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Co-deformation in Cu–6 wt.% Ag nanocomposites
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Scripta Materialia 64 (2011) 665–668 www.elsevier.com/locate/scriptamat
Co-deformation in Cu–6 wt.% Ag nanocomposites J.B. Liu,a,c L. Zhang,b Y.W. Zengc and L. Mengc,⇑ a
b
College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, China School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China c Department of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China Received 6 November 2010; revised 13 December 2010; accepted 15 December 2010 Available online 21 December 2010
The co-deformation behaviors of the Cu and Ag phases in Cu–6 wt.% Ag nanocomposites were investigated during cold drawing. The relationship between the drawing strains of both phases was determined and analyzed based on the strengthening mechanism. A parameter was proposed to evaluate the co-deformation ability. The orientation and the strain hardening ability are the main factors controlling the co-deformation in Cu–6 wt.% Ag. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Drawing; Transmission electron microscopy; Copper alloy; Co-deformation
Most industrially used alloys contain more than one phase. The co-deformation of all the phases is the basis of many industrial processes for the production of high-strength wires, such as Cu–Nb, Cu–Cr, Cu–Fe and Cu–Ag nanocomposites [1–4]. These nanocomposites can be used as conductor materials in pulsed high-field magnets due to their high strength and high electrical conductivity. A high deformation strain should be applied to these nanocomposites to obtain high strength. During deformation, both the matrix and the second phase are elongated and refined to nanofilaments. For the cases of Cu–Nb, Cu–Fe and other nanocomposite materials with a face-centered cubic (fcc)–body-centered cubic (bcc) lattice match system, bcc phases were found to adopt particularly convoluted cross-sectional shapes upon wire drawing [3,5–7]. The curved morphology resulted from the compatibility between axisymmetric deformation of the Cu matrix and plane strain deformation of the bcc phases. In those materials with an fcc–fcc lattice match system, such as Cu–Ag, the cross-sectional shapes of the embedded fcc phases remain unchanged even under the very large strains of wire drawing [8,9]. Generally, imposed plastic strains are not distributed equally between two phases. The strain partitioning is great for systems containing constituents with very different flow stress and strain hardening ability [10]. The strain partitioning between the two phases results
⇑ Corresponding
author. Tel.: +86 57187951027; 57187952358; e-mail: [email protected]
fax:
+86
in one phase undergoing additional deformation so as to accommodate the more rigid phase. A consequence of the non-uniform plasticity is the development of internal stress. Cu–Nb and Cu–Ag wires deformed to a drawing strain of 2.0 showed large internal strains of the order of 0.2–0.5% [11]. The strain partitioning is expected to be more heterogeneous as the scale of the slip approaches the scale of embedded phase [11]. For Cu–72 wt.% Ag, Cu and Ag eutectic laminas were considered to be deformed in a coordinated manner due to the similar microstructure scales of both laminas [12]. For Cu–6 wt.% Ag, the scale of the Ag precipitate is only about 24 nm, which is far smaller than the slip scale. How the Ag precipitates are co-deformed into nanofilaments still needs further study. As deformation increases and the scale of the microstructure decreases, the role of the interface becomes dominant in co-deformation. Slip transmission across the interface was considered to take place when the filaments reached the nanometer scale [13]. The co-deformation was determined by shear transfer across the phase interfaces, leading to mechanically induced chemical mixing. The structure of the interface also changes during the co-deformation. In a previous work [14], we observed the evolution of a semi-coherent interface into a coherent interface in Cu–6 wt.% Ag during cold drawing. With a much higher drawing strain, deformation-driven amorphization at some of the Cu–Nb interface was observed in Cu–Ag–Nb alloys [13]. It has been pointed out by Sinclair et al. [11] that the roles of the interface, the slip system match and internal stress were among the
