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Microstructure of a nickel-base superalloy after creep in [011] orientation at 1173 K
Materials Science and Engineering, A188 (1994) 147-152
147
Microstructure of a nickel-base superalloy after creep in [011] orientation at 1173 K Thomas Kuttner and Monika Feller-Kniepmeier Technische Universitiit Berlin, Institut fiir Metallforschung, Mikrostrukturanalyse, BH 18 Strafle des 17. Juni 135, W-l O587 Berlin (Germany) (Received October 28, 1993; in revised form January 14, 1994)
Abstract Tensile creep tests in the [011] direction have been performed on two specimens of SRR99 at 1173 K under a load of 300 MPa. The microstructure was analysed by transmission electron microscopy investigations after plastic strains of 0.1% and 0.29%. At both strains, the 7' phase is not sheared by dislocations. Plastic deformation is concentrated in roof matrix channels lying at an angle of 45 ° to the load axis. Gable matrix channels that contain the load axis are almost free of dislocations. This experimental result was shown to be due to the supe:rposition of coherency and external load stress tensors, leading to different levels of shear stress in the two types of matrix channel. The results obtained at 1173 K are compared with previous results at 1033 K.
1. Introduction
Creep lifetimes of single-crystal nickel-base superalloys strongly depend on the orientation of the load axis [1-5]. In all investigations the shortest creep lifetimes were observed in [011] orientation. So far, the majority of microstructural investigations have been performed for the [001] orientation. Recently a quantitative transmission electron microscopy (TEM) analysis of the microstructure of SRR99 after creep in [011] orientation at 1033 K [6-8] has been presented. It was shown that the superposition of load and coherency stress together with the restricted amount of glide systems leads to stress accumulation in matrix channels that are at an angle of 45 ° to the load axis. The same result is obtained by modelling by the finite element method (FEM) [9-12]. During creep at 1033 K, diffusion effects play a minor role and the cubic morphology of the 7' phase is maintained throughout the creep experiments [6, 7]. At higher temperatures (1223-1323 K) the effect of orientation and 7' size on the creep strength of superalloys was found to be considerably reduced [4]. In the present investigation, we are interested in the effects that control creep at high temperatures under medium load and on the temperature dependence of creep in [011] orientation.
tals were prepared by epitaxial crystallization. After the standard solution heat treatment (1553 K for 1 h + 1563 K for 2 h + 1573 K for 0.5 h + 1578 K for 0.5 h; cooling to 1273 K at 0.7 K s- ~) and annealing ( 1353 K for 4 h + 1143 K for 16 h), the microstructure consisted of 70 vol.% of cubic 7/' precipitates embedded coherently in the matrix. Two specimens were creep tested at 1173 K under a constant load of 300 MPa. The initial strain gauge length was 25 mm. Specimen 2 was cooled under load while, for specimen 1, cooling and unloading started at the same time. Details of the creep experiments are given in Table 1. Slices for scanning electron microscopy (SEM) and TEM investigations were cut parallel to (011), (100) and (001) planes. The microstructure was investigated using a 300 kV Philips CM30.
3. Results
3.1. Creep curves Creep curves of the two specimens are plotted in Fig. 1 [6]. The creep rate of specimen 2 reaches a quasi-stationary creep rate of g of about 4 x 10-9 sin the secondary stage of creep. The difference between the initial creep rates of the two specimens is considered to be connected to different densities of grown-in dislocations.
2. Experimental details
The single-crystal nickel-base superalloy used for the investigation was SRR99. The [011]-oriented crys0921-5093/94/$7.00 SSD1 0921-5093(94)09523-Y
3.2. Morphology of the 7' phase In specimen 1 (creep time, 7.45 h) the cubic 7' morphology is unchanged. After a creep time of © 1994 - Elsevier Sequoia. All rights reserved
148
T. Kuttner, M. Feller-Kniepmeier / Microstructureof Ni-base superalloy after creep
TABLE 1. Creep tests at 1173 K, and o = 300 MPa Specimen
Load axis
1
[3, 68, 73]
2
[2, 70, 72]
Creep time (h) 7.45
217.2
Plastic strain (%) 0.1
0.29
0.4 sp'ci--e-"~ .,.. ' ' specimen 2 o~
0.3-
.o O (D t,-, ¢2
Fig. 2. Overview of microstructure after e=0.1% in the (001) projection.
0.2-
0.1-
•
direction
D
0.0
o
5'0 . . . .
i;o
i;o . . . .
2;0 . . . .
