Mechanism of 1 1 2/3 slip initiation and anisotropy of g? phase in CMSX-4 during creep at 750 C and...

Mechanism of �1 1 2�/3 slip initiation and anisotropy of g? phase inCMSX-4 during creep at 750 8C and 750 MPa

Q.Z. Chen a, D.M. Knowles b,*a Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kongb Materials Performance Technologies, Gracefield Research Centre, P.O. Box 31-310, Lower Hutt, New Zealand

Received 21 November 2002; received in revised form 20 February 2003

Abstract

Creep deformation defects from tensile creep tests carried out at 750 8C under 750 MPa in the approximate orientations [1 3 6];[0 0 1], [0 1 1] and [1 1 1] for CMSX-4 single crystals have been identified carefully, using transmission electron microscope combined

with computer simulated microimages. A series of results have been obtained. (i) It was confirmed that �1 1 2�/3 slip in g? phase

mainly involved the reaction and dissociation of two �1 1 0�/2 dislocations which had different Burgers vectors and met at the g/g?interfaces where the product �1 1 2�/6 partials were trapped. (ii) At 750 8C and 750 MPa, the selectivity among {1 1 1}�1 1 2� slip

systems was sensitive to Schmid factors. The reason for the anisotropy was that the resolved shear stress of highly stressed

{1 1 1}�1 1 2� slip systems in the [1 3 6]; [0 0 1] and [0 1 1] orientations were just around the critical resolved shear stress of �1 1 2�/3

faulting in g? phase which was estimated to be �/300 MPa. Hence, a slight decrease of a RSS could switch off the operation of a

{1 1 1}�1 1 2� slip system, or vice versa. (iii) The activation of {1 1 1}�1 1 0� slip systems was a necessary but not sufficient factor of

initiating �1 1 2�/3 faulting in the g? particles. The operation of �1 1 2�/3 slip and density of superlattice stacking faults were

controlled by the RSSs acting on those {1 1 1}�1 1 2� slip systems.

# 2003 Elsevier Science B.V. All rights reserved.

Keywords: Single crystal superalloy; Stacking fault; Anisotropy; Creep; Critical resolved shear stress

1. Introduction

The creep life of single crystal (SX) superalloys varies

significantly as a function of loading orientation due to

their inherent anisotropy [1�/3]. The degree of aniso-

tropy is strongly influenced by both the temperature and

stress level. It is well documented that the greatest

sensitivity to orientation is observed around 750�/850 8C[4]. It is generally found that SXs orientated close to

[0 1 1] have much shorter creep lives than crystals

orientated near [0 0 1] [1,4,5]. The extremely high creep

strain rates and correspondingly short creep lives

observed near [0 1 1] orientations in Mar M200 and

CMSX-4 over a range of temperatures and stresses are

explained by the predominance of a single

{1 1 1}�1 1 2� slip system [3,5], though two

{1 1 1}�1 1 2� slip systems are nearly equivalently and

highly stressed. On the other hand, orientations close to

[0 0 1] have multiple highly stressed equivalent slip

systems in which rapid dislocation interactions ensue

causing transition to the secondary creep stage [5]. It has

been reported that for CMSX-4 stressed in the �0 0 1�orientation at 750 8C only two families of �1 1 2�stacking faults were observed during creep although

theoretically there are four nearly equally stressed

{1 1 1}�1 1 2� slip systems [3]. A similar phenomenon

was observed for {1 1 1}�1 1 0�-type slip. For the

�0 0 1� orientation eight �1 1 1��1 1 0� slip systems

are equally stressed. However, Pollock and Argon [6]

found in CMSX-3 stressed in the �0 0 1� orientation at

800�/900 8C that during the primary creep stage the gphase channels are locally filled with dislocations of a

single �1 1 0�/2 Burgers vector which are emitted from

the same dislocation source; and that at the end of the

primary stage dislocations with other Burgers vectors

emanate from other sources, the majority of the

dislocations having Burgers vectors of the most highly* Corresponding author. Tel.: �/64-4-569-0234.

E-mail address: [email protected] (D.M. Knowles).

Materials Science and Engineering A356 (2003) 352�/367

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0921-5093/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0921-5093(03)00148-5

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stressed slip systems. In practice, a single crystal cannot

be stressed strictly along �0 1 1� or �0 0 1� directions.

This might be one of the reasons why a single

{1 1 1}�1 1 2� slip system is observed near [0 1 1]

orientations while crystallographically two nearly

equivalent {1 1 1}�1 1 2� slip systems are highly

stressed, and why two dominant {1 1 1}�1 1 2� slip

systems were found near [0 0 1] orientations while four

nearly equivalent {1 1 1}�1 1 2� slip systems are highly

stressed. However in light of the observations by Pollock

and Argon, the relative importance of the local resolved

stress or the availability of local sources on activation of

slip systems is yet to be resolved. One of objectives of

this paper is thus to discuss the physical reasons for the

significant anisotropy of CMSX-4 at 750 8C and 750

MPa focusing on {1 1 1}�1 1 2�-type slip systems, which

generally dominates deformation under these condi-

tions. In order to achieve this aim, however, it is crucial

that the foil normal which is parallel to loading axis is

determined precisely in addition to the characterisation

of the creep deformation defects. In this investigation

convergent bean electron diffraction (CBED) technique

has been used in this regard.

With regard to the creep deformation mechanisms,

there have been a number of deep and systematic

investigations on single-phase g? alloys (Ni3Al struc-

ture), and the possible dislocation dissociations have

been well reviewed [7�/9]. However, the actual disloca-

Table 1

Specimen orientations

Specimen Angle from �0 0 1� Angle from �0 0 1��/�0 1 1� boundary Nominal orientation [uvw]

A 27.88 8.88 /�[1 3 6]

B 5.78 4.78 �/[0 0 1]

C 50.68 7.18 �/[0 1 1]

D 53.88 44.98 �/[1 1 1]

Fig. 1. Creep curves of CMSX-4 superalloy at different stress

orientations. All samples were tested until creep rupture, except for

specimen B which was interrupted at �/2.5% strain.

