ten Haken, B.

ten Kate, H.H.J.

van Eck, H.J.N.

Vargas, L.

English

A comparison is made between the critical current (Ic) versus bending strain and axial strain of superconducting multi-filamentary Bi2Sr2Ca2Cu3Ox (Bi-2223) AgMg sheathed tapes. For the bending strain measurement the tape is sandwiched between a curved base and cover plate. Six sets of bending plates introduce bending strains ranging from 0% to 1.0%. The measurements show a slight decrease in Ic after the first bending step after which the degradation becomes more pronounced. The Ic in a bent conductor is calculated assuming a linear axial strain profile inside the conductor. For this calculation the Ic degradation determined in an axial compression and elongation experiment is used. The model predicts an immediate decrease of Ic, caused by the compressive strain dependence. There is a good agreement (within 5%) between the measured data and the calculated values. Based on this good agreement it can be concluded that a possible shift in the neutral line or the formation of additional cracks due to bending has no significant influence on the Ic degradation. It is concluded that the influence of thermal contraction is crucial for a good calculation

University of Twente Research Information

INSTITUTE OF PHYSICS PUBLISHING SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 15 (2002) 1213–1215 PII: S0953-2048(02)36408-XBending and axial strain dependence ofthe critical current in superconductingBSCCO tapesH J N van Eck, L Vargas, B ten Haken and H H J ten KateLow Temperature Division, Faculty of Applied Physics, University of Twente, PO Box 217,7500 AE Enschede, The NetherlandsE-mail: h.j.n.vaneck@tn.utwente.nlReceived 30 April 2002Published 20 June 2002Online at stacks.iop.org/SUST/15/1213AbstractA comparison is made between the critical current (Ic) versus bending strainand axial strain of superconducting multi-filamentary Bi2Sr2Ca2Cu3Ox(Bi-2223) AgMg sheathed tapes. For the bending strain measurement thetape is sandwiched between a curved base and cover plate. Six sets ofbending plates introduce bending strains ranging from 0% to 1.0%. Themeasurements show a slight decrease in Ic after the first bending step afterwhich the degradation becomes more pronounced. The Ic in a bentconductor is calculated assuming a linear axial strain profile inside theconductor. For this calculation the Ic degradation determined in an axialcompression and elongation experiment is used. The model predicts animmediate decrease of Ic, caused by the compressive strain dependence.There is a good agreement (within 5%) between the measured data and thecalculated values. Based on this good agreement it can be concluded that apossible shift in the neutral line or the formation of additional cracks due tobending has no significant influence on the Ic degradation. It is concludedthat the influence of thermal contraction is crucial for a good calculation.1. IntroductionBismuth-based oxide high-temperature superconducting tapesare used in various applications. The conductors then undergomechanical deformations, for example, conductor winding,that can significantly degrade the critical current (Ic). Inorder to make optimal use of the conductor it is necessaryto be able to predict the transport properties under operatingconditions. Critical current versus bending measurementsperformed on Bi2Sr2Ca2Cu3Ox (Bi-2223) AgMg sheathedtapes are presented. The irreversible reduction of the criticalcurrent due to bending is calculated, assuming a linear axialstrain profile in the tape. For this calculation the results froman axial compression and elongation experiment are used.2. Experimental detailsThe test sample is sandwiched between a curved base plateand a curved cover plate as shown in figure 1. The sampleis mounted at room temperature and subsequently cooled toliquid nitrogen temperature. The plates are made from epoxyreinforced glass fibre (G10) to match the thermal contractionof the sample. After determination of Ic the sample is broughtto room temperature. At this temperature the sample is furtherdeformed using a different set of bending plates. Six sets ofbending plates are used, which introduce