compressive plastic strain of approximately εx = 0.30 was applied in the bending range, and then a tensile plastic strain was applied in the rebending range. Additionally, the tensile plastic strain in the rebending range decreased with the inverse rotation of the shaft and an increase in the angular velocity. This means that the movement of the shaft had a decisive effect on the plastic strain in the rebending range. This phenomenon was caused by the increase in the shearing plastic strain on the XY plane. In particular, a distinctive change occurred in the processing history in the case of inward bending. In the case of outward bending, it was confirmed that the same tensile plastic strain was continuously applied in the bending and rebending ranges at various velocities.
3.4. Change in texture during draw bending
Fig. 6. Change in hardness distribution of wire specimen in flexural center and after draw bending processed at angular velocity of 11.12 rad/s.
Fig. 9 shows the change in texture during draw bending with an angular velocity of 11.12 rad/s. The texture was measured by EBSP in the area shown in Fig. 2. The 0 0 1 and 1 1 1 textures were the main textures in the cross section of the WD specimen. On the inside of the bend at the flexural center, the textures were dispersed as shown in Fig. 9(b). On the other hand, after draw bending, the 0 0 1 and 1 1 1 textures increased in concentration (Fig. 9(d)), whereas on the outside of the bend the concentrations of the 0 0 1 and 1 1 1 textures were hardly changed as shown in Fig. 9(c). However, on the outside of the bend after draw bending, the textures were dispersed slightly. When the change behavior of the texture was compared at each measurement point, markedly different behavior was found on the inside and outside of the bend.
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Fig. 7. Results of the FEM simulation during draw bending at angular velocity of 11.12 rad/s: (a) equivalent true stress distribution and (b) equivalent true plastic strain distribution.
Fig. 8. Results of FEM simulation showing applied plastic strain in longitudinal direction: (a) definition of the range of deformation, (b) angular velocity of 33.36 rad/s, (c) angular velocity of 11.12 rad/s and (d) angular velocity of −11.12 rad/s.
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Fig. 9. Change in texture during draw bending: (a) WD specimen, (b) and (c) correspond to the specimen on the inside of the bend, (d) and (e) correspond to the specimen on the outside of the bend. (b) and (d) were obtained at the flexural center, (c) and (e) were obtained after draw bending.
4. Discussion
relationship between the mean distance between the dislocations and the dislocation density is
4.1. Relationship between elastic energy of dislocations and plastic strain energy
1 Rd = √
In this section, the plastic strain energy obtained from FEM analysis and the elastic energy obtained from the theory of elasticity of dislocations are compared, and the validity of the energy calculated by FEM analysis is discussed. Compressive deformation and tensile deformation occurred in the longitudinal direction of the wire specimen during draw bending, particularly on the inside of the wire (shown in Fig. 8). It was reported by Hasegawa et al. (1975) that the movement of dislocations in a grain is changed significantly by the reversal of stress. When the elastic energy of the dislocation motion and the plastic strain energy calculated from FEM analysis are predicted quantitatively, the correlation between them can be determined. First, the plastic strain energy on the inside of the bend during draw bending was calculated by FEM analysis. This value was used in our quantitative evaluation, and a value of 2.29 × 1010 J was obtained using the following equation:
EP =
ıW P =
ij · dεPij
(2)
On the other hand, to estimate the motion of dislocations, it is necessary to consider the energy required to move the dislocations inside a grain. The total elastic energy required to move the dislocations was considered in the following quantitative evaluation by Kato (2007) and is equal to the sum of the elastic energies of the screw dislocations and edge dislocations as follows. E T = E0s + E0e = =
b2 ln 4
R
1 B2 ln 2
d
r0
+
R
B2 ln 4 (1 − )
R d
r0
(3)
d
r0
here ET is the total self-energy per dislocation, E0s is the elastic energy of the screw dislocations, E0e is the elastic energy of the edge dislocations, is Lame’s constant (=41.4 GPa), b is the Burgers vector (=0.256 nm), Rd is the mean distance between dislocations, and r0 is the radius of the dislocation cores (=0.0224 nm). The
(4)
