GRAIN BOUNDARY INTERNAL FRICTION AND RELATIONSHIP TO INTERGRANULAR FRACTURE

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GRAIN BOUNDARY INTERNAL FRICTION AND RELATIONSHIP TO INTERGRANULAR FRACTURE

F. Cosandey

To cite this version:

F. Cosandey. GRAIN BOUNDARY INTERNAL FRICTION AND RELATIONSHIP TO IN- TERGRANULAR FRACTURE. Journal de Physique Colloques, 1988, 49 (C5), pp.C5-581-C5-586.

�10.1051/jphyscol:1988572�. �jpa-00228069�

JOURNAL DE PHYSIQUE

Colloque C5, suppl6ment au nOIO, Tome 49, octobre 1988

GRAIN BOUNDARY INTERNAL FRICTION AND RELATIONSHIP TO INTERGRANULAR FRACTURE

I?. COSANDEY

Rutgers, The State University of New Jersey, Department of Mechanics and Materials Science, Piscataway, NJ 08855-0909, U.S,A.

A b s t r a c t --

Creep r a t e , s t r e s s r u p t u r e and f r a c t u r e mode have been measured on Ni-20

W/O

C r a l l o y s c o n t a i n i n g 0 and 180 a t . ppm Ce. Grain boundary v i s c o s i t y and a n e l a s t i c r e l a x a t i o n phenomena have been determined by h i g h temperature i n t e r n a l f r i c t i o n measurements and r e s u l t s c o r r e l a t e d t o f r a c t u r e behavior.

I n t r o d u c t i o n

The phenomena o f h i g h temperature i n t e r g r a n u l a r f r a c t u r e w i t h i t s associated v e r y low a l l o y d u c t i l i t y i s a complex process which i n c l u d e c a v i t y n u c l e a t i o n , cav--

i t y growth, i n t e r l i n k a g e f o l l o w e d by f i n a l f r a c t u r e 11,21. I t i s now w e l l estab- l i s h e d t h a t l o c a l i z e d h i g h s t r e s s c o n c e n t r a t i o n i n excess o f a p p l i e d s t r e s s i s r e w i r e d f o r t h e n u c l e a t i o n o f c a v i t i e s 121. T h i s h i g h s t r e s s can be generated by, f o r instance, g r a i n boundary s l i d i n g . I n a d d i t i o n , g r a i n boundary segregation i s o f g r e a t importance since i t ' c a n reduce g r a i n boundary cohesion and surface f r e e energy which would i n t u r n reduce t h e c r i t i c a l s t r e s s r e q u i r e d f o r c a v i t y formation.

For instance, i t i s known t h a t t r a c e amounts o f S promote i n t e r g r a n u l a r f r a c t u r e 131, w h i l e o t h e r s such as Ce 141 o r 6 [51 r e s t o r e h i g h a l l o y d u c t i l i t y . F i n a l l y , f r a c t u r e p a t h i s a l s o determined by t e s t c o n d i t i o n s and i n general i n t e r g r a n u l a r f r a c t u r e i s observed predominantly a t h i g h temperatures and f o r low s t r a i n r a t e t e s t s . T h i s behavior i s observed because a t low temperatures and h i g h s t r a i n r a t e s , g r a i n boundaries a r e e s s e n t i a l l y immobile and t h e r e f o r e cannot generate t h e

r e q u i r e d l o c a l i z e d h i g h stresses. An upper bound s t r a i n r a t e , above which c a v i t a - t i o n does n o t occur, has been obtained by Crossman and Ashby (61 by c o n s i d e r i n g t h e balance between s t r e s s c o n c e n t r a t i o n generated by g r a i n boundary s l i d i n g and s t r e s s r e l a x a t i o n produced by d i s l o c a t i o n creep. This upper bound o r t r a n s i t i o n s t r a i n r a t e (TSTR) i s given by:

,n

U n - 1

where ngb denotes t h e g r a i n boundary s l i d i n g v i s c o s i t y , 6 t h e g r a i n boundary thickness, d t h e g r a i n size, n and A a r e t h e s t r e s s exponent and parameter o f t h e

power-law creep r e l a t i o n : n

;

= A(C)

IJ ^{( 2 )}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988572

C5-582 JOURNAL

DE

PHYSIQUE

w i t h

where Qc denoted t h e creep a c t i v a t i o n energy. A l l t h e parameters i n v o l v e d i n eq. 1 are known o r can be determined experimentally. I n p a r t i c u l a r , g r a i n boundary s l i d i n g v i s c o s i t i e s can be measured d i r e c t l y by the i n t e r n a l f r i c t i o n method [7,81.

