Relation of strength distribution of Nb3Al filaments to strength of multifilamentary superconducting composite wire

Cryogenics 36 (1996) 249-253 0 19% Elsevier Science Limited Printed in Great Britain. All rights reserved OOll-2275/96/$15.00 ELSEVIER

Relation of strength distribution of Nb,Al filaments to strength of multifilamentary superconducting composite wire S. Ochiai, T. Sawada, and Y. Yamada*

S. Nishino,

M. Hojo,

K. Takahashi*

Mesoscopic Materials Research Center, Faculty of Engineering, Kyoto University, Sakyo-ku, Kyoto 606-01, Japan “Sumitomo Electric Industries Ltd, Konohana-ku, Osaka 554, Japan Received 20 June 1995; revised 24 August

1995

The distribution of tensile strength of NbBAl filaments and its relation to tensile strength of NbBAl multifilamentary superconducting composite wire were studied. The main results can be summarized as follows .( 1-j The tensile-strength of the. extracted filaments with an average diameter of 24pm was estimated based on the two-parameter Weibull distribution function. The shape and scale parameters were 7.0 and 530 MPa (for a standard length of 1 m), respectively. (2) Although the scatter of the strength of the Nb3Al filaments was large, that of the multifilamentary composite was very small. This means that, when a large number of filaments are embedded in a composite, the stress leading to overall fracture of the composite is not very different from sample to sample, even though the strengths of the embedded filaments are significantly different. This feature was confirmed by means of a computer-aided Monte Carlo simulation. (3) It was shown by experiment and simulation that the strength of the NbBAl composite wire has a very slight dependence on length, although the strength of the NbBAl filament decreases markedly with increasing length. This result indicates that, even if the length of the composite wire is extended from a short, laboratory scale sample to an industrial scale, the reduction in strength will be very small. Keywords: Nb,AI; strength; Weibull distribution; fracture; length

Stresses are applied to a superconducting composite wire mechanically during fabrication and/or handling and also electromagnetically (Lorentz force) when in use. From this point of view, it is necessary to clarify the resulting mechanical behaviour. However, to date a detailed analysis of the deformation and fracture behaviour has not been done, while several efforts have been made to reveal the straineffect on the critical current and upper critical magnetic field’. Concerning Nb3Al superconducting composite wires, it is now known that this composite has high critical current densities at high magnetic fields, and high strain endurance and low strain sensitivity of the critical current’-6. However, there are no data on strength and its distribution in terms of Nb3A1 filaments at present. Also the relation of the strength distribution of the filaments to the overall strength of the resulting multifilamentary composite is unknown. Furthermore, the length dependence of the strength of such a composite wire is still unknown, although such information is needed for the purposes of reliability and design.

The aims of the present work are to measure the distribution of strength of Nb3Al filaments extracted from the composite wire and to clarify the relation of this distribution to the strength of the multifilamentary composite wire with the aid of a Monte Carlo simulation method, which has been demonstrated to describe well the experimental strength distributions of various kinds of fibrereinforced composite materials7-9. Furthermore, we attempt to predict the length dependence of the strength of the present composite wire from data obtained using short samples.

Experimental

procedures

The multifilamentary Nb3A1 superconducting composite wire was fabricated by means of the Jelly-roll method3,4,6 at Sumitomo Electric Industries. The cross-section of the composite wire with an overall diameter of 0.817 mm, being composed of 486 filaments with an average diameter of 24 pm and copper as a stabilizer, is shown in Figure 1.

Cryogenics

1996 Volume

36, Number

4

249

Strength

of Nb&V filaments

and multifilamentary

200pm Figure 1

Cross-section

of Nb3AI composite

wire

The volume fractions of the filaments and copper matrix were 0.42 and 0.58, respectively. Each filament was composed of copper in the central part, Nb3Al in the middle part and niobium in the outer part; overall the Nb3A1 occupied 60% of the cross-sectional area of the filaments. The filaments were extracted by etching away the copper stabilizer with a 30% HNO,+ 70% HZ0 solution. The tensile test procedure for the filament samples is schematically shown in Figure 2. For protection of the fibre during handling, both ends of a filament were glued on to a paper frame, the ends of the frame were set into grips and the frame was then cut. The tensile test was carried out at room temperature at the nominal strain rate of 3.3 x lo4 s-’ for gauge lengths of 20, 50 and 150 mm. More than 40 filaments were tested for each gauge length and the results were analysed statistically based on the two-parameter Weibull distribution function”. The multifilamentary composite samples were also tested at the same strain rate for gauge lengths of 20, 50, 150 and 350 mm. For each gauge length, more than 10 samples were tested to obtain average strength, and for the gauge

