AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF DAMAGE … · 2017-01-18 · A stress-assisted diffusion approach has been used to model oxygen penetration in the waisted specimen based

AN EXPERIMENTAL AND COMPUTATIONAL

STUDY OF DAMAGE AND CRACK GROWTH FOR A

NICKEL-BASED SUPERALLOY UNDER FATIGUE-

OXIDATION CONDITIONS

ALKISTIS KARABELA

BENG (HONS), MSC, MIET, AMIMECHE

The thesis is submitted in partial fulfilment of the requirements for the award of the degree of

Doctor of Philosophy

Of the

University of Portsmouth

This research was conducted in the Mechanical Behaviour of Materials laboratory, in the School of Engineering at the University of Portsmouth. The research was funded by the Faculty of Technology of the University of Portsmouth and the Engineering and Physical Sciences Research Council (EPSRC) of the UK. The test samples were provided by Rolls-Royce plc in Derby, the UK. The work was in a close collaboration with Cranfield University of the UK.

30 September 2011

2

ABSTRACT

Oxidation damage, in conjunction with fatigue, is a concern for nickel-based superalloys

utilised as disc rotors in high pressure compressor and turbine of aero-engines. A combined

experimental and numerical study has been carried out for alloy RR1000, developed at Rolls-

Royce plc through a powder metallurgy route to meet the demands for higher overall

pressure ratios, compressor discharge temperatures and rotational speeds for the latest

aero-engines.

Cyclic experiments have been carried out for waisted specimens at selected temperatures

(700C-800C), followed by microscopy examination using Focused Ion Beam (FIB). The

results suggest that the major mechanism of oxidation damage consists of the formation of

surface oxide scales and internal micro-voids and oxide particles beneath the oxide scales,

which becomes more severe with the increase of temperature. Applying a cyclic stress does

not change the nature of oxidation damage but tends to enhance the extent of oxidation

damage for temperatures at 750°C and 800°C. Further energy dispersive X-ray (EDX) analyses

show the enrichment of Cr and Ti, together with lower Ni and Co levels, in the surface oxide

scales, suggesting the formation of brittle Cr2O3, TiO2, NiO and Co3O4 oxides on the specimen

surface. Penetration of oxygen into the material and associated internal oxidation, which

leads to further material embrittlement and associated failure, are evidenced from both

secondary ion imaging and EDX analyses.

Scanning electron microscopy (SEM) studies of fracture surfaces have been performed for

dwell crack growth, and the results confirmed the transition from transgranular to

3

predominant intergranular cracking in alloy RR1000 for increased dwell time. This change in

fracture mode supports the oxidation-assisted crack growth mechanism via grain boundary

embrittlement. Oxidation embrittlement has also been supported by the FIB analyses of

fracture surfaces which confirmed the oxidation reaction for alloy RR1000 at high

temperatures.

A stress-assisted diffusion approach has been used to model oxygen penetration in the

waisted specimen based on Fick’s first and second laws. Grain microstructures were

considered explicitly in the model using a finite element submodelling technique, and the

grain boundary was taken as the primary path for oxygen diffusion. The material constitutive

behaviour was described by a crystal plasticity model to consider the effects of

heterogeneous deformation at grain level on oxygen diffusion. Two essential diffusion

parameters, i.e., oxygen diffusivity and pressure factor, have been obtained from the

simulated oxygen penetration as well as the FIB measurements of internal oxidation depth.

Using the obtained diffusion parameters, finite element analyses of a compact tension

specimen have been carried out to model oxygen diffusion, coupled with viscoplastic

deformation, near a fatigue crack tip. A failure curve for crack growth has been constructed

based on the consideration of both oxygen concentration and accumulated inelastic strain

near the crack tip. The failure curve was then utilized to predict crack growth rates under

fatigue-oxidation conditions for selected loading frequencies and dwell periods, with

comparison against the experimental results and those predicted from the viscoplastic model

alone.

4

TABLE OF CONTENTS

List of figures ............................................................................................................................................................ 9

Chapter 1 ................................................................................................................................................................ 18

1.1. Introduction .............................................................................................................................................. 18

1.2. References ................................................................................................................................................ 22

Chapter 2 ................................................................................................................................................................ 26

2.1. Introduction .............................................................................................................................................. 26

2.2. Oxidation of nickel and its alloys ............................................................................................................... 28

2.3. Damage caused by oxidation .................................................................................................................... 31

2.4. Effect of mechanical stress on oxidation .................................................................................................. 35

2.5. Oxidation-assisted crack growth ............................................................................................................... 37

2.5.1. Time-dependent crack growth due to oxidation .............................................................................. 37

2.5.2. Crack tip embrittlement mechanism—short range diffusion .......................................................... 39

2.5.3. Crack tip embrittlement mechanism—long range diffusion ............................................................ 41

2.5.4. Interaction between crack tip field and oxidation ........................................................................... 42

2.5.5. Crack growth prediction models ...................................................................................................... 44

2.6. Dynamic embrittlement mechanism ........................................................................................................ 47

2.7. Review of research on alloy RR1000 ......................................................................................................... 51

2.7.1. Crack growth study ........................................................................................................................... 52

2.7.2. Cyclic constitutive behaviour ........................................................................................................... 52

2.7.3. Modelling of crack tip deformation and growth .............................................................................. 55

2.7.4. Oxidation work ................................................................................................................................. 57

2.8. Conclusions ............................................................................................................................................... 60

2.9. References ................................................................................................................................................ 61

Chapter 3 ................................................................................................................................................................ 74

3.1. Introduction .............................................................................................................................................. 74

3.2. Material, specimen and experimental details........................................................................................... 76

5

3.2.1. Material ............................................................................................................................................ 76

3.2.2. Specimen geometry.......................................................................................................................... 76

3.2.3. Fatigue tests ..................................................................................................................................... 77

3.2.4. FIB analyses ...................................................................................................................................... 78

3.2.5. EDX analyses of the oxides ............................................................................................................... 80

3.3. Results ....................................................................................................................................................... 81

3.3.1. Stress analysis ................................................................................................................................... 81

3.3.2. Fatigue experiments ......................................................................................................................... 84

3.3.3. FIB examinations .............................................................................................................................. 86

3.3.4. Effect of stress level on oxidation damage ....................................................................................... 91

3.3.5. Composition of oxides ...................................................................................................................... 93

3.4. Discussions ................................................................................................................................................ 95

3.5. Conclusions ............................................................................................................................................... 99

3.6. References .............................................................................................................................................. 101

Chapter 4 .............................................................................................................................................................. 105

4.1. Introduction ............................................................................................................................................ 105

4.2. Microscopy analyses of CT specimens .................................................................................................... 106

4.2.1. SEM fractography ........................................................................................................................... 108

4.2.2. FIB examination .............................................................................................................................. 110

4.3. Microscopy analyses of CN specimens .................................................................................................... 114

4.3.1. SEM fractography ........................................................................................................................... 116

4.3.2. FIB examination .............................................................................................................................. 118

4.4. Conclusions ............................................................................................................................................. 124

4.5. References .............................................................................................................................................. 126

Chapter 5 .............................................................................................................................................................. 130

5.1. Introduction ............................................................................................................................................ 130

5.2. Modelling of oxygen diffusion................................................................................................................. 131

6

5.2.1. Governing equations ...................................................................................................................... 131

5.2.2. Oxygen flux boundary conditions ................................................................................................... 132

5.2.3. Crystal plasticity ............................................................................................................................. 132

5.2.4. Model parameters and UMAT ........................................................................................................ 133

5.2.5. Finite element model ..................................................................................................................... 134

5.3. Results and discussions ........................................................................................................................... 136

5.3.1. Natural diffusion ............................................................................................................................. 136

5.3.2. Effect of mechanical stress on oxygen diffusion ............................................................................ 140

5.3.3. Determination of pressure factor................................................................................................... 142

5.4. Conclusion ............................................................................................................................................... 145

5.5. References .............................................................................................................................................. 146

Chapter 6 .............................................................................................................................................................. 150

6.1. Introduction ............................................................................................................................................ 150

6.2. Viscoplasticity deformation analysis ....................................................................................................... 151

6.2.1. The material model ........................................................................................................................ 152

6.2.2. Finite element analysis ................................................................................................................... 154

6.2.3. Near-tip inelastic deformation ....................................................................................................... 156

6.2.4. Prediction of crack growth ............................................................................................................. 158

6.3. Coupled viscoplasticity-oxygen diffusion analysis .................................................................................. 162

6.3.1. Near-tip oxygen concentration ...................................................................................................... 163

6.3.2. Failure curve ................................................................................................................................... 165

6.3.3. Prediction of crack growth under fatigue-oxidation condition ...................................................... 167

6.4. Discussion ................................................................................................................................................ 174

6.5. Conclusions ............................................................................................................................................. 177

6.6. References .............................................................................................................................................. 178

7. Conclusions & Further Work ....................................................................................................................... 182

7.1. Conclusions ......................................................................................................................................... 182

7

7.2. Further work ....................................................................................................................................... 183

Appendix A............................................................................................................................................................186

Appendix B............................................................................................................................................................187

8

DECLARATION

Whilst registered as a candidate for the above degree, I have not been registered for any

other research award. The results and conclusions embodied in this thesis are the work of

the named candidate and have not been submitted for any other academic award. Some of

the results presented in this thesis have already been published.

Signed:

Date:

9

LIST OF FIGURE

Figure 2. 1: External oxide and internal voids formed in Ni 270 after air exposure at 1000°C for 200 hours [58]. 32

Figure 2. 2: Cracking of sub-surface carbides due to oxidation swelling [62]. ....................................................... 33

Figure 2. 3: Fatigue crack propagation behaviour in IN718 at ΔK=27.5MPa√m *74+. ........................................... 38

Figure 2. 4: Fatigue crack growth rate in air and vacuum at 650°C [87]. ............................................................... 38

Figure 2. 5: (A) Intergranular and (B) Transgranular fracture surfaces for crack growth in air and vacuum for Alloy

718 at 650°C [87]. ................................................................................................................................................... 39

Figure 2. 6: Fatigue crack growth rate as function of oxygen partial pressure [90]. .............................................. 40

Figure 2. 7: A schematic of the kinetic model [106]. .............................................................................................. 47

Figure 2. 8: At 650°C, cracking in 1atm of oxygen was completely arrested in about 10s, the time necessary to

evacuate the testing chamber below 10-2Pa. Cracking resumed when oxygen was re-admitted to the chamber

[107]. ...................................................................................................................................................................... 49

Figure 2. 9: Comparison of model simulations and experimental results: (a). Stress-strain loop at saturation

(dε/dt=0.05%/s and Δε=2%) (b). Stress relaxation behaviour during 100-second dwells at maximum and

minimum strain levels (dε/dt=0.5%/s and Δε=2%) *132+. ...................................................................................... 54

Figure 2. 10: Contour plot of the von Mises equivalent strain at the maximum strain level of the 2nd cycle (strain

rate dε/dt=0.005%/s, strain range Δε=20%, strain ratio =-1) [132]. ...................................................................... 54

Figure 2. 11: (a). The evolution of stress-strain loops over 30 cycles ahead of a stationary crack tip. (b). The

evolution of stress-strain loops registered at an integration point O as the crack grew towards it [133]. ........... 55

Figure 2. 12: Focused ion beam image of an oxidised RR1000 surface, exposed to 700°C for 200 hours [48]. .... 58

Figure 2. 13: Oxide layer on the fracture surface during dwell fatigue tests at 725°C [98]. .................................. 59

Figure 3. 1: Waisted specimen geometry and the three positions “A”, “B” and “C” selected for FIB examinations.

Drawing provided by Rolls-Royce Plc. Internal communication. ........................................................................... 77

Figure 3. 2: Waisted specimen surface, the Pt strip applied to protect the oxide scale and the first stage of rough

milling. .................................................................................................................................................................... 79

Figure 3. 3: (a). Secondary electron image (b). Secondary ion image. ................................................................... 80

Figure 3. 4: (a). Contour plot of the normal stress in the y direction for the waisted specimen under an applied

load of 10kN, where d is the distance from the narrowest section of the specimen (b). Stress concentration

factor, defined as the ratio of the normal stress in the y-direction (σyy) to the applied stress (σapp = 39.0MPa),

against the distance from the narrowest section of the specimen. ...................................................................... 83

10

Figure 3. 5: (a). The fracture surface of the specimen fatigue tested at 750°C. (b). Surface cracks on the side

surface of the specimen fatigue tested at 800°C. .................................................................................................. 85

Figure 3. 6: FIB images for position "A" at 700°C (a) secondary electron and (b) secondary ion, where the dashed

line in red indicates the original specimen surface. ............................................................................................... 88





Figure 3. 9: (a). Comparison of the thickness of the oxide scale and depth of internal damage, for positions A, B

and C at 700°C. (b). Comparison of thickness of oxide scale and depth of internal damage for positions A, B and

C at 750°C. (c). Comparison of thickness of oxide scale and depth of internal damage for positions A, B and C at

800°C. ..................................................................................................................................................................... 92

Figure 3. 10: Five spectrums selected for EDX analyses, over a depth of 2.2μm from the oxide scale surface and

with equal spacing (0.54μm) between each other. ............................................................................................... 93

Figure 3. 11: (a). EDX element profiles showing weight% of Cr, Ni, Ti and Co against the distance from the oxide

scale surface (750°C). (b). EDX element profiles showing weight% of O, Mo, Al and Ta against the distance from

the oxide scale surface (750°C). ............................................................................................................................. 94

Figure 3. 12: (a). EDX element profiles showing weight% of Cr, Ni, Ti and Co against the distance from the oxide

scale surface (800°C). (b). EDX element profiles showing weight% of O, Mo, Al and Ta against the distance from

the oxide scale surface (800°C). ............................................................................................................................. 94

Figure 4. 1: Fracture surface of a CT specimen tested at T=650°C for variable dwell times. ............................... 107

Figure 4. 2: SEM micrographs of the fractured surface of a CT specimen tested at 650°C under (a) 20s, (b) 300s

and (c) 1000s dwell. ............................................................................................................................................. 109

Figure 4. 3: SEM micrographs of the fractured surface of a CT specimen tested at 725°C under (a) 20s, (b) 300s

and (c) 1000s dwell. ............................................................................................................................................. 110

Figure 4. 4: Micrograph of the selected FIB location, which also shows the severe surface roughness. ............ 111

Figure 4. 5: The secondary electron image for FIB analysis which reveals a very thin and light oxide film built on

the surface. .......................................................................................................................................................... 112

Figure 4. 6: The secondary ion image for FIB analysis, showing the surface oxide scale and penetration of oxides

into the material along the path of a secondary crack. ....................................................................................... 113

Figure 4. 7: The secondary ion image for FIB analysis, which reveals a thicker oxide scale, built on the fracture

surface (Testing temperature at 725°C). .............................................................................................................. 113

Figure 4. 8: Fractured surface of the CN specimen tested at 650°C, with indications of the three FIB positions.

.............................................................................................................................................................................. 115

11


.............................................................................................................................................................................. 115


.............................................................................................................................................................................. 116

Figure 4. 11: SEM pictures of the fractured surface of the CN specimen R134 (a) room temperature fatigue and

(b) 1 hour dwell at 650°C. .................................................................................................................................... 117

Figure 4. 12: SEM pictures of the fractured surface of the CN specimen R134 (a) room temperature fatigue and

(b) 1 hour dwell at 700°C. .................................................................................................................................... 117

Figure 4. 13: SEM pictures of the fractured surface of the CN specimen tested at 750°C: (a) 0.25Hz followed by 1

hour dwell and (b) 1 hour dwell. .......................................................................................................................... 118

Figure 4. 14: Secondary Ion images at FIB position 1 for the specimens tested under one-hour dwell at (a) 650°C,

(b) 700°C and (c) 750°C. The colour lines indicate the surface oxide boundaries. .............................................. 119


(b) 700°C and (c) 750°C. The colour lines indicate the surface oxide boundaries. .............................................. 120


(b) 700°C and (c) 750°C. The coloured lines indicate the surface oxide boundaries. .......................................... 121

Figure 5. 1: (a) The 150-grain submodel with random orientation (b) Finite element mesh for the global model

and (c) Inverse pole figure for the 150 grains. ..................................................................................................... 135

Figure 5. 2: For 650°C the diffusion value has been determined using the Arrhenius equation and the

experimental values obtained for 700, 750 and 800°C, as shown on the graph. ................................................ 137

Figure 5. 3: Contour plots of oxygen concentration along the grain boundaries for natural diffusion: (a) 650°C

and (b) 800°C. ....................................................................................................................................................... 138

Figure 5. 4: Oxygen concentration against the distance from the specimen surface for four different

temperatures. ...................................................................................................................................................... 140

Figure 5. 5: Contour plot of the hydrostatic stress (peak load level) for the submodel after 33473 cycles at 800°C

for an applied load of 8kN. ................................................................................................................................... 141

Figure 5. 6: Contour plot of the oxygen concentration in the submodel at 800°C after 33473 cycles: (a) natural

diffusion and (b) with a pressure factor of 0.3MPa-1

. .......................................................................................... 142

Figure 5. 7: Depth of oxygen penetration against the pressure factor for T=750°C, where the penetration depth

(δ) under fatigue is normalized against that (δ0) for natural diffusion. ............................................................... 143

Figure 5. 8: Depth of oxygen penetration against the pressure factor for T=800°C, where the penetration depth

(δ) under fatigue is normalized against that (δ0) for natural diffusion. ............................................................... 144

12

Figure 6. 1:(a) Finite element mesh for a CT specimen and (b) refined mesh for the crack tip area (element size is

6.35μm). ............................................................................................................................................................... 156

Figure 6. 2: Contour plot of the accumulated inelastic strain near the crack tip after ten loading cycles for a

stress intensity factor range ΔK=30MPa√m and a loading frequency f=0.25Hz. ................................................. 157

Figure 6. 3: Contour plot of the accumulated inelastic strain near the crack tip after ten loading cycles for a

stress intensity factor range ΔK=30MPa√m and a dwell period of 1000s............................................................ 158

Figure 6. 4: Effects of loading frequency on crack growth rate for a triangular loading waveform with ΔK =

30MPa√m and load ratio R = 0.1 at 650°C, comparison of model prediction and experimental results *11, 12+.

.............................................................................................................................................................................. 160

Figure 6. 5: Effects of dwell periods on crack growth rate for a trapezoidal loading waveform with ΔK =

30MPa√m and load ratio R = 0.1 at 650°C, comparison of model prediction and experimental results [11, 12].

.............................................................................................................................................................................. 161

Figure 6. 6: (a) Contour plot of the oxygen concentration near the crack tip after 10 cycles for a frequency of

0.001Hz. ............................................................................................................................................................... 164

Figure 6. 7: Failure curve in terms of the accumulated inelastic strain and the oxygen concentration near the

crack tip (ΔΚ=30ΜPa√m, R=0.1, T=650°C). .......................................................................................................... 167

Figure 6. 8: Illustration of determining the number of cycles for the crack to grow, i.e., when the combination of

the accumulated inelastic strain and the oxygen concentration reached the failure curve, for different

frequencies. .......................................................................................................................................................... 169

Figure 6. 9: Illustration of determining the number of cycles for the crack to grow, i.e., when the combination of

the accumulated inelastic strain and the oxygen concentration reached the failure curve, for different dwell

time. ..................................................................................................................................................................... 170

Figure 6. 10: The effects of loading frequency on the crack growth rate for a triangular waveform with

ΔK=30MPa√m and load ratio R = 0.1 at 650°C; comparison of the model prediction and the experimental results

[11, 12]. ................................................................................................................................................................ 172

Figure 6. 11: The effects of dwell period on the crack growth rate for a trapezoidal loading waveform with

ΔK=30MPa√m and load ratio R = 0.1 at 650°C; comparison of the model prediction and the experimental results

[11, 12]. ................................................................................................................................................................ 173

13

DISSEMINATION

A. Karabela, L.G. Zhao, J. Tong, N.J. Simms, J.R. Nicholls and M.C. Hardy. Effects of

cyclic stress and temperature on oxidation damage of a nickel-based superalloy.

Materials Science and Engineering: A, 528(2011), 6194-6202.

Tong, J., Cornet, C., Lupton, C. and Karabela, A. (2010). Developing improved service

propagation lives in arduous cyclic environment (DISPLACE) project. TSB Project.

University of Portsmouth, Portsmouth, UK.

"Fatigue-oxidation interaction for a nickel-based superalloy", at EUROCORR'2010

(European Corrosion Congress, Moscow, Russia, 13-17 September 2010) was awarded

a Young Author's prize by the Russian Scientific Committee, with 500EUR prize.

14

ACKNOWLEDGEMENTS

My sincere gratitude to my supervisor Dr Liguo Zhao, who’s guidance and support have been

of great value and without whom this PhD thesis wouldn’t have been possible.

My gratitude also for my second supervisor Prof Jie Tong, who has been my reference point

as a woman and as an engineer, since I first arrived in Portsmouth.

Many thanks to Mr Colin Lupton, for his help and friendship, his advices and interest were

always very much appreciated.

Thank also to all the members of the Mechanical Behaviour of Materials Research group for

their friendship and support whenever it was needed, especially Dr Bing Lin with his help

with ABAQUS when it was needed.

The work has been funded by the EPSRC (Grant EP/E062180/1) of the UK and in a close

collaboration with Rolls-Royce plc. (Dr M.C. Hardy) and Cranfield University (Professor J.R.

Nicholls and Dr N.J. Simms) of the UK. The bursary and tuition fees have been provided by

the Faculty of Technology of the University of Portsmouth.

The waisted specimens were provided by Rolls-Royce plc of the UK.

Support has been provided by Dr Adriana Encinas-Oropesa and Mr Andrew Dyer in the use of

the FIB facilities at Cranfield University of the UK.

The crystal plasticity UMAT was originally developed by Professor Esteban Busso and his

associates, while he was with the Imperial College London of the UK.

15

Finally many thanks to all my friends here in Portsmouth, especially Dr Eleni Noussi, Dr Nick

Savage and Mr Gianluca Tozzi for their help, advices, and constant moral support on personal

matters that occurred these past few months of my PhD.

16

DEDICATION

To my parents Alexios and Anastasia

17

CHAPTER 1

INTRODUCTION

18

CHAPTER 1

1.1. INTRODUCTION

Increasing turbine entry temperatures and rotational speeds in order to increase fuel

efficiency and to reduce NOx/CO2 emissions are the pursuits of modern development and

design of aero engines. As a consequence, demand for increased performance has been

critically placed upon the nickel based superalloy materials, which are used in the hot section

of the engine, particularly the critical rotating turbine discs. RR1000 is one of the new

generation nickel alloys, developed by Rolls-Royce plc of the UK through the powder

metallurgy process, to meet such demands. Very recently, RR1000 has been put into

application for the turbine discs of the latest Rolls-Royce aircraft engines, which were

designed towards higher performance and increased failure resistance, to power the

dreamliner Boeing 787 aircrafts.

During a typical flight cycle, turbine discs are subjected to variable centrifugal and thermal

stresses with operation temperatures reaching up to 700C at the rim. Hence, failure of

turbine discs could result from the interaction of fatigue, creep and environmental effects.

