10. G . A . Gogotsi and G. N. T r e t ' y a c h e n k o , "A method of tes t ing br i t t le m a t e r i a l s in a steady t e m p e r a t u r e f ie ld , " in: High T e m p e r a t u r e Strength of Mater ia l s and Design Elements [in Russ ian] , Naukova Dumka, Kiev (1965).

11. G . A . Gogotsi , A. G. Gashchenko, and N. N. Radin, "A cooler for s amples in heat r e s i s t ance t e s t s , " Inven to r ' s Cer t i f ica te No. 394,707, Publ. Aug. 22, 1973.

12. G . A . Gogotsi , L. A. Kozdoba, and F. A. Kr ivoshe i , "Determining the heat r e s i s t ance and t he rmophys i - cal c h a r a c t e r i s t i c s of corundum m a t e r i a l s , " Probl . Prochn. , No. 1, 92-96 (1971).

13. V. Dauknis, K. Kazakyavichus , G. P ran t skyav ichyus , and V. Yurenas , Invest igat ion of the Heat R e s i s - tance of R e f r a c t o r y C e r a m i c s [in Russ ian] , Mintis, Vilnius (1971).

14. B . A . Boley and J. H. Weiner , Theory of T h e r m a l S t r e s s e s , Wiley (1960). 15. G. K a u d e r e r , Nonl inear Mechanics [Russian t rans la t ion] , Inos t r . Lit . , Moscow (196!). 16. V . M . Panfe rov , "The theory of e las t ic i ty and the deformat ion theory of ductility for solids with different

p r o p e r t i e s in c o m p r e s s i o n , tens ion, and t o r s i o n , " Dokl. Akad. Nauk SSSR, 180, No. 1, 41-44 (1968). 17. G . A . Gogotsi , "Rat ing the b r i t t l eness of r e f r a c t o r i e s tes ted for heat r e s i s t a n c e , " Probl . Prochn. ,

No. 10, 26-29 (1973). 18. A . A . I I 'yushin and P. M. Ogibalov, E l a s t i c - P l a s t i c Deformat ions of Hollow Cyl inders [in Russ ian] ,

Moscow State Univ. (1960).

T H E S T R E N G T H A N D D E F O R M A T I O N O F G R A P H I T E S

U N D E R C O N D I T I O N S O F A C Y C L I C V A R I A T I O N IN

L O A D A N D T E M P E R A T U R E

E . S. U m a n s k i i , E . I . U s k o v , A . V. B o g o m o l o v , a n d M. M. A l e k s y u k

UDC 539.4.419

Graphi te is being used m o r e and m o r e widely as a s t ruc tu ra l m a t e r i a l in var ious branches of technology, pa r t i cu l a r ly in a tomic energy . Graphi te products a re frequently used under complex operat ional conditions which involve high opera t ing t e m p e r a t u r e s and loads , the action of i r r ad ia t ion , co r ro s ive media , etc. The absence of sufficient informat ion on the behavior of graphi te under such conditions substant ial ly l imi ts the poss ib i l i t i es of us ing this h i g h - t e m p e r a t u r e ma te r i a l .

In this pape r the r e su l t s a re p resen ted of s tudies on the l o n g - t e r m s t r e n g ~ of two grades of r e ac to r graphi tes under conditions of constant and cycl ical ly vary ing loads and t e m p e r a t u r e s . The tes t s were ca r r i ed out on spec imens of VPG graphi te [1], and a graphite having an ave rage densi ty of 1.8 and 1.65 g/cm 3, which we shall subsequently r e f e r to as SPG graphite .

VPG and SPG are graphite m a t e r i a l s of ave rage granular i ty with a max imum grain s ize of 1.2 ram, p r e - pa red f rom calcined KNPS coke accord ing to e lec t rode technology. Crushed coke was impregnated with p e t r o - leum pitch and the m a s s fo rmed was p r e s s e d through a nozzle to obtain bi l le ts . The molded bil lets were an- nealed in a furnace of 1000-1300~ and then the final graphi t izat ion of the SPG ma te r i a l was ca r r i ed out at 2600-2800~ Before graphi t izat ion the bi l lets of VPG m a t e r i a l were impregnated twice with pitch and subse - quently annealed.