T h i s paper presents t h e r e s u l t s o f an i n v e s t i g a t i o n on t h e upper bound s t r a i n r a t e f o r i n t e r g r a n u l a r f r a c t u r e i n a Ni-20 C r a l l o y . F i r s t , the formalism o f i n t e r n a l f r i c t i o n measurements i s presented which i s f o l l o w e d by a d i s l o c a t i o n g l i d e d e s c r i p t i o n f o r g r a i n boundary r e l a x a t i o n time. I n t e r n a l f r i c t i o n and creep data a r e then used t o model t h e p r e d i c t e d t r a n s i t i o n s t r a i n r a t e which i s then compared t o experimental data. F i n a l l y , t h e p o s s i b l e r o l e s o f minor Ce a d d i t i o n s cn t h e observed suppression o f i n t e r g r a n u l a r f r a c t u r e a r e discussed i n l i g h t o f i n t e r n a l f r i c t i o n r e s u l t s .

I n t e r n a l F r i c t i o n Analysis

The i n t e r n a l f r i c t i o n technique, although i n d i r e c t , i s unique f o r t h e study of g r a i n boundaries and has been used s u c c e s s f u l l y t o determine g r a i n boundary s l i d i n ? k i n e t i c s [7,8] .and g r a i n boundary segregation phenomena [9]

.

Whenever g r a i n boundaries can move f r e e l y , viscous s l i d i n g occurs l e a d i n g t o an exponential increase i n h i g h temperature background. I f s l i d i n g i s impeded by p i n n i n g p o i n t s , a n e l a s t i c r e l a x a t i o n w i l l occur l e a d i n g t o a peak i n i n t e r n a l f r i c t i o n . T h i s r e l a x a t i o n process i s c h a r a c t e r i z e d by a r e l a x a t i o n time ^T which i s expressed as

A d e t a i l e d basic mechanism f o r g r a i n boundary i n t e r n a l f r i c t i o n has n o t y e t been c l e a r l y e s t a b l i s h e d , a1 though model s based on g r a i n boundary s l i d i n g by d i f f u s i o n have r e c e i v e d most a t t e n t i o n [7,8]. Since g r a i n boundaries a r e composed o f d i s c r e t e d i s l o c a t i o n s , g r a i n boundary s l i d i n g may be described a l s o by t h e c l i m b process o f these d i s l o c a t i o n s . I n t h i s case, t h e r e l a x a t i o n t i m e i s g i v e n by [ l o ] :

where vc i s t h e average d i s l o c a t i o n c l i m b v e l o c i t y , h t h e c l i m b distance, o t h e shear s t r e s s , Q t h e atomic volume, b t h e d i s l o c a t i o n burgers v e c t o r and M t h e m o b i l i t y . Two l i m i t i n g cases can be considered f o r t h e d i s l o c a t i o n m o b i l i t y [ l o ] . For a g r a i n boundary f r e e o f segregated i m p u r i t i e s t h e i n t r i n s i c d i s l o c a t i o n

m o b i l i t y i s g-iven by D b

1, = gb

kT ( 6 )

where D i s t h e g r a i n boundary d i f f u s i v i t y . For an a l l o y c o n t a i n i n g i m p u r i t y atoms, ?he d i s l o c a t i o n m o b i l i t y w i l l be l i m i t e d by t h e drag caused by segregated i m p u r i t i e s . 1.n t h i s case t h e d i s l o c a t i o n m o b i l i t y decreases t o [ l o ]

M =

---

Ds

2 ^{( 7 )}

b kTBCo

rlhere DS 1:s t h e s o l u t e d i f f u s i v i t y , f? t h e g r a i n boundary enrichment f a c t o r and Co t h e i m p u r i t y b u l k concentration.

F i n a l l y , g r a i n boundary v i s c o s i t y ngb i s r e l a t e d t o r e l a x a t i o n t i m e v i a t h e f o l l o w i n g equation [7,81

where E i s t h e modulus o f e l a s t i c i t ] , , 6 t h e g r a i n boundary thickness and L t h e

l e n g t h o f s l i ' d i n g q r a i n boundaries, i . e . d i s t a n c e between p i n n i n g points.. I n most studies, an equiaxed g r a i n s t r u c t u r e i s considered and L i s taken as t h e average g r a i n s i z e d.

Experimental Procedures

T e n s i l e t e s t s , creep t e s t s and i n t e r n a l f r i c t i o n measurements were performed on two Ni-20 W% C r a l l o y s c o n t a i n i n g 0 and 180 a t . ppm Ce. The a l l o y s were pre- pared by vacuum i n d u c t i o n m e l t i n g a t Special Metals Corporation, f o l l o w e d by c a s t i n g and h o t r o l l i n g . S i m i l a r heat treatments were performed on a l l a l l o y s c o n s i s t i n g o f a vacuum annealed a t 110O0C i n order t o o b t a i n s i m i l a r g r a i n s i z e s ( 4 0 ~ m ) f o l l o w e d by aging f o r 24 hours a t 80O0C.

