ENERAL ATOM

GA-A13524 u c - 7 7

-- L U

MECHANICAL PROPERTIES OF G RAPH ITE FOR H IG H-TEM PERATU R E

GAS-COOLED R EACBORS: A REVIEW

by R. J. PRICE

~ - ~- NOTICE

sponrored by the Umted Stater Cavernment. Neither the United Stater nor the Unated Stater Energy Research and Development Adminisfntion, nor any of them employees. nor any of their conlractors, wbcontnetarr, or thew employees. makes any wrranty. erpres 01 impbed. or auurnes any legal hbility or responsibility for the accuracy. completenea 01 u r f u l n e a of any tnformation. apparatus. product or process discloud. or rcprercnls that 11s u v would not

Prepared under Contract E(04-3)- 167

Project Agreement No. 17 for the

San Francisco Operations Office U.S. Energy Research and Development Administration

T h i s document is

Authofiing Omcid wt~ O U % / ~ o a 7

GENERAL ATOMIC PROJECT 3224 DATE PUBLISHED: SEPTEMBER 22, 1975

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

. _ . , . . . .. .' ..,I.

ABSTRACT

i"

Exper imenta l d a t a on t h e mechanica l p r o p e r t i e s of r e a c t o r g r a p h i t e s

( e x c l u d i n g i r r a d i a t i o n c r e e p and f a t i g u e ) under High-Temperature Gas-Cooled

Reac to r (HTGR) c o n d i t i o n s a re rev iewed.

U n i r r a d i a t e d g r a p h i t e e x h i b i t s a n o n l i n e a r (approximate ly p a r a b o l i c )

s t r e s s - s t r a i n c u r v e and a "permanent se t" when t h e l o a d i s reduced t o z e r o .

P o i s s o n ' s r a t i o d e c r e a s e s w i t h i n c r e a s i n g s t r a i n . The t e n s i l e s t r e n g t h

t e n d s t o d e c r e a s e w i t h i n c r e a s i n g specimen s i z e . The f l e x u r a l s t r e n g t h i s

h i g h e r t h a n t h e t e n s i l e s t r e n g t h by 30% t o 100%. Both Young's modulus and

s t r e n g t h i n c r e a s e w i t h i n c r e a s i n g measurement t e m p e r a t u r e , f r a c t i o n a l

i n c r e a s e s b e i n g g r e a t e r f o r t h e s t r e n g t h . The s t r e n g t h i s g e n e r a l l y lower

under b i a x i a l t e n s i o n - t e n s i o n o r tens ion-compress ion t h a n under u n i a x i a l

t e n s i o n . F a i l u r e under m u l t i a x i a l l o a d i n g a g r e e s b e s t w i t h E l y ' s c o n s t a n t

s t r a i n energy c r i t e r i o n . A l i m i t e d amount of work on notched t e s t samples

i n d i c a t e s t h a t f r a c t u r e mechanics a n a l y s i s may b e a p p l i c a b l e t o g r a p h i t e .

Some of t h e c h a r a c t e r i s t i c s of g r a p h i t e f a i l u r e are compat ib le w i t h t h e

Weibul l s t a t i s t i c a l t h e o r y of s t r e n g t h , b u t t h i s t h e o r y does n o t p r o v i d e a

r e l i a b l y s e l f - c o n s i s t e n t model. N o single t h e o r y h a s been found t o p r e d i c t

a f a i l u r e c r i t e r i o n a p p l i c a b l e under a l l c o n d i t i o n s of l o a d i n g .

O x i d a t i o n d r a s t i c a l l y r e d u c e s b o t h t h e s t r e n g t h and Young's modulus: a

1 % burn-off r e d u c e s t h e s t r e n g t h by a b o u t 10%.

Neut ron i r r a d i a t i o n changes t h e mechanica l p r o p e r t i e s of g r a p h i t e s by

( 1 ) p i n n i n g b a s a l d i s l o c a t i o n s and ( 2 ) c l o s i n g mic roc racks . I r r a d i a t i o n

p r o g r e s s i v e l y removes t h e c u r v a t u r e from t h e s t r e s s - s t r a i n c u r v e . Dynamic

d e t e r m i n a t i o n s of Young's modulus i n c r e a s e r a p i d l y and t h e n l e v e l o f f ; t h e

level of t h e p l a t e a u d e c r e a s e s w i t h

F u r t h e r i r r a d i a t i o n c a u s e s a second

4 f

*

i n c r e a s i n g i r r a d i a t i o n t e m p e r a t u r e .

i n c r e a s e and f i n a l l y a d e c r e a s e i n

iii

Young's modulus. The s t a t i c Young's modulus of i r r a d i a t e d g r a p h i t e a g r e e s

w i t h t h e dynamic modulus, whereas t h e s t a t i c modulus of u n i r r a d i a t e d

g r a p h i t e i s lower t h a n t h e dynamic modulus. No s y s t e m a t i c e f f e c t of i r r a d i -

a t i o n on P o i s s o n ' s r a t i o h a s been found. I r r a d i a t i o n i n c r e a s e s t h e t e n s i l e

and f l e x u r a l s t r e n g t h s . A t low i r r a d i a t i o n t e m p e r a t u r e s , t h e s t r e n g t h ,

S, and Young's modulus, E , of u n i r r a d i a t e d and i r r a d i a t e d samples arc!

r e l a t e d by t h e c o n d i t i o n of c o n s t a n t s t r a i n energy f r a c t u r e ; t h u s , S z - / E =

c o n s t a n t . A t h i g h e r i r r a d i a t i o n t e m p e r a t u r e s , t h e s t r e n g t h s are o f t e n

somewhat h i g h e r t h a n p r e d i c t e d by t h e c o n s t a n t s t r a i n energy c o n d i t i o n and

may approach t h e c o n d i t i o n S/E = c o n s t a n t . The e f f e c t of i r r a d i a t i o n on

t h e s c a t t e r i n s t r e n g t h v a l u e s i s n o t c l e a r l y d e f i n e d ,

')

Most p u b l i s h e d work on t h e e f f e c t of o x i d a t i o n i n a r a d i a t i o n f i e l d

r e l a t e s t o carbon d i o x i d e . Ox ida t ion by carbon d i o x i d e i n t h e p re sence of

i r r a d i a t i o n r e d u c e s t h e s t r e n g t h more g r a d u a l l y t h a n t h e o x i d a t i o n o f

u n i r r a d i a t e d g r a p h i t e .

Based on an assessment of t h e l i t e r a t u r e , recommendations a re made

f o r d e s i g n - b a s i s v a l u e s f o r t h e e l a s t i c p r o p e r t i e s and s t r e n g t h o f i r r a d i -

a t e d g r a p h i t e , and f a i l u r e c r i t e r i a are s u g g e s t e d f o r p a r t i c u l a r 1oad.ing

c o n d i t i o n s .

i v

CONTENTS

BSTFUCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . .

1.1. Scope of Review . . . . . . . . . . . . . . . . . . . . . 1.2. F a s t Neutron F luence U n i t s . . . . . . . . . . . . . . . .

2 . MECHANICAL PROPERTIES OF U N I W I A T E D GRAPHITE . . . . . . . . . Tempera ture . . . . . . . . . . . . . . . . . . . . . . .

2.2. Elas t ic Moduli a t Room Temperature . . . . . . . . . . . . 2.3. Lateral S t r a i n s and P o i s s o n ' s R a t i o . . . . . . . . . . .

2.1. U n i a x i a l S t r e s s - S t r a i n R e l a t i o n s h i p a t Room

2.4. Equa t ions f o r S t r e s s - S t r a i n Curves . . . . . . . . . . . . 2.5. E f f e c t of Specimen S i z e on T e n s i l e S t r e n g t h . . . . . . . 2.6. F l e x u r a l Tests a t Room Tempera ture . . . . . . . . . . . . 2.7. E f f e c t of Temperature on Mechanical P r o p e r t i e s . . . . . .

2.9. Application of Frac ture Mechanics t o G r a p h i t e . . . . . . 2.8. Mechanical Behavior Under M u l t i a x i a l S t r e s s e s . . . . . .

2.10. A p p l i c a t i o n of Weibul l S t a t i s t i c a l Theory t o G r a p h i t e . . . . . . . . . . . . . . . . . . . . . . . . .

2.11. F a i l u r e Criteria f o r G r a p h i t e . . . . . . . . . . . . . . 2.11.1. Maximum Normal Stress . . . . . . . . . . . . . . 2.11.2. Maximum Normal S t r a i n . . . . . . . . . . . . . . 2.11.3. Maximum Shear S t r e s s . . . . . . . . . . . . . . 2.11.4. D i s t o r t i o n Energy . . . . . . . . . . . . . . . . 2.11.5. Maximum S t r a i n Energy . . . . . . . . . . . . . . 2.11.6. Weibul l Theory . . . . . . . . . . . . . . . . . 2.11.7. F r a c t u r e Mechanics . . . . . . . . . . . . . . . 2.11.8. Mean Loca l S t r a i n Energy D e n s i t y i n P l a n e

of Crack . . . . . . . . . . . . . . . . . . . . 2.11.9. Conc lus ions on F a i l u r e Cri ter ia . . . . . . . . .

2.12. E f f e c t of O x i d a t i o n on S t r e n g t h of G r a p h i t e . . . . . . . 3 . MECHANICAL PROPERTIES OF IRRADIATED GRAPHITE . . . . . . . . . .

3.1. E f f e c t of I r r a d i a t i o n on S t r e s s - S t r a i n Curve . . . . . . .

iii

1-1

1-1

1-1

2-1

2-1

2-3

2-6

2-10

2-12

2-13

2-16

2-18

2-23

2-27

2-30

2-30 2-32

2-32

2-33

2-33

2-34

2-34

2-35

2-35

2-36

3-1

3-1

. c

U V

CONTENTS (Continued)

4 .

3 . 2 . E f f e c t of I r r a d i a t i o n on Young's Modulus . . . . 3 . 3 . E f f e c t of I r r a d i a t i o n on Other E l a s t i c C o n s t a n t s

3 . 4 . E f f e c t of I r r a d i a t i o n on P o i s s o n ' s R a t i o . . . . 3 . 5 . E f f e c t of I r r a d i a t i o n on S t r e n g t h . . . . . . . 3 . 6 . S t r e n g t h of G r a p h i t e Oxid ized Under I r r a d i a t i o n

RECOMMENDED DESIGN PRACTICE . . . . . . . . . . . . . 4 . 1 . B a s i s f o r Recommendations . . . . . . . . . . . 4 . 2 . Type of E l a s t i c Behavior . . . . . . . . . . . .

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. . . . . 4 . 3 . E l a s t i c C o n s t a n t s . . . . . . . . . . . . . . . . . . . . 4 . 4 . P o i s s o n ' s R a t i o . . . . . . . . . . . . . . . . . . . . . 4 . 5 . F a i l u r e Criteria . . . . . . . . . . . . . . . . . . . . . 4 . 6 . E f f e c t of I r r a d i a t i o n on S t r e n g t h . . . . . . . . . . . . 4 . 7 . S t a t i s t i c a l V a r i a t i o n i n S t r e n g t h . . . . . . . . . . . . 4 . 8 . Numerical Values f o r U n i r r a d i a t e d Mechanical

P rope r t ies . . . . . . . . . . . . . . . . . . . . . . . . 5 . REFERENCES.. . . . . . . . . . . . . . . . . . . . . . . . . .

FIGURES

1 . U n i a x i a l s t r e s s - s t r a i n c u r v e f o r EGCR-type AGOT g r a p h i t e ,

2 . T e n s i l e s t r e s s - s t r a i n c u r v e w i t h r e p e a t e d l o a d i n g f o r

3 .

p a r a l l e l t o e x t r u s i o n axis . . . . . . . . . . . . . . . . . . . u n s p e c i f i e d n u c l e a r g r a p h i t e , p a r a l l e l t o e x t r u s i o n a x i s . . . . Compressive s t r e s s - s t r a i n c u r v e w i t h r e p e a t e d l o a d i n g f o r u n s p e c i f i e d n u c l e a r g r a p h i t e , p a r a l l e l t o e x t r u s i o n a x i s . . . . A T J g r a p h i t e , i n t h e w i t h - g r a i n d i r e c t i o n . . . . . . . . . . . p a r a l l e l t o t h e e x t r u s i o n a x i s ( 1 2 c y c l e s ) . . . . . . . . . . . c u r v e s f o r n u c l e a r g r a p h i t e . . . . . . . . . . . . . . . . . . AGOT g r a p h i t e . . . . . . . . . . . . . . . . . . . . . . . . . s t r e s s - s t r a i n c u r v e (H-451 g r a p h i t e ) . . . . . . . . . . , . . .

4 . Composite t e n s i o n and compress ion d a t a f o r two specimens of

5. C y c l i c s t r e s s - s t r a i n c u r v e s f o r EGCR-type AGOT g r a p h i t e ,

6 . Schematic drawings of l o n g i t u d i n a l and l a t e r a l s t r e s s - s t r a i n

7 . T r a n s v e r s e - t o - l o n g i t u d i n a l s t r a i n r a t i o c u r v e s f o r EGCR-type

8 . C o r r e c t i o n f a c t o r s f o r b e n d - t e s t d a t a t o accoun t f o r n o n l i n e a r

3-4 3-1 2

3-20 3-20 3-39

4-1 4-1

4-2

4-2

4-5 4-5

4-6 4-6

4-8 5-1

2-2

2-4

2-5

2-7

2-8

2-9

2-1 1

2-1 5

v i V

FIGURES (Continued)

9 . T r a n s v e r s e t e n s i l e s t r e n g t h of H4LM g r a p h i t e a s a f u n c t i o n of

10. Dynamic Young's modulus v e r s u s t empera tu re f o r r e p r e s e n t a t i v e

t e m p e r a t u r e when t e s t e d i n s t a t i c he l ium a t 0.005/min

commercial g r a p h i t e s . . . . . . . . . . . . . . . . . . . . . . 11. S t r e n g t h of Graph-1-Tite t u b e s under combined stresses . . . . .

. . . . .

12. B i a x i a l f r a c t u r e d a t a f o r AXF-5Q g r a p h i t e t u b e s t e s t e d a t room t e m p e r a t u r e . . . . . . . . . . . . . . . . . . . . . . . .

13. B i a x i a l f a i l u r e envelopes p r e d i c t e d by d i f f e r e n t f a i l u r e c r i t e r i a f o r a n i s o t r o p i c g r a p h i t e w i t h P o i s s o n ' s r a t i o = 0.2 and u l t i m a t e compress ive s t r e n g t h = 3 x u l t i m a t e t e n s i l e s t r e n g t h . . . . . . . . . . . . . . . . . . . of t h e e x t e n t o f o x i d a t i o n . . . . . . . . . . . . . . . . . . . n e u t r o n f l u e n c e a t 15OOC; i s o t r o p i c n u c l e a r g r a p h i t e . . . . . . i r r a d i a t e d H-451 g r a p h i t e . . . . . . . . . . . . . . . . . . .

17. F r a c t i o n a l changes i n dynamic Young's modulus of PGA g r a p h i t e w i t h doub le p i t c h impregnat ion . . . . . . . . . . . . . . . . .

18. F r a c t i o n a l changes i n dynamic Young's modulus of ex t ruded petroleum-coke g r a p h i t e . . . . . . . . . . . . . . . . . . . .

19. F r a c t i o n a l changes i n dynamic Young's modulus of ex t ruded p i tch-coke g r a p h i t e . . . . . . . . . . . . . . . . . . . . . .

20. F r a c t i o n a l changes i n dynamic Young's modulus of molded

21. F r a c t i o n a l changes i n dynamic Young's modulus of molded

14. Compressive s t r e n g t h of P i l e Grade A g r a p h i t e a s a f u n c t i o n

15. V a r i a t i o n i n s t r e s s - s t r a i n c u r v e s i n t e n s i o n w i t h i n c r e a s i n g

16. T y p i c a l t e n s i l e s t r e s s - s t r a i n c u r v e s f o r u n i r r a d i a t e d and

p i t ch -coke g r a p h i t e . . . . . . . . . . . . . . . . . . . . . . Gi l soca rbon g r a p h i t e . . . . . . . . . . . . . . . . . . . . . .

22. F r a c t i o n a l changes i n dynamic Young's modulus, E , and s t r e n g t h , S , of i s o t r o p i c g r a p h i t e s a t t e m p e r a t u r e s of 350" t o 440°C i n Dounreay F a s t Reac to r and 700°C inBR-2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

23. F r a c t i o n a l changes i n Young's modulus v e r s u s f l u e n c e f o r a n a n i s o t r o p i c r e a c t o r g r a p h i t e . . . . . . . . . . . . . . . . . .

24a. Tens i l e s t r e n g t h and s t a t i c Young's modulus of H-327 need le - coke g r a p h i t e as a f u n c t i o n of f a s t n e u t r o n f l u e n c e . . . . . .

24b. T e n s i l e s t r e n g t h and s t a t i c Young's modulus of H-327 need le - coke g r a p h i t e as a f u n c t i o n of f a s t n e u t r o n f l u e n c e . E r r o r bands i n d i c a t e f one s t a n d a r d d e v i a t i o n . I r r a d i a t i o n t empera tu re 940" t o 12OOOC . . . . . . . . . . . . . . . . . . .

2-1 7

2-1 9 2-20

2-22

2-3 1

2-37

3-2

3-3

3-5

3-6

3-7

3-8

3-9

3-1 1

3-1 3

3-1 4

3-1 5 ,- .

v i i

FIGURES (Continued)

25. T e n s i l e s t r e n g t h and s t a t i c Young's modulus of H-451 near - i s o t r o p i c petroleum-coke g r a p h i t e as a f u n c t i o n of f a s t n e u t r o n f l u e n c e . . . . . . . . . . . . . . . . . . . . . . . .

26. T e n s i l e s t r e n g t h and s t a t i c Young's modulus of TS-1240 n e a r - i s o t r o p i c petroleum-coke g r a p h i t e as a f u n c t i o n of f a s t n e u t r o n f l u e n c e . . . . . . . . . . . . . . . . . . . . . . n e u t r o n f l u e n c e . . . . . . . . . . . . . . . . . . . . . . . . i r r a d i a t e d a t 350' t o 500°C . . . . . . . . . . . . . . . . . .

27. V a r i a t i o n of P o i s s o n ' s r a t i o of PGA g r a p h i t e w i t h f a s t

28. Mechanical p r o p e r t y changes i n ex t ruded i s o t r o p i c g r a p h i t e

29. S t r e n g t h - Young's modulus r e l a t i o n s h i p f o r i r r a d i a t e d g r a p h i t e . . . . . . . . . . . . . . . . . . . . . . . . . . . .

30. F l e x u r a l s t r e n g t h as a f u n c t i o n of s t a t i c Young's modulus

31. T e n s i l e s t r e n g t h and Young's modulus o f needle-coke H-327 g r a p h i t e i r r a d i a t e d i n c a p s u l e G - 1 3 a t 1100" t o 1150°C . . . . .

32a. F l e x u r a l s t r e n g t h of a x i a l specimens of needle-coke H-327 g r a p h i t e i r r a d i a t e d i n c a p s u l e s F-26, F-28, and F-29 a t 575" t o 7 7 5 " ~ . . . . . . . . . . . . . . . . . . . . . . . .

32b. F l e x u r a l s t r e n g t h of r a d i a l specimens of needle-coke H-327 g r a p h i t e i r r a d i a t e d i n c a p s u l e s F-26, F-28, and F-29

33. T e n s i l e s t rength-Young ' s modulus r e l a t i o n s h i p s f o r needle- coke H-327 g r a p h i t e i r r a d i a t e d i n c a p s u l e s OG-1 and OG-2 . . . .

34. T e n s i l e s t rength-Young ' s modulus r e l a t i o n s h i p s f o r nea r - i s o t r o p i c petroleum-coke H-451 g r a p h i t e i r r a d i a t e d i n

35. T e n s i l e s t rength-Young ' s modulus r e l a t i o n s h i p s f o r nea r - i s o t r o p i c petroleum-coke TS-1240 g r a p h i t e i r r a d i a t e d i n c a p s u l e OG-2 . . . . . . . . . . . . . . . . . . . . . . . . . .

36. Young's modulus and f l e x u r a l s t r e n g t h of AXF-5Q g r a p h i t e as a f u n c t i o n of f a s t n e u t r o n f l u e n c e . . . . . . . . . . . . . . .

37. E f f e c t of r a d i o l y t i c o x i d a t i o n by C02 on Young's modulus of P i l e Grade A and i s o t r o p i c g r a p h i t e s . . . . . . . . . . . .

38. E f f e c t of r a d i o l y t i c o x i d a t i o n by C02 on t h e s t r e n g t h of i s o t r o p i c g r a p h i t e s . . . . . . . . . . . . . . . . . . . . . .

39. F r a c t i o n a l i n c r e a s e i n s t a t i c Young's modulus as a f u n c t i o n of f a s t n e u t r o n f l u e n c e . . . . . . . . . . . . . . . . . . . . f u n c t i o n of f a s t n e u t r o n f l u e n c e . . . . . . . . . . . . . . . .

f o r i r r a d i a t e d g r a p h i t e . . . . . . . . . . . . . . . . . . . .

a t 575" t o 7 7 5 " ~ . . . . . . . . . . . . . . . . . . . . . . . .

c a p s u l e s OG-1 and OG-2 . . . . . . . . . . . . . . . . . . . . .

