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Cu superconducting composite
Cryogenics 43 (2003) 45–51 www.elsevier.com/locate/cryogenics
Fracture of filaments and its influence on critical current and residual strength of fatigued Nb–Ti/Cu superconducting composite S. Ochiai
a,*
, Y. Oki b, F. Sekino b, M. Hojo b, M. Tanaka b, H. Okuda a, H. Moriai c, S. Sakai c, K. Watanabe d a b
International Innovation Center, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Graduate School of Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan c Hitachi Cable Ltd., 3550 Kidamari-cho, Tsuchiura 300, Japan d Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan Received 20 September 2002; accepted 29 November 2002
Abstract Fatigue behavior at room temperature and its influence on critical current at 4.2 K and residual strength at room temperature of multifilamentary Nb–Ti/Cu superconducting composite wire with a filament volume fraction of 0.49 (copper ratio of 1.04) were studied. The fatigue crack nucleated in the copper in the circumferential region and propagated stably into the inner region, causing fracture of the Nb–Ti filaments in the late stage of the fatigue life. Once the fracture of the filaments started, the number of the fractured filaments increased steeply with increasing number of stress cycles, and correspondingly, the current-transportable and stress-carrying capacity of the composite decreased steeply. In this process, both the critical current and residual strength of the fatigued composite decreased nearly linearly with decreasing fraction of surviving filaments. Thus, the critical current of the fatigued composite was proportional to residual strength as a first approximation. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nb–Ti/Cu superconducting composite; Fatigue; Critical current
1. Introduction Superconducting composite wires for magnets are exposed to (i) the thermal stresses caused by cooling down from the fabrication temperature and also by cooling down and warming up of magnets, (ii) mechanical stresses during winding to the magnet coil and (iii) electromagnetic stresses (Lorentz force) during service [1,2]. Studies on the mechanical behavior of superconducting composite wire and its relation to the superconducting property are therefore important to assure the high reliability and safety for application. Among the stresses mentioned above, the electromagnetic stresses on the composite wires are cyclic during repeated energization of magnets. For this reason, the fatigue behavior and its influence on critical current of the Nb3 Sn/Cu [3–5], Nb3 Al/Cu [6–9], Nb–Ti/
*
Corresponding author. Tel.: +81-75-753-4834; fax: +81-75-7534841. E-mail address: [email protected] (S. Ochiai).
Cu [9–11], Bi-2223/Ag [12–14] and Y–Ba–C–O/buffer/ inconel [15] superconducting composite wires and tapes have been studied. Until now it has been shown qualitatively that, the fatigue damage, especially the fracture of the superconducting current-transportable filaments, causes the reduction of critical current [5,7–9,11–13]. As a next step, it is needed to investigate quantitatively the variation of the number of fractured filaments with stress cycles and its influence on the variation of the critical current. The filaments play a dominant role not only in transportation of the superconducting current but also in stress carrying capacity (strength) of the composite wire especially when the volume fraction of the filaments is high, since the strength of the filaments is far stronger than that of the stabilizer (copper and silver). The aims of the present work are (i) to reveal the influence of the number of stress cycles on the fracture of the filaments in the Nb–Ti/Cu composite wire with a high filament volume fraction (0.49), (ii) to reveal the relation of the fraction of the surviving filaments to the critical current and residual strength of the fatigued composite and
0011-2275/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0011-2275(02)00169-8
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(iii) to obtain the empirical correlation between the critical current and residual strength whose values are commonly reduced with progressing fatigue damage.
2. Experimental procedure A multifilamentary 37at.%Nb–Ti/Cu composite wire with a filament volume fraction 0.49 (corresponding to a copper ratio of 1.04) was used. The diameters of the composite and filaments were 0.4 mm and 20 lm, respectively. The number of filaments n0 was 192. Fatigue tests were carried out at room temperature with the computer aided servohydraulic-testing machine (Shimadzu EHF-ED1). The specimens of the composite as well as the filaments extracted from it with a gage length of 25 mm were fatigued for various prescribed stress cycles. The stress ratio R for the composite was 0.1 (¼rc;min =rc;max where rc;min and rc;max are the minimum and maximum stresses applied to the composite specimens during the fatigue test, respectively). The maximum stress rc;max was 750, 470 and 320 MPa, and the frequency of stress cycling 15 Hz. The residual strength (rc;r ) of the fatigued specimens was measured at room temperature at a strain rate of 1:67 104 /s. The fracture surface was observed with a scanning electron microscope (SEM), from which the number of fractured filaments was measured. The critical current (Ic ) was measured at 4.2 K at the magnetic field H from 6 to 8 T by a 1 lV/cm criterion using a WM-5 magnet of the High Field Laboratory for Superconducting Materials, Tohoku University. The specimens for measurement of critical current had been soldered. In order to avoid the influence of stress concentration at the soldered portions, the specimens having been used for measurement of critical current were not used for measurement of residual strength. Instead, the residual strength was measured using the separately prepared specimens under the same fatigue condition. Due to such a reason, the number of experimental data of Ic was different from that of rc;r in the data presented below.
