A critical test on theories of work-hardening for the case of drawn iron wire
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with G = 8430 kgf p e r sq m m , and 0~i = 15.6 kgf p e r sq m m the l i n e a r w o r k - h a r d e n i n g c o e f f i c i e n t in t e r m s of t r u e t e n s i l e s t r e s s - t r u e t e n s i l e s t r a i n , s e e Fig. 1. M i c r o g r a p h s of t r a n s m i s s i o n s p e c i m e n s , t r a n s v e r s e and p a r a l l e l to the w i r e a x i s , at e = 0.22, 1.12, 3.82, 6.02, and 7.36, r e s p e c t i v e l y , r e v e a l e d c r o s s s e c t i o n s of d i s l o c a t i o n c e l l s which, except at e = 0.22, a r e g r e a t l y e l o n g a t e d in the d i r e c t i o n p a r a l l e l to the w i r e a x i s . For the d e p e n d e n c e of the m e a n d i s t a n c e b e t w e e n t r a n s v e r s e i n t e r c e p t s of the c e l l w a l l s , d, on t e n s i l e s t r e s s , a, Langford and Cohen found a = a o + K d / - d = 3.4 + 0 . 0 1 2 2 / d [ k g f / m m a]
= a0 + 5 . 9 G b / d
[3]
with d m e a s u r e d in m m when o and (ro a r e m e a s u r e d in kgf p e r sq ram, and b = vr-3a/2 = 2.48A. In the t r a n s i t i o n s t a g e of a < (~*, the (If0> bcc w i r e t e x t u r e is f o r m e d , the c e l l s h a p e changes c o n s i d e r a b l y , and the n u m b e r of c e l l s found in an a v e r a g e w i r e c r o s s s e e -
[1]
with a ~ ~ . Here b i n d i c a t e s the B u r g e r s v e c t o r , p the d i s l o c a t i o n d e n s i t y , T the r e s o l v e d s h e a r s t r e s s a p p l i e d to the s p e c i m e n , and TO the f r i c t i o n a l p a r t of r that does not depend on t e m p e r a t u r e in the s a m e way as G. Beyond e ~- 1.0, the envelope of all the l i n e a r p o r t i o n s of the v a r i o u s s t r e s s - s t r a i n c u r v e s , plotted a c c o r d i n g to t r u e t e n s i l e s t r e s s , a, and t r u e t e n s i l e s t r a i n , e, i n c l u d i n g the s t r a i n s a c h i e v e d by w i r e d r a w ing a n d t e n s i l e t e s t i n g , was to a f i r s t a p p r o x i m a t i o n found as
2500
50
80
90
REDUCTIONIN AREA BY WIRE ~AWING, % 95 g8 99 99.5
992
9g,9
99.95
a : a* + 0~ie -~ 30 + 15.6e [ k g f / m m z] = a* + (V/540)e [2] 0
I.O
2.0
30
4,17
7.0
9
TRUE STRAIN
DORIS KUHLMANN-WILSDORFis University Professor of Applied Science, cooperating with the Department of Materials Science and with the Department of Physics, University of Virginia, Charlottesville, Va. Manuscript submitted February 27, 1970. METALLURGICAL TRANSACTIONS
Fig. 1--Effect of wire-drawing strain on the tensile s t r e s s strain curves (corrected for necking) of furnace-cooled iron, drawn and tested at room temperature. The circles are calculated values employing Eq. [33] with n = 3.3, f l / F = 1/680, (r~ = 30 kgf per sq mm, and E0 = 0.2; the remainder of the figure is a copy of the corresponding figure in Ref. 1. VOLUME 1,NOVEMBER 1970-3173
tion s t a y s m o r e o r l e s s c o n s t a n t o r r i s e s m i l d l y . At h i g h e r s t r a i n s , L a n g f o r d a n d Cohen found the n u m b e r of c e l l s in the a v e r a g
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