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The influence of second phase particles on the free dislocation density during creep of stainless steel
Scripta
MtiTAI,LUR(;ICA
V o l . 14, pp. 7 5 5 - 7 0 0 , 1980 Printed in the U.S.A.
Pergamon P r e s s I,td. All rights reserved.
THE INFLUENCE OF SECOND PHASE PARTICLES ON THE FREE DISLOCATION DENSITY DURING CREEP OF STAINLESS R. F. Singer*,
STEEL
W. Blum** and W. D. Nix***
*Brown Bovari Company,
Baden,
Switzerland
**Institut fur Werkstoffwissenschaften Universit~t Erlangen-N~rnberg ***Department of Materials Science and Engineering Stanford University, Stanford, California 94305
(Received April ( R e v i s e d May 9,
9, 1980) 1980)
It has been well established that during steady state creep of many pure metals and solid solutions the density of free dislocations p (dislocations not associated with subgrain boundaries) varies with the square of the stress ~ according to the relation 2 p = (a/G Gb) , (1) where G is the shear modulus, b is the Burgers vector and ~ is a constant almost equal to i [I]. Less is known about the dislocation density in particle hardened materials. Figure I shows a compilation of data taken from the literature. It seems that the dislocation density does vary with stress, but considerable deviations from Eq. (i) occur. Stress exponents larger than 2 are found. (The weak stress dependences in the dashed parts of the curves were attributed by the authors to changes in the deformation mechanisms). The constant a ranges from 0.3 to values as large as 2.4. The purpose of the work described in this paper was to study the dependence of the free steady state dislocation density on the interparticle distance. To separate the influence of stress and particles, the specimens were crept at the same stress. The material used in this study was the y' (Ni3(AI,Ti)) - hardened stainless steel A-286. This alloy is an "iron-base superalloy" which is used especially for turbine wheels [12]. Experimental The chemical composition as follows (in wt%): C 0.08
Cr 13.5-16
Ni 24-27
Procedure
of the alloy investigated was certified by the manufacturer Ti 1.9-2.3
AI 0.35
Mo 1.0-1.5
Mn 1-2
to be
Fe Balance
The material was received in the recrystallized condition. The grains were equiaxed and 70 + 5 ~m in diameter [13]. The age-hardening treatment, given by the manufacturer, involved solution heat treatment at 980°C for i h, followed by aging at 725°C for 8 h. The creep tests and the preparation of TEM foils were carried out as part of a more extensive study of the deformation behavior and the stability of y' particles during creep, conducted at the University of Erlangen [14]. Briefly, cylindrical creep specimens with a gage length of 30 mm and a diameter of 6 m m w e r e prepared by spark cutting and crept in tension at constant stress. In order to prevent changes of the dislocation structure, the load was maintained during cooling. Thin foils were prepared according to standard techniques. The electro-polishing was done in a Struers Tenupol twin jet electropolisher using a i0:i mixture of acetic acid and perchlorid acid at 8°C and 35V. The TEM study was carried out on a Philips EM 400 at 120 kV. The dislocation
density was measured by counting the number of intersections
755 0036-9748/80/070755-06502.00/0 Copyright (c) 1 9 8 0 P e r g a m o n Press
Ltd.
which dis-
7S6
FREE D I S L O C A T I O N
15 6 ~52 ~4E
DENSITY
20%Cr-35%Ni Stoinless Steel.single phose,Lognebocg 20%Cr-35%Ni Stainless Steel, ),,-port~cles, Log~eborq 20%Cr-25%Ni-Nb StainlessSteeI,NbCNporficles,Kno~.les 20%Cr-25%Ni-Nb Stoin[essSteel, tronsktionporticles, Kno*les •% TD-Ni, HOUSSelt ond Nix ,% TD-Ni, Cloue¢ ond Wilcox . crystoll O Cu -AI205 , OOr = 18.SMPo,Lloyd and Mortin] single E] Cu-AI203, Oor =IZgMPO'LIOyd °nd Martini> . ~ ~]3 AI-5%Cu. AI2Cu*p°rticle$' Blum o n a ~
Vol.
14, No.
