MATERIALS STUDIES FOR

SUPERCONDUCTING MACHINERY COIL COMPOSITES

J. W. Ekin

M. B. Kasen

D. T. Read

R. E. Schramm

R. L. Tobler

A. F. Clark

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Prepared for: Annapolis Laboratory

David W. Taylor Naval Ship Research and

Development Center

Annapolis, Maryland 21402

" QC

100

.056

80-1633

ly/y

November 1979

Interim Report

NBSIR 80-1633

Q,c

MATERIALS STUDIES FOR

SUPERCONDUCTING MACHINERY COIL COMPOSITES

J. W. Ekin

M. B. Kasen

D. T. Read

R. E. Schramm

R. L. Tobler

A. F. Clark

Thermophysical Properties Division

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Prepared for: Annapolis Laboratory

David W. Taylor Naval Ship Research and

Development Center

Annapolis, Maryland 21402

November 1979

Interim Report

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
;}

A

i
TABLE OF CONTENTS

Page

LIST OF TABLES v

LIST OF FIGURES vi

ABSTRACT xi

1. INTRODUCTION 1

1.1 SUMMARY OF PRIOR WORK by A. F. Clark 3

1.2 SUMMARY OF PRESENT WORK by A. F. Clark 16

2. MATERIALS FOR SUPPORT STRUCTURES 21

2.1 FIBERGLASS EPOXY IN A CONICAL SUPERCONDUCTING MOTOR SUPPORT

by R. E. Schramm and M. B. Kasen 21

2.2 FATIGUE RESISTANCE OF A UNIAXIAL S-GLASS EPOXY COMPOSITE

by R. L. Tobler and D. T. Read 34

3. COMPOSITE COIL MATERIALS 55

3.1 EFFECT OF STRAIN ON EPOXY-IMPREGNATED SUPERCONDUCTING

COMPOSITES by J. W. Ekin, R. E. Schramm, and A. F. Clark 55

3.2 YOUNG'S MODULI OF COMPOSITE COIL MATERIALS

by D. T. Read and A. F. Clark 67

4. CONDUCTORS 71

4.1 LOW TEMPERATURE TENSILE BEHAVIOR OF COPPER-STABILIZED

NIOBIUM-TITANIUM SUPERCONDUCTING WIRE by R. P. Reed,

R. P. Mikesell, and A. F. Clark 71 4.2 EFFECT OF STRAIN ON THE CRITICAL CURRENT OF COPPER-STABILIZED

AND ALUMINUM-STABILIZED NbTi MULTIFILAMENTARY COMPOSITES

by J. W. Ekin 89

4.3 MECHANISMS FOR CRITICAL-CURRENT DEGRADATION IN NbTi AND

Nb^Sn MULTI FILAMENTARY WIRES by J. W. Ekin 116
Appendices

Page

A1 Current Transfer in Multi filamentary Superconductors 131

I. Theory by J. W. Ekin

A2 Current Transfer in Multi filamentary Superconductors 135

II. Experimental Results by J. W. Ekin, A. F. Clark, and

J. C. Ho.

A3 Defining Critical Current by A. F. Clark and J. W. Ekin 138

A4 Orthorhombic Elastic Constants of an NbTi/Cu Composite

Superconductor by H. M. Ledbetter and D. T. Read 141

A5 Temperature Dependence of the Elastic Constants of an NbTi/Cu

Superconducting Composites by D. T. Read and H. M. Ledbetter 147

IV
LIST OF TABLES

Page

1-

1-1 Comparison of Static and Acoustic Measurements of Elastic

Modul i 5

2-

1-1 Mechanical Property Data Summary 25

2-2-1 Static Tensile Properties of S-901 Glass/Epoxy Specimens.

2-2-2a Fatigue Results for S-901 Glass/Epoxy at 295 K. ^5

2-

2-2b Fatigue Results for S-901 Glass/Epoxy at 4 K.

3-

1-1 Epoxy Properties 58

3-

2-1 Acoustic Modulus Specimen Characterizations 68

4-

2-1 Sample Characteristics

V
LIST OF FIGURES

Page

1-1-1 Young's moduli of coil materials as a function of temperature for different directions 7

1-1-2 Shear modulus versus temperature as measured acoustically

in the superconductina coil composite 7

1-1-3 Tensile properties of the Nb-Ti filaments, the superconducting wire composite, and copper wire 10

1-1-4 Thermal conductivity of the superconducting coil composite

materials 10

1-1-5 Thermal contraction of the superconducting coil composite

materials 12

1-1-6 Thermal contraction of the Cu/Nb-Ti superconducting wire

and its constituents 12

1-1-7 Specific heat of the superconducting coil composite materials 14

1-

1-B Cumulative circumferehtial stresses in the superconducting

wire for constant and programmed winding tension 14

2-

1-1 Fixture for measurement of cone stiffness as a function of

axial compressive force. Strain gages were bonded directly to the cone surface 23

2-1-2 Porosity lying on the interlaminar shear planes of 10 ply

NASA Resin 2 and E 787 composites tested in this program.

Transmitted light, a) 1581 S-glass/NASA Resin 2; b) 1581

S-gl ass/E-787 (Lot 1); c) 1581 S-glass/E-787 (Lot 2). 27

2-1-3 Deflection of the Resin 2 cone as a function of axial com- pressive force. Calculated stiffnesses are noted. 29

2-1-4 Localized strain variations in the Resin 2 cone as a function of axial compressive force. Numbers refer to strain

gages positioned as illustrated on Figure 2-1-1. 30

2-2-1 S-901 glass/epoxy test specimen... 36

2-2-2 Liguid helium fatigue cryostat 37

2-2-3a Static test records; ordinary failure. 41

2-2-3b Static test records; premature failure 42

2-2-4 Room temperature fatigue data, with stresses normalized to

the static strength, showing the agreement between present

results and those of Reference [5] 44

VI
Page

2-2-5 4 K fatigue results, demonstrating a superior low temperature fatigue resistance, as compared to room temperature

results. 47

2-2-6 Tensile (lower) and fatigue (upper) failures of specimens

tested at 4 K. 49

2-

2-7 Deflection-versus-cycles for specimens tested at 295 K,

showing the increase in compliance preceding failure 51

3-

1-1 Cross-sectional view of a superconducting composite ring

showing its components. 60

3-1-2 Schematic of the ring test setup showing the configuration

of force, F, applie'd to the D's, current I, applied to the

superconducting ring, and the resulting self-field B, calculated to be about 3 T at maximum current 61

3-1-3 Training behavior of each ring type as a function of applied strain. 63

3-

1-4 Critical -current degradation of each ring type as a function of applied strain 65

4-

1-1 Photomicrograph of the mul ti fil amentary superconducting

wire containing 180 filaments and a copper to conductor

(Nb-Ti) ratio of 1.8 to 1.0 74

4-1-2 Loading assembly for the wire specimens 77

4-1-3 Tensile and yield strengths as a function of temperature.

Yield strength for Nb-Ti twisted filaments was unobtainable due to their small amount of plastic deformation

(0.689 - 1Q4 psi = N/m^) 81

4-1-4 Stress-strain curves at 298, 76, and 4 K (0.689 x 104

psi = N/m^) ° 82

4-1-5 The effect of strain rate on tensile properties. All data were obtained at 4 K. Brackets represent spread of data

presented in Fig. 4-1-4 85

4-1-6 Anelastic recovery of mul ti fil amentary superconducting

wire as a function of maximum applied stress 86

4-2-1 Schematic diagram of the stress-I^ apparatus for testing

hairpin samples 91

4-2-2 Schematic diagram of the strain- apparatus for testing

straight samples 93

vii
Page

4-2-3a Crossectional view of sample 1 (NSRDC 4-2, NbTiiCu = 1:1. B) 96

4-2-3b Crossectional view of sample 3 96

4-2-4 Vol tage-current characteristics for NbTi mul ti fil amentary

wire (sample 1) as a function of stress and strain. Also

shown are 3 dashed lines corresponding to several critical-current criteria: an electric field along the wire of

3 MV/cm, and resistivities of 10"1^ and 10~H f2cm, nor- malized to the cross sectional area of NbTi in the conductor 97

4-2-5 Critical current as a function of stress at various applied magnetic fields. Solid curves correspond to the

critical current measured while the wire is under stress;

dashed curves represent the critical current measured

after load is applied and reduced to the prestress value.

(Sample 1) 99

4-2-6 Critical current as a function of stress at various applied magnetic fields. Solid curves correspond to the

critical current measured while the wire is under stress;

dashed curves represent the critical current measured

after load is applied and reduced to the prestress value.

(Sample 2) 100

4-2-7 Critical current as a function of stress at various applied magnetic fields. Solid curves correspond to the

critical current measured while the wire is under stress;

dashed curves represent the critical current measured

after load is applied and reduced to the prestress value.

( Sample 3) 101

4-2-8 Cri tical -current degradation in several multi fil amentary

NbTi:Cu composites (samples 1, 4, and 5) as a function of

strain. Critical current, is expressed as a fraction of the initial unstrained critical current, 103

4-2-9 Critical-current degradation in a mul ti fil amentary NbTi:Cu

composite (sample 1) as a function of strain at three applied magnetic fields. Critical current, 1^, is ex- pressed as a function of the initial unstrained critical

current,

4-2-10 Critical current vs. magnetic field at various applied

stress levels 105

4-2-lla Crossectional view of sample 4 107

4-2-llb Crossectional view of sample 5 107
4-2-12

4-2-13

4-2-14

4-2-15

4-3-1

4-3-2

4-3-3

Crossectional view of sample 6

Crossectional view of sample 7

Vol tage-current characteristics for sample 4, at several

values of magnetic field. Characteristics labeled by

upward-pointing arrows indicate the field was increased to

the value shown; downward-pointing arrows indicate the

field was decreased to the value shown

Comparison of critical current vs. strain characteri sties

for aluminum- and copper- stabi 1 i zed NbTi superconductors

( samples 4 and 5)

Summary of critical current degradation in mul tifil amentary NbTi and Nb 3 $n wires. Results were obtained at com- parable magnetic fields (0.45 H(- 2

) The two materials. Dashed lines for each case indicate the critical

current recovery value after unloading

Time i nvariance of the cri tical -current degradation. Vol

tage-current plot shows the extent of degradation in a NbTi wire at a stress of 8 x 10^ Pa. Voltage-time

insert indicates the constancy of the flux- flow voltage

during the 2 hour test when the wire was biased at a cur- rent of 208 A

Invariance of the critical current degradation with residual resistivity ratio (RRR) of the matrix. Under stress,

the RRR for the Cu-stabil izer decreased to 19, while RRR

for the A1 -stabi 1 izer decreased to 191. The stabilization

material for each conductor was contained within NbTi

tubes (69 Mm O.D., 39 Mm I.D.) embedded in a 5056 aluminum

alloy matrix.

Magnetic-field dependence of the critical -current degradation. Vol tage-current insert shows the large resistivity

(10"^ i^cm) of a highly strained superconductor at

high magnetic fields, compared with the very low resistivity (<10"^^ J2cm) of the same wire at zero applied

field. Dashed lines show the retrace curves as the wire

returned to the superconducting state after being driven

normal

Page

108

109

111

112

118

121

123

124

Material Studies for Superconducting Machinery Coil Composites

J. W. Ekin, M. B. Kasen, D. T. Read, R. E. Schramm,

R. L. Tobler, and A. F. Clark

The physical properties of a superconducting coil composite are studied to accurately predict the coil behavior under operating

conditions. Emphasized in this third interim report are studies on the

effect of stress and strain on the critical current of superconducting

wires. The report also includes data on several fibergl ass/epoxy support

structures for the coil and its dewar. Preliminary results are also

given for the effect of stress on small superconducting composite rings

used to model the full sized coil behavior. A summary of the program

results to date is included.

Keywords: Critical current; fibergl ass/epoxy composite; mechanical

properties; niobium-tin; niobium-titanium; strain; superconducting coil

composite; superconducting wire.

XI

1. INTRODUCTION

The distinct advantages of lighter weight, smaller size, and

higher magnetic fields for superconducting magnets have 1 ed to their

successful application in electrical motors and generators. This superconducting electrical machinery, especially for propulsion applications,

must operate in a variety of conditions. The objective of the research

reported here is to determine the physical and mechanical properties of

such a magnetic field coil and the effect of operating environments on its

superconducting behavior. Thus, not only must the properties of the coil

components be known and understood, but their interaction with the

stress and magnetic field environments as well. With this understanding

will come the ability to predict the operating behavior of the superconducting coil and the assurance to design for long term reliability.

This report is the third in a series of interim reports summarizing

the research which has principally been published in the open liter1 * ature. The first report presented some of the mechanical properties

and the thermal expansion of the coil structure and established the micromechanical constitutive relationships for comparison with constituent

2 properties. The second report completed most of the mechanical and

thermal properties of the coil material and compared them with values

predicted from its constituent properties. The properties measured

included Young's modulus, Poisson's ratio, shear modulus, tensile strength,

elastic constants, thermal conductivity, thermal expansion, and specific

heat. The report also included a stress analysis for a transversely

isotropic coil for the stresses induced by fabrication, cool-down, and

the magnetic field.

*References are numbered independently in each section.
This third report includes: a summary of past and present work

(Sec. 1); reports on two different structures for dewar support, fiberglass epoxy bands and cones (Sec. 2); some preliminary data on a small

coil simulation for testing coil materials under stress and in a magnetic field (Sec. 3); the mechanical properties of NbTi superconducting

wires and the effect of stress, strain, and magnetic field on the critical

current in these conductors (Sec. 4); and, as appendices, some related

publications on superconductors which were direct outgrowths of sponsored

work. A fourth report is in preparation and will include strain effect

studies on Nb^Sn and other developmental superconductors, fatigue effects

in conductors, and scaling laws for these effects on the critical properties.

New work is in progress in two principle areas: 1) further studies

on the effects of strain, fatigue, magnetic field, and temperature on

the critical behavior of wires, both those used in present electrical

machinery and developmental wires, and 2) a complete study of the superconducting composite ring (SCCR) as a simulation of the electrical

machinery environment (stress and field) on the superconducting behavior

of various different combinations of wires and epoxies for the coil

material

2
1.1 SUMMARY OF PRIOR WORK

by A. F. Clark

The superconducting coil composite is not a simple structure. It

contains solenoidal layers of superconducting wires (which are composites

themselves) separated by layers of fiberglass cloth, the whole of which

is potted in an epoxy. It is highly anisotropic and is subject to

highly anisotropic thermal, magnetic, and mechanical stresses. Just how

anisotropic and the basic property values can best be described by a

brief summary of the properties measurement program to date. A specific

coil description and a table, of all the coil and constituent properties

2 measured is in the second report and a progress report at the 6th

3 International Conference on Magnet Technology. For this discussion

the coil composite is assumed to be transversely isotropic with the

longitudinal, 1, direction along the wires, the radial, 2, direction perpendicular to the wires and glass cloth, and the axial, 3, direction perpendicular to the wires in the plane of the glass cloth.

1.1.1 Mechanical Properties

Several of the mechanical properties of the coil composite and a

similarly constituted fiberglass epoxy were measured: the Young's

modulus in all three principal directions, two shear moduli, several

Poisson's ratios, some acoustic measurements of the same properties,

and the tensile properties of the superconducting wire.

Young ' s Modul

i

. The specimen preparation and experimental arrangement are described in the first report.^ Briefly, the specimens were

machined from actual coil material, strain gauges applied, and measurements

performed at the three temperatures , 293, 76 and 4 K, in a normal low

temperature tensile arrangement.

Because of the relatively weak fracture properties of the epoxy

bond between wires, the load for the axial specimen was limited to

3
2 ^7.0 MN/m ('vloOO psi). The resultant strains were quite small and

yielded an estimated uncertainty of about 5%. The data for all of the

Young's moduli are tabulated in Table 1-1-1 and Young's moduli are

shown in Fig. 1-1-1

The Young's moduli all increase slightly with decreasing temperature with the longitudinal specimens having a higher modulus more

appropriate to that of the wire. The behavior of the axial Young's

modulus, is, as expected, very similar to that of the radial specimen, £^2 9nd is probably due almost entirely to the epoxy. The less

accurate Poisson's ratios also show a slight increase with decreasing

temperature,^ however the acoustic measurements described below show

4

a decrease.

Acoustic Measurements . Composite materials are usually highly

anisotropic and the determination of their elastic constants is much

more difficult than for the more usual quasi-isotropic engineering materials. Conventional methods of measuring the elastic properties of

solids have been applied to composites with only limited success because

these methods usually require relatively large specimens and consider4

able time and effort. The new application of an acoustic resonance

technique to this superconducting coil composite has permitted rapid

determination of the coil's elastic constants. It also has the advantage of giving data continuous with temperature.

The technique consists of bonding quartz-driver and quartz-guage

piezoelectric crystals to a specimen to produce and to detect a standing

longitudinal (or torsional) wave. Each component's length is adjusted

so that it's resonant frequency is closely matched to that of the other

components. The elastic constants and thus the moduli are obtained from

4
Table 1-1-1. Comparison of static and acoustic

measurements of elastic moduli.

Elastic Moduli (lO^^N/m^) Temperature (K)

293 76 4

11 acoustic 8.14 8.77 8.96

static 7.58 8.08 8.53

22

acoustic 3.14 4.07 4.17

static 2.76 3.79 4.12

'13 acoustic 0.76 1.09 1.12

static 0.74 1.16 1.22

fiberglassepoxy

acoustic 3.14 3.47 3.42

static 2.80 3.33 3.56

5
the resonant frequency (about 60 kHz) and the length and density of the

specimen.

An example of the continuous and accurate data for one of the shear

moduli is shown in Fig. 1-1-2. A comparison of the static and acoustic

data for several of the moduli is shown in Table 1-1-1. (The static

2 shear moduli were obtained by a torsional technique. ) The comparison

is very favorable and well within the large quoted accuracies for the

static data. The acoustic resonance technique should prove quite

useful

Mechanical Properties of the Superconducting Wire . The tensile

properties of the multifilamentary superconducting wire and its base

5 components, Cu and Nb-Ti, were measured at 298, 76 and 4 K. Conventional tensile properties yield strength, tensile strength, elongation and Young's modulus were obtained. Additionally, the influence of

strain rate on tensile behavior and the stress-strain hysteresis effects

of the superconducting wire were studied.

The Young's moduli of the wires were found to be lower than the

bulk values but were predictable from those values for copper and NbTi

using a law of mixtures. The tensile properties of the twisted Nb-Ti

filaments, the drawn copper wire, and the superconducting wire composite

are summarized in Fig. 1-1-3. The tensile and yield strengths (0.2%

offset) have no abnormalities as a function of temperature. The yield

strength of Nb-Ti could not be determined since the filaments did not

deform plastically 0.2%. Predicted values of the composite tensile

strength, based on the mixture law, fall about 25% below the actual

composite values; this discrepancy is thought to result from the harder

6
Fig. 1-1-1 Young's moduli of coil materials as a function of

temperature for different directions.

Fig. 1-1-2 Shear modulus versus temperature as measured acoustically

in the superconducting coil composite.

7
condition of the copper in the composite, compared to the copper wire.

This harder condition may have resulted from cold working in manufacture

and is indicated by hardness and residual resistivity measurements.

There is little dependence of the yield strength of the wire composite

on temperature.

Compressibility of Glass Cloth . The compressibility of the glass

cloth which separates succeeding magnet layers is an important factor

in the stress analysis for determining internal magnet stresses. A

brief literature survey disclosed no information on this topic so room

temperature compressive modulus tests on the glass cloth were per2 formed.

1.1.2 Thermal Properties

The thermal conductivity and thermal expansion of the composite

coil material and the thermal expansion of one of its constituents,

the Cu-NbTi superconducting wire were measured. The thermal conductivity is highly anisotropic, and contributes significantly to coil

stresses. The thermal expansion of the coil composite and the wire

behave more or less as expected. The specific heat is also reported

for the low temperature region.

Thermal Conductivity of the Coil Composite . Thermal conductivity

measurements were performed on longitudinal and transverse sections

g of the superconducting coil composite. The longitudinal specimen was

measured in direction 1, and the transverse specimen was measured in

direction 2 (radial). No measurements were performed in the transverseaxial direction but the thermal conductivity in this direction was calculated.

8
The results of the measurements on the longitudinal and transverse

coil composite specimens are given in Fig. 1-1-4. The interpolated curve

given for the longitudinal specimen in Fig. 1-1-4 is based on the typical

temperature dependence of OFHC copper. The measured data were compared to

values calculated from the properties of the constituents of the coil

by summing the area-weighted conductivities of each of the parts.

Because of the reasonable agreement obtained it was useful to estimate

values for the transverse-axial case by the same technique. These values

are also shown in Fig. 1-1.-4.

The thermal conductivity is the most highly anisotropic of all the

properties measured on the coil composite, the longitudinal value being

a factor of about 1000 times greater than the poorest conducting transverse value in the radial direction. Even the axial and radial thermal

conductivities differ by a factor of 10. These differences are not

unexpected because of the high thermal conductivity of copper compared

to epoxy and the obvious anisotropy in conducting paths. These differences will be of no consequence in steady state operation but will

have a significant effect on any transient behavior such as cooldown

or the propagation of a normal conducting zone in the wire.

Thermal Expansion of the Coil Composite . The thermal expansion of

several radial and longitudinal specimens as well as one of the fiberglass-epoxy were measured with a quartz tube dilatometer. ^ The results

are shown in Fig. 1-1-5. The radial specimens have nearly twice the total

thermal contraction to 4 K as both the longitudinal and fiberglass

epoxy specimens. This is consistent with the large known thermal

contraction of pure epoxy. The approximate equality of the contractions

of the longitudinal and fiberglass specimens shows that the fiberglass,

9
Fig. 1-1-3 Tensile properties of the

NbTi filaments, the superconducting wire composite,

and copper wire.

Fig. 1-1-4 Thermal conductivity of

the superconducting coil

composite materials.

TEMPERATURE.K
which is in both, inhibits the contraction of the epoxy and dominates the

composite behavior.

Thermal Expansion of the Superconducting Wire . The superconducting

wire properties are essential components of the composite analysis and

thermal contraction of the wire during cooldown is one of the major

sources of stress. Toward this end the low- temperature thermal expansion of the Cu-NbTi wire was measured using the quartz tube dilatometer

from room temperature to 4 K. The results can be compared with previous

measurements of the coil composite^ and with measurements of the

constituents of the wire in Fig. 1-1-6. The thermal expansion curve of

the coil composite in the direction parallel to the wires is shown also

in Fig. 1-1-6 and is just slightly larger than that of the wires. This would

be expected since the coil expansion should be dominated by the wires

but slightly enlarged by the weaker epoxy whose thermal expansion

coefficient is significantly larger.

Specific Heat of the Coil Composite and Fiberglass Epoxy . The

specific heat at low temperatures was measured for both the superconducting coil composite and the fiberglass-epoxy composite.^ Both

specimens were portions of the same material used for the thermal expansion measurements. The measurements were taken by adiabatic calorimetry and only from 4 K to about 25 K, and either further measurements

or extrapolations will be done to extend the data to room temperature.

The results are shown in Fig. 1-1-7. One can readily see the similar behavior

except for the small discontinuity in the coil composite due to the

superconducting-to-normal transition of the superconductor . This discontinuity reveals a broad critical temperature transition centered

about 9.3 K. That the transition is several tenths of a degree wide

11
L293

~ Lt

1-293

*40

Fig. 1-1-6 Thermal contraction of

the Cu/Nb-Ti superconducting wire and its constituents.

Fig. 1-1-5

Thermal contraction of

the superconducting coil

composite materials.

12
implies that there are regions of different due to cold working or

diffusion of the superconductor itself. The presence of a dominant

quadratic term in a polynomial fit of the data indicates the presence

of two-dimensional, rather than three-dimensional, arrays of atomic

oscillators. Whether the two dimensionality is due to the long, chainlike polymer molecules or to the reinforcement by the fiberglass is

uncertain and could be the subject of further study.

1.1.3 Stress Analysis of Transversely Isotropic Magnet Coils

g A simple, two dimensional analytical model was developed to

evaluate the stresses generated for the characterized coil when in use.

The model assumes cylindrical symmetry for the coil and a transverse

isotropy in the coil composite in order to make the calculation viable

without going to a long, finite element, three dimensional calculation.

The material properties used were those generated in the complete study.

Material properties calculated using composite techniques proved to be

2 quite accurate for values not actually measured. The stresses

accounted for included those due to (1) winding tension, (2) removal

of the support bobbin after epoxy impregnation, (3) cooldown to 4 K, and

(4) activation of the magnetic field.'

Typical results for one of the calculations of stresses along the

wire as a function of radius is shown in Fig. 1-1-8. The effects of the

four sources of stress are readily observable, and it also shows that

programming the winding tension can result in a much more uniform final

stress distribution. Other parameterization also graphically demonstrated the importance of anisotropic moduli, anisotropic contraction,

the stiffness of the winding bobbin, the compressibility of the glass

cloth, the role of external support, and several others, all of which

can be optimized.

13
40

Fig. 1-1-7 Specific heat of the superconducting coil composite

materi al s.

Fig. 1-1-8 Cumulative circumferential stresses in the superconducting

wire for constant and programmed winding tension.

14
1.1.4 Comparison with Predicted Values

Finally, the coil properties as measured were compared with predicted

values from the properties of the constituents. In most cases the predicted values were well within 10%, with the exception of the shear

related moduli. Thus, a set of constitutive relationships was generated

for the coil material and should be reliably predictable for any changes

of a component.

15
1.2 SUMMARY OF PRESENT WORK

bv A. F. Clark

The research covered in this third report is varied and complex.

Only a brief summary is given here because the details and results are

given later. The work is divided roughly into three categories. In

section 2 the results of studies on dewar support structures is given,

in section 3 some preliminary work on composite coil materials in the

form of the superconducting composite rings is reported, and in section

4, the research on a variety of niobium-titanium conductors is presented. The appendices also include several reprints of related work

which were direct outgrowths of sponsored work.

1.2.1 Support Structures

Fiberglass-epoxy cones, designed as a thermal standoff and mechanical

support at either end of the rotor in the 2.2 MW (3000 hp) superconducting motor, were made of type 1581 S-glass cloth/NASA Resin 2.

While in operation, the cones experience a temperature gradient from

room temperature to 4 K, but shipping and storage temperatures may reach

350 K. Accordingly, tensile, compressive, and interlaminar shear

properties were measured on flat sheets of the glass cloth/Resin 2

composite at 350, 295, 76, and 4 K. For comparison, similar tests were

performed on a composite of the same cloth in E-787 epoxy resin. Mechanically, the composite made with flexibilized NASA Resin 2 seriously

degrades above room temperature. Furthermore, low shear strengths

resulted from voids on the interlaminar planes of both composite types.

Comparison confirms greatly differing values obtained with guillotine

and short-beam methods. Also tested was a full scale support cone for

axial stiffness under compressive loading at 350, 295, and 76 K.

16
Similarly, filament wound-epoxy bands are used as support structures

in the 2.2 MW generator. Tensile strength is not as much a concern as

fatigue in these materials. Accordingly, tension-tension axial fatigue

tests of a uniaxial glass f i 1 ament-reinforced epoxy were conducted at

295 K and 4 K. The fatigue life was found to be an order of magnitude

greater at 4 K than at 295 K. These results are believed to be the first

4 K fatigue data reported for a composite material.

1.2.2 Composite Coil Materials

Mechanical property data are reported for three epoxy materials

commonly used to impregnate superconducting solenoids, a filled epoxy,

a flexibilized epoxy, and a low-viscosity epoxy suitable for vacuum

impregnation. Impregnated superconducting test rings were also constructed using each type of epoxy. The critical current and training

behavior of each composite ring was then measured as a function of hoop

stress applied to the ring and correlated with the tensile properties of

the corresponding epoxy. The ultimate strain, of the epoxy impregnate was a primary controlling factor in the superconducting performance

of each composite ring. At strains below e^, both critical-current

degradation and training were negligi6le. At strains near e^, however,

training became a serious problem with 5 to 10 quenches required to

reach full critical current. These data would indicate that the training

behavior of potted superdonducting magnets is associated with a process

involving relief of stress concentration within the epoxy impregnant.

