Elementary deformation processes during low temperature ...

Elementary Deformation Processes duringLow Temperature and High Stress Creep

of Ni-base Single Crystal Superalloys

Dissertation

zur

Erlangung des Grades

Doktor-Ingenieurin

der

Fakultat fur Maschinenbau

der Ruhr-Universitat Bochum

von

Xiaoxiang Wu

aus

Jiangxi, China

Bochum, 2016

Dissertation eingereicht am: 18.10.2016

Tag der mundlichen Prufung: 09.12.2016

Erster Referent: Prof. Dr. Gunther Eggeler

Zweiter Referent: Prof. Dr. Dierk Raabe

Abstract

Ni-base single crystal superalloys have been widely used as gas turbine materials due to

their superior creep and fatigue properties at high temperatures. In the form of single

crystals, high angle grain boundaries are absent, which are the preferred sites for crack

initiation. The outstanding mechanical properties originate from the microstructure.

Ni-base single crystal superalloys contain two phases: the matrix γ phase, which is

an FCC structure and the precipitate γ′ phase, which is an ordered FCC structure

called L12. Researchers have found that creep, the time-dependent plastic deformation

of materials strongly depends on microstructures and different temperature and stress

regimes feature different deformation mechanisms. The present work focuses on the

deformation regime of low temperature and high stress, i.e., 750 ◦C and 800 MPa.

The material investigated in present work is a second generation Ni-base single crys-

tal superalloy ERBO/1 with around 3% Re. Miniature creep specimens with a gauge

length of 9 mm have been precisely [001]-oriented using the Laue method. Uniaxial

tensile creep tests have been interrupted after strains of 0.1, 0.2, 0.4, 1, 2 and 5%,

respectively. Transmission electron microscopy has been mainly employed to investi-

gate the microstructure evolution during the creep process and to interpret the creep

behavior.

A peculiar type of creep behavior has been observed for the material at 750 ◦C and

800 MPa. It has been found that there are two creep rate minima, i.e, a fast decrease

of creep rate at 0.1% and a broader creep rate minimum at 5%. It can be referred to

as double minimum creep behavior. This kind of creep behavior has been observed by

other researchers as well, however, this has never been explained. An effort has been

made to rationalize this peculiar type of creep behavior. Three mechanisms have been

proposed for the first minimum of creep rate, i.e., the composite character of Ni-base

single crystal superalloys, an exhaustion mechanism for vertical channel dislocations

due to the high applied stress and a run and stop mechanism for horizontal channel

dislocations due to the irregular placement and size-distribution of γ′ particles. Both

planar defects and dislocations have been quantified and the increase of creep rate from

the first minimum is related to both kinds of defects. The strain hardening leads to

the second broad creep rate minimum.

Acknowledgement

This thesis was performed during my time at the Ruhr-Univeristat Bochum as a scholar

of the International Max-Planck Research School on Surface and Interface Engineering

in Advanced Materials (IMPRS SurMat). I would like to thank all members of the

Institute of Materials for their support. I also enjoyed the contacts with my colleagues

from SurMat.

My special thanks go to Prof. Eggeler for his support and for supervising this thesis.

Prof. Eggeler offered me the opportunity to study Ni-base single crystal superalloys and

supported me in my research work. He helped me become familiar with the fascinating

world of elementary deformation mechanism. Prof. Raabe is highly acknowledged for

the fruitful discussions and for co-advising my thesis, which opened my horizon and

inspired me to keep making progress.

I appreciate the tremendous help and support from Prof. Dlouhy as well, who intro-

duced me to diffraction contrast TEM for defect analyses and whom I had the oppor-

tunity to collaborate with in my research project. Everything would have been much

more difficult without the support and help from my direct supervisors, Dr. Somsen

and Dr. Kostka. They were always there for me whenever I had problems with TEM.

They also helped me with settlings in my new German research environment.

Without the kind help of my colleagues my research work could not have been carried

out in sort of good way. Dr. Parsa showed great patience and devoted lots of time

showing me TEM sample preparation. Philip Wollgramm kindly provided all the creep

specimens. Dr. Jaeger and Dr. Depka encouraged me to open up to other people.

Dr. Neuking and Dr. Frenzel are always so patient to answer my questions. Special

thanks also go to K. Strieso, S. Jordan, N. Linder, D. Rose and M. Bienek for their

kind support in sample preparation and SEM investigation. As a “trouble maker”, I’m

also very grateful for the help from Suzana, Frank and Denis. The list can go on and

on.

My deepest and most grateful thanks go to my family and friends. Their encourage-

ment and support make me feel that I am never alone far away from home. There are

no more words than sincere thanks for Yu, for his never-ending support and always

being by my side.

Contents

Abbreviations viii

Symbols x

1 Introduction 1

2 Background 32.1 Ni-base single crystal superalloys . . . . . . . . . . . . . . . . . . . . . 32.2 Creep deformation of metals and alloys . . . . . . . . . . . . . . . . . . 72.3 Creep deformation of Ni-base single crystal superalloys . . . . . . . . . 102.4 Miniature tensile creep testing . . . . . . . . . . . . . . . . . . . . . . . 182.5 Transmission electron microscopy of defects in Ni-base single crystal

superalloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Scientific Objectives 43

4 Materials and Experiments 454.1 Alloy and heat treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 454.2 Interrupted miniature creep tests at low temperature and high stress . 494.3 Scanning electron microscopy . . . . . . . . . . . . . . . . . . . . . . . 494.4 Transmission electron microscopy . . . . . . . . . . . . . . . . . . . . . 504.5 Determination of γ′ volume fractions, γ channel widths and γ′ cube edge

lengths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514.6 Planar faults quantification . . . . . . . . . . . . . . . . . . . . . . . . 524.7 Dislocation density quantification . . . . . . . . . . . . . . . . . . . . . 534.8 TEM foil thickness determination . . . . . . . . . . . . . . . . . . . . . 554.9 Tilt experiments for identification of linear and planar defects . . . . . 56

5 Results 615.1 Double minimum creep at low temperature and high stress . . . . . . . 615.2 Microstructure evolution . . . . . . . . . . . . . . . . . . . . . . . . . . 635.3 Evolution of dislocation and planar fault densities . . . . . . . . . . . . 775.4 Identification of dislocation character . . . . . . . . . . . . . . . . . . . 805.5 Identification of planar fault displacement vectors R . . . . . . . . . . . 87

6 Discussion 1016.1 On the need of further work to explain primary creep . . . . . . . . . . 1016.2 Composite character and stress transfer . . . . . . . . . . . . . . . . . . 1026.3 Exhaustion of grown-in misfit dislocations . . . . . . . . . . . . . . . . 1036.4 Interpretation of glide of grown dislocation . . . . . . . . . . . . . . . . 107

6.5 Time spent at the first local minimum . . . . . . . . . . . . . . . . . . 1076.6 Observation for intermediate local maximum . . . . . . . . . . . . . . . 1086.7 Strain hardening: towards a global minimum . . . . . . . . . . . . . . . 1106.8 Local TEM observations . . . . . . . . . . . . . . . . . . . . . . . . . . 111

7 Summary and Conclusions 117

References 123

Appendices 133

List of Figures

2.1 Microstructure and crystal structure of Ni-base single crystal superal-

loy. (a) STEM HAADF image. (b) FCC structure: γ phase. (c) L12

structure: γ′ phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 EPMA mapping showing large scale elements partitioning (dendritic and

interdendritic regions). (a) Al partitions to interdendritic regions. (b)

Re partitions to dendritic regions [14, 15]. . . . . . . . . . . . . . . . . 6

2.3 Segregation of elements in ID region to γ′ cubes (first row) and γ chan-

nels (second row) [14, 15]. . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Shape of a generic text book creep curve. (a) Strain ε plotted as a

function of time t. (b) Logarithmic strain rate plotted as a function of

strain [15, 18]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.5 Stress-rupture plot [17, 19, 20]. (a) Constant temperature. (b) Changing

temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.6 Creep curve shapes which are associated with density controlled (type

I, alloy type) and obstacle controlled (type II, pure metal type) creep

[23, 24]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.7 SEM images showing two types of rafting. (a) Rafting perpendicular to

the loading direction. (b) Rafting parallel to the loading direction [28]. 11

2.8 Three possible cutting mechanisms into the γ′ particles. (a) a〈112〉 cut-

ting, with generation of SISF and SESF. (b) a〈110〉 cutting with SISF.

(c) a〈110〉 cutting with SESF [47]. . . . . . . . . . . . . . . . . . . . . . 16

2.9 Detailed analysis of γ′ cutting mechanism. (a) A TEM image indicating

stacking fault cutting mechanism. (b) Proposed model corresponding to

the TEM image [47]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.10 Illustration of {111} projection of L12 structure, Al atoms are in gray

and Ni atoms are in white. Circles represent atoms at the top layer, while

rectangles and triangles represent middle and bottom layers respectively.

Three 〈110〉 and 〈112〉 directions are indicated, adapted and modified

from [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.11 Illustration of an APB generation due to the top layer shear of vector

bAPB=a/2[101], two dashed rectangles indicates the forbidden bond of

Al-Al, adapted from [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . 22

i

LIST OF FIGURES

2.12 Illustration of a SISF generation due to top layer shear of vector bSISF=a/3[211],

the top layer sits directly on top of the bottom layer [3]. The circles have

the same meaning as in Fig 2.10. . . . . . . . . . . . . . . . . . . . . . 23

2.13 Illustration of a SESF generation due to top layer shear of vector bSESF=a/3

[211]. A new top layer has generated. The symbols have the same mean-

ing as in Fig 2.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.14 Illustration of a CSF generation due to top layer shear of vector bCSF=a/6[112],

the top layer sits directly on top of the bottom layer and forbidden bonds

form. The symbols have the same meaning as in Fig 2.10, adapted from

[3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.15 Illustration of stacking sequence of intrinsic and extrinsic stacking faults

with regard to dislocations [66]. (a) S-fault. (b) D-fault. . . . . . . . . 26

2.16 Schematic drawing showing the generation of diffraction contrast [61]. . 28

2.17 Schematic drawing showing two-beam conditions with different s value.

(a) Exact two-beam condition, s =0. (b) Positive s. (c) Negative s [61, 62]. 29

2.18 Illustration of s value and intensity distribution with s value [62]. . . . 30

2.19 Illustration of different modes in conventional TEM. (a) BF. (b) DF. (c)

CDF. (d) WBDF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.20 Comparison between CTEM and STEM modes [68]. . . . . . . . . . . . 32

2.21 Illustration of STEM mode configuration [69]. . . . . . . . . . . . . . . 33

2.22 Two g-conditions for stereo images. (a) Before rotation. (b) After rotation. 34

2.23 STEM images showing dislocations in Ni-base single crystal superalloy

CMSX-4 type. (a) BF image. (b) HAADF image. . . . . . . . . . . . . 35

2.24 Illustration of dislocation contrast. (a) When dislocation is parallel to

reflecting planes. (b) When dislocation is not parallel to reflecting planes

[62]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.25 Computed stacking fault intensity image profile for α =+2π/3 with

anomalous absorption [61, 71]. . . . . . . . . . . . . . . . . . . . . . . . 37

2.26 TEM images showing contrast of stacking fault. (a) BF image. (b) CDF

image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.27 Systematic flow chart showing the criterion for SF nature determination

[61–63]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.28 TEM images showing the contrast of an APB. (a) The APB in contrast

with the superlattice diffraction (100). (b) The APB out of contrast

with the matrix diffraction (200) [73, 74]. . . . . . . . . . . . . . . . . . 41

4.1 (a) ERBO plate. (b) Cut-up plan. . . . . . . . . . . . . . . . . . . . . . 46

4.2 Schematic drawing showing multi-step heat treatment [14]. . . . . . . . 47

4.3 Flow chart showing solution heat treatment process. . . . . . . . . . . . 48

ii

LIST OF FIGURES

4.4 Flow chart showing precipitation heat treatment process. . . . . . . . . 48

4.5 (a) Size and geometry for the miniature creep specimen. (b) Miniature

specimen in furnace for high temperature creep [85, 86]. . . . . . . . . . 48

4.6 Illustration of TEM specimens cutting from the creep miniature speci-

men. (a) [001] cutting and (b) [111] cutting. . . . . . . . . . . . . . . . 51

4.7 Illustration of defect quantification. (a) TEM montage images taken af-

ter 2% strain, g : (111). (b) Field F1 from (a) at a higher magnification.

(c) Reference grid for determination of dislocation density from Field F2

of (a). (d) Illustration of counting procedure. . . . . . . . . . . . . . . . 54

4.8 Illustration of the thickness measurement using CBED. (a) A TEM im-

age with a white spot indicating beam position, with diffraction pattern

as an inset image. (b) Measurement of distance Dd between transmitted

and diffracted disks. (c) Measurement of fringe distances. (d) Calcula-

tion of foil thickness and extinction distance. . . . . . . . . . . . . . . . 57

4.9 Illustration of measurement of s. (a) Illustration of x and R value. (b)

Example of an operating g-condition. (c) Measurement of x and R from

the operating g diffraction pattern. . . . . . . . . . . . . . . . . . . . . 58

5.1 Creep curves from interrupted tests of ERBO / 1C (750 ◦C and 800 MPa).

(a) Strain ε as a function of time t. (b) Logarithm of creep rate as a func-

tion of strain. (c) Logarithm of creep rate as a function of logarithmic

strain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 TEM images showing microstructure of ERBO/1 at initial state. (a)

STEM BF image. (b) STEM HAADF image. (c) HRTEM of the γ

phase. (d) HRTEM of the γ′ phase. . . . . . . . . . . . . . . . . . . . . 65

5.3 SEM micrographs of the γ/γ′ microstructure of ERBO/1C before and

after creep at 750 ◦C and 800 MPa. (a) Initial state, [001] cross section.

(b) Initial state, [111] cross section. (c) After creep, [001] cross section.

(d) After creep, [111] cross section. . . . . . . . . . . . . . . . . . . . . 66

5.4 TEM montage for the initial state prior to creep, foil normal [111]. . . . 67

5.5 TEM montage for 0.1% deformation, foil normal [111], g=(111). . . . . 68

5.6 TEM montage image for 0.1% deformation, foil normal [001]. (a) TEM

montage with horizontal and vertical reference lines. (b) Histogram

showing γ channel width distribution. (c) Histogram showing γ′ cube

edge length distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.7 TEM montage for 0.2% deformation, foil normal [111]. g=(111). . . . . 71

5.8 TEM montage for 0.4% deformation, foil normal [111]. g=(111). . . . . 72

5.9 TEM montage for 1% deformation, foil normal [111]. g=(111). . . . . . 74

5.10 CTEM montage for 5% deformation, foil normal [111]. g=(111). . . . . 75

iii

LIST OF FIGURES

5.11 STEM montage for 5% deformation, foil normal [111]. g=(111). . . . . 76

5.12 Dependence of dislocation densities on creep strain. (a) Overall dislo-

cation density ργ/γ′ . (b) Dislocation density in the γ channels ργ. (c)

Dislocation density in the γ′ particles ργ′ . . . . . . . . . . . . . . . . . . 78

5.13 Evolution of planar faults with creep strain. (a) Number density of

planar faults per area nPF/am. (b) Projected area fraction APF . (c)

Intensity parameter IPF . For details see texts. . . . . . . . . . . . . . . 79

5.14 TEM micrographs of initial state under different two-beam conditions.

(a) to (k) Bright field images. (l) Kikuchi map indicating tilt positions

and g-vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.15 Four STEM images taken as a part of a tilt series for the determination

of Burger’s vector and displacement vectors of planar faults crept at

750 ◦C, 800 MPa, 1%. (a) to (c) STEM BF images. (d) HAADF image. 83

5.16 Anaglyph showing spatial arrangement of defects from Figure 5.15. . . 86

5.17 TEM micrographs taken after 2% strain under different two-beam con-

ditions. (a) Kikuchi map. (b) and (d) to (i) BF images. (c) CDF image. 89

5.18 (a) In-plane faults, STEM micrograph taken after 1% strain under two-

beam condition. (b) Kikuchi map indicating different tilt positions. . . 91

5.19 STEM BF micrographs taken after 1% strain under different two-beam

conditions for in-plane stacking faults and dislocations investigation. (a)

g1 : (111). (b) g2 : (202). (c) g3 : (200). (d) g4 : (111). (e) g5 : (022).

(f) g6 : (111). (g) g7 : (131). (h) g8 : (220). (i) g9 : (311). (j) g10 : (111).

(k) g11 : (113). (l) g12 : (002). . . . . . . . . . . . . . . . . . . . . . . . 92

5.20 An anaglyph under condition of (111) showing in-plane stacking faults

and dislocations. 750 ◦C, 800 MPa, 1% creep strain. . . . . . . . . . . . 93

5.21 An anaglyph under condition of (111) showing in-plane stacking faults

and dislocations. 750 ◦C, 800 MPa, 1% creep strain. . . . . . . . . . . . 94

5.22 HRTEM analysis for stacking faults. (a) Edge-on stacking faults in a

lower magnification. (b) Higher magnification for stacking faults. (c)

FFT. (d) Filtered HRTEM with an inset containing only one plane fil-

tered. (e) Determination of faults nature. (f). Determination for fault

shift. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

6.1 Composite character of SX Ni-base superalloys on two length scales.

Center: Small differences between prior dendritic and interdendritic re-

gions. Left and right: Micro composites with slightly higher (left: ID)

and slightly lower (right: D) γ′-volume fractions. . . . . . . . . . . . . . 104

iv

LIST OF FIGURES

6.2 Misfit dislocation model. (a) Dislocations in two slip systems. (b) 2D

projection of γ/γ′ model system with misfit dislocations. (c) Reaction of

misfit dislocations to applied load. (d) Annihilation of misfit dislocations

in vertical channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

6.3 STEM HAADF image showing microstructure of ERBO/1 at the initial

state, the dashed circles highlight tiny γ phases inside of the γ′ particles.

Courtesy of Dr. A. Parsa, same specimen as in [118]. . . . . . . . . . . 113

6.4 TEM micrographs of dislocation events. (a) Dislocation expanding along

γ -channel in (111) plane of TEM foil - 0.2% strain. (b) Irregularly

located γ′-particles impede dislocation motion - 0.2% strain. (c) γ′-

phase cutting by dislocations - 1% strain. (d) High dislocation densities

in all γ-channels after 5% strain. Central γ′-particle contains planar

faults and dislocations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

A.1 TEM images showing dislocation movements at 750 ◦C, 800 MPa, 0.2%.

(a) Dislocations gliding in one direction of γ channel. (b) Dislocations

gliding along two sides of one γ′ particle. (c) Dislocations expanding

from one central loop into other direction of γ channels. (d) More dis-

locations sending to the same direction of channel. . . . . . . . . . . . . 133

A.2 Comparison of a pair of plus and minus g-vector analyzing a stacking

fault at 750 ◦C, 800 MPa, 0.2%. (a) BF image under +g, the two outer-

most fringes are both dark. (b) BF image under -g, the two outermost

fringes are both bright. (c) CDF image corresponding to +g, the lower

outermost fringe is bright. (d) CDF image corresponding to -g, the up-

per outermost fringe is bright. (e) WBDF image corresponding to +g,

dislocations show better contrast. (f) WBDF image corresponding to

-g, both the stacking fault and dislocations are highlighted. . . . . . . . 134

A.3 A tilting series for a stacking fault analysis at the condition of 750 ◦C,

800 MPa and 0.2%. (a) BF image at [111]. (b) BF image at [020].

(c) BF image at [111], the stacking fault has been oriented edge-on, as

indicated by the white dashed line. (d) BF image at [220], stacking fault

is invisible. (e) BF image at [202]. (f) BF image at [022]. (g) BF image

at [311], the stacking fault is invisble. (h) BF image at [113]. (i) BF

image at [131]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

v

LIST OF FIGURES

A.4 Microstructure of 750 ◦C, 800 MPa, 1%, foil normal [001]. (a) CTEM

BF image showing SFs. SFs start from γ′ corners, direction indicated by

white dashed line. (b) CTEM CDF image for SF nature determination.

(c) CTEM BF image showing SFs at a higher magnification. (d) CTEM

WBDF image showing partial dislocation associated with SF. (e) Multi-

beam STEM image showing SFs and lower density of dislocations. (f)

Multi-beam STEM image showing SF and higher density of dislocations. 136

A.5 An anaglyph showing an inclined stacking fault at the condition of

750 ◦C, 800 MPa, 0.1%. . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

A.6 Illustration of (111) projection of L12 structure. The symbols have the

same meaning as in Figure 2.10. (a) Projection of (111) plane, with three

〈110〉 and 〈112〉 directions. (b) The top layer is shifted by 1/3 [112] and

a SESF is generated. (c) The top layer is shifted by 1/3 [121] and a

SESF is generated. (d) The top layer is shifted by 1/3 [211] and a SISF

is generated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

vi

List of Tables

2.1 Quantitative results of element distribution for ERBO/1C [14]. . . . . . 7

4.1 Chemical composition of ERBO/1C in wt.%. . . . . . . . . . . . . . . . 48

4.2 Parameters for thickness measurement. . . . . . . . . . . . . . . . . . . 56

5.1 Overview of experimental details characterizing the TEM foils investi-

gated in the present work. . . . . . . . . . . . . . . . . . . . . . . . . . 76

5.2 g-vectors and effective visibilities and invisibilities of dislocations from

Figure 5.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

5.3 Results from TEM tilt experiments after 1% creep strain for inclined

faults, g-vectors: g (1 to 11), defects: (1-9: dislocations, 10 and 11:

planar faults). Fields highlighted in gray: Figures 5.15(a) to (c). res :

residual contrast, do: double contrast, ? : no determination possible, b:

Burgers vector, R: planar fault displacement vector. . . . . . . . . . . . 85

5.4 g-vectors and effective visibilities and invisibilities of the stacking fault

in Figure 5.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

5.5 Results from STEM tilt experiments (Figure 5.19) after 1% creep strain

for in-plane fault with a summary of w value and visibility conditions.

