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Pinning of dislocations on the departure side of strengthening dispersoids
Scripta
METALLURGICA
V o l . 17, pp. Printed in
PINNING OF DISLOCATIONS
467-470, 1983 the U.S.A.
ON THE DEPARTURE
Pergamon P r e s s Ltd. All rights reserved
SIDE OF STRENGTHENING
DISPERSOIDS
Vincent C. Nardone and John K. Tien Henry Krumb School of Mines, Columbia University, New York, NY 10027 (Received November (Revised February
29, 1 9 8 2 ) 15, 1 9 8 3 )
In studying the microstructure of crept oxide dispersion strengthened (ODS) alloys, the type of dislocation/particle configuration shown in Figure la-d has consistently been observed. It appears that the dislocations are being pinned even though they are already on the departure side of the oxide dispersoids. This is shown schematically in Figure 2. Indeed, it appears that the stress on the dislocation if Figure l(d) as estimated from the bowed configuration is on the order of the Orowan stress for the two particles involved. In what follows, we offer two alternative explanations for the phenomenon. On the one hand it can be proposed that dislocation/particle association leads to a lower energy configuration relative to the case when the dislocation and diepersoid are not in contact. This lower energy configuration results in a "nonmechanical pinning" of the dislocation. We see that "nonmechanical pinning" refers to the phenomenon of a dislocation being prevented from escaping a particle because to do so would lead to a higher energy configuration. Such a concept is a reasonable way to account for the dislocation configurations shown in the figures. On the other hand, the dislocation particle configurations shown in the figures may be explained by the local climb of dislocations over particles as proposed, for example, by Ham and Brown [1] or Shewfelt and Brown [2]. Perhaps the figures show a dislocation after it has climbed over the particle even though it is not at this time pinned by the particle. Two questions come to mind when analyzing this latter proposal. First, can one expect a dislocation to remain next to a particle that it has surmounted by climb long enough to be observed? Intuitively, one would expect that the time spent in such a configuration would he extremely short. The second question that needs to be answered is whether or not one would expect only that portion of the dislocation in contact with the particle to climb. As pointed out by Lagneborg [3], a sharp bend of the dislocation line at the particle is not realistic because it is a high energy configuration. Lagneborg goes on to state that the dislocation line tension will tend to straighten out the bend. As shown in the figures, however, bending of the dislocation around the particles is seen. These apparent conflicts may be resolved by considering the character of the dislocation. If the dislocation is pure edge, the climb jogs would be glissile and rapid escape would most likely occur. If it is mixed, however, non-conservative job climb might be required for escape. In addition, strong pinning by mixed jogs could prevent the dislocation from straightening during the process of localized climb. The hypothesis that ths dislocation/particle association leads to a lower energy configuration is also capable of resolving both of the aforementioned questions. The reason one is able to observe the dislocation configurations shown in the figures is that there exists an attractive interaction between the particle and dislocation. The attractive interaction results in the dislocation being in contact with the particle after it has surmounted the particle by climb. The attractive interaction also explains why the dislocation is seen to wrap around the particle even though one would expect that the bends in the dislocation line would lead to a higher energy configuration. The reason for the configuration is that the increase in the energy of the system as a result of dislocation bending is more than compensated by a decrease in the energy due to the dislocation/particle association. In speculating on why a dislocation in contact with a dispersoid, i.e., in contact with a high energy incoherent interface, may result in a reduction in energy for the system, two possible reasons are evident: (i) the portion of the dislocation in contact with the dispersoid may be able to reduce its line energy; (ii) the particle/dislocation surface energy may be lower than the particle/matrix surface energy. If the dispersoid-matrix interface is unstrained 467 0036-9748/83/040467-04503.00/0 Copyright (c) 1 9 8 3 P e r g a m o n Press
Ltd.
468
PINNING
OF
DISLOCATIONS
Vol.
17,
No.
4
other than by the dislocation, the elastic energy would be repulsive if the elastic constants of the particle exceed that of the matrix and vice-versa. It is difficult to determine how the elastic constants of the particles compare with those of the matrlx due to the highly anlsotropic nature of these constants and the small size of the particles. The surface energy effect of a dislocation on an unstrained incoherent interface is unlikely to be significant. However, if thermal stresses were present, as for example from differential contraction while cooling from the creep temperature, dislocation trapping at the partlcle/matrix interface may occur to lower the total strain energy. In addition to accounting for the dislocation configurations shown in the micrographs, the hypothesis that the dlslocatlon/partlcle association leads to a lower energy configuration provides an alternative explanation for the existence of a threshold stress in ODS alloys. The applied stress would have to be of sufficient magnitude to force the dlslocatlon/particle system into a higher energy configuration (one where they are no longer in close contact) before the motion of dislocations could occur. Thus, plastic deformation will not occur until this critical stress (the threshold stress) for dislocation escape is exceeded. It is interesting to note that the concept of a "nonmechanical pinning" is also capable of answering the following question. Why is it that a threshold stress exists for ODS alloys but not for coherent precipitation (~') strengthened superalloys? The answer may be that, although localized climb to bypass particles occurs for both classes of alloys under conditions of low stress and high temperature, there is an additional attractive interaction between particle and dislocation for ODS alloys that is absent in superalloys. In the case of superalloys, climb is a sufficient condition for dislocations to escape while for ODS alloys it is not. The "nonmechanical pinning" which occurs in ODS alloys requires that a critical stress (the threshold stress) must be surpassed before dislocation escape can occur. Existing theories [1,4-6] for the existence of a threshold stress cannot explain why a threshold stress exists for particle strengthened ODS alloys but not for particle strengthened superalloys. Further ramifications of a "nonmechanlcal pinning" of dislocations by dispersolds as well as calculations estimating the threshold stress as a result of this energy reduction will be detailed in a future paper
[7] References i. 2. 3. 4. 5. 6. 7.