7
(9 A <> {-]
3.0
I
I
I
I
I
i
0 annealed • crept A crept
2.5
and annealed
u,~4
Ec 2.0 Q, 14.0
,.5 ~., 136
c~ 0
1.0 -__TO_
d
BEFORE
13.2
286 800°C
A-
Q5 L2B I
0 0
124
12o
-~
-~ ~ -3:2
-31o -2'8
0.5
I
1.0
I
,.5
log
-2!6 -2 io -212 -2o
TEST
I
I
z.o 2.5
I
3.0 3.5
(t/h)
log (O/G) Fig. i. Relation between steady state dislocation density and modulus compensated stress for particle hardened metals. The data were taken from the work of Lagneborg [2], Knowles [3], Hausselt and Nix [4], Clauer and Wilcox [5], Lloyd and Martin [6], and Blum and Singer [7]. For the shear modulus we used the data given in references [8-11].
Fig. 2. Mean diameter of the y' particles in A-286 as a function of the time of annealing or creep at 800°C [14]. The creep testing was done at 177 MPa.
locations make with the surface of the loll [15]. P = 2 N/A ,
The dislocation density is then given by (2)
where N is the number of intersections with both surfaces whose total area is A. The foils were tilted to obtain several operating reflections and to make all dislocations visible. The effect of tilting on the surface area A was taken into account. No dlslocatlonmotlon occurred even at the highest electron currents and in the thinnest parts of the foil. This indicates that the dislocations are immobile due to particle and solid solution hardening and that changes of the dislocation density during toll preparation or handling are unlikely to occur. In order to characterize the experimental error the 95% confidence limits are given in the paper. The interparticle distance in A-286 increases during creep due to Ostwald ripening. This result which has been reported and discussed elsewhere [14], is shown in Fig. 2. In order to obtain creep specimens with different interpartlcle distances, the creep tests were interrupted after different creep times or specimens were preheated for different times. The interparticle distance is specialized in this paper to mean the square lattice spacing L [16] e = (~/f)0"5-2)
(2/3) 0.5 r
(3)
where f is the particle volume fraction and r is the particle radius. From the number of particles per unit volume and the mean particle size we determined the v o l ~ e fraction to be 0.7%. The foil thickness determination which is necessary for the measurement of the number
Vol.
14,
No.
7
FREE
DISLOCATION
DENSITY
757
of particles per unit volume was done by deliberately tilting foils containing some n (Ni3Ti)-equilibrium particles. The tilting axis was the intersection line between the {Iii} habit plane of the plate-like ~ precipitates and the foil surface. Results and Discussion Figure 3 shows the dislocation and particle structure in specimens crept at 117 MPa and 800°C. The y' particles are coarser in the specimen which is shown in Fig. 3b because it was preheated and crept for a longer time. Micrographs like those in Fig. 3 were used for the measurement of the free dislocation density. The results are listed in Table i and are plotted as a function of the interparticle distance in Fig. 4. The data point marked with an arrow in Fig. 4 was provided by a creep specimen deformed at 121 MPa instead of 177 MPa. This point, therefore, gives a lower limit for the dislocation density at 177 MPa. The free dislocation density found by Lagneborg [2] in a similar material which did not contain particles is indicated by a dashed line. It is evident from Fig. 4 that the free dislocation density decreases with decreasing interparticle distance. Fig. 3b shows that subgrains are formed during creep of A-286. This represents an apparent contradiction to a result obtained by Lagneborg [2] who found no tendency for subgrain formation in a similar material. He studied the dislocation structure after a creep strain of 12.5% or less. However, rather large strains are necessary to develop a homogeneous subgrain structure. We found that subgrains were not present in some parts of the samples after 18% elongation. The subgrain structure shown in Fig. 3b was produced by a creep strain of more than 30%. Because of the inhomogeneity of subgrain formation in A-286 some measurements of the free dislocation density had to be made in subgrain free regions. The corresponding data points are marked in Fig. 4. The question arises whether these values are representative of the steady state. This alloy shows normal transient creep [14]* , and subgrain formation. The variation of the free dislocation density with creep strain for materials with this behavior has been studied frequently: stainless steel [18], alpha-iron [19], iron-silicon [20], aluminum [21]. The free dislocation density reaches the steady state value or an even somewhat higher value after very small strains (typically smaller than 1%) and remains constant or decreases, respectively, during primary creep. This means that the dislocation densities measured in subgrain free regions are equal to, or somewhat higher, than the steady state values. Our view is supported by two experimental observations: (a) The dislocation density in a specimen deformed for 0.7% at 121 MPa was found to be higher than that in a specimen deformed for 3.1% at 177 MPa, see Fig. 4 and Table I. This indicates that the steady state dislocation density, or an even somewhat higher value, is already reached after about 0.7% strain. (b) The steady state dislocation density was measured in subgrain free regions and in regions containing subgrains in the same specimen (Fig. 4 at log L = 2.54, Table i, #2). The dislocation density is equal within the limits of experimental error. The result that particles lead to a decrease of the free dislocation density agrees with the observation made by Lagneborg [2] and Blum and Singer [7] (see Fig. i). The different absolute values for the dislocation density in TD-nickel, Fig. i, can also be regarded as a confirmation of our result, since the creep data suggest that the material studied by Hausselt and Nix [4] was stronger than that studied by Clauer and Wilcox [5].