“+” indicates visibility, “-” indicates invisibility and “res” indicates

residual visibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

vii

Abbreviations

APB anti-phase boundary

APT atom probe tomography

BF bright field

CBED convergent beam electron diffraction

CDF centered dark field

CSF complex stacking fault

CTEM conventional transmission electron microscopy

D dendritic

D-dislocation double stacking fault dislocation

DF dark field

DM creep double minimum creep

EBSD electron back scattered diffraction

ECCI electron channelling contrast imaging

EDM electro discharge machining

EDX energy-dispersive X-ray

EPMA electron probe microanalysis

FCC face-centered cubic

FFT fast Fourier transformation

FS/RH finish to start/ right hand rule

GPA geometrical phase analysis

viii

ABBREVIATIONS

HAADF high angle angular dark field

HR EBSD high angular resolution electron back scatter diffraction

HTLS high temperature and low stress

ID interdendritic

IPM Institute of Physics of Materials

ITIS intermediate temperature and intermediate stress

K-M fringes Kossel-Moellenstedt fringes

L12 ordered FCC structure

LACBED large angle convergent beam electron diffraction

LTHS low temperature and high stress

MMCs metal matrix composites

ODS oxide-dispersion-strengthened

OPS oxide polishing suspension

S-dislocation single stacking fault dislocation

SEM scanning electron microscopy

SESF superlattice extrinsic stacking faults

SISF superlattice intrinsic stacking faults

SSF superlattice stacking faults

STEM scanning transmission electron microscopy

SX single crystal superalloy

TCP topologically close-packed

TEM transmission electron microscopy

WBDF weak beam dark field

WDX wavelength-dispersive spectroscopy

ix

Symbols

Symbol Meaning Unit

γ matrix phase in superalloy -

γ′ precipitate phase in superalloy -

◦C temperature in degree Celsius -

MPa mega Pascal = 106 Pascal, unit for mechanical stress -

δ misfit -

aγ lattice constant of γ phase nm

aγ′ lattice constant of γ′ phase nm

εmin minimum creep rate -

c constant -

σ applied stress MPa

n stress exponent -

Qapp apparent activation energy kJ/mol

R universal gas constant J/(mol·K)

T temperature Kelvin

c′

constant after introduction of back stress -

MAR-M-200 directionally solidified superalloy -

CMSX-6 third generation of superalloy -

CMSX-4 second generation of superalloy -

LEK 94 second generation of superalloy -

x

SYMBOLS

ERBO/1C 2nd generation superalloy used in present work -

s deviation vector from exact Bragg condition -

K0 incident beam -

θc convergent angle mrad

L camera length m

α phase factor -

R displacement vector -

b Burger’s vector -

u line direction of dislocation -

g a vector characterizing two-beam condition -

ξg extinction distance angstrom

w a parameter combing extinction distance and deviation

vector

-

aPF projected area of planar defects µm2

am montage area µm2

IPF an intensity parameter to quantify SF -

APF projected area fraction of SF -∑lH total length of horizontal line µm∑lV total length of vertical line µm∑NH ALL total count of horizontal intersection∑NV ALL total count of vertical intersection

ργ/γ′ average dislocation density m−2

ργ dislocation density of γ phase m−2

ργ′ dislocation density of γ′ phase m−2

fγ volume fraction of γ phase -

fγ′ volume fraction of γ′ phase -

xi

SYMBOLS

tF foil thickness nm

dhkl lattice spacing of hkl plane nm

Dd distance between transmitted and diffracted disk nm

li distance between first and ith fringe 1/nm

λ wave length nm

x distance between the center of transmitted beam and

the deficient line

mm

R distance between the center of transmitted and

diffracted beam

mm

D diffusion coefficient m2/s

X diffusion distance nm

t diffusion time s

µ shear modulus GPa

d diameter of dislocation loop nm

τor Orowan stress MPa

τor H horizontal Orowan stress MPa

τor V vertical Orowan stress MPa

τapp H horizontal applied stress MPa

τmis H horizontal misfit stress MPa

xii

1. Introduction

The present work focuses on the reason for a specific type of creep deformation which

is observed for Ni-base single crystal superalloys (superalloy SX). Superalloy SX are

fascinating materials, because they can withstand mechanical loads at temperatures

up to 1100 ◦C, where other metallic engineering materials are no longer solid. Ni-base

single crystal superalloys are produced in a directional solidification process and have

no high angle grain boundaries. Ni-base single crystal superalloys contain two phases

(i.e., γ- and γ′-phase), where the atoms of the two phases occupy one common lattice.

This will be discussed in detail throughout the present work. Here it is important

to point out that superalloy SX are used to make first stage blades for turbines in

aero engines and power plants. Superalloy SX outperform ceramic high temperature

materials in terms of ductility, which provides the required damage tolerance under

harsh operating conditions.

Research in the last three decades has shown that, creep, the time dependent plas-

tic high temperature deformation of materials, strongly depends on microstructure.

Different elementary deformation mechanisms govern the creep behavior in the high

temperature/low stress (HTLS) and low temperature/high stress (LTHS) regimes. For

the superalloy SX, 750 ◦C is not a high temperature. Throughout the present thesis,

750 ◦C is referred to as the low temperature creep regime. At this temperature, high

mechanical stresses (e.g. 800 MPa) are required, to cause creep deformation within

short laboratory time scale.

In the present work special emphasis is placed on a peculiar type of creep curve shape

that is observed for precisely oriented [001] tensile specimens in the LTHS regime.

It is well-known, that many engineering materials show one creep rate minimum. In

contrast, in the LTHS regime, two creep rate minima can be observed. This peculiar

behavior can be referred to as double minimum creep (DM creep). The first creep rate

minimum occurs at an early stage, after strains as small as 0.1%. Then within a very

1

CHAPTER 1. INTRODUCTION

small strain interval, creep rates increase towards an intermediate maximum. From

then on, the strain rates decrease down to a global minimum at a strain of 5%. This

behavior has been first reported more than 20 years ago, and was not explained so far.

The present work uses diffraction contrast transmission electron microscopy (TEM),

to study the evolution of the microstructure of a SX during LTHS creep. The scien-

tific objective of the present work is to provide a microstructural explanation for DM

creep. This work first gives an overview of the technological and scientific background

of the field. Specific research objectives are then briefly summarized. All informa-

tion regarding the material investigated in the present work and the mechanical and

microstructural experiments that were performed are then given. Based on the re-

sults, a sequence of elementary deformation events is proposed which rationalizes DM

creep. The current results are discussed in the light of previous findings reported in

the literature. Directions for further work are finally highlighted.

2

2. Background

2.1 Ni-base single crystal superalloys

Ni-base single crystal superalloys have been widely used in gas turbine blades for jet

engines and power plants due to their superior properties such as high temperature

strength, creep and fatigue resistance, and resistance to oxidation and corrosion at

elevated temperatures [1–4]. The superior high temperature properties of Ni-base sin-

gle crystal superalloys have been significantly improved from the first generation to

the second generation with the addition of 3 wt.% Re [5, 6]. Ni-base single crystal

superalloys are cast materials. As single crystals, they possess several advantages. The

elimination of high angle grain boundaries greatly reduces the risk of crack initiation,

since grain boundaries are the preferred sites for damage accumulation [7]. Moreover,

elements like boron and carbon, which are used to strengthen grain boundaries, are

no longer required. The generation or formation of carbides or borides can then be

avoided [8].

The excellent high temperature properties of SX are closely linked to their microstruc-

ture. It is well-known that there are two phases in Ni-base single crystal superalloys,

i.e., the matrix γ phase and the precipitate γ′ phase. The γ phase has a face-centered

cubic (FCC) structure where Ni and Al atoms are randomly distributed over the lattice

sites, while the γ′ phase is an ordered FCC structure called L12, where all Al atoms sit

at the corners of a cubic cell and all the Ni atoms occupy the face centers. A typical

microstructure is shown in Figure 2.1. Figure 2.1(a) is a scanning transmission electron

microscopy (STEM) image taken in high angle angular dark field (HAADF) mode. The

dark rectangular regions represent the γ′ phase while the bright channels surrounding

them are the γ phase. In Figures 2.1(b) and (c) the crystal structures of γ phase and

γ′ phase are shown. The γ′ phase is coherently embedded in γ matrix. However, there

is a slight difference of the lattice constants of these two phases. The misfit δ is defined

3

CHAPTER 2. BACKGROUND

Figure 2.1: Microstructure and crystal structure of Ni-base single crystal superalloy.(a) STEM HAADF image. (b) FCC structure: γ phase. (c) L12 structure: γ′ phase.

to quantify the difference, as described in the following Equation 2.1:

δ =2 · (aγ + aγ′)

aγ − aγ′(2.1)

where aγ is the lattice constant of the γ phase and aγ′ is the lattice constant of the γ′

phase. For most of the Ni-base single crystal superalloys, their misfit is negative, i.e.,

the lattice constant of the γ′ phase is slightly smaller than that of the γ phase. The

existence of misfit leads to misfit stresses. To relax misfit stress and keep the system

in a low energy state, misfit dislocations are generated to minimize the overall elastic

stress energy. In this respect it is not difficult to understand that misfit dislocations

are present before deformation. In the absence of an external stress, the stress state in

superalloys consists of two elements: the stress introduced by the lattice misfit and the

stress field of dislocations. The presence of misfit dislocations can play an important

role in creep. It is also noteworthy that misfit stress can be as high as 500 MPa [9].

The ordered γ′ phase Ni3Al has received a considerable amount of attention due to its

increase of yield stress with increasing temperatures [10, 11]. This abnormal strength-

ening effect is related to the formation of Kear-Wilsdorf locks, where mobile dislocations

from {111} planes cross slip to the {001} planes and become immobile, thus making

further deformation more difficult.

4


Another important microstructure aspect is heterogeneity which has large and small

scale. Since Ni-base single crystal superalloys are fabricated by casting, they have a

typical cast microstructure consisting of dendritic (D) and interdendritic (ID) regions.

This has been referred to as large scale heterogeneity. Typical primary dendrites spac-

ings are of the order of 400 µm [2, 3]. The small scale of heterogeneity of SX is related

to the γ/γ′ microstructure, which consists of approximately 70% volume fraction of

γ′ cubes with a typical edge length of 0.5 µm and approximately 30% volume fraction

of γ channels with a typical channel width of 0.1 µm [2, 3, 12]. Different γ′ volume

fractions have great influence on the creep properties of Ni-base single crystal superal-

loys. Murakumo et al. [13] have carried out a series of experiments investigating the

influence of γ′ volume fractions upon creep behavior at different temperature ranges.

They found out that 70% of γ′ volume fraction yields the longest rupture life at 900 ◦C,

while 55% of γ′ volume fraction is the optimum condition for the temperature 1100 ◦C.

In addition, volume fraction of γ′ phase is closely related to the composition [13], as

can be seen in Equation 2.2:

Ci = (1− f)Xi + fX′

i (2.2)

In Equation 2.2, i represents the element (Ni, Al, Co, Ti, etc.), f is the γ′ volume frac-

tion, Ci represents the composition of the alloy, Xi and X′i represent the composition

of γ and γ′ phases, respectively.

It has also been found that element partitioning occurs on both scales. Parsa et al. [14,

15] have conducted detailed element analysis by employing various kinds of techniques,

such as energy-dispersive X-ray (EDX) mapping, wavelength-dispersive spectroscopy

- electron probe microanalysis (WDX-EPMA) and atom probe tomography (APT).

From the results of WDX-EPMA in Figure 2.2, it can be seen that after heat treatment

there is more Al in interdendritic than in dendritic regions. In contrast, Re preferably

partitions to the dendritic regions [14, 15]. On the smaller scale, comparing the element

distributions in γ′ particles and γ channels in the same interdendritic regions, as shown

in Figure 2.3, it is clear that the γ′ phase is the preferred place for elements like Al, Ni,

Ti and Ta, while Co, Re, Cr and W show a higher concentration in the γ phase. The

partitioning of elements on the large scale (dendrite and interdendrite) and the small

scale (γ channels and γ′ particles) is compiled in Table 2.1 [14].

5


Figure 2.2: EPMA mapping showing large scale elements partitioning (dendritic andinterdendritic regions). (a) Al partitions to interdendritic regions. (b) Re partitions todendritic regions [14, 15].

Figure 2.3: Segregation of elements in ID region to γ′ cubes (first row) and γ channels(second row) [14, 15].

6


Table 2.1: Quantitative results of element distribution for ERBO/1C [14].

wt.% Al Co Cr Hf Mo Re Ta Ti W Ni

dendrite core 5.6 9.9 6.7 0.1 0.6 4.0 5.6 1.0 8.4 Bal

Interdendritic region 6.3 9.3 6.0 0.1 0.5 1.9 7.1 1.1 5.3 Bal

γ (ID) 0.6 18.4 15.6 - 0.6 11.1 0.8 0.4 10.9 41.6

γ′ (ID) 6.9 6.2 1.9 - 0.1 0.9 5.1 1.2 10.9 68.5

2.2 Creep deformation of metals and alloys

Creep is a plastic time-dependent deformation process under a constant stress or a

constant force at elevated temperature, which is usually higher than half of the melting

temperature of the material [16, 17]. Creep deformation is a process depending on

both temperature and stress. During creep, plastic strain increases with time slowly

but steadily. Typically there are three stages during a creep process, i.e., primary

creep, secondary creep and tertiary creep [16, 17], as can be seen in Figure 2.4 [15, 18].

Figure 2.4(a) is a typical strain-time creep curve where the aforementioned three stages

have been identified as I, II and III. To better illustrate the changes of creep rate with

increasing strain, logarithmic strain rate is plotted as a function of creep strain as is

shown in Figure 2.4(b).

Figure 2.4: Shape of a generic text book creep curve. (a) Strain ε plotted as a functionof time t. (b) Logarithmic strain rate plotted as a function of strain [15, 18].

From logarithmic strain rate vs. strain curves, we can see that the primary stage is

characterized as a stage of decreasing creep rate with increasing strain, while secondary

stage is the period where the creep rate stays almost constant and the minimum strain

rate is established. Most of the creep life of the material is spent in the secondary creep

stage. In the tertiary stage, the creep rate increases dramatically with increasing strain

7


Figure 2.5: Stress-rupture plot [17, 19, 20]. (a) Constant temperature. (b) Changingtemperatures.

until rupture occurs. The creep behavior and minimum creep rate have shown strong

dependences on temperature T and stress σ [1, 3, 17, 19, 20]. Figure 2.5(a) [17, 19, 20]

shows the creep rupture response under constant temperature. With a small decrease

of stress, creep lives can be greatly prolonged. Figure 2.5(b) [17, 19, 20] systematically

illustrates the influence of temperature. Under the same stress (horizontal dashed

reference line), an increase of temperature from T1 to T3 significantly shortens creep

life. In other words, to establish a targeted creep life, a lower temperature requires a

much higher stress.

For the influence of temperature and stress on minimum creep rate, it was often re-

ported that [1, 3, 17, 19, 20] the minimum strain rate εmin shows a power law depen-

dence on stress and an Arrhenius type dependence on temperature, as described by

Equation 2.3:

εmin = c · σn · exp

(−Qapp

T

)(2.3)

Here εmin is the minimum strain rate during secondary creep, c is a constant, σ is the

stress, n is the stress exponent, Qapp is the apparent activation energy of creep, R is

the universal gas constant and T is temperature in Kelvin. In practice, the value of n

and Qapp can be obtained by performing creep tests at different stresses for a constant

temperature and at different temperatures for constant stress. Accordingly, the stress

component n can be derived from the Norton plot, i.e., the log-log plot of minimum

creep rate vs. stress [16–22], while the apparent activation energy Qapp can be plotted

from the slope of logarithm of creep rate vs. the inverse of absolute temperature plot

[16–22]. Detailed descriptions can be found in [18].

Creep behavior of pure metals and single phase metals has been well investigated and

8


Figure 2.6: Creep curve shapes which are associated with density controlled (type I,alloy type) and obstacle controlled (type II, pure metal type) creep [23, 24].

documented. The well-known Orowan equation has been used to describe these two

types of creep deformation. In pure metals, at the early stage of deformation, there

are no obstacles for dislocations movement except for grain boundaries. The high

mobility of dislocations result in the early high strain rates. With increasing densities of

dislocations and other obstacles like subgrain boundaries, dislocation mobility decreases

and creep rates decrease accordingly. This has been classified as class II type of creep

behavior [23, 24]. For other solid solution alloys, the creep behavior is quite different.

Due to the dominance of solid solution strengthening, creep is controlled by solute drag

forces on dislocations, and in this case, the initial creep rate is very low. The creep

response for this kind of material has been described as alloy type behavior, and alloys

with this type of creep behavior are regarded as class I materials [23, 24]. For class

I materials, the dominating factor is the mobile dislocation density, which increases

during creep. These two controlling mechanisms are systematically summarized in

Figure 2.6 [23, 24].

9


Particle strengthening materials differ in creep behavior from pure metals and simple

alloys in two aspects. First, the minimum creep rate is obtained from the transition

of primary creep stage to tertiary creep stage due to the absence of a microstructural

steady state. Second, when using Equation 2.3 to represent minimum creep rate, n and

Q values are normally larger compared to simple metals [23, 24]. The introduction of

a back stress term [25, 26], which is subtracted from the applied stress, has been used

to rationalize the high Q and n values, as indicated in Equation 2.4.

εmin = c′ · (σ − σi)n (2.4)

Here c′ is a constant which reflects material properties and temperature dependence, n

is considered to be the true stress exponent, and σi has been considered as a threshold

value below which creep ceases [23].

2.3 Creep deformation of Ni-base single crystal su-

peralloys

As creep deformation is both temperature and stress dependent, the deformation mech-

anism for Ni-base single crystal superalloys differs significantly in different temperature

and stress regimes. Due to the influence of temperature and stress upon creep, it is rea-

sonable to consider three regimes, i.e., the high temperature low stress regime (HTLS),

the intermediate temperature and intermediate stress regime (ITIS) and the low tem-

perature high stress regime (LTHS).

High temperature and low stress regime

In high temperature and low stress regime, the operating temperature is higher than

0.7 of the melting temperature of the material. In this temperature range, there are two

characteristic features associated with the deformation of single crystal superalloys.

The first characteristic feature is rafting or directional coarsening. This event starts

in the early stage of creep. Rafting is a well-known phase instability of the γ/γ′

microstructure. As can be seen in Figure 2.1, for Ni-base single crystal superalloys,

10


Figure 2.7: SEM images showing two types of rafting. (a) Rafting perpendicular tothe loading direction. (b) Rafting parallel to the loading direction [28].

initially the γ channel phase is continuously surrounding the cuboidal γ′ particles. In

the case of rafting, γ channels are interrupted and are not continuous any more (see

Figure 2.7). In some extreme cases, isolated γ′ phase regions become continuous while

the continuous γ channels become isolated, which has been referred to as topograph-

ical inversion by some researchers [27]. The morphology of rafting depends on both

misfit and loading direction during deformation. Figure 2.7 shows two scanning elec-

tron microscopy (SEM) images indicating different rafted microstructures at different

conditions in Ni-base single crystal superalloys. For superalloys with a negative misfit,

if uniaxial tensile creep tests in a 〈100〉 direction are conducted, directional rafting has

been observed in the direction perpendicular to the tensile loading direction, Figure

2.7(a). On the contrary, if uniaxial compression tests are performed in this direction,

directional coarsening has been observed parallel to the compression loading direction,

as shown in Figure 2.7(b) [28].

For superalloys with a positive misfit, the direction of rafting is opposite [29, 30].

A series of experiments have been conducted for detailed analyses, and the volume

fraction of γ′ phase has also been found to be an important factor for rafting [29].

Although rafting has been commonly regarded as a phase instability phenomenon,

there are researches which highlight the strengthening effect of raft for superalloys [8].

Since rafting interrupts the continuous path for dislocations movement in γ channels

or at the γ/γ′ interface, it can make dislocation movement more difficult. Ott and

Mughrabi [28] have compared the influence of two types of rafting upon high temper-

11


ature fatigue properties. They found out that pre-rafted γ/γ′ microstructures with

rafts parallel to stress direction are beneficial for fatigue properties due to a decreased

rate of fatigue crack propagation [28]. Reed et al.[31] compared the creep behavior at

different temperatures and stresses. They concluded that the decrease of creep rate at

high temperature is associated with rafting, since rafting prevents the glide/climb of

{111}〈110〉 creep dislocations from the γ phase into the γ′ phase. Epishin and Link [32]

further confirmed that glide/climb of a/2〈101〉 interfacial dislocations perpendicular to

the loading direction is activated, and in combination with generated vacancies, the

creep response is greatly influenced.

The second characteristic feature of single crystal Ni-base superalloy crept at high tem-

peratures is the pairwise dislocations cutting into the γ′ phase. As early as in 1957,

Williams [33] proposed that two dislocations are needed to deform an ordered phase.

This type of pairwise dislocation movement has been first observed by Gleiter and

Hornbogen in a Fe-Cr-Al alloy, where two regular a/2〈110〉 dislocations jointly sheared

the γ′ phase, limiting an anti-phase boundary (APB) between the two dislocations

[34–36]. A leading dislocation cuts into the ordered γ′ phase, disturbs the order and

generates an APB. Since an APB has a high energy and is quite unstable, another dis-

location is needed to restore the lattice order and minimize the energy. Kear, Leverant

and co-workers excellently combined diffraction contrast TEM with mechanical and mi-

cromechanical analysis and confirmed experimentally the pairwise cutting mechanism

for the directionally solidified superalloy MAR-M-200 in the high temperature and low

stress regime [37, 38]. This pair-wise cutting has been further confirmed in the second

generation superalloys [39–41]. The two dislocations which limits an APB are referred

to as superpartials, and two superpartials are referred to as one superdislocation [3, 17].

For high temperature and low stress creep regime, dislocation activities have been con-

strained to the γ channels or to the regions near the γ/γ′ interface. With the activation

of more slip systems during creep deformation process, more types of dislocations are

generated from different slip systems. As a result, there will be more possible dislo-

cation reactions, thus forming non-slip dislocations. The generation and interaction

of slip dislocations lead to the formation of dislocation networks. It should also be

highlighted that Eggeler and Dlouhy [41] have explicitly explained and confirmed the

formation of 〈010〉 dislocations in CMSX-6 at high temperature and low stress creep,

which form by the reaction of two 60◦ deposited channel dislocations. Dislocation net-

works strengthen the material by making the dislocation movement more difficult, but

at the same time it provides more sources of superdislocations for pairwise cutting into

the γ′ particles.

12


Anisotropic properties for single crystal superalloys are also an important aspect. For

example, Agudo et al.[42] have compared the creep properties of LEK 94 for [001] and

[110] orientations at a high temperature (1293 K) and a low stress (160 MPa). It was

found that, in the early stage of creep, [001] oriented samples show higher minimum

creep rates than [110] oriented samples, due to the activation of more slip systems. In

contrast, at later creep stage, [110] oriented samples creep faster because rafting is less

pronounced and pairwise cutting is easier.

