NBSIR 73-349

r

CHARACTERIZATION OF A SUPERCONDUCTING COIL COMPOSITE

C. W. Fowlkes

P. E. Angerhofer

R. N. Newton

A. F. Clark

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Interim Report

December 1973

Prepared for: Annapolis Laboratory

Naval Ship Research and Development Center

Annapolis, Maryland 21402

NBSIR 73-349

CHARACTERIZATION OF A SUPERCONDUCTING COIL COMPOSITE

C. W. Fowlkes

P. E. Angerhofer

R. N. Newton

A. F. Clark

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

Interim Report

December 1973

Prepared for: Annapolis Laboratory

Naval Ship Research and Development Center

Annapolis, Maryland 21402

u s DEPARTMENT OF COMMERCE. Frederick B. Dent. Secretary

NATIONAL BUREAU OF STANDARDS Richard W RobeM-, Directcir

TABLE OF CONTENTS

Page

ABSTRACT 1

1. INTRODUCTION 1

2. MACROSCOPIC MATERIAL PROPERTIES 5

2.1 Simplified Material Properties 5

3. MICROMECHANICAL ANALYSIS 8

3.1 Volume-Fraction Determination 9

3.2 Predictive Laws 13

4. SPECIMENS 18

5. THERMAL EXPANSION 22

5.1 Procedure 22

5.2 Data 25

5.3 Discussion 29

6. YOUNG'S MODULI AND POISSON'S RATIOS 29

6.1 Procedure 29

6.2 Data 36

6.3 Discussion 36

7. PREDICTED VERSUS MEASURED PROPERTIES 40

7.1 Preliminary Coil Values 42

7.2 Effect of Curvature 44

8. CONCLUSIONS 44

9. ACKNOWLEDGEMENTS 45

REFERENCES . 46

iii
LIST OF FIGURES

Page

Figure 1. Cross section of the superconducting coil tested .... 3 Figure 2. Schematic of superconducting solenoid coil showing

construction and coordinate axes 4 Figure 3. Average spacing of coil composite wires 12

Figure 4. Two simple micromechanical models of a composite

material 14

Figure 5. Schematic of specimen structures and orientations

(a) Longitudinal specimen (b) Radial or transverse

specimen 19

Figure 6. Schematic of thermal expansion apparatus 23

Figure 7. Thermal expansion (a) and tensile (b) specimens .... 24

Figure 8. Thermal contraction of superconducting coil materials . 27

Figure 9. Thermal expansion coefficient of superconducting

coil materials 28

Figure 10. Strain gage location on tensile specimens 30

Figure 11. Tensile test apparatus 32

Figure 12. Schematic of gage circuit 33

Figure 13. Typical apparent stress strain curve 34

Figure 14. Young's modulus versus temperature for superconducting

coil materials 38

Figure 15. Poisson's ratio versus temperature for superconducting

coil materials 39

LIST OF TABLES

Table 1. Room-temperature constituent material properties

for micromechanics calculations 10

Table 2. Equivalent volume fractions for transverse directions. . 11

Table 3. Elementary micromechanics equations for predicting

composite properties 16

Table 4. Thermal contraction and coefficient of thermal

expansion for superconducting coil materials 26

Table 5. Young's moduli and Poisson's ratio for superconducting

coil materials 37

Table 6. Room- temperature properties of the superconducting

coil composite, calculated values and measured values. . 41

iv
CHARACTERIZATION OF A SUPERCONDUCTING COIL COMPOSITE

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

The superconducting coil composite material

utilized by the Annapolis Laboratory of the Naval

Ship Research and Development Center is characterized

by its mechanical and thermal properties. The

Young's moduli, Poisson's ratios, and thermal

contractions are measured from room temperature to

4 K and presented in this interim report. A

micromechanical analysis based upon volume fractions

of constituents is used to predict room-temperature

properties, and a comparison is made to the measured

values

.

1. INTRODUCTION

Operating conditions of superconducting motors or generators include

a very wide range of temperatures and mechanical stresses and high magnetic

fields. These complex and extreme environments add to the designer's problem of determining reliability and establishing realistic margins of safety.

A particularly difficult problem is the requirement of long life under

fatigue conditions. The coil-design process must include prediction of

electrical or magnetic performance, heat transfer characteristics, and

structural reliability. Analyses of structural reliability of the coil

depends on many construction variables and is hampered by lack of knowledge

of mechanical and thermal properties of the coil composite. The level of

investment in this type of equipment dictates a need for more refined and

accurate analyses.

Stress analysis of the coil structure in a superconducting motor

must consider (a) residual stresses due to winding and potting, (b) stresses

due to mechanical interaction of the coil structure with adjacent parts of

the machine and its support, (c) stresses within the composite winding

structure due to differential thermal contraction during cool-down and

(d) stresses due to magnetic forces.
The analyses of such a structure may be conveniently and clearly

divided into two different areas: macromechanical and micromechanical

.

Macromechanical analysis treats the composite coil structure as a homogeneous

material characterized by anisotropic material properties .[ 1 , 2 , 3 , 4 ] This

is a practical approach for a wide variety of engineering design problems

provided that the anisotropic material properties can be characterized

accurately. Micromechanical analysis focuses on the coil properties on a much finer scale, giving detailed consideration to the stress distribution

around superconducting wires embedded in an epoxy matrix, each characterized

by different sets of material properties, Micromechanical analysis can be

used to estimate the anisotropic moduli required for macroscopic analysis.

Conversely, given a regional (average) stress calculated from macromechanical

analysis, localized stresses in the epoxy and wires may be calculated using

micromechanics .

'

A great body of literature has been developed within the last decade on micromechanical analysis of composite materials, particularly with reference

to fiber-reinforced plastics (fiberglass, etc.). Studies of these materials

rely greatly on powerful finite-element mathematical techniques for stress

analysis ,[ 5 , 6 ] which have been developed extensively in the last decade,

where continuum analytical techniques are intractable. Portions of this

literature are applicable to the superconducting coil analyses, and implicit

reference to the composite materials literature must be recognized throughout this work.

This interim report focuses on the structural analysis of a particular

coil built at NSRDC . Measured materials property data such as Young's

modulus, Poisson's ratio, and thermal expansion, which are required input

to the coil design, are presented. A cross section and schematic of the

coil studied in this paper are shown in Figures 1 and 2. The test results

presented in this paper represent a first step toward establishing a data

base of material properties which will facilitate accurate analysis of

superconducting coil structures.
<—>-

0. 5 mm

Figure 1. Cross section of the superconducting coil tested.

3
2.. RADIAL

Figure 2. Schematic of solenoid coil showing construction and

coordinate axes.

4
2. MACROSCOPIC MATERIAL PROPERTIES

To pursue the analyses discussed in the introduction, mechanical and

thermal properties of the coil material must be measured. These properties

include mechanical constitutive relationships, thermal expansions, conductivities, and dif f usivities

.

