Damage accumulation during creep deformation of a single crystal superalloy at 1150 C

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1 Materials Science and Engineering A 448 (2007) Damage accumulation during creep deformation of a single crystal superalloy at 1150 C R.C. Reed a,, D.C. Cox b, C.M.F. Rae b a Department of Materials, Imperial College London, Prince Consort Road, London SW7 2BP, UK b Department of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge CB2 3QZ, UK Received 5 August 2006; received in revised form 28 September 2006; accepted 22 November 2006 Abstract Microstructural degradation in the CMSX-4 single crystal superalloy during creep deformation at 1150 C and 100 MPa is studied. Tensile deformation in the 001 direction is considered due to its technological importance. Under these conditions, rafting of the structure is completed quickly and within the first 10 h. It is demonstrated that the creep rupture event is highly localised, the instability being associated with a critical and well-defined strain being reached with failure occurring within a further few tens of hours. It is shown that the high strain rates and shear stresses associated with the rupture process are sufficient to cause realignment of the rafted structure with respect to the matrix. Creep cavitation damage near to the rupture surface is prevalent, at microporosity inherited from the casting process but more significantly, at topologically close-packed (TCP) phases and associated pores and voids formed in their vicinity which have formed via vacancy condensation. Hot isostatic pressing (HIPing) prior to creep testing reduces the incidence of casting microporosity, but the creep rupture life is not improved significantly. It is suggested that it is the formation of TCP phases which limits creep rupture life Elsevier B.V. All rights reserved. Keywords: Nickel superalloys; Creep deformation; Degradation mechanisms 1. Introduction In recent years, improvements in the high temperature creep performance of nickel-base single crystals superalloys [1] have enabled significant improvements to be made in the efficiency, weight and rate of carbon emissions associated with gas turbine engines. However, as turbine entry temperatures continue to rise, it is becoming increasingly important to understand and rationalise the physical phenomena occurring during creep deformation under conditions of temperature and stress, which push these materials to their very limits. Progress has been made in this regard and the behaviour of single crystals at lower temperatures particularly in the vicinity of 750 C is now reasonably well understood. There, provided that the threshold stress for particle cutting is exceeded, a considerable amount of primary creep occurs [e.g. 2,3]. This is associated with a macroscopic deformation of the form {1 1 1} [4] although it should be noted that primary creep can be suppressed when Corresponding author. Fax: address: roger.reed@imperial.ac.uk (R.C. Reed). creep dislocations of the required type are unavailable [5]. At temperatures around 950 C, the loading of all known oriented superalloy single crystals yields a creep strain rate which increases monotonically with creep strain, there existing little evidence of a steady-state regime [6,7]. This strain softening behaviour has been termed tertiary creep, and is associated with a proportionality of the creep strain rate and the accumulated creep strain [8 11]; the mode of deformation is octahedral slip with {111} 1 10 creep dislocations gliding and climbing around the particles, which remain intact [12]. Unfortunately, the creep deformation behaviour of single crystal superalloys at temperatures in excess of 1000 C remains less well understood. For instance, under these conditions the morphological instability of the / structure which has become known as the rafting effect [13 16] is prevalent, the mechanisms responsible for this being the subject of some controversy [17 19]. There is debate in the literature concerning whether benefit is derived from the rafting effect or not [20] and the extent to which rafting affects the creep strain evolution at differing strain levels and temperatures. Reed et al. [21] have established by extrapolation of creep data from low temperatures to the regime where rafting is operative that /$ see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.msea

2 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) rafting is indeed beneficial to creep life since it confers better creep performance than might be expected if rafting were not to occur; moreover the rafting effect suppresses the accumulation of creep strain until just a few hours before creep failure. However, a proper characterisation of the microstructural degradation mechanisms was not attempted. This is important since it will provide a basis for an interpretation of the factors, which lead to ultimate failure by rupturing. Since the levels of strain required for failure of 001 -oriented crystals under these conditions is low, perhaps 5%, this represents a critical issue from the point of view of the gas turbine engineer. The purpose of this work is to address these outstanding issues by considering the creep deformation behaviour of oriented CMSX-4 single crystals at very extreme conditions of temperature