Fatigue and creep failure behaviour of RR1000 at high temperatures was considerably

studied before its very recent application. Effects of load ratios, frequency, wave form and

dwell period on fatigue crack growth have been extensively studied in the Mechanical

Behaviour of Materials laboratory at the University of Portsmouth, and data and models are

already available for life assessment of RR1000 turbine discs [1-3]. In addition, experimental

and analytical studies on the constitutive behaviour (stress-strain relationship) of RR1000

19

have also been carried out in the MBM research group at Portsmouth [4-10] and applied for

the study of fatigue and creep crack growth behaviour [11-13]. However, environmental

effects on the crack growth behaviour for RR1000 [14, 15], which is a crucial factor for life

assessment of RR1000 turbine discs, have not been well studied yet. Crack growth

predictions in Zhao and Tong [16], based on viscoplastic deformation only, showed a great

discrepancy with experimental data for low frequencies and long dwell periods, which was

due to the neglect of oxidation effects at high temperature.

Recently, Encinas-Oropesa et al. [17] studied the oxidation of alloy RR1000 using circular disk

specimens that have been isothermally exposed to air at 700°C, 750°C and 800°C for 200

hours. Focused Ion Beam (FIB) examinations of oxidized samples for RR1000 revealed the

appearance of the oxide scale on the surface and the formation of recrystallized grains and

voids beneath the oxide scales [17]. The oxide scale, rich in Cr and Ti, has been found to grow

in a parabolic dependence with time. However, the work of Encinas-Oropesa et al. [17] was

carried out without considering the influence of mechanical loading such as fatigue, which

can have a significant effect on oxidation and corrosion damage for nickel and its alloys.

For polycrystalline turbine-disc made of nickel superalloys environmental effects, in

particular oxidation, were frequently observed to modify the fracture morphology from

transgranular to intergranular during fatigue crack growth, as well as to increase the growth

rates significantly at a given crack-tip stress intensity [18-21]. Several prediction models have

been developed for different nickel alloys based on different views of the fatigue-oxidation

interaction process, such as the oxide-depth based model [21], the oxide-passivation

(formation of protective Cr2O3) based model [22] and the multiplicative mechanical-

20

environmental damage model [23]. However, these life prediction models for crack growth

are highly empirical.

It has been widely acknowledged that oxygen-accelerated crack propagation behaviour in

nickel alloys is a result of oxygen diffusion into a local area with increasing tensile stress, such

as crack tips. The oxidising elements, by themselves or through chemical reactions with alloy

elements, attack the grain boundaries by lowering boundary cohesion and tend to introduce

accelerated intergranular cracking [e.g. 18, 20, 21, 24-26]. Oxygen diffusion at the crack tip is

a dynamic phenomenon, a combined effect of time, temperature and local deformation [24-

26]. This approach has been shown encouraging to predict crack growth rate for a nickel alloy

under fatigue oxidation conditions [27].

The aim of this PhD program was to study the oxidation damage under fatigue, and to model

crack growth under fatigue-oxidation conditions using a dynamic embrittlement approach for

alloy RR1000. Funded by the EPSRC [28], the work has been in close collaboration with Rolls-

Royce plc and Cranfield University. The objectives were:

To carry out a literature review on oxidation and its effect on crack growth for nickel

alloys (Chapter 2).

To carry out fatigue tests on waisted specimens at elevated temperature at

Portsmouth and examine fatigue-oxidation damage using the FIB and EDX facilities at

Cranfield (Chapter 3).

21

To carry out post-mortem SEM and FIB studies on fracture surfaces of compact

tension (CT) and corner notch (CN) specimens that have been tested under fatigue at

Portsmouth (Chapter 4).

To calibrate the diffusion parameters from oxygen diffusion analysis of waisted

specimen at grain level via a coupled crystal plasticity-diffusion approach (Chapter 5).

To carry out oxygen diffusion analysis, coupled with viscoplasticity deformation, near

the crack tip, and develop a model for crack growth prediction under fatigue-

oxidation conditions (Chapter 6).

To conclude the work and make suggestions for future work (Chapter 7).

The work is of great practical importance for “Damage Tolerance” lifing of critical rotating

turbine discs [29]. The investigation will provide a fundamental and scientific understanding

of oxidation damage and associated fast crack growth in the fatigue-creep regime for alloy

RR1000. RR1000 is representative of the best powder metallurgy, fine grained nickel-based

superalloys for service as aero-gas turbine discs. Such studies will provide support to Rolls-

Royce in ensuring the structural integrity of aero-engines through a close collaboration.

22

1.2. REFERENCES

[1]. Dalby, S. Tong, J. (2005). Crack growth in a new nickel-based superalloy at elevated

temperature, Part I: Effects of loading waveform and frequency on crack growth. Journal

of Materials Science, 40(5), 1217-1228.

[2]. Tong, J., Dalby, S. and Byrne, J. (2005). Crack growth in a new nickel-based superalloy

at elevated temperature, Part III: Characterisation. Journal of Materials Science, 40(5),

1237-1243.

[3]. Dalby, Sara. (2002). The effects of frequency and waveshape on the fatigue crack

growth of an advanced nickel based superalloy at elevated temperatures. PhD Thesis.


[4]. Zhao, L.G., Tong, J., Vermeulen, B. and Byrne, J. (2001). On the uniaxial mechanical

behaviour of an advanced nickel base superalloy at high temperature. Mechanics of

Materials, 33(10), 593-600.

[5]. Tong, J. and Vermeulen, B. (2003). The description of cyclic plasticity and

viscoplasticity of Wasploy using unified constitutive equations. International Journal of

Fatigue, 25(5), 413-420.

[6]. Tong, J., Zhan, Z.-L. and Vermeulen, B. (2004). Modelling of cyclic plasticity and

viscoplasticity of a nickel-based alloy using Chaboche constitutive equations, International

Journal of Fatigue, 26, 829-837 (2004).

[7]. Zhan, Z.-L. (2004). A study of cyclic plasticity and viscoplasticity in a new nickel-based

superalloy using unified constitutive equations. PhD Thesis. University of Portsmouth,

Portsmouth, UK.

[8]. Zhan, Z.-L., Tong J. (2007). A study of cyclic plasticity and viscoplasticity in a new

nickel-based superalloy using unified constitutive equations. Part I: Evaluation and

determination of material parameters. Mechanics of Materials, 39(1), 64-72.

[9]. Zhan, Z.-L., Tong J. (2007). A study of cyclic plasticity and viscoplasticity in a new

nickel-based superalloy using unified constitutive equations. Part II: simulation of cyclic

stress relaxation. Mechanics of Materials, 39(1), 73-80.

[10]. C. Cornet, L.G. Zhao and J. Tong. (2011). A study of cyclic behaviour of a nickel-

based superalloy at elevated temperature using a viscoplastic-damage model.

International Journal of Fatigue, 33(2), 241-249.

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[11]. Zhao, L.G., Tong, J. and Byrne, J. (2001). Finite element simulation of creep-crack

growth in a nickel base superalloy. Engineering Fracture Mechanics, 68(10), 1157–1170.

[12]. Zhao, L.G., Tong, J. and Byrne, J. (2004). The evolution of the stress-strain fields near

a fatigue crack tip and plasticity-induced crack closure revisited. Fatigue and Fracture of

Engineering Materials and Structures, 27(1), 19-29.

[13]. Cornet, C., Zhao, L.G. and Tong, J. (2009). Ratchetting strain as a damage

parameter in controlling crack growth at elevated temperature. Engineering Fracture

Mechanics, 76(16), 2538-2553.

[14]. Tong, J., Dalby, S., Byrne, J., Henderson, M.B. and Hardy, M.C. (2001). Creep,

fatigue and oxidation in crack growth in advanced nickel base superalloys. International

Journal of Fatigue, 23(10), 897-902.

[15]. Knowles, D.M. and Hunt, D.W. (2002). The influence of microstructure and

environment on the crack growth behaviour of powder metallurgy nickel superalloy

RR1000. Metallurgical and Materials Transactions A, 33(10), 3165-3172.

[16]. Zhao, L.G., Tong, J. (2008). A viscoplastic study of crack-tip deformation and crack

growth in a nickel-based superalloy at elevated temperature. Journal of the Mechanics

and Physics of Solids, 56(12), 3363-3378.

[17]. Encinas-Oropesa, A., Drew, G.L., Hardy, M.C., Leggett, A.J., Nicholls, J.R., Simms,

N.J. (2008). Effects of oxidation and hot corrosion in a nickel disc alloy. Champion,

Pennsylvania, USA : Wiley, Superalloys 2008. 609-618.

[18]. Andrieu, E., Hoshstetter, G., Molins, R. and Pineau, A. (1997). Oxidation and

intergranular cracking behaviour of two high strength Ni base superalloys. Corrosion

Deformation Interaction (EFC 21), edited by T. Magnin, 461-475.

[19]. Molins, R., Hochstetter, G., Chassaigne, J.C. and Andrieu, E. (1997). Oxidation

effects on the fatigue crack growth behaviour of alloy 718 at high temperature. Acta

Materialia, 45(2), 663-674.

[20]. Andrieu, E., Molins, R., Ghonem, H. And Pineau, A. (1992). Intergranular crack tip

oxidation mechanism in a nickel-based superalloy. Materials Science and Engineering: A,

154(1), 21-28.

[21]. Ghonem, H., Zheng, D. (1992). Depth of intergranular oxygen diffusion during

environment-dependent fatigue crack growth in alloy 718. Materials Science and

Engineering: A, 150(2), 151-160.

24

[22]. Ghonem, H. and Zheng, D. (1991). Oxidation-assisted fatigue crack growth behavior

in alloy 718-Part I. Quantitative modeling. Fatigue & Fracture of Engineering Materials &

Structures, 14(7), 749-760.

[23]. Miller, M. P., McDowell, D. L. and Oehmke, R. L. T. (1992). A creep-fatigue-

oxidation microcrack propagation model for thermomechanical fatigue. Journal of

Engineering Materials and Technology. 114, 282-288.

[24]. Krupp, U. (2005). Dynamic embrittlement: time-dependent quasi-brittle

intergranular fracture at high temperatures. International Materials Reviews, 50(2), 83-

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[25]. Krupp, U., Kane, W.M., Laird, C., McMahon Jr., C.J. (2004). Brittle intergranular

fracture of a Ni-base superalloy at high temperatures by dynamic embrittlement.

Materials Science and Engineering A, 13th International Conference on the Strength of

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[26]. Pfaendtner, J.A., McMahon Jr., C.J. (2001). Oxygen-induced intergranular cracking

of a Ni-base alloy at elevated temperatures—an example of dynamic embrittlement. Acta

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base superalloy under fatigue-oxidation conditions. Engineering Fracture Mechanics,

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http://onlinelibrary.wiley.com/doi/10.1111/ffe.1991.14.issue-7/issuetoc

25

CHAPTER 2

LITERATURE REVIEW

26

CHAPTER 2

2.1. INTRODUCTION

Due to their superior mechanical properties at elevated temperature, nickel based superalloy

are favoured for applications in rotating blades and discs in gas turbine engines. It has been

more than 70 years since their initial use as blade materials in aeroengines [1]. Gas turbine

discs are subjected to extremely severe operating conditions during the repeated start-up,

take-off and climb, cruising, landing and shut-down cycles. These include variable centrifugal

and thermal stress as well as the prolonged application of load in the presence of corrosive

exhaust gases at elevated temperature up to 700C. Consequently fatigue, creep and

environmental factors, as well as their interaction, are the major concerns for gas turbine

safety.

Investigation of fatigue [2-4], creep [5, 6] and fatigue-creep interaction [7-11] of nickel alloys

has been carried out using a variety of experimental, analytical and numerical approaches. In

particular, unified constitutive models, with both isotropic and kinematic hardening internal

variables, have been rapidly developed to facilitate the safe life assessment of nickel alloy

discs under creep-fatigue conditions [7-17]. On the other hand, considerable experimental

and modelling work has also been carried out to study the fatigue/creep crack growth in

nickel alloys. It is well known that the time-independent crack growth (also known as cycle-

dependent crack growth or fatigue crack growth) is predominantly transgranular and

depends on load ratio, maximum load and temperature [1, 18-31]. Material microstructure

including grain orientation exerts a strong influence on transgranular crack propagation and

27

the crack growth rate [e.g., 1, 18, 21-25, 32]; While for creep crack growth the principal

mechanisms are void growth and coalescence at grain boundaries under applied stresses. In

this case the fracture morphology is dominantly intergranular [33, 34]. Floreen [35] found

from a variety of nickel-base superalloys that creep crack growth rate is proportional to a

power of the stress intensity factor. Furthermore, the presence of a dwell (i.e., creep

deformation) at maximum load in fatigue cycle was shown to increase crack growth rates.

For example, Wei [36] conducted experiments on nickel-based superalloys in high purity

argon and oxygen at 873-973K, and showed that crack growth rates increased linearly with

increasing dwell time. Nicholas and Weerasooriya [37] showed that not only the dwell load

level played a significant effect on crack growth rate, but also the frequency at which the

dwell was imposed. The R-ratio was also shown to be an influencing factor for dwell time

effects. The effect of dwell periods at higher R-ratio values is greater than that at lower R-

ratio values [38].

These crack growth studies are of particular importance for damage tolerance assessment of

nickel alloy discs. Apart from creep and fatigue, oxidation damage, which is also the focus of

this work, is another crucial factor that contributes to the failure of turbine discs. Oxidation

affects the fracture morphology by inducing a passage from slow transgranular to fast

intergranular fracture [e.g., 39, 40, 41], which might lead to premature failure of turbine

discs. In this chapter, a literature review has been carried out regarding the existing research

work on oxidation damage and oxidation-assisted crack growth in nickel and its alloys.

28

2.2. OXIDATION OF NICKEL AND ITS ALLOYS

In 1936, Smithells and Ransley [42] studied nickel oxidation between 900°C and 1050°C using

thin-wall tubes. Their micrographs appeared to confirm grain-boundary oxygen penetration.

The results demonstrated that oxygen can penetrate large distances into materials by

preferential grain-boundary diffusion. Giggins and Pettit [43] studied the oxidation of Ni-Cr-Al

alloys and suggested that the mechanism of oxidation in these alloys could be divided into

three categories, based on the amount of Cr and Al that they contain, as follows:

Type I: An external layer of NiO is formed, with a subscale of Cr2O3, Al2O3 and /or

Ni(Cr,Al)2O4 when the alloy contain small amounts of Cr and Al.

Type II: An external layer of Cr2O3, with a subscale of Al2O3, when the alloy

contains higher Cr but lower Al.

Type III: The only scale formed is Al2O3 with no signs of internal oxidation when

the alloy contains sufficient Al.

These are rather generic categories for oxidation of nickel alloys, and they give an idea of the

oxide scale formation based on the contents of Cr and Al.

Literature [44-47] agrees that there is a preferential oxidation of the various alloying

elements (Nb, Ti, Al, Cr and Ni) in nickel alloys. The formed oxide layers are usually an

external layer of NiO and Cr2O3, a sub layer of Al2O3 and TiO2 and various carbides (TixNby)C.

Encinas-Oropesa et al. [48] studied the oxidation of a powder metallurgy nickel alloy in air at

700°C, 750°C and 800°C. Energy Dispersive X-ray (EDX) analyses showed a progressive

29

enrichment of Cr and Ti in the oxide scales with increasing time and temperature, coupled

with lower Ni and Co levels. In Geng et al. [45], a study of the surface oxidation behaviour of

Alloy 718 was conducted, by hot extruding and isothermally exposing the alloy at 1100°C.

The oxidation time was varied from 10 to 180h. Three distinct surface layers were observed

depending on the oxidation time. An outside layer of a single phase Nb-rich Cr oxides with

some voids and microcracks was formed after an exposure of 80h. A second layer with a

small amount of discontinuous phase of Al2O3 was observed after 10h, and a third layer with

complicated shapes and carbides, composed of various (TixNby)C with different shapes, was

observed after 40h of exposure.

Chen et al. [44] studied the oxidation of three different alloys, Astroloy, Waspaloy and

Udimet720 (the percentage of Cr for these alloys is less than 20wt %). The alloys were

exposed isothermally in air at a temperature varying between 750-1000°C for up to

1000hours. Oxidation kinetics was determined and scales were analysed by electron

microscopy and X-ray diffraction. Waspaloy showed the lowest weight gain, but the deepest

internal corrosion due to oxidation of the grain-boundary carbides. Energy Dispersive X-ray

Microanalysis (EDX) was used to identify the oxides composition. The major oxides detected

on the external scale were Cr2O3, TiO2 and NiCr2O4 spinel, with NiO occasionally detected

after 20hr at 750°C. Titanium in the alloys also oxidised, diffusing through the chromia

(Cr2O3) scale and formed rutile (TiO2) grains at the surface as well as TiO2 and TiN internally.

Alumina (Al2O3) formed as discrete internal oxides below the chromia scale. The internal

oxides developed predominantly along grain boundaries since they were short-circuit paths

for inward oxygen diffusion.

30

Miller et al. [46] determined the depth of internal oxides at a crack tip for nickel-alloys using

X-ray photoelectron spectroscopy (XPS), and found that the oxygen affected region and the

depth of internal oxides varied according to the alloy. Andrieu et al. [49] suggested two

oxidation mechanisms at a crack tip, namely, short range and long range oxygen diffusion

processes. For short range diffusion, an oxide layer is formed at the crack tip and the

thickness of the oxide layer depends on the operating and material parameters. For long

range diffusion, oxygen can penetrate into the material along grain boundaries and slip

planes. As a result, internal oxidation and cavity formation take place and the oxidation of

various alloying elements results in the release of embrittling agents into the material.

Oxidation is generally quantified by measuring the weight gain of the alloy and the thickness

or depth of oxide scale built on the surface [43-45, 47, 48]. Both can be described using the

parabolic law for either the oxide scale thickness or the weight gain due to oxidation:

where X is the oxide scale thickness or depth, ΔW the mass gain, t the time. The parabolic

oxidation factor follows the Arrhenius law:

where is a constant, Q the activation energy, R universal gas constant and T the

temperature. Materials with low rates of mass gain and growth of oxide scales are more

resistant to oxidation.

31

2.3. DAMAGE CAUSED BY OXIDATION

High temperature exposure in oxygen-containing environments leads to a degradation of the

mechanical properties for nickel alloys, often termed as oxygen embrittlement. Douglass [50]

showed the severe loss in tensile and creep ductility at 600°C following the prior exposure at

1200°C. Chang [51] showed a drastic loss in tensile ductility for a nickel alloy René-80

following air exposure for 150hr at 982°C. He also demonstrated similar effects in two other

nickel base superalloys, René77 and René100. The detrimental effect of prior high

temperature exposure on subsequent stress rupture life and fatigue response has been also

demonstrated for nickel alloys by Woodford [52] and Antolovich et al. [53].

Oxygen embrittlement has been attributed to the penetration of oxygen along the grain

boundaries. Direct evidence of the presence of oxygen on embrittled grain boundaries has

been demonstrated in nickel and its alloys by Auger microscopy [54], as also represented by

intergranular fracture morphology. There are a number of mechanisms by which a boundary

may be embrittled by oxygen penetration. These include oxide formation, cavity formation

and solute segregation. It is also possible for oxygen to take part in chemical reactions

releasing known embrittling agent into a grain boundary. Each or all of these may be

operative in any particular alloy under a given set of conditions.

32

Figure 2. 1: External oxide and internal voids formed in Ni 270 after air exposure at 1000°C

for 200 hours [58].

For instance, the experiments of Woodford and Bricknell [55] showed the presence of small

oxides on nickel grain boundaries. Another consequence of oxygen penetration which has

been studied in nickel is the formation of voids. Such voids have been previously attributed

to vacancy injection from the growing oxides [50, 56 and 57]. While in Bricknell and

Woodford [58, 59], it showed that these voids are in fact gas bubbles as seen in Figure 2.1.

Mrowec et al. [60] studied the oxidation kinetics of pure Ni as well as two binary alloys

composed of Ni-Cr and Ni-Na, respectively. It was shown that the predominant defects in

non stoichiometry Ni oxide are double ionized cation vacancies and electron holes, and the

oxide scale on Ni grows by outward volume diffusion of cations. They also showed that Ni-Cr

alloy has higher oxidation rate, compared to the oxidation rate of pure Ni. Apart from oxides

and void formation, Fournier et al. [61] as well as Reed [62] agreed that oxidised niobium

33

carbides are also responsible for the damage caused in nickel alloys due to their swelling, as

shown in Figure 2.2.

Figure 2. 2: Cracking of sub-surface carbides due to oxidation swelling [62].

In the work of Garat et al. [47], thin tensile specimens of alloy 718 were oxidised under

synthetic air, at 1000°C for different durations, then heat treated according to aeronautical

heat treatment before being tested on a tensile machine at room temperature. Mechanical

tests were performed in order to highlight the influence of the damaged zone upon a global

tensile behaviour. A significant drop in flow stress was seen for oxidised specimens. The

tensile curves suggest that the flow stress generally decreases as the oxidation duration

before mechanical testing increases. The oxide scale and the intergranular oxygen

penetration (a mean depth of about 7μm) were observed on specimen’s cross-sections. The

EDX analysis showed that the external oxide scale is Cr and Ti rich. Close to the oxide-alloy

34

interface Nb enrichment and Cr depletion were observed. The intergranular oxygen

penetration was found to contain Al and O2 as major chemical elements.

It was shown in Garat et al. [47] that the OAZ (oxidation affected zone), consisting of the

oxide scale and the intergranular oxygen penetration, is responsible for initiation of several

types of in-service damaging processes. By assuming that the OAZ is unable to support any

mechanical load, they derived the apparent yield stress from the applied load using the

formula:

where σ is the yield stress, F0, Fi, S0, Si are the corresponding loads and specimen sections

before and after oxidation, e is the thickness, l is the width of the specimen and δe is the

depth affected by oxidation.

Calvarin et al. [63] investigated the interaction between the oxidation mechanism and the

mechanical behaviour of a Ni-20Cr alloy. Tensile tests showed a decrease of ductility with

temperature increase, accompanied by more severe intergranular decohesion. While for

creep tests, the environmental effect only appears at 500°C and beyond this temperature the

behaviour seems to be the same in air and vacuum. The alloy creep resistance is improved in

air at high temperatures and low stresses; on the contrary at high stresses and low

temperatures, the creep behaviour is decreased in air. After creep tests in air, whatever the

temperature is, an external NiO scale systematically developed on the surface substrate. At

500°C-600°C an internal oxidation zone was observed under the oxidised surface. Beyond

35

these temperatures, this zone did not appear but a continuous chromia layer developed at

the oxide-alloy interface. The environmental effect in relation to the oxidation process was

described by two competing mechanisms that explain the effect of an oxide layer on the

mechanical behaviour:

The presence of internal oxides may strengthen the material, which then behaves as

oxide dispersion strengthened alloy with improved creep behaviour [64].

The formation of a scale by outward cationic diffusion towards the external surface of

the substrate (provided that the metal-oxide interface cannot move) might induce

vacancy injection into the alloy, resulting in an increase in the creep rate of the

material.

