2024 Volume 65 Issue 2 Pages 130-137
Wires of a Cu–3.8 wt% Zr alloy were produced by conform extrusion followed by wire drawing up to 0.2 mm in diameter (S wire), or by conform extrusion and subsequent annealing during wire drawing up to 0.2 mm (IA wire). The effects of microstructure on the strength and electrical conductivity of the S and IA wires were investigated. The severely drawn S and IA wires had a mixed microstructure consisting of a Cu parent phase with fine grains, fibrous eutectics elongated along the drawing direction, and granular eutectics. The 0.2% proof stress (σ0.2) and tensile strength (σu) of the S and IA wires increased monotonically with increasing drawing ratio (η). The S wire with η = 7.8 exhibited large values of σ0.2 = 1080 MPa and σu = 1320 MPa. The S and IA wires having the mixed microstructure are strengthened primarily by high density of dislocations and grain refinement in the Cu phase and by the presence of fibrous and granular eutectics. The electrical conductivity (E) of the S wire increased in the early stage of wire drawing and then began to decrease, dropping to 42% IACS at η = 7.8. The increase in E is caused by refining of the eutectics, which was formed during casting, toward the granular or fibrous form. The E value of the IA wire after annealing was high, 72%IACS, and then decreased as η increased. Values of E of the S and IA wires with the mixed microstructure was estimated by applying rules of mixtures. The estimated values of E are in agreement with the measured values of E. It is shown that the presence of the fibrous and granular eutectics significantly increases the electrical conductivity.
This Paper was Originally Published in Japanese in J. Japan Inst. Copper 60 (2021) 16–23.
Fig. 2 SEM images of the vertical cross-sections of (a) the as-cast, (b) conform-extruded, (c) 5S, (d) 0.6S, and (e) 0.6IA specimens.
Currently, the thickness of copper-alloy wires used as components in electronic devices is extremely small. This has led to a demand for highly conductive copper-alloy wires with higher strength to prevent breakage.
Muramatsu et al. conducted a series of studies on the mechanical properties and electrical conductivities of Cu–0.72 to 7.2 wt%Zr alloy wires (hereafter, wt% will be omitted in the notation) to develop copper-alloy wires with both excellent strength and electrical conductivity.1–3) In general, the strength increased with increasing Zr concentration, while the electrical conductivity decreased. In Cu–Zr alloys containing approximately 2% Zr or more, in addition to a primary Cu phase with dendritic structures, eutectics consisting of a Cu5Zr intermetallic compound phase and a Cu phase were clearly formed between the primary dendrite arms.3) The presence of these eutectics increases the strength of the drawn wires and decreases their electrical conductivity. The Cu–7.2(5 at%)Zr alloy wire with a drawing ratio of η = 8.6 achieved a remarkably high tensile strength, σu, of 2.2 GPa (η = ln(A0/A), where A0 and A represent the cross sectional area of a wire before and after deformation, respectively). However, the electrical conductivity, E, became significantly low (16%IACS). Based on microstructural observations of the drawn wires, the significant strengthening of the drawn wire was attributed to composite strengthening by a Cu phase and a Cu9Zr2 intermetallic compound phase or grain boundary strengthening by the formation of nanostructures of the Cu phase and the Cu9Zr2 intermetallic compound phase with a layered structure. However, detailed analyses of the strengthening mechanisms of drawn wires have not been carried out, and the reason for the low electrical conductivity of the drawn wires has not been quantitatively discussed.
Recently, Muramatsu et al.4) and Nomura et al.5) investigated the properties of a Cu–0.29Zr alloy subjected to intermediate annealing between casting followed by rolling and subsequent wire drawing or Cu–0.29Zr alloy subjected to equal-channel angular pressing (ECAP)-conform processing before rolling and wire drawing to improve the electrical conductivity and strength of the alloy. Although eutectics are present in this cast alloy, their effects on the strength and electrical conductivity can be neglected because only a small amount of eutectics are formed. For example, the grain size (grain-boundary spacing) was refined to 120 nm by the rolling and wire drawing with a deformation ratio of η = 5.4 after the ECAP-conform processing. The alloy showed good strength and ductility with a tensile strength, σu, of 790 MPa and a total elongation, εt, of 3.9%. However, the electrical conductivity of the drawn wire decreased from 88% to 73%IACS.5) Watanabe et al.6) and Kunimine et al.7) performed quantitative analyses of the obtained tensile properties and electrical conductivities based on detailed microstructural observations.
