Creep and Creep-Fatigue Interaction in New and Service ......creep-fatigue interaction may...
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Creep and Creep-Fatigue Interaction in New and Service Exposed P91 Steel A Thesis submitted for the Degree of Doctor Philosophy of Imperial College London and Diploma of Imperial College by Norhaida Ab Razak January 2018 Department of Mechanical Engineering Imperial College London SW7 2AZ
Transcript of Creep and Creep-Fatigue Interaction in New and Service ......creep-fatigue interaction may...
Creep and Creep-Fatigue
Interaction in New and Service
Exposed P91 Steel
A Thesis submitted for the Degree of Doctor Philosophy of
Imperial College London
and
Diploma of Imperial College
by
Norhaida Ab Razak
January 2018
Department of Mechanical Engineering
Imperial College London
SW7 2AZ
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Abstract
Power plant components that have been in operation for many years may have
accumulated significant creep damage. Cyclic operations at high temperature lead to
issues with interactive creep-fatigue failure of high temperature components. The
creep-fatigue interaction may accelerate the failure and reduce the service life of power
plant components. The aim of this research is to examine the effects of material’s
service exposure, including prior creep damage, on subsequent creep-fatigue crack
growth and low cycle fatigue behaviour. These effects which are important for safe
component operation have been included in predicting the remnant life of high
temperature material.
The material of interest is P91 steel, which is widely used in high temperature power
plant components due to its high material performance. Tensile and uniaxial creep
have been performed on the new and ex-service P91 steel at 620°C and 600°C,
respectively to obtain the material properties. The result of uniaxial creep tests have
been analysed and compared with available P91 data to examine the effect of long
term exposure of P91 materials at high temperature in lower stress level.
Creep-fatigue crack growth testing has been performed on compact tension specimen
at a range of temperature between 600°C to 625°C with hold time ranging from static to
600s to examine the CFCG behaviour. The CFCG results have been correlated with
stress intensity factor range, ΔK and creep fracture mechanic parameter, C* and
compared to the static creep, high temperature fatigue and CFCG test data available in
the literature for P91 steel. The CFCG rate and the creep crack initiation (CCI) time
have been compared to the NSW CCG model’s prediction. It is found that for low stress,
low ductility and increase in constraint, the plane strain NSW model can conservatively
bound the tests data at long terms which is more appropriate for components
operational times. An interaction diagram based on a linear cumulative damage rule
has been proposed to predict the creep-fatigue interaction results regardless of the
degradation of the steel under ex-service condition. It is shown that the mean CFCG
rates for ex-service steels are faster by a factor of 4 compared to the mean CCG data.
The increase in cracking rate is directly related to the reduction in creep ductility which
can occur both due to material degradation and under long term testing conditions.
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Fractography have revealed an intergranular ductile fracture surface for shorter term
tests performed, which is an indication of the creep dominance for the creep- fatigue
conditions.
Notched bar creep tests have been performed on new and ex-service material at
620°C and 600°C to examine the effect of multiaxial stress state on creep ductility.
Finite element analysis coupled with a damage model were performed to evaluate the
damage accumulation on the notched bar and predict the rupture life under multiaxial
stress conditions. The finite element rupture life predictions based on the remaining
creep ductility criteria were compared with short term experimental data and provide a
basis to predict the long term behaviour. Metallographic and microstructural
assessment on the notched bar have been performed to support the experimental
findings.
Prior creep strain/damage has been introduced into a material by performing
interrupted uniaxial creep testing. The uniaxial creep tests were interrupted at various
levels of creep strain. In order to examine the influence prior creep strain/damage on
tensile deformation, a series of tensile test have been performed on prior creep
specimens. In this work, room temperature tensile test have been performed. The
result of these tests have been analysed and compared with thermally aged specimen
and the one without prior creep strain. It has been shown that prior creep strain
reduces the 0.2% proof stress. Low cycle fatigue (LCF) tests have been performed on
the specimen with and without prior creep strain at various strain ranges to examine
the effects of prior creep strain/damage on the fatigue behaviour. It is shown that the
stress amplitude for material with prior creep strain is lower than the material without
prior creep strain which indicate that the material with prior creep strain reduces its
strength by means of material degradation during the creep test. The result from these
LCF tests are compared and analysed to provide a basis for the fatigue life prediction.
For the future works, further LCF tests on prior creep strain specimen and CFCG tests
need to be performed to confirm the observed trend. Instead of prior creep strain, the
influence of prior cyclic loading may be investigated and subsequent test may be
performed. Numerical modelling of the creep damage process to predict uniaxial and
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multiaxial failure under cyclic loading need to be performed and enhanced by taking
into account the actual material properties of the damaged material .This model can
also be used to show its relevance to component failure under creep/fatigue conditions.
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Acknowledgements
I would like to thank my supervisors, Prof.Kamran Nikbin and Dr. Catrin Mair Davies for
the continuous support, guidance, encouragement and advice given during my
research project.
I must also thank Scott Lockyer from Uniper Technologies Limited for providing the
material and required information. Special thanks go to all members in Flex-E Plant
project for their constructive discussion and sharing idea during the meeting.
I would like to extend my acknowledgements to Alex Toth, Suresh, Ruth, Tom and
technical experts for their assistance with my experiment. Many thanks also to my
friends, colleagues and members of staff at Imperial for their help and support.
Last but not least, I am sincerely grateful to my husband for the endless support,
encouragement and a shoulder to cry on during my tough time. And to my children Ain,
Aqilah, Asma and Ammar, thank you for always been a source of joy to me and make
me smile when I’m home.
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Copyright Declaration
The copyright of this thesis rests with the author and is made available under a
Creative Commons Attribution Non-Commercial No Derivatives licence. Researchers
are free to copy, distribute or transmit the thesis on the condition that they attribute it,
that they do not use it for commercial purpose and that they do not alter, transform or
build upon it. For any reuse or redistribution, researchers must make clear to others the
license terms of this work.
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Declaration
I hereby declare that the work presented in this dissertation titled ‘’Creep and
Creep-Fatigue Interaction in New and Service Exposed P91 Steel’’ is original and has
not been submitted for a degree or diploma at any other university or institution.
Information derived from the published and unpolished work of others has been
acknowledged in the text and references are given in the list of sources.
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Table of Contents
Abstract ................................................................................................................. i
Acknowledgements ................................................................................................... iv
Copyright Declaration ................................................................................................ v
Declaration ............................................................................................................... vi
Chapter 1 Introduction ........................................................................................... 1
1.1 Thesis Framework .......................................................................................... 2
1.2 Aims and Objectives ....................................................................................... 4
Chapter 2 Creep and Creep-Fatigue Review ......................................................... 5
2.1 Introduction ..................................................................................................... 5
2.2 P91 Steel and its Microstructure ..................................................................... 5
2.3 Elastic Plastic Deformation ............................................................................. 8
2.3.1 Uniaxial Deformation ............................................................................... 8
2.3.2 Multiaxial Deformation ............................................................................. 8
2.4 Creep Deformation ......................................................................................... 9
2.4.1 Creep Deformation Stages .................................................................... 10
2.4.2 Creep Constitutive Law .......................................................................... 12
2.4.3 Creep Power Law .................................................................................. 14
2.4.4 Average Creep Strain Rate .................................................................... 15
2.4.5 Creep Rupture Time .............................................................................. 15
2.4.6 Multiaxial Creep Deformation ................................................................. 17
2.4.7 Multiaxial Stress State on Ductility ......................................................... 18
2.5 Creep Damage Model ................................................................................... 19
2.5.1 Continuum Damage Mechanics ............................................................. 19
2.5.2 Cavity Growth Mechanics ...................................................................... 20
2.6 Fracture Mechanics Concept ........................................................................ 21
2.6.1 Linear Elastic Fracture Mechanics ......................................................... 21
2.6.2 Elastic Plastic Fracture Mechanics ........................................................ 23
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2.6.3 Creep Fracture Mechanics .................................................................... 24
2.6.4 NSW model ........................................................................................... 26
2.7 Creep- Fatigue Crack Growth ....................................................................... 28
2.7.1 Fatigue Crack Growth ............................................................................ 28
2.7.2 Creep-Fatigue Crack Growth Interaction................................................ 29
2.7.3 Creep Fatigue Crack Growth Damage Mechanism ................................ 30
2.8 Low Cycle Fatigue ........................................................................................ 31
2.8.1 Cyclic stress strain curve ....................................................................... 32
2.8.2 Cyclic hardening and cyclic softening .................................................... 33
2.8.3 Strain Life Prediction ............................................................................. 34
Chapter 3 Material and Experimental Procedure ................................................ 35
3.1 Introduction ................................................................................................... 35
3.2 Material Specification and Service Conditions .............................................. 35
3.2.1 New material ......................................................................................... 35
3.2.2 Ex-service material ................................................................................ 35
3.3 Specimen Orientation ................................................................................... 36
3.4 Introduction of creep stain/damage ............................................................... 38
3.4.1 Interrupted Creep Test ........................................................................... 39
3.5 Uniaxial and Notched Bar Creep Experiments .............................................. 42
3.5.1 Specimen Design .................................................................................. 42
3.5.2 LVDT ..................................................................................................... 42
3.5.3 Testing Procedure ................................................................................. 43
3.6 Creep-Fatigue Crack Growth Experiments ................................................... 46
3.6.1 Specimen Design .................................................................................. 46
3.6.2 Fatigue Pre-cracking ............................................................................. 46
3.6.3 Side Groove .......................................................................................... 47
3.6.4 Thermocouples ...................................................................................... 47
3.6.5 Load Line Displacement Measurement .................................................. 47
3.6.6 Crack Length Measurement................................................................... 47
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3.6.7 Testing Procedure ................................................................................. 48
3.6.8 Post-test Measurement .......................................................................... 48
3.6.9 Data analysis ......................................................................................... 48
3.7 Low Cycle Fatigue Experiments ................................................................... 53
3.7.1 Specimen Design .................................................................................. 53
3.7.2 Testing Machine .................................................................................... 53
3.7.3 Machine Alignment ................................................................................ 53
3.7.4 Extensometer ........................................................................................ 54
3.7.5 LCF Testing Procedure .......................................................................... 54
Chapter 4 Uniaxial and Multiaxial Creep Test Results and Analysis................. 58
4.1 Introduction ................................................................................................... 58
4.2 Tensile Test Result at Room and High Temperatures ................................... 59
4.3 Uniaxial Creep Test Result ........................................................................... 61
4.3.1 Minimum and average creep strain rate ................................................. 64
4.3.2 Creep Ductility ....................................................................................... 67
4.4 Analysis of Uniaxial Creep Data ................................................................... 68
4.4.1 Stress Rupture....................................................................................... 68
4.4.2 Minimum and Average Creep Strain Rate.............................................. 69
4.4.3 Creep ductility ........................................................................................ 72
4.5 Creep Life Prediction of P91 Steel ................................................................ 76
4.5.1 Larson Miller Parameter ........................................................................ 76
4.5.2 Monkman Grant Relation ....................................................................... 77
4.6 Notched Bar Creep Test Results .................................................................. 79
4.6.1 Axial Deformation .................................................................................. 79
4.6.2 Creep Rupture Life ................................................................................ 83
4.7 Analysis of Notched Bar Creep Data ............................................................ 85
4.7.1 Representative stress ............................................................................ 85
4.7.2 Multiaxial Stress State on Creep Ductility .............................................. 90
4.8 Microstructural Examination of Uniaxial and Notched Bar Creep Test .......... 92
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4.8.1 Uniaxial Creep ....................................................................................... 92
4.8.2 Notched bar ........................................................................................... 93
4.8.3 Fractography of notched bar .................................................................. 96
4.9 Discussion .................................................................................................... 97
4.10 Summary ...................................................................................................... 98
Chapter 5 Creep Fatigue Crack Growth Test Result and Analysis .................... 99
5.1 Introduction ................................................................................................... 99
5.2 Creep Fatigue Crack Growth ........................................................................ 99
5.2.1 Load Line Displacement ...................................................................... 101
5.2.2 Crack Growth Behaviour ...................................................................... 101
5.3 Analysis of CFCG ....................................................................................... 103
5.3.1 CFCG Correlation with Stress Intensity Factor Range ......................... 103
5.3.2 Crack Growth Correlation with C* parameter ....................................... 105
5.3.3 Creep Crack Initiation .......................................................................... 108
5.4 Creep-Fatigue Interaction ........................................................................... 110
5.5 Fractography .............................................................................................. 113
5.6 Discussion .................................................................................................. 117
5.7 Summary .................................................................................................... 118
Chapter 6 Finite Element Simulation of Notched Bar ....................................... 119
6.1 Introduction ................................................................................................. 119
6.2 Material model ............................................................................................ 120
6.3 Finite Element Model .................................................................................. 120
6.3.1 Finite Element Meshes ........................................................................ 120
6.3.2 Creep Damage Model.......................................................................... 122
6.3.3 Creep Damage Simulation ................................................................... 123
6.4 Notched Bar Simulation Result ................................................................... 123
6.4.1 Stress Distribution ............................................................................... 123
6.4.2 Axial Displacement .............................................................................. 128
6.4.3 Creep Damage .................................................................................... 130
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6.4.4 Prediction of Rupture Time .................................................................. 133
6.5 Discussion .................................................................................................. 135
6.6 Summary and Conclusion ........................................................................... 136
Chapter 7 Influence of Prior Creep Strain on Tensile Response and Low Cycle
Fatigue Behaviour .................................................................................................. 137
7.1 Introduction ................................................................................................. 137
7.2 Global Creep Damage Tests and Results ................................................... 138
7.2.1 Global Creep Tests on Standard Specimen ......................................... 138
7.2.2 Global Creep Tests on Large Uniaxial Specimen ................................. 143
7.2.3 Global Creep Tests on Large Notched Bar Specimen.......................... 143
7.3 Tensile Tests and Results .......................................................................... 145
7.3.1 Tensile Response ................................................................................ 145
7.3.2 Influence of Prior Creep Strain on Tensile Response .......................... 148
7.4 Low Cycle Fatigue Test and Result ............................................................ 152
7.4.1 Cyclic Stress Response ....................................................................... 152
7.4.2 Determination of Cycle to Failure ......................................................... 156
7.4.3 Cyclic Stress Strain Response ............................................................. 158
7.4.4 Influence of Prior Creep Strain on LCF behaviour ................................ 161
7.4.5 Life Prediction ...................................................................................... 169
7.4.6 Fracture behaviour .............................................................................. 172
7.5 Discussion .................................................................................................. 177
7.6 Summary .................................................................................................... 179
Chapter 8 Discussion, Conclusion and Future Work ...................................... 181
8.1 Introduction ................................................................................................. 181
8.2 Future Work ................................................................................................ 184
References…………………………………………………………………………………..186
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List of Tables
Table 2.1 Typical chemical composition for P91 steel [5] .............................................. 6
Table 3.1 Test matrix for interrupted creep testing using the 8mm and 18 mm diameter
uniaxial specimens. .................................................................................................... 40
Table 3.2 Test matrix for tensile and uniaxial creep testing. ........................................ 43
Table 3.3 Test matrix for uniaxial notched bar creep testing. ...................................... 44
Table 3.4 Test matrix for creep fatigue crack growth testing and fatigue crack growth.51
Table 3.5 Test matrix for low cycle fatigue testing. ...................................................... 55
Table 4.1 Tensile properties of P91 material ............................................................... 61
Table 4.2 Ramberg Osgood material parameter ......................................................... 61
Table 4.3 Summary of uniaxial creep tests for new and ex-service material ............... 62
Table 4.4 Test duration and strain accumulation in primary, secondary and tertiary
region ......................................................................................................................... 64
Table 4.5 Creep properties of new and ex-service material ........................................ 67
Table 4.6 Creep properties based on low stress and high stress regions .................... 70
Table 4.7 Notched bar test result ................................................................................ 80
Table 4.8 Skeletal stress ratio [75] .............................................................................. 86
Table 5.1 Test loading condition and durations ......................................................... 100
Table 5.2 Grade P91 CCG parameter [85] ................................................................ 106
Table 5.3 Fatigue and creep constant ....................................................................... 112
Table 7.1 Variation of interrupted creep strain and time, creep strain rate and the creep
strain fraction for the new and ex-service material .................................................... 141
Table 7.2 The values of Nsta,Ntan,Nf10 and Nfinal ............................................................ 157
Table 7.3 Half life cycle stress strain properties for LCF and GD material ................. 161
Table 7.4 LCF parameter of material with and without prior creep ............................ 170
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List of Figures
Figure 2.1 Schematic illustration of tempered martensite microstructure[17] ................. 6
Figure 2.2 Microstructure of P91 steel a) prior austenite grain boundaries and tempered
martensitic matrix b) carbides on prior austenite and lath boundaries [6]. ..................... 7
Figure 2.3 TEM micrograph of P91 during creep at 600ºC under 70 MPa a) As
tempered b) 30,030h c)70,000h d) 80,736 h [13]. ......................................................... 7
Figure 2.4 Schematic deformation mechanism map ................................................... 10
Figure 2.5 Typical creep curve .................................................................................... 11
Figure 2.6 Influence of stress or temperature on creep curve ..................................... 12
Figure 2.7 Creep strain response using strain and time hardening laws. .................... 14
Figure 2.8 Creep rupture law representation ............................................................... 16
Figure 2.9 The J-integral along a path around a crack tip ........................................... 24
Figure 2.10 The schematic of crack propagation a) fatigue dominated, b) creep
dominated, c) creep fatigue interaction and d) creep fatigue interaction [58] ............... 31
Figure 2.11 Typical stress strain loop under constant strain cycling [61]. .................... 32
Figure 2.12 Example of cyclic hardening and cyclic softening[59] ............................... 34
Figure 3.1 Schematic orientation of specimen geometry for new material ................... 36
Figure 3.2 (a) Pipe-B dimension and schematic orientation of specimen geometry for
ex-service material, (b)Block A, (c) Block B and (d) Block C ....................................... 37
Figure 3.3 Specimen geometry of large uniaxial creep sample. .................................. 41
Figure 3.4 Specimen geometry of large notched bar creep sample. ........................... 41
Figure 3.5 Standard uniaxial creep specimen geometry.............................................. 45
Figure 3.6 Notched bar creep specimen. .................................................................... 45
Figure 3.7 Compact tension specimen geometry. ....................................................... 51
Figure 3.8 Thermocouple and PD setup for CFCG test. .............................................. 52
Figure 3.9 Loading wave (a) CFCG test with a hold time, (b) FCG test. ...................... 52
Figure 3.10 Low cycle fatigue specimen geometry. ..................................................... 55
Figure 3.11 Machine alignment. .................................................................................. 56
Figure 3.12 Extensometer used in the LCF testing. ................................................... 56
Figure 3.13 Example of loading waveform for strain ranges of 0.8%. .......................... 57
Figure 4.1 Engineering stress strain behaviour of new and ex-service material at room
temperature and high temperature .............................................................................. 60
Figure 4.2 True stress strain curve of new and ex-service material at room temperature
and high temperature .................................................................................................. 60
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Figure 4.3 Creep curve for new material tested at 620°C under 130 MPa and 160 MPa
................................................................................................................................... 63
Figure 4.4 Creep strain plot versus time for ex-service P91-B tested at 600C. ............ 63
Figure 4.5 Minimum creep strain rate of new and ex-service material ......................... 65
Figure 4.6 Average creep strain rate of ex-service material ........................................ 66
Figure 4.7 Time to rupture of new and ex-service material .......................................... 66
Figure 4.8 Creep ductility variation in term of percentage of elongation with rupture life
for ex-service material ................................................................................................ 67
Figure 4.9 Stress rupture data for P91 material. ......................................................... 69
Figure 4.10 Plot of minimum creep strain rate with available data for ex-service material
................................................................................................................................... 71
Figure 4.11 Plot of average creep strain rate with available data for ex-service material
................................................................................................................................... 71
Figure 4.12 Time to rupture against stress .................................................................. 72
Figure 4.13 Creep ductility variation in term of percentage of elongation and reduction
of area with rupture life ............................................................................................... 74
Figure 4.14 Creep ductility variation in term of percentage of elongation with rupture
life ............................................................................................................................... 74
Figure 4.15 Creep ductility variation in term of percentage of elongation with stress ... 75
Figure 4.16 Creep ductility variation in term of percentage of elongation with
normalised applied stress ........................................................................................... 75
Figure 4.17 Stress versus Larson Miller parameter plot using C= 30 for literature and
experimental data. ...................................................................................................... 76
Figure 4.18 Monkman Grant plot of rupture life versus minimum creep strain rate ...... 78
Figure 4.19 Stress versus Monkman Grant creep ductility .......................................... 78
Figure 4.20 Axial displacement for blunt notched bar for new material ........................ 81
Figure 4.21 Axial displacement for medium notch bar new material ........................... 81
Figure 4.22 Axial displacement for blunt notched bar for ex-service material .............. 82
Figure 4.23 Axial displacement for medium notch bar for ex-service material ............. 82
Figure 4.24 Rupture life of notched bar for new material ............................................. 84
Figure 4.25 Rupture life of notched bar for ex-service material ................................... 84
Figure 4.26 Rupture Life for new material based on a) von Mises stress and b)
Maximum Principal stress ........................................................................................... 87
Figure 4.27 Rupture Life for ex-service material based on a) von Misses stress and b)
Maximum Principal stress ........................................................................................... 88
Figure 4.28 Rupture life based on representative stress for a) new material and b) ex-
service material .......................................................................................................... 89
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Figure 4.29 The effect of triaxial stress state on the failure strain of notched bar for new
(P91-A) and ex-service material (P91-B) a) using axial measurement and b) reduction
of area (ROA) ............................................................................................................. 91
Figure 4.30 Optical micrograph of P91 material prior to testing for a) new condition
b) ex-service condition ................................................................................................ 92
Figure 4.31 Optical micrograph of the new P91 steel tested under a) 80 MPa, stopped
creep test after 9800 h creep test and b) 100 MPa, stopped creep test after 9400h.