For a linear, elastic anisotropic solid the constitutive relationship

is Hooke ' s law, which is given as [7]

"ij = ^ijke ^kS' « = 1' 2, 3 (1)

where o^^ and are the stress and strain tensors. (Repeated indices are

summed. ) The constants c^^j^g can be measured in the laboratory and characterize the material. There are, in general, twenty-one independent constants,

The linear thermal expansion coefficients a^^ are defined by [8]

e . . = a . . AT ( 2

)

where AT is the temperature change. There are six independent thermal ex- pansion constants. Similarly the thermal conductivity tensor k^^ is defined

by [9]

BT f . = K. . ^

(3)

1 1

J 8x

.

where f is the heat flux, T is the temperature, and x^ are Cartesian

coordinates. There are six independent thermal conductivity constants.

The task of measuring the complete set of material properties for an anisotropic solid is difficult. However, there are several reasonable

simplifications due to approximate material symmetries in the superconducting coil problem at hand.

2.1 Simplified Material Properties

The coordinate axes used to discuss the material properties of the coil

material are illustrated in Figure 2. The anisotropic material properties

5
can be formulated more directly and simply if the coordinate axes are chosen to coincide with the natural or material axes. In Figure 2, the

longitudinal or "1" axis coincides with the axis of the superconducting

wire, which is assumed to have zero helix angle. The "2" and "3" axes

lie along the radius and coil axis, respectively, and form an orthogonal

set with the "1" axis.

The cylindrical symmetry of the coil reduces the number of independent

elastic constants from 21 to 9, as for an orthotropic material [2,10]. Since

this still represents a formidable and expensive series of laboratory tests, we choose for now to simplify the model still further by taking the reasonable approximation that the properties in the radial ("2") direction will

be the same as in the axial ("3") direction. This model is termed transversely isotropic [2], and the number of constants required to characterize

the material is now reduced to five. The accuracy of this approximation is

discussed later, with reference to our experimental measurements.

It is convenient at this point to replace the tensor notation with the

generally accepted contracted notation. Hooke ' s law is then written as

o.^C.e. i,j=l,2,....6 (4) 11]:)

where are the six stress components, and a^^ = for i = 1 to 3

,

= o^, o-j^^ = o^^ = o^, and o-j^^ = ^21 ~ ^6' '^ij

stiffness

matrix and are engineering strain components [10]. Alternatively the

stress-strain relationships can also be represented in terms of the com- pliance matrix S. . as

e . = S . . a . . (5)

1 ij D

The compliance matrix is the inverse of the stiffness matrix. It is con- venient to introduce S. . since its elements are more simply related to the

ij

familiar engineering constants: Young's modulus (E) , Poisson's ratio (v),

and shear modulus (G) . For a transversely isotropic, orthotropic material

6
^11 ^22 ^22

^23

^22 ^22

[S] - ^ 0 0 0 (6)

22

(symmetrical)

^22

^12

^12

where E^^ and "^22 ^"^^ Young's moduli respectively in the 1 direction and

in the isotropic 2-3 plane, v.. = Poisson's ratio = (-l)e./e., and G.. is

the shear modulus on the i plane in the j direction. Because the energy

of a strained lattice is a scalar quantity, the matrix must be symmetrical [10]

with the result

"21 "12

^22 ^11

The same symmetry considerations, simplifications, and choice of axes

lead to simplified thermal properties. The only non-zero components of the

conductivity tensor K^^, Equation (3), will be K^^, '^22' ^""^ ^33' Approximate transverse isotropy leads to ^22 ~ ^33' Similarly all components of the

thermal expansion tensor. Equation (2), are zero except a^^ and ~ "33*

All of the material properties vary with temperature, which dictates

measurements over a representative range of temperatures. Internal stresses

due to construction and epoxy impregnation of the coil are developed at room temperature and above, while additional stresses due to thermal contraction

and magnetic field develop at helium temperature. Experimental measurements

must cover this range. This variation of material properties with temperature introduces additional complications into the stress analyses and heat

transfer calculations.

7
3. MICROMECHANICAL ANALYSIS

In the field of structural composite materials considerable effort

has been directed toward the prediction of the properties of a composite

material given the properties and proportions of the constituent materials.

These predictive procedures are usually derived from simplified microstructure models using variational methods, theory of elasticity, or finite

element analysis [10,11,12,13]. There exist a large number of rules for

the prediction of elastic moduli and some rules for thermal properties.

Such predictions are always approximations but can give results surprisingly close to measured macro-properties. It is instructive to predict the

properties of the superconducting coil composite using micromechanics

.

The photograph in Figure 1 shows the cross section of the coil in

which four distinct phases can be identified: stranded superconductor,

copper matrix, glass cloth, and epoxy. Most micromechanical predictive

rules have been derived for only a two phase system, usually consisting of

a fiber and a matrix material. Some modifications of the two phase rules

could be made to accomodate four phases, but the equations would become

much more complicated. At present an alternative is to introduce simplifying assumptions about the material that will reduce it to two phases.

Since the glass cloth is only a small volume fraction it will be ignored

in the calculations. The copper wire containing imbedded superconductor

will be assumed to be a single material. The superconducting coil will

thus be modeled by a two-phase system consisting of wires imbedded in an epoxy matrix.

Since some of the properties of the actual wire can be measured, the

second assumption of a single material wire will not necessarily reduce

the accuracy of the micromechanics analyses. The longitudinal Young's

modulus of the wire has been measured at room temperature and is shown

in Table 1. Measuring longitudinal thermal expansion and thermal conductivi

of the wire presents no major experimental obstacles. However, transverse

properties are difficult to measure to a useable degree of accuracy.

8
For estimation of the superconducting coil properties, nominal values

of copper will be assumed if the wire property has not been measured. The

epoxy matrix will also be given nominal values. All of the room-temperature constituent material properties used in subsequent micromechanics

calculations are given in Table 1.

3.1 Volume-Fraction Determination

A cross section of an actual superconducting coil. Figure 1 was sur- veyed to estimate the volume fraction of wire in the coil. The schematic

of the coil cross section is shown in Figure 3, which presents average values

of wire dimensions and wire spacings in the axial and radial directions.

Note that the spacing of the wires differs considerably in the 2 and

3 directions contrary to the earlier assumption of isotropy in the 2-3 plane.

Since properties normal to the wire are very sensitive to the wire spacing,

an adjusted set of volume fractions were computed separately for the 2 and

the 3 directions. For example, since small spacings between wires are normal to the 2 direction, for some theoretical calculations the volume

fraction should be computed by assuming that all spacings are small. Similarly for the 3 direction, an effective volume fraction is computed by

assuming that all of the wire spacings have the larger value. The fiberglass is ignored because of its very small volume fraction.

Many of the theoretical solutions are based on an analytical model

consisting of a square array of circular filaments imbedded in a matrix [14,15]

But, the superconducting coil wires tend toward rectangular shape. Because

of this discrepancy another effective volume fraction was calculated. For

this calculation it was assumed that the coil was made up of circular wires

with diameters equal to the appropriate dimensions of the actual wires and

with spacings identical to those of the actual wires. These equivalent

volume fractions were computed for the 2 and the 3 directions and are shown

in Table 2. These values necessarily fall somewhere below and above the

actual volume fraction, respectively. The tabulated values include corrections for rounding of the corners of the nominally-square wire.

