Torsional damping in pyrolytic graphite

Torsional damping in pyrolytic graphite

TORSIONAL (;ttlf (ieneral Atomic DAMPING IN PYROLYTIC GRAPHITE ITOMAS E. FIRLE Incorpot-.iLed, San Diego, (‘Aif‘. 921 12. I’.S..\. Abstract-7‘he d...

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TORSIONAL

(;ttlf (ieneral

Atomic

DAMPING IN PYROLYTIC GRAPHITE ITOMAS E. FIRLE Incorpot-.iLed, San Diego, (‘Aif‘. 921 12. I’.S..\.

Abstract-7‘he damping and shear tt~odulus c-ltattges of’ pyrc&Lic graphice wet-c studit by internal friction techniques in torsion in the IO-c,‘s frequencp range. ‘1‘11~ tettlpwatttt‘c dependence of internal friction 2nd tiroclulus defect was determined frotn abot~t 3)” i0 ?dWK under stable and reversible conditions. T\\o broad peaks were hu11t1 ;II I~i.~” ;11tc1 230°K. Correlating these peak temperatures with data f’rottt the 1iterarur.c atltl asslttnittg a thermally activaled process, f=/,, esp (- IIIK’T), leads to activation paranicLcra of’ 0.40 e\’ (log ,f;, = 1.5..5) and 0.58 eLr (log /,, = 12. 3), respecti\el). ‘The rcproduc_ilAe atnplitntlc dependence was explored, f’or the ~ttne tetnperaturc range, f’or strains f’i.ottt .- 10 ’ to abonL .5 X IV”. A wtnparisoti with data front the literature for graphites itti~l other materials by way of the (;rattato-l.uecke approac~h showa only ;I clualitarivc fit ittto tltcs ordering scheme but no definite break-a\lav char;tcterisri( s. 1. INTRODUCTION

devoted

on the basic dynamic mechanical properties of materials has been conducted primarily ott metals and polynwrs but also to a much st~~aller degree on carbott and graphites [ 1J. In tnetals, research of dislwatiott and poittt defect phenomena has resultcd itt a sufficiently good understanding of’ the fttndan~en~al mechanisms [2) to relate macrosc.opic mechanical behavior to ittontislic properties. ‘l%e presetit status of work on thy basic physical m~c~hattisms operating in graphite has been reviewed recently [3]. A rather coml~rehensivc study of dynamic mcc-hattical behavior of‘ graphites and carbons, which is a continuation of the work b,- the l’ennsvl\ania State University group, is in the l~~ro~~ ot being published[4, 51. The groups at Union (Ln-bide, Oak Kidge Natiottal I~abot~;~tor~, 1.0s .~lanios Scientific L,aboratory, and .Jet Propulsion I,aboratorv have Kesearch

i-\l’ot-k supported in part by the U.S. \Lomic cttcrgy ~~otttniission. C0ntrac.t A’I‘ (O-I-:I)-167, l’r(?ject ~\grecm~nt So. 17.

sottie

of their

cff~orts

10 basic, srutlies

A French gt-otil) has lakeit an exJ~eritnetita1 alq~roacli ~c‘ry 4itnilar lo rhc one developed b) our Iabora~or~ [6], oi-iginally for %vork on refi-ac torj b.c.c. :nct;~ls 171 antI atlapd for the wet-k on ln rolytic. ptphi~e. Ill this IX\J,tT, the ct\ ttatnic tttc’(.h;ttiic;tl

in this

field.

JwoJ>erties f’rictioit ettcrg!~

are being exatiiitied tcchtiicJues[X-IO]. loss

;uitl

chatiq

d~~et~tiiitied

as a furiction

ttic~~lianic;tl

stress.

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Our

ilt

friction

peaks

related

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itiLcv~ti;tl ittlt’t~ti~il

of LetnJ~w;it ure aritl

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Lo

cottsitlcrs a~rtl

rci;tx;~all), lie

att ecluivalence to the Bordotti 1111 argues peak. tfowever, relaxation l~:;ik5 obsc~r~~~l in b.c.c. metals show a diff‘crent l~lietiotnettology alit1 the piclure is I‘urthcr c~onrl~lic~atctl by the complexity of‘ atielastic~ rcsl~otisc for even simple pure isotropic metals 112. l3j. Our results are cotiiparctl \\.itl: those of other workers in rhc fieltl. \Ve stuclied l~vrol~tic graphire of cliflerent cottr(7 tti;ucri;il,

T. E. FIRLE

596

in a different mode of excitation (torsion rather than longitudinal or flexural vibration), and at a different frequency, and it is significant that our results yield similar relaxation spectra. 2. EXPERIMENTAL