Arrows show the creep cavities. .................................................................................. 93
Figure 4.32 Optical microscope image for blunt notched (P91-A-UB2a) ..................... 94
Figure 4.33 Optical microscope image for medium notched (P91-A-UM2c) ................ 94
Figure 4.34 Optical microscope image for medium notched (P91-B-8a) showing the
crack initiate at the notch root a) high magnification images of region i and b) high
magnification of region ii ............................................................................................. 95
Figure 4.35 SEM micrograph of blunt notch specimen on a) fracture surface
(b) centre of notch throat ............................................................................................. 96
Figure 4.36 SEM micrograph of medium notch specimen on a) fracture surface
(b) centre of notch throat ............................................................................................. 96
Figure 5.1 Load line displacement versus normalised time. ...................................... 102
Figure 5.2 Crack extension versus normalised number of cycles. ............................. 102
Figure 5.3 Crack growth percycle da dN vs K for CFCG test data ........................ 104
Figure 5.4 Comparison of crack growth rate at various frequencies with available
literature data ............................................................................................................ 104
Figure 5.5 Correlation of creep fatigue crack growth data with C* ............................. 106
Figure 5.6 Correlation of creep fatigue crack growth data, CCG data band and
predictive NSWA model by using axialf ................................................................... 108
Figure 5.7 Correlation of creep crack initiation and predictive model using axial
measurement a) NSW-MOD model and b) NSWA model ......................................... 109
Figure 5.8 Frequency dependence of crack growth per cycle showing increase in
cracking rate for cyclic tests in the low frequency creep dominated region (ex-service
material) ................................................................................................................... 112
Figure 5.9 Cracking behaviour a) CT-B; b) CT-C1 ; c) CT-A ..................................... 114
Figure 5.10 High magnification images of CT-B region (a) i and (b) ii, showing cracks
and cavities near the crack ....................................................................................... 115
Figure 5.11 Fracture surface of CT-A and SEM images of fracture surface on the creep
fatigue crack growth region at different frequencies a) 0.0017 Hz (CT-B1) b) 0.015 Hz
(CT-B2), c) 0.027 Hz (CT-B3) and d) 10Hz (CT-B4) ................................................. 116
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Figure 6.1 Schematic of notched bar specimen a) whole specimen b) details of notch
throat ........................................................................................................................ 121
Figure 6.2 FE Mesh a) Blunt notch b) Medium Notch ............................................... 122
Figure 6.3 Von Mises stress distribution for blunt and medium notch at
net stress 187=MPa .................................................................................................. 125
Figure 6.4 Maximum principal stress distribution for blunt and medium notch net stress
= 187 MPa ................................................................................................................ 126
Figure 6.5 Hydrostatic stress distribution for blunt and medium notch bar at net stress =
187 MPa ................................................................................................................... 127
Figure 6.6 Variation of triaxility across the notch throat for blunt and medium notch at t
= 0.5tr ....................................................................................................................... 128
Figure 6.7 Comparison of FE prediction with test data for a) blunt notch b) medium
notch ......................................................................................................................... 129
Figure 6.8 Creep damage contour for blunt notched at net stress = 187 MPa ........... 131
Figure 6.9 Creep damage contour for medium notched at net stress = 187 MPa ...... 131
Figure 6.10 Damage evolution across the notch throat at net stress of 187 MPa for a)
blunt notch and b) medium notch .............................................................................. 132
Figure 6.11 FE Prediction of rupture life using f =0.30% and 0.12% for a) blunt notch
and b) medium notch ................................................................................................ 134
Figure 7.1 Creep deformation for interrupted creep tests for ex-service material. ..... 140
Figure 7.2 Creep deformation for interrupted creep tests for new material. ............... 140
Figure 7.3 Creep strain variation against time for ex-service material ....................... 142
Figure 7.4 Creep strain variation against time for new material ................................. 142
Figure 7.5 Variation of creep strain against time for large specimens. ...................... 144
Figure 7.6 Variation of displacement against time for large notched bar specimens. 144
Figure 7.7 Engineering stress strain curve for new material with and without prior creep
strain ......................................................................................................................... 146
Figure 7.8 True stress strain curve for new material with and without prior creep strain
................................................................................................................................. 146
Figure 7.9 Engineering stress strain curve for ex-service material with and without prior
creep strain ............................................................................................................... 147
Figure 7.10 True stress strain curve for ex-service material with and without prior creep
strain ......................................................................................................................... 147
Figure 7.11 Comparison of stress strain curve behaviour of ex-service and new
material at different levels of prior creep strain a) 6-7% b) 5% c) 3% d) 1% e) without
prior creep strain ....................................................................................................... 150
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Figure 7.12 Variation of tensile properties for different level of creep strain for new and
ex-service material .................................................................................................... 151
Figure 7.13 Variation of tensile tensile strain at failure and total strain for new and ex-
service material......................................................................................................... 151
Figure 7.14 Cyclic stress response for material without prior creep strain. ................ 154
Figure 7.15 Cyclic stress response of prior creep specimens ................................... 154
Figure 7.16 Cyclic stress response or prior creep notched specimen........................ 155
Figure 7.17 Dependence of the degree of softening on the total strain range. .......... 155
Figure 7.18 Definition of Nsta,Ntan,Nf10 and Nfinal for the GD2 specimen tested at strain
range of 0.5% ........................................................................................................... 157
Figure 7.19 Cyclic stress response for a) GD1 b) GD6A and c) GD2 ........................ 159
Figure 7.20 Half life cycle for LCF specimens (without prior creep) ........................... 160
Figure 7.21 Half life cycle for GD specimens (with prior creep) ................................. 160
Figure 7.22 Comparison of cyclic stress response of material with and without prior
creep strain at room temperature for strain ranges a) 1.2%, b) 1.0%, c) 0.8%, d) 0.6%
and e) 0.5% .............................................................................................................. 164
Figure 7.23 Comparison of cyclic stress response of material with no creep damage
(LCF), with creep damage (GD) and with notched creep damage (GN) at rom
temperature for strain ranges a) 0.5% and b) 0.8%, .................................................. 165
Figure 7.24 Comparison of cyclic stress stain behaviour of material with and without
prior creep strain at strain ranges a) 1.2%, b) 1.0%, c) 0.8%, d) 0.6% and e) 0.5% .. 167
Figure 7.25 Comparison of cyclic stress stain behaviour of material with no creep
damage (LCF), with creep damage (GD) and with notched creep damage (GN) at
strain ranges a) 0.5% and b) 0.8%. ........................................................................... 168
Figure 7.26 Basquin and Coffin –Mansion plots for material without prior creep strain
(LCF specimens) ...................................................................................................... 171
Figure 7.27 Basquin and Coffin –Mansion plots for material with prior creep strain (GD
and GN specimens) .................................................................................................. 171
Figure 7.28 Cracking behaviour of GD and GN specimens a) GD3,t =1.2%,
(b) GD1,t =0.8 %, (c) GD6A,
t =0.7 %, (d) GD4,t =0.6 % (e) GD2,
t =0.5 %
(f) GN1,t =0.8 %(g) GN2,
t =0.5 %. .................................................................. 173
Figure 7.29 Cracking behaviour of LCF specimens a) t =1.2%, (b)
t =0.8 %,
(c) t =0.7 %, (d)
t =0.6 % (e) t =0.5 %. ....................................................... 174
xviii
Figure 7.30 SEM images of GD4 specimen (t =0.6 %) (a) Fracture surface
containing crack propagation and fracture zone, (b) and (c) high magnification of crack
propagation zone. ..................................................................................................... 175
Figure 7.31 SEM images of LCF specimen (t =0.6 %)(a) Fracture surface containing
crack propagation and fracture zone, (b) and (c) high magnification of crack
propagation zone. ..................................................................................................... 176
1
Chapter 1
Introduction
Many conventional power plants which have been designed for based load operation
are now required to operate in a ‘flexible manner’ in response to energy demand and
increased use of renewable energy sources. This flexible operation will pose new
challenges to component integrity in ageing conventional plant, which it is widely
recognised will play a crucial role in maintaining materials performance and structural
integrity. Flexible operation implies that the mechanical and thermal loads on high
temperature components are cyclic, which may lead to issues with interactive creep-
fatigue failure of high temperature components.
Significant creep damage accumulation may exist in the component that is operated at
elevated temperature. The combination of creep fatigue interaction on the service
exposed material may accelerate the failure and reduce the components service life.
Therefore it is important to accurately predict the remnant life of power plant
components under the creep-fatigue and low cycle fatigue loadings. Current
methodologies for remnant lifetime prediction under these conditions are limited.
Therefore further work is required to enable accurate component failure analyses to be
achieved. This work is performed in collaboration with the EU MACPLUS Project [1],
EPSRC project Flex-E-Plant [2] and ASTM/EPRI [3].
The material of interest is P91 steel, which is widely used in high temperature power
plant components. P91 material is classified as martensitic steel and has high creep
strength, high thermal conductivity, low thermal expansion and high corrosion
resistance. Due to its high material performance, P91 steel widely used for long term
service at operating temperatures over 600ºC in high temperature component of boilers,
steam lines and pipes of power plant. For service exposed material, it is necessary to
investigate the creep deformation and material properties. Thus, a series of uniaxial
creep tests have been performed on the ex-service material to examine the creep
deformation and failure properties compared to new material.
2
Cyclic operation in high temperature component may induce creep-fatigue interaction
which can be more severe compared to static creep load alone. A characterisation of
creep fatigue interaction is therefore needed to be better understood and the
assessment of the long-term failure in high temperature component is important. Thus,
creep fatigue crack growth testing has been performed on the new and ex-service
material to examine the creep fatigue crack growth behaviour and we have proposed
an interaction diagram to evaluate the creep fatigue crack growth interaction.
Creep damage may exist in the power plant components that have been in operation
for many years. Creep damage is manifested by the formation and growth of creep
voids and cavities within the microstructure of the material. In P91 steel, it is usually
associated with the tertiary stage of creep regime; however it can also initiate at the
relatively early stages of creep and develop gradually throughout the creep life. Creep
strain/damage can be introduced into a material by performing interrupted uniaxial
creep testing. The uniaxial creep tests were interrupted at various level of creep
strain/damage. Subsequently, tensile testing on interrupted creep specimens was
performed in order to investigate the influence of creep strain/damage on tensile
deformation. In order to investigate the effect prior creep strain/damage of fatigue
behaviour, low cycle fatigue tests are performed on the material with and without prior
creep damage. The results of the tests are compared with both material conditions.
1.1 Thesis Framework
This thesis contains eight chapters and the summary of each chapter is presented as
follows:
Chapter 1 gives a general background of the overall research work. The aim of the
research and objectives are formulated to achieve the main purpose of the study.
Chapter 2 provides a general overview of the background knowledge relevant to this
research, elastic plastic, damage constitutive model, fracture mechanics concept,
creep fatigue crack growth and low cycle fatigue in relation to the P91 material.
Chapter 3 details the material condition and experimental procedures performed on
P91 material. The introduction of prior creep damage on the material, specimen
3
geometry and dimensions are described in this chapter. Experimental procedure and
analyses technique accordance to standard were used for notched bar creep, creep
fatigue crack growth and low cycle fatigue test have been described in Chapter 3.
Chapter 4 presents the results of the tensile, uniaxial and notched bar test on the
examined material. The main results of this chapter are to characterize the uniaxial and
multiaxial behaviour of P91 material. The short-term uniaxial creep tests results were
analysed and compared with available literature data to examine the long term
exposure of P91 material. The results of notched bar creep tests were analysed in
order to predict the creep rupture life under multiaxial stress state. The effect of
multiaxial stress state on creep ductility was examined by employing the cavity growth
model. At the end of Chapter 4, metallographic assessment on the uniaxial and
notched bar specimen were presented to identify the damage mechanism.
Chapter 5 presents the results and analyses of creep fatigue crack growth tests. The
short-term test results obtained are compared to the long term-data predicted by the
NSW model. A linear cumulative rule has been used to predict the tests results and an
interaction diagram has been plotted which provides a basis to predict the cracking
behaviour. Metallographic and fractographic assessment were also presented in this
chapter to investigate the failure mechanism.
Chapter 6 presents the finite element analyses performed on the notched bar. The
analyses were carried out to study the influence of notch geometry on the stress
distribution across the notch throat during the creep exposure. The finite element
analyses coupled with damage model have been used to evaluate the damage
evolution and predict the rupture life under multiaxial stress condition. The predictions
from the FE models are compared with experimental data for the material.
Chapter 7 provides the experimental results of the prior creep strain effect on tensile
behaviour and low cycle fatigue. In this chapter, the process of introducing creep strain
into the material is explained in detail and the global creep damage test results are
presented. The results of tensile and low cycle fatigue tests were analysed and
compared with the material without prior creep strain in order to examine the influence
of prior creep strain on monotonic and cyclic behaviour. Fractographic assessment has
been presented to examine the cracking and fracture behaviour.
4
Chapter 8 summarizes the overall works of this research. The general findings of each
chapter are discussed and presented in this chapter. Practical implications of the
findings and recommendations are given for the future works.
1.2 Aims and Objectives
The aim of this research is to examine the impact of plant cycling on the failure
behaviour of high temperature components and the effects of material’s service
exposure including prior creep damage on subsequent creep-fatigue crack growth and
low cycle fatigue behaviour. These effects which are important for safe component
operation have been included in predicting the remnant life of high temperature
material. The main objectives are:
1. To review data on creep, creep fatigue and assessment method under creep
and creep fatigue conditions
2. To examine the creep behaviour under uniaxial and multiaxial stress state and
characterised relevant material properties by performing uniaxial and notched
bar creep tests.
3. To examine the creep fatigue crack growth behaviour by performing creep
fatigue crack growth testing.