Table 2

Summary of the creep rupture strains and lives of CMSX-4 at 7508 and

750 MPa

Specimen orienta-

tion

Rupture strain (%) Creep life (h)

A*//[1 3 6] 3.58 293.2

B*/[0 0 1] Interrupted at �/2.5% Interrupted after 15.3 h

C*/[0 1 1] 15.6 4.3

D*/[1 1 1] 15.3 1434.5

Fig. 2. Stacking faults in the g? particles and dislocations in the g matrix in specimen A. The orientation is [1 3 6]: BD �/0 1 1, g�2 0 0:/

Q.Z. Chen, D.M. Knowles / Materials Science and Engineering A356 (2003) 352�/367 353

tion dissociations that occur in two-phase g/g? super-

alloys are different from single-phase Ni3Al alloys.

What has been widely cited is the assumption that two

perfect dislocations of the g matrix, with different

�1 1 0�/2 Burgers vectors, have reacted in order to

form a junction of �1 1 2�/2 Burgers vector, and thatfrom this junction the necessary �1 1 2�/3 partial

dislocation is subsequently nucleated [10]. Sass et al.

have found evidence in CMSX-4 for this mechanism

[2,11], which was reported as:

1

2[1 1 0]�

1

2[1 0 1] 0

1

3[2 1 1]�SSF�

1

6[2 1 1]; (1)

where SSF stands for superlattice stacking fault. On theother hand, several investigators [12�/17] have carried

out detailed transmission electron microscope (TEM)

investigations for SRR99 and CMSX-2 alloys and found

evidence that the operation of �1 1 2�/3 slip in g? phase

is associated with the dissociation of a single �1 1 0�/2

matrix dislocation when it meets the g? precipitate. One

of possible reactions is

1

2[1 0 1] 0

1

3[1 1 2]�SSF�

1

6[1 2 1]: (2)

In all previous TEM work [11�/16] except literature

[17], however, the Burgers vectors were identified using

the invisibility criteria g �/b�/0 for perfect dislocations

and g �/b�/9/1/3 for partial dislocations. This conven-

tional method has its limitations. Firstly, a perfect

dislocation on a g/g? interface can be either 9/�1 1 0�or 9/�1 1 0�/2; but g �/b�/0 can distinguish neither thetwo types nor their sign. Secondly, judging the visibility

of a partial dislocation, particularly �1 1 2�/3-type, can

be a tricky task in practice. The rigorous method of

Fig. 3. Stacking faults in specimen A. The foil normal [1 3 6]: BD �/0 1 1, g�1 1 1:/

Q.Z. Chen, D.M. Knowles / Materials Science and Engineering A356 (2003) 352�/367354

identifying dislocations is computer simulation. Using

this method, Bonnet and Ati [17] have confirmed the

dissociation in Eq. (2) of a single �1 1 0�/2 matrix

dislocation in CMSX-2. However, the reaction of Eq.(1) has not been strictly confirmed yet, and the question

whether or not different dissociation mechanisms occur

in different superalloys is still open. Therefore another

objective of this paper is to thoroughly identify the

dissociation mechanism of initiating �1 1 2�/3 faults in

g? phase of CMSX-4 through a detailed TEM investiga-

tion combined with computer-simulation analysis. Crys-

tallographically consistent conventions are keptthroughout the analysis process.

2. Materials and experimental procedures

CMSX-4 single crystal material was provided by

Rolls-Royce plc. in the fully heat treated condition,

comprising of a three-step solution treatment consisting

of a 1 h soak at 1280 8C, 2 h at 1290 8C and 6 h at

1300 8C, followed by a two-step ageing treatment of 6 h

at 1140 8C and 16 h at 870 8C. This produces a g?volume fraction of 70% in the form of regular cubes with

an edge length of approximately 0.45 mm. The initial

orientations of all rods were determined by automated

Laue back-scattered X-ray diffraction technique. The

orientations that were investigated are listed in Table 1.

Conventional creep specimens with a gauge length of 28

mm were machined from the bars and constant load

creep tests were performed at 750 8C and 750 MPa.TEM foils were sectioned in the plane perpendicular

to the tensile axis. They were mechanically thinned to

80�/100 mm and electropolished using a solution of 10%

perchloric acid in methanol at �/15 8C and 30 V,

followed by examination in a JEOL 2000FX micro-

scope.

3. Conventions

3.1. Definitions and notations associated with dislocations

The FS/RH definition [18] of Burgers vectors isadopted throughout the paper for the dislocations

both in g (FCC structure) and g? (L12) phase. The

Thompson tetrahedron used is the same as in Hirth and

Lothe [18]. In assigning partial dislocations bounding an

intrinsic stacking fault in a way consistent with the FS/

RH definition, the usual Thompson’s rule is valid only

for the FCC structure in which the Shockley partials are

of the �1 1 2�/6 type. For the L12 structure in which theShockley partials are �1 1 2�/3, the ‘Greek�/Roman’

notation [18] must be reversed. Thompson’s rule for

L12 structure thus reads: Look along the positive

dislocation line from outside the Thompson tetrahe-

dron; the partial on the left is Roman�/Greek, and that

on the right is Greek�/Roman to give an enclosed

intrinsic stacking fault. Finally, the definition of dis-placement vector R of stacking faults in Hirsch et al.’s

book [19] is used. i.e. R is the displacement of the crystal

below the stacking fault relative to the crystal above the

fault.