wire: S. Ochiai et al. length of 50 mm, 60 samples were tested to obtain strength distribution. To avoid breakage of the samples in the grips during the tesile test, the ends of the samples were embedded in bronze tubes and bonded with a cyano-acrylate adhesive, and then the ends of the samples were set into pneumatic grips with specially prepared fine faces (Shimadzu, 1 kN). The strength distribution of the composite wire was simulated by means of a computer-aided Monte Carlo simulation method7-9 in combination with a shear lag analysis”-13 to calculate the stress disturbances around the broken filaments. This method has been demonstrated to describe well the tensile fracture behaviour of boron and Tyranno fibre-reinforced aluminium matrix composites7-9. In the stimulation, the interface between the filaments and copper was treated so as to have a high enough bonding strength to prevent debonding, because no pull-out of the filaments was observed in the fracture surface, as shown in Figure 3. The following were used as input values: Young’s modulus of Nb3A1 150 GPa (estimated from the stress-strain curve of the filament); shear modulus of copper, 40 GPa; volume fractions of the filament and copper in the composite, 0.42 and 0.58, respectively; yield stress of copper (estimated from the measured Vicker’s hardness for the copper in the centre of the composite), 250 MPa; diameter of filament, 24 pm; and shape and scale parameters of the Weibull function for the strength distribution of the filament, 7.0 and 530 MPa, respectively (as shown later).

Results and discussion Average strength and distribution extracted filaments

of strength of

Figure 4 shows the distribution

of strength of the extracted filaments for gauge lengths L of 20, 50 and 150 mm. The average strengths were 850, 770 and 650 MPa for L = 20, 50 and 150 mm, respectively. For the description of the distribution of strength of metals and ceramics, the twoparameter Weibull distribution model is known to be useful. Recently it has been shown that the strength distribution of the Nb,Sn compound in multifilamentary superconducting composite wires can also be described using

Filament

Cut afte setting

Paper

I

Grip

100fim

0 Figure 2

250

Schematic

Cryogenics

representation

of tensile test for filaments

1996 Volume

36, Number

4

Figure 3

Fracture surface of composite

Strength

of Nb+V

filaments

and multifilamentary

;;i

wire: S. Ochiai et al.

1000

800 & z 600 c G 400 P g 200 0

100

200 300 Umm)

400

Figure 6 Measured average strengths of filaments a‘ ,ayej and composite wire a, ,ayej, plotteti against gauge length L, together with simulation result for comlJosite strength

bf (MPa) Figure4 Distribution of strength q of extracted filaments. Solid curves show distributions calculated using estimated values of m= 7.0 and G, = 530 MPa

this function’4,‘5. Thus in the present work, this function was applied. According to the two-parameter Weibull distribution”, the cumulative probability of failure F at a stress a, for a material of the length L is given by F = I-exp

{- (L/L,) ( ar/ao)‘“}

(1)

where m and a0 are the shape and scale parameters, respectively, and Lo is the standard length (taken to be 1 m in the present work). The parameter m is a measure of scatter; the smaller m is, the larger the scatter. The parameter a0 corresponds to the strength at F = l-l/e for a standard length, which can be regarded as a characteristic strength, independent of gauge length. Figure 5 shows the results of the Weibull plot [plot of 1n In {l/( 1-F)) against In (at)]. From the slope and intersection, the parameters were estimated to be m = 6.9, 7.0 and 7.0, and a0 = 510, 540 and 540 MPa for L (length of the samples) = 20, 50 and 150 mm, respectively. Within the accuracy of the present work, the values of m and a0 are almost identical for any length. Then averaging the results, m and a, were determined to be 7.0 and 530 MPa, respectively. Using these values, the strength distribution was recalculated using Equation (1). The results are shown by

the solid curves in Figure 4. The experimental results were fairly well described by these values. The scatter of the strength of the present filaments (m = 7.0) was smaller than for industrial metal materials (m >30-50), comparable with Nb,Sn (m = 7-12)14,15 but larger than for glass filaments (m = 3%6.4)16. Figure 6 shows the measured average strength a,,,,,, of the extracted filaments plotted against gauge length L. The strength decreases with increasing L. According to the Weibull distribution, the average strength a, (avej is given by a,,,,,=

a0 (LdL)“mY

(1 + l/m)

(2)