4. To identify the extent of creep/fatigue interaction and propose a simple linear
damage summation rule to predict creep/fatigue failure of new and service
exposed material.
5. To evaluate the damage evolution and predict the rupture life under multiaxial
stress condition by finite element analysis.
6. To examine the influence of prior creep strain/damage on monotonic tensile and
cyclic stress strain behaviour.
7. To perform metallographic and fractographic assessment to identify dominant
mechanism involved under multiaxial stress condition and creep fatigue
condition to support experimental findings.
5
Chapter 2
Creep and Creep-Fatigue Review
2.1 Introduction
This chapter mainly describes the general overview of the creep deformation, fracture
and damage mechanism. Concept of elastic plastic and creep fracture mechanics
assessment which are relevant to the following chapters are presented. Creep fatigue
crack growth behaviour is characterised and interaction effects are reviewed. Cyclic
deformation under low cycle fatigue loading which introduced the plastic behaviour and
cyclic hardening and cyclic softening are reviewed in this chapter.
2.2 P91 Steel and its Microstructure
P91 was originally developed by the Oak Ridge National Laboratory for reactor and
power plant applications [4]. In power plants, the P91 steel is used for high temperature
components which operate in creep regime. P91 steel known as modified 9Cr-1Mo
consists of 9% chrominum, 1% molydenum, and vanadium and niobium. Table 2.1
shows the ASMEl chemical composition of P91 steel [5].
Figure 2.1 shows the schematic illustration of tempered martensitic microstructure after
normalizing and tempering. The microstructure of P91 steel consists of prior austenite
grain boundaries and lath martensitic interfaces. The average values of prior austenite
grain boundaries is about 20 µm [6]. Carbides are present along the prior austenite
grain boundaries as shown in Figure 2.2(b). Both inter and intra granular carbides
precipitated appeared in different morphologies like that of globular, cylindrical and to
lenticular. The most common carbides in martensitic microstructure are M23C6 and MX.
MX carbides were found to be very fine (20-30nm) as compared to M23C6 (200-300nm).
The presence of very fine carbides along the lath interfaces would prevent the
migration of interface during long term exposures and thereby impart good high
temperature properties [6].
Figure 2.2 shows typical SEM micrograph of the P91 microstructure. It is similar among
creep strength enhanced ferritic steel Grade91, Grade 92 and Grade 122. The M23C6
are mainly distributed at lath, block, packet and prior austenite grain boundaries, while
6
fine MX carbonitrides are mainly distributed in the matrix within lath at the boundaries.
The martensitic grain structure of P91 produces high dislocation density which causes
a retardation of creep deformation. However during long term thermal exposure [6-13],
the dislocation structure of P91 steel changed. Figure 2.3 shows the TEM micrograph
of change in dislocation structure during creep at 600°C under 70 MPa for different
durations [13]. The as-tempered virgin material had fine sub-grains and high dislocation
density. At up to 30,000h there was no change in the fine dislocation structure. After
70,000 h, equiaxed sub grains were revealed and the sub-grains size gradually
increased. The dislocation density drastically decreased up to rupture, which degrades
the creep strength [13]. The change in microstructure was strongly accelerated by the
influence of the applied stress in creep [14]. The basic way in which creep resistant
steels can be strengthened are by solid solution hardening, precipitation or dispersion
hardening, dislocation hardening and boundary hardening [15, 16] .
Table 2.1 ASME P91 steel chemical composition [5]
C Si Mn P S Cr Mo V Nb N Ni Al
0.10 0.38 0.46 0.02 0.002 8.10 0.92 0.18 0.073 0.049 0.33 0.034
Figure 2.1 Schematic illustration of tempered martensite microstructure[17]
7
Figure 2.2 Microstructure of P91 steel a) prior austenite grain boundaries and tempered
martensitic matrix b) carbides on prior austenite and lath boundaries [6].
Figure 2.3 TEM micrograph of P91 during creep at 600ºC under 70 MPa a) As
tempered b) 30,030h c)70,000h d) 80,736 h [13].
8
2.3 Elastic Plastic Deformation
A material will experience deformation when subjected to an applied load. This
deformation can be classified as elastic and plastic deformation. The deformation
under uniaxial and multiaxial deformation and related formulae are described in the
following sections.
2.3.1 Uniaxial Deformation
When a specimen is loaded in a uniaxial direction, the total strain of the specimen
experienced is elastic, plastic and creep deformation (time dependent). The elastic
strain component is simply defined as stress divided by the elastic modulus, (E) and
the plastic strain is defined by the power law [18] and given by
NpA
(2.1)
where Ap and N are the material properties. In a normalised form, the stress strain
relationship can be expressed as
0 0
N
(2.2)
where , 0 and 0 are the material constants. The 0 usually can be represented by
yield stress, y . The total elastic plastic response may be given as Ramberg Osgood
[18] material model and is written by:
NpA
E
(2.3)
2.3.2 Multiaxial Deformation
Under multiaxial stess state, where the three principal stresses exist, there are two
generally accepted criteria for predicting the onset yielding or the failure of the material
which are Tresca criterion and von-Mises criteria. Tresca criterion assumes that
yielding occurs when maximum shear stress reaches the value of shear stress in the
uniaxial tensile test. Tresca yield criterion can be expressed as:
1 2 2 3 3 1max , ,e (2.4)
9
where 1 , 2 and 3 are the principal stresses 1 2 3 .
Von-Mises yield criterion implies that yielding depends on all three values of principal
stresses. Yielding occurs when the von Mises equivalent stress attains its critical value.
The equivalent stress or von Mises stress can be given by following expression:
1/22 22
1 2 2 3 3 11
2
(2.5)
The von Mises stress predicts the material will fail at a higher stress than the Tresca
criterion and von Mises stress criterion is usually used in the fracture mechanics.
In multiaxial stress state, the mean or hydrostatic stress is given by:
1 2 3
3m
(2.6)
where 1 , 2 and 3 are the principal stresses 1 2 3 . The mean stress is a
uniform stress applied to a body that is equal in all directions. The mean stress does
not contribute to deformation and can only cause elastic volumetric stain.
For multiaxial deformation, by assuming the Ramberg Osgood material model, the
equivalent plastic strain can be defined as
0
0
p Nep eA
E
(2.7)
where the e is the equivalent stress in Eqn (2.5).
2.4 Creep Deformation
A material may experience creep deformation when it is subjected to a stress at a
temperature that is greater than 30% of their absolute melting temperature. Creep is a
time dependent process which generally occurs at high temperature. Creep strain is a
permanent (non-recoverable) and can lead to failure (creep rupture and creep crack
growth) [19].
The creep mechanism can be represented by a schematic deformation map as shown
in Figure 2.4 in which the normalized stress (σ/E) is plotted as the function of
homologous temperature (T/Tm) where, σ is the stress, E is the elastic modulus, T is the
10
absolute temperature and Tm is the melting temperature in Kelvin. In this figure, the
creep mechanism can be categorised into two distinct regions namely, diffusion and
dislocation creep. Diffusion creep can be associated with low stress and high
temperature and occurs due to the diffusion of point defects in the material. The
dislocation creep known as power law creep occurs at high stresses and temperature
due to glide and climb of dislocation motion along the slip planes. This dislocation
motion also involves the diffusion of vacancies and thus the strain rate is thermally
activated by the influence of stress and temperature.
All creep tests in this work have been performed on P91 steel at 600 to 620°C under
relatively high stresses, therefore, dislocation creep is expected to be dominant
mechanism.
Figure 2.4 Schematic deformation mechanism map
2.4.1 Creep Deformation Stages
The creep deformation can be obtained from a uniaxial creep test in which a tensile
specimen is subjected to a constant load at elevated temperature until it ruptures. A
typical creep curve is plotted in terms of creep strain and time as shown in Figure
2.5.The slope of this curve is referred to as creep strain rate. As shown in Figure 2.5,
the creep curve can be categorised into three main regions namely, primary, secondary
and tertiary region. In the primary region, the strain rate decreases with time mainly
11
due to strain hardening process. This process resists the occurrence of deformation. In
the secondary creep region which is also known as steady state region, where the
longest time period may occur, the creep strain rate is almost constant and the slope of
the line is called as minimum or steady state creep stain rate, min or s . In this region,
a balance between recovery and strain hardening process occurs. In the tertiary region,
the strain rate rapidly increases and failure occurs in this region. The creep strain at
failure time, rt , is often called as the uniaxial creep ductility, f .The creep failure can
be caused by the necking and the microstructural changes such as grain boundary
separation and the formation of internal cracks, cavities and voids.
In the secondary or steady state creep region, the creep strain rate can be expressed
by Norton power law [20] given as:
ns A
(2.8)
where A is the material constant and n is the power law creep exponent. The constant
A and n are obtained by fitting it to the secondary creep region in the uniaxial test data.
A creep curve profile may vary at different stresses and temperatures as illustrated in
Figure 2.6. As shown in Figure 2.6, the creep strain will increase as stress and
temperature increases. The effects of stress and temperature on the creep ductility ( f )
of a material vary appreciably depending on the testing condition.
Figure 2.5 Typical creep curve
12
Figure 2.6 Influence of stress or temperature on creep curve
2.4.2 Creep Constitutive Law
As mentioned previously, the shape of creep curve as well as creep strain rate may
vary depending on the applied stress and temperature. A number of state variable
models have been proposed to describe creep throughout the entire life of a
component. The simplest constitutive relationships are the strain and time hardening
constitutive law. The strain hardening law is expressed as:
, ,c cf T (2.9)
where the creep strain rate as a function of stress, temperature and creep strain. Time
hardening law is expressed as a function of time and is given by:
, ,c f T t (2.10)
Figure 2.7 shows the illustration of the strain and time hardening when the stress and
temperature are varied. As shown in Figure 2.7 (a), when the strain hardening is
applied, the point A on the curve 1 1, T is transferred horizontally (constant creep strain)
to point B on the curve 2 2,T where the stress and temperature are increased. This
process is repeated where point B then moves to C and transferred horizontally to point
D and E which then makes a ABCDE curve in Figure 2.7 9(b). Similarly, when the time
hardening rule is applied, point A is transferred vertically to point B’ on the curve 2 2,T .
The same process is repeated until a curve AB’C’D’E’ is formed as shown in Figure
2.7(b). The strain hardening law may predict a higher creep strain accumulation than
13
the time hardening law if the primary strain is dominant. The time hardening law may
be applicable when a large tertiary creep region is dominant. During the secondary
creep, both strain and time hardening predict the same creep strain accumulation.
The strain and time hardening law can be written in the normalized form:
, ,c
c
ff T
(2.11)
, ,c
r
tf T
t
(2.12)
where f and rt is the creep ductility and time to rupture, respectively. Eqn (2.11) is
known as strain fracture rule and Eqn (2.12) is known as life fraction rule. The strain
and life fraction rule can be used to predict the failure under variable stress and given
as:
,
,1
,
c
fT
T
T
(2.13)
,
,1
,rT
t T
t T
(2.14)
The strain hardening law in Eqn (2.13) predicts the failure when the sum ratio of creep
strain accumulation and creep ductility attains unity. Similar to strain hardening law, the
rupture time can be predicted using the life fraction rule in Eqn (2.14).
14
Figure 2.7 Creep strain response using strain and time hardening laws.
2.4.3 Creep Power Law
Creep is a time dependent process which is similar to plasticity behaviour which is time
independent. Analogues to plasticity in Eqn (2.2), the creep strain rate in steady state
region can also be represented as power law relation which is known as Norton creep
law [20]. The power law relation can be given as:
00
nn
s A
(2.15)
where 0 and 0 are the normalising strain rate and stress for creep, respectively. The
parameter A 0 0n and n are the material constants which depend on temperature
and can be obtained by fitting the secondary creep region in logarithmic axes of creep
curve. The value of 0 is usually taken as 1h-1[21].
A power law relation in Eqn (2.15) is used to determine the creep strain rate in
secondary creep region. In the primary region, the creep strain may also be
represented by a power law relation [22] which can be written as follows:
15
pnc pp C t (2.16)
where C , pn and p are the time dependent material constants. By differentiating Eqn
(2.16) and using the strain and time hardening law, the primary creep strain can written
as Eqn (2.17) and (2.18), respectively.
/ 1 1/1/ pn p pc pp pC
(2.17)
1pn pcp pC t
(2.18)
2.4.4 Average Creep Strain Rate
The average creep strain rate, A , at a given stress can be defined by the ratio of the
uniaxial creep ductility, f , to the time to rupture, rt , i.e,
fA
rt
(2.19)
The average creep strain rate can be used to describe all the three regions in the creep
curve as illustrated in Figure 2.5. Similar to the steady state creep strain rate, the
average creep stain rate can be represented as power law creep as given by:
00
A
A
nnc
A AA
(2.20)
where AA and An are the material constants and can be obtained from the rupture
data. 0 and 0 are normalizing creep stress and creep strain rate, respectively and
0 often taken as 1h-1.
2.4.5 Creep Rupture Time
For most engineering alloys, the creep rupture time, rt , which has an inverse power
law dependency on stress can be described by:
0 0
r
rfr rt B
(2.21)
16
where f is the uniaxial failure strain at stress 0 . rB and r are the rupture constants
and can be obtained by fitting to the uniaxial creep data in logarithmic axes as
illustrated in Figure 2.8.
Figure 2.8 Creep rupture law representation
Creep rupture time can be related to average creep strain rate by combining Eqn (2.20)
and Eqn (2.21) as given by:
A rn vf A r A rt A B
(2.22)
Based on Eqn (2.22), the creep failure strain is independent of stress if A rn and n
the creep failure strain decreases when the stress decreases A rn .
Creep failure in uniaxial tension under constant stress can also been described by
Monkman Grant relation [23].In this model, the creep failure is controlled by steady
state or secondary region of creep curve;
s rt C (2.23)
where s is the secondary creep strain rate, rt is the rupture time, and C are the
material constants.
Creep ruptures behaviour for P91 steel has been reported by many researchers [17,
24-26]. In Abe [17], the proposed mechanism of P91 steel is due to the occurrence of
microstructure degradation during creep exposure and is classified as:
a) Preferential recovery of martensitic microstructure in the vicinity of prior
austenitic grain boundaries (PAGBs)
b) Static recovery of lath martensitic microstructure
17
c) Dissolution of fine MX carbonitrides and precipitation of Z-phase
d) Reduction of solid solution hardening due to precipitation of Fe2Mo Laves
phase
2.4.6 Multiaxial Creep Deformation
Uniaxial creep data is inadequate in predicting the creep deformation of material
subjected to multiaxial condition. This is due to the fact that that creep deformation and
creep rupture can be dependent upon different multiaxial stress state which cannot be
differentiated by uniaxial testing [27]. Therefore, a general constitutive equation for
multiaxial conditions is produced by generalising the one for uniaxial conditions [28, 29].
Creep deformation under uniaxial condition can be related to plasticity by replacing the
plastic strain with the creep strain rate. Thus, it is anticipated that the equivalent creep
strain rate under multiaxial stress conditions is a function of equivalent stress as shown
by
c f (2.24)
where the function f is defined is the same way under uniaxial conditions.
Creep rupture time under uniaxial conditions can be described by Eqn (2.21). Under
multiaxial conditions, the rupture time can be described by an equation similar to
uniaxial condition by replacing with a representative stress, rep which is expressed
as :
rr r rept B
(2.25)
The concept of representative stress has been introduced to predict the rupture life for
notched bar which consider the relative contribution of each stress components. This
concept was proposed by Hayhurst et.al [30, 31] based on the observation that failure
is often controlled by a combination of maximum principal stress, 1 , and von Mises or
equivalent stresses, or e . The combination of these stresses results in
representative stress and is given by:
1 1rep e (2.26)
where is the material constant and the value of determines the failure process.
The value of 1 indicates that the failure is controlled by maximum principal stress
and the value of 0 indicate that the failure is controlled by equivalent stress.
18
Based on experimental data on P91 material [32] the value of is 0.18 which
indicates failure is governed predominantly by equivalent stress. Other methods have
also been used to relate the maximum principal stress, equivalent stress and
hydrostatic stress in predicting the rupture time under multiaxial stress condition [27,
33].
2.4.7 Multiaxial Stress State on Ductility
It is well known that creep ductility exhibit a strong dependence on the multiaxial stress
state. Many models that can be used to predict this dependence such as Rice and
Tracey [34] , Cocks and Ashby [35] and Spindler [36]. These models show that the
ratio of multiaxility and uniaxial ductility, *f f , is a function of hydrostatic stress and
the equivalent stress, m e , which is often known as triaxility. The model developed
by Rice and Tracey for void growth by the rigid plastic deformation can be expressed in
terms of ratio between multiaxial failure strain to uniaxial failure strain that gives,
*3
1.652
f m
f e
(2.27)
An alternative model has been proposed by Cock and Ashby which assumed that grain
boundaries cavities grow by the power law creep of the surrounding material. The
multiaxial ductility predicted by this model is given by
*2( 1/ 2) 2( 1/ 2)
sinh sinh3( 1/ 2) ( 1 / 2)
f m
ef
n n
n n
(2.28)
where n is creep exponent. It should be noted that when n is large, Eqn (2.28) is
insensitive to small changes in n.
A model proposed by Spindler accounted that both cavity nucleation and growth
determine the ductility. The Spindler model expressed by;
*1 31
exp 12 2
f m
f e e
p q
(2.29)
where p and q are constants.
19
2.5 Creep Damage Model
Creep damage in polycrystalline materials is mainly due to the nucleation and the
growth of voids and micro cracks and coalescence into macro cracks at the grain
boundaries. This creep damage process causes a progressive increase in the creep
strain rate as well as a final rupture of the material. It is usually associated with the
tertiary creep region although the voids may develop in the primary and secondary
creep region.