The creep rate reaches a minimum value after less than 1% elongation and increases afterwards. The minimum is due to the balancing effects of strain hardening and softening due to Ostwald ripening and does not indicate that the steady state dislocation structure is formed (compare the discussion in reference [17]) .
758
FREE
DISLOCATION
DENSITY
Vol.
14,
No.
7
TABLE 1 Results for Transmission Electron Microscopy of A-286 Crept at 800°C
No. oIMPa
r/nm
L/nm
9/m
Subgrains
OOr/MPa
o01MPa
o maas P
/MPa
i
177
34.5
43.0
673
(i.i + 0.5) 1014
yes
48
129
129
2
177
18.0
21.8
342
(4.4 + 2.2) 1013
yes
94
83
81
177
18.0
21.8
342
(3.9 + i.i) 1013
no
94
83
75
3
177
3.1
14.3
244
(1.2 + 0.9) 1013
no
144
33
41
4
121
0.7
16.4
257
(1.3 + 0.8) 1013
no
125
-4
43
It is a common idea that the creep characteristics of particle hardened materials are essentially those of pure materials subjected to a smaller stress, e.g., [7,22,23]. A natural consequence of this idea is the expectation of smaller dislocation densities in the particle hardened material deformed at the same stress as a pure material. In particle hardened materials a smaller stress is available for the generation of dislocations, i.e., the applied stress G in Eq. (i) is replaced by o
=
O where o
~
-
c
(4)
P
describes the influence of particles. P
In solid solutions the contribution from foreign atoms has to be considered additionally, resulting in a further decrease of the stress available for the generation of dislocations. Both the contributions of particles and foreign atoms are expected to be strain rate and temperature dependent. The quantity O^ , calculated according to Eq. (4), is plotted in Fig. 5 as a function of the interparticle d~stance. We assumed that the contribution of foreign atoms can be neglected and that the contribution of particles is independent of the strain rate. This is almost certainly an oversimplification. However, it permits us to determine whether the experimental data are in accordance with the view outlined above. We assumed further that the particles are bypassed by the dislocations and that ~ is equal to the Orowan stress, which is to a first approximation given by [16] P GOr/3 = 0.8 Gb/L
(5)
where L is the interparticle distance as defined by Eq. (3). The assumption that the y'particles are bypassed rather than sheared seems to be valid since the self stress of an Orowan loop is not sufficient to shear the particles in the present case* . Moreover, we did not find any indication ~or cutting in the TEM investigation, o meas, calculated from the measured dislocation densities according to Eq. (i) using ~ = 0.~, is also plotted in Fig. 5. The l e p a s _ values are in excellent agreement with the op values calculated according to Eq. 4 2 O5 * For shearing to occur r must be smaller than2(Gb /2 y (2/3) " ) , where y is the stacking fault energy [16]. A value of y = 0.285 Jm(Raynor and Silcock for Ti:AI = 6:1, cited in [16]) gives a value of r = 7.5 nm. The particle radii in A-286 found in this study (Table i) are substantially larger than 7.5 nm.
Vol.
14,
No.
7
FREE DISLOCATION Dt!NSfTY
759
A ,I, P
Fig.
Fig. 3.
3a
Fig. 3b
Dislocation and particle structure in A-286 crept at 800°C and 177MPa. Fig. 3a. Crept 3,1% for 12 h. Fig. 3b. Preheated 625 h and crept 34.5% for 36 h.
I
I
I
[
i
14.4
200
. .~A6. E"~.R -oE '/ ~
P IN SINGLEPHASESTAINLESS STEEL,
I
. . . . . . .
14.(:
I
_
I
I
APPLIED
I
STRESS
160 N
13.6 o 120
'E
=O9,G Kb
cL 13.2 b
8c
0
--
128
12.4
J.J-
177 MPo
/ _.L
12.0 2.3
4o
800°C [] NO SUBGRAINS O SUBGRAINS 1
2.4
I
i
I
2.5 2.6 2.7 log ( L / n m )
0
C~OT 0
400
800
1200
I
28
29
Fig. 4. Free dislocation density as a function of the interparticle distance which is defined by Eq. (3). The specimens were crept at 800°C and 177 MPa.
