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Mechanical properties of Gd123 bulk superconductors at room temperature
Cryogenics 43 (2003) 345–350 www.elsevier.com/locate/cryogenics
Mechanical properties of Gd123 bulk superconductors at room temperature q A. Murakami a, K. Katagiri b,*, K. Kasaba b, Y. Shoji b, K. Noto b, H. Teshima c, M. Sawamura c, M. Murakami d a
Graduate School, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan Advanced Technology Research Laboratories, Nippon Steel Corporation, 20-1 Shintomi, Futtsu 293-8551, Japan d Superconductivity Research Laboratory, ISTEC, 1-16-25, Minato-ku, Tokyo 105-0023, Japan b
c
Received 20 September 2002; accepted 27 January 2003
Abstract In order to investigate the mechanical properties of Gd123 single-grain bulk superconductors fabricated using a modified quench and melt growth method, tensile tests in the direction parallel and perpendicular to the c-axis have been carried out at 293 K by using the small specimens cut from bulk superconductors. As for the mechanical properties perpendicular to the c-axis, there was no significant difference between those in the crystal growth direction and those perpendicular to it. While the average value of the YoungÕs modulus of the bulk sample with 33.0 mol%-Gd211 secondary phase particles, 118 GPa, was higher than that of the bulk sample with 28.7 mol%-Gd211, 111 GPa, the average value of the tensile strength of the former, 36 MPa, was lower than that of the latter, 40 MPa. The tensile strength and the YoungÕs modulus in the c-axis, 10 MPa and 37 GPa, were quite low compared with those mentioned above. PoissonÕs ratio based on the transverse strain in the c-axis, 0.15, was significantly smaller than that perpendicular to it, 0.30. In the specimens with higher length, however, the difference was decreased to some extent. With regard to the anisotropy of the PoissonÕs ratio, the effect of a pre-existing micro-crack opening in the c-axis direction was discussed coupled with the constraints at the interfaces between the specimen and the sample holder. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Gd123; Modified QMG; YoungÕs modulus; PoissonÕs ratio; Tensile strength
1. Introduction Highly textured single-grain bulk superconductors with large dimensions fabricated by melt-process are known to trap high magnetic field [1]. However, it has been reported that they often fractured during the magnetization process by the electromagnetic force [2], which is enhanced with the improved performance and enlarged size. Further, they are thought to be subjected to various kinds of external force and non-equilibrium thermal stresses. Hence, the investigations of mechanical q Translation of article originally published in Cryogenic Engineering (Journal of Cryogenic Association of Japan), Vol. 37, 2002, pp. 665–670. * Corresponding author. Tel.: +81-19-621-6412; fax: +81-19-6216412/+81-19-624-3951. E-mail address: [email protected] (K. Katagiri).
properties are indispensable for both the development in the fabrication processing of bulk superconductors with high performance and their applications to, for example, high performance quasi-permanent magnets and current leads [3]. Because bulk superconductors are brittle, their mechanical properties are generally evaluated by three or four point bending tests by using small specimens cut from them [4–6]. However, it is preferable to evaluate the strength by tensile tests, because there exist a stress gradient in the bending test. In order to investigate the detailed distribution of strength in the bulks, the tensile test using small specimens is preferable as compared with the bending test where the specimens with large dimensions are indispensable. Recently, Sakai et al. have carried out the tensile test by using the small specimens cut from the Sm–Ba–Cu–O bulks to investigate the effects of Ag addition and
0011-2275/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0011-2275(03)00047-X
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A. Murakami et al. / Cryogenics 43 (2003) 345–350
fabricating atmosphere on the strength [7,8]. Some of the present authors have reported that the origins of fracture are voids and sub-grains based on the observations for the fracture surfaces induced by the tensile test [9]. Besides the strength of bulk superconductors, the elastic parameters such as YoungÕs modulus and PoissonÕs ratio are necessary for the stress analysis in the magnetization process [2] and the practical applications. Evaluation of the fracture toughness by indentation fracture method [10] also needs the YoungÕs modulus. Although some data of elastic parameters evaluated by indentation and ultrasonic technique have been presented [11,12], those obtained by the mechanical testing, in which the macroscopic behavior is reflected, are also needed for the practical applications. The Gd–Ba–Cu–O bulk superconductors fabricated using the modified quench and melt growth (QMG) process in air [13,14] are expected to be widely used for the applications because of their high performance in the high magnetic field. In this study, tensile tests of the bulk superconductors have been carried out by using the specimens cut from them. In order to evaluate YoungÕs modulus and PoissonÕs ratio, longitudinal and transverse strains have been measured by using strain gages. The distribution of the tensile strength in the bulk superconductors was also revealed.
