AD-753 392

A LABORATORY METHOD FOR THERMALFRACTURE OF GRAPHITE

Hans U. Eckert

Aerospace Corporation

Prepared for:

Space and Missile Systems Organization

31 October 1972

DISTRIBUTED BY:

National Technical Information ServiceU. S. DEPARTMENT OF COMMERCE

1jPt~ R r-aý ,

AIR FORCE REPORT NO. AEROSPACE REPORTSAMSO-TR-72-275 TR-0073(3450-76)-1

A Laboratory Method for ThermalFracture of Graphite

Preparcd by H. U. ECKERT

Plasma Research Laboratory

L;'boratory Operations

7,2 OCT 31 .' ,.

IILI

Dcvclopmcnt Operations

THE AEROSPACE CORPORATION

Prcparcd for SPACE AND MISSILE SYSTEMS ORGANIZATION

AIR FORCE SYSTEMS COMMAND

LOS ANGELES AIR FORCE STATION

1.L.s AngcIcs (alhtornia

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2. REPORT TITLE

A LABORATORY METH-OD FOR THERMAL FRACTURE OF GRAPHITE

4. DESCRIPTIVE NOTES (1ype of "part and Inclusive dotes)

S. AU THORIS) (First mime. saiddleinitial, fastrIan)

Hans U. Eckert

6. REPORT DATE 78- TOTAL NO. OF PAGES 7b. NO4. OF REFS

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13. SUPPLEMENTARY NOTES 12. SPONS,PRING MILITARY ACTIVITY

Space and Missile Systems OrganizationAir Force Systems CommandLos Angeles, California

13.'ABSTORAC'

Development of a[ method for producing thra tesfiuei T-Sgraphite and the initial results are described. Test specimens are 10-cm-longhollow cylinders with outer and inner radii of 1. 9 and 0. 4 cm, respectively.The outside is heated by induction at a frequency of 1. 4 MHz by a 1l00-kW powerosciilator; the inside is kept below 1005C by forcing water at a rate of 5 gpmthrough the copper-coated bore. A special lead soldering technique has been

dvlpdto fasten the coolant ducts -to the specimen. The inductor coil is3 protected by an oil bath against heat and electric breakdown. F krom the

recorded rise in cooling water temperature, radial heat fluxes through thespecimen at. fracture have been determined to be 38 kW. The surface temp-e rature at fracture has been measured pyrometrically to be -1700 0C. The meanfradial temperature gradient at the section where fracture occurs is -1050 0 C/cm,which comes close to theoretical predictions. Fast heating seems to producefracture at lower power. Recommendations are given for improving and

j extending the measurements. A method is developed for calculating radialtemperature distributions that takes into account effects of heater frequency,temperature dependen~ce of thermal conductivity, and surface radiation.Sample calculations for ATJ graphite show nearly linear .temperature variations.Therefore, the mean gradient obtained from the measurements can be

e~petedto approximate values of the local temperature gradients.

oo) FORM 1473 J.6/UNCLASSIFIEDIFACSIMILEI Security Classification

U4NCLASSMFIED" 1.1+ Security Classifidation

KEY WORiS

Graphite"

Thermal Fracture

- Ynduction Heating

Distribution Statement (Continued)

Abstract (Continued)

Ii

UNCLASSIFIEDL _Security Classifi -ation

Air Force Report No. Aerospace Report No.SAMSO-TR-72-275 TR-0073(3450-76)- 1

A LABORATORY METHOD FOR THERMAL?RACTURE OF GRAPHITE

Prepared by

H. U. EckertPlasma Research Laboratory

Laboratory Operations

72 OCT 31

Development OperationsTHE AEROSPACE CORPORATION

Prepared forSPACE AND MISSILE SYSTEMS ORGANIZATION

AIR FORCE SYSTEMS COMMANDLOS ANGELES AIR FORCE STATION

Los Angeles, California

Approved for public release;distribution unlimited

-- =- , • • • • •

FOREWORD

This report is published by The Aerospace Corporation, Ei Segundo,

California, under Air Force Contract No. F04701-72-C-0073.

The author gratefully acknowledges the able assistance of R. G. Aurandt

in carrying out the experiments. D. Nunberg-did the photographic work.

This report, which documents research carried out from December 1970

;through May 197Z, was subinitted for-reView and approval on 16 October 197Z

to Lt Col E. W. Porter, DYA.

Approved

R. X. Meyer, D/rector R. B. Mortensen, DirectorPlasma Research Laboratory Hardened Reentry SystemsLaboratory Operations Ballistic Reentry Vehicles

Reentry Systems DivisionDevelopment Operations

Publication of this report does not constitute Air Force approval of the

report's findings or conclusions. It is published only for the exchange and

stimulation of ideas.