In addition, the vacuum impregnated composites show less training required than the wet layup composites.

17
The Young's modulus of the composite coil materials was also measured

by an acoustic resonance technique. All three of the coil materials

described above were compared at room temperature and the vacuum impregnated composite was measured at 77 and 4 K as well. The values compare

well with calculated values from a law of mixtures and values from conventional static tests.

1.2.3 Conductors

The tensile behavior of superconducting wire composed of twisted

filamentary niobium-titanium stabilized with copper was determined at

4, 76, and 300 K. Continuous stress-strain measurements were recorded

to fracture, allowing Young's modulus, yield strength, breaking strength,

elongation, and stress-strain curves to be determined. Hardness measurements along with the length of wire were also obtained. Various strainrates over three orders of magnitude were used.

The tensile and yield strengths of the Nb-Ti , copper, and wire

composite appear well behaved from 4 to 300 K. The Nb-Ti has very little

plastic deformation, signifying that little adiabatic heating can take

place in the superconducting filaments prior to fracture. No discontinuous

yielding was observed at 4 K. The yield strength was found to increase

slightly with increasing strain rate and the elongation to decrease

with increasing strain rate, both measured at 4 K. Anelastic unloading

behavior was observed by the wire composite at 4 K. The degree of recovery

was dependent on the maximum applied stress.

The first measurements of the effect of strain on the critical

current of NbTi multi filamentary wires are reported. The results show

a definite degradation of with applied uniaxial strain, starting at

about a strain of 0.5%. The effect amounts to about 5% at an applied

18
strain of 1%, rapidly increasing at still higher strain. The initial

20 to 30% decrease in critical current is almost totally reversible upon

strain removal. The data are used to generate strain-dependent

characteristics for magnet design.

A number of possible explanations of the observed degradation in

both NbTi and Nb^Sn superconductors were hypothesized. The experimental

evidence would suggest that the source of degradation is associated

with the superconductor itself, rather than with peripheral effects such

as matrix degradation, heat generated by plastic deformation, area

reduction, etc. At high strains in Nb^Sn where the degradation is

irreversible, the effect is well accounted for by > 100 nm cracks observed in the Nb^Sn reaction layer. Where the degradation is mostly

reversible (at lower strains in Nb^Sn and at all strains in NbTi), the

effect is most likely brought about either by a shift in the intrinsic

critical temperature and field due to strain, or by an alteration of the

vortex-pinning structure.

References

1. Fowlkes, C. W., Angerhofer, P. E., Newton, R. N., and Clark, A. F.

,

"Characterization of a Superconducting Coil Composite," NBSIR

73-349, National Bureau of Standards, Boulder, CO (1973).

2. Clark, A. F. , Weston, W. F. , Arp, V. D., Hust, J. G. , and Trapani,

R. J., "Characterization of a Superconducting Coil Composite and

Its Components," NBSIR 76-837, National Bureau of Standards,

Boulder, CO (1 976).

3. Clark, A. F. , Arp, V. D., and Ekin, J. W., "Properties of a Superconducting Coil Composite and Its Components," 6th International

Conference on Magnet Technol ogy-MT6 , Alpha, Bratislava (1978), p. 673.

19
4. Weston, W. F., "Low-Temperature Elastic Constants of a Superconducting Coil Composite," J. Appl . Phys. 46, 4458 (1975).

5. Clark, A. F., Mikesell, R. P., and Reed, R. P., "The Low-Temperature Tensile Behavior of Copper-Stabilized NbTi Superconducting

Wire," Proc. Int. Cry. Mat. Conf., Kingston, Ontario, 1975, Adv

in Cry. Eng

, Vol . 22, Plenum, New York (1976).

6. Must, J. G., "Low-Temperature Thermal Conductivity Measurements

on Longitudinal and Transverse Sections of a Superconducting Coil,"

Cryogenics 1^, 8 (1975).

7. Jelinek, F. J., and Collings, E. W., "Low Temperature Thermal

Expansion and Specific Heat Properties of Structural Materials,"

i n : Materials Research for Superconducting Machinery - III and V ,

Clark, A. F., Reed, R. P., and van Reuth, E. C., Editors,

DAD004586 (October 1974) and ADA030170 (April 1976).

8. Arp, V. D., "Stresses in Superconducting Solenoids, J. Appl.

Phys. 48, 2026 (1977).

20
2. MATERIALS FOR SUPPORT STRUCTURES

2.1

FIBERGLASS-EPOXY IN A CONICAL SUPERCONDUCTING MOTOR SUPPORT

by R. E. Schramm and M. B. Kasen

2.1.1 Introduction

A conical fiberglass-epoxy field magnet support was designed for

use in a 2.2 MW (3000 hp) model superconducting motor. Cone design was

based upon cryogenic static mechanical property data published by Toth,

^ a^. ^ for a type 1581 S-glass/E-787 epoxy resin composite. However, the

cone tested in this program was fabricated with type 1581 S-glass cloth

in an epoxy resin system known as NASA Resin 2. To check the material

properties against design criteria, we tested flat panels of composites

of the glass cloth with both types of resin. All tests were to failure

in tension, compression, and shear at 350, 295, 76 and 4 K. The parameters measured were moduli, strengths, failure strains, and Poisson's

ratios. Another objective was measurement of the cone's axial spring

constant at 295 K and 76 K as a function of axial compressive force up

to 89 KN (20,000 lb). However, as the flexibilizer in the NASA Resin 2

formulation was known to decrease the composite strength above room

temperature, the cone was also tested at a temperature of 350 K.

2.1.2 Materials and Test Methods

Type 1581 glass cloth has an unbalanced 57 x 54 warp and fill, with an

eight harness satin weave, i .e. , the filling thread floats over seven warp

threads and under one. This weave is especially adaptable for forming

2 compound curves. Specially developed for cryogenic service , NASA Resin 2

consists of Epon 828/DSA/EMPOL 1040/BDMA* in proportions 100/115.9/20/1

*DSA = dodecenyl succinic anhydride

BDMA = benzyl dimethyl amine

NMA = nadic methyl anhydride

The use of trade names in no way implies endorsement or approval by NBS

and is included only to assure complete identification of specimen materials.

21
by weight. Addition of EMPOL 1040 increases the flexibility of the

resin, reducing the tendency of the resin to crack when cooled to cryogenic temperatures . The E-787 resin (also designated 58-68R or the

Polaris formulation) consists of Epon 828/Epon 1 031/NMA/BDMA in proportions 50/50/90/0.55 by weight. Lot 1 of the E-787 composite had 52.2

and 55.6 fiber volume percent respectively in 10 and 15 ply panels.

Apparatus and procedures for tension and compression testing were

3 4 similar to those used in a prior program. ’ For the tensile tests, the

flat panels had 10 plies, and for the compression and shear tests they

had 15 plies. Tensile coupons were tapered similar to the MIL-HDBK 17A

specification (width = 1.3 cm (0.5 in); gage length = 5.40 cm (2,13 in);

thickness = 0.26 cm (0.10 in); and compression specimens were unsupported

columns 0.38 cm (0.15 in) square, gage length = 1.3 cm (0.5 in)).

Interlaminar shear strength (shear strength of the interface between

layers in a layered composite) was evaluated by the unsupported guillotine method (ASTM D 2733-70) and the short-beam shear test (ASTM D 2344-

72). All strain measurements came from strain gages bonded directly to

the specimen surface.

Figure 2-1-1 shows the fixture used for measuring the axial stiffness of the fiberglass epoxy cone at 350, 295, and 76 K. As illustrated

the cone skirt was seated in a recess on a 5 cm (2 in) thick clothreinforced phenolic base, machined to conform to the mating flange of

the motor assembly. A stainless steel support ring clamped the skirt to

the base. A 5 cm (2 in) thick cloth-reinforced phenolic plate, machined

to mate with the lip of the small diameter of the cone, served as a

pressure plate on the upper cone surface. Deflection was monitored by a

linear variable differential transformer (LVDT) mounted axially between

22
li

iiIII

'lII I iI I C\J

23

Fixture

for

measurement

of

cone

stiffness

asa

function

of

axial

compressive

force.

Strain

pages

were

bonded

directly

to

the

cone

surface.
the upper and lower phenolic plates. Four strain gages at the locations

indicated on Figure 2-1-1 provided localized strain data. Load was

applied by a hydraulic testing machine. Estimated inaccuracy of the

axial force was 3%; that of the LVDT was + 0.00254 mm (+ 10”^ in).

The LVDT was calibrated at 295 K and 76 K.

Liquid nitrogen was contained within a polyurethane foam ring,

sandwiched between sheets of stainless steel and bonded to the phenolic

base plate. The liquid level on both sides of the cone wall was midway

between the two copper conduction rings in the cone for most tests

(about halfway up the cone) as a simulation of the thermal gradient in

service. The cone was slowly cooled over a 20- to 30-min interval to

reduce thermal stresses between the copper conduction rings and the

compos i te.

2.1.3 Resul ts

Materials Characterization . The data in Table 2-1-1 are the results

of the destructive tests of the flat panels and represent the averages

of one to three tests; in general, the specimen-to-specimen variability

was about 10 to 15%. In most instances, the stress-strain curve displayed

the usual initial straight-line behavior (giving the primary modulus)

followed by a second straight line of slightly lower slope (giving the

secondary modulus) before going into plastic yield. The secondary

strength is the point between primary and secondary moduli.

8 2 The tensile Resin 2 strength increases from 4.8 to 8.6 x 10 N/m

as the temperature drops from 350 to 4 K. The increase in compressive

strength with temperature change is much more dramatic, going from 1.0

8 2 to 7.1 X 10 N/m . Interlaminar shear values from the guillotine test

24
Table

2-1-1

Mechanical

Property

Data

Summary 1 i LA -3- MD vD 1 1 1 vD

O CA 1 sOO CA 3 03 1 1 • • • • 1 1 1 • • 1 • • • 

J- (5vP 1 1 O CM CM 1 1 1 CM CM CM 1 ^ CM CM

4-J OJ OO

if) c o 00 LA -3" 1111 1 1 1 1 1 1 1 1 1 o — V.O CA OO till 1 I 1 CA 1 1 1 1 1 1 (/) +-J O t— 1 1 1 1 1 1 1 1 1 1 1 1 1 in 03 • 1 1 1 1 1 1 1 • 1 1 1 1 1 1 — a: o O o 1111 1 1 1 O 1 1 1 1 1 1 o

Q_

CME2 1 CM ^ o 1 1 1 1 LA CM LA 1 CM A- OO

u 1 • • • • 1 1 1 1 • • • 1 03 in CD 1 OA CA CA 0> -3* 1 1 1 1 CM vO O 1 CA

O OO

“D 3 O 1 CM CM T— r- CM 1 1 1 1 CM CM CA 1 CM CM CM C 1— t— o 3 o T3

03 o

21

—

inQ. 1 CA LA vO 1 1 1 1 SO CA CM 1 AO A*. 1 CA LA O OO LA 1 1 1 1 CM -3- 1 CA O ^

UD 1 • • • • 1 1 1 1 • • • 1 • • • o 1 CA CA CM CM CA 1 1 1 1 CA CA ^ 1 CA CA -3"

CME\ LA

OO 2 CA \o CA v£) \£) 1 1 1 O CM CA 1 CA CA CA 1 1 1 1 >- in 1

CA CA <7^ OO 1 1 1 CX3 ^ o 1 (TN A- CA

L. 3 O *— CnI CA CM CM CM CM 1 1 1 CM CA -3" 1

...

—«. (M CM CA

fD •— »—* CM T— CM b 3

•— “O c 4-1 4-J o #— o o

D- 3:

— in

in OJ LA CM <T\ CM ^ -3- 1 1 1 SD CM OO 1 'w' LA SD CA

Q. a: OO OO LA CA -3- CA »— 1 1 1 O LA LA 1 CM 0MX> • • • • • • 1 1 1 • • • 1 A^ • • • CD < CM CA -3’ CA CA ^ -^r 1 1 1 OO -3- -3- LA 1 CO -3“ CA ^ o lA A- 1

< 1 1 2 LiJ LO \ \ in in m

CM in in in E 03 vO 04 CTl CT\ 03 -3* 03 sD CO sD \ CM CA t— OO CA CA r— T— A^ 2 Ol 1 • • • 1 1 1 1 cn • • • 1 cn • • • -C 1 1 T— O ^ ^ 1 1 1 1 1 ^ CM 1 1 CM ^ T—

ro 4-> CO </3 1 <? 1 1 1 1 CO 1 on T3 o c c »— 1— o d) OO OO OO u i_ LA LA LA

(1) +j r—

</)

—

in vD CA 0^ 1 1 1 1 CM T- LA 1 CM 00 LA

Q- 1 • • * 1 1 1 1 • • • 1 • • • 1 00 -3- r**- OO 1 1 1 1 vO OO CA 1 ^ LA 00

CO ! T— CM CM CM CA CA CM CM O

CME CM LA \ O OO -3- OO LA O LA O <T\ OO O _3- va CA a^ 00 LA 2 OO -3- -3" LA <T\ <T\ O CM -3* O A- O vO OO LA CM

D • • • • • • « •

4-1 •M CO -a* LA <T\ 00

O CM v£>O o o v£) LA o O CA -3" A^

03 O)O

b c ^

•— <Du

r— +-> 3) (/) •-

in

O LA -3“ Q. (A O vD OO CM CA CA -3- -3-

CO CT\ CA -3* -3- CM 1— CA 1— CA CM CM CA CA t— OO vD vD vO O vO OO CA CM -3- O O <T\ A- r- LA sO O ' r— O LA v£) -3" O LA nX) -3- o LA -3- LA LA -3" LA LA O LA -3- ' LA LA <J^ LA (T\ CTs (T\ <T\ LA cn H fA CM CA CM CA CM CM CM CM CM CA CM

L.u L. +J 0) 03 03 0) 03 03 03

F 03 in > C C > c C C 03 >

0) 03 H in F 4-> in E E CO in

<D in CD 1- o 0) in 03 1- o 03 L,

m

f— 0) 03

— •— 03 »— CO *— 03 4-) 0)

u L. <l) •— L. L. d)

—U 03u L. in Q. 0) JZ — in CL 03 _c — 03 -C o CL c E CO 3 c E 4-J LO 3 4-> (/) E

(D

O

C C3 0)O c <3

C </)

O

1- o —

—

H

O

— ' ^ — '—

O

25

Interlaminar

350

2.16

0.1^9

Shear

295

1.99

0.137

(Guillotine) h

2.15

0.149
8 2 are disappointingly low at 0.1 - 0.2 x 10 N/m . All strengths of the

E-787 composites are quite comparable to the Resin 2 composites at cryogenic temperatures but are considerably higher at room temperature and

above.

In the course of testing, we noted that the panels contained large

voids visible to the naked eye. Further examination under a low-powered

microscope (Fig. 2-1-2) showed the porosity to be uniformly distributed.

A check of void content (ASTM D 2734-70) in two labs indicated less than

1% total voids; however, an analysis of the porosity on the shear

surface of failed interlaminar shear specimens showed in excess of 3.5%

voids lying on the interlaminar shear planes. The interlaminar shear

strength of the composite (Table 2-1-1) was significantly degraded by

2 the porosity, an average value of 0.9 MN/m reported for the same composite

type by Toth, ^ ^ The manufacturer was informed of the problem and

requested to supply a second lot of panels. Unfortunately, the porosity

problem continued. As shown on Table 2-1-1, the interlaminar shear

strengths of the second lot of E-787 panels remained low. Interlaminar

porosity was also present in the Resin 2 composite, although to a lesser

extent than in the E-787 material. The Resin 2 cone used in the stiffness

study was found to contain the same amount and distribution of porosity

as did the Resin 2 panels.

Axial Cone Stiffness . The first runs to a given axial force level

were made with liquid nitrogen covering half the cone height so as to

take advantage of the increased composite strength. Subsequent runs

were made at 295 K. Initial cycling was to 49 KN during which no problems

developed at either temperature. Subsequent cycling was to 89 KN. The

26
Fig. 2-1 Porosity lying on the interlaminar shear planes of 10 ply

NASA Resin 2 and E 787 composites tested in this program.

Transmitted light, a) 1581 S-gl ass/NASA Resin 2; b) 1581

S-glass/E-787 (Loti); c) 1581 S-gl ass/E-787 (Lot 2).

27
cone generated considerable noise during the first few cycles to this

level at 76 K, sharp cracking noises being accompanied by load drops of

220-440 N. Loading to 89 KiM at 295 K was uneventful. The cone survived

these tests without visible evidence of damage. Cone stiffness was the

same whether half covered or fully covered with liquid nitrogen.

The elevated-temperature runs (350 K + 5 K) were limited to 49 KN.

A commercial heat gun gradually heated the cone, allowing time for the

temperature to equilibrate. The surface temperature was 360 K at the

start of the test sequence, falling to 345 K after seven load cycles.

Cone stiffness data are summarized on Figure 2-1-3. The much lower

cone stiffness at 76 K compared to that at 295 K is almost certainly due

to restraint of the test fixture rather than to a changing material

property, as the compressive modulus of the composite increases by about

25% on cooling to 76 K (cf. Table 2-1-1). Restraint of the cone skirt

during cooling may distort the cone walls, permitting column bending

under load. Alternatively, thermal contraction may be causing the skirt

to pull away from its seat, in which case full cone stiffness would not

be achieved until the applied load is sufficient to force the skirt

tightly against the base. The increasing slope of the 76 K curve of

Figure 2-1-3 is consistent with the latter interpretation.

Strains measured by the four gages at the locations given in

Figure 2-1-1 are plotted as functions of axial compressive force to

49 KN on Figure 2-1-4 for temperatures of 350 K, 295 K, and 76 K. Only

the output of gage #3 could be monitored at 76 K, as the remaining gages

could not be stabilized. The observed strain at 49 KN was about 0.04%

(gage #3) at all three test temperatures . Gage #2 indicated compressive

28
NIAI 33U0J 3AISS3UdlAI03 1VIXV

oo CP CM

Im

<uu

s.o

<L> >

'r*

(/)

</) <u

S4- +-> C to c -o o o>

•r- +-> TO O I— 0) 3

<— O

I—

OJ 05 Q O

CO

I

I C\J

gOlxqi aodOJ 3AISS3UdlAI03 1VIXV

29

AXIAL

CONE

DEFLECTION,

in.
NIAI'33U0d 3AISS3UdlAI03 IVIXV

cOlxqi 33UOJ 3AiSSdUdlAI03 1VIXV

30

Localized

strain

variations

in

the

Resin

2

cone

as

a

function

of

axial

compressive

force.

Numbers

refer

to

strain

naoes

positioned

as

illustrated

on

Figure

2-1-1.
strains of similar magnitude. Compressive strains from gage #4 were

much smaller (about 0.005%). Strain at gage #1 reached about 0.03%.

The strain in the cone skirt (gage #3) shows little effect of temperature, but heating to 350 K did increase the output of all three gages

near the cone apex. The hoop strain at the top (gage #4) may be very

small due to the constraint of the test fixture. Comparison of gages #1

and #2 indicate a greater strain on the exterior than on the interior.

2.1.4 Pi scussion

The large amount of visual interlaminar porosity in the composite

test panels reflects manufacturing problems. Since there is a considerable discrepancy between the results of the ASTM 0 2734-70 test for void

content and visual observation, it appears prudent to heed the caveat

written into the test method, i . e

.

, accuracy depends on an assumption

that resin density is the same in bulk as in the composite but small

differences in formulation or curing could render this invalid. The

usual change between the two conditions make the void content appear

lower than it really is.

The presence of porosity is clearly reflected in the very low

interlaminar shear strengths measured in this program. Considerable

controversy surrounds the subject of interlaminar shear testing of

composites. We make no claim that the unsupported guillotine method

used in the present work is ideal; however, this method is considered

5 the best presently available for generating allowable strength data.

Our ultimate strengths from the guillotine shear tests are much lower

than those for 1581 S-Gl ass/E-787 reported by Toth, while the

present values from the tensile, compressive, and short-beam shear tests

agree very well with theirs. Apparently, only the guillotine test

31
method is sensitive to interlaminar porosity. This may be an important

factor to consider when using the relatively simple short beam method as

a quality control or screening test.

Despite the low shear strength, we observed no degradation in

strength or stiffness of the Resin 2 cone as the result of repeated

axial loading to 89 KN at 76 K, 295 K, and 350 K. The noise generated

during the 76 K loading undoubtedly reflected the onset of some "damage"

to the composite. However, it most likely reflected a shakedown of the

composite, not seriously affecting the strength and stiffness properties.

The axial stiffness of the Resin 2 cone was a constant at 295 K and

at 350 K for loads in excess of about 9 KN with a spring constant of

22.8-24.5 X 10^ N/m. At 76 K, the stiffness was a monotonical ly increasing

function of load, attaining a stiffness of about 14 x 10^ N/m at 89 K.

We interpret this as a geometric effect due to restraint on the cone skirt

during cooling. The unrestrained cone, tested at 76 K, should have a

stiffness exceeding that at the elevated temperatures , consistent with

the significant (25%) increase in the compressive modulus observed in

the Resin 2 composite test materials upon cooling.

Acknowl edgment

We wish to thank Michael J. Superczynski of the Naval Ship Research

and Development Center and Robert A. Ackerman of Intermagnetics General

Corporation for their cooperation in this program.

References

1. L. W. Toth, T. J. Boiler, I. R. Butcher, A. H. Kariotis and F. D.

Yoder, NASA CR-80061 (1966) N67-12051.

32
k!. L. M. Soffer and R. Molho, NASA CR-721 14 (1967) N67-25076.

3. M. B. Kasen and R. E. Schramm in: Materials Research in Support of

Superconducting Machinery-I; R. P. Reed, A. F. Clark, E. C.

van Reuth (Eds.); Nat. Bur. Stds., Boulder, CO; (March 1974) AD

780 596. See also: V. II (Oct. 1974) ADA 004 586, V. Ill (April

1975) ADA 012 365, V. IV (Oct. 1975) ADA 019 230.

4. R. E. Schramm and M. B. Kasen, Materials Science and Engineering ,

30 (1977) 197.

5. Advanced Composites Design Guide, third Ed., V. IV, Materials,

Wright-Patterson AFB, Ohio (1973) AD 916 6821.

33
2.2 FATIGUE RESISTANCE OF A UNIAXIAL S-GLASS/EPOXY

COMPOSITE AT ROOM TEMPERATURES

by Ralph L. Tobler and David T. Read

2.2.1 Introduction

Glass-reinforced epoxy composites are prospective structural

materials at cryogenic temperatures where high strength-to-densi ty and

strength-to-thermal -conductivity ratios are required and where relatively

low elastic moduli can be tolerated. At temperatures from 295 to 4 K, these

composites offer a combination of physical and mechanical properties

unmatched by structural metals. Unfortunately , structural design data

for composites at low temperatures are scarce, a fact which hinders

the utility of these materials.

The advent of superconducting machinery prompted the need for mechanical property data for materials in a liquid helium environment at 4 K.

Accordingly, programs were instituted to establish a data base.^

1 2 Kasen's review ’ of the mechanical behavior of glass-reinforced

composites concludes that tensile and fatigue strengths generally increase

between 295 and 76 K; but, on further cooling to 20 K, there is a high

1 2 probability that strengths will decrease. According to Kasen ’

,

below 20 K, tensile behavior has rarely been investigated, and fatigue

data are non-existent.

In this study, fatigue tests of a filamentary-reinforced composite

at room temperature and 4 K are described. Cycle life as a function of

applied stress is evaluated to provide baseline fatigue data for a specific

primary load carrying component of a superconducting motor. Some experimental aspects of fatigue testing at 4 K are discussed.

34
2.2.2 Experimental Procedure

The material tested was a unidirectional composite of Owens-Corning

S-901 glass roving and an epoxy resin, SCI REZ 30^.* Specimens were

fabricated in the form of 12.38 cm long bands, as shown in Figure 2-2-1,

using a single material lot and constant fabrication procedure. The

specimen is a scaled down version of 68.5 cm long support bands designed

for suspension of superconducting motor components in liquid helium.

All specimen dimensions, except length, are equal to those of the service

component. As specified by 'the manufacturer , the specimen fiber content

is 82% by weight, 69% by volume; the void content is less than 1% by

_3 volume, and the density is 2.1 g*cm at room temperature.

Using flanged bushings, the specimens were pinned to the grips of

a cryostat enabling fatigue tests in a liquid helium environment, as

shown in Figure 2-2-2. The cryostat frame has a load carrying capability

of 100 kN; it consists of two tubular compression members which are

bridged at the bottom. The lower halves of these members are AISI 304

stainless steel having a wall thickness of 3.18 mm. The upper sections,

which experience a thermal gradient during testing, were fabricated from

fiberglass-reinforced plastic tubes, 6.35 mm thick. This lightweight

construction provides high specific strength and low thermal conductivity, with some sacrifice of rigidity; the stiffness of the frame and

load train at 4 K is approximately 23 kN/mm. Details of this cryostat

3

design were described by Fowlkes and Tobler.

*Certain materials are identified in this paper in order to a. ;.l tely

specify the v^xper’''^ ; ’ procedure. In no case ' es such identir ication

imply recommer ;? i, . jn or endorsement by the Nat .ona'i Bureau of Standards,

nor does it imply rhat the material identified is necessarily the best

availatl.r for j purpose.

35
Fig. 2-2-1 S-901 glass/epoxy test

specimen.

36
Pull Rod

Fig. 2-2-2 Liquid helium fatigue cryostat.

37
Room temperature tests were performed with the apparatus in ambient

air at 295 + 2 K, and at a relative humidity of 30 + 5%. The tests at

4 K were accomplished using the double-dewar arrangement illustrated in

Figure 2-2-2. The specimen was enclosed in a fiberglass-reinforced

plastic dewar, having a volumetric capacity of 9 liters. This dewar is

vacuum insulated, and is surrounded by a fiberglass-epoxy dewar containing liquid nitrogen. Tests began by cooling the specimen and apparatus

to 4 K, according to the two and one-half hour cool-down procedure pre3 viously described. The liquid level was maintained several inches

above the specimen, and was constantly monitored with a carbon-resistor

level indicator. Liquid helium was continuously transferred into the

cryostat to replenish the large amounts evaporated during fatigue tests.

All tests were conducted using a 100 kN closed-loop servo-hydraul ic

test machine. Replicate tensile tests were conducted at a loading rate

of 5.7 N • s"^ to determine the nominal fracture strength and loaddeflection (P- 6 ) characteristics of virgin specimens. Load cell and

LVDT outputs were used in recording load-versus-actuator displacement

curves. The nominal fracture strength, a^, was calculated from the

maximum load, and the mean crass-section area 2A of the unloaded

rriax specimen at room temperature:

= P /2A max ( 1 )

The specimen stiffness, P/ 62 » was obtained by deducting the load

frame deflection, 6 p from the total actuator displacement, 6 j:

P_ _ P 6s

- (6t

- 6p)

’ ( 2 )

38
where the load frame stiffness was measured separately by replacing the

specimen with a rigid steel block. The nominal or effective value of

specimen modulus was also calculated:

= PL/ 2 A63 (3)

where L is the initial specimen length at room temperature, and 6 ^ is

the specimen deflection at a 10 kN load.

The axial fatigue tests, were conducted under controlled load,

using a sinusoidal load cycle, at frequencies from 25 to 27 Hz. The

ratio, R, of minimum/maximum load was 0.1, except as noted in the test.

A digital indicator was used to measured the peak loads, which were

controlled to within 2 % of the specified values.

2.2.3 Resul ts

A representative load-displacement record obtained at 4 K is shown in

Figure 2-2-3a, and static tensile results are listed in Table 2-2-1.

There was no measurable change in stiffness or modulus between 295 and 4

K, but tensile strength increased by 28% above room temperature value of

7 -2

133.4 X 10 N • m . The scatter in tensile strength at 4 K was higher

than at room temperature, with one specimen at 4 K failing at a stress

lower than any of the room temperature values. This anomalous result

was not included in the average value of fracture strength listed in

Table 2-2-1: the load-displacement record of the test of this specimen

shows a noticeable increment in the displacement without a corresponding

increase in the load at a low value of the load, as can be seen in

Figure 2-2-3b.

