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A comparison of dislocation densities in high temperature creep
Scripta METALLURGICA
Vol. 20, pp. 1373-1377, 1986 P r i n t e d in the U.S.A.
A COMPARISON OF D I S L O C A T I O N
DENSITIES
P e r g a m o n J o u r n a l s Ltd. All rights r e s e r v e d
IN HIGH T E M P E R A T U R E
CREEP
C. R. Feng, I. R. Kramer and R. J. A r s e n a u l t E n g i n e e r i n g M a t e r i a l s Group U n i v e r s i t y of M a r y l a n d C o l l e g e Park, MD 20742 (Received June 19, 1986) (Revised July 2, 1986) Introduction In previous i n v e s t i g a t i o n s of high t e m p e r a t u r e creep of ll00 AI (1,2), it was found that the d i s l o c a t i o n density, as d e t e r m i n e d by the X-ray d i f f r a c t i o n l i n e - b r o a d e n l n g technique, was i n d e p e n d e n t of stress in the power law region but dependent on stress in the power law b r e a k d o w n region. Also, it was found that the d i s l o c a t i o n density in the surface layer p,, and in the i n t e r i o r p~ of the sample was the same in the power law region. ~owever, in the power la~ breakdown region, the d i s l o c a t i o n density in the surface layer was g r e a t e r than that in the interior. Several questions have a r i s e n c o n c e r n i n g the results o b t a i n e d in the two previous investigations. Firstly, the d i s l o c a t i o n density did not follow a square dependency of the stress, i.e., p ~ ~ , where p is the d i s l o c a t i o n density and a is the a p p l i e d stress (3), and secondly, that the d i s l o c a t i o n density was d e t e r m i n e d i n d i r e c t l y from m e a s u r e m e n t s of the RMS m l c r o s t r a i n s o b t a i n e d from X-ray llne b r o a d e n i n g analysis (4). High t e m p e r a t u r e creep e x p e r i m e n t s which result in a r e t e n t i o n of the dislocation c o n f i g u r a t i o n and density that existed during the creep test are d i f f i c u l t to p e r f o r m in high purity metal samples. However, it has been claimed that AI-II% wt. Zn alloys have the same creep c h a r a c t e r i s t i c s as that of pure A1 (5-9). A further d i s t i n c t a d v a n t a g e of this AI-Zn alloy is that it can be aged under load to pin the d i s l o c a t i o n s into the c o n f i g u r a t i o n w h i c h they had d u r i n g the creep experiment. The purpose of this i n v e s t i g a t i o n was to d e t e r m i n e w h e t h e r there is a c o r r e l a t i o n in the d i s l o c a t i o n d e n s i t i e s as d e t e r m i n e d by X-ray d i f f r a c t i o n l l n e - b r o a d e n l n g and the t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y m e t h o d s in samples crept at high t e m p e r a t u r e s . The changes in the d i s l o c a t i o n d e n s i t i e s in the surface region and the i n t e r i o r were also i n v e s t i g a t e d , as a f u n c t i o n of stress. Experimental
Procedure
The alloy used in this study was an AI-II% wt. Zn alloy specimen. The alloy was a gift from A L C O A R e s e a r c h Laboratory. A 25 mm t h i c k section from a 152 mm d i a m e t e r ingot was rolled to a t h i c k n e s s of 3.63 mm. Then samples with a gage length of 31.8 mm and w i d t h of 6.4 mm and a t h i c k n e s s of 3.2 mm were m a c h i n e d from the strips (FIG. i). After m a c h i n i n g , the s a m p l e s were a n n e a l e d at 723 K for 1 hour and e l e c t r o c h e m i c a l l y p o l i s h e d in a H N O q - C H 3 0 H s o l u t i o n at 250 K to remove a p p r o x i m a t e l y 500 ~m from each side. The g ~ a i n size, after the a n n e a l i n g treatment, was about 1 mm. C o n s t a n t load creep tests were carried out in a clam shell radiant furnace at 573 K at stresses r a n g i n g from 0.98 to 14.63 MPa. The creep tests were p e r f o r m e d until steady state c o n d i t i o n s were reached. This r e q u i r e d that s p e c i m e n s be crept for d i f f e r e n t amounts of strain. Generally speaking, as the stress increased, the s t r a i n r e q u i r e d to reach steady state c o n d i t i o n s also increased. However, several tests were run
1373 0 0 3 6 - 9 7 4 8 / 8 6 $3.00 Copyright
+ .00
(c) 1986 P e r g a m o n Journals
Ltd.
1374
HIGH TEMPERATURE
CREEP
~
20, No.
i0
at v a r i o u s strains in the steady state region to determine the effect of strain on the d i s l o c a t i o n density. An i n c r e a s e in strain did not result in any s i g n i f i c a n t change in the d i s l o c a t i o n density. The specimens, while still u n d e r load, were rapidly cooled in a cold water bath and s u b s e q u e n t l y aged 5 days under load at room t e m p e r a t u r e after each test to pin the dislocations.