Under the present condition of the stress ratio for composite (R ¼ 0:1), the stress ratio for the filaments was calculated to be 0.2 by the method shown in our former work [7]. The result of the fatigue test of the extracted filaments under the condition of R ¼ 0:2 is shown in Fig. 1. The fracture strength was nearly the same as the static one (1150–1300 MPa) for any stress cycles. This result indicates that the filaments themselves are not damaged by fatigue when tested alone as long as the exerted maximum stress is lower than the static strength. Fig. 2 shows the variation of the fracture surface of the specimens fatigued at rc;max ¼ 470 MPa up to the indicated stress cycles N and then fractured by static tensile stress. The fatigue-damaged regions are surrounded by the broken curves. The regions outside the broken curves correspond to the fracture surface caused by the subsequent static tensile stress. The specimen for N ¼ 0 shown in (a) refers to the original composite without fatigue damage. Fig. 3 shows (a) the inner region of the statically fractured specimen and (b) damaged region of the fatigued specimen, observed at high magnification. Following features are found in Figs. 2 and 3. (1) In the fatigue damage process, first the cracking of the copper in the circumferential region occurred as indicated by the broken curves in Fig. 2(b). Then, the crack in the copper in the circumferential region grew into the inner region, causing further fracture of the copper and also fracture of the filament (c). Finally, the overall fracture occurred after the growth of the fatigue crack (d). Such a damage process was commonly observed for all the maximum stresses investigated (rc;max ¼ 750, 470 and 320 MPa).
3. Results and discussion 3.1. Fatigue fracture behavior of Nb–Ti filaments in the composite The filaments were extracted from the composite by etching away the copper with a dilute HNO3 solution. The static strength at room temperature of the extracted filaments measured in this work was in the range of 1150–1300 MPa (1230 MPa on an average) for 30 test specimens.
Fig. 1. S–N diagram of the extracted Nb–Ti filaments under the condition of R ¼ 0:2, corresponding to R ¼ 0:1 for the composite.
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Fig. 2. An example of the change in tensile fracture surface of fatigued specimens with increasing stress cycles. In this example, the specimens were fatigued for N ¼ 0, 2 104 , 3 104 and 3:4 104 cycles at rc;max ¼ 470 MPa and then fractured by applying static tensile stress.
(2) The composite without fatigue damage failed by necking (Fig. 2(a)). The Nb–Ti filament in the composite was originally ductile and was fractured in a ductile manner, as evidenced by the dimple pattern (Fig. 3(a)). On the contrary, in the fatigue-damaged region, the filaments were broken in a brittle manner as shown in Fig. 3(b). This result, in addition to the result that the filament is not damaged by fatigue up to the static tensile strength when tested alone as has been shown in Fig. 1, indicates that the filaments in the fatigue-damaged region was broken in association with the preceding copper crack. Such a behavior is similar to that of the Nb3 Al filament in the Nb3 Al/Cu composite on the point that the filament is not broken by fatigue when tested alone but is broken accompanying with the copper crack when embedded in composite [7,8], despite that Nb3 Al is brittle but Nb–Ti is ductile. It is emphasized that the ductile Nb–Ti filament is broken in a brittle manner under fatigue when embedded in the composite.
(3) In the present Nb–Ti/Cu composite, two fatigue cracks grew in one cross-section as shown Fig. 2(c) and (d). In the case of the Nb3 Al/Cu composite, such a case was rare and one crack was found in almost all specimens [8]. Such a difference between Nb–Ti/Cu and Nb3 Al/Cu composites could be attributed to the difference in fracture toughness of the filaments. The high crack arrest capacity of Nb–Ti filaments allows the co-existence of cracks. The high ductility of the Nb–Ti/Cu composite will be verified later in 3.5 from the analysis of the residual strength. (4) The fracture surface of the undamaged region outside the broken curves (Fig. 2(c) and (d)) was the same as that of the static one without fatigue damage. Thus undamaged region maintained the ductile nature. This suggests that the final fracture of the composite was not caused by the propagation of the fatigue crack but by the loss of stress carrying capacity due to the reduction of stress carrying area. Such a suggestion will be demonstrated to be valid in 3.5.
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Fig. 3. Comparison of (a) the static fracture surface of the specimen without fatigue damage with (b) the damaged region of the specimen fatigued for N ¼ 1:5 105 cycles at rc;max ¼ 320 MPa.
