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Stress–strain behavior and degradation of critical current of Bi2223 composite tapes
Physica C 402 (2004) 341–346 www.elsevier.com/locate/physc
Stress–strain behavior and degradation of critical current of Bi2223 composite tapes M. Sugano *, K. Osamura Department of Materials Science and Engineering, Kyoto University Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan Received 28 December 2002; received in revised form 15 October 2003; accepted 21 October 2003
Abstract Stress–strain curve of commercially available Bi2223 multi-filamentary tapes was measured at RT and 77 K, which are composed of Bi2223, Ag and Ag alloy. The yielding at 77 K takes place at larger applied strain than that at RT. This behavior was discussed in terms of the residual strain during cooling. The reversibility of strain dependence of Ic was investigated in detail in the low strain region. It recovered reversibly when the maximum strain was less than 0.33%. However, when the applied strain exceeded 0.38%, the irreversible behavior was clearly confirmed. This is the first result that the strain region of reversible change of Ic exists in Bi2223 composite tape. 2003 Elsevier B.V. All rights reserved. PACS: 85.25.K; 62.20.F; 74.60.J Keywords: Bi2223; Stress–strain curve; Residual strain; Reversible change of Ic
1. Introduction Bi2223 tapes are most promising candidate for large scale superconducting devices. However, the tapes with higher critical current density (Jc ) and mechanical tolerance are required for practical application [1]. Mechanical properties and transport properties under applied stress have been widely studied. In the case of application to superconducting magnets, the stress is divided into several complicated compositions; they are tensile, compressive and bending stresses, of which direc* Corresponding author. Tel.: +81-75-7535440; fax: +81-757535486. E-mail address: [email protected] (M. Sugano).
tion is longitudinal and/or transverse one depending on condition. Their influence on critical current (Ic ) has been extensively investigated [2– 11]. Bi2223 tapes are usually composed of Bi2223 filaments, Ag and Ag alloy. Mechanical property of these tapes depends on the property of constituents. During cooling from the annealing temperature, the difference of thermal expansion coefficient among constituents causes compressive and tensile residual stress in oxide and metal sheath, respectively. To investigate stress–strain behavior, such residual stress must be taken into consideration. For Ag/Bi2223 monocore tapes, the stress–strain curve has been analyzed according to the rule of mixture by Ochiai et al. [12]. Macroscopic fracture of oxide core appears as multiple
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.10.013
342
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346
fracture phenomenon and it can be detected as repetitive drops of stress in stress–strain curve. In addition, it has been reported that the pre-compression due to residual stress in Bi2223 tape has large influence to the strain dependence of Ic [4,7]. Long length Bi2223 tapes experience various kind of working even after heat treatment. Tensile and bending stresses are applied to tapes during winding into coils at RT and checking the distribution of Ic at each position in the direction of length at 77 K. Therefore, it is also important to know the temperature dependence of stress–strain curve in the view point of application. The Ic versus tensile strain curve has typically two regions such as the gradual decrease of Ic at low strain and its drastic reduction at higher one [6]. The latter has been attributed to macroscopic cracking in Bi2223 filaments. A few studies about the former phenomenon has been however reported [6,13]. In this paper, the reversibility of Ic and variation of V –I curves during uniaxially load–unload test at low strain region has been also investigated.
2. Experimental Commercially available multi-filamentary Bi2223 tape (VAM2) was supplied for VAMAS program. Property of the tapes is summarized in Table 1. The tape has pure silver matrix around Bi2223 filaments and AgMgNi alloy sheath is arranged as the outer sheath. Tensile test was carried out by using Instron type tensile testing machine (NMB TCM-500) and testing machine with an electromagnetic actuator (Shimadzu MMT-100N) at RT and 77 K. As shown in Fig. 1, sample and gage lengths of the specimen are 80 and 50 mm, respectively, and
Table 1 Property of the tape examined here Dimension, width · thickness (mm)
Critical current (A) (77 K, SF)
Number of filament
Sheath material
2.95 · 0.182
28
19
Ag/AgMgNi
Fig. 1. Experimental setup for measurement of Ic –e curve.