Elliott W. Porter, Lt Col, USAFAsst Dir, Development DirDeputy for Technology

.11

i -i

CONTENTS

FOREWORD ................................. iiABSTRACT . . . ............. .. . . ........ iii

1. Introduction . .1..... .. .. * ..........

z. Development of Induction Heating Apparatusfor Thermal Stress Experiments. .................. 3

2. 1 Basic Considerations ........... ...................... 3

2. 2 Shape of Specimen ................ .............. 5

Z. 3 Inductor Coil Design ... . .............. ...... 8

Z. 4 Present Apparatus and Results .......................... 11

3. Conclusions and Recommendations.......................... 19

REFERENCES . . . . . . . .. ............ ...... 21

APPENDIXES

I. Matching of Graphite Load to Impedanceof rf Oscillator ....... ........................... I-i

_ II. Calculation of Radial Temperature Distributionsfor Infinite Graphite Cylinder ........ ................... 1-1

fi]if[ ~Preceding pagl lanqk

z FIGURES'

1- Calculated distributions -of axial and azimuthal,strains along inor surface of hollow ATJ-Sgraphite cylinder ...............................

2. Shapes of graphite test specimens . - 63 Magnetic flux cohcentrator." 10

4. Present arrangement of graphite the rmal stresstest apparatus ............................... "12

5. Recordings of cooling water te~mperatiire in twoheating tests leading to -fracture ....................... 13

6. Temperature correction for pyrometer readingstaken through odl bath of-apparatus in Figure 4 ........ 15

7. Heating test in apparatus of Figure 4 , ............. 16

8. Fractured graphite specimens .... ................. 17

I-1. Schematic of rf oscillator load circuit .................. 1-2

II- 1. Variations of thermal conductivity K and electricalconductivity a with temperature for ATJ graphite 11-2

11-2. Heat conduction potential of ATJ graphite o........... 11-3

11-3. Radiation flux va heat conduction potential ofATJ graphite. .. ................................ 11-6

11-4. Calculated temperature distributions in induction-heated ATJ graphite cylinder; low input .............. 11.-7

I1-5. Calculated temperature distributions in induction-heated ATJ graphite cylinder; high input,f = 1.7 MHz .................................. .11-8

-vi-

L. introduction. .

The tests described here were pr6mpted'by the continuing nee-din reenfry

vehicle design for quantitative information on the thermal fracture of graphite.

It was important to determine whether the severe conditions leading to thermal

fracture could be produced in an inexpensive laboratory experiment or whether

one •.o•od-have to expand the mor, expensive thermostructural rocket test

program to satisfy the needs of the designer. One Vss.•j!•ty for a laboratory

experiment was induction-heating of graphite with the large rf plasma generator

of The Aerospace Corporation. Therefore, this facility was modified for the

purpose, and temperature gradients were produced in hollow graphite cylinders

by induction heating of the outer surface and water-cooling of the inner surface.

The two major problems encountered in this experiment were electric breakdown

caused by the nearness of the inductor coil to a hot surface and leakage at the

junctions of the expanding graphite and the coolant tubing. These and other

problems were gradually overcome in one year's time through numerous

changes to the apparatus. In the present arrangement, temperature gradients

in excess of 1000 0K/cm can be obtained; these have proved to be sufficient to

break ATJ-S graphite. No systematic effort was made to obtain the complete

information needed for establishing a fracture criterion, as this will be the

objective of the next phase. In this report, the development of the apparatus

and its final arrangement are described in sufficient detail for others to do

the testing. The important considerations for matching the specimen load to

the rf heater impedance are contained in Appendix I.

Because it is very difficult to measure the radial temperature distribution

in the specimen without affecting fracture resistance and heating pattern, a

simple calculation method is derived in Appendix H that is based on an analytical

solution of the energy balance equation for an infinite cylinder. The solution

takes into account the frequency dependence of the heat source ddistribution, the

7 "A recent survey of unclassified information on graphite nosetips was made byP. J. Schneider, et al. [1].

-----

temperature dependence of the-thermal conductivity, and~the radiation losses.

With reliable data 6n~material propertlies, the method should provide more.

accurate resilts than can be expected from measurements.

t

.- 2

Z. Development of Induction Heating Apparatus forThermal Stress Experiments

2.1. Basic Considerations

Some estimate of the power requirepd-to breaka specimen of ATJ-S

graphite by-thermal stresses can be obtained from calculations -reported by

W. R- Grabowsky. Figure 1, reproduced'from: thesecalculations, shows the

distributions of longitudinal and-azimuthal strains -along, the inner 'surface of -a

1hoflow cylinder whose dimensions are given in the top porti6n-of the figure.

With tmnpeiatures of -2600 -Kand 5000 K at the outer -and-, inner surfaces,respectively, it is expected that the strains, especlixly axial, will exceed the

breaking limit. The average temperature gradient for this cane is 2100 0K/

1.54 cm or 136 0 "K/crit; the average thermal coridudtivity, obtained liko.ri00o

Fig. II-1, is .- 0. 1 cal/sec cmKor -0.4 W/cm K. Thus, the heat flux per~cn

area is -550 W/cm or, for the total area of -100 cmru, 55 kW. With -the

addition of 10% for radiation and convertion losses, the total power requirement

is 60 kW. Although this valud is within the capability of the Aerospace rf

heater, it requires careful matching and efficient cbapling to the load. Efficient

coupling is obtained if the induction coil is close to the specimen, but as this

interferes with protecting, the coil from the heat, a compromise must be made.

