Evidence for subgrain formation in an al-mg alloy at low stresses
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h (cm) 30 -
{3rs-~ r~
.
350 o 300 ~ 250 ~
_>00o
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Fig. 3--A schematic diagram of the melt rising in the fused silica tube.
9
40
w h i c h r a i s e d the t e m p e r a t u r e of the s i l i c a a b o v e T A , the a m b i e n t t e m p e r a t u r e , a c c o r d i n g to q silica = 27r~'d'c'p' ( T m 2+ Ts
-
TA/
[6]
and t h a t h e a t is the t o t a l h e a t t r a n s f e r r e d i n t o the s i l i c a f r o m t h e s u p e r h e a t e d m e l t w h i c h h a s p a s s e d by it at v e l o c i t y v d u r i n g t h e f i l l i n g of the t u b e to a h e i g h t H, i . e . , q silica =
(4 m e l t -
[7]
q r a d i a t i o n ) H -u h
in w h i c h b o t h ~ melt and ~ radiation a r e t a k e n to be c o n s t a n t d u r i n g f i l l i n g of the t u b e . In o r d e r to e v a l u a t e melt a f t e r the t u b e h a s b e e n f i l l e d , we u s e a t a b u l a t e d s o l u t i o n , f (and i t s d e r i v a t i v e f ' ) of the d i f f u s i o n e q u a tion for a cylindrical specimen: z To T To- Tm = f
(r~)
[8 ]
w h e r e ot = k / p c is the t h e r m a l d i f f u s i v i t y of t h e m e l t . B e c a u s e we a r e c o n c e r n e d w i t h the m e l t at h e i g h t h, f is to be e v a l u a t e d f o r the t i m e s i n c e the m e l t at that h e i g h t h a s b e e n c o o l i n g , i.e., s i n c e it l e f t the r e s e r v o i r , and that t i m e is t = h / v . C o m b i n i n g the a b o v e e q u a t i o n s in a s t r a i g h t f o r w a r d m a n n e r l e a d s to the f o l l o w i n g e q u a t i o n in w h i c h e a c h t e r m is d i m e n s i o n l e s s :
r
/
"v r ~
--T-
+
2~'
1 +-d7s T h e f a c t o r (\ TToi -nT- TmA~ /
I
I
5O
6O 70 H (cm)
I
I
I
80
9O
~00
Fig. 4--Calcutated curves of h vs H for different superheats (T o - Tin), as marked, with experimental data (superheats given in each case). Calculated curves are for v = 20 crn/s. T h e r a t e of s o l i d i f i c a t i o n w a s not o b s e r v e d d i r e c t l y . T h e r e is s o m e l i m i t e d i n f o r m a t i o n by w h i c h the s o l i d i f i c a t i o n r a t e m a y be d e d u c e d f r o m the o b s e r v e d g r a i n s i z e , but it is not a p p l i c a b l e to a l l o y s of the c o m p o s i t i o n we w e r e c o n s i d e r i n g . 6 T h e a u t h o r s w i s h to a c k n o w l e d g e m a n y u s e f u l d i s c u s s i o n s on b o t h the e x p e r i m e n t a l and t h e o r e t i c a l a s p e c t s of t h i s i n v e s t i g a t i o n w i t h P r o f e s s o r P . G. W i n c h e l l . T h i s w o r k w a s s u p p o r t e d by the N a t i o n a l S c i e n c e F o u n d a t i o n M R L P r o g r a m G r a n t N o . GH33574. I. Quartz Scientific,Incorporated, catalogFused Quartz, p. 4, March 1976. 2. L. S. Darken and R. W. Gurry: Physical Chemistry of Metals, pp. 445-47, McGraw-HillBook Co., New York, 1953. 3. G. L. Kehl: The Principlesof Metallographic Laboratory Practice, p. 490, McGraw-HillBook Co., New York, 1
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