2. Experimental procedure Gd–Ba–Cu–O bulk superconductors with 46 mm in diameter and 25 mm in thickness used in this study were fabricated using the modified QMG method [13,14]. The precursors with 10 wt% of Ag2 O and 0.5 wt% of Pt were prepared such that GdBa2 Cu3 Ox :Gd2 BaCuO5 in molar ratio was 100 Z:Z (Z ¼ 28.7 and 33.0). They were heated in air up to 1150 °C, kept for 40 min and cooled down to 1035 °C. Then, they were cooled down to 975 °C for the crystal growth after a (Sm,Nd)–Ba–Cu–O seed crystal was placed on the top of them. The sample with 28.7 mol% of Gd2 BaCuO5 and one with 33.0 mol% are denoted Gd29 and Gd33, respectively. Three kinds of small specimens with the dimensions of 3 3 4 mm3 for the tensile tests were cut from the samples such that the longitudinal direction corresponds with the radial direction (parallel to the a=b-axis), circumferential direction (perpendicular to the a=b-axis) and the c-axis of the bulks. They were annealed in O2 atmosphere at 400 °C for 100 h. Tensile tests were carried out by the loading method proposed by Sakai et al. [8] at room temperature. The specimens glued to two aluminum alloy rods by the epoxy resin were loaded through the universal joint by using 300 kgf Shimadzu Survopulser testing machine under the stroke control mode, crosshead speed being
εT
εT
c
Strain gage
εL
εL c
Fig. 1. Schematic illustration of strain measurement.
0.15 mm/min. Both the longitudinal and the transverse strain of the specimens caused by the loading were measured by using strain gages attached to the opposite sides of the specimens. Because of the existence of the pre-existing micro-cracks perpendicular to the c-axis induced during the fabrication process, both transverse strains parallel and perpendicular to the c-axis were measured as shown in Fig. 1. Strain gages used for measuring longitudinal and transverse strain were Kyowa KFL-1-120-C1-16 and KFG-03-120-C1-16.
3. Results and discussion 3.1. Young’s modulus Stress–strain curves for the specimens with the highest YoungÕs modulus and those with the lowest among the specimens of Gd29 and Gd33 are shown in Fig. 2. The data points in the figure represent the stress and the strain at fracture of all the specimens tested. Stress– strain curves loaded in the direction perpendicular to the c-axis were almost linear until the fracture of the specimens. There was a scatter in the value of YoungÕs modulus among the specimens as in the case of tensile strength to be mentioned in the following. YoungÕs modulus of Gd29 varied from 101 to 120 GPa and that of Gd33 from 109 to 132 GPa. The scatter of YoungÕs modulus is presumably ascribed to the difference in the
Fig. 2. Stress–longitudinal strain curves.
A. Murakami et al. / Cryogenics 43 (2003) 345–350
ex ¼
1 frx mðry þ rz Þg E
ð1Þ
where ex is a strain component in x (longitudinal) direction, rx , ry , and rz are stress components, E is YoungÕs modulus, and m is PoissonÕs ratio. So the effects of the constraints on the YoungÕs modulus have been examined by using Gd29 specimens with higher length, 8 and 12 mm, and the same cross sectional area as the specimens with 4 mm in length. The relationship between the YoungÕs modulus and the length of the specimens is shown in Fig. 3. Both the average values of the YoungÕs modulus measured by using the specimens with 8 and 12 mm in length were 118 GPa, which were 6% higher than the average value by 4 mm and fall in the range of scatter. Because the result is contrary to the expectation, it is considered that the YoungÕs modulus obtained by the specimens with 4 mm length was not significantly affected by the constraints. 3.2. Poisson’s ratio The relationship between the stress in the direction perpendicular to the c-axis and the transverse strain of Gd29 is shown in Fig. 4. Data points in the figure represent the tensile strength and the strain at fracture. Stress–transverse strain curves with the highest transverse elastic modulus, slope of the curves, among the
Young's modulus, GPa
140
120
100
80
60 4
8
12
Length of specimen, mm Fig. 3. Relationship between YoungÕs modulus and length of specimen.