SURFACE REMOVED
~
Vol.
/ INTERIOR SAMPLES ~ - S U R ~ C E SAMPLE
The d i s l o c a t i o n d e n s i t i e s r e p o r t e d h e r e were c a l c u l a t e d by two d i f f e r e n t techniques. First, RMS (10) m ~ c ~ 9 ~ strain m e a s u r e m e n t s < were m a d e in the f o l l o w i n g manner: a conventional powder FIG. 1 type X-ray t e c h n i q u e e m p l o y i n g a GE XRD5 d i f f r a c t o m e t e r , a Cu Schematic of AI-II% wt. Zn creep sample from target, a 1 ° sllt and a Ni which the loll samples were obtained, filter w e r e used to obtain the d i f f r a c t i o n lines. A position sensitive detector with a s e n s i t i v i t y of 0.005 ° per c h a n n e l was used to record the X-ray data. The X-ray line p r o f i l e data were p r o c e s s e d with the aid of an Apollo computer to o b t a i n the F o u r i e r c o e f f i c i e n t s . The b e a m size was 1 × 1 mm and several different areas were m e a s u r e d on each s p e c l m e n ' s gage section. The K doublet separation into K and K c o m p o n e n t s was c a r r i e d out by the m e t h o d d ~ v e l o p e d by DeAngelis (ii). ~I 2 The equation used to c a l c u l a t e the d i s l o c a t i o n d e n s i t i e s m i c r o s t r a i n was given by W i l l l a m s o n and S m a l l m a n (4):
B[I/2L] 2 P
=
,,
from the RMS
(i)
Fb 2
where B is a constant r a n g i n g b e t w e e n 12 and 16 and d e p e n d e n t on the p a r t i c u l a r metal under c o n s i d e r a t i o n . L is the column length over w h i c h the RMS m i c r o strains are averaged, F is the d i s l o c a t i o n d i s t r i b u t i o n p a r a m e t e r , and b is the Burgers vector. In this i n v e s t i g a t i o n , B was set equal to 12, L was set equal to 5.0 nm and F was a s s u m e d to be equal to i. (These are the same values of B, L and F as used in the p r e v i o u s i n v e s t i g a t i o n s (1,2).) An i n c r e a s e in L to 15 nm had very little effect on the d i s l o c a t i o n density. The d i s l o c a t i o n densities were d e t e r m i n e d both at the surface and in the interior. After the surface m e a s u r e m e n t s were made, one Side of the sample was b l o c k e d off by epoxy paint and the other side of the s u r f a c e was e l e c t r o p o l l s h e d in a H N O 3 - C H 3 0 H s o l u t i o n at 250 K to remove 200 pm, and the X-ray m e a s u r e m e n t s were r e p e a t e a of the newly p o l i s h e d surface. These m e a s u r e m e n t s r e p r e s e n t e d data from the interior. The other m e t h o d used to d e t e r m i n e the d i s l o c a t i o n d e n s i t i e s was by transm i s s i o n e l e c t r o n m i c r o s c o p y (TEM). After the X-ray m e a s u r e m e n t s , several 3 mm d i a m e t e r c y l i n d e r s were e l e c t r i c a l l y d i s c h a r g e d m a c h i n e d (EDM) out from the gage l e n g t h of each specimen; then three slices (two i n t e r i o r foils and one surface foil) of a thickness of about 0.63 mm were diamond sawed from each of these c y l i n d e r s (FIG. i). Each slice was m e c h a n i c a l l y p o l i s h e d to a thickness of 0.13 mm. The i n t e r i o r samples were p o l i s h e d from both sides w h i l e the surface samples were p o l i s h e d f r o m one side. The TEM foils were p r e p a r e d by a twin jet technique, f o l l o w e d by a very short time I o n - m i l l l n g p r o c e d u r e . For t h i n n i n g of the surface samples, only the side away from the surface was exposed to the jet
Vol.
20,
No.
10
HIGH TEHPERATURE CREEP
and the ion-milllng. The TEM foils were e x a m i n e d scope at the Argonne N a t i o n a l Laboratory.