The length dependence of the average strength calculated using Equation (2) with m = 7.0 and a(, = 530 MPa is superimposed in Figure 6. The experimental results are well described by Equation (2). The reduction in strength of the filaments due to increase in length is very large in comparison with that of the composite wire, as shown below. Average strength and distribution composite wires

of strength

of

Figure 7 shows the distribution of the measured strength of the composite wire a, for a gauge length of 50 mm. The Weibull plot for this is superimposed in Figure 5. The m and a0 were estimated to be 160 and 550 MPa, respectively. The scatter of strength of the composite (m = 160, corresponding to a coefficient of variation (COV) = 0.0079) is very small in comparison with that of the extracted filaments (m = 7.0, COV = 0.16).

50 40

*-

* 20mm Filament 0 50mm Filament x 150mm Filament 0 50mm Composite

.

-61LA 5.8 6.0

ln( d Figure5 filaments

g

30

=

20 10

-

520

a

6.2 f),

6.4

6.6

ln( 0 C)

Weibull plots for measured (a‘) and composite wire (a,)

( 0

6.8

7.0

f, d

&4Pa)

strengths

d

7.2

of extracted

530

540

c(MPa)

Figure7 Distribution of measured strength a, of composite wire for a gauge length of 50 mm. Broken curves show distribution calculated using estimated values of m= 160 and g0 = 550 MPa

Cryogenics

1996 Volume

36, Number

4

251

Strength

of Nb&V filaments

and multifilamentary

The measured average strength of the composite plotted against gauge length L is presented in Figure 6. Within the range of the present gauge length of 20-350 mm, the average strength remained nearly constant, indicating that the length dependence of the composite strength is very small in comparison with that of the filaments. Substituting the estimated values of m = 160 and a,, = 550 MPa, and &, = 1 m into Equation (2), the length dependence of the measured average strength of the composite a, (avej is calculated, as shown by the solid curve in Figure 6. In this way, the experimentally observed average strength-length relation is well described using the Weibull parameters estimated from the strength distribution for a guage length of 50 mm. Relation of strength distribution strength of composite wire

of filaments

to

Summarizing the experimental results, the scatter of strength of the composite is very small in comparison with that of the filaments, as shown in Figure 5, and also the length dependence of the composite strength is very small in comparison with that of the filament, as shown in Figure 6.

In general, the scatter of strength of the composite results for the following reason 8*17,18. During deformation and fracture of the multifilamentary composite wire, weaker filaments are broken prior to stronger ones (Figure 8~). As a result, stress disturbances occur around the broken ends; the load bearing capacity of the broken filament is lost within a distance of half the critical length (1J2) from the broken ends (Figure 8b), and also stress is concentrated in the neighbouring filaments (Figure 8~). The number of breakages of filaments increases with increasing applied stress. The accumulated breakages work together to cause overall fracture of the composite. As the number, locations and

Filament

Matrix

wire: S. Ochiai et al. progress of accumulation of the breakages of filaments differ from sample to sample, the strength of the composite differs from sample to sample, resulting in the scatter of strength of the composite. The experimental results, however, showed that the scatter of composite strength is far smaller than that of the filaments. They also showed that the length dependence of the composite strength is very weak, in spite of the strong length dependence of the filament strength. These results indicate that the stress level needed to cause overall fracture of the composite by co-operation between the breakages of the filaments is not very different among samples and is affected only slightly by the length. In the present work, in order to examine whether such features can be realized theoretically for the present composite system, a Monte Carlo simulation method was applied. This method has been demonstrated to describe well the relation of strength distribution of fibres to the strength of continuous fibre-reinforced aluminium matrix composites7-9. Figure 9 shows the distribution of composite strength obtained by the simulation for L = 50 mm, together with the measured distributions of the filaments and composite for comparison. The length dependence of the simulated average strength of the composite is superimposed in Figure 6. The simulated strength distribution and length dependence of the average strength of the composite are in fairly good agreement with the experimental values. The slight difference in the results between the simulation and the experiment might arise from the assumption used in the simulation that the fracture of the filament is caused by the breakage of Nb3A1. This assumption results in a lower strength value in the simulation, since the fracture surface shown in Figure 3 indicates that niobium and copper in the filament can carry applied stress even after the breakage of Nb3Al. With this in mind, the present simulation should be modified for accurate reproduction of the experimental results. However, the features describing how the distribution of composite strength becomes very small in comparison with that of the filament strength, and how the reduction in composite strength with increasing length is very small in spite of the strong length dependence of the filament strength, are well realized in this simulation. In this way, it was shown by experiment and simulation that the strength of the Nb3A1 composite wire has a very small scatter, in spite of the large scatter of the filament strength, and also that it has a very slight dependence on length. This means that, even if the length of the composite wire is extended from a short, laboratory scale sample to