Two main approaches have been adopted in the literature to evaluate the creep
damage. The first approach is refereed to continuum damage mechanics (CDM)
method is based on phenomenological consideration. The second approach is cavity
growth mechanics (CGM) developed based on physical modelling for microstructure
evolution of material under external loading. The creep damage accumulation is
associated with void nucleation and growth which occurred predominantly on the grain
boundaries .Therefore it has adopted in many design code or assessment procedure to
predict the creep deformation and rupture at elevate temperature. A state of art review
of creep analysis and design under multiaxial stress state based on CDM and CGM
can be found in reference [37, 38]. Here a brief description and related formulae for
CDM and CGM are explained.
2.5.1 Continuum Damage Mechanics
The basis for the continuum damage mechanics theories and the concept of damage
parameter was pioneered by Kachanov [39]. In order to characterized a gradual
deterioration of material’s microstructure under creep condition, Kachanov introduced
the damage parameter, such that 0 1 . The value of 0 correspond to the
undamaged state and decreases as damage develop. Kachanov’s theory is based
on the assumption that two physical process-accumulation of damage (deterioration of
grain boundaries) and creep are independent. This theory was then modified by
Rabotnov [40, 41] where he suggested to account for coupling between the two
mentioned variable. The empirical equation have been proposed such that the
instantaneous creep strain rate, c and damage accumulation can be written as
0
0
1
1 1
n nc
m m
a
(2.30)
20
0
0
1
1 1
c
(2.31)
where the parameter , , , , ,m n a c and 0 are the material constants [41]. In a
general form, the rate of creep damage accumulation can be written as
,c
f
(2.32)
By integrating Eqn (2.32), damage parameter can be defines as [19]
c
f
(2.33)
Under multiaxial stress condition, the same equation can be used by replacing the
instantaneous creep strain and strain rate to the equivalent creep strain and strain rate
respectively, corresponding to the equivalent stress.
2.5.2 Cavity Growth Mechanics
Cocks and Ashby model [35] proposed a model based on the constrained cavity growth
mechanism. In this model, the ratio of the time to failure under multiaxial condition,*ft ,
and uniaxial condition, ft , is given as
*2 1/ 2
sinh3 1/ 2
1/ 2sinh 2
1/ 2
f
f m
e
nt n
t n
n
(2.34)
If the average power law creep strain rate is assumed to be applied, the following
expression may be written as
*
*
f fA
f ft t
(2.35)
The ratio of time and strain to failure under the multiaxial and uniaxial condition can be
related to multiaxial strain factor (MSF) which is similar to Eqn (2.28) can be given as
the following relationship:
21
* *2 1/ 2
sinh3 1/ 2
1/ 2sinh 2
1/ 2
f f
f f m
e
nt n
MSFt n
n
(2.36)
Cavity growth theory and model has been adopted in the design code for high
temperature e.g. R5 and multiaxial creep deformation criteria are therefore established
to analyse the creep behaviour of the creep behaviour of high temperature materials
under multaxial stress state. In British R5 Procedure [42], a ductility exhaustion
approach is used to evaluate the creep damage which can be expressed as
*0 ,
t
cf
dt
(2.37)
where c is the instantaneous equivalent creep strain rate and
*f is the multiaxial
creep ductility which is function of stress and equivalent creep strain rate [36]. Using
Eqn (2.37) to calculate creep damage there are two values that need to be known, c
and *f .
2.6 Fracture Mechanics Concept
Fracture mechanics concept have been classified into linear elastic fracture mechanics
(LEFM), elastic plastic fracture mechanic (EPFM) and time dependent fracture
mechanics (TDFM). LEFM can be used when the stress behaviour and load line
displacement is linear. The relevant crack tip parameter in LEFM is the stress intensity
factor, K. When the LEFM is no longer valid due to large plasticity, EPFM is used and
the relevant crack tip parameter is J-integral. Finally, TDFM which is also known as
creep fracture mechanics is used when the stress strain behaviour and load
displacement behaviour is time dependent. The crack tip stress and deformation field
changes with time and the relevant crack tip parameter is C* integral [28]. A brief
description and related formulae of this approach are presented in this section.
2.6.1 Linear Elastic Fracture Mechanics
In a cracked body, the linear elastic fracture mechanic parameter, the stress intensity
factor, is used to describe the magnitude of the stress field ahead of the crack tip is
22
dependent on the body geometry, crack size and applied load. The stress intensity
factor is determined by:
/K Y a W a (2.38)
where is the applied stress, a is the crack length and Y is the non-dimensional
shape function that is dependent on geometry. For conventional fracture geometry the
solution for /Y a W can be found in fracture mechanics text book [43]. For a compact
tension specimen the shape function can be given as:
3/2
2 // / /
1 /
a WY a W W a f a W
a W
(2.39)
where a is the crack length ,W is the thickness and /f a W is calculated using:
2 3 4/ 0.886 4.64 / 13.32 / 14.72 / 5.6 /f a W a W a W a W a W
(2.40)
The stress in Eqn (2.38) for compact tension specimen having a side groove can be
described as
N
P B
BW B
(2.41)
where P is the applied load, W is the specimen width. B and NB are the specimen
thickness and side groove specimen thickness , respectively. The stress component
ahead of the crack tip which is normal to the crack plane, yy is given by
2yy
K
r
(2.42)
where r is the distance from the crack tip.
23
2.6.2 Elastic Plastic Fracture Mechanics
For a non-linear or elastic plastic fracture mechanics, J integral can be defines as [44]
is i
uJ W dy T ds
x
(2.43)
where is an integration contour around the crack tip, iT is the traction vector, iu is the
displacement vector and ds is the distance along the contour as shown in Figure 2.9.
The strain energy density, sW can be expressed as:
0
ijs ij ijW d
(2.44)
where ij and ij are the stress and strain tensor, respectively. The traction vector is
evaluated by:
i ij jT n (2.45)
where jn is the unit vector normal at a given plane.
The stress and strain field around the crack tip under elastic plastic condition can be
describe by HRR solution presented by Hutchinson[45] and Rice and Rosengren [46],
such as shown below:
1
1
0 0 0
;Nij
ijp p p N
JN
I r
(2.46)
1
0 0 0
;
N
Nijij
p p p N
JN
I r
(2.47)
where ij and ij are the non-dimensional functions of power law hardening stress
exponents, N and crack tip angle,. A table of HRR solution for ij and ij is given by
Shih [47].
24
Figure 2.9 The J-integral along a path around a crack tip
2.6.3 Creep Fracture Mechanics
The C-integral parameter is analogous to J-integral by swapping the strain rate and
displacement with displacement rate. Under widespread and steady state creep, the
creep fracture mechanic, C* may be defined as:
* ii
uC Wdy T ds
x
(2.48)
where is an integration contour around the crack tip, iu is the displacement rate
vector and W is the strain energy rate density and is given by:
0
ij cij ijW d
(2.49)
where cij is the creep strain rate.
Under small scale and widespread creep condition, the crack tip stress and strain
distribution can be characterised using Riedel and Rice (RR) [48] expression as given
by:
25
1
1
0 0 0
*;
nijij
n
Cn
I r
(2.50)
1
1
0 0
*;
nijij
n
Cn
I r
(2.51)
where ij and ij are the stress and strain rate tensors functions of crack tip angle,
and creep exponent, n. The quantities of ij and ij has been reported by Shih [47]. 0
is the normalise stress, 0 is the normalise strain rate and r is the radial distance from
the crack tip. The dimensionless constant nI can in RR equations can be calculated
using [19]:
Plane Stress: 1 2.9
7.2 0.12NIn n
(2.52)
Plane strain: 1 4.6
10.3 0.13NIn n
(2.53)
The stress ij and strain ij can be correlated to the angular stress ij and strain ij by
a power law such as follow:
; ;n
eq eqn n (2.54)
For a power law creeping material, the creep fracture mechanics, C* can be estimated
using several methods including experimental [49], EPRI solution, and reference stress
method. By using the first method, the C* parameter can be determined experimentally
by following relation:
*
N
PC H
B W a
(2.55)
where P is the applied load and is the load line displacement rate. NB and W are
the specimen side groove thickness and width, respectively. H and are the geometry
26
dependent constants. For a compact tension specimen; 1H n n and =2.2 are
used [49].
For steady state creep dominant conditions, the crack growth rate is expected to be
described by the *C parameter:
*a DC (2.56)
where D and are the CCG power law coefficient and exponent respectively.
2.6.4 NSW model
A model that can be used to predict creep crack growth under static conditions is
known as NSW model [50]. The model assumed that the crack advanced occurred
when the creep ductility is exhausted at the growing tip. The creep crack growth rate as
a function of multiaxial ductility *f and *C is written as:
* 11/( 1)
*
1
n
nnNSW c
nf
n Ca Ar
I
(2.57)
where cr is creep process zone size that is usually related to material’s grain size.
A modified version, referred to NSW-MOD model [51, 52] has been derived to predict
the creep crack growth rate under steady state creep condition which consider the
dependence of creep strain on crack angle and creep exponent. By this model, the
creep crack growth rate is written as:
* 11/( 1)
*
max
,1
,
n
nn eNSW MOD c
n f
nCa n Ar
I n
(2.58)
where the crack growth is assumed to occur along the direction where the ratio of
equivalent strain to multiaxial failure strain, *eq f reaches a maximum. The angular
function of ,e n for both plane stress or plane strain conditions and
*, ,eq fn n are reported in Ref [47]. It is recommended that the multiaxial
27
creep ductility, *f ,may be estimated as the uniaxial failure strain, f ,under plane
stress condition and 30f under plane strain condition [53].
For a range of steels, the creep crack growth rate is most sensitive to the multiaxial
creep ductility and can be approximated reasonably as:
*0.85
*
3NSWA
f
Ca
(2.59)
where the unit of a and *C are mm/h and MPam/h, respectively. Eqn (2.59) is
referred as the approximate NSW (NSWA) model [50].
In static CCG test, a period of time exists prior to the on-set of crack extension which
often referred as creep crack initiation (CCI) time. Creep crack initiation time may be
defined as the time for a small amount of crack extension to occur, usually 0.2 mm [54].
It may be estimated by assuming that the crack grows at constant rate from the point of
initial loading and can be written as:
ia
ta
(2.60)
Lower and upper bound prediction of it may be obtained by using the initial CCG rate,
0a , or steady state CCG rate, sa . The CCI can be predicted by
0i
s
a at
a a
(2.61)
where 0 ( 1)sa a n . The creep crack initiation can be predicted by using NSW-MOD
and NSWA which can be expressed in Eqn (2.62) and (2.63), respectively.
* *1 1
* *1/ 1 1/ 1max max
1
n n
n nf fn nin n
e ec c
I Ia at
C Cn Ar Ar
(2.62)
28
0.85 0.85
1
3 3
fi
a nat
C C
(2.63)
The prediction using Eqn (2.62) and (2.63) will vary depending on whether plane stress
or plane strain conditions are assumed.
2.7 Creep- Fatigue Crack Growth
Most of the power plant components are subjected to non-steady operating conditions
which can lead to various combinations effects of creep, fatigue and thermal fatigue
crack growth [55, 56]. The failures in such conditions depend on heat treatment,
temperature, cyclic loading and operating environment. This section concerned mainly
with situations where creep and fatigue crack growth may take place.
2.7.1 Fatigue Crack Growth
Typical crack growth under cyclic loading condition can be divided into three regions,
namely, threshold, propagation and rupture which correspond to the three regions on
the fatigue crack growth curve. In linear fracture mechanics, the stress intensity factor
is introduced to describe the stress and strain fields around the crack tip. Under fatigue
control conditions, the crack growth rate percycle, /da dN can be described by the
elastic stress intensity factor using the Paris law [57] which can be expressed as:
pdaK
dN
(2.64)
where /da dN is fatigue crack growth rate in mm/cycle. and p is a material constant.
It is found that for most steels p=3-5. K is the stress intensity factor and can be
calculated using following equation:
1/2 3/21/2
2
1N
P a WK f a W
a WBB W
(2.65)
where P is the load range, a is the crack length, W is the width, B is the thickness,
NB is the thickness with side groove and f a W is calculated using:
29
2 3 40.886 4.64 13.32 14.72 5.6f a W a W a W a W a W
(2.66)
2.7.2 Creep-Fatigue Crack Growth Interaction
Combined creep and fatigue crack growth may take place at elevated temperatures. In
most cases fatigue dominates at higher frequencies (f > 1 Hz) and creep dominates at
lower frequencies (f > 0.1 Hz) and hold times [56]. The total crack growth per cycle is
contributed by the cyclic dependent (fatigue) component and the time dependent
component, which can be expressed as linear cumulative rule by:
total fatigue creep
da da da
dN dN dN
(2.67)
where totalda dN is the total crack growth rate in mm/cycle. fatigue
da dN and
creepda dN are the cyclic dependent (fatigue) component and time dependent (creep)
component, respectively. By considering the frequency effect the Eqn (2.67) can be
rewrite as:
3600
creep
total fatigue
da dtda da
dN dN f
(2.68)
where f is the frequency of load cycle in Hz. The fatigue crack growth rate in Eqn
(2.64) and creep crack growth rate in Eqn (2.56) can be substituted in Eqn (2.68) and
can be expressed as:
*
3600p
total
da DCK
dN f
(2.69)
where the constants and p determined from high frequency FCG testing and the
constant D and can be determined from static CCG [19].
30
2.7.3 Creep Fatigue Crack Growth Damage Mechanism
In high temperature power plant components which are subjected to the combined
cyclic and creep loading, the failure of the components may be due to the interaction
between creep and fatigue. The damage mechanism may be due to the creep fatigue
interaction which depends on the operating conditions such as temperature, frequency
and environmental effects. Depending on such conditions, the creep fatigue damage
mechanism may influence the cracking behaviour to be fatigued dominated, creep
dominate or the interaction between fatigue and creep.
The schematic of fatigue, creep and creep fatigue interaction damage mechanism is
shown in Figure 2.10. The crack initiation and growth is fatigue dominated in the
absence of a significant hold time or at a relatively high strain rate (Figure 2.10(a)).
The cracks were initiated near the surface and were propagated through the grains
where crack path was formed as a transgranular.
With increasing hold time at high temperature, the creep damage condition within the
structure becomes increasing influential to which the crack development becomes fully
creep dominated (Figure 2.10(b)). The initiation and cavities along the gain boundaries
lead to intergranular crack path where the creep damage dominated.
Fatigue cracking interacts with the creep damage developing at intermediate hold times
and strain rate which consequentially result in accelerated crack growth (Figure 2.10 c
and d). The initiation of the creep cavitation damage within the material and the surface
fatigue damage are independent of each other where the crack propagates in both
transgranular and intergranular.
31
Figure 2.10 The schematic of crack propagation a) fatigue dominated, b) creep
dominated, c) creep fatigue interaction and d) creep fatigue interaction [58]
2.8 Low Cycle Fatigue
Fatigue failures occurs when metal is subjected to a repetitive or fluctuating stresses or
strains and will fail at a stress or strain much lower than its required. Fatigue can be
divided into the two categories, namely high cycle fatigue (HCF) and low cycle fatigue
(LCF). High cycle fatigue (HCF) refers to the number of cycles greater than 105 whilst
low cycle fatigue (LCF) refers to the number of cycles between 104 and 105 [59].
Low cycle fatigue is concerned about fatigue failure at relatively high stress and low
number of cycles to failure. It is usually concerned with cyclic strain rather than cyclic
stress. The LCF testing is frequently performed in strain control condition with the
extensometer attached to the gauge length to measure the strain. Cyclic strain
controlled fatigue occurs when the strain amplitude is held constant at a constant strain
rate with a common triangular or sinusoidal waveform [60]. The LCF data is normally
present as a plot of plastic strain range against the number of cycles.
32
2.8.1 Cyclic stress strain curve
The response of material subjected to cyclic loading is cyclic stress strain curve which
is also known as hysteresis loop. Figure 2.11 shows the typical cyclic stress strain loop
under constant strain cycling. During initial loading, the component is in tension,
resulting the curve OA. On unloading, the strain response of the specimen follows the
curve from A to D. At D, the component is under no stress. The strain response follows
the curve from D to B as the component is subjected to compressive stress. As the
compressive stress is released from B and tensile stress is applied, the curve is
defined by B,C and A. Points A and B represent the cyclic stress and strain limits [61].
Figure 2.11 Typical stress strain loop under constant strain cycling [61].
33
The cyclic stress stain curve may be described by a power curve as:
'
'
2 2
np
K
(2.70)
where 2 and 2p are the stress amplitude and plastic stain amplitude in the
hysteresis loop, respectively. 'K and 'n is the cyclic strength coefficient and cyclic strain
hardening exponent, respectively.
2.8.2 Cyclic hardening and cyclic softening
The stress strain response during cyclic loading can change depending on the initial
condition of the metal. The metal may experience cyclic strain hardening , cyclic strain
softening, or remain stable [61]. Figure 2.12 shows an example of cyclic hardening and
softening behaviour. Cyclic hardening leads to increasing maximum stress with
increasing cycles while cyclic softening results in decreasing maximum stress with
increasing number of cycles.
Cyclic softening behaviour is often observed in P91 and P92 material [62-65].
Krishna[65] investigated LCF behaviour of P91 steel at strain amplitude of 0.7% to
1.2% at room temperature and elevated temperature (500 and 600°C).The cyclic
softening is observed with the rise of temperature due to microstructural evolution
including the decrease in dislocation density and coarsening and rearrangement of
martensitic lath and sub-grain structure[65]. Cyclic softening exhibited during cyclic
loading has been attributed to the decrease in dislocation density and changes in
dislocation substructure from the original lath martensitic structure to sub grain
structure [65, 66].