1375
in the 1 MV e l e c t r o n m i c r o -
The dislocation density w i t h i n the s u b g r a i n s was m e a s u r e d by c o u n t i n g the dislocation intersections on a straight llne of a g i v e n length in d i f f e r e n t areas of the subgrain. The e q u a t i o n used to relate the i n t e r s e c t i o n s to the dislocation density was as follows (12):
p = 2N/Lt
(2)
where N is the number of i n t e r s e c t i o n s , L is the length of line used, and t is the thickness of the TEM foil. In most cases, the t h i c k n e s s was about 700 nm. Experimental
Results
and D i s c u s s i o n
The general shapes of the plots of d i s l o c a t i o n density vs. stress o b t a i n e d by both the TEM and X-ray t e c h n i q u e s are in very good agreement. The c o m p u t e d values of dislocation d e n s i t i e s from the surface region (p_) and the i n t e r i o r s (p~) as a function of stress from the X-ray and TEM t e c h n i q u e s are p r e s e n t e d in FIGS. 2 and 3. The d i s l o c a t i o n d e n s i t i e s d e t e r m i n e d by the X-ray m e t h o d are one order of m a g n i t u d e larger than o] the d i s l o c a t i o n d e n s i t i e s obA l - Z n l l % wt (X-RAY) tained from the TEM method. It 9 573K should be noted• however, that s.o the X-ray t e c h n i q u e c o n s i d e r s s I-. the total d i s l o c a t i o n density• ? i.e.• the d i s l o c a t i o n s w i t h i n E 6 the s u b g r a i n b o u n d a r i e s as well as those in the i n t e r i o r of the o subgrains. However, the factor v 5 of I0 d i f f e r e n c e in d i s l o c a t i o n 4 density remains c o n s t a n t 3 ~ o ~ t h r o u g h o u t the entire stress 2 o g • range i n v e s t i g a t e d . • I
O
:
~
0
I 2
3
4
5 6
7 8
9
i i I0 Ill 12 13 '4 15
~(MPo)
FIG. The d i s l o c a t i o n the X-ray m e t h o d The open circles the surface and points o b t a i n e d
2
density as d e t e r m i n e d by vs. applied creep stress, are data points o b t a i n e d from the closed circles are data from the interior,
In a plot of log of creep (~) vs. log of o (FIG. 4) • there is no d i s c e r n i b l e s t r a i g h t line p o r t i o n to the curve, and the slope increases c o n t i n u o u s l y with stress. However, at an applied stress less than 7.2 MPa, it appears p o s s i b l e to presume that the power law is obeyed. The stress exponent (n) is near 3.5 in this region, and for s t r e s s e s that exceed 7.2, n i n c r e a s e s in stress. rate
In plots of d i s l o c a t i o n density vs. stress o b t a i n e d by both methods, if the stress is b e l o w 7.2 MPa, i.e., in the power law region, the d i s l o c a t i o n d e n s i t i e s are independent of stress and there is a d i f f e r e n c e b e t w e e n p and p_, i.e., p is greater than p _ which is contrary to the results obtained in the l~00 A1 all~y. For the II00 A~ alloy, in the power law region, p~ = p~ (2). The o b s e r v a t i o n that p > p_ when the AI-II% wt. Zn s p e c i m e n s wer~ cre~t at s t r e s s e s below 7.2 MPaSmay ~e indicative that a linear region does not truly exist. As the stress exceeds 7.2 MPa, (in the power law b r e a k d o w n region) where ~ increases rapidly with e, Pi is still i n d e p e n d e n t of stress, but p_ increases as the stress increases. The i n c r e a s e in the d i s l o c a t i o n densit~ in the surface region in the power law b r e a k d o w n region is in a g r e e m e n t with the results o b t a i n e d in the previous i n v e s t i g a t i o n s (1,2) of high t e m p e r a t u r e creep of ii00 A1 alloy. However, in a case of the ii00 A1 alloy, the d i s l o c a t i o n
1376
HIGH TEMPERATURE
|0
AI-ZnlI%wt (TEM) t~7000~ s-o I-,
9
573K
e
o
7 E 6 mo
o
:5
~4 3
o
o
~
o
o
2
"
"
I
,
"
"
"
I I'
0
2'
3
~
5'
~
FIG.
7' 8. . 9 ~(MPo)
.I0 . I'1 . 12. 13 14 15
3
The d i s l o c a t i o n density as d e t e r m i n e d by the TEM method vs. applied c r e e p stress. The open circles are data p o i n t s o b t a i n e d from the surface and the c l o s e d circles are data points o b t a i n e d from the interior,
-2
-3
A I - Z n I1% CREEPTEMP573K/
/
-4
•w
/
-5
Z2MPo
/ o -6
/A
3'5
-7
-8
'
-0.2
0
' 0.2
FIG. The log creep a p p l i e d creep
~
~
~
0.4 0.6 0.8 LOG ~ (MPo)
i 1.0
i 1.2
|.4
4
s t r a i n rate stress.
vs.
log of the
CREEP
Vol.
20, No.