40. F r a c t i o n a l i n c r e a s e i n t e n s i l e o r f l e x u r a l s t r e n g t h as a

3-1 6

3-1 7

3-21

3-25

3-27

3-28

3-30

3-31

3-32

3-34

3-35

3-36

3-37

3-40

3-41

4 -4

4-7

Y

v i i i

TABLES

1 . Summary of mechanica l p r o p e r t y d a t a on g r a p h i t e s i r r a d i a t e d i n

2 . Measured e l a s t i c compl iance moduli of g r a p h i t e b l o c k s i n

3a. P h y s i c a l and mechanica l p r o p e r t i e s of u n i r r a d i a t e d

c a p s u l e s OG-1 and OG-2 . . . . . . . . . . . . . . . . . . . . . 3-18

u n i t s of lO-I4 cm2/dyne . . . . . . . . . . . . . . . . . . . . 3-19

g r a p h i t e s . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-22

3b. Change i n mechanica l p r o p e r t i e s a f t e r n e u t r o n i r r a d i a t i o n . . , 3-23

4 . Weibul l a n a l y s i s of i r r a d i a t e d Poco AXF-5Q g r a p h i t e . . . . . . 3-38

5. T y p i c a l mechanica l p r o p e r t i e s of u n i r r a d i a t e d n e a r - i s o t r o p i c g r a p h i t e s . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9

i x

1. INTRODUCTION

1 . 1 . SCOPE OF REVIEW

The g r a p h i t e moderator b l o c k s i n t h e c o r e of a n HTGR s e r v e a s pr imary

s t r u c t u r a l components, Accura te v a l u e s f o r t h e e l a s t i c p r o p e r t i e s of t h e

b l o c k s under s e r v i c e Cond i t ions a re needed f o r stress c a l c u l a t i o n s , and

s t r e n g t h d a t a are needed t o assess t h e r e l i a b i l i t y of t h e d e s i g n .

i

I n t h i s r e p o r t t h e a v a i l a b l e d a t a ( i n c l u d i n g e f f e c t s of n e u t r o n i r ra-

d i a t i o n ) on s t r e s s - s t r a i n c u r v e s , e l a s t i c c o n s t a n t s , P o i s s o n ' s r a t i o ,

s t r e n g t h , f r a c t u r e toughness , f a i l u r e c r i t e r i a , and f a i l u r e under complex

stress sys tems a re reviewed. The l i t e r a t u r e on t h e u n i a x i a l mechanica l

p r o p e r t i e s of u n i r r a d i a t e d g r a p h i t e s i s covered on ly i n o u t l i n e because a

number of p u b l i s h e d r ev iew a r t i c l e s (Refs , 1-4) summarize t h i s area,

I r r a d i a t i o n - i n d u c e d creep w a s reviewed i n a p r e v i o u s r e p o r t (Ref. 5 ) , as

w a s f a t i g u e i n g r a p h i t e (Ref. 6 ) ; consequen t ly n e i t h e r t o p i c i s cons ide red

h e r e . F i n a l l y , d e s i g n - b a s i s c u r v e s f o r t h e e l a s t i c moduli and s t r e n g t h o f

HTGR g r a p h i t e s as f u n c t i o n s of i r r a d i a t i o n c o n d i t i o n s are recommended, and

s u g g e s t i o n s are made as t o a p p r o p r i a t e mechanica l f a i l u r e c r i t e r i a .

1 . 2 . FAST NEUTRON FLUENCE UNITS

I n many of t h e f i g u r e s i n t h i s review, f a s t n e u t r o n f l u e n c e s a r e g i v e n

i n t e r m s of n e u t r o n s w i t h e n e r g i e s g r e a t e r t h a n 0.18 MeV f o r specimens

i r r a d i a t e d i n tes t c a p s u l e s i n l igh t -water -modera ted t e s t r e a c t o r s

(E > 0.18 MeV, LWR). Some European d a t a are quoted i n terms of t h e N i c k e l

Dido Equ iva len t (NDE) f l u e n c e . For HTGR d e s i g n p u r p o s e s , u s u a l p r a c t i c e

u t i l i z e s t h e f l u e n c e of n e u t r o n s w i t h e n e r g i e s g r e a t e r t h a n 0.18 M e V i n

a graphi te -modera ted HTGR spec t rum (E > 0.18 M e V , HTGR). For comparisons

between d i f f e r e n t i r r a d i a t i o n f a c i l i t i e s , t h e p r e f e r r e d u n i t i s t h e

1-1 - - v

Equiva len t F i s s i o n F luence f o r G r a p h i t e Damage (EFFGD). Conversion f a c t o r s

between t h e d i f f e r e n t u n i t s can be c a l c u l a t e d on t h e b a s i s of t h e number of 4

-24 d i s p l a c e d carbon atoms; on t h i s b a s i s , 1 n/cm2 (EFFGD) d i s p l a c e s 720 x 10

carbon atoms p e r atom. C a l c u l a t e d f a c t o r s f o r conve r t ing f l u e n c e s i n t h i s

r e p o r t expressed as n/cm2 (E > 0.18 MeV, LWR) t o o t h e r u n i t s a r e as f o l l o w s :

F luence (NDE) = 0.6 x f l u e n c e (E > 0.18 M e V , LWR) ,

Fluence (E > 0.18 M e V , HTGR) = 0.89 x f l u e n c e (E > 0.18 MeV, LwR),

F luence (EFFGD) = 1 . 1 2 x f l u e n c e (E > 0.18 M e V , LWR).

1-2

2. MECHANICAL PROPERTIES OF UNIRRADIATED GRAPHITE

2 .1 . UNIAXIAL STRESS-STRAIN RELATIONSHIP AT ROOM TEMPERATURE

Although p o l y c r y s t a l l i n e g r a p h i t e i s g e n e r a l l y r ega rded as a b r i t t l e

mater ia l , a l i m i t e d amount of s l i p on t h e b a s a l p l a n e s i s p o s s i b l e even

a t room t e m p e r a t u r e , and consequen t ly t h e s t r e s s - s t r a i n c u r v e s are non-

l i n e a r , F i g u r e 1 shows a n example of a room-temperature s t r e s s - s t r a i n

c u r v e i n b o t h compression and t e n s i o n f o r a coa r se -g ra ined nuc lea r -g rade

g r a p h i t e (EGCR-type AGOT) (Ref. 3 ) . Both t h e t e n s i o n and compress ion

p o r t i o n s of t h e c u r v e a r e concave toward t h e s t r a i n a x i s . The s t r a i n a t

f a i l u r e under compression i s t y p i c a l l y t e n t imes h i g h e r t h a n t h e s t r a i n

a t f a i l u r e i n t e n s i o n ( t h e t e n s i l e f a i l u r e s t r a i n i s about 0.1% t o 0 . 2 % ) ,

w h i l e t h e u l t i m a t e compress ive s t r e n g t h i s t y p i c a l l y f o u r o r f i v e t i m e s

h i g h e r t h a n t h e u l t i m a t e t e n s i l e s t r e n g t h .

The u l t i m a t e t e n s i l e s t r e n g t h of specimens t a k e n from l a r g e b l o c k s of

coa r se -g ra ined nuc lea r -g rade g r a p h i t e f a l l s i n t h e r a n g e 1000 t o 3000 p s i .

The s t r e n g t h of l a r g e e x t r u s i o n s and moldings i s i n f l u e n c e d by t h e t y p e

of f i l l e r coke and p i t c h b i n d e r , the g r a i n o r i e n t a t i o n of t h e f i l l e r coke ,

and t h e amount of ca rbon d e r i v e d from impregnat ion . For e x t r u d e d s t o c k

t h e s t r e n g t h i s h i g h e r i n t h e a x i a l d i r e c t i o n t h a n i n t h e r a d i a l d i r e c t i o n ,

w i t h t h e s t r e n g t h a n i s o t r o p y r e f l e c t i n g t h e d e g r e e of o r i e n t a t i o n of t h e

f i l l e r coke; i n ex t ruded g r a p h i t e s made from n e e d l e cokes t h e a x i a l s t r e n g t h

may b e as much as t w i c e t h e r a d i a l s t r e n g t h , I n molded s t o c k t h e o r i e n t a t i o n

dependence i s r e v e r s e d . Specimens from t h e c e n t e r of a l o g a re u s u a l l y

weaker t h a n t h o s e from t h e p e r i p h e r y and ends of t h e l o g because of t h e

i n f l u e n c e of impregnant ca rbon .

When g r a p h i t e i s s u b j e c t e d t o a t e n s i l e stress c l o s e t o i t s u l t i m a t e

s t r e n g t h , f r a c t u r e may occur a f t e r a p e r i o d of t i m e w i t h no i n c r e a s e i n

2- 1

I I

TENS1 LE

1 1 ..'if/ 2000

0 . - - v) n CO MP R ESSl V E Y

$ -2000 - w a I- v)

-4000 -

-6000 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4

STRAIN (%)

2-2

stress (de layed f r a c t u r e o r s t a t i c f a t i g u e ) . T h i s e f f e c t i s u s u a l l y

masked by scat ter i n t h e d a t a . One series of tes ts on ex t ruded RC-4

g r a p h i t e t e s t e d as c a n t i l e v e r beams i n a i r a t room t e m p e r a t u r e (Ref . 7 )

w a s des igned t o a l l o w f o r t h e sp read i n s t r e n g t h s . I n t h e s e tests de layed 5 f r a c t u r e w a s shown t o occur a f t e r 10 sec i n specimens s t r e s s e d a t 97% of

t h e i r expec ted f r a c t u r e stress.

I f a load i s a p p l i e d and t h e n removed, t h e s t r e s s - s t r a i n cu rve does

n o t re t race i t s o r i g i n a l p a t h ; a r e s i d u a l s t r a i n remains when t h e stress

i s reduced t o z e r o ("permanent s e t " ) . Examples of s t r e s s - s t r a i n c u r v e s

produced d u r i n g l o a d c y c l i n g i n b o t h t e n s i o n and compress ion a r e shown i n

F i g s . 2 and 3 (Ref. 1 ) . I f t h e load i s r e a p p l i e d , t h e r e l o a d i n g cu rve

(dashed l i n e s i n F i g s , 2 and 3 ) d e v i a t e s s l i g h t l y from t h e un load ing c u r v e ,

r e s u l t i n g i n a narrow h y s t e r e s i s loop . The r e l o a d i n g c u r v e s r e j o i n t h e

o r i g i n a l l o a d i n g c u r v e s h o r t l y a f t e r t h e l o a d - r e v e r s a l p o i n t i s passed .

2 . 2 . ELASTIC MODULI AT ROOM TEMPERATURE

The non-Hookean behav io r c a u s e s a problem i n d e f i n i n g Young's modulus

f o r g r a p h i t e , Some commonly used Young's modul i are:

1.

2 .

3 .

4 .

Sonic modulus (dynamic modulus) o b t a i n e d from t h e f r equency of

v i b r a t i o n i n t h e l o n g i t u d i n a l s t r e t c h i n g o r f l e x u r a l mode.

Tangent modulus a t z e r o stress, i . e . , t h e s l o p e of t h e stress-

s t r a i n c u r v e a t t h e o r i g i n .

Q u a s i - e l a s t i c modulus a f t e r p r e l o a d i n g and u n l o a d i n g , i . e . ,

t h e s l o p e of a s t r a i g h t l i n e connec t ing t h e un load ing and r e l o a d i n g

p o i n t s on t h e c u r v e s i n F i g . 2 .

Chord modulus, i . e . , t h e s l o p e between two s p e c i f i e d stress

p o i n t s on t h e o r i g i n a l l o a d i n g cu rve .

2-3

125C

1000

- - 2 750 1

v3 m w a L

500

I I 1 1 " I , " "

LOAD I NG --.- - U N LOA"' AH

0 0.025 0.050 0.075 [).loo STRAIN (%)

F i g . 2 . T e n s i l e s t r e s s - s t r a i n c u r v e w i t h r e p e a t e d l o a d i n g f o r u n s p e c i f i e d n u c l e a r g r a p h i t e , p a r a l l e l t o e x t r u s i o n a x i s (from Ref . 1 )

2-4 L

3000

v, 2000 n - v) v) w a 5

1000

I I 1 I 1

LOADING

0 0.1 0.2 0.3 0.4 0.5 0.6 STRAIN (%)

c *

F i g . 3 . Compressive s t r e s s - s t r a i n c u r v e w i t h r e p e a t e d l o a d i n g f o r u n s p e c i f i e d n u c l e a r g r a p h i t e , p a r a l l e l t o e x t r u s i o n a x i s (from Ref , 1 )

2- 5

5. Secant modulus, i . e . , u l t i m a t e t e n s i l e s t r e n g t h d i v i d e d by t h e

s t r a i n a t f a i l u r e .

The t angen t modulus ( s l o p e a t t h e o r i g i n ) i s t h e same f o r compression

and t e n s i o n and i s u s u a l l y somewhat lower t h a n t h e s o n i c modulus (F ig , 4 )

(Ref. 2 ) . I n t e n s i o n , t h e q u a s i - e l a s t i c modulus i s c l o s e t o t h e t angen t

modulus and o n l y s l i g h t l y dependent on t h e amount of p r e l o a d ( s e e F ig . 2 )

(Ref. I ) , bu t i n compress ion t h e q u a s i - e l a s t i c modulus d e c r e a s e s w i t h

i n c r e a s i n g p re load (F ig . 3 ) (Ref. 1 ) . For e n g i n e e r i n g pu rposes , t h e t e n s i l e

q u a s i - e l a s t i c modulus i s t h e most u s e f u l Young's modulus, because i t c l o s e l y

approximates t h e e l a s t i c r e s p o n s e of a g r a p h i t e component a f t e r i n i t i a l

l o a d i n g and because it can b e more a c c u r a t e l y measured from a stress-

s t r a i n c u r v e t h a n t h e t a n g e n t modulus. With r e p e a t e d c y c l i n g , t h e wid th

of t h e h y s t e r e s i s l oop d e c r e a s e s d u r i n g t h e f i r s t few c y c l e s bu t t h e v a l u e

of t h e q u a s i - e l a s t i c modulus changes v e r y l i t t l e (F ig . 5 ) (Ref. 4 ) .

The Young's modulus of n u c l e a r , g r a p h i t e s f a l l s i n t h e r a n g e 0.5 t o 6 2 x 10 p s i , depending on t h e p r e f e r r e d o r i e n t a t i o n , d e n s i t y , and c r y s t a l -

l i n i t y of t h e material.

F i g u r e 3 shows t h a t e x t e n s i v e p r e l o a d i n g i n compression r e d u c e s t h e

q u a s i - e l a s t i c modulus. Compressive p r e l o a d i n g a l s o r e d u c e s t h e sonic:

modulus and t h e t e n s i l e modul i (Refs . 1,2,8). Anneal ing t o t h e g r a p h i t i -

z a t i o n t empera tu re r e s t o r e s t h e mechanica l r e s p o n s e of a p re loaded specimen

t o i t s o r i g i n a l c o n d i t i o n (Refs . 2 , 4 ) .

2.3. LATERAL STRAINS AND POISSON'S RATIO

Although t h e s t r e s s - l o n g i t u d i n a l s t r a i n c u r v e s have a symmetrica.1

shape i n t e n s i o n and compress ion (F igs . 1 and 4 ) , t h e s t ress- la teral s t r a i n

c u r v e s are s i g n i f i c a n t l y d i f f e r e n t i n t e n s i o n and compression (Refs . 2 , 4 ) .

During a t e n s i l e test t h e stress-lateral s t r a i n c u r v e i s convex toward t h e

s t r a i n axis , whereas d u r i n g a compress ive t es t t h e cu rve i s concave toward

t h e s t r a i n a x i s , An example i s shown i n F i g . 6 (Ref. 4 ) . One r e s u l t i s

2-6

12

I I I I 1

/&A- CO MP R ESS I O N y- 1 I I I

P

2.0 1.6 1.2 0.8 0.4 0 0.4 STRAIN (%)

.

F i g . 4 . Composite t e n s i o n and compression d a t a f o r two specimens of A T J g r a p h i t e , i n t h e w i t h - g r a i n d i r e c t i o n (from Ref . 2 )

2- 7

4000

3500

3000

2500 h - rn n 1

% 2000

L w DZ

1500

1000

. 500

0 0 0.1 0.2 0.3 0.4 0.5 0.6

LONGITUDINAL STRAIN, EA (%)

Fig. 5. Cyclic stress-strain curves for EGCR-type AGOT graphite, parallel to the extrusion axis (12 cycles) (from Ref. 4 )

2- 8 .

TENS1 0 N

,

4

z3

5 2

z '

1

n M 0

v) v) w CT

n " 0.02 0.01 0 0 0.1 0.2 0.3 0.4 LATERAL E LONGITUDINAL E

STRAIN (%)

COMPR ESSl 0 N

" 0.2 0.1 0 0 0.4 0.8 1.2 1.6 2.0

LATERAL E LONGITUDINAL E

STRAIN (%)

Fig. 6. Schematic drawings of longitudinal and lateral stress-strain curves for nuclear graphite (from Ref. 4 )

2- 9

t h a t a f t e r l oad ing i n t e n s i o n and r e t u r n i n g t o z e r o stress, t h e specimen

h a s a p o s i t i v e permanent se t i n b o t h t h e l o n g i t u d i n a l and t r a n s v e r s e

d i r e c t i o n s . Another r e s u l t i s t h a t P o i s s o n ' s r a t i o measured d u r i n g a

t e n s i l e t e s t d e c r e a s e s w i t h i n c r e a s i n g s t r a i n , bu t d u r i n g a compression

t e s t P o i s s o n ' s r a t i o i s r e l a t i v e l y i n s e n s i t i v e t o s t r a i n l e v e l . An

example i s shown i n F i g . 7 .

For a n i s o t r o p i c g r a p h i t e , P o i s s o n ' s r a t i o i s independent of d i r e c t i o n

and f a l l s i n t h e r ange 0.1 t o 0.25 (Refs . 9-11). For a needle-coke g r a p h i t e

stressed a long t h e a x i s of f a b r i c a t i o n , P o i s s o n ' s r a t i o i s t h e same i n

= - ( S / S ) I and i s t y p i c a l l y 0 .1 t o a l l o r t h o g o n a l d i r e c t i o n s [ v - 0.15. When stress i s a p p l i e d i n t h e r a d i a l d i r e c t i o n , P o i s s o n ' s ra t : io

c a l c u l a t e d from t h e s t r a i n measured i n t h e o t h e r r a d i a l d i r e c t i o n [p = 1 2 p21 = - ( S

"13 - '23 13 11

13 33 31 - '32

/ S ) ] i s abou t 0 .1 , w h i l e P o i s s o n ' s r a t i o f o r t h e a x i a l s t r a i n 12 1 1 - = - ( S / S ) ] i s somewhat l o w e r ( t y p i c a l l y 0.05) ( R e f . 4 ) ~ .

2 . 4 . EQUATIONS FOR STRESS-STRAIN CURVES

S e v e r a l workers have p o s t u l a t e d models t o r e p r e s e n t t h e s t r e s s - s t r a i n

behav io r of p o l y c r y s t a l l i n e g r a p h i t e . The one which h a s r e c e i v e d t h e most

a c c e p t a n c e i s t h a t of J e n k i n s (Ref. 1 2 ) . Th i s model p roposes a l i m i t e d

amount of p l a s t i c s t r a i n o c c u r r i n g i n i n d i v i d u a l g r a i n s ; t h e number of

g r a i n s w i t h p l a s t i c s t r a i n i n c r e a s e s as t h e a p p l i e d stress i n c r e a s e s .

R h e o l o g i c a l l y , t h i s i s e q u i v a l e n t t o a series of s p r i n g s and f r i c t i o n

e l emen t s . The i n i t i a l l o a d i n g c u r v e h a s t h e form

2 E = A O + B O ,

where E i s t h e s t r a i n , O i s t h e stress, A i s t h e r e c i p r o c a l of t h e t a n g e n t

modulus, and B i s a p l a s t i c compliance parameter . The e q u a t i o n f o r unload-

i n g from a peak stress, 0 and peak s t r a i n , E i s m ' m'

1 2 E - E = A ( o -0) + - B(Om-O) , m m 2

n

2-1 0

0 Ad 0.05 0.10 0.15 0 0.5 1 .o 1.5 2.0 0

LONGITUDINAL STRAIN IN COMPRESSION (%) LONGITUDINAL STRAIN IN TENSION (%)

- 'i

Fig. 7. Transverse-to-longitudinal strain ratio curves for EGCR-type AGOT graphite (from Ref. 4 )

2-1 1

and t h e e q u a t i o n f o r r e l o a d i n g from 0 i s 0

Although based on a v e r y s imple concep t , J e n k i n s ' e q u a t i o n s f i t t h e

mechanica l behav io r of n u c l e a r g r a p h i t e remarkably w e l l . An a l t e r n a t i v e

model by Hesketh (Ref. 13) v i s u a l i z e s a n a g g r e g a t e of g r a i n s w i t h a d l i s -

t r i b u t i o n of y i e l d stresses.

t h e form

Heske th ' s model p r e d i c t s a l o a d i n g c u r v e of

where E i s t h e s i n g l e c r y s t a l e l a s t i c modulus and E i s t h e s i n g l e c r y s t a l

y i e l d s t r a i n . Woolley (Ref , 1 4 ) d e r i v e d a model based on t h e mot ion of

b a s a l d i s l o c a t i o n s i n which g r a i n s become p l a s t i c p r o g r e s s i v e l y , The pre-

d i c t e d l o a d i n g c u r v e h a s t h e form

Y

o = E E 0 1- where E i s t h e t a n g e n t Young's modulus and E i s a c o n s t a n t . Both Heske th ' s

0

and Woolley 's e q u a t i o n s can b e made t o f i t observed i n i t i a l l o a d i n g c u r v e s ,

bu t u n l i k e J e n k i n s ' model t h e y cannot e a s i l y b e ex tended t o un load ing o r

r e l o a d i n g c u r v e s .

2.5. EFFECT OF SPECIMEN SIZE ON TENSILE STRENGTH

The e f f e c t of specimen s i z e on u l t i m a t e t e n s i l e s t r e n g t h h a s been t h e

s u b j e c t of several i n v e s t i g a t i o n s which gave no c o n s i s t e n c y of r e s u l t s .

Los ty and Orchard (Ref. 1 ) found t h a t t e n s i l e specimens of a n u n s p e c i f i e d 2 n u c l e a r g r a p h i t e w i t h c r o s s - s e c t i o n a l areas of 0 .5 , 0 ,250 , and 0.125 i n ,

had s i m i l a r t e n s i l e s t r e n g t h s , w h i l e specimens w i t h a 0.0625-in. area had

j u s t s i g n i f i c a n t l y lower s t r e n g t h s .

2

No s imi l a r s i z e e f f e c t w a s found f o r

?

n

2-1 2 a

f l e x u r a l spec imens , Digesu and P e a r s (Ref. 15) t e s t e d specimens of A T J

b g r a p h i t e whose d i a m e t e r s ranged from 0.063 t o 1 i n . The u l t i m a t e t e n s i l e

s t r e n g t h s w e r e s i m i l a r excep t f o r t h e 1- in . -diameter spec imens , whose

mean s t r e n g t h w a s 1 1 % lower , G r e e n s t r e e t e t a l . (Ref . 16) found no s i g n i -

f i c a n t e f f e c t of specimen s i z e on t h e s t r e n g t h of EGCR-type AGOT g r a p h i t e

f o r d i a m e t e r s i n t h e r a n g e 0 ,128 t o 0 .75 i n . I n c o n t r a s t , Lungagnani and

Kre fe ld (Ref. 17 ) found t h a t t h e mean s t r e n g t h of t e n s i l e specimens of a

Gilso-coke g r a p h i t e dec reased p r o g r e s s i v e l y as t h e specimen volume i n c r e a s e d

from 0.7 t o 6.2 c m 3 , w i t h t h e smallest specimens ave rag ing 30% s t r o n g e r t h a n

t h e l a r g e s t specimens. Experiments on n e a r - i s o t r o p i c H-451 g r a p h i t e a t

Genera l Atomic Company showed t h a t t e n s i l e specimens measuring 0.5 i n . i n

d i ame te r by 3 i n . i n l e n g t h ave rage abou t 5% weaker t h a n specimens measur ing

0.25 i n . i n d i ame te r by 0 . 9 i n . i n l e n g t h (Ref . 18) .

