- Email: [email protected]
26 Al2O3f composite
Materials
Science and Engineering
A201 (1995) 205-210
An evaluation of steady state creep mechanism in an Al- Mg/26 Al,O,f composite R.S. Mishra”, “Department
A.B. Pandeyb,
A.K. Mukherjee”
of Chemical Engineering and Materials Science, University bDefence Metallurgical Research Laboratory, Kanehanbagh, Received
23 June
1994; in revised
of California, Davis, CA 95616, USA Hyderabad
form 3 October
500258, India
1994
Abstract composite shows the substructure invariant creep mechanism to An analysis of the steady state creep data of Al-SMg/Al,O,, be operative. This is consistent with the dislocation creep mechanism map and a previous evaluation of steady state creep mechanism in 6061 Al/Sic composites. A temperature dependent threshold stress exists for the steady state creep mechanism. Keywords:
Steady state creep; Temperature
dependence;
6061 Al/Sic composites
1. Introduction
(2)
The steady state creep mechanism in aluminum alloy matrix composite has received considerable interest in recent years and several experimental investigations have been reported [ 1- 191. The interpretation of the steady state creep operating mechanism is a matter of
some controversy at present. Dragone and Nix [14] have recently reported the steady state creep behavior of Al-5 wt% Mg/26 vol.% A1203f composite (f denotes fibre). They expressed their results by a creep constitutive law 14
i=
1.63 x 103’s-’
0 ( a
E
exp
-
201 kJ mol RT
’
(1)
where i is the creep rate, 0 the applied stress, E the Youngs modulus, R the gas constant and T the test temperature. It can be noted that the stress exponent value of 14 and an activation energy value of 201 kJ molt ’ are much higher than predicted by any phenomenological or theoretical models for steady state creep. It is well accepted that the presence of a threshold stress can lead to significantly higher apparent stress exponent and activation energy values and in such a case the creep equation is written as, 0921-5093/95/$09.50 SSDI
0 1995 ~
0921-5093(94)09755-O
Elsevier
Science
S.A. All rights
reserved
where D is the self diffusion coefficient, G the shear modulus, b the Burgers vector, k the Boltzmann constant, g,, the threshold stress, n the true stress exponent, and A a dimensionless constant. For any analysis involving go a value of n has to be assumed. Mishra and Pandey [20] found that the data for 6061 Al matrix composites can be best explained by a substructure invariant model [21], for which a true stress exponent of 8 is expected along with an activation energy similar to that for lattice self diffusion. The ‘dislocation creep mechanism map’ developed by Mishra [22] also predicts the dominance of substructure invariant creep mechanism in solid solution aluminum matrix composites. Recently, Cadek et al. [23] have reanalyzed the data of Al-Mg/26 A&O,, composite [14]. They have concluded that the true stress exponent for the composite is close to 5 and the steady state creep is lattice diffusion controlled. However, they do not indicate or discuss the detailed micromechanism of steady state creep deformation and the influence of discontinuous reinforcement on the creep kinetics. One of the problems in selecting a proper stress exponent has been the visual
206
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
of looking at the plots of .?‘I”vs. cr and picking up the best n value. At times, this graphical method does not give a clear indication, particularly when the plotting is not done using a sensitive scale. Another important aspect which has not received due consideration is the ‘steady state creep kinetics’. The purpose of this paper is to evaluate the operating steady state creep mechanism in the Al-Mg/26 A&O,, composite, data for which was reported by Dragone and Nix [14] and reanalyzed by Cadek et al. [23]. It is suggested that if the graphical method of <‘I” vs. 0 plot is unable to yield a unique true stress exponent, the statistical analysis should be resorted to. The importance of the ‘steady state creep kinetics’ is also pointed out. It should become clear from the following sections that this can be a useful indication for monitoring change in the operating creep mechanism. way
. 0.08 . 0.07. e '; v)
0.06 -
E? ‘,
0.05 -
B
Dragone and NIX (1992)
(4
-
AI-MS 126% AI,O, Composcte o
473 K
o
573K 673 K
q
0 0
004-
!!