34
Figure 2.12 Example of cyclic hardening and cyclic softening[59]
2.8.3 Strain Life Prediction
The fatigue life plot was established based on power law relationship between elastic
and plastic strain amplitude with number strain reversal to failure 2 fN as given by
2 2 2
pt e
(2.71)
where the first term on the right hand side is the elastic plastic strain amplitude and the
second term is the plastic strain amplitude. The elastic and plastic strain amplitude
relation to 2 fN is given by the Basquin [67] and Coffin-Manson [68, 69] relationship.
The strain life relationship is given by:
'
'2 22
b cftf f fN N
E
(2.72)
where 2t is the total strain amplitude, and 2 fN is the number of cycle to failure,
E is the elastic modulus, 'f is the fatigue strength coefficient, '
f is the fatigue
ductility coefficient , b and c are the fatigue strength exponent and fatigue ductility
exponent , respectively.
35
Chapter 3
Material and Experimental
Procedure
3.1 Introduction
This chapter provides the details of the material under study and service conditions.
The technique to introduce prior creep strain/damage on the material has been
explained. The experimental procedure covers the uniaxial and notched bar creep tests
in order to characterise the creep properties and influence of triaxiality on creep
deformation. Creep fatigue crack growth tests were performed to examine the creep
fatigue crack growth behaviour under different hold times. The evaluation and
calculation of stress intensity factor range and fracture mechanics parameter, C* were
included. Low cycle fatigue tests were performed to examine the low cycle fatigue
behaviour of material with and without prior creep strain. The details of the
experimental procedure for all tests are explained in this chapter.
3.2 Material Specification and Service Conditions
The materials used in this research are new and ex-service P91 steel. The detailed
explanations for both materials are described in following section.
3.2.1 New material
The new material is provided by RWE [1] as a pipe section. The pipe section has a
diameter of 250 mm and a wall thickness of 50 mm as shown in Figure 3.1 . Note that
hereon for brevity, the new material is denoted ‘P91-A’.
3.2.2 Ex-service material
Two sets of ex-service materials which are denoted as P91-B and P91-C were
provided by Flex-E Plant Project [2] and ASTM Round Robin Project [3], respectively.
P91-B was previously in operation for over 110,000 hours at 590ºC and P91-C at
600ºC for over 100,000 hours.
36
P91-B was supplied as a pipe section. The details and dimensions of the pipe section
are shown in Figure 3.2 (a). In this figure, the diameter and thickness of the pipe are
465 mm and 70 mm, respectively. The pipe section was further divided in several small
parts and some of the specimens were extracted from this section.
As for the ex-service P91-C material, the material was provided in two sets of square
blanks, each having a cross section of 65mm and 63mm and a thickness of 15mm.
This material was only used for compact tension, C(T) specimen which contributed to
a larger ASTM organised round robin project as detailed in reference [3, 70].
3.3 Specimen Orientation
The new and ex-service materials were supplied in the forms of block and pipe section,
respectively. Both materials may not be fully homogenous and isotropic. Thus, it is
important that the specimens have a similar orientation. Schematics of specimen
orientations are shown in Figure 3.1 and 1.2 for the new and ex-service material,
respectively. All uniaxial, notched bar and low cycle fatigue specimens were extracted
such that the loading axis was parallel to the axial direction of the pipe components. All
the C(T) specimens were extracted with the loading axis parallel to the axial direction
and the crack plane direction.
Figure 3.1 Schematic orientation of specimen geometry for new material
37
(a)
(b) (c) (d)
Figure 3.2 (a) Pipe-B dimension and schematic orientation of specimen geometry for
ex-service material, (b)Block A, (c) Block B and (d) Block C
38
3.4 Introduction of creep stain/damage
The influence of prior creep strained on subsequent tensile properties and creep crack
growth behaviour on 316H stainless steel has been studied by Mehmanparast et.al [71].
In their research [71], the creep damage was introduced into a pre-compressed
material by performing uniaxial creep test. The uniaxial creep tests were then
interrupted at various stages of creep life to examine the influence of plastic strain and
tensile strain on the material. The results showed that the 0.2% proof stress increases
and the tensile strain at failure drops in the crept samples [71].
The influence of prior creep strained on low cycle fatigue test at elevated temperatures
has been investigated on CrMV [72] and P91[73] material. The prior creep plus fatigue
test specimens were crept under 176 MPa at 575°C and 314 MPa at 550°C [72].
Subsequently, the specimens were machined to the low cycle fatigue specimen and
the fatigue test were performed with a strain range of 1% and strain rate of 6%/min. It is
shown that the fatigue live increases for the crept sample under 175 MPa at 575°C [72].
For P91 material, the influence of prior creep strained on subsequent fatigue was
previously investigated by Takahashi [73]. Two samples were crept at 600°C under 140
MPa for 500h and 1000h. Subsequently fatigue tests were performed at a strain range
of 0.5%, strain rate of 0.1%s-1 and load ratio, R of -1. It is shown that the fatigue
reduces as the crept time increases.
Recently, Pandey et.al [74] investigated the effect of creep rupture on the subsequent
tensile properties of cast and forged P91 steel. The short-term creep tests were
performed at temperatures of 650 °C and 620 °C for a constant stress level of 120 MPa
on creep specimens having a gauge length and diameter of 120mm and 10mm,
respectively. After fracture, the sub-size tensile specimen (gauge length of 25mm and
diameter of 6.25 mm) were machined from the gauge area of fracture specimens and
subsequent room temperature tensile tests were performed after the specimens were
subjected to heat treatment.
In this work, the research aimed to examine the influence of prior creep strain on
tensile and low cycle fatigue behaviour. The prior creep strain was introduced into the
material under ex-service condition at elevated temperature by interrupting the uniaxial
creep tests on uniaxial creep sample at 600ºC and subsequent tensile and low cycle
fatigue tests were then performed. The results of the interrupted creep test prior to
tensile and low cycle fatigue are presented in Chapter 7.
39
3.4.1 Interrupted Creep Test
Prior to tensile testing, the interrupted creep tests were performed on the standard
8mm diameter uniaxial creep specimens. Table 3.1 shows the test matrix for the
interrupted creep tests for the new and ex-service material. The tests were performed
at 600ºC under 150 MPa on a dead weight lever arm creep machine.
Prior to low cycle fatigue tests, the creep damage was uniformly introduced into a large
uniaxial specimen as shown in Figure 3.3. The specimen’s gauge length and diameter
were 115mm and 18mm, respectively. As shown in Table 3.1, the interrupted creep
test on the 18mm diameter were performed on ex-service material denoted by GD1 to
GD6 at 600°C and 150 MPa.
Interrupted creep tests on two notched large specimens were also conducted. The
specimens were designed by adding a notch on the gauge length section as shown in
Figure 3.4. The net section diameter of the notched specimen was 12mm. It must be
noted that due to the large size of the uniaxial and notched creep damage specimen,
the test must be performed on a high load carrying capacities machines. In order to
introduce global creep damage into the material, the specimen was pulled in tension at
600°C until a defined creep strain rate was obtained. The net stress of 150 MPa was
applied for all the tests. A test rig including the adapter to attach the specimen with the
push rod and the extensometer mounting system were designed and manufactured to
accommodate the large uniaxial creep specimen. After the prior creep testing the
specimens were machined to the low cycle fatigue specimen. This practise would
eliminate the surface cracks and oxide layer that happens during the creep test and
can correctly examine the effect of creep alone on fatigue behaviour.
40
Table 3.1 Test matrix for interrupted creep testing using the 8mm and 18 mm diameter
uniaxial specimens.
Specimen
ID
Material
Condition
d
(mm)
Temp
(ºC)
Net Stress
(MPa)
ACD1 New 8 600 150
ACD2 New 8 600 150
ACD3 New 8 600 150
ACD4 New 8 600 150
BCD1 Ex-service 8 600 150
BCD2 Ex-service 8 600 150
BCD3 Ex-service 8 600 150
BCD4 Ex-service 8 600 150
GD1 Ex-service 18 600 150
GD2 Ex-service 18 600 150
GD3 Ex-service 18 600 150
GD4 Ex-service 18 600 150
GD5 Ex-service 18 600 150
GD6 Ex-service 18 600 150
GN1 Ex-service 12 600 150
GN2 Ex-service 12 600 150
41
Figure 3.3 Specimen geometry of large uniaxial creep sample.
Figure 3.4 Specimen geometry of large notched bar creep sample.
42
3.5 Uniaxial and Notched Bar Creep Experiments
Uniaxial creep testing was performed on both new and ex-service material at 620°C
and 600°C, respectively, to determine the creep properties. In order to study the creep
under the influence of triaxial stress state, the uniaxial notched bar creep testing were
performed on both new and ex-service material. The test matrices for uniaxial and
notched bar creep tests are shown in Table 3.2 and 3.3, respectively. The next section
describes the specimen design and experimental procedure for uniaxial creep and
notched bar creep testing.
3.5.1 Specimen Design
The uniaxial creep specimen geometry was designed according to the ASTM E8 M.
The specimen had an 8 mm diameter and 36 mm gauge length. Ridges were added to
the top and bottom of the gauge region for extensometer purposes. Figure 3.5 shows
the schematics of uniaxial creep specimen.
The notched bar specimen geometry was designed to correspond with that
recommended by the Code of Practise [75]. The circumferentially U type double notch
bar specimen was characterised by a radius and depth as shown in Figure 3.6. The
creep strain, and therefore damage is assumed to accumulate equally between the two
notches. However, when one notch fails, the remaining notch can be used to examine
damage mechanism that led to the former notch’s failure. Two type of notches namely
blunt and medium notch were used to generate different levels of triaxiality and their
influence on the creep deformation and rupture properties of the material can be further
studied. Prior to testing and after failure, the dimensions of the notched bar specimen
was measured using a shadow graph technique as shown in Table 3.3.
3.5.2 LVDT
Axial displacements were measured using linear voltage differential transducers
(LVDT). Prior to testing, the LVDT output was converted into displacement by
calibrating the LVDT using a micrometer fixture. The LVDT was mounted on the
specimens using a mounting clamp.
43
3.5.3 Testing Procedure
Prior to testing, two thermocouples were attached along the gauge length of the
specimen. The specimen was then mounted on a dead weight lever arm creep
machine equipped with the furnace. The LVDT was installed by using a clamp holder.
The specimen was heated up to the specified temperature. Once the temperature was
stabilised, the load was applied and the displacement during the load up was recorded
for each test. Both temperature and displacement were continuously measured during
the test.
Table 3.2 Test matrix for tensile and uniaxial creep testing.
Specimen
ID
Material
Condition
Test
type
Stress
(MPa)
Temp
(ºC)
P91-A-UT1 New Tensile - 25
P91-A-UT2 New Tensile - 620
P91-B-UT3 Ex-service Tensile - 25
P91-B-UT4 Ex-service Tensile - 600
P91-A-UC1 New Creep 80 620
P91-A-UC2 New Creep 100 620
P91-A-UC3 New Creep 130 620
P91-A-UC4 New Creep 160 620
P91-B-UC5 Ex-service Creep 130 600
P91-B-UC6 Ex-service Creep 140 600
P91-B-UC7 Ex-service Creep 150 600
P91-B-UC8 Ex-service Creep 160 600
44
Table 3.3 Test matrix for uniaxial notched bar creep testing.
Specimen
ID
Material
Condition
Description a/R d dnotch
A-UB1 New Blunt notch 1.5 7.99 2.85
A-UB2 New Blunt notch 1.5 8.08 2.83
A-UB3 New Blunt notch 1.5 8.12 2.90
A-UB4 New Blunt notch 1.5 7.99 2.85
A-UM2 New Medium notch 5.0 7.98 2.66
A-UM3 New Medium notch 5.0 7.99 2.67
A-UM4 New Medium notch 5.0 7.97 2.66
A-UM5 New Medium notch 5.0 7.96 2.65
B-UB2 Ex-service Blunt notch 1.5 7.97 2.81
B-2B Ex-service Blunt notch 1.5 7.95 2.81
B-3A Ex-service Blunt notch 1.5 7.99 2.80
B-4A Ex-service Blunt notch 1.5 7.99 2.81
B-UM8a Ex-service Medium notch 5.0 7.99 2.82
B-UM8b Ex-service Medium notch 5.0 8.02 2.83
B-UM6a Ex-service Medium notch 5.0 7.96 2.84
B-UM5A Ex-service Medium notch 5.0 7.98 2.83
45
Figure 3.5 Standard uniaxial creep specimen geometry.
Figure 3.6 Notched bar creep specimen.
R=1.882.34
1.17
Blunnt Notch a/R=1.5
R=0.571.14
1.17
Medium Notch a/R=5.0
0.6
46
3.6 Creep-Fatigue Crack Growth Experiments
Creep fatigue crack growth test were performed to examine the CFCG behaviour.
Creep fatigue crack growth testing was performed according to the testing standard,
ASTM E-2760 [76]. The tests were performed on the compact tension, C(T) specimens
at a range of temperatures between 600°C and 625°C for a range of hold times
between 30s and 600s. A high temperature fatigue crack growth (FCG) test at a
frequency of 10Hz was also performed. Table 3.4 shows the test matrix for the CFCG
tests. As shown in Table 3.4, one specimen was from the new material P91-A,
identified as CT-A, four specimens were from the ex-service materiel P91-B, identified
as CT-B1 to CT-B4 and two were from the ex-service material P91-C, identified as CT-
C1 and CT-C2. It must be noted that the test specimens CT-C1 and CT-C2 contributed
to a larger ASTM organised round robin project, as detailed earlier [3, 70]. The loading
and the hold time are tabulated in Table 3.4.
3.6.1 Specimen Design
Compact specimen, C(T) geometry was used in the CFCG testing. Figure 3.7 shows
the schematics of the specimen geometry. The height and width of the specimen was
60 mm and 50 mm, respectively. The standard thickness is 25 mm, however for the
two specimens; CT-C1 and CT-C2 had a thickness of 12.5 as they were provided in the
blank specimen with a 15mm thickness. The initial crack was cut using electrical
discharge machining (EDM) with the wire notch diameter of 0.25mm.
3.6.2 Fatigue Pre-cracking
CT-C1 and CT-C2 were fatigue pre-cracked to an initial crack length to width ratio,
0a W ~ 0.4. The pre-cracking was conducted on the fatigue machine at a room
temperature. In order to identify the appropriate load to be applied the stress intensity
factor was calculated first. Here the loading value was calculated at maxP =6.7kN.It is
important to take into consideration that if the frequency of the pre-cracking test is too
high, the maximum load will not be attained resulting in slower pre-cracking timing,
however if frequency too low, the reverse will occur. Therefore, after conducting trials
on the aluminium specimen, the pre-cracking test was able to establish the ΔP and
optimal frequency.
47
3.6.3 Side Groove
After the pre-cracking, the specimens were side grooved along the crack plane with a
depth of 10% of the specimen thickness. This was to reduce tunnelling along the crack
front and increase triaxiality to achieve plane strain and to promote a uniform crack
growth.
3.6.4 Thermocouples
The temperature during the CFCFG test was measured using the K-type
thermocouples. The thermocouples were spot welded on both specimen sides and
near the crack as shown in Figure 3.8 to ensure that the temperature was uniformly
measured on the specimens. The temperature was monitored to ensure that the
temperature gradient is less than or equal to 2°C.
3.6.5 Load Line Displacement Measurement
The load line displacement was measured using linear voltage differential transducer
(LVDT) which was mounted outside the furnace and attached to the specimen via the
LVDT mounting system as shown in Figure 3.8. The displacement was calibrated using
a micrometer fixture by converting the LVDT output voltage into a displacement
3.6.6 Crack Length Measurement
A direct current electrical potential drop (PD) method was used to measure the crack
length. A constant direct current was applied to the specimens and the changed in the
resistance of the specimen was measured which correlates directly with the crack
growth. Two input and output PD wires were attached on the specimens as shown in
Figure 3.8.
The estimated crack length can be calculated from the measured voltage as
recommended by ASTM as given by:
0
1 0
0 0
cosh 22
cosh 2cosh cosh
cosh 2
Y Wa W
Y WV
V a W
(3.1)
48
where 0a is the initial crack length, 0V is the initial voltage, 0Y is the half distance
between the output voltage leads and V is the instantaneous output voltage.
3.6.7 Testing Procedure
The CFCG testing was performed on a lever arm creep machine under load control
conditions. A pneumatic load-lifting equipment was used for lifting and lowering the
load according to the hold time specified. Prior to testing, the specimen was prepared
by spot welding all three thermocouples and both the input and output PD wires. The
specimen was then placed on the creep machine that is equipped with the heating
furnace. The displacement measuring by LVDT was mounted outside the furnace and
attached to the specimen via the LVDT mounting system. The specimen was then heat
up until reaching the specified temperature. Once the specified temperature stabilized
through the specimen, the load was applied. The displacement and PD reading was
recorded during the load-up. The test was monitored and stopped until the
displacement reached the tertiary creep region, the crack growth accelerated and the
final failure is imminent.
3.6.8 Post-test Measurement
All tests were stopped prior to the specimen fracture and each specimen was
subsequently broken open at room temperature by high frequency fatigue loading. The
initial and final crack length was measured using image correlation technique by
averaging 9 measurements along the crack front. The instantaneous crack length was
then computed using a linear correlation between the PD voltage and measured crack
length by the following equation:
00 0
0f
f
V Va a a a
V V
(3.2)
where fa , 0a and a are the final, initial and instantaneous crack lengths, respectively.
fV , 0V ,andV are the corresponding final, initial and instantaneous PD voltage value.
3.6.9 Data analysis
The load line displacement and crack length data was smoothened by eliminating the
noise and scatter on the data. The load line displacement and crack length were then
calculated using the seven point incremental polynomial method as recommended by
49
ASTM to analyse the crack growth data. The CFCG can be calculated in terms of
stress intensity factor range, K and C parameter as explained in the following
section.