1359-6462/$ - see front matter Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2010.12.015
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J. B. Liu et al. / Scripta Materialia 64 (2011) 665–668
dominant factors in the description of co-deformation. How the interface structure and orientation relationship influence the co-deformation of Cu–Ag alloys remains unclear. Furthermore, there is still no parameter with which to compare the co-deformation ability among various multi-phase alloys. The present study was initiated to investigate the co-deformation behavior of Cu and Ag phases during drawing and to establish a comparison standard of co-deformation ability. Cu–6 wt.% Ag was melted in a vacuum induction furnace. The Cu and Ag both had an initial purity of at least 99.95%. Cylindrical ingots of 23 mm diameter were cast under an Ar atmosphere at a pressure of 2.7 104 Pa. The ingots were solution treated at 780 °C for 4 h, followed by water quenching and then aged at 450 °C for 32 h. The cold deformation was performed by drawing. Drawing reduction was presented in terms of the logarithmic strain and referred to as the drawing strain: g ¼ lnðA0 =AÞ
ð1Þ
where A0 and A are the cross-section areas of the original and drawn specimens. The microstructure of the specimens at various drawing strains was observed by transmission electron microscopy (TEM) in a JEM-2010 microscope operating at 200 kV. There are a large number of rod-like Ag precipitates in the aged Cu–6 wt.% Ag (Fig. 1a). The average diameter of the Ag precipitates is about 24 nm. The selected area
electron diffraction (SAED) patterns (insert in Fig. 1a) indicate that there is a cube-on-cube orientation relationship, <0 1 1>Ag//<0 1 1>Cu and {1 1 1}Ag//{1 1 1}Cu, between the Ag precipitate and the Cu matrix. The interface is planar and parallel to ð111ÞCu or ð111ÞAg (Fig. 1b). The image from the inverse fast Fourier transformation (IFFT) shows some misfit dislocations at the interface. The Cu/Ag interface belongs to a typical semi-coherent interface in the aged Cu–6 wt.% Ag. The Ag precipitates are elongated and refined in drawing deformation (Fig. 1c–f). The average diameter and interval of Ag filaments decrease with increasing drawing strain. The morphology of the Ag particles embedded in the Cu matrix remains unchanged in the cross-section of the specimens. Figure 2a and b illustrates the measurement of the filament diameter and the interface interval. In a given square, the summated diameter of all the Ag filaments divided by the number (m) of Ag filaments in the square should equal the average diameter (d) of the Ag filaments. Therefore, the interface interval between the Ag filaments can be calculated approximately by s ð2Þ k ¼ pffiffiffiffi d m where s is the length of a side of the given square. More than 100 filaments were measured to calculate the average diameter and more than eight squares were assessed to obtain the interface interval at each chosen drawing strain in the investigation. The measured result (Fig. 2c) shows
Figure 1. (a) TEM image of the Ag precipitates. The inset shows the SAED patterns of the precipitate zone. (b) High-resolution TEM image of the Cu/Ag interface. The inset is the corresponding IFFT image using only (1 1 1) and ð111Þ reflections. Microstructures of (c) longitudinal and (d) transverse sections of Cu–6 wt.% Ag drawn to g = 2.2 and of (e) longitudinal and (f) transverse sections of Cu–6 wt.% Ag drawn to g = 5.2.
J. B. Liu et al. / Scripta Materialia 64 (2011) 665–668
667
Figure 2. (a) TEM image, (b) schematic arrangement of Ag filaments on transverse section and changes of (c) Ag filament diameter and interface interval and (d) gCu and gAg with drawing strain in Cu–6 wt.% Ag.
