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have not g a i n e d w i d e s p r e a d a c c e p t a n c e . In this p a p e r we p r o p o s e a new and s i m p l e e x p l a n a t i o n of t h e s e high c r e e p a c t i v a t i o n e n e r g i e s . We s u g g e s t that the high a p p a r e n t a c t i v a t i o n e n e r g i e s a r e c a u s e d by the t e m p e r a t u r e d e p e n d e n c e of the e l a s t i c m o d u l u s . DIRECT DETERMINATION OF CREEP ACTIVATION ENERGY The d a t a of W i l c o x and C l a u e r 2 on t h e r m o m e c h a n i c a l l y p r o c e s s e d Ni + 2 v o l p c t ThO 2 w i l l be used in t h i s a n a l y s i s . T h e r e a r e s e v e r a l r e a s o n s for c h o o s i n g this d a t a o v e r the d a t a of m a n y o t h e r i n v e s t i g a t o r s . F i r s t , the a c t i v a t i o n e n e r g y is high (795 k J / m o l (190 k c a l / m o l ) ) . Second, they s t u d i e d a s i m p l e m e t a l - o x i d e s y s t e m , Ni + 2 vol p c t ThO 2. This p r e c l u d e s any of the c o m p l i c a t i n g m e t a l l u r g i c a l e f f e c t s which might be found in p r e c i p i t a t i o n s t r e n g t h e n e d a l l o y s s i n c e the ThO 2 p a r t i c l e s a r e v i r t u a l l y i n s o l u b l e in p u r e n i c k e l . F i n a l l y , W i l c o x and C l a u e r a p p a r e n t l y e x e r c i s e d g r e a t c a r e in t h e i r e x p e r i m e n t s with the r e s u l t that t h e i r d a t a show v e r y l i t t l e s c a t t e r . W i l c o x and C l a u e r m a d e u s e of the c o n v e n t i o n a l p h e n o m e n o l o g i c a l c r e e p equation:

Qc ~s =A1 an exp (-~q-TC)

[1]

-

in the a n a l y s i s of t h e i r data, w h e r e ~s is the " s t e a d y s t a t e " o r m i n i m u m c r e e p r a t e , A, is a s t r u c t u r e s e n s i t i v e c o n s t a n t , a i s the s t r e s s , n is the s t r e s s e x p o nent, Qc is the c r e e p a c t i v a t i o n e n e r g y , R i s the gas c o n s t a n t , and T i s the a b s o l u t e t e m p e r a t u r e . They conducted c o n s t a n t s t r e s s e x p e r i m e n t s and o b t a i n e d the a c t i v a t i o n e n e r g y f r o m : Qapp (apparent) = Qc

C a In ~-9.s\

=

-- R \ ~ ( 1 / ' T ) }(r

[2]

H o w e v e r , if the t e m p e r a t u r e d e p e n d e n t d y n a m i c e l a s tic modulus i s i n c l u d e d in the c r e e p equation a s s u g g e s t e d o r i g i n a l l y by S h e r b y 12' 13 for p u r e m e t a l s and s o l i d s o l u t i o n s , we have:

[ a

\n

es = Ae I , E - - ~ }

[-Qc\ exp I--R-if--)

[3]

w h e r e E (T) i s the e l a s t i c modulus at the t e m p e r a t u r e of the t e s t . In t h i s c a s e the c r e e p a c t i v a t i o n e n e r g y is obtained as follows: VOLUME 6A, JULY 1975-1329

( a ln d s "~ Qc -- - R t

d In E (T) d (l/T)

j,-

[4]

or

T 2 dE Qc = Qapp + n R - ~ - d T

[5]

Eq. [3] h a s been shown to b e v a l i d in a l a r g e n u m b e r of c a s e s by Bird, M u k h e r j e e , and Dorn 14 and S h e r b y and Burke. 15 A l s o , the m o d u l u s c o m p e n s a t e d s t