3.2. Determination of Burgers vectors and displacement

vectors

The determination of the Burgers vectors of disloca-

tions and displacement vectors of stacking faults has

been made mostly in bright field double-beam diffrac-tion conditions. The nature of the Burgers vectors and

displacement vectors are estimated primarily through

their contrast visibility, and then determined exclusively

by using computer image simulation: an image compu-

tation program for PC based upon TWODIS [20]. The

electron beam direction BD is oriented towards the

electron gun and the foil normal is acute to BD. The foil

Fig. 4. Identification of stacking faults in specimen A. The orientation

is [1 3 6]: BD �/0 1 1; (a) Bright field g�1 1 1; (b) centre dark field

g�1 1 1: The analysed stacking fault AB is extrinsic.


normal is determined as BD when the foil is horizontally

placed, using the Kikuchi map obtained by CBED in

TEM mode. Practically, simulation of 2�/3 g vectors

around each of three BDs, amounting to a total 7�/9 g

vector analyses, was carried out for each dislocation.

4. Results and discussion

4.1. Creep tests

The creep curves for the different orientations are

shown in Fig. 1, which are generally in agreement with

previous work [1,3,4]. The rupture strains and creep lives

are listed in Table 2.

4.2. Identification of creep deformation defects

4.2.1. Specimen A*//[1 3 6]/

4.2.1.1. Identification of deformation mechanisms. The

foil normal [1 3 6] was determined using the Kikuchi

map of CBED. The typical deformation microstructure

is shown in Figs. 2 and 3. Two facts can be drawn fromobservations of this foil. (i) There are considerable

�1 1 0�/2 dislocations in the g channels, and the stacking

faults are the result of shear in the g? particles. It should

Fig. 5. Identification of stacking faults in CXSX-4. The foil normal is [1 3 6]: The stacking fault I was identified as a SISF. The configuration II is an

overlap of two SESFs. (a) BD �/0 1 1, g�[2 0 0]; (b) BD �/0 1 1, g�[1 1 1]; (c) BD �/0 0 1, g�/0 2 0; and (d) BD �/0 0 1, g�/2 0 0.


Fig. 5 (Continued)

Table 3

Simulation parameters of Figs. 5 and 6

Micrograph-simulated graph Configuration BD g t /jg w u

5a�/5a I 0, 7, 9 /2 0 0 3.05 �/0.15 /3 1 4

5a�/5a II 0, 7, 9 /2 0 0 3.77 �/0.05 /4 1 3

5b�/5b I /1; 18; 17 /1 1 1 4.4 0.0 /3 1 4

5b�/5b II /1; 18; 17 /1 1 1 5.3 0.1 /4 1 3

5c�/5c I 1, 0, 10 0 2 0 3.3 0.0 /3 1 4

5c�/5c II 1, 0, 10 0 2 0 3.95 0.0 /4 1 3

5d�/5d I 0, 1, 11 2 0 0 3.5 0.0 /3 1 4

5d�/5d II 0, 1, 11 2 0 0 3.93 0.0 /4 1 3

5a�/6a d2 0, 7, 9 /2 0 0 3.2 0.0 /4 1 3

5a�/6b d3 0, 7, 9 /2 0 0 3.2 0.0 /4 1 3

C11�/169 GPa; C12�/89 GPa; C44�/121 GPa [22]; foil normal fn�1 3 6; anomalous absorption coefficient (ANO)�/0.06.


be noted that 9/[1 1 0]/2, 9/[0 1 1]/2 and 9[1 0 1]=2

dislocations are invisible under the diffraction condition

g� [1 1 1] in Fig. 3. Hence, �1 1 0�/2 dislocations are

more prevalent than apparent in Fig. 3. (ii) All stacking

faults lie on the same {1 1 1} plane, and they are either

intrinsic or extrinsic. Using the center dark field (CDF)

technique and stacking fault identification method [21],

the stacking faults in the CDF (Fig. 4b) are extrinsic.

Therefore the extrinsic stacking faults have bright outer

fringes in the bright field of g� [1 1 1] in Figs. 3 and 4a,

and vice versa. In Fig. 3, the percentage of the numbers

of superlattice intrinsic stacking fault (SISF) and super-

lattice extrinsic stacking fault (SESF) is about 30 and

70%, respectively.

Identification of the defects with assistance of com-

puter simulation is carried out for the defects in Fig. 5.

The analysed defects are named, and dislocation line

directions are defined, as illustrated in Fig. 5a. The

parameters used in the simulation are listed in Table 3,

and all Burgers vectors b of dislocations and displace-

ment vectors R of stacking faults are summarised in Fig.

5b.

In configuration I, the trailing partial dislocation

[1 1 2]=6 is lying on the g/g? interface, while the leading

partial dislocation [1 1 2]=3 cuts into the g? particle,

generating a SISF. The reaction is thus proposed to be

1

2[1 0 1]�

1

2[0 1 1]

01

3[1 1 2]�SISF on (1 1 1)�

1

6[1 1 2]: (3)

This is in agreement with the work of Sass et al. in

CMSX-4 [2,11].

In configuration II, the trailing partial dislocation

[1 2 1]=6 is lying on the opposite g/g? interface of thesame g channel (its contrast in Fig. 5c and d is disturbed

by dislocation d3, and the match between the simulated

and experimental images are not as good as in Fig. 5a

and b), while two leading partial dislocations [2 1 1]=3

cut into the g? particle. The general reaction is proposed

Fig. 6. The simulated graphs of (a) dislocation d2 and (b) dislocation d3 in Fig. 3a.

Fig. 7. Dislocation pairs of opposite sign A�/A and B�/B on g/g?interfaces in CMSX-4. The foil normal [1 3 6]: BD �/001, g�/2 0 0.