In this study, the changes in the strength and electrical conductivity of a Cu–3.8Zr alloy subjected to wire drawing were investigated based on detailed microstructural observations. Electrical conductivity was quantitatively evaluated by applying the rules of mixtures.
Round bars of the Cu–3.8Zr alloy with a diameter, d, of 14 mm were produced via vertical upward continuous casting (VUCC). The round bars were subjected to the conform-extrusion process to reach d = 10 mm. Thereafter, the samples were processed by wire drawing to obtain d = 5 mm (η = 1.4), 0.6 mm (η = 5.6), and 0.2 mm (η = 7.8), which are referred to as “5S wire”, “0.6S wire”, and “0.2S wire”, respectively. The samples that were wire-drawn after conform-extrusion process are collectively referred to as “S wires”. The wheel diameter of the conform-extrusion machine was 350 mm, and the feed rate was 5 m/min. Furthermore, the 5S wires were subjected to an intermediate annealing at 650°C for 1 h and subsequently wire-drawn to d = 0.6 mm (η = 4.2) and 0.2 mm (η = 6.4), respectively. These wires are referred to as “5IA wire”, “0.6IA wire”, and “0.2IA wire”, respectively. In addition, these wires are collectively expressed as “IA wires”.
Microstructural observations of the samples were carried out using scanning electron microscopy (SEM; JSM-7100F, JEOL, Tokyo, Japan) and transmission electron microscopy (TEM; Tecnai G2 30, FEI, Hillsboro, OR, USA). The methods for preparing the samples for SEM observations have already been described in detail in our previous paper.6) For TEM observations, the wires were firstly polished into strips with a thickness of 100 µm, followed by ion beam processing at a voltage of 5.0 kV using an ion slicer (EM-09100IS, JEOL, Tokyo, Japan) to obtain thin-film specimens. However, the wires with diameters smaller than approximately 0.5 mm could not be processed for TEM observations because their dimensions were too small.
The samples before the wire drawing were tensile-tested using a universal testing machine (AUTOGRAPH AG-X, Shimadzu, Kyoto, Japan). Flat tensile specimens with shoulders and a gauge section were cut from the round bars and subjected to tensile testing. The gauge section was cut with a length of 5 mm, width of 3 mm, and thickness of 0.3 mm. Regarding the wire-drawn samples, tensile tests were carried out using a universal testing machine (AUTOGRAPH AG-I, Shimadzu, Kyoto, Japan) with a distance of 100 mm between the grippers.
Dislocation density was evaluated by the X-ray diffraction (XRD) experiments using an X-ray diffractometer (RINT-2500, Rigaku Corporation, Tokyo, Japan) with Cu-Kα radiation. The amount of strain was determined from the full width at half maximum (FWHM) of the XRD peaks corresponding to the (111), (200), (220), and (311) planes using the modified Williamson-Hall method8) and converted to the dislocation density.
The electrical conductivity was determined as E = (ρ0/ρ) × 100 using the measured resistivity, ρ, by the four-terminal method and the resistivity, ρ0, of pure copper (ρ0 = 17.24 nΩm).
Hardness tests were performed using a nanoindenter (Hysitron TI 980 Triboindenter, BRUKER, Billerica, MA, USA) at a peak force of 90 µN.
Figure 1 shows the electrical conductivity, E, as a function of the inverse of the sample diameter, d−1, for the as-cast bar, conform-extruded bar, S wires and IA wires. E first increased by the conform-extrusion process and subsequent wire drawing to at least d = 5 mm, and then decreased with an increase in d−1. E also increased by the treatment of intermediate annealing on the 5S wire, followed by a decrease after subsequent wire drawing.
Electrical conductivity (E) as a function of the inverse of the diameter (d−1) for the as-cast, conform-extruded, S, and IA specimens.
The tensile strength, σu, of the as-cast bar was 440 MPa. σu increased monotonically by conform-extrusion and subsequent wire drawing. The tensile strengths of the 5S and 0.2S wires were 800 and 1320 MPa, respectively. σu decreased by the recrystallization caused by intermediate annealing of the 5S wire but increased again with subsequent wire drawing.
