On the relation of hardness and microstructure of tempered and spheroidized carbon steels
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s t u d y r e p o r t s on the indentation h a r d n e s s of s e v e r a l t e m p e r e d and s p h e r o i d i z e d c a r b o n s t e e l s a s a function of i n d e n t e r g e o m e t r y , m i c r o s t r u c t u r e , and uniaxial stress-strain behavior. It is w e l l d o c u m e n t e d that h a r d n e s s and g r a i n s i z e of i r o n and low c a r b o n s t e e l s a r e e m p i r i c a l l y r e l a t e d b y an equation of the H a l l - P e r c h t y p e : H = H o + k H 1-1/z
[1]
w h e r e H is the m e a s u r e d h a r d n e s s , H o and k H a r e e x p e r i m e n t a l c o n s t a n t s , and l is the g r a i n s i z e . 1-5 In m e d i u m and h i g h - c a r b o n s t e e l s , a l s o , s o m e of the o b s e r v e d e f f e c t s of t e m p e r i n g t i m e and t e m p e r a t u r e on the h a r d n e s s of t e m p e r e d s t e e l s have b e e n i n t e r p r e t e d in t e r m s of the d i m e n s i o n s of the m i c r o s t r u c t u r e . F o r i n s t a n c e , Hyam and Nutting 6 noted a l i n e a r r e l a t i o n s h i p b e t w e e n the V i c k e r s h a r d n e s s of a n u m b e r of t e m p e r e d s t e e l s (0.12 to 0.98 p c t C) and the r e c i p r o c a l of the s q u a r e r o o t of a c a l c u l a t e d f e r r i t e g r a i n d i a m e t e r . The f e r r i t e g r a i n d i a m e t e r , in this c a s e , was c a l c u l a t e d f r o m the p a r t i c l e s p a c i n g , and it was a s s u m e d b y the a u t h o r s that a l l the c e m e n t i t e p a r t i c l e s a r e c o n n e c t e d b y g r a i n b o u n d a r i e s . T. Kun i t a k e 7 m e a s u r e d the V i c k e r s h a r d n e s s of t e m p e r e d and s p h e r o i d i z e d , l o w - a l l o y s t e e l s (0.13 to 0.57 pct C) and o b t a i n e d the following e m p i r i c a l f o r m u l a b y m u l t i regression analysis: H v = 0.8893 ;~-1/2 + 0.6884 l -I/2 + 8.02 w c + 41
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w h e r e Hv, X, l, and w c a r e the V i c k e r s h a r d n e s s , the c a r b i d e s p a c i n g (cm), the f e r r i t e m e a n i n t e r c e p t g r a i n s i z e (cm), and the a m o u n t of c a r b i d e (wt pct), r e s p e c t i v e l y . He found that the h a r d n e s s is not a function of a s i n g l e p r e d o m i n a t i n g p a r a m e t e r , but is a s u m m a t i o n of c o n t r i b u t i o n s f r o m s e v e r a l s t r e n g t h e n i n g f a c t o r s . R e l a t e d r e s u l t s w e r e o b t a i n e d b y Liu and G u r l a n d 8 f o r the flow s t r e s s in u n i a x i a l t e n s i o n of s p h e r o i d i z e d s t e e l s , o f . The H a l l - P e t c h equation: Of = Oof + k f A -l/a
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a p p l i e s o v e r a wide r a n g e of c o m p o s i t i o n s (0.06 to 1.46 p c t C) and s p a c i n g s at s t r a i n s b e y o n d 4 pct, p r o v i d e d J. GURLAND is with Division of Engineering, Brown University, Providence, Rhode Island. P. C. JINDAL was formerly with C. I. Hayes Co., Cranston, Rhode Island. Manuscript submitted February 1, 1974. METALLURGICAL TRANSACTIONS
that the m
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