Stress (MPa) 0.25
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,
@I 0.20 -
2. Analysis of the Al-Mg/26
Al,O,, composite data
If Eq. (2) is considered as an appropriate representation of the creep data, it is imperative that the true stress exponent be determined. Normally, the graphical method of plotting G1/, vs. 0 on a linear scale suffices the purpose. But it has been recently claimed [23,24] that for certain data sets the choice n = 5 or 8 can be equally satisfactory. If indeed this is the case, we suggest that (a) the graphs have to be plotted on sensitive scales (maximum possible enhancement) and (b) the coefficient of linear regression should be considered (and this, of course, would remove any manual, i.e., visual, bias). Fig. l(a)-(c) shows ;‘I, vs. g plots with n values of 3, 5 and 8. The values of the square of correlation coefficient for linear regression and calculated threshold stress are summarized in Table 1. It should be noted that the correlation coefficient for linear regression is best for PZ= 8 at all the temperatures. This contradicts the recent analysis of Cadek et al. [23], who reported that n = 5 is best. It is clear, however, from both Fig. 1 and Table 1 that n = 8 is the best choice for this data set. To strengthen this observation further, the variation of lattice diffusivity compensated strain rate, i/D, with normalized effective stress, (a - a,)/& is shown in Fig. 2 (where crOvalues calculated with n = 5 and IZ= 8 were used for Fig. 2(a) and Fig. 2(b), respectively). A simple comparison indicates that IZ= 8 is more appropriate for the data set under consideration. A closer examination reveals not only that the choice of n = 5 provides a poor correlation, but also that in fact the datum points from different temperatures have not truly merged. For example, the 473 K and 673 K data at equivalent effective stress of z 1 x 10 -’ - 6 x lop4 are quite far apart. Also, there is considerable curvature in the plots when n = 5 is used. These obser-
0
50
100
150
200
250
Stress (MPa) o.5-.,,,...,.,...,...,.,.,,......,..,.....,,........,
(4 0.4 -
0 A
0 0
A
A m A A
0 0
0
0
A
a ,a”
0 0
A
001 0
50
100
150
200
250
Stress (MPa) Fig. 1. The plots of 6’:” vs. applied stress on linear scales to find the true stress exponent and threshold stress with (a) n = 3, (b) n = 5 and (c) n=8.
vations further reinforce the notion that IZ= 8 is the proper choice. The threshold stress values are plotted against l/T in Fig. 3. It shows that the threshold stress is temperature dependent.
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
Table 1 Results of linear regression to obtain the true stress exponent Temp.
n=3
n=8
i-l=5
6)
413 573 673
00
r’
g0
rz
60
r2
112.6 52.3 34.3
0.746 0.850 0.794
91.2 43.6 29.2
0.871 0.918 0.905
55.8 30.0 21.2
0.931 0.938 0.952
3. Discusson
The present findings are in quantitative agreement with the phenomenological model of Sherby et al. [21] which predicts
where R is the subgrain size and A ’ is a dimensionless constant. This is different from the unreinforced Al-5 Mg alloy which shows n = 3, typical of solid solution type behavior [14]. It is clear from the data on Al-Mg alloy of Dragone and Nix [14] that the alloy behaves like a solid solution type at all the stresses investigated. Fig. 2(b) shows the data of Al-Mg as well. It should be noted that at equivalent stress levels (up to (a - 0,/E) -= 7 x 10p4) the behavior of composite is different in two ways: (a) the stress exponent is 8 instead of 3 and (b) the creep rates are much lower. Mishra [22] has pointed out that the presence of second phase particles can stabilize subgrains in solid solution type matrix. This is likely to change the creep behavior from solid solution type to constant substructure creep. Fig. 4 shows a ‘dislocation creep mechanism map’. The data range of Al-Mg/26 Al,O,, is shown in the map. Also depicted is the data range for some other data sets analyzed earlier by Mishra and Pandey [20]. In the absence of whisker dimensions, the interparticle spacing for Nieh’s data [2] has been taken as 5 pm as mentioned by Nieh [2] as particle free distance. It can be noted that the data analysis is consistent with the dislocation creep mechanism map, and the experimental The data lie in the constant substructure regime. reason for the differences in the creep behavior of unreinforced Al-Mg alloy and reinforced composite is not difficult to understand if the microstructural features are taken into consideration. The average interparticle spacing can be given by [25]
4=
fdP[(&F-(J)]
(4)
where V’ris the volume fraction of reinforcement phase and d, the average size. Taking the typical values for Al-Mg/Al,O, composite, d, = 7.4 pm (calculated using dp = (lf x df)‘.‘3, where If and df are average length and diameter of the fibre) and Vr = 0.26, we obtain R, = 4.5
201