13


Intermediate temperature and intermediate stress

regime

Intermediate temperature creep is the creep deformation of superalloys which occurs

in a temperature range between 0.6 and 0.7 of the melting temperature. Stresses are

higher at intermediate temperatures than in the high temperature range, but not as

high as in the low temperature range. Therefore, dislocation activities are still mostly

confined to the γ channels. During creep in this regime, the morphology of the γ′

phase does not change dramatically [43]. Creep behavior at this temperature regime

has been reported to be sensitive to both size and shape of the γ′ phase [43, 44].

The influence of specific elements (heavy refractory elements: e.g., Ru, W) upon creep

responses has also been studied. Hobbs et al. [45] investigated the influence of ruthe-

nium on creep behavior of Ni-base single crystal superalloy, and found out ruthenium

has a significant strengthening effect due to the fact that it effectively reduces the

stacking fault energy of the γ matrix phase. On the other hand, Murakami et al. [43]

carried out some research to figure out the influence of Co on anisotropy properties

of Ni-base single crystal superalloys at 800 ◦C and 735 MPa. Surprisingly, it has been

concluded that Co is not essential in improving creep rupture properties of Ni-base

single crystal superalloys, and {111}〈112〉 slip systems have been operative during the

first stage of creep. Although it is possible for planar faults cutting into γ′ particles,

it is not commonly reported due to the intermediate stress. Furthermore, incubation

period has been commonly observed and studied in detail at intermediate temperature

range for 〈001〉 CMSX-3 superalloy [8, 9, 46]. One characteristic feather of this temper-

ature range is the observation of dislocation morphology during the incubation period.

It has been found out that during the incubation period and also the early stage of

creep, dislocations prefer to glide in horizontal channels, which are perpendicular to the

loading axis [8]. It is due to the fact that resolved shear stress in horizontal channels

are much higher than the stress in vertical channels [8].

Overall, under the condition of intermediate temperatures and stresses, the deforma-

tion mechanism could be much more complex compared to high temperature or low

temperature creep.

14


Low temperature and high stress regime

At low temperature (when the temperature is lower than 0.6 of the melting tempera-

ture) and high stress regime, the deformation mechanism is significantly different com-

pared to high temperature and low stress regime. Low temperature regime normally

undergoes a considerable amount of primary creep strain, and no significant rafting

has been observed. It has been widely accepted that the dominative operating slip

systems at low temperature and high stress is {111}〈112〉 at primary creep for Ni-base

single crystal superalloys, e.g. [47–53]. According to Kear and Leverant [38, 47, 48],

there are three possible γ′ cutting mechanisms involving low energy stacking faults, as

shown in Figure 2.8. The Burger’s vectors are given following Thompson’s notation,

and dislocations involving superlattice extrinsic stacking faults (SESF) are differenti-

ated from dislocations involving superlattice intrinsic stacking faults (SISF) by putting

an over-bar. It can be seen that cutting of the γ′ particles can involve a net vector

of a〈112〉 and generates both SISF and SESF, as shown in Figure 2.8(a), or it can be

associated with a net vector of a〈110〉, as displayed in Figures 2.8(b) and (c). Com-

bined with a detailed TEM analysis, Kear and Leverant proposed a type of a〈112〉cutting, as can be seen in Figure 2.9. In fact, they are the first ones who exclusively

proposed a cutting model and proved with detailed TEM analyses. In Figure 2.9(a),

there are two groups of dislocations and stacking faults, marked as I and II under a

g-condition of (200). The schematic drawing for the cutting mechanism description is

shown in Figure 2.9(b), corresponding to group I dislocations and stacking faults. It

is similar to a〈112〉 cutting, as displayed in Figure 2.8(a). According to the analysis in

[47], dislocation 1 has a Burger’s vector of 1/3[112] and dislocation 2 has a Burger’s

vector of 1/6[112]. Dislocation 3 has a Burger’s vector of 1/6[112] and dislocation 4 has

a Burger’s vector of 1/3[112]. Written in Thompson’s notation, the cutting mechanism

can be summarized in the following two Equations 2.5 and 2.6:

3αB −→ 2αB + SISF + αB (2.5)

3αB −→ 2αB + SESF + αB (2.6)

The partial dislocations 3αB arrive at the γ/γ′ interface and dissociate into 2αB along

with the generation of a SISF and one αB left at the interface, as indicated in Equation

2.5. A second set of 3αB will arrive at the interface for further deformation to occur.

In the similar sense, 3αB will dissociate into 2αB and leave one αB at the interface,

with the generation of a SESF. It is then not possible to avoid the generation of

15


Figure 2.8: Three possible cutting mechanisms into the γ′ particles. (a) a〈112〉 cutting,with generation of SISF and SESF. (b) a〈110〉 cutting with SISF. (c) a〈110〉 cuttingwith SESF [47].

Figure 2.9: Detailed analysis of γ′ cutting mechanism. (a) A TEM image indicatingstacking fault cutting mechanism. (b) Proposed model corresponding to the TEMimage [47].

16


high energy anti-phase boundary between the two 1/6[112] dislocations. It has been

estimated that the APB energy in Ni3Al can be as high as 144±20 mJ/m2 and 102±11

mJ/m2 for {111} and {100} planes, respectively, while for a SISF the energy is as

low as 12 mJ/m2 [54]. However, due to the multi-element environment of Ni-base

single crystal superalloy, it is plausible that during the deformation process, there is

diffusion of certain element to planar defects and changes the stacking fault energy

correspondingly [50]. Viswanathan et al. [55] tried out high resolution EDX mapping

to detect elemental segregation around planar defects. They found out that more Co

and Cr segregate to the fault compared to the elements Ni and Al. It is still not

clear what kind of element and how element partitioning influence planar fault energy.

More work is required to figure out whether there are more heavy elements partitioned

to planar defects and the corresponding consequences for the change of planar fault

energy.

Apart from the activation of {111}〈112〉 slip systems, for low temperature and high

stress regime, lattice rotation has also been observed and this leads to changes of

the Schmidt factor. Lattice rotation phenomenon has been studied and confirmed by

several researchers [37, 38, 56]. Kear et al. [37, 38, 56] have measured lattice rotation

and compared the results with the creep behavior. It is concluded that crystal lattice

tends to rotate towards to [112], where the Schmidt factor is highest. Lattice rotation

can further convince activation of {111}〈112〉 slip system, since in single crystals lattice

rotates towards slip direction [37, 38, 56]. However, there are also researchers who

found out that the lattice rotation is not necessary for strain accumulation [49]. In this

case, there is sufficient source of 〈110〉 type of dislocations for the generation of 〈112〉dislocations, but it is not enough to prevent the cutting of 〈112〉 type.

Anisotropy at low temperature and high stress regime for Ni-base single crystal superal-

loy has been quite significant. In fact, it has been more pronounced at low temperature

than at high temperature. Sass et al.[57] compared anisotropic creep properties of a

second generation CMSX-4 superalloy containing 3% Re. They found out that at a

lower temperature, even a small misorientation from [001] and [011] significantly affects

the primary creep behavior. While at a higher temperature as in 1253 K, the degree of

anisotropy is not so pronounced. The reason for different anisotropy behavior at dif-

ferent temperatures is due to the operating mechanisms changing from heterogeneous

{111}〈112〉 slip to a more homogeneous {111}〈110〉 slip. Meanwhile, with a slight de-

viation from [001] orientation, it is possible to change from a single slip orientation to a

duplex-slip orientation [57]. For a single slip orientation, creep life is much shorter than

in a duplex-slip orientation due to a lack of work hardening. Knowles et al. [52, 58]

concluded that the low temperature anisotropy is closely related to the shear stress

17


activating {111}〈112〉 slip systems. By slightly changing the orientation, the Schmidt

factor changes dramatically and correspondingly changes the shear stress.

2.4 Miniature tensile creep testing

Miniature tensile creep tests have been conducted to investigate creep properties of Ni-

base single crystal superalloys. Compared to standard-sized creep specimens, miniature

creep specimens have two advantages. First, with miniature specimens it is easier to ori-

ent the specimen precisely. As it is clear that single crystal superalloys show anisotropic

properties, more precise orientations yield more reproducible creep responses. Secondly,

more creep specimens can be obtained from the same amount of oriented superalloy

plates.

Regarding the accuracy of creep tests with miniature specimens, from the research work

of Malzer [59], who compares the creep behavior of miniature specimen and standard

creep specimen (Figure 3 in [59]), it can be seen that the creep curves from miniature

specimens only deviates slightly from a standard size specimen starting from a strain of

0.2% on. Meanwhile, even the decrease of creep rate can be more clearly observed from

the miniature specimen. All the creep tests of the present work have been conducted

using miniature specimens. It should also be noticed that polycrystalline materials are

less suitable for miniature creep specimen testing since the grain sizes can be of the

order of the diameter of the miniature creep specimen, which can lead to considerable

scatter when comparing different specimens [60].

In the present work, back scattered Laue method is used for a precise orientation of

miniature creep specimens. The selected orientation is fixed by a three-axis goniometer.

The goniometer is also attached to an electro discharge machining (EDM) for miniature

specimen cutting. More details about miniature specimens can be found in chapter

Materials and Experiment of the present work.

18


2.5 Transmission electron microscopy of defects in

Ni-base single crystal superalloys

To better understand and interpret creep properties and mechanisms of Ni-base sin-

gle crystal superalloys, transmission electron microscopy has been employed for mi-

crostructure investigations. When the specimen is thin enough, electrons can transmit

the specimen and reach a screen where an image is formed. The wave-particle duality

properties allow to investigate phases and defects in the material from the aspect of

wave function by TEM. The TEM image is a result of the interaction of the electron

beam with the microstructural elements in the thin foil. For example, if foil regions are

oriented such that they can produce Bragg diffraction, then the beam loses intensity

and this region appears dark on the screen (diffraction contrast). However, crystalline

regions can also produce contrast because the atoms and electrons of the solid interact

with the electron beam and affect the wave function [61–63]. Before this is further

discussed, it is important to take a look at the crystal defects which can be present in

the crystalline planes of a Ni-base superalloy, especially the defects in the ordered γ′

phase and the corresponding contrast mechanism introduced by defects in TEM.

Line defects

Dislocations are one of the most common crystal defects which are characterized by a

Burger’s vector b and a line direction u. The “finish start/ right hand (FS/RH) rule”

has been employed to determine the direction of the Burger’s vector and of the sense

of the dislocation line. The direction of the Burger’s vector is determined from the

finish to start (FS) point of the Burger’s circuit. The positive line sense of a Burger’s

vector is associated with a clockwise circuit using the right hand rule [64–66]. From the

relationship of Burger’s vector direction and dislocation line direction, two simple types

of dislocations can be classified, i.e., edge and screw dislocations. If the dislocation

line is perpendicular to the Burger’s vector, this type of dislocation is called an edge

dislocation [64–66]. Edge dislocations are associated with an extra half plane, and they

can only slip in specific glide planes. However, edge dislocations can also climb when the

temperature is high and diffusion is fast. When the dislocation line direction is parallel

to the Burger’s vector, this is a screw dislocation. Screw dislocations are not confined

to one slip plane, instead, they can cross slip to another slip plane, which contains

the Burger’s vector [64–66]. For Ni-base single crystal superalloys, dislocations have

19


been commonly observed in the γ phase and at the γ/γ′ interfaces. The dislocations

have been mainly a/2〈110〉 type, as for FCC structures. Under certain deformation

conditions, dislocations can also be observed cutting into γ′ particles. Pairwise cutting

of the γ′ phase is a well-known process [37–41]. At low temperatures cutting process

produce varies planar faults which are limited by dislocation ribbons. There are also

mixed dislocations. For example, when a a/2〈110〉 type of dislocation enters a γ channel

in a {111} glide plane, a leading screw segment deposits 60◦ dislocation segments close

to the γ/γ′ interface. 60◦ dislocations have 2/3 edge and 1/3 screw character.

Planar defects

Planar defects play an important role in Ni-base single crystal superalloys, especially in

the ordered γ′ phase. In the present work, planar faults in the γ′ particles are focused.

The crystallographic projection of a (111) plane is used to indicate the ordered structure

of the γ′ phase, as shown in Figure 2.10 (adapted and modified from [3]). Figure 2.10

represents a 〈111〉 projection of three layers of atomic planes of the L12 lattice. The

empty and full circles represent Ni and Al atoms in the upper layer. Empty and full

squares represent Ni and Al atoms in the middle layer. And the bottom layers consist

of empty (Ni) and full (Al-atoms) triangles. Figure 2.10 shows three 〈110〉 and 〈112〉directions on the (111) plane.

Anti-phase boundary (APB)

An anti-phase boundary is a defect in an ordered alloy and is generated due to the

disturbance of the ordered structure. In Ni-base single crystal superalloys, an APB

can be created by pair-wise cutting of dislocations into the γ′ phase. As can be seen in

Figure 2.11, if the top layer (the circles) is shifted by a/2[101], an anti-phase boundary

is formed, as indicated in the dashed rectangular area, because of the formation of

forbidden bonds (like Al-Al or Ni-Ni bonds). This corresponds to the formation of a

planar defect which is referred to as anti-phase boundary and costs energy. It should

be noticed that the example illustrated here is the formation of an APB in the {111}plane of a L12 lattice. An APB can also be formed in {001} planes and the APB energy

in {111} and {001} planes are not the same.

20


Figure 2.10: Illustration of {111} projection of L12 structure, Al atoms are in grayand Ni atoms are in white. Circles represent atoms at the top layer, while rectanglesand triangles represent middle and bottom layers respectively. Three 〈110〉 and 〈112〉directions are indicated, adapted and modified from [3].

21


Figure 2.11: Illustration of an APB generation due to the top layer shear of vectorbAPB=a/2[101], two dashed rectangles indicates the forbidden bond of Al-Al, adaptedfrom [3].

22


Figure 2.12: Illustration of a SISF generation due to top layer shear of vectorbSISF=a/3[211], the top layer sits directly on top of the bottom layer [3]. The cir-cles have the same meaning as in Fig 2.10.

Superlattice stacking fault (SSF)

Superlattice stacking faults (SSF) are planar defects in the ordered γ′ phase. They

correspond to the case when the normal stacking sequence is changed. According to

the change, i.e., whether there is a new inserted layer or a missing layer, the type

of superlattice stacking faults can be classified as superlattice extrinsic and intrinsic

stacking faults (SESF and SISF) [62–66]. Superlattice stacking faults can be generated

by a/3〈112〉 shear vector. Figure 2.12 shows one example of SISF generation by a shear

vector of a/3[211]. In Figure 2.12, the top layer is sheared by a vector of a/3[211], the

direction is indicated by the arrow. The result of the shearing is that the top layer

atoms sit directly on top of the bottom layer, which has a similar effect as a layer

missing. With this kind of shearing a superlattice intrinsic stacking fault is formed.

23


Figure 2.13: Illustration of a SESF generation due to top layer shear of vectorbSESF=a/3 [211]. A new top layer has generated. The symbols have the same meaningas in Fig 2.10.

In the same manner, shearing of a/3〈112〉 can also generate superlattice extrinsic stack-

ing faults. It can be better shown when the projected plane is (111), as indicated in

Figure 2.13. In this case, the top layer is sheared by a/3[211] and a new top layer

formed on the middle layer and generates a SESF.

If the shearing vector is a/6〈112〉, not only the stacking sequence is disturbed, but also

the environment of neighboring atoms. As can be seen in Figure 2.14, the top layer is

sheared by a dislocation with a Burger’s vector of a/6[112]. The corresponding result is

that the top layer atoms sit directly on top of the bottom layer. In addition, forbidden

bonds form, as highlighted by dashed rectangles. The combination of a SISF and an

APB is called a complex stacking fault (CSF). It is not difficult to understand that a

CSF has a higher energy as compared to a single SISF or an APB.

24


Figure 2.14: Illustration of a CSF generation due to top layer shear of vectorbCSF=a/6[112], the top layer sits directly on top of the bottom layer and forbiddenbonds form. The symbols have the same meaning as in Fig 2.10, adapted from [3].

25


Figure 2.15: Illustration of stacking sequence of intrinsic and extrinsic stacking faultswith regard to dislocations [66]. (a) S-fault. (b) D-fault.

Intrinsic and extrinsic stacking faults have also been regarded as single stacking faults

and double stacking faults, as can be seen in Figure 2.15 [66]. These two situations were

firstly described by Weertman in the case of Frank sessile dislocations. By removal of

one layer of atoms, an intrinsic stacking fault is generated since the stacking sequence

has changed from normal FCC stacking sequence ABCABC to ABC|BC (| indicates the

missing layer), as shown in Figure 2.15(a), along with two bonding edge-dislocations

of opposite signs.

On the other hand, inserting a layer of atoms can also generate an extrinsic stacking

fault with two edge dislocations of opposite signs and stacking faults in between. At-

tention should be paid that in this case, there are two stacking faults generated, since

the stacking sequence is ABCBABC. To differentiate dislocations attached to these

two types of stacking faults, single stacking fault dislocations are called S-dislocations

and double stacking faults dislocations are called D-dislocations [66]. In this respect,

it is not difficult to imagine that the energy for a SESF should be slightly higher than

a SISF.

Contrast mechanism of defects

Since TEM has been widely employed for investigation and analysis of defects, it is

important to understand the contrast mechanism introduced by defects in TEM. The

principle contrast mechanism in TEM is diffraction contrast, where an objective aper-

ture is used to select either the transmitted or the diffracted beam [61], as shown in

Figure 2.16. Figure 2.16 shows a TEM bright field (BF) mode, where the transmitted

beam passes through the objective aperture. According to the selection of the beam, in

conventional TEM mode (when the beam is parallel), there are bright field mode, dark

26


field (DF) mode, centered dark field (CDF) mode and weak beam dark field (WBDF)

mode. These four modes can be better explained and differentiated with the intro-

duction of a two-beam condition, as can be seen in Figure 2.17 [61–63]. A two-beam

condition is the situation when TEM specimen is tilted in such a way that there are

only two beams: one transmitted beam and one diffracted beam.

An exact two-beam condition is shown in Figure 2.17(a). On the left part of Figure

2.17(a), both transmitted and diffracted beam are exactly on the Ewald sphere. The

corresponding g-vector is pointing from the transmitted to the diffracted beam. On

the right side of Figure 2.17(a), this two-beam condition is illustrated together with

a pair of corresponding Kikuchi lines. T and D represent spots which correspond

to the transmitted and diffracted beams, respectively. An exact two-beam condition

represents a case where the Kikuchi lines pass through the center of the spots associated

with the transmitted and the diffracted beams. However, in practice, the exact two-

beam condition is not established. Instead, one establishes a certain deviation from the

exact two-beam condition. To quantify this deviation from exact two-beam condition, a

deviation parameter s is used. Negative and positive s have been illustrated in Figures

2.17(b) and (c) respectively. A negative s indicates that the diffracted beam is outside

of Ewald sphere or the diffraction patterns are on the right side of the corresponding

Kikuchi lines. On the contrary, a positive s means the diffracted beam is inside of Ewald

sphere or the diffraction patterns are on the left side of the corresponding Kikuchi lines.

An exact two-beam condition is not ideal to image dislocations. Experimentally, pos-

itive deviation vector s is usually used during investigation due to a better contrast

[61–63]. This can be explained by the intensity distribution with different s values in

Figure 2.18 [62]. It can be clearly seen that with an increase of s value, the diffracted

beam intensity decreases and a better contrast can be obtained.

A schematic drawing is presented in Figure 2.19 for demonstration of different modes

in TEM under two-beam conditions. A white circle indicates the transmitted beam,

marked as “0”, and the gray circles indicate diffracted beams, marked as “g”, “2g”

etc., as first and second diffracted beams. The dashed circle indicates the position of

the objective aperture for the selection of a beam. As described previously, a two-

beam condition implies the situation where only the transmitted beam “0” and the

first diffracted beam “g” are used for diffraction contrast. A BF mode is obtained

when the transmitted beam is selected, as shown in Figure 2.19(a). If the objective

aperture is moved to select the first diffracted beam g, a DF mode is obtained. The

direction of the operating g-vector remains the same for both BF and DF modes, i.e.,

pointing from transmitted beam to diffracted beam. If the objective aperture is kept

27


Figure 2.16: Schematic drawing showing the generation of diffraction contrast [61].

28


Figure 2.17: Schematic drawing showing two-beam conditions with different s value.(a) Exact two-beam condition, s =0. (b) Positive s. (c) Negative s [61, 62].

29


Figure 2.18: Illustration of s value and intensity distribution with s value [62].

at the transmitted beam position as in the BF mode in Figure 2.19(a), however, -g

beam is tilted away to the transmitted beam position while the transmitted beam has

been tilted to the original g beam position. As a result, a centered dark field mode is

obtained. Compared to the normal dark field image, when the objective aperture is

moved, the g-vector direction is opposite to that in the bright field mode. In practice, a

CDF image can be obtained more efficiently since BF and CDF images can be switched

back and forth by simply pressing one button on the TEM console. Moreover, the

normal dark field (DF) image suffered from a slight loss of contrast compared with

CDF [62, 63].

Tilting g beam to the transmitted beam position, one can also establish weak beam

dark field mode. In this case, diffracted beam 3g is activated. WBDF has also been

called g-3g method. When the diffraction contrast is associated with 3g, we obtain a

weak beam dark filed image. By WBDF, crystal defects can be visible with a high res-

olution of diffraction contrast, since the defects contrast is only introduced by the core

of defects [62]. However, long exposure time is usually required. The WBDF technique

has been widely used for the investigation and analysis of dislocation reactions, partial

dislocations and planar defects. Stacking fault energies can be calculated using WBDF

images which allow to assess the distance of two partial dislocations which limit the

SFs [67].

These four modes have been widely used in conventional transmission electron mi-

croscopy (CTEM). A better contrast of microstructure can be obtained in STEM mode

when the specimen is not thin enough for CTEM investigation or TEM thin foil is bent,

which is very often the case in practice.

30


Figure 2.19: Illustration of different modes in conventional TEM. (a) BF. (b) DF. (c)CDF. (d) WBDF.

31


Figure 2.20: Comparison between CTEM and STEM modes [68].

STEM outperforms CTEM in certain aspects due to the convergent beam condition,

as can be seen in Figure 2.20 [68]. Figure 2.20(a) illustrates the normal CTEM mode.

