Deformation mechanism maps based on grain size
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IT is now r e c o g n i z e d that a number of distinct m e c h a n i s m s contribute towards the p l a s t i c deformation of a p o l y c r y s t a l l i n e m a t e r i a l under h i g h - t e m p e r a t u r e c r e e p conditions. Several of these m e c h a n i s m s have been identified and equations developed, e i t h e r t h e o r e t i c a l l y or e m p i r i c a l l y , to d e s c r i b e the r a t e of s t r a i n under s t e a d y - s t a t e conditions. As a r e s u l t of this i n c r e a s e in understanding, it has become p o s s i b l e to c o n s t r u c t deformation m e c h a n i s m maps of the type f i r s t indicated by Weertman z and m o r e r e c e n t l y developed in detail by Ashbyfl T r a d i tionally, these maps plot e i t h e r s t r e s s , a, o r n o r m a l ized s t r e s s , a/G (where G is the s h e a r modulus), as a function of e i t h e r t e m p e r a t u r e , T, in d e g r e e s Kelvin o r homologous t e m p e r a t u r e , T / T m (where T m is the melting point of the m a t e r i a l ) . By using the b e s t a v a i l able constitutive equation to d e s c r i b e each of the m e c h a n i s m s known to occur during s t e a d y - s t a t e flow, the map is then divided into fields of s t r e s s / t e m p e r a t u r e space within which a single m e c h a n i s m dominates the creep behavior. Such maps a r e now finding i n c r e a s i n g use in p r a c t i cal applications (for example, in d e s c r i b i n g the i n - r e a c t o r behavior of oxide nuclear fuelsS). However, a drawback of this f o r m of deformation m e c h a n i s m map is that it must be p r e p a r e d for one specific grain size.*
mental data a v a i l a b l e and the v a r i o u s c r e e p m e c h a n i s m s o c c u r r i n g at high t e m p e r a t u r e s a r e r e a s o n a b l y understood. A r e v i e w of the existing e x p e r i m e n t a l r e s u l t s for aluminum suggests that h i g h - t e m p e r a t u r e c r e e p a r i s e s p r i m a r i l y through four different deformation processe~ *Other deformation processes undoubtedly contribute to the overall strain rate under some experimental conditions of stress, temperature and grain size, but these contributions appear to be fairly minor and the processeshave not been formulated in any detail.
The constitutive equations for these four m e c h a n i s m s a r e l i s t e d in Table I, where d is the s t e a d y - s t a t e c r e e p r a t e , D l is the coefficient for l a t t i c e self-diffusion, b is the B u r g e r s v e c t o r (2.86 • 10 -s cm in A1), k is Boltzm a n n ' s constant, d is the grain size, a n d Dg b is the coefficient for grain boundary diffusion. The mechanisms: a r e d e s c r i b e d b r i e f l y below: i) Climb There is considerable evidence to suggest that pure aluminum probably deforms primarily by some form of dislocation climb process 4 at high temperatures and r e a s o n a b l y high s t r e s s l e v e l s . The e x p e r i m e n t a l data were analyzed by Bird et al, s and it was shown that the
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