39
Table

2-2-1

Static

tensile

properties

of

S-901

glass/epoxy

specimens

m •> fn 4=

00

C9

C

C 0) S 4-> O M z

CNI O

c/3

•H ^

0)

O 3

0) iH3

vw T3

<sI

O'o 0) n

0)C CO

4-1 CO

4-1 •H fL, U

CO Sz

»r>O 0u <

0) Csl 1 / X « C4

flj c 0> S p < u < £

c:

0*o

(Ua

CO

0)

ki3

i-i

<TJ

k-i (UO.Q

<u H

OZ

vO CO vO •>1 1 00 rH -a- • • • • < 1 • • • • •o CO rH CO / II II 00 CM vO o

CO CO 00 CO z 1 m 00 CM

1—

r-4 rH iH rH rH rH rH <z

00 00m • • • • CM rH o 'O vO vO <z

O' 00

m

CO

uo

CM 00 rv CM CO '« •a- CM

rH o 'O' r>> lO rH vO vO UO

vO vO vO v£> VO VO VO VO vO

h

CO CO CO CO CO CO CO CO CO

V • • • • • • • • •

(d (0 CM CO

CO O'

rH 'O • « • 'O rH O

'O 'O 'O

00 oVO

*0 lO CM

00>

00

m

O'

(M

00 5

40

Not

Included

In

the

average

(see

text)
LOAD,

kN

Fig. 2-2-3a Static test records; ordinary failure.

41
LOAD

Fiq. 2-2-3b Static test records; premature failure.

42
The room temperature fatigue results are shown in Figure 2-2-4,

where the maximum fatigue stress is plotted as a fraction of the static

strength. The data trend and scatter are similar to other results,

5 particularly those reported by Hofer and Olsen for a unidirectional

S-994 glass filament-reinforced epoxy. Hofer and Olsen's data pertain

to conventional hour-glass specimens having a tensile strength of about

7 -2

162 X 10 N • m . Although their material exhibited a higher cycle

life capability at a given absolute stress value, the results for both

composites can be normalized on the basis of differences in static

strength as shown in Figure 2-2-4. It is also significant to note that

these materials at room temperature do not exhibit a fatigue limit at

cyclic stress levels as low as 20% of the static strength.

The effect of varying the load ratio was investigated briefly at

room temperature where two specimens were fatigued to fracture at

R = 0.5. As shown in Figure 2-2-4, the cycle life appeared to improve

at the higher load ratio; further conclusions are not justified in view

of the limited data.

The fatigue data obtained at liquid helium and room temperatures

are summarized in Table 2-2-2 and Figure 2-2-5. These results clearly

demonstrate a superior fatigue resistance at 4 K. Two specimens survived

10^ stress cycles of maximum levels 29.0 and 30.0 x 10^ N • m ^ (17.6% of

tensile strength) at 4 K without failure; their tensile strength and

effective modulus after cycling were only slightly less than the average

values for virgin specimens, as shown in Table 2-2-2b. These high

values of residual strength and residual modulus indicate that cyclic

loading at these levels at 4 K does not significantly degrade the loadbearing capability of these composite specimens. A third specimen failed

43
QJ x:

4-J

i_) >-tJ

r>o

Hi‘JN3aiS DliViS / SS3yiS 3I3DAD ‘XW

o.c

'5o

to

+J

cr, c

<L» S- +J

to

+-> 03 +J

to

<L)

un

O I M

T3

<D

O)UC

N OJ

•I- $- r— <U

ro M- E

<D DC oc 4-O

to

(U (U

to to

tA

O

Oi ^!->

+-> to "Oc ^ fO M•r- to 5 +j

»• 3

<o to +J cu

fO i- TD

•*-> <L) C 3 O) cr to

O)

4-> S- TO O- D O) ^ <U 3 3

-> +J o oj - JD V

3--M = C

LI 0)

-> E

<U = cu 3 S_ 3 CO I ooI CM

CO

44
Table

2-2-2a

Fatigue

Results

for

S-901

glass/epoxy

at

295 K

li

i

!

i

1^

(

I

]

i

w

01 v£> < •c m U-l m CO sr CN -o- CO

rH O O O O o o O o o o o O o o

cj a

U( fH rH iH rH pH rH pH rH iH rH rH rH rH rH U 3 • X X X X X X X X X X X X X X

i-H 0

0» -H z sC 3 CO NT vO un C30 vO CN vO in CN ON cn o o

00 *4-1 CN rx m CO ON < 00 CN o ON o -O’

•U 0 sC CO i-n iH 00 CN CN cn CN uo

CO 4-) pL,

O

•H

i-H s

U D

Co CN u « 1 cn B

B cn • 3 <u Z

B M

•H U

X CO O

CO rH s s_x

m in CO CO CO o o o ON ON ON o CN m in ON CON ON rH rH rH rH rH m CN CN CN CN CN CO CO CO CO CO CO '5- m

C

<VE

•HU

0)a

C/)

O

z

ma^o^vooor^<NO'00 iH iH rH iH iH CN iH

CO CO (N m

CN CN CN

II

Pi

CO

45

0.50
Table

2-2-2b

Fatigue

results

for

S-901

glass/epoxy

at4K

(A33O£

<NI B

<0 o^ 3 O

CO

0) Pi

tod /• o>U I

c/5

I—

COd

*0

•H

CO

0)

0) iHU

>* U e2o % s.

to ^ u

CO

<N 00 < t • 00 m 2 cr» vO

o\ \o < cn m

iH rH 2

ys

4J 0) 4J 0) 3 M 3 U 0 3 0 3 1 5 iH 1 c II II II iH

•H (j •H 3 CO 3 CO

(4 V4-I (4 44 w V-/ VO NO m ST •«0 'O- -O 0 0 0 0 0 000 0

rH rH iH iH iH iH rH 1—

iH

XX

XX

X XXX

X

iH rH Ov vO CM iH iH rH CM ST cn OV m • • • • rH cs VO CM

iHO

D I a o * * _ CO z a CO 3 0) a M o •H iJ I-) X cnc

(U /“S a

•H o

CJ 2

a) S.X a

CT) 0 0 0 ov 00 CM rH 0 • • • t • • • • . OV rH '4- m CM ov CM

CM CO cn

m SO VO 00

00 r>»

CM CO

m VO

Xi

46

Cycled

at

Increasing

stress

levels.
;

I

i

I

v£>O

iT»O

ZDO

o

47

Fig.

2-2-5

^k

fatigue

results,

demonstrating

a

superior

low

temperature

fatigue

resistance,

as

compared

to

room

temperature

results.
after 1.49 x 10

4

cycles at a stress level of 71.0 x 10

7-2 N • m ,

exceeding the room temperature endurance by a factor of 30. A final

specimen was cycled for specified intervals at the increasing stress

levels listed in Table 2-2-2. The results show that the cycle life at

4 K is at least ten times greater than at room temperature for maximum

7 -2

cyclic stresses from 38 to 82 x 10 N • m .

Although a reliable S-N curve at 4 K could not be constructed

without more extensive data, it appears that the stress level required

for failure at a specified number of cycles may approach twice the value

required at room temperature. The improvement in fatigue resistance at

4 K exceeds that which might be predicted based on scaling the fatigue

stress levels to account for the increase in static strength alone.

Fatigue and tensile specimens fractured at 4 K are shown in Figure

2-2-6. Failure invariably occurred at points of tangency where the

specimen contacted the bushings. Fatigue cracks initiated concurrently

at all four of the points of tangency; the cracks penetrated the specimen

ligaments along planes normal to the tensile axis; and delaminations

subsequently emanated from the gripped regions. The delaminations

propagated gradually in a direction parallel to the loading axis, along

the entire length of the specimen. When fatigue damage reached critical

proportions the weakest ligament splintered inco filaments, which was

the failure mode of tensile sp^ciirens, as shown in Figure 2-2-6. The

epoxy at the four point': cF tangency in specimens fractured in fatigue

at both 4 K and 295 K was quite dark, possibly indicating charring.

Test temperature had no obvious influence on the appearance of these

failures.

48
Tensile (lower) and fatigue (upper) failures of specimens

i-ig. ^

49
Specimen deflection at maximum fatigue load increased progressively,

as shown in Figure 2-2-7 for room temperature specimens fatigued at 25.5 x

10 N • m . The rate of increase of deflection differed by an order of

magnitude for these specimens, as did their fatigue lifetimes, N^.

This suggests that scatter in cycle life is due to specimen-to-specimen

variability in resistance to fatigue damage propagation, as well as

initiation. The loss of stiffness was always most pronounced during the

last few cycles to failure, and extreme adiabatic heating was also

noted in the terminal stages of fatigue.

2.2.4 Pi scussion

Relating laboratory results to service behavior is a practical

problem which was minimized in this study by performing a limited

number of tests under conditions nearly equivalent to those of the service

application. The results must be regarded as lower bounds on the uniaxial

tensile properties of the material itself, since the gripping fixture

influenced the results. However, the gripping fixture is a practical

one for service applications, and the data reported here are directly applicable in design.

It can be concluded from the 4 K results and known trends between

2 295 and 20 K that the fatigue and tensile strengths of this material are

lower at room temperature than at any cryogenic temperature. In the

application under consideration, the component will experience temperatures ranging from 295 to 4 K. The room temperature properties are

therefore limiting, and should form the basis for design. In certain

applications where a component operates exclusively at cryogenic temperatures, it would also be possible to design conservatively on the basis

50
Specimen

13 ]

i|V

<u s:•4-> CD5O

to

Lr? O'. CMMra T3

oi

+-> to

o» • +-> oj

s- to 3

<U T- E *o a

<L) O)

Q.

C

to •!— o

a; o o *- O)

s- to Q.

<U •— <U 0 o

>>

C

U <T3 1 *1- tO r— 3 D.

to E 1- o

O)

u >I c C •!- o

•I- <p

4-> to U «o

<u <u r- S- M- U

O) c Q I CM

CM

cr>

iliiJ ‘•‘9 ‘iN3W3DV1dSia dOiVniDV

51
of room temperature properties. However, a maximum level of design

efficiency at cryogenic temperatures requires more extensive low temperature mechanical property data.

In many structural applications, it is essential to monitor fatigue

damage and to replace critical components before catastrophic failure

becomes probable. The occurrence of delaminations in this composite

after 25% of total cycle life provides obvious evidence of degradation.

Damage could be detected earlier by dismounting the specimen to examine

the surfaces in contact with the bushing. Surface deterioration and

discoloration were noted at these locations. The loss of stiffness also

provides a means of detecting fatigue damage. Thus, a simple inspection

of service components should provide ample evidence of degradation prior

to failure.

Cyclic stressing produces specimen heating and agitation of the

cryogen. This agitation increases the heat leak into the cryogen due to

convection, because the cryogen is splashed into the warmer regions of

the cryostat. The heat input to the cryogen from both of these sources

increases strongly with displacement. In these tests the helium loss

under static load was only 0.15 £ • h~^ . This increased during fatigue

tests, varying from 7 to 15 £ • h~\ over the range of stress levels

investigated.

Adiabatic heating in glass-reinforced plastics results from their

g high internal friction and low thermal conductivities. Internal

temperature rises as high as 40 K were noted in room temperature fatigue

tests of such materials.^ At 4 K, adiabatic heating should be more

significant since the thermal conductivity of glass reinforced epoxies

52
4

is lowered by a factor of three. Furthermore , the temperature in the

interior of the specimen depends on the specimen thickness and cycling

rate. Since the present data pertain to a specimen thickness and frequency equivalent to service conditions, the effects of adiabatic heating

on fatigue resistance here are academic from an applications viewpoint.

However, this effect must be accounted for in future tests if fatigue

results are to be independent of specimen geometry and test variables.

2.2.5 Concl usions

From these tests, the following conclusions can be drawn:

1. The tensile strength and fatigue resistance exhibited by a

glass roving reinforced epoxy plastic (GFRP) composite material indicate

that such composites can be attractive structural materials for cryogenic

appl ications

.

2. The fatigue life of a GFRP composite material can be an order

of magnitude greater at liquid helium temperature than at room temperature.

3. A measurable decrease in the stiffness of GFRP specimens

may precede high cycle fatigue fracture at 295 K.

Acknowledgment

The cooperation of M. Calderon of Airesearch, Torrance, California

in providing the specimens and reviewing the manuscript is gratefully

acknowledged.

References

1. R. P. Reed and A. F. Clark, Eds., "Materials Research for Superconducting Machinery," National Bureau of Standards, Boulder,

Colorado, AD 780596 and Ad/A 004 586, Nat. Tech. Inf. Serv.,

Springfield, Virginia (1974).

53
2. M. B. Kasen, "Mechanical and Thermal Properties of FilamentaryReinforced Structural Composites at Cryogenic Temperatures - I:

Glass-Reinforced Composites," Cryogenics, Vol . 15 (1975), p. 230.

3. C. W. Fowlkes and R. L. Tobler, "Fracture Testing and Results

for a Ti-6A1-4V Alloy at Liquid Helium Temperature," Eng. Fract.

Mechs., Vol. 8 (1976) p. 487.

4. M. Segimoto, "Qualification Test Results for Glass FilamentWound Support Bands," Report No. 7581, Structural Composites

Industries, Inc., California (Jan. 1975).

5. K. E. Hofer, Jr. and E. M. Olsen, "An Investigation of Fatigue and

Creep Properties of Glass Reinforced Plastics for Primary Aircarft Structures, "Report M6104, 111. Inst. Tech. Res. Inst. (Apr.

1967).

6. L. J. Broutman, "Fibre-reinforced Plastics," Chap. 13 in Modern

Composite Materials, L. J. Broutman and R. H. Krock, Eds., AddisonWesley, Massachusetts (1967).

7. R. B. Heywood, Present and Potential Fatigue and Creep Strengths of

Reinforced Plastics, Tech. Note. No: Chem. 1337, Royal Aircraft

Establishment, Ministry of Supply, London, W. C. 2 (Oct. 1958).

54
3. COMPOSITE COIL MATERIALS

3.1 EFFECT OF STRAIN ON EPOXY-IMPREGNATED SUPERCONDUCTING COMPOSITES

by J. W. Ekin, R. E. Schramm, and A. F. Clark

3.1.1 Introduction

Flux-jump stabilized superconducting magnets are usually impregnated with epoxy to prevent wire movement and enhance stability. Hoop

stress experienced by the windings when the magnet is energized would

otherwise cause wire movement, leading to localized heating and, quite

probably, thermal runaway.

Unfortunately, the epoxy itself can act as a source of localized

heating and initiate thermal runaway. This occurs when the epoxy is

stressed to the point of fracture by a combination of magnetic hoop

stress and stress introduced by differential thermal contraction betweeen

the epoxy and superconducting wire during cooldown. Usually, failures

take place only locally in regions of stress concentration. The local

density of released energy, however, is usually more than adequate to

initiate thermal runaway. Thus, epoxy impregnation of flux- jump stabilized

magnets would be expected to contribute to their stable operation only

at moderate stress levels. At some point of strain, localized failure

of the epoxy is expected to degrade magnet performance. The purpose of

this study is to see if this point can be predicted from the mechanical

properties of the epoxy. A further purpose is to determine if the epoxy

properties have any correlation with the common problem of magnet "training",

wherein a flux-jump stabilized magnet must be quenched a number of times

before it reaches the final design field.

This study is divided into two parts: first, a study of three

types of epoxies commonly used in the construction of potted magnets;

55
second, a preliminary study of superconducting rings potted with these

epoxies.

3.1.2 Epoxy Tests

Specimen Preparation and Tensile-Test Apparatus . Mixing of epoxy

components was according to manufacturers'* directions; in some cases,

_3 outgassing the mixture at about 600 Pa (6 x 10 atm) for 5 to 10 minutes

followed. Curing was in a silicone-rubber mold and yielded a flat,

tapered specimen, accoring to ASTM D 638, Type I;^ the gage length was 5

cm long and 1.3 cm wide with a thickness of about 0.5 cm. After the

prescribed cure, commercial metal-foil strain gauges were attached

directly to the specimen surface (the strain-gage-cement cure temperature

was well below that of the test epoxy cure temperature) . Specimen

conditioning prior to testing was at least 50 hours at 50% relative

humidity and 23°C (ASTM D 618, procedure A).^

The specimen grip system was 100 mesh stainless steel screen

wrapped around 2.5 cm of each end before clamping between two stainless

steel plates (0.6 cm thick) cross-serrated with 10 lines/cm. After

assembly in an alignment jig, three pairs of 10-32 screws, torqued to

*Epoxy A, Armstrong A12, manufactured by Armstrong Products Company,

Warsaw, Indiana; Epoxy B, Stycast 2850FT, manufactured by Emerson

and Cuming, Canton, Massachusetts; Epoxy C, Araldite 6004, manufactured

by Ciba Products Company, Summit, New Jersey, mixed with Lindride 16

hardener, manufactured by Lindau Chemicals, Inc., hardened and cured

for 8 h at 80°C. Trade names are used to define the materials that

were studied. Their use implies no endorsement of particular products

by NBS.

56
2.3 to 4.5 N-m (20 to 40 in-lbs), were used to clamp the grip onto the

specimen. Holes in the steel plates allowed a load pin attachment to

clevises on each pull-rod. The test frame design made it possible to

immerse the entire system in a dewar of liquid helium.

During the test, a two-pen X-Y plotter recorded strain gage output

as a function of load. Our procedure was to load cycle the specimen

(strain rate, e = 3 x 10 ^ s to 25 to 35% of its ultimate strength

four times with high sensitivity settings on the plotter; these data

yielded the elastic parameters. We decreased the plotter sensitivity on

the final loading cycle to record the fracture parameters.

Epoxy Results . Table 3-1-1 shows the mechanical property results

for three types of epoxies at both room temperature and at liquid helium

temperatures. The flexibilized epoxy A has a low modulus and high

ultimate strain at room temperature, but a much higher modulus and lower

ultimate strain at 4 K, about 0.4%. The filled epoxy B has the highest

modulus, but a relatively low ultimate strain, 0.32% at 4 K. The lowviscosity epoxy C has a low modulus at 4 K, but the highest ultimate

strain, about 0.8% at 4 K.

Note the substantial change in properties of flexibilized epoxy A

on cooling to 4 K. At liquid helium temperature, its elongation is

no better than the filled epoxy B. By contrast, the low-viscosity

epoxy C has, by far, the greatest elongation at 4 K. The comparative

differences in elongation at 4 K are the most important property for

the purposes of this study.

57
Table

3-1-1.

Epoxy

Properties

fO Q_C3

•oO

(/) CD

fO

S-CD ^

I— +-> Xo

Q.

K

CO

II II II > > > C_) o o

CO CO

CM

ro CO

a. o) Ln LO LO E i- CTl cn cn

O) =3 CM CM CM

CQ CQ

</) C

0)u

<uQ.

in +J

in

O) +J„

C7) coE

n3

+-> 03

*r—S-03>

4-O

+JE

O)

•r—(J

4-

CUOoo

58
j

1

'I

I

i 3.1.3 Composite Ring Tests

I Ring Specimens and Test Apparatus . Several superconducting comI

' posite rings were fabricated using each of these epoxies. Approximately

' 150 turns of copper-stabilized NbTi (1.8:1 copper-superconductor ratio)

, were wound into rings 15 cm in diameter, 1 cm thick by 1 cm high.

Fiberglass cloth was used to separate each layer of superconducting

wire. A cross-sectional view of the final ring structure is shown in

Fig. 3-1-1. For epoxies A and B, the rings were potted as they were

wound, using a wet layup technique. Rings made with the low-viscosity

^ epoxy C were vacuum impregnated after winding.

To stimulate the hoop stress that would be generated in an actual

magnet solenoid, a split-D fixture was used to apply stress to the ring,

as shown schematically in Fig. 3-1-2. With this arrangement, the stress is

concentrated in the gap region between the two D's and, unfortunately,

a significant amount of bending strain is also introduced. To better

simulate the actual hoop stress in a magnet, a mul tifingered-cone and

magnet arrangement is now being developed. Nevertheless, tests with the

simplified apparatus have served to give comparative results among the

different epoxy types, although the relative strain values indicated

below should not be taken to represent absolute hoop strain. Strain was

calculated from measurements of D separation using an extensometer.

These calculated values were also correlated with strain measured

directly with gages attached to various sections of the ring. The strain

values given in this paper represent the maximum combined hoop strain

and bending strain occurring in the ring.

59
Fiberglass Cloth

Epoxy Potting

Compound

Copper Wire

Matrix

Twisted Niobium-Titanium

Superconducting Wire

Fig. 3-1-1 Cross-sectional view of a superconducting composite

ring showing its components.

60
Fig. 3-1-2

Schematic of the ring test setup showing the configuration

of force, F, applied to the D's, current I, applied to the

superconducting rino, and the resulting self-field B, calculated to be about 3 T at maximum current.

61
Composite Ring Results . While under strain, each ring was energized

with current until it quenched. At constant strain, the quench current

kept increasing until it reached an ultimate value, i . e

, the ring

"trained". The number of quenches it took to reach the ultimate current

is shown in Fig. 3-1-3.

What causes training? We suggest that a dominant cause of the

training process in potted magnets may be associated with localized

fracture of the epoxy impregnant, as follows: When the coil is energized,

the magnetic hoop stress on the coil increases. This charging process

continues until a failure of the epoxy occurs in the region of stress

concentration sufficiently large to initiate thermal runaway. However,

the net result is that the stress concentration in the epoxy is relieved, and the next time the coil is energized, it can withstand a

higher hoop stress, allowing the coil to go to a higher current. This

process continues until the highest levels of stress concentration are

all relieved, or the superconducting wire reaches its short-specimen

critical current.

As may be seen from Fig. 3-1-3, all three epoxies showed little or

no training initially, but all trained to varying degrees at high

strain. The training in rings impregnated with epoxies A and B was more

severe, in correlation with their relatively low ultimate strain. In

contrast, the ring made with epoxy C showed significantly less training,

consistent with its much higher strain tolerance and the training mechanism described above.

62
I

63

Fig.

3-1-3

Training

behavior

of

each

ring

type

asa

function

of

applied

strain.
The ultimate critical current reached after training is plotted for

each ring type in Fig. 3-1-4. The critical current degradation shown in

Fig. 3-1-4 is mainly a function of the localized strain in the superconducting wire rather than the epoxy. Recently, it was shown in a

4

separate study on nonpotted NbTi wire specimens that the critical

current of NbTi will begin to degrade significantly at about 1% strain.

This effect is aggravated, however, by cracks in the epoxy, which lead

to localized strain in the superconductor. It is seen in Fig. 3-1-4 that

the critical -current degradation is most pronounced in the composite

rings potted with epoxies A and B, again correlating with the lower

strain tolerance of these epoxies compared with epoxy C.

The method of epoxy impregnation may also be playing a role in both

these results. Rings potted with epoxies A and B were fabricated using

a wet layup technique. The ring made with epoxy C was made using a

vacuum-impregnated technique. Voids introduced by the wet layup technique may well serve as crack initiation sites, leading to even lower

strain tolerance of epoxies A and B.

3.1.4 Conclusions . These preliminary data indicate that the training

process in potted superconducting magnets is associated with a succession

of stress-concentration relief in the epoxy impregnant. The elongation

of the epoxy at 4 K and the method of impregnation appear to be key

factors controlling training.

Acknowledgments

We are grateful to American Magnetics, Inc. and to M. J. Superczynski

and F. E'. McDonald of the Naval Ship Research and Development Center

64
1

I

I

( 3

| SS9 J1S 0J8Z io %) iNaauno ivoiiiao

I 1—

H

I CO

O')

65

Critical-current

degradation

of

each

ring

type

asa

function

of

applied

strain.
for fabricating the superconducting composite rings tested in this

study. We wish to particularly than M. J. Superczynski for his suggestions and helpful discussions relating to these results.

References

1. "Tensile Properties of Plastics", Annual Book of ASTM Standards ,

Part 35, ASTM D638-76, American Society for Testing and Materials,

Philadelphia, Pennsylvania (1977), p. 215.

2. "Conditioning Plastics and Electrical Insulating Materials for

Testing", Annual Book of ASTM Standards , Part 35, ASTM D618-61,

American Society for Testing and Materials, Philadelphia, Pennsylvania

(1977), p. 198.

3. R. P. Reed, in: Advances in Cryogenic Engineering, Vol . 7 ,

Plenum Press, New York (1962), p. 448.

4. J. W. Ekin, F. R. Fickett, and A. F. Clark, in: Advances in

Cryogenic Engineering, Vol. 22 (Proc. Int. Cryogenic Materials

Conf., Kingston, Ontario, Canada, 1975), Plenum Press, New York

(1977), p. 449.

66
I

, 3.2 YOUNG'S MODULUS OF COMPOSITE COIL MATERIALS

by D. T. Read and A. F. Clark

3.2.1 Introduction

Using the acoustic resonance technique described in the second

report^ the Young's moduli were determined for the various coil comi posites tested in the previous section. Samples were sectioned from

actual coils and, therefore, contained curved wire segments. The effect

of the curvature was assessed by measuring two different lengths and

I also comparing to one specimen from an intentionally straight segment

;i manufactured in an identical manner. These values can then be compared

h 1

j to the measurements reported earlier for the coil composite and to

I calculated values to assure repeatability in the ring structures.

I

j 3.2.2 Specimens

Listed in Table 3-2-1 are the various specimens measured, their

i

i

! source, size, epoxy, and measured density. All were made with a similar

copper-stabilized NbTi wire with a copper-to-superconductor ratio of

1.8:1. The wire in the A and B specimens was slightly larger. The

various epoxy formulations are listed in the prior section (3.1). All

specimens had the ends ground flat and their lengths were measured with

a precision micrometer. Densities were measured by a water displacement

method.

3.2.3 Results and Discussion

The values for the Young's modulus, E, are given in Table 3-2-1

and are accurate to + 5% overall. The densities are estimated to be

accurate to + 1%. Since these measured E values were so close to what

67
to

TDO

s; (o o C\J ^ cn tn 00

O- • • • • • • • • * • to CD «;j- LT) 00 cn ro 1

to OO - CO 00 1

1

cn

cn a-

—

1

1

E

Z3O

>-

+-> to to >1 CU CU +J oo V, ^

1/1 •r- E o o to o 1 CO c to u cn cn o o 1 oo cn cn o E \ • • • • • • 1 • • • •1— (U cn un un LO to to to 1 00 CO 1—

+->

Q

— (ON

•1

s_<u

4->

(_> (O

s-(O o -*-> cn CM CM 1 1 1 1 cn E CTi o o o cn 1 1 1 1 c E CJ • • • • • a 1 1 1 1 O) 0) 1— tn CM <vl- CM 1 1 1 1 1 E _l

•f—o

<uQ. 00

to3(

n

T3O

s: •%

n CL CL to o 3 3 CU

•1— >1 >1 E

4-> eo <a E E -t-> •r" to 1

r— 3 3 -E CQ >1 3

13 3 3 cn cn

X o 4-) +-> CJ • O "r- •1

a o +-> a O) O) OJ (O cn (O to tT3 E CL 3 c o s s > E > E E to CU ^ O E •r— 4-> +-> O -E 3 «s n »> E •> to to ca: o +-> 1

O <C CQ O o >>•1— 1 OO E E E X 3

CNJ >> >1 >1 o >) o • r— r—“ 4-> +J o 1 -o X X X E X E •r— r— CL »> CO E o o O 4- O 4- +-> • 3 3 CU T3

fO CL CL CL CL E 4- CU

a; 0) (U OJ +-> (U +-> CU OJ T3 o •> +J 1

r“ 3 3 E DC CU CU to to 03 #» • «% • " U " O QJ to to to E

<o •r" O) cn OJ cn O) OJ E OJ 3 3 to cn • 1— E •<-> E +J E +-> •< +-> ^ 3 OJ • QJ-—

(U •r— 'r- *r" "a •r- -CJ to to CU to CU cn E 1—

+J to E to E to d) to CU to E 1— E E CL

«3

OO o +-> o +-> • QJ « •rTM •!