K0 represents the incident beam and the dashed line represents the Ewald sphere. The

full black circles are interactions between incident beam and lattice planes which are

in Bragg condition. When the TEM foil is slightly bent, the full gray diffraction spot

in Figure 2.20(a) will not be in Bragg condition, and the contrast cannot be properly

displayed. On the contrary, in STEM mode, the incident beam is convergent and

can be considered as a cone area defined by an angle 2α and limited by two incident

beams K01 and K02 as shown in Figure 2.20(b). In this case, many Ewald spheres

are associated with the range limited by ES1STEM and ES2STEM . The advantage of

convergent beam is that, in this case, the full gray circle which is not in Bragg condition

in CTEM mode is now in contrast in STEM mode. In other words, better contrast and

more information can be obtained in STEM mode, even when the TEM foil is slightly

bent.

However, STEM mode also has certain disadvantages, especially when it comes to a

large tilt angle, since it will be difficult to get one appropriate focus value for the whole

tilted scanning area. As suggested by Agudo [68], dynamic focus must be applied to

improve the image quality in STEM mode.

Figure 2.21 illustrates the configuration of the STEM mode [69]. The convergence

angle is θC . The distance between the sample and the detector is called camera length,

which is an important parameter for the image contrast.

As can be seen in Figure 2.21, with the change of camera length L, the divergent angle

is also affected. When L is too small, there will be contributions of the diffracted

beam to BF signal [69]. On the other hand, if L is too large, the transmitted signal

will contribute to the ADF image. An adequate choice of camera length is required to

32


Figure 2.21: Illustration of STEM mode configuration [69].

obtain optimum contrast.

Apart from a two-beam condition, in STEM mode, a multi-beam condition is also

applicable by orienting the specimen to a specific zone axis. This kind of contrast

arises by averaging BF and ADF imaging intensities [69]. In principle, all the defects

should exhibit contrast except for those with displacement vectors parallel to the zone

axis.

Stereo TEM

Stereo TEM can be applied in both CTEM and STEM modes [68–70]. For Ni-base

single crystal superalloys, stereo TEM has been widely used for determination of the

position and distribution of dislocations and planar defects and also to obtain a spatial

impression of the cuboidal shape of γ′ phase. The basic principle for the stereo tech-

nique is to take two individual images under the same operating g-conditions [68, 70]

within a certain angular distance. A typical angle of 10 to 15◦ is used for adjustment of

the two g-conditions, as it is the suitable angle range for human eyes to get the stereo

impression. Normally these two conducting g-vectors are located on both sides of a

33


Figure 2.22: Two g-conditions for stereo images. (a) Before rotation. (b) After rota-tion.

zone axis, as can be seen in Figure 2.22(a). The two two-beam conditions g1 and g2 are

located at both sides of the [112] pole. For stereo effect observation, the corresponding

g-vectors should be rotated in a way such that they are parallel to the observer, as can

be seen in Figure 2.22(b). The image which rotated clock-wise from the zone is viewed

by the left eye (image taken under g2), while the one rotated anti-clockwise is viewed

by the right eye (image taken under g1) [68, 70]. An anaglyph can then be obtained

from these two images. Each gray scale image is subdivided into its underlying red

and cyan colored image. Then one red image for one gray scale stereo micrograph is

viewed together with the one cyan image for the other gray scale stereo micrograph

using colored glasses. Stereo impression can be obtained when the anaglyph is viewed

with colored glasses. It has been found out that the STEM mode gives a better stereo

impression than the CTEM mode due to the fact that STEM mode is not so sensitive

to the very strong contrast associated with two-beam conditions [68]. More detailed

information can be found in [68, 70].

Electron microscopy uses wave functions to describe diffraction contrast associated

with the presence of defects in crystals. Although there are kinematical and dynamical

theories for contrast mechanisms, the additional phase factor introduced by defects is

α, as shown in the following Equation 2.7 [61–63]:

α = 2π · g ·R (2.7)

In Equation 2.7, g is the two-beam diffraction condition and R is displacement vector.

The phase factor is used for the explanation of defect contrasts.

34


Figure 2.23: STEM images showing dislocations in Ni-base single crystal superalloyCMSX-4 type. (a) BF image. (b) HAADF image.

Contrast of dislocations

In the bright field mode of a TEM, dislocations normally appear as dark lines. An

example is shown in Figure 2.23(a), where dislocations in Ni-base single crystal su-

peralloys have been observed at the interface. One can also observe different types of

contrasts, i.e., dislocations appear as white lines in HAADF images, as shown in Figure

2.23(b).

The contrast of dislocations can be understood as follows:

(1) When the Burger’s vector of a dislocation is parallel to the reflecting planes, the

location of the atoms in the reflecting lattice planes are only slightly disturbed by

dislocations. The reflecting angle between incident beam and reflecting planes is the

same as the angle between incident beam and the Burger’s vector of dislocations.

There is no contrast difference between regions with and without dislocations. This

corresponds to a situation where dislocations are effectively invisible. However, when

the Burger’s vector of a dislocation is not parallel to the reflecting planes, the reflecting

planes have a positive deviation vector and thus the diffracted intensity decreases and

the image in BF mode, where no dislocation is contained, appear bright.

(2) When the electron beam approaches the dislocation, the deviation vector s is closer

to zero, and the diffracted beam intensity reaches a maximum value. In this case,

35


Figure 2.24: Illustration of dislocation contrast. (a) When dislocation is parallel toreflecting planes. (b) When dislocation is not parallel to reflecting planes [62].

dislocations appear as dark lines in BF images.

The two types of contrasts discussed in this section can be seen in Figure 2.24. Figure

2.24(a) represents a case where the Burger’s vector is parallel to the reflecting planes

and there is no change of reflecting angles for dislocations and reflecting planes. Figure

2.24(b), on the other hand, shows a situation where the Burger’s vector of a dislocation

and reflecting planes are not parallel [62]. The contrast differences result from the

change of reflecting angle and the corresponding change of the deviation vector s.

Contrast of stacking faults

From the wave function of stacking faults, the phase factor introduced by stacking

faults is 2π, and therefore, stacking faults have been referred to as 2π defects [61–63].

Using the dynamic theory, Hashimoto et al. [61, 71] have calculated the intensity

profile for stacking faults for the condition where the phase angle is 2/3π and a foil

thickness is 7.25ξg ( ξg: the extinction distance), as can be seen in Figure 2.25. The

solid line represents the intensity profile in a bright field image while the dashed line

represents the dark field case. It can be concluded that the contrast at the top and

the bottom side of the stacking fault in BF is the same, i.e., are symmetric. In DF,

the contrasts of the two outermost fringes of stacking faults are opposite to each other,

which referred to as asymmetric [61–63]. Combined with g-vectors obtained from BF

and DF images, the way in which stacking faults are inclined can be obtained, i.e., one

can determine the top and the bottom side of stacking faults. The contrast peaks also

explain why stacking faults have black and bright fringe contrasts. This 2π feature of

stacking faults provide the basis for further detailed analysis.

36


Figure 2.25: Computed stacking fault intensity image profile for α =+2π/3 withanomalous absorption [61, 71].

Contrast of APB

In the case of an APB, the phase factor is π rather than 2π, which makes an APB

a special type of planar defect. Since APBs are only observed in ordered phases, the

contrast of an APB can only be clearly distinguished when using superlattice diffraction

induced from ordered phase. Due to the high energy of an APB, the width of an

APB tends to be relatively small. To make sure the defect is APB, both matrix and

superlattice diffraction conditions have to be employed and compared. An example is

shown in the section Analysis of APB.

Analysis of defects

Analysis of perfect dislocations

For determination of Burger’s vector of perfect dislocations, two effective invisibility

conditions are needed. In other words, there should be two different two-beam con-

ditions (two different g-vectors) where dislocations are out of contrast. Applying the

effective invisibility criterion g ·b = 0, Burger’s vector b can be calculated. To be fully

correct, the line direction of a dislocation u has to be taken into consideration, because

the full invisibility condition is g · b × u = 0 and not single g · b = 0. However, it is

37


not always possible to account for u in practice. Nevertheless, it has been often shown

that effective invisibility conditions can be used to obtain Burger’s vectors of perfect

dislocations. More detailed examples will be shown in the result section (see section

5.4).

Analysis of partial dislocations

In the case of partial dislocations, the invisibility conditions are modified. The in-

visibility condition g · b = 0 is still applicable. However, there are other conditions

which yield invisibilities. For example, g · b = ±1/3 has also been reported as an

effective invisibility condition for partial dislocations [61, 72]. Moreover, according to

the value of w, (a parameter combining extinction distance and deviation vector from

exact two-beam condition: w = ξg · s), g ·b = −2/3 can yield the vanish of dislocation

contrast when w has a larger value than 1 [61, 72]. Kear and Oblak [47] have extended

the invisibility criterion to g · b = +4/3, which will yield the same contrast result as

g · b = −2/3. More attention must therefore be paid for the analysis of the contrast

of partial dislocations.

High resolution TEM has been a common technique for the analyses of dislocations

as well, when dislocations are oriented edge-on. Back to the definition of dislocations

using Burger’s circuit, it is possible to set up a Burger’s circuit around the dislocation

core and simply derive the Burger’s vector from a Burger’s circuit in the high resolution

image. A state-of-art way for analysis of high resolution image is to use geometrical

phase analysis (GPA) which is a plug-in in Gatan software and is based on geometric

phase algorithms. However, the HRTEM technique requires very thin foils (e.g., 50

nm) while for the anaglyph of collective dislocations it is necessary to have thick foils

which contain sufficient dislocations (e.g., thicker than 150 nm).

Analysis of stacking faults

For the analysis of stacking faults, both bright field and dark field images are needed

in order to confirm their nature. By comparing BF and DF images, three questions

can be addressed:

(1) What is the nature of the stacking fault: intrinsic or extrinsic?

38


Figure 2.26: TEM images showing contrast of stacking fault. (a) BF image. (b) CDFimage.

(2) Where is the top of the stacking fault intersecting the TEM foil?

(3) What is the sign of the displacement vector of the stacking fault: positive or

negative?

The analysis of stacking faults is closely related to the type of g-vector used for the

image. To better illustrate the analysis procedure, an example is given in Figure 2.26.

Figure 2.26(a) is a BF image and Figure 2.26(b) is a CDF image under g-vector of

〈111〉 type. It is noteworthy that the directions of the g-vector in BF and CDF images

are opposite. The contrast of the stacking fault F1 is symmetric in BF while in CDF

it is asymmetric. This contrast difference confirms the nature of a stacking fault. The

outermost fringes for stacking fault F1 are both dark. This indicates that the scalar

product between g-vector used in BF and the fault vector R is negative. Comparing to

the CDF image in Figure 2.26(b), it can be seen that the outermost fringes are black

and bright. Since it is a CDF image, the direction of the operating g-vector is opposite

to the BF image. The fringe, where the contrast is different in BF and CDF image, is

the top of the stacking fault (as highlighted by the arrow pointing to the left in both

BF and CDF images). The top of the SF fringe is where the stacking faults interact

with the upper part of the TEM foil.

The question whether the stacking fault is intrinsic or extrinsic can be answered from

the CDF image. The basic procedure is to put the g-vector of CDF in the center

of the stacking fault, as indicated by the dashed arrow in the middle of the stacking

39


Figure 2.27: Systematic flow chart showing the criterion for SF nature determination[61–63].

fault, and determine whether the g-vector points away or towards the outermost bright

fringe of the stacking fault. Based on the different types of g-vectors used for DF (CDF)

images, the conclusion will be different. A summary of the determination of stacking

faults nature from g-vectors has been shown in Figure 2.27 [61–63]. In the example in

Figure 2.26, we can see that the g-vector used in CDF is (111). It points towards the

bright fringe of the stacking fault F1. Using the criterion from Figure 2.27, it can be

concluded that F1 is a superlattice extrinsic stacking fault.

Analysis of APB

As a specific kind of planar defects, the contrast of the APB can be verified by compar-

ison of images from the matrix diffraction and the superlattice diffraction. An example

can be seen in a single crystal cobalt-base superalloy crept at 900 ◦C [73, 74] in Figure

2.28. The APB displays full contrast under superlattice diffraction (100) while there is

40


Figure 2.28: TEM images showing the contrast of an APB. (a) The APB in contrastwith the superlattice diffraction (100). (b) The APB out of contrast with the matrixdiffraction (200) [73, 74].

only residual contrast under diffraction (200). This kind of contrast comparison reveals

the nature of an APB, which is different from other kinds of planar defects. A more

detailed analysis about the displacement vector involves a tilt series in combination

with the consideration of matrix and superlattice diffractions.

Fault vector determination

Similar to dislocation analysis, fault vectors can be determined by conducting a series of

tilting experiments and calculated from corresponding invisibility conditions. However,

as the phase factor for stacking fault is 2π, stacking faults can be invisible not only

when g ·R = 0, but also when g ·R equals to an integer [61–63, 67, 75]. The invisibility

criterion for stacking faults makes the fault vectors determination more difficult than

for dislocations. The planes of the stacking faults can be determined when the stacking

faults are oriented edge-on. It should also be noticed that stacking faults are closely

related with the partial dislocations that generate the stacking faults. Especially when

it comes to cutting mechanism into the γ′ phase, the interactions between dislocations

and stacking faults must be considered. The detailed analysis is presented in the result

section 5.4.

41

3. Scientific Objectives

The scientific objective of the present work is to contribute to a better understanding

of the elementary deformation processes which govern low temperature and high stress

creep (temperature: 750 ◦C, stress: 800 MPa) of the Ni-base single crystal superalloy

ERBO/1C. The present work represents the first investigation of this kind at the Chair

for Materials Science and Engineering of the Ruhr Universitat Bochum. Previous

work focused on the high temperature (above 1000 ◦C) and low stress (below 200 MPa)

regime. Different deformation mechanisms govern creep at different temperature and

stress regimes.

A peculiar type of creep behavior at 750 ◦C and 800 MPa has been observed during

[001] tensile loading for ERBO/1C. This kind of behavior has been observed before

and never been explained. The peculiar creep behavior has been referred to as double

minimum creep, where two creep rate minima were recorded: a first local minimum

(after 30 minutes, 0.1% strain) and a second global minimum (after 260 hours, 5%

strain). The main focus of the present work is to understand and explain the reasons

for these two creep minima.

The present work provides new insights into the elementary deformation mechanisms of

creep of Ni-base single crystal superalloys for the low temperature regime, because all

creep specimens are crystallographically precisely oriented and the influence of crystal-

lographic deviations from targeted growth directions has been excluded, an uncertainty

which has affected most of the previous work in this area. A series of interrupted ten-

sile creep tests was conducted to further confirm double minimum creep behavior and

investigate this creep phenomenon in detail.

Diffraction contrast TEM is used to study the microstructural evolution during double

minimum creep. Due to microstructural scatter, both large and small scale investi-

gation (montage investigation and single defect analysis) are employed for a better

43

CHAPTER 3. SCIENTIFIC OBJECTIVES

interpretation of the creep response to achieve a better understanding of deformation

mechanisms.

To describe microstructural evolution, defects (dislocations and planar defects) have

been determined both quantitatively and qualitatively. An effort was also made in the

present work to describe the distributions of microstructural parameters like γ′ particle

edge lengths and γ channel widths. Close attention was paid to small deviations from

the regularity of the arrangement of cuboidal γ′-particles in the γ/γ′-microstructure.

Regarding the importance of TEM techniques used in the present work, there is a need

to explain the procedures and to document the experimental steps in sufficient detail.

The goal of the present work is to use TEM investigations to explain double mini-

mum creep. Microstructural reasons have been identified in the present work, which

rationalize this peculiar creep behavior.

44

4. Materials and Experiments

4.1 Alloy and heat treatment

In the present work, a CMSX-4 type of superalloy referred to as ERBO/1 from the joint

research center SFB/ Transregio 103 is used for investigation [76]. The master alloy was

provided by Cannon Muskegon. It was cast into single crystal plates following a specific

heat treatment procedure. A typical cast plate used in the present work is shown in

Figure 4.1(a) with a special color coding indicating orientation distributions detected

by electron back scatter diffraction (EBSD). From the color coding, it is clear that

the majority of the plate is in [001] orientation, but there is also a small region which

deviates from [001]. A cut-up plan which documents the location of creep specimens

is shown in Figure 4.1(b). Knowing the position of specimens in the plate, their creep

responses can be better interpreted in terms of differences in orientation. For the

current work, all creep specimens and the associated thin foils for TEM investigation

stem from part C, where the material is precisely 〈001〉-oriented.

The nominal composition of ERBO/1 is shown in Table 4.1. It can be seen that the

investigated material contains about 3% Re. It is a second generation Ni-base single

crystal superalloy. The addition of Re improves the creep properties of a Ni-base single

crystal superalloy since Re is a strong solid solution strengthener at high temperatures,

due to the fact that it has a large atom radius [3, 77] and a very low diffusion coefficient

[78, 79]. Elements like Cr, Co, Mo, and W have been used for γ phase strengthening,

and elements like Al, Ta and Ti promote the formation of the γ′ phase. On one hand,

the addition of refractory elements has greatly improved the creep properties of Ni-

base single crystal superalloys. However, it increases the possibility of the formation

of topologically closed packed (TCP) phases, which are thought of as decreasing creep

strength of SX superalloys due to the depletion of matrix strengthening elements and

the fact that they can act as crack nucleation cites [80, 81].

45

CHAPTER 4. MATERIALS AND EXPERIMENTS

A schematic chart for multi-step heat treatment of a Ni-base single crystal superalloy is

shown in Figure 4.2. A multi-step heat treatment has to be applied because the melt-

ing temperature of the interdendritic region is lower than the dissolution temperature

of the coarse γ′ phase, which needs to be dissolved [14]. To avoid incipient melting,

the starting temperature of heat treatment is set to be T1, which is slightly below

the melting temperature of the interdendritic regions in the starting material. During

a hold time at T1, interdiffusion occurs between dendritic and interdendritic regions.

Consequently, the melting temperature of interdendritic regions increases and the tem-

perature for the next-step heat treatment can be increased. When this procedure is

repeated a number of times, the melting temperature of interdendritic regions is even-

tually high enough, i.e., higher than the dissolution temperature of the γ′ phase. After

the coarse γ′ phase is dissolved, a precipitation heat treatment at lower temperature

leads to the formation of the derived fine γ/γ′ microstructure.

Although it is time-consuming, applying multi-step heat treatment is important to

homogenize the material. After full homogenization, the precipitation heat treatment

at T5 leads to the formation of the γ/γ′ microstructure. For the material investigated

in the present work, two specific heat treatments have been conducted: solution heat

treatment and precipitation heat treatment, as illustrated in Figure 4.3 and Figure 4.4.

Solution heat treatment has been designed for a more homogeneous microstructure

and a more uniform distribution of elements [82, 83]. As we know today, the following

precipitation heat treatment is designed for the evolution of cuboidal γ′ particles and

the formation of the γ/γ′ two-phase microstructure [82, 83], which will yield good creep

and fatigue properties.

Figure 4.1: (a) ERBO plate. (b) Cut-up plan.

46


The material investigated in the present work is referred to as ERBO/1C. Part of the

SX plate were precisely oriented and then miniature tensile creep specimens were cut

out using spark erosion. A real-time Laue camera of type MWL 120 from Multiwire

Laboratories is used for orientation. To obtain a specific orientation, a three-axis

goniometer is employed, which also fits into a electro discharge machine. More detailed

information about the orientation method and sample cutting parameters can be found

in [14, 18, 84]. The schematic drawing in Figure 4.5(a) shows the geometry of a

miniature specimen with a gauge length of 9 mm and a cross section of 2×3 mm2.

Figure 4.5(b) [85, 86] shows a miniature creep specimen in the load line, at the end of

an interrupted creep test after the furnace has been removed.

Figure 4.2: Schematic drawing showing multi-step heat treatment [14].

47


Figure 4.3: Flow chart showing solution heat treatment process.

Figure 4.4: Flow chart showing precipitation heat treatment process.

Figure 4.5: (a) Size and geometry for the miniature creep specimen. (b) Miniaturespecimen in furnace for high temperature creep [85, 86].

Table 4.1: Chemical composition of ERBO/1C in wt.%.

element Co Ta W Cr Al Re Ti Mo Hf Ni

wt.% 9.3 6.9 6.3 6.2 5.8 2.9 1.0 0.6 0.1 Bal.

48


4.2 Interrupted miniature creep tests at low tem-

perature and high stress

A series of interrupted tensile creep experiments have been conducted at a low tem-

perature (750 ◦C) and a high stress (800 MPa) for a [001] orientation. A standard

constant-load creep machine from Denison Mayers has been used to conduct miniature

creep testing. The creep machine is equipped with a vertically movable three-zone

furnace. Three control thermocouples are used to measure the temperature of three

heating zones and each heating zone is controlled by an Eurotherm controller. The

miniature creep specimens are placed in the temperature constant zone of the furnace.

For a precise temperature measurement, apart from three thermocouples at the fur-

nace, there are two measurement thermocouples fixed to the lower and upper ends

of the gauge lengths of miniature specimens. The creep temperature operated during

a creep tests at the gauge length of the specimen is 750 ◦C±1.5 ◦C. The miniature

specimens are mounted in special grips consisting of an oxide-dispersion-strengthened

(ODS) alloy PM 3030 from Plansee (Reutte, Austria) which are reinforced by ceramic

Al2O3 insets. Ceramic rods in tube extensometry and strain sensors positioned outside

the furnace are used for displacement measurement.

In the present work, the specimens were heated in 2 hours to the test temperature of

750 ◦C under a preload close to 20 MPa to keep the load line aligned. The specimens

were then loaded by balanced horizontal lever arms with load ratios of 1:15 to the

value corresponding to 800 MPa within a few seconds. In order to keep the level arm

in a horizontal position during the entire test, an electromechanical control system

has been used. The immediate elastic reaction of the specimen/grip assembly was not

considered as a creep strain. For a detailed investigation of double minimum creep

behavior, a series of interrupted creep tests was conducted after creep strain intervals

of 0.1, 0.2, 0.4, 1, 2, and 5% respectively.

4.3 Scanning electron microscopy

Scanning electron microscopy has been used to obtain overviews of the microstructure.

SEM investigations were performed using a Zeiss Leo Gemini 1530 VP. It is equipped

with a field emission gun and an in-lens detector. Secondary electron and back scattered

electron signals are used for imaging. Good image conditions were obtained using

49


secondary electrons at a voltage of 10 kV and a working distance of 10 mm.