Fig. 8. Activated {1 1 1}�1 1 2� slip systems and the stacking faults

caused by the slip systems when the stressed axis is at [1 3 6]:/


as follows

1

2[1 1 0]�

1

2[1 1 0]�

1

2[1 0 1]

01

3[2 1 1]�SESF�

1

3[2 1 1]�SISF�

1

6[1 2 1]: (4)

Since the leading dislocation [2 1 1]=3 generates a SESF,

the SISF in configuration II results from the overlap of

two closely spaced SESFs that were produced by the two

[2 1 1]=3 leading dislocations, as postulated by Kear and

Oblak [23]. Therefore, the following reactions are

proposed for configuration II:

1

2[1 1 0]�

1

2[1 0 1] 0

1

3[2 1 1]�SESF on (1 1 1)�

1

6[2 1 1]

1

2[1 1 0] 0

1

3[2 1 1]�SESF on (1 1 1)�

1

6[1 1 2]

1

6[2 1 1]�

1

6[1 1 2] 0

1

6[1 2 1]

:

8>>>>>>>><>>>>>>>>:

(5)

Hence the SISF part of the configuration II is the

overlap of two SESFs, which occurred on two closely

spaced (1 1 1) planes. Although the second disassocia-

tion of Eq. (5) is consistent with previous work [12�/17],

this type of disassociations were found to occur together

with the first type of reactions, and an isolated SSF was

seldom generated by the second type of disassociations.

In counting SISFs (�/30%) and SESFs (�/70%) of Fig.

3, the overlapping effect was taken into account. Their

percentages indicate that the [2 1 1]=3 (SESF) slip

direction is more highly activated than [1 1 2]=3 (SISF).

The dislocations d1�/d4 are on the g/g? interfaces.

They were identified firstly through their visibilities

under different diffraction g. For example, d1 and d2

are visible when g�1 1 1 (Fig. 5b) and reasonably

invisible when g�/0 2 0 (Fig. 5c), which indicates that

the Burgers vector of d1 and d2 is either 9[1 0 1] or

9[1 0 1]=2: The exclusive identification is made through

computer simulation, as illustrated in Fig. 6(a). Com-

paring Fig. 5(a) and Fig. 6(a), one can see that [1 0 1]=2

is the right Burgers vector for dislocations d1 and d2. In

the same way, d3 is identified as [1 1 0]=2; and d4 as

[0 1 1]=2:/Dislocation pairs of opposite sign are frequently

observed on the two parallel g/g? interfaces of a gchannel, as shown in Fig. 7. It is very probable that a

dislocation loop is trapped on the two interfaces of a gchannel during its propagation, leaving a pair of

Table 4

�1 1 0� slip systems, �1 1 2� slip systems which will lead to the production of intrinsic stacking faults, using the convention that the crystal above a

{1 1 1} plane moves relative to the crystal below, and the Schmid factors for slip in these directions with the two tensile axes

Slip plane (hkl) Slip direction [uvw] Schmid factor l

/[1 3 6] /[1; 0; 10] [1 6 5] [1 1 1]

(1 1 1) /[1 1 0] 0.283999 0.036379 0.395079 0

/[1 0 1] 0.496998 0.400164 0.316063 0

/[0 1 1] 0.212999 0.363786 �/0.079016 0

/[1 2 1] 0.040992 �/0.189029 0.273719 0

/[1 1 2] 0.409917 0.441067 0.136859 0

/[2 1 1] �/0.450909 �/0.252038 �/0.410578 0

/(1 1 1) [1 1 0] 0.177499 �/0.044463 0.460925 0.272166

/[0 1 1] 0.266249 0.444627 �/0.065846 0

[1 0 1] 0.443748 0.400164 0.395079 0.272166

/[2 1 1] �/0.358677 �/0.205364 �/0.494214 �/0.314270

/[121] �/0.051240 �/0.282376 0.304132 0.157135

/[1 1 2] 0.409917 0.487740 0.190082 0.157135

/(1 1 1) [1 1 0] 0.035500 �/0.036379 0 0.272166

/[1 0 1] 0.124249 0.400164 0 0

[0 1 1] 0.159749 0.363786 0 0.272166

/[2 1 1] �/0.051240 �/0.252038 0 0.157135

/[1 2 1] �/0.112727 �/0.189029 0 �/0.314270

/[1 1 2] 0.163967 0.441067 0 0.157135

/(1 1 1) [1 0 1] 0.177499 0.400164 �/0.079016 �/0.272166

[0 1 1] 0.319499 0.444627 �/0.144862 �/0.272166

/[1 1 0] 0.141999 0.044463 �/0.065846 0

/[2 1 1] �/0.020496 �/0.205364 0.007603 0.157135

/[121] �/0.266446 �/0.282376 0.121653 0.157135

[1 1 2] 0.286942 0.487740 �/0.129256 �/0.314270

Note a negative sign means that SESF is initiated if the �1 1 2� slip system is activated.


dislocation segments on the interfaces. The dislocations,

which are trapped on the opposite g/g? interfaces of the

same g channel, have opposite signs if viewed along the

same direction and will lead to the same faulting in the

two g? particles on either side of the g channel. In Fig. 5

the reaction of Eq. (3) occurs on the lower g/g? interface

and generates a SISF in the lower g? particle. If the

reaction of the opposite sign dislocations of Eq. (3)

1

2[1 0 1]�

1

2[0 1 1]

01

3[1 1 2]�SISF on (1 1 1)�

1

6[1 1 2] (6)

Fig. 9. Stacking faults in specimen B1. The orientation is [1 0 10]: Creep was interrupted at �/2.5%. (a) BD �/0 0 1 g�/0 2 0; (b) BD �/0 1 1,

g�[1 1 1]: Stacking faults of ‘A’ family are identified as SISFs of R�[111]=3; ‘B’ family, SISFs of R�[1 1 1]=3; and ‘C’ family, SISFs of R�[1 1 1]=3: (c) Stacking faults in specimen B. The orientation is [1; 0; 10]: Creep was interrupted at a �/2.5%. BD �/0 1 1, g�[1 1 1]: The

predominant faults are SISFs of R�[1 1 1]=3; and four framed faults of family ‘D’ are SISFs of R�/[1 1 1]/3.