,um. In the presence of particles, the subgrains can be stabilized. Weckert and Blum [26] have reported the variation of subgrain size with stress in an Al-5 wt.% Mg alloy. Using the correlation, at the maximum effective stress used by Dragone and Nix [14], (0 - a,)/E g 2.2 x 10 - 3, the stress-dependent subgrain size would be 8.3 pm. This is higher than the interparticle spacing. Therefore, the subgrain size is likely to be independent of the applied stress. Also, the reported average grain size is 15.7 pm [14]. The implication is that below the normalized effective stress of 1 x lo- 3, the subgrain size cannot change because of the grain size. From these microstructural considerations it is unlikely that either the stress-dependent substructure creep (leading n = 5) or the solid solution creep mechanisms (with n = 3) would be dominant in the Al-Mg/26 A&O,, composite. Another way to strengthen this conclusion is to look at the kinetics of each mechanism. The data for the unreinforced Al-Mg alloy can be represented by DGb rs 3.0 _ i = 7.2 kT 0 E
(5)
The data for Al-Mg alloy are shown in Fig. 5. The AI-Mg/Al,O, composite results follow Eq. (3) with A’ = 4.9 x 104. A comparison with the earlier data of Pandey et al. [13] on Al-SIC composites shows that the dimensionless constant for Al-Mg/Al,O,, composite, 4.9 x 104, is almost three orders of magnitude lower than the dimensionless constant for Al-SIC composites, 2.5 x lo7 [13], and it is more than four orders of magnitude lower than the dimensionless constant for pure aluminum, 1.5 x lo9 [21]. Fig. 5 also depicts the expected creep behavior of Al-Sic composites and pure aluminum for a constant subgrain size of 4.5 pm. It can be noted that the creep kinetics is slower for the constant substructure creep of Al-Mg/Al,O,,. Therefore, it is likely that the substructure strengthening would be dominant. The result of the present analysis shows that the presence of Mg in Al-Mg/Al,O, composites lowers the dimensionless constant for constant substructure creep (Eq. 3). This is the ‘kinetics aspect’ of creep. The present analysis is consistent with the recent investigation of the influence of Mg addition on the creep behavior of Al/Sic, composite [27]. Pandey et al. [27] found that the addition of 4 wt.% Mg in Al/Sic, composite makes the creep kinetics significantly slower while the substructure invariant creep mechanism remains dominant. These results help to emphasize that in most of the composites the microstructure is likely to remain constant during creep and because of the slower kinetics, the substructure invariant creep mechanism would dominate. The threshold stress values shown in Fig. 3 indicate that (a) it is temperature dependent, and (b) it is apparently higher for composites with whiskers than particulates. The temperature dependence of the
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
208 IO" 10'6 10'5 IO“'
, , ,*,,,,,, , ,,,.,l,I , l,.l,,,I ,,,1 Dragone and Nix (1992) AI-Mg / 26 Al,O, Composite o. calculated “sang n=5 o
573K
A
673K
0
IO" ,010
10'4 10'3
0
0
0
i
n
q
'
108
IO"
s
10'0
n
qA A A
,TLj 10s
h
7
%,,
,
I ,,.,,,,
,
,,,,, @I
573K
A
673K
0
0” 0
Al-5 wt.% Mg -
6061 AI/SIC composites (Mishra and Pandey, 1990)
,’
1
I
I
109
2
I
10s
A
d
IO'
,,,.,
473K
q
10'2
O&
,
o0calculated using n=6 0
0
10'2 -
0
#,.,
AI-Mg / 26 A1203 Composite
10'5
473K
q
r ,...
Dragone and Nix (1992)
IO'@
0
10'3
5
10"
(4
IO' A
io-‘F
104
1o-5
10-s
104
IO-IF
10-Z
10-s
3 ’
-~*---’
10-S
’
(o-o,)/E
‘11*11d
’
104
1’111*1’
10-a
’
’
--uJ 10-Z
(o-o&/E
Fig. 2. The variation of diffusivity compensated strain rate with normalized effective stress when the threshold stress is calculated using (a) n = 5 and (b) n = 8. It isclear that the choice of n = 8 results in a much better correlation. For the 6061 Al/SC composites n = 8 was used to determine the aa’values [20].
threshold stress in Al-Mg/Al,O,, is consistent with the general trend observed in 6061 Al-SC composites [20,24]. The observation of Pandey et al. [13] about the temperature-independent threshold stress does suffer from some uncertainty as there is considerable scatter in the 723 K data. It is possible that because of the higher scatter at higher temperatures, the conclusion about temperature-independent threshold stress might be erroneous. Based on the general trend [20,23,24], it is more likely that the true nature of the threshold stress is temperature-dependent. The temperature dependence of the threshold stress for Al-Mg/A1,03, can be written as
2 =4.5 x 10-5exp The temperature dependence of z 11 kJ mol - ’ is similar to the temperature dependence of the threshold stress for some other high temperature deformation mechanisms such as diffusional creep [28], dislocationparticle interaction controlled creep [29] and superplasticity [30,31]. Mishra et al. [28] have suggested that the temperature dependence of the threshold stress for diffusional creep could be due to jog nucleation energy required for vacancy formation. Mohamed [30] has proposed a model based on solute segregation for the
1o-2 .
AI-Mg126 AI,O, (Dragone and NIX 1990)
.
6061 A11174 Sic, (Nieh 1994)
A
6061 Al/26 5 SE, (Nieh 1964)
v
6061 All15 SIC, (Monmoto et al 1966)
105r-L
. 104
_.-,...A . ..R.:.-----::::::-::::
:,
7
w
10-3
‘0
e
b
103
:
*
x
--.
1
islocation-Particle interaction
102 ?