9
Table 1. Room temperature constituent material properties

for micromechanics calculations.

Superconducting

Wire

r- (b)

\^ oppe r

(b) Epoxy

E

4 Z 10 MN/m 7. 85-8. 20^^^ 11.7 0. 34

L (10 psi)

/II A 11 0\

( 1 1 . 4 - i i . V ) ( -1 '

)

0.33'"' 0. 345 0. 29

G

4 2 10 MN/m 3.00^"^ 6. 3 0. 19

6 (10 psi) (4.36)

(9. 1) (0. 28)

-1 K 17. 6 45. 0

-1 (°F ) (9. 8) (25. 0)

k W/mK 387 0.35

(Btu/hr ft F)

(224) (0. 2)

(a) Longitudinal modulus, measured at NBS, 8.03 x 10 MN/m

(11.65 X 10^ psi) used for calculations. In review, we note that our stress-strain data is significantly nonlinear, and that this stated modulus is valid for stresses

4 2 of about 4 to 7 X 10 MN/m (5 to 10 ksi) . The measured

modulus is lower at lower stress levels. We will investigate this non-linearity quite carefully in future

work.

(b) Nominal values.

(c) Assumed values.

10
Table 2. Equivalent volume fractions for transverse directions.

Volume Fraction

of Wire, Average

Values

Actual cross section of coil (measured) 0.73

Assume uniform

spacing of 0.03175 mm (0.00125 in.)

for properties along

3 axis

Actual wire (calculated) 0.803

Equivalently spaced

square array of circles (calculated) 0.72

Assume uniform

spacing of 0.1067 mm (0.0042 in.)

for properties along 2 axis

Actual wire (calculated) 0.652

Equivalently spaced

square array of circles (calculated) 0.55

11
. 5385 mm 'M .0212" %

.7087mm

^0279'^

.03175 mm

.00125"

. 1067 mm

.00^2"

WIRE

FIBERGLASS

CLOTH

Figure 3. Average spacing of coil composite wires

] 2
3.2 Predictive Laws

An elementary set of predictive laws can be derived from the parallel

and series models shown in Figure 4. Young's modulus (E) for the parallel

model is

E = V^E- + V E (8) c f f m m

where V is the volume fraction and the subscripts f, m and c denote properties associated with the fiber, matrix, and composite respectively. For

the superconducting coil the wires are considered as fibers and the epoxy

potting compound as the matrix.

Equation (8) is commonly referred to as "the law of mixtures". It can

be shown using the principle of minimum potential energy that the modulus

given by Equation (8) is an upper bound for the composite modulus [10], but

gives a reasonably accurate estimate of longitudinal modulus for structural

composites [16]

.

If shear stresses are ignored the series model yields the equation

E,E

E = E-E . (9) c E,V + E V.

f m m f

for the composite modulus. By applying the principle of minimum complementary energy it may be shown that Equation (9) is a lower bound on E^

.

Equations for thermal expansion of the parallel and series models can similarly be obtained if shear stress and bending are ignored. The parallel

model yields

a,V^E^ + a V E

a = -^^-^ ^^-^

(10) c E

and the series model yields

= V.a. + V (li; c r f mm

where a denotes the linear coefficient of thermal expansion [17].

13
Vf i —

Vmr

^—

1

Fiber

Matr I

X

PARALLEL MODEL

Vf H

1 1^

Fiber

V m

>

-IX

SERIES NODEL

Figure 4. Two simple micromechanical models of a composite material

14
The composite thermal conductivity for the parallel model will be

= "^f^f + V K (12) c r r m m

where K denotes thermal conductivity. The elements of the model are assumed to be separated by an infinitesimal adiabatic plane [18] , The

series model yields

^f^m

^c " K + K^V ^^^^ m f f m

The contact resistance is assumed to be zero between the elements, and the

temperature distribution is assumed to be one dimensional. For reference

the micromechanical equations, for the series and parallel models are shown

in Table 3.

Poisson's ratio (v) can be derived from the parallel model and is

given as [19]

v,„ = v^^ = V.v. + V (14) 12 13 f r mm

The first subscript in this notation always denotes the direction of applied

stress, while the second subscript denotes the direction of the Poisson contraction. Equation (7) is used to obtain v ^-^ from v^^ or vice versa. Using variational methods, Rosen et al., [20,21] derived an expression

for ^ random array of fibers. The equation is

f f 1 m m 2 m

'l3 V,E^L^ + V E

f f 3 m m 2 (15)

where

and

L, = 2v.(l - v^)V. + V^(l + v^)v^

1 f m f m mm

= Vf(l " ^f " 2^f^

^3 = 2(1 - v2)v, + (1 + v^)V^,

15
Table 3. Elementary mic romechanic s equations for

predicting composite properties

Parallel Model Series Model

Composite Young's

Modulus, E

i c

V E^ + V E II mm

(upper bound)

EEf m

E,V + E

f m m f (lower bound)

Composite Thermal

Expansion cx c

a V^E^ + a V E iff m m m

Hjc

Y a + V a 11 m M

Composite Thermal

Conductivity k

c

V.k. + V k ft mm 1 m

k V, + k V mi f m

16
The remaining Poisson's ratio v^^ is obtained using the equation [11]

1 + v_ - , (E /Et t ) f 1 + V - V E /E^ T ^ v„, = v^V^ + V V < ~ ^ . . . . (16) 23 f f mm,Ll-v 2 , ,^ ,^ , f + vVt-{E /E, , ) J m m 13 m 11

The shear modulus in the plane of isotropy, 2-3, can be computed using

the relationship among elastic constants of isotropic materials. For example, if E^2 and \> known, then is given by the familiar relationship

^33

^23 ~ 2(1 + V23) • ^^''^

The shear modulus in the 1-3 plane is an independent material property and

must be measured or calculated from a micromechanics

Assuming a simple model containing rectangular fibers, Ekvall [19]

derived

f m

(^gj 13 V + V^G

m f f m

for a lamina one filament thick.

Using variational methods Rosen, et al . [20,21] obtained upper and

lower bounds for the shear modulus. These are given as

G, (upper bound) = G (m^V, + V~) (19) 13 '^'^ m G 1 2 and

G

G, ^ (lower bound) = , —. „ . (20) 13 (V^/m^ + V2)

where

^ Tid + P^) -H 1 -

Tl(l - p^) + 1 -

and T] = Gj/G^, p = V^/V^^, V^^ = n/2y/3 = 1 - ^ random array of fibers

the bounds coincide and the modulus is given as

17
Tl ( 1 + V . ) +

t in ^13 " r|V + 1 + ' ^^^^

' m f

Another expression for G^^^^ derived by Foye [22] has been found to be in

good agreement with elasticity solutions for regularly spaced arrays. It is

Q

P ^ ^ 4 - TT + TtN 4N

^ 13 2 4 (4-Tt)N + TT ^"^^^ where

G.(7r + 4V^) + G^(7i - 4V,)

N = — - - — G^in - 4V^) + G in + 4V^)

r t m r

The equations presented in these sections on micromechanics are representative of the predictive equations available to the experimentalist and

analyst. Other valuable tools for modulus prediction are found in a number

of elasticity and finite element solutions for the transverse properties of

regular arrays of fibers [11,14,15]. Comparison of experimental results

with those predicted by the above relationships will be made in a later

section.

