The effect of atomic order on the Hall-Petch behavior in Ni 3 Fe
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AND
Y. H. LIU
In both disordered and ordered NisFe the flow stress obeys the generalized Hall-Perch relationship JE = ~o,E + kEd -I/2. At low strains the Hall-Perch slope be increases with increasing strain in both states of order and is always higher for the ordered state, k~ passes through a maximum in both states. The maximum occurs in the ordered alloy at nearly twice the strain for the disordered. The relative magnitude and the variation of the HallPetch slope as influenced by order can be accounted for by considering the differences in the cross slip behavior between ordered and disordered states. The parabolic increase in kE with strain up to the maximum can be interpreted in terms of a model which relates the average dislocation density to flow stress and strain, and to the attendant Hall-Petch slope. The observed decrease in the Hall-Perch slope beyond the maximum may be attributed to dynamic recovery in the alloy. The friction stress ~o,E increases with strain almost linearly in both ordered and disordered states and is always higher in the ordered alloy.
T H E r e l a t i o n s h i p between the l o w e r yield s t r e s s and g r a i n s i z e in p o l y c r y s t a l l i n e m e t a l s and a l l o y s was shown o r i g i n a l l y by Hall 1 and P e t c h 2 to be of the f o r m OILy = go + k L y d - f / 2
[1]
w h e r e a L y is the l o w e r y ie ld s t r e s s , d is the m e a n g r a i n d i a m e t e r and go and k L y a r e constants. S u b s e quently, it has been shown by A r m s t r o n g e t al., 3 T j e r k s t r a , ~ Meakin and P e t c h , 5 and o t h e r s that the flow s t r e s s of s e v e r a l m e t a l s and alloys m e a s u r e d at a given value of s t r a i n a l s o obeys a r e l a t i o n s h i p of the type given by Eq. [ 1]. F o ll o w in g Meakin and P e t c h 5 the g e n e r a l i z e d e x p r e s s i o n m a y be given by z~ = ao,E + k e d -1/2
[2]
w h e r e z~ is the flow s t r e s s , while ~o,~ and kE a r e c onst a n t s all m e a s u r e d at the s a m e value of s t r a i n ~. Eqs. [1] and [2] have been i n t e r p r e t e d in t e r m s of v a r i o u s t h e o r e t i c a l m o d e l s , none of which a r e capable of accounting f o r all of the o b s e r v e d phenomena. The t e r m ~o,~ is g e n e r a l l y i n t e r p r e t e d as the f r i c t i o n s t r e s s e x p e r i e n c e d by d i s l o c a t i o n s in the a b s e n c e of g r a i n b o u n d a r i e s . H o w e v e r , the s i g n i f i c a n c e of the slope t e r m , k, is s t i l l s u b j e c t to c o n s i d e r a b l e c o n t r o versy. The i n t e r p r e t a t i o n of the H a l l - P e t c h slope at the l o w e r y i el d point k L y has r e c e i v e d the g r e a t e s t amount of attention. One theory due to Petch, 2 C o t t r e l l , 7 and o t h e r s is b as ed on the idea that a slip band is a s t r e s s c o n c e n t r a t o r which acts at a g r a i n boundary to p r o p a gate p l a s t i c [low f r o m g r a i n to grain. The s o u r c e of the s t r e s s c o n c e n t r
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