10-l
AI-Mg,26 Al,O,, (Dragone and NIX 1990)
v 1
1.5
,
I
I
I
,
I
I
1.8
I
I
2.1
&
I
I
6061 Al/15 SIC, (Monmoto et al 1989)
&
2.4
l/T (xl 03) (K-l) Fig. 3. The variation of normalized threshold stress with the inverse of test temperature. Note the temperature dependence of co/E as well as the influence of reinforcement shape on the magnitude of threshold stress.
IO' : 102
103
104
105
E/(o-0,) Fig. 4. A dislocation creep mechanism map for Al-Mg matrix. The experimental range lies in the constant substructure regime and the results of the present analysis are consistent with the map.
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
209
4. Conclusions AI/SIC composites (Pandey et al, 1992) AI-MglAI,O,
com~os!te (Dragone and NIX. 1992)
(1) The steady state creep data of Al-Mg/Al,O,, composites follow the substructure invariant creep mechanism. (2) A temperature dependent threshold stress exists. The origin of the threshold stress is likely to be related to the stress independent load transfer mechanism.
References
111D. Webster, Metal/. Trans. A, 13 (1982) I51 1. 121T.G. Nieh, Metall. Trans. A, 15 (1984) 139.
[31 V.C. Nardone and J.R. Strife, Metali. Trans. A, 18 (1987) 109. [41 H. Lilholt and M. Taya, in F.L. Mathews, N.C.R. Buskell, J.M. Hodkinson and J. Morton (eds.), Proc. ICCM and ECCM VI, 2 (1987) 234.
Fig. 5. The variation of diffusivity compensated strain rate with normalized effective stress. The lines for pure Al, Al/Sic composites and AI-Mg/AI,O, composite is for a constant subgrain size of 4.5 pm. Note the change in creep kinetics.
threshold stress for superplasticity. The magnitude of the threshold stress for creep of composite, however, is much higher than that for diffusional creep and superplasticity. So, at present the temperature dependence of the threshold stress for creep of composite cannot be explained. The magnitude of the threshold stress appears to depend on the shape of reinforcement (Fig. 3). Pandey et al. [13] showed that the magnitude of the threshold stress also depends on the volume fraction of the reinforcement phase. Because of the rigid nature of the reinforcement, load transfer is likely to occur, which will reduce the stress available for the creep of matrix. Kelly and Street [32] have developed a theory for the steady state creep in discontinuous fibre composites. For the case of rigid fibres with perfect bond, the average stress on the fibre is [32] / , \ (n+ I ),‘?I (7) where
and grn is the matrix stress. It should be noted that the load transfer to the rigid fibres is proportional to the stress on the matrix. It follows that if cr,,= Ba (where B is a constant), the stress exponent would not change [13,32]. However, the apparent experimental stress exponent (12.2-15.5) is much higher than the true stress exponent of 8. Therefore, if the load transfer is the origin of the threshold stress, it has to be applied stress independently. A model based on the applied stress independent load transfer mechanism is required to explain the origin of the threshold stress for steady state creep in Al-matrix composites.
[51 T.G. Nieh, K. Xia and T.G. Langdon, J. Eng. Mater. Tech., 110 (1988) 77.
bl T. Morimoto, T. Yamaoka, H. Lilholt and M. Taya, J. Eng. Mater. Tech., 110 (1988) 70.
[71 S. Pickard and B. Derby, in P. Lamica and A. Massiah (eds.), Third Eur. Conf. Composites Materials, France, 1989, p. 199. VI K. Xia, T.G. Nieh, J. Wadsworth and T.G. Langdon, in P.K. Liaw and M.N. Gungore (eds.), Fundamental Relationships Between Microstructure and Mechanical Properties of Metal Matrix Composites, TMS, Warrendale, PA, 1990, p. 543. [91 A.B. Pandey, R.S. Mishra and Y.R. Mahajan, Scripta Metall. Mater., 24 (1990) 1565. UOI K.T. Park, E.J. Lavernia and F.A. Mohamed, Acta Metall. Mater., 38 (1990) 2147. IllI F.A. Mohamed, K.T. Park and E.J. Lavernia. Mater. Sci. Eng. A, 150 (1992) 21. [I21 R.B. Bhagat and M.B. House, Mater. Sci. Eng. A., 144 (1991)
319. [I31 A.B. Pandey, R.S. Mishra and Y.R. Mahajan,
Acta Metall.
Mater., 40 (1992) 2045.
1141T.L. Dragone and W.D. Nix, Acta Metall. Mater., 40 (1992) 2781.
1151G. Gonzalez-Doncel
and O.D. Sherby, Acta Metall. Mater., 41
(1993) 2797.
[I61 P.E. Krdjewki, J.E. Allison and J.W. Jones, Mefall. Tram A., 24 (1993) 2731.
[I71 A.B. Pandey, R.S. Mishra and Y.R. Mahajan, Scripfa Metall. Mater., 29 (1993) 1199.