L/nm
Fig. 5. The stress available for dislocation generation and the Orowan stress as a function of the interparticle distance. meas ~p was derived from the measured dislocation densities according to Eq. (I), O 0 was calculated using Eq. (4).
From Eq. (4) together with Eq. (i) it follows that the stress dependence of the dislocation density is stronger in particle hardened materials. Indeed stress exponents larger than 2 have been found in particle hardened materials, Fig. i. Stress exponents equal to or smaller than 2 might have been caused by:
760
FREE
DISLOCATION
DENSITY
Vol.
(a)
changes in the particle structure which decrease o
(b)
strain rate or temperature dependence of ~
(c)
P very small O -values, which can be neglected compared to the applied stress. P
14,
No.
7
with decreasing stress P due to climb over particles
The suggestion that O may be lower than the Orowan stress (due to climb over particles) is supported by the observation that A-286 can be plastically deformed below the Orowan stress without any dramatic change in deformation behavior [14]. Moreover, it explains why a negative value for G~alc is found at lower stresses (Table i, #4) when the Orowan stress is used as an approximation for Gp . We intend to study the temperature and strain rate dependence of Gp in a future investlgation more in detail. For this study a dispersion hardened material will-be used to avoid additional effects of changes in the precipitate structure. Sua~aary The free dislocation density was measured in a y'-hardened stainless steel (A-286). The dislocation density is smaller in specimens which contain particles with a smaller interparticle distance provided the specimens were crept at equal stresses. The decrease of the dislocation density may be considered as supporting the view that particle hardened materials behave llke pure materials subjected to a smaller stress. Acknowledgement This research was the result of a collaboration between the respective research groups at Stanford University and the University of Erlangen. It was made possible by a grant to R. Singer from the Deutsche Forschungsgemeinschaft which the authors would llke to gratefully acknowledge. The contributions of Professor B. llschner of the University of Erlangen to this work and to the preparation of this manuscript have been especially welcome. The assistance of Dipl.-Ing. D. Gulden in connection with experimental aspects of this work is also appreciated. References [i] [2] [3] [4] [5] [6] [7] [8] [9] [i0] [ii] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
S. Takeuchi, A. S. Argon, J. Mater. Sci. ii, 1542 (1976). R. Lagneborg, Metal Scl. J. 3, 18 (1969). G. Knowles, Metal Sci. J. ii, 117 (1977). J . H . Hausselt and W. D. Nix, Acta. Met. 25, 595 (1977). A . H . Clauer and B. A. Wilcox, Metal Sol. J. ~, 86 (1967). G . J . Lloyd and J. W. Martin, to be published in Acta Mat. W. Blum and R. Singer, to be published in Z. Metallkde. Mechanical and Physical Properties of Austenitic Cr-Ni-Stainless Steels at Ambient Temperature, The Int. Nickel Co., New York, 1963. D.M.I.C. Technical Note, TD Nickel-Chron~lum, A Report on Currently Available Information and Data, 1967 . W. Koster, Z. Metallkde. 39, i (1948). U . F . Kocks, A. S. Argon and M. F. Ashby, Progr. in Mater. Sci. 19, i (1975), p. 118. R . W . Fawley in: C. T. Sims and W. C. Hagel (Eds), the Superalloys, John Wiley and Sons, New York, 1972. D. Gulden, Diplomarbelt, University of Erlangen (1979). D. Gulden, R. Singer and B. llschner, to be published. R . K . Ham and N. G. Sharpe, Phil. Mag. 6, 1193 (1961). L . M . Brown and R. K. Ham, in: A. Kelly and R. B. Nicholson (Eds), Strengthening Methods in Crystals, Applied Publishers Ltd., London, 1971. R. Singer and W. Blum, Z. Metallkde. 68, 328 (1977). V . K . Sikka, H. Nahm and J. Moteff, Mater. Sci. and Eng. 20, 55 (1975). S. Karashlma, T. likubo, T. Watanabe and H. Oikawa, Trans. JIM 12, 369 (1971). C.R. Barrett, W. D. Nix and O. D. Sherby, Trans. ASM 59, 3 (1966). W. Blum, A. ABsenger and R. Feilhauer, in: P. Haasen, V. Gerold and G. Kostorz (Eds), Strength of Metals and Alloys, Proc. ICSMA~, Pergamon Press, Toronto, 1979, p. 265. R . W . Lurid and W. D. Nix, Acta Met. 24, 469 (1976). B. llschner, Hochtemperaturplastizit~t, Springer, Berlin, 1973, p. 158.