4. SPECIMENS

All specimen fabrication was performed by the sponsor using superconducting wires, epoxies, bonding techniques, etc. selected by them to meet

their program needs. The information in this section on sample prepa'ration

was obtained from the sponsor.

To measure the properties in the 1 direction, specimens were prepared

using straight wires, Figure 5a. In order to make these specimens representative of the actual material in the coil, efforts were made to reproduce the volume fractions of the components as well as the curing procedure.

To measure properties in the 2 and 3 directions, blocks were sectioned

from an actual coil. These blocks were then fabricated into specimens with

thin epoxy bond lines. A schematic of this specimen is shown in Figure 5b

along with the coordinate system relating the specimen orientation to the

coil. Figure 2.

18
LONGITUDINAL SPECIMEN

Load (expansion)

RADIAL OR TRANSVERSE

SPECIMEN

203.2 mm

8.00"

^1

000000

CC

9 , 525 mm

\ 6 . 35 mm

0 . 375" , t

0.25"

6 . 35 mm

0 . ?S"

\

I

1

Figure 5. Schematic of specimen structures and orientations

(a) Longitudinal specimen (b) Radial or transverse specimen

19
The superconducting wire used to wind the test coil and to produce the

longitudinal specimens was multifilament niobium-titanium embedded in a copper matrix. The copper-to-superconductor volume ratio is 1.8 to 1.

There are 180 superconducting strands having a twist pitch of 2 per inch.

The conductor is rectangular in cross-section measuring .56 mm (.022 in.)

by .72 mm (.0285 in.) including .020 mm (.0008 in.) electrical insulation.

The test coil was a simple solenoid containing 40 layers of wire. The

coil has an inside diameter of 19.38 cm (7.632 in.), an outside diameter of

24.47 cm (9.632 in.) and a length of 10 cm (4 in.). The wire was wound on

a stainless steel coil form (mandrel) . Before the wire is applied to the

mandrel it is cleansed of any residual oil and contaminants, and pretensioned

.

A wire guide and "finger" mechanism were used to place the wire in its exact

final position on the mandrel. This mechanism also provided approximately

2 lbs (9N) of side force to establish excellent wire packing horizontally.

The wire was cleaned after leaving the supply reel by drawing it through a solvent jet and several felt wiping pads. The pretension was developed by

applying reverse torque to the supply reel. The following pretension was

used in winding the test coil.

layer tension ( lbs .

)

(N)

1 thru 10 17.6 (78.3)

11 20 13.2 (58.7)

21 30 8.8 . (39.1)

31 40 4.4 (19.6)

The wire used to fabricate the longitudinal samples was pretensioned to

8.8 lbs (39N) . Before the first turn of wire was wound, one complete

layer of fiberglass cloth, .1 mm (.004 in.) thick, 3 oz. per sq . yd.

2 100 gm/m ) was applied to the coil form. The fiberglass had approximately .6 cm (1/4 in.) overlap at the ends and .3 cm (1/16 in.) turn up,

approximately two wire thicknesses, at the side flanges. The overlap

and turn up are necessary to provide reinforcement for the epoxy in

these critical areas. A layer of wire is then wound over the dry

20
fiberglass. Just after the wire moves up to the next layer another layer

of dry fiberglass cloth is installed in the same manner as the first layer.

The second layer of wire then proceeds as the first. The winding procedure

continues layer on layer until the coil is complete.

Mechanical measurements of the superconducting test coil were made

after winding, showing it to be very uniform. The maximum radial runout

over the entire surface of the coil was ± .15 mm (.006 in.).

After the superconducting coil is completely wound it is placed in a potting mold slightly larger than the coil outside diameter. The coil is

_2 then placed in a vacuiam chamber and evacuated to approximately 10 torr

2 (1.33 N/m ). This pressure is maintained for 8 hours at which time the

chamber heaters are turned on and the coil is raised to 150°F (65°C) . After

the coil, fiberglass, and chamber have fully degassed, they are ready to

receive the epoxy resin.

The epoxy used in the superconducting coil is Ciba 6005*. The epoxy

-2

is preheated to 150°F {65°C) then degassed to a pressure of 5 x 10 torr

2 (6.7 N/m ). This process takes approximately 15 minutes. After degassing

is complete the epoxy is piped into the potting mold until the entire coil

is completely covered. Then the chamber containing the coil is pressurized

2 to 100 psig (.69 MN/m ). This pressure is held for 8 hours at 150°F

(65°C) , until the epoxy system is entirely cured. The temperature is then

slowly decreased to 77°F (25°C) and the chamber is vented to atmospheric

pressure. The coil is then taken out of the chamber, and the potting mold

and all excess epoxy removed. The coil is now complete. The same process

was used for the longitudinal specimens.

*The use in this paper of trade names of specific products is essential

to a proper understanding of the work presented. Their use in no way

implies any approval, endorsement, or recommendation by NBS

21
5. THERMAL EXPANSION MEASUREMENT

5.1 Procedure

The low temperature thermal expansion of the specimens was measured

using a quartz tube dilatometer from room temperature to 4 K utilizing the

apparatus of Clark [23]. The specimen, approximately 20 cm (8 in.) long, is

slowly cooled by helium exchange gas after the apparatus is immersed in a cryostat containing liquid nitrogen. When the specimen has reached 77 K,

the cryostat is purged of liquid nitrogen and filled with liquid helium.

Cooling at a rate of 2-5 K/min was chosen as the best compromise between

speed of measurement and minimal temperature gradients in the specimens.

Using this cooling rate, the test took 3-4 hrs., which includes 1 hr for

purging of liquid nitrogen and filling with liquid helium. The differential

contraction is transmitted to a mechanical dial gauge at room temperature

by concentric quartz tubes. A schematic of the apparatus is shown in

Figure 6. The temperature of the specimen is determined by two chromelconstantan thermocouples attached directly to opposite sides of the specimen,

one about 5 cm (2 in.) down from the top of the specimen and the other

about 5 cm (2 in.) up from the bottom. This procedure gave rise to data

pairs that could be averaged to effectively eliminate thermal gradients

in the specimen [23]. The thermocouples were calibrated following the

procedure of Sparks and Powell [24]

.

Five specimens were tested: two radial, and two longitudinal coil

sections and one longitudinal epoxy-f iberglass . The specimens were fabricated to the dimensions 20 ± . 5 cm (8 in. ± 1/4 in.) long and approximately 1 cm (3/8 in.) square, with the exception of the radial specimens

that were made from a stack of 2.5 x .63 x .63 cm (1 in. x 1/4 in. x 1/4 in.)

radial segments epoxied end to end. The specimens are shown in Figure 7a,

This type of thermal expansion measurement is relative and must be

compared to a similar specimen of a known material. The calibration of the

apparatus was accomplished by repeated measurements of a specimen machined

from NBS Standard Reference Material 736, an OFHC copper reference standard

22
Ceiling Vent i

PRV

Stainless Steel Sample

Tube

Sample Heat Shield

Thermocoup I e s

Sam p le

Stainless Steel

Outer Dewar

Quartz Sample Support

and Rider

Figure 6, Schematic of thermal expansion apparatus.