[I81 J. Cadek, V. Sustek and M. Pahutova, Mater. Sci. Eng. A, 174 (1994) 174. 1191A.B. Pandey, R.S. Mishra and Y.R. Mahajan, Mater. Sci. Eng. A, in press. PO1 R.S. Mishra and A.B. Pandey, Metall. Trans. A, 21 (1990) 2089.
L-211O.D. Sherby, R.H. Klundt and A.K. Miller, Metall. Trans. A. 8A (1977) 843.
PI R.S. Mishra, Scripta Metail. Mater., 26 (1992) 309. ~231J. Cadek, V. Sustek and M. Pahutova, Mater. Sci. Eng., Al 74 (1994) 141.
~241F.A. Mohamed, K.T. Park and E.J. Lavernia, Mater. Sci. Eng., AI50 (1992) 21.
~251G. LeRoy, J.D. Embury, G. Edward and M.F. Ashby, Acta Metal/., 29 (1981) 1509.
WI E. Weckert and W. Blum, in H.J. McQueen, J.P. Bailon, J. I. Dickson, J.J. Jonas and M.G. Akben (eds.), Proc. 7th Int. Conf on the Strength of Metals and Alloys, Pergamon Press, Oxford, 1985, p. 773.
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
210
[27] A.B. Pandey, R.S. Mishra and Y.R. Mahajan, unpublished work. [28] R.S. Mishra, H. Jones and G.W. Greenwood, Philos. Msg., 60 (1989) 581. [29] R.S. Mishra, A.G. Paradkar and K.N. Rao. Acta MetaN. Mater., 41 (1993) 2243.
[30] F.A. Mohamed, J. Mater. Sci., 18 (1983) 582. [31] R.S. Mishra, T.R. Bieler and A.K. Mukherjee, Acta Metall. Mater., in press. [32] A. Kelly and K.N. Street. Proc. R. Sot. London A., 328 (1972) 283.
Science and Engineering
A201 (1995) 205-210
An evaluation of steady state creep mechanism in an Al- Mg/26 Al,O,f composite R.S. Mishra”, “Department
A.B. Pandeyb,
A.K. Mukherjee”
of Chemical Engineering and Materials Science, University bDefence Metallurgical Research Laboratory, Kanehanbagh, Received
23 June
1994; in revised
of California, Davis, CA 95616, USA Hyderabad
form 3 October
500258, India
1994
Abstract composite shows the substructure invariant creep mechanism to An analysis of the steady state creep data of Al-SMg/Al,O,, be operative. This is consistent with the dislocation creep mechanism map and a previous evaluation of steady state creep mechanism in 6061 Al/Sic composites. A temperature dependent threshold stress exists for the steady state creep mechanism. Keywords:
Steady state creep; Temperature
dependence;
6061 Al/Sic composites
1. Introduction
(2)
The steady state creep mechanism in aluminum alloy matrix composite has received considerable interest in recent years and several experimental investigations have been reported [ 1- 191. The interpretation of the steady state creep operating mechanism is a matter of
some controversy at present. Dragone and Nix [14] have recently reported the steady state creep behavior of Al-5 wt% Mg/26 vol.% A1203f composite (f denotes fibre). They expressed their results by a creep constitutive law 14
i=
1.63 x 103’s-’
0 ( a
E
exp
-
201 kJ mol RT
’
(1)
where i is the creep rate, 0 the applied stress, E the Youngs modulus, R the gas constant and T the test temperature. It can be noted that the stress exponent value of 14 and an activation energy value of 201 kJ molt ’ are much higher than predicted by any phenomenological or theoretical models for steady state creep. It is well accepted that the presence of a threshold stress can lead to significantly higher apparent stress exponent and activation energy values and in such a case the creep equation is written as, 0921-5093/95/$09.50 SSDI
0 1995 ~
0921-5093(94)09755-O
Elsevier
Science
S.A. All rights
reserved
where D is the self diffusion coefficient, G the shear modulus, b the Burgers vector, k the Boltzmann constant, g,, the threshold stress, n the true stress exponent, and A a dimensionless constant. For any analysis involving go a value of n has to be assumed. Mishra and Pandey [20] found that the data for 6061 Al matrix composites can be best explained by a substructure invariant model [21], for which a true stress exponent of 8 is expected along with an activation energy similar to that for lattice self diffusion. The ‘dislocation creep mechanism map’ developed by Mishra [22] also predicts the dominance of substructure invariant creep mechanism in solid solution aluminum matrix composites. Recently, Cadek et al. [23] have reanalyzed the data of Al-Mg/26 A&O,, composite [14]. They have concluded that the true stress exponent for the composite is close to 5 and the steady state creep is lattice diffusion controlled. However, they do not indicate or discuss the detailed micromechanism of steady state creep deformation and the influence of discontinuous reinforcement on the creep kinetics. One of the problems in selecting a proper stress exponent has been the visual
206
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
of looking at the plots of .?‘I”vs. cr and picking up the best n value. At times, this graphical method does not give a clear indication, particularly when the plotting is not done using a sensitive scale. Another important aspect which has not received due consideration is the ‘steady state creep kinetics’. The purpose of this paper is to evaluate the operating steady state creep mechanism in the Al-Mg/26 A&O,, composite, data for which was reported by Dragone and Nix [14] and reanalyzed by Cadek et al. [23]. It is suggested that if the graphical method of <‘I” vs. 0 plot is unable to yield a unique true stress exponent, the statistical analysis should be resorted to. The importance of the ‘steady state creep kinetics’ is also pointed out. It should become clear from the following sections that this can be a useful indication for monitoring change in the operating creep mechanism. way
. 0.08 . 0.07. e '; v)
0.06 -
E? ‘,
0.05 -
B
Dragone and NIX (1992)
(4
-
AI-MS 126% AI,O, Composcte o
473 K
o
573K 673 K
q
0 0
004-
!!