2.4. EFFECT OF MECHANICAL STRESS ON OXIDATION

In addition, it has been well acknowledged that the mechanical stress can further influence

oxidation and corrosion damage in nickel and its alloys. For instance, Moulin et al. [65]

studied the influence of various mechanical loading (fatigue, creep and creep-fatigue) on

oxygen diffusion during nickel oxidation. It was shown that a relative O enrichment was

observed in the oxide scale under mechanical loading, although with a decrease of oxygen

diffusivity in the oxide scale. In the substrate beneath the oxide scale, the ingress of oxygen

became easier with a constant tensile load (creep) and oxygen diffusion took place along

grain boundaries. The intergranular oxygen diffusion coefficient was increased by a factor of

10 with respect to other samples. A short fatigue period during creep-fatigue decreased the

sensitivity of nickel to intergranular oxygen diffusion.

36

In the work of Berger et al. [66, 67], stress-oxidation of nickel has been studied using a

nuclear microprobe method. The application of a constant load (up to 75MPa) induced

multiple cracks at the surface of oxide scale as well as an increase of oxygen diffusivity by

two orders of magnitude (typically from 10-15cm2/s to around 10-13cm2/s in NiO thermally

grown on nickel monocrystals), although the enhancement of oxygen diffusivity decreased

with the further increase of load level. Zhou et al. [68] investigated the oxidation kinetics and

the growth of oxide scales on pure nickel oxidized under tensile and compressive stress at

973 K. The oxidation kinetics curves gained by thermogravimetric analysis (TGA) indicate that

the oxidation rate of pure nickel was accelerated by the external stress. Compared with the

tensile stress, the effect of compressive stress on the oxidation kinetics was more

pronounced. Surface morphologies examined by scanning electron microscopy (SEM) reveal

that granular oxides formed on the stressed specimen, which increase the short-circuit

diffusion the oxidation [68]. A study of cast nickel superalloy IN100 by Reger and Remy [69]

showed that matrix oxidation was strongly enhanced by fatigue cycling.

Effects of applied tensile stress on the growth kinetics of oxide scales has also been studied

for Ni-20Cr alloys at 600°C and 900°C to understand the simultaneous effect of the

environment and mechanical loading [70]. Applying a tensile load did not modify the oxide

layer nature but oxidation rate was increased due to the increase of oxygen diffusion via fast

diffusion paths generated when the strain was higher than a critical value. Consequently, the

internal oxidation was promoted and the oxide layers were shown to be much thicker than

that formed without any load. At 900°C, for short oxidation time, the spinel oxide layer

(NiCr2O4) was enlarged; while for longer time, the spinel layer progressively disappeared and

37

the excess of oxygen diffusing inwards reacted with Cr to form a thicker Cr2O3 layer.

Mechanical stress was also found to promote internal nitridation of nickel alloy Inconel 718

[71].

2.5. OXIDATION-ASSISTED CRACK GROWTH

2.5.1. TIME-DEPENDENT CRACK GROWTH DUE TO OXIDATION

The service experience of gas turbines involves low cyclic frequencies, often with long hold

times at maximum load (dwells) and temperature, in an aggressive environment. Under such

conditions cyclic crack growth rate is greatly accelerated and the crack length is a function of

both cycle count and period as shown in various studies [21, 40, 41, 46, 61, 72-74]. The

processes that contribute to time dependent crack propagation are thermally activated and

therefore become increasingly important with increasing temperature [73] as illustrated in

Figure 2.3 for crack growth in IN718 [74]. At 400°C the alloy shows pure cycle dependent

crack growth at all frequencies, and air tests give the same propagation rates as vacuum

tests. But with increasing temperature and cycle period, the propagation rates in air become

more time dependent.

In early work, the time dependence was assumed to stem from the nature of creep

deformation at the crack tip and the term creep-fatigue was applied [75, 76]. However, for

nickel-based superalloys, it was demonstrated that the test environment in fact played the

dominant role [77-79], especially oxygen in air [80]. Many studies showed that nickel alloys

are sensitive to oxidation-assisted crack growth mechanisms [21, 39, 40, 41, 46, 61, 72-74,

38

81-87], as shown in Figure 2.4. The loading frequency as well as microstructural effects

appear only in air, and disappear under vacuum [86].

Figure 2. 3: Fatigue crack propagation behaviour in IN718 at ΔK=27.5MPa√m *74+.

Figure 2. 4: Fatigue crack growth rate in air and vacuum at 650°C [87].

39

Experiments show that the process of oxygen embrittlement during fatigue crack

propagation occurs at the crack tip. The role of oxygen is simply to reduce the grain boundary

energy in such a way that the crack growth path becomes intergranular [20, 21, 40, 41, 49,

61, 86-89], as shown in Figure 2.5. Miller et al. [46] concluded that environmentally

enhanced crack growth in IN718 occurs by the stress-enhanced oxygen diffusion ahead of the

crack tip, followed by the oxidation of Ti, Al, Cr and Nb if present at the grain boundaries. The

oxidation of all these elements was considered to affect the environmentally enhanced crack

growth. As mentioned in Section 2.2, oxidation mechanisms can be identified in terms of

oxygen short - and long- range diffusion processes [49, 88].

Figure 2. 5: (A) Intergranular and (B) Transgranular fracture surfaces for crack growth in air

and vacuum for Alloy 718 at 650°C [87].

2.5.2. CRACK TIP EMBRITTLEMENT MECHANISM—SHORT RANGE DIFFUSION

Short-range diffusion refers to the formation of an oxide layer at the crack tip with a depth

that depends on cycle and material parameters. The formation of this layer may cause high

stresses to occur and transmit to the substrate. This mechanism could also result in the

40

formation of wedge-shaped oxide intrusions along the crack front. When these wedges

rupture at the intersection of grain boundaries, accelerated intergranular crack growth may

be observed.

Figure 2. 6: Fatigue crack growth rate as function of oxygen partial pressure [90].

Oxygen partial pressure is an important factor associated with short-range oxygen diffusion

at the crack tip. Molins et al. work [90] showed a sharp transition in fatigue crack growth rate

at an oxygen pressure of 10-1Pa, as can be seen from Figure 2.6. Crack propagation mode is

transgranular with low growth rate when oxygen pressure is below 10-1Pa and becomes

intergranular with accelerated growth rate when oxygen pressure is over 10-1Pa. The results

of Andrieu et al. [91] also confirmed the strong pressure dependence for crack growth.

Between pressures of about 10-1Torr and 10-3Torr, the crack propagation rate dropped by

three orders of magnitude. This is because the pressure of oxygen controls the preferential

formation of particular species of oxides which may either 'shield or contribute' to the crack-

41

tip damage process through the passivation or the enhancement of the oxidation process,

respectively [88].

In particular, Andrieu et al. [49] conducted tests and analyses of oxide formation on

deformed and non-deformed free surfaces of alloy IN718 as a function of O2 partial pressure.

They suggested that the oxidation process starts with the formation of selective oxides of

FeO and NiO and their spinels, once the atmospheric O2 partial pressure is available at the

crack tip. These oxides are porous and thus permit the oxidation process to continue into the

base material. However, over a period of time (equal to or less than the oxide passivation

time), the O2 partial pressure tends to decrease at the oxide-substrate interface, which

provides the required reaction conditions for the formation of a less porous, denser sub-layer

of Cr2O3. This chromium layer, which is known to be thermodynamically stable at high

temperatures, limits the diffusion of oxygen and acts to protect the grain boundary material

from further oxidation. Fatigue crack growth experiments conducted by Ghonem [88]

showed that the delay in the formation of the protective Cr2O3 layer resulted in a higher

crack growth rate.

2.5.3. CRACK TIP EMBRITTLEMENT MECHANISM—LONG RANGE DIFFUSION

Long-range diffusion refers to the penetration of oxygen into the crack-tip material along

rapid diffusion paths, for example slip planes [88] and grain boundaries. This process is

characterised by internal oxide sites, cavity formations and/or solute segregation. Woodford

and Bricknell [80] showed that oxygen could also take part in chemical reactions, thus

releasing embrittlement agents onto a grain boundary. These processes prevent the sliding

and migration of boundaries, and therefore their ability to relieve the build-up of local

42

stresses during deformation is reduced and intergranular cracking is promoted. Either or

both of these oxidation processes could be operative at the same time under any particular

set of conditions. As discussed by Ghonem [88], it is acknowledged that oxidation

mechanisms due to short and long-range diffusion are not completely separable.

2.5.4. INTERACTION BETWEEN CRACK TIP FIELD AND OXIDATION

It is extremely difficult to study micro structurally the interaction of oxygen with the tip of a

propagating crack because of the small scale penetration involved at temperatures of

interest (i.e., 400°C-650°C). This process could occur over distances of just a few atom

spacing in the limit, and also the near-tip stress levels may become uncertain as the material

creeps. Nevertheless, there have been several attempts to examine the oxidation near crack

tip region in detail. For instance, Wei and co-workers [92] have examined the region ahead of

sustained load cracks and showed a correlation between environmental sensitivity and

niobium content for several nickel alloys. However, significant oxygen enhanced cracking was

also seen in a niobium free alloy in their later work [93]. Thus, it remains unclear the role that

niobium plays in the oxidation-embrittlement mechanism near the crack tip. It should be

noted that their work evidenced internal oxidation ahead of the crack tip during oxygen-

enhanced crack growth, with the depth of internal oxides determined using X-ray

photoelectron spectroscopy (XPS) [46, 94 and 95].

Both strain rate and stress and strain fields [18, 19 and 61] within the plastic zone ahead of

the crack tip play a significant role in the mechanism of oxygen-induced intergranular

fracture. Intergranular oxygen diffusion depends on the stress and strain states along the

affected grain boundaries [96-98]. Molins et al. [90] carried out experiments to study the

43

local interaction between oxidation and deformation rate at the crack tip, to identify the

damaging part in a mechanical cycle. It was found that the oxidation effects occurred only

between load ratios of R = 0.3 and R = 0.9, corresponding to the loading and un-loading

threshold. This suggests that the embrittlement process is a dynamic coupling between

oxidation and surface mechanical behaviour and controlled by crack-tip stress states.

Conditions that promote rapid stress relaxation near the crack tip significantly reduce the

extent of environmental damage and result in a decrease in the crack growth rate [65].

Studies have also been attempted to define an effective time tox for the damaging effect of

oxygen penetration to occur in a fatigue cycle, as the loading and unloading parts may play

different roles in the oxygen diffusion process. Molins et al. [90] studied the oxidation

assisted fatigue crack growth in nickel based superalloys by varying oxygen partial pressure

during a loading cycle. They found that oxidation effects occur primarily during the loading

part of the cycle and part (about 10%) of the unloading cycle when the crack tip is in traction.

Consequently, an oxidation sensitive time was proposed by Tong et al. [99] and correlated

reasonably with crack growth data, where only 10% of the unloading duration was used.

Other work proposed that it was half of the tensile part of the cycle [100] or all the loading

part [101]. On the contrary, an experimental attempt to measure tox concluded that, for the

same frequency, varying the ratio of loading and unloading portions of the cycle did not

influence the fatigue crack growth rate of IN718 at 650°C [87]. It was therefore concluded

that, for this alloy under these conditions, the cycle effective oxidation time was equal to the

total time of the cycle. Using this observation, and a derived relationship between K and the

intergranular oxygen diffusion rate, estimates were made of crack growth rates for several

44

test frequencies. Although the comparison is quite good, the range of test is limited and

dwell tests were not included.

2.5.5. CRACK GROWTH PREDICTION MODELS

Life prediction models were proposed through literature on how to characterise crack

growth by introducing an oxidation parameter, which have been mainly based on

phenomenological approaches rather than analytical or theoretical methods. The simplest

model for the effect of oxidation on fatigue involves the addition of an oxidation contribution

to a mechanical increment of crack growth:

where

is the total crack growth rate,

and

are the crack growth rates

contributed by mechanical deformation and oxidation, respectively.

King and Coterill [102] gave the crack growth as a result of oxidation as the time per cycle

multiplied by the average oxidation rate P:

where f is the loading frequency and P the oxidation rate1.

1 The oxidation rate P refers to the growth rate of oxide scale thickness, and can be expressed as P =

, where X

is oxide scale thickness and t is the time. The frequency f is defined as

, where T is the time for one fatigue

cycle.

45

Reuchet and Remy [103] have developed an equation that includes the oxidation in the

fatigue crack growth, which was expressed as:

where is the material constant for the oxidation constant of the material matrix and t the

cycle time.

The oxidation activation energy Q has also been used by many authors to quantify the effect

of oxidation in crack growth. For instance, Gao et al. [104] used Arrhenius relationship to

describe time-dependent crack growth response:

where and m are fatigue crack growth constants, K is the stress intensity factor, R the

universal gas constant and T the absolute temperature. Miller et al. [105] suggested that if

the crack is part of the oxidised material then the crack propagation should be directly

related to the cycle time of oxygen penetration:

where , m and ξ are constants, t is the cycle time and J is the J integral (see Appendix B).

Ghonem and Zheng [87] proposed that, in the environmental-dependent stage, crack growth

increment per cycle is equal to the intergranular oxygen diffusion depth X occurring during

the cycle effective oxidation time tox and expressed the fatigue crack greater as:

46

Where is the rate of intergranular oxygen diffusion depth at the crack tip, as a function of

stress intensity factor range K and time t.

Another interesting model [106] is shown schematically in Figure 2.7. For a given material at

a given K level, there exists a corresponding fatigue crack increment per cycle af which is

caused solely by the fatigue process without environmental effects. For an effective cycle

time period t the damaging species must move with the crack tip to be detrimental. During

this time the intergranular penetration distance is ap which may be increased by increasing

the temperature or reducing the frequency. If af is much greater than ap crack growth is

caused primarily by the fatigue process alone. In this case, da/dN is frequency independent

and given by the limit line of no environmental effect as shown in Figure 2.7. If ap is greater

than or equal to af the environment has its full effect on da/dN. Any further increase in ap

by increasing the temperature or by reducing the frequency will not increase da/dN. This

situation is thus depicted by the limit line of full environmental effect as shown in Figure 2.7.

The crack growth mode changes from transgranular without environmental effects to fully

intergranular with environmental effects. In the region between these two limits the rate

controlling environmental effect becomes important and da/dN is temperature and

frequency dependent. According to some crack growth experimental results on IN100 at

650C, the general applicability of the model appeared very good [106].

47

Figure 2. 7: A schematic of the kinetic model [106].

2.6. DYNAMIC EMBRITTLEMENT MECHANISM

Dynamic embrittlement was introduced to define a time-dependent intergranular brittle

cracking process in which the supply of embrittling elements is due to grain boundary

diffusion into an area of increasing tensile stress ahead of a crack tip [107-112]. The

embrittling element lowers the cohesion of grain boundaries, allowing for crack advance and

shifting crack tip, the stress and the diffusion gradient onward. The case of hydrogen

embrittlement of steels is one of the most important damage mechanisms that fit in the

dynamic embrittlement scheme [113]. Other established dynamic embrittlement cases

include sulphur-induced stress relief cracking in steels [112], S-induced cracking in Cu Cr

48

alloys [114], O-induced cracking in Cu Be alloys [115] and Ni3Al [111], and Sn-induced

cracking in Cu-Sn model alloys [112, 116].

The dynamic embrittlement has also been used to explain the oxidation-accelerated crack

growth in nickel alloy by Pfaendtner and McMahon [107], Krupp et al. [108] and Krupp [109]

in their studies of the intergranular crack propagation in Inconel 718 under four-point

bending. Firstly, the individual grain boundary facets were found to be smooth on the sub-

micrometer level, and oxidation of NbC precipitates was only observed on the fractured

surface where the crack front had passed. Secondly, tests found that the cracking process is

extremely sensitive to rapid changes under oxygen pressure. Crack growth could be stopped

in less than 10s, by alternately pumping oxygen from the chamber and re-admitting it, as

shown in Figure 2.8. Given the fact that oxidation kinetics for nickel alloys at 650°C is

extremely slow [117], there is insufficient time for oxide formation to happen ahead of the

crack tip within the order of seconds. Direct observations of internal oxidation and associated

damage were only available on smooth specimens or fractured surfaces, which have been

exposed to oxidizing environment for a sufficiently long time, mostly greater than 20 hours

[47, 48, 58, 70]. This mechanism seems to suggest that oxygen elements diffuse into the

crack tip along grain boundaries and attack the grain boundaries by themselves, which is

different from the internal oxide formation mechanism as discussed in Section 2.5. Here,

high-level stresses at the crack tip are regarded as the driving force to accelerate the

diffusion of embrittling elements into the crack tip and promote crack propagation by

weakening grain boundary cohesion, i.e., a dynamic process of embrittlement. It was further

shown by Krupp [109] that the character of grain boundaries plays a role in oxidation-

49

assisted crack growth of nickel alloy IN718. For instance, special grain boundaries with a high

fraction of coincident lattice sites exhibit a higher resistance to oxygen attack and reduced

crack growth rate, due to their low oxygen diffusivity, when compared to random high-angle

grain boundaries [109, 118].

Figure 2. 8: At 650°C, cracking in 1atm of oxygen was completely arrested in about 10s, the

time necessary to evacuate the testing chamber below 10-2Pa. Cracking resumed when

oxygen was re-admitted to the chamber [107].

An early model for dynamic embrittlement was developed analytically by Bika and McMahon

[110] to describe quantitatively the experimental results for S-induced stress relief cracking

of steel. They used diffusion differential equations for grain boundary diffusion under the

influence of stress, obtained using a fracture mechanics expression, ahead of the crack tip.

This allowed for a numerical solution that yields the concentration profiles of the embrittling

element ahead of the crack tip. An empirical fracture criterion, which provided a functional

50

connection between the embrittler concentration and the local critical tensile strength, was

proposed to predict the onset location and time of intergranular decohesion. Xu and Bassani

[119] developed a cohesive model for diffusion-controlled fracture. The constitutive

equations for the cohesive zone are coupled with stress-assisted diffusion of impurities into

the grain boundaries. A damage model was used to describe the effect of impurities

concentration on grain boundary strength and fracture.

Computational simulation of oxygen diffusion [108, 109, 120, 121] has been attempted based

on Fick’s first and second laws, where the effect of stress on oxygen diffusion is assumed to

be controlled by the gradient of hydrostatic stress [110, 122-124]. In this case, diffusion of

oxygen within the material is controlled by two essential parameters, namely, the oxygen

diffusivity and the pressure factor [108, 109, 120 and 121]. This approach has been applied to

study the oxygen embrittlement of engineering materials under mechanical loading

conditions, especially for prediction of crack growth under fatigue-oxidation conditions. For

instance, Carranza and Haber [120] presented a numerical investigation, based on finite

element calculation and cohesive interface model, of high temperature intergranular fracture

in nickel base superalloys subjected to oxygen embrittlement. The formulation includes

coupled models for the mechanical response, stress-assisted diffusion of oxygen and a

moving cohesive interface that determines crack initiation, growth and arrest. The cohesive

strength was expressed as a function of the concentration and both the strength and the

work of separation of the cohesive interface are reduced by the presence of oxygen. Zhao et

al. [121] carried out finite element analyses of oxygen diffusion, coupled with viscoplastic

deformation, near a fatigue crack tip for a nickel-based superalloy at elevated temperature.

51

Low frequencies and superimposed hold periods at peak loads significantly enhanced oxygen

concentration near the crack tip. Furthermore, a failure envelop for crack growth was

constructed based on the consideration of both oxygen concentration and accumulated

inelastic strain near the crack tip. Using the fatigue-oxidation failure envelop, crack growth

rates in a CT specimen were predicted for selected loading ranges, frequencies and dwell

periods. The predictions from the fatigue-oxidation failure envelop compared well with the

experimental results, with significant improvements achieved over those predicted from the

viscoplastic model alone [121].

It should be noted that, so far, simulation of stress-driven oxygen diffusion near a crack tip is

largely limited to the continuum level, where the material is treated as homogeneous

medium and no micro-structural details have been considered. In fact, for polycrystalline

nickel and its alloys, oxidation and the associated diffusion of oxygen are primarily along the

grain boundaries [47, 56, 80 and 118], therefore consideration of grain microstructure is

necessary in order to simulate the oxygen diffusion process properly.

2.7. REVIEW OF RESEARCH ON ALLOY RR1000

Alloy RR1000, also the material studied in this work, is one of the latest fine-grained nickel-

based superalloys, developed at Rolls-Royce plc of the UK through a powder metallurgy

process, to meet the increasing demand of mechanical performance for turbine discs in the

latest Trent 1000 Rolls-Royce aero engines. This section provides a review of the research

work carried out on this particular alloy.

52

2.7.1. CRACK GROWTH STUDY

Fatigue and creep behaviour of alloy RR1000 at elevated temperature have been

systematically studied through crack growth testing using compact tension (CT) and corner

notch (CN) specimens. Tong et al. [84] showed that mixed time and cycle dependent crack

growth seems to be the dominant crack growth mode for RR1000 at 650C. Knowles and

Hunt [85] investigated the influence of microstructure and environment on crack growth

behaviour of RR1000 at 725C. Both environment and exposure-induced sigma-phase

precipitation at grain boundaries were shown to increase the crack growth rate through

increased crack tip cavity nucleation, whilst rapid near-tip stress relaxation induced by

coarsening has a beneficial effect on the severity of crack tip cavity damage. For short crack

growth at elevated temperature, Pang and Reed [125] showed that RR1000 demonstrated

superior fatigue performance compared to Udimet 720 and was attributed to the benefit of

stress relaxation due to its alloy chemistry. Most recently, Dalby and Tong [30, 31, 99]

systematically studied the crack growth behaviour for RR1000 at elevated temperature by

considering a range of loading waveforms and frequencies. Accelerated crack growth rates

were observed in specimens tested at low frequencies, long dwell periods or under slow-fast

loading waveform, due to oxidation effects [99].

2.7.2. CYCLIC CONSTITUTIVE BEHAVIOUR

Comprehensive experimental and analytical studies [15-17] have also been carried out

towards a fundamental understanding of time-dependent deformation behaviour using

material constitutive models. Strain-controlled cyclic tests were carried out at 650C for

selected strain ratio, range and rate. A unified Chaboche viscoplastic model [126], with a

53

combined non-linear kinematic and isotropic hardening, was adopted and modified to

describe the time-dependent constitutive behaviour of RR1000 alloy. Model parameters

were determined from an optimisation of the basic monotonic, cyclic and creep experimental

data [15-17]. Model simulations compared very well with the experimental results for a

range of strain-controlled loading cases in terms of stress-strain loops, cyclic hardening

behaviour and stress relaxation behaviour. The cyclic behaviour of the material was also

linked with the evolution of dislocation patterns using TEM observations [127]. This model

was further enhanced by Cornet et al. [128-130] to simulate strain ratchetting and stress

softening by introducing a third kinematic hardening component and a damage variable,

respectively.

Very recently, crystal plasticity model has been developed by Lin et al. [131, 132] to simulate

the cyclic deformation of alloy RR1000 at elevated temperature using finite element and

representative volume element approach. The model simulated well the stress-strain loops,

cyclic hardening behaviour and stress relaxation behaviour, as shown in Figure 2.9. Stress and

strain distributions within the representative volume element were shown to be of

heterogeneous nature due to the orientation mismatch between neighbouring grains, as

shown in Figure 2.10 for the von Mises equivalent strain.

54

Figure 2. 9: Comparison of model simulations and experimental results: (a). Stress-strain

loop at saturation (dε/dt=0.05%/s and Δε=2%) (b). Stress relaxation behaviour during 100-

second dwells at maximum and minimum strain levels (dε/dt=0.5%/s and Δε=2%) *132+.