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346
rubber tabs are attached to both ends of the tape for preventing from breakage near chucks. Strain is measured by using a couple of very light extensometers, which are symmetrically positioned along the tape. The total weight of the extensometers is about 4.3 g. Gage length of the extensometer is 25 mm. V –I measurement was performed by four-probe technique at 77 K under self-field. Ic was determined by 1 lV/cm criterion. Strain dependence of Ic was measured by using the setup shown in Fig. 1. Voltage taps were attached inside the gage of the extensometer and distance between voltage taps is 20 mm. The advantages of this setup are possibilities to measure stress, strain and V –I curve simultaneously and to avoid the influence of contraction of the machine by controlling the load at almost zero during cooling to 77 K.
3.1. Stress–strain behavior measured at different temperatures Stress–strain curves measured at RT and 77 K are shown in Fig. 2. Both curves show clear yielding and become almost horizontal after that.
200 77 K RT
150
Stress (MPa)
In the present study, yield point is defined as that at which slope of stress–strain curve starts to be horizontal and it was determined by eye. The yield points for RT and 77 K are indicated by YRT and Y77 . Such behavior is common for both monocore and multi-filamentary Bi2223 tapes and the horizontal region is explained due to multiple fracture of oxide filaments [14,15]. Comparing with two curves, the strain at YRT is larger than that at Y77 . As shown in the following section, the strain of such yielding is suggested to correlate with the strain at which Ic starts to decrease abruptly. This is the evidence that the yielding is caused by macroscopic fracture of Bi2223 filaments. Temperature dependence of mechanical property can be explained in terms of thermal residual strain exerted in each component during cooling from annealing temperature to measured one. Residual strain is calculated by the equation, er;i ¼ ðac ai ÞðT TA Þ
3. Results and discussion
100
343
ð1Þ
where ac and ai are thermal expansion coefficients of composite tape and each component i (i ¼ Bi2223, Ag and AgMgNi alloy) and TA is annealing temperature. Yield stress of pure silver is very low and it deforms plastically during cooling. In this case, ac can be calculated approximately from Eq. (2), which is obtained from balance equation of residual stress in each component [16], ry;Ag ðT Þ ac ðT Þ ¼ aBi EBi VBi þ DT ry;Ag ðT Þ þ aAg þ KAg ðT Þ VAg EAg ðT ÞDT þ aAlloy EAlloy ðT ÞVAlloy EBi VBi þ KAg ðT ÞVAg þ EAlloy ðT ÞVAlloy ð2Þ
50
0
0
0.2
0.4
0.6
0.8
1
Strain (%) Fig. 2. Stress–strain curves of Bi2223 composite tape measured at RT and 77 K.
where ry;Ag , ey;Ag and KAg are yield stress, yield strain and work hardening coefficient of Ag, Ei and Vi are YoungÕs modulus and volume fraction of each component, DT is temperature difference between annealing and room or liquid nitrogen temperature. TA is assumed to be 1103 K here. From Eqs. (1) and (2), the difference in residual strain in Bi2223 between RT and 77 K was
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Table 2 Physical property of each component used for the calculation
Bi2223
RT 77 K RT 77 K RT 77 K
Ag Ag alloy
YoungÕs modulus (GPa)
Yield stress (MPa) (GPa)
Work hardening coefficient (GPa)
Thermal expansion coefficient (·106 K1 )
100 100 76 [18] 82 86 [18] 92
– – 11.2 [21] 13.2 [22] – –
– – 0.61 [22] 0.75 [22] – –
13.6 [22] 13.6 21.6 [22] 21.6 21.6 21.6
estimated. Physical properties used for the calculation are summarized in Table 2. YoungÕs modulus of Bi2223 at RT was estimated from the load–unload slope of stress–strain curve for the composite tape and its temperature dependence was neglected. Details of analysis are found elsewhere [17]. YoungÕs modulus of Ag and Ag alloy at RT are cited from Ref. [18] and the values at 77 K were deduced from the data of Neighbours and Alers [19]. Thermal expansion coefficients of Ag and Ag alloy are assumed to be the same [20]. Volume fraction of each component was determined from SEM image of transverse cross-section of the composite tape after polishing and etching [17]. In this sample, volume fraction of Bi2223, Ag and Ag alloy are 0.29, 0.31 and 0.40, respectively. Residual strains in Bi2223 are calculated to be )0.36% and )0.46% for RT (293 K) and 77 K, respectively. From Fig. 2, macroscopic yield strains at RT and 77 K are 0.30% and 0.44%, respectively. The difference of the strains at the yield 1.2
