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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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d. SAMSO-TR-72-27510. DISTR:rUTION STATEMENT
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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-