I n t e r p r e t a t i o n of t h e e f f e c t of specimen s i z e on s t r e n g t h i s d i s c u s s e d

i n S e c t i o n 2 . 1 0 of t h i s r e p o r t .

2 .6 , FLEXURAL TESTS AT ROOM TEMPERATURE

When g r a p h i t e specimens a r e t e s t e d i n bending and t h e bending moment

a t f a i l u r e i s used t o c a l c u l a t e t h e modulus of r u p t u r e assuming l i n e a r l y

e l a s t i c b e h a v i o r , t h e v a l u e s o b t a i n e d a r e between 1 .5 and 2 t i m e s h i g h e r

t h a n t h e u l t i m a t e t e n s i l e s t r e n g t h . G r e e n s t r e e t e t a l . (Ref , 16 ) performed

f l e x u r a l tests on EGCR-type AGOT g r a p h i t e and ana lyzed t h e r e su l t s t ak ing

n o n l i n e a r i t y i n t o a c c o u n t , They found t h a t t h e t r u e o u t e r f i b e r stress a t

f a i l u r e i n t h e bend tests ag reed w i t h t h e u l t i m a t e t e n s i l e s t r e n g t h a f t e r

t h e observed u l t i m a t e t e n s i l e s t r e n g t h had been i n c r e a s e d t o a l l o w f o r

nonun i fo rmi ty of s t r a i n around t h e c i r cumfe rence . I n c o n t r a s t , Brock lehur s t

and Darby (Ref. 19) found t h a t f o r a n i s o t r o p i c n u c l e a r g r a p h i t e , t h e con-

v e n t i o n a l modulus of r u p t u r e o v e r e s t i m a t e s t h e t r u e o u t e r f i b e r stress by

o n l y a few p e r c e n t .

A r i g o r o u s t r e a t m e n t of t h e e f f e c t s of n o n l i n e a r i t y on t h e f l e x u r a l

s t r e n g t h i s complex because such a t r e a t m e n t shou ld t a k e i n t o accoun t

t r a n s v e r s e s t r a i n s and t h e s h i f t i n t h e n e u t r a l a x i s of t h e beam, A

- 2-13 i

s i m p l i f i e d approach may b e made by u s i n g one of t h e e x p r e s s i o n s i n S e c t i o n

2 . 4 i n p l a c e of Hooke's l a w t o c a l c u l a t e t h e r e l a t i o n s h i p between bending

moment and o u t e r f i b e r s t r a i n of t h e beam. Woolley 's e q u a t i o n (Ref. 14)

re la tes stress, 0 , s t r a i n , E, Young's modulus, E , and a c u r v a t u r e pa rame te r ,

E : 0

0 = EE 0 [l - exp (- $-)I .

T h i s e q u a t i o n y i e l d s t h e f o l l o w i n g r e l a t i o n s h i p s between t h e modulus of

r u p t u r e (bend s t r e n g t h c a l c u l a t e d assuming e l a s t i c b e h a v i o r ) and t h e t r u e

o u t e r f i b e r s t r a i n a t f r a c t u r e , E f :

Rec tangu la r c r o s s - s e c t i o n beam

C y l i n d r i c a l beam

2 3 [i - 0.340 (2) + 8 . 3 3 ~ 1 0-2 (2) - 1 . 6 2 ~ 1 0-2 (::) 0 0

f MOR = E€

+ 2 . 6 0 ~ 1 0-3 (;r] .

C o r r e c t i o n f a c t o r s which may b e a p p l i e d t o c o n v e r t t h e c o n v e n t i o n a l l y

c a l c u l a t e d modulus of r u p t u r e t o t h e t r u e o u t e r f i b e r stress a t f r a c t u r e

are p l o t t e d i n F i g . 8 f o r a g r a p h i t e w i t h E = 0.004 ( a p p r o p r i a t e f o r a

n e a r - i s o t r o p i c petroleum-coke-based g r a p h i t e such as Great Lakes Carbon

Company g r a d e H-451). These c o r r e c t i o n f a c t o r s w e r e a p p l i e d t o t h e r e s u l t s

of f o u r - p o i n t bend tests conducted a t Genera l Atomic Company on H-451 nea r -

i s o t r o p i c g r a p h i t e (Ref. 18). The c o r r e c t e d f l e x u r a l s t r e n g t h s ave raged

0

t

n

2-1 4 E

co

11

ccn

(D

i-t m

0 1

w.

X

A

0

w

0

0

A

Kl

w

P

Ln

m

TRU

E O

UTER

FIB

ER S

TRES

S ,03

YOUN

G'S

MO

DULU

S N

W

P

about 50% h ighe r t h a n t h e t e n s i l e s t r e n g t h s of companion samples , whereas

uncor rec t ed moduli of r u p t u r e averaged 80% h i g h e r . It i s notewor thy t h a t

h igh bend s t r e n g t h - t o - t e n s i l e s t r e n g t h r a t i o s a r e a l s o found i n baked

ca rbon bod ies and n e u t r o n - i r r a d i a t e d g r a p h i t e s , even though t h e s e materials

e x h i b i t l i n e a r s t r e s s - s t r a i n behav io r .

n

The d i f f e r e n c e between bend and t e n s i l e s t r e n g t h s p robab ly o c c u r s

because t h e s t r e n g t h of g r a p h i t e i s c o n t r o l l e d by f l a w s . Models such as

t h e Weibull t h e o r y of f r a c t u r e ( d i s c u s s e d more f u l l y i n S e c t i o n 2.10)

assume t h a t t h e mater ia l c o n t a i n s a d i s t r i b u t i o n of weakening f l a w s , and

f a i l u r e i s l i n k e d t o t h e p r o b a b i l i t y of encoun te r ing a major f l a w i n a

h i g h l y s t r e s s e d zone, Weibul l c a l c u l a t i o n s have been found t o b e i n f a i r l y

good agreement w i t h t h e b e n d - t o - t e n s i l e s t r e n g t h r a t i o of u n i r r a d i a t e d

needle-coke H-327 g r a p h i t e (Ref . 20) and n e a r - i s o t r o p i c H-451 g r a p h i t e

( R e f . I S ) .

2 . 7 . EFFECT OF TEMPERATURE ON MECHANICAL PROPERTIES

A s t h e t e s t t empera tu re i s i n c r e a s e d , t h e s t r e n g t h of g r a p h i t e r ises

p r o g r e s s i v e l y up t o abou t 2500°C. A t y p i c a l example of t h e v a r i a t i o n of

u l t i m a t e t e n s i l e s t r e n g t h w i t h t e m p e r a t u r e (Ref. 21) i s shown i n F i g . 9 .

A t low s t r a i n ra tes ( l e s s t h a n 0 .5 /min) , t h e s t r e n g t h t y p i c a l l y i n c r e a s e s

over i t s room-temperature v a l u e by 25% a t 1000°C, by 50% a t 2000"C, and by

100% a t 2500°C. Above 2500"C, p l a s t i c de fo rma t ion becomes e x t e n s i v e and

t h e s t r e n g t h a g a i n d e c l i n e s .

Time-dependent c r e e p i s i n s i g n i f i c a n t a t t empera tu res below 2000°C

( excep t under t h e i n f l u e n c e of i r r a d i a t i o n ) , Above 2000"C, c r e e p r a t e s

i n c r e a s e s h a r p l y w i t h b o t h t e m p e r a t u r e and stress, and t e n s i l e e l o n g a t i o n s

t o f r a c t u r e r ise s t e e p l y from a f r a c t i o n of a p e r c e n t a t 2000°C t o s e v e r a l

p e r c e n t a t 2500°C. I n t h i s t empera tu re r ange , b o t h t h e e l o n g a t i o n and

s t r e n g t h d e c r e a s e w i t h i n c r e a s i n g s t r a i n ra te .

E l a s t i c modulus measurements a t h i g h t e m p e r a t u r e s have u s u a l l y employed

dynamic t e c h n i q u e s . Up t o abou t 2000"C, Young's modulus i n c r e a s e s w i t h n

2-1 6 i

..

,

4000

3500

3000

2500

2000

1500

1000

500

H4LM GRAPHITE ORIENTATION: TRANSVERSE ATMOSPHERE: HELIUM TESTING RATE: 0.005/MIN

K

I I 1 1 I 1 I I I I

0 250 500 750 1000 1250 1500 1750 2000 2250 2500

TEMPERATURE (OC)

Fig. 9. Transverse tensile strength of H4LM graphite as a function of - temperature when tested in static helium at 0.005/min (from Ref. 21)

2-1 7

t e m p e r a t u r e , i n c r e a s i n g by 10% t o 15% a t 1000°C and 30% t o 40% a t 2000°C.

An example i s shown i n F ig . 10 (Ref . 2 2 ) . The dynamic Young's modulus

p a s s e s through a maximum a t 2000" t o 2200°C (Ref. 23) . When measured by

s t a t i c t e c h n i q u e s , t h e i n i t i a l i n c r e a s e w i t h t empera tu re i s less marked

and t h e modulus s t a r t s t o d e c r e a s e a t a lower t e m p e r a t u r e , p o s s i b l y

because of t h e i n f l u e n c e of p l a s t i c s t r a i n (Ref. 2 4 ) .

2.8. MECHANICAL BEHAVIOR UNDER MULTIAXIAL STRESSES

S e v e r a l s t u d i e s have been made i n which g r a p h i t e t u b e s have been

t e s t e d t o f a i l u r e under a combina t ion of i n t e r n a l p r e s s u r e and a x i a l t e n s i o n

o r compress ion , The f a i l u r e p o i n t s have been compared w i t h t h e p r e d i c t i o n s

of v a r i o u s t h e o r i e s f o r f a i l u r e under m u l t i a x i a l s tress, bu t few d e f i n i t i v e

c o n c l u s i o n s have been r eached . The d i f f e r e n t f a i l u r e t h e o r i e s are sum-

mar ized i n S e c t i o n 2 . 1 1 , w h i l e t h e e x p e r i m e n t a l d a t a a r e o u t l i n e d i n t h i s

s e c t i o n .

Some r e s u l t s f o r Graph-1-Tite g r a d e s A and G o b t a i n e d by Ely (Ref. 25) a r e t y p i c a l and a re reproduced i n F i g . 11 . I n t h e t e n s i o n - t e n s i o n q u a d r a n t ,

f a i l u r e g e n e r a l l y o c c u r s under somewhat lower t e n s i l e stresses t h a n i n

u n i a x i a l t e n s i o n . I n t h e tens ion-compress ion q u a d r a n t , t h e t e n s i l e s t r e n g t h

i s n o t reduced u n t i l t h e a p p l i e d o r t h o g o n a l compress ive stresses exceed t h e

a p p l i e d t e n s i l e stress, b u t i t d e c r e a s e s toward z e r o as t h e compress ive

stress approaches t h e u n i a x i a l u l t i m a t e compress ive s t r e n g t h . E ly concluded

t h a t f a i l u r e co r re spond ing t o a maximum s t r a i n ene rgy , o r a m o d i f i c a t i o n of

t h e maximum s t r a i n energy f a i l u r e c r i t e r i o n due t o S t a s s i - D ' A l i a , w a s i n

f a i r agreement w i t h t h e d a t a i n t h e tens ion-compress ion q u a d r a n t , bur: t h e

t e n s i o n - t e n s i o n d a t a ag reed b e t t e r w i t h t h e maximum normal stress f a i l u r e

c o n d i t i o n . I n a l a t e r se r ies of tes ts (Ref. 26) , Ely concluded t h a t a n

a l t e r n a t i v e m o d i f i c a t i o n of t h e maximum s t r a i n energy c r i t e r i o n , i n which

t h e t h r e e p r i n c i p a l stresses are normal ized a c c o r d i n g t o t h e co r re spond ing

u l t i m a t e s t r e n g t h f o r t h e same d i r e c t i o n , f i t t e d t h e d a t a i n b o t h t h e

t e n s i o n - t e n s i o n and tens ion-compress ion q u a d r a n t s ( s e e S e c t i o n 2 . 1 1 ) .

f7 -

8

c

2-1 8

.

3.0

2.5

2.0

1.5

1 .o

0

-

AU C

-

H4LM

1 I I I 1000 1500 2000 2500

TEMPERATURE (OC)

0 500

Fig. 10. Dynamic Young's modulus versus temperature for representative commercial graphites (from Ref. 22)

2-1 9

h, I

rQ 0

6000

4000

2000

0

-2000

-4000

-6000

-8000

-1 0,000

-12,000

-14,000

-16.000

uo = 3500 PSI R = 3.5 p = 0.2

I I 1

0 2000 4000 6000 8000

uo = 3020 PSI R = 4.33 - p = 0.20

( B)

/ -/ ,

I 1 I

0 2000 4000 6000 8000

H O O P STRESS (PSI)

oo = 2840 PSI R = 3.6 !.I = 0.2

--- MAXIMUM STRAIN ENERGY

-.- MAXIMUM NORMAL STRESS

STASSI - 0 2000 4000 6000 8000

F i g . 1 1 . S t r e n g t h of Graph-1-Tite t u b e s under combined stresses: ( a ) g r a d e A , b a t c h 1 ; ( b ) g r a d e A , b a t c h 2 ; and (c) g r a d e G (from R e f . 25)

Broutman e t a l . (Ref. 27) t e s t e d Poco AXM-5Q g r a p h i t e and found t h a t

b i a x i a l t e n s i l e s t r e n g t h s i n t h e t e n s i o n - t e n s i o n quadran t were reduced con-

s i d e r a b l y below t h e u n i a x i a l t e n s i l e s t r e n g t h . They found t h a t t h e t e n s i o n -

compress ion f a i l u r e envelope w a s i n f a i r agreement w i t h t h e mod i f i ed maxi-

mum s t r a i n energy t h e o r y o r t h e Coulomb-Flohr t h e o r y (0 / S - 0 / S = 1 ,

where 0

S are t h e u l t i m a t e t e n s i l e s t r e n g t h and u l t i m a t e compress ive s t r e n g t h ) .

I n t h e t e n s i o n - t e n s i o n q u a d r a n t , t h e maximum s t r a i n energy t h e o r y w a s con-

s i d e r e d a b e t t e r f i t t h a n t h e maximum normal stress t h e o r y b u t s t i l l

o v e r e s t i m a t e d t h e s t r e n g t h .

- -

1 T 2 c and a2 are t h e maximum and minimum p r i n c i p a l stresses and S 1 T

and

C

ATJ-S c y l i n d e r s equipped w i t h s t r a i n gauges were t e s t e d by Babcock

e t a l . (Ref. 2 8 ) i n a n a p p a r a t u s which enabled t h e compression-compression

q u a d r a n t t o b e e x p l o r e d i n a d d i t i o n t o t e n s i o n - t e n s i o n and t e n s i o n -

compression. The compress ive f r a c t u r e stress d a t a c o u l d be approximated

by e i t h e r t h e Coulomb-Mohr t h e o r y o r N o r r i s ' m o d i f i c a t i o n of t h e Von Mises

y i e l d c r i t e r i o n . A p l o t of t h e s t r a i n s a t f a i l u r e was v e r y s c a t t e r e d and

showed no s y s t e m a t i c f a i l u r e envelope .

-

S i m i l a r tes ts on g r a d e A T J g r a p h i t e by Tu-Lung Weng (Ref . 29) showed

t h a t Ely's m o d i f i c a t i o n of t h e maximum s t r a i n energy f a i l u r e c r i t e r i o n made

t h e b e s t o v e r a l l f i t t o t h e d a t a i n a l l f o u r q u a d r a n t s .

S t ra in-gauged t u b e s of Poco AXF-5Q g r a p h i t e were t e s t e d under b i a x i a l

c o n d i t i o n s by J o r t n e r (Ref. 30) a t 70"F, and a d d i t i o n a l t e s t s w e r e made a t

3000" and 4000°F. The f a i l u r e stress and f a i l u r e s t r a i n enve lopes a t 70°F

are shown i n F i g . 12 ( a and b ) . The f a i l u r e stresses i n t h e t e n s i o n -

t e n s i o n enve lope were found t o f i t p r e d i c t i o n s based on t h e Weibul l t h e o r y

f o r t h e s t r e n g t h of b r i t t l e s o l i d s , b u t t h e Weibul l t h e o r y d o e s n o t p r e d i c t

t h e d e c r e a s e i n t e n s i l e s t r e n g t h a t h i g h o r t h o g o n a l compress ive l o a d s . The

maximum s h e a r stress (Mohr-Coulomb) f a i l u r e c r i t e r i o n w a s a b e t t e r f i t i n

t h i s r e g i o n . The t e n s i l e s t r a i n s a t f a i l u r e ( F i g . 12b) were reduced below

t h e u n i a x i a l f r a c t u r e s t r a i n i n t h e t e n s i o n - t e n s i o n quadran t and i n c r e a s e d

above i t i n t h e tens ion-compress ion q u a d r a n t . For t h e h i g h e r t e s t i n g

2 - 2 1

h, I N h)

8

-4 -2 0 2 4 6 8 10 12 14

uH i K S i i

I . A , I I

MAXIMUM PR IN C l PAL TENSILE STRESS I O R GRlFFlTH

STRESS

AXF-SO DATA, 7OoF A MEDIAN, 129 UNIAXIAL SPECIMENS 0 MEDIAN, BIAXIAL SPECIMENS

/

I I I I 1 I

0.010

0

-0.01 0

-0.320

(1-0) @

0

0

0 G3

0 (-2:l)

0

0

(-4:l) 0 O 00

0

-0.004 0 0.004 0.008 0.012

HOOP SiiiaiN

F i g . 12. Biaxial f r a c t u r e d a t a f o r AXF-5Q g r a p h i t e t u b e s t e s t e d a t room tempera tu re : ( a ) f r a c t u r e stresses; (b) f r a c t u r e s t r a i n s ( f rom Ref . 30)

f ') t emDera tures . t h e f r a c t u r e

room-temperature envelopes

B i a x i a l t e s t s by Yahr

s p e c i a l t y g r a p h i t e " showed

stress envelopes were s imilar i n shape t o t h e

b u t were d i s p l a c e d toward h i g h e r stresses.

e t a l . (Ref. 31) on a n u n s p e c i f i e d "ex t ruded

r e s u l t s i n r e a s o n a b l e agreement w i t h e i t h e r t h e

maximum normal s t r e s s c r i t e r i o n o r E l y ' s m o d i f i c a t i o n of t h e maximum s t r a i n

energy c r i t e r i o n . The maximum s h e a r stress c r i t e r i o n d i s a g r e e d w i t h t h e

tens ion-compress ion d a t a .

An assessment of t h e expe r imen ta l r e s u l t s summarized above and t h e

a l t e r n a t i v e f a i l u r e c r i t e r i a i s g iven i n S e c t i o n 2 . 1 1 .

2 .9 . APPLICATION OF FRACTURE MECHANICS TO GRAPHITE

The a n a l y t i c a l methods of f r a c t u r e mechanics a r e used t o p r e d i c t t h e

nominal stress l e v e l s a t which f l a w s i n a m a t e r i a l can p r o p a g a t e and c a u s e

b r i t t l e f r a c t u r e . Although o r i g i n a l l y deve loped f o r h i g h - s t r e n g t h s t e e l

s t r u c t u r e s , t h e t e c h n i q u e s should b e a p p l i c a b l e t o a b r i t t l e m a t e r i a l con-

t a i n i n g f l a w s , such a s g r a p h i t e . For c o n d i t i o n s of p l a n e s t r a i n ( t h o s e

most l i k e l y t o c a u s e a p ropaga t ing c r a c k ) , t h e b a s i c e q u a t i o n r e l a t i n g t h e

nominal f r a c t u r e stress, 0 , t o t h e f l a w s i z e , a , i s

where Q i s a f u n c t i o n of t h e

material p r o p e r t y c a l l e d t h e

l o a d i n g geome.try and f l a w s i z e and

p l a n e s t r a i n f r a c t u r e toughness o r

i s a

c r i t i c a l

stress i n t e n s i t y f a c t o r .

forming c o n t r o l l e d c r a c k s i n t e n s i l e o r beam specimens and measuring t h e

f r a c t u r e stress. Q i s e i t h e r c a l c u l a t e d a n a l y t i c a l l y o r measured from t h e

specimen compl iance under l o a d as a f u n c t i o n of t h e n o t c h d e p t h . The

machined n o t c h must b e s h a r p enough t o e n s u r e p l a n e s t r a i n c o n d i t i o n s a t t h e

t i p and must b e deep compared w i t h t h e i n h e r e n t f l a w s i n t h e m a t e r i a l . I f

t h e n o t c h i s n o t deep compared w i t h t h e i n h e r e n t f l a w s i z e , t h e m a t e r i a l

w i l l n o t b e n o t c h - s e n s i t i v e and E q . 1 w i l l n o t be v a l i d .

KIC i s u s u a l l y measured by machining n o t c h e s o r

2-23

S l i n d (Ref, 32 ) measured t h e l o a d r e q u i r e d t o p r o p a g a t e c r a c k s i n

doub le c a n t i l e v e r e d beam specimens of SGBF n u c l e a r g r a p h i t e . The tests

y i e l d e d c o n s i s t e n t v a l u e s f o r K which were independent of t h e specimen

wid th and c r a c k l e n g t h as expec ted from f r a c t u r e mechanics c o n c e p t s , A

mean v a l u e of 1 .39 k s i @ f o r w i t h - g r a i n f r a c t u r e s w a s ob ta ined f o r K

I C

I C '

Notched-beam specimens of EGCR-type AGOT g r a p h i t e were t e s t e d by

Corum (Ref , 33 ) . R e s u l t s were c a l c u l a t e d u s i n g b o t h t h e a n a l y t i c a l f r a c t u r e

mechanics formula and t h e a l t e r n a t i v e method i n which t h e compliance of

t h e beam i s measured as a f u n c t i o n of c r a c k d e p t h . The two methods gave

s i m i l a r r e s u l t s , C o n s i s t e n t r e s u l t s were ob ta ined p rov ided t h a t t h e r a t i o

of c r a c k d e p t h t o specimen wid th w a s g r e a t e r t h a n 0.1 t o 0 .2 . However,

Corum no ted t h a t i f t h e e f f e c t i v e c r a c k d e p t h w a s assumed e q u a l t o t:he

a r t i f i c i a l c r a c k dep th p l u s one o r two g r a i n d i a m e t e r s , c o n s i s t e n t r e s u l t s

would be o b t a i n e d f o r specimens w i t h a l l c r a c k d e p t h s . Mean values of K IC

were 0.84 k s i & f o r specimens s t r e s s e d p a r a l l e l t o e x t r u s i o n and 0.54

k s i 6 f o r specimens s t r e s s e d p e r p e n d i c u l a r t o e x t r u s i o n .

c a s e , there w a s no d i f f e r e n c e between t h e v a l u e s o b t a i n e d when c r a c k s

propagated p a r a l l e l and p e r p e n d i c u l a r t o e x t r u s i o n .