F r o m the bil lets so obtained, spec imens were p r e p a r e d for tes t ing, these being cut para l le l (H) to the axis of the bil let and perpendicu la r (J-) to it. The spec imen shape and dimensions a r e presented in Fig. 1.

The t e s t s we re conducted on the UDP-500 and UTP-1 units developed and constructed at the Insti tute of Strength P r o b l e m s of the Academy of Sciences of the Ukrainian SSR. On the f i r s t unit we studied the c reep and l o n g - t e r m s t rength of the graphi tes for constant and cycl ical ly vary ing tensi le loads under i so the rmal condi- t ions , and on the second unit we studied them for a constant tensi le load and a t empe ra tu r e varying cycl ical ly according to a given p r o g r a m . Tes t s of spec imens heated by a radiat ion method were conducted in an iner t a tmosphe re of technical ly pure argon (nitrogen 0.019%, oxygen 0~ A detailed descr ip t ion of the design of the units and t e s t p r o c e d u r e s is given in [2].

Kiev. T rans la t ed f rom Prob lemy Prochnos t i , No. 4, pp. 42-45, Apri l , 1978. Original a r t ic le submitted

June 29, 1977.

0039-2316/78/1004- 0413507.50 �9 1978 Plenum Publishing Corporat ion 413

= 8 5 0 s _

- + ~ = ss-~o.I - .

Fig. 1. T e s t spec imen .

The s t rength of the graphi tes was studied accord ing to th ree p r o g r a m s for va r i a t ions in t e m p e r a t u r e and load (Fig. 2). Tes t s in the a and b r e g i m e s were conducted at 800~ in the c r e g i m e they were conducted un- der conditions of t h e r m a l cycl ing accord ing to two p r o g r a m s for va r i a t ions in t e m p e r a t u r e (250-800~ and 250-1500~ In both cases the t ime p a r a m e t e r s of the t e m p e r a t u r e cycles w e r e the s a m e , v iz . , heat ing c o m - p r i sed 3 rain (2 min of them for holding at the appropr ia t e m a x i m u m t e m p e r a t u r e ) , cooling c o m p r i s e s 6 min , i .e . , a total cycle t ime of 9 min.

Load cycling ( reg ime b) was c a r r i e d out accord ing to a t r apezo ida l nonzero cycle having the following t ime p a r a m e t e r s : total cycle t ime equal to 30 rain (loading 10 min , exposure to m a x i m u m load 10 rain, unload- ing 10 min).

Taking into account a poss ib le t e m p e r a t u r e gradient over the c r o s s sect ion of the working p a r t of the spec imen during t e s t s under t he rm a l cycling conditions ( reg ime c), appropr i a t e ca l ibra t ions were c a r r i e d out and the magnitude of the t he rm a l s t r e s s e s produced was es t ima ted . It is e x t r e m e l y compl ica ted to de te rmine exper imenta l ly the s t r e s s e s caused by a change in t e m p e r a t u r e of the spec imen during tes t ing, so that the magnitude of the t he rma l s t r e s s e s was found by calculat ion, using the M a l i n i n - B i r g e r method. The bas is adopted for the calculat ion model was an infinite cyl inder having a t e m p e r a t u r e va ry ing with the radius . It was a s sumed that the t e m p e r a t u r e along the axis of the cyl inder was constant.

As shown by the calculat ions for VPG graphi te (~), for t e s t s under conditions of a t e m p e r a t u r e cycle having p a r a m e t e r s Tma x = 800~ Train = 250 ~ the m a x i m u m tens i le (at the center of the specimen) and c o m p r e s s i v e (on the su r face of the specimen) s t r e s s e s ~ in a heat ing semicyc le a re ~ 0.15-0.20 kgf /mm 2. While holding the spec imen at the m a x i m u m t e m p e r a t u r e of the cycle a level ing of the t e m p e r a t u r e occurs over the c ross sect ion and the quantity ~ is lowered apprec iab ly (down to 0.05 k~ /mm2) . In the cooling s e m i - cycle t he rma l s t r e s s e s of the opposi te sign appear in the spec imen.