3.2. Critical current and residual strength Figs. 4 and 5 show the changes of critical current Ic and residual strength rc;r with increasing number of cycles ðN Þ for the specimens fatigued at rc;max ¼ 750, 470 and 320 MPa. The number of stress cycles N in Figs. 4 and 5 is normalized with respect to the stress cycles to failure, Nf (¼7:5 103 , 3:5 104 and 2:6 105 for rc;max ¼ 750, 470 and 320 MPa, respectively). As N =Nf ¼ 1 corresponds to the fatigue life, the variation of Ic and rc;r in the life can be shown in a linear scale. As the specimens had been fractured at N =Nf ¼ 1, critical current could not be measured. As the specimens were fractured at N =Nf ¼ 1 by the applied stress corresponding to the maximum stress, the residual strength was taken to be the same as the maximum stress, as indicated by the closed circles in Fig. 5. The reductions of Ic and rc;r started in the late stage of the fatigue life, but once they started, both of Ic and rc;r decreased steeply with increasing N =Nf . This result suggests that it takes a big number of cycles for formation of the damages to cause reduction in Ic and rc;r , but once such damages forms, they grow quickly. It is noted that the
Fig. 4. Change of critical current Ic of the specimens fatigued up to the prescribed cycles (N ) at the maximum stresses rc;max ¼ 750, 470 and 320 MPa. The number of cycles is shown in the normalized form of N =Nf where Nf is the cycles to failure (7:5 103 , 3:5 104 and 2:6 105 at rc;max ¼ 750, 470 and 320 MPa, respectively).
Ic N =Nf and rc;r N =Nf curves show the similar tendency to each other. 3.3. Variation of fraction of the surviving Nb–Ti filaments From the fracture surface of the fatigued specimens, the fraction of the surviving Nb–Ti filaments psf , (¼1 nf =n0 where nf is the number of broken filaments and n0 is the total number of embedded filaments (¼192 in the present specimens)), was measured as shown in Fig. 6. The reduction in psf occurred in the late stage of the fatigue life and decreased steeply increasing N =Nf at
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Fig. 5. Change of residual strength rc;r of the specimens fatigued up to the prescribed cycles (N ) at the maximum stresses rc;max ¼ 750, 470 and 320 MPa. The number of cycles N is normalized with respect to the cycles to failure Nf similarly as that in Fig. 4.
all the maximum stresses as similarly as the reduction in Ic and rc;r . The filaments were fractured in association with the copper crack propagation, as has been shown in Section 3.1. As a result, the psf was nearly equal to 1 Sc =S0 where Sc and S0 are the fatigue cracked area and the overall cross-sectional one, respectively, as shown in Fig. 7. Thus the undamaged area, which can transport the superconducting current and carry applied stress, was equal to psf S0 . 3.4. Correlation between critical current and fraction of surviving filaments Cyclic stressing changes the strain of filaments and causes damages, both of which influence on critical cur-
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Fig. 6. Change of fraction of the surviving filaments psf with increasing number of stress cycles N normalized with respect to the stress cycles to failure Nf .
rent. The influence of the change of the filament strain is, however, not so large in the Nb–Ti/Cu composite wire, since the Ic -degradation is negligible for the strain less than 0.4% and the reduction in critical current from zero strain is around 5% for 1% strain, which is not serious problem in most magnet designs [16]. In the following discussion, the influence of the fatigue-induced strain is neglected to a first approximation. Under this approximation, the simplest assumption to describe Ic is that Ic is proportional to the fraction of surviving filaments psf in the cross-section with the narrowest undamaged regions along the length. Such a narrowest effective crosssection is the same as the cross-section that contains the widest damage regions, causing the overall fracture of the
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Fig. 7. Correlation of the fraction of the surviving filaments psf to the fraction of the main crack area Sc =S0 .
composite. Thus, the psf -values estimated from the fracture surface can be applied also to the description of Ic . Noting the critical current of the non-fatigued specimens without damage as Ic;0 , Ic will be given simply by psf Ic;0 if we assume that the narrowest effective cross-section determines the current-transporting capacity of the specimens. Thus, as a very rough expression, by using the psf -value measured from the fracture surface, Ic of the fatigued specimens can be expressed also by psf Ic;0 . Fig. 8 shows the measured values of Ic =Ic;0 plotted against psf . The straight line corresponds to Ic =Ic;0 ¼ psf . The experimental data are around this line, suggesting that psf Ic;0 roughly expresses the critical current.
Fig. 8. Measured values of the normalized critical current Ic =Ic;0 plotted against the fraction of the surviving filaments psf . The straight solid line shows the relation of Ic =Ic;0 ¼ psf .
approximately given by rc;r ¼ rc;0 ð1 Sc =S0 Þ ¼ rc;0 psf since psf ¼ 1 Sc =S0 as has been shown in Section 3.3. Thus, the residual strength normalized with respect to the original strength, rc;r =rc;0 , is equal to psf in the net stress criterion. As the present composite is composed of metallic Nb–Ti and copper, the ductility of composite is high and the undamaged region are fractured in a ductile manner similarly as the original composite, the net stress criterion is expected to describe the experimental results. Fig. 9 shows the experimentally measured rc;r =rc;0 plotted against psf . Fairly good linear relation is found, as expected.
