Analysis of dislocation structures after double shear creep deformation of CMSX6-superalloy single crystals at temperatures above 1000 °C

Analysis of dislocation structures after double shear creep deformation of CMSX6-superalloy single crystals at temperatures above 1000 °C

MATERIALS SCIENCE & ENGINEERIRC ELSEVIER Materials Science and Engineering A207 (1996) 51-63 A Analysis of dislocation structures after double shea...

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Materials Science and Engineering A207 (1996) 51-63


Analysis of dislocation structures after double shear creep deformation of CMSXG-superalloy single crystals at temperatures above 1000 “C C. Mayr, G. Eggelerl, A. Dlouhy2 Swiss Federal Institute of Technology, Materials Department, MX-D Ecublens, CH-1015 Lawanne, Switzerland Received 22 March 1995; in revised form 14 July 1995

Abstract Dislocation structures which form during pure shear creep deformation of the superalloy single crystal alloy CMSX6 at 1025 “C under a shear stress of 85 MPa were analysed using transmission electron microscopy. Two macroscopic crystallographic shear systems were studied: {111}(110) and {lOO}(OlO). At the minimum creep rate (observed at shear values of 0.02) the system

{ 11l}(llO) deforms by a factor of ten faster than the system { lOO}(OlO). This creep rate ratio could not be rationalised merely on the basis of an external resolved shear stress argument. Shear creep deformation was always associated with multiple slip and nucleation of dislocations was not difficult (absence of incubation periods for creep). A detailed study of dislocation networks around y/-particles underlined the importance of (1 lo){ 111) glide and climb processesin the y-channels in the formation of these networks. Microstructural parameters and processes which must be considered to fully account for the mechanism of creep in superalloy SX are outlined. Channel work hardening always preceded the cutting of y’-particles which started at the minimum creep rate. Keywords:

CMSX6-Superalloy; Dislocation structures; Shear creep deformation

1. Introduction

Cast nickel-base superalloy single crystals (SXs) are used for gas turbine blades operating at temperatures up to 1100 “C where creep is one of the life limiting factors. Superalloy SXs consist of two phases: (i) a high volume fraction of coherently precipitated y/-cubes (Ll,) separated by (ii) thin channels of face centred cubic (f.c.c.) y-matrix. In this contribution, dislocation structures which form during double shear creep deformation of superalloy SXs loaded on two macroscopic crystallographic shear systems (MCSSs), namely (lll)(llO) and {100}(010), are analysed. A double shear creep test technique which is suitable to deform superalloy SXs under conditions of pure shear has been

‘Present address: Ruhr-University Bochum, Institute for Materials, Universit%tsstral3e 150, D-44780 Bochum, Germany. ?On leave from: Institute of Physics of Materials, Academy of Sciences of the Czech Republic, Zizkova 22, 616 62 Brno, Czech Republic. 0921-5093/96/$15.00 0 1996 - Elsevier Science S.A. All rights reserved

described recently [1,2]. (Unfortunately, there was a mistake in the work of Mayr et al. [l]. Fig. 5(a) in that manuscript showed part of a dislocation network after the minimum creep rate, and Fig. 5(b) showed the filling of matrix channels with dislocations during primary creep. The corresponding figure captions were juxtaposed.) Pure shear testing has always been attractive to researchers concerned with plastic deformation of metals because it allows direct loading of specific microscopic crystallographic shear systems. It is particularly suitable for characterising creep anisotropy of superalloy SXs at temperatures above 1000 “C [2]. When SX superalloys are tested in pure shear on different MCSSs there is not only a difference in resolved shear stresses for different microscopic slip systems but the spatial distribution of the y/-cubes with respect to the macroscopic shear plane will also change, as schematically illustrated in Fig. 1 (above: shear system {lll}( IlO), below: shear system {100}(010)). This second factor of anisotropy may equally influence creep rate anisotropy. Rafting of the

C. Mayr et al. 1 Materids Science ml Engineering A207 (1996) 51-63

Fig. 2. TEM micrograph (dark field) of the as-received CMSX6 material (Table 2: reference 1).

Fig. 1. Particle morphology as observed on cross-sections of the as-received material when looking on the macroscopic crystallographic shear planes. Above: { 11l}-plane. Below: { lOO}-plane. The schematic drawings represent binary images which were obtained from SEM-micrographs using an image analysis system.

y’-phase occurs during creep but it is not explicitly considered in the present study.

