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On the saturation of radiation hardening
Volume 28A, number 9
ON
PHYSICS
THE
SATURATION
OF
LETTERS
RADIATION
10 February 1969
HARDENING
*
J . M. G A L L I G A N Brookhaven National Laboratory. Upton, New York Received 1 January 1969
A model of saturation of radiation hardening is given. This model suggests that saturation of the t h e r mal hardening component should occur at different fluence levels than would the athermal component.
It i s g e n e r a l l y o b s e r v e d in i r r a d i a t e d m e t a l s t h a t t h e1 y i e l d s t r e s s i n i t i a l l y v a r i e s with f l u e n c e a s (~t)~ [1, 2], a f t e r w h i c h t h e y i e l d s t r e s s g r a d u a l l y s a t u r a t e s . T h i s b e h a v i o r is thought to a r i s e f r o m a g e o m e t r i c a l o v e r l a p of d a m a g e z o n e s [3] w h i c h w o u l d b e e x p e c t e d on t h e b a s i s of s i m p l e p r o b a b i l i t y c o n s i d e r a t i o n s . In t h i s e x p l a n a t i o n no c h a n g e in t h e c h a r a c t e r of t h e d e f e c t s i n t r o d u c e d by i r r a d i a t i o n i s c o n s i d e r e d . F o r e x a m p l e , s u c h a m o d e l d o e s not d i s t i n g u i s h b e t w e e n t h e r a t e of c h a n g e of t h e r m a l and a t h e r m a l c o m p o n e n t s of h a r d e n i n g w i t h e x p o s u r e . W e w o u l d l i k e to i n t r o d u c e a s i m p l e m o d e l of r a d i a tion hardening which distinguishes between these two c o m p o n e n t s of t h e h a r d e n i n g and l e a d s to a s a t u r a t i o n of t h e c o m p o n e n t s at d i f f e r e n t e x p o sure levels. In t h i s m o d e l we s u g g e s t t h a t w h e n a d a m a g e z o n e is f o r m e d n e a r a p r e e x i s t i n g z o n e , t h i s s a t i s f i e s t h e c o n d i t i o n s f o r t h e f o r m a t i o n of a d i s l o c a t i o n loop, s u c h a s i s o b s e r v e d w h e n an i r r a d i a t e d s a m p l e i s a n n e a l e d [4]. A l s o , m u l t i p l e d a m a g e z o n e s w h i c h l e a d to d i s l o c a t i o n l o o p s can i n c r e a s e t h e d e f e c t d e n s i t y w i t h o u t d r a s t i cally changing the yield stress. This latter fact a r i s e s w h e n d i s l o c a t i o n l o o p s i n c r e a s e in s i z e , b u t not t h e i r s e p a r a t i o n . If l o o p s a r e s e p a r a t e d by a d i s t a n c e in s p a c e , ~, then ~ i s g i v e n a s [5] 3 ~ 212R
w h e r e 1 i s t h e s e p a r a t i o n of l o o p s in a s l i p p l a n e and 2R t h e i r a v e r a g e s i z e . T h e y i e l d s t r e s s w o u l d , in t h i s m o d e l , v a r y a s = [const(Nz) (1-f) +
_
c o n s t fl½ ~3 J
* This work was performed under the auspices of the US Atomic Energy Commission.