APPROACH

2.1 Apparatw The apparatus in which the micromechanical measurements were made is essentially an inverted torsion pendulum. In essence, a specimen is twisted from its relaxed position. Shear stress and shear strain can be determined from the applied torque and the resulting angular deflection. From the measurement of the power dissipated during stress-strain cycles, the internal friction can be inferred. If the specimen is set into oscillation, information relating to the internal restoring forces that determine the modulus is obtained. The apparatus therefore has provisions to twist a specimen and to measure the input power, strain angle, and period of oscillation. An important feature of the equipment is that the specimen temperature can be changed over a wide range without mechanically disturbing the specimen. The basic principle of the torsion pendulum approach has been described [lo, when dealing with an 14, 151. However, easily deformable material, the actual apparatus is important and is discussed in the Appendix. 2.2 Specimens The specimens?_ used primarily in this study are of deposited pyrolytic carbon, deposited at about 2100°C and graphitized by annealing under minimal loading for about 70 min at temperatures between 3000” and 3300°C. The density is near 2.6 g/cm3, tThe specimens were prepared by Dr. J. White and characterized by Dr. J. Bokros of the Gulf General Atomic Metallurgy Department.

about 1600 A, layer spacing 3.35 A, and the Bacon[lG] anisotropy factor-> 13. The specimens were cut, using airabrasive techniques, into flat slices with a gauge section typically 2 mm wide, 9mm long, and 1.5 mm thick. They were held in the apparatus by fitted reactor-grade graphite grips. Each sample was installed in such a way that during the measurements it was twisted about the a-axis, which introduced sufficient shear stress on the c-planes to result in anelastic strain. The specimens were not given any special heat or surface treatment after fabrication and were not deliberately cold worked; careful installation procedures were used to avoid disturbing the annealed state. L,

3. RESULTS

AND DISCUSSION

Most measurements were made at an oscillating frequency around 16 Hz using single free decays. Amplitude dependent runs were made at room temperature to a maximum oscillating angular strain of 5 X low4 rad. The curves of internal friction and period versus strain angle were examined carefully for any indication of changes in the micromechanical state. Because of (1) the lack of time dependence, (2) the constancy of the low amplitude modulus, and (3) the reproducibility of the internal friction spectrum before and after room temperature oscillations, no change in the mechanical state of the specimens was indicated. Temperature dependence experiments were conducted primarily from liquid nitrogen temperature to room temperature. However, measurements above room temperature

were made but are only summarized

these runs did show dependence on measurement chronology and previous specimen history. The following trends were found for the above-roomtemperature experiments: (1) as the specimens are taken to progressively higher temperatures the room temperature internal friction decreases; (2) as the maximum below

because

exceeds 4.X’K, the room temperature friction rapidly internal temperature approaches an equilibrium value; (3) the internal friction as measured at the maximum temperature becomes time dependent (on a scale of hours) for temperatures 2 450°K ( - 175°C:); this behavior may be rc:lated to observed stored elierg)- release for irradiated material [4, 171. Koom temperature measurements (‘an be alfectecl by mild disturbances at lower tcnrperatures. F‘ol- some specimens, oscillation while warming from ii” to 3OO”K, even \vitli strain amplitudes of as little as - IO-“, 1room iIiternal raises the temperature f’rictioll value. This effect is indicati\,e of the sensitivity of’ the material to microstresses. J‘he results of various low temperature tlependenw runs are shown in Fig. 1 fi)r the internal friction and in Fig. 2 for the (orresponding period. The .reproducibility of the clata of Figs. 1 and 2 was established b) repeating the low-est amplitude oscillation run b\ itself from ‘77” to 300°K and then c-hecking the amplitude dependence at room temperature; the re-runs agreed \\,ith the

OSCILLATING STRAIN

c

I

5c

I00

I50 TEMPERATURE

I

200

250

i

i 300

(“K)

Fig. 1. ‘Temperature dependence of internal fi-iction with oscillating strain amplitude as parameter.

000

-

602 604

L

\

60.6 50

IO0

150 TEMPERATURE

200

7"O

I'KI

(OKI

results of Figs. 1 and 2 withill the incticatecl scatter. ~1‘0 permit easier clualitativc~ conparisoll with data where L‘recl~wnc~ ~3. tenperattn‘e are measured. the period has hcer~ plotted inc-r-easing do\vrr\\w.tl. ‘1‘11~ ;r~~gular strain amplitude Fvas used ils ;I l)lotting parameter lvith the val~res irlcliwtetl OII tllc graphs.

-Flie overall damping vs. telllpera(uw dependence is similar IO that observed 1,). others [l, 4, 1X-20]. ‘l‘wo broad processes are operating, separated hy the transition at about 2OO”K, and are also I-eflccted in the period vs. temperature curve. The results show two regions of tlifYei-ellt temperature coefficients for the specimen stiffness. l‘he peaks in the internal f’ric.tion spectrum show an associated characteristic iti the period versus temperalure response. (It is precarious to interpret the peaks in an internal friction spectrum as mechanical relaxation peaks without ha\:ing observed the proper temperature dependence of‘ the period. A complete reversal of the stiffness vs. temperature behavior nlav be caused b)

T. E FIRLE

598

dislocations that are initially depinned and then immobilized, i.e. pinned at higher temperatures. This type of unstable, irreversible, behavior was not observed by us.) The temperature spectrum of internal friction and period shown in Figs. 1 and 2 indicates that the peak temperatures increase with increasing amplitude similar to the behavior observed for mechanical relaxation processes in metals. If a single relaxation process is assumed in a standard anelastic solid[21,22] then the internal friction is found to be [23]

T (DKI 350 300

250

200

150

100

-I11----0 . * . x +

R E.TAYLOR (THESIS 1967) TURLEY (TAYLOR’S REEI BLANKENHORN (TAYLOR’S REF.) TSUZUKU-SAITO lJ.APPL. PHYS.OAPAMl TSUZUKU-SAITO (REVIEW. IN PRESS) l TSUZUKU (CARBON 19641 i . 0 BAENNAN-KLINE (CARBON 1967) THIS STUDY

(1) f* = 2rf = angular oscillating frewhere quency, and T = relaxation time constant. Thermally activated movement of atoms is assumed to be of the form

where TV-’ = frequency factor, H = activation energy for the process, and T = absolute temperature. The internal friction will become a maximum for the condition UT=

1.