and stress: 1150 C and 100 MPa. The major aim is to further understanding of the microstructural degradation mechanisms occurring in the final few hours of the creep deformation that lead ultimately to final failure. An examination of the effects of hot isostatic pressing (HIPing) is a particular feature of this work. The information reported in this paper is also of use to those interested in designing models for the creep deformation of single crystal superalloys based on the general principles of damage mechanics [e.g. 22]; there is a need to ensure that the expressions used correctly reflect the forms of creep damage which are occurring. Fig. 1. Creep curves determined for un-hiped CMSX-4 tested at 1150 C and 100 MPa. British Standard UDC [24]. The specimens were tested at 1150 C and 100 MPa and some were interrupted at various amounts of accumulated creep strain. Since the tests were carried out at temperatures beyond 1000 C, some special precautions were taken. Platinum wound furnaces were used. Both pull rods and extensometers were machined from creep resistant MA Experimental details Ten creep strain test pieces of diameter 5.5 mm and gauge length 28 mm were machined from CMSX-4 single crystal material provided by Rolls-Royce pic, in the form of 1 cm diameter cast rods in the fully heat-treated condition. Four of the test pieces were placed in a hot isostatic press (HIP) to reduce casting porosity inherited from processing. The HIPing conditions were 3 h at 1310 C under the reduced stress of 100 MPa; this process was carried out between the solutioning and the ageing heattreatments. The chemical composition of the CMSX-4 material is given in Table 1; all were from the same investment casting. The axes of all rods were shown to lie within 10 of 001 by the indexing of back Laue patterns using the SCORPIO method [23]. Creep strain testing was carried out using 20 kn constant load creep testing machines; such testing was compliant with the Table 1 The chemical composition (in wt%) of the CMSX-4 material used in the present study Ni Balance Cr 6.4 Al 5.6 Ti 1.0 Mo 0.6 W 6.4 Ta 6.5 Co 9.7 Re 3.0 Hf 0.1 Fig. 2. Photograph of specimen F crept at 1150 C and 100 MPa interrupted just before rupture at 2.32% strain after 198 h.

3 90 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) oxide dispersion-strengthened mechanically alloyed material; the adaptors were machined from MA754 and MA758. Subsequently, analysis was carried out using scanning electron microscopy (SEM). First, the creep specimens were sectioned on the {001} plane, which contained the tensile axis. The surfaces were then polished according to standard metallurgical practice to a 1 m finish, and then for a further 20 min with colloidal silica and etched electrolytically (6 V dc) using a mixture of 12 ml perchloric, 47 ml sulphuric and 41 ml nitric acids. Microstructural examination was then carried out using a JEOL 6340F field-emission gun scanning electron microscope (FEGSEM) using both secondary and backscattered electron signals. Use was made of electron backscattering diffraction (EBSD) methods for the characterisation of the local orientation of the crystal lattice with respect to the specimen geometry. 3. Results 3.1. Behaviour of the Un-HIPed specimens The creep curves generated at 1150 C and 100 MPa for the six specimens tested in the un-hiped condition are given in Fig. 1. The samples have been given the labels A F. Tests C E were taken to failure whilst A, B and F were interrupted before this occurred. The following observations can be made: (i) initially a small amount of strain (in the range %) is accumulated but there exists a plateau in which the creep strain does not vary strongly with time, and the creep strain rate is low; (ii) at later times, the creep strain increases rapidly, with rupture occurring soon afterwards; (iii) the time at which the creep rate starts to accelerate, i.e. the time to rupture is not well defined and varies by 100 h; this corresponds to a factor of almost two for the samples tested. Further insight can be gained by plotting strain rate versus strain as was done in [21]. Initially, it is seen that there exists a decreasing strain rate regime with the strain rate eventually reaching a minimum, which occurs within the creep plateaux of Fig. 1. The minimum creep rate is reached consistently at a critical creep strain ϵ * of (0.7 ± 0.3)% [21]. Thereafter the creep strain rate increases dramatically in what will be termed the increasing creep rate regime. In the case of sample F it proved possible to interrupt the test whilst the creep strain was accelerating rapidly just prior to failure; this confirmed that the final fracture process is highly localised with severe reduction in area occurring within a few millimetres of the fracture surface, see Fig. 2. Examination of sample A using scanning electron microscopy confirmed that under these testing conditions, welldeveloped rafts had already formed after 10 h [21]. As expected, for a negatively misfitting alloy such as CMSX-4, the rafts form with their long axes normal to the tensile axis. In fact Fig. 3. Secondary electron micrographs from sample C showing the changing orientation of the rafts at (a) 0.2 mm, (b) 0.5 mm, (c) 2 mm and (d) 4 mm from the fracture surface. In each case the tensile axis is vertical.