2. Experimental The double shear specimens were obtained from 19 mm diameter cylindrical SX cast rods of the superalloy CMSX6. The chemical composition of the material is given in Table 1. The vacuum heat treatment of the as-received material consisted of annealing (i) 1 h at 1204 “C, (ii) 3 h at 1238 “C, (iii) 3 h at 1271 “C and (iv) 3 at 1280 “C followed by cooling under argon (cooling rate 300 “C min- ‘). A transmission electron microscopy (TEM) micrograph of the as-received material is shown in Fig. 2; the microstructure contains only a very low density of free dislocations. Double shear creep specimens were machined using an iterative procedure consisting of (i) orienting the material in a Laue camera and (ii) spark erosion cutting [2]. This yields double shear creep specimens with welldefined macroscopic crystallographic shear planes and shear directions. Details of the double shear creep test Table 1 Chemical composition of the CMSX6 material used

technique used in the present study are given elsewhere [2]. The creep curves of the two MCSSs which were considered in the present study are shown in Fig. 3. Fig. 3 represents creep data as the logarithm of shear rate i vs. shear y. All curves exhibit decreasing primary creep rates, a creep rate minimum and a slow and steady increase of shear rate after the minimum. Fig. 3 shows that there is a clear influence of crystallographic orientation on shear rates. The MCSS { 11 l} (110) deforms by a factor of ten faster than the MCSS { lOO}(OlO). Shear creep deformation starts with high primary creep rates in both MCSSs. An incubation period for creep-which is sometimes observed in uniaxial testing of superalloy SXs [3]-was not observed. Creep tests were interrupted during primary creep and after the minimum creep rate and the specimens were then analysed by TEM. Dislocation structures were analysed for all double shear creep tests listed in Table 2. TEM was performed using a Phillips CM20 operating at an accelerating voltage of 200 kV. Slices of 1 mm thickness were cut from the as-received material (initial state) and from the crept specimens.


0 .k IlOO~

10S 0

















< 0.03



T:1025“C c:85MPa

I 0.05


4 0.1




Fig. 3. Logarithm of shear rate as a function of shear for the two macroscopic shear crystallographies (11 l}(l IO) and { lOO}(OlO) (T = 85 MPa, T= 1025 “C).

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Table 2 Reference numbers for the initial state CMSX6 material and the double shear creep tests which were performed at 1025 “C and 85 MPa Material state As-received Macroscopic Macroscopic Macroscopic Macroscopic

material shear system shear system shear system shear system

(11 I)[01 i]/primary creep (11 l)[Oli]/creep rate minimum (OOl)[lOO]/primary creep (OOl)[lOO]/creep rate minimum

In the case of the deformed material states, specimens were taken parallel to the macroscopic crystallographic shear planes from a region where the macroscopic external stress state was purely biaxial [2]. For both macroscopic slip systems investigated, the normal n of the TEM-foils was, to a good approximation, perpendicular to the macroscopic crystallographic shear plane. Kikuchi line diffraction patterns (KLD-patterns) were used to orient the foil for TEM and to set appropriate conditions for good dislocation contrast. An example of two such KLD-patterns from the TEM foil coplanar with the (100) shear plane are shown in Fig. 4 (g: iii). The stereo pair shown in Fig. 5(a) and 5(b) were taken using the two two-beam conditions shown in Fig. 4. There is clear evidence for a cross slip event in the stereo pair shown in Fig. 5. Such cross slip events have been reported in the literature (e.g. see Refs. [3-51). As can be seen in Figs. 5, cube-projections are used to indicate the crystallographic orientation of each particular TEM micrograph. These cubes can be thought of as the projection of an enlarged crystallographic unit cell on the TEM image plane. Used in combination with stereo microscopy these cube projections-in which Thompson’s tetrahedron [6] is inscribed-give a direct visual impression of the orientation of { lOO}- and {Ill}-planes and of (lOO)- and (llO)-directions in space. All TEM micrographs were taken under two beam conditions using g-vectors of types (11 l), (200) and (220). The dislocation structures observed in the corresponding micrographs were then anaiysed with respect to the Burgers vectors b and associated slip planes of the dislocation segments. At least seven different g-vec-

Fig. 4. Part of a Kikuchi map of the TEM foil which is coplanar to the {loo} shear plane. This is a montage of two KLD patterns (g:



Reference number

0.020 0.140 0.013 0.046

1 2 3 4 5

tors were used for each particular location to assure the unambiguous analysis of Burgers vectors b by means of the effective invisibility criterion. The sense of the Burgers vectors was not determined. Stereo pairs of one area were taken using different low index g-vectors to obtain information on the spatial arrangement of the observed dislocation structure.