•r- CU E • s: Q. E <=L E CL (O CL (O E E E 3 O 3 JO -I- 4- E O E O E c E E OJ CU CJ •I- <U O E O E o cn o cn E o E •I— •r* • 4- E DC

CJ MU 4-

U OJU CU •r“ •r— *f~ 1— >1 1— to \ 3 E E o 4-> U JCI X JO I— >> 3 CU I— +-> 1— +-> r— CL r— CL CU to CU 2: o 2: -1- X O CU

•I- 3 •r- 3 •r- E E CL 4-> CL \ CL \ o O to to O O O CJ O T- o •>- to c/j to 3 CU 3 U CL

(_)

O C_J o —

C_J C_J UJ E

CUE QC CO CQ CD CM in CM tn CM CM <=c C_J U_ onj <C C 00 CQ O C_J 3 IS LlJ a.

cn

68
was reported earlier^ it was decided unnecessary to measure any other

elastic constants or any of their temperature dependences. Everything

could be scaled against the prior values and these were used for comparison only.

The differences in apparent E values between the 2 cm and 5 cm

specimens are about 5%. This is attributed to the effects of the

curvatures of the wires; the shorter, and thus straighten, specimens

having the higher values.

The velocity of a Young's modulus wave in the composite Cu/NbTi

wire used in the A and B epoxy bonded specimens was measured to be

5 3.71 X 10 cm/sec. The velocity of sound in the Cu/NbTi wire in the

C specimens was measured to be 3.69 x 10^ cm/sec. Estimating the density

3

of these materials at 8.3 gm/cm gives a Young's modulus of E. „

=

2 pv =114 GPa at room temperature. The polycrystal 1 ine Young's modulus

of copper at room temperature is 123 GPa. The value of E obtained for

the composite wire is within 1% of this and is considered reasonable

agreement.

Applying a law of mixtures, the estimated density for the wire

3 3

(8.3 g/cm ) and the density of epoxy (1.93 g/cm ) we have for a volume

fraction of epoxy, a,

(1 - a)8.3 + a (1 .93) = 5.9

a[l .93 - 83] = 5.9 - 8.3

a = .377

Applying a simple law of mixtures to the modulus, we have

E T = .623 X E . + .377 x E^

calc wire fg-ep

69
Using the wire modulus above and the measured modulus of the epoxyfiberglass (31 GPa)^ we have

^calc

= 83 GPa

This is within 1% of the measured value for C specimens and also agrees

well with the static value of

static

= 75.8 GPa

3.2.4 Summary

The Young's modulus, E, was measured using dynamic techniques at

300 K in a total of 6 specimens of 3 different types of copper-niobiumtitanium/epoxy-fiberglass composite in both the copper-niobium-titanium

wires, and in one fiberglass-epoxy without wires. The values are shown

in Table 3-2-1. The uncertainties are possibly effects of the curvature

of the wires within the specimens and the nonuniformity of the cross

section due to differences in manufacture and machining. The values of

E obtained are in good agreement with “the value calculated using a

simple law of mixtures and the values of the moduli of the components of

the composite. They also agree well with values determined by conventional

static techniques. Thus, the dynamic technique can readily be used for

coil composite materials, simple laws of mixtures do apply, and the

modulus behavior of one system can be extrapolated to others.

References

1. Clark, A. f., Weston, W. F., Arp, V. D., Must, J. G., and Trapani,

R. J., "Characterization of a coil composite and its constituents",

NBSIR 76-837, Nat. Bur. Stds., Boulder, CO (1976), p. 53.

70
4. CONDUCTORS

4.1 LOW TEMPERATURE TENSILE BEHAVIOR OF COPPERSTABILIZED NIOBIUM-TITANIUM SUPERCONDUCTING WIRE

by R. P. Reed, R. P. MikeseH, and A. F. Clark

4.1.1 Introduction

The main component of each superconductivity application is the

superconducting element. For most large-scale applications, such as

electrical machinery, thermonuclear fusion and energy storage, this basic

element is a mul tifilamentary wire usually wound into a solenoid.

These superconducting solenoi-ds are complex composites exposed to mechanical

stresses, magnetic fields, and thermal gradients. Mechanical stresses are

imposed by the preloading of the wire during winding, by thermal gradients

and component thermal expansion differences during cooldown, and by the

composite magnetic field. Reaction of the superconducting wire to

mechanical stresses at the magnetic operating temperature must be known

to insure optimum design and efficient and successful long-time operation

of the superconducting application.

There have been few measurements of the mechanical properties of

niobium-based superconductors at 4 K. Fox and Pryle^ examined the

tensile behavior of unstabilized monofilaments of Nb-25 wt.% Zr wire

at 298, 77 and 4 K. They reported extremely good properties at 4 K for

the 0.0125 and 0.025 cm diameter wire specimens: tensile strengths from

28 X 10^ N/m^ (420,000 psi) to 45 x 10^ N/m^ (640,000 psi). These

wires had insufficient elongation over the entire specimen length at

4 K to record a yield strength but exhibited between 20 and 50% elongation

at 298 K. Brechna presents one figure that includes the stress-
strain curves of Nb-43 wt.% Ti wire (0.0625 cm diameter) at 4 K and a

Cu-Nb/Ti (10 to 1 ratio) composite wire at 300 K. Cornish measured

the stress-strain behavior of Nb-Ti core, copper-stabilized wire at 77 K 8 2 and found good tensile strength (5.3 x 10 N/m , 80,000 psi) considering

4

that the copper-superconductor volume ratio was 2.74. Finally, Evans

briefly reported several stress-strain curves measured using a

clamp-on extensometer at 4 K of both Nb-Ti, twisted, multifilamentary

wire and Nb-Ti filaments. These stress-strain curves had numerous

sudden load drops, which were interpreted as discontinuous yielding

caused by local, adiabatic heating of the specimen. However, these

curves had no strain associated with the load drops, leading one to

suggest that the load drops originated in the gripping area, rather than

in the gauge length monitored by the extensometer.

As one part of a systematic evaluation of a particular supercon5 ducting coil, the tensile behavior has been measured at 298, 76, and

4 K of its superconducting wire, the Nb-Ti filaments contained in the

superconducting wire, and copper wire given the same thermal and mechanical treatments as the stabilizing copper of the superconducting wire.

For this application, a prototype dc motor for marine propulsion, the

wire is wound into a coil and then vacuum impregnated with epoxy. The

mechanical behavior of the wire is used to program the winding tension

properly, to correlate with the electrical degradation, and to

predict the stress limits for system operation.

4.1.2 Material

The superconducting wire composite consists of 180 filaments (0.032 mm

diameter, twisted, 0.8 twists/cm) of 55 wt.% (38 at.%) Nb-45 wt.%

72
I!

!|

I

I

I (62 at.%) Ti stabilized by oxygen-free, high-conductivity copper (Fig.

I

4-1-1). The volume ratio of copper to superconductor is 1.8 and the

I wire cross section is rectangular with dimensions of 0.07 x 0.055 cm.

To best approximate the expected copper properties in the superI'i

I conducting wire a specially worked and heat-treated oxygen-free copper

wire was supplied by the American Metals Climax, Inc. This copper wire

had been sequentially hot rolled at 1123 K to 0.6 cm diameter rod,

annealed at 1123 K for 0.5 hr, water quenched, cold drawn to 0.2 cm

wire, annealed at 773 K for 0.5 hr, water quenched, cold drawn to 0.07 cm

diameter wire, and finally annealed at 573 K for 1 hr. Its chemical

^ analysis was, in parts per million, 14Ag, 3Fe, < 3As, 2Sb, 6Pb, 4P,

IIS, 0.7Bi, < 2Te, < 2Sn, < IZn, 4Ni, < ICd, and 0.4Mn. Its residual

resistance ratio was reduced from 210 (AMAX data) to 146 (measured

at 4 K at NBS) by the sequential treatment listed above. Microhardness

measurements produced a DPH hardness number of 70 with variations of

+10 (2 g load) and the average grain diameter was 0.011 mm.

The copper-stabilizing material in the superconducting wire was

cold worked in the final condition, after receiving approximately

the same sequential mechanical and thermal treatments as the copper wire.

The average hardness of the copper in the superconducting wire was DPH

98 (2 g load) with variation of + 20, the residual resistance ratio

was 64, and the average grain size was 0.017 mm.

The hardness of annealed, high-conductivity copper in bulk form is

DPH 65 + 5, using a 2 g load. Comparatively, the copper wire has a

slightly higher hardness (DPH 70, 2 g load) and a spread of + 10,

while the copper of the superconducting wire has the highest hardness

(DPH 98, 2 g load) and greatest spread of (+ 20). This corresponds

73
Fig. 4-1 Photomicrograph of the mul tifil amentary superconducting

wire containing 180 filaments and a copper to conductor

(Nb-Ti) ratio of 1.8 to 1.0.

74
well with the residual resistance ratios of 210 for annealed copper,

146 for copper wire, and 64 for the copper of the superconducting wire

composite.

The Nb-Ti filament specimens were prepared by chemically removing

the copper from the superconducting wire. The desired length of wire

was immersed in dilute nitric acid for 2 hr to etch away all copper. No

attack of the Nb-Ti filaments by the dilute nitric acid was detected.

All strands (180), remaining twisted, were then used as the specimen.

Each filament diameter remained at 0.0322 mm.

The wire composite is coated with formvar insulation, a polyvinyl

formal resin. Low- temperature tensile tests with this coating remaining

on the wire produced load-time curves that resembled discontinuous

yielding curves. The load drops did not occur within the specimen gauge

length since no associated strain, as sensed by the strain gauge extensometer, was detected. Removal of the formvar coating using a commercial

stripping solution, which attacked only the coating, produced load-time

curves that had no load drops. Therefore, the load drops with the formvar

on the wire are thought to result from the cracking of the formvar on

the spool grips. Consequently, all reported data at all temperatures

represent tests on specimens having their grip length uncoated, although

from the limited comparative tests, no difference (other than the load

drops) was found.

4.1.3 Procedures

Tensile measurements were performed using a commercial screw-driven

tensile machine with a 4500 kg Toad capacity. Cryostat equipment has

been described by Reed.^ Commercial load cells of 45 kg capacity were

75
used. Strain was measured using conventional four-strain gauge extensometers, which were held to the wire specimens using spring tension on

knife edges. These extensometers were able to sense plastic deformation

over sufficient lengths to measure the total strain (0.01 to 0.04) of

the wire composite and twisted Nb-Ti filaments, all within a gauge

length of 2.5 cm. Approximately 10% elongation could be recorded for

the copper wire specimens. At room temperature an elongation of 1%

resulted in an output of approximately 5 mV. The sensitivity of the

extensometer decreased about 1% betweeen 298 and 4 K. The extensometers

were calibrated at 298, 76, and 4 K using a sensitive drum micrometer

and overlapping, concentric extension arms that were immersed in the

cryogens. Except where indicated, all cross-head speeds were 0.05 cm/min,

resulting in specimen strain rates during plastic deformation of about

0. 004/mi n. All tests were conducted in air (298 K) , liquid nitrogen

(76 K), and liquid helium (4 K) . At least four composite and copper

specimens and two Nb-Ti twisted filament specimens were measured at

each temperature.

Specimens were gripped as illustrated in Fig. 4-1-2. Two wire

segments carried the load and attached to each segment was one extensometer

beam. In the upper spool care was taken in the winding to ensure no

wire overlap. Wire overlap in the grip areas tended to promote erratic load

drops when testing at low temperatures. The arrangement produced wellaligned loading and the fractures occurred randomly along the spool

loading areas and along the open wire lengths. The recorded strain output

was the average of the independent flexing of both extensometer beams.

Microhardness of the three types of copper specimens was measured

using a standard microhardness machine. A 2 g load, small enough to

76
I

Fig. 4-1-2 Loading assembly for the

wire specimens.

77
prevent impingement of the indenter on the Nb-Ti filaments, and a diamond

pyramid indenter were used,

4.1.4 Results and Discussion

Hardness . The condition of the copper-stabilizing material in the

rectangular wire was rather nonuniform. This is indicated by the relatively large variation of hardness of the copper found along the wire

length. This large variation suggests variations in composite properties.

In practice, such large variations in composite yield or tensile strength

were not found. This implies that considerable "averaging" occurs

along the wire length during deformation; however, the tensile strength

may reflect fracture in the softer areas.

Young ' s Modul us . Using the Nb-Ti twisted filaments and oxygen-free

copper data, one can predict their composite Young's modulus (E) values

knowing the volume ratio (1.8 part Cu, to 1 part Nb-Ti, and

using the law of mixtures relationship.

E comp^Cu^Cu

^ ^Nb-Ti^Nb-Ti

^Cu

^ ^Nb-Ti

(

1 )

Two possible effects may contribute to a lower wire modulus, compared

to the bulk modulus of the Cu and Nb-Ti components: (1) the predominance

of <10O> copper texture in wire after small increments of plastic deformation,

and (2) the reduction of E from defect generation during plastic deformation.

Young's modulus of annealed copper crystals, pulled along <100>, is

8 9 relatively low, a typical room temperature value ’ being about 7.6 x

10^*^ N/m^. Other crystal orientations measured by Cuykendall and Sack^*^

10 2

had larger values of E ranging from 15.8 to 20 x 10 N/m . Soliman

78
n 12

et al . and Yeomens have indicated that a <100> texture is observed

after small plastic strain increments in copper. This texture gradually

shifts to half <100> and half <111> at larger strains. Low-temperature

(400 to 800 K) annealing was not found to change the wire microstructure

significantly.^^ Therefore, since the wire composite was strained and

finally annealed at low temperatures, it is probable that a <100>

texture does predominate and may contribute to a low value of E.

Concurrent with the change of crystal orientation, the presence of

lattice defects is known slightly to decrease elastic constants (see

O

Ledbetter and Naimon for specific references). Excessive defects,

generated during the composite forming process and not entirely removed

by the low- temperature anneals, are known to be present; this is indicated by the high hardness and low residual resistance ratio of the

copper.

The combination of preferred orientation and defects, usually found

only wire specimens, provides low values of Young's modulus. Soliman

et al.^^ measured minimum values of E at room temperature as a function

10 2 of plastic deformation of from 5.5 to 6.8 x 10 N/m for copper wire.

Unusually low values of E for bronze-mul tifilamentary Nb^Sn wire have

1

3

been reported by Old and Chari esworth , who found E for the composite

to be lower than both the bulk Nb^Sn and the bronze base elements.

Comparative elastic data for Nb-Ti and Cu, Nb-Ti composites are

scarce. The values of E for Nb-45 wt.% Ti and Nb-48 wt.% Ti in bulk

14

specimens at room temperature, as determined by Ledbetter , are 7.80

and 7.45 x 10^^ N/m^ (1.1 x 10^ psi). The Young's modulus of bulk
10 2 copper at room temperature is about 12.5 to 13.0 x 10 N/m (18 x

6 8 8 9

10 psi) , although considerable data scatter has been reported. ’

The values of E at room temperature determined for Cu, Nb-Ti wire by

Easton and Koch^^ range from 9.3 to 11.0 x 10^^ N/m^. The room

temperature data for E of Cu, Nb-Ti wire, measured using the strain

1 0 2

gauge extensometer in this study, range from 5.8 to 13.0 x 10 N/m .

Obviously the spread of values is too large and further research is

continuing to separate material variability from experimental imprecision

Tensile Properties . The tensile properties of the twisted Nb-Ti

filaments, the drawn copper wire, and the superconducting wire composite

are summarized in Figs. 4-1-3 and 4-1-4. The tensile and yield strengths

(0.2T offset) have no abnormalities as a function of temperature. The

yield strength of Nb-Ti could not be determined since the filaments did

not deform plastically 0.2%. Predicted values of the composite tensile

strength, based on the mixture law, fall about 25% below the actual

composite values; this discrepancy is thought to result from the harder

condition of the copper in the composite, manufacture cold working

subsequent to the 573 K anneal and is indicated by the hardness and

residual resistivity measurements. There is little dependence of the

yield strength of the wire composite on temperature.

The Nb-Ti multifilamentary composite is considerably weaker than

1 3 the monofilaments of Nb-Zr and Nb-Ti. However, the room temperature

multifilamentary Nb-Ti wire tensile properties compare favorably with

the the properties of Nb^Sn multifilamentary composite formed by tin

diffusion into niobium filaments.^ They also compare favorably to

80
Fig. 4-1-3 Tensile and yield strengths as a function of temperature.

Yield strength for Mb-Ti twisted filaments was unobtainable due to their small amount of plastic deformation

(0.6RP - 10^ psi = N/m^).

81
STRAIN

Fio. 4-1-4 Stress-strain curves at 298, 76, and 4 K (0.689 X 10^ psi = N/m^).

82
3 previous work at 77 K, although the tensile values are somewhat higher

as might be expected with a lower copper-to-superconductor ratio.

The stress-strain curves are presented in Fig. 4-1-4. Elongation

to fracture, recorded using the clip-on, strain gage extensometers , can

be obtained from these curves as the tensile strengths and strain to

failure represent average values. The elongation to fracture was about

twice as great at 76 and 4 K as compared to 298 K. Contrary to the

findings of others, ’ no significant discontinuous yielding was observed

in either the Nb-Ti or the wire composite. As mentioned earlier, prior

to the adoption of the present test technique (removal of wire coating

and no overlapping wire on the spools) load drops were commonly observed.

Occasionally, with the present test technique an independent load drop

was noticed on the load-time chart recordings, accompanied by an audible

click. But, none of these sudden load decreases occurred within specimen

gauge lengths, as associated strain increases were never recorded by the

extensometer. This has led to the conclusion that, for this wire, all

load discontinuities occurred in the grip area. Very little plastic

deformation of the Nb-Ti filaments was observed; this implies that

adiabatic heating cannot be a major influence on the filament deformation

processes. The appearance of discontinuous yielding in a superconductor

wire deformed at 4 K is a sufficient, but not a necessary, condition for

plastic deformation-induced adiabatic heating to induce training effects

in solenoids. Discontinuous yielding requires both large temperature

rises and a steep temperature dependence of the superconductor flow

stress. It is very unlikely that large temperature rises will occur in

the Nb-Ti filaments since very little plastic deformation of the filaments

83
occurs and also because these filaments are surrounded by copper, a good

thermal conductor.

The influence of strain rate on the tensile properties at 4 K of

the wire composite is shown in Fig. 4-1-5. The 4 K tensile strength is

essentially independent of strain rate, while there is a slight increase

of yield strength with increasing rate of loading. The largest strain

rate effect is the dependence of elongation; fracture of the composite

occurs at decreasing values of plastic deformation as the rate of loading

is increased. Even at high strain rates, no discontinuous yielding was

observed in this conductor, leading one to speculate that local, adiabatic

heating conditions are not the cause of irregular yielding reported to

4 8 occur in the specimens of Evans and Easton and Koch.

Finally, hysteresis of the stress-strain curve during sequential

specimen loading to the plastic deformation range and unloading to zero

load was examined. Specimens were loaded, unloaded, and then loaded

to a higher stress; this process was continued for 4 to 6 cycles

per specimen at 4 K. A measure of these effects can be estimated from

the parameter (e^ - £i)/e 2

» where £2 strain difference at onehalf the maximum stress and e-j the strain difference at zero stress.

A high value of i'^dicates substantial recovery, while a

zero value indicates perfect elastic behavior. The parameter (£2 -

£-|)/£2 is plotted vs. the maximum applied stress in Fig. 4-1-6 and is

shown to increase steadily with applied stress. Sizable data scatter is

observed. Continuation of the cycling process to the same maximum load

(fatigue) produces decreased values of £2 (corresponding to a decrease

in Young's modulus), but sufficient testing has not been completed to

document adequately the effect on £-|

84
Tensile

Strength

(O)

446uai 06d6 luo u| iusojad

‘N0I1V9N013

85

Fig.

4-1-5

The

effect

of

strain

rate

on

tensile

properties.

All

da

were

obtained

at4

K.

Brackets

represent

spread

of

data

presented

in

Fig.

4-1-4/
M-O

+JOn3

t/l fO

O)

Scnc

+Jo

=3 ocoo

sCL) Q.

13CO>1

s-n3

•!-> c

O)E

(O

M-

•r* -ME • CO 4- CO O OJ

S- >>-(->

S- CO

d)> T3 O <U O •!- O)

S- CL

cn.

O (T3 +j E

CO 3

(O E r *t“ CD X C tT3 cC E

COI

CO

86
4.1.5 Summary

In brief, the following comments summarize this study of the stressstrain behavior of one twisted multifilamentary, copper-stabilized, NbTi superconducting wire.

The tensile and yield strengths of the Nb-Ti, copper, and wire

composite are well behaved from 4 to 300 K. The Nb-Ti has very little

plastic deformation, signifying that little adiabatic heating can take

place in the superconducting filaments prior to fracture. No discontinuous

yielding was observed at 4 K. The yield strength was found to increase

slightly with increasing strain rate and the elongation to decrease

with increasing strain rate, both measured at 4 K.

Anelastic unloading behavior was observed by the wire composite at

4 K. The degree of recovery was dependent on the maximum applied

stress.

Acknowledgments

The authors would like to acknowledge the helpful assistance of

R. L. Durcholz and R. J. Trapani.

References

1. D. K. Fox and W. H. Pryle, in: Advances in Cryogenic Engineering,

Vol . 9, Plenum Press, New York (1963), p. 124.

2. H. Brechna, in: Superconducting Magnet Systems, Springer-Verlag,

Munich (1974), p. 413.

3. D. N. Cornish, in: Proceedings Intern. Conference on Magnet Technology, Ther Rutherford Laboratory, Oxford, England (1967), p. 507.

4. D. Evans, "An Hypothesis Concerning the Training Phenomenon Observed

in Superconducting Magnets," RL-73-092, Rutherford Lab., Harwell,

England (August 1973)

.

87
5. C. W. Fowlkes, P. E. Angerhofer, R. N. Newton, and A. F. Clark,

"Characterization of a Superconducting Coil Composite," NBS-IR73-349, National Bureau of Standards, Boulder, Colorado (Dec. 1973).

6. J. W. Ekin, F. R. Fickett, and A. F. Clark, in: Advances in Cryogenic

Engineering, Vol . 22, Plenum Press, New York (1976), p. 449.

7. R. P. Reed, in: Advances in Cryogenic Engineering, Vol. 7, Plenum

Press, New York (1961), p. 448.

8. H. M. Ledbetter and E. R. Naimon, J. Phys. Chem. Ref. Data 3(4):897

(1974).

9. R. P. Reed and R. P. Mikesell, "Low Temperature Properties of Copper

and Copper Alloys," NBS Monograph 101, U.S. Govt. Printing Office,

Washington, D.C. (1967).

10. T. R. Cuykendall and H. S. Sack, "Dynamic Elastic Properties of

Solids," PB 121701, NTIS, Springfield, Virginia (1955).

11. M. R. Soliman, T. H. Youssef, and R. A. Essawi, Indian J. Phys.

45:77 (1971).

12. D. D. Yeomans, J. Inst. Metals 82:653 (1953).

13. C. F. Old and J. P. Charlesworth, "Some Tensile Properties of Multifilamentary Nb^Sn Superconductors," AERE-R 7903, AERE Harwell,

England (December 1974).

14. H. M. Ledbetter, National Bureau of Standards, Boulder, Colorado,

private communication.

15. D. S. Easton and C. C. Koch, in: Advances in Cryogenic Engineering,

Vol. 22, Plenum Press, New York, (1976), p. 453.

88
4.2 EFFECT OF STRAIN ON THE CRITICAL CURRENT OF COPPERSTABILIZED AND ALUMINUM-STABILIZED NbTi MULTIFILAMENTARY COMPOSITES

by J. W. Ekin

4.2.1 Introduction

Superconducting composites within large-scale magnets can be subjected to high stresses. These stresses arise from several sources,

chief among them being the winding tension and prestressing during

construction of the magnet, thermomechanical forces incurred during

thermal cycling to cryogenic temperatures, and, especially in largescale systems, magnetomechanical forces generated when the magnet is

energized. These mechanisms can combine to exert large stresses on the

superconducting composite, with magnitudes approaching a significant

9 2 fraction of the ultimate strength of the wire itself [about 10 N/m

(^150 ksi) for NbTi:Cu composites].

Typically, data on the critical -current characteristics of superconducting composites are obtained on wires that are in an unstressed

state. Very little is known, however, about how the critical current

behaves in wires experiencing stresses of the type described above.

To measure these effects, short sample critical current tests were made

under conditions simultaneously simulating the mechanical and magnetic

environments of high-field superconducting magnets. The program was

initiated both to form a basis for the fundamental understanding of

strain effects on superconductor stability and to provide engineering

data for optimizing design and construction of high-field magnets. As

will be seen, the results show that mul tifilamentary superconducting

89
composite wires are not characterized by a single critical current vs.

field curve, but rather by a family of curves, each corresponding to a

different operating strain level.

4.2.2 Experimental Apparatus

Two types of apparatus were constructed for simultaneously applying

current, tensile force and a perpendicular magnet field to short wire

specimens at 4K. The first apparatus was designed for testing samples

that can be bent to a radius less than 1.25 cm; the second for testing

straight samples.

The first apparatus utilizes a 100 kOe simple solenoidal magnet

with the sample in a hairpin geometry (shown schematically in Fig. 4-2-1).

At the center of the magnet an approximately 2 m long wire sample is

passed around a pair of 2.5 cm diameter, nonmagnetic, stainless steel

rollers designed to provide a short straight section of the superconductor transverse to the maximum mangetic field. Voltage was detected

along a 3 cm section of the wire perpendicular to the applied field at

the center of the magnet. The wire ends were led out of the magnet

bore, wrapped around a 3.8 cm diameter friction grip, anchored, and

soldered to two 600 A current leads. Stress was applied to the wire

using dead-weight loading. Strains were measured with a clip gauge over

a 1.2 cm gauge length outside the magnet. Voltage across the perpendicular test section was measured with a sensitivity of 400 nV; current

was determined to within 0.5%, magnetic field to within 0.1%, stress to

within 1%, and strain to within 0.01%.

The second apparatus utilizes a 5 cm bore 7T split-pair superconducting magnet with 1.5 cm diameter radial access ports which per90
LOAD

Fig. 4-2-1 Schematic diagram of the stress-I apparatus for testing

hairpin samples. ^

91
mitted testing of long (35.5 cm) straight specimens (shown schematically

in Fig. 4-2-2). The specimens were gripped at either end outside the mag

netic field by soldering into copper sleeves attached to the load train

through self-aligning universal joints. In fracture tests, the specimens did not break at the grips, but fractured at random points along

the gauge length between the grips, indicating no stress concentration

at the copper-solder grips. This arrangement also allowed the introduction of current directly through the grips. The solder grip length

was 3.2 cm and the current-transfer length between each grip and the

4 cm center test section consisted of a ^10 cm length in a linear magnetic field gradient and a 0.5 cm length at full field. These lengths

are more than the theoretical minimum transfer length calculated from

Appendix A.l and A. 2 and, experimentally, no current transfer effects

were observed in the data (i.e., no finited slope to the V-I characteristics at low currents, and no heating at the grips). The critical

current criterion used was 2 uV/cm unless otherwise stated, see Appendix A. 3. Current was determined to within 0.5% and magnetic field to

within 0.1%. Tensile load for this second apparatus was supplied by a

servohydraul ic system which was capable of either load, stroke, or

strain control. Specimen strain was determined to within 0.01% and load

to within +1 lb.

4.2.3 Procedure

After the wire is cooled to 4K, a small preload ($5N) is applied.

This serves the purpose of minimizing wire movement in the presence of

the Lorentz force developed during testing. Critical current is determined by increasing the current through the wire until the voltage

92
Fig. 4-2-2 Schematic diagram of the strain-I^ apparatus for testing

straight samples.

93
across the transverse section of the sample starts to increase sharply

and exceeds the critical -current criterion. This increase is extremely

rapid and is reversible provided the voltage is not allowed to become

too great. Monitoring this reversible rise in voltage also allows a

distinction between the intrinsic critical current of the wire and

irreversible premature quenches occasionally generated by wire movement.

The following measurement procedure was adopted. Initially the

critical current was determined as a function of the magnetic field H

at the prestress level. For the first (second) apparatus, the load

(strain) was then increased and maintained constant while the vs. H

characteristic was determined. This was followed by reducing the load

to the prestress level and remeasuring the initial vs. H characteristic before proceeding to still higher loads. Using this procedure,

information was obtained on both the critical current degradation under

load, as well as any recovery that had occurred after the load was

reduced to the prestress level.