Table 1 summarizes the 0.2% proof stress, σ0.2, σu, total elongation, εt, and E for the 5S, 0.6S, 0.2S, 5IA, 0.6IA and 0.2IA wires. In all the cases with d = 5, 0.6, and 0.2 mm, σ0.2 and σu were higher in the S wires, while εt and E were higher in the IA wires. This was due to the recrystallization caused by intermediate annealing.
Figures 2(a) to (e) show SEM images of the vertical cross-sections of the Cu–3.8Zr alloy for the as-cast bar, conform-extruded bar, 5S wire, 0.6S wire, and 0.6IA wire. In the as-cast bar, dendritic primary Cu phases (black areas) and eutectics (white areas) were observed. According to Muramatsu et al.,3) eutectics are composed of a layered Cu5Zr phase and a Cu phase. After conform-extrusion, the eutectics were elongated in the direction at an angle of approximately 30° to the extrusion direction. This can be attributed to the shear stress applied during the conform-extrusion process. In addition, the primary Cu phase recrystallized and possessed equiaxed grains owing to the heat generated during the conform-extrusion process; the average grain size, DCu, was 480 nm. The recrystallization of the primary Cu phase during the conform-extrusion process has already been reported by Nomura et al.5) In the 5S wire, the initial morphology of the eutectics observed in the as-cast bar was fragmented into granular and fibrous forms, unlike that after the conform-extrusion process. The grains in the Cu phase were elongated along the wire-drawing direction, and the grain boundary spacing parallel to the wire-drawing direction was defined as DCu. The value of DCu was 280 nm for the 5S wire. In the 0.6S wire, the grains in the Cu phase were further elongated along the wire-drawing direction, and DCu was 130 nm. In addition, the fibrous eutectics elongated along the wire-drawing direction and the granular eutectics were mixed. Observations from the transverse cross-sections revealed that the eutectics were almost circular; thus, it was confirmed that the morphologies of the eutectics were fibrous and granular. The average diameter, Df, of the fibrous eutectics was 480 nm, and the average diameter, Dg, of the granular eutectics was 460 nm. For the 0.2S wire, a DCu of 90 nm, Df of 370 nm, and Dg of 450 nm were obtained. That is, when the wire-drawing process was performed from d = 0.6 mm to d = 0.2 mm, the grains in the Cu phase and fibrous eutectics were further elongated along the wire-drawing direction. However, the shapes and dimensions of the granular eutectics remained unchanged. A mixed microstructure composed of fibrous and granular eutectics after the wire-drawing process has previously been reported by Muramatsu et al.3)
SEM images of the vertical cross-sections of (a) the as-cast, (b) conform-extruded, (c) 5S, (d) 0.6S, and (e) 0.6IA specimens.
By contrast, in the 5IA wire, which was obtained by annealing of the 5S wire, the Cu phase recrystallized with an average grain size of 760 nm. Similar to the S wires, the grains in the Cu phase and fibrous eutectics were elongated along the wire-drawing direction during the subsequent wire-drawing process; however, no changes in the shapes and dimensions of the granular eutectics were observed. In addition, by comparing Figs. 2(d) and 2(e), the IA wires possessed a larger fraction of granular eutectics than the S wires.
Figure 3(a) shows the TEM image of the as-cast bar. The primary Cu phase can be observed on the left and right edges, with a eutectic between them. Figure 3(b) shows the selected-area diffraction pattern (SADP) corresponding to Fig. 3(a). With respect to the Cu phase, only [011]Cu SADP was observed, which indicated that the two areas of the primary Cu phase and the Cu phase in the eutectic possessed the same crystal orientation. Reflection spots other than those of the Cu phase were also observed. As a result of an analysis using the lattice constant of pure Cu (0.3615 nm), it was found that a phase other than the Cu phase in the eutectic was identified as a cubic Cu5Zr intermetallic compound with a lattice constant of 0.687 nm,9,10) and possessed a cube-on-cube orientation relationship with the Cu phase in the eutectic. The fact that the primary Cu phase and eutectics possessed the same crystal orientation was also revealed by crystal orientation analysis using electron backscatter diffraction (EBSD) with SEM. This crystal orientation relationship has previously been reported by Muramatsu et al.3) through similar crystal orientation analyses of as-cast Cu–0.72Zr, Cu–1.4Zr, and Cu–2.9Zr alloys. In addition, they observed a microstructure composed of a layered Cu phase and Cu5Zr phase by SEM;3) the microstructure shown in Fig. 3(a) is similar to this microstructure. Figure 3(c) depicts a dark-field image captured using a reflection spot of spherical fine particles with a face-centered cubic (fcc) lattice system, which appeared in the SADP obtained from the primary Cu phase on the left side in Fig. 3(a). Spherical fine particles were observed not only in the primary Cu phase but also in the Cu phase in the eutectic. These fcc fine particles precipitated during cooling with a lattice constant of 0.416 nm and possessed a cube-on-cube orientation relationship with the Cu parent phase.11) The average diameter of the fcc precipitates was approximately 10 nm.
