The dependence of the lower yield strength in iron and steel on grain size and temperature
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/ ' k model b a s e d on d i s l o c a t i o n d y n a m i c s was d e v e l oped and p r e s e n t e d in an e a r l i e r p u b l i c a t i o n ,1 defining the d e p e n d e n c e of the lower yield s t r e n g t h , aaF, on g r a i n b o u n d a r y i n t e r c e p t , l, d u r i n g the p r o p a g a t i o n of a L i i d e r ' s band in i r o n and s t e e l u n d e r a c o n s t a n t u n i a x i a l f o r c e . The r e l a t i o n d e r i v e d was g i v e n by, aaF = r + ( Vc/NOKI2) ilm* , w h e r e a~ is a l o n g - r a n g e , i n t e r n a l s t r e s s opposing the motion of mobile d i s l o c a tions in a finite r e g i o n at the tip of the band. Vc is the c r o s s - h e a d velocity, and N is the n u m b e r of L ( i d e r ' s b a n d s p r o p a g a t i n g . 0 is the a v e r a g e d i s l o c a tion velocity at u n i t effective s t r e s s and K is a s s u m e d to be a m a t e r i a l c o n s t a n t which has b e e n defined p r e v i o u s l y . 1 m* is the d i s l o c a t i o n v e l o c i t y - e f f e c t i v e s t r e s s exponent. T e s t r e s u l t s have been obtained f r o m the published l i t e r a t u r e ~-~ on the dependence of (~aF on g r a i n size for two i r o n s and three s t e e l s at t e m p e r a t u r e s between 90 ~ and 373~ T h e s e r e s u l t s a r e u t i l i z e d to check the v a l i d i t y of the r e l a t i o n p r o p o s e d . It is a s s u m e d in this e v a l u a t i o n that ~ is independent of t e m p e r a t u r e and at r o o m t e m p e r a t u r e where m* is taken equal to 4, the value of ~i can be obtained f r o m a H a l l - P e t c h plot. It was pointed out p r e v i o u s l y ~ that for m* = 4, the p r e s e n t r e l a t i o n r e d u c e s to the H a l l - P e t c h r e l a t i o n . It is shown in this paper that the a v a i l a b l e t e s t r e s u l t s fit the p r o p o s e d r e l a t i o n well and the dependence of m* on t e m p e r a t u r e a g r e e s with that d e t e r m i n e d in p o l y c r y s t a l l i n e i r o n f r o m s t r e s s r e l a x a t i o n t e s t s ~'8 and in p o l y c r y s t a l l i n e T i - s t a b i l i z e d i r o n f r o m double s t r a i n r a t e cyclic and p r e m a c r o y i e l d t e s t s . 9 The p a r a m e t e r s m* and 0 a r e d i s c u s s e d in t e r m s of t h e i r t e m p e r a t u r e d e p e n d e n c e and the r e l a t i o n s h i p between the c h a r a c t e r i s t i c s of d e f o r m a t i o n a t the tip of a L(ider's band d u r i n g i n h o m o g e n e o u s d i s c o n t i n u o u s yielding and homogeneous plastic deformation.
F. GAROFALO is Director, Steel Products, Inland Steel Research Laboratories, East Chicago, Ind. 46312 Manuscript submitted January 21, 1972. METALLURGICALTRANSACTIONS
MATERIALS EXAMINED A search of the literature revealed a limited number of investigations on the dependence of the lower yield strength on grain size in iron and steel at room temperature and at one or more other temperatures. The materials which were investigated2-6 are describ
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