that both d and k decrease with increasing g. According to Eq. (1), the drawing strains of the Cu and Ag phases can be presented as gCu ¼ 2 lnðk0 =kÞ
ð3Þ
gAg ¼ 2 lnðd 0 =dÞ
ð4Þ
where k0, k, d0 and d are the characteristic scales of the Cu and Ag phases in the original and drawn specimens, respectively. The gCu and gAg calculated from Figure 2c are shown in Figure 2d. The finding that values of gCu are approximately the same as those of gAg at every drawing strain indicate that deformation of the Cu and Ag phases remains concordant during cold drawing. Specifically, the synchronous deformation of the Cu and Ag phases should be a dynamic process since gCu is slightly higher or lower than gAg in different ranges of the drawing strain. It is easy to see that the absolute values of gCu and gAg are smaller than the corresponding values of g. The reason for this may be due to the outer part (rim) of the wires undergoing more deformation than the central part during drawing. Therefore, the microstructure scales of the rim should be finer than the average scales. The findings that gCu and gAg are smaller than g do not
affect the conclusion that the Cu and Ag phases can maintain a concordant deformation overall, since gCu and gAg were measured at the same selected area. The average drawing strains of the Cu and Ag phases could be estimated as gCu-ave = agCu and gAg-ave = bgAg, where a and b are the coefficient. Considering that the average drawing strains of the Cu phase, the Ag phase and the specimens are similar, the values of a and b could be estimated to be about 1.7. The relationship between gCu and gAg is shown in Figure 3a. The phenomenon that gCu is small higher or lower than gAg is probably due to the different strengthening mechanisms in the Cu and Ag phases. For the Ag filament with a diameter of only a few nanometers, it can be considered that the Ag filament tends to exhibit a whisker-type behavior, as observed in Nb nanoribbon in Cu–Nb nanocomposites [1,15]. The strength of the Ag filament can be expressed as [1] rAg ¼ rAg0 þ k Ag expðd ave =KÞ
ð5Þ
where rAg0 is the intrinsic strength and is negligible compared to the high strength of the filament structure, kAg and K are related coefficients, and dave is the average diameter of the Ag filaments.
Figure 3. (a) Experimental and predicted dependences of gCu on the gAg and (b) change in co-deformation ability with deformation strain of the Ag phase in different materials.
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J. B. Liu et al. / Scripta Materialia 64 (2011) 665–668
The strength of the Cu matrix embedded with lots of Ag filaments could be described by an Orowan-type strengthening mechanism [16]: rCu ¼ ðk Cu f 0:5 ln d ave Þ=d ave
ð6Þ
where kCu is a related coefficient and f is the volume percent of Ag phase and is estimated by f ¼
pd 2ave 4k2ave
ð7Þ
where kave is the average interval of Ag filaments. Considering the iso-stress for Cu and Ag phases during deformation, rCu should be equal to rAg: ð8Þ k Ag expðd ave =KÞ ¼ ðk Cu f 0:5 ln d ave Þ=d ave Combining d ave ¼ d 0 expð0:5gAg-ave Þ, kave ¼ k0 exp ð0:5gCu-ave Þ and Eq. (7) gives pffiffiffi k Cu p gCu ¼ 1:2 ln 1:2 lnðln d 0 0:85gAg Þ 2k0 k Ag 1:2d 0 expð0:85gAg Þ ð9Þ K The dependence of gCu on the gAg is presented in Figure 3a. The related parameters in Eq. (9) have been taken as d0 = 24 nm, k0 = 80 nm, K = 32.6, kAg = 0.5 and kCu = 5.8. The predicted result is in good agreement with the experimental data for the investigated range of the drawing strain. To compare the co-deformation ability in various double-phase alloys, the co-deformation factor (P) is defined as P ¼ ga =gb
ð10Þ