(a) Bright-field TEM image of the as-cast Cu–3.8Zr specimen, (b) [011]Cu SADP corresponding to (a), and (c) dark-field image of fcc precipitates in the same area as (a).
Figure 4(a) shows the TEM image of the conform-extruded bar. Recrystallized grains in the primary Cu phase were observed on the upper and lower sides of the figure, and eutectics were observed in the middle part of the figure. The average grain size in the Cu phase was 480 nm, which was the same as that measured by SEM. In area A, inside the eutectic, an intricate layered microstructure composed of a brighter Cu phase and darker Cu5Zr phase was observed. This layered microstructure was the same as that of the eutectics in the as-cast bar, as shown in Fig. 3(a). As shown in the SADP in Fig. 4(b) corresponding to area A, the cube-on-cube orientation relationship was maintained between the Cu and Cu5Zr phases in the eutectic. In contrast, in area B, no layered microstructure was observed; an intricate microstructure composed of the granular Cu and Cu5Zr phases were formed instead of the layered microstructure. As shown in the SADP in Fig. 4(c), corresponding to area B, the crystal orientations of the grains in the Cu and Cu5Zr phases inside the eutectic were different and did not match the crystal orientation of area A. In area B, it can be said that recrystallization occurred during the conform-extrusion process. Approximately 20% of the eutectics possessed recrystallized grains. In the recrystallized grains in the primary Cu phases and in the Cu phases inside the eutectics after the conform-extrusion process, both fcc fine precipitates formed during casting and those formed after recrystallization were observed.6) The former precipitates became incoherent with the Cu matrix owing to recrystallization, while the latter precipitates exhibited a cube-on-cube orientation relationship with the Cu matrix.
(a) TEM image of a conform-extruded Cu–3.8Zr specimen, (b) [011]Cu SADP corresponding to the area A in (a), and (c) SADP corresponding to the area B in (a).
In the 5S wire, both eutectic areas with a layered microstructure elongated along the wire-drawing direction, and eutectic counterparts with granular microstructures formed by the recrystallization were mixed inside the granular and fibrous eutectics, as observed by SEM. In addition, the layered Cu5Zr and Cu phases maintained a cube-on-cube orientation relationship, whereas the granular Cu5Zr and Cu phases exhibited different crystal orientations.
Figure 5 shows the TEM image of the 5IA wire obtained by performing intermediate annealing at 650°C for 1 h on the 5S wire. All the grains in the primary Cu phases were recrystallized by intermediate annealing, with an average grain size of 760 nm. As previously discussed, some of the grains in the eutectics were recrystallized by the conform-extrusion process; the number of recrystallized grains was further increased by intermediate annealing. Consequently, most of the granular eutectics observed by SEM were composed of recrystallized grains of the Cu and Cu5Zr phases, as shown in Fig. 5. By measuring the grain sizes of the Cu and Cu5Zr phases within the eutectics together, the average grain size was determined as approximately 120 nm. In contrast, few recrystallized grains were observed within the fibrous eutectics using SEM. The fine particles observed in the Cu phase on the lower side of Fig. 5 were fcc precipitates.
TEM image of the 5IA specimen.
