Stress/strain dependence of ac loss and critical current of Bi 2 Sr 2 Ca 2 Cu 3 O 10reinforced tapeGuo Min Zhang, Justin Schwartz, P. V. P. S. S. Sastry, Liang Zhen Lin, Li Ye Xiao, and Yun Jia Yu Citation: Applied Physics Letters 85, 4687 (2004); doi: 10.1063/1.1819995 View online: http://dx.doi.org/10.1063/1.1819995 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/85/20?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetic field dependent critical current density of Bi–Sr–Ca–Cu–O superconductor in bulk and tape form withaddition of Fe 3 O 4 magnetic nanoparticles J. Appl. Phys. 105, 07E311 (2009); 10.1063/1.3070628 Statistical analysis of the electromechanical behavior of AgMg sheathed Bi 2 Sr 2 Ca Cu 2 O 8 + xsuperconducting tapes using Weibull distributions J. Appl. Phys. 101, 073913 (2007); 10.1063/1.2715844 Experimental and numerical studies of the effect of phase difference between transport current andperpendicular applied magnetic field on total ac loss in Ag-sheathed ( Bi , Pb ) 2 Sr 2 Ca 2 Cu 3 O x tape J. Appl. Phys. 98, 073902 (2005); 10.1063/1.2064314 Significantly enhanced critical current density in Ag-sheathed ( Bi,Pb ) 2 Sr 2 Ca 2 Cu 3 O x compositeconductors prepared by overpressure processing in final heat treatment Appl. Phys. Lett. 84, 2127 (2004); 10.1063/1.1682675 In-plane and out-of-plane dissipation in c-axis-oriented (Bi,Pb) 2 Sr 2 Ca 2 Cu 3 O x silver-sheathed tapes J. Appl. Phys. 81, 1331 (1997); 10.1063/1.364177

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Stress/strain dependence of ac loss and critical current of Bi 2Sr2Ca2Cu3O10reinforced tape

Guo Min Zhanga)

Center for Advanced Power Systems, Florida State University, Tallahassee, Florida 32310 and Institute ofElectrical Engineering, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China

Justin SchwartzCenter for Advanced Power Systems, Florida State University, Tallahassee, Florida 32310 and NationalHigh Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310 andDepartment of Mechanical Engineering, FAMU-FSU College of Engineering, Tallahassee, Florida 32310

P. V. P. S. S. SastryCenter for Advanced Power Systems, Florida State University, Tallahassee, Florida 32310

Liang Zhen Lin, Li Ye Xiao, and Yun Jia YuInstitute of Electrical Engineering, Chinese Academy of Sciences, Beijing 100080,People’s Republic of China

(Received 7 June 2004; accepted 16 September 2004)

The critical current and ac loss of a stainless steel reinforced Bi2Sr2Ca2Cu3O10 compositesuperconducting tape were measured under tensile stress/strain at 77 K. By use of the definition ofirreversible strain, a formula describing the variation of the critical current with strain was proposed.A relationship between ac loss and tensile strain was developed from Norris’ formula and the criticalcurrent–strain relation. It is shown that the experimental results agree well with the values calculatedfrom our formulas. ©2004 American Institute of Physics. [DOI: 10.1063/1.1819995]

The mechanical properties are among the most importantparameters for high temperature superconductor(HTS)tapes. In practical applications, the HTS tapes will experi-ence different stress/strain, such as bending, pulling, and/ortorsion. Because HTS tape is composed of brittleBi2Sr2Ca2Cu3O10 sBi2223d filaments and sheathed by ductileAg (or Ag-alloy), the transport properties of HTS tapes, suchas the critical current and ac loss, are much affected by theapplied stress/strain. Therefore, the mechanical properties ofsuperconducting composite tapes are at least as important aswith applications of traditional metal LTS wires. Investigat-ing of the effects of stress/strain on HTS tapes is of greatimportance for practical applications.