MtiTAI,LUR(;ICA
V o l . 14, pp. 7 5 5 - 7 0 0 , 1980 Printed in the U.S.A.
Pergamon P r e s s I,td. All rights reserved.
THE INFLUENCE OF SECOND PHASE PARTICLES ON THE FREE DISLOCATION DENSITY DURING CREEP OF STAINLESS R. F. Singer*,
STEEL
W. Blum** and W. D. Nix***
*Brown Bovari Company,
Baden,
Switzerland
**Institut fur Werkstoffwissenschaften Universit~t Erlangen-N~rnberg ***Department of Materials Science and Engineering Stanford University, Stanford, California 94305
(Received April ( R e v i s e d May 9,
9, 1980) 1980)
It has been well established that during steady state creep of many pure metals and solid solutions the density of free dislocations p (dislocations not associated with subgrain boundaries) varies with the square of the stress ~ according to the relation 2 p = (a/G Gb) , (1) where G is the shear modulus, b is the Burgers vector and ~ is a constant almost equal to i [I]. Less is known about the dislocation density in particle hardened materials. Figure I shows a compilation of data taken from the literature. It seems that the dislocation density does vary with stress, but considerable deviations from Eq. (i) occur. Stress exponents larger than 2 are found. (The weak stress dependences in the dashed parts of the curves were attributed by the authors to changes in the deformation mechanisms). The constant a ranges from 0.3 to values as large as 2.4. The purpose of the work described in this paper was to study the dependence of the free steady state dislocation density on the interparticle distance. To separate the influence of stress and particles, the specimens were crept at the same stress. The material used in this study was the y' (Ni3(AI,Ti)) - hardened stainless steel A-286. This alloy is an "iron-base superalloy" which is used especially for turbine wheels [12]. Experimental The chemical composition as follows (in wt%): C 0.08
Cr 13.5-16
Ni 24-27
Procedure
of the alloy investigated was certified by the manufacturer Ti 1.9-2.3
AI 0.35
Mo 1.0-1.5
Mn 1-2
to be
Fe Balance
The material was received in the recrystallized condition. The grains were equiaxed and 70 + 5 ~m in diameter [13]. The age-hardening treatment, given by the manufacturer, involved solution heat treatment at 980°C for i h, followed by aging at 725°C for 8 h. The creep tests and the preparation of TEM foils were carried out as part of a more extensive study of the deformation behavior and the stability of y' particles during creep, conducted at the University of Erlangen [14]. Briefly, cylindrical creep specimens with a gage length of 30 mm and a diameter of 6 m m w e r e prepared by spark cutting and crept in tension at constant stress. In order to prevent changes of the dislocation structure, the load was maintained during cooling. Thin foils were prepared according to standard techniques. The electro-polishing was done in a Struers Tenupol twin jet electropolisher using a i0:i mixture of acetic acid and perchlorid acid at 8°C and 35V. The TEM study was carried out on a Philips EM 400 at 120 kV. The dislocation
density was measured by counting the number of intersections
755 0036-9748/80/070755-06502.00/0 Copyright (c) 1 9 8 0 P e r g a m o n Press
Ltd.
which dis-
7S6
FREE D I S L O C A T I O N
15 6 ~52 ~4E
DENSITY
20%Cr-35%Ni Stoinless Steel.single phose,Lognebocg 20%Cr-35%Ni Stainless Steel, ),,-port~cles, Log~eborq 20%Cr-25%Ni-Nb StainlessSteeI,NbCNporficles,Kno~.les 20%Cr-25%Ni-Nb Stoin[essSteel, tronsktionporticles, Kno*les •% TD-Ni, HOUSSelt ond Nix ,% TD-Ni, Cloue¢ ond Wilcox . crystoll O Cu -AI205 , OOr = 18.SMPo,Lloyd and Mortin] single E] Cu-AI203, Oor =IZgMPO'LIOyd °nd Martini> . ~ ~]3 AI-5%Cu. AI2Cu*p°rticle$' Blum o n a ~
Vol.
14, No.
7
(9 A <> {-]
3.0
I
I
I
I
I
i
0 annealed • crept A crept
2.5
and annealed
u,~4
Ec 2.0 Q, 14.0
,.5 ~., 136
c~ 0
1.0 -__TO_
d
BEFORE
13.2
286 800°C
A-
Q5 L2B I
0 0
124
12o
-~
-~ ~ -3:2
-31o -2'8
0.5
I
1.0
I
,.5
log
-2!6 -2 io -212 -2o
TEST
I
I
z.o 2.5
I
3.0 3.5
(t/h)
log (O/G) Fig. i. Relation between steady state dislocation density and modulus compensated stress for particle hardened metals. The data were taken from the work of Lagneborg [2], Knowles [3], Hausselt and Nix [4], Clauer and Wilcox [5], Lloyd and Martin [6], and Blum and Singer [7]. For the shear modulus we used the data given in references [8-11].