Figure 2. 10: Contour plot of the von Mises equivalent strain at the maximum strain level of

the 2nd cycle (strain rate dε/dt=0.005%/s, strain range Δε=20%, strain ratio =-1) [132].

(a) (b)

55

2.7.3. MODELLING OF CRACK TIP DEFORMATION AND GROWTH

All the constitutive models, as described above, have been implemented in the finite element

software ABAQUS via a user-defined material subroutine (UMAT), and applied for modelling

of crack tip deformation and crack growth.

Figure 2. 11: (a). The evolution of stress-strain loops over 30 cycles ahead of a stationary

crack tip. (b). The evolution of stress-strain loops registered at an integration point O as the

crack grew towards it [133].

Using the viscoplasticity model, finite element analyses for stationary cracks showed

distinctive strain ratchetting behaviour near the crack tip, leading to progressive

accumulation of tensile strain normal to the crack growth plane [130, 133] (Figure 2.11(a)).

This is also true for time-independent cyclic loading cases [134]. Low frequencies and

superimposed hold periods at peak loads significantly enhanced strain accumulation at crack

tip. Finite element simulation of crack growth was carried out under a constant K-controlled

loading condition, again ratchetting was observed ahead of the crack tip (Figure 2.11(b)),

similar to that for stationary cracks. Further on, a crack growth criterion based on strain-

56

accumulation is proposed where a crack is assumed to grow when the accumulated strain

ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has

been utilised in the prediction of crack growth rates in a CT and CN specimens at selected

loading ranges, frequencies and dwell periods [130, 133], and the predictions were compared

with the experimental results.

In addition, the viscoplasticity-damage model was utilised to investigate the damage

evolution near a crack tip for a Single Edge Notch Tension specimen (SENT), where the

damage accumulation rate with respect to cycles was found to be linear once an inelastic

strain threshold was reached [128, 129]. The damage development seems to be localized to

the crack tip and becomes more significant at lower frequencies and longer dwell periods

[128, 129]. While a crystal plasticity model was applied to study the near-tip deformation of a

transgranular crack, in a compact tension specimen using a submodelling technique [132].

Grain microstructure is shown to have an influence on the von Mises stress distribution near

the crack tip and the grain texture heterogeneity disturbs the well-known butterfly shape

obtained from the viscoplasticity analysis at continuum level. The stress-strain response near

the crack tip, as well as the accumulated shear deformation along slip system, is influenced

by the orientation of the grain at the crack tip, which might dictate the subsequent crack

growth through grains. Individual slip systems near the crack tip tend to have different

amounts of accumulated shear deformation, which was utilised as a criterion to predict the

zigzag crack growth path [132]. Moreover, simulation of creep crack growth in RR1000

showed the creep-brittle nature due to its limited creep deformation [135, 136].

57

2.7.4. OXIDATION WORK

Very recently, oxidation damage of alloy RR1000 has been investigated by Encinas-Oropesa

et al. [48] at temperatures between 700C and 800C. Oxidation kinetics of RR1000 has been

characterized by mass change data from thermogravimetric analyses of small disc samples at

temperatures from 700C to 800C, where the oxide scale rich in Cr and Ti, confirmed from

EDX analyses, has been found to grow in a parabolic dependence with time. On the other

hand, FIB examinations of oxidised samples for RR1000 revealed the appearance of the oxide

scale on the surface and the formation of recrystallised grains and voids beneath the oxide

scales [48], as shown in Figure 2.12. The voids are considered to be the result of the loss of

base alloy elements (e.g., Cr, Ti Ni), which diffuse outwards to the specimen surface to form

the oxide scale. Also voids are mainly located along the grain boundaries which are the

preferential diffusion paths. The oxidation-linked microstructure damage becomes more

significant with the increase of testing temperature. The thickness of oxide scale and the

depth of internal damage, exemplified as voids along grain boundaries, are more than tripled

at 800C when compared to those at 700C. In addition, oxide particles can also be observed

on the surface of those internal micro-voids from the FIB images [48].

58

Figure 2. 12: Focused ion beam image of an oxidised RR1000 surface, exposed to 700°C for

200 hours [48].

Oxidation was also observed in fatigue crack growth by Tong et al. [99] and Figure 2.13 shows

the oxide layers formed on a fracture surface of RR1000 CT specimen during dwell fatigue

tests at 725C [99]. The oxide layer was considered to consist of outer nickel oxides and a

denser chromia layer underneath, and the chromia layer indicates a stage of oxidation

saturation on the alloy. Microscopy examination of crack tip regions in Knowles and Hunt

[85] also revealed oxidation near the crack tip, extending continuously along the grain

boundaries. No evidence of discrete damage was observed, indicating that the operating

environmental damage mechanism is highly localised at the crack-tip region.

59

Figure 2. 13: Oxide layer on the fracture surface during dwell fatigue tests at 725°C [98].

Modelling of oxidation for RR1000 has been first attempted by Zhao [137] using the oxygen

diffusion approach and finite element method, with and without mechanical loading. Grain

microstructures were considered explicitly in the finite element model, where the grain

boundary was taken as the primary path for oxygen diffusion. The diffusion of oxygen,

coupled with crystal plasticity deformation, was controlled by the parabolic oxidation rate,

oxygen diffusivity and pressure factor. It was found that heterogeneous deformation

presented at grain level imposes a great influence on oxygen diffusion at 750C and above,

leading to further penetration of oxygen into the bulk material. In the case of an existing

surface microcrack, oxygen tends to accumulate around the crack tip due to the high stress

level presented near the crack tip, which promotes localized material embrittlement and

rapid crack propagation. However, in Zhao's work [137], no attempt was made to model

60

chemical reaction kinetics, vacancy formation, the transport of other species and effect of

oxygen partial pressure, mechanisms which might also be operative in RR1000 [48].

2.8. CONCLUSIONS

The literature review shows that a large amount of work has been carried out to study the

oxidation damage and oxidation-assisted crack growth in nickel and its alloys. In particular,

the oxygen diffusion approach has been proposed and used to model crack growth under

fatigue-oxidation conditions, and the results are very encouraging. For nickel alloy RR1000,

although oxidation kinetics studies have also been carried out, the influence of fatigue was

not considered. Also, crack growth predictions, based on viscoplastic deformation alone,

showed a great discrepancy with experimental data for low frequencies and long dwell

periods, which was due to the neglect of oxidation effects at high temperature. Existing life

prediction models for fatigue-oxidation crack growth are still highly empirical. These research

gaps led to this PhD programme in which a combined experimental and computational study

has been carried out to investigate the effect of fatigue on oxidation damage and model the

oxidation-assisted crack growth in alloy RR1000.

61

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CHAPTER 3

EXPERIMENTAL WORK

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CHAPTER 3

3.1. INTRODUCTION

Oxidation damage of alloy RR1000 has been investigated by Encinas-Oropesa et al. [1] at

temperatures between 700C and 800C. Oxidation kinetics of RR1000 has been

characterized by mass change data from thermo gravimetric analyses of small disc samples at

temperatures from 700C to 800C, where the oxide scale rich in Cr and Ti has been found to

grow in a parabolic dependence with time. On the other hand, Focused Ion Beam (FIB)

examinations of oxidized samples for RR1000 revealed the appearance of the oxide scale on

the surface and the formation of re-crystallized grains and voids beneath the oxide scales [1].

The oxidation-linked microstructure damage becomes more significant with the increase of

testing temperature. The thickness of oxide scale and the depth of internal damage,

exemplified as voids along grain boundaries, are more than tripled at 800C when compared

to those at 700C. In addition, oxides can also be observed on the surface of those internal

micro-voids from the FIB images [1] as also confirmed in our recent study [2].

However, the work of Encinas-Oropesa et al. [1] was carried out without considering the

influence of mechanical loading such as fatigue, which can have a significant effect on

oxidation and corrosion damage for nickel and its alloys. For instance, Moulin et al. [3]

studied the influence of external mechanical loading on oxygen diffusion during nickel

oxidation. It was shown that relative oxygen enrichment is observed in the oxide scale under

mechanical loading and the ingress of oxygen in the substrate beneath the oxide scale

becomes easier with a constant tensile load (creep). In the work of Berger et al. [4, 5], the

75

application of a constant load induced multiple cracks at the surface of nickel oxide scale as

well as an increase of oxygen diffusivity by two orders of magnitude, although the

enhancement of oxygen diffusivity decreases with the further increase of load level. The

oxidation kinetics curves gained by thermogravimetric analysis (TGA) indicate that the

oxidation rate of pure nickel was accelerated by both tensile and compressive external stress

[6]. A study of cast nickel superalloy IN 100 showed that matrix oxidation was strongly

enhanced by fatigue cycling [7]. Effects of applied tensile stress on the growth kinetics of

oxide scales were also studied for Ni-20Cr alloys [8], where the internal oxidation and the

oxide layers are shown to be much thicker than that formed without load. This was also the

case for internal nitridation of nickel alloy Inconel 718 under mechanical stress [9]. Stress-

enhanced oxidation was also found for other metallic materials such as Cr-Mo steel, where

both oxide layer and penetration of oxide along preferential paths (e.g., cracks, grain

boundaries) increased significantly under strain-controlled low cycle fatigue [10, 11].

The objective of this chapter is to investigate, experimentally, the effects of cyclic stress and

exposure temperature on oxidation damage of alloy RR1000. Waisted specimens were tested

under cyclic loads in laboratory air at three temperatures (700C, 750C and 800C). FIB

microscopic analyses were performed to examine the effects of cyclic stress level on

oxidation damage at three selected surface locations. Measurements were made for the

thickness of surface oxide scale, the depth of internal damage caused by the oxidation

process as well as the combination of the two. Energy dispersive x-ray (EDX) analyses were

also carried out to identify the chemical composition of the oxides and the element

concentration at varying depth from the specimen surface.

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3.2. MATERIAL, SPECIMEN AND EXPERIMENTAL DETAILS

3.2.1. MATERIAL

The alloy under investigation is fine grain RR1000, produced through a powder metallurgy

route by Rolls-Royce for disc rotor applications in the latest aero-engines. The chemical

composition of RR1000 is 18.5Co-15Cr-5Mo-3.6Ti-3Al-2Ta-0.5Hf-0.03C-0.02B-0.06Zr and

balance Ni in weight percentage. The alloy has a two-phase microstructure consisting of γ

matrix and strengthening γ΄precipitates Ni3(Al, Ti, Ta) which are largely responsible for the

elevated temperature strength of the alloy. An average grain size of 4 to 5µm was

determined from an EBSD (Electron Backscatter Diffraction) analysis [12].

3.2.2. SPECIMEN GEOMETRY

Waisted specimens, as shown in Figure 3.1, were provided by Rolls-Royce for fatigue testing

in air at high temperatures. The specimen has a diameter of 4.4mm for the narrowest section

and 18mm for the section at the ends. All specimens have been carefully cleaned before the

fatigue tests by longitudinal and cross-hatch polishing before the fatigue tests. A surface

roughness analysis was performed on the specimen using a Mitutoyo Surface tracer SV-C524

and the arithmetic mean value, Ra, was found to be: 0.788μm.

The waisted specimen was chosen for its gradual variation of the cross sectional area, from a

diameter of 4mm at the middle section to a diameter of 18mm at the ends (Figure 3.1).

Under fatigue loading, this will produce a variable stress level across the specimen length.

This specific geometry allows the investigation of the effect of the cyclic stress on oxidation

damage by carrying out the fatigue test on a single specimen for a given temperature.

77

Figure 3. 1: Waisted specimen geometry and the three positions “A”, “B” and “C” selected

for FIB examinations. Drawing provided by Rolls-Royce Plc. Internal communication.

3.2.3. FATIGUE TESTS

The tests were carried out on a computer controlled Instron 8500 servo-hydraulic machine

with a load cell of ±25kN. The machine has a SF868E furnace mounted which can be heated

up to 1100°C. The temperature was monitored by three K-type thermocouples placed on the

side of the specimen. The temperature has a variation of ±2°C between the thermocouple

calibrator and the digital controller, and a variation of less than ±5°C along the specimen. The

tests were conducted in laboratory air condition with vapour content less than 5ppm.

78

Fatigue tests were carried out at three temperatures: 700°C, 750°C and 800°C, under a

triangular loading waveform. For 700°C and 750°C, a load of 10kN was applied, with a load

ratio of R = 0.1 and a loading frequency f = 0.25Hz. For 800°C, the load was reduced to 8kN,

considering the reduced mechanical properties at such a high temperature, while the load

ratio and loading frequency remain unchanged (R = 0.1 and f = 0.25Hz).

3.2.4. FIB ANALYSES

FIB system was used to cut trenches on the specimen surface to reveal and examine the

nature of the oxidised surface after the fatigue tests. The equipment is an FEI Strata 200xP

FIB with a fine gallium (Ga+) beam. The specimen was mounted onto a special grip and then

placed inside the FIB chamber where vacuum conditions apply (1.6×10-5 mbar for the

platinum strip deposition, 5.9×10-6 mbar for the coarse milling and 3.3×10-6 mbar for the fine

cross sectional milling). An area of interest, with a dimension of 25μm2μm1μm, was

selected and a layer of platinum (Pt) deposition was applied on the selected surface to avoid

both contamination and stray sputter damage during the FIB milling operations (Figure 3.2).

The cutting operation using the Ga+ beam was initially in coarse steps (at a current I =

6600pA), followed by finer steps (at a current I = 1000pA) to produce one flat side to the

trench [1, 2]. FIB images were produced via detected back scattered electrons that resulted

from bombardment of the sample using low power Ga+ ion beam, which scans the flat side of

the trench.

79

Figure 3. 2: Waisted specimen surface, the Pt strip applied to protect the oxide scale and

the first stage of rough milling.

In the present work, two different modes have been used for the FIB imaging, i.e., secondary

ions and secondary electrons. FIB secondary ion images (Figure 3.3(b)) are particularly

sensitive to the presence of oxides and carbides in metallic systems due to the effect of these

elements on the secondary ion yield of the metal, which is ideal to reveal oxides and carbides

as the oxygen or carbon “enhanced yield” increases the brightness of the area. FIB secondary

electron imaging (Figure 3.3(a)) is very effective in revealing the grain orientation and

contrast without having to use chemical or electrolytic etching on the material [13].

80

Figure 3. 3: (a). Secondary electron image (b). Secondary ion image.

FIB has been carried out for all specimens to observe the oxide scale and the associated

damage inside the material under fatigue-oxidation conditions. Three locations on each

specimen, as illustrated by "A", "B", "C" in Figure 3.4, were chosen for the FIB analysis to see

the influence of cyclic stress levels on oxidation damage. Point A is located at the narrowest

section, which has the highest stress level, while points B and C are 15mm and 30mm,

respectively, away from the point A and have reduced stress levels due to the increased

cross-sectional areas.

3.2.5. EDX ANALYSES OF THE OXIDES

Energy dispersive X-ray analyses (EDX) of both surface and internal oxides were carried out in

a Field Emission Gun Scanning Electron Microscope (FEG-SEM). Locations at selected

distances from the oxide scale surface were examined to identify the chemical composition

of the oxides at different depths into the specimen. Concentrations of the detected elements

81

were measured in weight percentage and compared with each other to reveal the nature of

oxidation ingress into the substrate beneath the surface oxide scale.

3.3. RESULTS

3.3.1. STRESS ANALYSIS

Finite element analyses were first carried out to compute the stress concentration factor for

the specimen. A quarter of the specimen was considered due to the geometrical symmetry

and meshed into 8-node axisymmetric elements with full integration [14]. The right and

bottom edges are constrained in the x and y directions, respectively, to remove the rigid

body motion. A distributed load of 39MPa, equivalent to 10kN for concentrated load, was

applied to the top surface of the specimen. Contour plot of the normal stress in the y

direction is shown in Figure 3.4(a), where the highest stress concentration is located in the

narrowest section. The stress concentration factor, defined as the ratio of the normal stress

in the y-direction (yy) to the applied stress (app = 39MPa), was calculated for the specimen

and shown in Figure 3.4(b), against the vertical distance from the narrowest section. The

middle section has a stress concentration factor as high as 17. The stress concentration is

gradually reduced towards the ends of the specimen, which allows the study of the influence

of cyclic stress level on the oxidation damage. The stress concentration factors are 17.1, 8.9

and 2.5 for point A, B and C, respectively. Specifically, under the load of 10kN, the stress level

is 670MPa, 350MPa and 100MPa, i.e., 65%, 34% and 10% of 0.2% proof stress of the material

at 650C, at point A, B and C, respectively (see Table 3.1).

82

Table 3. 1: Stress level at the three positions selected on the waisted specimen under a

10kN load.

Position Stress level (MPa) % of proof stress

A 650 65

B 350 34

C 100 10

83

Figure 3. 4: (a). Contour plot of the normal stress in the y direction for the waisted

specimen under an applied load of 10kN, where d is the distance from the narrowest

section of the specimen (b). Stress concentration factor, defined as the ratio of the normal

stress in the y-direction (σyy) to the applied stress (σapp = 39.0MPa), against the distance

from the narrowest section of the specimen.

A

B

C

84

3.3.2. FATIGUE EXPERIMENTS

At 700°C, the specimen was loaded for 176,763 cycles, approximately 196 hours, and

survived the test duration without failure; while fatigue failure occurred in specimens tested

at 750°C and 800°C, with complete fracture at the narrowest section. The fatigue life is

174,392 cycles (194h) at 750°C and 33,473 cycles (38h) at 800°C, indicating a dramatic

reduction of fatigue resistance at temperatures up to 800°C.

Microscopic examination of the fracture surface is shown in Figure 3.5Error! Reference source

not found.(a), for the specimen tested at 750°C, where fatigue crack seems to initiate from the

surface and propagate through the cross section till the final fracture. The side surface was

also examined and shown in Figure 3.5(b) for the specimen tested at 800°C, which shows

numerous surface cracks near the fracture surface. Observed surface cracks for 800°C

specimen represents the fracture of the surface oxide layer, which was essentially caused by

localized severe deformation near the waisted section as a result of the reduced mechanical

properties at 800°C. Surface cracks, i.e., cracking of oxide layers, were not observed for

specimens tested at 700°C and 750°C due to the less extent of oxidation damage and

mechanical deformation near the waisted section.

85

Figure 3. 5: (a). The fracture surface of the specimen fatigue tested at 750°C. (b). Surface

cracks on the side surface of the specimen fatigue tested at 800°C.

86

3.3.3. FIB EXAMINATIONS

FIB analyses were performed to examine the oxidation damage for the tested specimens and

the secondary electron images taken for position "A" are shown in Figure 3.6(a), Figure 3.7(a)

and Figure 3.8(a) for the three temperatures, all of which reveal the surface oxide scales and

internal micro-voids beneath the oxide scale. At 700°C, the oxidation is limited to the surface

area of the specimen. The oxide nodules on the surface do not appear to be uniform, with

patches of oxidised and un-oxidised areas. The micro-voids are almost invisible. The oxide

scale above the surface has a thickness of up to 0.8μm and the depth of internal damage

(below the surface and into the material) is measured up to 1.0μm. The thickness of oxide

scale was measured as the distance between the identified specimen surface and the surface

of the oxide scale; while the depth of internal damage was measured as the distance

between the identified specimen surface and the very tips of internal damage. The

measurements were based on the FIB projections at the selected positions (see Appendix A),

which will vary if a different FIB position is selected.

At 750°C and 800°C, as shown in Figure 3.7(a) and Figure 3.8(a), the specimens showed more

severe oxidation damage when compared to that at 700°C, with a thicker oxide scale and a

deeper damage into the specimen. At 750°C, the thickness of oxide scale is measured up to

1.6μm from Figure 3.6 (a), almost twice as much as that for the 700°C specimen. The depth

of internal damage measured from the obtained FIB image is up to 2.5μm, which is more

than doubled when compared to that for the 700°C specimen. At 800°C, the thickness of

oxide scale and the depth of internal damage have values up to 1.7μm and 7.0μm,

respectively (Figure 3.6Error! Reference source not found.(a)). There is an increased propensity for

87

voids at higher temperatures of 750°C and 800°C, as shown in Figure 3.7(a) and Figure 3.8(a).

The voids are considered to be the result of the loss of base alloy elements (e.g., Cr, Ti Ni),

which diffuse outwards to the specimen surface to form the oxide scale. Also voids are

mainly located along the grain boundaries which are the preferential diffusion paths.

In addition, internal oxide particles can be clearly seen from the secondary ion images in

Figure 3.6(b), Figure 3.7(b) and Figure 3.8(b), where the bright areas below the specimen

surface indicate the oxides within the material. A comparison with the electron images

(Figure 3.6(a), Figure 3.7(a), and Figure 3.8(a)) suggests that internal oxides tend to follow

the traces of the micro-voids formed beneath the oxide scale. Therefore, in addition to the

outwards diffusion of alloy elements (e.g., Cr, Ti, Ni) to form surface oxides, oxygen also

transports into the material through the porous oxide scale and internal voids along the grain

boundaries, and chemically reacts with the alloy elements to form internal oxide particles,

especially, on the surface of the voids.

88

Figure 3. 6: FIB images for position "A" at 700°C (a) secondary electron and (b) secondary

ion, where the dashed line in red indicates the original specimen surface.

89



90



91

3.3.4. EFFECT OF STRESS LEVEL ON OXIDATION DAMAGE

To examine the effects of cyclic stress level on oxidation damage, FIB images, taken at the

three locations A, B and C, were compared. The same types of oxidation damage were

observed at all three locations, i.e., the oxide scales built on the surface and the internal

micro-voids along the grain boundaries. This can be seen from the FIB images of oxidation

damage presented in Error! Reference source not found. for position B and C at 800°C.

Furthermore, the thickness of surface oxide scale and the depth of internal damage were

measured for the three locations and presented in Error! Reference source not found.(a), (b) and

(c) for 700°C, 750°C and 800°C, respectively. It can be seen that, at 750°C and 800°C, the

cyclic stress has a notable influence on the severity of the oxidation damage. Both the oxide

scale and the depth of internal damage increased with the increase of the stress level. At

800°C, the scale of overall damage at the highest stress area (Point A) nearly doubled that at

the lowest stress area (Point C), with a measured difference of 3.8μm. At 750°C, the scale of

total oxidation damage at Point A is 0.5μm more than that at Point C. However, at 700°C, the

effect of cyclic stress on oxidation damage seems to be less clear, as shown in Error! Reference

source not found.(a). This might be due to the relatively low level of oxidation kinetics at this

temperature [1].

92

Figure 3. 9: (a). Comparison of the thickness of the oxide scale and depth of internal

damage, for positions A, B and C at 700°C. (b). Comparison of thickness of oxide scale and

depth of internal damage for positions A, B and C at 750°C. (c). Comparison of thickness of

oxide scale and depth of internal damage for positions A, B and C at 800°C.

93

3.3.5. COMPOSITION OF OXIDES

Figure 3. 10: Five spectrums selected for EDX analyses, over a depth of 2.2μm from the

oxide scale surface and with equal spacing (0.54μm) between each other.

As shown in Error! Reference source not found.(b), Figure 3.7(b) and Figure 3.8(b), secondary ion

imaging confirms the formation of oxides both on the specimen surface and in the specimen.