L.M. Brown and R.K. Ham in Stren~thenin~ Methods in Crystals, A. Kelly and R.B. Nicholson, eds., Applied Science Publ., London, 1975, p. 75. R.S.W. Shewfelt and L.M. Brown, Phil. Mag., 1977, vol. 35, p. 945. R. Lagneborg, Scripta Met., 1973, vol. 7, p. 605. R.W. Lund and W.D. Nix, Acta Met., 1976, vol. 24, p. 467. J.H. Hausselt and W.D. Nix, Acta Met., 1977, vol. 25, p. 1491. W.C. Oliver and W.D. Nix, Acta Met., 1982, vol. 32, p. 1335. V.C. Nardone, D.E. Matejczyk and J.K. Tien, Acta Met., to be published.
Acknowledsements This contribution was reviewed twice by Scripta Metallurgica. We wish to thank both reviewers and note that the astute comments made by the second reviewer have been integrated in this final version. We also thank the Materials Science Division of the NSF for supporting this work under Grant DMR 80-11402. Dr. Robert Reynik and Dr. Ron Gibala were the program managers of this grant.
Vol.
17,
No.
4
PINNING
OF
DISLOCATIONS
469
(a)
(b)
(c)
(d) FIG. 1
TEM micrographs of Inconel MA 754, an ODS and solid solution strengthened nlckel-base alloy, crept to 2% strain at 2 2 1 M P a and 760°C, cooled on load.
470
PINNING
OF D I S L O C A T I O N S
O
Vol.
17,
O FIG. 2
A schematic illustration of the dislocation configurations shown in Figure i.
No.
4
METALLURGICA
V o l . 17, pp. Printed in
PINNING OF DISLOCATIONS
467-470, 1983 the U.S.A.
ON THE DEPARTURE
Pergamon P r e s s Ltd. All rights reserved
SIDE OF STRENGTHENING
DISPERSOIDS
Vincent C. Nardone and John K. Tien Henry Krumb School of Mines, Columbia University, New York, NY 10027 (Received November (Revised February
29, 1 9 8 2 ) 15, 1 9 8 3 )
In studying the microstructure of crept oxide dispersion strengthened (ODS) alloys, the type of dislocation/particle configuration shown in Figure la-d has consistently been observed. It appears that the dislocations are being pinned even though they are already on the departure side of the oxide dispersoids. This is shown schematically in Figure 2. Indeed, it appears that the stress on the dislocation if Figure l(d) as estimated from the bowed configuration is on the order of the Orowan stress for the two particles involved. In what follows, we offer two alternative explanations for the phenomenon. On the one hand it can be proposed that dislocation/particle association leads to a lower energy configuration relative to the case when the dislocation and diepersoid are not in contact. This lower energy configuration results in a "nonmechanical pinning" of the dislocation. We see that "nonmechanical pinning" refers to the phenomenon of a dislocation being prevented from escaping a particle because to do so would lead to a higher energy configuration. Such a concept is a reasonable way to account for the dislocation configurations shown in the figures. On the other hand, the dislocation particle configurations shown in the figures may be explained by the local climb of dislocations over particles as proposed, for example, by Ham and Brown [1] or Shewfelt and Brown [2]. Perhaps the figures show a dislocation after it has climbed over the particle even though it is not at this time pinned by the particle. Two questions come to mind when analyzing this latter proposal. First, can one expect a dislocation to remain next to a particle that it has surmounted by climb long enough to be observed? Intuitively, one would expect that the time spent in such a configuration would he extremely short. The second question that needs to be answered is whether or not one would expect only that portion of the dislocation in contact with the particle to climb. As pointed out by Lagneborg [3], a sharp bend of the dislocation line at the particle is not realistic because it is a high energy configuration. Lagneborg goes on to state that the dislocation line tension will tend to straighten out the bend. As shown in the figures, however, bending of the dislocation around the particles is seen. These apparent conflicts may be resolved by considering the character of the dislocation. If the dislocation is pure edge, the climb jogs would be glissile and rapid escape would most likely occur. If it is mixed, however, non-conservative job climb might be required for escape. In addition, strong pinning by mixed jogs could prevent the dislocation from straightening during the process of localized climb. The hypothesis that ths dislocation/particle association leads to a lower energy configuration is also capable of resolving both of the aforementioned questions. The reason one is able to observe the dislocation configurations shown in the figures is that there exists an attractive interaction between the particle and dislocation. The attractive interaction results in the dislocation being in contact with the particle after it has surmounted the particle by climb. The attractive interaction also explains why the dislocation is seen to wrap around the particle even though one would expect that the bends in the dislocation line would lead to a higher energy configuration. The reason for the configuration is that the increase in the energy of the system as a result of dislocation bending is more than compensated by a decrease in the energy due to the dislocation/particle association. In speculating on why a dislocation in contact with a dispersoid, i.e., in contact with a high energy incoherent interface, may result in a reduction in energy for the system, two possible reasons are evident: (i) the portion of the dislocation in contact with the dispersoid may be able to reduce its line energy; (ii) the particle/dislocation surface energy may be lower than the particle/matrix surface energy. If the dispersoid-matrix interface is unstrained 467 0036-9748/83/040467-04503.00/0 Copyright (c) 1 9 8 3 P e r g a m o n Press
Ltd.