(3)

Therefore, at a given oscillation frequency there will be a corresponding temperature at which a maximum in the internal friction may be observed; i.e. an internal friction peak exists. However, rarely do internal friction peaks satisfy the criteria for a single relaxation process except for the special cases of, for example, Snoek [24,25] interstitial peaks. If an assumption can be made as to the frequency factor,&, = ~~-l, which is of the order 101’-10’4 for dislocation interactions [‘i, 111 and of the order 1O’j for point defects in metals, an activation energy can be calculated. In Fig. 3 we have compiled experimental

_ -.i_i_2

__j

IL___-_

3

4

5

6

7

8

9

10

1000/T

Fig. 3. Log frequency

vs. reciprocal peak temperature.

data of various investigators for irradiated and unirradiated material. The data points for a given frequency scatter .for many specimen materials reasons, e.g. different ranging from glassy to polycrystalline carbon to nearly perfect pyrolytic graphites, different amplitudes, methods of material preparation, and modes of excitation. Following the Taylor analysis [4,5], in Fig. 3, data are grouped that appear to belong to the same process. Taylor’s LY (T - 260”K), P(T - 165”K), and -y(T - 340” K) peak regions are plotted, leaving out the very low temperature ( < 60°K) peak and the 6 peak he finds at - 440°K. The grouping of our results at f‘= 16 Hz, which show a broad low amplitude peak at 135’K, with the p process appears to be supported by the 3Hz data of Turley,? although the latter data may have been taken at amplitudes > 10P6. It appears that our resulting fit, as indicated by the solid line in Fig. 3, is reasonable for TAs cited in reference

[4].

TORSIONAL

the

DAMPIN<;

IN PYROLYTIC:

p process.

The fit gives a value of log may be indicative that a point defect type mechanism is operative. ITsing the indicated fit, we find for the activation energy of‘ the p process. Hti = Cl.40 t OC5 r\.. ‘I‘he assi~rimctit of our %O”K peak data ib rtitt ~lcar. ‘l’n~lot-[4] has suggested that his ct process is similar to the Uordoni peaks ol~sierwrl in f’w metals. a~lccw-dingly, he cxamittcd the behavior of‘ his a peak data ag;titisl tlltp t’caturw definitig[l 1, X] the l~ordor~i peak. It is difficult to assign our XiO” peak data to his N process primarily fbl I\\-(> rt’asons: i 1) out- data would f’orc-e the c~owlitsiort that the peak temper;3turc is I twluenc\independent, and (2) out data I3hO\\ :tn amplitude depettdcnce of‘ the peak tctnperatuw. Assuming that the (Y l”‘“c“‘s\ is tcrtlpel’ature act iwted \Vlt II log /(la ~otticwh~r~ t)etween I’L and 16, the pro,ic*c-tvtl cy peak tentpet-aturc ti)r our vihratitig I’t~~~tt~t~cv of 16 HY predicts 7;, to lie bethveen IXO” arid L’IX”k. which does 1101 sc’en~ to he the case fitr our daa.

f,,fi= 1.4.5,tvhich

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to

1ww1~.~~

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Olll‘

.l’tiese

L’3~” p4cs

prominenr in strcttgth af’tcr irradialioti and arc quite sensitive to ~~ultqtietit tctnpcrature atttieal. Lsirig the l)r’irratIiatiotl data (solid circles in Fi::. 3) ;ind our ‘2X% peaks, a y activation process ix ot)taitwtl \\.hich leads to log /,,, = I?*.? \vith att ;tcti\:atioti etieqgy 01’ HY = O*.%IT 04f;

CL..

5’W

1;RAPHI~I‘E

If’ all processes f’ollow the equation (2) one can sutiiniari~e as shown in -1’ahle I. The limits the ac-tivatiotr energies arc Itazerl log /,, v&c. (II‘ extremes for th tltr.

data

compiled

in

Fig.