For SEM investigations, samples were ground using emery paper and polished using

diamant suspension (particle size 6 µm to 1 µm) with ethanol. A final well-polished

surface can be obtained using oxide polishing suspension (OPS) with distilled water.

For the optimum image contrast, two etching methods can be used. To etch out the

γ′ phase, a solution which consists of 40 ml distilled H2O, 20 ml HCl (37%) and 10 ml

H2O2 (30%) was used and the sample was etched for about 3 seconds. To etch out the

γ channel phase, the sample is electrochemical polished using electrolyte A2, which

contains 700 ml of ethanol, 120 ml distilled water, 100 ml of diethylene glycol diethyl

ether and 78 ml of perchloric acid with a concentration of 70 to 72% at an applied

voltage of 5 V and a flow rate of 12 for about 3-5 seconds. The γ/γ′ microstructure

can then be observed using secondary electrons. The dendritic and interdendritic

microstructure can be observed using back scattered electrons when the sample is not

etched.

4.4 Transmission electron microscopy

Transmission electron microscopy investigations were conducted using two TEMs. One

is a Tecnai Supertwin F20 G2 equipped with a high angle angular dark field detector

and an energy-dispersive X-Ray analysis system and operated at 200 kV. The other

microscopy is Jeol JEM-2100 F located at the Institute of Physics of Materials (IPM) in

Brno which also works at 200 kV. Both conventional TEM and scanning TEM modes

have been used for overview images and detailed defect analysis. To get a spatial

impression, a STEM stereo method was used for the observation of defects. For the

sake of a better contrast and a larger field of view, TEM montages were performed under

both CTEM and STEM image conditions. Each montage consists of nine individual

TEM images taken under the same two-beam condition and magnification.

TEM thin foils were obtained mainly by double jet electrochemical polishing. The

specimens were firstly cut into thin slices with a thickness of 0.4 µm using an Accutom 5

cutting disk from Struers. The thin slices were cut in both [001] and [111] orientations,

as can be seen in Figure 4.6. The thin slices were then ground to a thickness of

90 µm using emery paper of 4000 mesh size. The following double jet electrochemical

thinning process was performed in a TenuPol-5. The electrolyte used is of type A7,

which consists of 70 vol.% methanol, 20 vol.% glycerine and 10 vol.% perchloric acid.

50


Optimum thinning conditions were obtained at a temperature of −20 ◦C. Different flow

rates (of the order 20) and voltages (of the order 10 V) had to be applied for specimens

in different conditions.

Figure 4.6: Illustration of TEM specimens cutting from the creep miniature specimen.(a) [001] cutting and (b) [111] cutting.

4.5 Determination of γ′ volume fractions, γ channel

widths and γ′ cube edge lengths

To better characterize the material, the γ′ volume fraction was determined using a

simplified area fraction method. At the early stage of creep, i.e., at 0.1% creep strain,

a TEM foil of [001] orientation was made. A TEM montage was used to determine

the γ′ volume fraction. For a specific area in the montage, a large rectangle is used for

identification of the whole two-phase region. Each γ′ particle within the area is then

depicted with a small rectangle adjusted to its size. The γ′ volume fraction is then

determined using the sum of all γ′ rectangle areas divided by the large rectangular area

of the probe field, see in Figure 5.6.

Simple line intersection methods were used to obtain the distributions of γ channel

widths and γ′ particle edge lengths. Two vertical and two horizontal lines through

the montage area have been used and the length for γ channel width and γ′ particle

51


edge length have been measured. The intersection of γ channel and γ′ particles has

been marked with a single line, whose length will be measured. A single line section

has been used to mark each γ channel and the particle size of γ′ cube edge length can

be measured accordingly. The size distribution of γ channel width and γ′ cube edge

length can then be obtained. The quantification results will be shown in the result

section. The demonstration of these two methods along with the quantification results

can be seen in the result section (Figure 5.6).

4.6 Planar faults quantification

Dislocation and planar defects densities have been calculated based on quantitative

micrographic data from montages from [111] TEM foils. An example is shown in Figure

4.7, where a TEM montage image was taken at a g of (111), for an accumulated creep

strain of 2%. Figure 4.7(b) reveals a rectangular area F1 in Figure 4.7(a) at a higher

magnification while Figure 4.7(c) is the rectangular area F2 at a higher magnification.

Other numbers in Figures 4.7(a) and (b) will be used later for reference in the result

section. The number of stacking fault nPF has been counted. The individual projected

areas of planar defects aPF have been approximated as rectangles and both lengths L

and widths W were measured, as shown in Figure 4.7(b). The total projected area

fraction of all planar defects APF has been determined using the following Equation

4.1:

APF =

nPF∑i=1

aPF,i/am (4.1)

In Equation 4.1, aPF,i is the projected area of the ith planar defect (i corresponds to

the number of stacking fault.) and am is the investigated montage area. There are

planar defects on different planes. Some planar defects appear nearly edge-on, thus

yielding a very small projected area. The influence of such kind of planar defects may

be underestimated when simply using Equation 4.1. On the other hand, there are

planar faults which are fully contained in the foil plane. Furthermore, as the TEM

foil represents a thin slice which probes the single crystal superalloy microstructure,

such planar faults have a higher possibility of not being captured by the TEM foil

sampling. Taking these effects into consideration, a qualitative intensity parameter

IPF was introduced as a reasonable compromise. IPF is based on both APF and nPF

and normalized by the thickness of TEM foil tF , as can be seen in Equation 4.2:

IPF = (nPF · APF )/tF (4.2)

52


4.7 Dislocation density quantification

To obtain dislocation densities, Ham’s method [87, 88] has been employed. As can be

seen in Figure 4.7(c), a system of thin horizontal and vertical lines is used. The total

length of all horizontal (H) and vertical (V) lines in the evaluation grid is∑lH and∑

lV respectively. The counting procedure is demonstrated in Figure 4.7(d) at a higher

magnification for the rectangular region highlighted in Figure 4.7(c). Each white dot

in Figure 4.7(d) represents one intersection between dislocations and horizontal and

vertical reference lines, and this yields the average dislocation density ργ/γ′ in the γ/γ′

microstructure using the following evaluation:

ργ/γ′ = (1/tF ) ·(∑

NH ALL/∑

lH +∑

NV ALL/∑

lV

)(4.3)

In Equation 4.3, NH ALL and NV ALL stand for the total number of intersections be-

tween dislocation segments and horizontal and vertical reference lines, respectively. By

applying the method described above, it is possible to distinguish and track the posi-

tion of dislocations, i.e., whether the dislocation is in the γ phase or in the γ′ phase.

The volume fractions of the γ phase fγ and the volume fraction of γ′ phase fγ′ have

been taken into consideration as well.

The dislocation densities in the γ phase ργ and in the γ′ phase ργ′ have been described

in Equations 4.4 and 4.5, respectively:

ργ =1

tF

( ∑nH−γ∑fγ · lH

+

∑nV−γ∑fγ · lV

)(4.4)

ργ′ =1

tF

( ∑nH−γ′∑fγ′ · lH

+

∑nV−γ′∑fγ′ · lV

)(4.5)

In Equations 4.4 and 4.5, nH−γ and nV−γ stand for the number of intersections between

dislocations in the γ phase with reference lines in horizontal and vertical directions,

respectively. nH−γ′ and nV−γ′ specify the intersection in the γ′ phase.

As dislocation density is a microstructural parameter which shows high scatter, there

are regions where dislocation density is high (Figure 4.7(a), arrow 1) while there are

other regions where the dislocation density is very low (Figure 4.7(a), arrow 2). This

kind of scatter is determined by two highest/lowest measured dislocation densities and

this information is used for the upper and lower limits of the error bars, which are

53


Figure 4.7: Illustration of defect quantification. (a) TEM montage images taken after2% strain, g : (111). (b) Field F1 from (a) at a higher magnification. (c) Referencegrid for determination of dislocation density from Field F2 of (a). (d) Illustration ofcounting procedure.

54


shown in the result section together with the mean value.

4.8 TEM foil thickness determination

The quantification of planar fault and dislocation densities requires the information of

TEM foil thickness. In the present work, foil thicknesses were measured using Kossel-

Moellenstedt (K-M) fringes technique as described in [63, 89] using the convergent

beam electron diffraction (CBED) mode. Figure 4.8 gives an example of the thickness

measurement. The white circle in Figure 4.8(a) indicates the location in the foil where

the thickness is measured. The inset in the lower right of the micrograph indicates

the diffraction pattern taken with selected aperture for the g-condition used. Using

the information from the diffraction pattern it is possible to measure lattice spacing

dhkl for the corresponding g-condition. Kossel fringes can be better observed at a

larger camera length, as shown in Figure 4.8(b), the distance between transmitted and

diffracted disk is measured as Dd. Measurement of fringe distances can be seen in a

higher magnification in Figure 4.8(c). The right edge of the first fringe is set as a

reference. The distance between the second and first fringes is marked as l1 while the

distance between the third fringe and the first fringe is marked as l2 and so forth. All

the measured values are listed in Table 4.2. The fewer number of fringes correspond to

the thinner TEM foils. The increase of one fringe reflects a thickness increase by one

extinction distance ξg [63].

A series of deviation value si can be obtained for the nth fringe using the following

equation [63]:

si = λli

Dd · d2hkl(4.6)

For an operation of 200 kV, the wave length λ is 0.0025 nm, and dhkl has been measured

to be 0.2067 nm. Foil thickness and extinction distance can then be fitted out using

Equation 4.7 as follows [63]:

(sini

)2

+ (1

ξg · ni)2

=1

t2(4.7)

In Equation 4.7, ni is an integer and corresponds to the number of fringes. With all

the calculated s value, a line can then be fitted, as shown in Figure 4.8(d). Both

extinction distance ξg and foil thickness t can be obtained, since the slope of the fitted

55


line is −1/ξg2 and the intercept with y axis is 1/t2, Figure 4.8(d). The foil thickness

is estimated to be 335 nm and an extinction distance to be 217 nm. It is a trial-and-

error process to get the optimum fitted line, but there is software which can easily

fit the curve.

Table 4.2: Parameters for thickness measurement.

i li/nm−1 si/nm−1 (si/ni)2/nm−2

1 0.54 0.0069 4.79× 10−5

2 1.11 0.0141 4.98× 10−5

3 1.65 0.0210 4.89× 10−5

4 2.20 0.0279 4.88× 10−5

5 2.84 0.0362 5.24× 10−5

4.9 Tilt experiments for identification of linear and

planar defects

Burger’s vectors b for dislocations and displacement vectors R for planar faults can be

determined by tilting experiments. The tilt positions are established with the Kikuchi

diffraction patterns for orientation [61–63]. At least seven g-vectors should be used and

a minimum of two invisibility conditions should be obtained, as has been described in

the background section. In the present work, tilt experiments are performed mainly for

TEM samples with a [111] foil normals in CTEM mode. To obtain optimum contrast

conditions, low-index g-vectors are used, such as {200}, {111} and {220}. Due to the

limited tilt range available in the TEM, and the large angular distance between 〈111〉and 〈110〉 poles, {200} g-vectors cannot be easily established.

Analyses of perfect dislocations and planar defects are conducted in a similar manner,

except that there are more invisibility possibilities for planar faults. A precise deter-

mination of the displacement vectors of planar faults need to account for the partial

dislocations which limit the planar faults. A series of systematic tilting experiments

have been conducted with a positive deviation parameter s (See section 2.5). There

are also cases where both positive and negative g-vectors were applied.

As w plays an important role in partial dislocation analysis, it is necessary to describe

56


Figure 4.8: Illustration of the thickness measurement using CBED. (a) A TEM imagewith a white spot indicating beam position, with diffraction pattern as an inset image.(b) Measurement of distance Dd between transmitted and diffracted disks. (c) Mea-surement of fringe distances. (d) Calculation of foil thickness and extinction distance.

57


Figure 4.9: Illustration of measurement of s. (a) Illustration of x and R value. (b)Example of an operating g-condition. (c) Measurement of x and R from the operatingg diffraction pattern.

briefly how the value of w can be calculated. The parameter w is defined as ξg · s [61–

63], where ξg is the extinction distance, which is related to the material, the operating

voltage and the g-vector. The measurement of w is illustrated in an example, as shown

in Figure 4.9.

The deviation parameter from exact Bragg condition s is defined using the following

Equation 4.8:

s =x

R· |g|2 · λ (4.8)

In Equation 4.8, x is the distance between the center of the transmitted beam and

the deficient line, and R is the distance between the center of transmitted beam and

diffracted beam, as demonstrated in Figure 4.9(a). |g| can be calculated as 1/d, d is

the lattice spacing and λ is the wave length of the electron in the TEM. The value of

ξg was taken for pure nickel from [61].

An example is shown in Figures 4.9(b) and (c). Figure 4.9(b) is one two-beam condition

and the operating g-condition is indicated as the central white arrow. For a more

precise determination of the circle center and the measurement of R, the choice of the

circle size is based on the disk size for the transmitted and diffracted beams in Figure

58


4.9(b). Figure 4.9(c) is the same image as in Figure 4.9(b) with enhanced contrast in

order to better figure out the position of Kikuchi lines and to facilitate the distance

measurement for better identification. When the Kikuchi lines corresponding to the

operating g-vector are determined, the value of x and R can be measured. With the

measured x and R values, as well as ξg , the value of w can be calculated.

59

5. Results

5.1 Double minimum creep at low temperature and

high stress

Interrupted creep test results for 0.1, 0.2, 0.4, 1, 2, and 5% accumulated strains at

750 ◦C and 800 MPa are shown in Figure 5.1. It can be seen that all creep curves

fall into one narrow scatter band and the creep results are quite reproducible. Figure

5.1(a) shows creep data plotted as strain ε vs. time t. Figure 5.1(b) shows logarithmic

creep rates plotted as a function of strain and in Figure 5.1(c) the logarithm of creep

rates is plotted as a function of the logarithm of strain. It should be noted that Figure

5.1(c) is not a traditional way to present creep curves, in this type of plots, the peculiar

change of creep rates with strain can be best appreciated. From Figures 5.1(b) and

(c), it can be seen that there is an initial sharp decrease of strain rate. A first creep

rate minimum is reached at 0.1% strain after 30 minutes. Then there is an increase

of strain rate towards an intermediate local maximum at 1% strain reached after 1.5

hours. Subsequently, strain rate steadily decreases towards a broad minimum at 5%,

reached after 260 hours. Figures 5.1(b) and (c) clearly show that in the LTHS regime,

the evolution of creep rates cannot be simply referred to as primary, secondary and

tertiary creep. For clarity, the creep deformation process has been divided into three

stages: stage I, stage II and stage III, as indicated in Figure 5.1(c). Stage I is the

period up to 0.1% strain, where the first local minimum is reached. In stage II, strain

rates increase towards an intermediate maximum at 1%. The decrease of creep rate

towards a broad minimum is indicated as stage III. TEM samples were prepared from

each interrupted creep test to study the evolution of microstructure during this peculiar

type of creep behavior.

61

CHAPTER 5. RESULTS

Figure 5.1: Creep curves from interrupted tests of ERBO / 1C (750 ◦C and 800 MPa).(a) Strain ε as a function of time t. (b) Logarithm of creep rate as a function of strain.(c) Logarithm of creep rate as a function of logarithmic strain.

62

CHAPTER 5. RESULTS

5.2 Microstructure evolution

TEM montages have been used for the investigation of microstructure evolution, as

described in the background section of the work. Before showing full montages, it is

worth to take a closer look at the microstructure of the initial state, prior to creep.

The TEM microstructure of the initial state in [001] orientation is shown in Figure 5.2.

Figures 5.2(a) and (b) were taken under a multi-beam condition in STEM mode in

the [001] zone. Figure 5.2(a) is a STEM BF image and Figure 5.2(b) shows a STEM

HAADF micrograph. High resolution TEM (HRTEM) can be used to identify the γ

channels and the γ′ particles, as shown in Figures 5.2(c) and (d), respectively.

For the [001] orientation, horizontal (parallel to the [010] direction) and vertical chan-

nels (parallel to the [001] direction) can be easily distinguished. From the STEM

BF and HAADF images in Figures 5.2(a) and (b), some interesting local microstruc-

tural features can be observed. Arrows 1 and 2 in Figure 5.2(a), point to some small

spheroidal γ′ particles which appear inside of γ channels, and have been referred to as

the secondary γ′ particles. Moreover, dislocations, as highlighted by arrows 3 and 4 in

Figure 5.2(b), have been observed at the γ/γ′ interface. Close to the γ/γ′ interface,

these dislocations are associated with grooves, as was reported earlier in [90].

The normal FCC structure of the γ phase and ordered L12 structure of the γ′ phase

can be detected by performing a fast Fourier transformation (FFT) analyses for these

two phases. In Figures 5.2(c) and (d), two small white rectangles indicate the positions

where this type of analyses were performed. The corresponding FFTs can be seen in

the lower right corner of Figures 5.2(c) and (d). Comparing the FFT images in Figures

5.2(c) and (d), it can be seen that in Figure 5.2(c), for the γ matrix phase, it is a classic

FCC structure with a four-fold symmetry in [001] orientation. In contrast, extra {100}superlattice spots are observed, highlighted by small white arrows in Figure 5.2(d).

They indicate the presence of the ordered γ′ phase. The filtered high resolution images

in the middle of Figures 5.2(c) and (d) provide clearer images of the arrangement of

atoms in the two phases.

In addition to TEM investigations, SEM investigations were carried out to obtain

an impression on how much the γ/γ′ microstructure changes with exposure of low

temperature and high stress creep. Figures 5.3(a) and (b) show [001] and [111] cross

sections of the initial state. Figures 5.3(c) and (d) were taken after 5% creep at 750 ◦C

and 800 MPa. The specimens from which the SEM images in Figures 5.3(a) and (c)

63

CHAPTER 5. RESULTS

were obtained, were in [001] orientation, while Figures 5.3(b) and (d) show [111] cross

sections. By comparing [001] and [111] cross sections, we can see that in [111] cross

sections, the projections of the γ′ particles often appear as triangles (Figure 5.3(b),

small arrow pointing up) and hexagons (Figure 5.3(b), small arrow pointing down).

Moreover, it can be seen that even after 5% creep strain at 750 ◦C and 800 MPa, there

is no significant rafting. This indicates that the peculiar creep curves shown in Figure

5.1 cannot be rationalized on the basis of rafting.

A TEM montage of a {111} cross section of the initial state is shown in Figure 5.4.

The morphology of the projected γ′ particles shapes show the triangular and hexagonal

features which are also observed in SEM. In this type of cross sections, the γ channels

cannot be easily distinguished as horizontal and vertical channels. In this case, hori-

zontal and vertical channels have been identified when necessary. At two locations, the

γ channels and γ′ particles for [111] cross sections are indicated by white arrows.

Dislocations can also be observed in the initial state. From the montage in Figure

5.4 we can see that there are some randomly distributed dislocations at the γ/γ′ inter-

faces. The overall dislocation density appears to be quite low in the initial state.

Figure 5.5 shows a montage of TEM micrograph which characterizes the material state

after 0.1% creep deformation. The TEM image was taken at a g-condition of (111).

It can be clearly seen that there are new features as compared to the microstructure

of the initial state. The first feature is the appearance of a small number of inclined

stacking faults, as highlighted by two black arrows pointing to the left.

Even though 0.1% is a small amount of deformation, a small number of stacking faults

can already be observed. The second feature is revealed by the dark dislocation lines.

Unlike in the initial state, where dislocations are distributed randomly, at 0.1% strain,

dislocations are observed to glide in specific γ channels, as highlighted by two dashed

rectangles 1 and 2. At this point, it appears as if dislocations glide more in one type

of channel while other channels remain empty. Extended dislocation segments can be

observed in the dashed rectangle 2. In the direction which is indicated by the long

black arrow in the rectangle, dislocation segments seem to fill that channel while in

other directions dislocations gliding appear to be absent.

Figure 5.6 shows quantification results for γ channel width and γ′ cube edge length from

TEM montage images. Figure 5.6(a) shows the montage of a state which was deformed

to 0.1% strain. A system of reference lines was used for quantitative evaluation as

64

CHAPTER 5. RESULTS

Figure 5.2: TEM images showing microstructure of ERBO/1 at initial state. (a) STEMBF image. (b) STEM HAADF image. (c) HRTEM of the γ phase. (d) HRTEM of theγ′ phase.

65

CHAPTER 5. RESULTS

Figure 5.3: SEM micrographs of the γ/γ′ microstructure of ERBO/1C before and aftercreep at 750 ◦C and 800 MPa. (a) Initial state, [001] cross section. (b) Initial state,[111] cross section. (c) After creep, [001] cross section. (d) After creep, [111] crosssection.

66

CHAPTER 5. RESULTS

Figure 5.4: TEM montage for the initial state prior to creep, foil normal [111].

67

CHAPTER 5. RESULTS

Figure 5.5: TEM montage for 0.1% deformation, foil normal [111], g=(111).

68

CHAPTER 5. RESULTS

was described in the chapter materials and experiment. Figures 5.6(b) and (c) show

histograms which present the distribution of the γ channel width and γ′ cube edge

length. A mean value for γ channel width is measured to be 65 nm and the average

γ′ cube edge width is estimated to be 442 nm. It is clear from Figures 5.6(b) and (c)

that local microstructural parameters (γ channel width and γ′ cube edge length) are

distributed quantities which can vary between 10 and 130 nm for γ channel width and

between 50 to 800 nm for γ′ cube edge length. This suggests that when discussing local

events in the γ/γ′ microstructure, it is not sufficient to simply refer to the average γ

channel width and γ′ cube edge length. Volume fraction of γ channel phase and γ′

particles have also been estimated from Figure 5.6: 27% and 73% respectively. These

values are in good agreement with the result of 72% γ′ volume fraction using another

method for the same material [14].

As creep deformation increased from 0.1% to 0.2%, creep rate starts to increase again.

From the microstructure in Figure 5.7, it can be seen that there are more dislocation

and stacking fault activities during the deformation process. Compared to 0.1% creep

strain, there are more dislocations filling in γ channels. Similar to previous deforma-

tion stage, there is also one leading direction where there are more dislocation activities

compared to other directions. Moreover, more stacking faults are cutting into γ′ par-

ticles. The observed stacking faults are inclined in the same way, and the quantity for

stacking faults is still quite small.