time [h] Fig. 1. Creep curves of specimens 1 and 2 (T=l173K; o = 300 MPa). A
A
Fig. 3. Orientation of glide systems relative to the load axis. 217.2 h, the y' precipitates have achieved a rod morphology, with the long axis parallel to the [100] direction. This morphology change is consistent with the growth direction, deduced from F E M calculations of the elastic energy for a superalloy with negative misfit and [011] tensile axis [11] and with previous experimental observations [13]. 3.3. Dislocation structures at ep = 0.1% and ep = 0.29% An overview in (001) projection of the microstructure strained to 0.1% is shown in Fig. 2. The two essential observations are that the 7' phase is not sheared at this stage of creep and that (001) and (010) matrix channels contain interfacial dislocations while (100) channels are almost free of dislocations. For the [011] load direction, two types of matrix channel can be distinguished. Those that build an angle of 45 ° with the load axis which will be denoted as roof channels, and the (100) channels that contain the load axis and are denoted as gable channels. The matrix dislocation loops were analysed to be on the octahedral slip systems with the highest Schmid factors. Dislocations with ½[i01] and ½[i10] Burgers vectors operate on the (111) plane and those with ½[101] and ½[110] on the ( i l l ) plane. In Fig 3 the orientations of glide systems relative to the load axis are depicted. Neither {111} cross-slip nor cubic slip occurs. In contrast with observations made after creep
in the [011] orientation at 1033 K, dissociation of the gliding matrix dipole segments into Shockley partials was not observed at 1173 K. Figure 4 shows an overview of the microstructure after 0.29% strain in the (001) projection. Interfacial ½(110) dislocations with mainly 60 ° character on (111) and (i11) planes are seen to form rectangular networks. In this specimen, detailed analysis of the interfacial dislocation networks was performed. An example is shown in Fig. 5 with compilation in Table 2. Network formation of a ½1110] dislocation dipole, having screw character in its interfacial segments, with a sessile ½[011] dislocation is observed at node 5-3-4. The reaction product ½[]01] lies on the (1]1) plane, which is inactive. Reaction of a dislocation from an active glide system with one of an inactive system, in this case, leads to an inactive reaction product. At node 7-6-8, a reaction including dislocations from the ( i 11) and (111 ) planes is analysed. ½1110] + ½[]01]-- ½[011]
(1)
As long as the resulting ½1011] dislocation keeps the [i01] line vector of dislocation 6, it is on the (11i) plane. However, in the analysed configuration, this dislocation has climbed into an edge position with the
7". Kuttner, M. Feller-Kniepmeier
/
149
Microstructure of Ni-base superalloy after creep
[010] line vector and lies on the (100) plane. Although the total dislocation configuration is pinned at the node, dislocation 6 is observed to bow out into a gliding dipole. Using Thompson's [14] notation, two types of dislocation reaction for the formation of immobile dislocation segments can be classified. For the given tensile direction, A D slip systems with A C D and A B D planes or BC Burgers vector are inactive (see Fig. 3). The immobile dislocation BC can be built by reaction of two glissile dislocations on the same active glide plane: A B C plane: B A + AC --"BC
(2)
B C D plane: BD + DC--" BC
(3)
In Fig. 6 the area in Fig. 5 has been tilted in such way that the two active glide planes (111) and (i 11) are edge on. At the leading part of dipole 9, the contrasts almost overlap each other, indicating the (] 11) glide plane. However, directly after the leading segment, the
Immobile A D dislocations are built by reaction of dislocations from the two glide planes: AC(ABC.' + CD(BcD ) --*A D
(4)
AB/ABC / + BD/BcD) --"A D
(5)
For the reaction of a glissile dislocation with an immobile segment, two reaction types can be determined. If the reaction product lies on the glide plane of the gliding dislocation, it is always glissile:
Fig. 5. Network formation of interfacial dislocations. (ko= [001]; g(200)).
A B C plane: A B + BC --"AC
TABLE 2. Dislocation properties and glide planes analysed from Fig. 5
(6)
AC+CB~AB
(7)
B C D plane: DB + BC ~ DC
(8)
DC + C B - , D B
(9)
The mobility of reaction products of glissile dislocations with the sessile dislocation AD, lying on inactive glide planes, is determined by the line vector of the glissile dislocation. Depending on the character of the gliding dislocation, the reaction product is on a glide plane with a high or low Schmid factor. All the five possible reactions have been observed.
Dislocation number
b
s oc
< (s, b)
s x b
oc
(°)
Schmid factor ms
1
2-5-7-9 3 4 6 8 10
(a/2)[llO]
(a/2)[llO] (a/2)[Oll] (a/2)[i01] (a/2)[101] (a/2)[O11] (a/2)[lO1]
[i12] [110] [ilO] [110] [il0] [010] [110]
60 Screw 60 60 60 45 60
1 i 1) 11 i ) 1 i 1) 111) 100) ill)
0.002 0.395 ~1 0.025 0.002 0.420 0.018 0.410
aFor the ( ] 11 ) slip plane.
~L J 500rim
Fig. 4. Overview of microstructure after e = 0.29% in the (001) projection.
Fig. 6. Same area as Fig. 5, sharing_cross-slip and climb of interfacial dislocations (ko = [101]; g = ( 111 )).
150
T. Kuttner, M. Feller-Kniepmeier / Microstructure of Ni-base superalloy after creep
60*-dislocat227 ion: (%n-Ccp+al,~ _) MPa
(001)-roof channel (01iO)-roof channel screwdislocatio122 n:MPa(%) 60*'dislocatili°n:Oi)ilqa~ ~ /
Fig. 7. Variationin shear stresses as a function of matrix channel orientation for the slip system (a/2)[]01]( 111 ). (Jr L is the external load, and o~p and o~, are stress components of coherency stress acting parallel and normal respectivelyto the y-y' interfaces.
~-~ 1200 ~L
I
....