3 ate

rclat ion of’ the results ittdicatcd in ott ;t single $1” cad 01’ t;thcn,

otw

tor the pl‘o”“~s I,alltls. Ior III< 0t)tailts high ai4 low temperature liiriitr\ rcslwclivc~h~: f-I? = 0~6-I i.1’ and 11~5-1c\’ t\,ith log ftbY= mtl I”*X, ;ttd II,{ =z 0~3!~ atttl 0. 43 VI’ 11-i lvith log- /,,/< = I-l.6 ait(1 Ifi.!).) I‘lre L~IIC.CI‘Iaiiit!. hgc

itt

/,, wot~ltl,

of’ (x)Lttw.

dc~~t~~x~

il’ ;t

trqt~et~y

sltif’t cotrltl IK tn;~(l~ 011 ;t tq)rehetrt;ttive spec‘itrtctt, /)I .\//a, ;~tt(l tot. ttjc s;ttne tnotlc of t.il)ratioil. ll is \igtti ticail that sttclr tlivtiw data t~*lww~tttiiig tlifl~~r~rtt c~otttliliottc atld matwialb (‘ait 1)~ gt,ottlw(I ;tt alI.

‘I’he tlytt;mtiC nlotliJltls clcfcc.t I.;111 i,e detcrmitted f‘rotlt the pcriotl of oscill;tlioit arid the wav it ~lia~t~es bitlt 41rititt ;tntl)lirittlc o1‘tctll~watLlt’e.

T. E. FIRLE

600

f=

state, measured frequency, G* = effective shear modulus, and G = reference (elastic) shear modulus. If the frequency fr can be determined for a state where the total strain is only elastic at the measurement temperature, i.e. neither dislocations nor point defects are mobile, then G is the elastic shear modulus and the quantity expressed by equation (4) is the modulus defect. It should be noted that f can be a function of both stress and temperature, while Jr is stress-amplitude independent but contains the contribution of the temperature dependence of the elastic constants. If the absolute modulus defect cannot readily be determined, as is the case for graphite, a reference for intercomparison of the specimen can be chosen by extrapolation of the frequency vs. temperature curve to 0°K and the frequency vs. strain curve to E = 0. A direct intercomparison of the temperature dependence of frequency for different samples is not very useful because of geometry factors, excitation mode, etc. The quantity that is more descriptive of the intrinsic materials properties is the change of the modulus with temperature (or some other variable), i.e. the modulus defect. The modulus defect calculated from back extrapolation neglects any dislocation relaxations that may exist at temperatures lower than those for which data have been reported. These dislocation relaxations can lead to an error of a few per cent in the absolute value of modulus defect at O”K by analogy with the work of Alers and Thompson1271 on highly purified copper single crystals. This procedure, however, wili not invalidate the overall temperature dependence of the modulus, which is of primary interest here. From Fig. 4 it can be seen that the specimen used by Brennan and Kline[l] had the lowest anelastic strain component, i.e. was most highly pinned. This type of representation permits some direct comparison con-

cerning the relative amounts strain contribution due either materials, irradiation, heat working, etc.

2

TWS

4

RE

STUDY

TAYLOR (THESIS 19671

50

*

of anelastic to different treatment,

100

150

200

250

300

T (“Kl Fig.

4. Temperature dependence of normalized modulus defect.

Both the internal friction and the period of oscillation have been seen, in Figs. 1 and 2 to be amplitude dependent at the lowest temperature in the study. Internal friction is plotted in Fig. 5 vs. the logarithm of the oscillating strain amplitude with temperature as a parameter to show the amplitude dependence in more detail. An amplitude-independent region has not been reached, even for strains of about 5 X 10U7,

‘4oor----‘“’ -

!

f =16Hr

1 1

0

! ,o-7

L--.

*

*

i_

-_i._--_i_LL_i___I_iij

6 *,+i OSCILLATING

10-5 STRAIN

10-4

AMPLITUDE

Fig. 5. Amplitude dependence of internal friction.

‘I‘OKSl<~NAL

DAMPING

IN

at .N”K. An extrapolation to E = IOF’ indicates a nearly amplitude-independent value of‘ Q-’ = 110 X IO-‘. The background damping of the apparatus is estimated at about 20-30 X I OF”. The strain sensitivity at these low applied stresses is indicative of‘ I-c~wonably good pyrolytic graphite, implying that sufficient dislocations are available to give anelastic strain and that the specimen is I’ree enough of impurities for them to traverse reasonable distances. lioom temperature data of‘ internal lrict ioll vs. the logarithm of‘ strain amplitude are shown in Fig. 6 along with data determined 1)~ ‘l‘suzuku [ 18, I!)] on his pyrolytic graphite, th;it was given a high-temperature treatment. .~~ltliougli his measurements were male in tl1(h longitudinal mode at audio frequencies, Iwth the I’nIIctional dependence and amplituclc are similar to our results in torsioii at I6 f-l/. KeceIit work by Merliri et cd. [28] \vorking also with a torsion pendulum, c~)uld not reasonably be incorporated in Fig. Ci sirIce their principal alnplitude rangca lies alwvc ours. However, they find very steep anrplitude dependence and high internal I’rict ion valties, particularly for the stress a~rnealcd pyrolytic Cgrapliite from Carbonel,orraine. .\mplitude dependence analysis has been tisctl irl attempts to relate experimental

l’YKOl~\‘-I-1(: (;R.-\PHI7‘k

Ii0 I

results in metals with theoretical models, ill particular, the Granato-Luecke ((i-1.) theory [%, SO]. Tsuzuku and Saito [S, 18, 201 have attempted to obtain a fit ot’ their data f’or various carbons and graphitc$ I))- wa> ot’a G-i, plot, namely, aniplitud~~ dependent intwnal triction times strain amplitude plotted against reciprocal straits iniiplitiIdC. Disa~~eenicnt exists betw.c~cw ‘l‘ruzuku and Saito’s results aiid the nIc’;i~IIrc’itic’nts of klerlin it (11.[28] who filld no ~tr;~ight-lilrc, relation o\wini anil~litutle rdilGgc f’roni - 1OF to 4 X IW” fiji- their sj)ecinlClls 01 graphite, Ilucleal~ p);roIyti(~ ~~;1I~1~oti. or pyrolytic graphite. IlIste;l
G-1.

type

T. E. FIRLE

602

:

;;“,~;A;“G”,“,P;~;~i

MERLIN

ET AL.