is considered, it produces a SISF in the upper g?particles, as plotted in Fig. 8. The above discussion

also applies to the SESFs of configuration II in the

upper g? particle. i.e. the reaction of dislocations of

opposite sign to the first reaction in Eq. (5)

1

2[1 1 0]�

1

2[1 0 1]

01

3[2 1 1]�SESF on (1 1 1)�

1

6[2 1 1]: (7)

can take place at the lower g/g? interface and produces a

SESF in the lower g? particles, as shown in Fig. 8. The

scenario plotted in Fig. 8 is frequently observed in

practice, as seen later in Figs. 10�/13. In this way,

�1 1 2�/3 faulting can spread throughout the two-phase

g/g? alloys.

In summary, when the tensile stress axis is in the

[1 3 6] orientation, two slip directions [2 1 1]=3 and

[1 1 2]=3 on the same (1 1 1) slip plane are activated.

They generate SESFs (�/70%) and SISFs (�/30%)

respectively, which indicates that SESF slip system

(1 1 1)/[2 1 1] is more strongly activated than the SISF

slip system (1 1 1)/[1 1 2]:/

Fig. 10. Identification of stacking faults in specimen B1. The orientation is [1 0 10]: Creep was interrupted at �/2.5%. (a) BD �/0 0 1, g�/0 2 0; (b)

BD �/0 1 1, g�1 1 1:/

Table 5

Simulation parameters of Fig. 10

Micrograph-simulated graph S.F. BD G t /jg w u

10a I 1, 0, 6 0 2 0 4.3 0.0 1 1 2

10a II 1, 0, 6 0 2 0 3.45 0.0 1 0 1

10a III 1, 0, 6 0 2 0 3.25 0.0 /0 1 1

10b III 1, 7, 6 /1 1 1 3.9 0.0 /0 1 1

10b IV 1, 7, 6 /1 1 1 3.35 0.0 1 0 1

10b V 1, 7, 6 /1 1 1 3.9 0.0 /1 1 2

C11�/169 GPa, C12�/89 GPa, C44�/121 GPa; fn�1; 0; 10; anomalous absorption coefficient (ANO)�/0.06.


4.2.1.2. Schmid factor. Schmid factors were calculated

for [1 3 6]; as summarised in Table 4. In Table 4, �1 1 2�slip systems which will lead to the production of SISFs

are given, the slip direction representing the movement

of the crystal above a {1 1 1} plane relative to the crystal

below. Hence, a positive Schmid factor means SISFs will

be initiated if the slip system is activated, and a negative

Schmid factor means SESFs will be produced if the slip

system is activated [24].

In the [1 3 6] column of Table 4, the (1 1 1)/[1 0 1] slip

system that is needed by both sets of reactions Eqs. (3)

and (4) has the largest Schmid factor 0.497. The (1 1 1)/

[2 1 1] slip system has the second largest Schmid factor

�/0.451. This negative Schmid factor means that the g?crystal above a (1 1 1) plane shears along [2 1 1] direc-

tion relative to the crystal below the (1 1 1) plane. The

leading partial 9[2 1 1]=3 (9/ sign is determined by the

definition of positive dislocation line direction) gener-

ates a SESF in the g? phase, which is configuration II in

Fig. 5. This consistence between the experimental

Fig. 11. Activated {1 1 1}�1 1 2� slip systems and the stacking faults

caused by the slip systems when the stressed axis is at [1 0 10]:/

Fig. 12. Deformation microstructure in specimen C. The orientation is [1 6 5]. (a) BD �/0 1 0, g�/2 0 0; (b) BD �/0 1 0, g�/2 0 2; (c) BD �/1 1 0,

g�1 1 1; and (d) BD �/0 1 0, g�/2 0 0. The predominant stacking faults are identified as SESFs of R�[1 1 1]=3: The stacking fault as marked by an

arrow in (d) is an SESF of R�[1 1 1]=3:/


observation and Schmid factor calculation also exists for

(1 1 1)/[1 1 2] slip system. (1 1 1)/[1 1 2] has a positive

Schmid factor 0.410 and thus produces SISFs. Config-

uration I in Fig. 5 is one of these SISF. Furthermore, the

Schmid factors l(1 1 1)/[2 1 1]/�/�/0.451 and l(1 1 1)/[1 1 2]/

�/0.410 indicate that the (1 1 1)/[2 1 1] slip system is

stressed more intensively than (1 1 1)/[1 1 2]; and conse-

quently the number of SESFs is larger than that of

SISFs. This prediction is in agreement with the experi-

mental observation in Fig. 3: �/70% SESFs and �/30%

SISFs.

The (1 1 1)/[1 0 1] slip system that has the largest

Schmid factor l(1 1 1)[101]�/0.497 produces 9[1 0 1]=2

dislocations for the reactions of Eqs. (3) and (4).

Although another two key slip systems (1 1 1)/[1 1 0]

and (1 1 1)/[0 1 1] have lower Schmid factors:

l(1 1 1)[110]�/0.284 and l(1 1 1)[011]�/0.213, their resolved

shear stress (RSS) t(1 1 1)[/110]/�/213 MPa and

t(1 1 1)[011]�/160 MPa are both much higher than the

critical resolved shear stress (CRSS) of {1 1 1}�1 1 0�/2

shear of g phase (�/35 MPa between 1000 and 1050 K)

[25]. The present TEM observation also shows that they

were activated in the g channels (Fig. 5b) supporting

their role in initiation of stacking faults in the g?particles.