Although much work has been reported on the effects ofstress/strain,1–14 most focus on the effects of stress/strain onthe critical current. Research concerning the influence ofstress/strain on ac losses is relatively less. It is proved thatimprovement of mechanical property of the sheath of HTStape can restrain the degradation of critical current.3–5 Thus,reinforced HTS tapes, such as stainless steel reinforced tape,are manufactured to improve the mechanical behavior. Asmentioned above, HTS tapes are brittle ceramics embeddedinto flexible metal(Ag, etc.). Its mechanical properties aremore complex than that of the traditional LTS wires. Up tonow, no theoretical formulas on the effects of stress/strain onac losses of HTS tape are established.

In this letter, the critical current and ac loss were mea-sured for different tensile stress/strain. A formula to describethe relationship between the critical current and the tensilestress/strain was proposed first by use of the definition ofirreversible strain. The relation of ac loss and stress/strain

was developed based on theIc,« (critical current strain)relation and Norris’ formula.

The sample used in the experiment was a 55-filamentarystainless steel reinforced Bi2223/Ag tape manufactured byAmerican Superconductor Corp. Its cross section is4.1 mm30.3 mm and the critical current is 131 A. Thelength of the sample is 12 cm.

The stress/strain measurement system is shown as inFigs. 1 and 2. The tensile strain is measured by use of aU-shaped slice made of piezoelectric material. The slice isembedded in two metal notches glued on the sample with adistance of 6 cm. Potential taps are soldered on the samplebeyond the notch. The distance between the potential taps is8 cm. When the sample is subjected to the pulling forcesgenerated by a screw and read by a spring balance, theU-shaped slice will be deformed by the strain in the tape.Such deformation of the slice is converted into a measurablevoltage signal. The strain is calculated from the voltage dif-ference between the strained state and the original state. The

a)Electronic mail: gzhang@caps.fsu.edu FIG. 1. Measurement setup.

APPLIED PHYSICS LETTERS VOLUME 85, NUMBER 20 15 NOVEMBER 2004

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stress/strain is applied simultaneously at LN2 during themeasurement of critical current and ac loss.

The critical current of the tape was measured with thefour-contact method and a 1mV/cm criterion. Ac loss wasmeasured using electrical method.7 The frequency of trans-port current is 60 Hz. To avoid background magnetic fieldnoise, we adopted “8” shaped potential leads.

The dependence of the critical current on stress/strain forHTS tape is much different from that of the LTS wire be-cause of its complicated structure. It is reported that the de-crease of the critical current with increasing stress/strain ismainly caused by the mechanical damage of the supercon-ductor core.8–10

To estimate the stress/strain tolerance of HTS tapes, theirreversible(critical) strain «irr is introduced. Generally, theirreversible strain is defined as the strain corresponding tothe irreversible decrease of the critical current.11 Because thedegradation of the critical current has a transition process,the irreversible strain is, in practice, defined as the strainwhen the critical current decreases to a certain percentage ofthe original(virgin) critical current. For example, the straincorresponding to a critical current reduction of 10% of thevirgin critical current is adopted as irreversible strain.4

For much research concerning the relationship betweencritical current and strain, the critical current is generallyexpressed as follows:8

Ics«d = hs«dIc0, s1d

whereIc0 is the critical current for zero strain(virgin state),Ics«d is the critical current under strain, andhs«d is a func-tion of strain which satisfies 1ùhs«dù0. The expression ofhs«d has different empirical forms. One is given by:13

hs0d = 1 « ø «irr , s2ad

hs«d = e−As«−«irrd « . «irr . s2bd

There are other forms ofhs«d. Ten Haken14 suggestedthat the critical current is in proportion to strain before itreaches the irreversible strain, i.e.,

hs«d = 1 −C«, for « ø «irr with C = 4 ± 1. s3d

Kiss et al.8 assumed thaths«d satisfies the Weibull func-tion:

hs«d = 1 − expF− S« − «irr

aDbG, for « ù «irr , s4ad

hs«d = 0, for 0ø « , «irr , s4bd

wherea is a scale parameter andb is a numerical constant.

According to the definition of irreversible strain, we sug-gest thaths«d has the following form:

hs«d = hs0d < 1, for « , «irr s5ad

hs«d = hs«irrdexpS−« − «irr

hs0d − hs«irrdD, for « ù «irr .

s5bd

The measured result of the variation of the normalizedcritical current with tensile strain is given in Fig. 3. Here wenormalized the critical current under strainfIcs«dg to thecritical current of virgin statesIc0d. It shows that the criticalcurrent varies little when the stress/strain is less than irre-versible strain, then decreases very quickly.