GLASSY,AMORPHO”S

CARBON

(TSUZUKU

1

;;$y,‘“]

TANTALUM

CRYSTAL

0 “NPlNNEO TUNGSTEN CRYSTAL 0 BORON FIBERS (FIRLE 1968)

,,-I: : 0

/

2

3

4

5

1967 19641

(CHAMBERS

19661

(CARPENTER-BAKER

6

7

6

19651

9

IO

(< x IO?

Fig. 7. Granato-Lxecke plot for various graphites and other materials. a high temperature anneal [7]. The pyrolytic graphite shows behavior similar to that of unpinned pure tantalum and tungsten [34] and a bol u I fiber [35]. The graphites examined show little tendency to exhibit simple pinning breakaway behavior, but irradiation mly bring this about. 4. CONCLUSIONS

The existence of a number of broad damping peaks with associated modulus defect has been confirmed for pyrolytic graphite using internal friction techniques at low frequency in torsion. Comparison with results obtained by longitudinal or flexural vibration measurements shows that the nature of these peaks is basic to graphite as such; they exist in graphites having different structures, impurities, and fabrication histories. From other work, it appears that dislocations, microstructure, and point defects have

anelastic interacting roles in determining strain behavior, but some can be identified by internal friction measurements. Two damping peaks were found: one has an activation energy of 0.58 eV, assuming log fo = 12.5, and the other has an activation energy of 0.40 eV, assuming logf, = 15.5. Internal friction data on pyrolytic graphite fit qualitatively into the phenomenology developed principally for f-.c.c. and recently for b.c.c. metals. Since the peaks are generally broad, it is essential to conduct experiments over a wide temperature (or frequency) range. An ability to make in situ, wide-range frequency shifts in the same excitation mode is necessary to identify separate mechanisms contributing anelastic strain. The micromechanical state can easily be disturbed unintentionally. Therefore, for pyrolytic graphite, as for metals with high dislocation mobility, the determination of the amplitude dependence of both damping and modulus is essential. True mechanical relaxation peaks and associated periods of oscillation are stable with time, number of cycles oscillated, and temperature cycling. The peaks at 135” and 250°K satisfy this condition. Both the internal friction and period were found to be amplitude dependent over the entire temperature range studied. Pyrolytic graphite shows amplitude dependence into the 10m7 strain range at 50°K. Annealing effects can take place even at room temperature after small oscillations ( - 10m5)at lower temperatures. From a study of the amplitude dependence of imernal friction it was found that pyrolytic graphite fits qualitatively into the ordering suggested for metals by a Granato-Luecke type approach but does not show the sharp breakaway required to give a fit with the model. Acknowledgments-The author wishes to thank Drs. J. Bokros and R. J. Price for encouragement during the course of this work; Dr. J. L. White for making the specimen material available;

TORSIONAL

DAMPING

and Dr. G. W. Hinman, chairman of the Physics Department, for making this study possible. Dr. .J. D. Diefendorf of Rensselaer Polytechnic Institute made valuable suggestions for the specimen fabrication and characterization. Dr. R. E. Taylor, now at Purdue University and Professor ‘I‘. rsuruku of Nihon University, Tokyo, generously provided some of their data prior to publicarion, and stimulating discussions were held with Dr. B. T. Kelly of UKAEA, Culcheth. Thanks go also to Dr. .J. H. Filloux and Mr. H. H. Moeller f&r their assistance in development of the apparatus and instrumentation. Past association with Dr. K. H. Chambers while investigating refractor! b.c.c. metals has been valuable. Special acknowledgement is given to Mr. H. Harper, who made the measurer&nts and carried out much of the data reduction. The reviewer’s comments and suggestions have resulted in a considerably dift‘erent and better manuscript; I appreciate the assistance he has given me and the service he hits rendered the readers.