w h e r e N Z i s t h e n u m b e r of d a m a g e z o n e s in a s l i p p l a n e a n d f i s a f a c t o r w h i c h t a k e s into a c count the p r o b a b i l i t y of f o r m i n g a z o n e n e a r a p r e e x i s t i n g z o n e . It is e x p e c t e d that t h e f o r m a tion and g r o w t h of such d i s l o c a t i o n l o o p s w o u l d l e a d to an i n c r e a s e in t h e s t r e s s f o r y i e l d i n g , which w o u l d b e g e n e r a l l y i n d e p e n d e n t of t e m p e r ature, such as a forest hardening mechanism. A c c o r d i n g l y , t h e a t h e r m a l c o m p o n e n t of t h e r a d i a t i o n h a r d e n i n g would s t i l l b e i n c r e a s i n g when t h e t h e r m a l c o m p o n e n t t e n d s to s a t u r a t e . T h e f i n a l s a t u r a t i o n of t h e h a r d e n i n g - t h e r m a l and a t h e r m a l - would o c c u r , in t h i s m o d e l , w h e n the a p p a r e n t i n c r e a s e in d i s l o c a t i o n loop s i z e and density reaches a steady-state value determined by r a d i a t i o n a n n e a l i n g . T h e p r e s e n t m o d e l is c o n s i s t e n t with s o m e r e c e n t m e a s u r e m e n t s in r a d i a t i o n d a m a g e [4] and r a d i a t i o n h a r d e n i n g [2] in p l a t i n u m . It i s a l so c o n s i s t e n t with s o m e r e c e n t o b s e r v a t i o n s on t h e s i z e d i s t r i b u t i o n of d e f e c t s in n e u t r o n i r r a d i a t e d n i o b i u m [6]. S o m e p e r t i n e n t m e a s u r e m e n t s on r a d i a t i o n h a r d e n i n g on n e u t r o n i r r a d i a t e d t u n g s t e n and p l a t i n u m w i l l be r e p o r t e d in the n e a r f u t u r e .
References
1. J. Diehl, Radiation damage in metals (Int. Atomic Energy Commission, Vienna, 1962). 2. J. M. Galligan and M. J. Attardo, Phys. Stat. Sol. 27 (1968) 383. 3. M.J. Makin and F . J . Minter, Aeta Met. 8 (1960) 691. 4. M.J. Attardo and J. M. Galligan, Phys. Rev. 161 (1967) 558. 5. J. Friedel, Dislocations (Pergamon P r e s s , London, 1964). 6. S. M. Ohr and R. P. Tucker. J. Metals 20 (1968) 80a.
609
ON
PHYSICS
THE
SATURATION
OF
LETTERS
RADIATION
10 February 1969
HARDENING
*
J . M. G A L L I G A N Brookhaven National Laboratory. Upton, New York Received 1 January 1969
A model of saturation of radiation hardening is given. This model suggests that saturation of the t h e r mal hardening component should occur at different fluence levels than would the athermal component.
It i s g e n e r a l l y o b s e r v e d in i r r a d i a t e d m e t a l s t h a t t h e1 y i e l d s t r e s s i n i t i a l l y v a r i e s with f l u e n c e a s (~t)~ [1, 2], a f t e r w h i c h t h e y i e l d s t r e s s g r a d u a l l y s a t u r a t e s . T h i s b e h a v i o r is thought to a r i s e f r o m a g e o m e t r i c a l o v e r l a p of d a m a g e z o n e s [3] w h i c h w o u l d b e e x p e c t e d on t h e b a s i s of s i m p l e p r o b a b i l i t y c o n s i d e r a t i o n s . In t h i s e x p l a n a t i o n no c h a n g e in t h e c h a r a c t e r of t h e d e f e c t s i n t r o d u c e d by i r r a d i a t i o n i s c o n s i d e r e d . F o r e x a m p l e , s u c h a m o d e l d o e s not d i s t i n g u i s h b e t w e e n t h e r a t e of c h a n g e of t h e r m a l and a t h e r m a l c o m p o n e n t s of h a r d e n i n g w i t h e x p o s u r e . W e w o u l d l i k e to i n t r o d u c e a s i m p l e m o d e l