'
'
'
I
'
'
60O-dislocatinns Screw dislocations
microstructure of SRR99 after [011] creep at 1033 K [6-8]. This effect is due to the superposition of coherency and external stresses, leading to different shear stresses that are experienced by dislocations in the two types of matrix channel. An example for the ½[i01](111 ) slip system is depicted in Fig. 7. In order to estimate the influence of the projected matrix with d on the expansion of dislocation dipoles, the equilibrium of forces A UL(d)/d, due to the formation of an interfacial dislocation segment and the Peach-Koehler force FpK per unit length was calculated:
~-~ lO00l
~q t~
800-
6000
400~
"7.
.a
2oo-
o o
20
'
Matrix
'
'
40 '
'
Channel
'
'
60 ~
Width
'
'
'
8'0
Fig. 9. Overview of [011] creep specimen (T= 1033 K; a = 680 MPa; e = 0.47%) during secondary creep.
100
l [nrn]
Fig. 8. Equilibrium shear stress for dipole expansion as function of matrix width. Dislocation characters are given for the interfacial segments.
dipole segments spread, showing that they have left the glide plane. Also, dipoles 10, 5 and 6 have connecting planes that differ from their glide planes. Detailed analysis revealed that interfacial dipole segments with screw character cross-slip on {001} interfaces where high shear stresses are active. 60 ° interracial dipole segments climb in the 7-Y' interfaces. It is noticeable that the interfacial screw segments of dipoles 2, 5, 7 and 9 have a minimum curvature. This is interpreted as repeated slip on the (] 11) glide plane after cross-slip on the (001) interface has occurred.
4. Discussion Selection of matrix channels Different densities of interfacial dislocations in roof and gable channels have already been observed in the
AV(d)
Fpz = - d
(10)
The equilibrium shear stress r e is given by the component Fg of the Peach-Koehler force in the glide plane normalized to unit length:
re Ibl (bo)p
(11)
The critical equilibrium shear stress r e necessary to expand a dipole in the matrix is then given by
%=
Ibll
with l being the nominal matrix width. A UL, the elastic energy of interfacial dipole segments, was calculated by numerical integration considering the anisotropy of the material. Using the coherency stress components at 1173 K, Ocp = - 2 0 2 MPa and acn=56 MPa [9, 12], the plot of equilibrium shear stress r e vs., channel width l in Fig. 8 is obtained. Owing to the superposition of external and coherency stresses, the shear
T. Kuttner, M. Feller-Kniepmeier
/
Microstructure of Ni-base superalloy after creep
stresses available in roof channels are 227 MPa for 60 ° interfacial dislocations and 122 MPa for screw interfacial dislocations. In gable matrix channels, dipoles with 60 ° interfacial segments experience a shear stress of 17 MPa only. Compared with the common mean matrix channel width of 50 nm after standard heat treatment, matrix channels after a strain ep of 0.29%, due to the change of the 7' morphology, have a mean roof channel width of about 150 nm and a mean gable channel width of 50 nm or less. It is seen from Fig. 8 that, under these conditions, screw and 60 ° interfacial segments can expand only in roof channels and not in gable channels [6, 7]. 4.2. Properties of matrix dipoles In contrast with results obtained at 1033 K, gliding segments of dislocation dipoles in matrix roof channels are not dissociated into Shockley partials. In principle this could be due to an increase in the stacking-fault energy, to the temperature dependences of elastic constants and misfit or to the different load levels. The elastic constants for the two temperatures differ by only 2%, so that this effect is negligible. The temperature dependences of the misfit [9] and therefore of the coherency stresss together with the lower external load are of major influence. Under the assumption that the stacking fault energy of 40 mJ m -2 measured at 1033 K [6, 7] does not increase, a dissociation width of only about 3 nm would result. A major difference between the microstructure at 1173 K and that at 1033 K is the pronounced interfacial climb of interfacial dislocations and the variety of interfacial dislocation reactions. Interfacial cross-slip and climb to some extent relax the slip restrictions imposed by the reduced amount of slip systems with the lack of {111} cross-slip. The analysed interfacial dislocation reactions of creation and annihilation of glissile and sessile dislocation segments stabilize an equilibrium between hardening and softening. 4.3. Correlation between microstructure and creep rates at T = l173 K Under the experimental conditions used at 1173 K, the 7' phase is not sheared. The creep curve up to an elongation of 0.29% is therefore determined by deformation processes occurring in matrix channels and at the 7-7' interfaces. As neither cubic nor single slip is observed, arguments based on these events cannot be used to describe our experimental results. In our interpretation, the concentration of slip in roof matrix channels and the low strain hardening is considered to be the reason for the bad creep performance of the [011] orientation. Because interfacial dislocations can only compensate stress components parallel to the Y-Y' interfaces, stress
151
components of the external load cannot be reduced and a high von Mises stress level remains in the roof channels, independent of interfacial dislocation density. Our observations and their representation by a model based on slip crystallography are supported by stress and strain calculations for creep in [011] direction using a micromechanical model and the FEM [10-12]. At 1173 K, interracial slip and climb play a major part in the quasi-stationary state of creep between strains of 0.1 and 0.29%. Mutual formation and annihilation of glissile and sessile interracial dislocations promote a quasi-stationary creep rate. Generally, in addition to {111} slip, plastic deformation is supported by the analysed interracial cross-slip and climb events that are the result of high shear stresses operating on {100} planes for the [011] load axis. 4.4. Temperature dependence of creep in [011] orientation The microstructure analysed in the present investigation can be compared with that of [011]-oriented SRR99 after creep at 1033 K under a constant load of 680 MPa [6, 7]. Under both testing conditions, cubic slip in the matrix or in the y' volume did not occur and plastic deformation starts by multiple ½(110){111} slip in matrix channels. The types of activated ½(110){111} matrix slip system and the stress concentration in matrix roof channels are common for both temperatures. Also, interfacial cross-slip of screw dislocations is observed in the secondary stage of creep at both test temperatures. Differences in the microstructures arise mainly from the different levels of the external load, the temperature dependence of misfit and from climb processes activated at the higher temperature. The high external load of 680 MPa applied at 1033 K enables shearing of the y' phase at the onset of secondary creep. At this time, stress reduction in the roof matrix channels by 60 ° interfacial dislocations is sufficient for a stress build-up in the y' phase until the 7' yield stress is reached. The decrease in creep rate at the onset of secondary creep results from dislocation hardening in both phases and at the interfaces. As climb processes have no measurable influence at this temperature, plastic strain in the secondary stage of creep is achieved by dipole expansion in the matrix, cross-slip of screw segments at the 7-7' interfaces and common shear of both phases by 2A6 superpartials [6, 7]. Generally, the restriction to few slip systems, the remaining high von Mises stress level in matrix roof channels and the common slip of both phases are considered to be the reasons for the low creep lifetimes of the [011] orientation at 1033 K.
