An improved equation relating hardness to ultimate strength
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STRAINHARDENINGCOEFFICIENT
Fig. 1--Relation of ultimate strength to hardness and strain h a r d e n i n g coefficient.
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1. F. J. Centolanzi, H. B. Probst, C. E. Lowell, and N. B. Zimmerman: NASA TM X-62092, October 1971. 2. J. D. Whittenberger: NASATN D-6797. 3. F. Seitz: ActaMet, 1953, vol. 1, pp. 355-69. 4. J. A. Brmkman: Acta Met., 1955, vol. 3, pp. I40-45.
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0,6
[5]
By d i f f e r e n t i a t i n g Eq. [5] with r e s p e c t to -g one o b t a i n s the t r u e s t r a i n at the u l t i m a t e n o m i n a l s t r e s s a s 3 = n
[6]
T h e r e f o r e f r o m Eq. [5], the u l t i m a t e n o m i n a l s t r e s s i s given by
An Improved Equation Relating Hardness to Ultimate Strength
If it i s a c c e p t e d that the t r u e s t r e s s on a s t r e s s - s t r a i n c u r v e at a s t r a i n of 0.08 i s given a p p r o x i m a t e l y by / / / 2 . 9 a s s u g g e s t e d by T a b o r ~ and s u p p o r t e d by Cahoon et al. 4. then it is e a s i l y shown that
J . R. CAHOON
IN 1951
*Tabor1 suggestsvalues in the range 1t/2.9 to HI3 while Cahoon et al. 4 suggests values m the range H/2.9 to 11/3 1.
T a b o r 1 obtained the e x p r e s s i o n
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[1]
= g-d.9 \0.-Th--q)
[8]
r e l a t i n g u l t i m a t e n o m i n a l s t r e s s , au, to the V i c k e r s P y r a m i d H a r d n e s s , H, and the s t r a i n h a r d e n i n g c o e f f i cient, n. T a b o r a s s u m e d that t r u e s t r e s s in the p l a s t i c r e g i o n i s a p p r o x i m a t e d by the f a m i l i a r equation
It i s s u g g e s t e d that Eq. [8] i s a s i m p l e r and m o r e a c c u r a t e e x p r e s s i o n r e l a t i n g u l t i m a t e t e n s i l e s t r e n g t h to h a r d n e s s . The r e s u l t s c a l c u l a t e d f r o m Eq. [8] a r e c o m p a r e d to t h o s e c a l c u l a t e d by T a b o r (Eq. [1]) in F i g . 1. T a b o r 1 noted that his r e s u l t s c a l c u l a t e d f r o m Eq. [1] = k~ [2] a g r e e d w e l l with the e x p e r i m e n t a l d a t a ( c o n v e r t e d f r o m w h e r e ~ i s the t r u e s t r a i n and k i s a c o n s t a n t . To o b the B r i n e l l r e s u l t s of O ' N e i l l 5) for l o w e r v a l u e s of the tain the n o m i n a l s t r e s s , a, T a b o r u s e d the a p p r o x i m a t i o n s t r a i n h a r d e n i n g c o e f f i c i e n t , but d e v i a t e d c o n s i d e r a b l y f r o m the e x p e r i m e n t a l d a t a a t l a r g e r v a l u e s of n. k'~n O ' N e i l l ' s e x p e r i m e n t a l p o i n t s a r e i n c l u d e d in F i g . 1 or= (1 +E) [3] which shows that the p r e s e n t e x p r e s s i o n , Eq. [8], a g r e e s w e l l with the e x p e r i
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