I0
densitj in the i n t e r i o r also i n c r e a s e d in the power law b r e a k d o w n region, but there is an i n d i c a t i o n from the ii00 A1 data that if the test in the ii00 AI were c o n d u c t e d at a lower t e m p e r a t u r e than in the p o w e r law b r e a k d o w n region, the density in the i n t e r i o r w o u l d not be a f u n c t i o n of stress. In a plot of log of disl o c a t i o n d e n s i t y , p_, as determ i n e d by the TEM me~hod, vs. log of stress, FIG. 5 shows that for s t r e s s e s above 7.2 MPa the stress d e p e n d e n c e of the d i s l o c a t i o n density is p r o p o r tional to the o "~. In this p a r t i c u l a r plot only the disl o c a t i o n density m e a s u r e d in the s u b g r a i n i n t e r i o r was used. B a r r e t t (13) also found the same type of results in terms of stress d e p e n d e n c e . In hls work he used an e t c h - p i t techn i q u e on the s u r f a c e to m e a s u r e the d i s l o c a t i o n d e n s i t i e s in the s u b g r a i n i n t e r i o r s in Fe3.1% wt. Si alloy after high t e m p e r a t u r e creep test. He found the stress dependency of p was p r o p o r t i o n a l to a ~ at high s t r e s s e s while at low s t r e s s e s the stress dependencj falls off c o n s i d e r a b l y . However, his creep tests were c a r r i e d out in the p o w e r law region. For h i g h t e m p e r a t u r e creep test of AI-II% wt Zn, H a u s s e l t and Blum (6) and Morris (14) both found that the stress d e p e n d e n c y of p is p r o p o r t i o n a l to o in the p o w e r law b r e a k down region. The d i s l o c a t i o n density they m e a s u r e d corresponds to our TEM data o b t a i n e d from m e a s u r e m e n t s in the i n t e r i o r of the specimen; however, we found the d i s l o c a t i o n density to be i n d e p e n d e n t of stress. The d i f f e r e n c e b e t w e e n the investigation cited above and our i n v e s t i g a t i o n is that the f o r m e r was c o n d u c t e d at a lower t e m p e r a t u r e , i.e., 523 K.
Vol.
20, No.
i0
HIGH T E H P E R A T U R E
CREEP
137~
Conclusions i. AI-ZnlI%
wt(TEM)
573K 14.0
2. 138
3. v
m
1.9
13.6
13.4
4.
13.2
13.0
0
~
O.Z
=
0.4
~
0.6
~
0.8
LOG ~
FIG.
L
LO
=
1.2
~
1.4
1,6
5.
(MPa)
5
The log of dislocation density in the surface region as determined by the TEM method vs. the log of applied creep stress.
The d i s l o c a t i o n densities determined by the TEM technique are approximately a factor of i0 smaller than that obtained by the X-ray method. The d i s l o c a t i o n densities determined by the TEM technique and the X-ray t e c h n i q u e show the same stress dependency. In the high temperature creep of AI-II% wt. Zn, similar to the behavior of ll00 A1, power law breakdown occurs when the dislocation density in the surface region becomes significantly greater than that of the dislocation density in the interior, i.e., p is greater than p~. s The d i ~ l o c a t l o n densities in the surface region are stress dependent in the power law breakdown region and are stress independent in the power law region. The d i s l o c a t i o n densities in the interior were found to be stress independent, as determined both 0y X-ray technique and the TEM method.
Acknowledyements The authors wish to acknowledge the support of the National Science Foundation under grant No. DMR-81-08422-A03, and the support of the Argonne National Laboratory HVTEM facility. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ii. 12. 13. 14.
I. R. Kramer, C. R. Feng and R. J. Arsenault, Metall. Trans., 15A, 1571 (1984). I. R. Kramer, C. R. Feng and R. J. Arsenault, to be published in Mat. Sci. and Eng. A. K. Mukherjee, "Treatise on Materials Science and Technology," Ed. by R. J. Arsenault, Academic Press, p. 163 (1975). G. K. Williamson and R. E. Smallman, Phil. Mag., Series 8, i, 34 (1956). W. Blum, Phys. Stat. Sol., (b) 45, 561 (1971). J. Hausselt and W. Blum, Acta Met., 24, 1027 (1976). G. Konig and W. Blum, Acta Met., 25, 1531 (1977). W. Blum, Z. Metallkde, 484 (1977). W. Blum, A. Absenger and R. Feilhauer, Proc. 5th Int. Conf. on Strength of Metals and Alloys, Aachen, 265 (1979). B. W. Warren and B. L. Averbach, J. Appl. Phys., 234, 382 (1948). R. J. DeAngelis, Metallography, 6, 243 (1973). P. B. Hirsch, A. Howie, R. B. N i c h o l s o n and M. J. Whelen, "Electron Microscopy of Thin Crystal," London, 1965. C. R. Barrett, Trans. of AIME, 239, 1726 (1967). M. Morris, Doctor's Thesis, Swiss Institute of Techonology (1984).