3.5. Correlation between residual strength and fraction of surviving filaments The residual strength is determined by the largest defect. For description of the strength, two criteria, depending on the ductility of the material, can be mentioned. If the material is brittle or if the material contains brittle filaments such as A15 compounds, the stress intensity factor criterion can be applied, according to which the fracture of composite occurs when the stress intensity factor based on the fracture mechanical approach reaches a critical value as has been shown in our former work for Nb3 Al/Cu composite [7]. On the other hand, if the material has a very high ductility as in the present case, it is expected that the overall fracture of the composite occurs when the applied load carried by the cross-section with the widest damaged regions along the specimen length reaches the static ultimate load (net stress criterion). In such a case, noting the strength of the non-fatigued (original) composite as rc;0 , the residual strength rc;r is
Fig. 9. Measured values of the normalized residual strength rc;r =rc;0 , plotted against the fraction of the surviving filaments psf . The straight solid line shows the linear relation between rc;r =rc;0 and psf .
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3.6. Correlation of critical current and residual strength As shown above in Sections 3.4 and 3.5, the crosssection containing the widest damaged regions along the specimen length was regarded to be responsible for determination of both current-transporting capacity and stress carrying capacity of the specimens. Then, using the psf -value measured from the fracture surface, both Ic =Ic;0 and rc;r ; =rc;0 were shown to be roughly equal to psf . This suggests that the relation of Ic =Ic;0 ¼ rc;r =rc;0 is retained to a first approximation. While the relation Ic =Ic;0 ¼ rc;r =rc;0 obtained in the present work is very rough, this kind of relation can be a useful tool for rough prediction of critical current from the room temperature-residual strength that can be estimated easily.
4. Conclusions Fatigue behavior of a Nb–Ti/Cu multifilamentary composite wire with a low copper ratio (1.04, corresponding to filament volume fraction of 0.49) at room temperature and the relations of fatigue damage to critical current at 4.2 K and to residual strength at room temperature were studied. Main results are summarized as follows. (1) The fatigue damage progresses in the order of formation of cracks in the copper in the circumferential region, stable propagation of the fatigue crack into the inner region and overall fracture of the composite. In this process, the originally ductile Nb–Ti filaments in the composite are fractured in a brittle manner in association with the propagation of the copper crack. (2) The critical current and residual strength decreased in the late stage of fatigue life where the currenttransportable and stress-carrying capacities were reduced due to the fracture of the filaments. (3) The critical current decreased linearly with decreasing fraction of the surviving filaments to a first approximation. (4) The residual strength was controlled by the net stress criterion; namely it decreased linearly with decreasing fraction of the surviving filaments to a first approximation. (5) As a result of (3) and (4) mentioned above, the critical current of the fatigued composite was approximately proportional to the residual strength.
Acknowledgements The authors wish to express their gratitude, to MesserÕs K. Sai and Y. Ishikawa at the High Field Laboratory for Superconducting Materials at Tohoku
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University for their help in the critical current measurement, to IEC National Committee TC90/WG5 in the New Materials Center, Osaka Science and Technology Center for the support and encouragement, and to The Ministry of Education, Science and Culture, Japan, for the grant-in-aid (no. 14350360).
References [1] Ekin JW. Strain effects in superconducting compounds. Adv Cryog Eng 1984;30:823–36. [2] Osamura K. In: Osamura K, editor. Composite superconductors. New York: Marcel Dekker Inc.; 1994. p. 137–71. [3] Cogan SF, Rose RM. Fatigue effects in unidirectional composites: application to Nb3 Sn superconductors. Appl Phys Lett 1979; 35(11):884–6. [4] Kasahara H, Torii S, Akita S, Uyeda K, Ogawa T, Ikeno Y, et al. Critical current of Nb3 Sn superconductors for generators under cyclic mechanical load. IEEE Trans Magn 1994;30(4): 1927–30. [5] Ochiai S, Osamura K. Influence of cyclic loading at room temperature on critical current of superconducting Nb3 Sn composite wire. Cryogenics 1992;32(6):584–90. [6] Katagiri K, Ohgami M, Okada T, Kuroda K, Wada H, Innoue K, et al. Strain effect in Nb3 Al multifilamentary wires. Adv Cryog Eng 1992;38:827–33. [7] Ochiai S, Sawada T, Sekino F, Hojo M, Yamada Y, Takahashi K, et al. Fatigue behavior at room temperature and its influence on superconducting property at 4.2 K of multifilamentary Nb3 Al composite wire. Supercond Sci Technol 1998;11:322–32. [8] Ochiai S, Ohno H, Sekino F, Oki Y, Hojo M, Koganeya M, et al. Progress of fatigue damages and its influence on critical current of multifilamentary Nb3 Al superconducting composite. Supercond Sci Technol 1999;12:499–506. [9] Ochiai S, Oki Y, Sekino F, Ohno H, Hojo M, Moriai H, et al. Differences and similarities in fatigue behavior and its influence on critical current and residual strength between Ti–Nb and