3. Analysis of dislocation structures

3.I. Shear system (11 l)[Ol 17 The dislocation structure which develops during primary creep is shown in Fig. 6. All results of the g*b-analysis and the evaluations of stereo pairs are summarised in Tables 3 and 4. From Figs. 6(a)-6(d) it can be concluded that a considerable part of the overall dislocation density is associated with long dislocation segments (dislocation family 1 in Tables 3 and 4). These are visible in Figs. 6(b) and 6(c) and show only residual contrast in Figs. 6(a) and 6(d). Stereo microscopy confirmed that the long segments of dislocation family 1 are associated with the (1 1 1)-plane. Their Burgers vector b, was found to be of type + a,/2. [Oil 1. In some areas, irregular dislocation networks were observed, like the network in the upper left part of Figs. 6(a) to 6(c). These networks contain other dislocation segments which do not belong to dislocation family 1. Some dislocation segments are not associated with the primary (111) slip plane, These dislocation segments cross the TEM foil from the top to the bottom and several types of different Burgers vector were observed. The most frequently detected types of segment belong to dislocation families 2 and 3, Tables 3 and 4. Stereo pair analysis suggests that if these dislocation families were associated with crystallographic slip then the corresponding slip planes were both of type (1 Ii). The dislocation structure which has developed after the minimum shear rate is shown in the TEM micrographs of Fig. 7. It consists of three types of dislocation segments which are referred to as dislocation families 4 to 6 in Tables 5 and 6. While dislocation family 4 is invisible in Fig. 7(a), the second system of dislocation segments (family 5) is invisible in Fig. 7(b) and disloca-

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Fig. 5. Stereo pair of TEM micrographs obtained using the two two-beam conditions of Fig. 4,

tion segment family 6 is invisible in Fig. 7(c). All dislocation segments are visible in Fig. 7(d). Stereo analysis of the dislocation network shown in the left parts of Figs. 7(a) to 7(d) showed that the dislocation segments with Burgers vectors b, are parallel to the shear plane (111). The dislocation segments of family 5 were often found to cross the TEM foil from the top to the bottom. This excludes the possibility that this system results from slip on the (111) shear plane. The dislocation family 5 (b5) arrived at the y/-interface due to glide on the (1 Ii)-plane. Dislocation segment family 6 with Burgers vector (b6 = f a,/2. (iO1) is a result of dislocation reactions between families 4 and 5. Since dislocation segments of system 6 are rather short, stereo analysis could not clearly identify corresponding crystallographic directions and planes. The results are consistent in that dislocation families 1,2 (primary creep) and 4,5 (after minimum creep rate) belong to the same microscopic crystallographic slip systems. Fig. 8 summarises schematically the TEM results obtained for the MCSS (lll)[Oli]. It shows how dislocation families 1,4 and 2,5 are deposited in the y/y’-interfaces. (Note that b, equals b, and that b, equals b,.) 3.2. Shear system (OOl)[lOO]

Dislocation structures which form during primary creep in the MCSS (OOl)[lOO] are shown in Figs. 9(a) to 9(d). The results of the visibility/invisibility-analysis for four dislocation families is summarised in Table 7. The resulting Burgers vectors, together with slip planes which were determined using stereo microscopy, are given in Table 8. The dislocation families 9 and 10 were most frequently observed. Their Burgers vectors were determined as bg = _+a,/2. (iO1) and b,,, = I a,/2 -*(101). The other two types of dislocation segment (families 7 and 8) occurred less frequently. They have Burgers vectors of type b, = + a,/2. (Oil) and b, = + a,/2* (011). A detailed assessment of stereo pairs