152
T. Kuttner, M. Feller-Kniepmeier /
Microstructure of Ni-base superalloy after creep
At 1173 K under only 300 MPa load, the decrease in von Mises stresses in roof channels is insufficient for the yield stress of 7' particles to be reached. In order to overcome the 7' particles, interfacial slip and climb are activated. Therefore interfacial dislocation reactions and climb processes increasingly determine the creep rate. The transformation to a quasi-stationary state in this case is obtained by the analysed interfacial dislocation reactions that promote an equilibrium between hardening and softening events in matrix and interfaces. The observed reduction in creep rate anisotropy at higher temperatures [4], from the analysis of the microstructure, is considered to be connected with the different load levels applied, leading to different mechanisms for the onset of secondary creep, and to the relaxation of strictly crystallographic slip by climb processes.
5. Conclusions (1) During creep in [011] orientation at 1173 K under 300 MPa the morphology of the Y' phase changes from cubes to rods with [100] direction. (2) Plastic deformation occurs by ½(110){111 } slip on (111) and ( i 11) planes in matrix channels oriented at 45 ° to the load axis. (3) In matrix channels containing the load axis, dislocation expansion is not possible, because of superposition of external and coherency stresses and elastic interactions in narrow matrix channels. (4) Up to a strain of 0.29%, the 7' phase is not sheared during secondary creep. (5) Cross-slip on {100} 7-7' interfaces and interfacial climb play major parts in plastic deformation. (6) By reaction of interfacial dislocations, glissile and sessile dislocation segments are built and stabilize equilibrium between hardening and softening events. (7) The T E M results can be rationalized by applying a model of dislocation loop expansion in narrow matrix channels.
(8) By comparison with an investigation of the microstructure after [011] creep at 1033 K, the temperature dependence of creep under [011 ] load can be discussed.
Acknowledgments The authors are indebted to Deutsche Forschungsgemeinshaft for financial support, to Dr. Ing. U. Paul of Rheinisch-Westf~ilische Technische Hochschule Aachen for casting the single crystals and to Motorenund Turbinen- Union GmbH, Miinchen, for processing and testing of the creep specimens.
References 1 B. H. Kear and B. J. Piearcey, Trans. A1ME, 239 (1967) 1209. 2 R. MacKay and R. D. Maier, Metall. Trans. A , 13 (1982) 1747. 3 R. MacKay, R. L. Dreshfield and R. D. Maier, in J. K. Tien, S. T. Wlodek, H. Morrow III, M. Gell and G. E. Maurer (eds.), Superalloys 1980, Proc. 4th. Int. Symp. on Superalloys, Seven Springs, PA, 1980, American Soc. for Metals, Metals Park, OH, 1980, p. 385. 4 P. Caron Y. Ohta, Y. G. Nakagawa and T. Khan, in S. Reichman, D. N. Duhl, G. Maurer, S. Autolovich and C. Lund (eds.), Superalloys 1988, Metallurgical Society of AIME, Warrendale, PA, 1988, p. 215. 5 P. Caron, T. Khan and Y. G. Nakagawa, Scr. Metall., 20 (1986) 499. 6 T. Kuttner, Ph.D. Thesis. Technische Universit/it Berlin, 1993. 7 M. Feller-Kniepmeier and T. Kuttner, Acta Metall. Mater., in press. 8 T. Kuttner and M. Feller-Kniepmeier, J. de Physique IF, 3 (1993)325. 9 L. Miiller, T. Link and M. Feller-Kniepmeier, Scr. Metall. Mater., 26 (1992) 1297. 10 L. Miiller and M. Feller-Kniepmeier, Scr. Metall. Mater., 29 (1993)81. 11 L. Miiller, Ph.D. Thesis, Technische Universit~it Berlin, 1993. 12 L. M/iller, U. Glatzel and M. Feller-Kniepmeier, Acta Metall. Mater., 41 (1993) 3401. 13 J. K. Tien and S. M. Copley, Metall. Trans., 2 (1971 ) 543. 14 N. Thompson, Proc. Phys. Soc. B, (1953) 481.
