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