where ga and gb are the drawing strains of the two phases in the alloys. The changes of the co-deformation ability with the deformation strain of the Ag phase in Cu–6 wt.% Ag, Cu–72 wt.% Ag and Ni–Ag composites are shown in Figure 3b [17,18]. The dashed line of P = 1 indicates that the two phases have excellent co-deformation ability. For the Cu–6 wt.% Ag in this study, the value of P quickly approaches 1 and fluctuates along the dashed line as the drawing strain of the Ag phase increases. The value of P in Cu–72 wt.% Ag increases with the drawing strain of the Ag phase and may approach 1 at high drawing strains. However, the value of P in Ag/Ni composite is rather smaller than 1. It is clear that Cu–6 wt.% Ag has the best co-deformation ability among the three materials. Cu and Ag phases are in the form of eutectic lamina in Cu–72 wt.% Ag, which should be more beneficial for co-deformation than the Cu and Ag phases in Cu– 6 wt.% Ag, which has a morphology of Ag nanofilaments embedded in Cu matrix. However, Cu–72 wt.% Ag has a poorer co-deformation ability than Cu–6 wt.% Ag. The main reason for this may lie in the orientation relationship of the Cu and Ag phases. It has been pointed out that the match of the dislocation sliding system between both phases was the key issue controlling the co-deformation [11]. The cube-on-cube orientation of Cu matrix and Ag precipitates in Cu–6 wt.% Ag can guarantee the close match of the dislocation sliding system. The co-existence of cube-on-cube and hetero-twin orientation of Cu and
Ag eutectic in Cu–72 wt.% Ag may weaken the match of the dislocation sliding [19]. Considering that Ni has a much greater strain hardening ability than Cu and Ag, the discrepancy in strain hardening ability between Ni and Ag is greater than that between Cu and Ag. It is easy to understand why Ni/Ag composites have worse codeformation ability than Cu–Ag alloys, which suggests that the strain hardening ability of both phases also plays an important role in their co-deformation. Therefore, it can be concluded that the orientation and strain hardening ability are the main factors controlling co-deformation in double-phase alloys. In summary, both Cu and Ag phases are elongated and refined during cold drawing while the morphology remains unchanged in the cross-section of Cu–6 wt.% Ag wires. The values of gCu are similar to those of gAg at every drawing strain, showing that there is dynamic co-deformation behavior of the Cu and Ag phases. The relationship between the drawing strains of both phases depends on the strengthening mechanisms of each phase. The ratio of the true drawing strains of the two phases could evaluate the co-deformation ability in double-phase alloys. Orientation and strain hardening ability are the main factors controlling the co-deformation behavior. The project is supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. Y4100193) and National Natural Science Foundation of China (Grant No. 50671092). [1] L. Thilly, M. Veron, O. Ludwig, F. Lecouturier, J.P. Peyrade, S. Askenazy, Philos. Mag. A82 (2002) 925–942. [2] D. Raabe, K. Miyake, H. Takahara, Mater. Sci. Eng. A291 (2000) 186–197. [3] C. Biselli, D.G. Morris, Acta Mater. 44 (1996) 493–504. [4] S.I. Hong, M.A. Hill, Acta Mater. 46 (1998) 4111–4122. [5] J. Bevk, J.P. Harbison, J.L. Bell, J. Appl. Phys. 49 (1978) 6031–6038. [6] W.A. Spitzig, A.R. Pelton, F.C. Laabs, Acta Metall. 35 (1987) 2427–2442. [7] Z.W. Wu, J.J. Liu, Y. Chen, L. Meng, J. Alloys Compd. 467 (2009) 213–218. [8] A. Benghalem, D.G. Morris, Acta Mater. 45 (1997) 397– 406. [9] J.B. Liu, L. Meng, Y.W. Zeng, Mater. Sci. Eng. A435– 436 (2006) 237–244. [10] T. Ozturk, J. Mirmesdagh, T. Ediz, Mater. Sci. Eng. A175 (1994) 125–129. [11] C.W. Sinclair, J.D. Embury, G.C. Weatherly, Mater. Sci. Eng. A272 (1999) 90–98. [12] G. Frommeyer, G. Wassermann, Acta Metall. 23 (1975) 1353–1360. [13] D. Raabe, S. Ohsaki, K. Hono, Acta Mater. 57 (2009) 5254–5263. [14] J.B. Liu, L. Zhang, D.W. Yao, L. Meng, Acta Mater. 59 (2011) 1191–1197. [15] L. Thilly, P.O. Renault, V. Vidal, F. Lecouturier, S.V. Petegem, U. Stuhr, H.V. Swygenhoven, Appl. Phys. Lett. 88 (2006) 191906. [16] E. Orowan, Inst. Metals (1948) 451. [17] F. Heringhaus, Ph.D. thesis, Germany, 1998. [18] J.M. Lee, B.R. Lee, S.B. Kang, Mater. Sci. Eng. A406 (2005) 95–101. [19] J.B. Liu, Y.W. Zeng, L. Meng, J. Alloys Compd. 464 (2008) 168–173.