Vol. 20, pp. 1373-1377, 1986 P r i n t e d in the U.S.A.
A COMPARISON OF D I S L O C A T I O N
DENSITIES
P e r g a m o n J o u r n a l s Ltd. All rights r e s e r v e d
IN HIGH T E M P E R A T U R E
CREEP
C. R. Feng, I. R. Kramer and R. J. A r s e n a u l t E n g i n e e r i n g M a t e r i a l s Group U n i v e r s i t y of M a r y l a n d C o l l e g e Park, MD 20742 (Received June 19, 1986) (Revised July 2, 1986) Introduction In previous i n v e s t i g a t i o n s of high t e m p e r a t u r e creep of ll00 AI (1,2), it was found that the d i s l o c a t i o n density, as d e t e r m i n e d by the X-ray d i f f r a c t i o n l i n e - b r o a d e n l n g technique, was i n d e p e n d e n t of stress in the power law region but dependent on stress in the power law b r e a k d o w n region. Also, it was found that the d i s l o c a t i o n density in the surface layer p,, and in the i n t e r i o r p~ of the sample was the same in the power law region. ~owever, in the power la~ breakdown region, the d i s l o c a t i o n density in the surface layer was g r e a t e r than that in the interior. Several questions have a r i s e n c o n c e r n i n g the results o b t a i n e d in the two previous investigations. Firstly, the d i s l o c a t i o n density did not follow a square dependency of the stress, i.e., p ~ ~ , where p is the d i s l o c a t i o n density and a is the a p p l i e d stress (3), and secondly, that the d i s l o c a t i o n density was d e t e r m i n e d i n d i r e c t l y from m e a s u r e m e n t s of the RMS m l c r o s t r a i n s o b t a i n e d from X-ray llne b r o a d e n i n g analysis (4). High t e m p e r a t u r e creep e x p e r i m e n t s which result in a r e t e n t i o n of the dislocation c o n f i g u r a t i o n and density that existed during the creep test are d i f f i c u l t to p e r f o r m in high purity metal samples. However, it has been claimed that AI-II% wt. Zn alloys have the same creep c h a r a c t e r i s t i c s as that of pure A1 (5-9). A further d i s t i n c t a d v a n t a g e of this AI-Zn alloy is that it can be aged under load to pin the d i s l o c a t i o n s into the c o n f i g u r a t i o n w h i c h they had d u r i n g the creep experiment. The purpose of this i n v e s t i g a t i o n was to d e t e r m i n e w h e t h e r there is a c o r r e l a t i o n in the d i s l o c a t i o n d e n s i t i e s as d e t e r m i n e d by X-ray d i f f r a c t i o n l l n e - b r o a d e n l n g and the t r a n s m i s s i o n e l e c t r o n m i c r o s c o p y m e t h o d s in samples crept at high t e m p e r a t u r e s . The changes in the d i s l o c a t i o n d e n s i t i e s in the surface region and the i n t e r i o r were also i n v e s t i g a t e d , as a f u n c t i o n of stress. Experimental
Procedure
The alloy used in this study was an AI-II% wt. Zn alloy specimen. The alloy was a gift from A L C O A R e s e a r c h Laboratory. A 25 mm t h i c k section from a 152 mm d i a m e t e r ingot was rolled to a t h i c k n e s s of 3.63 mm. Then samples with a gage length of 31.8 mm and w i d t h of 6.4 mm and a t h i c k n e s s of 3.2 mm were m a c h i n e d from the strips (FIG. i). After m a c h i n i n g , the s a m p l e s were a n n e a l e d at 723 K for 1 hour and e l e c t r o c h e m i c a l l y p o l i s h e d in a H N O q - C H 3 0 H s o l u t i o n at 250 K to remove a p p r o x i m a t e l y 500 ~m from each side. The g ~ a i n size, after the a n n e a l i n g treatment, was about 1 mm. C o n s t a n t load creep tests were carried out in a clam shell radiant furnace at 573 K at stresses r a n g i n g from 0.98 to 14.63 MPa. The creep tests were p e r f o r m e d until steady state c o n d i t i o n s were reached. This r e q u i r e d that s p e c i m e n s be crept for d i f f e r e n t amounts of strain. Generally speaking, as the stress increased, the s t r a i n r e q u i r e d to reach steady state c o n d i t i o n s also increased. However, several tests were run
1373 0 0 3 6 - 9 7 4 8 / 8 6 $3.00 Copyright
+ .00
(c) 1986 P e r g a m o n Journals
Ltd.
1374
HIGH TEMPERATURE
CREEP
~
20, No.
i0
at v a r i o u s strains in the steady state region to determine the effect of strain on the d i s l o c a t i o n density. An i n c r e a s e in strain did not result in any s i g n i f i c a n t change in the d i s l o c a t i o n density. The specimens, while still u n d e r load, were rapidly cooled in a cold water bath and s u b s e q u e n t l y aged 5 days under load at room t e m p e r a t u r e after each test to pin the dislocations.