60 50
ε T⊥ c ε T || c
40
Stress, MPa
density of voids and to the existence of the cracks parallel to the c-axis [15]. The average value, 118 GPa, for Gd33 with high density of secondary phase particles was 6% higher than that for Gd29, 111 GPa. It has been reported that the YoungÕs modulus of the Y211 secondary phase particles measured by the indentation technique was higher than that of the Y123 matrix [11]. Since no significant difference of the void fraction between the Gd29 and Gd33 could be found on the fracture surfaces, it is considered that the difference in the average value of the YoungÕs modulus was mainly caused by the density of the secondary phase particles. Stress–strain curves in the c-axis showed a non-linear behavior. It is presumably ascribed to the non-linear behavior of the opening of the pre-existing micro-cracks perpendicular to the c-axis or to their slow speed propagation. The average value of the YoungÕs modulus evaluated from the early stage of loading was 37 GPa for both Gd29 and Gd33, which was one-third of that in the direction perpendicular to the c-axis. It is probable that the transverse strain measured is lower than that intrinsic to the bulks, if the transverse strain was affected by the constraints at the interfaces between the short specimen and the sample holder (see the next section). Then, the YoungÕs modulus measured becomes higher from the three-dimensional HookeÕs law described below:
347
30 20 10 0 0.000
0.004
0.008
0.012
0.016
Transverse strain, % Fig. 4. Stress–transverse strain curves.
specimens and those with the lowest are also shown. It was found that the transverse elastic modulus based on the strain parallel to the c-axis was higher than that based on that perpendicular to it. One of the reasons for it is considered to be the opening of the pre-existing micro-cracks perpendicular to the c-axis. The crack opening induced by the constraints at the interfaces between the specimen and the sample holder reduces the shrinkage of the specimen in that direction. Therefore, PoissonÕs ratio, the ratio of transverse strain with respect to the longitudinal strain, becomes different depending on the transverse directions. The PoissonÕs ratio based on the transverse strain parallel to the c-axis varied from 0.11 to 0.19 and that based on the strain perpendicular to it varied from 0.24 to 0.35. The average values of them were 0.15 and 0.30, respectively. The effects of the constraints on the transverse strain were examined by using the specimens with higher length as in the case of the YoungÕs modulus. The relationship between the PoissonÕs ratio and the length of
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A. Murakami et al. / Cryogenics 43 (2003) 345–350 0.5
ε T⊥ c ε T || c
Poisson's ratio
0.4
0.3
0.2
0.1
0.0
4
8
12
Length of specimen, mm Fig. 5. Relationship between PoissonÕs ratio and length of specimen.
the specimen is shown in Fig. 5. Average values of the PoissonÕs ratio based on the strain perpendicular to the c-axis by using the specimens with 8 and 12 mm were 0.38 and 0.36, which were 20–30% higher than that with 4 mm. On the other hand, the PoissonÕs ratio based on the strain parallel to the c-axis by using 8 and 12 mm were 0.23 and 0.26, which were 50–70% higher than that with 4 mm. It was found that both the transverse strains parallel and perpendicular to the c-axis were affected by the constraints, and the effect was larger in the former, where the opening behavior of the pre-existing microcracks reduces the shrinkage.
Fig. 6. Distribution of tensile strength: (a) Gd29 and (b) Gd33.
3.3. Tensile strength The distribution of the tensile strength in Gd29 and Gd33 is shown in Fig. 6(a) and (b). Tensile strength in the direction perpendicular to the c-axis widely scattered as in the case of Sm–Ba–Cu–O bulk [7,8]. The average value of Gd29 was 40 MPa, which is slightly higher than that of the Ag added Sm–Ba–Cu–O reported, 37 MPa [7]. Tensile strength of the circumferential region in the bulks was slightly higher than that of the central region. This is contrary to the report on (Sm,Gd)–Ba–Cu–O [16]. With regard to the distance from the top surface, the strength of the specimens in the first layer from the top surface was also slightly higher than that in the second layer. It has been reported that the sub-grains were elongated in the radial crystal growth direction, aor b-axis [17]. The area of the sub-grain boundary is larger when the specimens are loaded perpendicular to it. While the maximum value of tensile strength in the growth direction was lower than that in the direction perpendicular to it, the average value was 40 MPa for both directions. The scatter of the tensile strength is presumably ascribed to the difference in the net stress and the stress concentration originated from the distri-
bution of the size, shape and density of voids, the origin of cracks, or to the pre-existing cracks parallel to the caxis [15]. It has been reported that the secondary phase particles were effective in suppressing crack propagation [11,18] and improving the fracture toughness evaluated by the indentation method in Y–Ba–Cu–O bulk [19]. On the other hand, it has recently been clarified that the tensile strength of Nd–Ba–Cu–O bulk increased with increase in secondary phase particle content from 13.0 to 20.0 mol% and then decreased at 23.1% [15]. The present authors have also shown that the tensile strength of (Nd,Eu,Gd)–Ba–Cu–O bulk with 40 mol% secondary phase particles was lower than that with 30 mol% [20], which was higher than the content showing the highest strength in Nd–Ba–Cu–O bulk. In this study, the average value of the tensile strength of Gd33 with high density of the secondary phase particles, 36 MPa, was lower than that of Gd29, 40 MPa. The cohesive force between the secondary phase particles and the matrix is deduced to be lower than the strength of the secondary phase particles and that of the matrix. Many secondary phase particles and depressions formed by decohesion of
A. Murakami et al. / Cryogenics 43 (2003) 345–350
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factor m, a measure of scatter, for Gd29 (m ¼ 4:51) and that for Gd33 (m ¼ 4:87), respectively. These values were slightly higher than 3.03 for Sm–Ba–Cu–O with 10 wt% Ag reported [8]. Although, no intrinsic difference from others was observed on the fracture surface for two specimens of Gd29 with erratically lower strength, the m value reaches to 8.39 (averaged tensile strength being 43 MPa) if the two data were deleted. The maximum and the minimum values of the tensile strength in the c-axis were 11 and 9 MPa. These values were quite lower than those in the direction perpendicular to the c-axis. There was no significant scatter of the tensile strength. Judging from this, the size and the distribution of the pre-existing micro-cracks perpendicular to the c-axis are deduced to be rather uniform.