showed that none of the observed segments can be clearly associated with one particular slip plane. However, in the case of dislocation families 8, 9 and 10 there is clear evidence that dislocation line segments can be associated with the (lli)- or (lil)-plane. Some of the segments of dislocation family 9 have also been observed on the (lOl)-plane. The situation after the shear rate minimum in the case of the MCSS (OOl)[lOO] is illustrated in the TEM micrographs of Figs. 10(a) to 10(d). The networks consist of three dislocation families (1 1- 13). While the first two systems (family 11 and 12) are visible in Fig. 10(a), they only are in residual contrast in Fig. IO(b). The dislocation family 13 is invisible in Figs. 10(a), 10(c) and 10(d) and is in full contrast in Fig. IO(b). The first dislocation system (family 11) is invisible in Fig. 10(c) and visible in Fig. 10(d), while the opposite holds for dislocation family 12 (summaries of the results are given in Tables 9 and 10). Stereo pair analysis on the network shown in Fig. 10 revealed that this part of the network is nearly parallel to the (OOl)-plane. This is in agreement with what has been reported in the literature for the case of uniaxial tests in (100) direction where networks were observed close to the (100) interfaces (e.g. see Ref. [7]). The (001) plane is the macroscopic crystallographic shear plane and it is parallel to the TEM-foil which, therefore, is particularly suitable for the assessment of possible slip planes. The segments of dislocation families 11 and 12 intersect at an angle which is close to 90”. The angles between the dislocation segments of these two families and the crystallographic directions [loo] and [OIO] are very close to 45”. Therefore it can be concluded that the dislocation loops which deposited these segments at the y/y/-interfaces propagated on (ill) and (lli) planes, as described by Feller-Kniepmeier and Link [8,9] for the case of uniaxial creep of SRR99. This is schematically illustrated in Fig. 11. Dislocation family 13 consists of segments which are parallel to [OlO] (Figs. 10 and 11). While

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(4 Fig. 6. TEM micrographsof dislocationsin the matrix channel taken under different two-beam conditions for the macroscopicshearsystem (lll)[Oli]. Test interrupted during primary creep(Table 2: reference2): (a) g: (Iii), (b) g: (irl), (c) g: @Ii), (d) g: (200). there is some evidence that segments of dislocation family 13 locally moved on (lOi) planes, there are other cases where these segments are parallel to the inlersection of the planes (Iii) and (001). Reaction products resulting from interactions of these three basic families were also observed frequently. There are mainly two reaction products with Burgers vectors f 42. [l lo] and + 42. [TlO] which appear as short segments stabilising the network. Occasionally, segments resulting from dislocation reactions with Burgers vectors

Table 3 Dislocationfamilies1, 2 and 3 in the MCSS (11l)[Oli] which formed during primary creep(Fig. 6, Table 2: reference2) and their visibility (+) and/or effectiveinvisibility (-)

+ 42.

[OlO] were also observed.

3.3. Cutting of f-particles minimum

after the shear rate

A common microstructural feature of both macroscopic crystallographic shear systems investigated in the present study was that cutting of $-particles was not observed during primary creep but did occur after the

Table 4 Burgers vectors and slip planes of dislocations in the MCSS (lll)[Oli] which formed during primary creep (Fig. 6, Table 2: reference2)

Dislocation family g

1 2 3

(iTi) (iTi) (iii)

(202) (022) (Zoo) (020)

+ +

4+ +

+ -

+ + -

f -I-

+ -

+ -I+


* 2b/a

Planeof dislocation segments

1 2 3



[ii01 P111

(iii) (Iii)

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Cd) Fig. 7. TEM micrographsof a y/y’-dislocationnetwork of one area taken under different two-beamconditionsfor the macroscopicshearsystem (11l)[Oli]. Test interrupted after the shearrate minimum (Table 2: reference3): (a) g: (il I), (b) g: (iii), (c) g: (lil), (d) g: (ZOZ).

shear rate minimum. An example of pairwise cutting of a y/-particle in the MCSS {ill 1 is given in Fig. 12. Pairwise cutting of y’-particles in SX superalloys has been extensively investigated in the literature and will not be discussed. Here, it is important that cutting starts at the minimum shear creep rate.