4.2.4 Results: NbTi -Copper

Unless otherwise noted, results are reported here for sample 1, a

multifilamentary NbTi composite which consisted of 180 NbTi filaments in

an "oxygen-free" copper matrix having an initial resistance ratio (R295

k'^^ 9K^

of 70. Copper-to-superconductor ratio was 1 8:1 and the NbTi alloy was

composed of 55 wt-% Ti and 45 wt-% Nb. Twist pitch was 1.3 cm and the

overall wire dimensions were 0.53 x 0.68 mm. A crossectional view is

shown in the top half of Fig. 4-2-3. The specifications are tabulated

in Table 4-2-1; mechanical properties are described in Sec. 4.1.

A typical set of voltage-current characteristic for this conductor

is shown in Fig. 4-2-4. Also shown in Fig. 4-2-4 are three dashed reference

94
Table

4-2-1.

Sample

Characteristics

>> 50 o o o

S- s- s- s~ 1— ( 1

r“ r—

O) OJ O) cu r- 1

<C rQ. CL CL CL fO fO <o Q. Cl Q. CL CU cu

sz •IO •<- o O o •r“ S- r— • 1— 1

•f— S- 1—

•1o 1—

O h- C_) sO o 1— 3 ear (— c 1— 3 C

LO o O) cn CL LO CL

-l-> IX)

O LOO •r- Q. •r- U. •1- u_ un CO LO CO CO

•1

1 zc 1 zc 1— O. 1—

O 1— o 1 cn LO 1 LO 1 CT) LO

</1 JO u_ JD U_ -Q

O JO CO JO CO JO 1 o JO 3 O JO 1 O o 2: o 2: o 2: c_) 2 a. 2 Q- 2 LO LO 2 C_J LO 2 LO LO

ClEO CO «d- o o CO CM CO o CO CO 1— CO o cn o CO CO ro CO CO CO CO CO CO 1— ^ CM CO 1—

LO

•r- x: E E E E E E 2 +-> u u <j u o u

1— CD3 CO cn CO cn CO • CU • • • « » • I— _J f—

'

r” I

1

E . . . . <0 E CO Q Q CO

•1— E « • • • Q E O O *—1 E •vj- E 3 • 3 LO 3 E E E E E

r— CM CM 3 3 3 3 3

•rO . LO • U- CO o CO CD. CD> CD CD CO CO CO CO CO oCO +oCM

U) LO

CU CU jQ JD 3 3

+J +J LO CO X

LO LO o CO CM E E E E E E E E E E E E E

00 o (O <0 fO CO LO CO 00 •r“ •f— •r- CO CO CM

cu . -o o X( • • • N CO CD o o 1—

•p“ E E E

CO

X

X E E E X

X

X

CO CO

O CO o CO CO o

LO CO CO LO LO o • • . « • . . . o o o o o 1

acu -O ,—-s N

cu 4-> *rTM N C n— '—*' CU • r- — CO f— CvJ CD E XD JO 1 cu • 1

1 1 (O <o ta r— -Q r— r— -(-> _i r—

CL fO •r— CO '

•X—

E 4-> o C_) M- •r— (O fO o

CO COQ

Q

O E E o o o

CO QC QC

C 3 <C S- o o

s- cn cn o C o cu rTM (/) CU 2 2 s: •r— 21 u_ < <

CL V, ^ 

E ^ x»

— ''

—

CO. 3

CM CO LO CO 00 o c

95 9

(NSRDC

13-2)

0,89

mm

121“

cm

37%

Nb-53Ti

18%

4-9

pure

A1
Fig. 4-2-3a Crossectional view of sample 1 (NSRDC 4-2, NbTirCu

1 : 1 . 8 ).

Fig. 4-2-3b Crossectional view of sample 3.

96
«3 I— •!-

4-> <C 4-> C •!- <U i. E • O

«o c

(O »o

$- s- <4-

•r“

'sE

M

to o

c

fO

<U I "O

s- s- c • 1-0 0

5 c U

QJ »> O) f if

TO o I—

.-I XI

tou

Mto

<u

4-

>

<o

5-fO

<u

ii-3

a

I <uCD

<D +J

to

to CJ

<u c

S- *r- •M TO

to c

o

M-o

c:o

•!-> o

c

3

MQ.

to

(U

iS-o

a

to

dJ

to "O

«o <u x: —' to

f-< (tJ c

O) I— ro

CLE o

to S- to lO

a; 5

S- o

I- X

5 to

X!I— X <u c

•I- to 4- o0*-H

•r- Io +-> .-I 0

<D 4- 1— O

cu to c <u to -r4->

•• >

to •!-

•r- +J

5- to

o; •!-

-t-> to

•I- Ol

S- 1. a X •M c

C to

OJ

S- E

3 (J U

1 >- r- 0. toO CO

toc

o

•Mo

<u

to

to

too

i.u

<v

XOJN^ sto o

E -M

I CM

CD

CO evj

(A^) 39VnOA

97
lines corresponding to several critical current criteria: an electric

field along the wire of 2 x 10" V/cm, and two resistivity levels of

10"^^ ^^cm and 10”^^ ficm (normalized to the cross-sectional area of NbTi

in the composite wire). For consistency, the electric-field criterion

has been used throughout the following discussion.

From Fig. 4-2-4, it can be seen that the critical current for this

particular NbTi wire was found to be about 230 A at low stress. However

as stress on the wire was increased, the critical current systematically

degraded until eventually a critical current of less than 190 A was

reached just prior to fracture.

In Fig. 4-2-5, has been plotted as a function of stress. Here the

open circles correspond to the critical current measured while the wire

is under load and crosses represent the critical current measured after

the load is applied and reduced to the prestress value. (The dotted

line is included as a reference indicating the initial critical -current

value measured at the preload level; the large X represents the point of

fracture.

Also tested were two other NbTi wires: the first was similar to

the one described above, except larger in size (0.63 x 0.80 mm); the

second was a monofilamentary wire shown in the bottom half of Fig. 4-2-3.

Specifications for both are tabulated in Table 4-2-1. Critical -current

results for each wire are shown in Figs. 4-2-6 and 4-2-7. Note that the

qualitative form of the dependence of critical current on stress was the

same in each case, i.e., the geometry of the wire did not significantly

affect the results. Furthermore, when the results are normalized by the

zero-strain value of the critical current, and plotted as a function

98
(S3a3diftiv) iN3dyno nvoiiiao

LO

(XI

«dCD

99

Critical

current

as

a

function

of

stress

at

various

applied

magnetic

fields.

Solid

curves

correspond

to

the

critical

current

measured

while

the

wire

is

under

stress;

dashed

curves

represent

the

critical

current

measured

after

load

is

applied

and

reduced

to

the

prestress

value.

(Sample

1).
CRITICAL

CURRENT

(AMPERES)

Fig. 4-2-6 Critical current as a function of stress at various

applied magnetic fields. Solid curves correspond to the

critical current measured while the wire is under stress

dashed curves represent the critical current measured

after load is applied and reduced to the prestress value

(Sample 2).

100
CRITICAL

CURRENT

(AMPERES)

Fiq 4-2-7 Critical current as a function of stress at various

applied magnetic fields. Solid curves correspond to the

critical current measured while the wire is under stress;

dashed curves represent the critical current measured

after load is applied and reduced to the prestress value.

(Sample 3).

101
of strain, there were quantitatively the same to within 5 to 10%. Such

a universal strain plot is shown in Fig. 4-2-8 where the normalized

results of sample 1 are compared with two other NbTi samples (4 and 5)

having different amounts of copper and different filament sizes.

Three features of these data are emphasized.

1) The decrease in commences at about 0.5% strain but does

not become appreciable (i.e., greater than 5%) until strains

exceeded about 1%.

2) A surprisingly large part of the degradation is recoverable.

This can be seen most easily by comparing the two sets of data

(circles and crosses) at the higher stress levels in Fig. 4-2-5.

The residual critical -current degradation upon load removal

was directly proportional to the residual strain remaining in

the wire. [In fact a plot of vs. residual strain upon

load removal would fall right on top of the curves shown in

Fig. 4-2-8.]

3) The magnetic field dependence in the 3 T to 7 T range was

relatively small and is shown for sample 1 in Fig. 4-2-9.

Based on all results to date, Fig. 4-2-9 is nearly universal

and may be used for design purposes in most NbTi magnet systems.

From an engineering viewpoint, this stress degradation can be of

importance in setting operating-current levels with adequate safety

margins. As seen in Fig. 4-2-10, the usual vs. H characteristic becomes

a family of curves, each corresponding to a different stress level. At

o 2

a low stress level of 1.12 x 10 N/m (16 ksi) these data agree within 1%

2 with independent data obtained on the same wire using a standard zerostress technique. However, as can be seen in Fig. 4-2-10, at higher

102
7

TESLA

OOj

y

103

Fig.

4-2-8

Cri

tical

-current

degradation

in

several

mul

tifil

anentary

NbTi

:Cu

composites

(samples

1,

4,

and

5)

asa

function

of

strain.

Critical

current,

is

expressed

asa

fraction

of

the

initial

unstrained

critical

current,

Ij^o*
104

Critical

-current

degradation

in

a

mul

tifil

amentary

NbTirCu

composite

(sample

1)

asa

function

of

strain

at

three

applied

magnetic

fields.

Critical

current,

Iq,

is

expressed

as

a

function

of

the

initial

unstrained

critical

current,

Iqq*
H ( kOe)

Fig. 4-2-10 Critical current vs. magnetic field at various applied

stress levels.

105
stress levels (but still considerably below the ultimate) the

characteri Stic is significantly depressed. As a percentage of the total

critical current, the change for this particular sample varies from

about 1% at half the ultimate strength (5 x lO^N/m^) to about 2.^% near

p p the ulimate (10 x 10°N/m^). The percentage change in operating safety

margins can be correspondi ngly greater, especially in large-scale

applications involving high magnetomechanical stress levels.

4.2.5 Results: NbTi -Aluminum

Because aluminum costs less than copper, has a smaller magnetoresistance than copper, and weighs less than copper, it would be advantageous to use aluminum rather than copper to stabilize superconducting

composites. Strain-effect data are reported here on the first attempts

at fabricating aluminum-stabilized multi filamentary conductors.

Three types of aluminum-stabilized conductors were studied, the

first type (tubular geometry) consisted of NbTi tubes filled with a

high-purity aluminum stabilizer and embedded in a low conductivity 5056

aluminum-alloy matrix (shown in Fig. 4-2-lla); the second type (cable

geometry) consisted of filaments of NbTi embedded in a 5056 aluminumalloy matrix cabled with high-purity aluminum (shown in Fig. 4-2-12);

and the third type (high-conductivity alloy) consisted of filaments of

NbTi embedded in a higher conductivity 1100 aluminum-alloy matrix which

was surrounded by high-purity aluminum (shown in Fig. 4-2-13). Results

for each of these will be discussed in turn:

Tubular Geometry. Because pure aluminum is so much softer than

pure copper, it is metal 1 urgical ly very difficult to fabricate a

conductor similar to that shown in Fig. 4-2-3 by simply replacing the

106
Fig. 4-2-llb Crossectional view of sample 5.

Fig. 4-2-lla Crossectional view of sample 4.

107
Pb-Sn 99.999% Al Nb-46.5 T

Fig. 4-2-12 Crossectional view of sample 6.

108
Fig. 4-2-13 Crossectional view of sample 7.

109
matrix by a pure aluminum matrix. The aluminum is too soft to uniformly

reduce the NbTi filaments when the composite is drawn into wire (D.

Koop, private communication). Consequently the first geometry studied

consisted of NbTi tubes embedded in a relatively tough 5056 aluminum

alloy matrix with the soft, pure aluminum stabilization material on the

inside of each NbTi tube, as shown in Fig. 4-2-lla. (Further details

are given in Table 4-2-1.)

Figure 4-2-14 shows a typical set of voltage-current characteristics

for this specimen. The conductor was stable, but as seen in Fig. 4-2-14,

it exhibited a hysteresis in its critical current characteristics

depending on whether the magnetic field was being increased or decreased.

This resulted from magnetic flux trapped in the tubes and indicated that

self-field ac losses would be large for this tubular geometry. All

subsequent data reported here were obtained with field increasing to the

indicated value.

In an effort to compare the strain effects of aluminum stabilization

vs. copper stabilization directly, two wires were tested under tension

which were alike in every way, except one (Fig. 4-2-lla) was stabilized

by high purity aluminum (RRR=5000), the other (Fig. 4-2-llb) by OFHC

copper (RRR=70). Both consisted of NbTi tubes embedded in a 5056 aluminum

alloy matrix with the stabilization material on the inside of the tubes.

(Further details are given in Table 4-2-1.) Results for the two wires

are shown in Fig. 4-2-15. As seen in Fig. 4-2-15, the strain degradation

of the critical current for the two wires was identical to within 1%.

The magnitude of the effect, however, was greater for this tubular

geometry than for the strain effect in non-tubular NbTi copper conductors

(shown in Fig. 4-2-3).

no
(Arf) 39VnOA

i

111

Fiq

4-2-14

Voltage-current

characteristics

for

sample

4,

at

several

values

of

’

magnetic

field.

Characteristics

labeled

by

upward-pointing

arrows

indicate

the

field

was

increased

to

the

value

shown;

downward-pointing

arrows

indicate

the

field

was

decreased

to

the

value

shown.
O}o

03

CC

h—

CO

(s8J3diue) i|\|3«an3 IVDIilbO

Ln

C\J

I

cn

(s8J3duie) iN3danO IVOliiaO

Comparison

of

critical

current

vs.

strain

characteristics

for

aluminumand

copper-stabilized

NbTi

superconductors

(samples

4

and

5).
other problems with this geometry are:

1) the current transfer length (Appendix A.l) will be much longer

than for typical NbTi copper conductors because the NbTi tubes

are separated by a high-resistivity aluminum-alloy matrix.

2) The ratio of stabi 1 izer-to-superconductor is limited to low

values because only the NbTi tube cores are available for

stabilization material.

Cable Geometry . To avoid the problems associated with tubes, the

second geometry tested consisted of several strands of NbTi filaments in

a 5056 aluminum alloy matrix. The strands were cabled with several

additional strands of high-purity (5-9 grade) aluminum to provide stabil

ization, see Fig. 4-2-12. The entire cable was soldered together by

nickel plating the individual strands and soldering with 50/50 PbSn

solder. (Sample details are given in Table 4-2-1.) Unfortunately, this

cable geometry was found to be unstable, probably because of the high

resistivity 5056 matrix surrounding the filaments. At 5T, only 68% of

critical current could be achieved before thermal run away would occur.

The full critical current could be achieved only in an isolated strand,

surrounded completely with helium.

The 4K resistivity of the 5056 aluminum alloy matrix was about 1.4

ufi-cm, comparable to that of tin bronze used in the manufacture of

multifilamentary Nb^Sn conductor. But the filament size ‘in this cable

was about 7 times that in a typical multifilamentary Nb^Sn wire. Thus,

as far as the future direction of work is concerned, it is noted that

choosing an aluminum alloy only slightly more conductive than 5056 and

reducing the filament size to less than 10 microns should increase the

113
stability of the cable to a practical level (at least comparable to

multifilamentary Nb^Sn).

High-Conductivity Aluminum Alloy Conductor . The third type of

conductor studied was fabricated much the same as commercial copper NbTi

(Fig. 4 2-3a)but with the copper replaced by a higher-conductivi ty 1100

aluminum alloy surrounded by 4-9 purity aluminum, see Fig. 4-2-13. The

1100 alloy has a 4K resistivity considerably less than that of the 5056

alloy. The conductor was stable and had a critical current density

typical of copper-stabilized NbTi. The only problem was fabrication.

Only short lengths could be drawn because of breakage and necking in the

NbTi filaments.

4.2.6 Aluminum Conductors: Conclusion

These data suggest that a workable method of fabricating an aluminumstabilized conductor would be to use an aluminum-alloy matrix with a

resistivity somewhat less than 5056 aluminum (e.g., 1 u^^-cm or less) and

reduce the NbTi filament diamters to the 10 um range. Such a conductor

would be both fabricable and stable (although not as stable as typical

copper:NbTi multi filamentary conductors).

Perhaps the best method for utilizing the advantages of pure

aluminum as a stabilizer without encountering the fabrication problems

of such a soft metal is to bond the pure aluminum stabilizer to the NbTi

after fabrication. With present joining technology, there is no reason

why pure aluminum could not be bonded to a copper-fabricated multifilamentary NbTi core. This could be particularly advantageous in the

production of cryostabil ized conductors where the required amount of

stabilization material is many times that actually needed to fabricate

the NbTi filaments.

114
References

1 ) Superconducting Machines and Devices, Large Systems Applications

(S. Foner and B. B. Schwartz, eds.), Plenum Press, New York (1974);

H. Brechna, Superconducting Magnet Systems , Springer-Verlag, Munich

(1973).

2) Magnetic Corporation of America and Westinghouse Electric Corporation,

private communication.

115
4.3 MECHANISMS FOR CRITICAL-CURRENT DEGRADATION IN NbTi

AND Nb^Sn MULTIFILAMENTARY WIRES

by J. W. Ekin

Abstract

Critical currents of NbTi and Nb^Sn mul tifilamentary wires have

been studied in magnetic fields to 9 T as a function of mechanical load

applied at 4 K. Degradation of the critical current in NbTi is limited

to about 30% with the effect becoming large only at strains above ^1%.

The change in critical current with strain is much larger in Nb^Sn,

commencing at strains of 0.1 to 0.3%. For both superconductors, the

first 20 to 30% decrease in critical current is almost totally reversible.

A number of possible explanations of the observed degradation are considered,

including filament breakage, heat generation by mechanical creep, degradation of the stabilizing matrix, and defect formation in the superconductor

itself. Results of experiments to test the source of degradation

are reported. Evidence for microcrack damage in the Nb^Sn reaction layer

has been found and it is suggested that defect size variations on the

order of a coherence length ('^5 nm) can account for the reversibil ity

of the degradation as well as low-strain enhancement effects.

4.3.1 Introduction

1 -4

Recently it has been shown that when NbTi or Nb^Sn multifilamentary

wires are uniaxial ly stressed at liquid helium temperatures, the critical

current of these superconducting wires undergoes a nearly reversible

degradation. In this paper we consider various possible sources of

this degradation and report the results of several experiments to test

these explanations.

116
A summarized comparison of the results given in Refs. 1 and 2 for

NbTi and Nb^Sn is shown in Fig. 4-3-1. As shown by the solid curve

labeled NbTi, the effect in NbTi commences at about 0.5% strain and grows

to about a 30% degradation as the ultimate strength of the wire is

approached. The recovery curve for NbTi (dashed line in Fig. 4-3-1) shows

that the critical current recovers to about 95% of its unstressed value

upon load removal. That is, the effect is highly reversible; large

degradation occurs only when the wire is actually under stress.

In Nb^Sn, the degradation threshold occurs at lower strains and is

dependent on reinforcement and cabling techniques used in the wires'

construction. As shown by the curve labeled Nb^Sn in Fig. 4-3-1, the

effect typically starts at threshold strains in the range 0.1 -0.3%

depending on wire configuration and condition. The cri tical -current

degradation is almost totally reversible up to strains about double the

threshold strain. At higher strains, however, much of the damage is

permanent, and recovery is only partial.

To summarize the observations on mul tifilamentary wires:

(1) The first 20 to 30% decrease in critical current, I^, is

almost totally reversible for both NbTi and Nb^Sn.

(2) Total degradation before fracture is limited to about 30% in

NbTi, with the effect becoming large only at strains above ^1%.

(3) The change in with strain is much larger in Nb^Sn and

commences at strains of 0.1-0. 3% depending on wire configuration

and condition.

A number of possible explanations have been suggested. Included

among them are the following: simple filament breakage, reduction in

117
(3| SS8JIS 0J3Z p

o/„) iN3 ayno ivoiiiao

118

STRAIN

(percent)

Summary

of

critical

current

degradation

in

mul

tifil

amentary

NbTi

and

Nb^Sn

wires.

Results

were

obtained

at

comparable

magnetic

fields

(0.45

the

two

materials.

Dashed

lines

for

each

case

indicate

the

critical

-current

recovery

value

after

unloading.
cross-sectional area of the wire, heat generation by steady-state creep,

degradation of the stabilizing matrix conductivity, stress-induced

martensite formation, and microcrack formation in the superconductor.

Results of experiments to test several of these explanations are presented

below.

4.3.2 Mechani sms

Filament Breakage . As noted above, the first 20 to 30% decrease in

is almost totally reversible for both NbTi and Nb^Sn. Significant

filament breakage would not produce a reversible effect. Furthermore,

SEM examination of stressed wires used in obtaining the experimental

data in Fig. 4-3-1 showed the filaments to be intact after testing.

However, in the irreversible, high-strain region for Nb^Sn, cracking of

the Nb^Sn reaction layer was observed. This will be discussed in more

detail in Section 3.

Area Reduction . An elastic reduction in cross-section area of the

superconductor would produce a proportional increase in current density

and a reversible decrease in I^. However, the average cross-sectional

area reduction for the samples shown in Fig. 4-3-1 was on the order of

1-2%, too small to account for the 30%+ effects observed.

Creep . Low temperature creep in metals is small and usually charac5 terized by a time-varying logarithmic dependence. If heat generation

by slow plastic deformation of the superconductor were responsible for

the decrease in I^, then the degradation under static loading would be

expected to vary with time. The degradation would be largest when

the load is first applied, but decreasing with time as the creep rate

and rate of heat generation decrease.

119
To test for this, a constant bias current of 208 A was passed

through a NbTi wire as shown in Fig. 4-3-2. At his current, the fluxflow voltage along a 3 cm-length of wire was less than 0.5 uV. However,

g

upon stressing the wire to 8 x 10 Pa (^80% of the ultimate stress), the

critical current decreased to the point where there was a large increase

in flux flow voltage to 15 yV. As shown in the insert in Fig. 4-3-2, the

voltage along the wire remained constant at 15 uV over the entire test

period of 2 hours. Upon unloading the wire, the voltage dropped immediately

to 0.05 uV. No time-dependent changes in the cri tical -current degradation

were observed during the two hour period.

The analysis can be carried slightly further to establish an upper

limit on the temperature change in the wire. dl^/dT for the wire was

measured to be 62A/K at 4 K. This would mean the wire would have to

rise 400 mK in temperature to account for the degradation shown in

Fig. 4-3-2. The change in voltage during the two hour test was less

than 0.5 yV, which, combined with the V-I slope of 0.28 A/yV, results in

the temperature change of the wire being less than 2 mK during the test.

The magnitude and time invariance of the effect would thus suggest that

the observed degradation is not associated with a stress-induced

heating effect.

Matrix Degradation . degradation curves were obtained on two

NbTi wires, one stabilized by high-purity aluminum. Both wires were

essentially identical in every respect except for the stabilization

material. The OFHC copper stabilizer had a residual resistivity ratio

(RRR) of 23; the aluminum stabilizer had a RRR of 580. The stabilization

material is contained inside the superconducting filaments and has an

average cross section diameter of 39 ym.

120
\

I

!

i o

CO LO CO CSI (Ag.Ol) 30VnOA

00

03

(Uo.E

CO

121

Fig.

4-3-2

Time

invariance

of

the

critical

-current

degradation.

Vol

tage-current

plot

shows

the

extent

of

degradation

in

a

NbTi

wire

at

a

stress

of

8

8

X

10

Pa.

Voltage-time

insert

indicates

the

constancy

of

the

fluxflow

voltage

during

the 2

hour

test

when

the

wire

was

biased

ata

current

of

208

A.
Results for these two wires are shown in Fig. 4-3-3. A close

comparison of the two sets of data shows the degradation in both wire

types to be essentially identical, even though the starting RRR's for

the two stabilizing materials differed by more than an order of magnitude.

Moreover, a measurement of the change in RRR (R293 K

^ ^ c wires after stressing (but kept at 77 K) showed that the RRR of the

high-purity A1 had decreased to less than half its initial value (RRR =

191). By contrast, stress affected the relatively impure copper much

less, decreasing its already low RRR from 23 to 19. So not only was the

starting RRR of each material different, but the stress-induced change

in RRR during testing was very dissimilar. Yet, in spite of these

differences in matrix conductivity, the degradation of the two wires

was essentially the same. These data suggest that the matrix is not

playing major role in degradation of the critical current. (Of course,

if the matrix degradation becomes too great, eventually the thermal vs.

magnetic diffusivity balance is upset and the wire becomes unstable.)

It is also interesting to note the effects of stress on the superconductor cooling current, that is, the current at which a wire sample

returns to the superconducting state after being driven normal (dashed

lines in Fig. 4-3-4). It varied very little with stress, even under

loads which degraded the critical current by more than 90%. Since this

2

current is mainly a functin of I R heating in the matrix, this, too,

would focus attention on the superconductor, rather than the matrix, as

the source of degradation.

Magnetic-Field Dependence . The degradation effect was found to be

strongly dependent on magnetic field intensity. For example, one Nb^Sn

122
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123

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Invariance

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Under

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the

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for

the

Cu-stabil

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decreased

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19,

while

RRR

for

the

Al-stabilizer

decreased

to

191.

The

stabilization

material

for

each

conductor

was

contained

within

NbTi

tubes

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39

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in

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124
wire was strained to such an extent that a resistivity of more than 10~

Q. cm was measured at a current of lOA in a field of 9 T ; see Fig. 4-3-4.

However, when the same damaged wire was tested at zero applied field,

-13

its resistivity was less than 10 n cm at currents up to 257 A (at

which point flux instabilities drove it normal). The stress-induced

resistivity is thus observed to be strongly field dependent, suggesting

the effect has its origin in vortex movement within the superconductor.

4.3.3 Superconductor Degradation -- Discussion

Briefly summarizing the results thus far, degradation in NbTi

and Nb^Sn does not appear to be caused by any of a number of peripheral

effects associated with degradation of the stabilizing matrix, heating

of the wire caused by plastic deformation of the composite conductor,

elastic reduction of the crossectional area, etc. Rather, it appears to

be due to stress-induced changes in the superconductor itself.

For the case of high strains in Nb^Sn, the irreversible degradation

can well be accounted for by the relatively wide (>100nm) transverse

cracks we have observed in highly stressed samples using SEM techniques.

Enhanced current density in the regions near the crack sites will induce

large flux-flow voltages along the -wire at low currents, resulting in a

substantial decrease in I^. Also the associated flux-flow resistivity

will be strongly field dependent as observed in the above studies.

Details of the mechanism are not so clear in NbTi, however, nor in

Nb^Sn at low strains where the degradation is reversible and I enhancements

sometimes occur. ^ For these cases, the critical current could be affected

by two general types of changes within the superconductor -- either by a

shift in the intrinsic critical temperature and field, or by an alteration

of the vortex-pinning structure.

125
Stress-induced band structure changes and/or martensitic transformations

are possible and it is conceivable that these would lead to critical

temperature-field properties different enough to produce the observed

changes in However, the effect would have to be unusually reversible

(for the martensitic transformation) and produce at least a 20% change

in vs. e vs. T data (and/or direct metallurgical observation) are

needed to determine the existence of such an effect.

On the other hand, rather large changes in would also be produced

if the vortex pinning structure of the superconductor were altered

by stress. In particular, a number of observations have been made which

show the critical current of hard superconductors to increase as defect size

g decreases. Recently it has also been experimentally shown that if the

defect size is made too small (small compared with the superconducting

coherence length C)> eventually stops increasing and starts to precipitously

9 decrease. Maximum vortex pinning occurs when the average defect size

is on the order of the vortex core size, given by the Ginzburg-Landau

5(T) = 0.85(e^«,)''/^(l - 0 )

Here is the BCS coherence length and £ the electronic mean free

path. Using measured values of H ^2 Nb^Sn^^’^^ and Nb45Ti^^,

5(4.2 K) may be approximately determined using the relation:

5^(4. 2 K) = y27TH^2(^-2 K) ( 2 )

126
In Nb-45Ti, ?{4.2 K) is found to be on the order of 5.5 nm; in Nb^Sn,

5(4.2 K) is approximately 4 nm. Changes in the metallurgical structure of

the superconductor on this size scale will strongly affect I^. Thus

for these two superconductors, a growth in either defect strength, or

defect size to the order of 10 nm would initially enhance I^. Further

defect growth under the action of strain, however, will make the defects

less effective pinning centers and I will decrease. I recovery is

also possible if, upon stress removal, the defect size returns toward

the '^^l 0 nm level

.