I n t e r n a l f r i c t i o n measurements were performed a t low frequency (0.5

-

3 Hz) i n a c l a s s i c a l t o r s i o n pendulum and data deduced from t h e wave form a n a l y s i s o f t h e f r e e decay s i g n a l [I11

.

S t r a i n amplitude was 5 x and h e a t i n g and c o o l i n g r a t e s Z0K/min.

Stress exponents and creep a c t i v a t i o n energies were obtained u s i n g a constant l o a d creep t e s t e r . A l l data were analyzed by c o n v e r t i n g r e s u l t s t o t r u e s t r e s s data by measuring t r u e s t r a i n a t minimum s t r a i n r a t e [121. D u c t i l i t i e s , f r a c t u r e modes and t r a n s i t i o n s t r a i n r a t e data were obtained by combined creep and t e n s i l e t e s t i n g using a constant crosshead v e l o c i t y machine [ 4 ] .

Results and Discussion --

A t y p i c a l i n t e r n a l f r i c t i o n spectrum Q-1 measured on a f u n c t i o n o f temperature i s d e p i c t e d i n Fig. 1 f o r t h e a l l o y w i t h o u t Ce. The spectrum r e v e a l s a peak which i s superposed t o an exponential background. The a c t i v a t i o n energy f o r t h e peak Q, and r e l a x a t i o n time, -ro, have been determined f o r both a l l o y s by measuring t h e s h i f t i n peak temperature T as a f u n c t i o n o f frequency i n an Arrhenius t y p e p l o t . These r e s u l t s a r e summarize1 i n Table I. By i n s p e c t i o n o f t h i s Table i t can be seen t h a t t r a c e a d d i t i o n s o f Ce decreases t h e a c t i v a t i o n energy from a h i g h value o f 370 kJ/mole t o a lower value o f 200 kJ/mole and decreases t h e peak temperature measured a t 1 Hz. I n t h e l i t e r a t u r e i t i s g e n e r a l l y observed [ I 4 1 t h a t small a d d i t i o n s o f both s u b s t i t u t i o n a l and i n t e r s t i t i a l atoms increase t h e peak a c t i v a t i o n energy w i t h t h e appearance o f a new peak a t l a r g e concentrations. I n a d d i t i o n , if t h e r a t e c o n t r o l l i n g process f o r g r a i n boundary i n t e r n a l f r i c t i o n i s t h e g l i d e and c l i m b process o f g r a i n boundary d i s l o c a t i o n s , then t h e a c t i v a t i o n energy increases from g r a i n boundary d i f f u s i v i t y t o t h a t o f i m p u r i t y s e l f d i f f u s i v i t y . T h i s r e s u l t seems t o i n d i c a t e t h a t a d d i t i o n s o f Ce decreases t h e i m p u r i t y c o n t e n t of t h e a l l o y and t h e i r segregation t o g r a i n boundaries. The p r e c i s e g r a i n boundary chemistry i s n o t known f o r these a l l o y s b u t a r e d u c t i o n i n b u l k 0 and S c o n t e n t has been measured upon Ce a d d i t i o n s [131. I n view o f t h e s t r o n g tendency of 0 and

S

t o segregate a t g r a i n boundaries, ( i . e . l a r g e 6 values) a s i m i l a r decrease i n g r a i n boundary chemistry i s expected.

Table I I n t e r n a l f r i c t i o n peak temperature, Tp, measured a t 1 Hz, r e l a x a t i o n time TO, a c t i v a t i o n energy Q and r e l a x a t i o n s t r e n g t h A as a f u n c t i o n o f Ce concen- t r a t i o n . Also shown a r e t h e g r a i n boundary v i s c o s i t i e s q evaluated a t 700°C.

Ce Concentration Tp To

Q

A rl

[ a t . ppml ["CI [ s l [KJ/molel [ x [~s/rn'l

JOURNAL DE PHYSIQUE

Temp. C K I

Figure 1 I n t e r n a l f r i c t i o n spectrum Q - ~ versus temperature f o r Ni-20Cr a l l o y c o n t a i n i n g 0 ppm Ce. The background i s f i t t e d w i t h a s i n g l e exponential.

I ^I I I I I 1

400 500 600 700 800 900 TEMPERATURE (%)

F i g u r e 2 F r a c t u r e behavior as a f u n c t i o n o f s t r a i n r a t e and temperature f o r f l i - 2 0 ~ r a l l o y w i t h o u t Ce. F i l l e d , open and h a l f open symbols represent i n t u r n , transgranular, i n t e r g r a n u l a r and mixed f r a c t u r e modes. Numbers r e p r e s e n t elonga- t i o n a t f r a c t u r e . The TSTR l i n e i s t h e t h e o r e t i c a l t r a n s i t i o n s t r a i n r a t e .