REFERENCES I. Brennan ,J. .J. and Kline I). E., Carbon 5, 181 (1967). by W. P. Mason), 2. Physical Acoustics (Edited Vol. III, Pt. A. Academic Press, New York (1966). -1‘. and Saito M. H., In ~~~~~t~ and 3. Tsutuku Hyics qfCnrbon (Edited by P. L. Walker,,Jr.), \‘ol. 4. ht. Dekker, New York (1968). ,4. ‘l‘aylor R. F,., Ph. D. thesis, Pennsylvania State University (1967). 3a Taylor R. E., Kline D. E. and Walker P. I,.,jr., 8th Biennial Carbon Cov$ Bz(faEo, New Yod, June 1921, 1967, Paper M 138. lib ‘Taylor K. E:. and Kline D. E., Carbon 6, 749 (1968). 6 Firlc Tomas E., General Dynamics, General Atomic Division Rep. Ivo. CA-8214 (1965). 7. Chambers R. H., In Physical Acozlstics (Edited 1~) W. P. Mason), Vol. III, Pt. A, (Ihap. 4, 1.‘. 123. Academic Press, New York (1966). 8 Zener (:., Elnsticity and Anelasticity. University of Chicago Press, Ghicago (1948). !I. Nowick A. S., In Progress in Metal Phy,sics (Edited by B. Chalmers), Vol. 4, p. 1. Pergamon Press, Cjxford (1953). C., In Modern’ Research Techniques in IO. %ert Phy.s~&a~i~~et~l~ur~, p. 229. Am. Sot. Metals, (Cleveland (I 953). II. Niblett D. I-I.. In Phvsical Acoustics (Edited bv W. P. Mason), Vol. iI1, Pt. A, Chap. 3, p. ‘i’i. Academic Press, New York (1966).

1:AK Vol. 7. NoS--F

IN PYRC)LY~I‘l(:

fio:3

GR.L\PHITE

R. H. and Schultz ,J., Acta Mrt. 10, 12. Chambers 466 (1962). D. 0. and Holmes D. K., ,f. [email protected] 13. Thompson Phys. 30,525 (1959). 14. Nielson 1,. E., Rev. Sci. Imtr. 22, 690 (1951). 15. Butera R. A. and Gaig R. S., Kev. Sci. Instr. 37,401 (1966). Chem. 6, 477 (19%). 16. Bacon G. E., J. A#. .J. H. W., In Radiution Damage in 17. Simmons Grafihitc, p. 172. Pergamon Pres?, Osfitrd (1965). 18. 7suzuku T., Curbon 1.25 (1963). 19. Tsuzuku T., Carbon 1,51 I (1964). 20. ‘i’suzuku T. and Saito \I., ,I. [email protected] Phy,\. ,/[email protected] 6, 54 (1967). 21. Barry A. S. and Nowick 11. S., In f’hv.+cll /Icttusiics (Edited by W. I”. MaSon), 1-01: III, Pt. A, p. 1. Academic Press, New York (1966). 22. Nowick A. S., In Infevrlcll Fraction, Dnvnping, and Cyclic Plasticity, AST>I Publication No. 378. p. 21, AS’TM, Philadelphi;l (1965). 23. Mc(:lintock F. A. and Argon A. S.. In /!l&unicnl Nehmior of Materids, p. ,177. ;\ddisonWesley, i,oncl& (1966). “4. Snoek.1, I... Phy.sica8,711 (1941). 25. Ikslrers I). N.. In A&*anrer in NIaterials Re,searrh (Edited I>\: H. Herman). Vol. I. p. I!#. Intcrscience, New Yorh (1967). 26. Niblet I). Il. and 12:ilkh ,J., .4diU?/. I’+. 9, I (1960). 27. Aiers G. A. and ~l.~lonll~s~)n II. 0.. j. ~4~~~~~. I’@\. 32. 283 (1961). 28. \feriin .J._ Gobin P., Jorquct (;. and Kapptqlcau ,J. ,,I. h’ucl. Mater. 24, JO0 (1967). 29.

30. 31. 32.

33. 34.

35.

(;l-allalo

A.

ar1tl

I.ueckt*

IL.,

,I.

A/q/l.

/‘/rys.

27, .585 ( 19%). (;ranato A. and Luecke K.. ,I. /ij+,. P1~v.t. 27, 789 (19.56). Jenkins (;. XI., Brit.J. ,4p,b/. r’!q. 13, it0 (l!ttZ?). Jenkins (;. M. and Williamson (;. K., ,I. .Ippl, &slys. 34, 2837 (I 963). Jenkins G. Zl., Williamson C;. K. and Barnet J. l‘., Curbovz 3, I ( 1965). <;arl>etlter S. H. and Baker t;. S. Aclrc ;IIe/. 13, 917 (196:i). I;ir-le .I’. E., ,I. [email protected] f’hw. 39, 283!) (1968~. APPENDIX

As

show1

specimen tube,

ill

Fin

2

*he

is -‘__

called

specimen torque

is clamped transmitting

to the end of‘ a rigid tube, the drive tube,

604

T. E. FIRLE

which is suspended from the top by a fine tungsten wire, acting as a lossless pivot. The upper end of the suspension wire is attached to a rocker arm, which is supported on a knife edge. The opposite arm is used to counterbalance the weight of the drive tube assembly. Using an appropriate counter weight the specimen can be unloaded, although in practice a tensile force of less than has been 100 psi ( - 7 X 106 dyne/cm2) maintained to provide lateral stability. The desired driving torque is applied via magnetic coupling from air core coils to high permeability magnets mounted symmetrically on outriggers on the drive tube. An external power supply (not shown) controls the current through the coils. It can be used in a loop of a self-excited oscillator system. Operation may be in a number of modes, two of which were used for these experiments: (1) bringing the specimen to a given strain amplitude and then letting it ‘free decay,’ or (2) keeping the input power constant and measuring the resulting strain amplitude. strain amplitude is The total angular observed by a very high sensitivity optical lever system?. The strain readout is achieved by reflecting a light beam from a mirror attached to the drive tube and detecting any angular deflection by a set of differential photocells. The electric signal, analogous to the rotational strain, controls the torque amplifier and is used for instantaneous strain indication or digital data printout. From a measurement of the period of torsional oscillations the frequency is obtained. Simultaneously the oscillation amplitude is determined. The recording and data handling system permits analysis of both internal friction and modulus as a function of strain amplitude from a single free decay. Thus, changes in the micromechanical state due to

tFor details, request Gulf General Information Sheet on Optical Lever.