Stress (MPa) 0.25
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
,,,,,,,,,
@I 0.20 -
2. Analysis of the Al-Mg/26
Al,O,, composite data
If Eq. (2) is considered as an appropriate representation of the creep data, it is imperative that the true stress exponent be determined. Normally, the graphical method of plotting G1/, vs. 0 on a linear scale suffices the purpose. But it has been recently claimed [23,24] that for certain data sets the choice n = 5 or 8 can be equally satisfactory. If indeed this is the case, we suggest that (a) the graphs have to be plotted on sensitive scales (maximum possible enhancement) and (b) the coefficient of linear regression should be considered (and this, of course, would remove any manual, i.e., visual, bias). Fig. l(a)-(c) shows ;‘I, vs. g plots with n values of 3, 5 and 8. The values of the square of correlation coefficient for linear regression and calculated threshold stress are summarized in Table 1. It should be noted that the correlation coefficient for linear regression is best for PZ= 8 at all the temperatures. This contradicts the recent analysis of Cadek et al. [23], who reported that n = 5 is best. It is clear, however, from both Fig. 1 and Table 1 that n = 8 is the best choice for this data set. To strengthen this observation further, the variation of lattice diffusivity compensated strain rate, i/D, with normalized effective stress, (a - a,)/& is shown in Fig. 2 (where crOvalues calculated with n = 5 and IZ= 8 were used for Fig. 2(a) and Fig. 2(b), respectively). A simple comparison indicates that IZ= 8 is more appropriate for the data set under consideration. A closer examination reveals not only that the choice of n = 5 provides a poor correlation, but also that in fact the datum points from different temperatures have not truly merged. For example, the 473 K and 673 K data at equivalent effective stress of z 1 x 10 -’ - 6 x lop4 are quite far apart. Also, there is considerable curvature in the plots when n = 5 is used. These obser-
0
50
100
150
200
250
Stress (MPa) o.5-.,,,...,.,...,...,.,.,,......,..,.....,,........,
(4 0.4 -
0 A
0 0
A
A m A A
0 0
0
0
A
a ,a”
0 0
A
001 0
50
100
150
200
250
Stress (MPa) Fig. 1. The plots of 6’:” vs. applied stress on linear scales to find the true stress exponent and threshold stress with (a) n = 3, (b) n = 5 and (c) n=8.
vations further reinforce the notion that IZ= 8 is the proper choice. The threshold stress values are plotted against l/T in Fig. 3. It shows that the threshold stress is temperature dependent.
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
Table 1 Results of linear regression to obtain the true stress exponent Temp.