The (1 1 1)[1 1 2] slip system appears to have the same

Schmid factor 0.410 as (1 1 1)/[1 1 2]: In addition, the

two slip systems (1 1 1)[0 1 1] and (1 1 1)/[1 0 1] that

provide �1 1 0�/2 dislocations for (1 1 1)[1 1 2] faulting

have Schmid factors 0.266 and 0.444. Their RSSs are

200 and 333 MPa, respectively, which are sufficient to

support their role in initiation of stacking faults in the g?particles. However, very few (1 1 1) stacking faults were

observed in the specimens. This fact indicates that the

RSSs on suitable {1 1 1}�1 1 0� systems in g phase are

not a sufficient factor for the activation of

{1 1 1}�1 1 2� slip systems in g? phase though necessary

to generate �1 1 0�/2 dislocations for the initiation of

Fig. 13. Simulated graphs of three stacking faults in Fig. 8a. The foil normal is [1 6 5]. (a) R�[1 1 1]=3; u�/[1 0 1], SESF. (b) R�[1 1 1]=3; u�/

[1 1 0], SESF. (c) R�[1 1 1]=3; u�/[2 1 1], SESF. (d) Shear mechanism in g? particles.

Table 6

Simulation parameters of Fig. 12a

Micrograph-simulated graph S.F. BD g t /jg w u

12a�/13a I 0, 6, 1 2 0 0 4.1 0.0 1 0 1

12a�/13b II 0, 6, 1 2 0 0 2.75 0.0 1 1 0

12a�/13c III 0, 6, 1 2 0 0 3.2 0.0 2 1 1

C11�/169 GPa, C12�/89 GPa, C44�/121 GPa; foil normal fn�/[1 6 5]; anomalous absorption coefficient (ANO)�/0.06.


�1 1 2�/3 SSFs. The following two reasons are probably

responsible for the lack of (1 1 1)[1 1 2] faults. (i) The

errors in the orientation measurements are inevitable,

and the two slip systems (1 1 1)[1 1 2] and (1 1 1)/[1 1 2]

do not have the same Schmid factors actually. It is most

likely that the (1 1 1)[1 1 2] slip system has a slightly

lower Schmid factor than (1 1 1)/[1 1 2]: (ii) It is probably

that the CRSS for stacking faulting is just around

0.410�/750 MPa�/307 MPa at 750 8C in this materials.

This inference is identical to the value determined for

Fig. 14. �1 1 0�/2 dislocations in specimen D. The orientation is [1 1 1]. (a) BD �/1 1 0, g�[1 1 1]; 9/[0 1 1]/2 dislocations in AC, i.e. (1 0 0) gchannels. (b) BD �/1 1 0, g�[1 1 1]; 9/[1 0 1]/2 dislocations in BC, i.e. (0 1 0) g channels. (c) BD �/1 1 2, g�[1 1 1]; 9/[1 1 0]/2 dislocations in AB,

i.e. (0 0 1) g channels.

Table 7

Summary of highly stressed {1 1 1}�1 1 2� slip systems, their Schmid factors and RSS during creep at 750 8C and 750 MPa at different loading

orientations

Specimen Actual stress axis Slip system, defect Amount Schmid factor RSS (MPa)

A [1 3 6] /[1 3 6] (1 1 1)/[2 1 1]; SESF Predominant (�/70%) �/0.451 338

(1 1 1)/[1 1 2]; SISF Predominant (�/30%) 0.410 307

/(1 1 1)[1 1 2]; SISF Very few 0.410 307

B [0 0 1] /[1; 0; 10] /(1 1 1)[1 1 2]; SISF Predominant 0.488 366

/(1 1 1)/[1 1 2], SISF Predominant 0.488 366

(1 1 1)/[1 1 2]; SISF A few 0.441 331

/(1 1 1)[1 1 2]; SISF A few 0.441 331

C [0 1 1] [1 6 5] /(1 1 1)/[2 1 1], SESF Predominant �/0.494 371

(1 1 1)/[2 1 1]; SESF Very few �/0.411 308

D [1 1 1] [1 1 1] /(1 1 1)/[2 1 1], SESF None �/0.314 236

/(1 1 1)/[1 2 1], SESF None �/0.314 236

/(1 1 1)/[1 1 2], SESF None �/0.314 236


CRSS of g? phase in SRR99 which is mainly deformed

by SSFs at 760 8C [26]. Hence, a slight variation of the

Schmid factor around CRSS dramatically changes the

number of stacking faults on the respective slip systems.This may be the physical reason why the greatest

sensitivity of creep to orientation is observed around

750 8C and 750 MPa.

4.2.2. Specimen B*/[0 0 1]

4.2.2.1. Identification of deformation mechanisms. Thefoil normal of this specimen was determined to be

[1; 0; 10]: Figs. 9 and 10 show SSFs in the foil. There

are some �1 1 0�/2 dislocations in g channels. The SSFs

in Fig. 9 are analysed as follows. If the stress axis was

exactly along the [0 0 1] direction, four {1 1 1} planes

would be symmetric about the loading axis and would

thus have stressed equally. Under the diffraction condi-

tion BD �/0 0 1 and g�/0 2 0 (Fig. 9a), the 9/(1 1 1) and

9(1 1 1) stacking faults both lie along [1 1 0] direction;

and 9(1 1 1) and 9(1 1 1) stacking faults both align

along the [1 1 0] line. To distinguish them the diffraction

condition BD �/0 1 1 and g� 1 1 1 was adopted, as

shown in Fig. 9b. Under this diffraction condition, 9/

(1 1 1) stacking faults are visible and 9(1 1 1) are

invisible; 9(1 1 1) plane is edge-on appearing as a

narrow line; and 9(1 1 1) inclines with a considerable

angle appearing as a wide faulting plate. It is found that

most of the stacking faults along [1 1 0] line in Fig. 9a

exhibit a considerable width in Fig. 9b, implying they

are9(1 1 1) faults (‘A’ family); and that a few of them as

marked by arrows are edge-on, which indicates that they

are9(1 1 1) faults (‘B’ family). All stacking faults along

the [1 1 0] line of Fig. 9a are invisible in Fig. 9b,

indicating that they are 9(1 1 1) faults (‘C’ family).