This general picture of vortex-defect interactions has been presented

mainly to set the size-scale for further study in this area. The sizescaling mechanism is independent of the type of defect considered.

Mechanical twins, martensite platelets, cell boundaries, dislocations,

and grain-boundary stress fields could all serve the purpose, provided

their size varied with the amount of stress applied to the superconductor.

In brittle Nb^Sn, grain boundary damage actually develops into largescale cracks which are readily observable. In ductile NbTi, such gross

defects do not develop and direct observations of the ^10 nm defect

structure have not yet been obtained. However, such a change in vortexpinning structure could account for the large scale of I^ degradation

in Nb^Sn compared with NbTi, the slight enhancement in I^ at low strain

levels, the reversibility of the effect at intermediate strains, and

the strong dependence on magnetic field.

4.3.4 Conclusion

In summary, the experimental evidence would suggest that the source

of I^ degradation is associated with the superconductor itself, rather

127
than with the peripheral effects such as matrix degradation, area

reduction, etc. At high strains in Nb^Sn where the degradation is

irreversible, the effect is well accounted for by >100 nm cracks observed

in the Nb^Sn reaction layer. Where the degradation is mostly reversible

(at lower strains in Nb^Sn and at all strains in NbTi), the effect is

most likely brought about either by a shift in the intrinsic critical

temperature and field, or by an alteration of the vortex-pinning. No

direct observations of reversible defect behavior have yet been obtained.

However, it is suggested that defect size variations on the order of

a coherence length (^5 nm) could be playing an important role in this

reversible regime, explaining such effects as recovery and lowstrain I enhancement,

c Acknowledgments

I am grateful to A. F. Clark, F. R. Fickett, R. P. Reed, M. Suenaga,

and M. J. Superczynski for a number of stimulating discussions relating

to these results.

References

1. J. W. Ekin, F. R. Fickett, and A. F. Clark, "Effect of Stress

on the Critical Current of NbTi Multifilamentary Composite Wire,"

Proceedings of the Int. Cryogenic Materials Conference, Kingston,

Ontario, 1975, Adv. in Cry. Eng. , Vol . 22, pp. 449-452, Plenum,

New York (1976)

2. J. W. Ekin, "Effect of Stress on the Critical Current of Nb^Sn

Mul tifilamentary Composite Wire," Appl . Phys. Lett. 218 (1976).

3. J. W. Ekin and A. F. Clark, "Effect of Strain on the Critical Current

of Nb^Sn and NbTi Multifilamentary Composite Wires," Proceedings

128
of the Joint MMM-Intermad. Conf., Pittsburgh, PA (1976) (to be

published by the Am. Inst, of Phys.).

4. D. S. Easton and R. E. Schwall, "Performance of Multifilamentary

Nb^Sn Under Mechanical Load", Appl . Phys. Lett, (to be published).

5. See for example, J. Weertman and J. R. Weertmann, "Mechanical

Properties, Strongly Temperature Dependent" in Physical Metallurgy ,

edited by R. W. Cahn, North-Hol land Pub. Co. (1965), Chapter 16,

pp. 793-804.

6. See also J. L. McDougall, IEEE Trans, on Mag. 1J_, 1467 (1975).

7. E. Buehler and H. J. Levinstein, "Effect of Tensile Stress on the

Transition Temperature and Current-Carrying Capacity of Nb^Sn,"

Jour. Appl. Phys. 3856 (1965); D. Easton, Ref. 4; T. Luhman

and M. Suenaga, paper W-4 in this conference.

8. See, for example, D. Dew-Hughes, in Superconducting Machines and

Devices, Large System Applications , edited by S. Foner and B. B.

Schwartz, Plenum, New York (1974), Chapter 2, pp. 109.

9. J. W. Ekin, "Critical Currents in Granular Superconductors," Phys.

Rev. B U 2676 (1975).

10. G. Otto, E. Saur, and H. Wizgall, J. Low Temp. Phys. X, 19 (1969).

11. S. Foner, E. J. McNiff, Jr., B. J. Matthias, T. H. Geballe, R. H.

Willens, and Corenzwit, Phys. Lett. 31A 349 (1970).

12. B. G. Lazarev, 0. N. Ovchavencko, A. A. Matsakova, V. G. Volotskaya,

Zh. Eksp. Teor. Fiz. 1031 (1968); Trans. Sov. Phys. JETP XZ.»

549 (1968).

129
13. D. S. Easton and C. C. Koch, "Mechanical Properties of Superconducting NbTi Composites," Proc. Inti. Cry. Mat. Conf., Kingston,

Ontario, 1975, Adv. in Cry. Eng. , Vol . 22, Plenum, New York (1976)

14. R. P. Reed, R. P. Mikesell, and A. F. Clark, "The Low-Temperature

Tensile Behavior of Copper-Stabilized NbTi Superconducting Wire,"

Proc. Int. Cry. Mat. Conf., Kingston, Ontario, 1975, Adv. in

Cry. Eng. , Vol. 22, Plenum, New York (1976).

130
Appendix 1

Current transfer in multifilamentary syperconductors. I. Theory®^’*"^

J. W. Ekin

Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302

(Received 21 February 1977; accepted for publication 10 January 1978)

In short-specimen critical current measurements, inadequate separation between current and voltage contacts results in a finite linear slope in the measured voltage-current characteristic at low currents. A

simple approximate analytic expression is developed for estimating the magnitude of this slope from wire parameters. Current-transfer lengths are evaluated for multifilamentary NbTi and NbjSn composite

superconductors. PACS numbers: 74.60.Jg, 74.70.Dg, 74.70.Lp, 85.25. -fk

I. INTRODUCTION

In multifilamentary superconducting wires, there is a resistive transition from the superconducting to nor- mal state as current through the wire is increased

above the critical current [Fig. 1(a)]. This resistive transition is highly variable from wire to wire; for magnet design it must be measured in order to determine operating currents, cooling requirements, and

internal heat -transfer conditions. Often this involves

measurement of very low wire resistivities (10**^ ficm or less), especially when the Joule heating re- quirements of the magnet system are stringent.

An experimental problem in performing such measurements on short -specimen multifilamentary composites is that an additional voltage can be generated near the current contacts as the current penetrates the normal matrix material from the outer to the inner

superconducting filaments [Fig. 1(b)]. This currenttransfer voltage can be significant over surprisingly

long distances from the current contacts, 10—100 wire

diameters or more, depending on the particular superconductor and application. In this paper, we derive a simple approximate formula for quantitatively esti- mating the magnitude of current-transfer effects. This

theoretical result will be compared with an experimental study of current transfer in the following paper. ^

In Sec. II, a model first presented by Wilson^ is used to calculate the electric field E{x) along a wire

due to current transfer among the filaments within the wire. In Sec. Ill, it is shown that for most practical purposes, the integral equation for E{x) from Sec. II can be reduced to a simple analytic expression. This is then used to determine an apparent resistivity from

current transfer, p(x), and a current-transfer length

^min> where the latter is defined as the distance along

the wire needed for p(x) to decay to a negligible value.

In Sec. rv, is calculated for multifilamentary

NbTi and NbjSn. In Sec. V, the effect of current transfer on the shape of the superconductor voltage-current

characteristics is discussed.

II. MODEL EQUATIONS

In this section, a model originally presented by

Wilson in an unpublished lab note^ is used to derive an

integral expression for the current-transfer electric

field. In Wilson’s model, it is assumed that current is fed in from the outer radius of a multifilamentary

superconducting composite. In particular, the transfer

of current between two concentric filament rings is considered, eacfh of mean radius and and thickness

and fg! see Fig. 2. If a current AJ^2-!rr^tj^ crosses from ring 1 to ring 2 over a distance Ax, the resulting

potential difference between the two rings is

FIG. 1. Schematic representation of the superconducting

composite’s V-I characteristics in two regions: (a) far from

the current contact where the wire undergoes the usual resistive transition as 7 approaches 7^ and (b) near the current contact where the characteristic exhibits a linear region at low

currents.

^'Contribution of the National Bureau of Standards.

'"'Supported by the Naval Ship Research and Development Center, Annapolis, Md and the NBS Superconducting Standards Program.

FIG. 2. Schematic representation of current transfer between two concentric rings of superconducting filaments.

3406 J. Appl. Phys. 49(6), June 1 978 3406

131
( 10 ) V^(x) - V^ix) = - (AJ^/Ax)rJ^f3^ Inir^/r^), (1) where p„ is the transverse resistivity of the matrix.

Jj can be related to by applying the boundary conditions that the total current in the rings is constant and that at x = « the current density in the conductor

becomes uniform and equal to J„. This yields

J^r^t^+J^r^t2=Jjr^ti+r2t2). ( 2 ) Current will not penetrate to the inner ring of fila- ments unless the resistance of the outer superconductor

filaments becomes comparable to the matrix resistance

separating the filaments. This will occur when the current density J in the outer filaments approaches the

critical current density. The filaments will then exhibit the usual resistive transition behavior, which for

this calculation is assumed to be given by the empirical

formula

P=krF, (3) where p is the effective resistivity of the superconducting composite layer, J is the current density, and n

is a constant representative of the material being considered (e. g. , w = 30 is typical for NbTi ^). The proportionality constant k may be determined from a specific

value of the resistivity at some arbitrary current density; for example, the effective resistivity p„ at yields

k=pJJl. (4) Using Eqs. (3) and (4), the electric field along the outer ring in the x direction can be represented by

= Pi(x)Ji(x)

and along the inner ring it is

£2(x) = -

dx

(5)

Then, after integrating and applying the boundary condition that when y= 1, Eq. (7) becomes

? = (^)

( 11 ) where Y is the initial value of y at the current junction.

Note from Eqs. (5) and (9) that the electric field along

the outer cylinder is given by (the subscript 1 will be omitted for the remainder of this paper)

E=pJ=p„J,(J/J.)"*i=E.y"*i, (12)

where

(13)

In this model, only two concentric annuli of filaments

have been considered, whereas a practical superconducting composite contains many such rings. To obtain an exact solution, another integration should be

carried out with respect to the radius, subjected to the boundary condition that the total current in the wire

is constant. Also, the precise solution will be dependent

on the initial current distribution at the current junction,

which can vary considerably from apparatus to apparatus. All that is really needed, though, is some idea

of the magnitude of current-transfer effects for apparatus design. For this purpose, the entire wire may

be simply approximated by two cylinders of filaments,

the outer one hollow and the inner one solid. Assume

that they have equal cross-sectional area, in which

case 6 = 1, rj/r2 = l+r2 , and — where D is the overall radius of the wire. Then, Eq. , (10) reduces

to X (w + 2)^'^^ fX dy

•'y where

\ = 0.23(p„/pJ‘/^D.

(14)

(15) = J^{x)P2ix) (6)

Differentiating Eq. (1) with respect to x and combining

with Eqs. (2), (5), and (6), there results

dx^ J^p„ \rj

V«>/ \ ^2^2 '^•>^2^2/

Let us define the following parameters:

^2 ^:ZhPjl • rirm In

P.

y =

(7)

( 8 )

(9)

The above results are essentially those obtained by

Wilson,^ but involve several different assumptions.

They are presented here to serve as a starting point for the derivation of a much simpler expression. In Eq. (14), we have used a different geometry for the relative size of the two rings comprising the wire, and

in Eq. (11) no assumption has been made about the relative thicknesses of the two rings, which were as- sumed to be of equal thickness in the original derivation.

In Secs. Ill—V, the integrals in Eqs. (11) and (14) are reduced to an analytic expression that should be useful

for quick calculations of current transfer effects over most of the wire’s length, without numerical integration or a priori knowledge of the wire’s intrinsic resistivity (p„) and initial electric field (T).

III. CURRENT-TRANSFER LENGTH

For short-specimen testing, an estimate is needed

of how close to the current contacts the voltage taps

3407 J. Appl. Phys., Vol. 49, No. 6, June 1978 132

J.W. Ekin 3407
FIG. 3. Relationship between the normalized electric field from current transfer E/E„ and the normalized distance along

the superconductor x/x {from Eq. (17)1, plotted for several

values of the resistive transition parameter n [defined in Eq, (3)].

can be placed without having the current-transfer volt- age interfere with measurement of the wire’s intrinsic V-I characteristics. Let us denote this minimum separation as the current-transfer length To determine Eq, (14) [or alternatively Eq. (11)] has to be solved for E{x). Fortunately, for most experimental

situations the integral can be greatly simplified and a numerical integration avoided.

Consider the denominator of the integral in Eq. (14), For E/E^ = y"*^> 10, the numerical constant (near

unity) is negligible compared with the first term

Furthermore, in most practical superconductors, the resistive transition is very sharp and n is large (usually 30 or more). Thus, even though y"*^»l, y is nevertheless close to unity and the middle term is a number

less than unity raised to a high power. Consequently,

in practice it can be neglected compared with both the

first and last terms. The result is that for E/E^ > 10,

Eq, (14) reduces to

or using Eq. (12),

I (^)

These considerations are not specific to Eq. (14) but

3408 J. Appl. Phys., Vol. 49, No. 6, June 1 978

apply to the more general integral in Eq. (11) as well

(provided 6 does not deviate too much from unity).

Equation (11) has been evaluated numerically by Wilson

for w = 30, (F/F,„)j„,,,ji = 10^ and 10^, and several values

of Xj/Xj. The difference between these specific numerical results and Eq. (17) is less than 1% for E/E^> 10,

A graph of Eq. (17) for several values of n is shown

in Fig. 3 [where we have assumed {E/E„)^^^^^^^^

»{E/E„)]. Also shown in this graph is the first-order

correction to Eq, (17) in the region below E/£„=10,

which we have evaluated analytically by including the constant term in the denominator of Eq. (11). The small

deviation from Eq. (17) is evident at values of E/E„

> 2. For E/E„ less than 2, an exact numerical integration is required. For w = 30, where Wilson made his

calculations, the numerical solution is shown. The important point, however, is that the deviation from the simple analytic form in Eq. (17) is small at all but

the lowest values of E/E„.

Equation (17) can be simplified even further by as- suming the typical case that w» 1 and iE/E„\^^^^^^

»{E/E„). Then, we have

E{x)/E^^{2/n){X/xY, (18)

and taking X from Eq. (15), E{x)/E^ - (0. l/n){pJpJ{D/x)\ (19)

This result can also be expressed in terms of the ef- fective current-transfer resistivity p(x) =E(x)/J(x).

From Eqs. (12) and (13), £(x)/E„ =

y"*i = [j(x)/J„][p(x)/p„] =

^Pjx)

P« P,

’

since for n»l, y is close to unity, even though y”*^ » 1. Thus, for the usual case of large n and {E/E„)^^^^^^

»E/E„, Eq. (17) reduces finally to p(x)-(0.1/n)p„(Il/x)^ (20)

where n [defined in Eq. (3)] is determined by the superconductors’s resistive transition, is the transverse

resistivity of the matrix, and D is the wire diameter.

It is emphasized that Eq. (20) is an approximate ex- pression based on a simple two-cylinder model. The

numerical coefficient 0. 1 is dependent on the assumptions made about the initial current distribution, i. e.

,

the size of the two cylinders. The expression should

nevertheless serve to give an order-of-magnitude es- timate of the current-transfer length for most practical

situations.

From Eq. (20), a current-transfer length can be

calculated. is defined as the distance required for

p(x) to decay to some negligible value p*. Inverting

Eq. (20),

x^,, = {0.1/nY'HpJp*Y^^D. ( 21 )

The value of p* will depend on the particular application. For a short-specimen apparatus, it will usually

be determined by the resistivity detection limit of the

J.W. Ekin 3408 133
equipment. For example, if the noise in the system

only permits measurement of resistivities greater

than 10‘“ ncm, the required separation between the current and voltage contacts may be determined from

Eq. (21) by taking p* = 10"“ f2cm. A separation greater

than is unnecessary since the specimen’s resistivity could not be detected at lower levels anyway. Note

also that Eq. (21) can be used to obtain some idea of the required junction length when joining two superconducting wires in a magnet. The junction must be long

enough so that its resistivity is less than some acceptable level that depends on the requirements of the magnet. In this case, an estimate of the minimum

junction length may be obtained from Eq. (21) by taking

p* to be the desired maximum resistivity of the junction.

IV. EXAMPLES

To illustrate the application of Eq. (21) to practical

superconductors, the approximate current-transfer

length is evaluated for multifilamentary NbTi and

NbgSn.

A. NbTi

The wire is assumed to consist of NbTi filaments

embedded in a cold-worked “oxygen-free” copper matrix, The transverse resistivity of the matrix will consequently be about 1. 4x 10'® 0 cm at 4 K. For NbTi,

a typical value of n representing the resistive transition is « = 30,^ Substituting these values in Eq, (21), the relative transfer length is obtained as a function of the resistivity limit p*. The results are shown in the left-hand curve in Fig. 4. Thus, for ex- ample, if the detection limit of the measurement ap- paratus is 10"^^ O cm, a transfer length of about 7 wire

diameters is needed.

B. NbjSn

For NbjSn wires, the wire is assumed to consist

of NbjSn filaments that have been reacted in a tin- bronze matrix with a residual 4 K resistivity of about

2xi0‘® Ocm. For the resistive transition in NbgSn,

a typical value for n is 60.^ Substituting in Eq, (21), the results for the relative transfer length in a typical

NbjSn wire are shown by the right-hand curve in Fig. 4. From this curve, for example, it is seen that a detection limit of 10"^^ cm would require a transfer length

of about 60 wire diameters.

V. VOLTAGE-CURRENT CHARACTERISTICS

Suppose the transfer length is inadequate for a particular experimental apparatus. How will this affect

the apparent V-l characteristics? It is seen from Eq.

(20) that the effective resistivity from current transfer

is nearly independent of current magnitude. A linear V-I relationship thus would be expected, just as for a

FIG. 4. Current-transfer length for typical NbTi and Nb3 Sn multifilamentary superconductors, where D is the wire

diameter and p* is the resistivity limit (usually determined by

the apparatus detection limit). The approximate currenttransfer length for other values of n and p„ may be obtained from Eq. (21),

normal metal; see Fig. 1(b). Eventually at high currents, the wire’s intrinsic flux-flow resistivity will dominate the current-transfer resistivity given by Eq.

(20). The V-l characteristic will then deviate from its linear shape, showing the usual upturn as the critical current is approached. So, the net effect of current

transfer when the transfer length is inadequate is to alter the usual flux-flow transition shown in Fig. 1(a)

to that shown in Fig. 1(b). Equation (20) gives an esti- mate of the expected slope of the linear region.

To a first approximation, intrinsic V-l data can

still be obtained when measurable current-transfer

effects are present. Provided the current-transfer

slope does not dominate too much, the linear region can be extrapolated to high currents, and the flux-flow

resistivity is taken as the difference between the measured result and this extrapolated baseline.

ACKNOWLEDGMENT

The author is grateful to Martin Wilson for helpful

discussions and for communicating his lab note. Ref. 2,

^J.W. Ekin, A. F, Clark, andJ.C, Ho, following paper,

J. Appl. Phys. 49, 3410 (1978). ^M. N. Wilson, Rutherford Laboratory, Report SMR/l,

Chilton, Oxfordshire, England, 1977 (unpublished).

3409 J. Appl. Phys., Vol. 49, No. 6, June 1978 134

J.W. Ekin 3409
Appendix 2

Current transfer in multifilamentary superconductors. II. Experimental results®^**^

J. W. Ekin and A. F. Clark

Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302

J. C. Ho

Physics Department, Wichita State University, Wichita, Kansas 67208

(Received 21 February 1977; accepted for publication 10 January 1978)

Measurements are reported of the current-transfer effect in a 0.58x0.68-mm NbTi (180 filament) copper- matrix wire, and in a 0.33x0.66-mm Nb3Sn (3553 filament) bronze-matrix wire at magnetic fields from 2

to 8 T. With a voltage sensitivity of 100 nV, the effect of current transfer in the copper: NbTi wire was

too small to be measured at a distance 1 cm from the current contact. In the bronze :Nb3 Sn wire, however, the effect was relatively large and resulted in voltage-current characteristics which had an

extensive linear region. The slope of the linear region decreased with distance x from the current contact

as X

“2*®^ and reached a value of 10“'^ ftcm, for example, at a distance of 3±0.5 cm. Both the magnitude and functional dependence of the measured current-transfer effects correspond closely to that predicted by

theory. PACS numbers: 74.60. Jg, 74.70.Dg, 74.70.Lp, 85.25. 4-k

I. INTRODUCTION

In this paper, experimental results will be presented

which show that current transfer occurs over a length

which is considerably shorter in a typical copper- matrix NbTi composite than in a similar- sized bronzematrix Nb3 Sn composite. The approximate theoretical

model presented in the preceding paper, ^ hereafter

called paper I, is found to predict these results accurately.

II. EXPERIMENTAL APPARATUS

Experimentally, current penetration may be realized

either by increasing the current carried by the conductor (at constant magnetic field) or by increasing the magnetic field B in order to lower the critical current

density {B) (with the applied current kept constant).

Either method forces current transfer from the outer superconducting filaments to the inner filaments. The

results reported here were obtained using the first procedure, although the data should apply approximately to the second case as well. [This is because the rate of current penetration is determined mainly by the matrix

resistivity, rather than by the method for making J in the outer filaments approach JciB); see Sec. II of paper

I.]The wire specimens were wound on a 3. 8-cm-diam.

Bakelite tube and inserted into a 10-T simple solenoidal

magnet. The sample was mechanically held in place by

wrapping it in a spiral groove cut around the circumference of the tube with a twist length of 0. 42 cm (that is, the entire length of the sample was within about 3

“ of being perpendicular to the field). Current bus bars were

soldered to the outer copper surface of the wire speci- men about 3 cm from the specimen ends. 60/40 Sn-Pb

Contribution of the National Bureau of Standards.

'“’Supported by the Naval Research and Developnaent Center,

the Air Force AeroPropulsion Laboratory, and the NBS

Superconducting Standards Program.

solder was used, and the solder junction length was

about 3 mm.

Current was supplied by a programmed 600-A current source and controlled to within 0. 1%. Voltage taps were

spot soldered with the same Sn-Pb solder to the speci- men at several points along its length. Distance be- tween contacts was calculated from voltage measurements obtained while the specimens were at room temperature. Voltage sensitivity for the 4 K measurements was about 100 nV.

Ml. SPECIMENS

Two specimens were tested. The first was a rectangular 0. 58 X 0. 68-mm NbTi : Cu (1 : 1. 8) composite containing 180 filaments with a nominal twist length of 1.2 cm. The NbTi comprising the composite consisted of 55 wt% Nb and 45 wt% Ti, and the matrix was “oxygenfree” copper with a resistance ratio (p293 k/PtJ of 126.

The second specimen was a rectangular 0. 33 x 0. 66-

mm Nb3 Sn: bronze composite containing 3553 filaments

with a nominal filament twist length of 1. 1 cm. The

composite consisted of 65% bronze, ~ 12% Nb3 Sn, and

~ 5% unreacted Nb (by volume). Around the outside of the bronze -Nb3 Sn composite was an “oxygen-free”

copper sheath (11% by volume), separated from the bronze by a tantalum diffusion barrier (7% by volume).

The resistance ratio (p293 k/PtJ of the bronze matrix was 1. 87, measured with the copper and tantalum

removed.

From the standpoint of the present study, the major

difference between the two specimens is the resistivity

of the matrix material. For the NbTi composite, the entering current must penetrate an “oxygen-free” copper

matrix with a 4 K residual resistivity of 1. 38 xlO ‘ cm.^

On the other hand, in the Nb3 Sn composite the entering current must cross copper-tantalum-bronze interfaces

and then penetrate a bronze matrix with a significantly

higher 4 K residual resistivity of 1.98xl0‘® flcm.

3410 J. Appl. Phys. 49(6), June 1978 135

3410
CURRENT (amperes)

FIG. 1. Effect of current transfer on the short- specimen V-I

characteristics. TTie top curve was obtained by measuring

voltage between two taps located 0. 5 and 1 cm from the current contact. Location of voltage taps for th'^ middle and lowest curves are similarly indicated on the graph. Data were

obtained at 2 T on a 0. 33 x 0. 66-mm Nb3 Sn bronze composite.

IV. EXPERIMENTAL RESULTS

For the NbTi specimen, we can only report an upper

limit for the transfer length. For our apparatus, the voltage induced by currents in the matrix was immeasurably small, even at the voltage contact closest to the current lead. From the measurement sensitivity, we

could determine that the current- transfer resistivity of this conductor dropped to less than 10"*^ n cm in a dis- tance less than 10 equivalent wire diameters, at all magnetic fields. (The equivalent wire diameter is taken

to be the diameter of a round wire of equivalent crosssectional area.)

For the NbsSn specimen, however, the effective wire

resistivity resulting from current transfer was significantly larger and measurable results were obtained.

These are outlined below

A. V-! characteristics The effect of current transfer on the V-1 characteristics is shown in Fig. 1. The top curve represents the voltage as measured between voltage taps located 0. 5 and 1 cm from the current contact. Location of the voltage taps for the middle and lowest curves are similarly indicated on the curves in Fig. 1. Note that the additional voltage generated by current flowing through

the bronze matrix gives the V-I characteristic a finite linear slope over most of the current range. This is exactly what would be expected in the current- transfer

region, based on the theoretical analysis of paper I (see Sec. V). The slope of the V-I characteristic in this linear region will be referred to as the current-trans- fer resistivity for the remainder of this paper. By contrast, the wire’s intrinsic flux-flow resistivity dominates at high current levels. Here, the V-I characteristics show the usual nonlinear upturn as current approaches the critical current.

3411 J. Appl. Phys., Vol. 49, No. 6, June 1 978

FIG. 2. Current-transfer resistivity as a function of distance X from the current contact. Data were obtained at 2 T on a

0. 33x0. 66-mm Nb3 Sn bronze composite. ITie solid line represents the theoretical result obtained by evaluating Eq. (20) of Ref. 1 using the characteristics of this specimen (i. e.

an equivalent diameter D of 0. 53 mm; a transverse matrix

resistivity P( of 1.98x 10'® fi cm; n = 60).

B. Resistivity decrease with distance

From the slope of the linear region of the V-I characteristics in Fig. 1, the magnitude of the currenttransfer resistivity has been evaluated and plotted as a

function of distance from the current contact in Fig. 2.^ A log- log plot has been used in order to facilitate comparison with the theoretically predicted rate of decrease

shown in Fig. 4 of paper I. There it is shown that the current- transfer resistivity is expected to decrease

with distance from the current contact approximately

as In spite of the theoretical approximations in- volved, the data in Fig. 2 are in good agreement with

this prediction. Specifically, the experimentally measured resistivity is seen to decrease with distance as

Furthermore, the absolute value of the current- transfer resistivity predicted in paper I is in surprisingly

good agreement with these data. Using Eq. (20) in Ref. 1, the theoretically expected current- transfer resistivity

has been calculated for specimen II and is shown by the

solid line in Fig. 2. A comparison with the experimental

data shows the agreement is well within the uncertainty

of the approximate calculation described in paper I.

C. Magnetic field dependence

The data presented in Fig. 2 were obtained at a magnetic field of 2 T. Similar measurements were-'Also

carried out at 4 and 8 T. All the results were essentially the same within experimental error, indicating no

large magnetic field dependence. This is expected due

to the relatively small magnetoresistance (< 1%) of alloy materials such as Cu-Sn bronze.

For the copper : NbTi wire, on the other hand, some

magnetic field dependence would be expected had we

been able to measure the effect. The magnetoresistance

of “oxygen-free” copper is considerably greater than

bronze (30% at 2 T, 80% at 8 T), but not large enough

Ekin, Clark, and Ho 341

136
to permit measurement at the sensitivity level of our

apparatus.