When creep strain reaches 0.4%, the creep rate is close to the intermediate maximum

at 1% strain. As compared to 0.2% strain, there is a significantly higher density

of dislocations in the γ channels and there are much more stacking faults in the γ′

particles at 0.4% creep strain, as shown in Figure 5.8. The white dashed line is used

to indicate horizontal channel direction where the dislocation density is higher. When

the term “horizontal channel” is used (here and in the following), it is referred to the

γ channels which are horizontal during [001] tensile creep testing. They cannot be

easily recognized when a {111} foil is cut out of a [001] specimen after deformation.

As expected for high symmetry 〈001〉 loading, planar faults can be observed in the γ′

phase on all four {111} type planes. At 0.4% strain, planar faults on three different

slip planes have been clearly observed, as indicated by arrows 1, 2 and 3. Arrow 1

indicates the planar faults which are parallel to the TEM foil normal. Arrows 2 and 3

indicate planar faults which are inclined in two slip planes. It is clear that the contrasts

of stacking faults which are parallel to the foil normal is different from those of the

inclined stacking faults. Another kind of planar faults is oriented edge-on and thus out

of contrast under the operating g-condition. It should also be highlighted that at this

stage there are few dislocations which have entered the γ′ particles. One example is

69

CHAPTER 5. RESULTS

Figure 5.6: TEM montage image for 0.1% deformation, foil normal [001]. (a) TEMmontage with horizontal and vertical reference lines. (b) Histogram showing γ channelwidth distribution. (c) Histogram showing γ′ cube edge length distribution.

70

CHAPTER 5. RESULTS

Figure 5.7: TEM montage for 0.2% deformation, foil normal [111]. g=(111).

71

CHAPTER 5. RESULTS

Figure 5.8: TEM montage for 0.4% deformation, foil normal [111]. g=(111).

shown in the dashed circular area where one dislocation seems to be interacting with

a stacking fault.

At a strain of 1%, where the creep rate is at the intermediate maximum, the microstruc-

ture looks similar to the previous deformation stage at 0.4% strain, as displayed in

Figure 5.9. Under this operating g-condition, planar faults which are edge-on can be

more clearly observed, as highlighted by two arrows in the lower left part of the image.

It is apparent that the dislocation density is still high and stacking faults are now a

prominent feature of the microstructure.

As creep strain approaches 5%, the second broad creep rate minimum is obtained. For

comparison with previous deformation stages, montage images at the CTEM mode are

72

CHAPTER 5. RESULTS

shown in Figure 5.10. The microstructure at 5% creep strain is more homogeneous

and overall uniform. The dislocation densities are high in all γ channels and it is now

difficult to tell which channel is horizontal. Due to the very high dislocation density,

HAADF STEM imaging gets advantages giving better contrast, as can be seen in Figure

5.11. Dislocations and planar defects show a bright contrast. After 5% creep strain,

the density of planar faults decreased. Moreover, it can be clearly observed that there

are more dislocations inside the γ′ particles, and there are more frequent observation

of interactions between dislocations and planar faults, as highlighted by three dashed

circles in Figure 5.11.

An overview summary of experimental details which characterize the TEM specimens

of the present work is given in Table 5.1. These details include the foil thickness, the

operating g-vector, the montage area and the number of the γ′ particles within the

montage area. It should be noticed that in 〈001〉 tensile testing, eight microscopic

crystallographic slip systems experience the same resolved shear stress. Therefore it is

reasonable to assume that each g-vector of 〈111〉 type shows a representative part of

the overall dislocation substructure. Table 5.1 shows that the montage area for each

deformation stage is similar and comparable.

73

CHAPTER 5. RESULTS

Figure 5.9: TEM montage for 1% deformation, foil normal [111]. g=(111).

74

CHAPTER 5. RESULTS

Figure 5.10: CTEM montage for 5% deformation, foil normal [111]. g=(111).

75

CHAPTER 5. RESULTS

Figure 5.11: STEM montage for 5% deformation, foil normal [111]. g=(111).

Table 5.1: Overview of experimental details characterizing the TEM foils investigatedin the present work.

strain/% tF/nm g-vector am/µm2 number of γ′ particles

0.1 335 (111) 32.1 111

0.2 160 (111) 33.2 122

0.4 260 (111) 29.4 117

1.0 295 (111) 24.2 102

2.0 373 (111) 33.7 112

5.0 238 (111) 29.3 104

76

CHAPTER 5. RESULTS

5.3 Evolution of dislocation and planar fault densi-

ties

Dislocation and planar fault densities, as derived from TEM montages, are plotted with

the evolution of deformation strain as a function of creep strain in Figures 5.12 and

5.13. Figure 5.12(a) shows the evolution of the overall dislocation density in the γ/γ′

microstructure ργ/γ′ with creep strain. Figures 5.12(b) and (c) differentiate between

the dislocation densities in the γ channels ργ and in the γ′ particles ργ′ respectively.

The increase of dislocation density in the γ′ particles indicated in Figure 5.12(c) is

fully in line with the qualitative impression which one obtains when comparing Figure

5.8 (low dislocation densities in the γ′ particles) and Figures 5.10 and 5.11 (elevated

dislocation densities in the γ′ particles). Dislocation densities increase in the later stage

of deformation for both γ channels and γ′ particles. Figure 5.13 shows the evolution

of planar faults with deformation. In Figure 5.13(a) we can see the number density of

planar faults per area of corresponding montage area aPF/am plotted as a function of

strain. Figure 5.13(b) illustrates how projected area fraction APF evolves with creep

strain. Finally, the intensity of the planar fault activity as captured by the parameter

IPF (see Equation 4.2) is plotted as a function of creep strain.

It is suggested from Figure 5.13 that at the early stage of deformation there is only a

small amount of planar faults. Then it seems that there is an optimum condition for

the formation of planar faults in the γ′ phase at accumulated strains between 0.4% and

1% strain. With further increasing strain, the condition for planar fault cutting is not

optimum anymore, and there is a decreasing contribution of planar fault cutting into

the γ′ phase.

77

CHAPTER 5. RESULTS

Figure 5.12: Dependence of dislocation densities on creep strain. (a) Overall dislocationdensity ργ/γ′ . (b) Dislocation density in the γ channels ργ. (c) Dislocation density inthe γ′ particles ργ′ .

78

CHAPTER 5. RESULTS

Figure 5.13: Evolution of planar faults with creep strain. (a) Number density of planarfaults per area nPF/am. (b) Projected area fraction APF . (c) Intensity parameter IPF .For details see texts.

79

CHAPTER 5. RESULTS

5.4 Identification of dislocation character

Initial state

Burger’s vectors of dislocations in ERBO/1C in its initial state have been determined

using the effective invisibility criterion. Figure 5.14 shows one example of a tilt series

under different two-beam conditions. Figures 5.14(a) to (k) are bright field images.

Figure 5.14(l) is the kikuchi map indicating all corresponding tilt positions and g-

vectors. Six dislocations have been analyzed, marked as 1 to 6. Dislocation 6 is

effectively invisible in Figure 5.14(a) under a g-vector of (111) but in full contrast in

Figure 5.14(b) of g-vector (111). Other invisibilities for dislocation 6 can be found in

Figures 5.14(g) (131) and (k) (020). With these three invisibility conditions and by

the applying effective invisibility criterion, the Burger’s vector can be identified using

scalar operation. Dislocation 6 is then identified as of type ±a/2 [101].

The same procedure can be used for the other dislocations. The visibility and invisi-

bility conditions for all the dislocations under investigation have been summarized in

Table 5.2. Visibility is represented by a “+” symbol and invisibility is represented by

a “-” symbol. From Table 5.2 we can see that all observed dislocations at the initial

state are of 〈011〉 type, which is consistent with previous reports [15, 90].

Creep state

Applying similar tilting experiments, Burger’s vectors b of dislocations and displace-

ment vectors R for stacking faults were analyzed after 1% creep strain at 750 ◦C and

800 MPa in STEM mode. As can be seen in Figure 5.15, nine dislocations (marked

as numbers 1 to 9) and two stacking faults (marked as numbers 10 to 11) have been

analyzed. The four images presented in Figure 5.15 are part of a full tilting series of 11

g-vectors. Figures 5.15(a) to(c) were taken in bright field mode under g-vectors (200),

(111), and (111) respectively, while Figure 5.15(d) was taken in the HAADF mode un-

der the same g-condition as Figure 5.15(b). A combination of BF and HAADF images

can be used for the identification of the nature of a stacking fault.

Dislocation 1 is in full contrast in Figure 5.15(a) under the condition g=(200), while

it is out of contrast in Figure 5.15(b) for g=(111). Dislocations 3, 4, 5, and 7 show no

80

CHAPTER 5. RESULTS

Figure 5.14: TEM micrographs of initial state under different two-beam conditions.(a) to (k) Bright field images. (l) Kikuchi map indicating tilt positions and g-vectors.

81

CHAPTER 5. RESULTS

Table 5.2: g-vectors and effective visibilities and invisibilities of dislocations from Fig-ure 5.14.

1 2 3 4 5 6

g1 (111) + + + + + -

g2 (111) - - + + + +

g3 (111) + + - - - +

g4 (220) + + + + + +

g5 (202) + + + + + +

g6 (022) + + + + + +

g7 (131) + + + + + -

g8 (311) - - + + + +

g9 (113) + + - - - +

g10 (200) - - + + + +

g11 (020) + + + + + -

±2b/a [011] [011] [110] [110] [110] [101]

contrast in Figure 5.15(c) while they are fully visible in Figure 5.15(b). The same type

of contrast analysis can be applied for other dislocations. A summary of dislocation

visibilities is shown in Table 5.3. There are also cases where it is difficult to conclude

whether a dislocation is visible or not. Situations like this have been marked with a

“?”. In relative higher order g-conditions such as {022} or {113}, dislocations can

show residual or double contrast, which is indicated as “res” or “do”.

An anaglyph made from a stereo pair has been taken to illustrate the spatial arrange-

ment of dislocations and stacking faults, as shown in Figure 5.16. When viewed with

colored glasses (red: left eye, blue: right eye), it can be seen that dislocations are

inclined at the interface of the γ/γ′ microstructure or lie in the γ channel phase except

for dislocation 6, which is inside of a γ′ particle. The analysis of dislocations involves

the theory for partial dislocation determination. The complete invisibility of disloca-

tion 6 in Figure 5.15(c) under the condition of (111) indicates that the dislocation 6

lies in (111) plane. As mentioned earlier, for partial dislocations a scalar product of

1/3 also indicates invisibility. A trial-and-error analysis for dislocation 6 suggests that

the dislocation is of type 1/6 [211]. For dislocation 6, the calculated value in brackets

after the visibility indications in Table 5.3 matches this conclusion. If the dislocation

is of type 1/3 [211], it would be visible for g2, g5 and g11, which is not consistent with

the experimental results.

82

CHAPTER 5. RESULTS

Figure 5.15: Four STEM images taken as a part of a tilt series for the determinationof Burger’s vector and displacement vectors of planar faults crept at 750 ◦C, 800 MPa,1%. (a) to (c) STEM BF images. (d) HAADF image.

83

CHAPTER 5. RESULTS

From the results in Table 5.3, we can conclude that all dislocations are of 〈110〉 type

except for dislocation 6. This is similar to what was found for the initial state. Different

types of dislocations also indicate activation of different slip systems. The Burger’s

vector of dislocations inside of the γ′ particle are different from the dislocations at the

interface. Partial dislocation inside of γ′ particles are closely associated with stacking

faults. In Table 5.3 the first three rows have been highlighted in gray, indicating the

g-vectors for which micrographs are shown in Figure 5.15 (Figure 5.15(d) shows the

same region as in Figure 5.15(b), only in dark field mode.). The corresponding TEM

images at other g-conditions are not shown here.

The analysis of stacking faults requires careful examination of the contrast of fringes.

To explain this, Figure 5.15(d) shows two insets at higher magnification of stacking

faults. The contrasts of the outermost fringes can be clearly observed. From the two

insets, we can see that for stacking fault 10, g-condition (111) points away from the

bright outermost fringe. This allows to conclude that stacking fault 10 is a superlattice

intrinsic stacking fault (SISF) based on the criteria summarized in Figure 2.27. For

stacking fault 11, g-condition (111) points towards a bright outermost fringe, which

indicates that the stacking fault is a superlattice extrinsic stacking fault (SESF). At

the condition of 1% deformation strain at 750 ◦C, 800 MPa, both SISF and SESF can

be found. Both stacking faults 10 and 11 have been out of contrast at g-conditions of

(111), (022), (131) and (113). The plane stacking faults inclined is (111) and there are

three possible displacement vectors on this plane, i.e., [211], [121], [112]. It is difficult

to decide which displacement vector is the correct one and to determine the pre-factor.

Additional methods are needed to reach the final conclusions. More information for

stacking faults analysis can be found in the next section.

84

CHAPTER 5. RESULTS

Tab

le5.

3:R

esult

sfr

omT

EM

tilt

exp

erim

ents

afte

r1%

cree

pst

rain

for

incl

ined

fault

s,g

-vec

tors

:g

(1to

11),

def

ects

:(1

-9:

dis

loca

tion

s,10

and

11:

pla

nar

fault

s).

Fie

lds

hig

hligh

ted

ingr

ay:

Fig

ure

s5.

15(a

)to

(c).

res:

resi

dual

contr

ast,do

:dou

ble

contr

ast,?

:no

det

erm

inat

ion

pos

sible

,b

:B

urg

ers

vect

or,R

:pla

nar

fault

dis

pla

cem

ent

vect

or.

gan

dd

12

34

56

78

910

11

1:(2

00)

++

++

-+

(±2/

3)+

+-

++

2:(1

11)

-+

++

+-

(±1/

3)+

++

++

3:(1

11)

+-

--

--

(0)

-re

s-

--

4:(0

22)

+re

s/do

++

+-

(0)

++

+-

-

5:(1

11)

+-

--

+-

(±1/

3)-

-+

++

6:(1

31)

-+

/do

++

+-

(0)

++

+-

-

7:(2

20)

++

++

+-

(±1/

3)+

++

++

8:(3

11)

++

++

res

+(±

2/3)

++

res

++

9:(1

13)

++

/do

++

+-

(0)

++

+-

-

10:

(002

)+

?+

+?

?+

?+

++

11:

(202

)+

--

-+

-(±

1/3)

-re

s+

++

2b/a

and

3R/a±

[101

]±

[101

]±

[101

]±

[101

]±

[011

]±

1/3

[211

]±

[101

]±

[101

]±

[011

]±

[112

]±

[112

]

85

CHAPTER 5. RESULTS

Figure 5.16: Anaglyph showing spatial arrangement of defects from Figure 5.15.

86

CHAPTER 5. RESULTS

5.5 Identification of planar fault displacement vec-

tors R

Displacement vectors R for stacking faults have been analyzed using conventional tilt-

ing experiments and high resolution TEM. Both inclined stacking faults and in-plane

stacking faults (parallel to foil normal) are investigated. For the low temperature and

high stress creep regime, as considered in the current work, the activity of planar faults

is closely related to dislocations. In the case of in-plane stacking faults, it is easier to

observe the interactions between dislocation and planar faults, thus both defects will

be jointly analyzed.

Inclined stacking fault

A set of TEM images was obtained after 2% creep strain with a (111) TEM foil, as

shown in Figure 5.17. A schematic kikuchi map is firstly shown in Figure 5.17(a),

indicating all the tilt positions and g-vectors close to the [111] zone. Figures 5.17(b)

to (i) are TEM images corresponding to different g-vectors. Except for Figure 5.17(c)

which was taken in the CDF mode, the other TEM images were taken in BF mode.

From the TEM images it can be seen that the stacking fault under investigation is

oriented nearly edge-on under the g-condition of (002) and it is effectively invisible

under g-condition of (202). All the effective visibility and invisibility conditions have

been summarized in Table 5.4 for the stacking fault investigated in Figure 5.17. With

these two invisibilities, it can be concluded that the stacking fault lies in the (111)

plane and its displacement vector is of type 〈121〉.

Figures 5.17(b) and (c) illustrate the change of contrast of the fringes and the two insets

make it possible to distinguish fringe contrast. From the inset in Figure 5.17(b) we can

see that both outermost fringes are bright, while in Figure 5.17(c) the two outermost

fringes display opposite contrast. The small black arrow in Figure 5.17(b), indicating

the fringe where the contrast is the same in both BF and CDF images, points to the

top of the stacking fault, i.e., the position of SF interacting with TEM foil. The bright

fringe in the BF image suggests that the scalar product of the operating g-vector and

the displacement vector is positive. Possible displacement vectors could be [121], [211],

or [112]. Furthermore, in Figure 5.17(c), as g points towards the bright fringe, it can

be concluded that the stacking fault is a SESF. Taking crystallographic information of

87

CHAPTER 5. RESULTS

Table 5.4: g-vectors and effective visibilities and invisibilities of the stacking fault inFigure 5.17.

g (111) (111) (220) (202) (002) (022) (111) (111)

SF + + + - + + + -

the ordered L12 structure into consideration, as for (111) plane, a displacement vector

of 1/3 [211] will introduce a SISF. In contrast, 1/3 [121] and 1/3 [112] displacement will

generate SESFs (see Figure A.6). As it is clear that the stacking fault is extrinsic

in nature, a vector of 1/3 [211] can be ruled out. However, a vector of 1/6 [211] can

generate a CSF composed of a SESF and an APB. A CSF normally requires much

higher energy to form and there is no clear evidence of the formation of an APB under

this condition. Therefore it seems reasonable to conclude that the fault has a vector

of 1/3 [121] or 1/3 [112]. More methods such as large angle convergent beam electron

diffraction (LACBED) have to be employed to precisely distinguish the vector of the

stacking fault.

When the leading partial dislocation is possible to detect, the stacking fault generated

by the dislocation can also be figured out. However, for the current example, the

leading dislocation is in most cases difficult to distinguish due to the relative small

size of the associated dislocation and difficult contrast determination at different tilt

positions. In this case, the example of in-plane stacking fault is considered, as can be

seen in the following section.

In-plane stacking fault

For the creep strain of 0.4% or higher, there are more slip systems activated and

stacking faults can be observed in more than one {111} plane. TEM foils with a normal

orientation of [111] contain inclined stacking faults and stacking faults which lie in the

plane of the foil. The in-plane stacking faults hold certain advantages compared to

the inclined ones. Dislocations associated with in-plane stacking faults are usually

relatively easier to distinguish.

Figure 5.18 shows examples of stacking faults in the foil plane after 1% deformation,

and the contrast of this kind of stacking fault is different compared with the inclined

stacking faults. Unlike dark and bright fringes of inclined stacking faults, in-plane

stacking faults show higher intensities as compared with background contrast or the

88

CHAPTER 5. RESULTS

Figure 5.17: TEM micrographs taken after 2% strain under different two-beam condi-tions. (a) Kikuchi map. (b) and (d) to (i) BF images. (c) CDF image.

89

CHAPTER 5. RESULTS

contrast from the γ′ particles. In Figure 5.18(a), there are three in-plane stacking faults

which have been marked as f1, f2, and f3 under investigation. A number of dislocations,

either bounding the stacking faults or in the γ matrix phase have been identified and

investigated. They are marked as 1 to 8. Figure 5.18(b) documents the conducting

g-vectors used for the tilting experiments.

A full tilt series is presented in Figure 5.19, and the investigated area has been tilted

to twelve different g-vectors. Under some g-conditions stereo images are made. In this

case, the images under similar g-conditions are not shown in Figure 5.19, rather shown

as anaglyphs, like those shown in Figure 5.20 and Figure 5.21.

The three in-plane faults, i.e., f1 to f3, are effectively invisible for all three 〈220〉 type

of g-vectors, in line with a fault plane of (111). From the stereo images in Figure 5.20

and Figure 5.21, it can be better seen that the faults are in-plane and not inclined.

Figure 5.20 was taken under the condition of (111) and Figure 5.21 was taken under

the condition of (111).

The analysis of partial dislocations requires the knowledge of the value of w and a

comparison of contrast. A summary of the w value and the visibility conditions is

shown in Table 5.5. It is necessary to bring in the criterion for the determination

of partial dislocation with regard to w value. It has been well-accepted that a value

of ±1/3 of scalar product g · b yields an invisibility regardless of w value [61, 72].

When w is small, a value of ±2/3 of scalar product g · b also indicates a visibility

[61, 72]. However, when w is larger than 1, a value of +2/3 of scalar product g · bguarantees visibility, while a value of -2/3 implies an invisible condition [61, 72]. With

this aforementioned criterion, both the magnitude and the sign of the Burger’s vector

for dislocations can be determined. Dislocations 1 and 2 and dislocations 2 and 3 are

used as two pairs of examples to clarify this point.

The results presented in Figure 5.19 and Table 5.5 suggest that dislocation 1 is effec-

tively invisible for g-vectors (111), (220) and (111) while it is in contrast for all other

diffraction conditions. These invisibilities ascertain that the investigated dislocations

are partial dislocations. The result obtained for the diffraction condition g8(220) in

Figure 5.19(e) allows to conclude that the Burger’s vectors for dislocation 1 to 5 lie

in (111) plane and there are three possible types of partial dislocations, i.e., ± [112],

± [121] and ± [211]. A trial-and-error practice by taking the visibilities and invisibili-

ties into consideration enables us to narrow down the possibilities of Burger’s vector to

±a/6 [112] for dislocation 1. Burger’s vectors of ±1/3 [121] indicate visibility for dislo-

90

CHAPTER 5. RESULTS

Fig

ure

5.18

:(a

)In

-pla

ne

fault

s,ST

EM

mic

rogr

aph

take

naf

ter

1%st

rain

under

two-

bea

mco

ndit

ion.

(b)

Kik

uch

im

apin

dic

atin

gdiff

eren

tti

ltp

osit

ions.

91

CHAPTER 5. RESULTS

Figure 5.19: STEM BF micrographs taken after 1% strain under different two-beamconditions for in-plane stacking faults and dislocations investigation. (a) g1 : (111).(b) g2 : (202). (c) g3 : (200). (d) g4 : (111). (e) g5 : (022). (f) g6 : (111). (g) g7 : (131).(h) g8 : (220). (i) g9 : (311). (j) g10 : (111). (k) g11 : (113). (l) g12 : (002).

92

CHAPTER 5. RESULTS

Figure 5.20: An anaglyph under condition of (111) showing in-plane stacking faultsand dislocations. 750 ◦C, 800 MPa, 1% creep strain.