where is the dislocation density (=4.8 × 1014 m−2 ) of the WD specimen. This value was empirically estimated by Tokutomi et al. (2012) by removing a thin cross-sectional sample from a WD specimen using a focused ion beam (FIB) then observing the dislocations in a grain using a transmission electron microscope (TEM). The number of dislocations in each grain was derived from the relationship between the mean distance between dislocations and the spacing between neighboring agglomerations of dislocations. Additionally, if the spacing between agglomerations of dislocations is assumed to be half of the grain diameter, the number of dislocations can be shown to be L 2R √ L = 2
n=
(5)
here n is the number of dislocations in a grain and L is the grain diameter (=0.145 m). Therefore, from the product of Eqs. (3) and (5), the total elastic energy of all dislocations in a grain is ET =
1 nb2 ln 2
R r0
(6)
The total elastic energy of all the dislocations in a grain was estimated to be 7.87 × 1010 J using Eq. (6). The total elastic energy of all the dislocations in a grain required for their motion and the plastic strain energy determined by FEM analysis were compared. The generation and annihilation of dislocations during draw bending cannot be estimated using Eq. (6). Therefore, it is very difficult to precisely estimate the plastic strain energy. However, we consider that a rough estimate of the plastic strain energy is possible, because the elastic energy of all the dislocations inside a grain and the plastic strain energy determined by FEM analysis have the same order of magnitude. Changes in the hardness and mechanical properties are closely related to the metallographic structure. In particular, the change in hardness may be strongly affected by the dislocation substructure. Therefore, the plastic strain energy obtained by FEM analysis can explain the decrease in hardness during draw bending.
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4.2. Relationship between HV and plastic strain energy We next discuss the correlation between the change in HV on the inside of the bend and the plastic strain energy obtained from FEM analysis. Then, the change in the metallographic structure is considered on the basis of this discussion. As shown in Fig. 7, the principal stress and principal strain were in the longitudinal direction of the wire specimen. The plastic strain energy was calculated using Eq. (2) for various angular velocities and both rotational directions of the shaft, particularly on the inside of the bend. The residual energy on the inside of the bend during draw bending is denoted by E and is given by E = Ebending − Erebending
(7)
here Ebending is the plastic strain energy in the bending range and Erebending is the plastic strain energy in the rebending range. Ebending and Erebending were both obtained from Eq. (6). It was confirmed that the main types of plastic strain energy in the bending range and rebending range were compression and tension, respectively, in the longitudinal direction of the wire specimen. In Eq. (7), E is the mean compressive residual energy during draw bending, namely, a large amount of compression energy remained after draw bending and rebending. Fig. 10 shows the relationship between the compressive residual energy and HV on the inside of the bend. The HV was measured at the position of the node used to calculate the plastic strain energy. The HV decreased substantially as the compressive residual energy was increased. The relationship between the change in HV and the compressive residual energy was closely related to the microstructural evolution. It is assumed that the dislocations were in a stable state owing to the tensile energy during WD, since the energy in the compression direction maintained the state of the dislocations. Since the compression energy was loaded on the inside of the bend during draw bending, it can be considered that the compression energy also induced the piling up of dislocations in the opposite direction. Consequently, a difference in hardness occurred since
Fig. 10. Change in HV of wire specimens during drawing as a function of compressive residual energy.
the dislocation substructures were changed. Note that the angular velocity and rotational direction of the shaft may be used to control the compressive energy. 4.3. Change in formation of texture In this section, the relationship between the changes in the principal stress during draw bending and the texture is discussed. We clarified that tension and compression on the inside and
Fig. 11. Comparison of the measured and the texture predicted change in texture during draw bending with an angular velocity of 11.12 rad/s: (a) inverse pole figure map for various cross sections, (b) stress distribution in longitudinal direction and measurement cross sections and (c) rotations in a fcc metal under tension and compression (Calnan and Clews, 1950).