147
Microstructure of a nickel-base superalloy after creep in [011] orientation at 1173 K Thomas Kuttner and Monika Feller-Kniepmeier Technische Universitiit Berlin, Institut fiir Metallforschung, Mikrostrukturanalyse, BH 18 Strafle des 17. Juni 135, W-l O587 Berlin (Germany) (Received October 28, 1993; in revised form January 14, 1994)
Abstract Tensile creep tests in the [011] direction have been performed on two specimens of SRR99 at 1173 K under a load of 300 MPa. The microstructure was analysed by transmission electron microscopy investigations after plastic strains of 0.1% and 0.29%. At both strains, the 7' phase is not sheared by dislocations. Plastic deformation is concentrated in roof matrix channels lying at an angle of 45 ° to the load axis. Gable matrix channels that contain the load axis are almost free of dislocations. This experimental result was shown to be due to the supe:rposition of coherency and external load stress tensors, leading to different levels of shear stress in the two types of matrix channel. The results obtained at 1173 K are compared with previous results at 1033 K.
1. Introduction
Creep lifetimes of single-crystal nickel-base superalloys strongly depend on the orientation of the load axis [1-5]. In all investigations the shortest creep lifetimes were observed in [011] orientation. So far, the majority of microstructural investigations have been performed for the [001] orientation. Recently a quantitative transmission electron microscopy (TEM) analysis of the microstructure of SRR99 after creep in [011] orientation at 1033 K [6-8] has been presented. It was shown that the superposition of load and coherency stress together with the restricted amount of glide systems leads to stress accumulation in matrix channels that are at an angle of 45 ° to the load axis. The same result is obtained by modelling by the finite element method (FEM) [9-12]. During creep at 1033 K, diffusion effects play a minor role and the cubic morphology of the 7' phase is maintained throughout the creep experiments [6, 7]. At higher temperatures (1223-1323 K) the effect of orientation and 7' size on the creep strength of superalloys was found to be considerably reduced [4]. In the present investigation, we are interested in the effects that control creep at high temperatures under medium load and on the temperature dependence of creep in [011] orientation.
tals were prepared by epitaxial crystallization. After the standard solution heat treatment (1553 K for 1 h + 1563 K for 2 h + 1573 K for 0.5 h + 1578 K for 0.5 h; cooling to 1273 K at 0.7 K s- ~) and annealing ( 1353 K for 4 h + 1143 K for 16 h), the microstructure consisted of 70 vol.% of cubic 7/' precipitates embedded coherently in the matrix. Two specimens were creep tested at 1173 K under a constant load of 300 MPa. The initial strain gauge length was 25 mm. Specimen 2 was cooled under load while, for specimen 1, cooling and unloading started at the same time. Details of the creep experiments are given in Table 1. Slices for scanning electron microscopy (SEM) and TEM investigations were cut parallel to (011), (100) and (001) planes. The microstructure was investigated using a 300 kV Philips CM30.
3. Results
3.1. Creep curves Creep curves of the two specimens are plotted in Fig. 1 [6]. The creep rate of specimen 2 reaches a quasi-stationary creep rate of g of about 4 x 10-9 sin the secondary stage of creep. The difference between the initial creep rates of the two specimens is considered to be connected to different densities of grown-in dislocations.
2. Experimental details
The single-crystal nickel-base superalloy used for the investigation was SRR99. The [011]-oriented crys0921-5093/94/$7.00 SSD1 0921-5093(94)09523-Y
3.2. Morphology of the 7' phase In specimen 1 (creep time, 7.45 h) the cubic 7' morphology is unchanged. After a creep time of © 1994 - Elsevier Sequoia. All rights reserved
148
T. Kuttner, M. Feller-Kniepmeier / Microstructureof Ni-base superalloy after creep
TABLE 1. Creep tests at 1173 K, and o = 300 MPa Specimen
Load axis
1
[3, 68, 73]
2
[2, 70, 72]
Creep time (h) 7.45
217.2
Plastic strain (%) 0.1
0.29
0.4 sp'ci--e-"~ .,.. ' ' specimen 2 o~
0.3-
.o O (D t,-, ¢2
Fig. 2. Overview of microstructure after e=0.1% in the (001) projection.
0.2-
0.1-
•
direction
D
0.0
o
5'0 . . . .
i;o
i;o . . . .
2;0 . . . .