Nb3 Al superconducting composite wires. Supercond Sci Technol 2000;13:396–404. [10] Bray SL, Ekin JW, Waltman DJ, Superczynski MJ. Quench energy and fatigue degradation properties of Cu-stabilized and Al/ Cu-stabilized Nb–Ti epoxy-impregnated superconductor coils. IEEE Trans Appl Supercond 1995;5(2):222–5. [11] Hojo M, Iwasaki N, Sekino F, Ochiai S, Sakai S, Watanabe K. Fracture behavior under fatigue loading at room temperature and its influence on critical current of Nb–Ti/Cu composite wire. Cryogenics 1999;39(7):627–36. [12] Malachevsky MT, Esparza DA. Metal-ceramic interface response to bending and fatigue cycles in superconducting Ag–Bi2223 composites. Physica C 1999;324(3–4):153–60. [13] Sugano M, Osamura K, Ochiai S. Influence of dynamic and static stresses to mechanical and transport properties of Ag/Bi2223 composite superconductors. IEEE Trans Appl Supercond 2001; 11(1):3022–5. [14] Masur LJ, Kellers J, Li F, Fleshler S, Podtburg ER. Industrial high temperature superconductors: Perspectives and milestones. IEEE Trans Appl Supercond 2002;12(1):1145–50. [15] Ekin JW, Bray SL, Cheggour N, Clickner CC, Foltyn SR, Arendt PN, et al. Transverse stress and fatigue effects in Y–Ba–Cu–O coated IBAD tapes. IEEE Trans Appl Supercond 2001; 11(1):3389–92. [16] Matsushita T, Ekin JW. In: Osamura K, editor. Composite superconductors. New York: Marcel Dekker Inc.; 1994. p. 21– 136.
Fracture of filaments and its influence on critical current and residual strength of fatigued Nb–Ti/Cu superconducting composite S. Ochiai
a,*
, Y. Oki b, F. Sekino b, M. Hojo b, M. Tanaka b, H. Okuda a, H. Moriai c, S. Sakai c, K. Watanabe d a b
International Innovation Center, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan Graduate School of Engineering, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan c Hitachi Cable Ltd., 3550 Kidamari-cho, Tsuchiura 300, Japan d Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan Received 20 September 2002; accepted 29 November 2002
Abstract Fatigue behavior at room temperature and its influence on critical current at 4.2 K and residual strength at room temperature of multifilamentary Nb–Ti/Cu superconducting composite wire with a filament volume fraction of 0.49 (copper ratio of 1.04) were studied. The fatigue crack nucleated in the copper in the circumferential region and propagated stably into the inner region, causing fracture of the Nb–Ti filaments in the late stage of the fatigue life. Once the fracture of the filaments started, the number of the fractured filaments increased steeply with increasing number of stress cycles, and correspondingly, the current-transportable and stress-carrying capacity of the composite decreased steeply. In this process, both the critical current and residual strength of the fatigued composite decreased nearly linearly with decreasing fraction of surviving filaments. Thus, the critical current of the fatigued composite was proportional to residual strength as a first approximation. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Nb–Ti/Cu superconducting composite; Fatigue; Critical current
1. Introduction Superconducting composite wires for magnets are exposed to (i) the thermal stresses caused by cooling down from the fabrication temperature and also by cooling down and warming up of magnets, (ii) mechanical stresses during winding to the magnet coil and (iii) electromagnetic stresses (Lorentz force) during service [1,2]. Studies on the mechanical behavior of superconducting composite wire and its relation to the superconducting property are therefore important to assure the high reliability and safety for application. Among the stresses mentioned above, the electromagnetic stresses on the composite wires are cyclic during repeated energization of magnets. For this reason, the fatigue behavior and its influence on critical current of the Nb3 Sn/Cu [3–5], Nb3 Al/Cu [6–9], Nb–Ti/
*
Corresponding author. Tel.: +81-75-753-4834; fax: +81-75-7534841. E-mail address: [email protected] (S. Ochiai).
Cu [9–11], Bi-2223/Ag [12–14] and Y–Ba–C–O/buffer/ inconel [15] superconducting composite wires and tapes have been studied. Until now it has been shown qualitatively that, the fatigue damage, especially the fracture of the superconducting current-transportable filaments, causes the reduction of critical current [5,7–9,11–13]. As a next step, it is needed to investigate quantitatively the variation of the number of fractured filaments with stress cycles and its influence on the variation of the critical current. The filaments play a dominant role not only in transportation of the superconducting current but also in stress carrying capacity (strength) of the composite wire especially when the volume fraction of the filaments is high, since the strength of the filaments is far stronger than that of the stabilizer (copper and silver). The aims of the present work are (i) to reveal the influence of the number of stress cycles on the fracture of the filaments in the Nb–Ti/Cu composite wire with a high filament volume fraction (0.49), (ii) to reveal the relation of the fraction of the surviving filaments to the critical current and residual strength of the fatigued composite and
0011-2275/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0011-2275(02)00169-8
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(iii) to obtain the empirical correlation between the critical current and residual strength whose values are commonly reduced with progressing fatigue damage.