I n t h e l a t t e r

The most e x t e n s i v e series of f r a c t u r e mechanics tes ts r e p o r t e d t o

d a t e was performed by Yahr e t a l . (Refs . 34-36). Notched beams of Poco

AXM g r a p h i t e and Union Carb ide A T J g r a p h i t e were t e s t e d w i t h seve ra l . d i f -

f e r e n t s i z e s and n o t c h shapes and d e p t h s , t o g e t h e r w i t h notched t e n s i l e

specimens and doub le c a n t i l e v e r e d beams (Ref , 3 4 ) . KIC v a l u e s showed a

tendency t o d e c r e a s e a s t h e c r a c k s h a r p n e s s i n c r e a s e d , and t h e y were inde-

pendent of specimen c o n f i g u r a t i o n provided t h a t t h e c r a c k depth- to-specimen

wid th r a t i o w a s g r e a t e r t h a n 0.1 f o r A T J g r a p h i t e o r 0.05 f o r t h e f i n e r -

g r a i n e d AXM.

o b t a i n e d :

The f o l l o w i n g v a l u e s f o r KIC (? one s t a n d a r d d e v i a t i o n ) were

AXM, a l l o r i e n t a t i o n s : 1 . 1 7 2 0.08 k s i ,/in.

A T J , w i t h - g r a i n l o a d i n g , w i th -g ra in c r a c k i n g :

0.82 2 0.05 k s i d i n .

2-24

A T J , wi th-gra in l o a d i n g , a c r o s s - g r a i n c r a c k i n g :

0.81 2 0.06 k s i 6;

A T J , a c r o s s - g r a i n l o a d i n g , w i th -g ra in c r a c k i n g :

0.69 2 0.04 k s i d i n .

It w a s no ted t h a t i f t h e s e v a l u e s a re combined w i t h t h e observed t e n s i l e

s t r e n g t h of t h e materials, c r i t i c a l f l a w s i z e s of 0 .01 i n . f o r A T J

g r a p h i t e and 0.003 i n . f o r AXM g r a p h i t e are c a l c u l a t e d . These s i z e s a re i n

r e a s o n a b l e agreement w i t h t h e l a r g e s t i n t e r g r a n u l a r p o r e s observed micro-

g r a p h i c a l l y .

Two l a t e r ser ies of t e s t s (Refs . 35 ,36) examined t h e a p p l i c a t i o n o f

f r a c t u r e mechanics t o t h e same two g r a p h i t e s under complex stress c o n d i t i o n s .

I n t h e f i r s t se r ies , c i r c u l a r o r e l i p t i c a l d i s k s of A T J and A D 1 g r a p h i t e w i t h

s l i t s c u t a t t h e c e n t e r were loaded i n compression a l o n g t h e d i a m e t e r o r

major a x i s u n t i l f a i l u r e o c c u r r e d by c r a c k s p ropaga t ing from t h e s l i t s

(Ref. 3 5 ) . The stress a t t h e c e n t e r i s b i a x i a l ; t h e p r i n c i p a l s tresses

are t e n s i o n p e r p e n d i c u l a r t o l o a d i n g and compression p a r a l l e l t o l o a d i n g .

It w a s found t h a t t h e l o a d a t f a i l u r e could r e a s o n a b l y be p r e d i c t e d from

f r a c t u r e mechanics c o n s i d e r a t i o n s , u s i n g t h e v a l u e s of K l i s t e d above ,

provided t h a t t h e t e s t i n g geometry w a s n o t i n v a l i d a t e d by c r u s h i n g a t t h e

p o i n t s of c o n t a c t w i t h t h e l o a d i n g p l a t e n s , The second ser ies of t e s t s

(Ref. 36) used t h i c k - w a l l e d , c losed-end c y l i n d e r s w i t h c i r c u m f e r e n t i a l

n o t c h e s machined d i a g o n a l l y a t t h e wall-to-end j u n c t i o n , The c y l i n d e r s

w e r e p r e s s u r i z e d u n t i l t h e y f a i l e d by t h e end b reak ing o f f . The f a i l u r e

p r e s s u r e s were i n good agreement w i t h p r e d i c t i o n s based on f r a c t u r e

mechanics .

IC

Mean K v a l u e s of 1 .54 and 1.36 k s i 6 were o b t a i n e d f o r two United I C Kingdom n u c l e a r i s o t r o p i c g r a p h i t e s by M a r s h a l l and P r i d d l e , who used t h e

compact t e n s i o n " notched s l a b specimen (Ref , 3 7 ) . I n a subsequent paper I 1

(Ref, 3 8 ) ) t h e same a u t h o r s sugges t ed t h a t f r a c t u r e mechanics c o n c e p t s

might b e used t o e x p l a i n t h e d i f f e r e n c e between t h e f l e x u r a l s t r e n g t h and

t e n s i l e s t r e n g t h of g r a p h i t e specimens. I f a f l e x u r a l o r t e n s i l e specimen

1 2-25

i s r ega rded as a uniform beam w i t h a n edge n o t c h e q u a l t o t h e maximum p o r e

s i z e , f r a c t u r e mechanics formulae may be used t o p r e d i c t t h e r a t i o o f bend

s t r e n g t h t o t e n s i l e s t r e n g t h . The specimens t e s t e d were 6 mm wide and con-

t a i n e d p o r e s between 0 . 6 and 2 mm wide. For t h e s e f l a w s i z e s , t h e picedicted

bend- to - t ens i l e s t r e n g t h r a t i o i s 1 . 2 t o 1 . 5 , i n rough agreement w i t h t h e

e x p e r i m e n t a l r e s u l t s . However, t h i s approach cannot b e c o r r e c t i n g e n e r a l

because i t would r e q u i r e t h a t i f l a r g e specimens o r f ine -pored g r a p h i t e s are

u s e d , t h e f l e x u r a l s t r e n g t h w i l l e q u a l t h e t e n s i l e s t r e n g t h , and t h i s is

n o t observed .

Andersson and S a l k o v i t z (Ref. 39) measured t h e f r a c t u r e toughness o f

Union Carb ide g r a d e s ZTA and A T J and Poco g r a p h i t e g r a d e s AXZ and AXF-5Q

g r a p h i t e s . They used center -notched p l a t e specimens under u n i a x i a l t e n s i o n

and used t h e r e s u l t s t o c a l c u l a t e b o t h K and t h e c r i t i c a l s t r a i n energy

re lease r a t e ,

v i s P o i s s o n ’ s r a t i o and E i s Young’s modulus.] The r e s u l t s were as follows:

2 2 IC ( 1 - V )/E, where -

- 5 c [For p l a n e s t r a i n c o n d i t i o n s , GIG.

O r i e n t a t i o n ( t o molding

a x i s ) ( d e g r e e s ) Ma t e r i a 1

Z TA 0

ZTA 90

AT J 0

AT J 90 AXF- 54 -- AXZ --

( p s i - i n .

6 6 0

1440

7 50

905

1120

7 20

GI c ( p s i - i n . )

0.660

0 .760

0.580

0.580

0.590

0.360

The d a t a i n d i c a t e t h a t , f o r a g i v e n ma te r i a l , GIC i s less o r i e n t a t i o n -

F u r t h e r , GIC f o r t h e f o u r g r a p h i t e g r a d e s i s approxi - dependent t h a n K

mate ly a l i n e a r f u n c t i o n of t h e f r a c t i o n a l p o r o s i t y , e x t r a p o l a t i n g t o 0.97

p s i - i n , f o r f u l l y d e n s e mater ia l .

I C ’

To summarize, a n a l y s e s based on f r a c t u r e mechanics may be a p p l i e d t o

notched g r a p h i t e t e s t specimens provided t h a t t h e n o t c h d e p t h i s l a r g e /7

2-26

compared with the inherent pore size and that the conditions at the crack

tip are approximately plane-strain. Experimental values for K range

between 0.5 and 1.5 k s i - K with no clear systematic dependence on graphite

type.

IC

GIC values appear to increase with decreasing porosity.

2.10. APPLICATION OF WEIBULL STATISTICAL THEORY TO GRAPHITE

Several characteristics of the strength of many brittle solids (for

example, the variability in strength, the dependence of mean strength on

specimen volume, and the difference between ultimate tensile strength and

flexural strength) are qualitatively consistent with Weibull's statistical

theory of strength (Refs. 4 0 , 4 1 ) . IJeibull's model assumes that the material

contains a distribution of flaws of varying size. When the material is

subjected to a tensile stress, the strength is controlled by the combination

of the highest local stress and the most severe flaw. The probability of

survival, S ( O ) , of a small volume element under a tensile stress o is assumed to have the form

This yields the following expression for the failure probability of

the bulk specimen, F:

F = 1 - exp [-( (-r dV] ,

where 0 is the tensile stress in the element, Ou is the "minimum failure

stress" below which the failure probability is zero, 0 is a normalizing

parameter, and m is a parameter called the Weibull modulus, O u , 0 0 ' and

m are determined from experimental strength measurements by best-fit

methods. For simple non-uniform stress systems, E q . 2 may be integrated

analytically to give the following type of expression for the ratio of the

0

2-27

median s t r e n g t h under non-uniform stress, 0 t o t h e median t e n s i l e

s t r e n g t h , 0 : nu ’

t

f(m, stress g r a d i e n t ) , 0 nu

t nu (3 )

where V

s t ress specimens, r e s p e c t i v e l y . The l a s t t e r m i n Eq. 3 depends on t h e

s t ress g r a d i e n t and i s d i f f e r e n t f o r t h ree -po in t bending , four -poin t

bending , t u b e s w i t h i n t e r n a l p r e s s u r i z a t i o n , b i a x i a l l o a d i n g , e t c . ; i t s

v a l u e depends on t h e Weibul l modulus, m. Some numer i ca l v a l u e s a re g i v e n

i n Ref. 20.

and Vnu are t h e volume of t h e t e n s i l e specimens and non-uniform t

S e v e r a l tes ts of t h e a p p l i c a b i l i t y of t h e Weibul l model t o g r a p h i t e

have been made. G r e e n s t r e e t e t a l . (Ref. 1 6 ) t e s t e d b a t c h e s of 2 4 t o 32

r e p l i c a t e specimens of AGOT, u s i n g two s i z e s of t e n s i l e specimen and two

s i z e s o f bend specimen. Each s e t of d a t a w a s ana lyzed t o o b t a i n m , 0

and 0 . Reasonably c o n s i s t e n t v a l u e s f o r m ( i n t h e r a n g e 3 t o 4 ) were

o b t a i n e d , e x c e p t f o r t h e d a t a on l a r g e bend spec imens , b u t no c o n s i s t e n t

v a l u e s f o r 0 and O0.

w a s much less marked t h a n t h a t p r e d i c t e d by E q . 3. I t was concluded t h a t

t h e d a t a d i d n o t f i t t h e Weibul l t h e o r y ,

U’

0

The dependence of mean s t r e n g t h on specimen s i z e U

By c o n t r a s t , Lungagrami and K r e f e l d (Ref. 17) t e s t e d t e n s i l e specimens

of a Gilsocarbon-based n u c l e a r g r a p h i t e w i t h volumes between 0 . 7 and 6 . 2

c m 3 and o b t a i n e d a s i n g l e set of v a l u e s f o r m , 0

s t r e n g t h d i s t r i b u t i o n of a l l specimen s e t s w i t h t h e p o s s i b l e e x c e p t i o n of

and 0 which f i t t e d t h e U ’ 0

t h e smallest s i z e .

P r i c e and Cobb (Ref. 20) f i t t e d Weibul l pa rame te r s t o s e t s of t e n s i l e

d a t a on H-327 needle-coke g r a p h i t e from d i f f e r e n t p a r t s of t h e l o g . Bend

t e s t s and th i ck -wa l l ed tube -bur s t t es t s showed h i g h e r mean s t r e n g t h s t h a n

t h e t e n s i l e tests; however, t h e d a t a could b e made t o f i t t h e Weibull. model

o n l y i f t h e volume dependence term (Eq. 3) w a s i g n o r e d .

c

2-28

Brock lehur s t and Darby (Ref. 19) drew somewhat s imi l a r c o n c l u s i o n s from

t e n s i l e , bend, t u b e - b u r s t , and r i n g d i a m e t r a l compression t e s t s on i s o t r o p i c

n u c l e a r g r a p h i t e . They observed t h e expec ted i n c r e a s e i n mean s t r e n g t h w i t h

i n c r e a s i n g stress g r a d i e n t , b u t found t h a t t h e m-value deduced from t h e

d i s t r i b u t i o n of t e n s i l e s t r e n g t h s g r e a t l y o v e r e s t i m a t e d t h e volume dependence

of s t r e n g t h , w h i l e s l i g h t l y u n d e r e s t i m a t i n g t h e dependence on s t ress gra-

d i e n t . It was concluded t h a t w h i l e i t i s p o s s i b l e t o e v a l u a t e Weibul l

pa rame te r s f o r a s i n g l e t e s t , no c o n s i s t e n t v a l u e s c a n b e d e r i v e d which

f i t a l l t h e d a t a .

Comparison of bend and t e n s i l e t es t s on a v a r i e t y o f Pechniney

g r a p h i t e s (Ref. 42) a l s o l e d t o t h e c o n c l u s i o n t h a t t h e 1Je ibu l l model

o v e r e s t i m a t e s t h e specimen volume e f f e c t .

Experiments a t Genera l Atomic Company on n e a r - i s o t r o p i c H-451 g r a p h i t e

(Ref . 18) showed t h a t t h e d i s t r i b u t i o n of t e n s i l e s t r e n g t h s was f a i r l y w e l l

r e p r e s e n t e d by a Weibul l d i s t r i b u t i o n f u n c t i o n w i t h a n m-value averaging

a b o u t 9. The mean t e n s i l e s t r e n g t h of 0 .5- in . -d iameter b:- 3- in . - long

specimens w a s a b o u t 5% lower t h a n t h a t of 0 .25- in . -d iameter by 0.9- in . -

l o n g spec imens , whereas t h e Weibul l model w i t h m = 9 would p r e d i c t a d i f -

f e r e n c e i n mean s t r e n g t h s of 25%. The f l e x u r a l s t r e n g t h of 0 .25- in . -

d i a m e t e r specimens averaged 50% h i g h e r t h a n t h e t e n s i l e s t r e n g t h s of

companion spec imens , i n f a i r l y good agreement w i t h a v a l u e of 59% p r e d i c t e d

by t h e Weibul l t h e o r y .

The l a s t f o u r s t u d i e s a l l a s s i g n e d a v a l u e of z e r o t o o , T h i s i s a U

c o n s e r v a t i v e assumpt ion , and i t h a s been j u s t i f i e d by measurements on

Poco g r a p h i t e which showed t h a t t h e r e w a s no s i g n i f i c a n t d i f f e r e n c e i n t h e

f i t of t h e e x p e r i m e n t a l d a t a o b t a i n e d by t a k i n g a b e s t - f i t v a l u e f o r 0

and t a k i n g 0 = 0 (Ref , 4 3 ) . u

U

It may b e concluded t h a t w h i l e t h e Weibul l model a p p e a r s t o f i t t h e

t e n s i l e s t r e n g t h d i s t r i b u t i o n and r a t i o s of t e n s i l e s t r e n g t h t o t u b e - b u r s t

s t r e n g t h and f l e x u r a l s t r e n g t h o f many g r a p h i t e s , i t g r e a t l y o v e r e s t i m a t e s

2-29

t h e volume e f f e c t . Thus, i t does n o t c o n s t i t u t e a s e l f - c o n s i s t e n t model

f o r t h e behav io r of most g r a p h i t e s .

2 . 1 1 . FAILURE C R I T E R I A FOR GRAPHITE

S i n c e p l a s t i c f l o w i n g r a p h i t e i s n e g l i g i b l e , f a i l u r e o c c u r s by

b r i t t l e f r a c t u r e w i t h t h e p r o p a g a t i o n of a c r a c k a c r o s s a load-bear ing

s e c t i o n . When u n i a x i a l t e n s i l e o r compress ive tests a re conducted , t h e

c o n d i t i o n f o r f a i l u r e may a r b i t r a r i l y b e t a k e n as a c r i t i c a l stress, a

c r i t i c a l s t r a i n , o r some o t h e r parameter c a l c u l a t e d from t h e s t ress o r

s t r a i n . However, when g r a p h i t e i s loaded by a complex o r non-uniform

sys tem of stresses, t h e q u e s t i o n of choos ing a f a i l u r e c r i t e r i o n becomes

i m p o r t a n t .

A number of d i f f e r e n t f a i l u r e c r i t e r i a have been s u g g e s t e d , b u t none

h a s been g e n e r a l l y adopted as a p p l i c a b l e t o g r a p h i t e under a l l l o a d i n g

c o n d i t i o n s . Several of t h e s e f a i l u r e c r i t e r i a may b e d i s t i n g u i s h e d by

t h e i r d i f f e r e n t p r e d i c t e d f a i l u r e envelopes f o r m u l t i a x i a l s t ress sys tems.

The f a i l u r e enve lopes f o r a n i s o t r o p i c g r a p h i t e ( w i t h P o i s s o n ’ s r a t i o = 0 . 2

and t h e u l t i m a t e compress ive s t r e n g t h t h r e e t imes t h e u l t i m a t e t e n s i l e

s t r e n g t h ) unde r a b i a x i a l stress are shown i n F i g . 13 f o r s i x of t h e most

commonly t e s t e d c r i t e r i a . I n t h e d e f i n i t i o n s of f a i l u r e c r i t e r i a which

f o l l o w , i s o t r o p i c e l a s t i c behav io r i s assumed. 0 0 and 0 are t h e

t h r e e p r i n c i p a l stresses;

p r i n c i p a l s tresses; ST and S

s t r e n g t h s , r e s p e c t i v e l y ; v i s P o i s s o n ’ s r a t i o ; and E i s Young‘s modulus.

1 ’ 2’ 3 and 0 are t h e maximum and minimum ‘max min

a re t h e u l t i m a t e t e n s i l e and compress ive C

2 . 1 1 . 1 . Maximum Normal S t r e s s

0 = ST max o r 0 = sc min

”

T h i s i s t h e s i m p l e s t and most commonly used f a i l u r e c r i t e r i o n . I t i s con-

s e rva t ive when used t o p r e d i c t f a i l u r e i n sys tems w i t h a stress g r a d i e n t ,

such as beams i n bending , b u t t e n d s t o o v e r e s t i m a t e t h e s t r e n g t h o f g r a p h i t e

9 i n b i a x i a l t e n s i o n ( s e e S e c t i o n 2 .8 ) .

2-30

0- 0

0 0

0 0

0- 0

0 0

0

-01 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a

MAX. NORMAL STRESS - - - - MAX. NORMAL STRAIN *-• -* MAX. SHEAR STRESS (COULOMB) 0 0 . 0 0 0 0 0 MAX. OlSTORTlON ENERGY (VON MISES) -- MAX. STRAIN ENERGY (ELY) - - - WEIBULL (M = 5)

2

I ' I 0

' . I 1 t le.

I' 1;

I

i I

I I

I I

I I

I I

I

.-- ,

F i g . 13. B i a x i a l f a i l u r e enve lopes p r e d i c t e d by d i f f e r e n t f a i l u r e c r i t e r i a f o r a n i s o t r o p i c g r a p h i t e w i t h P o i s s o n ' s r a t i o = 0.2 and u l t i m a t e compress ive s t r e n g t h = 3 x u l t i m a t e t e n s i l e s t r e n g t h

2-3 1

2.11.2. Maximum Normal Strain

'T ' 0 - v ( a + o ) = 1 2 3

I t h a s been sugges t ed t h a t f a i l u r e i n g r a p h i t e shou ld b e c o n t r o l l e d by a

l i m i t i n g t e n s i l e s t r a i n , l a r g e l y on t h e grounds t h a t p r o c e s s e s which i n c r e a s e

Young's modulus (such as n e u t r o n i r r a d i a t i o n ) o r d e c r e a s e Young's modulus

( such as g r a p h i t i z a t i o n ) have a s i m i l a r e f f e c t on t h e s t r e n g t h . However,

examinat ion of b a t c h e s of t e n s i l e d a t a f rom r e p l i c a t e specimens shows

l a r g e r c o e f f i c i e n t s of v a r i a t i o n f o r t h e f r a c t u r e s t r a i n s t h a n f o r t h e

f r a c t u r e stresses. Fur the rmore , a c o n s t a n t s t r a i n c r i t e r i o n would imply

s u b s t a n t i a l l y h i g h e r s t r e n g t h s i n b i a x i a l t e n s i o n t h a n u n i a x i a l t e n s i o n

( s e e F i g . 1 3 ) , which i s c o n t r a r y t o o b s e r v a t i o n s . There seems t o be no

e x p e r i m e n t a l j u s t i f i c a t i o n f o r such a f a i l u r e c r i t e r i o n .

2.11.3. Maximum Shear Stress (Coulomb, Tresca, o r Mohr C r i t e r i o n )

- = I - ( s h e a r stress a t f a i l u r e ) . 'min ' max

2 max

T h i s c r i t e r i o n i s o f t e n a p p l i e d t o y i e l d i n g i n metals . When a p p l i e d t o

t h e f a i l u r e of b r i t t l e mater ia ls , i t i s n e c e s s a r y t o a s s i g n a c o e f f i c i e n t

of f r i c t i o n between t h e s h e a r p l a n e s t o accoun t f o r t h e h i g h e r u l t i m a t e

s t r e n g t h i n compress ion as compared w i t h t e n s i o n (F ig . 1 3 ) . A number of

a u t h o r s (Refs . 27 ,28 ,30) have compared b i a x i a l f a i l u r e r e s u l t s w i t h t h i s

c r i t e r i o n and observed f a i r agreement w i t h e x p e r i m e n t a l d a t a i n t h e t e n s i o n -

compression quadran t . However, two o b j e c t i o n s may b e r a i s e d a g a i n s t t h e

a p p l i c a t i o n of t h i s c r i t e r i o n t o g r a p h i t e : ( 1 ) a c r i t e r i o n based on

y i e l d i n g i n s h e a r i s n o t r e a l i s t i c f o r g r a p h i t e , which f r a c t u r e s by c r a c k

p r o p a g a t i o n ; and (2) t h e c r i t e r i o n r e q u i r e s t h a t t h e s h e a r s t r e n g t h be

h a l f t h e u n i a x i a l t e n s i l e s t r e n g t h , which i s n o t t r u e f o r g r a p h i t e .

n

2-32

2.11.4. D i s t o r t i o n Energy ( O c t a h e d r a l Shear S t r e s s o r Von Mises C r i t e r i o n )

(a , -02) 2 + (a -0 l 2 + (0 -0 ) 2 y 2 = v5 ST . [ 2 3 3 1

T h i s y i e l d c r i t e r i o n a l s o w a s developed from t h e p l a s t i c y i e l d of meta ls .