IB- 72537 1
Figure 7. Thermal expansion (a) and tensile (b) specimens.

24
available from the Office of Standard Reference Materials, National Bureau

of Standards, Washington, D.C. The specimen was stress relieved at 1112 °F

(600°C) for 1 hour before testing. The reproducibility of the calibration

was better than 0.3%. The high degree of reproducibility was maintained

throughout the test program. The difference between an average of this

calibration data and the primary standard reference data accounts for

residual differential contractions in the quartz tubes, and was used as a correction to all other specimen measurements. The correction (Table 4) was

less than 5% throughout the temperature range.

5.2 Data

A computer curve-fitting program was developed to fit the experimental

data and to reduce the data to standard tabular form. Several polynomials

in temperature were tried and simple power series limited to T^ were usually

best. The expansion coefficient (a K was obtained by taking the derivative of each equation. The final tabular values were determined by visual

inspection of each of the curve fits; the fit to the thermal contraction

being selected if the curve visually fit the data points and the correspond3 ing derivative was "regular" (i.e., approached T = 0 as T and approached a constant at the higher temperatures)

.

The data are compiled in a standard tabular form in Table 4 showing

both the thermal expansion referred to room temperature, ^^293 ~

''^T^ '^'^293

'

and the thermal expansion coefficient, a = {l/L^^^'^ (dL/dT) . The best

approximation of a single equation for each specimen is presented as curves

for both the thermal contraction and the thermal expansion coefficient in

Figures 8 and 9.

The variation between selected values for the averaged curve fits was

at most ± 1.0 X 10~^ or ± 1%, whichever is greater, for the thermal con- traction values; for the thermal expansion coefficient values the variation

— 6 —1 was at most ± 0.1 x 10 K or ± 2i , whichever is greater. This accuracy

is probably greater than the differences that might be expected due to

variability among composite specimens made in different ways. Nevertheless,

the values measured should be representative of this type of composite

within ± 5% for an equivalent volume fraction.

25
u u ^

ro fM CO

rvj 00 ro ^

O O CT- o o

o CO CO

un CO CO

LTl ^

00-£)O^CO COOJOt^

L/> sO in C —' (NJ CO Ttro o ^ o LTI r-J

00 0~ O O —

'

r- r~ 00 00

(Nl f-J O O <N1 ^ O LTi

fN] fNI (N] rg (\J

CO no in ^

ro (NJ no

(NJ (Nl ro ro no

on un lTi ^ ro ^ on ro ^ (NJ O N

3

—. PO

00 o o ^ r- 00

Ln 00 CO

00 o —^ ro CO ro ro m ro ro CO m

nja

Xw

s

l-i V

s:H

Hi

<uC

o

c

00 00 00 r~ in

oo rvj ro ro ro

o ld -f^* o o

rO r-H r- ro (NJ CO no po

no 00 00 00 o o in

CO 00 00 00 00

r-m in oD 00

00 00 t— O m

nO o in in

00 00 00 OJ 00

o o 00 oj ^ 00 in OO 00 —I —I —

I

00 ^ p-1 ^

o —< <NJ 00

00 00 00 00

-"ti 00 ^ ro) r~

00 00 —

00 OO OO 00

00 ON ^ o- o ^

O O CT^ sD r- O CTcti (Ti (T3 nJ OO 00 00 00

00 00 00 00

00 00 o 00

-0 T!

ro o

o o -H on in

ON in ^ ^ ^ ^

ON CO in o 00

r- -H 00

ro m r~ 00 00 00

00 O 00 vD 00

in m OO

''J^

in cj^ o

vX5 00 ON

no on 00 00 o • O nD 00 in 00 -H

nJ 00 ON -H 00

nO vO o ^

00 O O nO

no ^

T3 T) ^ in O O 00 o

o o o o o

^ OO no

r}< -H ^ O 00

00 O ^ fO

00 o ^ in in 00 00 m

o o o o o

in v£) 00 ON o o o o o O 00 %D 00 o o o o

o nJ on

in 00 OO O^

on on 00 on nO in on ON in 00 o^ 0- -£) in o o in on 00 o ON 00 00 O sO 00 in 00 o o in

Nt on on m OO 00 00 ro

ro O no O

00 ON o

00 OO 00 no

Oa

u

Xw
0 30 60 90 120 150 180 210 240 270 300

TEMPERATURE, K

Figure 8. Thermal contraction of superconducting coil materials.

27
30

28 G Fiberglass - Epoxy ^ Coil Composite - Longitudinal

26 Coil Composite - Radial

V Copper

24

TEMPERATURE, K

Figure 9. Thermal expansion coefficient of superconducting coil materials.
5.3 Discussion

The radial specimens showed nearly twice the thermal contraction of

both the longitudinal and the fiberglass specimens. This is consistent

with the known large thermal contraction of pure epoxy [26] , and the

fact this orientation is more accurately represented by the series

model, Equation (11) , than the parallel model. Equation (10) . The approximate equality of the contractions of the fiberglass and the longitudinal

coil specimens shows that fiberglass, like the metallic conductors, inhibits

the thermal contraction of the epoxy.

The relatively large expansivity of the fiberglass specimen below 70 K

is apparently real, but is not understood at this time.

The important feature of this result is that the coil structure tends

to contract significantly more in the radial direction than in the longitudinal

direction. This means that, at 4 K prior to energizing the coil, the superconducting wire will experience stresses due to additive effects of winding

tension during fabrication and thermal contraction during cooldown.

Further, the coil will tend to contract more than the f iberglass-epoxy overwrap. Both of these may diminish the allowable magnetic field pressure

which the coil can tolerate before yielding. These effects need careful

investigation, and analytical studies in this direction are proceeding.

6. YOUNG'S MODULI AND POISSON'S RATIOS

6.1 Procedure

Young's moduli and Poisson's ratios were measured for three specimen

orientations at room temperatures as well as at the normal boiling points

of nitrogen, 77 K (-320°F) , and helium, 4 K (-425°F) . Tensile specimens

were instrumented with strain gages, as shown in Figure 10. Gages were

placed longitudinally (along the axis of pull) in order to measure Young's

modulus, i.e., strain in the longitudinal direction, as well as transversely

(90° to the direction of pull) to measure strain due to the Poisson effect.

Corresponding gages on opposite faces were connected in series to eliminate

any spurious output due to bending.

29
Figure 10. Strain gage location on tensile specimens.

30
Specimens were tested on a universal testing machine (Figure 11)

.

The lower specimen grips were attached to the support frame, which in

turn was secured to the movable cross-beam of the test machine. The

upper grips were connected via a .63 cm (1/4 in.) titanium rod to the

load cell, mounted at the top of the testing machine.