3.6.9.1 K Calculation
For a side groove C(T) specimen, the stress intensity factor range parameter can be
calculated by:
1/2 3/21/2
2
1N
P a WK f a W
a WBB W
(3.3)
where P is the load range, a is the crack length, W is the width, B is the thickness,
NB is the thickness with side groove and f a W is calculated using
2 3 40.886 4.64 13.32 14.72 5.6f a W a W a W a W a W (3.4)
3.6.9.2 C* Calculation
In CFCG, during the hold time, the creep deformation and damage may be developed
during this period, thus the C* may suitable to describe the crack growth behaviour .For
steady state creep dominant conditions, the crack growth rate is described by the *C
parameter which can be determined experimentally by:
* P
C HB W a
(3.5)
where P is the applied load, is load line displacement rate, H and are the
dimensionless coefficient that depend on the specimen geometry. For a C(T) specimen,
1H n n where n is the power law creep exponent and =2.2 [49].
The validity criteria for the use of C* are specific in ASTM E1457 [54] has been
applied to the CFCG experimental data. The criteria are described as:
i. The creep load line displacement rate calculated using the equation given in
ASTM E1457 [54] should constitute at least half of the total load line
displacement rate, i.e 0.5c T
50
ii. Data point at 0.2t t obtained prior to a crack extension a of 0.2 mm
should be excluded as they are considered to be within the transient crack
growth regime where damage is developed to a steady state at the crack tip
iii. The transition time, Tt , from an elastic crack tip field should be exceeded.
The transition time may be described by:
2
' *max
1T
Kt
E n C
(3.6)
51
Table 3.4 Test matrix for creep fatigue crack growth testing and fatigue crack growth.
Specimen
ID
Material
Condition
Test
type
Temp
(ºC) B
(mm) 0 /a W ht
(s)
maxP
(kN)
CT-A New CFCG 620 25 0.45 600 15.0
CT-B1 Ex-service CFCG 600 25 0.50 600 13.0
CT-B2 Ex-service CFCG 600 25 0.50 60 12.0
CT-B3 Ex-service CFCG 600 25 0.50 30 12.0
CT-B4 Ex-service FGC 600 25 0.50 0 13.0
CT-C1 Ex-service CFCG 625 12.5 0.42 600 7.5
CT-C2 Ex-service CFCG 625 12.5 0.44 600 9.0
Figure 3.7 Compact tension specimen geometry.
52
Figure 3.8 (a) Schematic diagram of CFCG setup with LVDT mounting system
b) Thermocouple and PD setup for CFCG test.
Figure 3.9 Loading wave (a) CFCG test with a hold time, (b) FCG test.
(a) (b)
Pmax
Pmin
th
Time,t
Pmax
Pmin
Time,t
(a) (b)
53
3.7 Low Cycle Fatigue Experiments
The low cycle fatigue tests were performed to examine the stress response and stress
strain behaviour under cyclic loading. Cyclic stress strain hysteresis loops were
obtained to determine the cycle dependent changes in the stress and plastic strain
amplitude. The cyclic stress strain behaviour at half life cycle to failure were analysed
to evaluate the basic fatigue properties of the examined material.
The LCF tests were performed at room temperature on the servo hydraulic testing
system in total strain control mode. The tests were conducted in accordance to the
ASTM-E606 standard [77] under fully reversed triangular waveform with R-ratio of -1 at
a strain rate of 0.1% for a strain range of 0.5 to 1.2%. Table 3.5 shows the test matrix
for the low cycle tests. The specimen design, machine configuration and testing
procedure are explained in detail in the following section.
3.7.1 Specimen Design
The LCF specimen was characterised by a cylindrical specimen with a 15 mm gauge
length and a 7mm diameter. Both ends were all threaded with 12mm diameter and
35mm length and curvature radii of 25mm were machined. The LCF specimen
geometry with all the dimensions are shown in Figure 3.10. The specimen was
finished by polishing in axial direction to have a surface roughness of 0.2 µm.
3.7.2 Testing Machine
The low cycle fatigue test were conducted on a 100kN Instron 8801 servo hydraulic
machine. The machine testing system consists of two supported load frames, an
adjustable upper cross head, a load cell, a servo-electric actuator controller and a
console software. The specimens were mounted and secured on the machine using
the hydraulic grips which were equipped with the wedge shaped jaw faces in order to
align and to provide sufficient contact with the specimen.
3.7.3 Machine Alignment
Misalignment is an major concern in the LCF testing as it could result bending in the
specimen [78]. Thus, according to the ASTM E606 [77] the testing machine along with
any fixtures used in the test program must meet the bending strain criteria. Prior to LCF
54
testing, the machine alignment was performed using an aligning tool called Instron
AlignPro. A trial test specimen with longitudinal strain gauges placed at four equidistant
locations around the minimum diameter that is called an alignment cell was mounted
on the testing machine as shown in Figure 3.11. Once the alignment cell was installed
on the testing machine, the AlignPro measured and calculated the bending strain due
to angular and concentric alignment error. The angular and concentric alignment error
was adjusted manually by fixing the aligning fixture so that the maximum bending strain
did not exceeded 5% of the minimum axial strain range as a requirement in ASTM
E606 [77].
3.7.4 Extensometer
A room temperature extensometer was used for measuring axial strain in the gauge
section. The knife-edge type extensometer has a 12.5 mm gauge length with a travel of
±2.5 mm. The LCF test was controlled in terms of total strain which were measured by
this extensometer. The extensometer was mounted to the gauge length specimen
using spring and rubber band to exert sufficient clamping force to prevent slippage.
Figure 3.12 shows the configuration of extensometer attachment to the specimen.
3.7.5 LCF Testing Procedure
Prior to testing, the machine was set up following several procedures. After the
machine alignment, the specimen was placed into the machine grip. The extensometer
was then mounted on the specimen gauge length for the strain measurement. The
extensometer was calibrated for each test.
A triangular loading waveform was set up in the machine software. An example of
loading waveform is shown in Figure 3.13 with a strain range of 0.8%. The strain range
was varied between 0.5% and 1.2% with a constant strain rate of 0.1%s-1 and the
frequency was calculated as shown in Table 3.5.
The machine was set to stop when it reached 50% of the minimum load after 100th
cycle. This cycle is considered as the stabilising cycle for this type of material. About
1000 data points were recorded per cycle for constructing the stress strain hysteresis
loop. The 50% failure criterion was chosen based on trial tests to prevent the
specimens from totally fracture and the extensometer falling off. The mechanical strain
was set 0.1 higher than the applied strain amplitude and the displacement was set
55
about 2 mm from the current position as another setting for specimen and machine
protection. All the test data were monitored and recorded automatically using the
Instron computer software.
Table 3.5 Test matrix for low cycle fatigue testing.
Specimen ID Material Condition (%) f (Hz)
LCF1 Ex-service 1.2 0.0417
LCF2 Ex-service 0.5 0.1000
LCF4 Ex-service 0.8 0.0625
LCF5 Ex-service 0.6 0.0833
LCF6 Ex-service 1.0 0.0500
GD1 Ex-service +GCD 0.8 0.0625
GD2 Ex-service + GCD 0.5 0.1000
GD3 Ex-service +GCD 1.2 0.0417
GD4 Ex-service +GCD 0.6 0.0833
GD5 Ex-service +GCD 1.0 0.0500
GD6 Ex-service +GCD 0.7 0.1667
GN1 Ex-service +GCD 0.8 0.0625
GN2 Ex-service +GCD 0.5 0.1000
Figure 3.10 Low cycle fatigue specimen geometry.
56
Figure 3.11 Machine alignment.
Figure 3.12 Extensometer used in the LCF testing.
57
Figure 3.13 Example of loading waveform for strain ranges of 0.8%.
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 10 20 30 40
Mechanic
al S
train
(%
)
Time (s)
58
Chapter 4
Uniaxial and Multiaxial Creep Test
Results and Analysis
4.1 Introduction
Tensile tests at both room and high temperatures have been performed on new and
ex-service material. The uniaxial and notched bar creep testing has been performed at
620ºC and 600ºC on the new and ex-service material, respectively. The test
temperature for new material was specified by MACPLUS project [1]. For the ex-
service material, the test temperature of 600°C is selected, as it is the maximum design
temperature for P91 material. The main results of this chapter are to characterize the
uniaxial and multi-axial behaviour of new and ex-service material.
Uniaxial creep test results have been analysed and compared to the available P91 data
to obtain the reliable creep properties. The experimental results are also analysed with
available P91 data to examine the effect of long term exposure of P91 materials at high
temperature in lower stress levels which simulates the most likely scenario during the
component service.
Notched bar creep test results have been analysed in order to predict the creep rupture
life under multiaxial stress state. The notched bar analysis was necessary to establish
the material’s multiaxial behaviour under relatively short term test times. The results
have been used to predict the long term behaviour from the short term tests. The effect
of multiaxial stress state on creep ductility was examined by employing cavity growth
models. Metallographic assessment has been performed on the uniaxial and notched
bar specimens to identify the damage mechanism.
59
4.2 Tensile Test Result at Room and High
Temperatures
Tensile tests have been performed on new and ex-service material at room and high
temperatures. Figure 4.1 and 4.2 show the engineering stress strain and true stress
strain of new and ex-service material, respectively. Table 4.1 shows the tensile
properties of both new and ex-service material which were derived from Figure 4.1. As
seen in Figure 4.1 the yield strength and ultimate tensile strength of new material are
considerably increased at room temperature. A comparison of 0.2 % proof stress
shows that the new material exhibit larger strength (570 MPa) than ex-service material
(490 MPa). The tensile elongation shows that the ex-service material exhibits larger
elongation than the new material. The tensile deformation shows significant decrease
at high temperature compared to the one at room temperature. Ramberg Osgood
power law has been fitted to the high temperature tensile data and the parameter is
tabulated in Table 4.2.
60
Figure 4.1 Engineering stress strain behaviour of new and ex-service material at room
temperature and high temperature
Figure 4.2 True stress strain curve of new and ex-service material at room temperature
and high temperature
0
100
200
300
400
500
600
700
800
0 0.1 0.2 0.3
σen
g(M
Pa)
εeng (mm/mm)
New materialEx-service material
25°C
25°C
620°C
600°C
0
100
200
300
400
500
600
700
800
900
0 0.05 0.1 0.15 0.2
σ tru
e(M
Pa)
εtrue (mm/mm)
New material
Ex-service material
25°C
25°C
620°C
600°C
61
Table 4.1 Tensile properties of P91 material
Material Material
Condition
Temp
(°C) 0.2%
(MPa) UTS
(MPa)
E(GPa)
f
%
P91-A New 25 570 663 203 20
P91-B Ex-service 25 490 655 233 26
P91-A New 620 340 360 127 25
P91-B Ex-service 600 287 308 - 30
Table 4.2 Ramberg Osgood material parameter
Material P91-A P91-B
Temperature 620°C 600°C
pA 4.74x10-3 2.02x10-3
N 0.03 0.04
1.02 1.01
0p 4.65x10-3 2.00x10-3
0p 325 287
4.3 Uniaxial Creep Test Result
The uniaxial creep tests were performed on standard creep specimens to determine
the creep properties for new and ex-service materials. Table 4.3 gives a summary of all
uniaxial creep tests. A total number of 8 specimens were subjected to uniaxial creep
test at 620°C and 600°C for new and ex-service material, respectively. Detail
explanation on material service conditions can be found in Chapter 3. Creep strain at
failure known as creep ductility was calculated based on axial measurement and
reduction of area. As seen in Table 4.3, two specimens denoted as P91-A-UC1 and
P91-A-UC2 which were tested at low stresses were stopped at 9848 and 9420 hours,
respectively due to longer time required to rupture the specimens. Both specimens
were sliced and metallography was performed on the specimens and explained in the
next section.
62
Creep deformation for new and ex-service materials are shown in Figure 4.3 and
Figure 4.4, respectively. The creep deformation of P91 steel can be characterized by a
small primary region, secondary region and tertiary creep region. This characteristic is
in agreement with those reported for martensitic steel [25, 26, 79, 80]. The
accumulation of strain in tertiary region is large compared to that in primary and
secondary region. A rapid creep strain accumulation in tertiary region is observed as a
result of necking just prior to fracture. The detail of test duration and strain
accumulation in primary, secondary and tertiary region is shown in Table 4.4. As seen
in Table 4.4, the test duration in primary creep region is small and the primary creep
strain is less than 5%.
Table 4.3 Summary of uniaxial creep tests for new and ex-service material
Specimen
ID
Stress Temp rt min A f f
Axial ROA
(MPa) (ºC) (h) (h-1) (h-1) (%) (%)
P91-A-UC1 80 620 +9848 7.6x10-7 - 1 9
P91-A-UC2 100 620 +9420 2.0x10-6 - 3 12
P91-A-UC3 130 620 443.3 7.3x10-5 7.8x10-4 36 92
P91-A-UC4 160 620 ~52 3.7x10-4 6.7x10-4 - -
P91-B-UC5 130 600 5818 6.0x10-6 4.7x10-5 27 82
P91-B-UC6 140 600 1125 8.3x10-6 2.5x10-4 28 87
P91-B-UC7 150 600 954 5.0x10-5 3.1x10-4 30 89
P91-B-UC8 160 600 297 3.0x10-4 1.3x10-3 34 89
63
Figure 4.3 Creep curve for new material tested at 620°C under 130 MPa and 160 MPa
Figure 4.4 Creep strain plot versus time for ex-service P91-B tested at 600C.
0.0
8.0
16.0
24.0
32.0
40.0
0 200 400 600
εc(%
)
Time (h)
160 MPa
130 MPa(a)
620°C0.0
1.0
2.0
3.0
4.0
5.0
0 2000 4000 6000 8000
εc(%
)
Time (h)
100 MPa
80 MPa(b)
620°C
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
0 1000 2000 3000 4000 5000 6000
Cre
ep S
tra
in (
%)
Time (h)
600°C160 MPa150MPa140 MPa130 MPa
P91-B
64
Table 4.4 Test duration and strain accumulation in primary, secondary and tertiary
region
Specimen
ID
Stress prit sect tert pri sec ter
(MPa) (%) (%) (%) (%) (%) (%)
P91-A-UC1 80 20.3 - - - - -
P91-A-UC2 100 31.9 - - - - -
P91-A-UC3 130 11.3 51.0 33.9 3.8 6.6 89.2
P91-A-UC4 160 19.2 48.1 48.1 2.1 6.9 7.8
P91-B-UC5 130 12.7 43.0 40.0 3.2 5.8 91.1
P91-B-UC6 140 31.1 44.4 20.0 4.7 9.4 86.1
P91-B-UC7 150 12.9 44.7 39.0 4.0 8.5 86.2
P91-B-UC8 160 16.8 42.1 25.3 4.5 8.5 85.5
4.3.1 Minimum and average creep strain rate
A total of eight uniaxial creep tests have been performed at 600°C and 620°C for
ex-service and new material, respectively to obtain the creep properties. The variation
of minimum creep strain rate with applied stress for new and ex-service material is
plotted in Figure 4.5. It should be noted that the two test data (P91-A-UC1 and P91-A-
UC2) were stopped as explained in Section 4.3. In Figure 4.5, a regression line has
been fitted to the experimental data to obtain the creep properties for both tested
material. The minimum creep rate is taken as a slope of the creep curve in the
secondary creep region. The stress dependence of minimum creep rate obeyed
Norton’s power law (Eqn (2.8)) where A and n are the stress coefficient and stress
exponent, respectively. The material constant of A and n are given in Table 4.5.
As can be seen in Figure 4.5, the minimum creep rate increases with increase in
applied stress for both materials. It can be seen also that the new material exhibit
better creep resistance than those in ex-service material over the entire stress range
used. The magnitude of minimum creep rate in new condition is about one order of
magnitude less than of service exposed P91 steel. The stress exponent, n in ex-service
65
material exhibit larger value than that in new material as shown in Table 4.5. However
more tests are required to confirm this behaviour. The average creep rate was plotted
with applied stress in Figure 4.6 for ex-service material. For new material, the test data
is not enough to a plot graph. Similar to minimum creep strain rate plot, the same
procedure has been used to obtain the material constant as given in Table 4.5.
Figure 4.7 shows the time to rupture with applied stress for new and ex-service
material. The stress dependence of rupture life also obeyed power law as given in
Eqn (2.21) where rB and rv are the stress coefficient and stress exponent, respectively.
The material constant of rB and rv are also given in Table 4.5. The arrow are showed
for the two new material test data (see Section 4.3) indicated that the tests were
stopped, thus longer rupture life should be predicted.
The creep properties in Table 4.5 shall not be representing the material behaviour as
limited test data available. Therefore, analyses of the creep test data with available
literature data are presented in Section 4.4 to obtain reliable creep properties of the
material.
Figure 4.5 Minimum creep strain rate of new and ex-service material
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
10 100 1000
Min
inum
cre
ep s
train
rate
(h
-1)
Stress (MPa)
New material
Ex-service material
66
Figure 4.6 Average creep strain rate of ex-service material
Figure 4.7 Time to rupture of new and ex-service material
1.E-05
1.E-04
1.E-03
1.E-02
10 100 1000
Ave
rag
e
cre
ep
str
ain
ra
te (
h-1
)
Stress (MPa)
Ex-service material
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
10 100 1000
t r(h
)
Stress (MPa)
New material
Ex-service material
67
Table 4.5 Creep properties of new and ex-service material
Material A n AA nA Br vr
Condition (MPa)-n h-1 (MPa)-n h-1 (MPa) h
New 4.0x10-25 10 - - 4.0x1019 8
Ex-service 2.0x10-44 18 7.0x10-35 14 3.0x1031 13
4.3.2 Creep Ductility
The creep ductility for new and ex-service material is shown in Table 4.3. The creep
ductility or creep strain at failure was calculated using both axial measurement and
reduction of area (ROA). For the new material, the test data is not enough to plot a
graph, thus only ex-service material test data is plotted. It should be noted that the
creep ductility in Table 4.3 for two test data (P91-A-UC1 and P91-A-UC2) are not
representing the creep ductility at final rupture. As can be seen in Figure 4.8 , the result
show that creep ductility measured by reduction of area is significantly greater than the
axial measurement probably due to significant plasticity effect after necking especially
to final rupture. For the stress range examined, the creep ductility is seen to reduce in
longer rupture time. However due to limited test data, no conclusive trend can be
inferred. The analysis of the creep ductility will be discusses further in Section 4.4.3.