93

CHAPTER 5. RESULTS

Figure 5.21: An anaglyph under condition of (111) showing in-plane stacking faultsand dislocations. 750 ◦C, 800 MPa, 1% creep strain.

94

CHAPTER 5. RESULTS

cations under the (111) condition, while Burger’s vectors of ±1/6 [211] only satisfy the

invisibility condition under the (111) condition. To differentiate these two candidates,

the value of w is considered. As we can see, under the g-vector of (311), w has a value

which is larger than 1. Based on the criterion mentioned earlier, a scalar product of

+2/3 corresponds to a visibility condition, while -2/3 corresponds to invisibility. The

visibility of dislocation 1 at the condition of (311) suggests that the scalar product of

g9 and the Burger’s vector of dislocation 1 is +2/3. In this case, it can be concluded

that the Burger’s vector for dislocation 1 is +a/6 [112]. For dislocation 2, the analysis

follows the same process and the sign of the vector is deduced from the contrast of g9,

where the value of w is larger than 1. A scalar product of +4/3 indicates an invisibility

(or residual contrast) when w is larger than 1 and fits to all the contrast conditions.

This suggests a Burger’s vector of +a/3 [112].

The contrasts of dislocations 2 and 3 are the same at all the conditions except for g9

(311). Since w value for g9 is larger than 1, and it is clear that the change of sign

of scalar product will change the visibility correspondingly, an opposite sign for the

Burger’s vector of dislocation 3, i.e., +a/3 [112] will satisfy all the contrast conditions.

It is noteworthy that under g9, the contrasts for dislocations 2 and 3 are complementary

to each other.

Interface dislocations (d5 to d8) have been analyzed and three types of dislocations were

found. From the invisibility conditions, it can be seen that the dislocations are mainly of

〈110〉 type. The conventional effective visibility/invisibility criterion of g · b = 0 could

yield the type of dislocation while leaving the pre-factor undetermined. Although

LACBED [91–93] method has not been used, it is well-accepted that the interface

dislocations for Ni-base single crystal superalloys are of type a/2 〈110〉 [42, 90, 94–96].

Different types of dislocations indicate that there are different slip systems activated

which allow to deposit dislocation segments at the interface. Attention must be paid to

the fact that the two types of interface dislocations d5 (±a/2 [011]) and d6 (±a/2 [101])

provide the possibility to generate the [112] type of partial dislocations.

The analysis of in-plane stacking faults undergoes the same tilting and analysis pro-

cedure as described previously. The three stacking faults under investigation have

the same contrast. As combined with the orientation of the TEM foil, the in-plane

stacking faults should have a vector of ±a/3 [111]. It is difficult to determine the sign

of the vector. While for the inclined stacking faults, the sign can be determined by

the contrast of the first fringe. The conventional tilting analysis does not help to de-

termine the pre-factor of the fault vector. A pre-factor of a/3 is only determined by

taking the crystallographic information of the FCC structure into consideration. The

95

CHAPTER 5. RESULTS

in-plane stacking fault investigation has certain advantages when one aims at inves-

tigating stacking faults which are related to partial dislocations. But it suffers from

the completely different contrast compared with inclined stacking faults, and the crite-

rion which help to determine inclined stacking faults cannot be applied to characterize

in-plane faults.

HRTEM Analysis

High resolution TEM was applied for the investigation of stacking faults. A TEM

specimen taken from a crept specimen after 5% deformation at 750 ◦C and 800 MPa is

used for HRTEM investigation. While TEM foils with [111] orientation show obvious

advantages in observing dislocation gliding behavior, a large angle of tilt is required

from 〈111〉 to 〈110〉 poles to get stacking faults edge-on such that HRTEM can be

performed. Using HRTEM analysis, both the nature of the stacking fault and a rough

estimation of its displacement vector can be achieved.

Figure 5.22 shows one example of a HRTEM analysis for an edge-on stacking fault.

In Figure 5.22(a), a few stacking faults are orientated edge-on inside one γ′ particle.

A small white rectangle indicates the location where higher magnification is applied,

Figure 5.22(b). From FFT in Figure 5.22(c), the ordered structure of the γ′ phase has

been confirmed by the observation of superlattice reflections. The long streaks in the

direction of [111] show clear evidence for the presence of stacking faults. They indicate

that the stacking faults lie in the plane of [111] with the direction of ± [112]. The

plane of the stacking faults can be further confirmed when the plane [111] is filtered

out, which is shown in the inset of Figure 5.22(d). The “twisted” region is the area of

the stacking fault.

The determination of the fault nature and vector can be seen in Figures 5.22(e) and

(f). In Figure 5.22(e), a normal FCC stacking sequence is constructed, where white

circles represent the “A”, red circles the “B” and green circles the “C” layers. The

stacking sequence is constructed in a normal way (ABCABC) until the stacking fault

is approached. An extra “C” layer has been found to fit the sequence. With this extra

“C” layer it can be concluded that the stacking fault is of extrinsic nature, according

to the definition of a SESF. The measurement of the shift has been demonstrated in

Figure 5.22(f). The white line indicates the normal position of atom columns. Due

to the introduction of stacking faults, the columns are shifted. This normal lattice

spacing shift associated with the stacking fault were 0.21 and 0.073 nm, respectively.

96

CHAPTER 5. RESULTS

Tab

le5.

5:R

esult

sfr

omST

EM

tilt

exp

erim

ents

(Fig

ure

5.19

)af

ter

1%cr

eep

stra

info

rin

-pla

ne

fault

wit

ha

sum

mar

yof

wva

lue

and

vis

ibilit

yco

ndit

ions.

“+”

indic

ates

vis

ibilit

y,“-

”in

dic

ates

invis

ibilit

yan

d“r

es”

indic

ates

resi

dual

vis

ibilit

y.

g1:(

111)

g2:(

202)

g3:(

200)

g4:(

111)

g5:(

022)

g6:(

111)

g7:(

131)

g8:(

220)

g9:(

311)

g10:(

111)

g11:(

113)

g12:(

002)

b/R

w0.

330.

320.

420.

940.

780.

500.

881.

031.

140.

501.

370.

80

d1

-(-

1/3)

+(-

1)-

(+1/

3)-(

+1/

3)+

(+1)

+(+

2/3)

res

(-2/

3)-

(0)

+(+

2/3)

-(-

1/3)

+(+

4/3)

+(-

2/3)

a/6

[112

]

d2

+(-

2/3)

+(-

2)+

(+2/

3)+

(+2/

3)+

(+2)

res

(+4/

3)re

s(-

4/3)

-(0

)re

s(+

4/3)

+(-

2/3)

+(+

8/3)

+(-

4/3)

a/3

[112

]

d3

+(+

2/3)

+(+

2)re

s(-

2/3)

res

(-2/

3)+

(-2)

+(-

4/3)

+(-

4/3)

-(0

)+

(-4/

3)+

(+2/

3)+

(-8/

3)re

s(+

4/3)

a/3

[112

]

d4

-(1

/3)

+(+

1)-

(-1/

3)-

(-1/

3)+

(-1)

+(-

2/3)

+(+

2/3)

-(0

)-

(-2/

3)-(

+1/

3)+

(-4/

3)+

(+2/

3)a/6

[112

]

d5

+(±

1)+

(±1)

-(0

)+

(±1)

+(±

2)+

(±1)

+(±

2)+

(±1)

-(0

)-

(0)

+(±

1)+

(±2)

±a/2

[011

]

d6

-(0

)+

(±2)

+(±

1)-

(0)

+(±

1)+

(±1)

-(0

)+

(±1)

+(±

2)+

(±1)

+(±

2)+

(±1)

±a/2

[101

]

d7

+(±

1)-

(0)

+(±

1)+

(±1)

+(±

1)-

(0)

res

(±1)

+(±

1)+

(±1)

-(0

)+

(±1)

+(±

1)±a/2

[101

]

d8

+(±

1)+

(±1)

-(0

)+

(±1)

+(±

2)+

(±1)

+(±

2)+

(±1)

-(0

)-

(0)

+(±

1)+

(±2)

±a/2

[011

]

f1+

(±1/

3)-

(0)

+(±

2/3)

+(±

1/3)

-(0

)+

(±1/

3)re

s(±

1/3)

-(0

)re

s(±

1/3)

+(±

1/3)

res

(±1/

3)+

(±2/

3)±a/3

[111

]

f2+

(±1/

3)-

(0)

+(±

2/3)

+(±

1/3)

-(0

)+

(±1/

3)re

s(±

1/3)

-(0

)re

s(±

1/3)

+(±

1/3)

res

(±1/

3)+

(±2/

3)±a/3

[111

]

f3+

(±1/

3)-

(0)

+(±

2/3)

+(±

1/3)

-(0

)+

(±1/

3)re

s(±

1/3)

-(0

)re

s(±

1/3)

+(±

1/3)

res

(±1/

3)+

(±2/

3)±a/3

[111

]

97

CHAPTER 5. RESULTS

This shift is roughly 1/3 on the direction of [112]. Due to the limited accuracy of this

analysis, alternative methods should be used to further confirm this result.

98

CHAPTER 5. RESULTS

Figure 5.22: HRTEM analysis for stacking faults. (a) Edge-on stacking faults in alower magnification. (b) Higher magnification for stacking faults. (c) FFT. (d) FilteredHRTEM with an inset containing only one plane filtered. (e) Determination of faultsnature. (f). Determination for fault shift.

99

6. Discussion

6.1 On the need of further work to explain primary

creep

Low temperature and high stress creep investigation of Ni-base single crystal superal-

loys have been performed in the literatures (e.g., [37, 50, 51, 57, 97]). Regardless of

superalloy compositions and differences of temperature and stress conditions, double

minimum creep behavior has always been observed, for example, in Mar-M200 [37],

CMSX-4 and SRR 99 [50, 51, 57, 97]. However, there is no explanation of the reason

for this peculiar type of creep behavior. Thus, the present work is intended to shed

some light on this peculiar double minimum creep phenomenon.

In the low temperature and high stress regime, a large amount of primary creep strain

has been accumulated and observed. Moreover, γ′ cutting mechanism has been found to

be associated with {111}〈112〉 slip systems. Rae and Reed [51] have conducted a series

of experiments at different temperatures, stresses and orientations to figure out the

origin and mechanism of primary creep at a temperature range of 750 - 850 ◦C. They

concluded that three elementary process are involved in the high primary creep strain

accumulation observed at low temperature and high stress. First, 〈112〉 dislocation

ribbons must form by reactions of different a/2〈110〉 γ channel dislocations. Second, the

resolved shear stress (driving force) must be high enough for γ′ cutting to occur. Finally,

they point out that an optimum γ channel dislocation density must be established,

which is high enough to promote the reactions for the formation of 〈112〉 ribbons,

but at the same time, not too high to suppress all dislocations achieving by stress

work hardening interacts. Cutting of the γ′ particles by a single a/2〈110〉 dislocation

has also been observed, where superlattice intrinsic and extrinsic stacking faults were

reported to be involved [98]. While stacking faults have been commonly detected in the

101

CHAPTER 6. DISCUSSION

low temperature regime, the appearance of stacking faults does not necessarily imply

a〈112〉 cutting mode: a detailed analysis with the associated dislocations is necessary

for the confirmation of the cutting mode. Kear et al. [37, 47] have conducted a series

of TEM analysis for detailed dislocation and stacking fault analysis. They confirmed

a cutting mechanism which is associated with a planar fault with a total displacement

vector of [112] on the (111) plane.

So far work on low temperature and high stress creep of the Ni-base single crystal

superalloys has mainly focused on the reasons for conventional primary creep. However,

as has been reported in the present work, a first local minimum precede the second

global minimum. This peculiar creep behavior is difficult to describe by simply using

the term primary, secondary and tertiary creep. Moreover, there is a need to explain

why the creep rate reaches an early local minimum by an intermediate maximum.

6.2 Composite character and stress transfer

The first local minimum is observed at 0.1% creep strain after creep of 30 minutes at

750 ◦C and 800 MPa. It is important to highlight that strain accumulation commences

immediately in all creep tests, as soon as the load is applied. In other words, no

incubation period has been observed in the present work for low temperature and high

stress creep, which is not consistent with what has been reported in previous work

[9, 37, 99]. It is also noteworthy that the durations of the incubation period in [9, 37]

are of the same order of the intervals required to reach stage II. Further investigation

is needed to clarify this point.

One part of the explanation of the first rate minimum (shown in Figure 5.1(b)) is

based on the macroscopic heterogeneity of Ni-base superalloys SX, which result from

the solidification process. Ni-base superalloys SX are produced in a Bridgeman type of

process, where dendrites grow into an undercooled melt. The dendrite structure of the

material used in the present work has been described elsewhere [14]. Most importantly

the average chemical compositions between prior dendritic and interdendritic regions

differ. As a result, dendritic regions have a lower γ′ volume fraction than interdendritic

regions [14]. It is therefore reasonable to assume that the interdendritic regions are

stronger than dendritic regions. This is schematically illustrated in the lower part

of Figure 6.1, which also shows that the average dendrite spacing is of the order of

500 µm. One can interpret the difference between dendritic and interdendritic regions

102


as a large scale microstructural heterogeneities. In fact, the material represents a

composite consisting of dendritic and interdendritic regions (center of Figure 6.1). The

mechanical analogon in the middle top of Figure 6.1 suggests, that dendritic regions

deform easier than interdendritic regions. As a consequence, there is a stress transfer

from dendritic to interdendritic regions. This stress transfer results in a decrease of

creep rate and may explain one part of the decrease of creep rate towards the first

minimum.

Figure 6.1 also suggests, that there is a smaller scale heterogeneity associated with the

γ/γ′ microstructure. This can also be thought of as a composite consisting of harder

(γ′ particles) and softer (γ channels) regions. There is also a stress transfer on this

smaller scale, as will be discussed later.

Classically, composite materials combine a soft matrix phase with a hard strengthening

phase. One class of the well-studied composite materials are fiber reinforced Al-alloy

metal matrix composites (MMCs) [100, 101], where the stress transfer mechanism from

softer to harder regions explains the decrease of primary creep. The situation of Ni-base

SX is different, where all available evidence suggests, that two softer phases combine to

form one stronger microstructure [8, 17, 102]. Bulk Ni3Al species are probably softer

than γ′ particles in SX-microstructure, because the latter are dislocation-free while bulk

materials contain dislocations. The key to understand the superior creep properties of

SXs lies in understanding the way to inject dislocations from the γ channels into the

ordered γ′ particles. This probably requires a critical stress. Similarities can be found

between threshold event between conventional MMCs and the γ/γ′ micro composite.

For short fiber reinforced Al-MMCs, fiber breakage didn’t occur immediately [100,

101]. However, stress transfer from the softer matrix phase to the fibers is required

and further deformation continues until the critical stress is reached. For Ni-base

single crystal superalloys with a γ/γ′ microstructure, cutting events are not observed

until stress transfer from plastically deformed γ channels to dislocation-free γ′ particles

occurs. At larger strains, the two phases deform in parallel and must accumulate similar

amounts of strain.

6.3 Exhaustion of grown-in misfit dislocations

An exhaustion mechanism is proposed as a second elementary process which contributes

to the first local minimum. This is related to the decrease of dislocation density in the

103


Figure 6.1: Composite character of SX Ni-base superalloys on two length scales. Center:Small differences between prior dendritic and interdendritic regions. Left and right:Micro composites with slightly higher (left: ID) and slightly lower (right: D) γ′-volumefractions.

104


vertical γ channels. A simplified dislocation model has been introduced in Figure 6.2.

In Figure 6.2(a), there are two slip systems, as indicated by the two crossed dashed lines.

When an external tensile stress is applied (shown by two vertical arrows), dislocations

move along slip planes, as depicted by the small arrows. The “+” and “-” symbols

next to dislocation at the lower right of Figure 6.2(a) indicate that in addition to the

external stress (large vertical arrows), there are local strain fields around dislocations.

In case of an edge dislocation, there can be positive (+) and negative (-). Here 60◦

interface dislocations are important, which behave like edge dislocations with respect

to the presence of compressive and tensile stress states which surround them.

The established dislocation model is accommodated to misfit dislocations in the γ/γ′

microstructure. Figures 6.2(b) to (d) schematically show a 2D projection of four γ′

particles and a γ channel crossing. As mentioned in the background section, the Ni-

base single crystal superalloy investigated in the present work has a negative misfit.

Consequently, the γ′ phase, with a smaller lattice constant, undergoes tension while the

γ phase, with a larger lattice constant, undergoes compression. The two long arrows

indicate misfit stress state inside of the microstructure. This internal misfit stresses

attract dislocations to the interfaces of the γ/γ′ microstructure, as can be seen in Fig-

ure 6.2(b). The misfit stress can be as high as 500 MPa [9, 103]. Dislocations are

accommodated in such a way that the compressive/tensile stress state of dislocations

are directed towards tensile/compressive stress state of the γ/γ′ microstructure. When

a high external stress is applied, as shown in Figures 6.2(c) and (d), dislocations move

in the direction defined in Figure 6.2(a). Dislocations in horizontal channels are pushed

toward the interfaces. On the contrary, dislocations in the vertical channels are pulled

away. After a short glide time, dislocations move towards the center of the vertical γ

channels where they annihilate, as indicated in Figure 6.2(d). The corresponding con-

sequence for the different ways of movement for dislocations in horizontal and vertical

channels is that the mobile dislocation density in vertical channels is decreasing. The

early decrease of the density of in-grown dislocations contributes to the decrease of

creep rate. It represents an exhaustion mechanism. As already mentioned by Leverant

and Kear [37], the density of in-grown dislocations plays an important role in the early

stages of creep.

105


Figure 6.2: Misfit dislocation model. (a) Dislocations in two slip systems. (b) 2D pro-jection of γ/γ′ model system with misfit dislocations. (c) Reaction of misfit dislocationsto applied load. (d) Annihilation of misfit dislocations in vertical channels.

106


6.4 Interpretation of glide of grown dislocation

There is a third mechanism which contributes to the decrease towards the first creep

rate minimum. As can be seen from both SEM and TEM images (e.g., Figures 5.3

and 5.6), the morphology of the γ′ phase is in general cuboidal, but the γ′ cubic

edge length reveals some scatter. More importantly, the γ′ cubes are not regularly

arranged as is often assumed. The dashed line in Figures 5.3(a) and (b) show free γ

channel segments which end at a location where an irregularly positioned γ′ particle is

present. This is the basis of a third mechanism which probably contribute to the early

first local creep rate minimum. This deformation process involves immediate glide

of pre-existing dislocations through continuous parts of the channel network. These

gliding process are interrupted when dislocation segments run into irregularly located

γ′ particles, as can be seen in several locations in Figures 5.5, 5.6 and 5.7. This has

been referred to as run and stop mechanism. The interruptions of dislocation glide

also contribute to the first local creep rate minimum. It should be noted that this

mechanism cannot be rationalized when the presence of in-grown dislocations is not

considered or when a highly regular spatial arrangement of the high asymmetry of γ′

particles in the γ/γ′ microstructure is assumed, as in most micromechanical models

[104–106]. At high temperatures and low stresses regimes, there is no intermediate

minimum observed [18, 42, 84, 94]. Peach-Koehler stresses are not high enough to

pull in-grown misfit dislocations away from the γ/γ′ interfaces. Furthermore, climbing

processes at higher temperatures make it easier for dislocations to overcome constraints

imposed by crystallographic slip or microstructural irregularities.

6.5 Time spent at the first local minimum

The time needed to pass the first local minimum (the duration of stage I) is of the order

of 30 minutes. It is worth highlighting that this time needed to overcome the first creep

rate minimum does not represent an incubation period, where no strain accumulates.

Leverant and Kear [37] interpreted this period as an incubation time which is needed to

produce dislocations. They did not observe such an incubation period after introducing

a high dislocation density by applying shock waves. Pollock and Argon in their well-

cited paper [9] suggested that dislocations emanate from ingrown nests which act as

dislocation sources during the incubation period. The TEM montages of the present

work, e.g., Figures 5.5 and 5.7, suggest that the increase of dislocation density can

also be associated with local sources. Ram et al. in their recent paper [107] explicitly

investigated and explained the main sources for creep dislocations by using high angular

107


resolution electron back scatter diffraction (HR EBSD), electron channelling contrast

imaging (ECCI) under controlled diffraction conditions. The main message from the

investigation is that the main sources for creep dislocations are individual, isolated

dislocations rather than low-angle boundaries. Their work is consistent with the TEM

results retrieved from the montages in the present work.

The time spent at the first local minimum suggests that diffusion is involved. It is

reasonable to assume that dislocations can climb in vertical γ channels to reach the

next horizontal γ channel, where glide can be resumed.

To prove this hypothesis, a dislocation climb process which takes about 30 minutes

is considered. A relevant diffusion distance is related to a fraction of the γ′ size, for

example, 0.2× 10−6m. The diffusion coefficient D can be approximated using the well-

known equation:

X2 = 4 ·D · t (6.1)

where X is the diffusion distance and t is the diffusion time. By applying the aforemen-

tioned value, a diffusion coefficient of 0.6× 10−17m2 s−1 is obtained. This is consistent

with the values of diffusion coefficients for relevant d-shell elements in Ni [3, 108]. Due

to the multi-element composition of Ni-base single crystal superalloys, it cannot be

expected that the calculated diffusion coefficient fully matches the Ni-data which are

reported in the literature. However, the rough estimation suggests that the time spent

at the first local minimum is related to short range diffusion processes which govern

dislocation climb.

6.6 Observation for intermediate local maximum

In stage II, as defined in Figure 5.1(c), the strain rate increases to a local intermediate

maximum. Several other researchers have also observed this early increase of creep rate

[50, 51, 97, 109–112]. From the overview of the SEM image (Figure 5.3) and montage

images (Figures 5.6, 5.7 and 5.8) we can see that the increase of creep rate is not related

to rafting of the microstructure. On the other hand, the quantitative results presented

in Figures 5.12 and 5.13 clearly show that the increase of creep rate in stage II of DM-

creep is associated with the increase of dislocation densities and planar faults densities.

The results show that up to 1% strain, dislocation densities reach a peak value in the

interrupted creep experiments. More dislocations offer more sources for the formation

108


of stacking faults. Thus, the amount of stacking faults seems to reach a maximum

value as well. This may indicate that there is an optimum condition for the formation

of stacking faults and this optimum condition has been referred to as “the opening of

Rae window”, since Pollock et al. have summarized this condition from the work of

Rae [50, 51] and describe it as a window of opportunity for the formation of stacking

faults [8]. As there are more dislocations in γ channels, there are more sources for

dislocation reactions which can provide for the formation of 〈112〉 type of dislocations

for further γ′ particle shearing. Both dislocations and stacking faults contribute to the

intermediate maximum of strain rate.