For further information, EDX analyses of the trench at position "A" were performed for

specimens tested at 750°C and 800°C to analyse the chemical composition of those oxides at

five different depths from the surface. As shown in Figure 3.10, the five spectrums selected

for EDX analyses spread over a depth of 2.2μm from the oxide scale surface, with equal

spacing (0.54μm) between each other. Specifically, the first spectrum is located at the oxide

scale surface while the fifth spectrum has a depth of 2.2μm into the material. The obtained

element profiles at the five spectrums are shown in Figure 3.11 and Figure 3.12 for 750°C and

800°C, respectively.

94

Figure 3. 11: (a). EDX element profiles showing weight% of Cr, Ni, Ti and Co against the

distance from the oxide scale surface (750°C). (b). EDX element profiles showing weight%

of O, Mo, Al and Ta against the distance from the oxide scale surface (750°C).

Figure 3. 12: (a). EDX element profiles showing weight% of Cr, Ni, Ti and Co against the

distance from the oxide scale surface (800°C). (b). EDX element profiles showing weight%

of O, Mo, Al and Ta against the distance from the oxide scale surface (800°C).

As seen from Figure 3.11(a) and Figure 3.12(a), the surface oxide scale mainly consists of Ni,

Cr, Ti and Co oxides, indicating the formation of Cr2O3, TiO2, NiO and Co3O4 oxides on the

specimen surface, which is consistent with the work of Encinas-Oropesa et al. [1]. The

formation of the Cr2O3 layer indicates a stage of saturation during the oxidation process of

95

the alloy, which may act as a protection from further oxidation. Cr and Ti levels decreased

progressively with the increase of depth, accompanied by the progressive increase of Ni and

Co levels, a result of approaching the base material. The oxides also contain a small

percentage of Mo, Al and Ta, as shown in Figure 3.11(b) and Figure 3.12(b). The level of O

decreases with the increase of depth at 750°C (Figure 3.11(b)), while it seems to remain

steady at 800°C (Figure 3.11(b)) probably due to the presence of multiple surface cracks

which facilitated the penetration of oxygen into the specimen. This suggests the ingress of

oxygen into the material and formation of internal oxide particles, as also evidenced from the

secondary ion images (Figure 3.6(b), Figure 3.7(b) and Figure 3.8(b)). At 800°C, a reduced

percentage of O element was obtained when compared to that at 750°C (see Figure 3.11(b)

and Figure 3.11(b)), which may be due to the lower density of oxides at 800°C caused by the

increased propensity and depth of micro-voids (Figure 3.7(a) and Figure 3.8(a)), as well as the

multiple surface cracks (Figure 3.5(b)) generated under fatigue loading. The patchy presence

of oxide scales for the specimen tested at 700°C made the EDX analyses rather difficult and

inaccurate. Also, the internal damage for the 700°C specimen is too limited to obtain a

meaningful concentration-depth profile and therefore EDX analyses were not carried out for

700°C specimen.

3.4. DISCUSSION

Oxidation damage of alloy RR1000 has been investigated by Encinas-Oropesa et al. [1] for

small disc samples at temperatures between 700C and 800C, in the absence of mechanical

loading. Oxidation kinetics has been characterized by mass change data from

thermogravimetric analyses, where the mass gain has been found to grow in a parabolic

96

function with time. In addition, FIB examinations of oxidised samples revealed the

appearance of the oxide scale, rich in Cr and Ti, on the surface and the formation of

recrystallised grains and micro-voids beneath the oxide scales [1]. Internal oxide particles can

also be observed on the surface of those micro-voids from the FIB images. The thickness of

oxide scale and the depth of internal damage at 800C are more than tripled when compared

to those at 700C. Our results suggest the same types of oxidation damage for alloy RR1000

in the presence of fatigue loading. Fatigue tends to increase the thickness of oxide scale and

depth of internal damage for temperatures at 750°C and above. For instance, at 750°C, the

added measurements of oxide scale and internal damage are 4.1µm, 3.3µm and 3.2µm for

Position A, B and C, respectively, as compared to 2.0µm reported in Encinas-Oropesa et al.

[1]. At 800°C, the oxidation damage becomes much more severe under fatigue loading. The

added measurements of oxide scale and internal damage are 8.7µm, 5.7µm and 4.8µm for

Position A, B and C, respectively, as compared to 3.9µm reported in Encinas-Oropesa et al.

[1]. The considerably increased oxidation damage for position A at 800°C may be due to the

numerous surface cracks formed near the fractured section (Figure 3.5(b)) which act as short

circuits for oxygen penetration. At 700°C, fatigue influence seems to be negligible on the

oxidation damage, at least for the load level considered in the present work. The measured

oxidation damage for the three positions A, B and C is in the range of 1.7µm to 1.9µm, which

is comparable to the measurement of 1.5µm in Encinas-Oropesa et al. [1]. It should be

pointed out that the specimens used in Encinas-Oropesa et al. [1] has a surface finish of

0.25µm, which is different from the 0.79µm surface finish of the waisted specimen tested in

the present work. This might have an influence on the measured oxidation damage.

97

EDX analyses in Encinas-Oropesa et al. [1] were reported for the surface oxides, which show

the enrichment of Cr and Ti as well as low Ni and Co level. This is consistent with the results

in the present work. Similar oxides were also found for other types of nickel superalloys. For

instance, Chen et al. [35] studied the oxidation behaviour for nickel alloys Waspaloy, Astroloy

and Udimet 720 after isothermal exposures at temperature between 750°C and 1,000°C. It

was reported that X-ray diffraction detected Cr2O3, TiO2 and NiCr2O4 oxides on the surface of

the materials [15]. In addition, NiO was also found in Astroloy after a 20 hour exposure at

750°C [15]. Surface oxides for Inconel 718 were reported to consist of Ni or Nb rich Cr2O3 [16,

17]. It was well recognized that the formation of Cr2O3 is largely responsible for the superior

oxidation resistance of nickel-based superalloys.

During oxidation, outwards diffusion of alloy elements (Cr, Ni and Co) leads to the growth of

surface oxides, as well as resulting in the formation of internal voids due to the loss of alloy

elements. The voids seem to locate along the grain boundaries, indicating the primary path

of alloying elements diffusion. Interestingly, internal oxidation was indentified from the

secondary ion imaging (Figure 3.6(b), Figure 3.7(b), Figure 3.8(b)), suggesting the

simultaneous inwards diffusion of oxygen to form internal oxide particles. Penetration of

oxygen was also confirmed by the presence of O element from the EDX analyses at the

selected depths into the material (Figure 3.9 and Figure 3.12). Internal oxide particles are

considered to be a mixture of TiO2 and Al2O3 [2, 16, and 17]. Internal oxidation, especially

along grain boundaries, may lead to critical embrittlement of the material and results in

significantly shortened fatigue life via intergranular fracture process. As shown in Zhao [18],

simulation of internal oxidation can be done from oxygen diffusion analyses based on Fick’s

98

first and second laws. The depth of oxygen penetration and concentration-depth profile can

be predicted from the oxygen diffusion analyses and further utilized to quantify the material

embrittlement caused by internal oxidation process.

Investigation of the effect of mechanical stress on oxidation has significant implications for

the oxidation-accelerated crack growth and failure behaviour. For polycrystalline nickel

superalloys, environmental effects were frequently observed to modify the fracture

morphology from transgranular to intergranular during crack growth, as well as to increase

the crack growth rates significantly for a given stress intensity factor [19-22]. Recently, it has

been acknowledged and evidenced that the strong environmental effect on crack growth of

nickel based superalloy is due to the penetration of oxygen into a crack tip. Under the

influence of a tensile stress, oxygen may move into the grain boundaries by diffusion,

attacking the grain boundaries by themselves or through chemical reactions with alloy

elements. The oxygen diffusion process at a crack tip is a dynamic process, a combined effect

of time, temperature, local deformation and microstructure. Oxygen diffusion may be

facilitated by high tensile stresses near the crack tip [23-26], especially for superimposed

dwell periods at the maximum load where the crack tip is fully open and experiences

sustained high tensile stresses. The work of Zhao et al. [27] showed that crack growth rates in

air at high-temperature can be well predicted from a dynamic embrittlement hypothesis.

For modelling of stress-assisted oxygen diffusion near the crack tip, a coupling between the

oxygen diffusion and the mechanical deformation is generally required to include the effect

of crack tip deformation (stress fields) on oxygen diffusion process [27, 28]. In this case,

diffusion of oxygen within the material is controlled by two essential parameters, namely,

99

the oxygen diffusivity and the pressure factor [27, 28]. So far, no direct measurements are

available for oxygen diffusion parameters in nickel alloys. In fact, the present work measured

the scale of oxidation damage as well as the concentration of O element under varying cyclic

stress levels from the fatigue-oxidation tests on waisted specimens, which are useful in the

determination of the two essential parameters in oxygen diffusion analyses. Some pilot work

has been carried out in Zhao [18], where modelling of oxygen diffusion along grain

boundaries was attempted under creep loading condition based on the coupling of crystal

plasticity with oxygen diffusion. In Chapter 4, finite element simulations are presented for

calibration of the oxygen diffusion parameters based on the modelling of oxygen diffusion

and penetration in waisted specimen under fatigue.

3.5. CONCLUSIONS

Formation of surface oxide scales (Cr, Ti, Ni and Co oxides) and micro-voids beneath the

oxide scales seem to be the major mechanisms for oxidation damage of alloy RR1000 under

fatigue loading conditions. Both surface oxides and internal voids could lead to crack

initiation and subsequent propagation into the substrate under mechanical loading

conditions, resulting in material failure as occurred for the cyclic tests at 750C and 800C.

Cyclic stress influenced oxidation damage at 750C and 800C, and the thickness of oxide

scale and the depth of internal damage were enhanced by the increase of stress level. Both

EDX analyses and secondary ion imaging show the penetration of oxygen into the material to

form internal oxide particles, which leads to further embrittlement of the material.

Measurements of oxidation damage and oxygen concentration have been carried out, and

100

could be utilised to estimate the oxygen diffusivity and the pressure factor which are two

essential parameters for modelling of oxidation damage and prediction of crack growth

under fatigue-oxidation conditions.

101

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104

CHAPTER 4

MICROSCOPY ANALYSES OF FRACTURE

SURFACES IN DWELL CRACK GROWTH

105

CHAPTER 4

4.1. INTRODUCTION

Damage tolerance approaches have been used to evaluate the service life for critical

structural components such as gas turbine discs made of nickel alloys [1]. Such

methodologies require data and predictions for crack growth rates under service loading

conditions. For alloy RR1000, crack growth tests on CT specimens have been carried out at

elevated temperature to investigate the effects of loading frequency, waveform and dwell

time on crack growth [2, 3]. In the frequency domain, the majority of the crack growth rate

data seem to have three distinct regimes, cycle-dependent, time-dependent and the mixed

cycle/time-dependent crack growth [4]. Similar clarifications can also be found in literatures

[5-9]. Time-dependent crack growth is usually observed at low frequencies with

predominantly intergranular cracking while cycle-dependent crack growth occurs at high

frequency with transgranular cracking [4]. Transitional frequencies indicate mixed

cycle/time-dependent crack growth behaviour [4]. Predominantly time-dependent crack

growth may be because of creep or environmental embrittlement due to oxidation [10]. For

alloy RR1000, as creep deformation was found extremely limited within the temperature

range of interest [11, 12], oxidation embrittlement was thought to be the dominant

mechanism for time-dependent crack growth [4].

Crack growth tests, with a dwell period (ranging from 1s to 1000s) imposed at the maximum

load, showed an increased crack growth rate with the increase of the dwell period [2, 3]. For

instance, at 650C, crack growth rate for 1000s dwell is about 20 times that for 1s dwell

106

under K=30MPam and load ratio R = 0.1 (see Figure 6.5 in Chapter 6). Recent tests on

coarse grain RR1000 showed that crack growth rate for 1 hour dwell can be 60 times that

without dwell at 700C [13]. The accelerated crack growth under long dwell has been

attributed to the oxidation embrittlement, i.e., time-dependent crack growth. In this chapter,

scanning electron microscopy (SEM) has been used to examine the fracture surface of CT and

CN specimens tested under selected dwell times, in order to further establish the

mechanisms for crack growth under such conditions. Focussed Ion Beam (FIB) analysis of

fracture surfaces was also performed to examine the oxidation damage during crack growth

under dwell loading conditions. Table 4.1 gives a list of the specimens examined using the

SEM and FIB.

Table 4. 1: Specimens used for SEM and FIB examinations (tested under selected

temperatures and dwell times).

Specimen type Temperature (°C) Dwell time (s)

CT 650 & 725 20, 300, 1000

CN 650, 700 & 750 3600

4.2. MICROSCOPY ANALYSES OF CT SPECIMENS

Standard CT specimens [14], cut from an unused turbine disk of fine grain RR1000

(FGRR1000) supplied by Rolls-Royce plc, were used for dwell fatigue tests at 650C and 725C

by Dalby and Tong [2, 3]. The tests were performed on a servo-hydraulic Instron machine and

crack growth was monitored using a Direct Current Potential Drop (DCPD) method [2, 3]. A

constant K was applied with a load ratio of 0.1 and a base-line frequency of 0.25Hz. During

107

the testing, a dwell period between 20s and 1000s was introduced at the maximum load. The

microscopy analyses of CT specimens [2, 3] were carried out for comparison purposes with

the CN specimens of coarse grain RR1000 (Section 4.3). Figure 4.1 shows a view of the

fracture surface, with indication of crack growth direction and imposed variable dwell time.

As can be seen, the surface within the crack growth area shows varying darkness and

brightness due to the variation of dwell time introduced in the testing. The measured crack

growth rates were shown to increase with the increase of dwell time for both temperatures

[2, 3]. Specifically, at 650C, crack growth rate for 1000s dwell is about 20 times that for 1s

dwell under K=30MPam and load ratio R = 0.1 (see Figure 6.5 in Chapter 6). While at

725C, crack growth rate for 1000s dwell is about 30 times that for 1s dwell under

K=30MPam and load ratio R = 0.1 [2, 3].

Figure 4. 1: Fracture surface of a CT specimen tested at T=650°C for variable dwell times.

108

4.2.1. SEM FRACTOGRAPHY

SEM has been employed to study the fracture modes with respect to the dwell time at both

temperatures and the results are shown in Figures 4.2 and Figure 4.3. The influence of load

level was removed by the K-controlled testing methods such that all micrographs taken

were at a similar stress intensity level. As seen from Figures 4.2 and 4.3, a mixture of

transgranular and intergranular crack growth was observed for all cases, although the

proportion of the transgranular crack growth decreased as the temperature and dwell time

increased. No cavities in the vicinity of the crack tip or grain boundaries were observed in all

cases studied, indicating a lack of creep deformation, consistent with previous experimental

and numerical studies [2, 3, 11, and 12]. Figures 4.2 shows the micrographs of fracture

surfaces of the specimen tested under 20s, 300s and 1000s dwell at 650C. Typical features

of transgranular cracking can be observed at 20s dwell with clearly visible striations,

characteristic of cycle-dependent fatigue crack growth. At 300s dwell, some fatigue striations

are still visible but with a reduced proportion, and a fair amount of intergranular cracking can

be observed. At 1000s dwell, the fracture surface exhibits a predominant intergranular

cracking, although transgranular cracking is still present. The general morphology of the

fracture surface seems to be consistent with the SEM micrographs, with a smooth and flat

surface at 20s dwell as opposed to a much rougher surface at 1000s dwell; while the

roughness of fracture surface at 300s dwell lies in between. It seems that as the dwell time

increased, the proportion of intergranular cracking also increased and became predominant

at 300s dwell and above.

109

Figures 4.3 shows the micrograph of fracture surfaces of the specimen tested under 20s,

300s and 1000s dwell at K = 30MPam and 725C. The fracture mode, as indicated in Figure

4.3, is mainly intergranular for all three dwell times, a direct result of temperature increase.

Some transgranular cracking is still present, but the proportion is reduced with the increase

of dwell time. The surface is generally rougher when compared to those shown in Figure 4.2

for 650C. A closer look also indicates the presence of oxides on fracture surfaces at this

temperature, which is believed to be the main mechanism for intergranular cracking due to

grain boundary, decohesion by oxidation.

Figure 4. 2: SEM micrographs of the fractured surface of a CT specimen tested at 650°C

under (a) 20s, (b) 300s and (c) 1000s dwell.

110

Figure 4. 3: SEM micrographs of the fractured surface of a CT specimen tested at 725°C

under (a) 20s, (b) 300s and (c) 1000s dwell.

4.2.2. FIB EXAMINATION

It is well known that nickel-based alloys are particularly susceptible to oxygen exposure at

intermediate temperatures. Oxide formation may reduce boundary mobility and prompts

crack initiation and growth. The oxide deposits have been observed on fracture surfaces

using SEM examination for all specimens tested at 650C and 725C [2, 4]. To further

examine the oxide morphology, FIB analyses have been carried out here following the same

procedures as described in Chapter 3. The FIB Position at the final crack front, as indicated in

Figure 4.1, was chosen for the FIB analysis. A micrograph of FIB position is shown in Figure

111

4.4, which reveals the severe roughness of the fracture surface. This roughness tended to

spatter the Pt ions on the surface and made FIB analysis very difficult.

Figure 4. 4: Micrograph of the selected FIB location, which also shows the severe surface

roughness.

Figure 4.5 shows the secondary electron image taken for FIB position, which reveals a very

thin and light oxide film built on the surface. Grain microstructure can also be clearly seen

from the picture. For a clearer view of the surface oxides, secondary ion images were also

taken and shown in Figure 4.6. In addition to the surface oxide scale, occasional penetration

of oxides into the material, about 3.6μm, can be seen, and seems to follow the path of a

secondary crack. Overall, the oxide scale is very thin for 650C and generally below 1μm, as

shown by the measurements in Figure 4.6.

Figure 4.7 shows the secondary ion FIB image at 725C, which again reveals the oxide scale

built on the fracture surface. The oxide scale has an increased thickness when compared to

112

that at 650C, and measured to be between 0.7 and 1.6μm, which is consistent with the SEM

examination by Dalby and Tong [2, 4].

Figure 4. 5: The secondary electron image for FIB analysis which reveals a very thin and

light oxide film built on the surface.

113

Figure 4. 6: The secondary ion image for FIB analysis, showing the surface oxide scale and

penetration of oxides into the material along the path of a secondary crack.

Figure 4. 7: The secondary ion image for FIB analysis, which reveals a thicker oxide scale,

built on the fracture surface (Testing temperature at 725°C).

114

4.3. MICROSCOPY ANALYSES OF CN SPECIMENS

Recently, dwell tests as long as 1 hour have been carried out for coarse grain RR1000 alloy in

corner notch (CN) specimens at Portsmouth, as part of the DISPLACE programme [13]. The

specimens were provided by Rolls-Royce plc. Tests were carried out at 650C, 700C and

750C on Single Screw Instron 1362 machine with crack length monitored by a DCPD system

[13]. The tests were carried out under constant load. For 650°C, a load of 31.5kN was applied

and for 700 and 750°C, the applied load was 21.6kN. The fracture surfaces of three tested

specimens are shown in Figures 4.8, 4.9, and 4.10, respectively, with indications of the

testing conditions as well as the three positions chosen for the FIB analyses. Variation of

surface morphologies can be observed, reflecting the variation of testing conditions. Imposed

one-hour dwell leads to severe roughness of the fracture surfaces when compared to those

for pure fatigue tests at both room and elevated temperature.

115

Figure 4. 8: Fractured surface of the CN specimen tested at 650°C, with indications of the

three FIB positions.



116



4.3.1. SEM FRACTOGRAPHY

Figure 4.11 shows the SEM micrographs of fracture surfaces of the specimen tested at 650C,

dominantly transgranular cracking can be observed for room temperature fatigue, with the

presence of fatigue striations which indicate the crack growth path. For one-hour dwell, the

fracture surface clearly exhibits intergranular cracking growth. This is also the case for the

specimen tested at 700°C, as shown in Figure 4.12, i.e., intergranular crack propagation for

one-hour dwell condition and transgranular mode for crack growth at room temperature.

This is consistent with the general morphology of the fracture surface, with a smooth and flat

surface at room temperature fatigue and a much rougher surface at 3600s dwell (Figures 4.8

and 4.9).

117

At 750C, SEM examinations (Figure 4.13) also confirm intergranular fracture for one-hour

dwell and transgranular cracking for room temperature fatigue. While a mixture of

transgranular and intergranular cracking can be seen for 0.25Hz fatigue tests, without dwell,

at 750C, indicating a combined nature of cycle and time dependent crack growth. The

yellow line in Figure 4.13(a) indicates the boundaries of crack growth between 0.25Hz fatigue

and the one-hour dwell at 750C.

Figure 4. 11: SEM pictures of the fractured surface of the CN specimen R134 (a) room

temperature fatigue and (b) 1 hour dwell at 650°C.

Figure 4. 12: SEM pictures of the fractured surface of the CN specimen R134 (a) room

temperature fatigue and (b) 1 hour dwell at 700°C.

118

Figure 4. 13: SEM pictures of the fractured surface of the CN specimen tested at 750°C: (a)

0.25Hz followed by 1 hour dwell and (b) 1 hour dwell.

4.3.2. FIB EXAMINATION

A closer look at SEM pictures, particularly those at 750C (Figure 4.13), shows bright-colour

oxides built on the fracture surface. For further examination, FIB analyses of fracture surfaces

have been carried out for all three specimens. The three selected FIB locations for each

specimen are indicated in Figures 4.8, 4.9 and 4.10, respectively. Position 1 is close to the

free surface while positions 2 and 3 are located in the middle section. More specifically,

Position 2 is located close to the final crack front while Position 3 is at the starting crack front

for the one-hour dwell test. Secondary Galium ion scan was used in the FIB analyses. Figure

4.14 gives a comparison of the FIB images at position 1 for the three temperatures, all

showing the oxide scales built on the fracture surface. The oxide scales have been traced

using colour lines which clearly show the increase of oxide scale thickness with the increase

of temperature. Penetration of oxides into the material is evidenced at 750C; similar results

were also obtained for Positions 2 and 3, as shown in Figures 4.15 and 4.16. There seems no

119

discernible difference in the apparent oxide thickness for the three different positions at a

given temperature.

Figure 4. 14: Secondary Ion images at FIB position 1 for the specimens tested under one-

hour dwell at (a) 650°C, (b) 700°C and (c) 750°C. The colour lines indicate the surface oxide

boundaries.

120


hour dwell at (a) 650°C, (b) 700°C and (c) 750°C. The colour lines indicate the surface oxide

boundaries.

121


hour dwell at (a) 650°C, (b) 700°C and (c) 750°C. The coloured lines indicate the surface

oxide boundaries.

For nickel alloys, an appreciable increase in crack propagation rate in air is generally

observed when static loading periods (dwells) are included in the fatigue cycle [16, 17]. This

increase may be due to oxidation-caused embrittlement in oxygen environment, i.e.,

environmentally enhanced crack growth [18]. This is also the case for crack growth in alloy

RR1000 [2-4]. Nickel alloys are particularly sensitive to oxidation-assisted crack growth

mechanisms [18-20], and the loading frequency as well as micro structural effects appear

122

only in air, and disappear under vacuum [21]. The process of oxidation embrittlement occurs

at the crack tip during fatigue crack propagation. The abrupt change in fracture mode (from

transgranular to intergranular cracking) confirms [22] that the role of oxygen is to reduce the

grain boundary cohesion in such a way that the crack growth path becomes intergranular.