Atomic

COUNTER WEIGHT

SUSPENSION WIRE

Fig.

8. Schematic representation torsion pendulum.

of inverted

the measurement itself can be readily detected. A liquid helium cryostat and furnace thermometry, appropriate system with controllers, and recorders provides continuous coverage over a large temperature range. This permits in silu measurements of internal friction and modulus as a function of temperature while amplitude measurements are being taken. Such measurements are possible

Gnte the time constant for the specitnen f’rw deca), is much smaller than its time rate of’change with temperature. ‘l‘he torsion pendulum system is supported ott an isolation system to avoid spurious excitations f’rom man-made and microseismic noise. PIlic pendulum portion is Itc)t~setl iii a vacuum and gas exchange UK losurc to eliminate drag effects due to the air and to prevent elects due to humidit\, oxidation, and condensation while allowing good heat transt‘c~r to the specimen.

ble to electrically simulate a knowlt amount ‘external I‘riction’ that acts like a hrakc. the other friction

extreme (vet-\; high

is the case of high damping-

rapid

of At

iltterttal tlrcxy):

here a knowA, constant amount of elierg) is supplied during the dcc;i\z. For both c’as;c’s the ttieasur~ttictit resolution is improv~tl I)\ the itlcreased ttutnher 01 oscilfatiotts tvttltitt r;tti,gc. lit the ritc‘ast1t‘c’a gi\,eri atuplitudc mcnt ptxmxtut-es outlined ahove. 1tici \lxhc.inxn itig

is ttrst

brought

to 2 ptxwlec~tetl

05~ illal-

Ic\.el; internal f tic-tiott and modultis are then mcasurcd as the amplitude ~N;I\ \. It is essrttrial lo ktiow if’ tltc spcscitt;c.tt’s overall tiicclianic;il state (lialiges. .l’lti\ i\ detected I)! tnottitoring tltc tint. c1cpct~tfcttc.c~ of the tnodulus alit1 itttc’t.tt;il fric~rion. ()Itcli this is cotinf)itied with atnf~li~utl~ tlep~tttl~~tic (8 tnea~ur~m~tits t,v using I tic ‘cfrivett’ motl~, whet-e the ittpul ponder is Iivltl cx~tistattl. .l.tlc power necessary to sustain owillatiotts at ;I strain

‘1‘11~ in[crttal f’riction and modulus detect mcasttretttents \verc tnade in torsion at IOTZ f’tquc7tc~ie4 in contrast to flexural, Iorigi-tutlitlal. or ~cfto techniques, which range f’t-c,111 the audio t’requencies through ultr;tsotiics ittto the niegac-ycles. -I‘lle iltternal f‘riction can be determined in :I I ~utnber of’ \~a\ s. l‘he usual method consists given atnplitude is c;tlihr~tt~~l using 2 aitlglc of‘ setting a specimen into oscillation and then L’ree-decav. ,\lic.t-otnec.l1;1~~i(.~~l state ( lidt~gc~s ohscrvitig lhc decrease of oscillating ampliare thus Lqed to tlte itipnl potvet. rcyttirctl tttt 1~. Gth time. From the amplitude decay, to sustain constant aniplittitfc oscillariott~. c~;Alcti ft-ce decxy. the logarithmic decrement fill teclitiicfit~s cat1 1x5 ttsctl ci(trct isoC;III tw okrittvd, whiclt, for low amplitudes is thermally. or with the tetnprr~~tttre chatlging f~t~of~ot~tiott;il to tlie internal friction. The ilt ;t delinite IV;IV with titw, c’.g. liti~at~l~, l’li~ sItcar_ modulus GII~ be derived from the simul1attcT is ;t vcq &~nvettiettl \~a\ lo dct~~rtiiit~c tatteotrs mt’xuwtttent of the period of the intcrtial f’riction ~p~~~lt~utn il the littic osc~illatiott. rcquitwl lo mc~isurc ititt’t.ti;ll IricTiott ;itj(f \lore important than the cleterminatiot~ of modulus is shot-t, and the, tit;gtiiludv 01 1Itcsc the absolute magnitude of these quantities quatttities does not ch;~tigc ttitt~~li itt tlic is tlicb ahilit) to measure any small chattg~s cot.t.esf”)tt(fitig tenifxxit uty ittterv;tl. I+ that occur. l-he ntore obvious changcas at-e t\t‘rc‘tl the tticixitiiuni atttl mitlitttunt osc-ill;tI)rottght about II)- externally applied mec.hanitiotts ol’ t~cpeatcd l’t-re t1ec.1~ ,. ;I lxge ~tttttll)~t. (21 stresses, temperature cvcling, exposure to of’ mtplitudcs can 1~ sclcx lctl foi \chic~lt tljt* tlifferctrt anthicttt gases or liquids, exposure itttertt~tl Iriction and ttiotlt~l~rs \;tlur~ c;~tt IX% l(! it~r;ttliatioti, etc-. More advanced tnocl~~s ohtaitictf. I’tttts, front ;I \ittgIci c.\f)c.t.ittlr*ttt 01 opcratiott werca developed. The cn\&pe through ;I large ~etitfwratttt~~ ~‘;~ttg::(x. 1II<* 01 sue-cessivc strain amplitude maxitrt,~, the attiplit utlc cl~~pctidenct~ 101~ ;1tt\ :gibclt I ICC’ tlcca) nlotk, is used for calibration and tctnpct~ature can Iw c~sltxl~YI I)\ ( I~OSS-plot t-t~f’crewc \\:hetlcver possible. However, \vith attalvsis. ;I I-~a1 spcc-imctt under various operating cottditiott>, tlte mechanical response can t-:~ttge widelv. For very low internal f’t-ictiott, ,\ coml,inatioti block atttl How tfiagrattt 1%hit h Icxl\ to long decay times, it is pef’ct-a(I;ig. \I) SIIOM~S the c.ssctrti;tl features of‘ the