Fig. 2. Mean diameter of the y' particles in A-286 as a function of the time of annealing or creep at 800°C [14]. The creep testing was done at 177 MPa.
locations make with the surface of the loll [15]. P = 2 N/A ,
The dislocation density is then given by (2)
where N is the number of intersections with both surfaces whose total area is A. The foils were tilted to obtain several operating reflections and to make all dislocations visible. The effect of tilting on the surface area A was taken into account. No dlslocatlonmotlon occurred even at the highest electron currents and in the thinnest parts of the foil. This indicates that the dislocations are immobile due to particle and solid solution hardening and that changes of the dislocation density during toll preparation or handling are unlikely to occur. In order to characterize the experimental error the 95% confidence limits are given in the paper. The interparticle distance in A-286 increases during creep due to Ostwald ripening. This result which has been reported and discussed elsewhere [14], is shown in Fig. 2. In order to obtain creep specimens with different interpartlcle distances, the creep tests were interrupted after different creep times or specimens were preheated for different times. The interparticle distance is specialized in this paper to mean the square lattice spacing L [16] e = (~/f)0"5-2)
(2/3) 0.5 r
(3)
where f is the particle volume fraction and r is the particle radius. From the number of particles per unit volume and the mean particle size we determined the v o l ~ e fraction to be 0.7%. The foil thickness determination which is necessary for the measurement of the number
Vol.
14,
No.
7
FREE
DISLOCATION
DENSITY
757
of particles per unit volume was done by deliberately tilting foils containing some n (Ni3Ti)-equilibrium particles. The tilting axis was the intersection line between the {Iii} habit plane of the plate-like ~ precipitates and the foil surface. Results and Discussion Figure 3 shows the dislocation and particle structure in specimens crept at 117 MPa and 800°C. The y' particles are coarser in the specimen which is shown in Fig. 3b because it was preheated and crept for a longer time. Micrographs like those in Fig. 3 were used for the measurement of the free dislocation density. The results are listed in Table i and are plotted as a function of the interparticle distance in Fig. 4. The data point marked with an arrow in Fig. 4 was provided by a creep specimen deformed at 121 MPa instead of 177 MPa. This point, therefore, gives a lower limit for the dislocation density at 177 MPa. The free dislocation density found by Lagneborg [2] in a similar material which did not contain particles is indicated by a dashed line. It is evident from Fig. 4 that the free dislocation density decreases with decreasing interparticle distance. Fig. 3b shows that subgrains are formed during creep of A-286. This represents an apparent contradiction to a result obtained by Lagneborg [2] who found no tendency for subgrain formation in a similar material. He studied the dislocation structure after a creep strain of 12.5% or less. However, rather large strains are necessary to develop a homogeneous subgrain structure. We found that subgrains were not present in some parts of the samples after 18% elongation. The subgrain structure shown in Fig. 3b was produced by a creep strain of more than 30%. Because of the inhomogeneity of subgrain formation in A-286 some measurements of the free dislocation density had to be made in subgrain free regions. The corresponding data points are marked in Fig. 4. The question arises whether these values are representative of the steady state. This alloy shows normal transient creep [14]* , and subgrain formation. The variation of the free dislocation density with creep strain for materials with this behavior has been studied frequently: stainless steel [18], alpha-iron [19], iron-silicon [20], aluminum [21]. The free dislocation density reaches the steady state value or an even somewhat higher value after very small strains (typically smaller than 1%) and remains constant or decreases, respectively, during primary creep. This means that the dislocation densities measured in subgrain free regions are equal to, or somewhat higher, than the steady state values. Our view is supported by two experimental observations: (a) The dislocation density in a specimen deformed for 0.7% at 121 MPa was found to be higher than that in a specimen deformed for 3.1% at 177 MPa, see Fig. 4 and Table I. This indicates that the steady state dislocation density, or an even somewhat higher value, is already reached after about 0.7% strain. (b) The steady state dislocation density was measured in subgrain free regions and in regions containing subgrains in the same specimen (Fig. 4 at log L = 2.54, Table i, #2). The dislocation density is equal within the limits of experimental error. The result that particles lead to a decrease of the free dislocation density agrees with the observation made by Lagneborg [2] and Blum and Singer [7] (see Fig. i). The different absolute values for the dislocation density in TD-nickel, Fig. i, can also be regarded as a confirmation of our result, since the creep data suggest that the material studied by Hausselt and Nix [4] was stronger than that studied by Clauer and Wilcox [5].