2. Experimental procedure A multifilamentary 37at.%Nb–Ti/Cu composite wire with a filament volume fraction 0.49 (corresponding to a copper ratio of 1.04) was used. The diameters of the composite and filaments were 0.4 mm and 20 lm, respectively. The number of filaments n0 was 192. Fatigue tests were carried out at room temperature with the computer aided servohydraulic-testing machine (Shimadzu EHF-ED1). The specimens of the composite as well as the filaments extracted from it with a gage length of 25 mm were fatigued for various prescribed stress cycles. The stress ratio R for the composite was 0.1 (¼rc;min =rc;max where rc;min and rc;max are the minimum and maximum stresses applied to the composite specimens during the fatigue test, respectively). The maximum stress rc;max was 750, 470 and 320 MPa, and the frequency of stress cycling 15 Hz. The residual strength (rc;r ) of the fatigued specimens was measured at room temperature at a strain rate of 1:67 104 /s. The fracture surface was observed with a scanning electron microscope (SEM), from which the number of fractured filaments was measured. The critical current (Ic ) was measured at 4.2 K at the magnetic field H from 6 to 8 T by a 1 lV/cm criterion using a WM-5 magnet of the High Field Laboratory for Superconducting Materials, Tohoku University. The specimens for measurement of critical current had been soldered. In order to avoid the influence of stress concentration at the soldered portions, the specimens having been used for measurement of critical current were not used for measurement of residual strength. Instead, the residual strength was measured using the separately prepared specimens under the same fatigue condition. Due to such a reason, the number of experimental data of Ic was different from that of rc;r in the data presented below.
Under the present condition of the stress ratio for composite (R ¼ 0:1), the stress ratio for the filaments was calculated to be 0.2 by the method shown in our former work [7]. The result of the fatigue test of the extracted filaments under the condition of R ¼ 0:2 is shown in Fig. 1. The fracture strength was nearly the same as the static one (1150–1300 MPa) for any stress cycles. This result indicates that the filaments themselves are not damaged by fatigue when tested alone as long as the exerted maximum stress is lower than the static strength. Fig. 2 shows the variation of the fracture surface of the specimens fatigued at rc;max ¼ 470 MPa up to the indicated stress cycles N and then fractured by static tensile stress. The fatigue-damaged regions are surrounded by the broken curves. The regions outside the broken curves correspond to the fracture surface caused by the subsequent static tensile stress. The specimen for N ¼ 0 shown in (a) refers to the original composite without fatigue damage. Fig. 3 shows (a) the inner region of the statically fractured specimen and (b) damaged region of the fatigued specimen, observed at high magnification. Following features are found in Figs. 2 and 3. (1) In the fatigue damage process, first the cracking of the copper in the circumferential region occurred as indicated by the broken curves in Fig. 2(b). Then, the crack in the copper in the circumferential region grew into the inner region, causing further fracture of the copper and also fracture of the filament (c). Finally, the overall fracture occurred after the growth of the fatigue crack (d). Such a damage process was commonly observed for all the maximum stresses investigated (rc;max ¼ 750, 470 and 320 MPa).
3. Results and discussion 3.1. Fatigue fracture behavior of Nb–Ti filaments in the composite The filaments were extracted from the composite by etching away the copper with a dilute HNO3 solution. The static strength at room temperature of the extracted filaments measured in this work was in the range of 1150–1300 MPa (1230 MPa on an average) for 30 test specimens.
Fig. 1. S–N diagram of the extracted Nb–Ti filaments under the condition of R ¼ 0:2, corresponding to R ¼ 0:1 for the composite.
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Fig. 2. An example of the change in tensile fracture surface of fatigued specimens with increasing stress cycles. In this example, the specimens were fatigued for N ¼ 0, 2 104 , 3 104 and 3:4 104 cycles at rc;max ¼ 470 MPa and then fractured by applying static tensile stress.
(2) The composite without fatigue damage failed by necking (Fig. 2(a)). The Nb–Ti filament in the composite was originally ductile and was fractured in a ductile manner, as evidenced by the dimple pattern (Fig. 3(a)). On the contrary, in the fatigue-damaged region, the filaments were broken in a brittle manner as shown in Fig. 3(b). This result, in addition to the result that the filament is not damaged by fatigue up to the static tensile strength when tested alone as has been shown in Fig. 1, indicates that the filaments in the fatigue-damaged region was broken in association with the preceding copper crack. Such a behavior is similar to that of the Nb3 Al filament in the Nb3 Al/Cu composite on the point that the filament is not broken by fatigue when tested alone but is broken accompanying with the copper crack when embedded in composite [7,8], despite that Nb3 Al is brittle but Nb–Ti is ductile. It is emphasized that the ductile Nb–Ti filament is broken in a brittle manner under fatigue when embedded in the composite.