4 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) Fig. 5. Secondary electron micrograph from sample C showing the precipitation of secondary upon cooling. Fig. 4. For sample C, estimates of (a) the angle through which the / matrix had rotated away from the tensile axis at distances close to the fracture surface, and (b) angle through which the rafts had rotated relative to tensile axis. the rafts exhibited remarkable stability within the creep plateau of Fig. 1, with no further lengthening or isotropic coarsening being detected in samples B and C. Only at the very late stages of deformation and very close to the fracture surface was there a substantial change in their morphology. This is illustrated in Fig. 3, which shows the variation in microstructure of sample C at four distances from the fracture surface. At a distance of 200 m, the rafts were found to have brokened up and the precipitates were approximately 45 to the tensile axis, whereas 4 mm from the fracture the microstructure was essentially unchanged and the rafts were still intact. To examine this further, EBSD methods were used to compare the degree of raft rotation and the matrix orientation in the vicinity of the fracture surface. This revealed that although a significant rotation of the / interfaces had taken place, only a small rotation of the crystallographic lattice had occurred, see Fig. 4. These observations suggest a rapid reorientation of the raft morphology in the vicinity of the localised fracture as a consequence of the differing state of triaxial stress there, as in [25]. Sample C also revealed the presence of a significant amount of secondary which was not observed in the interrupted samples A, B or F, see Fig. 5. This secondary will have dissolved during the creep testing and re-precipitated on cooling as particles of size 50 nm. Only the ruptured samples exhibited this secondary, as they cooled rapidly from the test temperature due to the fracturing which removed the testpiece from the creep furnace rather quickly. By comparison samples A, B and F which were interrupted prior to failure cooled more slowly and this, which allowed the supersaturated to reprecipitate onto the existing rafts. Fig. 6 is a plot of the calculated volume fraction of as a function of temperature obtained using the commercial software package Thermo-Calc [26]. This graph is in good agreement with the experimental findings of Roebuck et al. [27]. Indicated on this figure is the test temperature used in this study, and it can be seen that at 1150 C the volume fraction is approximately 45% significantly lower than the 70% at ambient conditions. Thus substantial dissolution can be expected during testing. The orientation of the secondary in Fig. 5 can be used to judge the relative orientation of the matrix with respect to the / interfaces, thus further confirming the rotation of the rafts in the vicinity of the fracture surface. In samples other than A, particles of topologically closepacked phases (TCPs) formed predominantly in the tungsten Fig. 6. Plot of volume fraction of as a function of temperature. The filled circle denotes the temperature of the creep tests undertaken in the present study.

5 92 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) Fig. 8. Backscattered electron image showing creep cavitation of porosity in sample C. Fig. 7. Backscattered electron images showing TCP phase formation and porosity in (a) sample B (100 h) and (b) sample C (170 h). and rhenium rich dendritic core regions. Fig. 7a and b show typical TCP particles in samples B and C, respectively imaged in the SEM, using backscattered signals to obtain atomic number contrast from the high levels of rhenium and tungsten they contain. These observations are consistent with work [28] which has reported that CMSX-4 is prone to the precipitation of both µ and R phases in roughly equal proportions when exposed to heat treatment at 1150 C. The TCP particles were almost always enclosed in since their composition is largely made up from elements found in the phase it is possible that this is the reason why the particles do not grow beyond a certain size; once a TCP particle has formed and dissolved the elements locally, it is then surrounded by and the TCP/ elements are required to diffuse through the to the TCP particle. As can be seen, the TCP particles act as sites for the nucleation of pores, which presumably arise as a consequence of the condensation of vacancies. The TCP-related pores were observed to be prone to creep cavitation, but only in the vicinity of the fracture surface, see Fig. 8. It should be emphasised that these TCP-related pores are in addition to the microporosity present in the interdendritic region as a consequence of the casting process; in the material considered such casting pores were found to outnumber the TCP pores by a factor of approximately 25:1. The casting pores