For tests in nitrogen (liquid) , a slit-silvered dewar was placed

around the test frame. For runs at helium temperatures, an additional

outer "shield" dewar was mounted around the inner dewar and filled with

LN2. After purging the fill tubes and inner dewar with helium gas, liquid

helium was transferred until the liquid level rose above the upper specimen

grips. One filling lasted for 1-1/2 hours, sufficient for several series

of runs. The strain gages were attached to a Wheatstone bridge balance, and the

circuit was initially balanced. During loading and unloading, the resulting

imbalance was then amplified and read as an apparent strain on an X-Y recorder. The output of the load cell was connected to the remaining axis

(Figure 12). Typical resulting curves are shown in Figure 13.

Between 5 and 10 runs were made for each set of gages at each temperature, whereafter the complementary gages were connected. The system bridge

was rebalanced, the load-unload test sequences were repeated, and the output

was recorded on the same piece of graph paper for easy comparison. Since

there was a small loading and unloading hysteresis, only that portion of the

test curve above and below this effect was used. From each set of test

curves, two were designated "representative" and values from them were

averaged

.

2 2 Longitudinal specimens were loaded to about 8 3 MN/m to 110 MN/m

(12000 - 16000 psi) . At loads much above this, the specimens would break

at the grip holes. Therefore, as an added precaution, the grips were

epoxied to the specimens, and an epoxy fillet was added along the gripspecimen boundaries. Similarly, in order to keep within the elastic ranges,

2 the f iberglass-epoxy specimen was loaded to only 55 MN/m (8000 psi).

31
32
LOAD

CELL

DC

AMP X - Y

RECORDER

SPECIMEN

BR DGE

BALANCE

DC

AMR

Figure 12. Schematic of gage circuit.

33
isd 'SS3dlS
Since the radial tensile specimens were fabricated from sections of an

2 actual coil which were epoxied together, loads were kept to about 5.5 MN/m

2 (800 psi) . The epoxy bond at the butt-joints failed at loads about 7 MN/m

(1000 psi). Load was converted to stress by the relationship

= L/A (23)

where

= apparent stress;

L = load, i.e., measured output of load cell;

A = cross sectional area of the specimen,

measured at the gage.

True strain was calculated from apparent strain, compensating for transverse gage effects by the following formulae:

(e^ - ke^ ) (1 - Upk)

e, = ^ . (24)

(1 - k^)

(e^ - ke^ ) (1 - Hgk)

e. = — 5 (25)

(1 - k^)

where e^^ = true longitudinal strain

8^ = true transverse strain

= apparent longitudinal strain

a = apparent transverse strain

a

k = transverse correction factor, = -0.034

[1q = Poisson's ratio of the material upon which

strain gage was calibrated (1018 Steel), = 0.285.

These corrections were negligible for the longitudinal gages (< 1%), but

proved to be considerable 20%) for the transverse gages.

Since gage factors vary as a function of temperature, corrections had

to be made to the strain gage output whenever tests were done at temperatures other than room temperature. These corrections were taken from curves

supplied by the manufacturer of the strain gages, extrapolated to include

the data taken at helium temperatures.

35
6.2 Data

From the true strains. Young's modulus and Poisson's ratio were calculated from

L/A

r (26)

e and

(27)

The data are plotted in Figures 14 and 15 and listed in Table 5. Instrument errors are nominally set at ± 0.5%, this being the un- certainty quoted for the electrical components. The gage factors are ± 1%,

at room temperature, but may be higher at low temperature which leads to

an estimated error for the longitudinal and f iberglass-epoxy specimens of

about 2 or 3%.

Since the radial specimens were so fragile, loads were kept to

2 5.5 MN/m (800 psi) or less. The resulting strains were quite small (on

-4

the order of 10 for the Poisson gage output) , and the noise level re- sulted in resolution errors several times higher than the above uncertainty.

These instrumental errors are probably small compared to variability which

could reasonably be expected in the composite sample fabrication.

6 . 3 Discussion

Young's modulus of every specimen decreased slightly with increasing

temperature, as shown in Figure 14. Poisson's ratio also appears to de- crease with increasing temperature. Figure 15, but the curvature is of

opposite sign. The 4 K (-452°F) data point for radial specimen # 1 may

be in error. The large variations in Poisson's ratio between the two

radial specimens may be due to markedly different compositions, different

curvatures in the respective constituent wires, or perhaps to local debonding near the strain gage. This is being investigated further.

The general behavior is similar to the thermal expansion in that the

longitudinal moduli are similar to the superconducting copper wire and

the transverse are similar to the epoxy

.

36
Table 5. Young's Moduli and Poisson's Ratios for

superconducting coil materials

4 2 6 YOUNG'S MODULI 10 MN/m (10 psi)

Specimen

293

T" p TTTnp T*?^ I'll r p TCpI vi n 77 4

Radial #1 (E22) 2. 82 (4. 10) 3. 82 (5. 53) 4. 15 (6. 01)

Radial #2 (E22) 2. 68 (3. 89) 3. 75 (5. 43) 4. 08 (5. 91)

i-.ong, ?fi (h^iD 7( . R 7 A M 1 Q7^ 0. 1 ^ \ L c, . 0 1 } Long. #3 (Ell) 7. 39 (10. 72) 7. 89 (11. 44) 8. 31 (12. 05)

F. E. #1 (Ell) 2. 82 (4. 10) 3. 33 (4. 82)

POISSON'S RATIOS

3. 56 (5. 16)

Specimen

293

Temperature, Kelvin

77 4

Radial #1 (V21) 0. 146 0. 202 0. 196

Radial #2 (V21) 0, 199 0. 248 0. 256

Long. #3 (V13) 0. 333 0. 352 0. 352

F. E. #1 (V13) 0. 149 0, 209 0. 221

37
15x10

O

0

T r

1

r

1 r

Longitudinal No. I ,E^^

Longitudinal No. 3, E

Radial No.l, E,

Radial No.2,E,

Fiberglass Epoxy No. I, E^

J I I L 100 200

TEMPERATURE,

10x10

CVJ

ZD

-I

5 g

O

CO

"CD

O>-

0

300

Figure 14. Young's modulus versus temperature for superconducting

coil materials ,

38
0.4

1 ^ T T \ T

0.3

•Longitudinal No.3 , 2/13

<

Radial No.2,Z/,

21

O

CO

O Q2

Fiberglass Epoxy No. 1,1/

IS

Radial NoJiZ/g,

0.1 J I L J \ \ \ I \ L 100 200

TEMPERATURE, K

300

Figure 15. Poisson's ratio versus temperature for superconducting

coil materials

.

39
7. PREDICTED VERSUS MEASURED PROPERTIES

The micromechanical laws discussed in previous sections were evaluated

using available, appropriate volume fractions and constituent properties.

These predicted results are compared with measured room temperature properties in Table 6. The predicted value preferred on a theoretical basis

is underlined.