FIG. 4. ac losses of stainless steel reinforced Bi2223/Ag tape under differ-ent tensile load.

FIG. 2. Schematic drawing of sample tape with potential leads and strainmeasurement setup.

FIG. 3. Normalized critical current of stainless steel reinforced Bi2223 tapevs tensile strain. The solid line is the calculated values, and the dotted line isthe measured results.

4688 Appl. Phys. Lett., Vol. 85, No. 20, 15 November 2004 Zhang et al.

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From the experimental results, we know that the irre-versible strain is 0.46%, i.e.,hs«irr =0.46d=0.9, then Eqs.(5a) and (5b) can be further expressed as:

hs«d = hs0d < 1 for « , «irr . s6ad

hs«d = 0.9 expS−« − 0.46

1 – 0.9D for « ù «irr . s6bd

Figure 3 also compares the normalized critical currentbetween the measured results and the calculated values usingEqs. (6a) and (6b). It can see that the calculated values fitrather well with the measured results.

Ac losses of HTS tapes in the virgin state can be de-scribed by Norris’ formula.15 When the superconducting tapeexperiences stress/strain, the critical current decreases and aclosses increase. Because stress/strain does not affect the in-trinsic pinning properties of the HTS tape,12 the increased acloss can be regarded as resulting from the decrease of thecritical current caused by the damage of the superconductorcore. Thus, ac loss under stress/strain can be estimated bymodifying Norris’ formula, i.e., by replacing the critical cur-rent Ic0 (virgin state) in Norris’ formula with the critical cur-rent under strainIcs«d. Using the same method as in Ref. 7,we obtain the relationship between ac loss and tensile strainas:

Ps«d =m0Ic0

2

p

1 +i

2hs«d

hs«dS1 +i

2D fs1 − idlns1 − id + s2 − idi/2g,

s7d

wherei = Im/ Ic0, Im is the peak current.Applying relation(5a) and(5b) into Eq.(7), then ac loss

under stress/strain becomes:

Ps«d =m0Ic0

2

p

1 +i

2hs0d

hs0dS1 +i

2Dfs1 − idlns1 − id

+ s2 − idi/2g, for « , «irr s8ad

Ps«d =m0Ic0

2

p

1 +i

2hs«irrdexpS−« − «irr

hs0d − hs«irrdD

hs«irrdexpS−« − «irr

hs0d − hs«irrdDS1 +

i

2D

3fs1 − idlns1 − id + s2 − idi/2g, for « ù «irr .

s8bd

Applying hs«irr =0.46d=0.9 into formulas(8a) and (8b),ac losses of HTS tapes for different tensile strain can beeasily calculated.

The measured results of ac loss versus transport currentfor different loads are given in Fig. 4. It shows that ac losscurves almost unchanged for smaller tensile forces, but whenthe tensile force is high enough, ac loss curves rise quickly.

To see clearly the variation of ac loss with strain, wegive ac losses versus strain curve as in Fig. 5. It can be seenthat ac loss hardly changes with stress/strain when the stress/strain is less than the irreversible stress/strain. However,when the stress/strain is larger than irreversible stress/strain,ac loss increases rapidly with stress/strain.

Comparing Fig. 3 with Fig. 5, we can see that the in-crease of ac loss with stress/strain is approximately the in-verse of the decrease of the critical current. It indicates thatthe increase of ac losses is mainly caused by the decrease ofthe critical current. Comparison of the measured results forstrain dependent ac losses with that of the calculated valuesby use of expression Eqs.(8a) and (8b) (see Fig. 5) showsthat the calculated values fit rather well with the measuredresults.

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FIG. 5. Ac losses of stainless steel reinforced Bi2223 tape vs tensile strainfor different transport currents. The dotted lines represent the measured data,and the solid lines represent the calculated values from(8a) and (8b).

Appl. Phys. Lett., Vol. 85, No. 20, 15 November 2004 Zhang et al. 4689

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