SURFACE REMOVED
~
Vol.
/ INTERIOR SAMPLES ~ - S U R ~ C E SAMPLE
The d i s l o c a t i o n d e n s i t i e s r e p o r t e d h e r e were c a l c u l a t e d by two d i f f e r e n t techniques. First, RMS (10) m ~ c ~ 9 ~ strain m e a s u r e m e n t s < were m a d e in the f o l l o w i n g manner: a conventional powder FIG. 1 type X-ray t e c h n i q u e e m p l o y i n g a GE XRD5 d i f f r a c t o m e t e r , a Cu Schematic of AI-II% wt. Zn creep sample from target, a 1 ° sllt and a Ni which the loll samples were obtained, filter w e r e used to obtain the d i f f r a c t i o n lines. A position sensitive detector with a s e n s i t i v i t y of 0.005 ° per c h a n n e l was used to record the X-ray data. The X-ray line p r o f i l e data were p r o c e s s e d with the aid of an Apollo computer to o b t a i n the F o u r i e r c o e f f i c i e n t s . The b e a m size was 1 × 1 mm and several different areas were m e a s u r e d on each s p e c l m e n ' s gage section. The K doublet separation into K and K c o m p o n e n t s was c a r r i e d out by the m e t h o d d ~ v e l o p e d by DeAngelis (ii). ~I 2 The equation used to c a l c u l a t e the d i s l o c a t i o n d e n s i t i e s m i c r o s t r a i n was given by W i l l l a m s o n and S m a l l m a n (4):
B[
=
,,
from the RMS
(i)
Fb 2
where B is a constant r a n g i n g b e t w e e n 12 and 16 and d e p e n d e n t on the p a r t i c u l a r metal under c o n s i d e r a t i o n . L is the column length over w h i c h the RMS m i c r o strains are averaged, F is the d i s l o c a t i o n d i s t r i b u t i o n p a r a m e t e r , and b is the Burgers vector. In this i n v e s t i g a t i o n , B was set equal to 12, L was set equal to 5.0 nm and F was a s s u m e d to be equal to i. (These are the same values of B, L and F as used in the p r e v i o u s i n v e s t i g a t i o n s (1,2).) An i n c r e a s e in L to 15 nm had very little effect on the d i s l o c a t i o n density. The d i s l o c a t i o n densities were d e t e r m i n e d both at the surface and in the interior. After the surface m e a s u r e m e n t s were made, one Side of the sample was b l o c k e d off by epoxy paint and the other side of the s u r f a c e was e l e c t r o p o l l s h e d in a H N O 3 - C H 3 0 H s o l u t i o n at 250 K to remove 200 pm, and the X-ray m e a s u r e m e n t s were r e p e a t e a of the newly p o l i s h e d surface. These m e a s u r e m e n t s r e p r e s e n t e d data from the interior. The other m e t h o d used to d e t e r m i n e the d i s l o c a t i o n d e n s i t i e s was by transm i s s i o n e l e c t r o n m i c r o s c o p y (TEM). After the X-ray m e a s u r e m e n t s , several 3 mm d i a m e t e r c y l i n d e r s were e l e c t r i c a l l y d i s c h a r g e d m a c h i n e d (EDM) out from the gage l e n g t h of each specimen; then three slices (two i n t e r i o r foils and one surface foil) of a thickness of about 0.63 mm were diamond sawed from each of these c y l i n d e r s (FIG. i). Each slice was m e c h a n i c a l l y p o l i s h e d to a thickness of 0.13 mm. The i n t e r i o r samples were p o l i s h e d from both sides w h i l e the surface samples were p o l i s h e d f r o m one side. The TEM foils were p r e p a r e d by a twin jet technique, f o l l o w e d by a very short time I o n - m i l l l n g p r o c e d u r e . For t h i n n i n g of the surface samples, only the side away from the surface was exposed to the jet
Vol.
20,
No.
10
HIGH TEHPERATURE CREEP
and the ion-milllng. The TEM foils were e x a m i n e d scope at the Argonne N a t i o n a l Laboratory.