point between RT and 77 K is 0.14%. This value is close to the difference of the calculated residual strains in Bi2223 (0.1%). Therefore, it is suggested that the temperature dependence of stress–strain curve for Bi2223 tape is attributed to the difference of residual strain at RT and 77 K in Bi2223. Bi2223 is still in compressive state at the yield point from our estimation. This contradiction is caused by many assumptions for calculation of residual strain. For more precise discussion, temperature dependence of thermal expansion coefficient should be taken into consideration. 3.2. Transport property under tensile test Fig. 3 show the change of Ic and the stress as a function of strain. In this figure, macroscopic yield strain is indicated by point A. Fig. 3(b) is the enlarged view of Ic –e curve. The Ic decreased linearly with increasing strain up to point B and then it reduces more steeply. At point C, Ic is degraded 1.02
200
(a)
(b)
A 1
1
0.4
c0
100
0.96 B
c
c0 c
I /I
0.6
0.98
I /I
B
0.8
Stress (MPa)
150
0.94
50 0.92
0.2 C 0
0
0.1
0.2
0.3
Strain (%)
0.4
0 0.5
0.9
0
0.1
0.2
0.3
Strain (%)
Fig. 3. Ic –e curve and stress–strain curve (a) and enlarged Ic –e (b).
0.4
0.5
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346
shown in Fig. 4, where the stress was increased up to a maximum point (emax ) and then released up to zero. Change of Ic during load–unload test is shown in Fig. 5. In the conditions between emax ¼ 0:23% and 0.32%, Ic recovered reversibly during loading and unloading processes. On the other hand, the irreversible reduction of Ic appeared for emax ¼ 0:38%. The V –I curves for emax ¼ 0:32% and 0.38% are shown in Fig. 6. The curves shown in this figure correspond to the results of the points indicated by arrows in Fig. 5. For emax ¼ 0:32%, Ic recovers reversibly in the shape of V –I curves before and after loading. On the other hand, for emax ¼ 0:38%, the low voltage region in V –I curve starts to be broadened at the strain more than 0.36%. In such low voltage region, the voltage is suggested to generate predominantly at the part with microcracks in the Bi2223 filament because the cross-section of the oxide filament is smaller by cracks and the current density becomes higher locally. On the other hand, the origins of the reversible decrease of Ic with increasing stress and whether such behavior is common under compressive loading are not clear. One of the possibilities is related to the grain connectivity such as weak link. In order to ensure the possibility, it is necessary to measure the change of intragranular and intergranular Ic under applied stress separately.
almost zero. To comparison with the strain at A and C, the strain corresponding to rapid reduction of Ic agrees well with the macroscopic yielding in the stress–strain curve. The reversibility of Ic degradation was examined in the following. A certain tensile stress was applied and then it was released down to zero. During this process, the Ic was measured under stress. The trace of experimentally applied stress is
200
Stress (MPa)
150
100
50
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Strain (%) Fig. 4. Conditions of load–unload and monotonic stress–strain curve.
εmax=0.23%
εmax=0.26%
1
c
I /I
c0
1
345
0.99
0.99
0.98
0.98
εmax=0.32%
εmax=0.38%
1
0.99
I /I
c0
1
c
0.98 0.98 0.96
0.97 0
0.1
0.2
Strain (%)
0.3
0.4
0
0.1
0.2
0.3
Strain (%)
Fig. 5. Change of Ic during load–unload test for different maximum strain (emin ).
0.4
346
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346 10-3
10-3
Before Loading
Before Loading
10-4
0.30% Load 0.32% Load 0.29% Unload 0.13% Unload
0.34% Load 0.36% Load
log(E) (V/cm)
log(E) (V/cm)
10-4
-5
10
10-6
0.38% Load -5
10
0.36% Unload 0.16% Unload
10-6
10-7
10-7
20
30
40
log(I) (A)
20
30
40
log(I) (A)
Fig. 6. V –I curves before and under applied tensile stress for different maximum strain (emin ).