a maximum strainat the matrix surface of 0%, 0.2%, 0.4%, 0.6%, 0.8% and1.0% for a 0.27 mm thick conductor. The total length of thesample is 80 mm and the distance between the voltage tapsis 30 mm. The Ic is defined, with a four-point measurementmethod, at an electric field criterion of 10−4 V m−1. For theaxial compression and elongation measurement, two tapes ofthe same batch are investigated. One piece is used in thecompressive strain regime and the other in the tensile strainregime. The sample is soldered to a brass U-shaped sampleholder. After cooling to liquid nitrogen temperature, strain isapplied to the sample by a force that acts on the legs of theU-shaped sample holder. The strain can be varied in the range0953-2048/02/081213+03$30.00 © 2002 IOP Publishing Ltd Printed in the UK 1213H J N van Eck et alFigure 1. The sample is sandwiched between a curved base andcover plate.Figure 2. Axial strain dependence of the critical current of sampleA as measured on a brass bending spring at 77 K (data) and thedescription (model).from −1% to +1%. A detailed description of this measurementmethod is given elsewhere [1].3. Uniaxial strainThe measured axial strain (εa) dependence of tape A is plottedin figure 2. The Ic curve can be defined by three differentexponents for the different strain regimes [2]:I : εa < 0 Ic ∝ eεaα1,II : 0 < εa < εirr dIc/dεa = 0,III : εa > εirr Ic ∝ e−εaα3 .The compressive regime (I) shows a relatively slow degradingof Ic, starting immediately from εa = 0. In the limit for smallcompressive strains the Ic degradation can be approximatedby a linear dependence (Ic ∝ 1 − α1εa). This behaviourhas been reported earlier on several BSCCO conductors [3].The mechanism behind this irreversible reduction still remainsunclear. Other authors even reported a strain insensitiveplateau in their data, using a different measurement method[4]. The tensile strain behaviour has been described by variousauthors [5–7]. The Ic in the second strain regime (II) shows avery small decrease and is often considered to be constant upto an irreversible strain level (εirr). Beyond this strain levelthe Ic falls abruptly (III). This strong reduction is commonlyattributed to crack formation and propagation. The value ofεirr depends on the pre-compression on the superconductingfilaments after cool down. The pre-strain of the filaments ina bare tape at a certain temperature depends on the matrixmaterial, the superconductor to matrix ratio and the reactiontemperature. This pre-strain can be estimated if the mechanicalproperties of the matrix and the filaments are known. Adetailed analysis of this problem is made by Passerini [7].After soldering the tape to the brass sample holder, the thermalcontraction is determined by the holder. The amount of pre-strain of the filaments (εfil) can then be calculated withεfil(T ) = εfil(Tsolder) +∫ TTsolder(αbrass − αfil) dT , (1)where α is the thermal contraction coefficient.4. Bending strainThe bend strain is defined as the maximum axial strain on thematrix surface: εb = εmax = D/2Rb where D is the thicknessof the sample and Rb is the curvature radius. In the case ofa tape conductor with elastic properties, there will be a linearaxial strain profile from −εmax to +εmax along the height ofthe conductor. Together with the description for the threeaxial strain regimes the critical current density (Jc) becomes afunction of the height (−D/2 < x < +D/2) along the conductorcross-section. Assuming a homogeneous Bi-2223 distribution,the Ic of the conductor can be calculated by direct integrationof Jc over the entire cross-section.In the case of small strains (εmax < εirr, i.e. large bendingradius), the third strain regime (III) will not occur inside thetape. Therefore, a simple dependence for the normalizedcritical current (ic) of a bent tape can be derived for arectangular cross-section (using the linear approximation forthe compressive regime):ic = 1 − α14D2Rb. (2)If the maximum value of the axial strain becomes too large(εmax > εirr, i.e. small bending radius) then the third strainregime has to be considered. This leads to a different icdependence for a rectangular cross-section (using the linearapproximation for the