V. SUMMARY

Summarizing the experimental results, current-transfer effects have been measured in a bronze :Nb3 Sn wire

specimen and were found to agree quite well with the theoretical model predictions discussed in Ref. 1. In particular, it is found that:

(1) The composite’s V-I characteristics have an extensive linear region when measured by voltage taps

placed near the current contact.

(2) The slope of this linear region decays with dis- tance from the current contact as

(3) The absolute magnitude of this slope agrees with

that predicted by Eq. (20) of Ref. 1 to within the combined theoretical and experimental uncertainties. The

magnitude of the current-transfer resistivity in other

specimens with different diameters and matrix resistivities may be estimated from Eq. (20) in Ref. 1. This

is only a suggested empirical procedure; the dependence on D and have not been tested directly. However, the X dependence and absolute- value predictions

of the theory from which it is derived are well substantiated by these data. Based on the evidence thus far, the procedure should provide a fairly accurate prediction of

current- transfer resistivity, particularly for design of short- specimen testing apparatus and instrumentation of test coils. If current- transfer effects actually do affect the results of a particular measurement, they can be

detected from the shape of the V-I characteristics (as in Fig. 1). ACKNOWLEDGMENTS

Private communications with M. N. Wilson, D. C.

Larbalestier, R. L. Powell, and F. R. Fickett are

gratefully acknowledged.

*J.W. Ekin, preceding paper, J. Appl, Phys. 49, 3406 (1978). ^G. T. Meaden, Electrical Resistance of Metals (Vlemm,

New York, 1966). ^J.E. Magraw and D.C. Larbalestier, Rutherford Laboratory

internal report SMR/14 (unpublished); F. Fickett (private

communic ation)

.

^The average resistivity measured between two voltage contacts located at points x^ and ^3 (^1 closest to the current

junction) is not representative of the instantaneous resistivity at a point halfway between and X2

. Rather it corresponds to a point slightly closer to x^, due to the rapid de- crease of p with X. In particular, the data points in Fig. 2 were plotted at a weighted point x, which we determined by

iterative procedure to be x"^ = x^X2

. This weighting has very

little effect on the data. The difference between x and the midpoint, \(x^ + X2

) is indicated by the horizontal error bars

in Fig. 2.

3412 J. Appl. Phys., Vol. 49, No. 6, June 1978 137

Ekin, Clark, and Ho 3412
38 Appendix 3

DEFINING CRITICAL CURRENTt

A. F. Clark and J. W. Ekin*

ABSTRACT

The critical current of a practical superconductor

can be defined in a variety of ways such as a specific

voltage level, an apparent resistivity, or even the point of the irreversible superconducting-to-normal

transition. The resultant values may differ very little or be meaningless for one given condition, but when

comparing superconductors under a variety of conditions,

such as different magnetic fields or applied stresses,

these various definitions can give apparently different behavior. This is illustrated using data on the effects of stress on the critical current behavior

in wires. As part of an initial effort at the National Bureau of Standards to develop standard practices and definitions for practical superconductors, several critical current criteria are proposed and discussed.

INTRODUCTION

The transition between superconducting and normal states is a topic of more than just academic interest.

Superconductivity is finding acceptance in fields such

as high energy physics, power transmission and storage,

rotating electrical machinery, and controlled thermonuclear fusion. Thus, practical superconductors must

not only be characterized under a variety of operating

conditions but their production must be monitored,

design criteria established, and specifications pre- pared for the tons of material to be used. At the National Bureau of Standards we are attempting to develop standard definitions and practices for practical superconductors, and it is the purpose of this paper to stimulate discussion on one of the supercon- ducting parameters, the critical current.

A variety of criteria have been used to define the current at which a practical superconductor is no longer superconducting. This is because the currentvoltage (I-V) characteristic for most practical super- conductors is not a step function but shows a rising

voltage with current until enough heat is generated to initiate an irreversible thermal runaway. The current

at this point of thermal runaway has been used as the critical current, but it is strongly dependent on the current ramping rate, the cooling medium, and the specific test configuration. It is also of little value in defining operating criteria. An experimentally easy definition is one based on a minimum detectable voltage,

but it, too, depends strongly on the experimental

equipment and sample configuration. A voltage level does have the advantage of being sensitive to shape

changes in the I-V characteristics and usable over wide

ranges of current values. Apparent resistivity is commonly used because it is intrinsic to the conductor,

and a constant power criterion is sometimes used because

of its applicability to heat removal.

All of these criteria and many related ones have

been used in the literature with a variety of experimental conditions and make comparisons extremely difficult. In the remainder of the paper these various

criteria are discussed, their effect on a sample of

data will be shown, other factors are considered, and

some conclusions regarding their use are presented.

Manuscript received August 17, 1976.

Cryogenics Division, National Bureau of Standards,

Boulder, Colorado 80302. tContribution of NBS, not subject to copyright.

THE VARIOUS CRITERIA

An idealized current-voltage characteristic is shown in Fig. 1 where, as the current is increased, an increasing amount of voltage appears across the detection probes until the heat deposited in the supercon- ductor raises its temperature above its transition

temperature. The region then transforms to the normal state with a high resistance. Ideally the critical current can be defined as' "that electrical current, I^., above which an ideal superconductor abruptly transforms into the normal state ..." However, in practical superconductors the transition is seldom abrupt and

no specific point on the current axis can be identified

in this manner. Superimposed on the current-voltage

curve in Fig. 1 are several of the common criteria

used to establish a value for the critical current. These four basic kinds of criteria and their limitations are discussed below.

Fig. 1. The current-voltage characteristic of a practical superconductor with transition, power, electric field, and resistivity criteria for critical current.

Superconducting-to-Normal Transition

When a recorder pen slams into its stop as it flies off the chart paper, it appears to be indicating a very definitive transition. However, this point

of thermal runaway on the current axis depends very strongly on the specific conductor configuration, how

it is stabilized, how it is cooled, the current ramping rate, the external conditions and many more experimental parameters. Also, this transition criterion is of little value in the determination of operating cur- rents because it must be avoided under operating con- ditions and gives no information about power dissipation or cooling requirements.

On the positive side, because the superconductingto-normal transition is so readily observable and its detection requires no sensitive equipment, it is

Copyright © 1977 by The Institute of Electrical and Electronics Engineers, Inc. Printed in IJ.S. A. Annals No. 70IMA009

138
39 commonly used for parameterization studies. That is,

in cases where the experimental conditions remain constant and only specimen variables are changed (e.g.

heat treatment), the transition can provide quick

comparisons. The difficulty arises on trying to compare with other work; there can be no value correspondence, only trends. This reason alone is sufficient

to discourage the use of this criterion in the literature.

Voltage

A minimum detectable voltage has been traditionally used as a critical current criterion and its extension to a specified voltage level has eliminated

the obvious detector dependence. It still is strongly

dependent upon the experimental conditions, e.g. probe

separation, and is an extrinsic property of the superconductor, depending upon the wire size, etc. A

voltage criterion has the distinct advantage of being constant over a wide range of currents and, as we

shall see in the example below, can be used to define

critical current over the widest range of conditions.

Even further advantages are gained if -the electric field, or voltage per unit length, is used. The

dependence on probe separation is removed and the electric field is a property of the conductor although

still not intrinsic with the material. It has also

been shown by one of us^ that the electric field in the conductor is directly relatable to the power and refrigeration requirements for a given system and

thus becomes a very useful design parameter.

Resistivity

The resistivity, or resistance x(area/length)

,

is also purely a property of the conductor and should

be independent of the experimental arrangement. It still depends on the normal material -to-superconductor

ratio of the specific wire configuration. (The intrinsic property of the superconductor is the "superconductor critical current density" normalized to the superconductor alone.) The resistivity can also be directly related to power requirements when multiplied

by the current density, and is a useful design para- meter when weight and/or size become the principal

design variable (i.e. current density). The resistivity criterion has the disadvantage of not reflecting changes in the current-voltage characteristic at low current levels, and multiple values may have to

be used as criteria.

Power

A power (the product of current and voltage)

criterion is also insensitive at low current values,

is not intrinsic to the conductor, and is very dependent on the specific configuration. Power density is,

however, intrinsic to the conductor. Since the power

required per unit field generated is usually the quantity of design interest, it must also be nor- malized by the current in order to be a design parameter. Since the superconducting-to-normal transition occurs when the heat generated can no longer be carried away (i.e. a heat transfer limit) it has also

been suggested^ that a power per unit surface area be used, particularly where cooling problems are anticipated and accurate design simulation tests are possible.

EFFECT OF CRITERIA ON DATA

As part of a program to study the effect of

strain on superconductors, we have generated a family

of current-voltage curves for a Nb3Sn wire under different applied stresses as shown in Fig. 2.^

0 20 40 60 80 100 CURRENT (Amperes)

rig. 2. The effect of stress on the current-voltage

characteristic of a Nb 3 $n multifi lamentary conductor.

Superimposed upon these curves are several different

criteria for determining critical current values. One

can see immediately how the power criterion intersects

fewer of the current-voltage curves at high stresss

and also how the sample's resistivity exceeds a 10*'1 n cm value at high stress levels and never reaches

10"'*^ SI cm at low stresses before going normal. All of the curves shown were reversible with current and

the superconducting-to-normal transition points were

taken at definite breaks in the curves (off scale in Fig. 2) where irreversibility took place.

Figure 3 shows the degradation of the critical current with applied stress utilizing transition, power, electric field, and resistivity criteria as described

above. The last three criteria were picked to give

similar critical current values at the lowest stress

level. Note that the critical current scale is logarithmic and the degradation as determined by the different criteria varies by as much as a factor of 10. The i rreversible transition values would underestimate

the effect for operating conditions, the power determined values saturate and the resistivity determined

values go to zero with increasing stress. Under such wide ranging conditions, the electric field determined

values appear to be a good compromise, maintain sensitivity over the whole range of stress, and serve to reflect the added power dissipation requirements of a system per unit field. Conceivably there are other

families of curves that would yield different results. The point to be made is that the choice of a criterion

for determining critical current can dramatically

affect the results of a test.

OTHER FACTORS

There are many other factors, both semantic and experimental, which we have ignored in this simple

approach to the problem of defining critical current.

The National Bureau of Standards will publish soon'

a set of definitions which should alleviate some of

the semantic confusion. The experimental problems are somewhat more elusive. For example, it is still

undetermined how far from a current contact a voltage

139
40

STRESS (10®Pa)

Fig. 3. The critical current of a Nb3 Sn multifilamentary conductor as a function of applied stress for various critical current criteria.

probe must be to eliminate any normal matrix resistive

component due to the transfer of current into the superconductor. For that matter, the type of voltage

probe, welded, soldered, or pressure, may affect the results. The mechanism of the voltage generation has not yet been clearly established much less its dependence on conductor configuration or enivronmental

conditions. Current ramping rate and circuit para- meters have only been mentioned and other than fourprobe techniques have not. It is possible to obtain

critical currents from magnetization curves^ but only

for specific configurations.

CONCLUSIONS

It has been shown that a problem in defining the critical current of practical superconductors exists.

Many definitions for a variety of measurement tech- niques have been used and make literature comparisons

extremely difficult. The electric field and resis-

,tivity criteria are the easiest to relate to both experimental conditions and system design needs. The

choice of definition can dramatically affect the results of parameterization studies even when per- formed on a single specimen. There is a definite

need to establish standard definitions and measurement techniques in this area.

ACKNOWLEDGMENTS

The authors would like to thank F. R. Fickett

and R. L. Powell for helpful discussions and the latter for assistance in an accurate choice of terms. The data usedwere generated in a program sponsored

by the Naval Ship Research and Development Center,

Annapolis, Maryland.

REFERENCES

1. R. L. Powell, to be published, nBS report.

2. J. W. Ekin, Appl . Phys. Lett. 218 (1976).

3. M. S. Walker, personal communication.

4. J. W. Ekin and A. F. Clark, Proc. Joint MMM-Intermag

Conf., Pittsburgh, PA (1976), AIP Conf. Proc., to

be published.

5. W. A. Fietz and W. W. Webb, Phys. Rev. 17^ 657 (1969).

140
Appendix 4

Orthorhombic elastic constants of an NbTi/Cu composite

superconductor

H. M. Ledbetter and D. T. Read*

Cryogenics Division, Institute for Basic Standards, National Bureau of Standards, Boulder, Colorado 80302

(Received 18 October 1976; accepted for publication 11 January 1977)

Elastic properties of a niobium-titanium-filament copper-matrix composite superconductor were studied experimentally at room temperature. Ultrasonic pulse and resonance measurements showed the material has orthorhombic symmetry and, therefore, nine independent elastic constants. With respect to copper, C;,,

C22, and C33 are about 7% lower; C44, C55, and Qe are about 15% lower; the off-diagonal elastic constants

are the same; and the bulk modulus is about 5% lower. Deviations from isotropic elastic behavior are

small.

PACS numbers: 62.20.Dc, 74.70. Rv, 74.30.Gn

I. INTRODUCTION

The purpose of this paper is to report a room- temperature experimental study of the elastic properties of a composite material. The study emphasizes elastic symmetry and applies familiar single-crystal methods

to composites. The studied composite has unidirectional

niobium- titanium (NbTi) filaments in a copper (Cu)

matrix and it is designed as a superconductor for magnets. Manufacture and morphology suggest that the fila- ment direction is an elastic-symmetry axis. Thus, the macroscopic elastic symmetry is orthorhombic, tetra- gonal, hexagonal, or cubic. Oblique axis systems

triclinic, monoclinic, trigonal— are excluded. The present study shows that the studied composite is orthorhombic, but deviations from isotropy are small,

and it can be referred to other coordinate axes (for ex- ample, hexagonal) without introducing large errors; advantages of this simplification are discussed in Sec. V

Nevertheless, a complete set of nine orthorhombic

elastic constants was determined. The elastic constants reported here may differ from those of apparently identical composites for reasons discussed in Secs. IIIC and

VF.

Experimentally, two dynamic methods were used: pulse and resonance. Most measurements were made by

a pulse method; 18 ultrasonic wave velocities were measured along the orthorhombic (100) and (110) directions.

Resonance experiments were done for two reasons: to look for dispersion, the variation of sound-velocity with

frequency, and to confirm the off-diagonal elastic constants.

II. WAVE MOTION IN ORTHORHOMBIC MEDIA

Usual crystallographic notations for vectors and elastic constants are used in this paper. Since all components of the studied composite are polycrystalline, the symmetries discussed here are strictly macroscopic.

The filament direction of the composite is designated

[001], and the principal directions perpendicular to the filaments are [lOO] and [OlO]. These directions are in- dicated in Fig. 1. As stated above, the studied material has orthorhombic symmetry, and, therefore, nine independent elastic

constants. These are displayed in Eq. (1) in the Voigt

contracted notation in matrix form.

^11 ^12 ^13 0 0 0

^22 ^23 0 0 0

^33 0 0 0

C44 0 0

C55 0

( 1 )

where the matrix is symmetrical about its main dia- gonal. The Christoffel equations, which relate the

elastic constants to the plane monochromatic phase

velocities, are*

pvhi,)pi = 0, ( 2 ) where is the fourth- rank elastic-stiffness tensor, n is the wave-propagation direction, p is the mass density, V is the wave velocity, 6^ is the Kronecker delta.

FIG. 1. Schematic geometries of four pulse specimens. Fila- ments along [001] are indicated by striping. The wave-propagation directions (indicated by dashed lines) and displacement

vectors are given in Table I. The x, y, and z axes are equivalent to the [100], [010], and [001] axes that are used in the

text and tables.

1874 Journal of Applied Physics, Vol. 48, No. 5, May 1977 Copyright © 1977 American Institute of Physics 141

1874
and p is the displacement vector. It is easy to show that the resulting secular equation is diagonal for the [lOO],

[OlO], and [OOl] directions; that is, waves traveling

along (100) directions are pure modes. Their velocities are determined by Cji, C55, Cgg; Cjj, C44, Cgg; and C33,

C44, C55, respectively. Thus, all diagonal elastic constants, Cjj, can be determined by propagating waves in (100) directions. For each direction there is one longitudinal wave and there are two shear waves; the three waves are polarized mutually orthogonally. Thus,

checks on each of the three shear elastic constants, C44,

C55, and Cgg, are available. The off-diagonal elastic constants Cj2, Cj3, and C23 must be determined by measurements where the n vectors are oblique to (100)

directions.

In general, waves traveling along lower- symmetry

directions are not pure modes. ^ For n = (110), there is a single pure mode whose velocity is determined by

2 (^55 ^gg)) 2(^44 +Cgg), and 2(044 + C55) for the [oil],

[101], and [110] directions, respectively. These provide additional checks on the three Cjj shear constants measured along (100) directions. The two impure modes

that propagate along each (110) direction can be determined from the Christoffel equations.

The (Oil) propagation-direction case is now outlined.

The Kelvin-Christoffel elastic stiffnesses

are for the case n = (l//2) [Oil]:

55 ^G6 ® 0

0

0 ^23 "^^^^ "44 ^51 "hC 33 Thus, one solution is = 2(^55 +Cgg),

(3)

(4)

(5) a torsion mode. And the remaining two roots are

pV^ ~2{C22 + C33 ± [(C 22 ~ ^33 ) + 4(C23 + C44)2]1/2}+C44. (6) Experimentally, pv^ is measured and C23 is unknown.

Thus, by rearrangement,

^23 — ^ {[ 2 oi’^ ~ 2 (^22 + C33 +

“ ^(^33 “ ^22)^}*^^ “ ^44«

The spurious second value of C23 from this equation can be discarded on physical grounds. Similarly, [lOl] and

[110] planes can be used to determine Cjg and Cjj, respectively. For these cases

^13 = {[2pi’^ — 2 (Cjj + C33 + 2055)]^ — i(^33 ~ ~ ^55

and

Further details on the problem of wave propagation in orthorhombic media were given by Musgrave.^

III. EXPERIMENTAL

A. Material

The samples used in this study were cut from a short

section of a Kryo 210 superconductor. (A trade name is used to describe the studied material; its use is not an NBS endorsement of the product. ) This is a coppermatrix niobium-titanium-filament composite material.

The Cu/NbTi volume ratio is 6:1, and the bar contains

2640 filaments with a twist each 7.6 cm. The filament

distribution is shown in Fig. 2. The sample obtained for

this study was about 20 cm long, 1. 0 cm wide, and 0. 5 thick. Four samples were cut for ultrasonic pulse measurements, one with its surfaces perpendicular to the symmetry axes of the material and three with the largest surface oriented at 45° to two symmetry axes. Sample geometries are shown in Fig. 1. Samples were

studied in the as-received condition, that is, optimized

by the manufacturer for use as a superconductor. The

thermal and mechanical treatments that optimize such

superconductors were described by Mclntiirff and

Chase.'’ The specimen with {lOO} surfaces was 0. 5 XI. 0X1.0 cm, while the three off-axis specimens had

thicknesses of 5, 3, and 2 mm. All specimens were

ground sufficiently flat and parallel for ultrasonic

study.

B. Procedures

Eighteen ultrasonic-wave modes were studied in these

four specimens at room temperature. Quartz-crystal

transducers either 9. 5 or 6. 4 mm in diameter with fun- damental resonance frequencies between 5 and 10 MHz

were bonded to one specimen surface with phenyl

salicylate (salol). Ultrasonic pulses were generated and

detected in the transducer using an electronic apparatus

described previously.® The time interval between the arrival of selected pulses from the ultrasonic echo train was measured using an oscilloscope with a delaying

time base calibrated against a precision time- mark

• 0 . M - 9 •• .• -•I**

^12 — ^ {[2pt^^ — 2 (Cii + C33 + 2Cgg)]^

— 4(022 — — Cgg.

FIG. 2. Photomicrograph showing distribution of filaments. Plane of photo is perpendicular to filaments. Width shown

corresponds to 4.3 mm in specimen. Vertical direction is (9) x= [100] and horizontal direction is y

= [010].

1875 J. Appl. Phys., Vol. H.M. Ledbetter and D.T. Read 1875 48, No. 5, May 1977

142
TABLE I. Room-temperature elastic constants C^J for a NbTi/Cu composite with macroscopic orthorhombic symmetry. The

wave-front normal is denoted by n and the displacement direction by p. Both and have units of lO” N/m^

Measurement

Specimen number n p pv\ pv\ 1Cij Derived C^^ A 1 100 100 1.834 Cij = 1.834 ±0.005

2 010 0.404 ^66 Cgg = 0.414 ± 0.007

3 001 0.407 ^55 C55 = 0.40 7 ± 0.011

4 010 010 1.878 ^22 C22 = 1.8 78 ± 0.015

5 100 0.413

6 001 0.413 C44 €44 = 0.416 ± 0.003

7 001 001 1.880 C33 €33 = 1.880 ± 0.002

8 100 0.414 C55

9 010 0.419 ,

1 ^44 B 10 oil 011» 1.713 1^z{C22 + C33 ^ f(t^22 ~ ^33^^ + 4(C23 + C44 (€23 = 0.715)”

11 011^ 0.419 j €23 = 1.041 ±0.040

12 100 0.407

> 2(^55 + Cgj)

C 13 101 101

1.740 1 + C33 ± [(Cii — €33)^ + 4 (Cj3 + 055)^]*^^}+ C55

,0 0 00 0

II 14 101

0.409 j €43 = 1.039 ±0.040

15 010 0.408 5 (C44 + Ceg) D 16 110 110^ 1.744 1|MCii + C22 ± l(Cn — €22)^ + 4:(Ci 2 + Cgg)^]'^^}+ Cgg (€12 = 0.804)” 17 iIo» 0.400 ! €12 = 1. 056 ±0.040

18 001 - 0.394 2(^44 + 055)

^•Impure modes. '’Values discarded for reasons discussed in text.

generator. The ultrasonic echo patterns obtained in this study were of good quality. They had between 3 and 30

well-defined echoes.

Using the velocity v of the ultrasonic wave (obtained

from the transit time and the path length) and the speci- men mass density p, the room- temperature elastic constants were calculated from

C=pv\ (10)

a simplified form of Eq. (2), where C is a combination

of the Cij’s depending on the mode. Results derived from

Eq. (2) for the 18 modes studied here are given in Table

I.

Resonant-bar elastic-constant measurements were

performed on two other specimens at room temperature.

These specimens were 4.8-mm-diam cylinders with

lengths of 1. 9 and 3. 1 cm prepared with filaments along

the specimen axis. In the resonant-bar technique, the sample is excited into longitudinal or torsional reso- nance by an attached quartz-crystal driver of appropriate mode and frequency. Resonance is detected using a quartz gauge crystal attached to the driver. The driver, gauge, and specimen form a composite oscillator. The

appropriate elastic constant of the specimen can be cal- culated from the resonant frequency of the composite

oscillator, the specimen density, and known properties

of the driver and gauge crystals. Since the compositeoscillator resonant frequency is often tens of kilohertz,

this technique is sometimes called a kilohertz technique, but it is called a composite-oscillator technique

in the literature.® No correction was made for specimen

geometry. According to the well-known formulas of Rayleigh, in this case, the correction multiplier is 1.003 for Young’s moduli and 1.000 for torsional

moduli.

1876 j, Appl. Phys., Vol. 48, No. 5, May 1977

C. Uncertainties

Experimental uncertainties of the elastic constants are discussed in two parts: imprecision and systematic

error. Imprecisions affect many conclusions of the study; systematic errors do not; they affect only the Ci/s themselves.

Bounds on the Cj^’s in Table I are imprecisions ex- pressed as ±<J, where cr is the standard deviation based

on a normal distribution. For the diagonal Cj^’s, these

imprecisions are based on two to five pure-mode measurements. Imprecisions of the nondiagonal Cj^’s depend

both on these values and on an assumed imprecision of 0.005 in the quasitransverse values of pv^. Sources of imprecision include deviations of specimens from flat and parallel, specimen- length mismeasurements,

specimen-to-specimen bond variations, transit-time

mismeasurement, and, for this material, specimen

inhomogeneity.

There are two principal systematic errors, one

arising from the mass density and one from the trans- ducer-bond coupling to the specimen. Maximum error in the mass densFy is estimated to be less than 0. 15%.

Transit-time error due to the ultrasonic wave traveling

through the transducer and the coupling agent is esti- mated to be less than 1%; and, when corrected for,

increases the pv"^ values. Thus, the overall uncertainty

in the Cj^’s is estimated to be less than ±1. 5%.

A possible source of sample-to-sample variation in the elastic constants of any composite material is its thermal-mechanical treatment, which may vary considerably for the type of material reported on here. For

example, for copper, elastic-constant differences up to 10% have been reported for annealed and deformed

specimens.^ Such variations can also occur in copperbase composites. Residual stresses of the order of the yield strength may occur in the composite, but simple

H.M. Ledbetter and D.T. Read 1876

143
TABLE n. Elastic compliances of a NbTi/Cu composite mea^

sured by a resonance method at room temperature. Units are 10-“ mVN.

Observed Calculated from Cj^’s

^33 0.873 ±0.009 0.878 ±0.073 from quasishear

modes

(0. 692 from quasilongitudinal

modes)

2

(S44 + S55) 2. 398 ±0.024 2.430 ±0.041

computations show that these would change the elastic constants by less than 1%.

IV. RESULTS

TABLE in. Room-temperature elastic stiffnesses and

elastic compliances of a NbTi/Cu composite and copper.

C^J units are 10“ N/m2 and S{j units are 10"^* m^/N. Values in parentheses are derived from 2C44 = Cjj - C^2 and S 44 = 2 (Sjj -Sjj).

ij Composite

^ij ^ij

Copper^

11 1.834 0.924 2.006 0.780

22 1.878 0.894

33 1,880 0.879

44 0.416 2.404 0.477 2.096

55 0.407 2.457

66 0.414 2.415

12 1.056 -0.341 (1.052) (-0.268)

13 1.039 - 0. 322 23 1.041 -0.307

^Reference 7.

Results of the study are displayed in Tables I— II. In Table I the observed room- temperature values of pv^ are given for the 18 measurement modes. Table I also

contains expressions for in terms of the Cj^’s.

These expressions were derived from the Christoffel

equations. When a plus- minus sign occurs, the plus

sign corresponds to the longitudinal mode and the minus

sign corresponds to the transverse mode. Estimated

errors for the derived elastic constants are also in Table I. The basis for estimating these errors was described above.

Results of the resonance studies are in Table II. S33

is the reciprocal Young’s modulus along the filament

direction and 1(544+555) is the reciprocal torsion (or

shear) modulus around that direction.

The elastic compliances, 5 j^’s, are given in Table HI

along with a summary of the C,^ data. The 5j^’s were

determined by inverting the matrix displayed in Eq.

( 1 ) and substituting the Cjy values from Table I. Except

for 544, 555, and 5gg, which are simple reciprocals of the corresponding Ci/s, errors in the 5<y’s are larger

than those in the Cf/s because of error accumulation.

The practical elastic constants {E = Young’s modulus,

G= shear modulus, and v— Poisson’s ratio) are given in Table IV. These parameters are related to the 5,y’s as

displayed in the matrix equation

1/^22 ~ *^32/^33 ^ S{j= 1/^33 0

1 /G44

0

0

0

0

0

0

0

0

0

1/^66

( 11 ) where the matrix is symmetrical about its main

diagonal and the Poisson ratios are defined by

- 54y/5j4 (no sum). (12)

V. DISCUSSION

A. Symmetry

On the basis of its internal and external geometry,

the composite appears to be orthorhombic. If an object

has three mutually perpendicular twofold axes, then it belongs to the orthorhombic symmetry system. These

rotation axes are labeled x, y, and 2 in Figs. 1 and 2 . Other possible symmetry systems can be excluded.

Triclinic has no symmetry axis. Monoclinic has a single

TABLE rv. Practical elastic constants; E= Young’s modulus, G= shear modulus, v = Poisson’s ratio for NbTi/Cu composite in different coordinate systems at room temperature. Units are 10^^ N/m^, except v’s, which are dimensionless.

Elastic constant Orthorhombic

basis

Tetragonal

basis

Hexagonal

basis

Isotropic basis Copper^

values

Static results'* (hexagonal basis)

^11 1.082 1.100 1.100 1.112 1.282 1.22

£22 1.119

®33 1.138 1.138 1.138 1.19

G44 0.416 0.411 0.411 0.412 0.477 0.448

G55 0.407

Ggg 0.414 0.414 (0. 398) “ (0.431)“

*'21 0.381 0.381 0.381 0.415

*’31 0.365 0.357 0.357 0.347

*’32 0.349

^Reference 7. “Quantities in parentheses are derived from given data using '’References. Ggg = £11/2(1 + ^42).