4. Conclusions Stress–strain behavior of commercial Bi2223 tapes and transport properties under applied stress was investigated. The yielding point in the stress– strain curves at 77 K becomes larger than that at RT. From the calculation based on the rule of mixture, difference of yield strain can be attributed to that of compressive residual strain in Bi2223. Reversible recovery of Ic during load–unload test at low strain was observed. Irreversible degradation of Ic was detected in the change of V –I curves, when the maximum strain exceeded 0.36%. This is the first result that the strain region of reversible change of Ic exists in Bi2223 composite tape. References [1] P. Vase, R. Fl€ ukiger, M. Legissa, B. Golowaki, Supercond. Sci. Technol. 13 (2000) R17. [2] A. Otto, L.J. Masur, J. Gannon, E. Podtburg, D. Daly, G.J. Yurek, A.P. Melozemoff, IEEE Trans. Appl. Supercond. 3 (1993) 915. [3] M. Lahtinen, J. Paasi, Z. Han, J. Sarkaniemi, Physica C 277 (1997) 238. [4] S. Ochiai, K. Hayashi, K. Osamura, Cryogenics 33 (1993) 976. [5] P. Kovac, P. Bukva, Supercond. Sci. Technol. 14 (2001) L8.
[6] B. ten Haken, A. Beuink, H.H.J. ten Kate, IEEE Trans. Appl. Supercond. 7 (1997) 2034. [7] R. Passerini, M. Dhalle, E. Giannini, G. Witz, B. Seeber, R. Fl€ ukiger, Physica C 371 (2002) 173. [8] H. Kitaguchi, K. Itoh, H. Kumakura, T. Takeuchi, K. Togano, H. Wada, IEEE Trans. Appl. Supercond. 11 (2001) 3058. [9] Y. Viouchkov, J. Schwartz, IEEE Trans. Appl. Supercond. 11 (2001) 3062. [10] S.L. Bray, J.W. Ekin, C.C. Clicker, J. Appl. Phys. 88 (2000) 1178. [11] R.L. Holtz, IEEE Trans. Appl. Supercond. 11 (2001) 3238. [12] S. Ochiai, K. Hayashi, K. Osamura, J. Mater. Sci. 25 (1990) 3467. [13] B. ten Haken, H.J. ten Kate, IEEE Trans. Appl. Supercond. 5 (1995) 1298. [14] K. Osamura, S. Nonaka, Y. Katsumura, S. Ochiai, Adv. Supercond. VIII (1996) 787. [15] K. Osamura, M. Sugano, Physica C 357–360 (2001) 1128. [16] K. Osamura, M. Sugano, K. Matsumoto, IEEE Trans. Appl. Supercond. 13 (2003) 3540. [17] M. Sugano, K. Osamura, M. Hojo, Supercond. Sci. Technol. 16 (2003) 571. [18] K.C. Goretta, J.L. Routbort, R.L. Thayer, J.P. Caroll, J. Wolfenstine, J. Kessler, J. Schwartz, Physica C 265 (1996) 201. [19] J.R. Neighbours, G.A. Alers, Phys. Rev. 111 (1958) 707. [20] J. Tembrink, H. Krauth, Supercond. Sci. Technol. 7 (1994) 754. [21] S. Ochiai, K. Hayashi, K. Osamura, Cryogenics 32 (1992) 799. [22] S. Ochiai, K. Hayashi, K. Osamura, Cryogenics 31 (1991) 954.
Stress–strain behavior and degradation of critical current of Bi2223 composite tapes M. Sugano *, K. Osamura Department of Materials Science and Engineering, Kyoto University Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan Received 28 December 2002; received in revised form 15 October 2003; accepted 21 October 2003
Abstract Stress–strain curve of commercially available Bi2223 multi-filamentary tapes was measured at RT and 77 K, which are composed of Bi2223, Ag and Ag alloy. The yielding at 77 K takes place at larger applied strain than that at RT. This behavior was discussed in terms of the residual strain during cooling. The reversibility of strain dependence of Ic was investigated in detail in the low strain region. It recovered reversibly when the maximum strain was less than 0.33%. However, when the applied strain exceeded 0.38%, the irreversible behavior was clearly confirmed. This is the first result that the strain region of reversible change of Ic exists in Bi2223 composite tape. 2003 Elsevier B.V. All rights reserved. PACS: 85.25.K; 62.20.F; 74.60.J Keywords: Bi2223; Stress–strain curve; Residual strain; Reversible change of Ic
1. Introduction Bi2223 tapes are most promising candidate for large scale superconducting devices. However, the tapes with higher critical current density (Jc ) and mechanical tolerance are required for practical application [1]. Mechanical properties and transport properties under applied stress have been widely studied. In the case of application to superconducting magnets, the stress is divided into several complicated compositions; they are tensile, compressive and bending stresses, of which direc* Corresponding author. Tel.: +81-75-7535440; fax: +81-757535486. E-mail address: [email protected] (M. Sugano).