time [h] Fig. 1. Creep curves of specimens 1 and 2 (T=l173K; o = 300 MPa). A
A
Fig. 3. Orientation of glide systems relative to the load axis. 217.2 h, the y' precipitates have achieved a rod morphology, with the long axis parallel to the [100] direction. This morphology change is consistent with the growth direction, deduced from F E M calculations of the elastic energy for a superalloy with negative misfit and [011] tensile axis [11] and with previous experimental observations [13]. 3.3. Dislocation structures at ep = 0.1% and ep = 0.29% An overview in (001) projection of the microstructure strained to 0.1% is shown in Fig. 2. The two essential observations are that the 7' phase is not sheared at this stage of creep and that (001) and (010) matrix channels contain interfacial dislocations while (100) channels are almost free of dislocations. For the [011] load direction, two types of matrix channel can be distinguished. Those that build an angle of 45 ° with the load axis which will be denoted as roof channels, and the (100) channels that contain the load axis and are denoted as gable channels. The matrix dislocation loops were analysed to be on the octahedral slip systems with the highest Schmid factors. Dislocations with ½[i01] and ½[i10] Burgers vectors operate on the (111) plane and those with ½[101] and ½[110] on the ( i l l ) plane. In Fig 3 the orientations of glide systems relative to the load axis are depicted. Neither {111} cross-slip nor cubic slip occurs. In contrast with observations made after creep
in the [011] orientation at 1033 K, dissociation of the gliding matrix dipole segments into Shockley partials was not observed at 1173 K. Figure 4 shows an overview of the microstructure after 0.29% strain in the (001) projection. Interfacial ½(110) dislocations with mainly 60 ° character on (111) and (i11) planes are seen to form rectangular networks. In this specimen, detailed analysis of the interfacial dislocation networks was performed. An example is shown in Fig. 5 with compilation in Table 2. Network formation of a ½1110] dislocation dipole, having screw character in its interfacial segments, with a sessile ½[011] dislocation is observed at node 5-3-4. The reaction product ½[]01] lies on the (1]1) plane, which is inactive. Reaction of a dislocation from an active glide system with one of an inactive system, in this case, leads to an inactive reaction product. At node 7-6-8, a reaction including dislocations from the ( i 11) and (111 ) planes is analysed. ½1110] + ½[]01]-- ½[011]
(1)
As long as the resulting ½1011] dislocation keeps the [i01] line vector of dislocation 6, it is on the (11i) plane. However, in the analysed configuration, this dislocation has climbed into an edge position with the
7". Kuttner, M. Feller-Kniepmeier
/
149
Microstructure of Ni-base superalloy after creep
[010] line vector and lies on the (100) plane. Although the total dislocation configuration is pinned at the node, dislocation 6 is observed to bow out into a gliding dipole. Using Thompson's [14] notation, two types of dislocation reaction for the formation of immobile dislocation segments can be classified. For the given tensile direction, A D slip systems with A C D and A B D planes or BC Burgers vector are inactive (see Fig. 3). The immobile dislocation BC can be built by reaction of two glissile dislocations on the same active glide plane: A B C plane: B A + AC --"BC
(2)
B C D plane: BD + DC--" BC
(3)
In Fig. 6 the area in Fig. 5 has been tilted in such way that the two active glide planes (111) and (i 11) are edge on. At the leading part of dipole 9, the contrasts almost overlap each other, indicating the (] 11) glide plane. However, directly after the leading segment, the
Immobile A D dislocations are built by reaction of dislocations from the two glide planes: AC(ABC.' + CD(BcD ) --*A D
(4)
AB/ABC / + BD/BcD) --"A D
(5)
For the reaction of a glissile dislocation with an immobile segment, two reaction types can be determined. If the reaction product lies on the glide plane of the gliding dislocation, it is always glissile:
Fig. 5. Network formation of interfacial dislocations. (ko= [001]; g(200)).
A B C plane: A B + BC --"AC
TABLE 2. Dislocation properties and glide planes analysed from Fig. 5
(6)
AC+CB~AB
(7)
B C D plane: DB + BC ~ DC
(8)
DC + C B - , D B
(9)
The mobility of reaction products of glissile dislocations with the sessile dislocation AD, lying on inactive glide planes, is determined by the line vector of the glissile dislocation. Depending on the character of the gliding dislocation, the reaction product is on a glide plane with a high or low Schmid factor. All the five possible reactions have been observed.
Dislocation number
b
s oc
< (s, b)
s x b
oc
(°)
Schmid factor ms
1
2-5-7-9 3 4 6 8 10
(a/2)[llO]
(a/2)[llO] (a/2)[Oll] (a/2)[i01] (a/2)[101] (a/2)[O11] (a/2)[lO1]
[i12] [110] [ilO] [110] [il0] [010] [110]
60 Screw 60 60 60 45 60
1 i 1) 11 i ) 1 i 1) 111) 100) ill)
0.002 0.395 ~1 0.025 0.002 0.420 0.018 0.410
aFor the ( ] 11 ) slip plane.
~L J 500rim
Fig. 4. Overview of microstructure after e = 0.29% in the (001) projection.
Fig. 6. Same area as Fig. 5, sharing_cross-slip and climb of interfacial dislocations (ko = [101]; g = ( 111 )).
150
T. Kuttner, M. Feller-Kniepmeier / Microstructure of Ni-base superalloy after creep
60*-dislocat227 ion: (%n-Ccp+al,~ _) MPa
(001)-roof channel (01iO)-roof channel screwdislocatio122 n:MPa(%) 60*'dislocatili°n:Oi)ilqa~ ~ /
Fig. 7. Variationin shear stresses as a function of matrix channel orientation for the slip system (a/2)[]01]( 111 ). (Jr L is the external load, and o~p and o~, are stress components of coherency stress acting parallel and normal respectivelyto the y-y' interfaces.
~-~ 1200 ~L
I
....
'
'
'
I
'
'
60O-dislocatinns Screw dislocations
microstructure of SRR99 after [011] creep at 1033 K [6-8]. This effect is due to the superposition of coherency and external stresses, leading to different shear stresses that are experienced by dislocations in the two types of matrix channel. An example for the ½[i01](111 ) slip system is depicted in Fig. 7. In order to estimate the influence of the projected matrix with d on the expansion of dislocation dipoles, the equilibrium of forces A UL(d)/d, due to the formation of an interfacial dislocation segment and the Peach-Koehler force FpK per unit length was calculated:
~-~ lO00l
~q t~
800-
6000
400~
"7.