n=3
n=8
i-l=5
6)
413 573 673
00
r’
g0
rz
60
r2
112.6 52.3 34.3
0.746 0.850 0.794
91.2 43.6 29.2
0.871 0.918 0.905
55.8 30.0 21.2
0.931 0.938 0.952
3. Discusson
The present findings are in quantitative agreement with the phenomenological model of Sherby et al. [21] which predicts
where R is the subgrain size and A ’ is a dimensionless constant. This is different from the unreinforced Al-5 Mg alloy which shows n = 3, typical of solid solution type behavior [14]. It is clear from the data on Al-Mg alloy of Dragone and Nix [14] that the alloy behaves like a solid solution type at all the stresses investigated. Fig. 2(b) shows the data of Al-Mg as well. It should be noted that at equivalent stress levels (up to (a - 0,/E) -= 7 x 10p4) the behavior of composite is different in two ways: (a) the stress exponent is 8 instead of 3 and (b) the creep rates are much lower. Mishra [22] has pointed out that the presence of second phase particles can stabilize subgrains in solid solution type matrix. This is likely to change the creep behavior from solid solution type to constant substructure creep. Fig. 4 shows a ‘dislocation creep mechanism map’. The data range of Al-Mg/26 Al,O,, is shown in the map. Also depicted is the data range for some other data sets analyzed earlier by Mishra and Pandey [20]. In the absence of whisker dimensions, the interparticle spacing for Nieh’s data [2] has been taken as 5 pm as mentioned by Nieh [2] as particle free distance. It can be noted that the data analysis is consistent with the dislocation creep mechanism map, and the experimental The data lie in the constant substructure regime. reason for the differences in the creep behavior of unreinforced Al-Mg alloy and reinforced composite is not difficult to understand if the microstructural features are taken into consideration. The average interparticle spacing can be given by [25]
4=
fdP[(&F-(J)]
(4)
where V’ris the volume fraction of reinforcement phase and d, the average size. Taking the typical values for Al-Mg/Al,O, composite, d, = 7.4 pm (calculated using dp = (lf x df)‘.‘3, where If and df are average length and diameter of the fibre) and Vr = 0.26, we obtain R, = 4.5
201
,um. In the presence of particles, the subgrains can be stabilized. Weckert and Blum [26] have reported the variation of subgrain size with stress in an Al-5 wt.% Mg alloy. Using the correlation, at the maximum effective stress used by Dragone and Nix [14], (0 - a,)/E g 2.2 x 10 - 3, the stress-dependent subgrain size would be 8.3 pm. This is higher than the interparticle spacing. Therefore, the subgrain size is likely to be independent of the applied stress. Also, the reported average grain size is 15.7 pm [14]. The implication is that below the normalized effective stress of 1 x lo- 3, the subgrain size cannot change because of the grain size. From these microstructural considerations it is unlikely that either the stress-dependent substructure creep (leading n = 5) or the solid solution creep mechanisms (with n = 3) would be dominant in the Al-Mg/26 A&O,, composite. Another way to strengthen this conclusion is to look at the kinetics of each mechanism. The data for the unreinforced Al-Mg alloy can be represented by DGb rs 3.0 _ i = 7.2 kT 0 E
(5)
The data for Al-Mg alloy are shown in Fig. 5. The AI-Mg/Al,O, composite results follow Eq. (3) with A’ = 4.9 x 104. A comparison with the earlier data of Pandey et al. [13] on Al-SIC composites shows that the dimensionless constant for Al-Mg/Al,O,, composite, 4.9 x 104, is almost three orders of magnitude lower than the dimensionless constant for Al-SIC composites, 2.5 x lo7 [13], and it is more than four orders of magnitude lower than the dimensionless constant for pure aluminum, 1.5 x lo9 [21]. Fig. 5 also depicts the expected creep behavior of Al-Sic composites and pure aluminum for a constant subgrain size of 4.5 pm. It can be noted that the creep kinetics is slower for the constant substructure creep of Al-Mg/Al,O,,. Therefore, it is likely that the substructure strengthening would be dominant. The result of the present analysis shows that the presence of Mg in Al-Mg/Al,O, composites lowers the dimensionless constant for constant substructure creep (Eq. 3). This is the ‘kinetics aspect’ of creep. The present analysis is consistent with the recent investigation of the influence of Mg addition on the creep behavior of Al/Sic, composite [27]. Pandey et al. [27] found that the addition of 4 wt.% Mg in Al/Sic, composite makes the creep kinetics significantly slower while the substructure invariant creep mechanism remains dominant. These results help to emphasize that in most of the composites the microstructure is likely to remain constant during creep and because of the slower kinetics, the substructure invariant creep mechanism would dominate. The threshold stress values shown in Fig. 3 indicate that (a) it is temperature dependent, and (b) it is apparently higher for composites with whiskers than particulates. The temperature dependence of the
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
208 IO" 10'6 10'5 IO“'
, , ,*,,,,,, , ,,,.,l,I , l,.l,,,I ,,,1 Dragone and Nix (1992) AI-Mg / 26 Al,O, Composite o. calculated “sang n=5 o
573K
A
673K
0
IO" ,010
10'4 10'3
0
0
0
i
n
q
'
108
IO"
s
10'0
n
qA A A
,TLj 10s
h
7
%,,
,
I ,,.,,,,
,
,,,,, @I
573K
A
673K
0
0” 0
Al-5 wt.% Mg -
6061 AI/SIC composites (Mishra and Pandey, 1990)
,’
1
I
I
109
2
I
10s
A
d
IO'
,,,.,
473K
q
10'2
O&
,
o0calculated using n=6 0
0
10'2 -
0
#,.,
AI-Mg / 26 A1203 Composite
10'5
473K
q
r ,...