This has also been evidenced from our SEM studies of fracture surfaces, especially for the

long dwell tests.

At the crack front, intergranular diffusion of oxygen takes place, which also depends on the

stress and strain states along the affected grain boundaries [23–25]. Miller [26] showed that

environmentally enhanced crack growth in IN718 occurs by the stress-enhanced oxygen

diffusion ahead of the crack tip, followed by the oxidation of Ti, Al, Cr, as well as Nb if

present. The oxidation of all these elements was considered to affect (either favourably or

otherwise) the environmentally enhanced crack growth. So far, there have been no direct

measurements of oxygen ahead of the crack tip, probably due to very limited level of

oxidation into the crack tip as well as the insufficient resolution of current facilities. For

instance, when oxidation was studied by photo-electron spectroscopy [27], it was found that

the oxide thickness was in the order of the escape depth of photoelectrons. Similarly, in our

work FIB analyses only reveal oxides on the fracture surfaces while oxides ahead of the crack

front could not be seen. However, the rate of oxide formation in the steady state oxygen-

affected area was found to be compatible with the oxygen atom flux at the crack tip [27], an

indirect support for oxygen flux into the crack tip.

As discussed by Ghonem [28], oxygen tends to penetrate the crack-tip material along rapid

diffusion paths, for example, slip planes and grain boundaries, which may be characterised by

123

internal oxide sites, cavity formations and/or solute segregation. Oxygen could also take part

in chemical reactions, thus releasing embrittlement agents onto a grain boundary [29]. These

processes prevent the sliding and migration of boundaries, and reduce the ability of the

material to relieve the build-up of local stresses during deformation. Consequently, grain

boundary cracking, which leads to intergranular cracking, tends to occur. This has been

evidenced from the SEM examinations in the current work, which shows pre-dominant

intergranular cracking with the increased dwell time. Oxygen penetration into the crack tip is

both time and deformation dependent. High-level stress and strain fields [30-33], as well as

strain rates, ahead of the crack tip could play a significant role in the mechanism of oxygen-

induced intergranular fracture. This is especially true for superimposed dwell periods at the

maximum load, where the crack tip is fully open and experiences sustained high tensile

stresses.

Oxygen partial pressure is another important factor which influences oxidation and oxygen

diffusion at the crack tip. The pressure of oxygen controls the preferential formation of

particular species of oxides which may either shield or contribute to the crack-tip damage

process through the passivation or the enhancement of the oxidation process, respectively

[28]. For instance, Andrieu et al. [33] carried out tests and analyses of oxide formation on

deformed and non-deformed free surfaces of large grain sized alloy IN718 as a function of

oxygen partial pressure. The oxidation process starts with the formation of selective oxides

of FeO and NiO and their spinels once the atmospheric oxygen partial pressure is available at

the crack tip. These oxides are porous and thus permit the oxidation process to continue at

the base grain boundary material, hence contributes to the crack-tip damage process. Over a

124

time equal to or less than the oxide passivation time, the oxygen partial pressure tends to

decrease at the interface thereby, providing the required reaction conditions for the

formation of a less porous, denser sub-layer of Cr2O3, which may shield the crack-tip damage

process. These aspects have not been studied in this work.

In addition, the well-known tunnelling phenomenon in crack growth can be clearly observed

for the CN specimens tested under 1 hour dwell (Figures 4.8 to 4.10), i.e., faster crack growth

in the middle section than near the free surface. This has been attributed to the stronger

crack-tip constraint in the middle section, exemplified by higher T-stress level, which

facilitates crack growth by limiting the near-tip plastic deformation [34]. On the other hand,

an oxidation-based rationale has also been proposed to explain the observed tunnelling

phenomenon in crack growth in air, i.e., due to more severe oxidation damage in the middle

section than near the free surface. However, such rationale could not be supported from the

observed oxide accumulation on the fracture surface, as oxides accumulation does not

appear to have a link with the position on the surface, according to our FIB examinations

(Figures 4.14 to 4.16). Further and in-depth investigation is required in order to understand

the true mechanisms for tunnelling crack growth.

4.4. CONCLUSIONS

SEM studies of fracture surfaces of samples tested under dwell conditions have been carried

out, and the results confirmed the transition from transgranular to predominantly

intergranular cracking in alloy RR1000 for increased dwell time. This change in fracture mode

supports the oxidation-assisted crack growth mechanism via grain boundary embrittlement,

125

as creep deformation is very limited for alloy RR1000 [2, 3, 11, 12]. FIB analyses of fracture

surfaces also confirmed the presence of oxidation for alloy RR1000 at the temperatures

studied.

Oxygen penetration into the crack tip, which is both time and deformation dependent, is

believed to be the source for grain boundary embrittlement ahead of the crack tip and

subsequent intergranular crack growth; although experimental evidence of crack tip oxygen

diffusion process and measurements of oxygen concentration near the crack tip are yet to be

available.

126

4.5. REFERENCES

[1]. King, J.E. (1983). Fatigue crack propagation in nickel-base superalloys—effects of

microstructure, load ratio, and temperature. Materials Science and Technology, 3(9), 750-

764.

[2]. Dalby, S. (2005). The effects of frequency and waveshape on the fatigue crack growth of

an advanced nickel based superalloy at elevated temperatures. Ph.D. Thesis. University of





[4]. Tong, J., Dalby, S. and Byrne, J. (2005). Crack growth in a new nickel-based superalloy at

elevated temperature Part III Characterisation. Journal of Materials Science, 40(5), 1237-

1243.

[5]. Branco, C.M. and Byrne, J. (1996). Elevated temperature fatigue of IN718: Effects of

stress ratio and frequency. In: Proceedings of the 81st Meeting of the AGARD/SMP, Thermal

Mechanical Fatigue of Aircraft Engine Materials, Oct 2–4 1995; Banff, Canada (1996) [AGARD

Rep. 669, Paris, France. p. 6-1–6-12].

[6]. Pineau, A. (1984). High Temperature Fatigue: Creep--Fatigue--Oxidation Interactions in

Relation to Microstructure. Subcritical Crack Growth Due to Fatigue, Corrosion and Creep;

Ispra; Italy; 19-23 Oct. 1981, 483-530.

[7]. Nicholas, T., Weerasooriya, T., and Ashbaugh, N.E. (1985). A model for creep/fatigue

interaction in alloy 718. Fracture mechanics, 16th Symposium. American Society for Testing

and Materials, Special Technical Publications, 868; 167-80.

[8]. Weerasooriya, T., and Venkataraman, S. (1987). Frequency and environment effect on

crack growth in Inconel 718. Effects of load and thermal histories. Warrendale (PA):

Metallurgical Society of AIME; 101-8.

[9]. Weerasooriya, T. (1988). Effect of frequency on fatigue crack growth rate of Inconel 718

at high temperature. Fracture mechanics, 19th Symposium American Society for Testing and

Materials, Special Technical Publications, 969; 907-23.

[10]. Tong, J., Dalby, S., Byrne, J., Henderson, M.B. and Hardy, M.C. (2001). Creep, fatigue

and oxidation in crack growth in advanced nickel base superalloys. International Journal of

Fatigue, 23(10), 897-902.

127

[11]. Zhao, L.G. and Tong, J. (2005). Crack growth in a new nickel-based superalloy at

elevated temperature Part II Finite element analysis of crack growth. Journal of Materials

Science, 40(5), 1229-1235.


growth in a nickel base superalloy. Engineering Fracture Mechanics, 68(10), 1157-1170.

[13]. Tong J. (2009-2011) Developing improved service propagation lives in arduous cyclic

environments (DISPLACE). TSB funded project.

[14]. ASTM Standards. (1995). Standard test method for measurement of fatigue crack

growth rates. ASTM E647-95a, 557-593.

[15]. Tong, J., Cornet, C., Lupton, C. and Karabela, A. (2010). Developing improved service

propagation lives in arduous cyclic environment (DISPLACE) project. TSB Project. University of


[16]. Shahinian, P., and Sadananda, K. (1976). Crack growth behavior under creep-fatigue

conditions in alloy 718. Proceedings ASME-MPC Symposium on Creep-Fatigue Interaction,

New York, 365-390.

[17]. Wei, R.P. and Huang, Z. (2002). Influence of dwell time on fatigue crack growth in

nickel-base superalloys. Materials Science and Engineering A, 336(1–2), 209-214.

[18]. Floreen, S., and Kane, R.H. (1979). Effects of environment on high-temperature fatigue

crack growth in a superalloy. Metallurgical and Materials Transactions A, 10(11), 1745-51.

[19]. Shahinian, P., and Achter, M.R. (1957). A comparison of the creep–rupture properties of

nickel in air and in vacuum. Trans. Metall. Soc. AIME, 215, 37-41.

[20]. Sadananda, K. and Shahinian, P. (1983). Creep crack growth behavior of several

structural alloys. Metallurgical and Materials Transactions A, 14(7), 1467-1480.

[21]. Pedron, J.P. and Pineau, A. (1982). Effect of microstructure and environment on crack

growth behaviour in Inconel 718 alloy at 650°C under fatigue, creep, and combined loading.

Materials Science and Engineering, 56, 143-156.

[22]. Osinkolu, G.A., Onofrio, G. and Marchionni, M. (2003). Fatigue crack growth in

polycrystalline IN 718 superalloy. Materials Science and Engineering A, 356(1–2), 425-433.

[23]. Sadananda, K. and Shahinian, P. (1985). Effects of environment on high temperature

crack growth behavior of several nickelbase alloys. Corrosion of nickel-base alloys. Cincinnati

(OH), American Society for Metals, 101-115.

128

[24]. Balsone, S.J., Nicholas, T. and Khobaib, M. (1990). Effects of stress history on the

magnitude of the environmental attack in Rene 80. Environmentally assisted cracking:

Science and Engineering, ASTM STP 1049, Special Technical Publications, 303-318.

[25]. Coffin, Jr. L.E. (1963). Cyclic-strain-induced oxidation of high temperature alloys. Trans.

Am. Soc. Met. , 56, 339-344.


oxygen enhanced crack growth in P/M Ni-based superalloys. Scripta Materialia, 48(1), 103-

108.

[27]. Gao, M., Dwyer, D.J. and Wei, R.P. (1995). Niobium enrichment and environmental

enhancement of creep crack growth in nickel-base superalloys. Scripta Metallurgica et

Materialia, 32(8), 1169-1174.

[28]. Ghonem, H., Nicholas, T. and Pineau, A. (1993). Elevated temperature fatigue crack

growth in alloy 718—Part II: Effects of environmental and material variables. Fatigue &

Fracture of Engineering Materials & Structures, 16(6), 577-590.

[29]. Woodford, D.A. and Bricknell, R.H. (1983). Environmental embrittlement of high

temperature alloys by oxygen. Treatise on Materials Science and Technology, 25, 157-199.

[30]. Clavel M. and Pineau, A. (1978). Frequency and wave-form effects on the fatigue crack

growth behaviour of alloy 718 at 298 K and 823 K. Metallurgical and Materials Transactions

A, 9(4), 471-480.

[31]. Andersson, H. and Persson, C. (2001). Crack growth in IN718 at high temperature.


[32]. Fournier, L., Delafosse, D. and Magnin, T. (2001). Oxidation induced intergranular

cracking and Portevin-Le Chatelier effect in nickel base superalloy 718. Materials Science and

Engineering: A, 316(1), 166-173.

[33]. Andrieu, E., Molins, R., Ghonem, H. And Pineau, A. (1992). Intergranular crack tip


154(1), 21-28.

[34]. Zhao, L.G., Tong, J. and Byrne, J. (2001). Stress intensity factor K and the elastic T-stress

for corner cracks. International Journal of Fracture, 109(2), 209-225.

129

CHAPTER 5

MODELLING OF FATIGUE-ASSISTED

OXYGEN DIFFUSION AT GRAIN LEVEL

130

CHAPTER 5

5.1. INTRODUCTION

Stress-assisted oxidation has been confirmed for RR1000 in the fatigue-oxidation study in

Chapter 3, where penetration of oxygen and associated internal oxidation are facilitated by

the influence of fatigue from a temperature of 750°C and above. A diffusion approach can be

used to model oxygen penetration and associated internal oxidation damage of the material

at high temperatures. Generally, computational simulation of oxygen diffusion [1-4] are

based on Fick’s first and second laws, where the effect of stress on oxygen diffusion is

assumed to be controlled by the gradient of hydrostatic stress [5-8]. In this case, diffusion of

oxygen within the material is controlled by two essential parameters, namely, the oxygen

diffusivity and the pressure factor [1-4]. This approach has been applied to study the

hydrogen and oxygen embrittlement of engineering materials under mechanical loading

conditions, especially for prediction of crack growth under fatigue-oxidation [3, 4].

Very recently, simulation of stress-driven oxygen diffusion for RR1000 has been carried out at

grain level, where the material micro-structure was explicitly considered [9]. The

heterogeneous deformation at grain level, caused by the orientation mismatch between

neighbouring grains, introduces a large local stress gradient and was shown to have

significant influence on the oxygen diffusion process along the grain boundaries [9].

However, the diffusion parameters used in [9] were estimated from the surface oxide scale

growth, rather than the depth of internal oxidation.

131

The objective of this chapter is to model the oxygen diffusion process for alloy RR1000 at

grain level, aiming to quantify the oxidation damage and, more importantly, to calibrate the

diffusion parameters based on the internal oxygen penetration. Finite element method has

been used to simulate the diffusion process for a waisted specimen, where the grain

boundaries were taken as the primary path for oxygen diffusion and subsequent internal

oxidation. Both the natural and the fatigue-influenced diffusion processes were modelled. A

sequentially coupled mechanical-diffusion analysis was adopted to account for the effects of

deformation on diffusion during fatigue loading with the assistance of a finite element

submodelling technique. Diffusion parameters have been obtained by matching the

simulated results with FIB measurements of internal oxidation depth in Chapter 3.

5.2. MODELLING OF OXYGEN DIFFUSION

5.2.1. GOVERNING EQUATIONS

Under applied stress, the oxygen transport inside the material can be modelled as [5-7]:

where C is the concentration of the solute, t the time, the gradient, D the oxygen

diffusivity, P the hydrostatic stress (pressure) and M the pressure factor. The constitutive

law shown in Equation (5.1) has been used to account for the influence of mechanical stress

on mass transport [1-8, 10, 11]. The gradient of hydrostatic stress has been regarded as the

driving force for stress assisted diffusion. In the absence of M ( M = 0 ) the constitutive law

will be reduced to natural diffusion. As shown in Suo et al. [12] and El Kadiri et al. [13],

132

oxidation, by itself, can generate growth stresses, which have been neglected in this work for

simplification.

5.2.2. OXYGEN FLUX BOUNDARY CONDITIONS

The boundary condition for oxygen diffusion from the surface into the material follows the

parabolic law, which can be determined from the oxidation kinetics study. The oxidation

kinetics of RR1000 have been studied in [14] for temperatures between 700C to 800C. The

mass gain due to oxidation is a parabolic function of time and can be expressed as:

Δ

where Δ is the mass gain, the parabolic oxidation rate and the time.

The flux of oxygen into the material at the surface can be derived by performing

differentiation with respect to time for equation (5.2), which gives:

Equation (5.3) has been applied as flux boundary condition in the diffusion analyses, where

the value of is given in Encinas-Oropesa et al. [14] for RR1000.

5.2.3. CRYSTAL PLASTICITY

The crystal plasticity theory was used to describe the material deformation at grain level. The

flow rule is expressed in terms of, slip resistance and back stress [15].

133

where, k is the Boltzmann constant, the resolved shear stress on the slipped system ,

the absolute temperature, and are the shear moduli at and 0 Kelvin, respectively, and

, , , and are material constants.

The two internal variables, the slip resistance in each slip system and back stress , are

introduced at the slip system level, which represent the state associated with the current

dislocation network and can be expressed as [16]:

and

where and are hardening constants and and describe the dynamic recovery

behaviour.

Equation (5.5) describes the grain interior deformation without taking into account the grain

boundary deformation, as our simulation is focussed on the effects of heterogeneous stress

(caused by the mismatched mechanical behaviour of the individual grains) on oxygen

diffusion. This is believed to be a major source of stress gradient generated across the grain

boundaries and also the driving force for stress assisted diffusion.

5.2.4. MODEL PARAMETERS AND UMAT

Crystal plasticity formulation was implemented numerically into the finite element code

ABAQUS [17] via a user-defined material subroutine (UMAT), where the fully implicit (Euler

backward) integration algorithm was adopted [18, 19]. Values of the model parameters were

fitted from the uniaxial experimental data of alloy RR1000 at 650°C [20, 21], which give a

very good simulation of the material’s constitutive behaviour tested for a wide range of

strain-controlled loading conditions [22, 23].

134

5.2.5. FINITE ELEMENT MODEL

For natural diffusion analyses, an FE model consists of 150 grains (Voronoi tessellation, with

randomly assigned orientation), as shown in Figure 5.1(a) and (c), was created and meshed

into 1,450 four-node first-order elements with full integration using ABAQUS [17]. The

element size is about 1μm, quarter of the average grain size (4 to 5μm) of the material.

Specifically, each grain has about 20 to 30 finite elements. A local stress-strain study has

been carried out in the recent work [22, 23] and the results verified the convergence of the

mesh density. Grain boundaries have been meshed into one-dimensional diffusion elements

[17], which share the same nodes with the bulk elements. On the right edge, the oxygen flux

boundary condition, as given by Equation (5.3), was applied to each node to represent the

surface oxidation process.

To study the effects of mechanical stress on oxygen diffusion, a quarter of the waisted

specimen geometry was considered under fatigue loading condition and the finite element

mesh for the global model, as shown in Figure 5.1(b), consists of first-order elements with full

integration [17]. The sub model is the same as that used for natural diffusion in Figure 5.1(a).

To solve the fatigue-oxidation problem, a sequentially coupled mechanical-diffusion analysis

was performed to include the dependence of oxygen diffusion on the stress state. The

mechanical analyses for the global model and sub-model were carried out first, with the

history of hydrostatic stress for each node stored in the ABAQUS [17] output files. Crystal

plasticity model has been used for the sub-model FE analyses, while elasticity has been used

for the global model analyses as the applied load is below the yield level as described in

135

Chapter 3. During the diffusion analysis, the output files were then used as inputs to include

the effect of hydrostatic stress gradient on oxygen diffusion.

Oxygen diffusion was assumed to occur along the grain boundaries only, as for polycrystalline

nickel and its alloys; oxidation and the associated diffusion of oxygen are primarily along the

grain boundaries. Oxygen diffusion in bulk material was excluded in the diffusion analyses by

assigning negligible diffusivity to the bulk elements.

Figure 5. 1: (a) The 150-grain submodel with random orientation (b) Finite element mesh

for the global model and (c) Inverse pole figure for the 150 grains.

136

5.3. RESULTS AND DISCUSSION

5.3.1. NATURAL DIFFUSION

Modelling of natural diffusion of oxygen has been carried out first, where the oxygen

diffusivity was calculated using the depth of oxygen penetration measured in Chapter 3. The

diffusivity (or diffusion coefficient) was calculated based on [24]:

where is the diffusivity, is the depth of internal oxidation measured from the FIB analysis

in Chapter 3 (position C for the waisted specimen) and is the time. The obtained values for

700C, 750C and 800C are given in Table 5.1, where the value for 650C has been fitted

using an Arrhenius equation (

, with D0 = 205.504mm2/s, Q = 270 kJ/mol and R

= 8.314J/(Kmol)).

Table 5. 1: Oxygen diffusivity at four different temperatures.

T (°C) D(mm2/s)

650 1.085E-13

700 1.397E-12

750 5.859E-12

800 1.423E-11

137

Figure 5. 2: For 650°C the diffusion value has been determined using the Arrhenius

equation and the experimental values obtained for 700, 750 and 800°C, as shown on the

graph.

The contour plot of oxygen concentration for temperatures 650C and 800C are shown in

Figure 5.3 after 200 hours of oxidation, where grain boundaries in red colour show the

penetration of oxygen into the material. It is seen that, for 800C, the depth (10.135µm) of

oxygen penetration along grain boundary is about four times that (2.753µm) for 650C due

to the significantly increased oxygen diffusivity at 800°C (Table 5.1).

0

0.5x10-11

1.0x10-11

1.5x10-11

960 1020

eqn: y=a*exp(-270000/(8.314472*x)), R:1.88e-012,a=205.504

Temperature (K)

Diffu

sio

n (

mm

2/s

)

138

Figure 5. 3: Contour plots of oxygen concentration along the grain boundaries for natural

diffusion: (a) 650°C and (b) 800°C.

139

Results in Figure 5.4 show the predicted oxygen concentration against the distance from the

surface after 200 hours of oxidation at four different temperatures. For 650C and 700C,

oxygen penetration is very limited, about 1 to 3μm, with very low values of oxygen

concentration as well. Severe oxygen penetration can be seen for 750C and 800C,

accompanied by high values of oxygen concentration. The depth of oxygen penetration along

grain boundaries is about 6.0μm for 750C and 10.0μm for 800C, indicating a strong

dependency of oxidation on temperature.

In the absence of mechanical stress, oxygen diffusion purely depends on the temperature,

which is consistent with the experimental study of oxidation of alloy RR1000 [14]. The

oxidation damage of alloy RR1000 has been investigated by Encinas-Oropesa et al. [14] at

temperatures between 700C and 800C. Oxidation kinetics of RR1000 has been

characterized by mass change data from thermogravimetric analyses of small disc samples at

temperatures from 700C to 800C, where the oxide scale rich in Cr and Ti have been found

to grow in a parabolic dependence with time. Mass gain increased significantly with the

increase of temperature. On the other hand, Focused Ion Beam (FIB) examinations of

oxidized samples for RR1000 revealed the appearance of the oxide scale on the surface and

the formation of recrystallised small grain and large voids beneath the oxide scales [14]. The

oxidation-linked microstructure damage becomes more significant with the increase of the

testing temperature. The thickness of oxide scale and the depth of internal damage at 800C

are more than tripled when compared to those at 700C. Internal oxides can also be

observed on the surface of those voids from the FIB images [14]. However, in the present

140

work, no attempt was made to model chemical reaction kinetics, vacancy formation or the

transport of other species [14]. Further work is required to address these issues.

Figure 5. 4: Oxygen concentration against the distance from the specimen surface for four

different temperatures.

5.3.2. EFFECT OF MECHANICAL STRESS ON OXYGEN DIFFUSION

To study the effects of mechanical stress on oxygen penetration, finite element analyses of

the global model and sub-model were first carried out for 800C under fatigue loading

condition using elasticity and crystal plasticity material model, respectively. Figure 5.5 shows

the contour plot of the hydrostatic stress for the sub-model loaded for 33473 cycles at an

applied load of 8kN (f = 0.25Hz and R = 0.1). Heterogeneous stress distributions can be clearly

observed and the maximum value of the local hydrostatic stress (~328MPa) is about twice

0

0.2

0.4

0.6

0.8

1

1.2

0 0.002 0.004 0.006 0.008 0.01

Co

nce

ntr

atio

n (

mg/

mm

3)

Distance from specimen surface (mm)

T=650°C

T=700°C

T=750°C

T=800°C

141

the global hydrostatic stress (~181MPa). A closer inspection shows that most stress

concentrations are located at the triple or multiple points along grain boundaries due to the

mismatch of the mechanical properties of multiple grains.