Another compromise is necessary:with respect to'the operating fre-

quency. At the conductivity'of graphite, a- ; 4000 to 1500 mho/dm, a fre-

quePcy of 104 to 105 Hz, skin depth -1 cni, would be desirable for efficient

volume hegting. But this would require major changes in the circuitry of the

oscillator that previously has operated in the MHz range. In the calculations

of Appendix I, therefore, f = 1 MHz has been assumed. Actual tests were run

at f 1.4 to 1.7 MHz.

MW. R. Grabowsky (The Aerospace Corporation, SBO) Memorandum to TheAerospace Corporation, GO, Subject: Graphite Thermal Stress Experiment(23 January 1969).

- -3-

el,:

r.:0.4 cmJ r2 = 1.9'4, cm

0.8m AXIAL STRAIN Ti = 505*K

-T2= 2690°K

HOOP STRAIN REGION OF"I- I PROBABLECj FAILURE

Z

S.20 -

0 2 4 6 8 10LENGTH, cm

'Figure 1. Calculated distributions of axial andazimuthal strains along inner surfaceof hollow ATJ-S graphite cylinder

-4-

2. 2. Shape of Specimen

All specimens tested were hollow ATJ-S graphite cylinders with an

o. d. of 3.8 cm and a length of 10 cm. These dimensions turned out to be,

nearly optimal for the production of fracture, with the available laboratory

facilities, in a heating zone that was nearly uniform axially. For an apprec-

iably longer cylinder, the generator." power would have been insufficient and

problems also might.have arisen in the-coolant flow because of -the larger

resistance' and the higher exit temperature (boiling). •For a cylinder with

an appr&ciably lower 1/d ratio, it would have been difficult to obtain a-

sufficiently uniform axial temperature in the midzone where fracture -was

likely to occur. Changes wvere mide only in the diameter, of the bore and in

the method of connection with the coolant flow tubing. The first configuration

is shown in Fig. 2a. Except for the conical sink at the front surface, this

shape is the same as' that used in earlier experiments at the Aerodynamics.

and Propulsion Research Laboratory. The use of a threaded neck and

Swadgelok fitting to connect the specimen to copper tubing of slightly smaller

diameter than that of the bore ensures freedom from mechanical stresses.

The gap between tubing and cylinder is filled with A gallium-indium alloy,

which consists of 767o Ga and 247o In, that is liquid at rob ii temperature and

provides thermal contact. Although the boiling point of this alloy is above

2000°K, it was useful only as long as the heating rates were below -1.5 kW/cm.

At higher rates, it was partly driven out of the gap, probably by gas liberated

in the hot graphite, and seemed to make only spot contact. This was indicated

by the low temperature gradients inferred from pyrometer readings at the

front surface that were found to be -- 200°K/cm and corresponded to radial

heat fluxes of only 0. 7 kW/cm. Therefore, most of the heat input must have

been conducted in the axial direction toward the neck.

In order to avoid these problems, the neck, inner tubing, and liquid metal

were eliminated, and the cooling water was led directly into the bore after the

graphite pores had been sealed with an electrolytically deposited copper coating

that was 0. 05 to 0. 1 mm thick. Also, the bore was widened from 8 to 13 mm

diameter for the following reasons: First, calculations described in Appendix II

-5-

3 V&4mmL 38mm1 7\3-~8mm _k-Bamm -4ki 4-.mm

EE

E-

~~; ;I 4"-o8mm -4m. k-8.23mm

Figure 2. Shapes of graphite test specimens

had indicated that, at a desired inpu: of 4 kWicm, the temperaiure at the

outer surface would exceed the apparatus safety limit of a20O0eK (Fig.!- 5).

Second, the wider cross section allowed the cooling flow rate zo be raised from

-2. 5 to 4 gpm, which eliminated shaking of the specinm.en caused by nucleate

boiling. Copper tubing ends, with the same i.d., were threaded 0. 5 in- deep

into the graphite and sealed with Viton 0-rings (Fig. Zb). Because the 0-rings

burned up on the graphite side dtring heating, they were replaced by- V-profile

copper rings, which were compressed for proper sealing. This intruced

mechanical stresses into the specimen that were not considered admissiL-=e;

therefore, tke gaskets were eliminated, azid the tubing was soft-soldered to

the copper coating.

When the solder melted during testing, silver soldering -as considered,

which requires silver coating of the graphite interior. This approach was

abandoned because the silver adhered to the graphite only after the binding

material of the graphite had been driven oujt by heating the sample in a furnace.

Finally, lead was used because it has a sufficiently high melting point, and

could be soldered onto the copper.