In the t e s t s of SPG graphi te , the e las t ic i ty modulus of which is apprec iably lower , the t he rma l s t r e s s e s produced in the spec imens a r e lower than in the t e s t s of VPG graphi te . Taking into account that the s t rength c h a r a c t e r i s t i c s of the graphi tes have a co r re l a t ion with the i r densi ty and e l ec t r i ca l r e s i s t i v i t y [3], the spe c i - mens were separa ted before tes t ing accord ing to weight (owing to the sl ight d i f ference in the geomet r i ca l d i - mens ions of the spec imens the i r densi ty was not determined) and speci f ic r e s i s t a n c e into groups having ap p ro x - imate ly equal s t rength. This enabled us to reduce the s ca t t e r in the expe r imen ta l data c h a r a c t e r i s t i c of graphi tes .

The r e su l t s of tes t ing VPG and SPG graphi tes under the va r ious conditions a re p resen ted in Figs . 3 -5 , in the f o r m of curves for c reep and l o n g - t e r m strength.

Over the t e m p e r a t u r e - t i m e range inves t iga ted , the re la t ionships in s emi loga r i t hmic coordinates between s t r e s s a and t ime to f r a c t u r e T (see Fig. 4) or the number of heat change cycles N (see Fig. 5) a re approximated by s t ra igh t l ines and may be r e p r e s e n t e d by the exponential function

= Ae -~a , (1)

where A and cz a r e coefficients.

For all types of t es t s the graphite m a t e r i a l s cited exhibit a substant ia l an isot ropy in s t rength c h a r a c - t e r i s t i c s . Thus , t he s t rength of ~he spec imens cut pa ra l l e l (ll) to the axis of p repa ra t ion is m o r e than twice that of spec imens cut perpendicu la r (• to it. I so the rma l t e s t s at 800~ (see Fig. 4) and t he rma l cycling over the range 2 5 0 ~ 800~ (Fig. 5, curves 2-4) showed that for a cor responding di rec t ion of cutting of the spec imens the l o n g - t e r m s t rength of the dense r VPG graphi te is twice that of SPG graphite . With an inc rease in the level of the m a x i m u m cycle t e m p e r a t u r e to 1500~ the t h e rma l cycling l o n g - t e r m s t rength of VPG graphi te i n c r ease s

414

, ,

\,p

a

\ p

C T

/T

b

F ig . 2. P r o g r a m s fo r v a r i a t i o n in t e m p e r a - t u r e and load . a , b) I s o t h e r m a l t e s t s fo r c o n - s t a n t and c y c l i c l o a d s ; c) t h e r m a l c y c l i n g at c o n s t a n t l oad (P - load ; T - t e m p e r a t u r e ; and r - t i m e ) .

i

O,2O

0,~0

O, O5

0

: = / , , 6 5 kgf / Imm21 1 ""-- "~ ..

I ~ ~ ' - Ass

iiI~ ~"/, as ~:s

- - w o :U

I a

0,40

0,2C

VPG (Z) ~:~65 kgf/ mm I

o, ss ~ ' " "-~- x-.-

u

0,:O o

Fig. 3.

~0 80 /20 /6'0 200 b

C r e e p c u r v e s fo r VPG g r a p h i t e a t 800~

(see F ig . 5), which a g r e e s wi th the r e s u l t s of i s o t h e r m a l t e s t s on s h o r t - t e r m and l o n g - t e r m streng%h a t the c o r r e s p o n d i n g t e m p e r a t u r e (as i s w e l l known, wi th an i n c r e a s e in t e m p e r a t u r e the s t r e n g t h of g r a p h i t e i n - c r e a s e s , in c o n t r a s t to o t h e r m a t e r i a l s [4]) o v e r a de f in i t e t e m p e r a t u r e r a n g e .

F r o m the c u r v e s p r e s e n t e d in F ig . 3 fo r the c r e e p of VPG g r a p h i t e , p lo t t ed f r o m the r e s u l t of t e s t s u n - d e r i s o t h e r m a l cond i t ions at 800~ i t fo l lows tha t the r e l a t i v e p l a s t i c d e f o r m a t i o n e v a r i e s f r o m 0.2 to 0.4%, the r e s i d u a l e longa t ion Al not e x c e e d i n g 0.2 m m .