Scripta Materialia 64 (2011) 665–668 www.elsevier.com/locate/scriptamat
Co-deformation in Cu–6 wt.% Ag nanocomposites J.B. Liu,a,c L. Zhang,b Y.W. Zengc and L. Mengc,⇑ a
b
College of Materials Science and Engineering, China Jiliang University, Hangzhou 310018, China School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing 100083, China c Department of Materials Science and Engineering, Zhejiang University, Hangzhou 310027, China Received 6 November 2010; revised 13 December 2010; accepted 15 December 2010 Available online 21 December 2010
The co-deformation behaviors of the Cu and Ag phases in Cu–6 wt.% Ag nanocomposites were investigated during cold drawing. The relationship between the drawing strains of both phases was determined and analyzed based on the strengthening mechanism. A parameter was proposed to evaluate the co-deformation ability. The orientation and the strain hardening ability are the main factors controlling the co-deformation in Cu–6 wt.% Ag. Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Drawing; Transmission electron microscopy; Copper alloy; Co-deformation
Most industrially used alloys contain more than one phase. The co-deformation of all the phases is the basis of many industrial processes for the production of high-strength wires, such as Cu–Nb, Cu–Cr, Cu–Fe and Cu–Ag nanocomposites [1–4]. These nanocomposites can be used as conductor materials in pulsed high-field magnets due to their high strength and high electrical conductivity. A high deformation strain should be applied to these nanocomposites to obtain high strength. During deformation, both the matrix and the second phase are elongated and refined to nanofilaments. For the cases of Cu–Nb, Cu–Fe and other nanocomposite materials with a face-centered cubic (fcc)–body-centered cubic (bcc) lattice match system, bcc phases were found to adopt particularly convoluted cross-sectional shapes upon wire drawing [3,5–7]. The curved morphology resulted from the compatibility between axisymmetric deformation of the Cu matrix and plane strain deformation of the bcc phases. In those materials with an fcc–fcc lattice match system, such as Cu–Ag, the cross-sectional shapes of the embedded fcc phases remain unchanged even under the very large strains of wire drawing [8,9]. Generally, imposed plastic strains are not distributed equally between two phases. The strain partitioning is great for systems containing constituents with very different flow stress and strain hardening ability [10]. The strain partitioning between the two phases results
⇑ Corresponding
author. Tel.: +86 57187951027; 57187952358; e-mail: [email protected]
fax:
+86
in one phase undergoing additional deformation so as to accommodate the more rigid phase. A consequence of the non-uniform plasticity is the development of internal stress. Cu–Nb and Cu–Ag wires deformed to a drawing strain of 2.0 showed large internal strains of the order of 0.2–0.5% [11]. The strain partitioning is expected to be more heterogeneous as the scale of the slip approaches the scale of embedded phase [11]. For Cu–72 wt.% Ag, Cu and Ag eutectic laminas were considered to be deformed in a coordinated manner due to the similar microstructure scales of both laminas [12]. For Cu–6 wt.% Ag, the scale of the Ag precipitate is only about 24 nm, which is far smaller than the slip scale. How the Ag precipitates are co-deformed into nanofilaments still needs further study. As deformation increases and the scale of the microstructure decreases, the role of the interface becomes dominant in co-deformation. Slip transmission across the interface was considered to take place when the filaments reached the nanometer scale [13]. The co-deformation was determined by shear transfer across the phase interfaces, leading to mechanically induced chemical mixing. The structure of the interface also changes during the co-deformation. In a previous work [14], we observed the evolution of a semi-coherent interface into a coherent interface in Cu–6 wt.% Ag during cold drawing. With a much higher drawing strain, deformation-driven amorphization at some of the Cu–Nb interface was observed in Cu–Ag–Nb alloys [13]. It has been pointed out by Sinclair et al. [11] that the roles of the interface, the slip system match and internal stress were among the
1359-6462/$ - see front matter Ó 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.scriptamat.2010.12.015
666
J. B. Liu et al. / Scripta Materialia 64 (2011) 665–668
dominant factors in the description of co-deformation. How the interface structure and orientation relationship influence the co-deformation of Cu–Ag alloys remains unclear. Furthermore, there is still no parameter with which to compare the co-deformation ability among various multi-phase alloys. The present study was initiated to investigate the co-deformation behavior of Cu and Ag phases during drawing and to establish a comparison standard of co-deformation ability. Cu–6 wt.% Ag was melted in a vacuum induction furnace. The Cu and Ag both had an initial purity of at least 99.95%. Cylindrical ingots of 23 mm diameter were cast under an Ar atmosphere at a pressure of 2.7 104 Pa. The ingots were solution treated at 780 °C for 4 h, followed by water quenching and then aged at 450 °C for 32 h. The cold deformation was performed by drawing. Drawing reduction was presented in terms of the logarithmic strain and referred to as the drawing strain: g ¼ lnðA0 =AÞ