were found to be spherical in the un-crept material and sample A, but examination of the samples tested to longer times indicated that they grow and facet as shown in Fig. 9a. Others develop conical tunnels extending along the directions perpendicular to the tensile axis, see Fig. 9b, thus increasing the cross-sectional area of the pores. Given the highly localised nature of the final fracture event, see Fig. 2, it is interesting to characterise the extent of porosity as a function of the gauge length. Sample F was used for this purpose. Fig. 10 shows the total number of pores counted within each 2 mm section along the gauge length; also shown is a histogram of the number of pores which exhibited obvious creep cavitation. One can see that the total density of pores varied by a factor of about four along the gauge length. Significantly, only a fraction of these exhibit some form of creep cavitation damage, and all those that do are located in the vicinity of the fracture surface Behaviour of the HIPed specimens Prior to testing, several pieces of un-crept HIPed material were examined in the SEM to establish whether casting porosity

6 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) Fig. 10. Plot of total and cavitated number of pores counted as a function of sample gauge length in sample F. Fig. 9. (a) Secondary electron image of casting pore and (b) backscattered electron image of TCP pore, illustrating the two types of porosity observed in sample C (170 h). Fig. 11. Secondary electron image showing porosity in HIPed CMSX-4. had been significantly reduced by the HIPing operation. It was found that the microporosity had been almost entirely removed, with only the occasional pore remaining, see Fig. 11; even then these had a diameter of less than 0.5 m, which times smaller than a typical casting pore in the unhiped state. Creep testpieces were then machined and tested as before, and the creep curves obtained are given in Fig. 12. In these testpieces, the minimum creep rate was reached consistently at a critical creep strain ϵ * of (0.3 ± 0.2)%, which is about half that of the un-hiped specimens. Nevertheless, comparison with Figs. 1 and 12 shows that despite the scatter in the data the form of the creep curves is not strongly affected by the HIPing treatment. In particular, the average time to rupture is not substantially improved, as might have been expected. Fig. 12. Creep curves determined for HIPed CMSX-4 tested at 1150 C and 100 MPa.

7 94 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) Fig. 13. Backscattered electron image showing TCP phase particles and porosity in crept HIPed material. Following creep testing, the microstructure of the failed HIPed specimens was examined. Far away from the fracture surface, significant numbers of pores were again found, but these were often associated with TCP particles as had been observed for the un-hiped specimens, see Fig. 13; there was no evidence of any casting porosity. Interestingly, in the vicinity of the fracture surface, porosity was again observed in the interdendritic region, see Fig. 14, and these diminished in both number and size with distance away from the fracture surface; they were generally larger than the TCP pores. These were most definitely not associated with TCPs, but rather was casting porosity which had re-opened during creep deformation. Very close to the fracture surface, the larger pores were often found to have coalesced via creep cavitation. Fig. 15 shows this, and it can be seen that these pores are associated unambiguously with TCP phase formation. Fig. 14. Optical micrographs showing the distribution of porosity and creep cavitation near to the fracture surface in (a) HIPed and (b) un-hiped CMSX-4. In (a), note the location of the casting porosity in the interdendritic (light etching) regions. 4. Discussion The observations made here in particular the stability of the / structure during the time which corresponds to the creep plateaux of Figs. 1 and 12 support the view that the reduction of the creep rate in the decreasing creep rate regime [21] arises as a consequence of the rafting effect, and its effect on the underlying dislocation processes occurring. It can be presumed that rafts of, once formed, prevent the glide/climb of a/ {lll} creep dislocations necessary to percolate the / microstructure. Since the rafts remain as continuous and unbroken except in the region very close to fracture in the necked region, it is probable that the precipitates continue to act as barriers to the movement of dislocations right up to the onset of fracture. As creep dislocations of a given a/ {lll} form are introduced into the structure, the stress field from the applied load interacts with the internal stress fields of the dislo- Fig. 15. Secondary electron image of crept HIPed CMSX-4, illustrating severe creep damage associated with porosity around TCPs.