Figure 6(a) shows the TEM image of a fibrous eutectic elongated along the wire-drawing direction in the 0.6S wire, and Fig. 6(b) shows the SADP corresponding to the fibrous eutectic observed in the middle part of Fig. 6(a). The grains of the Cu and Cu5Zr phases in the eutectics, elongated along the wire-drawing direction, were significantly refined, and the grain boundary spacing, DCu, was 20–50 nm. After the wire-drawing process from d = 10 mm to 0.6 mm, a cube-on-cube orientation relationship was maintained between the Cu5Zr intermetallic compound in the eutectics and Cu matrix. Figure 6(c) shows the TEM image of a granular eutectic in the 0.6S wire. The crystal orientations of the grains in the Cu and Cu5Zr phases differed. After the wire-drawing process to d = 0.6 mm, the mixed microstructure of the eutectics composed of the layered and granular microstructures were not present within the granular or fibrous eutectics, as observed by SEM. As shown in Figs. 6(a) and (c), the mixed microstructure of the eutectics was divided into layered and granular microstructures during the wire-drawing process; the layered and granular microstructures existed, separately. The 0.6IA wire also exhibited a similar microstructure.
(a) TEM image of a fibrous eutectic in the 0.6S specimen, (b) [011]Cu SADP corresponding to the area A in (a), and (c) TEM image of a granular eutectic in the 0.6S specimen.
As mentioned above, the shapes and dimensions of the granular eutectics did not change by the wire-drawing process from d = 0.6 mm to 0.2 mm. In contrast, the fibrous eutectics were elongated along the wire-drawing direction. Therefore, the presence of fibrous eutectics after the wire-drawing process can be attributed to the fact that the Cu and Cu5Zr phases within the eutectics had a cube-on-cube orientation relationship such that both phases were sheared by dislocations during wire drawing. In contrast, the presence of granular eutectics indicates that no macroscopic shear deformation occurred in the grains of the Cu and Cu5Zr phases with different crystal orientations, which were formed by the conform-extrusion process or intermediate annealing. In addition, as can be seen in Figs. 2(d) and 2(e), the reason for the presence of larger fraction of granular eutectics in the drawn IA wires, compared to the drawn 0.6S and 0.2S wires, is that the granular Cu and Cu5Zr phases increased by intermediate annealing.
Table 2 summarizes the volume fraction of the fibrous eutectics, ff, volume fraction of the granular eutectics, fg, dislocation density in the Cu phase, ρd, grain size in the Cu phase, DCu, mean linear intercept length of the Cu phase, LCu, and Zr concentration in the Cu phase, CZr, in the 5S, 0.6S, 0.2S, 5IA, 0.6IA, and 0.2IA wires. The area fractions of the fibrous and granular eutectics were determined from the SEM observations and considered as ff and fg, respectively. Details about the CZr will be explained later. In the following sections, the electrical conductivity and yield strength of each wire were evaluated using these values.
The 0.6S, 0.2S, 0.6IA, and 0.2IA wires can be considered as composite materials composed of the Cu phase, fibrous eutectics, and granular eutectics. In the 5S and 5IA wires, the eutectics generated during casting were dividing into fibrous and granular eutectics, and it could be considered that they had entirely divided into fibrous and granular eutectics. However, the 5S wire possessed a complex mixed microstructure composed of layered and granular structures within the fibrous and granular eutectics, respectively, as observed by SEM. TEM data for the 0.2S and 0.2IA wires were not available; therefore, their electrical conductivities could not be calculated. Therefore, in the present study, we attempted to estimate the electrical conductivities of 0.6S, 5IA, and 0.6IA wires using two types of rules of mixtures.
Let us consider the shape of the fibrous eutectic as a spheroid and assume that its aspect ratio is infinite. The electrical conductivity, E1, can then be expressed by the following simple parallel-type rule of mixtures12) using the electrical conductivity, ECu, of the Cu phase and electrical conductivity, Eef, of the fibrous eutectic.
| \begin{equation} E_{1} = f_{\text{Cu}}E_{\text{Cu}}/(f_{\text{Cu}} + f_{\text{f}}) + f_{\text{f}}E_{\text{ef}}/(f_{\text{Cu}} + f_{\text{f}}) \end{equation} | (1) |
Although it is difficult to determine the aspect ratio from the SEM and TEM images, it was estimated to be approximately 10 for the 0.6S, 0.6IA, and 5IA wires. In this study, the analysis was performed using eq. (1). In addition, when granular eutectics are dispersed in the Cu phase, the particle-dispersed-type rule of mixtures expressed by eq. (2)12,13) was used to evaluate the electrical conductivity, E2.