C y c l i c v a r i a t i o n s in t e m p e r a t u r e o v e r the r a n g e 250 ~ 800~ for c o n s t a n t load ing (based on 103 cyc les ) and load cyc l i ng o v e r the r a n g e 0-0 .8 k g f / m m 2 a t 800~ (based on 2 �9 10 ~ cyc l e s ) have no m a r k e d e f fec t on the duc t i l i t y c h a r a c t e r i s t i c s of the g r a p h i t e m a t e r i a l s c o n s i d e r e d .

The v a l u e s of Al and e ob ta ined d u r i n g c y c l i n g t e s t s a r e in good a g r e e m e n t wi th the da ta f r o m the i s o - t h e r m a l t e s t s a t 800~

M o r e o v e r , t h e r m a l c y c l i n g a c c o r d i n g to the r e g i m e w h e r e the l e v e l of the m a x i m u m cyc le t e m p e r a t u r e i s a p p r e c i a b l y h i g h e r (Tma x = 1500~ l e a d s to an i n c r e a s e in the duc t i l i t y of the g r a p h i t e s c o n c e r n e d and the r e l a t i v e e longa t ion e r e a c h e s 0.5-0.6% (Fig . 6).

415

/& a~

~.~.__ VPG {L/) o oo oo

oo c o

S PG (I/] o

i

" SPG (1} "

V P G (~J . . . . . I . . , , �9 . . . . . . I . . . . . /0- /0 ~ r, h

a b

Fig. 4. L o n g - t e r m s t r eng th of g raph i t e s at 800~

4

g,: " __._..____

0,'.

0,2 ,, /0'

0,/

:0 ~ ~ cycles i ~ t f r i

I 2 Z /0 ~JO r

4a/F4 .~ l

~

0, 0,

L q ..... I , ....... s.~" 7 ~ /0' ' . . . . . . ~ . . . . . . ~ cycles

VPG( • )

- " " "S~G(n !~ ~50:~ 800"C

Fig. 5 Fig. 6

Fig. 5. L o n g - t e r m s t r eng th of g raph i t e s on t h e r m a l cyc l ing . 1) VPG (• g raphi te 250 ~ 1500~ 2 ) VPG O-) graphi te 250 r 800~ 3) SPG (I[) g r aph i t e 250 ~800~ 4) SPG (• g r aph i t e 250 ~ 800~ (N - the n u m b e r of t h e r m a l change c y c l e s ; -r - the total t i m e of holding at the m a x i m u m t e m p e r a - t u re of the cyc le) .

Fig. 6. Dependence of the r e s i d u a l p l a s t i c d e f o r m a t i o n of g raph i t e s on the n u m b e r of hea t change cyc l e s . 1) a = 0.75 kgf/mm2; 2) ~ = 0.7 kgf /mm2; 3) cr = 0.65 kg f /mm 2.

Over the t e m p e r a t u r e - t i m e range inves t iga ted , the r e l a t i onsh ip in l o g a r i t h m i c coo rd ina t e s fo r VPG graphi te (• between the r e l a t ive p la s t i c de fo rm a t i on e and the n u m b e r of hea t change cyc l e s N is l i nea r and may be r e p r e s e n t e d by the equat ion

e = B N fs, (2)

whe re B and fl a r e coef f ic ien ts .

The va lues fo r the r e s idua l e longat ion Al and the r e l a t i v e p l a s t i c d e f o r m a t i o n e a f te r t e s t ing VPG (-) graphi te for v a r i o u s s t r e s s e s and t h e r m a l cyc l ing o v e r the r ange 250 ~- 1500~ (the cont inuous l ine in Fig. 6) have a m a r k e d s c a t t e r , owing to its spec i f i c p r o p e r t i e s . The s c a t t e r in the e x p e r i m e n t a l points d e c r e a s e s if account is taken of the r e s u l t s of t e s t ing fo r one s t r e s s .