The specimens were then prepared by the following procedure: Lead was

filed into fine particles that were mixed with conventional paste soldering flux

(Douton Co. 's NOKORODE). This mixture was then painted onto both mating

surfaces, which had been prewarmed to assist in the flowing of tihe flux and

solder. These surfaces were then heated separately to a temperature at which

the lead filings would melt and wet the associated surfaces. Excess solder was

wiped from the tube and shaken from the sample. The now lightly leaded

surfaces were alio'.ved to cool to a point where they were still warm, given a

light coating of the flux and solder mixture, and then put together in their

finished positions. When the fit was loose, a sufficient amount of the lead

filings was placed around the tubing, at the point where it entered the sample,

to fill the annulus. The entire assembly was then heated to the rn-elting point

of lead and allowed to cool slowiy. The b~are of the sample and associated end

fittings were then given a coating of conventional lead and tin s.ider (Johnson's

FLUX-'N-Solder) paste and again heated to the appropriate temperature to seal

-7-

any porosity in ike copper plating. The lead and tin solder is adute in

this appIic~ction, as it is in direc1x contact witth the water flow..

Because the desired power inputs. ap to 5 kV4Icm (Fig. UI-5), could not

be generated over the full length of the sample. ar- attempt was made to pro-

duce such iputs locally by tapering the ends (Fig. 2c). Here heating occurred

over the full length, witereas cooling waz limited to one-half of the specimen

lemgth so that anm axia! converggence of the beat flux in the ratio 2:1' occurred.

However, fracture could not be achieved widn this sha.ve, as the total om-er

innut had to be limited to -ZO k" because of the increased surface temýrature.

Also, it wrould be more difficult to determine the magnitude of the thermal

stress from the two-di-mensional heat flux zvattern in this geometry..

.In the subseczent version (Fig. Zd), a_-al coc-ergence &-as a am oned in

favor of increased radial convergence that resulted frod red-,-cing •he bore

diameter again to 8 mm.. The coolant flow rate 'was maintained and eventually

even increased to 5 op..- by .utting a booster Pump imto the city water line.

Also, it was possible to eliminate the threading and still retain sufficient

rigidity. Finally, the sharp edge at the lower end, adjacent to the s-de of the

inductor carrying the high rf potential, was rounded off to reduce the form ation

of corona discharges. This spec-nen shape, which .-s also shown in the final

arrange-nent in Fig. 4, was used in later tests where fracture occurred.

2.3. Inductor Coil Design

From the considerations in Appendix .I it follows that the inductor coil

should have at least 16 turns over a length of 10 cm. In order to produce this

turn density, hollow-core, rectangular copper tubing, with a cross section

of 3.2 x 6.4 mm Z. was wound over the small side into a 17-turn coil that had a

2.6-cm inner radius. The coil was then silver-plated and connected to the

terminals of the plate tank circuit, which also provided waterflow for cooling.

In the first heating tests, the coil was operated in air and separated from the

graphite specimen by a clear quartz tube. When the rf voltage on the coil had

reached -6 kV and the graphite surface be:ame red hot, corona filaments

formed on the graphite surface next to the end of the coil carrying the high

potential These filaments gradualy grew into arcs, softened the quartz, and

finally pierced !t At other times flashovers occurred between the coil turns,

which caused irrepa l leaks.

In order to avoid these problems, aa alternative configAration was tested

that dates back to an idea of Babat and Losinsky [2]; it is termed a magnetic

flux r. A photograph of the device is showa in Fig. 3; the

ie si in inches can be inferred from the size of•the 6-in. scalW ie the

picture. The device consists of t- coaxial, slotted, copper cylinders that

are silver-plated and are connected at the slots by trapezoidal copper plates.

The length of the interior cylinder, at 5 in., is only one-third that of the outer,

tkus, the linear density of a current induced in the latter is increased by a factor

of 3. T1e tightly fitting inductor coil has 20 turns of square copper tubing and

is insulated by a pyrex trbe from the concenrator that is at floating potentiaL

The graphite specimen fits cdosiy into the inner cylinder and is not near a high

rf potential. The danger of arcing between coil turns is also greatly reduced by

I the wide tarn spacing. *The entire lengthý of the specimen can be observed

through the slot.

In tests with this configuration, the plate voltage of the generator could

be run im to its maximum value of 10 kV without a breakdown. But the powerinput to the graphite at this voltage, and at a frequency f -2 WMHz, was only

15 kW, which is not higher than could be obtained with the small inductor coil

at -7 Mr. Probably, the poor efficieccy resulted from poor coupling, which

was caused by the large difference in coil and load diameters, and from ohmic

losses in the concentrator. Tapping the inductor coil, which lowered the

impedance of the system, brought little improvement in efficiency. Although

some improvement could have been obtained by optimizing the design, it was

still questionable whether the needed power input could ever bt. reached,

Therefore, efforts were focused on overcoming the problems associated with

direct heating, and further 'ork with the flux concentrator was abandoned.