| \begin{align} &E_{2} = (3/4)\Big[\{(f_{\text{a}} - 1/3)E_{\text{Cu}} + (f_{\text{b}} - 1/3)E_{\text{eg}}\}\\ &\quad + \sqrt{\{(f_{\text{a}} - 1/3)E_{\text{Cu}} + (f_{\text{b}} - 1/3)E_{\text{eg}}\}^{2} + (8/9)E_{\text{Cu}}E_{\text{eg}}}\Big] \end{align} | (2) |
Here, Eeg is the electrical conductivity of the granular eutectics, fa and fb can be written as fa = fCu/(fCu + fg) and fb = fg/(fCu + fg).
First, the specific electrical resistance of the Cu phase, ρCu, which is the reciprocal of the electrical conductivity, ECu, of the Cu phase, is determined by the following calculation. The ρCu can be expressed by the following eq. (3) using the specific electrical resistance, ρ0, of pure Cu, dislocation density, ρd, grain-boundary density, Sv, and the Zr concentration in the Cu phase, CZr.14)
| \begin{equation} \rho_{\text{Cu}} = \rho_{0} + \varDelta \rho_{\text{dis}} \cdot \rho_{\text{d}} + \varDelta \rho_{\text{gb}} \cdot S_{\text{v}} + \varDelta \rho_{\text{Zr}} \cdot C_{\text{Zr}} \end{equation} | (3) |
Here, the Sv is given as Sv = 2/LCu.15) Δρdis and Δρgb are the contributions per unit dislocation density and grain boundary density to the specific electrical resistance, respectively; the theoretical values reported by Karolik et al.16) are Δρdis = 1.9 × 10−16 nΩm3 and Δρgb = 2.1 × 10−7 nΩm2. ΔρZr is the amount of change in the specific electrical resistance per unit Zr concentration in the Cu phase; the value of ΔρZr = 110 nΩm/at% has been reported.17) The contribution of precipitates to the specific electrical resistance can be considered negligible.18) ρCu was calculated by substituting the values of Δρdis, Δρgb, and ΔρZr, and the values of ρd, LCu, and CZr listed in Table 2 into eq. (3). The calculated ρCu was converted to ECu.
The CZr values listed in Table 2 were obtained from the literature.19) These values were obtained based on calculations using eq. (3) from specimens prepared by the same processes performed in this study using an as-cast Cu–0.29Zr alloy as the primary material, which can be practically regarded as single-phase Cu. It has been revealed that fine spherical fcc precipitates with a cube-on-cube orientation relationship to the Cu matrix were mechanically dissolved owing to the motion of dislocations caused by shear deformation during the wire-drawing process of the Cu–0.29Zr alloy.6,19) Differences in the sizes and volume fractions of these fcc precipitates and in the drawing ratio appeared as the difference in the Zr concentration in the Cu phase listed in Table 2. It was confirmed that the sizes and distributions of the fcc precipitates in the 0.6S, 5IA, and 0.6IA wires were almost the same as those in the Cu–0.29Zr alloy prepared by the same processes.
Next, the electrical conductivities of the eutectics, Eef and Eeg, were determined. The fibrous eutectics were composed of the Cu and Cu5Zr phases elongated along the wire-drawing direction, whereas the granular eutectics consisted of granular Cu and Cu5Zr phases. Thus, the electrical conductivities were estimated using the parallel-type rule of mixtures, expressed by eq. (1), and the particle-dispersed-type rule of mixtures, expressed by eq. (2), respectively. Because the specific electrical resistance of intermetallic compounds is generally much higher than that of Cu, the electrical conductivity of the Cu5Zr intermetallic compound in the eutectics was approximated as 0 Sm−1. Through SEM observations of the as-cast alloy, the volume fraction ratio of the Cu5Zr and Cu phases within the eutectics was determined to be 48:52. The electrical conductivity of the Cu phase within the eutectics was determined using eq. (3) in the following way. The average linear intercept length, L, measured without distinguishing between the elongated Cu and Cu5Zr phases within the eutectics was approximately 80 nm for the 0.6S and 0.6IA wires and approximately 310 nm for the 5IA wire. Similar measurements of the L values of the equiaxed grains within the granular eutectics revealed that the L values for all the 0.6S, 0.6IA, and 5IA wires were approximately 120 nm. The contribution of the grain boundaries to the electrical conductivity of the Cu phase within the eutectics, obtained using these values, did not consider the presence of the Cu5Zr/Cu interface. Here, 52% of the calculated value was used as the actual contribution from the grain boundaries of the Cu phase. In addition, the values used as CZr for the Cu phase within the eutectics were those for the Cu matrix in Table 2. With respect to ρd, the value in Table 2 was used for the 0.6S wire. In the 5IA wire, the granular eutectics exhibited a recrystallized granular microstructure. Although the fibrous eutectics in the 5IA wire were not recrystallized, ρd is expected to be low. Thus, the values of ρd for the granular and fibrous eutectics were set as 0. Because the grain shapes and sizes of the Cu and Cu5Zr phases within the granular eutectics in the 0.6IA wire were the same as in the 5IA wire, a low ρd is also expected for the 0.6IA wire and it was set as 0. Value of ρd in Table 2 was used for the Cu phase within the fibrous eutectics in the 0.6IA wire.