The predicted value of E^^ was approximately 13% below the measured

value. This was probably due to the value of E^ used for the wires as well

as to the fact that the contribution of the fiberglass was ignored. The

tensile test of the wire showed an increase in E^ with increasing stress

(a behavior typical of a stranded specimen) . Since the coil is fabricated

with considerable tension in the conductor this tension may slightly alter

the mechanical properties of the wire.

The predicted values for v^^^ were about 5% below the measured value.

Due to the complexity of the transverse geometry and the fact that for

the wire was assumed to be the same as copper, this agreement is probably

fortuitous

.

The predicted value of v^j^ was 0.11. The measured value of v^^ was between 0.146 and 0.199. If the material were truly transversely isotropic in the 2-3 plane then v^^^ = ^21" '^^^ discrepancy in these values

probably reflects a lack of isotropy which must exist in the 2-3 plane.

This also is being experimentally measured.

The transverse modulus, ^22' """^ difficult to predict due to the complex

stress distribution and to the fact that the transverse properties of fibers

or wires are generally not known. The usual procedure is to assume that the

transverse fiber properties are equal to the longitudinal properties. The

lower bound is given by the series model or equation (12) . The most accurate

values are produced by the elasticity solutions of Adams [11,14], which

bracket the experimental values. The value of ^'^^ the nominal volume

fraction of 0.7 3 is approximately 8% higher than the average measured value.

3 2 The predictions of shear modulus G^^, vary between 3.45 x 10 MN/m

(0.5 X 10^ psi) and 9.16 x 10^^ MN/m^ (1.33 x 10^ psi) for four different

40
Table 6. Room temperature properties of the superconducting coil composite, calculated values and measured values.

Property

Model or

Autiior (Ref. Equation

Is'umbe r Calculated Values Experimental

Values Notes

1

Parallel [ 8] 0. 73 6. 66 (9. 66)' 7. 39 (10. izr

7. 72 (11.21)^

With Ef 11. 64 X 10°Dsi and neglecting fiberglass

13 Parallel

Rosen (20)

[14J [14]

0. 73

0. 803 0.319

0. 324

0. 333 With V£ = 0. 33 and using

volume fraction corresponding to 3 direction.

0. 73

0. 803

0. 320

0. 324

31 Calcote (7) N. A. 0. 11 0. 146 - 0. 199'" "Experimental values

actually v^j and assuming transverse isotropy.

23 Adv. Comp. Design

Guide (11) [16] 0. 650. 73

0. 803

0. 355

0. 349

0. 335

To be measured

'22 Series

(lower bound)

[ 9] 0. 73

0. 65

1. 12 (1. 67)"^ 0. 90 (1. 30)^2. 82 (4. 10)^

2. 68 (3. 89)^ Adams (et al. ) (14) 0. 73

0. 65

2. 97 (4. 32)'

1. 96 (2. 85)"

The transverse modulus

of the wire is assumed

equal to the measured

longitudinal modulus.

13 Adams (et al. ) (14) 0. 65

0. 73

0. 630 (0. 914) ^

0. 916 (1. 33)^ To be measured

Ekvall (19) [18] 0. 65

0. 73

0. 803

0. 346 (0. 502)^ 0.433 (0. 629)^

0. 564 (0. 818)^

The shear modulus of the wire was determined from

the measured longitudinal

modulus and the assumed

V = 0. 33 by G = E/2(1-hv).

Rosen (20) [19]

[20]

[21]

0. 73

0. 73

0. 73

0. 545 (0. 791)' 0.443 (0. 643)'

0. 660 (0. 958)'

Foye (22) [22] 0. 73 0. 544 (0. 789)'

1

Parallel [12] 0. 73 282 W/mK

(163 Btu/hr ff'F) To be measured Constituent properties

assumed are shown in Table 1.

22 Series [13] 0. 65 9. 95 W/mK

(5. 75 Btu/hr ft°F) To be measured

11 Parallel [10] 0. 73 14. 2 X 10-°/K

(7. 91 X 10"°/ 'F)

14. 0 X 10"^/K

(7. 78 X 10-6/°F)

22 Series [11] 0. 65

0. 83

27. 25 X 10-°/K

(15. 14 X 10-°/°F)

21. 96 X 10'

22. 9 X 10-^/K

(12. 7 X lO-^/'F)

(12. 20 X 10 "/K

"*/ = F)

Volume fraction of 0. 83 was computed assuming a series of rectangles spaced

as shown in schematic of

coil cross section Fig. 3.

^Units of lo'* MN/m^ (lO^psi).

41
micromechanical solutions as well as a range of representative volume

fractions. Since the shear modulus of the wire is not known these values

must be considered tentative approximations until the composite shear modulus

is measured.

The simple series and parallel models were used along with the appropriate

volume fractions to predict the linear coefficients of thermal expansion at room temperature. The agreement between predicted and measured values is

within a few percent for both the longitudinal and transverse specimens.

Since the actual constituent properties were unknown, nominal values for

copper and epoxy were used in the equations. Because of these approximations

the close agreement is surprising and perhaps fortuitous.

The general agreement of measured properties and properties predicted

by micromechanical methods indicates that these laws can be used to generate

composite coil properties sufficiently accurate for preliminary design purposes. Experimental values should be obtained whenever feasible, especially

at room temperature. The change of coil composite mechanical properties with

temperature can probably be extrapolated very accurately by noting the change

with temperature of the major constituent.

7.1 Preliminary Coil Values

By combining the measured properties and the theoretically predicted

properties, a set of constitutive relationships for this superconducting

coil composite can be established. These properties should be considered

as tentative until additional measurements are completed. They are, however, accurate enough for some practical analyses and may actually introduce

less error than the analytical model or solution method itself.

The experimental values as well as the calculated values for the properties are average or best values in our judgement. The calculated values

are noted by an asterisk. We assume

42
ID

^11 = 7 4 2 .58 X 10 N/in = (11 x 10^ psi)

p — ^22 ~ z

4 P ./DXXU IN / III — A i U p & X ;

''13 " U

5 "3 "3 . 0 0 J

^23 = 0 .335*

^13 = 0 .69 X 10^ N/m^* = (1 x 10 psi)*

into the compliance matrix. Equation 7,

13.18 -12.07 -12.07 0

-12.07 36.25 -12.14* 0 -12.07 -12.14* 36.25 96.79

0 0 0 0

0 0 0 0

0 0

0 0

lO^S.. (N/m^) = -12.07 -12.14* 36.25 96.79 0 0 (28)

72.50* 0

0 72.50*

To obtain the equation in English units, in the form

Q 10 (psi) = [matrix]

,

multiply all elements of the matrix on the right hand side of Equation 28

by 6.895.

The thermal conductivity at room temperature is given by the matrix

282* 0 0

K. . (W/mK) = 0 9.95* 0 (29)

1]

0 0 9.95

to obtain K(Btu/hr ft °F) multiply the given matrix elements by 0.578.

The thermal expansion coefficient at room temperature is given by the

matrix

14.0 0 0

lO^a . . (k"-"-) = 0 22.9 0 (30)

ID

0 0 22.9

to obtain lO^a , .(°F~'''), multiply the given matrix elements by 5/9.

