Substructure strengthening mechanisms
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I T has b e e n known for many y e a r s that the s t r u c t u r e of a d e f o r m e d m e t a l is i n h o m o g e n e o u s on the s c a l e of about 1 # m ; the " c r y s t a l l i t e s " d e s c r i b e d by X - r a y i n v e s t i g a t o r s I a r e now u s u a l l y called " s u b s t r u c t u r e . " It is b e c o m i n g c o n v e n t i o n a l to r e f e r to s u b s t r u c t u r e s p r o d u c e d at low homologous t e m p e r a t u r e as " c e l l s " and those at h i g h e r t e m p e r a t u r e s as " s u b g r a i n s , " and that t e r m i n o l o g y is u s e d h e r e a l s o . The b a s i s for the d i s t i n c t i o n , which is not always easy to make, is the obvious, tangled d i s l o c a t i o n s t r u c t u r e of cell walls,* c o m p a r e d to the n a r r o w , w e l l - d e f i n e d walls *Amongthe very first observationsin thin foilswas thiscellstructure.2 of s u b g r a i n s . As will be s e e n , the d i s t i n c t i o n can be a n i m p o r t a n t one. The p r i n c i p a l q u e s t i o n to be a n s w e r e d in a d i s c u s s i o n of s t r e n g t h e n i n g m e c h a n i s m s i s , why does the s t r e n g t h e n i n g o c c u r ? In the c a s e of cell s t r u c t u r e s , the a n s w e r is s i m p l e : they contain high d i s l o c a t i o n d e n s i t i e s . Sinker and Holt 3 m e a s u r e d the d e n s i t y in cell walls, and found the r e l a t i o n s h i p shown in Fig. 1, that
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w h e r e ~- is the s h e a r flow s t r e s s , ot is a c o n s t a n t of o r d e r 0.5, G the s h e a r modulus, b the B u r g e r s v e c t o r , and p the d i s l o c a t i o n d e n s i t y . T h i s r e l a t i o n , of c o u r s e , is v e r y well known; it can be d e r i v e d f r o m a l l the e x i s t i n g t h e o r i e s of work h a r d e n i n g4 and has for s o m e t i m e been well e s t a b l i s h e d e x p e r i m e n t a l l y ) What is i m p o r t a n t h e r e is that the p v a l u e s w e r e m e a s u r e d in cell w a l l s . Michel, et al 6 have made s i m i l a r findings for 316 s t a i n l e s s s t e e l . Broadly, then, t h e r e is nothing unique about cells beyond t h e i r high d i s l o c a t i o n d e n s i t i e s . S u b g r a i n s a r e somewhat d i f f e r e n t (see below). A m o r e complex and difficult q u e s t i o n about s t r e n g t h e n i n g is, what a r e the d e t a i l e d m e c h a n i s m s , and how do they depend on e x p e r i m e n t a l v a r i a b l e s ? U n d e r s t a n d i n g of d e f o r m a t i o n and work h a r d e n i n g b e h a v i o r i s not yet adequate to p r o v i d e c o m p l e t e a n s w e r s . T h i s p a p e r d e s c r i b e s what is now known, f i r s t about how s u b s t r u c t u r e s f o r m and then how they affect the flow s t r e s s . Q u e s t i o n s of u n d e r l y i n g m e c h a n i s m s a r e d e f e r r e d to the D i s c u s s i o n . In this way the p r e s e n t a t i o n c o n f o r m s to A r i s t o t l e ' s d i c t u m , ANTHONY W. THOMPSON, forme
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