Searching over a large region, four 9/(1 1 1) faults (‘D’

family) were founded as shown in Fig. 9c. It is

concluded that for [1; 0; 10] orientation 9(1 1 1) and

9(1 1 1) stacking faults are predominant and a few 9/

(1 1 1) and 9(1 1 1) faults form.

Rigorous identification was carried out for partial

dislocations of five stacking faults in Fig. 10. The

simulation parameters are listed in Table 5. The Burgers

vectors of partial dislocations and the displacement

vectors of stacking faults are given in Fig. 10. The

following reactions are proposed for (1 1 1)=3 and

(1 1 1)=3 fault configurations according to their Burgers

vectors.

and

Configurations I and III are extending in opposite

directions on the same slip system 9[1 1 2](1 1 1); as

summarised in Fig. 11. Configurations II (IV) and V are

broadening in opposite directions as well on another slip

system 9[1 1 2](1 1 1):/

4.2.2.2. Schmid factor. The Schmid factors for loading

axes [1; 0; 10] are given in Table 4 as well. It can be seen

that the (1 1 1)[1 1 2] and (1 1 1)/[1 1 2] slip systems both

have the highest positive Schmid factor 0.488. Theyproduce SISFs through the movement of the leading

partials 9[1 1 2]=3 and 9/[1 1 2]/3. Referring back to

Fig. 10, one can see that the key shearing mechanisms

predicted above and the predominant SISFs observed in

this specimen (Fig. 10) are consistent.

Although another two slip systems (1 1 1)/[1 1 2] and

(1 1 1)[1 1 2] have a high Schmid factor of 0.441 (RSS�/

331 MPa), the TEM observation has illustrated thattheir activity is significantly less than the dominant slip

systems (Fig. 9b and c). The required {1 1 1}�1 1 0� slip

systems have Schmid factors 0.400 and 0.364. Their

1

2[1 0 1]�

1

2[0 1 1] 0

1

3[1 1 2]�SISF on (1 1 1)�

1

6[1 1 2] (Configuration II and IV)

1

2[1 0 1]�

1

2[0 1 1] 0

1

3[1 1 2]�SISF on (1 1 1)�

1

6[1 1 2] (Configuration V)

;

8>>><>>>:

(8)

1

2[1 0 1]�

1

2[0 1 1] 0

1

3[1 1 2]�SISF on (1 1 1)�

1

6[1 1 2] (Configuration I)

1

2[1 0 1]�

1

2[0 1 1] 0

1

3[1 1 2]�SISF on (1 1 1)�

1

6[1 1 2] (Configuration III)

:

8>>><>>>:

(9)


RSSs are 300 and 273 MPa, respectively, which are

much higher than the CRSS of {1 1 1}�1 1 0�/2 slip (�/

35 MPa), and should have produced sufficient �1 1 0�/2

dislocations. Hence, the amount of SSFs is mainly

controlled by the RSSs of �1 1 2� shearing rather than

the activation of �1 1 0�/2 slip. A slight reduction of the

RSS of a {1 1 1}�1 1 2� slip system dramatically reduces

the number of SSFs.

Since specimen B was interrupted in the primary creepstage (Fig. 1), one may argue that the density of

deformation defects at the early stage may also largely

depend on the availability of local dislocation sources.

This effect is excluded for the following two reasons. (i)

At very early stage, the density of �1 1 0�/2 dislocations

might be well controlled by the availability of local

sources, but a local source emanates dislocations of the

same Burgers vector [6] which is not sufficient to initiateSSFs, as a successful nucleation process of a SSF

configuration needs at least two types of �1 1 0�/2

dislocations, as expressed in Eqs. (3)�/(9). Hence, when

the amount of �1 1 0�/2 dislocations is controlled by

local sources, it is unlikely to form SSFs. (ii) If one local

sources can emit two types of �1 1 0�/2 dislocations and

the density of SSFs is controlled by the availability of

local sources, one could expect defects of the same�1 1 2�/3 Burgers vector in one region, and another

�1 1 2�/3 faults were predominant in another region.

The present TEM observation over large areas (e.g. Fig.

3) in several foils shows no evidence of this distribution.

It is therefore concluded that the density of

{1 1 1}�1 1 2� SSFs is, from the very beginning of their

formation, determined by the Schmid factor on that slip

system, neither by the RSSs acting on suitable{1 1 1}�1 1 0� slip systems nor by the availability of

the local sources.

4.2.3. Specimen C*/[0 1 1]

4.2.3.1. Identification of shearing mechanisms. The foil

normal of specimen C was measured to be [1 6 5] using

Kikuchi map. If the sample was stressed exactly along

[0 1 1] orientation, the Schmid factors of (1 1 1)/[2 1 1]and (1 1 1)/[2 1 1] would have been equally high and

activated. However, Fig. 12 indicates a single

{1 1 1}�1 1 2� slip system, which is in agreement with

previous observation [5]. Computer simulation was

made for three stacking faults in Fig. 12a, as illustrated

in Fig. 13. The simulation parameters are listed in Table

6. The result is that the strongly predominant SESFs are

R�(1 1 1)=3 and they are produced by [2 1 1]/3 shear-

ing (the Burgers vector of the leading partials). The

following reactions are proposed according to the

crystallographic identification.