Figure 5. 5: Contour plot of the hydrostatic stress (peak load level) for the submodel after

33473 cycles at 800°C for an applied load of 8kN.

Following the mechanical deformation analyses, diffusion analyses was carried out for a

chosen pressure factor of 0.3MPa-1, where the stress-driven oxygen diffusion was accounted

for through Equation (5.1). A contour plot of the oxygen concentration is shown in Figure

5.6(b) for 800C, where fatigue loading tends to induce a non-uniform distribution of oxygen

concentration along the grain boundaries when compared to the case for natural diffusion

(Figure 5.6(a)). As illustrated in Figure 5.6(b), the maximum depth of oxygen penetration into

the material is found to be = 7.313μm, which is twice more than that for natural diffusion

(0 = 3.207μm).

Grain

142

Figure 5. 6: Contour plot of the oxygen concentration in the submodel at 800°C after 33473

cycles: (a) natural diffusion and (b) with a pressure factor of 0.3MPa-1.

5.3.3. DETERMINATION OF PRESSURE FACTOR

According to Equation (5.1), two parameters (diffusivity and pressure factor) are essentially

required to model fatigue-assisted oxygen diffusion. Diffusivity has been calculated from the

143

FIB measurements of depth of internal oxidation and given in Table 5.1. To work out the

pressure factor, FE analyses have been carried out to obtain the depth of oxygen penetration

for different pressure factor values, and the results are shown Figures 5.7 and 5.8 for 750°C

and 800°C, respectively. For both temperatures, the oxygen penetration depth () is

normalised against that (0) for natural diffusion.

Figure 5. 7: Depth of oxygen penetration against the pressure factor for T=750°C, where the

penetration depth (δ) under fatigue is normalized against that (δ0) for natural diffusion.

At 750°C, the penetration depth of oxygen follows a linear trend with the increase of the

pressure factor (Figure 5.7). While, at 800°C, the penetration depth of oxygen has a linear

trend for pressure factor up to a value of 0.17MPa-1, then followed by a sudden increase

(Figure 5.8). According to the FIB measurements in Chapter 3, oxygen penetration depth has

a normalised value (δ/δ0) of 1.209 for 750C and 2.012 for 800C, which corresponds to a

0.95

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11

δ/δ

0 (

μm

)

Pressure factor (MPa-1)

Pressure factor = 0.068MPa-1

δ/δ0=1.209 (FIB measurement)

144

pressure factor value of 0.068MPa-1 and 0.188MPa-1 for 750C and 800C respectively, as

indicated in Figure 5.7 and Figure 5.8.

Figure 5. 8: Depth of oxygen penetration against the pressure factor for T=800°C, where the

penetration depth (δ) under fatigue is normalized against that (δ0) for natural diffusion.

The obtained values for 750C and 800C are given in Table 5.2, where the values for 650C

and 700C have been fitted using an Arrhenius equation (

, with

, Q = 270 kJ/mol and R = 8.314J/(Kmol)).

Table 5. 2: Oxygen pressure factor at four different temperatures.

T (°C) Pressure Factor (MPa-1)

650 0.001558

700 0.0098

750 0.068

800 0.188

0.9

1.15

1.4

1.65

1.9

2.15

2.4

0 0.05 0.1 0.15 0.2 0.25 0.3

δ/δ

0 (

μm

)

Pressure factor (MPa-1)

Pressure factor = 0.188MPa-1

δ/δ0=2.012 (FIB measurement)

145

5.4. CONCLUSION

Finite element analyses of oxygen diffusion along grain boundaries have been carried out for

a waisted specimen using a submodelling technique. Oxygen diffusivity was calculated from

the FIB measurements of depth of internal oxidation in Chapter 3. For natural diffusion,

oxygen penetration and concentration along grain boundaries are controlled by the

diffusivity, which is temperature dependent. The higher is the temperature, the deeper is the

oxygen penetration. Penetration of oxygen is facilitated by the presence of fatigue for both

750°C and 800°C, and the simulation results have been used to obtain the pressure factor

which has been further used to model the oxidation-accelerated fatigue crack growth in

Chapter 6.

146

5.5. REFERENCES





fracture at high temperatures. International materials reviews, 50(2), 83-97.

[3]. Carranza, F.L., Haber, R.B. (1998). A numerical study of intergranular fracture and oxygen

embrittlement in an elastic-viscoplastic solid. Journal of the Mechanics and Physics of Solids,

47(1), 27-58.

[4]. Zhao, L.G., Tong, J. and Hardy, M.C. (2010). Prediction of crack growth in a nickel-based


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[5]. Li, J.C.M., Oriani, R.A. and Darken, L.S. (1966). The thermodynamics of stressed solids. Z.

Phys. Chem. Neue Folge, 49, 271-290.

[6]. Larchè, F.C., and Cahn, J.W. (1982). The effect of self-stress on diffusion in solids. Acta

Metallurgica, 30(10), 1835-1845.

[7]. Stephenson, G.Brian. (1988). Deformation during interdiffusion. Acta Metallurgica,

36(10), 2663-2683.

[8]. Bika, D. and McMahon Jr, C.J. (1995). A model for dynamic embrittlement. Acta

Metallurgica et Materialia, 43(5), 1909-1916.

[9]. Zhao, L.G. (2011). Modelling of oxygen diffusion along grain boundaries in a nickel-based

superalloy. ASME Journal of Engineering Materials and Technology, 133(3), 031002.

[10]. Sofronis, P. and Mc Meeking, R.M. (1989). Numerical analysis of hydrogen transport

near a blunting crack tip. Journal of the Mechanics and Physics of Solids, 37(3), 317-350.

[11]. Yokobori Jr., A.T., Chinda, Y., Nemoto, T., Satoh, K. and Yamada, T. (2002). The

characteristics of hydrogen diffusion and concentration around a crack tip concerned with

hydrogen embrittlementnext term. Corrosion Science, 44(3), 407-424.

[12]. Suo, Z., Kubair, D.V., Evans, A.G., Clarke, D.R. and Tolpygo, V.K. (2003). Stresses

induced in alloys by selective oxidation. Acta Materialia, 51, 959-974.

147

[13]. El Kadiri, H., Horstemeyer, M.F. and Bammann, D.J. (2008). A theory of stress-driven

interfacial damage upon cationic-selective oxidation of alloys. Journal of the Mechanics and

Physics of Solids, 56, 3392-3415.




[15]. Busso, E.P. (1990). Cyclic deformation of monocrystalline nickel alluminide and high

temperature coatings. (Ph.D. Thesis )Department of Mechanical Engineering, Massachusetts

Institute of Technology. Cambridge, MA, USA.

[16]. Denis, R.J. (2000). Mechanistic modelling of deformation and void growth behaviour in

superalloy single crystals. (PhD Thesis). Imperial College London. London, UK.

[17]. ABAQUS, 2009, Version 6.8, Dassault Systemes Simulia Corp., Providence, USA.

[18]. Busso, E.P., Meissonnier, F.T. and O'Dowd, N.P. (2000). Gradient-dependent

deformation of two-phase single crystals. Journal of the Mechanics and Physics of Solids,

48(11), 2333-2361.

[19]. Meissonnier, F.Y., Busso, E.P. and O'Dowd, N.P. (2001). Finite element implementation

of a generalised non-local rate-dependent crystallographic formulation for finite strains.

International Journal of Plasticity, 17(4), 601-640.

[20]. Zhan, Z.L. (2004). A study of cyclic plasticity and viscoplasticity in a new nickel-based


Portsmouth, U.K.

[21]. Zhan, Z.L., Tong J. (2007a). A study of cyclic plasticity and viscoplasticity in a new nickel-

based superalloy using unified constitutive equations. Part I: evaluation and determination of

material parameters. Mechanics of Materials, 39, 64-72.

[22]. Lin, B., Zhao, L.G., Tong, J. and Christ, H.-J. (2010). Crystal plasticity modeling of cyclic

deformation for a polycrystalline nickel based superalloy at high temperature. Materials

Science and Engineering: A, 527(15), 3581-3587.

[23]. Lin, B., Zhao, L.G. and Tong, J. (2011). A crystal plasticity study of cyclic constitutive

behaviour, crack-tip deformation and crack-growth path for a polycrystalline nickel-based

superalloy. Engineering Fracture Mechanics, 78(10), 2174-2192.

148

[24]. Azari, Z., Abbadi, M., Moustabchir, H., Lebienvenu, M. (2008). The influence of fatigue

cycling on the oxidation kinetics and crack initiation of a Cr-Mo steel. International Journal of

Fatigue, 30(3), 517-527.

149

CHAPTER 6

MODELLING OF CRACK GROWTH UNDER

FATIGUE-OXIDATION CONDITION

150

CHAPTER 6

6.1. INTRODUCTION

For nickel alloys, it was experimentally observed that oxidation modifies the fracture

morphology from transgranular to intergranular during crack growth, as well as increases the

growth rates significantly at a given stress intensity factor [1-4]. The effect of oxidation on

crack growth becomes more pronounced at low frequencies and long dwell periods.

Recently, it has been acknowledged [5-7] that oxidation-assisted crack propagation in nickel

alloys is a result of oxygen diffusion into a local area with increasing tensile stress, such as

crack tips. The oxygen element attacks the grain boundaries by lowering boundary cohesion

and prompts accelerated intergranular cracking [5-7]. The diffusion process is facilitated by

high tensile stresses near the crack tip [8, 9] especially for superimposed dwell periods at the

maximum load where the crack tip is fully open and experiences sustained high tensile

stresses.

Modelling of oxygen diffusion coupled with viscoplasticity has been developed to study

oxidation-assisted crack growth for alloy RR1000 [10]. A failure envelope, expressed in terms

of oxygen concentration and accumulated inelastic strain, has been constructed and utilised

to predict crack growth rates in a CT specimen under fatigue-oxidation conditions. The

predictions were evaluated against the experimental results for triangular and dwell loading

waveforms, with marked improvements achieved over those predicted from the mechanical

deformation alone, i.e., neglecting the influence of oxidation [10]. However, one major

limitation of the work is the use of assumed values of the two essential diffusion parameters,

151

namely the oxygen diffusivity and pressure factor, required in the modelling of oxygen

diffusion near the crack tip.

The objective of this work is to further investigate the process of oxygen diffusion into a

crack tip and its subsequent effects on crack growth, using the newly obtained diffusion

parameters in Chapter 5. Finite element analyses of a compact tension (CT) specimen were

carried out to model crack-tip oxygen diffusion, and more importantly, construct a failure

curve for crack growth based on the consideration of both oxygen concentration and

accumulated inelastic strain near the crack tip. The failure curve was then utilized to predict

crack growth rates under fatigue-oxidation conditions for selected loading frequencies and

dwell periods, with comparison against the experimental results [11, 12] and those predicted

from the viscoplastic model.

6.2. VISCOPLASTICITY DEFORMATION ANALYSIS

Mechanical deformation, mainly fatigue and creep, must be considered when designing and

assessing the service life of high temperature turbines. Viscoplastic or time-dependent

inelastic behaviour plays a very important role in crack tip deformation and crack

propagation for nickel alloys subjected to high temperature cyclic loading. Reduced loading

frequency and imposed hold time at the maximum load often lead to increased deformation

near the crack tip and plastic zone size. Here, finite element analyses have been carried out

first to investigate the role of viscoplasticity in crack growth.

152

6.2.1. THE MATERIAL MODEL

Unified constitutive equations, developed by Chaboche [13], were adopted to describe the

viscoplastic deformation for RR1000. The isotropic and kinematic hardening

variables are considered during the transient and saturated stages of cyclic response [13]. A

small strain hypothesis is used where the strain rate tensor is divided into two parts an

elastic part and a plastic part [13]:

It is assumed that the elastic strain obeys Hooke’s law:

Where and are the Young’s modulus and Poisson’s ratio

respectively, σ and I are the stress tensor and unit tensor of rank two respectively and tr is

the trace.

The inelastic strain represents both plastic and creep strains. A power relationship

adopted for the viscoplastic strain rate is expressed as [13]:

where is the yield function, the back stress or kinematic hardening variable, and are

material constants and the bracket "<>" is defined by:

153

According to the von Mises yield criterion, the yield function is defined as:

where is the isotropic hardening variable and the initial value of the radius of the yield

surface and denotes the von Mises distance in the deviatory stress space:

where and are the deviators of and and : represents the inner product of two

tensors. Plastic flow occurs under the condition: and

For this model, the motion of yield surface continues to hold but the stress in excess of the

yielding stress is now admissible and often termed as overstress.

The evolution of the kinematic stress tensor and the isotropic stress may be described

through the following rules [13]:

154

here , , , , and are six material and temperature-dependent constants, which

determine the shape and amplitude of the stress-strain loops during the transient and

saturated stage of cyclic response, and is the accumulated inelastic strain rate defined by:

The constitutive equations contain eleven material parameters: , , , , , , , , ,

and . The kinematic hardening behaviour is described by , , and , where and

are the saturated values of the kinematic hardening variables and and indicate the

speed with which the saturation is reached. The isotropic hardening is depicted by and ,

where is the asymptotic value of the isotropic variable at saturation and indicates the

speed towards the saturation. The initial size of the yield surface is represented by , and

and are the viscous parameters. The model has already been established [14-16], with

parameters optimised from cyclic test data of RR1000 at 650°C. The model has also been

programmed into a UMAT [17], using a fully implicit integration and the Euler backward

iteration algorithm, and implemented in the finite element software ABAQUS [18].

6.2.2. FINITE ELEMENT ANALYSIS

A standard compact tension (CT) specimen is considered for the finite element study of

fatigue crack-tip deformation and crack growth, and has the same geometry as that used for

the crack growth testing by Dalby and Tong [11, 12]. The specimen (width W = 26mm and

height H = 15.6mm), was meshed into 2D plane strain elements. As shown in Figure 6.1,

refined mesh (4-node, full integration) has been used for the crack tip area, while slightly

155

coarse mesh (3-node, full integration) was used outside the crack tip area in order to save

the computation time. At the crack tip, the element has a size of 6.35μm, which is about the

average grain size (5~6μm) of the material [11, 12]. The crack length was chosen to be a =

13mm, half of the specimen’s width (a/W = 0.5). All FE analyses have been carried out with a

constant stress intensity factor range of and ratio of R = 0.1. The load was

applied to the specimen through a rigid pin, modelled as a pair of contact surfaces in

ABAQUS. For pure fatigue loading, a triangular waveform was used and frequencies varied

from 0.001 to 2.5Hz. For dwell loading, a trapezoidal waveform was used with a 1-X-1-1

pattern, where X is the dwell time and varies from 1 to 1000s [11, 12].

156

Figure 6. 1:(a) Finite element mesh for a CT specimen and (b) refined mesh for the crack tip

area (element size is 6.35μm).

6.2.3. NEAR-TIP INELASTIC DEFORMATION

Figure 6.2 shows the contour plot of the accumulated inelastic strain obtained from the finite

element analyses after ten loading cycles at an applied frequency of . The

accumulated inelastic deformation is highly localized in the vicinity of the crack tip. Figure 6.3

shows the contour plot of the accumulated inelastic strain after ten loading cycles for an

imposed dwell time of . It can be seen that imposed 1000s dwell period introduces

more severe inelastic deformation (a maximum value of 0.892) near the crack tip when

compared to that (a maximum value of 0.732) for pure fatigue (Figure 6.2). For a given

157

number of cycles, the lower the frequency or the longer the dwell period, the more severe

the accumulated inelastic deformation near the crack tip.

Figure 6. 2: Contour plot of the accumulated inelastic strain near the crack tip after ten

loading cycles for a stress intensity factor range ΔK=30MPa√m and a loading frequency

f=0.25Hz2.

2 In Figures 6.2 and 6.3, different contour colours in a single finite element represent different values obtained

at four different integration points using ABAQUS [18].

158

Figure 6. 3: Contour plot of the accumulated inelastic strain near the crack tip after ten

loading cycles for a stress intensity factor range ΔK=30MPa√m and a dwell period of 1000s.

6.2.4. PREDICTION OF CRACK GROWTH

Similar to the work of Zhao et al. [10], the accumulated inelastic strain has been used here as

a criterion to predict crack growth rate in CT specimens at 650C for selected loading

conditions. The choice of accumulated inelastic strain seems justified in that, under fatigue

loadings, the reversed deformation during unloading is accounted for as well as that during

loading. In the FE analyses, the number of cycles was recorded when the inelastic strain

accumulation over the characteristic distance d* = 6.35m ahead of the crack tip reached a

critical value of 0.35. This critical value 0.35 was back calculated using finite element analysis,

159

which predicts the same crack growth rate (2.72107 m/cycle) as the experimental result in

Dalby and Tong [11, 12] for a base-line fatigue test ( f = 2.5 Hz and R = 0.1)

at 650C. The average crack growth rate was then calculated by dividing the characteristic

distance with the recorded number of cycles.

The predicted effects of loading frequency on crack growth rates are shown in Figure 6.4 for

a triangular waveform with and load ratio R = 0.1, including the test data

for CT specimens at 650C [11, 12]. The predictions showed the same trend as the

experimental data, i.e., the increase of crack growth rate with the decrease of loading

frequency, due to the enhanced crack tip deformation for lower frequencies. The predictions

agree well with the test data for higher frequency region (f > 0.1Hz), while marked difference

is noted in the lower frequency region (f < 0.01Hz). This difference may be due to the

oxidation effect at high temperature, which was not taken into account in the model

prediction.

The effects of dwell period on crack growth rates are predicted by considering a trapezoidal

loading waveform (1-X-1-1 pattern) with , baseline frequency f = 0.25 and

load ratio R = 0.1. The predictions are presented in Figure 6.5, including the experimental

data [11, 12] for CT specimens at 650C under the same loading conditions. Again the

predictions show the same trend as the experimental data, i.e., the increase of crack growth

rate with the increase of hold period. On the other hand, the predictions show an increasing

difference between the prediction and the experimental data as the dwell period is

increased, especially when the dwell period is over 60 seconds. Again, this difference may be

160

due to the oxidation effect at high temperature, which is not accounted for in the current

model prediction.

Figure 6. 4: Effects of loading frequency on crack growth rate for a triangular loading

waveform with ΔK = 30MPa√m and load ratio R = 0.1 at 650°C, comparison of model

prediction and experimental results [11, 12].

0.00E+00

5.00E-07

1.00E-06

1.50E-06

2.00E-06

2.50E-06

0.001 0.01 0.1 1 10

da/

dN

(m

/cyc

le)

Frequency (Hz)

Prediction - accumulated inelastic strain

Experimental data

161

Figure 6. 5: Effects of dwell periods on crack growth rate for a trapezoidal loading

waveform with ΔK = 30MPa√m and load ratio R = 0.1 at 650°C, comparison of model

prediction and experimental results [11, 12].

The detrimental effects of environmental factors, in particular oxygen, on high-temperature

crack growth behaviour in nickel alloys have been well demonstrated by experimental results

[19, 20]. Oxidation-accelerated crack growth is a direct consequence of oxygen diffusion into

the material, which attacks the grain boundary through chemical reaction with alloy

elements or oxygen segregation at grain boundaries. The diffusion process becomes more

significant with the assistance of high tensile stress near crack tip [21], especially for

superimposed dwell periods at the maximum load where the crack tip is fully open and

experiences the highest tensile stress level. As a consequence, a coupled mechanical-

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1 10 100 1000

da/

dN

(m

/cyc

le)

Dwell time [s]

Prediction - accumulated inelastic strain

Experimental data

162

diffusion analysis [22] is required to account for the effects of oxygen diffusion as well as that

of viscoplasticity on crack growth.

6.3. COUPLED VISCOPLASTICITY-OXYGEN DIFFUSION ANALYSIS

Here we are concerned with the diffusive transport of oxygen into the crack tip under the

influence of a mechanical loading field. The analyses follows exactly the same method as

described in Chapter 5, where the gradient of hydrostatic stress (or pressure) is considered to

be the driving force for the stress-assisted diffusion process.

To solve the overall fatigue-oxidation problem, a sequentially coupled mechanical-diffusion

analysis was performed to include the dependence of oxygen diffusion on the stress state.

The mechanical analyses were carried out first, with the history of hydrostatic stress for each

integration point stored in the ABAQUS output files. During the diffusion analysis, the output

files were then used as inputs, to include the effect of hydrostatic stress gradient on oxygen

diffusion. Although the availability of oxygen may vary in the vicinity of the crack tip, as does

the oxygen partial pressure, the oxygen intake on the crack surface was assumed to be

uniform and follows the Equation (3) in Chapter 5.

The diffusion parameters were already obtained in Chapter 5 from the FE analyses

performed on the waisted specimen and, at 650°C, they are found to be

= 1.67×10-13mg2/mm4/s for the parabolic rate constant, D = 1.085×10-13mm2/s for the

diffusivity and M = 1.585×10-3mm2/N for the pressure factor.

163

6.3.1. NEAR-TIP OXYGEN CONCENTRATION

Figure 6.6(a) shows the contour plots of oxygen concentration near a fatigue crack tip after

10 loading cycles, where the stress intensity factor range , load ratio R = 0.1

and loading frequency f = 0.001Hz. Figure 6.6(b) shows the contour plot of oxygen

concentration after 10 cycles for the 1000s dwell loading situation, where the dwell is

superimposed at peak loads of a 0.25Hz base line fatigue waveform. Both results show the

penetration of oxygen into the crack tip, as well as the crack flanks, due to oxygen diffusion

process. It is also noted that the oxygen concentration level ahead of the crack tip is less

severe compared to the one on the fracture surface, which may be due to the limited oxygen

availability at the crack tip. This is consistent with the FIB experimental examinations in

Chapter 4, where oxides are mainly observed on fracture surfaces. Also, for a given number

of cycles, the lower the frequency or the longer the dwell period, the more severe the near-

tip oxygen concentration becomes.

164

Figure 6. 6: (a) Contour plot of the oxygen concentration near the crack tip after 10 cycles

for a frequency of 0.001Hz.

(a)

Crack tip

165

Figure 6. 6: (b) Contour plot of the oxygen concentration near the crack tip after 10 cycles

for a dwell period of 1000s.

6.3.2. FAILURE CURVE

In order to predict the crack growth rates under fatigue-oxidation conditions, it is necessary

to formulate an appropriate criterion to account for the contributions from both mechanical

deformation and oxidation. Two parameters, the accumulated inelastic strain and oxygen

concentration, have been used to represent the viscoplastic deformation and the oxidation

effect, respectively. The idea is to use the two parameters to construct a failure curve from

which crack growth prediction under fatigue-oxidation may be made. Experimental crack

growth data for selected loading frequencies at [11, 12] were utilised to

determine the number of cycles required to grow the crack in the FE model. Specifically, the

(b)

Crack tip

166

number of cycles was calculated by dividing the near-tip element size (6.35µm) with the

measured crack growth rate. FE analyses were then carried out for the calculated number of

cycles, i.e., just before the crack grows into the next element, and the values of the two

parameters were extracted. The extracted values of the two parameters were then plotted

against each other to obtain a failure curve. The results (give in Table 6.1) are presented in

Figure 6.7, where all the data seem to follow the fitted failure curve. As shown in Figure 6.7,

the failure curve indicates a "safe zone" outside which the crack will grow.