4. Conclusion
Fig. 7. A sub-grain and secondary phase particle on the fracture surface of Gd29.
them from the matrix were found on the fracture surfaces as shown in Fig. 7. In this figure, they are clearly seen in the regions of both matrix with numerous steps perpendicular to the c-axis and a sub-grain. Although, the secondary phase particles may suppress initial propagation of cracks, they appear to decrease the tensile strength by decohesion. Weibull plots of the tensile strength are shown in Fig. 8. There was no significant difference between the shape 2
1
Gd 29 Gd 33
0
lnln{1/(1-F)}
m (Gd33) = 4.87
-1
-2 m (Gd29) = 4.51
-3
Tensile tests of the Gd123 bulk superconductors fabricated using the modified QMG method have been carried out at room temperature by using the specimens cut from them. We obtained the following conclusions: (1) Stress–strain curves in the direction perpendicular to the c-axis were almost linear until the fracture of the specimen. There was no significant difference in the YoungÕs modulus and the tensile strength between the samples loaded in the crystal growth direction, a=b-axis, and those perpendicular to it. While the average value of the YoungÕs modulus of Gd33 with high density of 211 secondary phase particles, 118 GPa, was higher than that of Gd29, 111 GPa, the average value of the tensile strength of the former, 36 MPa, was lower than that of the latter, 40 MPa. These are presumably due to the higher YoungÕs modulus of 211 particles and the low cohesive force between the 211 particles and the matrix. (2) The average values of the YoungÕs modulus and the tensile strength in the c-axis, 37 GPa and 10 MPa, were quite lower than those in the direction perpendicular to it because of the existence of the pre-existing micro-cracks perpendicular to the c-axis. (3) Average PoissonÕs ratio based on the transverse strain parallel to the c-axis, 0.15, was lower than that based on the strain perpendicular to it, 0.30. This is presumably ascribed to the opening of the pre-existing micro-cracks accompanied by the shrinkage of the matrix. The extent of the anisotropy was affected by the extent of the constraints at the interfaces between the specimen and the sample holder. The effect of constraint was not so significant in the YoungÕs modulus.
-4 3.0
3 .5
4.0
ln(σ) Fig. 8. Weibull plots of tensile strength in direction perpendicular to caxis.
Acknowledgements We appreciate helpful assistance in the experiment by M. Takahashi of Iwate University. This work was
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A. Murakami et al. / Cryogenics 43 (2003) 345–350
partially supported by Japan Science and Technology Corporation under the Joint-research Project for Regional Intensive in Iwate Prefecture on ‘‘Development of practical applications of magnetic field technology for use in the region and in everyday living’’ and also partially supported by NEDO.
References [1] Ikuta H, Mase A, Yanagi Y, Yoshikawa M, Itoh Y, Oka T, et al. Supercond Sci Technol 1998;11:1345. [2] Miyamoto T, Nagashima K, Sakai N, Murakami M. Physica C 2000;340:41. [3] Murakami M. Cryo Eng (J Cryo Assoc Jpn) 1999;34:92 [in Japanese]. [4] Singh JP, Leu HJ, Poeppel RB, Voorhees EV, Goudey GT, Winsley K, et al. J Appl Phys 1989;66:3154. [5] Joo J, Kim JG, Nah W. Supercond Sci Technol 1998;11:645. [6] Goretta KC, Diko P, Jiang M, Cuber MM. IEEE Trans Appl Supercond 1999;9:2081. [7] Sakai N, Seo SJ, Inoue K, Miyamoto T, Murakami M. Physica C 2000;335:107.