-9-

Figure 3.. Magnetic flux concentrator

2. 4. Present Apparatus and Results

Iu the final apparatus, the original inductor coil was used again, bet itwas placed in a bath of circulating oil (Fig. 4). The purpose of the oil was to

provide insulatio and additional cooling. The first tests were miade with

Sbell Diala OCI AX, which smoked heavily wbeA the graphite became red hot

adproduced a fire hazard. NoncbatmMosnocra heion

candidate, apparently has poor insulating qualities, because it permitted small

sparks to for•i at the high oltage end of the zoil and it decomposed into black

-f3)ibm-nts, possiy carb6=, wDi.ch after a short time produced breakdown

between turns of tfe coil The Ifiml choice was Kinney vacuum oil Kinlube 220,

which is hig•ly viscous at room tenmperatmre, but has a flash point of 5001F

and generally proved satisfactory after outgassing. The GE perficoricated

oils were considered, iut were mot used because, althouh they may- be ideal

for this purpose, the cost is prohibitive.

Is shown in Fig. 4 there is, in addition to the 'j-ycor tube o the cil -essel,

a quartz tube sepa-ratig the c fa from the graphite sample. For cooling, nitro-

gen gas wras blown, at 30 psi, through the narrow annular gap between the

tubes. A radiation shield, which consisted of a slotted tantalum cylinder, ras

inserted into the gap, but proved to be useless. The metal was apparently

heated by capacitive currents and gradually burned up. The quartz tube can

be replaced by a specially fabkicated thin-walled Mullite tube (Coors, Golden,

Col.o) that can stand temperatures about 400WC higher, but for ATJ-S graphite

this has not been necessary.,

The flow, rate of the cooling water through the sample is metered, and

the difference between inlet-and outlet temperatures is registered, through a

£ therminstor bridge, on an X-Y recorder. Examples of two tracings are hbown

in Fig. 5. Power input is raised gradually over periods of 4 to 5 mrin by

increasing the plate voltage from 3 kV (onset of oscillations) to -8.5 kV, withI ' minor retuning in between. This increase in plate voltage is shown to corres-

pond to an increase in water temperature of 28 C. At a flow rate of 5 gpm,

this temperature rise corresponds to a heat flux through the sample of 38 kWV.

At this point, fracture occurs and the generator is turned off automatically by

-I1-

HIGH SPEEDWATER

T U B E •- ---- T U B,, WCOR TUBE

•:, ~- BATH_ _-

PLASTIC

S•N2 LOWc m .4 -_ _ _2_

Figure 4. Present arrangement of graphitethermal stress test apparatus

-12-

L

150WAEOF

40i W i R I I I I

AT = 55-27 28"C

30i• HE'AT FLUX AT FRACTURE = L35- 28

= 38 kW

0 5I 100 150 2)O 250 300 350 400sec

Figure 5. Recordings of cooling water temperature

in two heating tests leading to fracture

-13-

the sudden clarage in lood so that the cooulan temperature drops instanta-

neously. Also, dependimg on the maer of fr-acturing, a certain am~owt of

Spillage takes place and the HlOW is svhut off amauallyr within sec~zds. The

temperature rises 2V.in tempora.i:IT. At a How rate of 5 gpm, water pres-

zvres upstream and downstream of the specimen are -28 amd 7 psi, respec-

tively,. These pressures are negjigbe compared with the thousands of psi

induced tR!malY.

The surface temperatvre of the specimen is measured with an opticalpyrometer ('Py-ro • ergenfie, ',% J.j either at the =per front surface wifth

the aid of a 4-5-devg mirror or on the side between the tur= spacings.. In the latter

case, a small correction must be applied because of optical absorption by the

oil. This correction ibas been obtained from the c-__r in Fig. 6. S-ie-on and

end-o= photograp&s Of apparatus 2nC samples taken duringe a heating test are-show-n in Figs. lia a=:d 77b. The brioghtness distribution of thwe specimen in

Fig. 7a indicates that the longitudinal distribution of the surface temperature

is molt uniform, but has a =aximum near .the. midsection.. Us value at the

mome•t of fracture has been measured, in two cases, to be between 19OO and

2000 -K Assuming the temperature at the inner surface to equal the water

boiliog temperature, we obtain a temperature difference between the surfacesof !600'K or an average gradient , l05OKlcm. The diameter of the sample

in Fig. -7b has been compared v'ath Oreat before heating, and %as found to have

exoanded bmil..,5p.

Ill twelve samples that were fractured with the apparatu were leak-

tested and carefully inspected for cracks before installation. Mhotographs of

four samples are shown in Fig. 8. The sample in Fig. 8b, -aIhich has several

lengthwise hairline cracks, is representative of several that were heated faster

(total heating time -2 mini) than the others. Ihe fast-heated samples seem to

break at -10 lower power and usually stay in one piece; whereas, the samples

heated normally over 4 to 5 min break into two or three pieces, as seen in

Figs. 8Sa, c, and d,.