I n t h e form g i v e n above, i t p r e d i c t s symmetrical behav io r i n t e n s i o n -

t e n s i o n and compression-compression ( s e e F i g . 1 2 ) . A m o d i f i c a t i o n by N o r r i s

(Ref. 44) a l l o w s t h e f a i l u r e envelope t o p a s s through t h e u n i a x i a l com-

p r e s s i v e s t r e n g t h p o i n t ; i n t h i s form t h e c r i t e r i o n h a s been a p p l i e d t o

tens ion-compress ion f a i l u r e i n g r a p h i t e (Refs . 28 ,29) . However, i t pre-

d i c t s t h a t b i a x i a l s t r e n g t h i n t h e t e n s i o n - t e n s i o n quadran t s h o u l d b e

h i g h e r t h a n t h e u n i a x i a l t e n s i l e s t r e n g t h , which i s c o n t r a r y t o o b s e r v a t i o n s .

2 .11.5. Maximum S t r a i n Energy

The s t r a i n energy c r i t e r i o n most o f t e n used f o r g r a p h i t e i s t h a t of

Ely (Ref. 2 6 ) . For an i s o t r o p i c g r a p h i t e under b i a x i a l l o a d i n g , t h e appro-

p r i a t e e q u a t i o n s f o r t e n s i o n - t e n s i o n and tens ion-compress ion , r e s p e c t i v e l y ,

are

and

T h i s f a i l u r e c r i t e r i o n h a s been found t o b e i n r e a s o n a b l e agreement w i t h

b o t h t e n s i o n - t e n s i o n and tens ion-compress ion expe r imen t s (Refs . 25-27,

29,31) and c o r r e c t l y p r e d i c t s t h e lowered s t r e n g t h s i n b i a x i a l t e n s i o n -

t e n s i o n .

2-33

/7 2 . 1 1 . 6 . Weibull Theory

A s discussed in Section 2.10, the Weibull statistical theory goes a

long way toward explaining many aspects of failure in graphite, but fails

t o provide a completely self-consistent model because it overestimates the

effect of specimen volume. The theory may be extended to multiaxial stress

states because, if the internal flaws are considered planar, the surkival

probability is influenced by the presence of multiaxial stresses (Refs. 20,

4 0 ) . The failure envelope for a graphite with a Weibull modulus, m, of

5 is shown in Fig. 13. The predicted envelope is in fairly good agreement

with experimental data in the tension-tension quadrant (Ref. 3 0 ) , but fails

to predict a decrease in strength as the ultimate compressive strength is

approached.

The application of the Weibull theory to multiaxial stress states for

the purpose of designing with brittle materials is covered in detail in

Ref. 4 5 . .

2.11 .7 . Fracture Mechanics

In principle, the techniques of fracture mechanics (Section 2.9) can

be extended to any complex stress state. Yahr et al. (Refs. 35,36) success-

fully applied fracture mechanics calculations to the biaxial stress state

present in circular and eliptical graphite disks loaded along the major

axis and to pressurized closed-end cylinders with circumferential notches

at the wall-end junction. However, analytical expressions have been worked

out only for a few stressing modes and crack geometries, and it is not yet

possible to quote generalized failure criteria based on fracture mechanics.

Fracture mechanics techniques may be used during the engineering design

o f brittle materials to impose a conservative stress limit (Ref. 4 6 ) . If

the material is likely to contain weakening flaws, the size of the largest

flaw which could escape detection by nondestructive examination is sub-

stituted into the appropriate formula (Eq. I ) , and if the corresponding

2-34

stress i s lower t h a n t h e s a f e working stress o b t a i n e d from s t r e n g t h measure-

ments , t h e more c o n s e r v a t i v e v a l u e must be u s e d .

2 .11.8. Mean Loca l S t r a i n Energy D e n s i t y i n P l a n e of Crack

B r o c k l e h u r s t and Darby (Ref. 19) advanced t h e h y p o t h e s i s t h a t , i n t h e

c a s e of f o u r - p o i n t bend tes ts and p r e s s u r i z e d c y l i n d e r s , f r a c t u r e o c c u r s

when t h e mean s t r a i n ene rgy d e n s i t y averaged o v e r t h e t e n s i l e p a r t o f t h e

f a i l u r e c r o s s s e c t i o n e q u a l s t h e s t r a i n energy d e n s i t y f o r t e n s i l e f r a c t u r e ,

S T / 2 E .

b e 1 .73 times t h e u l t i m a t e t e n s i l e s t r e n g t h , and t h a t t h e f a i l u r e hoop

stress, S H Y i n a n i n t e r n a l l y p r e s s u r i z e d c y l i n d e r o f d i a m e t e r r a t i o R

( i n t e r n a l r a d i u s d i v i d e d by e x t e r n a l r a d i u s ) shou ld be g i v e n by

2 T h i s approach p r e d i c t s t h a t t h e f o u r - p o i n t f l e x u r a l s t r e n g t h s h o u l d

Although n e i t h e r r e l a t i o n s h i p e x a c t l y f i t s t h e d a t a , t h e g e n e r a l

t r e n d s a re accoun ted f o r . However, t h i s c r i t e r i o n cannot b e a p p l i e d t o

cases where t h e stress v a r i e s i n two dimensions (such as a t h r e e - p o i n t

bend t e s t ) because t h e r e s u l t depends on t h e volume of ma te r i a l o v e r which

a v e r a g i n g i s c a r r i e d o u t .

2 . 1 1 . 9 . Conc lus ions on F a i l u r e Cri ter ia

It may b e concluded t h a t t h e maximum normal stress f a i l u r e c r i t e r i o n

i s a d e q u a t e f o r g r a p h i t e under a p redominan t ly un i fo rm, u n i a x i a l stress

(p rov ided t h a t t h e s t a t i s t i c a l v a r i a t i o n i n s t r e n g t h i s t a k e n i n t o a c c o u n t ) .

It i s c o n s e r v a t i v e when a p p l i e d t o sys t ems w i t h a stress g r a d i e n t , b u t non-

c o n s e r v a t i v e when a p p l i e d under m u l t i a x i a l stresses. Under m u l t i a x i a l

stresses, E l y ' s maximum s t r a i n ene rgy c r i t e r i o n p r o v i d e s t h e b e s t o v e r a l l

agreement w i t h t h e d a t a . Where a stress g r a d i e n t i s p r e s e n t , t h e f a c t o r s

p r e d i c t e d by W e i b u l l ' s t h e o r y f i t t h e o b s e r v a t i o n s b e s t , b u t t h i s model

2-35

o v e r e s t i m a t e s t h e e f f e c t of specimen volume. C l e a r l y , t h e s u b j e c t of

f a i l u r e c r i t e r i a i n g r a p h i t e would b e n e f i t from more t h e o r e t i c a l and e x p e r i -

mental investigation.

2 . 1 2 . EFFECT OF O X I D A T I O N ON STRENGTH OF GRAPHITE

Oxid iz ing g a s e s a t t a c k t h e b i n d e r phase of p o l y c r y s t a l l i n e g r a p h i t e

i n p r e f e r e n c e t o t h e f i l l e r . T h i s r e s u l t s i n a v e r y r a p i d d e c r e a s e i n

s t r e n g t h and e l a s t i c modulus. Most of t h e pub l i shed d a t a r e f e r t o n u c l e a r

g r a p h i t e s o x i d i z e d i n carbon d i o x i d e o r a i r a t t empera tu res between 500"

and 1000°C (Refs . 47-50). The r e s u l t s show a p a r a l l e l d e c l i n e in t e n s i l e ,

compress ive , f l e x u r a l , and s h e a r s t r e n g t h , w i t h t h e s t r e n g t h s f a l l i n g 50%

f o r weight l o s s e s between 5% and 10%. T y p i c a l r e s u l t s (Ref . 4 7 ) are shown

i n F i g . 14. Young's modulus d e c r e a s e s a t about t h e same r a t e as t h e

s t r e n g t h , l e a v i n g t h e s t r a i n t o f a i l u r e a lmost unchanged.

The o n l y a n t i c i p a t e d o x i d i z i n g i m p u r i t y i n t h e HTGR c o o l a n t i s a small

amount of water vapor f rom o c c a s i o n a l heat-exchanger l e a k s . Measurements

of t h e t e n s i l e s t r e n g t h o f H-327 g r a p h i t e o x i d i z e d i n a steam-helium m i x -

t u r e (Ref. 51) are v e r y s imilar t o t h e r e s u l t s on g r a p h i t e o x i d i z e d in a i r

o r carbon d i o x i d e , w i t h t h e s t r e n g t h dropping by h a l f a f t e r about 5%

burnof f .

K r e f e l d e t a l . (Ref. 52) have r e p o r t e d expe r imen t s

f e r e n t t y p e s of g r a p h i t e were a l t e r n a t e l y l o a d e d and un

i n which f o u r

oaded i n t e n s

w h i l e exposed t o a n a rgon - 1500 vpm water a tmosphere a t 1000°C. The:

of o x i d a t i o n (as measured by t h e change i n g a s composi t ion) i n c r e a s e d

d i f -

on

ra te

by a f a c t o r of 3 t o 6 when t e n s i l e stresses between 280 and 770 p s i were a p p l i e d .

2-36

6.0

5 .O

M I z X

4.0

w

v) v) w

2 2.0

a a 5 0

1 .o

0

0 OXIDIZED IN C02 AT 875O-96OoC AOXIDIZED IN AIR AT 7OO0C

0 5 10 15 20 25 30 35 40

BURN-OFF (%)

F i g . 14. Compressive strength of Pile G r a d e A graphite as a function of the extent of oxidation ( f r o m Ref. 4 7 )

3 . MECHANICAL PROPERTIES OF IRRADIATED GRAPHITE

3.1. EFFECT OF IRRADIATION ON STRESS-STRAIN CURVE

The most i m p o r t a n t e f f e c t s of n e u t r o n i r r a d i a t i o n on t h e mechanica l

p r o p e r t i e s of g r a p h i t e r e s u l t from t h e p inn ing of b a s a l d i s l o c a t i o n s by

i r r a d i a t i o n - i n d u c e d d e f e c t c l u s t e r s . T h i s r e d u c e s t h e amount of b a s a l

s l i p i n a c r y s t a l l i t e d u r i n g mechanica l l o a d i n g and i n c r e a s e s t h e e f f e c t i v e

s h e a r modulus. One r e s u l t i s t o r e d u c e g r e a t l y t h e c u r v a t u r e of t h e stress-

s t r a i n c u r v e , T a y l o r e t a l . (Ref . 10) found t h a t i r r a d i a t i o n a t 150°C

p r o g r e s s i v e l y s t r a i g h t e n e d t h e s t r e s s - s t r a i n c u r v e s of Uni ted Kingdom

i s o t r o p i c g r a p h i t e b o t h i n t e n s i o n and compression. An example i s shown

i n F ig . 15.

Everett and R idea lgh (Ref. 53) found t h a t c u r v a t u r e j.n t h e t e n s i l e

s t r e s s - s t r a i n c u r v e of a p r e s s e d Gi l soca rbon g r a p h i t e (Dragon code No. 95)

was g r e a t l y reduced , b u t n o t e l i m i n a t e d , a f t e r i r r a d i a t i o n a t 1200°C t o

1021 n/cm (NDE). The "permanent se t" observed d u r i n g mechanica l l o a d i n g

of u n i r r a d i a t e d g r a p h i t e w a s reduced t o less t h a n 0 .01% s t r a i n ( a f t e r

l o a d i n g t o 70% o f t h e t e n s i l e s t r e n g t h and unloading) f o l l o w i n g i r r a d i a t i o n .

2

S t r e s s - s t r a i n measurements a t Genera l A t o m i c Company on H-451 n e a r -

i s o t r o p i c g r a p h i t e and H-327 needle-coke g r a p h i t e i r r a d i a t e d a t tempera-

t u r e s between 600" and 1 3 5 O O C i n c a p s u l e OG-1 (Ref , 54) showed t h a t t h e

e l i m i n a t i o n o f c u r v a t u r e i s more n e a r l y complete a t low i r r a d i a t i o n t e m -

p e r a t u r e s t h a n a t h i g h i r r a d i a t i o n t e m p e r a t u r e s , Examples of s t r e s s - s t r a i n

c u r v e s are shown i n F ig . 16. I n t h e t e s t s from which t h e s e c u r v e s were

o b t a i n e d , t h e stress w a s f i r s t i n c r e a s e d t o 1000 p s i , t h e n reduced t o

100 p s i , and t h e n i n c r e a s e d u n t i l t h e specimen f a i l e d .

3- 1

3.0

- a 2.0 5 --. a Y

m v3 w

Y

a + m

1 .o

0 0

0 UNIRRADIATED 0 1.55 X 1020 N/CM2 A 11.5 X 1020 N / C M ~ 0 MEAN VALUES

pd

0.1 0.2

STRAIN (%)

Fig . 15. V a r i a t i o n i n s t r e s s - s t r a i n c u r v e s i n t e n s i o n w i t h i n c r e a s i n g n e u t r o n f l u e n c e a t 150°C; i s o t r o p i c n u c l e a r g r a p h i t e (from I tef . IO)

3- 2

u

0

0

ru CD

L

0

(Ed) SS3tllS 311SN31

3-3

3 . 2 . EFFECT OF IRRADIATION ON YOUNG'S MODULUS

I r r a d i a t i o n - i n d u c e d p i n n i n g of b a s a l d i s l o c a t i o n s i n c r e a s e s t h e e f f e c -

t i v e C s h e a r modulus of t h e c r y s t a l l i t e s , which i n t u r n i n c r e a s e s t h e

e l a s t i c moduli of t h e b u l k specimen. Most r e p o r t e d measurements of

i r r a d i a t i o n - i n d u c e d i n c r e a s e s i n Young's modulus have been o b t a i n e d from

s o n i c measurements of t h e v i b r a t i o n a l f r equency of c y l i n d r i c a l s amples ,

because such measurements are n o n d e s t r u c t i v e and t h e specimen may be

r e i r r a d i a t e d . O the r r e p o r t e d d a t a are d e r i v e d from s t a t i c s t r e s s - s t r a i n

c u r v e s . It i s impor t an t t o n o t e t h a t t h e two t e c h n i q u e s may n o t givl.

i d e n t i c a l r e s u l t s , e s p e c i a l l y w i t h u n i r r a d i a t e d o r l i g h t l y i r r a d i a t e d

ma te r i a l , I n p a r t i c u l a r , t h e f r a c t i o n a l i n c r e a s e i n s o n i c modulus may b e

lower t h a n t h e f r a c t i o n a l i n c r e a s e i n s t a t i c modulus, because t h e s o n i c

modulus of u n i r r a d i a t e d material i s u s u a l l y h i g h e r t h a n t h e s t a t i c modulus,

whereas t h e two measurements are c l o s e r i n i r r a d i a t e d ma te r i a l . A l l

measurements r e p o r t e d so f a r have been made a t room t e m p e r a t u r e .

4 4

The l a r g e s t body of d a t a on t h e e f f e c t s of n e u t r o n i r r a d i a t i o n on

Young's modulus of g r a p h i t e s comes from Dragon p r o j e c t s o n i c modulus

measurements on c y l i n d r i c a l specimens i r r a d i a t e d t o p r o g r e s s i v e l y h i g h e r

f l u e n c e s (Ref s . 55-59). Curves showing t h e p e r c e n t i n c r e a s e i n s o n i c

modulus as a f u n c t i o n of f a s t n e u t r o n f l u e n c e a re shown i n F i g s . 1 7 t h rough

21 f o r ( 1 ) ex t ruded a n i s o t r o p i c pe t ro l eum coke g r a p h i t e (Dragon code No,

5 9 / 2 ) ; ( 2 ) e x t r u d e d n e a r - i s o t r o p i c petroleum-coke g r a p h i t e (Dragon code No,

1 2 0 ) ; ( 3 ) ex t ruded p i t ch -coke g r a p h i t e (Dragon code No. 1 0 0 ) ; ( 4 ) molded

p i t ch -coke g r a p h i t e (Dragon code No. 113); and (5) molded G i l s o c a r b o n

g r a p h i t e (Dragon code No. 95 ) .

The Dragon d a t a show t h a t t h e i r r a d i a t i o n - i n d u c e d changes i n You.ng's

modulus f o l l o w a s i m i l a r p a t t e r n i n a l l t y p e s of g r a p h i t e . A r a p i d i n i t i a l

i n c r e a s e i s fo l lowed by a p l a t e a u whose leve l d e c r e a s e s w i t h i n c r e a s i n g

i r r a d i a t i o n t e m p e r a t u r e . The p l a t e a u i s fo l lowed by a second r i s e i n

modulus which may e x t e n d t o 2 . 5 t imes t h e u n i r r a d i a t e d l e v e l . The modulus

t h e n passes th rough a maximum and t h e n d e c r e a s e s , f i n a l l y f a l l i n g below

3-4

s I

w 2 100 a vi a 80

u 60

3 40

2 Q I

c/) 3 J

0 0 H

a z 3

p 20

0 0

0 0 6OO0C 0 9oooc

Fig. 17. Fractional changes in dynamic Young's modulus of PGA graphite with double pitch impregnation (Dragon code No. 5 9 / 2 ) 56)

(from Ref.

3-5

w I o\

s - W w 1 a m-

z +80 a +60

2 +40

w L3

I

m 3

0

g +20 I" a 0

0 -20

-40

z 3

>

4OO0C

A R 0 4OO0C 0 0 6OO0C

9oooc A A 12OOOC V V 140OOC

1200oc A--

Y 1400°C

-\ v I I 1 I I 1 I I f I I I I 1 1

2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 0.5 1 .o 1.5 2 .o FAST N E U T R O N F L U E N C E (1021 NKM* NDE)

in dj ; i iamic T T - - . - - - I - F i g , 18. Fracti=nal changes ~ U U L I ~ s iiiocluius v i extruded petro- leum-coke graphite (Dragon code No. 120) (from R e f . 59)

c

s - w w . a + l o o m- w g +80 a 5 +60

2 +40 m

3

A R 0 4OO0C 0 060OoC 0 rn 9oooc A A 12OO0C

0 1 .o 2.0 3.0 4.0 5.0 6.0 7.0

FAST N E U T R O N F L U E N C E (1021 N K M ~ NDE)

F i g . 19. F r a c t i o n a l changes i n dynamic Young's modulus of e x t r u d e d p i tch-coke g r a p h i t e (Dragon code No. 100) (from Ref . 59)

I,

I

I 1

I1

0 0

0

0

0

N .f‘ 7

uo

ou

uo

0

000 00

00

00

0

OO

ON

d

em

O3

-7

00

0 0

0

0

NO

00

s-

c

9

a5

9

b

=! n ?

d

? 3

3 ? >

LLI 0

z

H

u

z

N

1

- N 0 c I

W

0

z

W

3

-J

LL

z

0

[r

I- 3

W z

L 2

I .G

U

u

-ti a

a

al a

rl

0

E- m

440

0

0-

>

00

.rl z

E

CdaJ ca

hO

m

u

cc

rlc

ma

ca

O

h

.d

M

u

Va

l

h0

k

0

3-8

e

w I

LD

+160

+140

+120 A s I

w w . a + l o o vi w cl z I 0

3 J 3 0 0

a

v) +80

z ,v) +60 0 z 3 0 >

+40

+20

c 0

A R 0 0 60O0C 0 m 9oooc

A A 750-800°C V V 1400°C

0 + 120oOc

0

I 1 1 _ ~ - I 1 .o 2.0 3.0 4.0

N E U T R O N FLUENCE ( 1 0 2 ~ N K M ~ NDE)

5.0

Fig . 2 1 . F r a c t i o n a l changes i n dynamic Young's modulus of molded Gi l soca rbon g r a p h i t e (Dragon code No. 95) (from Ref . 58)

t h e u n i r r a d i a t e d l e v e l a t v e r y h i g h f l u e n c e s . The second i n c r e a s e i n

modulus s ta r t s soone r a t h i g h e r i r r a d i a t i o n t e m p e r a t u r e s ; however, t h e

h e i g h t of t h e subsequen t peak i s less f o r t h e h i g h e s t i r r a d i a t i o n tempera-

tures s t u d i e d (1300" t o 1400°C) t h a n i t i s i n t h e v i c i n i t y of 1000°C. The

sequence of changes may be e x p l a i n e d i n terms of s t r u c t u r a l changes i n t h e

g r a p h i t e . The r i se t o t h e f i r s t p l a t e a u may b e a t t r i b u t e d t o t h e p i n n i n g

of b a s a l d i s l o c a t i o n s by s m a l l p o i n t d e f e c t c l u s t e r s . The second r i s e may

be e x p l a i n e d by t h e p r o g r e s s i v e t i g h t e n i n g of t h e s t r u c t u r e as mic roc racks

c l o s e and i n t e r c r y s t a l l i n e r e s t r a i n t i n c r e a s e s . The f i n a l d e c l i n e i s pro-

bab ly caused by t h e opening of new i n t e r c r y s t a l l i n e p o r e s as t h e g r a p h i t e

e n t e r s i t s volume expans ion phase .

With t h e e x c e p t i o n of h i g h l y o r i e n t e d g r a p h i t e s , t h e f r a c t i o n a l change

i n Young's modulus i s s i m i l a r f o r t h e ax ia l and t h e r a d i a l d i r e c t i o n ; ? .

There a re some d i f f e r e n c e s i n b e h a v i o r between d i f f e r e n t t y p e s of g r a p h i t e .

The i n c r e a s e s a re g e n e r a l l y h i g h e r f o r Gilsocarbon-based g r a p h i t e s (F ig .

21) t h a n f o r petroleum-coke- o r pi tch-coke-based g r a p h i t e s . There i,? a l s o

a tendency f o r t h e maximum i n t h e modulus-fluence c u r v e of petroleum-coke

o r p i t ch -coke g r a p h i t e s t o b e h i g h e r f o r p r e s s e d g r a p h i t e s t h a n f o r g r a p h i t e s

e x t r u d e d u s i n g t h e same f i l l e r (compare F i g s . 19 and 20) .

S o n i c modulus measurements on i s o t r o p i c g r a p h i t e s i r r a d i a t e d a t lower

t e m p e r a t u r e s by United Kingdom Atomic Energy A u t h o r i t y workers ( R e f s . 60-

62) show t r e n d s s imi l a r t o t h e Dragon d a t a . A t a n i r r a d i a t i o n t e m p e r a t u r e

of 350" t o 440"C, modulus i n c r e a s e s up t o 300% were observed a f t e r i r r a d i -

a t i o n i n t h e Dounreay F a s t R e a c t o r t o 2 x 10

example i s shown i n F ig . 22. French d a t a on a G i l s o c a r b o n g r a p h i t e fLrradi-

a t e d a t 500" t o 700°C (Ref. 63) and German d a t a on G i l s o c a r b o n and petroleum-

coke g r a p h i t e s i r r a d i a t e d a t 600" t o 1200°C (Ref. 64) a l s o show t r e n d s

s imilar t o t h e Dragon r e s u l t s .