[8] Sakai N, Mase A, Ikuta H, Seo SJ, Mizutani U, Murakami M. Supercond Sci Technol 2000;13:770. [9] Katagiri K, Kasaba K, Shoji Y, Chiba A, Tomita M, Miyamoto T, et al. Physica C 2001;357–360:803. [10] Yoshino Y, Iwabuchi A, Noto K, Sakai N, Murakami M. Physica C 2001;357–360:796. [11] Goyal A, Oliver WC, Funkenbusch PD, Kroeger DM, Burns SJ. Physica C 1991;183:221. [12] Reddy RR, Murakami M, Tanaka S, Reddy PV. Physica C 1996;257:137. [13] Morita M, Sawamura M, Takebayashi S, Kimura K, Teshima H, Tanaka M, et al. Physica C 1994;235–240:209. [14] Sawamura M, Morita M. Supercond Sci Technol 2002;15:774. [15] Matsui M, Sakai N, Murakami M. Physica C 2003;384:391. [16] Katagiri K, Murakami A, Sato T, Okudera T, Sakai N, Muralidhar M, et al. Physica C 2002;378–381:722. [17] Morita M, Trouilleux L, Miyamoto K, Hashimoto M. In: Proc 5th U.S.–Japan Workshop on High Tc Superconductors, 1992. p. 95. [18] Murakami A, Katagiri K, Kasaba K, Shoji Y, Noto K, Sakai N, et al. Supercond Sci Technol 2002;15:1099. [19] Fujimoto H, Murakami M, Koshizuka N. Physica C 1992;203:103. [20] Murakami A, Katagiri K, Noto K, Kasaba K, Shoji Y, Muralidhar M, et al. Physica C 2002;378–381:794.
Mechanical properties of Gd123 bulk superconductors at room temperature q A. Murakami a, K. Katagiri b,*, K. Kasaba b, Y. Shoji b, K. Noto b, H. Teshima c, M. Sawamura c, M. Murakami d a
Graduate School, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan Advanced Technology Research Laboratories, Nippon Steel Corporation, 20-1 Shintomi, Futtsu 293-8551, Japan d Superconductivity Research Laboratory, ISTEC, 1-16-25, Minato-ku, Tokyo 105-0023, Japan b
c
Received 20 September 2002; accepted 27 January 2003
Abstract In order to investigate the mechanical properties of Gd123 single-grain bulk superconductors fabricated using a modified quench and melt growth method, tensile tests in the direction parallel and perpendicular to the c-axis have been carried out at 293 K by using the small specimens cut from bulk superconductors. As for the mechanical properties perpendicular to the c-axis, there was no significant difference between those in the crystal growth direction and those perpendicular to it. While the average value of the YoungÕs modulus of the bulk sample with 33.0 mol%-Gd211 secondary phase particles, 118 GPa, was higher than that of the bulk sample with 28.7 mol%-Gd211, 111 GPa, the average value of the tensile strength of the former, 36 MPa, was lower than that of the latter, 40 MPa. The tensile strength and the YoungÕs modulus in the c-axis, 10 MPa and 37 GPa, were quite low compared with those mentioned above. PoissonÕs ratio based on the transverse strain in the c-axis, 0.15, was significantly smaller than that perpendicular to it, 0.30. In the specimens with higher length, however, the difference was decreased to some extent. With regard to the anisotropy of the PoissonÕs ratio, the effect of a pre-existing micro-crack opening in the c-axis direction was discussed coupled with the constraints at the interfaces between the specimen and the sample holder. Ó 2003 Elsevier Science Ltd. All rights reserved. Keywords: Gd123; Modified QMG; YoungÕs modulus; PoissonÕs ratio; Tensile strength
1. Introduction Highly textured single-grain bulk superconductors with large dimensions fabricated by melt-process are known to trap high magnetic field [1]. However, it has been reported that they often fractured during the magnetization process by the electromagnetic force [2], which is enhanced with the improved performance and enlarged size. Further, they are thought to be subjected to various kinds of external force and non-equilibrium thermal stresses. Hence, the investigations of mechanical q Translation of article originally published in Cryogenic Engineering (Journal of Cryogenic Association of Japan), Vol. 37, 2002, pp. 665–670. * Corresponding author. Tel.: +81-19-621-6412; fax: +81-19-6216412/+81-19-624-3951. E-mail address: [email protected] (K. Katagiri).