Table I 1 Stress exponent ( n ) , p r e s t r e s s exponent c o e f f i c i e n t s (A) and A,, and creep a c t i v a t i o n energy (Qc) as a f u n c t i o n o f Ce c o n c e n t r a t i o n .

Ce Concentration n A

Qc

[ a t . ppml [ l / s l [ l / s l [ k J / m o l e ~

I n order t o determine t h e t r a n s i t i o n s t r a i n r a t e , creep s t r e s s exponents and creep a c t i v a t i o n energies have been measured f o r v a r i o u s Ce c o n t a i n i n g a l l o y s [121.

The r e s u l t s a r e summarized i n Table 11. Contrary t o g r a i n boundary r e l a x a t i o n data, creep a c t i v a t i o n energy increases w i t h Ce content. However, Ce has l i t t l e e f f e c t on t h e s t r e s s exponent n which i s equal t o 5.2 f o r a l l compositions. This increase i n a c t i v a t i o n energy was a t t r i b u t e d t o an increase i n b u l k d i f f u s i v i t y 1121.

F i n a l l y , a l l o y d u c t i l i t y and f r a c t u r e mode have been measured as a f u n c t i o n o f t e s t s t r a i n r a t e and temperature [41. The r e s u l t s f o r t h e a l l o y w i t h o u t Ce a r e represented i n Fig. 2 i n a t e m p e r a t u r e - s t r a i n r a t e - f r a c t u r e mode graph. The experimental data can be d i v i d e d i n t o t h r e e broad c a t e g o r i e s according t o t h e i r f r a c t u r e path. A t h i g h t e s t temperatures and low s t r a i n - r a t e s the f r a c t u r e mode i s i n t e r g r a n u l a r w i t h an associated low d u c t i l i t y . A t low temperatures and h i g h stresses, t h e f r a c t u r e mode i s t r a n s g r a n u l a r w i t h a corresponding h i g h d u c t i l i t y . I n between these two broad categories, mixed mode o f f r a c t u r e i s observed. A d r a s t i c a l l y d i f f e r e n t p i c t u r e i s obtained f o r t h e a l l o y c o n t a i n i n g 180 a t . ppm Ce.

T h i s a l l o y remains d u c t i l e f o r a l l t e s t c o n d i t i o n s and f r a c t u r e mode remain t r a n s - g r a n u l a r .

These experimental r e s u l t s can now be compared w i t h t h e o r e t i c a l p r e d i c t i o n s given by eq. 1. The c a l c u l a t e d TSTR values drawn i n F i g . 2 show a reasonable agreement between t h e o r y and experimental r e s u l t s , and eq. 1 can t h e r e f o r e be used t o estimate t h e d u c t i l e - b r i t t l e t r a n s i t i o n i n a l l o y s which a r e s u s c e p t i b l e t o i n t e r g r a n u l a r f r a c t u r e .

For Ce c o n t a i n i n g a l l o y s - i n t e r g anu a r f r a c t u r e i s n o t observed even a t t h e lowest creep s t r a i n r a t e s o f ^E =

lo-?

s - I . This r e s u l t i n d i c a t e s t h a t e i t h e r much l a r g e r stresses a r e r e q u i r e d f o r t h e f o r m a t i o n o f c a v i t i e s and/or t h a t stresses can be r e l i e v e d much more r e a d i l y . Furthermore, a pronounced i n t e r n a l f r i c t i o n h y s t e r e s i s between heating and c o o l i n 9 c y c l e s was measured f o r t h e

180 ppm Ce a l l o y 1151. T h i s h y s t e r e s i s which was n o t observed f o r t h e a l l o y w i t h o u t Ce was a t t r i b u t e d t o a d e s t a b i l i z a t i o n o f t h e g r a i n boundary p i n n i n g p o i n t s a t h i g h temperature. T h i s i n t u r n c o u l d minimize s t r e s s c o n c e n t r a t i o n p o i n t s and t h e r e f o r e reduce t h e n u c l e a t i o n r a t e o f c a v i t i e s and r e s t o r e h i g h temperature d u c t i l i t y .

Acknowledgements

We thank G.E. Maurer o f Special Metal Corporation f o r c o n t r i b u t i o n o f t h e a l l o y s . Special thanks t o R. S c h a l l e r , J.J. Ammann and W. B e n o i t f o r v e r y p r o f i t - a b l e discussions and f o r t h e i r c o n t r i b u t i o n i n i n t e r n a l f r i c t i o n measurements.

T h i s work i s supported i n p a r t by t h e N a t i o n a l Science Foundation under g r a n t s NSF-i)irlR-84-06005 and NSF-Int-85-15321.

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