of r a d i a tion hardening which distinguishes between these two c o m p o n e n t s of t h e h a r d e n i n g and l e a d s to a s a t u r a t i o n of t h e c o m p o n e n t s at d i f f e r e n t e x p o sure levels. In t h i s m o d e l we s u g g e s t t h a t w h e n a d a m a g e z o n e is f o r m e d n e a r a p r e e x i s t i n g z o n e , t h i s s a t i s f i e s t h e c o n d i t i o n s f o r t h e f o r m a t i o n of a d i s l o c a t i o n loop, s u c h a s i s o b s e r v e d w h e n an i r r a d i a t e d s a m p l e i s a n n e a l e d [4]. A l s o , m u l t i p l e d a m a g e z o n e s w h i c h l e a d to d i s l o c a t i o n l o o p s can i n c r e a s e t h e d e f e c t d e n s i t y w i t h o u t d r a s t i cally changing the yield stress. This latter fact a r i s e s w h e n d i s l o c a t i o n l o o p s i n c r e a s e in s i z e , b u t not t h e i r s e p a r a t i o n . If l o o p s a r e s e p a r a t e d by a d i s t a n c e in s p a c e , ~, then ~ i s g i v e n a s [5] 3 ~ 212R
w h e r e 1 i s t h e s e p a r a t i o n of l o o p s in a s l i p p l a n e and 2R t h e i r a v e r a g e s i z e . T h e y i e l d s t r e s s w o u l d , in t h i s m o d e l , v a r y a s = [const(Nz) (1-f) +
_
c o n s t fl½ ~3 J
* This work was performed under the auspices of the US Atomic Energy Commission.
w h e r e N Z i s t h e n u m b e r of d a m a g e z o n e s in a s l i p p l a n e a n d f i s a f a c t o r w h i c h t a k e s into a c count the p r o b a b i l i t y of f o r m i n g a z o n e n e a r a p r e e x i s t i n g z o n e . It is e x p e c t e d that t h e f o r m a tion and g r o w t h of such d i s l o c a t i o n l o o p s w o u l d l e a d to an i n c r e a s e in t h e s t r e s s f o r y i e l d i n g , which w o u l d b e g e n e r a l l y i n d e p e n d e n t of t e m p e r ature, such as a forest hardening mechanism. A c c o r d i n g l y , t h e a t h e r m a l c o m p o n e n t of t h e r a d i a t i o n h a r d e n i n g would s t i l l b e i n c r e a s i n g when t h e t h e r m a l c o m p o n e n t t e n d s to s a t u r a t e . T h e f i n a l s a t u r a t i o n of t h e h a r d e n i n g - t h e r m a l and a t h e r m a l - would o c c u r , in t h i s m o d e l , w h e n the a p p a r e n t i n c r e a s e in d i s l o c a t i o n loop s i z e and density reaches a steady-state value determined by r a d i a t i o n a n n e a l i n g . T h e p r e s e n t m o d e l is c o n s i s t e n t with s o m e r e c e n t m e a s u r e m e n t s in r a d i a t i o n d a m a g e [4] and r a d i a t i o n h a r d e n i n g [2] in p l a t i n u m . It i s a l so c o n s i s t e n t with s o m e r e c e n t o b s e r v a t i o n s on t h e s i z e d i s t r i b u t i o n of d e f e c t s in n e u t r o n i r r a d i a t e d n i o b i u m [6]. S o m e p e r t i n e n t m e a s u r e m e n t s on r a d i a t i o n h a r d e n i n g on n e u t r o n i r r a d i a t e d t u n g s t e n and p l a t i n u m w i l l be r e p o r t e d in the n e a r f u t u r e .
References
1. J. Diehl, Radiation damage in metals (Int. Atomic Energy Commission, Vienna, 1962). 2. J. M. Galligan and M. J. Attardo, Phys. Stat. Sol. 27 (1968) 383. 3. M.J. Makin and F . J . Minter, Aeta Met. 8 (1960) 691. 4. M.J. Attardo and J. M. Galligan, Phys. Rev. 161 (1967) 558. 5. J. Friedel, Dislocations (Pergamon P r e s s , London, 1964). 6. S. M. Ohr and R. P. Tucker. J. Metals 20 (1968) 80a.
609