Mechanical properties of sheet columbium (niobium) alloy SU31
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per unit volume is independent of grain size. This postulation, which is critical to the Brown-Lukens theory, has yet to be experimentally verified, but Brentnall and Rostoker~ showed that inclusions have great control over the distribution of dislocation sources.
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ACKNOWLEDGMENT
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Thanks a r e due to Dr. K. T a n g r i for useful d i s c u s s i o n s , and to the National R e s e a r c h Council of Canada for financial support.
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I. N. Brownand J. F. LuckensJr.: A cta Met., 1961,vol.9, pp. 106-11. 2. R. D. Carnahanand J. E. White:Phil. Mag., 1964,vol. 10, pp. 513-26. 3. W.D. Brentnalland W. Rostoker:ActaMet,, 1965,vol. 13, pp. 187-98.
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cr vs D
,PLASTIC STRAIN I 0 0 x l 0 6 -
(2) A
o- vs Ds
, PLASTIC STRAIN I00 xlO- e -
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o
(4)1o 0
-512 -312
( I ) []
0.005
vs 65/2, PLASTIC STRAIN -512
cr vs Ds ~ 0.01
, PL/~STIC STRAIN I 0.015 0.02
D- s 1 2 o r
D s 3la (/.t.m -312 )
20 x K) e a o ~ 16 6
0.025
Fig. 3--The flow stress as a function of D -3/2 and Ds-3/2 A linear relation at a plastic strain of 20 • 10-6 is in accordance with the theory of Brown and Lukens. 1 and 150 • 10-6 the m a t e r i a l obeyed the Petch law. They o b t a i n e d a t h r e e stage s t r e s s - s t r a i n c u r v e (which was not duplicated in the p r e s e n t s e r i e s of t e n s i l e t e s t s ) , and consequently it i s not p o s s i b l e to d e t e r m i n e whether t h e i r r e s u l t s would a g r e e with the B r o w n - L u k e n s theory at lower s t r a i n s . T e n s i l e t e s t s on c o m m e r c i a l grade nickel by B r e n t n a l l and Rostoker s indicate that the flow s t r e s s is p r o p o r t i o n a l to D - I / z down to s t r a i n s of 1 x 10 -6, but even at this low s t r a i n the m e a s u r e d flow s t r e s s was 5.8 k g / m m e for a m a t e r i a l of 81 # m g r a i n s i z e , and t h e r e f o r e the r e s u l t s a r e not c o m p a r a b l e to those in the p r e s e n t i n v e s t i g a t i o n . In c o n c l u s i o n , the p r e s e n t r e s u l t s s e e m to support the B r o w n - L u k e n s theory d u r i n g the e a r l y s t a g e s of p l a s t i c d e f o r m a t i o n , but at higher s t r a i n s the u s u a l P e t c h r e l a t i o n s h i p e x i s t s . F o r the f i n e r g r a i n e d m a t e r i a l the flow s t r e s s dependence b a s e d on e i t h e r the g r a i n d i a m . D or the s u b g r a i n d i a m . D s a r e c o m p a t i b l e , but at l a r g e g r a i n s i z e s ( i . e . over 100 pro) the s u b g r a i n d i a m . is the c o n t r o l l i n g f a c t o r , and the g r a i n diam. should not be used. The t r a n s i t i o n b e tween D s -~/'e and D s -3/z dependence of the flow s t r e s s is p r o b a b l y due to a n i s o t r o p i c b e h a v i o r , for in the f i r s t s t a g e s of p l a s t i c d e f o r m a t i o n , not all the g r a i n s or s u b g r a i n s a r e f a v o r a b l y o r i e n t a t e d for slip, hence i n i t i a l d e f o r m a
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