tion is longitudinal and/or transverse one depending on condition. Their influence on critical current (Ic ) has been extensively investigated [2– 11]. Bi2223 tapes are usually composed of Bi2223 filaments, Ag and Ag alloy. Mechanical property of these tapes depends on the property of constituents. During cooling from the annealing temperature, the difference of thermal expansion coefficient among constituents causes compressive and tensile residual stress in oxide and metal sheath, respectively. To investigate stress–strain behavior, such residual stress must be taken into consideration. For Ag/Bi2223 monocore tapes, the stress–strain curve has been analyzed according to the rule of mixture by Ochiai et al. [12]. Macroscopic fracture of oxide core appears as multiple
0921-4534/$ - see front matter 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2003.10.013
342
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346
fracture phenomenon and it can be detected as repetitive drops of stress in stress–strain curve. In addition, it has been reported that the pre-compression due to residual stress in Bi2223 tape has large influence to the strain dependence of Ic [4,7]. Long length Bi2223 tapes experience various kind of working even after heat treatment. Tensile and bending stresses are applied to tapes during winding into coils at RT and checking the distribution of Ic at each position in the direction of length at 77 K. Therefore, it is also important to know the temperature dependence of stress–strain curve in the view point of application. The Ic versus tensile strain curve has typically two regions such as the gradual decrease of Ic at low strain and its drastic reduction at higher one [6]. The latter has been attributed to macroscopic cracking in Bi2223 filaments. A few studies about the former phenomenon has been however reported [6,13]. In this paper, the reversibility of Ic and variation of V –I curves during uniaxially load–unload test at low strain region has been also investigated.
2. Experimental Commercially available multi-filamentary Bi2223 tape (VAM2) was supplied for VAMAS program. Property of the tapes is summarized in Table 1. The tape has pure silver matrix around Bi2223 filaments and AgMgNi alloy sheath is arranged as the outer sheath. Tensile test was carried out by using Instron type tensile testing machine (NMB TCM-500) and testing machine with an electromagnetic actuator (Shimadzu MMT-100N) at RT and 77 K. As shown in Fig. 1, sample and gage lengths of the specimen are 80 and 50 mm, respectively, and
Table 1 Property of the tape examined here Dimension, width · thickness (mm)
Critical current (A) (77 K, SF)
Number of filament
Sheath material
2.95 · 0.182
28
19
Ag/AgMgNi
Fig. 1. Experimental setup for measurement of Ic –e curve.
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346
rubber tabs are attached to both ends of the tape for preventing from breakage near chucks. Strain is measured by using a couple of very light extensometers, which are symmetrically positioned along the tape. The total weight of the extensometers is about 4.3 g. Gage length of the extensometer is 25 mm. V –I measurement was performed by four-probe technique at 77 K under self-field. Ic was determined by 1 lV/cm criterion. Strain dependence of Ic was measured by using the setup shown in Fig. 1. Voltage taps were attached inside the gage of the extensometer and distance between voltage taps is 20 mm. The advantages of this setup are possibilities to measure stress, strain and V –I curve simultaneously and to avoid the influence of contraction of the machine by controlling the load at almost zero during cooling to 77 K.
3.1. Stress–strain behavior measured at different temperatures Stress–strain curves measured at RT and 77 K are shown in Fig. 2. Both curves show clear yielding and become almost horizontal after that.