J. Tokutomi et al. / Journal of Materials Processing Technology 212 (2012) 2505–2513
outside of the bend were applied to the wire specimen (shown in Fig. 8). Moreover, a change in texture during draw bending was confirmed (shown in Fig. 9). The general behavior of rotations in a face-centered cubic (fcc) metal, such as pure copper or copper alloy, under tension and compression was reported by Calnan and Clews (1950) and Calnan (1954). When their theory is applied to the calculation of stress by FEM, the results of which are shown in Fig. 8, the change in texture can be predicted. Fig. 11 shows a comparison of the measured and predicted change in texture during draw bending with an angular velocity of 11.12 rad/s. The measured changes in the texture showed good qualitative agreement with the change in texture calculated by FEM analysis. Namely, the deformation-induced texture formation of a copper polycrystal is affected by the applied stress during draw bending. Additionally, the direction of the principal stress obtained by FEM analysis may qualitatively indicate the change in orientation. 5. Conclusions The mechanical behaviors of Cu–Sn alloy wire specimens processed by rotational draw bending and the relationship between the HV on the cross section and the compressive residual energy during draw bending were systematically investigated. During draw bending, particularly on the inside of the bend, the WD specimen was subjected to compressive/tensile strain in the longitudinal direction, and the softening induced by plastic deformation was promoted by increasing the compressive residual energy. Additionally, it is considered that the increase in the compressive residual energy is related to the change in mechanical properties. Consequently, there was a large difference in the hardness distributions on the inside and outside of the bend, namely, the mechanical properties of the wire specimen were changed greatly during draw bending. The change in the texture obtained by FEM analysis of the stress and the measured change in the texture showed good qualitative agreement.
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Acknowledgments This study was financially supported by a grant-in-aid for Scientific Research on Innovative Areas, “Bulk Nanostructured Metals”, through MEXT, Japan (Contract No. 22102005), which is gratefully appreciated. Yazaki Parts Company is also acknowledged for supplying the copper rods used in this study. References Azushima, A., Kopp, R., Korhonen, A., Yang, D.Y., Micari, F., Lahoti, G.D., Groche, P., Yanagimoto, J., Tsuji, N., Rosochowski, A., Yanagida, A., 2008. Severe plastic deformation (SPD) processes for metals. CIRP Annals–Manufacturing Technology 57, 716–735. Calnan, E.A., Clews, C.J.B., 1950. Deformation textures in face-centered cubic metals. Philosophical Magazine 41, 1085–1100. Calnan, E.A., 1954. Deformation textures of face-centred cubic metals. Acta Metallurgica 2, 865–873. Hanazaki, K., Shigeiri, N., Tsuji, N., 2010. Change in microstructures and mechanical properties during deep wire drawing of copper. Materials Science and Engineering A 527, 5699–5707. Hasegawa, T., Yakou, T., Karashima, S., 1975. Deformation behaviour and dislocation structures upon stress reversal in polycrystalline aluminium. Materials Science and Engineering 20, 267–276. Kato, M., 2007. Introduction to the Theory of Dislocations, Sixth ed. Shokabo, Tokyo, pp. 42–48. Negroni, F.D., Thomsen, E.G., Kobayashi, S., 1986. A drawing modulus for multi-pass drawing. CIRP Annals–Manufacturing Technology 35, 181–183. Saito, Y., Utsunomiya, H., Tsuji, N., Sakai, T., 1999. Novel ultra-high straining process for bulk materials-development of the accumulative roll-bonding (ARB) process. Acta Materialia 47, 579–583. Segal, V.M., 1995. Materials processing by simple shear. Materials Science and Engineering A 197, 157–164. Tokutomi, J., Hanazaki, K., Tsuji, N., Yanagimoto, J., 2012. Changes in mechanical characteristics of pre-annealed wires of Cu–Sn alloy manufactured by continuous draw bending. Materials Transactions 53, 116–122. Valiev, R.Z., Korznikov, A.V., Mulyukov, R.R., 1993. Structure and properties of ultrafine-grained materials produced by severe plastic deformation. Materials Science and Engineering A 168, 141–148. Yanagimoto, J., Tokutomi, J., Hanazaki, K., Tsuji, N., 2011. Continuous bendingdrawing process to manufacture the ultrafine copper wire with excellent electrical and mechanical properties. CIRP Annals–Manufacturing Technology 60, 279–282.