Elastic constants of binary iron-base alloys
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SPEICH,
A. J. SCHWOEBLE,
AND
W. C. LESLIE
The Y o u n g ' s m o d u l u s (E) and s h e a r m o d u l u s (G) of i s o t r o p i c Fe and b i n a r y F e - C , F e - C o , F e - C r , F e - I r , F e - M n , F e - N i , F e - P t , F e - R e , F e - R h , and F e - R u a l l o y s have b e e n d e t e r m i n e d a s functions of c o m p o s i t i o n (0 to 10 at. pct) and t e m p e r a t u r e (77 to 473 K) by a p u l s e - e c h o technique (100 kHz e l a s t i c waves). P o i s s o n ' s r a t i o (v) and the bulk m o d u l u s (K) have b e e n d e r i v e d f r o m the v a l u e s of E and G. The r a t e s of change of E and G with c o m p o sition (LxE/,Xcand AG/Ac) depend on the change of l a t t i c e p a r a m e t e r with c o m p o s i t i o n and upon the p o s i t i o n of the solute in the p e r i o d i c table. Both n e g a t i v e and p o s i t i v e v a l u e s of AE/Ac and LxG/Acare o b s e r v e d . The v a l u e s of ~E/Ac and ~G/Ac a r e g e n e r a l l y different so that P o i s s o n ' s r a t i o m a y i n c r e a s e or d e c r e a s e with c o m p o s i t i o n . C o m p a r a b l e c h a n g e s in the value of K/G also o c c u r . T h e s e c h a n g e s cannot be u s e d to p r e d i c t the effects of a l l o y ing additions on the t o u g h n e s s of i r o n . The t e m p e r a t u r e d e p e n d e n c e of E and G of the a l l o y s is s i m i l a r to that of i r o n , d e c r e a s i n g in a n o n l i n e a r m a n n e r f r o m 77 to 473 K. A knowledge of the effects of s o l u t e s on the e l a s t i c c o n s t a n t s of i r o n is e s s e n t i a l to an u n d e r s t a n d i n g of the effects of such e l e m e n t s on m e c h a n i c a l p r o p e r t i e s s i n c e the a v e r a g e s t r e s s and the s t r a i n e n e r g y within the e l a s t i c s t r a i n fields of individual d i s l o c a t i o n s a r e p r o p o r t i o n a l to the s h e a r m o d u l u s . ~ Also, i n t e r a c t i o n of solute a t o m s with d i s l o c a t i o n s m a y occur b e c a u s e of a d i f f e r e n c e of the s h e a r m o d u l u s of the- solute and solvent a t o m s . Such i n t e r a c t i o n s m a y play a r o l e in solid solution h a r d e n i n g . 2 M o r e o v e r , it has been s u g gested that the r a t i o of the bulk m o d u l u s (K) to the s h e a r m o d u l u s (G) m a y d e t e r m i n e the t o u g h n e s s of m e t a l s . 3,4 Although s o m e e a r l i e r data a r e a v a i l a b l e on the effects of a l l o y i n g e l e m e n t s on Y o u n g ' s m o d u l u s (E) for i r o n - b a s e b i n a r y a l l o y s , 5-9 much l e s s is known of the effect of alloying e l e m e n t s on G. In g e n e r a l , both q u a n t i t i e s have not been m e a s u r e d on the s a m e set of a l l o y s so that c a l c u l a t i o n of v a l u e s of K f r o m v a l u e s of E and G to t e s t the c o r r e l a t i o n of K/G with t o u g h n e s s is not p o s s i b l e . The p r e s e n t work was u n d e r t a k e n to fill this gap in our knowledge of i
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