1375
in the 1 MV e l e c t r o n m i c r o -
The dislocation density w i t h i n the s u b g r a i n s was m e a s u r e d by c o u n t i n g the dislocation intersections on a straight llne of a g i v e n length in d i f f e r e n t areas of the subgrain. The e q u a t i o n used to relate the i n t e r s e c t i o n s to the dislocation density was as follows (12):
p = 2N/Lt
(2)
where N is the number of i n t e r s e c t i o n s , L is the length of line used, and t is the thickness of the TEM foil. In most cases, the t h i c k n e s s was about 700 nm. Experimental
Results
and D i s c u s s i o n
The general shapes of the plots of d i s l o c a t i o n density vs. stress o b t a i n e d by both the TEM and X-ray t e c h n i q u e s are in very good agreement. The c o m p u t e d values of dislocation d e n s i t i e s from the surface region (p_) and the i n t e r i o r s (p~) as a function of stress from the X-ray and TEM t e c h n i q u e s are p r e s e n t e d in FIGS. 2 and 3. The d i s l o c a t i o n d e n s i t i e s d e t e r m i n e d by the X-ray m e t h o d are one order of m a g n i t u d e larger than o] the d i s l o c a t i o n d e n s i t i e s obA l - Z n l l % wt (X-RAY) tained from the TEM method. It 9 573K should be noted• however, that s.o the X-ray t e c h n i q u e c o n s i d e r s s I-. the total d i s l o c a t i o n density• ? i.e.• the d i s l o c a t i o n s w i t h i n E 6 the s u b g r a i n b o u n d a r i e s as well as those in the i n t e r i o r of the o subgrains. However, the factor v 5 of I0 d i f f e r e n c e in d i s l o c a t i o n 4 density remains c o n s t a n t 3 ~ o ~ t h r o u g h o u t the entire stress 2 o g • range i n v e s t i g a t e d . • I
O
:
~
0
I 2
3
4
5 6
7 8
9
i i I0 Ill 12 13 '4 15
~(MPo)
FIG. The d i s l o c a t i o n the X-ray m e t h o d The open circles the surface and points o b t a i n e d
2
density as d e t e r m i n e d by vs. applied creep stress, are data points o b t a i n e d from the closed circles are data from the interior,
In a plot of log of creep (~) vs. log of o (FIG. 4) • there is no d i s c e r n i b l e s t r a i g h t line p o r t i o n to the curve, and the slope increases c o n t i n u o u s l y with stress. However, at an applied stress less than 7.2 MPa, it appears p o s s i b l e to presume that the power law is obeyed. The stress exponent (n) is near 3.5 in this region, and for s t r e s s e s that exceed 7.2, n i n c r e a s e s in stress. rate
In plots of d i s l o c a t i o n density vs. stress o b t a i n e d by both methods, if the stress is b e l o w 7.2 MPa, i.e., in the power law region, the d i s l o c a t i o n d e n s i t i e s are independent of stress and there is a d i f f e r e n c e b e t w e e n p and p_, i.e., p is greater than p _ which is contrary to the results obtained in the l~00 A1 all~y. For the II00 A~ alloy, in the power law region, p~ = p~ (2). The o b s e r v a t i o n that p > p_ when the AI-II% wt. Zn s p e c i m e n s wer~ cre~t at s t r e s s e s below 7.2 MPaSmay ~e indicative that a linear region does not truly exist. As the stress exceeds 7.2 MPa, (in the power law b r e a k d o w n region) where ~ increases rapidly with e, Pi is still i n d e p e n d e n t of stress, but p_ increases as the stress increases. The i n c r e a s e in the d i s l o c a t i o n densit~ in the surface region in the power law b r e a k d o w n region is in a g r e e m e n t with the results o b t a i n e d in the previous i n v e s t i g a t i o n s (1,2) of high t e m p e r a t u r e creep of ii00 A1 alloy. However, in a case of the ii00 A1 alloy, the d i s l o c a t i o n
1376
HIGH TEMPERATURE
|0
AI-ZnlI%wt (TEM) t~7000~ s-o I-,
9
573K
e
o
7 E 6 mo
o
:5
~4 3
o
o
~
o
o
2
"
"
I
,
"
"
"
I I'
0
2'
3
~
5'
~
FIG.
7' 8. . 9 ~(MPo)
.I0 . I'1 . 12. 13 14 15
3
The d i s l o c a t i o n density as d e t e r m i n e d by the TEM method vs. applied c r e e p stress. The open circles are data p o i n t s o b t a i n e d from the surface and the c l o s e d circles are data points o b t a i n e d from the interior,
-2
-3
A I - Z n I1% CREEPTEMP573K/
/
-4
•w
/
-5
Z2MPo
/ o -6
/A
3'5
-7
-8
'
-0.2
0
' 0.2
FIG. The log creep a p p l i e d creep
~
~
~
0.4 0.6 0.8 LOG ~ (MPo)
i 1.0
i 1.2
|.4
4
s t r a i n rate stress.
vs.
log of the
CREEP
Vol.
20, No.
