Positron lifetime & X-ray particle size measurements during the high cycle fatigue of AISI 4340 steel
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~kT
1.5p
~)Gb - --eZc
kT (b-E)
(T/C).
[5]
As m e n t i o n e d e a r l i e r , it has b e e n r e p o r t e d z'4 that p d u r i n g the H a r p e r - D o r n c r e e p in pure A1 is low (104 cm -e) and independent of s t r e s s level. Also, isolated bits of evidence in other m a t e r i a l s suggest that the dependence of p on s t r e s s d e c r e a s e s zz,e3 at lower s t r e s s e s , and the value e s s e n t i a l l y b e c o m e s constant and independent of s t r e s s 24 at r//G < 2 • 10 -~. T h i s r a i s e s the p o s s i b i l i t y that the o b s e r v a t i o n made on A1 c o n c e r n i n g the low d i s l o c a t i o n d e n s i t y might be valid for other s y s t e m s . A c c o r d i n g l y , if it is a s s u m e d that p i n Eq. [5] is equal to the value r e p o r t e d for A1, a H a r p e r - D o r A - c r e e p type of equation for A1-Mg solidsolution alloys is obtained as, SkT ~)Gb = ( A g o ) A l l ~
(T/G)
[6]
with
(AHD)AIIoy _ 1.5 X
104
kT
[7]
To e x a m i n e the absolute r a t e p r e d i c t i o n of Eq. [6], the following v a l u e s for the A1-2 pct Mg a l l o y a r e taken: e = 0.12, c = 0.02, G = 1.6 • 104 M N / m 2, and D -~ D = 5.3 x 10 -~ cm2/s (Ref. 16). With these v a l u e s , the p r e d i c t e d value of (AHD)Alloy is 4.5 x 10 -11, which c o m p a r e s well with the e x p e r i m e n t a l l y e s t i m a t e d value of 3.5 x 10 -~1. This favorable c o r r e l a t i o n is also shown in Fig. 1. A s i m i l a r Newtonian b e h a v i o r has b e e n r e ported in an A1-3 pct Mg alloy, n and it is i n t e r e s t i n g to e x a m i n e the c o r r e s p o n d e n c e b e t w e e n data of this alloy and Eq. [6]. F o r the A1-3 pct Mg alloy, (AHD)AIIoy was e s t i m a t e d as 3 x 10- n u n d e r the f o l l o w i n g condit i o n s : T = 855 K, c = 0.03, e = 0.12, D - D = 2 x 10 -~ cm=//s, and G = 1.6 x 104 M N / m 2. T h i s value of (AHD)AIIoy also c o m p a r e s f a v o r a b l y with the e x p e r i m e n t a l l y r e p o r t e d value of 2 x 10 - ~ , An i n v e s t i g a t i o n of the effect of solute content along with a c o m p a r i s o n between s u b s t r u c t u r e s developed in both A1 and A1-Mg alloys at v e r y low s t r e s s e s could d e t e r m i n e the validity of the p r o p o s e d p r o c e s s . C r e e p r a t e s will be a function of solute c o n c e n t r a t i o n if the modified v i s c o u s - g l i d e p r o c e s s c o n t r o l s the Newtonian b e h a v i o r of A1-Mg a l l o y s . Also, the modified v i s c o u s - g l i d e p r o c e s s , which is b a s e d on an int e r a c t i o n between solute a t o m s and d i s l o c a t i o n s , is not applicable to pure A1, so s u b s t r u c t u r e s developed u n d e r v i s c o u s - g l i d e conditions in A1-Mg alloys should be d i f f e r e n t f r o m those in A1. F o r e x a m p l e , r e c e n t e x p e r i m e n t a l evidence 2 shows that s u b g r a i n s a r e f o r m e d d u r i n g H a r p e r - D o r n c r e e p in A1. On the other hand, if the modified v i
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