-14-

17 /C>o,17 _ RIJN2/o / -

S13

Uj if-9'I7I°..

8 10 12 14 16 18 20TEMPERATURE x f00°C (AIR)

Figure 6. Temperature correction for pyrometer readingstaken through oil bath of apparatus in Fig. 4.Oil: Kinlube 220 of Kinney Vacuum Equipment Co.

,, -15 -

(a) SIDE-OGN VIEW (b) END-ON VIEW OF SAMPLE

Figure 7. Heating test in apparatus of Fig. 4

-16-

CI

(a) 72 MAR 17 (b) 72 APR 28

(c) 72 MAY 5 (d) 72 MAY11

Figure 8. Fractured graphite specimens

j -17-

&3 C6nclusions.• iid Recommendations

The- resulits of this first expioraory :phase-:have demonstrated that the

apparatus, and technique developed at the' Plasma Reis earch1 Laboratory can

produce thermal failure, in ATJ-S graphite cylinders. Since the load-matching

procedure was not carried to th6e optimum-an~d the full pate voltage was not,

required :for fracture, jheremis still. a, c6nsideraible poWf, 'r reserve, inthe. sys-

tern, which might be used'either to break ,str6nger types of graphite-,or to

improve conditions for difficult measuremlents.

Although the data obtained in this• phase- axe neither cOmplete nor

systematic, they already permit some tentative ýc6nclusions. First,. there i's,

no striking disagreement with the theoretical predictions reported~by W., R.

Grabowsky. Whereas 1the temperature gradients measured are.,,-25% lower

than those calculated in the -example. in Fig; '1, the failure limit is, exceeded

by the axial strain in that example by -•30%. Therefore,, there is no need at,

this, time to revise design specifications, based on that theory.

Second, the' rate of rise in power input appears to affect fractural

behavior, which means that the fracture criterion depends on the flight trajec.-

tory; therefore, a closer investigation of this phenomenon is recommended.

With the present self-excited oscillator, full power output could not be reachedbefore 90 see because the plate voltage must be raised gradually; however, faster,rises could be obtained by operating the installation as a power amplifier with

an available 5-kW Lepel induction heater as the modulator. This would allow

continuous application of full plate voltage, with the output determined by the

degree of modulation. It is expected that the transition from zero to full output

could then be accomplished in 1 sec or less.

In order to obtain a more nearly uniform temperature distribution over

the length of the sample, an inductor coil with higher turn density at the ends

is recommended to compensate for end losses by increased heating. Although,

for a fixed turn spacing, the distribution can be strictly uniform for one

temperature only, the coil would reduce considerably the two-dimensionality

of the temperature field so that simple one-dimensional calculations,

- 19- Preceding page blank

similar to those in Appendix :, could be applied with confidence. Also, it

would give more significance to the total heat flux measurements that, at

present, are averagesý of an-unknown distribution.

Finally, in order-to check more directly the theoretical predictions as

exemplified in Fig. 1, itwould be desirable to measure the axial and- radial

strains of the inner surface at the moment of:failure. For the specimens

tested, the absolute axial dilatation would be -0.5 amn. It could be, measured

accurately with an optical interference system that is attached to the coolant

tube stubs and combined with a fringe (pulse) counting. recorder.

Measurement of the radial dilatation at the inner radius is more -difficult

because it is smaller and interfered with by the coolant. It may be possible

to make the measurement by means of the photographic technique used'to

measure the dilatation at the outer radius (Fig. 7b). If the facility is operated

as a power amplifier, as, mentioned before, it may be possible to cause frac-

ture by shock heating and eliminate the need for water-cooling. In this case

the bore of the cylinder would bezome accessible to direct strain measurements%;

The feasibility of this idea can be determined only by experiments.

-20-

REFERENCES

1 1, P. J. Schneider, et al.. '9Design of Graphite Nosetips for Ballistic

Reentry". Paper No. 72--.05 presented AIAA 5.h Fluid and Plasma

Dyramics Conference, Boston, 26-28 3une 1972.

2. G. Babat and M. Losinsky, "Concentrator of Eddy Currents for Zonal

Heating of Steel Parts, " 3. Appl. Phys. 11. 816-Z3 (1940).

3. E. May, Industrial High Frequency Electric Power. Chapman and Hall

Ltd., London (1949).

4. Y. S. Touloukian, ed., Thermophysical Properties of High Tempezature

Materials, Vol. -1, The Mac.Millan Co., New York (1967).