At this stage, it is necessary to discuss two main types of stacking faults shearing

mechanisms from dislocations in the γ channel phase. Several authors have proposed

that a〈112〉 dislocation ribbons shear the γ′ phase [47, 49–53, 113]. One possible

mechanism can be seen from Equations 6.2 to 6.4. Two different channel dislocations

react and form a 〈112〉 dislocation, as described in Equation 6.2.

a/2[101] + a/2[011]→ a/2[112] (6.2)

The resulting a/2[112] can further decompose into two partial dislocations, as shown

in Equation 6.3:

a/2[112]→ a/3[112] + SISF + a/6[112] (6.3)

For the ordered γ′ phase, a dislocation with a Burger’s vector of a/3[112] is able to cut

into γ′ phase and generates a SISF while the trailing dislocation a/6[112] cannot enter

the γ′ phase and remains at the γ/γ′ interface.

A second pair of channel dislocations is needed for the formation of a/2[112] disloca-

tions which eventually can decompose into a/3[112] and a/6[112] with the generation

of a SESF, indicated in Equation 6.4:

a/2[112]→ a/3[112] + SESF + a/6[112] (6.4)

The newly generated a/6[112] can then jointly enter γ′ together with the former

a/6[112] left at the interface, when the driving force is high enough. Meanwhile, it

is unavoidable to form an anti-phase boundary between these two dislocations, and a

109


SISF/APB/SESF ribbon is formed.

A second type of stacking fault shear involves one single a/2[110] dislocation cutting

event. One a/2[110] dislocation cuts into the γ′ phase and creates an APB [98]. In a

second step, the a/2[110] dislocation further dissociates into two types of [112] disloca-

tions, as assumed in Equation 6.5, and generates a SISF. The APB area is eventually

consumed by the SISF and the low energy SISF remains.

a/2[101]→ a/3[211] + SISF + a/6[121] (6.5)

Regarding the results and the scope of the present work, it is clear that both SISF and

SESF have been observed. It seems that both types of stacking faults shearing mech-

anisms are related and it is difficult to conclude which mechanism is dominant. Apart

from the formation of SISF and SESF, under certain conditions, complex stacking faults

and deformation twins have also been reported as alternative γ′ cutting mechanisms

[113]. While it is clear that the increase of strain rate at stage II is closely related

to stacking fault cutting, further work is needed to clarify the displacement vectors of

stacking faults. This can help to differentiate between these two types of mechanisms.

6.7 Strain hardening: towards a global minimum

After an intermediate maximum at 1%, the creep rate starts to decrease towards a

global minimum. The decrease of strain rate in stage III of double minimum creep

coincides with the closure of the “Rae window”, i.e., the condition for stacking fault

shear is not optimum anymore. The overall dislocation density keeps the increasing

trend till 5%, which is consistent with the montage image in Figure 5.11. By comparison

with the montage image at 0.4% (Figure 5.8), it can be seen that at 0.4% strain only one

direction of the γ channel is full of dislocations while in other directions dislocation

densities are low. The dashed line indicates a horizontal channel where dislocation

density is highest among three directions of channels. As a striking contrast, at 5%

strain, all three directions of γ channels have been full of dislocations. Dislocations

cannot enter all channels by glide since there are interrupted movements of dislocations

by irregularly spaced γ′ particles, as shown in Figures 5.3, 5.7 and 6.4. It is plausible

to conclude that stacking fault shear is an alternative mechanism, which accounts for

the increase of dislocation density in channels with unfavourable stress states. As the

110


relative empty channels (the channels receiving dislocations) fill up with dislocations

(initiated by dislocations from sources in horizontal channels), back stresses build up

and there is increasing difficulty to inject more dislocations into the receiving channels,

whether it is by dislocation glide or by stacking fault shear.

To sum up, the decrease of creep rate in stage III can be rationalized by three factors.

First, it is the closure of Rae window. The condition for dislocation and stacking faults

is not optimum. It depends on interactions between source channel dislocations and

the formation of low energy networks, for interfacial dislocation segments stabilization.

Second, back stresses build up in the receiving channels and it is more difficult for

dislocations to move to the relatively empty channels. Last but not least, it is also

reasonable to assume that the inherent resistance for stacking fault shear in γ′ particles

increases, which could be related to chemical changes on the nanoscale [114–117] and

the increase of dislocation density in the γ′ particles.

6.8 Local TEM observations

Initial state

From the STEM images of initial state in Figure 5.2 and the STEM HAADF image in

Figure 6.3, tiny γ particles can be clearly observed inside of the γ′ cubes, as highlighted

in Figure 6.3 by the white dashed circles. A recent paper by Yardley et al. [118] has

specifically combined thermodynamic calculations with characterization to explain the

formation of γ particles inside of the γ′ cubes. Their calculation indicates that a change

of volume fraction and chemical compositions at a high-temperature thermodynamic

equilibrium leads to a reestablishment at low-temperature equilibrium. To be more

specific, at the high-temperature equilibrium, heavy elements such as Re, Co and Cr

diffuse into the γ′ cubes [118]. When it comes to a lower temperature, these heavy

elements are not able to diffuse back to the γ channel phase and at the same time they

cannot be accommodated in the γ′ particles. As a consequence, tiny γ particles form

inside of γ′ cubes and accommodates the heavy elements [118].

On the other hand, secondary γ′ particles have been observed inside of γ channels. The

formation of secondary γ′ particles inside the γ phase can result from precipitation from

an oversaturated solid solution during cooling from higher temperatures. Secondary γ′

111


particles have been a prominent feature associated with grooves and ledges at the γ/γ′

interface of Ni-base single crystal superalloy [90]. Xiang et al. have conducted more

detailed work regarding secondary γ′ particles in γ matrix phase and at the dislocation

nodes [119]. They found out these two kinds of secondary γ′ particles differ in size,

morphology and element composition [119].

Creep state

In Figure 6.4, there are four local TEM observations at different stages of deformation.

Figure 6.4(a) shows dislocation movement in γ channels after 0.2% creep strain. The

dashed line indicates horizontal channel direction, as for the [001]-oriented sample.

Figure 6.4(a) further confirms the run and stop mechanism. As highlighted by two

white arrows, 1 and 2, we can see that dislocations make an attempt to enter non-

horizontal γ channels but it is not successful. Local stresses can be estimated by

approximating semicircles of leading dislocations and measuring the radii. The radii

of the two dislocation tips have been estimated to be 27 nm and 55 nm for dislocation

tips 1 and 2 respectively.

Local Orowan stresses have been calculated using the following well-known Orowan

Equation 6.6:

τor = 0.8 · µ · b/d (6.6)

Where µ is the shear modulus and b is Burger’s vector and d the diameter of the

dislocation loop.

Elastic constants of the ERBO/1 Ni-base single crystal superalloy were widely inves-

tigated at different temperatures for different orientations [120]. A value of 100 GPa

has been estimated for shear modulus for 750 ◦C and [001]-oriented specimen, and the

magnitude for Burger’s vector is taken as 0.254 nm. For dislocation 1, with a radius of

27 nm and a diameter of 54 nm, the calculated Orowan stress τor H is around 376 MPa.

Since dislocation 1 is in horizontal channel, it is also necessary to calculate the stress in

horizontal channel. The total applied stress in the whole experiment series is 800 MPa,

with a Schmidt factor of 0.408, the applied horizontal stress τapp H is 326 MPa. In

addition, horizontal misfit stress has also to be taken into consideration, which has

supposed to be 50 MPa, and the horizontal applied misfit stress τmis H is 20 MPa. In

this case, horizontal channel stress is the sum up of applied stress τapp H and misfit

112


Figure 6.3: STEM HAADF image showing microstructure of ERBO/1 at the initialstate, the dashed circles highlight tiny γ phases inside of the γ′ particles. Courtesy ofDr. A. Parsa, same specimen as in [118].

113


stress τmis H , which is 346 MPa. It is clear that the horizontal stress (346 MPa) is not

high enough to overcome the Orowan stress (376 MPa), and dislocation is not able to

move further.

In the case of “vertical” channel (as opposed to horizontal channel), the Orowan stress

and vertical channel stress have been calculated in the similar way. The vertical Orowan

stress has calculated to be 185 MPa but the vertical channel stress is only 126 MPa.

Both horizontal and vertical stresses have been estimated to be not high enough to

supress Orowan stress. This has been the reason why the dislocation loops cannot

expand into the two highlighted locations.

In Figure 6.4(b), a full white circle indicates an irregularly placed γ′ particle imped-

ing the continuous dislocation glide between the upper and lower part of γ channels,

marked by two arrows pointing up and down respectively. It can also be seen that

there are dislocations that succeed to circumvent blocking particles by expanding into

non-horizontal channels. At this creep strain stage, dislocation activities are restricted

in the γ channels. When the creep strain increases to 1%, as documented in Fig-

ure 6.4(c), dislocations can be observed inside of γ′ particles, as highlighted by two

white arrows. When creep strain increases further to 5% (Figure 6.4(d)), two relevant

microstructural features have been observed: (i) Dislocation densities in γ channels

increased significantly. Compared with early stages, dislocation density has increased

in a significant way. (ii) γ′ particles are sheared by both dislocations (marked by the

arrow pointing to the lower left) and stacking faults (marked by the arrow pointing to

the upper left).

114


Figure 6.4: TEM micrographs of dislocation events. (a) Dislocation expanding alongγ -channel in (111) plane of TEM foil - 0.2% strain. (b) Irregularly located γ′-particlesimpede dislocation motion - 0.2% strain. (c) γ′-phase cutting by dislocations - 1%strain. (d) High dislocation densities in all γ-channels after 5% strain. Central γ′-particle contains planar faults and dislocations.

115

7. Summary and Conclusions

The present work aims to contribute to a better understanding of the elementary

processes that govern low temperature and high stress creep (750 ◦C and 800 MPa)

of precisely [001] oriented (±1◦) single crystal Ni-base superalloy tensile specimens.

Special emphasis was placed on the evolution of creep rates during creep and quantifi-

cation of corresponding microstructures and defects related to plasticity. A set of six

interrupted creep specimens, which were interrupted after strains between 0.1% to 5%

and microstructures were evaluated using diffraction contrast transmission electron mi-

croscopy. The results of the present work are summarized and a number of conclusions

are drawn:

(1). Low temperature and high stress creep always starts as soon as the load is applied.

No incubation periods of creep have been observed. This is not in line with results

reported in the literature, and further work is required to clarify this point. Creep

results in present work suggest that the details of the loading procedure are critically

important. Most probably a step-wise loading procedure used in present work does

not allow to document the processes. When studying early creep phenomena it is

important to document the heating/loading procedure precisely. Without this kind of

information it is difficult to compare with creep results from previous researches.

(2). During high temperature and low stress creep, double minimum creep behavior has

been confirmed and reproduced. There is a first sharp decrease of creep rate towards

a first local minimum (0.1% strain, 30 minutes). This result confirms mechanical

data which were published by researchers from the University of Erlangen (Schneider

et al., Superalloy Conference 1992). Then creep rates pass through an intermediate

maximum (1%, 1.5 hours). Then creep rates decrease towards a global minimum after

260 hours (corresponding to 5%). Finally creep rates increase towards final rupture

(not investigated in the present work).

117

CHAPTER 7. SUMMARY AND CONCLUSIONS

(3). Classical creep concepts do not allow addressing this type of creep behavior. In

the classical picture of creep of materials there is one decrease of creep rate due to

an increase of back stress. A secondary or steady state creep regime characterizes

a scenario where an increase of dislocation density (strain hardening) is balanced by

a decrease of dislocation density (dynamic recovery). Finally tertiary creep accounts

for softening and damage processes. Clearly, this traditional way of viewing a creep

process is not suitable to rationalize DM-creep. Current engineering definitions of

primary creep incorporate the stages I (decrease to first local creep rate minimum) and

stage II (increase towards an intermediate creep rate maximum) of DM creep. In the

present work it is outlined why this definition of primary creep requires refinement.

(4). Even though considerable scatter is shown, the microstructural results obtained in

the present work do allow interpretation of DM creep. The good quantitative metal-

lographic results obtained in the present work rely on five boundary conditions. First,

the tensile creep specimens which were investigated in the present work were precisely

oriented. Second, the TEM foils were cut out parallel to {111} planes. This allows

obtaining TEM foils which contain long dislocation segments. Third, it is important

to study TEM foils with thicknesses larger than 150 nm. Only such TEM foils allow

characterization of relevant features of the dislocation substructure. Thinner TEM

foils are less suitable in this respect. Fourth, it is important to characterize sufficiently

large regions to obtain statistically relevant information on elementary deformation

mechanisms. For this purpose, montages of TEM micrographs were produced, which

contained 100 or more γ′ particles. And finally, it is important to establish well-defined

contrast conditions.

(5). The present work applies well-established methods like Ham’s method and the

effective invisibility approach to measure/identify dislocation densities and the Burger’s

vectors of dislocations. In order to quantify the density of planar faults, an intensity

parameter was developed, which gives fair credit to such planar faults which are fully

contained in the TEM foil, because their fault plane is parallel to TEM foil normal and

others which intersect the TEM foil in an angle. With the help of this parameter it

was possible to quantitatively describe the opening and the closing of the Rae window,

which qualitatively describes the transient from stage I to stage III of DM-creep.

(6). An important result obtained in the present work is related to the fact that

dislocation plasticity in γ -channels always precedes stacking fault shear of γ′-particles.

The γ/γ′-microstructure represents a composite where stresses are transferred from

the softer γ-channels to the harder γ′-particles via dislocations. The deposition of

dislocations at γ/γ′-interfaces or the sudden interruption of dislocation movements

118


by irregularly positioned γ′-particles represent microscopic stress transfer processes.

Stacking faults represent dislocation ribbons. The presence of a stacking fault indicates

that a group of dislocations jointly shears an ordered lattice. The results obtained in the

present work strongly suggest, that stacking faults should not be considered as planar

defects which operate on their own. They are always linked to dislocation plasticity.

(7). The present work interprets stage I of DM creep (decrease of creep rate towards

an early local minimum) on the basis of three elementary deformation processes. First,

an exhaustion mechanism, where the high external stresses which govern low tempera-

ture and high stress creep, pull misfit dislocations away from γ/γ′-interfaces. This first

mechanism represents an interpretation, which requires further validation by additional

experiments. Second, a run and stop mechanism, where favorably oriented dislocation

segments start to glide along open γ-channels before they hit irregularly positioned γ′-

particles. The present work provides direct TEM evidence for this second mechanism.

And finally the present work suggests, that a larger scale stress transfer from interden-

dritic (higher γ′ volume fraction) to dendritic regions (lower γ′ volume fractions) also

contributes to the decrease of deformation rate in the early stages of creep. The fact

that these two regions have different strengths was concluded from experimental and

theoretical results, which showed that interdendritic regions contain higher γ′-volume

fractions than dendritic regions. Although this appears to be reasonable, further work

is required to validate this conclusion.

(8). The increase of creep rate from the first local minimum towards the intermediate

maximum (stage II of DM-creep) is characterized by an increase of overall dislocation

density in the γ-channels and an increase of the density of planar faults in the γ′-

particles. During stage I a dislocation scenario evolves in the γ-channels, which provides

optimum conditions for γ′-particle cutting. There are enough dislocations available to

form the type of dislocation pairs which are required for cutting. The γ′-particles

still have perfect lattices and no obstacles hamper the movement of planar faults.

And the receiving γ-channels, on the other side of the γ′-particle are empty and can

accommodate dislocations. In the present work quantitative data are presented which

fully support this scenario. The situation was qualitatively described previously by

Rae et al. (MSEA, 2001) and was referred to as “opening of the Rae window”.

(9). The decrease of creep rate in stage III of DM-creep is governed by several ele-

mentary processes. There is normal strain hardening in the γ-phase. The dislocation

density in the receiving γ channels is so high that they can no longer integrate new

dislocations which arrive by either hampered channel glide or by delayed stacking fault

shear. Stacking fault shear itself can become more difficult, because dislocations strain

119


harden the γ′-phase. Moreover, the stabilization of interface dislocation networks and

atomic re-ordering processes may slow down stacking fault shear.

(10) The current work provides some insights into the physical nature of the process

by which dislocations from the γ channels manage to penetrate and move through the

γ′ particles. Diffraction contrast TEM analysis has proved a number of points. First,

most γ channel dislocations which we observed are of a/2〈110〉 type. Dislocation reac-

tions between such γ channel dislocations lead to the formation of planar faults in the

γ′ phases with overall displacement vector of 〈112〉. This finding is in agreement with

those of the previous work accepted in the literature. It seems likely that the dissoci-

ation of γ channel dislocation into a/6〈112〉 types precedes all cutting events. Further

work is required to clarify this hypothesis, which so far could not be experimentally

observed.

120


Further work and outlook

Results obtained in the present work indicate that systematic and careful quantifica-

tion of microstructures and associated defects enable to explain the double minimum

creep behavior observed at LTHS regime. There are situations where no direct mi-

crostructural observation is available, while there are cases when no certain conclusion

about stacking fault displacement vectors or the interaction between dislocation and

stacking faults can be reached. The following points can be suggested for further work

in this field:

(1) With regard to the accurate determination (both sign and magnitude) for inclined

and in-plane stacking faults, conventional TEM with a plus and minus g-vector con-

ditions can be applied. For certain TEM samples (with appropriate foil thickness),

LACBED can be applied.

(2) Correlative TEM/APT experiments shall be conducted to evaluate the influence of

elements segregating into the planar faults and associated change of the SF energy.

(3) A further correlative simulation work (calculation of SF energy) can be compared

with experimental results. The change of SF energy may play a significant role in

determining deformation mechanism.

(4) Double shear creep experiments can be employed to activate a precisely selected

single slip system, contributing to a better understanding of double minimum creep

behavior at low temperature and high stress regime.

(5) New insight for alloy design can be obtained, based on the influence of elements

upon creep behavior. As most of the creep life is in secondary creep region, a high

primary creep strain is detrimental to the material in the respect of creep life. Certain

elements which can avoid large primary strain is more beneficial to the material.

121

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Appendices

Figure A.1: TEM images showing dislocation movements at 750 ◦C, 800 MPa, 0.2%.(a) Dislocations gliding in one direction of γ channel. (b) Dislocations gliding alongtwo sides of one γ′ particle. (c) Dislocations expanding from one central loop into otherdirection of γ channels. (d) More dislocations sending to the same direction of channel.

133

APPENDICES

Figure A.2: Comparison of a pair of plus and minus g-vector analyzing a stacking faultat 750 ◦C, 800 MPa, 0.2%. (a) BF image under +g, the two outermost fringes are bothdark. (b) BF image under -g, the two outermost fringes are both bright. (c) CDFimage corresponding to +g, the lower outermost fringe is bright. (d) CDF image cor-responding to -g, the upper outermost fringe is bright. (e) WBDF image correspondingto +g, dislocations show better contrast. (f) WBDF image corresponding to -g, boththe stacking fault and dislocations are highlighted.

134

APPENDICES

Figure A.3: A tilting series for a stacking fault analysis at the condition of 750 ◦C,800 MPa and 0.2%. (a) BF image at [111]. (b) BF image at [020]. (c) BF image at[111], the stacking fault has been oriented edge-on, as indicated by the white dashedline. (d) BF image at [220], stacking fault is invisible. (e) BF image at [202]. (f) BFimage at [022]. (g) BF image at [311], the stacking fault is invisble. (h) BF image at[113]. (i) BF image at [131].

135

APPENDICES

Figure A.4: Microstructure of 750 ◦C, 800 MPa, 1%, foil normal [001]. (a) CTEM BFimage showing SFs. SFs start from γ′ corners, direction indicated by white dashedline. (b) CTEM CDF image for SF nature determination. (c) CTEM BF imageshowing SFs at a higher magnification. (d) CTEM WBDF image showing partialdislocation associated with SF. (e) Multi-beam STEM image showing SFs and lowerdensity of dislocations. (f) Multi-beam STEM image showing SF and higher densityof dislocations.

136

APPENDICES

Figure A.5: An anaglyph showing an inclined stacking fault at the condition of 750 ◦C,800 MPa, 0.1%.

137

APPENDICES

Figure A.6: Illustration of (111) projection of L12 structure. The symbols have thesame meaning as in Figure 2.10. (a) Projection of (111) plane, with three 〈110〉 and〈112〉 directions. (b) The top layer is shifted by 1/3 [112] and a SESF is generated.(c) The top layer is shifted by 1/3 [121] and a SESF is generated. (d) The top layer isshifted by 1/3 [211] and a SISF is generated.

138

Publications

Part of the work has been published in the following journal / proceeding:

• X. Wu, P. Wollgramm, C. Somsen, A. Dlouhy, A. Kostka, G. Eggeler, Double

minimum creep of single crystal Ni-base superalloys, Acta Mater. 112 (2016)

242-260.

• P. Wollgramm, X. Wu, G. Eggeler, On the temperature dependence of creep

behavior of Ni-base single crystal superalloys, Superalloys 2016.

Part of the work has been presented in the following conferences:

• Junior EuroMat, July 2016, Lausanne, Switzerland

• Superalloys 2016, Sep. 2016, Pennsylvania, USA

Curriculum Vitae

Personal Information

Name: Xiaoxiang Wu

Gender: Female

Date of birth: 09/11/1988

Nationality: Chinese

Education

Oct. 2013 - present Ph.D. student at the Chair of Materials Science in Ruhr Uni-

versity Bochum

Sep. 2010 – June 2013 Master degree in engineering at the Faculty of Materials Sci-

ence in Kunming University of Science and Technology

Sep. 2006 – June 2010 Bachelor degree in engineering at the Faculty of Mechanical

Engineering in East China Jiaotong University

Sep. 2003 – June 2006 High school education and college entrance exam

Academic / work Experiences

Oct. 2013 - present Research assistant (Ph.D. student) at the Chair of Materials

Science in Ruhr University Bochum.

Main activity: TEM investigation for Ni-base single crystal

superalloy.

Sep. 2010 – June 2013 Research assistant (master student) at the Faculty of Materi-

als Science in Kunming University of Science and Technology.

Main activity: tensile tests for copper alloys and XRD char-

acterization.

Language Abilities

Chinese: Native speaker

German: B1

English: proficient level: BEC (higher)

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