8 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) cations, such that a build-up of back stresses occurs. At this point other a/ {lll} forms become favoured with the cellular dislocation structures eventually being formed on the / interfaces [29 31]. The suggestion that the decreasing creep rate regime arises because of the formation of the rafted structure and its effect on the dislocation accumulation kinetics is supported further by the quantitative analysis presented in [21]. It is however the effects which precipitate creep rupture under these conditions which are of the greatest curiosity, since the creep rate accelerates quickly just before the onset of fracture even though the accumulated creep strain is still rather modest: about 1% or less. Thus in this sense the material exhibits only limited ductility. The considerable variation in the time to rupture is consistent with the observation that accumulation of creep damage in the form of cavitation of porosity is the life limiting factor, since the coalescence of incipient cracks will depend upon the statistical distribution of pores in any given specimen. The implication of this is that elimination of porosity should have a beneficial effect on the time to rupture, and indeed it was this which prompted the testing of the material in the HIPed condition. Unfortunately, although HIPing was successful in eliminating the presence of casting microporosity, the creep life remains unaffected. This suggests that either (i) it is the formation of cavitation at pores associated with TCP phases which is the rate limiting factor in determining creep life, or alternatively that (ii) it is cavitation at casting microporosity which is relevant, and that HIPing is ineffective in increasing creep life since the casting pores re-open during the later stages of creep deformation. From our observations, it is suggested that the formation of the TCP phases and the associated porosity is the more potent form of damage, although further work is needed to confirm this unambiguously. Creep life in this regime would then be improved only through changes in alloy composition, which confer better high temperature resistance to the formation of TCP phases. An open question then remains about the origin of the vacancies needed to cause the significant size of the voids formed during creep deformation. Whilst the precipitation of TCP phases by diffusional processes could conceivably cause the formation of Kirkendall porosity, it seems unlikely that the Kirkendall process alone is sufficient to provide the number of vacancies which are required [32]. Neither can it explain observations of damage, which is unassociated with the TCPs, for example at re-opened casting microporosity. Instead, in view of the small size and quite low volume fraction of the TCP phases, there must be another mechanism which supplies vacancies and contributes to void growth. Recently, Epishin and Link [30,31] have completed elegant work which has demonstrated that non-conservative movement (by glide/climb) of a/ dislocations deposited on the / interfaces produces most of the creep strain expected in these materials during the creep plateaux of the type displayed by Figs. 1 and 12, when the creep strain rate is extraordinarily low. Significantly, the interfacial climb required to form the equilibrium dislocation nets on the / interfaces generates vacancies, which diffuse either to pores or else to a interfacial dislocations, assisting their climb. Metallographical evidence has been provided to support this, in the form of a correlation between creep strain and porosity levels. It seems to us that this mechanism is able to provide the vacancies required to cause the damage seen under the creep conditions employed here. More significantly, the evidence seems to be that vacancy condensation is preferred at TCP phases, as is seen clearly in the micrographs presented in [31,32], although the role of TCPs was not commented upon. 5. Summary and conclusions The following conclusions can be drawn from this work: 1. At 1150 C and 100 MPa, rafting in CMSX-4 occurs rapidly and is completed within 10 h; whilst this is occurring and for a considerable period thereafter the creep rate decreases with increasing strain. Thus a creep hardening effect is operative at this stage. 2. Once a critical strain is reached, the creep strain increases dramatically and failure occurs within a few tens of hours. 3. Ultimate failure is highly localised. High stresses and strain rates in the fracture zone are sufficient to cause reorientation of the rafts, due to the changing triaxiality of the stress state in the vicinity of the fracture surface. 4. Under these conditions, CMSX-4 is prone to the formation of topologically close packed (TCP) phases. 5. In the unhiped material, two forms of porosity are observed: (i) casting porosity which is predominantly in the interdendritic regions and (ii) porosity in association with the TCPs, which will have formed via the condensation of vacancies. 6. In the unhiped testpieces, both casting porosity and TCPrelated pores are subject to creep damage in the form of cavitation; however this is restricted to the vicinity of the fracture surface. 7. HIPing was found to remove the casting porosity almost completely, but following rupture, pores and creep cavitation are again found to be prevalant. This is associated predominantly with TCP phase formation. It appears that casting porosity re-opens in the narrow region near to the fracture surface. 8. Under these conditions, the creep rupture life and behaviour of CMSX-4 is not affected substantially by the HIPing operation. This leads one to conclude that it is the precipitation of the TCP phases with associated porosity, which controls creep life. 9. A recently proposed mechanism for the formation of vacancies which invokes the rearrangement of interfacial dislocations at / interfaces caused by climb processes is suggested to be the origin of the quantity of vacancies required for the creep porosity to occur under these conditions. Acknowledgements Two of the authors (RCR and CMFR) acknowledge collaboration with Rolls-Royce plc over many years. The authors thank the referees for helpful and thought-provoking reviews, which have improved the manuscript considerably.