F r a c t u r e s of the s p e c i m e n s show the m a t e r i a l to be nonun i fo rm with s e p a r a t e inc lus ions of coke powder and an app rec i ab l e n u m b e r of po res .

Fig. 7. Typ ica l b r e a k in a s p e c i - m e n of VPG graphi te (J-).

416

Frac tu re of the specimens commences at the external surface or close to it, which is charac te r i s t ic of a heterogeneous , britt le mate r ia l , which is distinguished by a predominant effect of the state of the surface on its strength [5].

At the breaks charac te r i s t i c "steps" are observed which indicate the position of nucleation and advance of the cracks .

Figure 7 shows a photograph of a typical break in a specimen of VPG graphite (• f rac tured after 96 h when tested for long- te rm strength at T = 800~ and ff = 0.7 kgf/mm 2. At the left are seen three steps and be- yond them three shelves in the break of the specimen.

1.

2.

3.

4.

5.

L I T E R A T U R E C I T E D

V. N. Barabanov and Yu. S. Virg i l ' ev , The Radiation Resis tance of Structural Graphite [in Russian], Atomizdat , Moscow (1976). E. I. Uskov, A. V. Bogomolov, and M. M. Aleksyuk, "Apparatus for studying the mechanical proper t ies of mater ia l s under varying strength and thermal loads ," Probl. Prochn. , No. 11, 117-121 (1976). E. N. Marmer , Ca rbon -Graph i t e Materials (a handbook) [Russian translat ion], Metallurgiya, Moscow

0973). E. N. Marmer , O. S. Gurvich, and L. F. Mal ' t seva , High-Tempera ture Materials [Russian translat ion], Metal lurgiya, Moscow (1967). Yu. B. Fr idman, The Mechanical P roper t i e s of Metals, Pa r t 1 [in Russian], Mashinostroenie, Moscow (1974).

THE STRENGTH OF ENGINEERING GLASS UNDER

PROLONGED STATIC AND CYCLIC LOADS

V. G. Soluyanov and A. P. Poleshko UDC 666.1:620.173.25

Among the numerous fac tors that affect the strength of technical glass in some degree or other , the dura - tion and repeated nature of the load action should be noted.

While the question of the long- te rm strength of glass has been well documented in domest ic and foreign l i te ra ture [1-8], the question of the cyclic action of loads has been investigated very little [5, 10, 11]. Almost all these investigations were conducted under bending, although the most promis ing loading range for glass is under compress ion.

Previous investigation of the long- te rm strength of engineering glass have been under compress ion under the ext remely unfavorable conditions for this mater ia l of d i rec t contact between the testpiece and the metall ic plates of the loading equipment [12]. . . . .

The aim of the presen t work is to investigate the effects of duration and repeated nature of the applied loads on the strength of type 13v glass under monoaxial compress ion in air at normal temperature .

The tes tpieces used were cyl inders of d iameter 10 mm with f i re-pol ished surfaces . The ends of the tes t - pieces were fastened by an epoxy adhesive based on type ED-6 res in in the sockets of the metal yokes. The pa rame te r s of the composite tes tpieces corresponded to the data in [9].

The test ing for long- te rm strength was ca r r i ed out in a type P D P S - l m at tachment [12].

The endurance of the glass was determined at the four s t r e ss levels 0.8, 0.71, 0.62, and 0.58 of the sho r t - t e rm strength f rom data using five tes tpieces for each s t ress level. According to the resul ts f rom tes t - ing 75 tes tp ieces , the s h o r t - t e r m strength (breaking point under compression) of type 13v glass in air at no r - mal t empera tu res ab = 224.5 kgf/cm 2 (coefficient of variat ion was 9%). The test basis (duration) at a s t r e ss level ~ = 0.58a b was equal to 24,000 h (~ 3 years) . Under these conditions all of the testpieces failed.

Institute of Strength P rob lems , Academy of Sciences of the Ukrainian SSR, Kiev. Translated f rom Problemy Proehnost i , No. 4, pp. 46-48, Apri l , 1978. Original ar t ic le submitted April 26, 1977.

0039-2316/78/1004- 0,117907.50 �9 1978 Plenum Publishing Corporation 417