properties are indispensable for both the development in the fabrication processing of bulk superconductors with high performance and their applications to, for example, high performance quasi-permanent magnets and current leads [3]. Because bulk superconductors are brittle, their mechanical properties are generally evaluated by three or four point bending tests by using small specimens cut from them [4–6]. However, it is preferable to evaluate the strength by tensile tests, because there exist a stress gradient in the bending test. In order to investigate the detailed distribution of strength in the bulks, the tensile test using small specimens is preferable as compared with the bending test where the specimens with large dimensions are indispensable. Recently, Sakai et al. have carried out the tensile test by using the small specimens cut from the Sm–Ba–Cu–O bulks to investigate the effects of Ag addition and
0011-2275/03/$ - see front matter Ó 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0011-2275(03)00047-X
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A. Murakami et al. / Cryogenics 43 (2003) 345–350
fabricating atmosphere on the strength [7,8]. Some of the present authors have reported that the origins of fracture are voids and sub-grains based on the observations for the fracture surfaces induced by the tensile test [9]. Besides the strength of bulk superconductors, the elastic parameters such as YoungÕs modulus and PoissonÕs ratio are necessary for the stress analysis in the magnetization process [2] and the practical applications. Evaluation of the fracture toughness by indentation fracture method [10] also needs the YoungÕs modulus. Although some data of elastic parameters evaluated by indentation and ultrasonic technique have been presented [11,12], those obtained by the mechanical testing, in which the macroscopic behavior is reflected, are also needed for the practical applications. The Gd–Ba–Cu–O bulk superconductors fabricated using the modified quench and melt growth (QMG) process in air [13,14] are expected to be widely used for the applications because of their high performance in the high magnetic field. In this study, tensile tests of the bulk superconductors have been carried out by using the specimens cut from them. In order to evaluate YoungÕs modulus and PoissonÕs ratio, longitudinal and transverse strains have been measured by using strain gages. The distribution of the tensile strength in the bulk superconductors was also revealed.
2. Experimental procedure Gd–Ba–Cu–O bulk superconductors with 46 mm in diameter and 25 mm in thickness used in this study were fabricated using the modified QMG method [13,14]. The precursors with 10 wt% of Ag2 O and 0.5 wt% of Pt were prepared such that GdBa2 Cu3 Ox :Gd2 BaCuO5 in molar ratio was 100 Z:Z (Z ¼ 28.7 and 33.0). They were heated in air up to 1150 °C, kept for 40 min and cooled down to 1035 °C. Then, they were cooled down to 975 °C for the crystal growth after a (Sm,Nd)–Ba–Cu–O seed crystal was placed on the top of them. The sample with 28.7 mol% of Gd2 BaCuO5 and one with 33.0 mol% are denoted Gd29 and Gd33, respectively. Three kinds of small specimens with the dimensions of 3 3 4 mm3 for the tensile tests were cut from the samples such that the longitudinal direction corresponds with the radial direction (parallel to the a=b-axis), circumferential direction (perpendicular to the a=b-axis) and the c-axis of the bulks. They were annealed in O2 atmosphere at 400 °C for 100 h. Tensile tests were carried out by the loading method proposed by Sakai et al. [8] at room temperature. The specimens glued to two aluminum alloy rods by the epoxy resin were loaded through the universal joint by using 300 kgf Shimadzu Survopulser testing machine under the stroke control mode, crosshead speed being
εT
εT
c
Strain gage
εL
εL c
Fig. 1. Schematic illustration of strain measurement.
0.15 mm/min. Both the longitudinal and the transverse strain of the specimens caused by the loading were measured by using strain gages attached to the opposite sides of the specimens. Because of the existence of the pre-existing micro-cracks perpendicular to the c-axis induced during the fabrication process, both transverse strains parallel and perpendicular to the c-axis were measured as shown in Fig. 1. Strain gages used for measuring longitudinal and transverse strain were Kyowa KFL-1-120-C1-16 and KFG-03-120-C1-16.
3. Results and discussion 3.1. Young’s modulus Stress–strain curves for the specimens with the highest YoungÕs modulus and those with the lowest among the specimens of Gd29 and Gd33 are shown in Fig. 2. The data points in the figure represent the stress and the strain at fracture of all the specimens tested. Stress– strain curves loaded in the direction perpendicular to the c-axis were almost linear until the fracture of the specimens. There was a scatter in the value of YoungÕs modulus among the specimens as in the case of tensile strength to be mentioned in the following. YoungÕs modulus of Gd29 varied from 101 to 120 GPa and that of Gd33 from 109 to 132 GPa. The scatter of YoungÕs modulus is presumably ascribed to the difference in the
Fig. 2. Stress–longitudinal strain curves.