Figure 4.8 Creep ductility variation in term of percentage of elongation with rupture life
for ex-service material
0.0
20.0
40.0
60.0
80.0
100.0
1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05
ε f(%
)
tr(h)
Axial
Reduction of area
600°C
68
4.4 Analysis of Uniaxial Creep Data
In this work, the uniaxial creep test performed on new and ex-service material was
limited due to time and material constraint. However, the analyses of the uniaxial creep
data were not limited to the test results from the current works. Thus, the long-term
test data and available literature data (up to 100,000h tests) were compared and
analysed with the present test data in order to better characterise the material over a
longer time range.
Creep data from National Institute of Material Science (NIMS) [81] for a range of
temperature from 500 to 700°C has therefore been used in this analysis. It should be
noted that the NIMS creep data obtained from different batches of material subjected
to different heat treatment process prior to testing [26]. However, within the range of
data scatter they may be treated as single data set. The trends and the bounds that are
established help in better assessment of failure in this steel. The analysis in this section
was to examine the effect of long term exposure of P91 materials at high temperature
in lower stress levels which simulates the most likely scenario during the component
service.
4.4.1 Stress Rupture
The stress with rupture time is plotted in Figure 4.9 for the ex-service material tested at
600°C. NIMS creep data [81] for a range of temperature from 550 to 650°C has been
included in the figure. As shown in Figure 4.9, the tests data for ex-service material
which were tested at high stress (130 MPa to 160 MPa) for short term tests lies on the
NIMS data set at the same temperature. It can be seen in Figure 4.9, the data range
between 100 to 10000 hours, follow the power relation in Eqn (2.21) however at longer
creep life, the data demonstrate dramatically degradation in creep strength. The
prediction of rupture under low stress at longer period is important as it simulated the
actual life of power plant. The change in the creep strength appears to occur at
10,000 hours for temperature of 600 and 650°C. The reason for a marked drop in creep
rupture strength can be explained in terms of microstructural evolution where the sub
grain size gradually increased and abruptly coarsened up to creep failure [13].
69
Figure 4.9 Stress rupture data for P91 material.
4.4.2 Minimum and Average Creep Strain Rate
The minimum creep strain rate have been plotted and compared with NIMS creep
data [81] for the temperature of 600ºC as shown in Figure 4.10. Note that only data at
600°C was analysed as it is the most frequent applicable operating temperature for
P91 material. It should be noted that the NIMS data in Figure 4.10 was obtained from
different batches of material subjected to different heat treatment prior to testing but it
is treated as single data set as no trend can be observed between the different batches.
The power law relation as shown in Eqn (2.15) has been fitted to the data to obtain the
creep properties. It can be seen in Figure 4.10 that there exists two main regions,
namely low stress and high stress region and can be regarded as long term and short
term test, respectively. The creep properties of these two regions are tabulated in
Table 4.6. As shown in Figure 4.10 a change in stress exponent n, can be observed
from the low stress to the high stress at 600ºC. At the low stresses, the value of stress
exponent is 6 and at high stresses the value of stress exponent is larger than 10 as
given in Table 4.6. A change in the slope is at a minimum creep rate of 5x10-6 h-1.The
10
100
1000
1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06
Str
ess
(M
Pa
)
tr (h)
Test data ex-servcie
550
600
650
°C
°C
°C
Literature data
70
test data which was tested at high stresses appear to lie along a line having a slope of
n=13. Similar results have been reported for the stress exponent in the high stress
region at 600°C [26, 82]. The different in the stress exponent value which is the change
in the slope may indicates a shift in the creep mechanism from power law creep where
the stress exponent is above 10 to viscous creep where the stress exponent is about
1[12].
As the minimum creep strain rate is calculated in the secondary creep region, the
average creep strain rate comprises all the three creep regions. The average creep
strain rate have been plotted and compared with available NIMS creep data [81] for the
temperature of 600ºC as shown in Figure 4.11. The average creep strain rate is always
higher than the minimum creep strain rate and the difference between them could vary
between one and two orders of magnitude. Similar to minimum creep strain rate, a
power law relation have been fitted to the lower stresses and high stresses regions and
the creep constants are given in Table 4.6. As can be seen in Figure 4.10, a change in
the average creep strain rate exponent can be observed from the low stress region to
the high stress region.
Figure 4.12 shows a plot of time to rupture was plotted with stress. Similar to minimum
and average creep strain rate, power law relation (Eqn(2.21)) has been fitted to the
high stress and low stress region to obtain the creep properties. The material constants
of rB and rv are also given in Table 4.6.
Table 4.6 Creep properties based on low stress and high stress regions
Region A n AA nA Br vr
(MPa)-n h-1 (MPa)-n h-1 (MPa) h
High stress
( 130 MPa) 1.0x10-33 13 2.0x10-31 13 7.0x1028 12
Low stress (
130 MPa) 2.0x10-18 6 2.0x10-20 7 2.0x1013 4
71
Figure 4.10 Plot of minimum creep strain rate with available data for ex-service material
Figure 4.11 Plot of average creep strain rate with available data for ex-service material
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
10 100 1000
Min
inum
cre
ep str
ain
rate
(h
-1)
Stress (MPa
NIMS data
Test data ex-service
600°C
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
10 100 1000
Ave
rag
e c
ree
p
stra
in r
ate
(h
-1)
Stress (MPa
NIMS data
Test data ex-service
600°C
72
Figure 4.12 Time to rupture against stress
4.4.3 Creep ductility
One of the key indicators of creep fracture behaviour is creep strain at failure or creep
ductility. The creep ductility was calculated using axial measurement and reduction of
area (ROA). As shown previously in Figure 4.8, there is no conclusive trend on creep
ductility can be inferred due to limited of test data. Therefore, the test data have been
analysed with available data [81] as shown in Figure 4.13. In Figure 4.13, creep
ductility has been plotted in terms of axial and reduction of area measurement with the
rupture life at temperature of 600°C. It should be noted that creep ductility for new
material was not enough to compare, thus only creep ductility for ex-service material is
plotted. The variation of creep ductility for the temperature examined exhibit scatter as
the data in this figure was obtained from different batches of material subjected to
different heat treatment prior to testing. However, within the range of data scatter they
may be treated as single data set as no trend can be observed between the different
batches. As can be seen in Figure 4.13, the creep ductility calculated by both
measurements decrease as rupture life increased. Creep ductility measured from ROA
is much higher than that from elongation, probably due to significant plasticity effects
after necking especially to final rupture. Creep ductility data for P91 steel tested at
600°C show that for similar creep rupture life there can be a large variation in the axial
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
10 100 1000
t r(h
)
Stress (MPa)
Experimental data (P91-B)
NIMS data
600°C
73
measurement and ROA. Due to this variation, an analysis has been performed on the
creep ductility by axial measurement to obtain the minimum and average values.
Figure 4.14 and 4.15 shows the creep ductility axial measurement plot with rupture life
and stress, respectively. As shown in Figure 4.14, a regression line has been fitted to
the data to show a clear reduction of the ductility, particularly at period longer than
10,000 hours. Figure 4.15 shows the stress dependency of creep ductility at 600°C at a
wider stress range. A regression line is also fitted to the data and it is shown that a
strong stress dependency may be inferred in the creep ductility at wider stress range.
The stress dependency for this material satisfy Eqn (2.22) where A rn v and the
constants of An and rv are given in Table 4.6. The dependency of failure strain on the
stress at high temperature could be due to effect of aging which is accelerated at
higher temperature.
In order to investigate the level of plasticity, the creep ductility is plotted against
normalized stress for the test data and NIMS data [81] as shown in Figure 4.16. In
Figure 4.16, the level of plasticity in the material is indicated by the ratio of the applied
stress to the 0.2% proof stress. The 0.2% proof stress, 0.2 , is taken as the yield
strength of the material for a uniaxial sample. For the ex-service material, the 0.2%
proof stress is 287 MPa. It can be seen in Figure 4.16 that the effect of plasticity can be
negligible for the examined data. As can be seen in Figure 4.16, the test data lies
within the scatter of NIMS data [81], and the stress dependency of creep ductility at
600°C shows a trend for the limited ex-service test data. However for the NIMS data
[81] at 600°C, no particular trend within a wide scatter can be observed in the creep
ductility data. If the tensile strength at any temperature is assumed to represent the
highest level of plasticity [83], this could be aligned with the upper bound for creep
ductility as shown in Figure 4.16. The upper bound of value of the tensile strain at
failure at 600°C is 30%.It is clear from Figure 4.16 that very little data available at
600°C to determine the transition lower bound thus no lower shelf behaviour is
apparent. This could be because there is no longer term data available or possibly due
the inherent brittle nature of P91 which fails at very low 0.2 values of between 0.3-
0.6 0.2 over the whole of the stress range observed. If the lowest value of creep
ductility is to be taken as the lower bound, from Figure 4.16, the lower bound would be
12% of creep ductility.
74
Figure 4.13 Creep ductility variation in term of percentage of elongation and reduction
of area with rupture life
Figure 4.14 Creep ductility variation in term of percentage of elongation with rupture
life
0.0
20.0
40.0
60.0
80.0
100.0
1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06
ε f(%
)
tr(h)
Axial
ROA
600°C
AxialROA
Literature data
Experimental data (P91-B)
10.0
100.0
1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06
ε fax
ial (%
)
tr (h)
Literature data
Experimental data (P91-B)
600°C
75
Figure 4.15 Creep ductility variation in term of percentage of elongation with stress
Figure 4.16 Creep ductility variation in term of percentage of elongation with
normalised applied stress
10.0
100.0
10 100 1000
ε fax
ial (
%)
Stress (MPa)
Literature data
Experimental data (P91-B)
600°C
10.0
100.0
0.1 1
ε fa
xia
l (%
)
σ/σ0.2% (MPa)
Literarure data
Experimental data (P91-B)
Tensile failure strainεf =30%
600°C
76
4.5 Creep Life Prediction of P91 Steel
4.5.1 Larson Miller Parameter
Several parametric approaches for life prediction such as Larson Miller, Manson-
Haferd, Orr-Sherby-Don are available in literature. In this work, Larson Miller parameter
was used for creep life prediction. Larson Miller parameter (LMP) is defined as;
( ) log rP LMP T C t (4.1)
where LMP is the parameter as function of applied stress, T is the temperature in
Kelvin, tr is the rupture time in hour and C is a material parameter. Figure 4.17 shows
the Larson Miller parameter with applied stress for NIMS data [81] and experimental
data at 600°C. The material parameter, C of 30 has been used which is the best fit
value for Grade P91 steel [84] .From Figure 4.17 it can be seen that the experimental
data agree well with the literature data.
Figure 4.17 Stress versus Larson Miller parameter plot using C= 30 for literature and
experimental data.
1.E+01
1.E+02
1.E+03
27 28 29 30 31
Str
ess (
MP
a)
LMP =T(C+log10 tr)
Ex-service material (P91-B)
NIMS data
600°C
77
4.5.2 Monkman Grant Relation
Creep rupture life data has been analysed in terms of Monkman-Grant relation
(Eqn(2.23)). Figure 4.18 shows the Monkman Grant plot of minimum creep strain rate
against rupture time for experimental data and available data in the literature [81, 85,
86].The value of C=0.3079 and α=0.79 were obtained from the straight line fit to the
data. Chetal [87] found the value of α=0.815 for grade 91 steel tested at 700°C. The
observed lower value of α less than unity can be ascribed to the loss of creep ductility
and its associated effect on creep rupture properties [87].
The creep failure strain is the strain at time to failure. The creep deformation as shown
in Figure 4.4 shows a large increase of strain to failure in the tertiary creep region
which can be due to the considerable amount of necking prior to rupture. Therefore, the
failure strain at the secondary region or known as Monkman Grant ductility may be
appropriate to define the strain at failure. The Monkman Grant ductility may also be
calculated from minimum creep strain rate and the rupture life. Figure 4.19 shows the
Monkman Grant creep ductility ,εfMG against stress. The test data (P91-B) and literature
data [81] has been included. As shown in Figure 4.19, the Monkman Grant creep
ductility data show less scatter compared to Figure 4.16 and the dependence of
Monkman Grant creep ductility to stress is apparent. This approach has been used in
P91 material [79, 85] and is expected to be more appropriate and more conservative
in prediction of long term component behaviour.
78
Figure 4.18 Monkman Grant plot of rupture life versus minimum creep strain rate
Figure 4.19 Stress versus Monkman Grant creep ductility
1.0E+00
1.0E+02
1.0E+04
1.0E+06
1.0E-08 1.0E-06 1.0E-04 1.0E-02 1.0E+00
Ru
ptu
re li
fe, t
r(h
)
Mininimum creep strain rate (h-1)
[NIMS 2014]
[Maleki 2015]
Test data ex-service
CMG=0.3079n=0.79
600°C
10
100
1000
0.1 1 10 100
Str
ess
(M
Pa)
Ɛf MG (%)
NIMS data
Ex-service test data (P91-B)
600°C
79
4.6 Notched Bar Creep Test Results
Notched bar creep tests have been performed on blunt and medium notched bar with
notch acuities (a/R) of 1.5 and 5 for new and ex-service material. The test data and
results are shown in Table 4.7. For the new material 8 notched bar specimens have
been tested from which 2 were interrupted. All the test specimens have double notches
and the failure strain is calculated both on the failed and unfailed notched specimen by
measuring the diameter of the notch. As shown in Table 4.7, the von Mises skeletal
point, ske ,and maximum principal, 1
sk , skeletal stress is determined based on
previous study [88].
4.6.1 Axial Deformation
Figure 4.20 to Figure 4.23 show the axial displacement for blunt and medium notched
bar creep tests. For the tests which are tested at lower stress, the axial deformation
does not show pronounced tertiary region but shows rapid fracture. It should be noted
that the final point on the graph represents the post-test elongation measurement.
Similar to creep behaviour of uniaxial specimen, the time to failure increase as the net
stress decreases.
80
Table 4.7 Notched bar test result
Specimen
ID a/R net sk
e 1sk rt axial
f ROAf
MPa MPa MPa h % Failed
notch
Unfailed
notch
Ne
w m
ate
ria
l
A-UB1 1.5 165 127 173 1655 6.94 62.2 0.7
A-UB2 1.5 130 9653+ - - -
UB2a 1.5 197 152 207 63 8.89 64.7 16.2
A-UB3 1.5 211 163 222 56 10.25 81.8 5.6
A-UB4 1.5 180 139 189 216 8.67 73.1 10.1
A-UM2a 5.3 50 33 57 7250+ - - -
A-UM-2c 5.3 235 156 269 43 7.78 52.2 23.2
A-UM3a 5.3 201 133 229 458 6.75 65.5 15.5
A-UM4 5.3 216 142 246 210 7.67 71.1 1.5
UM5 5.3 227 150 258 110 8.28 74.6 0.8
Ex-
serv
ice
mate
ria
l
B-UB-2a 1.5 187 144 196 942 5.69 57.3 13.7
B-2B 1.5 222 171 233 139 7.22 68.8 9.8
B-3A 1.5 244 188 256 49 8.94 70.7 16.2
B-4A 1.5 202 156 212 778 5.97 51.7 8.0
B-UM-8a 5.3 199 131 227 2840 3.72 10.7 2.1
B-UM-8b 5.3 259 171 295 98 7.72 49.6 9.0
B-UM-6A 5.3 237 156 270 198 6.81 38.2 2.8
B-UM-5A 5.3 226 149 257 336 6.33 33.4 6.6
81
Figure 4.20 Axial displacement for blunt notched bar for new material
Figure 4.21 Axial displacement for medium notch bar new material
0.0
1.0
2.0
3.0
4.0
5.0
0 500 1000 1500 2000
Axi
al D
ispla
cem
ent (
mm
)
Time (h)
Blunt Notch211 MPa197 MPa180 MPa165 MPa
620°C
σnet
0.0
1.0
2.0
3.0
4.0
5.0
0 50 100 150 200 250 300 350 400 450 500
Axia
l Dis
pla
cem
en
t (
mm
)
Time (h)
Medium Notch 235 MPa
227 MPa
216 MPa
201 MPa
620°C
σnet
82
Figure 4.22 Axial displacement for blunt notched bar for ex-service material
Figure 4.23 Axial displacement for medium notch bar for ex-service material
0.0
1.0
2.0
3.0
4.0
5.0
0 200 400 600 800 1000
Axi
al D
isp
lace
me
nt
(m
m)
Time (h)
Blunt Notch 244 MPa
222 MPa
202 MPa
187 MPa
600°C
σnet
0.0
1.0
2.0
3.0
4.0
5.0
0 500 1000 1500 2000 2500
Axi
al D
isp
lace
me
nt
(m
m)
Time (h)
Medium Notch 259 MPa
237 MPa
226 MPa
199 MPa
600°C
σnet
83
4.6.2 Creep Rupture Life
The notched bar rupture data for blunt and medium notch have been plotted with net
section stress in Figure 4.24 and 4.25 for new and ex-service material, respectively.
The uniaxial data for new and ex-service material were also included in both figures. A
regression line has been made to the data for each notch type. The regression line for
uniaxial data has been fitted to the uniaxial data which was taken from the NIMS data
[81] and the uniaxial test data. In both figures, it can be seen that the medium notch
results in longer failure times than the blunt notch for both material conditions.