200 77 K RT
150
Stress (MPa)
In the present study, yield point is defined as that at which slope of stress–strain curve starts to be horizontal and it was determined by eye. The yield points for RT and 77 K are indicated by YRT and Y77 . Such behavior is common for both monocore and multi-filamentary Bi2223 tapes and the horizontal region is explained due to multiple fracture of oxide filaments [14,15]. Comparing with two curves, the strain at YRT is larger than that at Y77 . As shown in the following section, the strain of such yielding is suggested to correlate with the strain at which Ic starts to decrease abruptly. This is the evidence that the yielding is caused by macroscopic fracture of Bi2223 filaments. Temperature dependence of mechanical property can be explained in terms of thermal residual strain exerted in each component during cooling from annealing temperature to measured one. Residual strain is calculated by the equation, er;i ¼ ðac ai ÞðT TA Þ
3. Results and discussion
100
343
ð1Þ
where ac and ai are thermal expansion coefficients of composite tape and each component i (i ¼ Bi2223, Ag and AgMgNi alloy) and TA is annealing temperature. Yield stress of pure silver is very low and it deforms plastically during cooling. In this case, ac can be calculated approximately from Eq. (2), which is obtained from balance equation of residual stress in each component [16], ry;Ag ðT Þ ac ðT Þ ¼ aBi EBi VBi þ DT ry;Ag ðT Þ þ aAg þ KAg ðT Þ VAg EAg ðT ÞDT þ aAlloy EAlloy ðT ÞVAlloy EBi VBi þ KAg ðT ÞVAg þ EAlloy ðT ÞVAlloy ð2Þ
50
0
0
0.2
0.4
0.6
0.8
1
Strain (%) Fig. 2. Stress–strain curves of Bi2223 composite tape measured at RT and 77 K.
where ry;Ag , ey;Ag and KAg are yield stress, yield strain and work hardening coefficient of Ag, Ei and Vi are YoungÕs modulus and volume fraction of each component, DT is temperature difference between annealing and room or liquid nitrogen temperature. TA is assumed to be 1103 K here. From Eqs. (1) and (2), the difference in residual strain in Bi2223 between RT and 77 K was
344
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346
Table 2 Physical property of each component used for the calculation
Bi2223
RT 77 K RT 77 K RT 77 K
Ag Ag alloy
YoungÕs modulus (GPa)
Yield stress (MPa) (GPa)
Work hardening coefficient (GPa)
Thermal expansion coefficient (·106 K1 )
100 100 76 [18] 82 86 [18] 92
– – 11.2 [21] 13.2 [22] – –
– – 0.61 [22] 0.75 [22] – –
13.6 [22] 13.6 21.6 [22] 21.6 21.6 21.6
estimated. Physical properties used for the calculation are summarized in Table 2. YoungÕs modulus of Bi2223 at RT was estimated from the load–unload slope of stress–strain curve for the composite tape and its temperature dependence was neglected. Details of analysis are found elsewhere [17]. YoungÕs modulus of Ag and Ag alloy at RT are cited from Ref. [18] and the values at 77 K were deduced from the data of Neighbours and Alers [19]. Thermal expansion coefficients of Ag and Ag alloy are assumed to be the same [20]. Volume fraction of each component was determined from SEM image of transverse cross-section of the composite tape after polishing and etching [17]. In this sample, volume fraction of Bi2223, Ag and Ag alloy are 0.29, 0.31 and 0.40, respectively. Residual strains in Bi2223 are calculated to be )0.36% and )0.46% for RT (293 K) and 77 K, respectively. From Fig. 2, macroscopic yield strains at RT and 77 K are 0.30% and 0.44%, respectively. The difference of the strains at the yield 1.2
point between RT and 77 K is 0.14%. This value is close to the difference of the calculated residual strains in Bi2223 (0.1%). Therefore, it is suggested that the temperature dependence of stress–strain curve for Bi2223 tape is attributed to the difference of residual strain at RT and 77 K in Bi2223. Bi2223 is still in compressive state at the yield point from our estimation. This contradiction is caused by many assumptions for calculation of residual strain. For more precise discussion, temperature dependence of thermal expansion coefficient should be taken into consideration. 3.2. Transport property under tensile test Fig. 3 show the change of Ic and the stress as a function of strain. In this figure, macroscopic yield strain is indicated by point A. Fig. 3(b) is the enlarged view of Ic –e curve. The Ic decreased linearly with increasing strain up to point B and then it reduces more steeply. At point C, Ic is degraded 1.02
200
(a)
(b)
A 1
1
0.4
c0
100
0.96 B
c
c0 c
I /I
0.6
0.98
I /I
B
0.8
Stress (MPa)
150
0.94
50 0.92
0.2 C 0
0
0.1
0.2
0.3
Strain (%)
0.4
0 0.5
0.9
0
0.1
0.2
0.3
Strain (%)
Fig. 3. Ic –e curve and stress–strain curve (a) and enlarged Ic –e (b).