43
7.2 Effect of Curvature

Since the radial tensile specimen was fabricated from slugs machined

from an actual solenoidal coil, some shear is introduced away from the

centerline of the specimen due to the curvature of the wires, Figure 16a.

A question arises as to the effect of this curvature on the experimental

values.

A preliminary calculation indicates that the upper bound on the possib

error in the calculated moduli from this effect is no more than 10%, and

probably much less. We conclude that this can be neglected in the studies

at hand

.

, 8 . CONCLUSIONS

(1) Comparison of measured macroscopic coil properties to those

predicted from constituent properties by micromechanical analyses is

reasonably accurate, giving confidence to our formulation of the mea- surement program.

(2) The modulus and expansion coefficient parallel to the superconducting wire is best predicted by the micromechanical models of binary

materials in parallel, while perpendicular to the wire the best predictions

come from the series model.

(3) Measurements of the shear moduli and Poisson's ratios are incomplete at this time.

(4) The anisotropy of the material properties is very real, and of

such magnitude as to have a strong effect on the stresses on the coil body

as a function of operating conditions.

Work is continuing on the following topics

(1) Shear moduli, Poisson's ratios, and thermal conductivity of

coil materials.

(2) Moduli, conductivity, and thermal expansion of the superconducting wire.

(3) Analysis of internal strains in the coil structure as a

function of winding tension and anisotropic thermal contraction.

4 4
(4) Instrumentation procedures on a coil to further test

and confirm our experimental and analytical work.

9 . ACKNOWLEDGEMENTS

The authors are indebted to M. J. Superczynski of the Annapolis

Laboratory - Naval Ship Research and Development Center for providing

specimens, the general description of the coil and its manufacturers,

and helpful discussions. R. J. Trapani performed several of the calculations for which we are thankful. The critical reading of the manuscript

by V. D. Arp is greatly appreciated.

45
REFERENCES

1_. Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity Third Edition,

McGraw-Hill Book Company, New York (1970), pp 433-484.

2. Frederick, D, and Chang, T. S., Continuum Mechanics Allyn and Bacon, Inc.,

Boston, (1965), pp 166-172.

3. Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Elastic Body , translated from Russian by P. Fern, Holden Day, San Francisco (1963).

4. Hearmon, R. F. S., An Introduction to Applied Anisotropic Elasticity , Oxford University Press, New York (1961)

.

5. "Element Methods in Stress Analysis", TAPIR, The Technical University

of Norway, Trodheim, Norway (1970) .

6. Zienkiewicz, 0. C. and Cheung, Y. K., The Finite Element Method in

Structural and Continuum Mechanics , McGraw-Hill, London, (1967),

pp 148-191.

7. Calcote, L. R. , Introduction to Continuum Mechanics , D. Van Nostrand

Company, New York (1968), pp 67-76.

8. Landau, L. D. and Lifshitz, E. M. , Theory of Elasticity , Translation

by Sykes, J. B. and Reid, W. H., Pergamon Press, Reading, Mass.

(1959) , pp 14-17.

9. Carslaw, H. S. and Jaeger, J. C, Conduction of Heat in Solids , second

edition, Oxford at the Clarendon Press (1959), pp 38.

10. Calcote, L. R. , The Analysis of Laminated Composite Structures , Van

Nostrand Reinhold, New York (1969) .

11. Advanced Composites Design Guide, Volume 11, Analysis, Air Force

Materials Laboratory (AFML/LC) , Wright-Patterson Air Force Base,

Ohio 45433 (January 1973).

12. Modern Composite Materials , ed . Broutman, L. J. and Krock, R. H.,

Addison-Wesley Publishing Company, Reading, Mass. (1967),

13. Paul, B., "Prediction of Elastic Constants of Multiphase Materials",

Transactions AIME 218, 36-44 (1960) .

14. Adams, D. F. and Doner, D. R., "Transverse Normal Loading of a Unidirectional Composite", J. Composite Materials 1, 152 (1967).

15. Chen, C. H. and Cheng, S., "Mechanical Properties of Fiber Reinforced

Composites", J. Composite Materials ^, 30 (1967).

16. Whitney, J. M. and Riley, M. B., "Elastic Properties of Fiber-Reinforced

Composite Materials", AIAA Journal 4, 1537-1542 (September 1966).

17. Davis, L. W. and Bradstreet, S. W., "Control of Thermal Expansion

Through Composite Design", Ceramic Bulletin 5_0, No. 12 (1971).

18. Schneider, P. J., Conduction Heat Transfer , Addison-Wesley, Cambridge,

Mass. (1957) pp 21-26.

19. Ekvall, J. C, "Elastic Properties of Orthotropic Monofilament Laminates",

ASME Paper 61-AV-56, presented at Aviation Conference, Los Angeles,

California (March 12-16, 1961) . 46
20. Rosen, B. W. , Dow, N. F., and Hashin, Z., "Mechanical Properties of

Fibrous Composites", NASA CR-31 (April 1964).

21. Hashin, Z. and Rosen, B. W. , "The Elastic Moduli of Fiber-Reinforced

Materials", Paper No. 63-WA-175, J. Appl . Mech., ASME (June 1964).

22. Foye, R. L., "Advanced Design Concepts for Advanced Composite Airframes",

AFML-TR-68-91, Vol. 1 (July 1968).

23. Clark, A. F., Cryogenics 8, 282 (1968).

24. Sparks, L. L., Powell, R. L. and Hall, W. J., "Reference Tables for

Low-Temperature Thermocouples", NBS Monograph 124 (June 1972).

25. Automation Industries, Inc., "Technical Data 10-701", (1969).

26. Corruccini, R. J. and Gniewek, J. J., "Thermal Expansion of Technical

Solids at Low Temperatures", NBS Monograph 29, (1961).

47
FORM NBS-1 14A (1-71) 2. Gov't Accession No.

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 73-349

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

CHARACTERIZATION OF A SUPERCONDUCTING COIL

COMPOSITE

5. Publication Date December 1973

6. Performing Organization Code

7. AUTHOR(S)

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

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS ... DEPARTMENT OF COMMERCE

Washington, D.C. 20234

10. Project/Task/Work Unit No. 2750538

11. Contract/Grant No.

12. Sponsoring Organization Name and Address Annapolis Laboratory

Naval Ship Research and Development Center

Annapolis, Maryland 21402

13. Type of Report & Period Covered

NBSIR

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summaty of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The superconducting coil composite material being utilized by the

Annapt.Iis Laboratory of the Naval Ship Research and Development Center

is characterized by its mechanical and thermal properties. The Young's

moduli, Poisson's ratios, and thermal contractions are measured from

room temperature to 4K and reported in this interim report. A micro

mechanical analysis based upon volume fractions of constituents is used to

predict room-temperature properties, and a comparison is made to the

measured values.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Composite; low^ temperature; Poisson's ratio; superconductor; thermal expansion;

Young's modulus.

18. AVAILABILITY STATEMENT

Hn UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

22. Pr

USCOMM tRL USCOMM-DC 66244.P7I