(3) In the present Nb–Ti/Cu composite, two fatigue cracks grew in one cross-section as shown Fig. 2(c) and (d). In the case of the Nb3 Al/Cu composite, such a case was rare and one crack was found in almost all specimens [8]. Such a difference between Nb–Ti/Cu and Nb3 Al/Cu composites could be attributed to the difference in fracture toughness of the filaments. The high crack arrest capacity of Nb–Ti filaments allows the co-existence of cracks. The high ductility of the Nb–Ti/Cu composite will be verified later in 3.5 from the analysis of the residual strength. (4) The fracture surface of the undamaged region outside the broken curves (Fig. 2(c) and (d)) was the same as that of the static one without fatigue damage. Thus undamaged region maintained the ductile nature. This suggests that the final fracture of the composite was not caused by the propagation of the fatigue crack but by the loss of stress carrying capacity due to the reduction of stress carrying area. Such a suggestion will be demonstrated to be valid in 3.5.
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Fig. 3. Comparison of (a) the static fracture surface of the specimen without fatigue damage with (b) the damaged region of the specimen fatigued for N ¼ 1:5 105 cycles at rc;max ¼ 320 MPa.
3.2. Critical current and residual strength Figs. 4 and 5 show the changes of critical current Ic and residual strength rc;r with increasing number of cycles ðN Þ for the specimens fatigued at rc;max ¼ 750, 470 and 320 MPa. The number of stress cycles N in Figs. 4 and 5 is normalized with respect to the stress cycles to failure, Nf (¼7:5 103 , 3:5 104 and 2:6 105 for rc;max ¼ 750, 470 and 320 MPa, respectively). As N =Nf ¼ 1 corresponds to the fatigue life, the variation of Ic and rc;r in the life can be shown in a linear scale. As the specimens had been fractured at N =Nf ¼ 1, critical current could not be measured. As the specimens were fractured at N =Nf ¼ 1 by the applied stress corresponding to the maximum stress, the residual strength was taken to be the same as the maximum stress, as indicated by the closed circles in Fig. 5. The reductions of Ic and rc;r started in the late stage of the fatigue life, but once they started, both of Ic and rc;r decreased steeply with increasing N =Nf . This result suggests that it takes a big number of cycles for formation of the damages to cause reduction in Ic and rc;r , but once such damages forms, they grow quickly. It is noted that the
Fig. 4. Change of critical current Ic of the specimens fatigued up to the prescribed cycles (N ) at the maximum stresses rc;max ¼ 750, 470 and 320 MPa. The number of cycles is shown in the normalized form of N =Nf where Nf is the cycles to failure (7:5 103 , 3:5 104 and 2:6 105 at rc;max ¼ 750, 470 and 320 MPa, respectively).
Ic N =Nf and rc;r N =Nf curves show the similar tendency to each other. 3.3. Variation of fraction of the surviving Nb–Ti filaments From the fracture surface of the fatigued specimens, the fraction of the surviving Nb–Ti filaments psf , (¼1 nf =n0 where nf is the number of broken filaments and n0 is the total number of embedded filaments (¼192 in the present specimens)), was measured as shown in Fig. 6. The reduction in psf occurred in the late stage of the fatigue life and decreased steeply increasing N =Nf at
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Fig. 5. Change of residual strength rc;r of the specimens fatigued up to the prescribed cycles (N ) at the maximum stresses rc;max ¼ 750, 470 and 320 MPa. The number of cycles N is normalized with respect to the cycles to failure Nf similarly as that in Fig. 4.
all the maximum stresses as similarly as the reduction in Ic and rc;r . The filaments were fractured in association with the copper crack propagation, as has been shown in Section 3.1. As a result, the psf was nearly equal to 1 Sc =S0 where Sc and S0 are the fatigue cracked area and the overall cross-sectional one, respectively, as shown in Fig. 7. Thus the undamaged area, which can transport the superconducting current and carry applied stress, was equal to psf S0 . 3.4. Correlation between critical current and fraction of surviving filaments Cyclic stressing changes the strain of filaments and causes damages, both of which influence on critical cur-
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Fig. 6. Change of fraction of the surviving filaments psf with increasing number of stress cycles N normalized with respect to the stress cycles to failure Nf .
rent. The influence of the change of the filament strain is, however, not so large in the Nb–Ti/Cu composite wire, since the Ic -degradation is negligible for the strain less than 0.4% and the reduction in critical current from zero strain is around 5% for 1% strain, which is not serious problem in most magnet designs [16]. In the following discussion, the influence of the fatigue-induced strain is neglected to a first approximation. Under this approximation, the simplest assumption to describe Ic is that Ic is proportional to the fraction of surviving filaments psf in the cross-section with the narrowest undamaged regions along the length. Such a narrowest effective crosssection is the same as the cross-section that contains the widest damage regions, causing the overall fracture of the
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Fig. 7. Correlation of the fraction of the surviving filaments psf to the fraction of the main crack area Sc =S0 .