5. H. U. Eckert, "Analysis of Thermal Induction Plasmas Dominated by

Radial Conduction Losses," 3. Appl. Phys. 41, 1520-28, (1970).

t• -21 -

atching of Graphite -Lad to Impedance of irf COillator

The rf hese 3- ,The Aerospace Corlration. is a tune-plate. tuned-

grid, self-excited oscillatr operating in or near the class B mode with four

GE 830 triodes in paralleL Each tube is rated for a plate current of 5 A. At

this current and at the maximum available plate voltage of 10 kV, an internal

resistance of -8001 per tube is obtained from the tube char. The internai

resistance of the heater is therefore

R_ - 20021 (1)

For maximum power transfer, R, must be matched by the exter-nal resistance

R e. Since Re results from a complex a-rangement and can be determined only

approximately and since a mismatch is much less critical if R > Ri, we aim for- e 1

R = 4001• (2)eAs indicated schematically in Fig. 1-1, R is formed by the resonating plate tank

circuit C R and the secondary or load circuit LzR2 if the small impedance

Sof the blocking capacitor CB is disregarded. The two circuits are coupled

through the mutual inductance M. The value of R is given bye

R Leff (3)e CReff

where Leff and Rfef are the effective inductance and resistance, respectively,

as seen by the resonating circuit. Their values are determined by the relation-

ships [3]

2 +2

LC CB

u01CM R2

?7"7

Figure I-1. Schematic of rf oscillator load circuit.Only one of four tubes is shown

28

Re = a,+• +•) ="

"wbere = u 'Th prPacrica lowser 1it• a sh gwemratorfraueacy is

believed to be abvai 1-t(~

DTsregazdig the effect of Rea freuecy. we use the ep

an T rhe r- ft dr ei± is take asand R~~~eff =3 •{2

The ircuplatin ourent Of the tn circ u a istam as lrtdb emsil

ULU0f(1)

Lef 1.6 xZ6- (19)

rWitpe (2) and (3), we then obtain for the tank capacitanceC = 009 pF (10)

and further LFef=6H(11)

and R lf = 3 100E (12)

The circulating current in the tank circuit is limited by the permissible

rf peak voltage U1, which should stay --10% below the plate voltage U.p

With U p max = 10 WV, we have U1 9 kV and the miaximum power dissipation,

which includes circuit losses, is

PmxZ 1 100 kW (13)e

-1-3- ;A '.

This ~ ~ ~ ~ * Go. i - ee I E W estwa"e Ibr b~e speciwsm is

Sectim ZýL

t nhe -=•tn =WLti

170 A (14)

The aistrapsam Ti e secsrfae rseen, ey tisonde gUapate - c, WWI

apfos im -e = 1L a = 10 cby tis chahe-oterize bow -2 ki

& 1. 1 56. e-- 10t a o r p oprandt e 6. U aX 1 0 tsie 1o

6=0. 16 evn16

and

- I1 (171)

are obtained0 Tbhe resistance laa seen by the voltage UZ induced ariund the

peripherry is

--

2 Edr0

For - -> 10, the variation of the induced electric field E: with r is closely

approximated by the power law r2

E =Ez (I'll ZT (19)Zr.

$The data in Fig- 11- 1 indicate that a miore~ appropriate mean value for a' wouldbe 1400 m~ho/cm. These data were obialned. ater the calculations in thisappendix had been made. Because of their exploratory nature and as t-enters only with the square root, a revision was mot considered worthwhile.

-2-4

M A

To >> s i wh e cWan seAtj 2 N, r-33

uliere N is trhe ••=ber of tias over the-lenth of the work piece. With

' 1 = I 1 = 170 A, disregarding end effects, we obtain for the =ber

of tMurs of the imanctr coil

NI = 210 16 turns, (24)

The value of L follows from the forn•.a or a coil of finite !ength [3]

1.36 x - (25)

Therefore, wL2 = 8. 5 X 10-2 z 10 R2., and it is permissible to disregard"R 2 . com ison v (,Lz)z2 in zqs. (4) and (5). It and L. are related

through

M, = SLzkz (26)

With Eq. (23) and N2 1, Eq. (26) yields

IA = N 1 z (27)

-'5

*4 isLC ("Z*6 S

1. r 2

pyc21. -~~s~ ?-l 1.7. itae

IcM~ etrl;o b "ysclA- -ic .-Hw

=1= 0 !ý &dytae aas rI c=zi IFrm-b1-6-ot i

Calexu~a~m of 32aa R FVII for

InSee sftate,, Lbe speci~c Uoses tF~e heaz gwmated brw C&=ic disý-

bemd low ama =ai be &iSregArdied.. dato is accomted for in tec bommury

cEui6m for tze omtr smrface.. 7The emergy EiaU.-e eqc!io;a com2sists,,theefoeof~ amt5 e &cUOx-Ing VU0 terms

r ar t - =ra

77se Varialioms GE thermma1 *r 2a~ electrical UT -r % imi

te~eraure fo grahte are slomsm in RFi. HI~ [4]. Whereas for or

a mcam Dralmee, Fr n3a be used vni-thout sewerelT affectimg the results, this doesnot secem yex-missible for X.. To line-arize the equationp, it is therefore

adranageoms to Introdbnce the beat comcbdcton Potential S as is common= %wth

gaseous paasmas U-4 S is defec-m by

S =fJdT (10

The em-alcation off Bq. (31) is shown in Fig.. H-2. For the -ariation of Ewith r, we use Eq. (19). Setting rIrz 2 -= x, we can write Eq. (30) in the form

I d (xdS 2.. Z2q (2

where q r2 16 for r2 16 > 2 [4]. The first integration of Eq. (32) yields

2- 2dS r 2 O"E-2 Zq +Z

X X - (33)

*Property data for ATJ-S graphite were not available at the time thesecalculations were made.