The above shear mechanism was illustrated in Fig. 13d.The lead partials are moving in opposite directions in

these two configurations. In addition, only one [1 1 1]=3

stacking fault was found, as marked in Fig. 12d.

4.2.3.2. Schmid factor. From the [1 6 5] column of Table

4, one can see that (1 1 1)[2 1 1] slip system has thelargest negative Schmid factor �/0.494, which means the

crystal above the (1 1 1) plane shears along the [2 1 1]

direction relative to the crystal below (1 1 1); producing

SESFs. This shearing mechanism is consistent with the

observed predominant SESFs (Fig. 12aFig. 13). The

(1 1 1)/[2 1 1] slip system has a higher Schmid factor �/

0.411 (RSS�/308 MPa), which is very close to the

inferred CRSS (307 MPa). The suitable slip systems(1 1 1)/[1 1 0] and (1 1 1)/[1 0 1] have Schmid factor 0.395

and 0.316, respectively. Their RSSs are 296 and 237

MPa, which are high enough to produce the necessary

�1 1 0�/2 dislocations. However only one (1 1 1)-type

SESF (Fig. 12d) was found. This supports the conjecture

that the RSS of (1 1 1)/[2 1 1] is indeed close to its CRSS,

confirming that the CRSS of {1 1 1}�1 1 2� slip system

is about 300 MPa.

4.2.4. Specimen D*/[1 1 1]

4.2.4.1. Identification of shear mechanisms. The accurate

foil normal is still [1 1 1] for this specimen. Stacking

faults were seldom observed. Many �1 1 0�/2 disloca-

tions appear in the g channels, as illustrated in Fig. 14.

For convenience, the three sets of g channels that are

parallel to (1 0 0), (0 1 0) and (0 0 1) planes are named

(1 0 0)-, (0 1 0)- and (0 0 1)-g channels, respectively.

Thus in Fig. 14, the g channels aligning in the AC, BCand AB directions are (1 0 0)-, (0 1 0)- and (001)-gchannels, respectively. In Fig. 14a, the predominant

dislocations in (1 0 0)-g channels (in AC direction) are

1

2[1 0 1]�

1

2[1 1 0] 0

1

3[2 1 1]�SESF on (1 1 1)�

1

6[2 1 1] (Configuration II and III)

1

2[1 0 1]�

1

2[1 1 0] 0

1

3[2 1 1]�SESF on (1 1 1)�

1

6[2 1 1] (Configuration I)

:

8>>><>>>:

(10)


identified as 9/[0 1 1]/2. In Fig. 14b, the major disloca-

tions in (0 1 0)-g channels (in BC direction) are identified

as 9/[1 0 1]/2. In Fig. 14c, the predominant dislocations

in (0 0 1)-g channels (AB direction) are identified as 9/

[1 1 0]/2. Trace analysis shows that the dislocations

observed above are screw type. In Fig. 14c, for instance,

the projection traces of b�/9/[1 1 0]/2 dislocations in AB

g channel lie along 9[1 1 1] direction. The project

direction of u�/9/[1 1 0] line in Fig. 14c is BD�u�BD�9[1 1 1]: This indicates that b�/9/[1 1 0]/2 dislo-

cations in Fig. 14c lie along 9/[1 1 0], and hence are

screw in character. It can be seen that the dominant

shear direction in each set of g channels is selected to be

perpendicular to the g channel layer normal (i.e. parallel

to the g channel layer), consistent with the observation

of Kolbe et al. [27].

4.2.4.2. Schmid factor. The Schmid factors at [1 1 1]

orientation are generally low (Table 4). The largest

Schmid factor on (1 1 1)�1 1 2� family is 0.314. Their

RSS is 236 MPa which is lower than the estimated CRSS

value (307 MPa) of (1 1 1)�1 1 2�-type slip systems.

Three slip directions [1 1 0], [1 0 1] and [0 1 1] have the

same Schmid factor of 0.272, and their RSS equals 204

MPa which is large enough to activate {1 1 1}�1 1 0�slip system in the soft g matrix.

5. Summary

The above identification of deformation defects has

no doubt confirmed that �1 1 2�/3 slip in g? phase of

CMSX-4 largely involves the reaction and dissociation

of two �1 1 0�/2 dislocations which have different

Burgers vectors. TEM observation has also shown that

the operation of {1 1 1}�1 1 2� slip systems and the

density of SSFs are very sensitive to the stress orienta-

tion at 750 8C and 750 MPa, being determined by the

RSSs on those slip system as indicated by Schmid factor

calculation. Around [1 3 6] or [0 1 1] a minor reduction

of a Schmid factor switches off the activation of the slip

system. A slight offset from [0 0 1] symmetric axis

dramatically reduces the number of SSFs on some slip

systems. It is explained that at 750 8C and 750 MPa the

RSSs of highly stressed {1 1 1}�1 1 2� slip systems at the

[1 3 6]; {0 0 1} and [0 1 1] orientations are just above

their CRSS (�/300 MPa), and thus a slight decrease of a

RSS may switch off the operation of a {1 1 1}�1 1 2�slip system, or vice versa. The highly stressed

{1 1 1}�1 1 2� slip mechanisms, their Schmid factors

and RSSs are summarised in Table 7.

Acknowledgements

The authors acknowledge Rolls-Royce plc. for sup-

plying the bars used in the investigation, and Dr S.S.K.Gunturi for carrying out the creep test and providing the

TEM foils. The authors also wish to thank Professor

Alan Windle for provision of the research facilities

whilst D.M. Knowles and Q.Z. Chen were working at

the University of Cambridge. The authors also wish to

thank Materials Performance Technologies and the

University Research Committee (URC Hong Kong)

which has continued to support this work.

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Mechanism of 1 1 2/3 slip initiation and anisotropy of g? phase in CMSX-4 during creep at 750 C and...

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