A. Murakami et al. / Cryogenics 43 (2003) 345–350
ex ¼
1 frx mðry þ rz Þg E
ð1Þ
where ex is a strain component in x (longitudinal) direction, rx , ry , and rz are stress components, E is YoungÕs modulus, and m is PoissonÕs ratio. So the effects of the constraints on the YoungÕs modulus have been examined by using Gd29 specimens with higher length, 8 and 12 mm, and the same cross sectional area as the specimens with 4 mm in length. The relationship between the YoungÕs modulus and the length of the specimens is shown in Fig. 3. Both the average values of the YoungÕs modulus measured by using the specimens with 8 and 12 mm in length were 118 GPa, which were 6% higher than the average value by 4 mm and fall in the range of scatter. Because the result is contrary to the expectation, it is considered that the YoungÕs modulus obtained by the specimens with 4 mm length was not significantly affected by the constraints. 3.2. Poisson’s ratio The relationship between the stress in the direction perpendicular to the c-axis and the transverse strain of Gd29 is shown in Fig. 4. Data points in the figure represent the tensile strength and the strain at fracture. Stress–transverse strain curves with the highest transverse elastic modulus, slope of the curves, among the
Young's modulus, GPa
140
120
100
80
60 4
8
12
Length of specimen, mm Fig. 3. Relationship between YoungÕs modulus and length of specimen.
60 50
ε T⊥ c ε T || c
40
Stress, MPa
density of voids and to the existence of the cracks parallel to the c-axis [15]. The average value, 118 GPa, for Gd33 with high density of secondary phase particles was 6% higher than that for Gd29, 111 GPa. It has been reported that the YoungÕs modulus of the Y211 secondary phase particles measured by the indentation technique was higher than that of the Y123 matrix [11]. Since no significant difference of the void fraction between the Gd29 and Gd33 could be found on the fracture surfaces, it is considered that the difference in the average value of the YoungÕs modulus was mainly caused by the density of the secondary phase particles. Stress–strain curves in the c-axis showed a non-linear behavior. It is presumably ascribed to the non-linear behavior of the opening of the pre-existing micro-cracks perpendicular to the c-axis or to their slow speed propagation. The average value of the YoungÕs modulus evaluated from the early stage of loading was 37 GPa for both Gd29 and Gd33, which was one-third of that in the direction perpendicular to the c-axis. It is probable that the transverse strain measured is lower than that intrinsic to the bulks, if the transverse strain was affected by the constraints at the interfaces between the short specimen and the sample holder (see the next section). Then, the YoungÕs modulus measured becomes higher from the three-dimensional HookeÕs law described below:
347
30 20 10 0 0.000
0.004
0.008
0.012
0.016
Transverse strain, % Fig. 4. Stress–transverse strain curves.
specimens and those with the lowest are also shown. It was found that the transverse elastic modulus based on the strain parallel to the c-axis was higher than that based on that perpendicular to it. One of the reasons for it is considered to be the opening of the pre-existing micro-cracks perpendicular to the c-axis. The crack opening induced by the constraints at the interfaces between the specimen and the sample holder reduces the shrinkage of the specimen in that direction. Therefore, PoissonÕs ratio, the ratio of transverse strain with respect to the longitudinal strain, becomes different depending on the transverse directions. The PoissonÕs ratio based on the transverse strain parallel to the c-axis varied from 0.11 to 0.19 and that based on the strain perpendicular to it varied from 0.24 to 0.35. The average values of them were 0.15 and 0.30, respectively. The effects of the constraints on the transverse strain were examined by using the specimens with higher length as in the case of the YoungÕs modulus. The relationship between the PoissonÕs ratio and the length of
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ε T⊥ c ε T || c
Poisson's ratio
0.4
0.3
0.2
0.1
0.0
4
8
12
Length of specimen, mm Fig. 5. Relationship between PoissonÕs ratio and length of specimen.
the specimen is shown in Fig. 5. Average values of the PoissonÕs ratio based on the strain perpendicular to the c-axis by using the specimens with 8 and 12 mm were 0.38 and 0.36, which were 20–30% higher than that with 4 mm. On the other hand, the PoissonÕs ratio based on the strain parallel to the c-axis by using 8 and 12 mm were 0.23 and 0.26, which were 50–70% higher than that with 4 mm. It was found that both the transverse strains parallel and perpendicular to the c-axis were affected by the constraints, and the effect was larger in the former, where the opening behavior of the pre-existing microcracks reduces the shrinkage.
Fig. 6. Distribution of tensile strength: (a) Gd29 and (b) Gd33.