0.4
0.5
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346
shown in Fig. 4, where the stress was increased up to a maximum point (emax ) and then released up to zero. Change of Ic during load–unload test is shown in Fig. 5. In the conditions between emax ¼ 0:23% and 0.32%, Ic recovered reversibly during loading and unloading processes. On the other hand, the irreversible reduction of Ic appeared for emax ¼ 0:38%. The V –I curves for emax ¼ 0:32% and 0.38% are shown in Fig. 6. The curves shown in this figure correspond to the results of the points indicated by arrows in Fig. 5. For emax ¼ 0:32%, Ic recovers reversibly in the shape of V –I curves before and after loading. On the other hand, for emax ¼ 0:38%, the low voltage region in V –I curve starts to be broadened at the strain more than 0.36%. In such low voltage region, the voltage is suggested to generate predominantly at the part with microcracks in the Bi2223 filament because the cross-section of the oxide filament is smaller by cracks and the current density becomes higher locally. On the other hand, the origins of the reversible decrease of Ic with increasing stress and whether such behavior is common under compressive loading are not clear. One of the possibilities is related to the grain connectivity such as weak link. In order to ensure the possibility, it is necessary to measure the change of intragranular and intergranular Ic under applied stress separately.
almost zero. To comparison with the strain at A and C, the strain corresponding to rapid reduction of Ic agrees well with the macroscopic yielding in the stress–strain curve. The reversibility of Ic degradation was examined in the following. A certain tensile stress was applied and then it was released down to zero. During this process, the Ic was measured under stress. The trace of experimentally applied stress is
200
Stress (MPa)
150
100
50
0 0
0.1
0.2
0.3
0.4
0.5
0.6
Strain (%) Fig. 4. Conditions of load–unload and monotonic stress–strain curve.
εmax=0.23%
εmax=0.26%
1
c
I /I
c0
1
345
0.99
0.99
0.98
0.98
εmax=0.32%
εmax=0.38%
1
0.99
I /I
c0
1
c
0.98 0.98 0.96
0.97 0
0.1
0.2
Strain (%)
0.3
0.4
0
0.1
0.2
0.3
Strain (%)
Fig. 5. Change of Ic during load–unload test for different maximum strain (emin ).
0.4
346
M. Sugano, K. Osamura / Physica C 402 (2004) 341–346 10-3
10-3
Before Loading
Before Loading
10-4
0.30% Load 0.32% Load 0.29% Unload 0.13% Unload
0.34% Load 0.36% Load
log(E) (V/cm)
log(E) (V/cm)
10-4
-5
10
10-6
0.38% Load -5
10
0.36% Unload 0.16% Unload
10-6
10-7
10-7
20
30
40
log(I) (A)
20
30
40
log(I) (A)
Fig. 6. V –I curves before and under applied tensile stress for different maximum strain (emin ).
4. Conclusions Stress–strain behavior of commercial Bi2223 tapes and transport properties under applied stress was investigated. The yielding point in the stress– strain curves at 77 K becomes larger than that at RT. From the calculation based on the rule of mixture, difference of yield strain can be attributed to that of compressive residual strain in Bi2223. Reversible recovery of Ic during load–unload test at low strain was observed. Irreversible degradation of Ic was detected in the change of V –I curves, when the maximum strain exceeded 0.36%. This is the first result that the strain region of reversible change of Ic exists in Bi2223 composite tape. References [1] P. Vase, R. Fl€ ukiger, M. Legissa, B. Golowaki, Supercond. Sci. Technol. 13 (2000) R17. [2] A. Otto, L.J. Masur, J. Gannon, E. Podtburg, D. Daly, G.J. Yurek, A.P. Melozemoff, IEEE Trans. Appl. Supercond. 3 (1993) 915. [3] M. Lahtinen, J. Paasi, Z. Han, J. Sarkaniemi, Physica C 277 (1997) 238. [4] S. Ochiai, K. Hayashi, K. Osamura, Cryogenics 33 (1993) 976. [5] P. Kovac, P. Bukva, Supercond. Sci. Technol. 14 (2001) L8.
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