composite. Thus, the psf -values estimated from the fracture surface can be applied also to the description of Ic . Noting the critical current of the non-fatigued specimens without damage as Ic;0 , Ic will be given simply by psf Ic;0 if we assume that the narrowest effective cross-section determines the current-transporting capacity of the specimens. Thus, as a very rough expression, by using the psf -value measured from the fracture surface, Ic of the fatigued specimens can be expressed also by psf Ic;0 . Fig. 8 shows the measured values of Ic =Ic;0 plotted against psf . The straight line corresponds to Ic =Ic;0 ¼ psf . The experimental data are around this line, suggesting that psf Ic;0 roughly expresses the critical current.
Fig. 8. Measured values of the normalized critical current Ic =Ic;0 plotted against the fraction of the surviving filaments psf . The straight solid line shows the relation of Ic =Ic;0 ¼ psf .
approximately given by rc;r ¼ rc;0 ð1 Sc =S0 Þ ¼ rc;0 psf since psf ¼ 1 Sc =S0 as has been shown in Section 3.3. Thus, the residual strength normalized with respect to the original strength, rc;r =rc;0 , is equal to psf in the net stress criterion. As the present composite is composed of metallic Nb–Ti and copper, the ductility of composite is high and the undamaged region are fractured in a ductile manner similarly as the original composite, the net stress criterion is expected to describe the experimental results. Fig. 9 shows the experimentally measured rc;r =rc;0 plotted against psf . Fairly good linear relation is found, as expected.
3.5. Correlation between residual strength and fraction of surviving filaments The residual strength is determined by the largest defect. For description of the strength, two criteria, depending on the ductility of the material, can be mentioned. If the material is brittle or if the material contains brittle filaments such as A15 compounds, the stress intensity factor criterion can be applied, according to which the fracture of composite occurs when the stress intensity factor based on the fracture mechanical approach reaches a critical value as has been shown in our former work for Nb3 Al/Cu composite [7]. On the other hand, if the material has a very high ductility as in the present case, it is expected that the overall fracture of the composite occurs when the applied load carried by the cross-section with the widest damaged regions along the specimen length reaches the static ultimate load (net stress criterion). In such a case, noting the strength of the non-fatigued (original) composite as rc;0 , the residual strength rc;r is
Fig. 9. Measured values of the normalized residual strength rc;r =rc;0 , plotted against the fraction of the surviving filaments psf . The straight solid line shows the linear relation between rc;r =rc;0 and psf .
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3.6. Correlation of critical current and residual strength As shown above in Sections 3.4 and 3.5, the crosssection containing the widest damaged regions along the specimen length was regarded to be responsible for determination of both current-transporting capacity and stress carrying capacity of the specimens. Then, using the psf -value measured from the fracture surface, both Ic =Ic;0 and rc;r ; =rc;0 were shown to be roughly equal to psf . This suggests that the relation of Ic =Ic;0 ¼ rc;r =rc;0 is retained to a first approximation. While the relation Ic =Ic;0 ¼ rc;r =rc;0 obtained in the present work is very rough, this kind of relation can be a useful tool for rough prediction of critical current from the room temperature-residual strength that can be estimated easily.
4. Conclusions Fatigue behavior of a Nb–Ti/Cu multifilamentary composite wire with a low copper ratio (1.04, corresponding to filament volume fraction of 0.49) at room temperature and the relations of fatigue damage to critical current at 4.2 K and to residual strength at room temperature were studied. Main results are summarized as follows. (1) The fatigue damage progresses in the order of formation of cracks in the copper in the circumferential region, stable propagation of the fatigue crack into the inner region and overall fracture of the composite. In this process, the originally ductile Nb–Ti filaments in the composite are fractured in a brittle manner in association with the propagation of the copper crack. (2) The critical current and residual strength decreased in the late stage of fatigue life where the currenttransportable and stress-carrying capacities were reduced due to the fracture of the filaments. (3) The critical current decreased linearly with decreasing fraction of the surviving filaments to a first approximation. (4) The residual strength was controlled by the net stress criterion; namely it decreased linearly with decreasing fraction of the surviving filaments to a first approximation. (5) As a result of (3) and (4) mentioned above, the critical current of the fatigued composite was approximately proportional to the residual strength.
Acknowledgements The authors wish to express their gratitude, to MesserÕs K. Sai and Y. Ishikawa at the High Field Laboratory for Superconducting Materials at Tohoku
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University for their help in the critical current measurement, to IEC National Committee TC90/WG5 in the New Materials Center, Osaka Science and Technology Center for the support and encouragement, and to The Ministry of Education, Science and Culture, Japan, for the grant-in-aid (no. 14350360).
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