22 n/cm2 (NDE) (Ref. 6 2 ) , An

S o n i c modulus d a t a have been measured on many var ie t ies of g r a p h i t e

i r r a d i a t e d a t P a c i f i c Northwest L a b o r a t o r y (Ref s . 65-68). U n f o r t u n a t e l y ,

much of t h e d a t a i s so s c a t t e r e d t h a t i t i s i m p o s s i b l e t o compare w i t h

o t h e r r e s u l t s . Some smoothed c u r v e s o b t a i n e d from a needle-coke g r a p h i t e n

3-10

0 1 2 3 x 1022

NEUTRON DOSE ( N / c M ~ )

Fig. 22. Fractional changes in dynamic Young's modulus, E, and strength, S, of isotropic graphites at temperatures of 350" to 440°C in Dounreay Fast Reactor and 700°C in BR-2 (from Ref. 62)

3-1 1

(g rade CSF) are shown i n F ig . 23 ( R e f . 66 ) . Although t h e c u r v e s show an

i n i t i a l temperature-dependent rise rough ly s imilar t o t h e Dragon c u r v e s ,

t h e y do n o t show t h e second r i s e and peak i n modulus c h a r a c t e r i s t i c of t h e

Dragon r e s u l t s . It may b e t h a t t h e scat ter i n t h e d a t a masks t h e d e t a i l s

of t h e cu rves .

Young's modulus w a s measured from t h e s t r e s s - s t r a i n cu rves of t e n s i l e

specimens i r r a d i a t e d a t 600" t o 1400°C i n c a p s u l e s OG-1 and OG-2 by Genera l

Atomic Company (Refs . 6 9 , 7 0 ) . The specimens were 0 .25- in . -d iameter by

O.g-in.-long c y l i n d e r s of H-327 ( n e e d l e coke) , H-451 , and TS-1240 (near -

i s o t r o p i c pe t ro l eum coke) g r a p h i t e s i r r a d i a t e d i n b a t c h e s of 8 t o 1 2

r e p l i c a t e s and subsequen t ly t e n s i o n - t e s t e d t o f a i l u r e . The modulus w a s

measured from t h e r e l o a d i n g p a r t of t h e cu rve a f t e r l o a d i n g t o 1000 p s i ,

un load ing t o 100 p s i , and r e l o a d i n g t o f a i l u r e ( s e e F ig . 1 6 ) . The i n c r e a s e

i n modulus i s shown i n F i g s . 24 through 26 and t h e a b s o l u t e v a l u e s are l i s t e d

i n Table 1 . The e r r o r b a r s on t h e cu rves i n d i c a t e 2 one s t a n d a r d d e v i a t i o n .

The f r a c t i o n a l i n c r e a s e s i n modulus a r e c o n s i d e r a b l y g r e a t e r t h a n would b e

expec ted from t h e Dragon c u r v e s . The most p robab le c a u s e of t h e d i s c r e p a n c y

i s t h a t t h e s o n i c modulus of t h e u n i r r a d i a t e d g r a p h i t e s t e s t e d by t h e Ilragon

p r o j e c t i s s i g n i f i c a n t l y h i g h e r t h a n t h e s t a t i c modulus measured from t h e

s t r e s s - s t r a i n c u r v e ; b u t a f t e r i r r a d i a t i o n t h e s o n i c and s t a t i c modul i

a g r e e . The Genera l Atomic Company s t a t i c modulus i n c r e a s e s and t h e Dragon

s o n i c modulus i n c r e a s e s can b e brought i n t o agreement i f t h e s t a t i c modulus

of u n i r r a d i a t e d g r a p h i t e i s assumed t o b e 80% of t h e s o n i c modulus (see

S e c t i o n 4 .3 ) .

3.3. EFFECT OF IRRADIATION ON OTHER ELASTIC CONSTANTS

The o n l y measurements of e l a s t i c c o n s t a n t s o t h e r t h a n Young's modulus

f o r i r r a d i a t e d p o l y c r y s t a l l i n e g r a p h i t e were r e p o r t e d by Goggin and

Reynolds (Ref. 9 ) . Complete sets of e l a s t i c c o n s t a n t s were o b t a i n e d on

a needle-coke g r a p h i t e (PCA) and a n e a r - i s o t r o p i c g r a p h i t e i r r a d i a t e d a t

25°C u n t i l t h e i n i t i a l i n c r e a s e i n modulus w a s comple te ( lo1 ' n/cm N D E ) .

The r e s u l t s are shown i n Tab le 2 . It may be s e e n t h a t a l l t h e compliance

c o n s t a n t s d e c r e a s e i n abou t t h e same r a t i o ,

2

3-1 2

a 0

0 0

0

m

I

I 0 0

0

M

I I I I I I \ \ \

a 1

u

0

m

0 ?

\ E

\ \ I I I I I I I I I I I I

0

0

0

m

0

Ln

c

7

I 0 0

0 E

/ Ln

a I

u

0

Lo

I- N

c

I 0

Ln

N

m

0

0

c3

Lo

N

0

N

In

- 0

c

m

0

3-13

4000

3000

2000

1000

0

4000

3000

2000

1000

0

T I R R = 640°-7400C AXIAL o = EDGE A = CENTER

A

T I R R = 75O0-9OO0C AXIAL o = EDGE A = CENTER

T

I

0 2 4 6 8

T ~ A R = 64O”-74O0C AXIAL o = EDGE A = CENT€R

I I 1 I

T I R R = 750”-9OO0C AXIAL 0- EDGE A = CENTIA

1 I 1 -- 0 ’ 0 2 4 6 8

FLUENCE X lowz1 (NICM’I (E > 0.18 MeV)

Fig . 24a. T e n s i l e s t r e n g t h and s t a t i c Young’s modulus of H-327 needle- coke g r a p h i t e as a f u n c t i o n of f a s t n e u t r o n f l u e n c e . E r r o r bands i n d i c a t e k one s t a n d a r d d e v i a t i o n . t u r e 640” t o 900°C. (From Ref . 70)

I r r a d i a t i o n tempera-

3-14

4000

3000

2000

- v, 1000 4 I

W z UJ m I- v)

A

v) z W + W

t u 0 -

2 ' 4000 I 5 3

3000

2000

1000

0

T ~ R R = 940°-10350C CENTER 0 = A X I A L 0 = RADIAL

T

I

TIRR = 1040°-12000C A X I A L 0 = EUGE A = CENTER

1 I I I

0 2 4 6 8

TIRR = 940°-10350C CENTER 0 = A X I A L 0 = RAUlAL

T 1

I I I 1

TIRR = 104O0-12OO0C A X I A L 0 = EUGE A = CENTER

I I I I 0 2 4 6 8

FLUENCE X (N/CM*I ( E > 0.18 MeV)

Fig. 24b. Tensile strength and static Young's modulus of H-327 needle- coke graphite as a function of fast neutron fluence. Error bands indicate t one standard deviation. Irradiation tempera- ture 940" to 1200°C.(From Ref. 70)

3-15

3000

2000

T I R R = 58O0-63OoC AXIAL

-

O L ' I I I I

W + W c 4 1000 I f 2

T ~ R R = 89Oo-97O0C 0 = AXIAL 0 = RADIAL

TI = 58On-63OoC AXIAL

0

0 0

3000 -

-r 1000 -

T ~ R R = 134Oo-137O0C AXIAL

0 " I 1 I 0 2 4 6 0 2 4 6

0

T ~ R R = 89Oo-97OnC 0 = AXIAL 0 = RADIAL

I I I I

j/

1

T t R R = 1340'-1370°C AXIAL

0 0 2 4 6

FLUENCE X (N/CM2) ( E > 0.18 MeV)

Fig . 25. T e n s i l e s t r e n g t h and s t a t i c Young's modulus o f H-451 n e a r - i s o t r o p i c petroleum-coke g r a p h i t e as a f u n c t i o n o f f a s t n e u t r o n f luenc ' e . E r r o r bands i n d i c a t e k one s t a n d a r d d e v i a t i o n . (From R e f . 70)

3-16

3000 - 2

3000 3

1000 I

TIRR = 1105'C A X I A L

I 1 1 O I

r+ T l ~ ~ = 765'-920'C 0 = A X I A L

T I R R = 1105°C A X I A L

0 ' I I I

0 = R A D I A L

1 I I 1

3

Fig. 26. Tensile strength and static Young's modulus of TS-1240 near- isotropic petroleum-coke graphite as a function of fast neutron fluence. Error bands indicate 2 one standard deviation. (From Ref. 70)

3-1 7

oa,

-t

:

E-

aJu -

u-.o c

c

Uv

A

dW

l

rr

-

XG

m

C

TI

U

m U

C

.d

!4 0

NN

NO

U~

m

b

aa

-

a

uu

mm

ma

m

r-

mu

- I ...... 1

.

I .... I.

1 ..... ..

I .

. .

I .

INNNNN-I- I

--

--

I-

I

NN

NN

NN

NI

~~

~I

-

mo

-o

um

wm

m

o~

r-

m-

-a

~o

m~

r-

o-

om

ma

mm

o

ON

-N

N-

OO

-

-~

--

N-

N

-e

um

~u

mm

~m

w-

o~

0

00

00

00

00

0

00

00

00

0

00

00

00

00

00

00

0

.............................. +

I +

I +I +

I +I

+I

+I +

I +I

+I

+I

+I +

I +

I +I +

I +

I +I

+I +

I +I

+I +I

+I +

I +

I +I

+I +

I +I

em

~e

am

mo

m

ON

NW

~O

O o

mr

-m

~m

~~

mm

om

um

-

a~

mo

mr

.o

co

mr

-r

-a

am

m

m~

r-

mo

em

mm

m-

~a

~

-C

VN

NN

N-

--

o----o-

-~

~~

mr

~~

~-

mm

mo

-

..............................

00

00

00

0

0

00

0

0

00

00

00

0

00

0

0

iuamuoo~m iuobmim imo-ummm~oma~r-

I-

--

ON

OI

-

i-

-o

oi

m

ir

-m

m~

r.

wm

~o

mm

~o

N

NN

N"

N

N

NN

N -

------- W

NN

7

m m

u m

a -

mm

mm

m

mooaoeo

m-r-

u

o-

~~

mm

mo

m

o-

-~

mo

- o

~e

m~

ma

bo

w~

mo

m

..

..

..

.

..

..

.

..

..

..

..

..

.

I

0

oo

oo

or-

0

mm

mm

r-

m

m

aa

ac

nm

-

m

II

II

II

II

0

00

00

0 I

O

ww

w-

me

o

I

0

N

0

II

I

O

Q

7

b4

L.iL

.iL.iN

NL

.iL.iL

.i L.iL.iL.iL.iL.iL.i&

NU

L4

L.iL

.iL.iN

L.i

LI

N

aJ

a,m

ma

,aJ

a,a

,a,

a,a,a,aJa,a,a,

ma

,a

,a

,a

,m

a,

a,

m

a,

uu

uu

uu

uu

u u

uu

uu

uu

uu

uu

uu

uu

~a

,a

,a

,u

u

CC

CC

CC

CC

C

CG

CG

CC

C

CG

CC

CC

CC

MM

MM

CC

a

,a,a

,a,a

,a,a

,aJ

a

mm

a,

ma

,a

,a

a

,a

Ja

,a

ra

,a

,a

,a

,a

am

va

,a

,

uu

uu

uu

uu

u u

uu

uu

uu

uu

uu

uu

uu

a,

a,

a,

a,

uu

I

II

II

II

II

I

II

II

II

I

II

II

II

II

II

II

I

n

3-1 8

Mat e r i a 1 ~

PGA

P GA

P GA

P GA

P GA

P GA

P GA

I s o t r o p i c

I s o t r o p i c

Is0 t r o p i c

Is0 t r o p i c

TABLE 2 MEASURED ELASTIC COMPLIANCE M O D U L I OF GRAPHITE BLOCKS

IN UNITS OF 10-14 C M ~ / D Y N E (FROM REF. 9 )

Modulus

s1 1

s33 ( f rom s / S )

( f r o m s / S )

( f r o m S / S )

'1 3 1 3 33

'1 3 13 11

s12 1 2 11

s44

s12 ( f r o m 1 / 2 s~~ + S l l - S 1 2 )

s1 1

s12 ( f r o m s / S )

s12 ( f r o m S

12 11

11 - 1 / 2 S44)

s44

2

I r r a d i a t e d Value o f Modulus x 1014 (cm / d y n e )

U n i r r a d i a t e d

2150

1087

-162

-123

-1 27

-530

3333

1370

-148

-145

3030

5 20

279

-42

-1 9

-4 1

-1 2 3

925

355

- 32

-99

909

3-19

3.4. EFFECT OF IRRADIATION ON POISSON'S RATIO

I n t h e work d e s c r i b e d above, Goggin and Reynolds (Ref . 9 ) measured

P o i s s o n ' s r a t i o f o r an i s o t r o p i c g r a p h i t e i r r a d i a t e d a t room tempera tu re .

Compressive l o a d s of 5 t o 40 p s i were a p p l i e d , and t h e s t r a i n s were measured

by Cornu ' s method,

of t h e l o a d and e x t r a p o l a t e d t o i n f i n i t e l o a d . The v a l u e s o b t a i n e d dec reased

s l i g h t l y from 0.108 ( u n i r r a d i a t e d ) t o 0.090 ( a t lo1' n/cm ) .

t h r e e P o i s s o n ' s r a t i o s of t h e h i g h l y o r i e n t e d PGA g r a p h i t e w e r e a s f o l l o w s :

The observed v a l u e s were p l o t t e d a g a i n s t t h e r e c i p r o c a l

2 Changes i n t h e

. u n i r r a d i a t e d 0.059, i r r a d i a t e d 0.079 2

1 - -*

'1 3 - -: u n i r r a d i a t e d 0.057; i r r a d i a t e d 0.037 s1 1

'1 3 - -: u n i r r a d i a t e d 0.149; i r r a d i a t e d 0.150 s33

B r o c k l e h u r s t and Lyman (Ref . 71) found t h a t t h e P o i s s o n ' s r a t i o s of

PGA g r a p h i t e (measured under compress ive l o a d s between 400 and 4000 p s i )

i n c r e a s e d on i r r a d i a t i o n a t 150"C, w i t h - ( S / S ) changing from 0.13

b e f o r e i r r a d i a t i o n t o abou t 0 . 3 a t a n exposure of 6 .5 x lo2' n/cm2.

d a t a are shown i n F ig . 2 7 . I n c o n t r a s t , Tay lo r e t a l . (Ref . lo), u s i n g a

s imilar t e c h n i q u e , found no s y s t e m a t i c t r e n d s i n t h e P o i s s o n ' s r a t i o

( i n i t i a l l y 0.17) of two t y p e s of i s o t r o p i c g r a p h i t e i r r a d i a t e d a t 150°C

t o a peak f l u e n c e of 1.1 x 1021 n/cm

13 33 The

2 (NDE). The d a t a are g i v e n i n T,sble 3 .

It may b e concluded t h a t expe r imen t s s o f a r have found no s y s t e m a t i c

e f f e c t of i r r a d i a t i o n on P o i s s o n ' s r a t i o ,

3.5. EFFECT OF IRRADIATION ON STRENGTH

Los ty and Orchard (Ref. 1 ) measured t h e f l e x u r a l s t r e n g t h of an

u n s p e c i f i e d t y p e of r e a c t o r g r a p h i t e a f t e r i r r a d i a t i o n a t 60°C t o fluc. ances n

3- 20

0.5

a

0 0.4 l- a a v)

z 0.3

2 n 0

0.2

0.1

0

ERROR LIMITS ARE ? STANDARD DEVIATIONS O F A SINGLE OBSERVATION. 1 MEASUREMENTS A T CENTER O F SPECIMEN

4 MEASUREMENTS 1/4 WAY FROM ONE END OF SPECIMEN 4

P.G.A. PARALLEL

P.G.A. PERPENDICULAR 200'-2 5OoC

-Yt P.G.A. PERPENDICULAR

7

I 1 I I I I I I I 0 1 2 3 4 5 6 7 8 9 10 x 1020

FAST NEUTRON D O S E ( N / c M * )

F i g . 27 . V a r i a t i o n of P o i s s o n ' s r a t i o of PGA g r a p h i t e with f a s t neu t ron fluence (from Ref. 71)

3-2 1

1 w I

4.95 4.781

7.65 7.23)

6.75 6.85 1

h, 2 h,

0 * 3 5

0.43

0.57 3

-

1.78 20.05

1.85 t0.04

1.86 t0.04

6

P a r a l l e l P e r p e n d i c u l a r

P a r a l l e l P e r p e n d i c u l a r

P a r a l l e l P e r p e n d i c u l a r

D i r e c t i o n of c u t 3

(g/cm )

TABLE 3A PHYSICAL AND MECHANICAL PROPERTIES OF UNIRRADIATED GWHITES (FROM REF. 10)

Mean C . T . E .

(2O0-12O"C)

(x deg/K)

3.4 3.8

3.5 4.1

3.0 3.4

Mean K (ca l /cm/ sec/ 'K)

. 0.335 0.315

0.320 0.290

0.390 0.370

t Average S t r e n g t h

Tens ion

S tanda rd D e v i a t i o n

2 ( k g / m )

0.13

0.21

0.22

Average % S t r a i n

t o F r a c t u r e

0.244 0.260

0.215 0.215

0.19 0.20

1

Compress i o n

S tanda rd Average Dynamic Modulus

1

I F r a c t u r e q 2.50

9.7 8.7

11.4 10.4

12.0 11.0

c

Type 1 M a t e r i a l

' c'

Type 2 M a t e r i a l Type 3 E l a t e r i a l

w I h, w

0 .75

1.85 1 .88

0.47 0 . 4 0

2 . 1 3 2.01

0.64 0 .64

0 . 1 3

16

i1.2 0 . 3

4 . 8 4 . 9

D i r e c t i o n P r o p e r t y I of c u t 1.55

2.09 2.02

0.66 0.63

2.51 2 .55

0.70 0.64

0.17

55

13.3 12.3

5.1 6.1

2.91

1.71 1 .90

0 . 5 3 0 .68

2 .90 2.90

0 . 7 1 0 . 6 4

0 .19

'0

12.1 13.0

6 .7 6 . 9

Compressive s t r e n g t h T e n s i l e s t r e n g t h

3.60 7 . 5 11.5

2.07 2.08 1.75 1.97 1.94 2.05

0 .97 0.49 0.59 0.77 0 .62 0 .69

2.99 3.11 3.21 3 .04 3 . 2 3 3.47

0.84 0 .62 0 .58 0 .86 0 . 5 9 0.51

0 .22 0 . 1 3 0.14

79 147 167

1 3 . 3 11.9 9 . 3 13.6 12.0 1 1 . 7

6 . 8 6 . 9 8 . 1 6 . 7 7.5 7 . 9

0 .85

1.49 1 .35

0.57 0 . 5 5

2.08 1 .88

0.61 0.65

_ _ 4

4 .5 7 . 2

9 . 7 7 . 2

1 1

1 1

1 1

1 1

0.1;

16.5

5 .9 6.6

4 . 7 4.5 -

2.9(

1 .5t 1 .9(

0 .7; 0.91

2.5t 2.41

0.8: 1 . 1 ;

_ _ 75

7 .8 15.4

8 . 6 6 .6

Change i n t e n s i l e s t r e n g t h , oT/oTo

Change i n t e n s i l e s t r a i n t o f r a c t u r e

Change i n compress ive s t r e n g t h , oC/oCo

Change i n compress ive s t r a i n t o f r a c t u r e

P o i s s o n ' s r a t i o

Hardness (kg/mm ) 2

S t r a i n e n e r y (dynes x 10 2 )

I I 1

I I 1

I1 1

/ I 1

_ _

_ _ I 1 1

0(a - 1 1

1 1

1 1

1 1

0 . 1

19.8

9 .8 9.4

5 . 0 5 . 2 -

~

0 . 7 5

2 .11 1 .97

0 . 7 4 0 . 7 1

1 . 9 5 1 .97

0 . 6 3 0 . 5 8

0 . 1 7

. 2

-

8 . 2 6 .0

5 .1 5 . 4 -

1.55

2.40 1.95

1.3c 0 . 8 5

2.32 2.30

0.69 0.59

0.17

'4

-

8.7 9 .2

5 .2 6 . 1 -

2.70

2.00 1.90

0.69 0 .98

2 .65 2.54

0.75 0 .58

0 .18

-

90

18 .0 17.8

7 . 4 7 . 3

3.60

1 .92 1.81

0 . 9 7 0 .93

2.76 2.90

0 .88 1 .oo

0.21

-

00

23.0 16.5

7 . 2 8 .7

7 .5

1.79 1.81

0 .48 0 .95

3.02 3.00

0 .58 0 .46

0 . I O

-

1 35

14.9 16.9

S . 8 8 . 3 -

- 11.5 -

1.98 1 . 7 1

0 . 6 3 0 .38

2.94 3.14

0.56 0.47

0.09

58

15.5 12.8

8 . 3 9 .6

1

1 1

1 1

1 1

_-

18.5

5 . 2 8 . 2

6 . 0 5 .1

4.70

1.05 1 . 6 3

0 .53 0.72

3.04 2.91

0.51 0.52

_ _ IO

2 .3 10 .2

20.3 9.8

7.5

1 .65 1 .45

0.52 0.49

3.30 3.25

0 . 5 3 0.56

_ _

122

10.8 9 . 2

10.2 1 1 . 1

(a )See Table 3A f o r a b s o l u t e v a l u e s o f f r a c t u r e s t r e n g t h and s t r a i n .

up t o 1019 n/cm2. They found t h a t t h e s t r e n g t h i n c r e a s e d a t a s lower r a t e

t h a n Young's modulus, w i t h t h e s t r a i n energy p e r u n i t volume t o f r a c t u r e

(assuming l i n e a r e l a s t i c b e h a v i o r ) remain ing approx ima te ly c o n s t a n t . The

s t r e n g t h , S , and Young's modulus, E , f o r several f l u e n c e s and bo th o r i e n -

t a t i o n s were r e l a t e d by t h e e x p r e s s i o n

~

where K i s c o n s t a n t .

T e n s i l e and compress ive s t r e n g t h s of t h r e e p r o t o t y p e g r a d e s of 21 i s o t r o p i c petroleum-coke g r a p h i t e s i r r a d i a t e d a t 150°C t o 1 . 1 x 10

n/cm (NDE) were r e p o r t e d by Tay lo r e t a l . (Ref. l o ) . The da ta are shown

i n T a b l e 3. The t e n s i l e s t r e n g t h of a l l t h r e e mater ia l s r o s e r a p i d l y t o

about twice t h e u n i r r a d i a t e d v a l u e , w h i l e t h e compress ive s t r e n g t h i n c r e a s e d

more s l o w l y t o abou t t h r e e t i m e s t h e u n i r r a d i a t e d level . I n c o n t r a s t t o t h e

r e s u l t s of Los ty and Orchard , t h e s t r a i n energy t o f a i l u r e i n c r e a s e d s i g n i , f -

i c a n t l y on i r r a d i a t i o n , w h i l e t h e f r a c t u r e s t r a i n d e c r e a s e d . The s h e a r

s t r e n g t h of several samples was measured and w a s found t o i n c r e a s e i n t h e

same p r o p o r t i o n as t h e t e n s i l e s t r e n g t h .