The creep rate reaches a minimum value after less than 1% elongation and increases afterwards. The minimum is due to the balancing effects of strain hardening and softening due to Ostwald ripening and does not indicate that the steady state dislocation structure is formed (compare the discussion in reference [17]) .
758
FREE
DISLOCATION
DENSITY
Vol.
14,
No.
7
TABLE 1 Results for Transmission Electron Microscopy of A-286 Crept at 800°C
No. oIMPa
r/nm
L/nm
9/m
Subgrains
OOr/MPa
o01MPa
o maas P
/MPa
i
177
34.5
43.0
673
(i.i + 0.5) 1014
yes
48
129
129
2
177
18.0
21.8
342
(4.4 + 2.2) 1013
yes
94
83
81
177
18.0
21.8
342
(3.9 + i.i) 1013
no
94
83
75
3
177
3.1
14.3
244
(1.2 + 0.9) 1013
no
144
33
41
4
121
0.7
16.4
257
(1.3 + 0.8) 1013
no
125
-4
43
It is a common idea that the creep characteristics of particle hardened materials are essentially those of pure materials subjected to a smaller stress, e.g., [7,22,23]. A natural consequence of this idea is the expectation of smaller dislocation densities in the particle hardened material deformed at the same stress as a pure material. In particle hardened materials a smaller stress is available for the generation of dislocations, i.e., the applied stress G in Eq. (i) is replaced by o
=
O where o
~
-
c
(4)
P
describes the influence of particles. P
In solid solutions the contribution from foreign atoms has to be considered additionally, resulting in a further decrease of the stress available for the generation of dislocations. Both the contributions of particles and foreign atoms are expected to be strain rate and temperature dependent. The quantity O^ , calculated according to Eq. (4), is plotted in Fig. 5 as a function of the interparticle d~stance. We assumed that the contribution of foreign atoms can be neglected and that the contribution of particles is independent of the strain rate. This is almost certainly an oversimplification. However, it permits us to determine whether the experimental data are in accordance with the view outlined above. We assumed further that the particles are bypassed by the dislocations and that ~ is equal to the Orowan stress, which is to a first approximation given by [16] P GOr/3 = 0.8 Gb/L
(5)
where L is the interparticle distance as defined by Eq. (3). The assumption that the y'particles are bypassed rather than sheared seems to be valid since the self stress of an Orowan loop is not sufficient to shear the particles in the present case* . Moreover, we did not find any indication ~or cutting in the TEM investigation, o meas, calculated from the measured dislocation densities according to Eq. (i) using ~ = 0.~, is also plotted in Fig. 5. The l e p a s _ values are in excellent agreement with the op values calculated according to Eq. 4 2 O5 * For shearing to occur r must be smaller than2(Gb /2 y (2/3) " ) , where y is the stacking fault energy [16]. A value of y = 0.285 Jm(Raynor and Silcock for Ti:AI = 6:1, cited in [16]) gives a value of r = 7.5 nm. The particle radii in A-286 found in this study (Table i) are substantially larger than 7.5 nm.
Vol.
14,
No.
7
FREE DISLOCATION Dt!NSfTY
759
A ,I, P
Fig.
Fig. 3.
3a
Fig. 3b
Dislocation and particle structure in A-286 crept at 800°C and 177MPa. Fig. 3a. Crept 3,1% for 12 h. Fig. 3b. Preheated 625 h and crept 34.5% for 36 h.
I
I
I
[
i
14.4
200
. .~A6. E"~.R -oE '/ ~
P IN SINGLEPHASESTAINLESS STEEL,
I
. . . . . . .
14.(:
I
_
I
I
APPLIED
I
STRESS
160 N
13.6 o 120
'E
=O9,G Kb
cL 13.2 b
8c
0
--
128
12.4
J.J-
177 MPo
/ _.L
12.0 2.3
4o
800°C [] NO SUBGRAINS O SUBGRAINS 1
2.4
I
i
I
2.5 2.6 2.7 log ( L / n m )
0
C~OT 0
400
800
1200
I
28
29
Fig. 4. Free dislocation density as a function of the interparticle distance which is defined by Eq. (3). The specimens were crept at 800°C and 177 MPa.