9 96 R.C. Reed et al. / Materials Science and Engineering A 448 (2007) References [1] R.C. Reed, Superalloys: Fundamentals and Applications, Cambridge University Press, [2] V. Sass, U. Glatzel, M. Feller-Kniepmeier, in: R. Kissinger, D.J. Deye, D.L. Anton, A.D. Cetel, M.V. Nathal, T.M. Pollock, D.A. Woodford (Eds.), Creep Anisotropy in the Monocrystalline Nickel-base Superalloy, in Superalloys 1996, The Minerals, Metals and Materials Society, Warrendale, PA, USA, 1996, pp [3] C.M.F. Rae, R.C. Reed, Acta Mater., in press. [4] N. Matan, D.C. Cox, P. Carter, M.A. Rist, C.M.F. Rae, R.C. Reed, Acta Mater. 47 (1999) [5] C.M.F. Rae, N. Matan, R.C. Reed, Mater. Sci. Eng. 300 (2001) [6] F.R.N. Nabarro, H.L. de Villiers, The Physics of Creep, Taylor and Francis, [7] P. Caron, T. Khan, Mater. Sci. Eng. 61 (1983) [8] B.F. Dyson, M. McLean, Acta Metall. 31 (1983) [9] P.J. Henderson, M. McLean, Acta Metall. 31 (1983) [10] R.N. Ghosh, R.V. Curtis, M. McLean, M., Acta Metall. Mater. 38 (1990) [11] L.M. Pan, I. Scheibli, M.B. Henderson, B.A. Shollock, M. McLean, Acta Metall. Mater. 43 (1995) [12] T.M. Pollock, A.S. Argon, Acta Metall. Mater. 40 (1992) [13] C. Carry, J.L. Strudel, Acta Metall. 26 (1977) [14] M.V. Nathal, L.J. Ebert, Metall. Trans. 16A (1985) [15] A. Epishin, T. Link, U. Bruckner, P.D. Portella, Acta Mater. 49 (2001) [16] K. Serin, G. Gobenli, G. Eggeler, Mater. Sci. Eng. A (2004) [17] I.L. Svetlov, B.A. Golovko, A.I. Epishin, N.P. Abalakin, Scripta Mater. 26 (1992) [18] F.R.N. Nabarro, Metall. Trans. 27A (1996) [19] N. Matan, D.C. Cox, C.M.F. Rae And, R.C. Reed, Acta Mater. 47 (1999) [20] M. Kamaraj, Sadhana 28 (2003) [21] R.C. Reed, N. Matan, D.C. Cox, M.A. Rist, C.M.F. Rae, Acta Mater. 47 (1999) [22] R.W. Evans, B. Wilshire, Structural Materials: Engineering Application Through Scientific Insight The Donald McLean Symposium, The Institute of Materials, London UK, 1996, pp [23] M.J. Goulette, P.D. Spilling, R.P. Arthey, in: M. Gell, C.S. Kortovich, et al. (Eds.), Cost Effective Single Crystals in Superalloys 1984, The Metallurgical Society of AIME, Warrendale, PN, USA, 1984, pp [24] British Standard UDC 629.7, The British Standards Institution, London (1965). [25] M. Kamaraj, K. Serin, M. Kolbe, G. Eggeler, Mater. Sci. Eng. A (2001) [26] B. Janssen, B. Sundman, J.O. Andersson, Calphad 9 (1985) [27] B. Roebuck, D.C. Cox, R.C. Reed, Scripta Mater. 44 (2001) [28] C.M.F. Rae, R.C. Reed, Acta Mater. 49 (2001) [29] R.D. Field, T.M. Pollock, W.H. Murphy, in: S.D. Antolovich, R.W. Stusrud, R.A. Mackay, D.L. Anton, T. Khan, R.D. Kissinger, D.L. Klarstrom (Eds.), Superalloys 1992, The Minerals, Metals and Materials Society, Warrendale, Pennsylvania, USA, 1992, pp [30] A. Epishin, T. Link, in: K.A. Green, T.M. Pollock, H. Harada, T.E. Howson, R.C. Reed, J.J. Schirra, S. Walston (Eds.), Mechanisms of High Temperature Creep of Nickel-Base Superalloys Under Low Applied Stress in Superalloys 2004, TMS (The Minerals, Metals and Materials Society), Warrendale, Pennsylvania, USA, [31] A. Epishin, T. Link, Philos. Mag. 84 (2004) [32] M.E. Kassner, T.A. Hayes, Int. J. Plast. 19 (2003)