2

Re fe rence 62 i n c l u d e s d a t a on t h e f r a c t i o n a l i n c r e a s e i n t h e t e n : s i l e

s t r e n g t h and b r i t t l e - r i n g s t r e n g t h ( s i m i l a r t o f l e x u r a l s t r e n g t h ) of

molded and ex t ruded i s o t r o p i c g r a p h i t e s i r r a d i a t e d i n t h e Dounreay F a s t

Reac to r a t 350" t o 440°C. The t y p e of f i l l e r coke w a s n o t s p e c i f i e d b u t

w a s s a i d t o have a m i c r o s t r u c t u r e s imi la r t o Gi l soca rbon . The r e s u l t : ; are

i n c l u d e d i n F ig . 22.

modulus. The f r a c t i o n a l s t r e n g t h i n c r e a s e s were p r o p o r t i o n a l t o t h e

s q u a r e r o o t of t h e f r a c t i o n a l Young's modulus i n c r e a s e s , i n agreement w i t h

Los ty and O r c h a r d ' s s u g g e s t i o n o f a c o n s t a n t s t r a i n energy t o f r a c t u r e .

Data on samples t a k e n t o h i g h e r exposures a t 350" t o 500°C a r e r e p o r t e d i n 22 2

Ref , 7 2 and are reproduced i n F i g . 28. Beyond about 2 x 10 n/cm t h e

s t r e n g t h f e l l below t h e leve l p r e d i c t e d by t h e c o n s t a n t s t r a i n ene rgy

The s t r e n g t h i n c r e a s e d a t a lower r a t e t h a n Young's

n

3-24

0 m . 2 w a z I u I l- a z w [r I- m

a 2 t A 2 A

I I

0 1 2

NEUTRON O O S E x 10-22 (NICM~)

I 0 I

0 0

1 I I 0 1 2

NEUTRON DOSE x 10-22 ( N / c M ~ )

3

I 3

Fig. 28. Mechanical property changes in extruded isotropic graphite irradiated at 350" to 500°C (from Ref. 72): (a) strength; (b) Young's modulus

3-25

r e l a t i o n , b u t remained above t h e u n i r r a d i a t e d level . The f a l l - o f f was

a t t r i b u t e d t o p o r e g e n e r a t i o n .

S t r e n g t h measurements on specimens i r r a d i a t e d a t h i g h e r t empera tu res

by t h e Dragon p r o j e c t are reviewed i n Ref. 53. A series of c y l i n d r i c a l

specimens about 0.4 i n . i n d i a m e t e r by 4 i n . l ong made from p r e s s e d G i l s o c a r - 2 bon g r a p h i t e (Dragon code No, 95) were i r r a d i a t e d a t 1200°C t o 1 x 1021 n/cm

(NDE) d u r i n g t h e c o u r s e of a n i r r a d i a t i o n c r e e p exper iment i n t h e Dra.gon

r e a c t o r , A f t e r t h e c r e e p exper iment w a s completed, some of t h e s t r e s s e d

specimens and some u n s t r e s s e d companions were t e s t e d i n t e n s i o n . The

s t r e n g t h s were found t o b e c l o s e l y p r o p o r t i o n a l t o t h e s o n i c modulus, w i t h

d a t a f o r u n i r r a d i a t e d and i r r a d i a t e d (bo th s t r e s s e d and u n s t r e s s e d ) s p e c i -

mens f a l l i n g on t h e same l i n e (see Fig . 29) . A c u r v e co r re spond ing t o t h e

c o n s t a n t s t r a i n energy c o n d i t i o n (S2 = KE) d i d n o t f i t t h e d a t a .

Four-point bend- t e s t specimens measur ing 0 . 2 i n . i n d i ame te r by 2 . 6 i n .

i n l e n g t h and made from ex t ruded Gi l scocarbon-based g r a p h i t e f u e l s l e e v e s

were t e s t e d a f t e r i r r a d i a t i o n i n f o u r Dragon f u e l e l emen t s (Ref . 53) .

Tempera tures ranged from 850" t o 1250°C and f l u e n c e s ranged up t o 3 x 10

n/cm (NDE). The r e s u l t s are shown i n F i g . 30. A s i n t h e c a s e of t h e

c r e e p specimens, t h e s t r e n g t h i n c r e a s e s were i n b e t t e r agreement w i t h a n

S = KE r e l a t i o n s h i p t h a n an S2 = KE r e l a t i o n s h i p .

21

2

A few bend s t r e n g t h r e s u l t s on a f i n e - g r a i n e d petroleum-coke g r a p h i t e

i r r a d i a t e d i n t h e Dragon r e a c t o r and t h e P e t t e n High F lux Reac tor (HFR) 2

t o 5 t o 6 x 1021 n/cm (NDE) a t 600" , 900", and 1100°C were r e p o r t e d .by

Del le (Ref. 6 4 ) . A t 600" , 900", and 1100°C t h e s t r e n g t h i n c r e a s e s w e r e

40%, 25%, and 20%, r e s p e c t i v e l y . O the r d a t a showed t h e bend s t r e n g t h

i n c r e a s i n g a f t e r i r r a d i a t i o n approx ima te ly w i t h t h e s q u a r e r o o t of Young's

modulus, bu t t h e i r r a d i a t i o n c o n d i t i o n s were n o t s t a t e d .

The f i r s t expe r imen t s i n t e n d e d t o show t h e e f f e c t s of i r r a d i a t i o n on

t h e s c a t t e r of t h e s t r e n g t h measurements were r e p o r t e d by Lungagnani and

Kre fe ld (Ref. 1 7 ) . Groups of 12 t o 35 bend specimens of a Gi l soca rbon n

3-26

Fig. 29. Strength - Young's modulus relationship for irradiated graphite (Dragon code No. 95). Fluence = 1 x n/cm2 (NDE temperature = 1200°C (from Ref. 53)

3-27

0

5000 LBf/lN.2

- I CONTROLS

1

RELATIVE E = 30 28 26 25 F.E. 701 CordTROL. ELASTIC STRAIN F.E. 704

A h

FUEL PEAK DOSE TEMPERATURE ELEMENT (1021 N / C M ~ ) R A N G E p c )

V 311 0.4 900-1250 A 700 0.3 900-1 250 0 701 1.7 900-1 250 0 704 3 850-1 150 0 NON-IRRADIATED CONTROLS

0 MEAN OF NON-IRRADIATED CONTROLS USING ES MEAN OF NON-IRRADIATED CONTROLS USING KNOWN VALUE OF ED

2 X lo6 LBf/lN.2

F i g . 30. F l e x u r a l s t r e n g t h a s a f u n c t i o n of s t a t i c Young's modulus f o r i r r a d i a t e d g r a p h i t e (from Ref . 53)

3-28

g r a p h i t e were i r r a d i a t e d i n t h e HFR ( P e t t e n ) a t 600" and 1150°C t o f l u e n c e s

up t o 7 x lo2' n/cm For i r r a d i a t i o n a t 600"C, b o t h t h e s t r e n g t h

and t h e e x p e r i m e n t a l sca t te r i n c r e a s e d w i t h i r r a d i a t i o n . A t 115OoC, t h e

s t r e n g t h f i r s t i n c r e a s e d , as expec ted , b u t t h e n r a p i d l y d e c r e a s e d t o below

t h e p r e i r r a d i a t i o n l e v e l . These r e s u l t s were i n s t r i k i n g c o n t r a s t t o a l l

p r e v i o u s measurements and cou ld n o t b e confirmed i n subsequen t t e s t s . It

w a s l a t e r concluded t h a t t h e specimens had been s l i g h t l y o x i d i z e d d u r i n g

i r r a d i a t i o n (Ref. 73 ) , and t h e r e s u l t s of t h e s e tests shou ld b e d i s r e g a r d e d .

2 ( N D E ) .

A c o n s i d e r a b l e amount of mechan ica l p r o p e r t y d a t a w a s o b t a i n e d on

H-327 ( n e e d l e coke) g r a p h i t e i r r a d i a t e d by Genera l Atomic Company i n

c a p s u l e s G-13, F-26, F-28, and F-29 (Ref , 74 ) . R e s u l t s of t e n s i l e tests on

0 .2- in . -d iameter t e n s i l e specimens i r r a d i a t e d a t 1100" t o 1150°C t o f l u e n c e s

up t o 5 x I O 2 ' n/cm2 (E > 0.18 MeV) i n c a p s u l e G-13 are shown i n F i g . 31.

The t e n s i l e s t r e n g t h and Young's modulus i n c r e a s e w i t h f l u e n c e . A con-

s i d e r a b l e number of bend tests were performed on H-327 specimens i r r a d i a t e d

i n c a p s u l e s F-26, F-28, and F-29 a t t e m p e r a t u r e s i n t h e r ange 575" t o 775°C

t o f l u e n c e s up t o 8 x 10

mid- length r e g i o n of t h e p a r e n t l o g and r a d i a l specimens from t h e end

r e g i o n of t h e l o g were t e s t e d i n a he l ium a tmosphere a t room t e m p e r a t u r e o r

a t a h i g h e r t e m p e r a t u r e , e i t h e r c l o s e t o t h e i r r a d i a t i o n t e m p e r a t u r e o r a t

1000" t o 1 2 O O 0 C . The f l e x u r a l s t r e n g t h measurements are shown as a func-

t i o n of f l u e n c e i n F i g , 32. Although t h e d a t a a r e q u i t e s c a t t e r e d , t h e

f l e x u r a l s t r e n g t h s g e n e r a l l y i n c r e a s e w i t h i n c r e a s i n g f l u e n c e . The e f f e c t

of t e s t i n g t e m p e r a t u r e i s n o t v e r y w e l l d e f i n e d , b u t i n g e n e r a l t h e

s t r e n g t h s of samples t e s t e d a t e l e v a t e d t e m p e r a t u r e s l i e toward t h e t o p

of t h e sca t te r bands , w h i l e t h e room-temperature s t r e n g t h s t end t o b e

lower .

21 n/cm2 ( E > 0 .18 MeV). A x i a l specimens from t h e

Groups of 8 t o 12 r e p l i c a t e specimens of H-327 ( n e e d l e c o k e ) , H-451,

and TS-1240 ' ( n e a r - i s o t r o p i c pe t ro l eum coke) g r a p h i t e s were t e s t e d i n

t e n s i o n a t room t e m p e r a t u r e a t Genera l Atomic Company a f t e r i r r a d i a t i o n i n

t h e Oak Ridge Reac to r (ORR) i n c a p s u l e s OG-I and OG-2 (Ref s . 6 9 , 7 0 ) . The

r e s u l t s are summarized i n T a b l e 1 , and t h e i n c r e a s e s i n s t r e n g t h , t o g e t h e r

3-29

4000

I - v) n -

3000 cl 2 w a I- v)

w -J

v) -

2000 I-

I-

5

w

a

5 - 3

1000

0

AXIAL / 0

/- I,/ 0' 0

/

A

0

-8- /-

I A -- --e- /-- A

RADIAL- - - A A

I /. L

I I I I I 0 1 2 3 4 5

/

AXIAL,

/'

/

8-

A

/- 0.

0

A I I ---- - A A RADIAL /-

/- A /-- /.

0 1 2 3 4 5

FAST NEUTRON FLUENCE X (N/CM2) (E > 0.18 MeV)

F i g . 31. T e n s i l e s t r e n g t h and Young's modulus of needle-coke H-327 g r a p h i t e i r r a d i a t e d i n c a p s u l e G-13 a t 1100" t o 1150°C (Ref . 74)

3-30

n

aooo

6000

4000

2000

0 '

2000

0

A X I A L - MIDLENGTH - SAMPLES FROM CENTER O F LOG

I I I I

6000

4000

AXIAL - MIDLENGTH SAMPLES FROM EDGE O F LOG

1

0 ROOM TEMPERATURE TESTS 0 HIGH TEMPERATURE TESTS

1 1 I 2 4 6 a 10 0

F i g . 32a. F l e x u r a l s t r e n g t h of axial specimens of needle-coke H-327 g r a p h i t e i r r a d i a t e d i n c a p s u l e s F-26, F-28, and F-29 a t 575" t o 7 7 5 ° C . Closed p o i n t s were o b t a i n e d a t room t e m p e r a t u r e and open p o i n t s a t e l e v a t e d t e m p e r a t u r e . cates t h e i r r a d i a t i o n t e m p e r a t u r e and t h e second number i n d i c a t e s t h e t e s t i n g t e m p e r a t u r e . (Ref. 7 4 )

The f i r s t number by each p o i n t i n d i -

3-31

h - v) a

W

3

3 a U 0 m 3 J 3 0 0 I

I

a

k

- 6000

4000

2000

8000

6000

4000

2000

RADIAL - END SAMPLES FROM EDGE OF LOG

I 1 1 I O h

- 700110

@ ROOM-TEMPERATURE TESTS RADIAL - END 0 H I G H -T EM P E RAT U R E TESTS SAMPLES FROM CENTER O F LOlG

0 0 2 4 6 8 10

FAST NEUTRON FLUENCE X (N/CM2) (E > 0.18 MeV)

F i g . 32b. F l e x u r a l s t r e n g t h of r a d i a l specimens of needle-coke H-327 g r a p h i t e i r r a d i a t e d i n c a p s u l e s F-26, F-28, and F-29 a t 575" t o 775". Closed p o i n t s were o b t a i n e d a t room t empera tu re and open p o i n t s a t e l e v a t e d t empera tu re . The f i r s t number by each p o i n t i n d i - cates t h e i r r a d i a t i o n t e m p e r a t u r e and t h e second number i n d i c a t e s t h e t e s t i n g t empera tu re . (Ref . 7 4 )

3-32

w i t h s t a n d a r d d e v i a t i o n s , are p l o t t e d i n F i g s . 24 th rough 2 6 . The coef -

f i c i e n t of v a r i a t i o n of t h e s t r e n g t h v a l u e s showed no s y s t e m a t i c and

s t a t i s t i c a l l y s i g n i f i c a n t change w i t h i r r a d i a t i o n , w i t h t h e e x c e p t i o n of

t h e groups of TS-1240 and H-327 specimens i r r a d i a t e d t o t h e h i g h e s t f l u e n c e s

and t e m p e r a t u r e s , where t h e c o e f f i c i e n t of v a r i a t i o n underwent a s i g n i f i c a n t

i n c r e a s e a t t h e 95% conf idence l e v e l .

The t e n s i l e s t r e n g t h s o f t h e specimens i r r a d i a t e d i n c a p s u l e s OG-7

and OG-2 are p l o t t e d a g a i n s t Young's modulus (measured from t h e r e l o a d i n g

p o r t i o n of t h e cu rve ; see F i g . 1 6 ) i n F i g s . 33 t h rough 35. L i n e s c o r r e s -

ponding t o S / E = K and S / E = K a r e drawn through t h e d a t a p o i n t s o b t a i n e d

f o r u n i r r a d i a t e d specimens. For H-327 and TS-1240 g r a p h i t e s , t h e d a t a

p o i n t s o b t a i n e d f o r i r r a d i a t e d specimens a r e i n f a i r l y good agreement w i t h

Los ty and O r c h a r d ' s c o n s t a n t s t r a i n energy c o n d i t i o n ( S / E = K ) . For t h e

H-451 g r a p h i t e , t h e d a t a p o i n t s f o r i r r a d i a t e d specimens g e n e r a l l y f a l l

above t h e S / E = K l i n e . I f t h e d a t a p o i n t s from t h e lowes t t empera tu re

and f l u e n c e c o n d i t i o n s ( c l o s e d s q u a r e s i n F i g . 3 4 ) are exc luded , t h e

remain ing measurements on a x i a l specimens of H-451 g r a p h i t e are i n f a i r

agreement w i t h t h e S / E = K f a i l u r e c o n d i t i o n proposed i n Ref . 5 3 .

2

2

2

A d d i t i o n a l r e s u l t s on t h e e f f e c t of i r r a d i a t i o n on t h e s p r e a d i n

s t r e n g t h s have been p u b l i s h e d by Matthews (Ref . 7 5 ) . Rec tangu la r specimens

( 2 i n , by 0 . 2 4 i n . by 0.12 i n . ) of Poco AXF-54 g r a p h i t e were i r r a d i a t e d a t

400°C t o fluences up to 3 x I O 2 ' n/cm2 ( E > 1 M e V ) .

measured from t h e f r equency of f l e x u r a l v i b r a t i o n s , and t h e modulus of

r u p t u r e of g roups of 11 t o 29 specimens w a s measured i n f o u r - p o i n t bending.

The mean s t r e n g t h s i n c r e a s e d p r o p o r t i o n a l l y t o t h e s q u a r e r o o t of t h e

i n c r e a s e i n Young's modulus (F ig . 3 6 ) , i n acco rdance w i t h t h e c o n s t a n t

s t r a i n energy f a i l u r e c o n d i t i o n . The d i s t r i b u t i o n of s t r e n g t h s w i t h i n

each group w a s f i t t e d t o t h e Weibul l d i s t r i b u t i o n f u n c t i o n (Eq. 2 ) ,

assuming cs = 0 . The r e s u l t s f o r 0 and m are g iven i n Tab le 4 , t o g e t h e r

w i t h t h e co r re spond ing stress f o r a f a i l u r e p r o b a b i l i t y of I t w a s

found t h a t t h e s p r e a d i n s t r e n g t h s i n c r e a s e d somewhat a f t e r i r r a d i a t i o n

(shown by t h e d e c r e a s e i n m), w i t h t h e r e s u l t t h a t stress c a l c u l a t e d f o r

Young's modulus was

U 0

3-33

4000

3000

2000

1000

3000

2000

1000

1000

500

0

1 2 3 4

H-327 GRAPHITE, AXIAL, CENTER OF LOG c I

A o A e

1 2 3 4

1 H-327 GRAPHITE. RADIAL, CENTER O F LOG 4--

0, - - FLUENCE TEMPERATURE

0 0 e 2 5-2 9 640- 740 0 2 1 770- 810

750- 81 0 A 5 0 835-850 A 2 6 860- 900

SYMBOL (1021 N ~ C M ~ ) ( O C )

W 4 0 0

3 0-3 4 960- 1035 6 4 940- 1035

V 3 1 1050-1 100 1040- 1105

0

v 7 0

7 S - ' E = K - S'E = K --- I I

0 1 2 3

YOUNG'S MOOULUS X (PSI)

Fig. 33. Tensile strength-Young's modulus relationships for needle-coke H-327 graphite irradiated in capsules OG-1 and OG-2

3-34

,-

3000

Fig.

F L U EN CE TEMP E R ATU R E

0 0, SYMBOL (1021 N / C M ~ ) (OC) - - 0 0 0 2.2 0 2.9

- 580-620 590

2000

1.6 A 3.1 A 3.4

5.9 8 3.6

- SIE = K

- - - S2/E = K -

610-630 900-950 910-950 890-970 1340-1370

eu 0 /p ‘I A

H-451 GRAPHITE, AXIAL , CENTER O F L O G

1000 I 1

3000

2000

O0

H-451 GRAPHITE, RADIAL, CENTER O F LOG /

1000 / 1 0 1 2

YOUNG‘S MODULUS X (PSI)

3

3 4 . Tensile strength-Young’s modulus relationships for near-isotropic petroleum-coke H-451 graphite irradiated in capsules OG-1 and OG-2

3-35

3000

2500

2000

1500

1000

500

2500

2000

1500

1000

500

F L U EN C E TEMPERATURE SYMBOL (1021 N / C M ~ )

1.3 / 0 / - 0 1.9 765-805

0

/ /

/ /

9 n

0

0

TS-1240 GRAPH P r l l T r " n r I n,

ITE, A X I A L , ~ C I V I c n u r LUG

1 I I 1

/ ' I

/

TS-1240 GRAPHITE, R A D I A L , CENTER O F LOG

0 0.5 1 .o 1.5 2.0 2.5

YOUNG'S MODULUS X (PSI)

Fig. 35. Tensile strength-Young's modulus relationships for near-isotropic petroleum-coke TS-1240 graphite irradiated in capsule OG-2

3-36

20

19

18

17

16

15

14

13 ' I I 1 I I A 1 V

115

110

105

100

95

90

A V

-

0 EXPERIMENTAL APREDICTED

I 1 1 1 1 1 A I V

0 2 4 6 8 10 30

Fig . 3 6 . Young's modulus and f l e x u r a l s t r e n g t h of AXF-5Q g r a p h i t e as a f u n c t i o n of f a s t n e u t r o n f l u e n c e ( E > 1 MeV) a t 400°C ( f rom Ref . 75)

3-37

TABLE 4 WEIBULL ANALYSIS OF IRRADIATED POCO AXF-5Q GRAPHITE

(from Ref. 75)

~ 24

28

29

11

26

29

I I

As-received

1 .1

3 . 3

6.0

10

30

93 .4

102.5

103.2

108.2

109.5

111.1

m

16

15

10

11

8

11

00 (m/m2>

61 .5

6 6 . 0

4 5 . 0

49.4

37.2

4 9 . 3

0 10-6 (MN / m2 )

40.5

41.2

29.0

:32.6

:21 . o :32.1

-6 a f a i l u r e p r o b a b i l i t y of 10 dec reased . Matthews a s s o c i a t e d t h e i n c r e a s e d

s p r e a d w i t h t h e volume expans ion expe r i enced by Poco g r a p h i t e on i r r a d i a t i o n ,

which may i n d i c a t e t h a t a new sys tem of i n t e r n a l c r a c k s was g e n e r a t e d .

A t v e r y h i g h n e u t r o n f l u e n c e s , where g r a p h i t e swells r a p i d l y and new

p o r e s are g e n e r a t e d , i t i s p r o b a b l e t h a t t h e s t r e n g t h f a l l s . However, no

d e f i n i t i v e d a t a have been p u b l i s h e d .

The p u b l i s h e d d a t a on t h e s t r e n g t h of i r r a d i a t e d g r a p h i t e may b e sum-

mar ized as f o l l o w s . The t e n s i l e and f l e x u r a l s t r e n g t h i n c r e a s e w i t h n e u t r o n

f l u e n c e i n a manner r e l a t e d t o t h e i n c r e a s e i n Young's modulus. For i r r a d i -

a t i o n t empera tu res below about 5 0 0 " C , t h e f r a c t i o n a l i n c r e a s e i n s t r e n g t h

i s p r o p o r t i o n a l t o t h e s q u a r e r o o t of t h e f r a c t i o n a l i n c r e a s e i n Young's

modulus. T h i s i s e q u i v a l e n t t o t h e s t r a i n energy t o f r a c t u r e remain ing

c o n s t a n t , p rov ided t h a t Young's modulus i s measured i n a s t a t i c t es t t o a

h i g h s t r a i n and n o t i n a dynamic t es t . A t h i g h e r i r r a d i a t i o n t e m p e r a t u r e s ,

t h e s t r e n g t h i n c r e a s e f o r some i s o t r o p i c g r a p h i t e s i s somewhat h i g h e r t h a n

expec ted from t h e c o n s t a n t s t r a i n energy f a i l u r e c o n d i t i o n .