By substituting the obtained Eef, Eeg, and ECu, and the listed ff, fg, and fCu in Table 2 into eqs. (1) and (2), the amounts of changes in electrical conductivity due to the fibrous eutectics, ΔEef, and due to the granular eutectics, ΔEeg, were determined. The electrical conductivity of each wire was determined by adding ΔEef and ΔEeg to the ECu of each wire. The calculation results are presented in Table 3. For all the wires, the calculated values agreed with the measured values, indicating that the measured values could be explained using the rules of mixtures. The contributions of the fibrous and granular eutectics to the electrical conductivity are shown in parentheses in Table 3. For example, the presence of eutectics reduced the electrical conductivity by 17%IACS for the 0.6S wire and by 21%IACS for the 0.6IA wire. It can be assumed that the presence of eutectics reduces the electrical conductivity; indeed, it was confirmed that the electrical conductivity was significantly reduced by eutectics.
As shown in Fig. 1, when the as-cast round bar was subjected to the conform-extrusion process and subsequent wire drawing, the electrical conductivity, E, first increased and then decreased after d = 5 mm. Next, this result will be discussed. The eutectics in the as-cast alloy possessed a three-dimensional shape, covering the dendrites composed of the primary Cu phase (Fig. 2(a)). This morphology of the eutectics inhibits electron flow, resulting in low electrical conductivity. Through the conform-extrusion and wire-drawing processes, the net-like eutectics were broken by shear deformation and simultaneously aligned along the wire-drawing direction, as shown in Figs. 2(b) and (c). This microstructural change led to an increase in the electrical conductivity owing to the elimination of the barriers composed of Cu5Zr phase with low electrical conductivity that impeded the electron flow. After the wire drawing to d = 5 mm, it can be considered that the electrical conductivity was decreased mainly due to the increase in dislocation density, grain boundary density, and Zr concentration in the Cu phase.
4.2 Evaluation of yield strengthTable 4 lists the nanoindentation hardness of the Cu phase, HCu, and of the eutectics, He, in the 0.6S, 0.2S, 0.6IA, and 0.2IA wires. Because no differences in hardness were observed between the fibrous and granular eutectics in the wires, the average values of hardness measured within the fibrous and granular eutectics are shown in Table 4. As expected, the hardness of the eutectics was clearly harder than that of the Cu phase. The 0.2% proof stress of the Cu phase, $\sigma_{0.2}^{\text{Cu}}$, and the eutectics, $\sigma_{0.2}^{\text{e}}$, in each wire shown in Table 4 was determined as follows. Table 4 also lists the $\sigma_{0.2}^{\text{Cu}}$ values measured by Watanabe19) for the 0.6L and 0.2L wires produced by the same process as the 0.6S and 0.2S wires, using the as-cast Cu–0.29Zr alloy that can be regarded as a Cu single-phase. The HCu values for the 0.6L and 0.2L wires obtained in the present study are also shown. The $\sigma_{0.2}^{\text{Cu}}$ and HCu values for the 0.6L and 0.2L wires gave $\sigma_{0.2}^{\text{Cu}}$/HCu ≈ 0.134. Therefore, the $\sigma_{0.2}^{\text{Cu}}$ of the Cu phase and $\sigma_{0.2}^{\text{e}}$ of the eutectics in each wire were estimated by assuming yield strength/hardness = 0.134.