606

T. E. FIRLE

PROGRAMMER -START/STOP -CYCLE AVERAGING

SCOPE

FULL WAVE RECTIFIER

HELMHOLTZ COILS

VOLTAGE TO FREOUENCY CONVERTER

-

‘““‘““““r”“’

Ed=E+-kc7

au BAR

STABILIZED DC SUPPLY 20 TVRN POTENTlOMETER MlNIJS ZERO-PLUS STEP BIAS OPTION

MAGNET

_-

ANGULAR POSITIONING REFERENCE

RESISTANCE THERMOMETER

L&N K3 POTENTIOMETER -READ AN0 BUCK TEMPERATURE-

JUNCTION

VOLTAGE TO FREOUENCY CONVERTER

I

+

I

CTEMPERAT”RE

-

dPERlO0

I

Fig. 9. Block

and flow diagram

for essential

torsion

I

COUNTER

COUNTER

COUNTER -

QAMPUTUDE

I

pendulum

I

instrumentation.

-

TORSIONAI>

instrumentation I’arious

and

linear

to angular

rotation

components,

of the

highly unit,

each

signals

are

pair

linear, high-gain, amplified differential for

a programmer, pulses

that

Inen

oscillations.

which digital

ca11 be

period read

printout.

the modulus

Ggnal

and

of specicounter

oscillations.

recorded

information

the strain rectified

is stop

on

the is of‘

photocell

signal

amplitude. and

The

voltage-to-

For

range

can

be covered

optical

by switching

lever sensitivities.

through

resistor

or

input

temperature

a controller

regulates

specimen

Helium

to

is possible.

controlled

to the

can be which

resolution

precision

gas

chamber

pressure

is used as a heat exchange

at

reduced medium

to the specimen. Very

low can

frequency be

made

01

creep

using

hoI/. coils. fixed,

‘l’he

current

corresponding or

be

desired mechanical support

tube

for

tion,

or for balancirkg The components. when

can

curves fractional

be

from

driven

drive

controlled

working

of

01 A

for the

and can be the

specimen

out large Helmhob

with a periodic

used

to generate

very

low frequencies

cycle range.

stress

;I varic.ty functiorls.

positioning

(in torsion) current,

to

driving

is servo

it! sifu

be held

a constant

programmed angular

stable,

current supply, IO a set of Helm-

ca11 either to

stress-bias

measure-

a highly

positive-Lero-negative d.c. which controls the current

strain

various

temperature

winding.

recorded

printer as the A large dynamic:

liquid

or a carbon

measurements,

power

measurements

same line on the digital corresponding period data).

the

a germanium

furnace

used

011 the

for

either

higher

isothermal

profile the

permits

although

counter readout strain amplitude

are

where

thermometer

routinely

frequency converted. A results which gives precise (which

is measured

except

is used. The temperature information recorded bvith the digital printer,

bias,

defect.

607

temperature

range,

meuts

using

and its changes or for calculations

differential

is full-wave

start

of these

The

It controls

number

or the modulus

is llsed to measure

its own signal

specimen

thermocouples

O.l”K

output

electronic

and/or

This

amplified

in a selfThe

amplifier.

emits

An

optical source,

drives

d.c.

gate a selected

vibration frequencv used either directly The

lever.

(;RAPHITF.

resistance

specimen

of functions.

which

the

helium

photocell

a number

dc~ermines

analogous

light

of photocells stable

used

by

housed

the optical

‘l‘he

system.

upper

stabilized

IN PYROI.YTI(:

photocells

to its lower end. The

photodetectors

contained

silicon

electrical

end with respect

from

handling

sets of differential

provide

and

data

DAMPING

c3-eep coil f’unc-

stress-s,tmin into

the