&’

K

-Measured

40

t

200

(4 Figure8 Schematic representation of: (a) breakages of filaments in the composite; (b) loss of stress carrying capacity of broken filament; (c) stress concentration in neighbouring filament; and (d) modelling for the Monte Carlo simulation

252

Cryogenics

1996 Volume

36, Number

4

d f

I

400

600

800

1000

1200

Strength(MPa) Figure 9 Comparison of distribution of strength of the filament with that of the composite. The gauge length for both the filament and composite was 50 mm

Strength

of Nb&I

a practical scale, the reduction in strength is very small. According to the Weibull distribution function, the strength for a length L’ becomes (L/L’)“” times higher than the strength for a length L. According to this relation, even if the length of the present composite sample becomes 300 m, for instance, 95% of its strength can be retained. Thus it is predicted that the strength of the present Nb3A1 composite wire can remain high compared to the strength of short samples. This indicates that the strength data for short samples can be used for predicting the strength of long wires to a first approximation.

Conclusions

filaments

Acknowledgements The authors wish to express their gratitude to M. Nakagawa and M. Unesaki at Kyoto University for help in the SEM

wire: S. Ochiai et al.

and EPMA studies, to M. Seki at Shimadzu Corp. for his help in the measurement of composite strength with pneumatic grips, to the Japan Atomic Energy Research Institute for support and encouragement and to the Ministry of Education, Science and Culture of Japan for the grant-in-aid for Scientific Research (No. 06452320).

References 1 2 3

The tensile strength distribution of the extracted Nb,Al filaments was described by the two-parameter Weibull distribution function, where the shape and scale parameters were 7 and 530 MPa (for a standard length of 1 m), respectively. The strength distribution of the multifilamentary composite was very small in comparison with that of Nb3Al filaments. This feature was reproduced by a Monte Carlo simulation. It was shown by experimental and simulation that the strength of the Nb3Al composite wire has a very slight dependence on length. It was predicted that, if the length of the composite wire was extended from a short, laboratory scale sample to a practical scale, the reduction in strength would be very small.

and multifilamentary

4 5 6 I 8 9 10 11 12 13 14

Ekin, J.W. Composite Superconductors (Ed Osamura, K.) Marcel Dekker, Inc., New York, USA (1994) 85 Kuroda, T., Wada, H., Bray, S.L. and Ekin, J.W. Fusion Eng Des (1993) 20 271 Zeritis, D., Iwasa, Y., Ando, T., Takahashi, Y., et al. IEEE Tram Magn (1991) MAG-27 1829 Specking, W., Kiesel, H., Nakajima, H., Ando, T. et al. IEEE Tram Appl Supercond(1993)3 1342 Ekin, J.W. Adv Ctyog Eng (1984)

30 823

Ando, T., Takahashi, Y., Sigimoto, M., Nishi, M. et al. IEEE Tram Appl Supercond (1993) 3 492 Ochiai. S.. Osamura. K. and Abe. K. Z Merallkd ( 1993) 76 402 Ochiai; S: and Hojo, M. Mate& (Bull Jpn Inst Met&) (1994) 33 1397 Ochiai, S., Matsunaga, K., Waku, Y., Yamamura, T. et al. Metal1 Trans (in press) Weihull, W. J Appl Phys (195 1) 28 293 Zwehen, C. Eng Frac Mech ( 1974) 6 1 Ochiai, S., Abe, K. and Osamura, K. Z Metallkd (1985) 76 299 Ochiai, S. and Osamura, K. J Mater Sci ( 1989) 24 3865 Ochiai, S., Osamura, K. and Watanabe, K. J Appl Phys ( 1993) 74 440 Ochiai, S., Nishino, S., Hojo, M., Osamura, K. and Watanabe, K. Cryogenics (1995) 35 55 Yokobori, T. Zairyou-kyodogaku Gihoudou (Tokyo) (1967) 4 (in Japanese) Ocbiai, S. Mechanical Properties of Metallic Composites (Ed Ochiai, S.) Marcel Dekker Inc., New York, USA (1994) 474 Ochiai, S. and Hojo, S. Camp Interfaces (1994) 5 365

Cryogenics

1996 Volume

36, Number

4

253