3.3. Tensile strength The distribution of the tensile strength in Gd29 and Gd33 is shown in Fig. 6(a) and (b). Tensile strength in the direction perpendicular to the c-axis widely scattered as in the case of Sm–Ba–Cu–O bulk [7,8]. The average value of Gd29 was 40 MPa, which is slightly higher than that of the Ag added Sm–Ba–Cu–O reported, 37 MPa [7]. Tensile strength of the circumferential region in the bulks was slightly higher than that of the central region. This is contrary to the report on (Sm,Gd)–Ba–Cu–O [16]. With regard to the distance from the top surface, the strength of the specimens in the first layer from the top surface was also slightly higher than that in the second layer. It has been reported that the sub-grains were elongated in the radial crystal growth direction, aor b-axis [17]. The area of the sub-grain boundary is larger when the specimens are loaded perpendicular to it. While the maximum value of tensile strength in the growth direction was lower than that in the direction perpendicular to it, the average value was 40 MPa for both directions. The scatter of the tensile strength is presumably ascribed to the difference in the net stress and the stress concentration originated from the distri-
bution of the size, shape and density of voids, the origin of cracks, or to the pre-existing cracks parallel to the caxis [15]. It has been reported that the secondary phase particles were effective in suppressing crack propagation [11,18] and improving the fracture toughness evaluated by the indentation method in Y–Ba–Cu–O bulk [19]. On the other hand, it has recently been clarified that the tensile strength of Nd–Ba–Cu–O bulk increased with increase in secondary phase particle content from 13.0 to 20.0 mol% and then decreased at 23.1% [15]. The present authors have also shown that the tensile strength of (Nd,Eu,Gd)–Ba–Cu–O bulk with 40 mol% secondary phase particles was lower than that with 30 mol% [20], which was higher than the content showing the highest strength in Nd–Ba–Cu–O bulk. In this study, the average value of the tensile strength of Gd33 with high density of the secondary phase particles, 36 MPa, was lower than that of Gd29, 40 MPa. The cohesive force between the secondary phase particles and the matrix is deduced to be lower than the strength of the secondary phase particles and that of the matrix. Many secondary phase particles and depressions formed by decohesion of
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factor m, a measure of scatter, for Gd29 (m ¼ 4:51) and that for Gd33 (m ¼ 4:87), respectively. These values were slightly higher than 3.03 for Sm–Ba–Cu–O with 10 wt% Ag reported [8]. Although, no intrinsic difference from others was observed on the fracture surface for two specimens of Gd29 with erratically lower strength, the m value reaches to 8.39 (averaged tensile strength being 43 MPa) if the two data were deleted. The maximum and the minimum values of the tensile strength in the c-axis were 11 and 9 MPa. These values were quite lower than those in the direction perpendicular to the c-axis. There was no significant scatter of the tensile strength. Judging from this, the size and the distribution of the pre-existing micro-cracks perpendicular to the c-axis are deduced to be rather uniform.
4. Conclusion
Fig. 7. A sub-grain and secondary phase particle on the fracture surface of Gd29.
them from the matrix were found on the fracture surfaces as shown in Fig. 7. In this figure, they are clearly seen in the regions of both matrix with numerous steps perpendicular to the c-axis and a sub-grain. Although, the secondary phase particles may suppress initial propagation of cracks, they appear to decrease the tensile strength by decohesion. Weibull plots of the tensile strength are shown in Fig. 8. There was no significant difference between the shape 2
1
Gd 29 Gd 33
0
lnln{1/(1-F)}
m (Gd33) = 4.87
-1
-2 m (Gd29) = 4.51
-3
Tensile tests of the Gd123 bulk superconductors fabricated using the modified QMG method have been carried out at room temperature by using the specimens cut from them. We obtained the following conclusions: (1) Stress–strain curves in the direction perpendicular to the c-axis were almost linear until the fracture of the specimen. There was no significant difference in the YoungÕs modulus and the tensile strength between the samples loaded in the crystal growth direction, a=b-axis, and those perpendicular to it. While the average value of the YoungÕs modulus of Gd33 with high density of 211 secondary phase particles, 118 GPa, was higher than that of Gd29, 111 GPa, the average value of the tensile strength of the former, 36 MPa, was lower than that of the latter, 40 MPa. These are presumably due to the higher YoungÕs modulus of 211 particles and the low cohesive force between the 211 particles and the matrix. (2) The average values of the YoungÕs modulus and the tensile strength in the c-axis, 37 GPa and 10 MPa, were quite lower than those in the direction perpendicular to it because of the existence of the pre-existing micro-cracks perpendicular to the c-axis. (3) Average PoissonÕs ratio based on the transverse strain parallel to the c-axis, 0.15, was lower than that based on the strain perpendicular to it, 0.30. This is presumably ascribed to the opening of the pre-existing micro-cracks accompanied by the shrinkage of the matrix. The extent of the anisotropy was affected by the extent of the constraints at the interfaces between the specimen and the sample holder. The effect of constraint was not so significant in the YoungÕs modulus.
-4 3.0
3 .5
4.0
ln(σ) Fig. 8. Weibull plots of tensile strength in direction perpendicular to caxis.
Acknowledgements We appreciate helpful assistance in the experiment by M. Takahashi of Iwate University. This work was
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partially supported by Japan Science and Technology Corporation under the Joint-research Project for Regional Intensive in Iwate Prefecture on ‘‘Development of practical applications of magnetic field technology for use in the region and in everyday living’’ and also partially supported by NEDO.
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