ð1Þ
where A0 and A are the cross-section areas of the original and drawn specimens. The microstructure of the specimens at various drawing strains was observed by transmission electron microscopy (TEM) in a JEM-2010 microscope operating at 200 kV. There are a large number of rod-like Ag precipitates in the aged Cu–6 wt.% Ag (Fig. 1a). The average diameter of the Ag precipitates is about 24 nm. The selected area
electron diffraction (SAED) patterns (insert in Fig. 1a) indicate that there is a cube-on-cube orientation relationship, <0 1 1>Ag//<0 1 1>Cu and {1 1 1}Ag//{1 1 1}Cu, between the Ag precipitate and the Cu matrix. The interface is planar and parallel to ð111ÞCu or ð111ÞAg (Fig. 1b). The image from the inverse fast Fourier transformation (IFFT) shows some misfit dislocations at the interface. The Cu/Ag interface belongs to a typical semi-coherent interface in the aged Cu–6 wt.% Ag. The Ag precipitates are elongated and refined in drawing deformation (Fig. 1c–f). The average diameter and interval of Ag filaments decrease with increasing drawing strain. The morphology of the Ag particles embedded in the Cu matrix remains unchanged in the cross-section of the specimens. Figure 2a and b illustrates the measurement of the filament diameter and the interface interval. In a given square, the summated diameter of all the Ag filaments divided by the number (m) of Ag filaments in the square should equal the average diameter (d) of the Ag filaments. Therefore, the interface interval between the Ag filaments can be calculated approximately by s ð2Þ k ¼ pffiffiffiffi d m where s is the length of a side of the given square. More than 100 filaments were measured to calculate the average diameter and more than eight squares were assessed to obtain the interface interval at each chosen drawing strain in the investigation. The measured result (Fig. 2c) shows
Figure 1. (a) TEM image of the Ag precipitates. The inset shows the SAED patterns of the precipitate zone. (b) High-resolution TEM image of the Cu/Ag interface. The inset is the corresponding IFFT image using only (1 1 1) and ð111Þ reflections. Microstructures of (c) longitudinal and (d) transverse sections of Cu–6 wt.% Ag drawn to g = 2.2 and of (e) longitudinal and (f) transverse sections of Cu–6 wt.% Ag drawn to g = 5.2.
J. B. Liu et al. / Scripta Materialia 64 (2011) 665–668
667
Figure 2. (a) TEM image, (b) schematic arrangement of Ag filaments on transverse section and changes of (c) Ag filament diameter and interface interval and (d) gCu and gAg with drawing strain in Cu–6 wt.% Ag.
that both d and k decrease with increasing g. According to Eq. (1), the drawing strains of the Cu and Ag phases can be presented as gCu ¼ 2 lnðk0 =kÞ
ð3Þ
gAg ¼ 2 lnðd 0 =dÞ
ð4Þ
where k0, k, d0 and d are the characteristic scales of the Cu and Ag phases in the original and drawn specimens, respectively. The gCu and gAg calculated from Figure 2c are shown in Figure 2d. The finding that values of gCu are approximately the same as those of gAg at every drawing strain indicate that deformation of the Cu and Ag phases remains concordant during cold drawing. Specifically, the synchronous deformation of the Cu and Ag phases should be a dynamic process since gCu is slightly higher or lower than gAg in different ranges of the drawing strain. It is easy to see that the absolute values of gCu and gAg are smaller than the corresponding values of g. The reason for this may be due to the outer part (rim) of the wires undergoing more deformation than the central part during drawing. Therefore, the microstructure scales of the rim should be finer than the average scales. The findings that gCu and gAg are smaller than g do not
affect the conclusion that the Cu and Ag phases can maintain a concordant deformation overall, since gCu and gAg were measured at the same selected area. The average drawing strains of the Cu and Ag phases could be estimated as gCu-ave = agCu and gAg-ave = bgAg, where a and b are the coefficient. Considering that the average drawing strains of the Cu phase, the Ag phase and the specimens are similar, the values of a and b could be estimated to be about 1.7. The relationship between gCu and gAg is shown in Figure 3a. The phenomenon that gCu is small higher or lower than gAg is probably due to the different strengthening mechanisms in the Cu and Ag phases. For the Ag filament with a diameter of only a few nanometers, it can be considered that the Ag filament tends to exhibit a whisker-type behavior, as observed in Nb nanoribbon in Cu–Nb nanocomposites [1,15]. The strength of the Ag filament can be expressed as [1] rAg ¼ rAg0 þ k Ag expðd ave =KÞ
ð5Þ
where rAg0 is the intrinsic strength and is negligible compared to the high strength of the filament structure, kAg and K are related coefficients, and dave is the average diameter of the Ag filaments.