N e i t h e r t h e e f f e c t of i r r a d i a t i o n on t h e s c a t t e r i n t h e s t r e n g t h

measurements no r t h e e f f e c t of t e s t i n g t e m p e r a t u r e on t h e s t r e n g t h of

i r r a d i a t e d g r a p h i t e i s w e l l d e f i n e d . The s h e a r s t r e n g t h of g raph . i t e

3-38

i n c r e a s e s on i r r a d i a t i o n i n about t h e same r a t i o as t h e t e n s i l e s t r e n g t h ,

w h i l e t h e compress ive s t r e n g t h i n c r e a s e s are h i g h e r . The s t r a i n t o f a i l u r e

i s reduced by i r r a d i a t i o n .

3.6. STRENGTH OF GRAPHITE O X I D I Z E D UNDER I R R A D I A T I O N

A c o n s i d e r a b l e amount of work h a s been r e p o r t e d on t h e e f f e c t of oxida-

t i o n by ca rbon d i o x i d e i n a r a d i a t i o n f i e l d on t h e s t r e n g t h of r e a c t o r

g r a p h i t e s (Ref s . 76 ,77 ) . The r a d i o l y t i c d i s s o c i a t i o n of ca rbon d i o x i d e by

gamma r a d i a t i o n i n c r e a s e s t h e o v e r a l l c o r r o s i o n r a t e , b u t c a u s e s t h e a t t a c k

t o b e less l o c a l i z e d t h a n d u r i n g o x i d a t i o n i n t h e absence of r a d i a t i o n .

The r a t e of decrease i n s t r e n g t h w i t h burn-off i s t h e r e f o r e lower t h a n f o r

o u t - o f - r e a c t o r expe r imen t s . Re fe rence 7 7 i n c l u d e s d a t a on t h e s t r e n g t h of

t e n s i l e spec imens , d i a m e t r i c a l l y compressed r i n g s , and i n t e r n a l l y p r e s -

s u r i z e d r i n g s of i s o t r o p i c g r a p h i t e o x i d i z e d i n f lowing ca rbon d i o x i d e i n

t h e BR-2 and D I D O r e a c t o r s a t 300" t o 500°C. The d i r e c t e f f e c t of r a d i -

a t i o n damage on t h e mechanica l p r o p e r t i e s w a s separa ted o u t by i r r a d i a t i n g

some companion specimens sealed i n s i l i c a c a p s u l e s and by a n n e a l i n g o u t

t h e i r r a d i a t i o n damage i n some o x i d i z e d specimens b e f o r e t e s t i n g . The

d e c r e a s e i n Young's modulus and s t r e n g t h w i t h weight l o s s i s shown i n

F i g s . 37 and 38. The d a t a show about a 20% r e d u c t i o n i n Young's modulus

and s t r e n g t h f o r 5% burn -o f f , compared w i t h up t o 50% r e d u c t i o n f o r 5%

burn-off i n o u t - o f - r e a c t o r tests ( s e e S e c t i o n 2 . 1 2 ) . There w a s no i n d i -

c a t i o n of d i f f e r e n t behav io r f o r d i f f e r e n t g r a p h i t e t y p e s , i r r a d i a t i o n

f a c i l i t i e s , o r t es t methods. It w a s concluded t h a t t h e e f f e c t s of i rra-

d i a t i o n damage and o x i d a t i o n are s e p a r a b l e , and o x i d a t i o n e f f e c t s may b e

a l lowed f o r by m u l t i p l y i n g t h e expec ted s t r e n g t h of i r r a d i a t e d , unox id ized

g r a p h i t e by a f a c t o r o b t a i n e d from p l o t s such as F i g . 38. L a t e r r e s u l t s

(Ref. 72) s u g g e s t t h a t s t r e n g t h s c a l c u l a t e d i n t h i s way may u n d e r e s t i m a t e

t h e t r u e s t r e n g t h .

No e q u i v a l e n t body of d a t a r e l a t i n g t o i n - r e a c t o r o x i d a t i o n by w e t

he l ium have been p u b l i s h e d i n t h e open l i t e r a t u r e , b u t measurements on

g r a p h i t e i r r a d i a t e d i n t h e Dragon r e a c t o r s u g g e s t t h a t b o t h t h e o x i d a t i o n

3-3 9

w I c- 0

1 .o

0.8

0.6

0.4

0.2

0

- P.G.A. (HAWKINS)

- BR-2 A ISOTROPIC

A

- Dl00 0 ISOTROPIC 0 P.G.A.

b,

20 30 40 0 10

WEIGHT LOSS (%)

F i g . 37. E f f e c t of r a d i o l y t i c o x i d a t i o n by C02 on Young's modulus of P i l e Grade A and i s o t r o p i c g r a p h i t e s (from R e f . 7 7 )

I 8 . , a?

8 c

w I f

1.2

1 .o

0.8

0.6

0.4

0.2

0 0

. +

BR-2 0 TENSILE 0 COMPRESSIVE SMALL \A A COMPRESSIVE

\ 0 DIAMETRAL ] DISKS

DIDO ATENSILE

DIAMETRAL ] 0 PRESSURE

t 10 20

WEIGHT LOSS (%)

30 40

F i g . 38 . E f f e c t of r a d i o l y t i c o x i d a t i o n by C02 on t h e s t r e n g t h of i s o t r o p i c g r a p h i t e s (from R e f . 7 7 )

r a t e and t h e s t r e n g t h v e r s u s burn-off r e l a t i o n ( S e c t i o n 2 . 1 2 ) are u n a f f e c t e d

by i r r a d i a t i o n . It i s notewor thy t h a t t h e oxida t ion- induced f r a c t i o n a l

d e c r e a s e i n Young's modulus i s s u f f i c i e n t l y c l o s e t o t h e d e c r e a s e i n s t r e n g t h

t h a t t h e e l a s t i c s t r a i n t o f a i l u r e remains a lmos t unchanged.

.

3-42

4 . RECOMMENDED D E S I G N P R A C T I C E

4 .1 . BASIS F O R RECOMMENDATIONS

The recommendations p r e s e n t e d i n t h i s s e c t i o n a re based on a c r i t i c a l

assessment of t h e l i t e r a t u r e combined w i t h in-house d a t a on t h e mechan ica l

p r o p e r t i e s of n e a r - i s o t r o p i c g r a p h i t e s . Because many gaps s t i l l remain i n

t h e expe r imen ta l r e s u l t s , i t h a s been sometimes n e c e s s a r y t o make "bes t -

guess ' ' judgments . Wherever s i g n i f i c a n t u n c e r t a i n t y remains , a c o n s e r v a t i v e

approach h a s been t a k e n . For example, Young's modulus of u n i r r a d i a t e d

g r a p h i t e i s known t o i n c r e a s e w i t h measurement t e m p e r a t u r e , b u t no e x p e r i -

men ta l measurements a t e l e v a t e d t e m p e r a t u r e s have been made on i r r a d i a t e d

material . Young's modulus of i r r a d i a t e d g r a p h i t e h a s t h e r e f o r e been assumed

t o i n c r e a s e w i t h t empera tu re s i m i l a r l y t o t h a t of u n i r r a d i a t e d g r a p h i t e ,

On t h e o t h e r hand, t h e s t r e n g t h of u n i r r a d i a t e d g r a p h i t e i n c r e a s e s w i t h

t empera tu re somewhat f a s t e r t h a n Young's modulus, b u t t h e d a t a on i r r a d i -

a t e d mater ia l are inadequa te t o prove t h e e x i s t e n c e of a s imi l a r i n c r e a s e

w i t h t e m p e r a t u r e . T h e r e f o r e , no co r re spond ing i n c r e a s e i n s t r e n g t h w i t h

t empera tu re h a s been assumed f o r i r r a d i a t e d g r a p h i t e .

The l a r g e s t remain ing area of u n c e r t a i n t y s u r r o u n d s t h e s e l e c t i o n of

f a i l u r e c r i t e r i a . There i s no s i n g l e model f o r f a i l u r e which h a s been

shown t o a p p l y t o g r a p h i t e under a l l c o n d i t i o n s of l o a d i n g . Even t h e

Weibul l s t a t i s t i c a l t h e o r y , which f i t s many a s p e c t s of g r a p h i t e s t r e n g t h

b e h a v i o r , h a s n o t been demonst ra ted t o p r o v i d e a s e l f - c o n s i s t e n t model.

The a p p l i c a t i o n of d e s i g n c r i t e r i a based on f r a c t u r e mechanics cons ide r -

a t i o n s i s n o t y e t v e r i f i e d by expe r imen ta l d a t a from l a r g e g r a p h i t e s t r u c -

t u r e s . I n t h e absence of a u n i v e r s a l and v e r i f i e d f a i l u r e c r i t e r i o n , d i f -

f e r e n t f a i l u r e c r i t e r i a are recommended f o r d i f f e r e n t l o a d i n g c o n d i t i o n s ,

based on t h e r e s u l t s of tes ts under a similar stress s t a t e .

4- 1

It shou ld b e no ted t h a t t h e t e r m " f a i l u r e c r i t e r i o n " r e f e r s h e r e t o

t h e stress c o n d i t i o n s which can b e assumed t o c a u s e f a i l u r e i n a s i n g l e

e lement of material, such as a c r a c k a c r o s s t h e web between a f u e l and

c o o l a n t h o l e i n an HTGR modera tor b l o c k .

4.2 . TYPE OF ELASTIC BEHAVIOR

For g r a p h i t e i r r a d i a t e d under any c o n d i t i o n s , Hookean behav io r can b e

assumed.

For u n i r r a d i a t e d g r a p h i t e , t h e d e p a r t u r e from l i n e a r i t y may b e g r e a t

enough t o i n t r o d u c e impor t an t e r r o r s i f l i n e a r e l a s t i c i t y i s assumed. The

f o l l o w i n g r e l a t i o n s h i p s between u n i a x i a l stress, 0 , and s t r a i n , E, based

on t h e work of J e n k i n s (Ref. 1 2 ) , are recommended f o r u n i r r a d i a t e d g r a p h i t e :

2 I n i t i a l l o a d i n g cu rve : E = A 0 + Ba

Unloading from peak stress, 0 and peak s t r a i n , E : m y m

1 2 - E = A(om-a) + 7 B(Om-O) , 'm

Reloading from cr : 0

It shou ld b e no ted t h a t i g n o r i n g t h e n o n l i n e a r i t y and assuming A =

l /Young's modulus and B = 0 w i l l g e n e r a l l y r e s u l t i n o v e r e s t i m a t i o n o f

stresses and t h e r e f o r e errs on t h e s i d e of conse rva t i sm.

4 . 3 . ELASTIC CONSTANTS

Young's modulus under service c o n d i t i o n s shou ld b e o b t a i n e d by m i i l t i -

p l y i n g t h e a p p r o p r i a t e room-temperaturey u n i r r a d i a t e d v a l u e , Eo, by a

4-2

c

-. f a c t o r a c c o u n t i n g f o r t h e i n c r e a s e i n modulus w i t h t e m p e r a t u r e and a

second f a c t o r g i v i n g t h e i n c r e a s e w i t h i r r a d i a t i o n . Thus,

E = E 0 ( 1 + 1 . 5 ~ 1 0 - ~ ~ ) F l ( @ t , T i r r ) )

where T i s t h e t e m p e r a t u r e i n 'C.

i r r a d i a t e d g r a p h i t e , t h e t e m p e r a t u r e dependence t e r m w a s t a k e n from t h e

I n t h e absence of e x p e r i m e n t a l d a t a on

measurements of t h e dynamic modulus of u n i r r a d i a t e d g r a p h i t e by Mason and

Knibbs (Ref. 78) . These d a t a were used i n p r e f e r e n c e t o t h e l e s s - t e m p e r a t u r e -

dependent r e s u l t s on t h e s t a t i c modulus of u n i r r a d i a t e d g r a p h i t e (Ref. 2 4 ) )

because t h e s t a t i c e l a s t i c modulus of i r r a d i a t e d g r a p h i t e a g r e e s w i t h t h e

dynamic modulus. Values f o r F l ( $ t ) T i r r ) are shown i n F ig . 39.

The v a l u e s f o r F , ( $ t ) T i r r ) w e r e c a l c u l a t e d from Dragon p r o j e c t dynamic

modulus d a t a (Ref, 59) on a p i t ch -coke g r a p h i t e (code No. l o o ) , whose pro-

p e r t i e s and i r r a d i a t i o n b e h a v i o r resemble t h o s e of n e a r - i s o t r o p i c petroleum-

coke g r a p h i t e s , by making t h e f o l l o w i n g a s sumpt ions :

2 1 . Fluence i n u n i t s of n/cm (NDE) = 0 .6 x f l u e n c e i n u n i t s of

n/cm2 (E > 0.18 MeV).

2. S t a t i c Young's modulus of u n i r r a d i a t e d g r a p h i t e = 0 . 8 x dynamic

Young's modulus.

3. S t a t i c Young's modulus o f i r r a d i a t e d g r a p h i t e = dynamic Young's

modulus.

The c u r v e s c a l c u l a t e d u s i n g t h e s e a s sumpt ions (F ig . 39) are i n good ag ree -

ment w i t h measurements of t h e s t a t i c Young's modulus of g r a p h i t e i r r a d i a t e d

i n c a p s u l e s OG-1 and OG-2 (Re f s . 6 9 , 7 0 ) . Values p r e d i c t e d from F i g . 39 are i n c l u d e d i n T a b l e 1 f o r comparison w i t h t h e measurements.

4-3

\

c- I c-

140

120

100

80

60

40

20

0 0 1 2 3 4 5 6 1 8

FAST NEUTRON FLUENCE x io -z i (NICM~

F i g . 39 . F r a c t i o n a l i n c r e a s e i n s t a t i c Young's modulus as a (recommended f o r d e s i g n p u r p o s e s )

E > 0.18 MeV)

f u n c t i o n of f a s t n e u t r o n f l u e n c e

. For conditions where oxidation by low-level impurities is significant,

the value of Young's modulus should be reduced by multiplying by a factor

(1-WL)", where WL is the fractional weight loss due to oxidation.

4 .4 . POISSON'S RATIO

In the absence of definitive data establishing a trend for the effect

of irradiation on Poisson's ratio, it may be assumed that Poisson's ratio

does not change on irradiation.

4 . 5 . FAILURE CRITERIA

1 . Predominantly uniform uniaxial tension or compression:

= S (tension) , T cs max

= S (compression) , C cs min

and omin are the maximum and minimum principal max

where CT

stresses, and S and S are the ultimate tensile and compressive

strengths, respectively. T C

2. Stress gradient progressing from tension to compression:

where S is the flexural strength. F

3. Biaxial stresses: The effect of biaxial stresses is not fully

defined at present. For interim calculations the use of Ely's

maximum strain energy criterion is suggested:

4-5

where 0 and 0 are t h e p r i n c i p a l stresses and v i s P o i s s o n ' s

r a t i o . 1 2

4 . 6 . EFFECT OF IRRADIATION ON STRENGTH

The t e n s i l e , f l e x u r a l , and compress ive s t r e n g t h s may b e assumed t o

i n c r e a s e on i r r a d i a t i o n i n p r o p o r t i o n t o t h e s q u a r e r o o t of t h e f r a c t i o n a l

i n c r e a s e i n Young's modulus. Thus,

where F2($ t ,T

room tempera tu re .

i n c r e a s e s shown i n F ig . 39, are p l o t t e d i n F ig . 40. S t r e n g t h v a l u e s p r e -

d i c t e d from Fig . 40 are i n c l u d e d i n Tab le 1 f o r comparison w i t h measure-

ments on specimens i r r a d i a t e d i n c a p s u l e s OG-1 and OG-2. For H-451 g r a p h i t e

and most H-327 spec imens , t h e s t r e n g t h v a l u e s p r e d i c t e d by F ig . 40 a r e

c o n s e r v a t i v e . However, t h e r e are n o t y e t s u f f i c i e n t e x p e r i m e n t a l measure-

ments t o j u s t i f y t h e u s e of a s t rength-modulus r e l a t i o n s h i p less c o n s e r v a t i v e

t h a n t h a t shown i n F ig . 4 0 .

) =dw and S i s t h e u n i r r a d i a t e d s t r e n g t h measured a t i rr 0 0 Values of F2($ t ,T i r r ) , c a l c u l a t e d from t h e modulus

When o x i d a t i o n by low- leve l i m p u r i t i e s i n t h e c o o l a n t g a s i s s i g n i f i - 10

c a n t , t h e s t r e n g t h v a l u e s shou ld b e m u l t i p l i e d by (1-WL) , where WL is

t h e f r a c t i o n a l weight l o s s due t o o x i d a t i o n .

4 .7 . STATISTICAL VARIATION I N STRENGTH

S t r e n g t h d a t a r e p o r t e d i n t h e l i t e r a t u r e have been expres sed e i t h e r

i n terms of t h e Weibul l d i s t r i b u t i o n pa rame te r , m y o r i n terms of a s t a n d a r d

d e v i a t i o n . There are i n s u f f i c i e n t d a t a t o e s t a b l i s h t h e form of t h e d i s -

t r i b u t i o n f u n c t i o n . For c a l c u l a t i o n a l convenience i t i s recommended t h a t n

4-6

0

co

V

0 0

0

m

u

0

0

0

N -

0

7

0

N

0

m

0

d

0

Lo

(%) H

19N3H

lS lV'tlnX314 80

311SN31 NI 3SV3t13NI lN33t13d :'4

0

4-7

t h e s t r e n g t h s of i n d i v i d u a l samples be assumed t o have a Gauss ian d i s t r i -

b u t i o n , Evidence on t h e e f f e c t o f i r r a d i a t i o n on t h e s p r e a d o f s t r e n g t h s

i s n o t w e l l d e f i n e d . However, s t r e n g t h measurements on n e a r - i s o t r o p i c

(H-451) g r a p h i t e samples i r r a d i a t e d i n c a p s u l e s OG-1 and OG-2 (Table 1 )

showed no s i g n i f i c a n t change i n c o e f f i c i e n t of v a r i a t i o n from t h e u n i r r a d i -

a t e d r e s u l t s . It i s recommended t h a t t h e c o e f f i c i e n t of v a r i a t i o n ( s t and-

a r d d e v i a t i o n d i v i d e d by t h e mean) b e assumed t o remain c o n s t a n t d u r i n g

i r r a d i a t i o n .

4.8. NUMERICAL VALUES FOR UNIRRADIATED MECHANICAL PROPERTIES

R e p r e s e n t a t i v e v a l u e s f o r t h e mechanica l p r o p e r t i e s o f t h e u n i r r a d i a t e d

n e a r - i s o t r o p i c petroleum-coke g r a p h i t e s H-451, TS-1240, and SO-818 are shown

i n Tab le 5. Measurements are g i v e n f o r t h e mid leng th -cen te r (weakest

l o c a t i o n ) and midlength-edge r e g i o n s of a " t y p i c a l " l o g . The da ta i n

Tab le 5 are i n t e r i m v a l u e s based on a l i m i t e d number of t e s t s on p r o t o t y p e

l o t s and may n o t b e t y p i c a l of p r o d u c t i o n material .

4- 8

n

I e

Grade

H-451

H-45 1

H-45 1

H-451

TS- 1 240 c- I

\D TS-1240

TS-1240

TS-1240

SO-818

SO-8 18

SO-8 18

SO-818

Orien- t a t i o n

Ax ia l

A x i a l

Rad ia l

Rad ia l

Ax ia l

Axia l

Rad ia l

Rad ia l

Ax ia l

Ax ia l

Rad ia l

Rad ia l

TABLE 5 TYPICAL MECHANICAL PROPERTIES OF UNIRRADIATED NEAR-ISOTROPIC GRAPHITES (t STANDARD DEVIATION)

Loca t ion

r l id length - c e n t e r

Midlength - edge

r l id length - c e n t e r

Midlength - edge

Midlength - c e n t e r

Midlength - edge

Midlength - c e n t e r

Midlength - edge

Midlength - c e n t e r

Midlength - edge

Midlength - c e n t e r

Midlength - edge

Young ' s Modulus

10-6(a) ( p s i )

1 . 1 7 t 0.09

1.26 t 0.09

0 .98 t 0.08

1 .03 t 0.09

1 .14 t 0.12

1 . 1 7 ? 0.10

1.02 t 0.07

1 .06 t 0.06

1.09 t 0.11

1.16 t 0.12

1 . 0 3 t 0.07

1.04 ? 0.11

P o i s s o n ' s Ra t io

0 .13 t 0.01

0 .12 t 0.01

0 .13 2 0.01

--

0 .11 2 0 .01

_ _

_-

-- --

_-

_-

--

P r o u e r t v (Mean V a l u e t 1 S tanda rd Dev ia t ion )

T e n s i l e S t r e n g t h

( p s i )

2011 t 211

2686 2 306

1557 t 293

1964 t 342

2122 2 364

2301 t 406

1572 2 503

1802 2 354

1980 2 216

2267 2 290

1851 t 206

1797 ? 203

. .

Compressive S t r e n g t h

( p s i )

8350

8300 t 1 7 8

7867 t 1 5 3

_ _ 7288 t 1 3 2

7808 ? 376

-_

_ _ 8303 f 1 7 5

_ _

8583 2 306

_-

F l e x u r a l

( p s i )

3690 2 371

i332 t 425

1257 t 414

3706 2 380

_-

_-

_ _ --

_ _

3603 t 476

_ _

2900 t 358

S t r e s s - S t r a i n Curve A

.Parameter x 1 0 ~ ' ~ ) ( p s i - l )

0.91 2 0.07

0.87 t 0.07

1,.04 i 0.06

1 .04 t 0.06

1.02 t 0 .05

1 .05 t 0.10

1.14 t 0.04

1 .12 t 0.06

0 . 9 3 t 0 .05

0.86 t 0.04

0.89 t 0.05

0.96 t 0.02

S t r e s s - S t r a i n Curve B

10 (c) Parameter x 10 (ps i -2 )

1 .8 2 0.6

1 . 1 2 0.2

1 .8 2 0 .6

1 . 4 t 0 . 3

1 .6 t 0 .1

1 . 7 ? 0 . 3

1 . 7 t 0 . 1

1 . 7 t 0 . 3

1 . 3 t 0 .1

1.6 t 0 .1

1 . 7 ? 0.1

1 .9 2 0.2

(a)Measured f o r t h e 100- t o 1000-psi p o r t i o n of t h e r e l o a d i n g cu rve a f t e r l o a d i n g t o 1000 p s i , u n l o a d i n g t o 100 p s i , and r e l o a d i n g t o f a i l u r e .

(b)Modulus of r u p t u r e , n o t c o r r e c t e d f o r n o n l i n e a r i t y of t h e s t r e s s - s t r a i n cu rve .

= AD + Bo2 ( u i n p s i ) .

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