Effect of grain boundary dislocations on the slope of the Hall-Petch relation

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2.6 Effect of Grain Boundary Dislocations on the Slope of the HalI-Petch Relation

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Y. T. CHOU AND C. S. PANDE

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d e r i v e s the H a l l - P e t c h r e l a t i o n u s i ng a m o d e l in which a d o u b l e - e n d e d pileup is pinned at the g r a i n b o u n d a r y ledge d i s l o c a t i o n s with a B u r g e r s v e c t o r d i f f e r e n t f r o m that of the l a t t i c e d i s l o c a t i o n s . F o l l o w i n g Hall ~ and P e r c h , 2 it has now b e e n w e l l e s t a b l i s h e d that the y i el d s t r e s s o of 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 can be g i v e n as

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TIME- MINUTE5 Fig. 1--Fraction of 1.0 g specimen herd on magnetic probe after 400~ reduction treatment with 10,000 v corona discharge [], and without discharge | v i s u a l c o m p a r i s o n s of m a g n e t i t e line i n t e n s i t i e s in D e b y e - S c h e r r e r X - r a y d i f f r a c t i o n p a t t e r n s of the r e duced h e m a t i t e s a m p l e s . It was p o s s i b l e to d e t e c t v i s u a l l y d i f f e r e n c e s in m a g n e t i t e content of a n y two s p e c i m e n s that e x h i b i t e d 20 pct o r m o r e d i f f e r e n c e in s u s c e p t i b i l i t y to a t t r a c t i o n by the m a g n e t i c p r o b e . It was noted h o w e v e r , that e v e n the m o s t s t r o n g l y m a g net i c s p e c i m e n s a p p e a r e d , f r o m X - r a y p a t t e r n s , to be only o n e - t h i r d to o n e - h a l f c o n v e r t e d to m a g n e t i t e .

RESULTS T h e r e s u l t s of t e s t s on r e d u c e d s p e c i m e n s with the magnetic probe after reduction treatments for varying p e r i o d s of t i m e at 400~ in 95 pct A r , 5 pct H g a s , F i g . 1, show that a f t e r an induction p e r i o d of 5 m i n the corona d i s c h a r g e - t r e a t e d specimens underwent conv e r s i o n to m a g n e t i t e at an a p p a r e n t l y c o n s t a n t r a t e while without the d i s c h a r g e only a s m a l l a m o u n t of c o n v e r s i o n o c c u r r e d and this did not i n c r e a s e s i g n i f i c a n t l y upon m o r e p r o l o n g e d t r e a t m e n t at t e m p e r a t u r e . T h i s r e s u l t s u g g e s t s that, f o r this p a r t i c u l a r type of reduction roasting process where complete conversion to the r e d u c e d p h a s e is not r e q u i r e d , c o r o n a d i s c h a r g e a c t i v a t i o n of the r e d u c i n g g a s m a y a f f e c t the r e d u c t i o n k i n e t i c s s u f f i c i e n t l y to m a k e p o s s i b l e a r o a s t i n g p r o c e s s at a s q b s t a n t i a l l y l o w e r t e m p e r a t u r e than w as heretofore possible.

1. D. W. Scott"Mming Congr. J., 1963, vol.49, p. 78. 2. D. J. Hams:Magnetizing Roasting, Ch. fromIron Ore Reduction, ElectroMETALLURGICALTRANSACTIONS

w h e r e a* is the l a t t i c e f r i c t i o n s t r e s s , k is the constant of p r o p o r t i o n a l i t y known a s the H a l l -

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