Table 5 Dislocation families 4, 5 and 6 in the MCSS (lll)[Oli] after the minimum creeprate (Fig. 7, Table 2: reference3) and their visibility ( + ) and/or effectiveinvisibility( - )

4. Discussion 4.1. Creep nniso tropy The creep results which were obtained for the two MCSSs are presented in Fig. 3. In the beginning of creep the MCSS (11 l)[Olij deforms by a factor of five

Table 6 Burgers vectors and slip planes of dislocations in the MCSS (11l)[Oli] after the minimum creeprate (Fig. 7, Table 2: reference3) Dislocationfamily

2 2bja

Plane of dislocation segments

4 5

[oil] [ii01 [ioil

(111) (1ii) -n

Dislocationfamily g

4 5 6


(iTi) (iii)

(202) (022) (002) (020)

+ L

+ +

+ + +

i+ -


+ +

i + -


“Dislocationsegmentstoo short for a clear identificationof correspondingcrystallographicslip plane.

C. Map et al. 1 Materials Science and Engineering A207 (1996) 51-63


4.3. Recovery processes

Fig. 8. Schematic drawing illustrating the deposition of dislocation segments at y/y’-interfaces during primary creep as well as after the minimum shear rate in the MCSS (Ill)[Oli]. (Note that b, equals b, and that b, equals b2.)

than the MCSS (OOl)[lOO]. This difference in creep rates increases during creep. At the minimum creep rate the MCSS (11 l)[Oli] deforms by a factor of ten faster than the MCSS (OOl)[lOO]. This is a clear indication of creep anisotropy of SX superalloys at temperatures above 1000 “C.


4.2. Absence of single slip

One conclusion which can be drawn from the TEM results obtained is that plastic deformation during high temperature shear creep deformation in superalloy SXs never is associated with single slip as would be expected in the case of pure copper at 293 K. Here, uniaxial tension specimens which were oriented for single slip remained during 0.1 shear within the single slip regime [IO]. For the material investigated in the present study, even in primary creep at shear strains y smaller than 0.02, there is clear evidence for more than one activated slip system in both MCSSs investigated. Only in the case of primary creep in the (lll)[Oli]-system is the directly loaded slip system dominant (dislocation family 1, Fig. 6). After the shear rate minimum, each of three dislocation families, associated with different microscopic slip systems, contribute the same amount to the overall dislocation density. In the case of the (OOl)[lOO]system this holds for early and later stages of creep (Figs. 9 and lo), a clear overweight of one family of dislocations is never observed.

High temperature creep in superalloy SX does involve diffusion controlled recovery processes. Evidence for this has been shown in the literature. Pollock and Argon [3] take the bowing out of dislocations lines from sharp corners after cross slip events as direct experimental evidence. Keller et al. [7] observe deviations from regular network structures which they rationalise on the basis of non-conservative dislocation movement. The formation of a low energy dislocation network itself may be considered as a recovery process. However, Figs. 8 and 11 suggest that dislocation glide in the y-channels is also important in the formation of such networks. Networks were not observed in the undeformed parts of the double shear creep specimens. Networks do not form easily, as misfit stresses relax in the absence of external stresses. In this context it is interesting to note that in the case of SRR99 it takes 1000 h to form misfit dislocation networks around the y/-particles after pure annealing at 980 “C. At the same temperature, networks with much higher network dislocation densities form during creep in only 40 h [8]. Recovery may also drive climb processes in the y-channels which finally result in the annihilation of channel dislocations of opposite sign. In the case of SRR99 and CMSX4 [11,12] there is no apparent increase in dislocation density as strain increases after the minimum creep rate. (High dislocation densities near rupture surfaces which are associated with necking in the l?nal stages of creep need not be considered.) As early as 1978, Carry and Strudel [13] take the view that during creep of y/y’-microstructures internal stresses build up by the formation of dislocation networks piled up against the y/y/-interfaces and oppose the applied stress. Climb of dislocations in the y/y’-interfaces and associated recovery processes then become important in controlling the strain-rate [ 131.

4.4. Cutting of y’-particles after the minimum creep rate

Cutting of y/-particles was only observed after the minimum of the shear creep rate. This is typical for the high temperature low stress regime of creep of superalloy SXs and has also been reported for other superalloy SXs [3,14,15]. The scenario is similar to what has been observed in room temperature in situ TEM experiments on the SX alloy MC2 [16,17]: y-channel work-hardening precedes the shearing of precipitates. Another mechanism which decreases the density of channel dislocations during creep may be associated with cutting of the y’-phase, Fig. 12. Two channel dislocation jointly shear the y/-phase and annihilate with two channel dislocations of opposite sign when entering the channel on the opposite side of the y’-particle.