Figure 3. (a) Experimental and predicted dependences of gCu on the gAg and (b) change in co-deformation ability with deformation strain of the Ag phase in different materials.
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J. B. Liu et al. / Scripta Materialia 64 (2011) 665–668
The strength of the Cu matrix embedded with lots of Ag filaments could be described by an Orowan-type strengthening mechanism [16]: rCu ¼ ðk Cu f 0:5 ln d ave Þ=d ave
ð6Þ
where kCu is a related coefficient and f is the volume percent of Ag phase and is estimated by f ¼
pd 2ave 4k2ave
ð7Þ
where kave is the average interval of Ag filaments. Considering the iso-stress for Cu and Ag phases during deformation, rCu should be equal to rAg: ð8Þ k Ag expðd ave =KÞ ¼ ðk Cu f 0:5 ln d ave Þ=d ave Combining d ave ¼ d 0 expð0:5gAg-ave Þ, kave ¼ k0 exp ð0:5gCu-ave Þ and Eq. (7) gives pffiffiffi k Cu p gCu ¼ 1:2 ln 1:2 lnðln d 0 0:85gAg Þ 2k0 k Ag 1:2d 0 expð0:85gAg Þ ð9Þ K The dependence of gCu on the gAg is presented in Figure 3a. The related parameters in Eq. (9) have been taken as d0 = 24 nm, k0 = 80 nm, K = 32.6, kAg = 0.5 and kCu = 5.8. The predicted result is in good agreement with the experimental data for the investigated range of the drawing strain. To compare the co-deformation ability in various double-phase alloys, the co-deformation factor (P) is defined as P ¼ ga =gb
ð10Þ
where ga and gb are the drawing strains of the two phases in the alloys. The changes of the co-deformation ability with the deformation strain of the Ag phase in Cu–6 wt.% Ag, Cu–72 wt.% Ag and Ni–Ag composites are shown in Figure 3b [17,18]. The dashed line of P = 1 indicates that the two phases have excellent co-deformation ability. For the Cu–6 wt.% Ag in this study, the value of P quickly approaches 1 and fluctuates along the dashed line as the drawing strain of the Ag phase increases. The value of P in Cu–72 wt.% Ag increases with the drawing strain of the Ag phase and may approach 1 at high drawing strains. However, the value of P in Ag/Ni composite is rather smaller than 1. It is clear that Cu–6 wt.% Ag has the best co-deformation ability among the three materials. Cu and Ag phases are in the form of eutectic lamina in Cu–72 wt.% Ag, which should be more beneficial for co-deformation than the Cu and Ag phases in Cu– 6 wt.% Ag, which has a morphology of Ag nanofilaments embedded in Cu matrix. However, Cu–72 wt.% Ag has a poorer co-deformation ability than Cu–6 wt.% Ag. The main reason for this may lie in the orientation relationship of the Cu and Ag phases. It has been pointed out that the match of the dislocation sliding system between both phases was the key issue controlling the co-deformation [11]. The cube-on-cube orientation of Cu matrix and Ag precipitates in Cu–6 wt.% Ag can guarantee the close match of the dislocation sliding system. The co-existence of cube-on-cube and hetero-twin orientation of Cu and
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