.a
2oo-
o o
20
'
Matrix
'
'
40 '
'
Channel
'
'
60 ~
Width
'
'
'
8'0
Fig. 9. Overview of [011] creep specimen (T= 1033 K; a = 680 MPa; e = 0.47%) during secondary creep.
100
l [nrn]
Fig. 8. Equilibrium shear stress for dipole expansion as function of matrix width. Dislocation characters are given for the interfacial segments.
dipole segments spread, showing that they have left the glide plane. Also, dipoles 10, 5 and 6 have connecting planes that differ from their glide planes. Detailed analysis revealed that interfacial dipole segments with screw character cross-slip on {001} interfaces where high shear stresses are active. 60 ° interracial dipole segments climb in the 7-Y' interfaces. It is noticeable that the interfacial screw segments of dipoles 2, 5, 7 and 9 have a minimum curvature. This is interpreted as repeated slip on the (] 11) glide plane after cross-slip on the (001) interface has occurred.
4. Discussion Selection of matrix channels Different densities of interfacial dislocations in roof and gable channels have already been observed in the
AV(d)
Fpz = - d
(10)
The equilibrium shear stress r e is given by the component Fg of the Peach-Koehler force in the glide plane normalized to unit length:
re Ibl (bo)p
(11)
The critical equilibrium shear stress r e necessary to expand a dipole in the matrix is then given by
%=
Ibll
with l being the nominal matrix width. A UL, the elastic energy of interfacial dipole segments, was calculated by numerical integration considering the anisotropy of the material. Using the coherency stress components at 1173 K, Ocp = - 2 0 2 MPa and acn=56 MPa [9, 12], the plot of equilibrium shear stress r e vs., channel width l in Fig. 8 is obtained. Owing to the superposition of external and coherency stresses, the shear
T. Kuttner, M. Feller-Kniepmeier
/
Microstructure of Ni-base superalloy after creep
stresses available in roof channels are 227 MPa for 60 ° interfacial dislocations and 122 MPa for screw interfacial dislocations. In gable matrix channels, dipoles with 60 ° interfacial segments experience a shear stress of 17 MPa only. Compared with the common mean matrix channel width of 50 nm after standard heat treatment, matrix channels after a strain ep of 0.29%, due to the change of the 7' morphology, have a mean roof channel width of about 150 nm and a mean gable channel width of 50 nm or less. It is seen from Fig. 8 that, under these conditions, screw and 60 ° interfacial segments can expand only in roof channels and not in gable channels [6, 7]. 4.2. Properties of matrix dipoles In contrast with results obtained at 1033 K, gliding segments of dislocation dipoles in matrix roof channels are not dissociated into Shockley partials. In principle this could be due to an increase in the stacking-fault energy, to the temperature dependences of elastic constants and misfit or to the different load levels. The elastic constants for the two temperatures differ by only 2%, so that this effect is negligible. The temperature dependences of the misfit [9] and therefore of the coherency stresss together with the lower external load are of major influence. Under the assumption that the stacking fault energy of 40 mJ m -2 measured at 1033 K [6, 7] does not increase, a dissociation width of only about 3 nm would result. A major difference between the microstructure at 1173 K and that at 1033 K is the pronounced interfacial climb of interfacial dislocations and the variety of interfacial dislocation reactions. Interfacial cross-slip and climb to some extent relax the slip restrictions imposed by the reduced amount of slip systems with the lack of {111} cross-slip. The analysed interfacial dislocation reactions of creation and annihilation of glissile and sessile dislocation segments stabilize an equilibrium between hardening and softening. 4.3. Correlation between microstructure and creep rates at T = l173 K Under the experimental conditions used at 1173 K, the 7' phase is not sheared. The creep curve up to an elongation of 0.29% is therefore determined by deformation processes occurring in matrix channels and at the 7-7' interfaces. As neither cubic nor single slip is observed, arguments based on these events cannot be used to describe our experimental results. In our interpretation, the concentration of slip in roof matrix channels and the low strain hardening is considered to be the reason for the bad creep performance of the [011] orientation. Because interfacial dislocations can only compensate stress components parallel to the Y-Y' interfaces, stress
151
components of the external load cannot be reduced and a high von Mises stress level remains in the roof channels, independent of interfacial dislocation density. Our observations and their representation by a model based on slip crystallography are supported by stress and strain calculations for creep in [011] direction using a micromechanical model and the FEM [10-12]. At 1173 K, interracial slip and climb play a major part in the quasi-stationary state of creep between strains of 0.1 and 0.29%. Mutual formation and annihilation of glissile and sessile interracial dislocations promote a quasi-stationary creep rate. Generally, in addition to {111} slip, plastic deformation is supported by the analysed interracial cross-slip and climb events that are the result of high shear stresses operating on {100} planes for the [011] load axis. 4.4. Temperature dependence of creep in [011] orientation The microstructure analysed in the present investigation can be compared with that of [011]-oriented SRR99 after creep at 1033 K under a constant load of 680 MPa [6, 7]. Under both testing conditions, cubic slip in the matrix or in the y' volume did not occur and plastic deformation starts by multiple ½(110){111} slip in matrix channels. The types of activated ½(110){111} matrix slip system and the stress concentration in matrix roof channels are common for both temperatures. Also, interfacial cross-slip of screw dislocations is observed in the secondary stage of creep at both test temperatures. Differences in the microstructures arise mainly from the different levels of the external load, the temperature dependence of misfit and from climb processes activated at the higher temperature. The high external load of 680 MPa applied at 1033 K enables shearing of the y' phase at the onset of secondary creep. At this time, stress reduction in the roof matrix channels by 60 ° interfacial dislocations is sufficient for a stress build-up in the y' phase until the 7' yield stress is reached. The decrease in creep rate at the onset of secondary creep results from dislocation hardening in both phases and at the interfaces. As climb processes have no measurable influence at this temperature, plastic strain in the secondary stage of creep is achieved by dipole expansion in the matrix, cross-slip of screw segments at the 7-7' interfaces and common shear of both phases by 2A6 superpartials [6, 7]. Generally, the restriction to few slip systems, the remaining high von Mises stress level in matrix roof channels and the common slip of both phases are considered to be the reasons for the low creep lifetimes of the [011] orientation at 1033 K.