Table 6. 1: The accumulated inelastic strain and oxygen concentration obtained from the FE

analyses for different frequencies (ΔΚ=30ΜPa√m, R=0.1, T=650°C).

Frequency (Hz) Number of cycles Acc. inelastic strain Oxygen con. (mg/mm3)

0.001 3.05E+00 0.095539 9.23565E-04

0.0033 3.30E+00 0.097097 5.33232E-04

0.01 5.21E+00 0.130146 3.78586E-04

0.1 9.38E+00 0.189051 1.57638E-04

0.25 1.17E+01 0.217812 1.10645E-04

1 1.60E+01 0.265895 6.4548E-05

2.5 2.33E+01 0.35038 4.95818E-05

167

Figure 6. 7: Failure curve in terms of the accumulated inelastic strain and the oxygen

concentration near the crack tip (ΔΚ=30ΜPa√m, R=0.1, T=650°C).

6.3.3. PREDICTION OF CRACK GROWTH UNDER FATIGUE-OXIDATION

CONDITION

Using the failure curve constructed above, crack growth rates in a CT specimen at 650C

were predicted from the finite element analyses for selected loading frequencies and dwell

time at . During the analyses, the accumulated inelastic strain and the

oxygen concentration over the characteristic distance d* = 6.35m ahead of the crack tip

were recorded against the number of cycles. The results were then used to obtain the

number of cycles for the crack to grow, i.e., when the combination of the accumulated

inelastic strain and the oxygen concentration reached the failure curve. The average crack

growth rate was then calculated by dividing the characteristic distance with the number of

168

cycles. The procedures have been illustrated in Figures 6.8 and 6.9, and the obtained

numbers of cycles for the crack to grow are given in Tables 6.2 and 6.3.

Table 6. 2: The obtained number of cycles for crack to grow for different frequencies.

Frequency (Hz) Critical number of cycles

0.001 3

0.0033 4

0.01 5

0.1 9

0.25 11

1 16

2.5 17.5

169

Figure 6. 8: Illustration of determining the number of cycles for the crack to grow, i.e.,

when the combination of the accumulated inelastic strain and the oxygen concentration

reached the failure curve, for different frequencies.

170

Figure 6. 9: Illustration of determining the number of cycles for the crack to grow, i.e.,

when the combination of the accumulated inelastic strain and the oxygen concentration

reached the failure curve, for different dwell time.

Table 6. 3: The obtained number of cycles for crack to grow for different dwell time.

Dwell time (s) Critical number of cycles

1 10

20 6.5

60 5.25

120 4.5

300 3.5

1,000 2.75

171

The predicted effects of loading frequency on crack growth rates are also shown in Figure

6.10 for a Κ , in a direct comparison with test data for CT specimens at 650C

[11, 12]. For the predictions based on fatigue-oxidation failure curve, excellent agreements

were achieved for all loading frequencies.

The predicted effects of dwell time on crack growth rates is also shown in Figure 6.11 for

, in a direct comparison with test data for CT specimens at 650C [11, 12]. The

predictions from accumulated inelastic strain show increased deviations from the

experimental data as the dwell period is increased, especially when a dwell period is over 60

seconds. Again, this difference is much reduced when the fatigue-oxidation failure curve was

used for the prediction.

172

Figure 6. 10: The effects of loading frequency on the crack growth rate for a triangular

waveform with ΔK=30MPa√m and load ratio R = 0.1 at 650°C; comparison of the model

prediction and the experimental results [11, 12].

1.00E-07

1.00E-06

1.00E-05

0.001 0.01 0.1 1 10

da/

dN

(m

/cyc

le)

Frequency (Hz)

Experimental data

Prediction - Accumulated inelastic strain

Prediction - Fatigue-oxidation

173

Figure 6. 11: The effects of dwell period on the crack growth rate for a trapezoidal loading

waveform with ΔK=30MPa√m and load ratio R = 0.1 at 650°C; comparison of the model

prediction and the experimental results [11, 12].

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1 10 100 1000

da/

dN

(m

/cyc

le)

Dwell (s)

Experimental data

Prediction - Accumulated inelastic strain

Prediction - Fatigue-oxidation

174

6.4. DISCUSSION

For polycrystalline nickel alloys under low cycle fatigue at elevated temperature above

500C, a transition from cycle-dependent transgranular crack propagation to time-dependent

intergranular crack propagation may occur, when the frequency is sufficiently low and/or the

hold period at peak loads is sufficiently long, resulting in significant increase in crack growth

rates. As frequency or cycle duration does not seem to influence the crack propagation rate

at low temperatures or under vacuum conditions, oxygen from the environment may be the

key factor for the time-dependent crack propagation behaviour, which is attributed to the

oxidation reaction at grain boundaries in most studies. For instance, Miller et al. [19, 20]

proposed that the formation of thin intergranular Nb2O5 films, which fracture in a brittle

manner, leads to high crack propagation rates. This was also supported by studies on Ni-

18Cr-18Fe and powder-metallurgical superalloys with varying Nb concentrations, where the

material’s sensitivity to environmental attack depends solely on the Nb content. On the other

hand, strong environmental effects on fatigue crack propagation were also observed by

Molins et al. [2, 4] in Ni-Cr model alloys without any Nb. Molins et al. [4] proposed that

epitactic NiO-formation ahead of the crack tip introduced the vacancies into near-tip

materials, which act as nucleation sites for pores and microcracks and thereby give rise to

high crack propagation rates. High Cr contents were suggested to bring beneficiary effects

due to the much slower kinetics of Cr2O3 formation than that of NiO formation, and, in

addition, Cr could scavenge O2 near the crack tip and reduces the level of elemental O

required for oxidation reaction [4].

175

The oxidation-reaction mechanism has been challenged by the dynamic embrittlement

hypothesis in recent studies of crack growth in nickel alloys under fatigue-oxidation

conditions [5, 7]. Dynamic embrittlement was introduced to define a time-dependent

intergranular brittle cracking process in which the supply of embrittling elements is due to

grain boundary diffusion into an area of increasing tensile stress ahead of a crack tip [21, 22].

The embrittling elements lower the cohesion of the grain boundary and facilitate the crack

advance. The case of hydrogen embrittlement in steels is one of the most important damage

mechanisms that fit in the dynamic embrittlement scheme [23]. Other established dynamic

embrittlement cases include: sulphur-induced stress relief cracking in steels [22], S-induced

cracking in Cu Cr alloys [24], O-induced cracking in Cu Be alloys [25] and Ni3Al [21], and Sn-

induced cracking in Cu-Sn model alloys [22, 26].

Dynamic embrittlement for nickel superalloys has been supported by experimental

observations in Inconel 718 for four-point bending tests [5-7]. First, the individual grain

boundary facets were found to be smooth on the sub-micrometer level and oxidation of NbC

precipitates was only observed on the fractured surface where the crack front had passed.

Second, the cracking process was found to be extremely sensitive to rapid changes in oxygen

pressure. Crack growth could be turned off and on in less than 10s by alternately pumping

oxygen from the chamber and re-admitting it. Given the fact that oxidation kinetics for nickel

alloys at 650°C is extremely slow [27], there is insufficient time for oxide formation to happen

ahead of the crack tip within the order of seconds. Direct observations of internal oxidation

and associated damage were only available on smooth specimens, which have been exposed

to oxidizing environment for a considerably long time, mostly greater than 20 hours [8, 28-

176

30]. The current work also showed that, the crack growth rates in air at high-temperature,

can be predicted well from the dynamic embrittlement hypothesis, though collecting

experimental evidence of crack tip oxygen diffusion and measurements of oxygen

concentration near the crack tip, are challenging tasks and yet to be accomplished.

The construction of a failure curve and associated crack growth predictions, are based on the

values of the accumulated inelastic strain and the oxygen concentration averaged over the

element just ahead the crack tip, which corresponds to a characteristic distance of 6.35µm

ahead of the crack tip. The need to specify a critical distance in association with a fracture

criterion is well established [31-40], particularly for sharp cracks, where, due to the stress

and strain singularities, numerical results are non-unique unless a critical distance is

specified. McClintock [32, 33] developed a mechanistic analysis of crack extension by fatigue,

employing a failure criterion based on plastic strain accumulation over a “structural size” of

the material. Quantitatively, a structural size of 5m seems to fit well with the experimental

results for three types of materials [33]. Krafft [34] proposed that ductile fracture would

occur when the instability strain for a uniaxial tensile specimen is achieved at the crack tip

over a distance equal to the spacing of void nucleating particles. Ritchie et al. [35]

successfully predicted fracture when the critical stress was achieved over two grain sizes.

Rawal and Gurland [36] reported a critical stress was achieved over a critical distance about

1.3 grain-sizes. Chen et al. [38] reported a characteristic distance of 13m for crack tip

fracture in C-Mn steel, over which the critical strain, the critical stress and the critical stress

triaxiality criteria are satisfied simultaneously. Said and Tasgetiren [39] used the

characteristic distance of 0.8-1.37 mean grain size to determine the static and dynamic

177

fracture toughness for bcc metals and alloys using the critical stress criterion. In the present

work, the chosen characteristic distance 6.35µm is on the similar order to the others [32-36,

38, 39] and it is about the average grain size, where crack growth is assumed to be associated

with the cracking of a grain. Our mesh sensitivity study showed that the strain distribution

ahead of the crack tip has reached a good convergence at d* μ [17].

6.5. CONCLUSIONS

In this chapter, the diffusion parameters obtained in Chapter 5 from the FE analyses of

waisted specimen were used to model near-tip oxygen diffusion process and predict the

oxidation-assisted crack growth in CT specimens for different frequencies and dwell times.

The FE analyses were carried out for selected loading frequencies to construct a failure curve

based on the accumulated inelastic strain versus the oxygen concentration near the crack tip.

The failure curve was then used to predict the critical number of cycles for crack to grow at

selected loading frequencies and dwell time.

Simulations showed that the crack growth rates predicted from the fatigue-oxidation failure

curve compare well with the experimental results, with marked improvements achieved over

those predicted from the viscoplastic model alone.

178

6.6. REFERENCES

[1]. Andrieu, E., Molins, R. (1992). Intergranular crack tip oxidation mechanism in a nickel-

based superalloy. Materials Science and Engineering: A, 154, 21-28.


environment-dependent fatigue crack growth in alloy 718. Materials Science and Engineering:

A, 150(2), 151-160.

[3]. Andrieu, E., Hoshstetter, G., Molins, R., Pineau, A. (1997). Oxidation and intergranular

cracking behaviour of two high strength Ni-base superalloys. Magnin T, editor. Corrosion-

Deformation Interactions (EFC 21), p. 461-475.

[4]. Molins, R., Hochstetter, G., Chassaigne, J.C. and Andrieu, E. (1997). Oxidation effects on

the fatigue crack growth behaviour of alloy 718 at high temperature. Acta Materialia, 45(2),

663-674.

[5]. Pfaendtner, J.A., McMahon Jr., C.J. (2001). Oxygen-induced intergranular cracking of a

Ni-base alloy at elevated temperatures—an example of dynamic embrittlement. Acta

Materialia, 49(16), 3369-3377.





fracture at high temperatures. International Materials Reviews, 50(2), 83-97.

[8]. Calvarin-Amiri, G., Huntz, A.M., Molins, R. (2001). Effects of an applied stress on the


18(2), 91-99.

[9]. Bika, D., McMahon Jr, C.J. (1995). A model for dynamic embrittlement. Acta Metallurgic

Materialia, 43, 1909-1916.

[10]. Zhao, L.G., Tong, J. and Hardy, M.C. (2010).Prediction of crack growth in a nickel-based


938.

[11]. Dalby, Sara. (2002). The effects of frequency and waveshape on the fatigue crack

growth of an advanced nickel based superalloy at elevated temperatures. PhD Thesis.


179




[13]. Chaboche, J.L. (1989). Constitutive equations for cyclic plasticity and cyclic

viscoplasticity. International Journal of Plasticity, 5(3), 247-302.

[14]. Zhan, Z.-L. (2004). A study of cyclic plasticity and viscoplasticity in a new nickel-based


Portsmouth, U.K.

[15]. Zhan, Z.-L., Tong J. (2007). A study of cyclic plasticity and viscoplasticity in a new nickel-

based superalloy using unified constitutive equations. Part I: evaluation and determination of

material parameters. Mechanics of Materials, 39, 64-72.

[16]. Zhan, Z.-L., Tong J. (2007). A study of cyclic plasticity and viscoplasticity in a new nickel-

based superalloy using unified constitutive equations. Part II: simulation of cyclic stress

relaxation. Mechanics of Materials, 39, 73-80.

[17]. Zhao, L.G. and Tong, J. (2008). A viscoplastic study of crack tip deformation and crack

growth in a nickel based superalloy at elevated temperatures. Journal of the Mechanics and

Physics of Solids, 56(12) , 3363-3378 .

[18]. ABAQUS. Version 6.8. (2009). Providence, USA. Dassault Systemes Simulia Corp.

[19]. Miller, C.F., Simmons, G.W. and Wei, R.P. (2001). Mechanism for oxygen enhanced

crack growth in inconel 718. Scripta Materialia, 44(10), 2405-2410.


oxygen enhanced crack growth in P/M Ni-based superalloys. Scripta Materialia, 48(1), 103-

108.

[21]. Liu, C.T., White, C.L. (1987). Dynamic embrittlement of boron-doped Ni3Al alloys at

600°C. Acta Metallurgica, 35(3), 643-649.

[22]. Bika, D. (1992). Dynamic embrittlement in metallic alloys. PhD Thesis. University of

Pensylvania, Philadelphia, PA, U.S.A.

[23]. Birnbaum, H.K., Sofronis, P. (1994). Hydrogen-enhanced localized plasticity—a

mechanism for hydrogen related fracture. Materials Science and Engineering: A, 176(1-2),

191-202.

180

[24]. Misra, R.D.K., Prasad, V.S. (2000). On the dynamic embrittlement of copper-chromium

alloys by sulphur. Journal of Materials Science, 35(13), 3321-3325.

[25]. Misra, R.D.K., McMahon Jr., C.., Guha, A. (1994). Brittle behavior of a dilute copper-

beryllium alloy at 200°C in air. Scripta Metallurgica et Materialia, 31(11), 1471-1474.

[26]. Bika, D., Pfaendtner, Menyhard, M., J.A., McMahon Jr., C.J. (1995). Sulfur-induced

dynamic embrittlement in a low-alloy steel. Acta Metallurgica e Materialia, 43(5), 1895-1908.

[27]. Krupp, U., Kane, W., Pfaendtner, J.A., liu, X., laird, C., McMahon Jr., C.J. (2004).

Oxygen-induced intergranular fracture of nickel-base alloy IN718 during mechanical loading

at high temperature. Materials Research, 7(1), 35-41.

[28]. Bricknell, R.H., Woodford, D.A. (1982). The mechanism of cavity formation during high

temperature oxidation of nickel. Acta Metallurgica, 30(1), 257-264.

[29]. Garat, V., Brucelle, O., Clouè, J.M., Rebeyrolle, V., Monceau, D., Viguier, B., Andrieu, E.

(2004). Comparing different methods to dtermine the intergranular oxidation damage on a

nickel based superalloy. Materials Science Forum, 461-464, 537-544.




[31]. Riedel H. and Rice J.R. (1980). Tensile cracks in Creeping Solids. Fracture Mechanics:

Twelfth Conference, ASTM STP 700, 112–130.

[32]. McClintock F.A. (1958). Ductile instability in shear. ASME J Appl. Mech. 25, 582-588.

[33]. McClintock F.A, Irwin G.R. (1965). Plasticity aspects of fracture mechanics. Fracture

Toughness Testing and its Applications, ASTM STP 381, 84-113.

[34]. Krafft J.M. (1964). Crack toughness and strain hardening of steels. Applied Materials

Research, 3, 88-101.

[35]. Ritchie, R.O., Knott, J.F., Rice, J.R. (1973). On the relationship between critical tensile

stress and fracture toughness in mild steel. Journal of the Mechanics and Physics of Solids,

21(6), 395-410.

[36]. Rawal, S.P., Gurland, J. (1977). Observations on the effect of cementite particles on the

fracture toughness of spheroodized carbon steels. Metallurgical and Materials Transactions A,

8(5), 691-698.

181

[37]. Neville, D.J. (1988). On the distance criterion for failure at the tips of cracks, minimum

fracture toughness, and non-dimensional toughness parameters. Journal of the Mechanics

and Physics of Solids, 36(40), 443–457.

[38]. Chen, J.H., Wang, Q., Wang, G.Z., Li, Z. (2003). Fracture behavior at crack tip—A new

framework for cleavage mechanism of steel. Acta Materialia, 51(3), 1841-1855.

[39]. Said, G., Tasgetiren, S. (2004). An express technique for the determination of static and

dynamic fracture toughness (KIC, Kid) of bcc metals and alloys. Mechanics of Materials, 36(11),

1129-1142.

[40]. Neimitz, A., Graba, M., Galkiewicz, J. (2007). An alternative formulation of the Ritchie-

Knott-Rice local fracture criterion. Engineering Fracture Mechanics, 74(8), 1308-1322.

182

7. CONCLUSIONS & FURTHER WORK

7.1. CONCLUSIONS

Formations of surface oxide scales (Cr, Ti, Ni and Co oxides) and micro-voids beneath the

oxide scales are the major mechanisms for oxidation damage of alloy RR1000 with or

without fatigue loading. Oxidation damage becomes more severe with the increase of

temperature. The internal voids, created by the outwards diffusion of alloy elements to

form the oxide scale on the specimen surface, could lead to crack initiation and

subsequent crack propagation under mechanical loading condition.

Cyclic stress was shown to have an influence on oxidation damage for temperatures at

750C and above, and the thickness of oxide scale and the depth of internal damage

were enhanced by the increase of cyclic stress level. This has been confirmed from the

FIB measurements of the thickness of oxide scale and the depth of internal damage. In

addition, both EDX analyses and FIB secondary ion imaging showed the presence of

internal oxides, indicating the oxygen penetration into the material.

The SEM studies of the fracture surfaces in dwell crack growth confirmed the transition

from transgranular to predominant intergranular cracking in alloy RR1000 for increased

dwell time. This change in fracture mode supports the oxidation-assisted crack growth

mechanism via grain boundary embrittlement, considering that creep deformation is

extremely limited for alloy RR1000. Oxidation has also been evidenced by the FIB

analyses of both CT and CN specimens which revealed the oxides accumulated on the

fracture surface.

183

Finite element analyses of oxygen diffusion along the grain boundaries have been carried

out for a waisted specimen using a submodelling technique. For natural diffusion,

oxygen penetration and concentration along grain boundaries are controlled by the

diffusivity, which is temperature dependent. The higher the temperature, the deeper the

oxygen penetration. Fatigue-assisted penetration of oxygen was modelled for both

750°C and 800°C, and the simulation results have been used to obtain the pressure

factor for modelling the oxidation-assisted fatigue crack growth.

Oxygen diffusion process, coupled with viscoplasticity, near a crack tip has been

modelled using the diffusion parameters obtained from the FE analyses of the waisted

specimen. A failure curve for crack growth under fatigue-oxidation condition has been

constructed based on the consideration of both the accumulated inelastic strain and the

oxygen concentration near the crack tip. Crack growth rates, predicted from the failure

curve for selected frequencies and dwell periods, compare well with the experimental

results, with marked improvements achieved over those predicted from the viscoplastic

model alone.

7.2. FURTHER WORK

It is suggested to carry out fatigue-oxidation experiments on a notched specimen and

examine the effects of fatigue on oxidation damage near the notch area, as the

stress/strain field near the notch area resembles that near a crack tip. Waisted specimen

belongs to the smooth specimen family, and could not properly represent the high stress

triaxiality presented near the crack tip, which might influence the oxidation process

significantly.

184

FIB examinations of fracture surface oxides could not support the oxidation-based

rationale to explain the observed tunnelling phenomenon in dwell crack growth in CN

specimens, as there seems no difference in oxides accumulation between the middle

section and the free surface for a given temperature. Further and in-depth investigation

is required in order to understand the complex mechanisms for crack growth tunnelling.

For simplicity, oxygen diffusion approach has been used in the preset work to quantify

the oxidation damage of alloy RR1000 under fatigue. No attempts have been made to

model the chemical reaction kinetics, vacancy formation, transport of other species and

recrystallization, which are the mechanisms physically operative during the oxidation

process of RR1000. Further work is undergoing to address these issues.

The crystal plasticity formulation describes grain interior deformation without

consideration of grain boundary deformation. Grain boundary deformation is controlled

mainly by sliding and diffusion, which can be described by constitutive laws stating the

evolution of the normal and shear tractions in terms of both normal and tangential

displacements along the grain boundaries. Cohesive element approach has been

generally used to model grain boundary deformation, where the tensile and shear

tractions of the cohesive elements embedded along the grain boundaries can be

calculated. Further work is required to address the influence of grain boundary

deformation on oxygen diffusion.

The current work showed that, the crack growth rates in air at high-temperature, can be

predicted well from the dynamic embrittlement hypothesis (stress-assisted oxygen

diffusion into the crack tip). However, so far, there have been no direct evidence and

185

measurements of oxygen ahead of the crack tip, probably due to very limited level of

oxidation into the crack tip as well as the insufficient resolution of current facilities.

These challenging tasks are yet to be accomplished in further work.

186

APPENDIX A

MEASUREMENTS FROM THE FIB IMAGES

187

APPENDIX B

THE J INTEGRAL

In modelling material failure various energy methods are used which provide an insight into

fracture. For 2-D domains containing cracks, Rice in 1968 presented the J-integral.

Considering a 2-D linear body of linear or nonlinear elastic material free of body forces and

subjected to a 2-D deformation field (plane strain, plane stress) so that all stresses σij depend

only on two Cartesian coordinates (x, y). Suppose the body contains an edge crack as shown

in Figure B1.

Define the strain-energy density W as:

where ε=(εij) is the infinitesimal strain tensor. Now, define the J-integral as

As shown in Figure B1, Γ is the curve surrounding the notch tip; the integral being evaluated

counter clockwise starting from the lower surface and continuing along the path Γ to the

upper surface. In the J-integral equation, T is the traction vector defined according to the

outward normal along Γ, u is the displacement vector and ds is an element arc length along Γ.

Rice (1968) proved the path independent concepts and found that for small-scale yielding the

stress energy release rate G is equal to the J-integral. Therefore, the stress intensity factor

can be evaluated as follows:

188

where

for plane strain and for plane stress.

Figure B1: Crack tip coordinate system and typical line integral contour.

References:

Riveros, G.A. (2006). Numerical Evaluation of Stress Intensity Factors (KI) J-Integral Approach.

ERDC/CHL CHETN-IX-16. US Army Corps of Engineers.

Rice, J.R. (1968). A path independent integral and the approximate analysis of strain

concentrations by notches and cracks. Journal of Applied Mechanics. 35. 379-386.

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AN EXPERIMENTAL AND COMPUTATIONAL STUDY OF DAMAGE … · 2017-01-18 · A stress-assisted diffusion approach has been used to model oxygen penetration in the waisted specimen based