025 +2500

C)0 0

It41P

NOJO-D lo - t;0

005- 500

0 00 5W0 I00M 15W0~ 2500 3000 3500

TEMPERATURE, OK

Figure 11-1- Variations of ihe=.ai conductivity Kand electricai conductivity a withtemperature for ATJ graphite

I-319-2-S...... £• -.

A

400

* ICOO4D

TEMPERATURE, OK

Figure U-2. Heat conduction potential of AT5 graphite

-JI-3- .0

-5p=_-.0

The constant C is determinued at the outer boundary r. where x = I and

= C=( ~r 2 Z 1E22

=(9h: + -2qTz- (34)

Here., the heat flux is balanced by gray body radiation from the surface.

Therefore

2 - CZT4-- f (SZ) (35)-

The second integration of Eq. (33) yields

2- 2r 2 z •E2Zj

S+ r2q+) 2 x~q+ 2 = C Inx+C' (36)( ~(Zq+Zýz

After evaluation of C' at the inner boundary ri, where x = x. and

S = Si, Eq. (36) can be written

SS. +C In X r E22 F2 2 q+ 2q+2 (37)I xi (x i )

or, when using Eqs. (34) and ý35) and considering that the power dissipated

per unit length is

Zirr zFE 2 1P - 2 2 xi2q + (38)

-1

-i 2 1 2+f- X.1

2q+2 2q+2

)x

(n. - X (39)

31L

The function f (S?) in Eq. (35) has :been evaluated for - 0. 85 and is plotted

in Fig. 11-3. Writing Eq. (39) for the outer boundary x= 1 yields an implicit

equation for S2 that can be evaluated with, the aid of Fig. 11-3 so that-f (S2 ) also

is determined. S(x) can then be calculated from Eq. (39). T(x) finally can

be obtained from the function S(T) in Fig. H-I2.

Some examples of temperature distributions obtained by this method

are shown-in Figs. 11-4 and U-5. Figure 11-4 shows, the, effect..of frequency

for I = 1 kW/cm and an innier'surface temperature of 1000 0 C at r. = 0.4 cm.These conditions represent appkoximately those in the early tests- with

specimen (a) in Fig. 2. Results for~f = 1.7 1Hz are shown in Fig. 11-5;

ST. =.273°K,,P/1 = 3, 4 and 5 kW/cm, r. = 0.4 and 0.-63 cm are values that

represent conditions in the later tests. The curve for -- 4 kW/cm and.

r. = 0. 4 cm, in particular, is believed to represent closely the conditions atwhich fracture occurred, although a steady state may not have been reached.

in every test. The mean gradient is -1300°K/cm. It is remarkable i

that all curves show a nearly linear distribution, although the heat flux is

strongly convergent. This is caused by the strong increase in thermal conduc-

tivity toward the cool inner surface, which compensates for the effect of con-.

£ vergence. If this result is generally true and if it holds in particular also

for ATJ-S graphite, the situation is greatly simplified. Then the value of the

mean gradient, which is determined experimentally from the temperature

difference between inner and outer surfaces, also approximates that of the

local gradient at any radial position and makes detailed measurements or

calculations unnecessary.

-11-5-

.- p

10 69 K 01400

120~1000 20 0 102o2 0o 2800

800 2400,o/ -_,/ -- •2o/ "-

2000

Tk~ -116010-' 1600 10

,,4 04012

2 i 1000100 150 200 250 300 350 400

S2 caL/cm sec

Figure 11-3. Radiation flux vs heat conductionpotential of ATJ graphite

-" "33 -1%-6-

i I

I I. -I" ~1000 "

f 17M1I I P/t : kW/cm f: 17MHzf --- 0

• 500

0~

Ii w* I

' I!- I I- ,I I 0

0 1 2 3 4 5 10 15 19r, mM

Figure 11-4. Calculated temperature distributions in induction-heated ATJ graphite cylinder; low inputP 1 kW/cm, ---- f 1.7 MHz,-f --*0I

-"-7- 3

" I2500

I% Iii--'

<1 2 000 •" I I

>150

(I)

S uI-5P: 15000

I II

, , , ,,,I I 100

0 1 2 3 4 5 10 15 19r, mm

Figure !1-5. Calculated temperature distributions in induction-heated ATJ graphite cylinder; high input, f = 1. 7 MHz.Inner surfacd temperature 373'K; outer surfacetemperature determined by radiation equilibriu-

-11-8-