152
T. Kuttner, M. Feller-Kniepmeier /
Microstructure of Ni-base superalloy after creep
At 1173 K under only 300 MPa load, the decrease in von Mises stresses in roof channels is insufficient for the yield stress of 7' particles to be reached. In order to overcome the 7' particles, interfacial slip and climb are activated. Therefore interfacial dislocation reactions and climb processes increasingly determine the creep rate. The transformation to a quasi-stationary state in this case is obtained by the analysed interfacial dislocation reactions that promote an equilibrium between hardening and softening events in matrix and interfaces. The observed reduction in creep rate anisotropy at higher temperatures [4], from the analysis of the microstructure, is considered to be connected with the different load levels applied, leading to different mechanisms for the onset of secondary creep, and to the relaxation of strictly crystallographic slip by climb processes.
5. Conclusions (1) During creep in [011] orientation at 1173 K under 300 MPa the morphology of the Y' phase changes from cubes to rods with [100] direction. (2) Plastic deformation occurs by ½(110){111 } slip on (111) and ( i 11) planes in matrix channels oriented at 45 ° to the load axis. (3) In matrix channels containing the load axis, dislocation expansion is not possible, because of superposition of external and coherency stresses and elastic interactions in narrow matrix channels. (4) Up to a strain of 0.29%, the 7' phase is not sheared during secondary creep. (5) Cross-slip on {100} 7-7' interfaces and interfacial climb play major parts in plastic deformation. (6) By reaction of interfacial dislocations, glissile and sessile dislocation segments are built and stabilize equilibrium between hardening and softening events. (7) The T E M results can be rationalized by applying a model of dislocation loop expansion in narrow matrix channels.
(8) By comparison with an investigation of the microstructure after [011] creep at 1033 K, the temperature dependence of creep under [011 ] load can be discussed.
Acknowledgments The authors are indebted to Deutsche Forschungsgemeinshaft for financial support, to Dr. Ing. U. Paul of Rheinisch-Westf~ilische Technische Hochschule Aachen for casting the single crystals and to Motorenund Turbinen- Union GmbH, Miinchen, for processing and testing of the creep specimens.
References 1 B. H. Kear and B. J. Piearcey, Trans. A1ME, 239 (1967) 1209. 2 R. MacKay and R. D. Maier, Metall. Trans. A , 13 (1982) 1747. 3 R. MacKay, R. L. Dreshfield and R. D. Maier, in J. K. Tien, S. T. Wlodek, H. Morrow III, M. Gell and G. E. Maurer (eds.), Superalloys 1980, Proc. 4th. Int. Symp. on Superalloys, Seven Springs, PA, 1980, American Soc. for Metals, Metals Park, OH, 1980, p. 385. 4 P. Caron Y. Ohta, Y. G. Nakagawa and T. Khan, in S. Reichman, D. N. Duhl, G. Maurer, S. Autolovich and C. Lund (eds.), Superalloys 1988, Metallurgical Society of AIME, Warrendale, PA, 1988, p. 215. 5 P. Caron, T. Khan and Y. G. Nakagawa, Scr. Metall., 20 (1986) 499. 6 T. Kuttner, Ph.D. Thesis. Technische Universit/it Berlin, 1993. 7 M. Feller-Kniepmeier and T. Kuttner, Acta Metall. Mater., in press. 8 T. Kuttner and M. Feller-Kniepmeier, J. de Physique IF, 3 (1993)325. 9 L. Miiller, T. Link and M. Feller-Kniepmeier, Scr. Metall. Mater., 26 (1992) 1297. 10 L. Miiller and M. Feller-Kniepmeier, Scr. Metall. Mater., 29 (1993)81. 11 L. Miiller, Ph.D. Thesis, Technische Universit~it Berlin, 1993. 12 L. M/iller, U. Glatzel and M. Feller-Kniepmeier, Acta Metall. Mater., 41 (1993) 3401. 13 J. K. Tien and S. M. Copley, Metall. Trans., 2 (1971 ) 543. 14 N. Thompson, Proc. Phys. Soc. B, (1953) 481.