I0
densitj in the i n t e r i o r also i n c r e a s e d in the power law b r e a k d o w n region, but there is an i n d i c a t i o n from the ii00 A1 data that if the test in the ii00 AI were c o n d u c t e d at a lower t e m p e r a t u r e than in the p o w e r law b r e a k d o w n region, the density in the i n t e r i o r w o u l d not be a f u n c t i o n of stress. In a plot of log of disl o c a t i o n d e n s i t y , p_, as determ i n e d by the TEM me~hod, vs. log of stress, FIG. 5 shows that for s t r e s s e s above 7.2 MPa the stress d e p e n d e n c e of the d i s l o c a t i o n density is p r o p o r tional to the o "~. In this p a r t i c u l a r plot only the disl o c a t i o n density m e a s u r e d in the s u b g r a i n i n t e r i o r was used. B a r r e t t (13) also found the same type of results in terms of stress d e p e n d e n c e . In hls work he used an e t c h - p i t techn i q u e on the s u r f a c e to m e a s u r e the d i s l o c a t i o n d e n s i t i e s in the s u b g r a i n i n t e r i o r s in Fe3.1% wt. Si alloy after high t e m p e r a t u r e creep test. He found the stress dependency of p was p r o p o r t i o n a l to a ~ at high s t r e s s e s while at low s t r e s s e s the stress dependencj falls off c o n s i d e r a b l y . However, his creep tests were c a r r i e d out in the p o w e r law region. For h i g h t e m p e r a t u r e creep test of AI-II% wt Zn, H a u s s e l t and Blum (6) and Morris (14) both found that the stress d e p e n d e n c y of p is p r o p o r t i o n a l to o in the p o w e r law b r e a k down region. The d i s l o c a t i o n density they m e a s u r e d corresponds to our TEM data o b t a i n e d from m e a s u r e m e n t s in the i n t e r i o r of the specimen; however, we found the d i s l o c a t i o n density to be i n d e p e n d e n t of stress. The d i f f e r e n c e b e t w e e n the investigation cited above and our i n v e s t i g a t i o n is that the f o r m e r was c o n d u c t e d at a lower t e m p e r a t u r e , i.e., 523 K.
Vol.
20, No.
i0
HIGH T E H P E R A T U R E
CREEP
137~
Conclusions i. AI-ZnlI%
wt(TEM)
573K 14.0
2. 138
3. v
m
1.9
13.6
13.4
4.
13.2
13.0
0
~
O.Z
=
0.4
~
0.6
~
0.8
LOG ~
FIG.
L
LO
=
1.2
~
1.4
1,6
5.
(MPa)
5
The log of dislocation density in the surface region as determined by the TEM method vs. the log of applied creep stress.
The d i s l o c a t i o n densities determined by the TEM technique are approximately a factor of i0 smaller than that obtained by the X-ray method. The d i s l o c a t i o n densities determined by the TEM technique and the X-ray t e c h n i q u e show the same stress dependency. In the high temperature creep of AI-II% wt. Zn, similar to the behavior of ll00 A1, power law breakdown occurs when the dislocation density in the surface region becomes significantly greater than that of the dislocation density in the interior, i.e., p is greater than p~. s The d i ~ l o c a t l o n densities in the surface region are stress dependent in the power law breakdown region and are stress independent in the power law region. The d i s l o c a t i o n densities in the interior were found to be stress independent, as determined both 0y X-ray technique and the TEM method.
Acknowledyements The authors wish to acknowledge the support of the National Science Foundation under grant No. DMR-81-08422-A03, and the support of the Argonne National Laboratory HVTEM facility. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. ii. 12. 13. 14.
I. R. Kramer, C. R. Feng and R. J. Arsenault, Metall. Trans., 15A, 1571 (1984). I. R. Kramer, C. R. Feng and R. J. Arsenault, to be published in Mat. Sci. and Eng. A. K. Mukherjee, "Treatise on Materials Science and Technology," Ed. by R. J. Arsenault, Academic Press, p. 163 (1975). G. K. Williamson and R. E. Smallman, Phil. Mag., Series 8, i, 34 (1956). W. Blum, Phys. Stat. Sol., (b) 45, 561 (1971). J. Hausselt and W. Blum, Acta Met., 24, 1027 (1976). G. Konig and W. Blum, Acta Met., 25, 1531 (1977). W. Blum, Z. Metallkde, 484 (1977). W. Blum, A. Absenger and R. Feilhauer, Proc. 5th Int. Conf. on Strength of Metals and Alloys, Aachen, 265 (1979). B. W. Warren and B. L. Averbach, J. Appl. Phys., 234, 382 (1948). R. J. DeAngelis, Metallography, 6, 243 (1973). P. B. Hirsch, A. Howie, R. B. N i c h o l s o n and M. J. Whelen, "Electron Microscopy of Thin Crystal," London, 1965. C. R. Barrett, Trans. of AIME, 239, 1726 (1967). M. Morris, Doctor's Thesis, Swiss Institute of Techonology (1984).