Dragone and Nix (1992)
IO'@
0
10'3
5
10"
(4
IO' A
io-‘F
104
1o-5
10-s
104
IO-IF
10-Z
10-s
3 ’
-~*---’
10-S
’
(o-o,)/E
‘11*11d
’
104
1’111*1’
10-a
’
’
--uJ 10-Z
(o-o&/E
Fig. 2. The variation of diffusivity compensated strain rate with normalized effective stress when the threshold stress is calculated using (a) n = 5 and (b) n = 8. It isclear that the choice of n = 8 results in a much better correlation. For the 6061 Al/SC composites n = 8 was used to determine the aa’values [20].
threshold stress in Al-Mg/Al,O,, is consistent with the general trend observed in 6061 Al-SC composites [20,24]. The observation of Pandey et al. [13] about the temperature-independent threshold stress does suffer from some uncertainty as there is considerable scatter in the 723 K data. It is possible that because of the higher scatter at higher temperatures, the conclusion about temperature-independent threshold stress might be erroneous. Based on the general trend [20,23,24], it is more likely that the true nature of the threshold stress is temperature-dependent. The temperature dependence of the threshold stress for Al-Mg/A1,03, can be written as
2 =4.5 x 10-5exp The temperature dependence of z 11 kJ mol - ’ is similar to the temperature dependence of the threshold stress for some other high temperature deformation mechanisms such as diffusional creep [28], dislocationparticle interaction controlled creep [29] and superplasticity [30,31]. Mishra et al. [28] have suggested that the temperature dependence of the threshold stress for diffusional creep could be due to jog nucleation energy required for vacancy formation. Mohamed [30] has proposed a model based on solute segregation for the
1o-2 .
AI-Mg126 AI,O, (Dragone and NIX 1990)
.
6061 A11174 Sic, (Nieh 1994)
A
6061 Al/26 5 SE, (Nieh 1964)
v
6061 All15 SIC, (Monmoto et al 1966)
105r-L
. 104
_.-,...A . ..R.:.-----::::::-::::
:,
7
w
10-3
‘0
e
b
103
:
*
x
--.
1
islocation-Particle interaction
102 ?
10-l
AI-Mg,26 Al,O,, (Dragone and NIX 1990)
v 1
1.5
,
I
I
I
,
I
I
1.8
I
I
2.1
&
I
I
6061 Al/15 SIC, (Monmoto et al 1989)
&
2.4
l/T (xl 03) (K-l) Fig. 3. The variation of normalized threshold stress with the inverse of test temperature. Note the temperature dependence of co/E as well as the influence of reinforcement shape on the magnitude of threshold stress.
IO' : 102
103
104
105
E/(o-0,) Fig. 4. A dislocation creep mechanism map for Al-Mg matrix. The experimental range lies in the constant substructure regime and the results of the present analysis are consistent with the map.
R.S. Mishra et al. / Materials Science and Engineering A201 (1995) 205-210
209
4. Conclusions AI/SIC composites (Pandey et al, 1992) AI-MglAI,O,
com~os!te (Dragone and NIX. 1992)
(1) The steady state creep data of Al-Mg/Al,O,, composites follow the substructure invariant creep mechanism. (2) A temperature dependent threshold stress exists. The origin of the threshold stress is likely to be related to the stress independent load transfer mechanism.
References
111D. Webster, Metal/. Trans. A, 13 (1982) I51 1. 121T.G. Nieh, Metall. Trans. A, 15 (1984) 139.
[31 V.C. Nardone and J.R. Strife, Metali. Trans. A, 18 (1987) 109. [41 H. Lilholt and M. Taya, in F.L. Mathews, N.C.R. Buskell, J.M. Hodkinson and J. Morton (eds.), Proc. ICCM and ECCM VI, 2 (1987) 234.
Fig. 5. The variation of diffusivity compensated strain rate with normalized effective stress. The lines for pure Al, Al/Sic composites and AI-Mg/AI,O, composite is for a constant subgrain size of 4.5 pm. Note the change in creep kinetics.
threshold stress for superplasticity. The magnitude of the threshold stress for creep of composite, however, is much higher than that for diffusional creep and superplasticity. So, at present the temperature dependence of the threshold stress for creep of composite cannot be explained. The magnitude of the threshold stress appears to depend on the shape of reinforcement (Fig. 3). Pandey et al. [13] showed that the magnitude of the threshold stress also depends on the volume fraction of the reinforcement phase. Because of the rigid nature of the reinforcement, load transfer is likely to occur, which will reduce the stress available for the creep of matrix. Kelly and Street [32] have developed a theory for the steady state creep in discontinuous fibre composites. For the case of rigid fibres with perfect bond, the average stress on the fibre is [32] / , \ (n+ I ),‘?I (7) where
and grn is the matrix stress. It should be noted that the load transfer to the rigid fibres is proportional to the stress on the matrix. It follows that if cr,,= Ba (where B is a constant), the stress exponent would not change [13,32]. However, the apparent experimental stress exponent (12.2-15.5) is much higher than the true stress exponent of 8. Therefore, if the load transfer is the origin of the threshold stress, it has to be applied stress independently. A model based on the applied stress independent load transfer mechanism is required to explain the origin of the threshold stress for steady state creep in Al-matrix composites.
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