1877 J. Appl. Phys., Vol. 48, No. 5, May 1977 H.M. Ledbetter and D.T. Read 1877

144
TABLE V. Checks for various symmetries for NbTi/Cu composite. For hexagonal and cubic cases, relationships (1), (2), and (3) also hold. For an isotropic case, all eight relationships must hold, either (4) or (8) is redundant.

Symmetry

system Relationships

Ratio of LHS/RHS

for NbTi/Cu

Tetragonal (1) C22 = Cjj 1.024 ± 0.020

(2) C55 = C44 0.978 ± 0.014

(3) C23 = Cj3 1.002 ± 0. 040

Hexagonal (4) Cgg = 5 (Cjj — Cj2) 1.064 ± 0. 020

Cubic (5) C33 = Cjj 1.025 ±0.007

(6) Cj2 = Ci3 1.016 ± 0.040

(7) Cgj = C55 1.017 ±0.018

Isotropic (8) C44 = i(Cji — Cj 2

) 1.069 ±0.016

twofold axis. Trigonal has a single threefold axis.

Clearly, these three systems are less symmetrical than

the composite.

Orthorhombic symmetry includes four other symmetry systems: tetragonal, hexagonal, cubic, and isotropic. Relationships among the C^’s for these systems

are given in Table V together with tests of the relationships. Clearly, from Table V, none of the higher- symmetry systems can be used to describe exactly the observed Cij’s, but the deviations are small for any of these four symmetry choices. The advantage of describing an object by its highest symmetry is that there are fewer independent elastic constants: six for tetragonal,

five for hexagonal, three for cubic, and two for isotropic. Thus, measurements and calculations are simplified to various degrees. In Table IV, present orthorhombic results are also expressed in higher- symmetry

coordinates to facilitate comparisons with other studies.

When necessary, elastic constants were simply

averaged.

B. Off-diagonal elastic constants The off-diagonal (i*j) elastic constants are more

difficult to determine and almost always have higher

uncertainties than the diagonal (i=j) elastic constants. This problem is reflected in the present study in Table

I. The problem arises because the off-diagonal elastic constants are not related simply to any pure mode of mechanical deformation. This is best shown in the Sfj

matrix displayed in Eq. (11). All the diagonal S{/s are

related reciprocally to either a Young’s modulus or to a shear modulus; but all the off-diagonal S,^’s are related

to a Young’s modulus and a Poisson’s ratio, which is in turn determined by two other elastic constants, as shown

in Eq. (12).

In the present study, another difficulty arose in determining the off-diagonal elastic constants. As shown

in Table I, different values of the off-diagonal Ci/s were obtained depending on whether the observed pvj or

the observed pv^ was substituted into the appropriate

Cij expression given in the table. For example, in the [oil] direction the quasitransverse datum gave C23 = 0.715, while the quasilongitudinal datum gave C23

1878 J. Appl. Phys., Vol. 48, No. 5, May 1977

= 1.041. The C ,2 and C ,3 cases are similar. On the basis of small imprecisions of the measurements and

on the basis of the correctness of the value of the third (pure shear) mode, it seemed that the off-diagonal

terms should be less uncertain than this and that one

of two values was perhaps correct. To resolve this uncertainty in the off-diagonal elastic constants, an independent experiment was done: some

of the Sij’s were determined by a resonance method.

Dilatational and shear modes were measured on a cylindrical specimen with filaments along the cylinder axis. Results shown in Table n for the torsional mode l(S44

-

1-S 55 ) agree exactly with the value calculated from the Ci/s. (The Si/s are computed from the Ci/s by inverting the Cij matrix). Similarly, exact agreement is also

obtained for the dilatational mode S33 if the Cij data from

quasitransverse modes rather than quasilongitudinal

modes are used. Thus, it was concluded that the quasi- transverse velocity data are both correct and consistent

with other data. However, the quasilongitudinal wave

velocities are low by about 5%. This slowing can be in- terpreted as a longer path length in the specimen due to interactions between the quasilongitudinal waves and

internal boundaries due to the presence of filaments.

C. Comparison with copper

It is useful to compare the elastic constants of the composite with those of the matrix material, unalloyed

copper,^ to determine the effects of the filaments.

Comparative data are shown in Table IV. Both the Young’s moduli and the shear moduli of the composite

are about 15% lower than those of copper. The

compressibility,

T, Sij, (13)

i,y=l,3

of the composite is about 5% higher. The off-diagonal

Ci/s are identical to the value for copper, within 1 %.

This result may be accidental since it has no obvious

physical interpretation.

D. Comparison with previous studies The elastic constants of this composite were measured by Sun and Gray* using static methods, assuming

hexagonal symmetry, and their results are shown in Table IV. Considering the higher inaccuracies usually

associated with static methods, the agreement between

the two sets of data is surprisingly good. The static Young’s and shear moduli are up to 9% higher than the values reported here. The largest discrepancy is in 1^21 and is due probably to error accumulation in the computed static value. Possibly, the differences in the two

data sets are real, but this cannot be decided without

knowing the uncertainties of the static values. A real

difference is unlikely because, ignoring dispersion

effects, dynamic elastic moduli are almost always high- er than static elastic moduli, and the opposite effect is observed in this case.

E. Dispersion

No dispersion effects were observed, either in the limited 5— 10- MHz region that was studied or in comH.M. Ledbetter and D.T. Read 1878

145
paring the MHz pulse data with the 60- kHz resonance

data. By dispersion is meant the dependence of sound

velocity on frequency. Dispersive effects have been

reported in many composite materials; they are usually

due to either relaxation or resonance effects. Their

absence here is attributed to assumed coherent interfaces between the filaments and the matrix and to the small difference in acoustic impedance between the fila- ments and the matrix. Absence of dispersion is also

consistent with the well-defined echo patterns that were

obtained.

F. Relationship to similar composites

Elastic-property data have not been reported for NbTi/Cu composites with different ratios of NbTi or

with different thermal-mechanical treatments. The

present data can be applied to other NbTi/Cu composites

through predictive schemes that relate the elastic constants of a composite to those of its components. Using

the values of the NbTi elastic constants given by Sun

and Gray® and formulas summarized by them, it follows

that the present material obeys approximately simple

rules of mixtures. Thus, similar composites would also

be expected to follow these rules approximately. The

present study is a useful guide to the elastic properties

of any NbTi/Cu composite, but it is a source of exact

elastic data only for the particular material studied.

Even when the filament matrix volume ratio is adjusted

for, several other variables remain that can affect

elastic properties. These include the state of mechanical deformation (the number and distribution of lattice defects), composition of the NbTi filaments, preferred

orientations in either the filaments or the matrix, and

degree of coherency of the filament- matrix interfaces.

G. Low-temperature elastic constants Since this composite is intended for use as a superconductor, its low-temperature elastic properties are

important. Studies down to liquid- helium temperature

are underway in our laboratory and results will be re- ported subsequently. Preliminary results are that the composite behaves on cooling approximately like unalloyed copper; but the magnitudes of the elastic constant changes are slightly different and there are some

anomalous effects that are both reproducible and

reversible.

VI. CONCLUSIONS

The chief results and conclusions of this study are

as follows:

(1)

Ultrasonic (5—10 MHz) waves, both dilatational and shear, can be propagated in an NbTi/Cu composite

in directions parallel, perpendicular, and oblique to the filaments.

(2) Except as noted below, usual single-crystal elasticity techniques could be used to establish the complete

set of elastic constants of the composite.

(3) Longitudinal waves propagated obliquely to (100)

directions have velocities about 5% lower than expected.

Obliquely propagated shear waves travel at their ex- pected velocities.

(4) The studied composite has orthorhombic symmetry and, therefore, nine independent elastic constants; but the deviations from isotropy are small.

(5) Compared to copper, the C i/s {i =j) of the composite are lower by about 7% for C,i, C22, and C33, and

by about 15% for C44, C55, and Cgg; but the C{/s (i*j) are about the same. The composite’s compressibility

is about 5% higher than copper’s.

(6) The present dynamic results agree reasonably

well with existing static measurements.

(7) Advantages of combining pulse-echo measurements

and resonance measurements were found.

(8) No dispersion, change of velocity with frequency, was observed.

ACKNOWLEDGMENTS

This study was supported by the Advanced Research

Projects Agency of the U.S. Department of Defense.

G. A. Miranda of Los Alamos kindly contributed a photomicrograph of the studied material. W.H. Gray of Oak Ridge National Laboratory contributed a critical reading of the manuscript.

*NRC-NBS Postdoctoral Research Associate, 1975—1976.

^L.D. Landau and E. M. Lifshitz, Theory of Elasticity

(Pergamon, London, 1959), p. 104. ^J.R. Neighbors andG.E. Schacher, J. Appl. Phys. 38, 5366-5375 (1967). ®M.J.P. Musgrave, Crystal Acoustics (Holden-Day, San

Francisco, 1970), p. 117—123.

^A.D. Mclnturff and G.G. Chase, J. Appl. Phys. 44, 2378—

2384 (1973). ^E.R. Naimon, W. F, Weston, andH.M. Ledbetter, Cryogenics 14, 246-249 (1974).

®J. Marx, Rev. Sci. Instrum. 22, 503—509 (1951). ^H. M. Ledbetter and E.R. Naimon, J. Phys. Chem. Ref. Data 3, 897-935 (1974). ®C.T. Sun and W.H. Gray, Sixth Symposium on Engineering

Problems of Fusion Research, San Diego, Calif., 1975

(unpublished); W.H. Gray and C.T. Sun, Oak Ridge National Lab. Report TM-5331, 1976 (unpublished).

1879 J. Appl. Phys., Vol. 48, No. 5, May 1977 146

H.M. Ledbetter and D.T. Read 1879
Appendix 5 Temperature dependence of the elastic

constants of an NbTi/Cu superconducting

composite

D.T. READ and H.M. LEDBETTER

Low-temperature elastic properties are reported for a commercial superconducting composite consisting of niobium-titanium filaments in a copper

matrix. Both an ultrasonic (10 MHz) pulse-superposition technique and a composite-oscillator (100 kHz) technique were used. Seven of the composite's

nine independent elastic constants were determined between 76 and 300 K; Young's modulus along the filament axis and a shear modulus perpendicular

to that axis were determined between 4 and 300 K; all showed irregular

temperature behaviour.

Superconducting composites consisting of niobium/titanium

filaments in a copper matrix are now available commercially

for applications in which high electrical-current density must

be obtained in high magnetic fields. Current-carrying

capacity of these conductors can be degraded by very small

strains, which may arise from the large forces to which

components containing these conductors are often

subjected. Reinforcing materials for strain relief consume

valuable space in a cooled volume; cool-down costs and

fabrication are further disadvantages of excess reinforcement.

Thus, mechanical design of large components containing

superconductors must be optimized. Elastic constants of

such conductors are useful for two reasons: for computing

the recoverable deflections due to applied loads, and for computing thermoelastic stresses due to either temperature

changes or differential thermal contractions. Also elastic constants provide a valuable characterization of a material. For composites, accurate elastic data provide key tests for theories that relate macroscopic elastic properties to the

elastic properties of the constituents. The particular NbTi/Cu composite reported here has orthorhombic symmetry, and the room temperature values of all nine independent elastic constants, the Cjj’s have been

reported previously.' The present study determined the temperature dependences to 77 K of seven elastic constants:

^ii> C22, C33, Css, C33, and 2/(544 "* ‘^ss)> where C33 is Young’s modulus along the filament axis and + Sss)

is the torsion modulus about that axis. Two elastic constants, C33 and Cee, were determined to 4 K. The temperature

dependences of the other elastic constants, such as C12 and

Ci 3, were not determined because they are measured

indirectly and they have larger errors. Symmetries discussed here are strictly macroscopic. The filament direction of the composite is designated [001 ] , and the principal directions perpendicular to the filaments are (lOO) and [010) .These

directions are indicated in Fig. 1.

Cryogenics Division, Institute for Basic Standards, National Bureau

of Standards, Boulder, Colorado, USA.

EXPERIMENTAL

Material Specimens were cut from a sample bar of a commercially

available multifilamentary superconductor, a copper matrix,

niobium/titanium-filament composite. The sample obtained

for this study was about 200 mm long, 10 mm wide, and

5 mm thick. The material was studied in the as-received condition. Thermal and mechanical manufacturing treatments of such superconductors have been described by Critchlow,

Gregory, and Zeitlin.^ The Cu/NbTi volume ratio of the conductor is 6 : 1 , and the bar contains 2640 filaments with

a twist pitch of 76 mm. The NbTi filaments contain 45% by

weight of titanium. Four specimens were cut for ultrasonic pulse measurements, one with its surfaces perpendicular to the symmetry axes of the material and three with their largest surface oriented at 45° to two symmetry axes. Specimen

geometries are shown in Fig. 1. The specimen with [100 [surfaces was 5 mm by 10 mm by 10 mm, while the three off-axis specimens had thicknesses of 5 mm, 3mm, and 2 mm. All four specimens were ground sufficiently flat and parallel for ultrasonic study. Two composite-oscillator specimens were

prepared. These were right circular cylinders 4.8 mm in diameter and 31 mm and 19 mm long for the extensional

and torsional measurements, respectively.

Procedures

The temperature dependences of five of the elastic stiffnesses, Cn, C22, C33, Css, and C^, were measured using

a pulse-superposition technique in which the ratio of the

ultrasonic velocity, v, at low temperatures to its value at room temperature was measured every five degrees between room temperature and the lowest temperature obtained

during each cooling. These ratios of sound velocities were

used to compute the temperature dependence of the appropriate elastic constant, C, from C = pv^ where p is the specimen’s mass density. Each specimen was cooled by

enclosing it in a chamber and lowering it gradually into the

100 COMPOSITES . APRIL 1978

147
Fig. 1 Schematic geometries of four pulse specimens; filaments along [001 ) are indicated by striping. In specimen a, waves were

propagated along the [100], and [010] directions; in b along [011];

in c along [101 ] ; and in d along [110]

ullage of a Dewar containing either liquid nitrogen of liquid helium. The low temperature apparatus and techniques have been described previously.^

The temperature dependence of the Young’s modulus and

the torsional modulus were measured using a compositeoscillator technique. Briefly, the resonant frequency is measured of a composite oscillator consisting of a specimen,

a quartz crystal driver, and a quartz crystal gauge. This composite oscillator is also cooled by insertion into a chamber and lowering into the ullage of a Dewar. The

resonant frequency of the specimen is computed from the resonant frequency of the composite oscillator, the masses and geometries of the specimen and the quartz crystals, and

resonant frequencies of the gauge and quartz crystals. From

its resonant frequency, the elastic constant of the sample

can be computed simply. The apparatus and techniques used

in such measurements have been described previously.'*

Errors

Errors in the reported low temperature moduli arise from

errors in the measured ultrasonic transit times, the resonance

frequencies, and the temperature. Relative transit time errors

are estimated to be about ± 1 x 10'^; relative resonance frequency errors are estimated to be ± 1 x

10“'*. Modulus

errors due to temperature mismeasurement are estimated

to be much less than one percent.

Systematic ejurors are the major sources of uncertainties in the present results. Sources of these are: errors in the room

temperature modulus values, changes of the specimen density

and length with temperature, variation of the Cu/NbTi ratio across the cross sections of the specimens, and errors arising

from the twist pitch of the filaments in the superconductor.

Errors in the room temperature moduli were reported

previously.* These errors are ± 1.5%, and they are the source of almost all the uncertainty in the low temperature moduli.

Due to cancellation of lengths in the density and velocity in the relationships used to compute the moduli, each low

temperature modulus has an error equal to the length change

of the specimen between room temperature and the measure- ment temperature. The maximum thermal contraction modulus error can be estimated by assuming copper’s

expansivity; this gives a maximum thermal contraction error,

at 4 K, of 0.3%. The sound waves used in this study traversed only part of the cross-section of the composite super- conductor. The Cu/NbTi ratio varied over the cross-section of the specimen; no filaments occur at the centre or at the perimeter of the conductor. The variation of the ultrasonic

velocity across the specimen was determined by making

velocity measurements with a transducer positioned either

at the centre of the specimen or off-centre. Both longitudinal- wave and shear-wave velocities were checked, and no

significant differences were found. This lack of dependence

of ultrasonic velocity on position indicated that the specimens

could be considered homogeneous units; the microscopic

basis for this behaviour was not studied. An equation

derived by Whitney® was used to compute the effect of

twist pitch of the fibres on the Young’s modulus, and it was found to be about 0.03%. This value is useful as a qualitative estimate of the effect of twist pitch on all the moduli; it shows that twist pitch errors are negligible in specimens

Fig. 2 The variation with temperature of the Young's modulus of an NbTi/Cu composite along [001] compared with the Young's modulus behaviour of polycrystalline copper

COMPOSITES . APRIL 1978 101 148
52

Temperature (K)

Fig. 3 The variation with temperature of the shear, or torsional, modulus of an NbTi/Cu composite around the [001 ] , or filament,

axis compared with the shear modulus behaviour of polycrystalline copper

shorter than one twist length. Thus, the total uncertainty of

the reported moduli values is estimated to be ± 2%.

RESULTS

The measured value of £"33 (Young’s modulus along the fila- ment direction) is shown in Fig. 2; Young’s modulus, E, of

polycrystalline copper is shown for comparison. The copper

values were obtained from the single-crystal data of Overton and Gaffney* using the arithmetic average of the Hashin- Shtrikman bounds. The composite’s Young’s modulus is about ten percent lower than copper’s, and it increases about

ten percent during cooling from room temperature to 4 K.

Irregularities in the composite’s temperature behaviour are

significant deviations from the temperature dependence of

Young’s modulus of typical materials; the upturn in the curve below 20 K is believed to be real. The values of 2/(544 + >^55), the modulus of torsion about

the filament axis, is shown in Fig. 3. Shown also is the

torsional or shear modulus, G, of copper. It is clear that the temperature behaviour of 2/(544 + 5ss) differs from that of

£’33, and that its relationship to the torsional modulus of copper is nearly the same as the relationship of E33 to the Young’s modulus of copper. The dashed part of the curve

is an extrapolation based on the usual behaviour of elastic constants at low temperatures and the behaviour of the

elastic constants of this composite that were measured to 4 K. The extrapolation represents probable behaviour based on available data, but other behaviour is possible.

The Poisson ratios that relate the strain along the filament

axis (produced by a stress along that axis) to the strains perpendicular to the axis were found to be 0.366 and 0.349

along the x and y axes respectively, at room temperature.'

The temperature dependences of these ratios are not easily

measured by dynamic techniques, and they were not measured in this study. However, since Poisson’s ratio for copper decreases by two percent on cooling from 300 to 4 K, a similar change would be expected for the composite’s

Poisson’s ratio. The elastic stiffness coefficients, the Cjj’s, are given in Table 1 . Although Cn, C22 and C33 were all measured, the data for C22 practically coincide with those for C33 , so only Cl 1 and C33 , normalized separately to their 300 K values are shown in Fig. 4 together with the longitudinal modulus, C|, of copper. The dashed curves are extrapolations. Again, these

Table 1. Elastic constants of an NbTi/Cu composite and

polycrystalline copper at selected temperatures in units of 10'^ N/m^, except n, which is dimensionless; numbers in parentheses are based on extrapolated data

300 K 200 K 100 K 0 K

NbTi/Cu composite:

C33 1.138 1.189 1.238 1.287

G|| 0.417 0.427 0.445 (0.454)

0.365 - - -

^32 0.349 - - -

1.834 1.865 1.908 (1.915)

C22 1.878 1.911 1.952 (1.957)

C33 1.880 1.919 1.965 (1.983)

C55 0.407 0.418 0.436 (0.442) Cee 0.414 0.425 0.442 0.456

Polycrystalline

copper®:

E 1.282 1.329 1.369 1.386 G 0.477 0.496 0.512 0.519

u 0.344 0.341 0.339 0.338

Cl 2.006 2.053 2.093 2.111

Ct 0.477 0.495 0.51

1

0.518

® Reference 6, single crystal data converted using arithmetic average of Hashin-Shtrikman bounds

102

149

COMPOSITES . APRIL 1978
Fig. 4 The temperature variation of the longitudinal elastic stiffnesses of an NbTi/Cu composite in the [ 100 ] and [ 001 ] directions compared with the temperature dependence of

longitudinal elastic modulus of polycrystalline copper

Fig. 5 The temperature dependence of the shear modulus of an NbTi/Cu composite compared to the behaviour of the shear modulus

of polycrystalline copper; Cjg corresponds to the shear resistance on a (100) plane in a [010] direction, or a (010) plane in a [100]

direction

elastic constants are about seven percent lower than those of copper, and they increase about five percent on cooling. As in the case of the practical elastic constants, irregularities

in the Qj’s are observed during cooling.

The temperature dependence of C(^, normalized to 300 K,

is shown in Fig. 5. Css was measured between 300 and 76 K;

the resulting data nearly coincide with those for Cf^ and

they are not shown. Css ^nd for the composite are about

14% lower than the value for copper, and they increase about 10% on cooling. They also exhibit irregular temperature behaviour. The datum point shown as an open square

at 4 K in Fig. 5 represents an absolute, rather than a relative, elastic constant measurement; it confirms the overall elastic constant change due to cooling.

C33 and Css, ^ longitudinal and a transverse stiffness of the composite material, are shown in Fig. 6 together with Q,

and Ct, the longitudinal and transverse moduli of polycrystalline copper. In both copper and the composite, the

transverse (shear) moduli have stronger temperature

dependences than the longitudinal moduli. Surprisingly, the temperature dependences of both the transverse and

longitudinal moduli of the composite are between those of

the two copper moduli. Based on simple rule-of-njixture

arguments it follows from Fig. 6 that the shear modulus of NbTi must increase with decreasing temperature in a way

similar to that of copper, but the longitudinal modulus of NbTi must increase considerably more than that of copper

if stress effects from differential thermal contraction are small.

DISCUSSION

In a previous study,’ it was shown that the room temperature

elastic constants of an Nb Ti/Cu composite can be predicted

approximately from a rule of mixtures from the known

elastic constants of copper and NbTi. It was also shown

that the observed values of the practical elastic constants £33 and 2/(544 + -^ss) were consistent with the measured

values of the elastic stiffnesses, the Cjj’s.

Rules of mixtures could not be used to predict the temperature dependence of the composite material studied here because the temperature dependences of the elastic constants of the NbTi alloy have not been reported. An

attempt to obtain such data failed.’ Weston* reported the temperature dependences of the

elastic constants fo an NbTi/Cu fibre^ass/epoxy coil composite. Although that composite included fibreglass and

epoxy, the temperature dependence of its elastic constants

reflects that of NbTi/Cu because the stiffness of the

fibreglass epoxy is low and it constitutes only about one

quarter of the total volume. The sign and magnitude of the temperature dependences observed by Weston were about

the same as those reported here. For most of the elastic constants, Weston reported very small deviations from the

usual temperature behaviour of ordinary materials, but, in the Young’s modulus along the filaments, Weston found a large deviation from usual temperature behaviour. However, none of the elastic constants of the coil composite studied by Weston showed the type of irregularities observed in the present study.

Fig. 6 Comparison of a longitudinal and a sfiear elastic constant of the composite; C33 is measured in the [001] direction, along the

filament axis; C55 corresponds to the shear resistance on a ( 100) plane

in a [001 ] direction or of a (001 ) plane in a [001 ] direction; values

for copper are s' own for comparison

COMPOSITES . APRIL 1978

150

103
The observed increase in all the elastic stiffnesses of about

ten percent on cooling from 295 K to 4 K is expected for

this material. Elastic constants of most metals increase between five and fifteen percent on cooling to zero temperature;’ the polycrystalline longitudinal modulus Q

of copper increases four percent on cooling.

As shown in Figs 2-6, all the measured elastic constants reported here have irregular temperature dependences

compared to copper. Experimental evidence for these

irregularities is strong: they occur in seven different measured elastic constants; they were observed on measurements made during both heating and cooling; and they occurred

in repeated experiments. These irregularities are probably

insignificant from the viewpoint of engineering design

because of the relatively small deviations from regular

behaviour.

The cause of these irregularities is uncertain. Two hypotheses

can be suggested. First, since elastic constants are changed

by stress, the irregularities may arise from internal stress changes due to differential thermal contraction during

cooling. Second, the irregularities may arise from similar

irregularities in the temperature dependences ofthe elastic constants of the NbTi filaments. Similar irregularities have

been observed in niobium and in other transition metals,

where they are ascribed to the electronic structure,*’’ " and

in a niobium/zirconium alloy, where they are attributed to the formation of omega phase. *^

CONCLUSIONS

The following principal results and conclusions emerge from

the present study. The Young’s modulus along the filaments,

E33, increases 1 2% on cooling from 300 to 4 K, compared

to 8% for copper. The extrapolated torsional modulus

around the filaments, C||, increases 9% on cooling, the same

as copper. The extrapolated elastic stiffnesses Cn, C22 and

C33 increase by 5% on cooling, compared to 4% for copper. The shear elastic constants Css and Cf^ increase 1 0% on

cooling, compared to 9% for copper. All measured elastic constants have irregular temperature dependences.

ACKNOWLEDGEMENTS

This study was supported by the Advanced Research

Projects Agency of the US Department of Defense. Dr D.A.

Colling of Magnetic Corporation of America, the manufacturer

of the composite, made valuable comments on the manuscript.

References

1 Ledbetter, H.M. and Read, D.T.J Appl Phys (in press) 2 Critchiow, P.R., Gregory, E. and Zeitlin, B. Cryogenics 11 (1971) pp 3-10

3 Naimon, E.R., Weston, W.F. and Ledbetter, H.M. Cryogenics

14 (1974) pp 246-249

4 Marx, J./Sc/ Instrum 22 (1951) pp 503-509

5 Whitney, J.M. Textile Res J 36 (1966) p 765

6 Overton, W.C. and Gaffney, J. Phys Rev 98 (1955) pp 969-977

7 Reid, C.N., Routbort, J.L. and Maynard, R.A. J Appl Phys 44

(1973) pp 1398-1399

8 Weston, W.F. J Appl Phys 46 ( 1 975) pp 4458-4465

9 Hearmon, R.F.S. in Numerical data and functional relation- ships in science and technology. Group III, vol 1, edited by

K.H. Hellwege and A.M. Hellwege (Springer-Verlag, Berlin, 1969)

10 CarroU, Vi.i.J Appl Phys 36 (1965) pp 3689-3690

1 1 Featherston, F.H. and Neighbors, J.R. Phys Rev 130 (1963) pp 1324-1333

12 Goasdue,C., Ho, P.S. and Sass, S.L. Acta Met 20 (1972) pp 125-133

104

151

COMPOSITES . APRIL 1978
NBS-114A (REV. 0-76)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 80-1633

4. TITLE AND SUBTITLE 5. PuDMcation Date June 1980

Material Studies for Superconducting Machinery Coil Composites

7. AUTHOR(S)

J. W. Ekin, M. B. Kasen, D. T. Read, R. E. Schramm,

R. L. Tobler, and A. F. Clark

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

it. i%ject/Tasi(/Work t^U

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fSrrMr, City, state, zip)

Annapolis Laboratory

David W. Taylor Naval Ship Research & Development Center

Annapolis, Maryland 21402

13. Type of Report & Period Covered

14. Sponsoring Agency Code

.

15. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200^word or less factual sunimary of most significant information. If document includes a significant bibliography or

literature survey, mention it her©.^

The physical properties of a superconducting coil composite are studied to accurately predict the coil behavior under operating conditions. Emphasized in this third

interim report are studies on the effect of stress and strain on the critical cur- rent of superconducting wires. The report also includes data on several fiberglass/

epoxy support structures for the coil and its dewar. Preliminary results are also

given for the effect of stress on small superconducting composite rings used to

model the full sized coil behavior. A summary of the program results to date is

included.

17. KEY WORDS (six to twelve entries; atphabetica! order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Critical current; fiberglass/epoxy composite; mechanical properties; niobium-tin;

niobium-titanium; strain; superconducting coil composite; superconducting wire.

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