L/nm
Fig. 5. The stress available for dislocation generation and the Orowan stress as a function of the interparticle distance. meas ~p was derived from the measured dislocation densities according to Eq. (I), O 0 was calculated using Eq. (4).
From Eq. (4) together with Eq. (i) it follows that the stress dependence of the dislocation density is stronger in particle hardened materials. Indeed stress exponents larger than 2 have been found in particle hardened materials, Fig. i. Stress exponents equal to or smaller than 2 might have been caused by:
760
FREE
DISLOCATION
DENSITY
Vol.
(a)
changes in the particle structure which decrease o
(b)
strain rate or temperature dependence of ~
(c)
P very small O -values, which can be neglected compared to the applied stress. P
14,
No.
7
with decreasing stress P due to climb over particles
The suggestion that O may be lower than the Orowan stress (due to climb over particles) is supported by the observation that A-286 can be plastically deformed below the Orowan stress without any dramatic change in deformation behavior [14]. Moreover, it explains why a negative value for G~alc is found at lower stresses (Table i, #4) when the Orowan stress is used as an approximation for Gp . We intend to study the temperature and strain rate dependence of Gp in a future investlgation more in detail. For this study a dispersion hardened material will-be used to avoid additional effects of changes in the precipitate structure. Sua~aary The free dislocation density was measured in a y'-hardened stainless steel (A-286). The dislocation density is smaller in specimens which contain particles with a smaller interparticle distance provided the specimens were crept at equal stresses. The decrease of the dislocation density may be considered as supporting the view that particle hardened materials behave llke pure materials subjected to a smaller stress. Acknowledgement This research was the result of a collaboration between the respective research groups at Stanford University and the University of Erlangen. It was made possible by a grant to R. Singer from the Deutsche Forschungsgemeinschaft which the authors would llke to gratefully acknowledge. The contributions of Professor B. llschner of the University of Erlangen to this work and to the preparation of this manuscript have been especially welcome. The assistance of Dipl.-Ing. D. Gulden in connection with experimental aspects of this work is also appreciated. References [i] [2] [3] [4] [5] [6] [7] [8] [9] [i0] [ii] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
S. Takeuchi, A. S. Argon, J. Mater. Sci. ii, 1542 (1976). R. Lagneborg, Metal Scl. J. 3, 18 (1969). G. Knowles, Metal Sci. J. ii, 117 (1977). J . H . Hausselt and W. D. Nix, Acta. Met. 25, 595 (1977). A . H . Clauer and B. A. Wilcox, Metal Sol. J. ~, 86 (1967). G . J . Lloyd and J. W. Martin, to be published in Acta Mat. W. Blum and R. Singer, to be published in Z. Metallkde. Mechanical and Physical Properties of Austenitic Cr-Ni-Stainless Steels at Ambient Temperature, The Int. Nickel Co., New York, 1963. D.M.I.C. Technical Note, TD Nickel-Chron~lum, A Report on Currently Available Information and Data, 1967 . W. Koster, Z. Metallkde. 39, i (1948). U . F . Kocks, A. S. Argon and M. F. Ashby, Progr. in Mater. Sci. 19, i (1975), p. 118. R . W . Fawley in: C. T. Sims and W. C. Hagel (Eds), the Superalloys, John Wiley and Sons, New York, 1972. D. Gulden, Diplomarbelt, University of Erlangen (1979). D. Gulden, R. Singer and B. llschner, to be published. R . K . Ham and N. G. Sharpe, Phil. Mag. 6, 1193 (1961). L . M . Brown and R. K. Ham, in: A. Kelly and R. B. Nicholson (Eds), Strengthening Methods in Crystals, Applied Publishers Ltd., London, 1971. R. Singer and W. Blum, Z. Metallkde. 68, 328 (1977). V . K . Sikka, H. Nahm and J. Moteff, Mater. Sci. and Eng. 20, 55 (1975). S. Karashlma, T. likubo, T. Watanabe and H. Oikawa, Trans. JIM 12, 369 (1971). C.R. Barrett, W. D. Nix and O. D. Sherby, Trans. ASM 59, 3 (1966). W. Blum, A. ABsenger and R. Feilhauer, in: P. Haasen, V. Gerold and G. Kostorz (Eds), Strength of Metals and Alloys, Proc. ICSMA~, Pergamon Press, Toronto, 1979, p. 265. R . W . Lurid and W. D. Nix, Acta Met. 24, 469 (1976). B. llschner, Hochtemperaturplastizit~t, Springer, Berlin, 1973, p. 158.