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Fig. 9. TEM micrographs of y/$-dislocations taken under different two-beam conditions for the macroscopic shear system (OOl)[lOO]. Test interrupted during primary creep (Table 2: reference 4): (a) g: (020), (b) g: (200), (c) g: (iii), (d) g: (1 Ii).

4.5. Coarsening of the f-phase

Under conditions of shear stress and temperature the y’-morphology is not stable and directional coarsening of the y/-phase is a fast process [ll, 18,191. In uniaxial creep (of SX superalloys with negative misfit) in the (100) direction, it was shown that the y-channels which are parallel to the applied stress close, while those perpendicular to the applied stress widen as a

function of time and strain. The influence of rafting on creep rate must therefore be considered. It should also be emphasised that the y’-morphology is never ideally geometrically homogeneous: channel widths and sizes of y/-cubes in the initial state are distributed quantities. Thus a full account of TEM observations can only be given on the basis of such irregularities in the y’-morphology. This has not been explicitly considered in the present work.

Table 7 Dislocation families 7, 8, 9 and 10 in the MCSS (OOl)[lOO] which formed during primary creep (Fig. 9, Table 2: reference 4) and their visibility ( + ) and/or effective invisibility ( - )

Table 8 Burgers vectors and slip planes of dislocation segments in the MCSS (OOl)[lOO] which formed during primary creep (Fig. 9, Table 2: reference 4)

Dislocation family

Dislocation family

g (020) (200) (iii)





I 8

+ +


t -


t -

t +


















7 8 9 10


[oil] Pill [roil [iof]

Plane of dislocation -n (1 ii) 0;;;’


“Dislocation segments too short for a clear identification sponding crystallographic plane.

of corre-

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Fig. 10. TEM micrographs of a y/y’-dislocation network of one area taken under different two-beam conditions for the macroscopic shear system (OOl)[lOO]. Test interrupted after the shear rate minimum (Table 2: reference 5): (a) g: (020) (b) g: (TOO),(c) g: (ill), (d) g: (lli).

4.6. Applied stress and resolved hens stresses

The macroscopic or external loading condition in the present study was pure shear loading of superalloy SXs on the (lll)[Oli] and (OOl)[lOO] MCSSs. This loading drives slip in several microscopic slip systems of type {ll l)(llO). The ratios of the resolved to the applied shear stresses as calculated for all microscopic crystallographic slip systems of the two MCSSs are listed in Table 11. Slip on { 11 l}( 1 lO)-systems is clearly faTable 9 Dislocation families 11, 12 and 13 in the MCSS (OOl)[lOO] after the minimum creep rate (Fig. 10, Table 2: reference 5) and their visibility ( + ) and/or effective invisibility ( - ) Dislocation family

11 12 13

voured in the case of the (11 l)[Oli] MCSS compared with the (OOl)[lOO] MCSS. However, the resolved shear on one microscopic slip system does not depend only on the external loading; other stress terms must also be considered. 4.7. Misfit stresses In the case of the SX superalloys investigated, there is a misfit between the y’-cubes and the y-channels

Table 10 Burgers vectors and slip planes of dislocation segments in the MCSS (OOl)[lOO] after the minimum creep rate (Fig. 10, Table 2: reference 5)

g (020) (Zoo) (iii)





+ t -

t -

t +

+ t

+ + t


+ -

Dislocation family

&- 2b/a

Plane of dislocation segments

11 12 13

Ull 10111 Cl011

(ii 1) (iii) (iii), (loi)

C. May et al. 1 Materials Science and Engineering A207 (1996) 51-63 Table 11 Ratios of resolved to applied shear stresses in the 12 crystallographic { 11 I} (110) slip systems for the two macroscopic crystallographic shear systems (lll)[Oli] and (OOl)[lOO] MCSS

Number of microscopic slip systems

Ratio of resolved to applied 7


1 2 4 1 4

1.00 0.67 0.50 0.33 0.17


8 4

0.41 0.00

System 11 i;= a/2 [OTl] slip plane

(ii 1)

J System 12

System 13

E;=a/z [oil]


slip plane (1 IT)

slip plane (1 oi)



Fig. 11. Schematic drawing illustrating the deposition of dislocation segments at y/$-interfaces during primary creep as well as after the minimum shear rate in the macroscopic shear system (OOl)[lOO].