468
PINNING
OF
DISLOCATIONS
Vol.
17,
No.
4
other than by the dislocation, the elastic energy would be repulsive if the elastic constants of the particle exceed that of the matrix and vice-versa. It is difficult to determine how the elastic constants of the particles compare with those of the matrlx due to the highly anlsotropic nature of these constants and the small size of the particles. The surface energy effect of a dislocation on an unstrained incoherent interface is unlikely to be significant. However, if thermal stresses were present, as for example from differential contraction while cooling from the creep temperature, dislocation trapping at the partlcle/matrix interface may occur to lower the total strain energy. In addition to accounting for the dislocation configurations shown in the micrographs, the hypothesis that the dlslocatlon/partlcle association leads to a lower energy configuration provides an alternative explanation for the existence of a threshold stress in ODS alloys. The applied stress would have to be of sufficient magnitude to force the dlslocatlon/particle system into a higher energy configuration (one where they are no longer in close contact) before the motion of dislocations could occur. Thus, plastic deformation will not occur until this critical stress (the threshold stress) for dislocation escape is exceeded. It is interesting to note that the concept of a "nonmechanical pinning" is also capable of answering the following question. Why is it that a threshold stress exists for ODS alloys but not for coherent precipitation (~') strengthened superalloys? The answer may be that, although localized climb to bypass particles occurs for both classes of alloys under conditions of low stress and high temperature, there is an additional attractive interaction between particle and dislocation for ODS alloys that is absent in superalloys. In the case of superalloys, climb is a sufficient condition for dislocations to escape while for ODS alloys it is not. The "nonmechanical pinning" which occurs in ODS alloys requires that a critical stress (the threshold stress) must be surpassed before dislocation escape can occur. Existing theories [1,4-6] for the existence of a threshold stress cannot explain why a threshold stress exists for particle strengthened ODS alloys but not for particle strengthened superalloys. Further ramifications of a "nonmechanlcal pinning" of dislocations by dispersolds as well as calculations estimating the threshold stress as a result of this energy reduction will be detailed in a future paper
[7] References i. 2. 3. 4. 5. 6. 7.
L.M. Brown and R.K. Ham in Stren~thenin~ Methods in Crystals, A. Kelly and R.B. Nicholson, eds., Applied Science Publ., London, 1975, p. 75. R.S.W. Shewfelt and L.M. Brown, Phil. Mag., 1977, vol. 35, p. 945. R. Lagneborg, Scripta Met., 1973, vol. 7, p. 605. R.W. Lund and W.D. Nix, Acta Met., 1976, vol. 24, p. 467. J.H. Hausselt and W.D. Nix, Acta Met., 1977, vol. 25, p. 1491. W.C. Oliver and W.D. Nix, Acta Met., 1982, vol. 32, p. 1335. V.C. Nardone, D.E. Matejczyk and J.K. Tien, Acta Met., to be published.
Acknowledsements This contribution was reviewed twice by Scripta Metallurgica. We wish to thank both reviewers and note that the astute comments made by the second reviewer have been integrated in this final version. We also thank the Materials Science Division of the NSF for supporting this work under Grant DMR 80-11402. Dr. Robert Reynik and Dr. Ron Gibala were the program managers of this grant.
Vol.
17,
No.
4
PINNING
OF
DISLOCATIONS
469
(a)
(b)
(c)
(d) FIG. 1
TEM micrographs of Inconel MA 754, an ODS and solid solution strengthened nlckel-base alloy, crept to 2% strain at 2 2 1 M P a and 760°C, cooled on load.
470
PINNING
OF D I S L O C A T I O N S
O
Vol.
17,
O FIG. 2
A schematic illustration of the dislocation configurations shown in Figure i.
No.
4