In Table 4, $\sigma_{0.2}^{\text{Cu}}$ of the 0.6S and 0.6L wires, and $\sigma_{0.2}^{\text{Cu}}$ of the 0.2S and 0.2L wires were almost equal, respectively. In addition, $\sigma_{0.2}^{\text{Cu}}$ of the 0.2S wire was higher than that of the 0.6S wire. The yield strengths of the Cu matrix in these wires are affected by solid-solution, precipitation, grain boundary, and dislocation strengthening mechanisms. Our previous studies6,19) showed that the effect of solid-solution strengthening caused by the CZr values listed in Table 2 on the yield strength was low. It was also analyzed that the contribution of fcc precipitates to the yield strength was low during the wire-drawing process. Therefore, no significant difference in the dislocation density, ρd, and grain size, DCu, is expected between the 0.6S and 0.6L wires and between the 0.2S and 0.2L wires. Indeed, no significant difference was observed between the 0.6S and 0.6L wires and between the 0.2S and 0.2L wires. For example, the values of ρd and DCu in the 0.6L wire were reported as $\rho_{\text{d}} = 1.7 \times 10^{ 15}$ m−2, and $D_{\text{Cu}} = 140$ nm, respectively.19) These values are almost equal to the values of ρd and DCu in the 0.6S wire listed in Table 2, which explains why $\sigma_{0.2}^{\text{Cu}}$ of the 0.6S and 0.6L wires and $\sigma_{0.2}^{\text{Cu}}$ of the 0.2S and 0.2L wires are almost equal, respectively. In addition, higher $\sigma_{0.2}^{\text{Cu}}$ value of the 0.2S wire than that of the 0.6S wire is attributed to a higher ρd and lower DCu of the 0.2S wire than that of the 0.6S wire, as shown in Table 2. The same can be said for the 0.6IA and 0.2IA wires. DCu decreased and ρd increased as the wire drawing progressed for both the S and IA wires, as shown in Table 2. Therefore, the increase in $\sigma_{0.2}^{\text{Cu}}$ of the Cu phase in the S and IA wires with the wire drawing can be attributed to the decrease in DCu and increase in ρd.
Since the strength of the eutectic is much higher than that of the Cu phase, as shown in Table 4, the presence of eutectics obviously leads to an increase in the strength as a composite material. The values of σ0.2 for the 5S, 0.6S, and 0.2S wires listed in Table 1 were 680, 790, and 1080 MPa in sequence. In contrast, the $\sigma_{0.2}^{\text{Cu}}$ values for the 5L, 0.6L, and 0.2L wires of the Cu–0.29Zr alloy were 400, 610, and 740 MPa, respectively.19) Thus, the amounts of strengthening owing to the presence of eutectics were 280, 180, and 340 MPa, respectively. Although the amount of strengthening did not have a strong correlation with the drawing ratio, the average value was 270 MPa, indicating that the presence of eutectics resulted in a significant increase in strength. The difference between the σ0.2 values of the 0.2S and 5S wires was 400 MPa, which is roughly identical to the difference of 340 MPa between the $\sigma_{0.2}^{\text{Cu}}$ values of the 0.2L and 5L wires. The same results were obtained for the IA wires. Therefore, in the case of wires with microstructures consisting of the Cu phase, fibrous eutectics, and granular eutectics, the increase in the 0.2% proof stress after wire drawing can be mainly attributed to the increase of the 0.2% proof stress in the Cu phase.
Thus, it can be concluded that the S and IA wires with the mixed microstructures were mainly strengthened by the high dislocation density and grain refinement in the Cu phase as well as the presence of fibrous and granular eutectics.
The effects of microstructures on strength and electrical conductivity were investigated for wires of a Cu–3.8 wt%Zr alloy processed by conform-extrusion process, followed by wire drawing to d = 0.2 mm (S wires), and for wires of the same alloy intermediately annealed during wire drawing to d = 0.2 mm after the conform-extrusion process (IA wires). The results are summarized as follows.
This research was supported by a Grant-in-Aid for the 2019 academic year from the Japan Institute of Copper.