which arises from a difference in the lattice constants between these two phases [3,20,21]. This results in misfit stresses which depend on the location in the microstructure. If one performs 3D FEM calculations for matrix channels which creep by a Norton law and y’-precipitates which are purely elastic then misfit stresses relax relatively quickly [21]. However, the kinetics of the formation of misfit networks is slow [8] (at temperatures up to 1000 “C). 4.8. Internal stresses

Internal stresses represent one of the classic concepts of creep research which have received much attention in the literature. Creep rates decrease during primary creep because back stresses pi build up and oppose the applied stress ~~~~ [22,23]. It is only the effect of the remaining effective stress ~~~which drives plastic deformation:

geff =

gaPP -



Internal stresses are caused by stress fields of dislocations [24]. This reflects the simple fact that the more dislocations fill the channel the more difficult it is to squeeze another one in. However, in superalloy SXs, misfit stresses also contribute to gi and, since dislocations move through thin matrix channels, Orowan stress terms must also be considered [16,17]. 4.9. Stsesses at y/y’-inte$aces The y/y/-interface represents an obstacle to the motion of channel dislocations. It exerts a stress on a channel dislocation segment at the interface. The physical nature of this repulsive force is associated with the antiphase boundary energy which is needed for cutting. Thus, most probably, a first interface dislocation segment which is deposited early in creep is very near or just in the y/-phase. In order to start pairwise cutting (which has been observed on many occasions in the literature and is not discussed here) a second channel dislocation segment must approach the first segment against the repulsive forces which the two segments of equal sign exert on each other. This results in a critical interface stress for cutting. It is important that cutting of y/-particles can only start when the resolved shear stress which acts on two interface dislocation segments exceeds the critical interface stress. 4.10. A pyelimincwy jhme for discussirtg srlperdloy SX creep anisotropy

The shear stress which acts on a particular dislocation segment in a given slip system depends on time t and on the position and orientation of this segment in the y/y’-microstructure. The space co-ordinates and the orientation are implicit in the following set of equations and are not explicitly given. The shear stress is Fig. 12. Pairwise cutting of ;1’-particles in the MCSS { 1 11}( 110) after the shear rate minimum.

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where F, is the ratio between the applied stress and raPP the resolved shear stress in the specific slip system (‘Schmid factor’), zcs is a coherency stress term, Zis describes internal stresses and rrs represents an interface stress term. The velocity v(t) of a dislocation segment depends on rs (3)

4t) =f(d

One can now assume that all dislocation segments in one slip system have a unit length 1. The overall shear rate in one specific slip system is then obtained by adding the contributions of all individual dislocation segments iSCt)





where vi is the velocity of the ith dislocation segment of unit length 1, b is the magnitude of the Burgers vector and V is the crystal volume under consideration. The same procedure can be applied to all other activated slip systems. Then one can calculate the shear displacement which each individual slip system contributes to the macroscopic shear displacement using a geometric projection factor for the jth slip system. Considering the contributions of all slip systems, the macroscopic shear rate is obtained as (5) where j(t) is given in Eq. (4). Dislocation climb does not significantly contribute to the overall creep strain but it can influence the creep rate by changing not only the density and spatial arrangement of dislocations but also the rafting of y’-cubes. The climb process can, for example, influence the stress component his in that it helps to decrease overall dislocation density and consequently change the zs. The stress component which assists dislocation climb is odt> = Fcrapp + CCC(~)+ aidt)


A part of the applied shear stress (Fcr,,,), the coherency and internal stress components (act and sic) thus contribute to the climb stress component. The contribution of the interface stress term here is neglected. 4.11. Results of the present stud} It is now assumed that the function be represented by a simple power law v(t) = uo[rs(t)]”

f in Eq. (3) can (7)

In a first order approximation we only consider the contribution of the external resolved shear stresses to zs in Eq. (2), thus ignoring some of the microstructural

and Blgineering





Table 12 Fs-values of activated slip systems identified by TEIM MCSS

Slip system


(iii)[oii] (ii i)[oii]

(11-l)lOi11 - (b,, bz,)

(001)[100] (001)[100]

(iwoiii (1 li)Pl11

1 0.17 0.41 0.41

(111N1101 (b>W

parameters contributing obtained as

(b,> b,,) (b b,,)

to zs. Then the overal shear is

(8) where summation is performed over all activated slip systems. pj is the dislocation density associated with the jth activated slip system. We now evaluate the ratio I between the macroscopic shear rates of the (lll)[Oli] and (OOl)[lOO] MCSSs, which was experimentally determined as 10 in the later stages of creep:


It is now further assumed that dislocation densities pj in different crystallographic slip systems are approximately the same, and since only the macroscopic shear strain component yi2 is considered: gj = FSj

In the experimental part of this work, two activated microscopic crystallographic slip systems have been identified for each MCSS. In a first step, only these are considered to calculate the ratio I’: (i (F’j)‘*il)(ll~)[ol~ I’= j=l



In this simplified treatment the ratio of the shear rates of the two MCSSs is obtained as a function of the stress exponent n in Eq. (7). The (Fsj) used for the calculation of I’ are listed in Table 12. The results for i for n-values of 1, 2 and 3 are presented in Table 13. In a second step we perform the same calculation for both MCSSs assuming the 12 (11 l}( 110) slip systems Table 13 Results for the ratio r between the creep rates of the IMCSSS (11 l)[Oli] and (OOl)[lOO] when only considering external resolved shear stresses n




iidentified slip systems)




L12 slip systems)





C. Mayr et al. / Materials Science and Engineering A207 (1996) 51-63

listed in Table 11 together with their corresponding Fsj-factors. The results for r for n-values of 1, 2 and 3 are presented in Table 13. It seems reasonable to assume that the movement of dislocations in channels of superalloy SXs is solute drag controlled. Then the n-value in Eq. (7) should be 1 [25] and the results of both calculations (1: only slip systems detected in the TEM, 2: 12 slip systems) underestimate the experimentally observed ratio of minimum strain rates in the two MCSSs since a ratio of 10 was experimentally observed. Nevertheless, the results go in the right direction. The MCSS with the higher external resolved shear stresses creeps faster. It is not surprising that the calculation performed in this section does not reproduce the strain rate ratio which was found experimentally. Work hardening and recovery-as outlined in the previous sections-have not been considered. Further work is required to rationalise the mechanical results obtained in the present study on a micro-mechanical basis. It clearly is not possible to rationalise high temperature creep data merely on a basis of external resolved shear stresses. From a microstructural point of view this sheds some doubt on some of the models which only use external resolved shear stress arguments to rationalise creep anisotropy of superalloy SXs [26,27].

5. Summary and conclusions This paper adds an investigation of the dislocation substructure which formed during pure shear deformation to the large body of microstructural observations which were made after uniaxial creep testing of superalloy SXs. The double shear creep test technique applied in the present paper has recently been described in the literature [1,2]. The following conclusions can be drawn. (1) In the case of double shear testing of CMSX6 at 1025 “C and 85 MPa, the MCSS (lll)[Oli] deforms-from the minimum creep rate onwardsby a factor of 10 faster than the MCSS (OOl)[lOO]. Double shear testing represents a convenient tool for studying creep anisotropy in superalloy SXs at temperatures above 1000 “C. (2) Under the conditions of stress and temperature of the present study, shear creep deformation was always associated with multiple slip. Single slip (which sometimes is intuitively associated with pure shear deformation) was never observed. (3) A detailed study of dislocation networks around underlined the importance of y’-particles (110){111} glide in the formation of networks. This is in agreement with observations which were made in uniaxial testing. (4) The creep rate ratio of the two MCSSs could not be

rationalised merely on the basis of an external resolved shear stress argument. The paper qualitatively outlines which other microstructural parameters and processes must be considered to fully account for the mechanism of creep. (5) The shear creep rate minimum was observed at shear strains of 0.02. Under the conditions of this study dislocation nucleation is not difficult. Tests which were interrupted early in primary creep showed a homogeneous dislocation substructure. Incubation periods for creep were not observed. (6) Matrix channel work hardening always preceded the cutting of y’-particles. Cutting of y/-particles started at the minimum creep rate. Cutting can result in a decrease of overall dislocation density. (7) Rafting occurs under the creep conditions of the present study. This was not explicitly considered in the present study. Work is underway to provide a description of the rafting process in superalloy SXs under conditions of pure shear.

Acknowledgements The authors would like to acknowledge funding from the Swiss National Foundation (contract 21-29844.90, CM.), the Swiss Priority Program for Materials (project l.A. 1, G.E.) and the Commission Fed&ale Suisse de Bourses pour Etudiants Etrangers (A-D.).

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