compressive regime):ic = 1 − α14D2Rb+RbD(1α3(1 − e−α3x) − x), (3)wherex = D2Rb− εirr. (4)With (2) and (3) the bending strain dependence can bepredicted using the uniaxial strain data.5. ResultsThe constants Ic(0)∗, α1, α3 and εirr are determined fromthe Ic(εa) data shown in figure 2. Ic(0)∗ is a fictionalcurrent predicted by the Ic description in the strain-freecase. Due to differences in the measurement method between1214Bending and axial strain dependence of the critical current in superconducting BSCCO tapesFigure 3. Critical current reduction as a function of bending strainof sample A, measurement (data) and calculation (model). Thedashed line represents the value of εirr.Table 1. Sample properties.Sample A Sample BIc(0)∗ (A) 71 61α1 30 40α3 1000 550εirr (%) 0.22 0.24(0.45 − 0.23) (0.47 − 0.23)Number of filaments 55 57the bending and the axial strain measurements, the pre-compression of the filaments will be different in both cases.In the bending experiment, the strain is introduced at roomtemperature. However, the axial strain measurement isperformed at liquid nitrogen temperature. In order to comparethese measurements εirr has to be altered by the difference inpre-strain. This difference can be calculated by comparingthe thermal contraction of the sample holder with respect tothe filaments, hereby neglecting the initial difference in pre-compression between solder and room temperature (≈0.01%).With an estimated contraction of ε = 0.65% for the brasssample holder and ε = 0.42% for the ceramic filaments, thedifference is 0.23%. Table 1 shows the fitted values of Ic(0)∗,α1, α3 and εirr for the two different conductors.The results of the measurement and calculation of Ic as afunction of the bending strain are shown in figures 3 and 4.The first part of the curve, where 0 < εmax< εirr, is determinedby the compressive strain dependence. The calculated slopeof approximately 1% per percent strain is supported bythe measurement. The second part, εmax > εirr, is mainlydetermined by the tensile strain dependence. The strong Icreduction above εirr results in a more pronounced decrease.Overall there is a good agreement (within 5%) between themeasured data and the calculated values. This good agreementimplies that an eventual shift in the neutral line, as canbe induced by non-elastic deformations, or the formationFigure 4. Critical current reduction as a function of bending strainof sample B, measurement (data) and calculation (model). Thedashed line represents the value of εirr.of additional cracks due to bending has no significantinfluence.6. Conclusions• The proposed model can be used to approximate thebending strain dependence of Ic using the measured axialstrain dependence of Ic.• The model predicts an immediate decrease of Ic, evenin the case of a large bending radius, caused by thecompressive strain dependence. No strain-insensitiveregime exists in the case of bending.• Because of the good agreement between the measuredand calculated data no shift in neutral line or formation ofadditional cracks due to bending the conductor is expectedto influence Ic.• The influence of thermal contraction is crucial for a goodcalculation of the bending strain dependence.References[1] ten Haken B, Godeke A and ten Kate H H J 1999 J. Appl. Phys.85 3247–53[2] ten Haken B, Godeke A, Schuver H-J and ten Kate H H J 1996IEEE Trans. Magn. 32 2720–3[3] ten Haken B, Godeke A, Schuver H-J and ten Kate H H J 1997Adv. Cryog. Eng. 42 651–8[4] Viouchkov Y and Schwartz J 2001 IEEE Trans. Appl.Supercond. 11 3062–5[5] Ekin J W, Finnemore D K, Li Q, Tenbrink J and Carter W 1992Appl. Phys. Lett. 61 858–60[6] Kitaguchi H, Itoh K, Kumakura H, Takeuchi T, Togano K andWada H 2001 IEEE Trans. Appl. Supercond. 11 3058–61[7] Passerini R, Dhallé M, Witz G, Seeber B and Flükiger R 2001IEEE Trans. Appl. Supercond. 11 3018–211215

Bending and axial strain dependence of the critical current in superconducting BSCCO tapes

Vargas Llona, Laura Dolores

ten Haken, Bernard

ten Kate, Herman H.J.

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Bending and axial strain dependence of the critical current in superconducting BSCCO tapes

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