It is shown in Figure 4.24 and 4.25 that the presence of notches results in longer
rupture times than the uniaxial test at the same net section stress. This behaviour is
similar to the one reported by Goyal [32, 89] who investigated the effect of notch
constraint on P91 steel at 600°C.The behaviour is known as ‘notch strengthening’
which is caused by the reduction of equivalent stress or von Mises stress in the
notched bar. This behaviour is typically observed in ductile materials [90, 91].
84
Figure 4.24 Rupture life of notched bar for new material
Figure 4.25 Rupture life of notched bar for ex-service material
50
500
10 100 1,000 10,000
Ne
t st
ress
(M
Pa
)
Time to rupture (h)
P91-A-Blunt notch
P91-A- Medium notch
P91-A-Uniaxial
620°C
Fit to medium notchFit to blunt notchFit to NIMS and uniaxial test data
50
500
10 100 1,000 10,000
Net st
ress
(M
Pa)
Time to rupture (h)
P91-B-Blunt notch
P91-B- Medium notch
P91-B-Unixial
600°C
Fit to medium notchFit to blunt notchFit to NIMS and uniaxial test data
85
4.7 Analysis of Notched Bar Creep Data
The high temperature components are generally designed based on uniaxial creep
data. However the components experience multiaxial stress state as a result of change
in geometry, material and loading condition. In order to assess the life of such
components, it is important to predict the creep rupture life under multiaxial stress state.
The notched bar analysis was necessary to establish the material’s multiaxial
behaviour under relatively short term test times. The results have been used to predict
the long term behaviour from short term test. The effect of multiaxial state of stress on
creep ductility has been evaluated by employing cavity growth models.
4.7.1 Representative stress
In Section 4.6.2, the creep rupture life of P91 steel has been plotted in terms of net
section stress for the notched bar. However, the net section stress does not correctly
predict the creep rupture of notched bar [30] because the creep rupture behaviour of
the notched bar depends on maximum principal stress, hydrostatic stress and von
Mises stress.
A concept of representative stress has been introduced to predict the rupture life for
notched bar which was based on the observation that failure is often controlled by a
combination of maximum principal stress, 1 , and von Mises stress, e [30]. The
combination of these stresses results in representative stress and is given by Eqn (2.26)
The material constant in Eqn (2.26) described the relative importance of maximum
principal stress and von Mises stress where for =1 the failure is controlled only by
the maximum principle stress whilst for =0 the failure is controlled by the von Mises
stress.
The value of maximum principal stress and von Misses stress in Eqn (2.26) were
determined by skeletal stress analysis. In this analysis, it is assumed that the skeletal
stress can be used as a basis for interpreting the overall behaviour of the notched bar.
This approach allows the creep response of materials under multiaxial stress state to
be examined without the need to perform numerical computer calculation. The skeletal
representative stress, ske net value is defined at a skeletal point where the
variations of the stress component for different creep exponent intersect. The values of
86
the skeletal stresses ratio for blunt and medium notch have been reported by Webster
[75] and it is given in Table 4.8.
The skeletal von Mises and maximum principal stress for blunt and medium notch are
plotted in Figure 4.26 and 4.27 for new and ex-service material, respectively. The
uniaxial data have been included in Figure 4.27. Similar to Figure 4.24 and 4.25, the
regression line in Figure 4.26 and 4.27 has been made to uniaxial data and NIMS data
[81] at the same temperature. From both figures, it can be seen clearly that the
maximum principal skeletal stress does not accurately represent the experimental data
for notched specimen. The test data for uniaxial and notched bar specimen could be
represented reasonably well using the von Mises skeletal stress as shown in Figure
4.26 and 4.27. This may indicate that the von Mises stress dominates the fracture
behaviour of this material. In order to obtain more accurate way of representing the
creep rupture data under multiaxial stress state, Eqn (2.26) has been plotted by using
=0.06 and 0.05 for new and ex-service material, respectively as shown in Figure
4.28. With this value of , the creep rupture life for notched bar is considered to be
governed predominantly by von Mises stress with only 6% and 5% maximum principal
stress for new and ex-service material, respectively.
Table 4.8 Skeletal stress ratio [75]
a/R ske net sk
m net 1sk
net
1.5 0.77 0.54 1.05
5 0.66 0.73 1.14
87
Figure 4.26 Rupture Life for new material based on a) von Mises stress and b)
Maximum Principal stress
50
500
10 100 1,000 10,000
σ esk
ele
tal s
tre
ss (
MP
a)
Time to rupture (h)
P91-A-Blunt notch
P91-A-Medium notch
620°C
a)
Fit to medium notchFit to blunt notchFit to NIMS and uniaxial test data
50
500
10 100 1,000 10,000
σ 1 s
kele
tal s
tress (
MP
a)
Time to rupture (h)
P91-A-Blunt notch
P91-A-Medium notch
620°C
b)
Fit to medium notchFit to blunt notchFit to NIMS and uniaxial test data
88
Figure 4.27 Rupture Life for ex-service material based on a) von Misses stress and b)
Maximum Principal stress
50
500
10 100 1,000 10,000
σ e s
kele
tal s
tress (
MP
a)
Time to rupture (h)
P91-B-Blunt notch
P91-B-Medium notch
P91-B-Uniaxial
600°C
a)
Fit to medium notchFit to blunt notchFit to NIMS and uniaxial test data
50
500
10 100 1,000 10,000
σ 1 s
ke
leta
l str
ess (
MP
a)
Time to rupture (h)
P91-B-Blunt notch
P91-B-Medium notch
P91-B-Uniaxial
600°C
b)
Fit to medium notchFit to blunt notchFit to NIMS and uniaxial test data
89
Figure 4.28 Rupture life based on representative stress for a) new material and b) ex-
service material
50
500
10 100 1,000 10,000
σ rep
skele
tal s
tre
ss (
MP
a)
Time to rupture (h)
P91-A-Blunt notch
P91-A-Medium notch
Fit to all notches
Fit to uniaxial data
620°C
a)
α=0.06
50
500
10 100 1,000 10,000
σ rep
ske
leta
l str
ess
(M
Pa
)
Time to rupture (h)
P91-B-Blunt notch
P91-B-Medium notch
Fit to all notches
Fit to uniaxial data
600°C
b)
α=0.05
90
4.7.2 Multiaxial Stress State on Creep Ductility
The effects of stress on rupture life have been discussed previously where the concept
of representative stress has been employed. In this section, the effect of multiaxial
state of stress on creep ductility has been evaluated. It is well known that creep ductility
exhibits a strong dependence on the multiaxial stress state. Many models that can be
used to predict this dependence such as Rice and Tracey [34] , Cocks and Ashby [35]
and Spindler [36]. These models show that the ratio of multiaxiality and uniaxial ductility,
*f f , is a function of hydrostatic stress and the equivalent stress, m e , which
is often known as triaxiality.
The multiaxiality creep ductility models described by Eqns (2.27) to (2.29) are
compared with the test data for new and ex-service material condition as shown in
Figure 4.29. In Figure 4.29(a) and (b), the failure strain for uniaxial test are based on
the axial measurement where 30%f and ROA measurement where
80%f .The multiaxial failure strain for notched bar are tabulated in Table 4.7. The
stress triaxiality, m e , for the test data was analysed by using the skeletal point
analysis as given in Table 4.8. For the Spindler model, p=0.15 and q=1.25 has been
used [36]. The creep exponent, n of 13 was used for the Cocks and Ashby model.
It can be seen in Figure 4.29(a) that the Spindler and Cocks and Ashby models are in
reasonable agreement with the test data at high triaxiality, though the Cocks and Ashby
model over predict at low triaxiality. Note that the Rice and Tracey model is based on
perfectly plastic material response and therefore has no dependence on creep
exponent (see Eqn (2.29)). As shown in Figure 4.29(b) where the failure strain
measured based on ROA, most of the test data lies above the prediction models. This
may imply that the model conservatively predicts the test result. It should be noted that
the new and ex-service materials tested at 620ºC and 600ºC, respectively would also
include some temperature effect of creep ductility. The prediction of the rupture life and
the effect of creep ductility on notched bar will be investigated further using numerical
analyses.
91
Figure 4.29 The effect of triaxial stress state on the failure strain of notched bar for new
(P91-A) and ex-service material (P91-B) a) using axial measurement and b) reduction
of area (ROA)
0.1
1.0
0.0 0.3 0.6 0.9 1.2 1.5 1.8
Nom
aliz
ed D
uctilit
y
σm /σ
P91-A Blunt notch
P91-A-Medium notch
P91-B-Blunt notch
P91-B-Medium notch
Uniaxial
Rice and Tracey model
Spindler model
Cocks and Ashby model (n=13)
εf axial =30%
a)
0.1
1.0
0.0 0.3 0.6 0.9 1.2 1.5 1.8
No
ma
lize
d D
uct
ility
σm /σ
P91-A-Blunt notch
P91-A-Medium notch
P91-B-Blunt notch
P91-B-Medium notch
Uniaxial
Rice and Tracey model
Spindler model
Cocks and Ashby model (n=13)
b)
εf ROA =80%
92
4.8 Microstructural Examination of Uniaxial and
Notched Bar Creep Test
Metallographic examination prior to testing has been performed on the new and ex-
service P91 material. Both materials were etched using Villela agent (containing 1g of
picric acid, 5 ml of HCI and 100 ml of ethanol). Figure 4.30 shows similar
microstructure for new and ex-service materials where the expected lath martensitic
microstructure is observed.
4.8.1 Uniaxial Creep
Microstructural analysis has been performed on new creep specimen which were
stopped at 9800h and 9400h. The specimens were sliced in the gauge length and were
polished and etched to reveal the microstructure. Figure 4.31 shows the optical
micrograph of new P91 steel tested at 80 MPa and 100 MPa. It is shown in Figure 4.31
that there is no significant difference between the specimen tested under 80 and 100
MPa at 620ºC. Arrows in Figure 4.31 show the creep cavities in the microstructure.
According to [92],the carbide and nitride precipitates form on prior austenite grain
boundaries, subgrain boundaries and on martensitic laths. When the materials are put
into service in power plant at temperature below the tempering temperature, further
particles may precipitate which are thermodynamically unstable at the tempering
temperature.
(a)
(b)
Figure 4.30 Optical micrograph of P91 material prior to testing for a) new condition
b) ex-service condition
93
Figure 4.31 Optical micrograph of the new P91 steel tested under a) 80 MPa, stopped
creep test after 9800 h creep test and b) 100 MPa, stopped creep test after 9400h.
Arrows show the creep cavities.
4.8.2 Notched bar
Microstructure examination has been performed on the notched bar specimens to
investigate the failure mechanism. The unfailed notched specimens were sliced and cut
approximately 2 mm from the notch throat. The specimens were mounted, polished
and etched. Figure 4.32 and 4.33 show the optical microscope images for P91-A-UB2
and P91-A-UM2, respectively. In Figure 4.32, the P91-A-UB2 specimen was initially
tested at 620°C under low load and was interrupted at 9653 h. The same specimen
designated as UB2a, was then further tested at high load and ruptured at 63h. It can be
seen that in Figure 4.32 that for the unfailed blunt notch, the creep damage is visible at
the center of the notch throat. No sign of micro-crack is seen in this figure.
For the new material denoted as P91-A-UM2, the specimen was initially tested at
620°C under low stress and was interrupted at 7250 h. The same specimen designated
as UM2c was further tested at high load and ruptured at 43h. From Figure 4.33, it can
be seen that the creep damage is more dense at the notch root rather than at the notch
centre. It may suggest that for the medium notched specimen, the void may start to
coalescence near the notch root and grow toward the centre of the notch throat. This is
confirmed by looking at Figure 4.34 where the cracks are initiated at the notch root for
medium notch specimen tested at low stress (P91-B-UM8a). High magnification
images at both notch roots are shown in Figure 4.34 a) and b) showing that the cracks
starts to initiate at the notch root and coalescence with the void nearby and grow
toward the centre of the notch throat.
94
Figure 4.32 Optical microscope image for blunt notched (P91-A-UB2a)
Figure 4.33 Optical microscope image for medium notched (P91-A-UM2c)
95
Figure 4.34 Optical microscope image for medium notched (P91-B-8a) showing the
crack initiate at the notch root a) high magnification images of region i and b) high
magnification of region ii
96
4.8.3 Fractography of notched bar
Fracture surface for both blunt and medium failed notched has been examined using
scanning electron microscope. Figure 4.35 and 4.36 show SEM images for blunt and
medium notched specimens, respectively. It can be seen in Figure 4.35 that typical cup
and cone is observed on the fracture surface of blunt notch specimen. Dimple fracture
was dominantly observed at the centre of the notch throat as shown in Figure 4.35 (b).
From this observation, it may suggest that for the blunt notch, the failure mechanism is
intergranular ductile failure. Different fracture behaviour was observed for medium
notch specimen as shown in Figure 4.36. A relatively flat surface can be seen on the
fracture surface in Figure 4.36 (a) and a mixed mode failure appearance comprising of
ductile dimples at the notch center as shown in Figure 4.36 (b).
Figure 4.35 SEM micrograph of blunt notch specimen on a) fracture surface
(b) centre of notch throat
Figure 4.36 SEM micrograph of medium notch specimen on a) fracture surface
(b) centre of notch throat
97
4.9 Discussion
The stress rupture data in Figure 4.9 has shown that at the at longer creep life
(>10,000h) the creep strength degrades dramatically. The prediction of rupture under
low stress at longer periods is important as it simulated the actual life of power plant.
The reason for a marked drop in creep rupture strength can be explained in terms of
microstructural evolution where the sub grain size gradually increased and abruptly
coarsened up to creep failure [13].
Creep ductility has shown a lot of scatter as shown in Figure 4.13 to 4.16. It is seen
that at longer rupture life, the creep ductility reduced significantly. This degrading
phenomenon can be regarded with creep cavitation growth process. The present short
term tests when compared with the longer tests in the data sets confirm this effect. It is
therefore important to note that the fractography presented here showing the short term
test behaviour with increased ductility may not be representative of long term plant
behaviour.
In the notched bar analysis, the behaviour of the notch strengthening is seen in Figure
4.24 and 4.25. This behaviour depends on the notch shape, notch acuity, testing
condition and material ductility. The extend of strengthening in higher notch acuity has
been reported for the P91 material [32] and 2.25Cr-1Mo steel [93].
The models based on cavity growth used to predict the influence of multiaxiality show
that the Spindler and Cocks and Ashby models are in reasonable agreement with the
test data at high triaxiality though the Cocks and Ashby model over predict at low
triaxiality. Most of the test data lies above the prediction models when the ROA is used
as a failure strain which may imply that the model conservatively predicts the test data.
The prediction of the rupture life and the effect of creep ductility on notched bar will be
investigated further using the numerical analysis.
Microstructural examination reveals that for blunt notch specimen the creep damage
appears at the notch centre whilst for medium notch specimen the creep damage may
start to coalescence near the notch root and grow toward the centre of the notch throat.
This has been confirmed by the Figure 4.34 that the crack starts to initiate at the notch
root and coalescence with the void nearby and grow toward the centre of the notch
throat.
a) b)
98
4.10 Summary
The uniaxial creep tests have been performed on the new and ex-service
material tested at 620°C and 600°C, respectively.
Creep deformation of both material conditions show that the strain accumulation
in tertiary region is large compared to that in primary and secondary region.
The short-term creep test data have been analysed with available literature for
P91 material to examine the effect of long term exposure.
The stress rupture data have shown that at longer creep life (>10,000h) the
creep strength degrades dramatically (Figure 4.9).
The minimum and average creep strain plot have shown that there exist two
main regions, namely low stress and high stress region which can be regarded
as long term and short term test, respectively. The change in the slope from
long term test to short term test may indicate the shift of the creep mechanism.
Analysis of creep ductility has shown the stress dependency on creep ductility
at 600°C at a wider stress range ( Figure 4.15).
The notched bar creep tests have been performed on the blunt and medium
notched type for new and ex-service material.
The creep rupture life of notched specimens was found to be higher than the
uniaxial specimens. This behaviour is known as notch strengthening which is
caused by the reduction of equivalent stress in the notched bar.
The concept of representative stress has been employed to examine the effect
of multiaxial stress on the rupture life. A skeletal stress analysis has been used
to determine the value of the stress components.
The effect of multiaxial stress state on creep ductility has been examined by
employing the void growth models. It is shown that the Spindler and Cocks and
Ashby models in a reasonable agreement with the test data at high triaxiality
though the Cocks and Ashby model over predict at low triaxiality.
Microstructural examinations have been performed on the unfailed notched bar
specimens.
The microstructure reveals that for blunt notch specimen the creep damage
appear at the notch centre whilst for medium notch specimen the creep damage
may start to initiate and coalescence near the notch root and grow toward the
centre of the notch throat.
99
Chapter 5
Creep Fatigue Crack Growth Test
Result and Analysis
5.1 Introduction
Cyclic operation in a high temperature component may lead to a combination of creep
and fatigue failure which can be more severe compared to static creep load alone.
A characterisation of creep fatigue interaction therefore is needed to be better
understood and the assessment of long term failure in high temperature component is
crucial. The industrial design code such as R5 [42] and BS7910 [94], assumes a linear
accumulation of creep and fatigue damage but does not consider any long-term
material degradation. In this work, creep fatigue crack growth (CFCG) tests have been
performed on compact tension, C(T) specimens at a range of temperature between
600ºC to 625°C with hold times ranging from static to 600s. The main results of this
chapter are to characterize the CFCG behaviour of new and ex-service material.
In this chapter, the experimental result were analysed and compared to static creep,
high cycle fatigue and CFCG test data available in the literature on P91 steel. The
CFCG data was characterised using stress intensity factor parameter range, K and
creep fracture mechanics parameter, C*. The CFCG rate and the time for 0.2mm creep
crack growth extension have been compared to the NSW CCG model’s prediction.
A linear cumulative rule was used to predict the CFCG experimental result.
Metallography and fractography assessments were performed to investigate the
dominant failure mechanism. Part of this work has been published in preliminary form
in the journal [95].
5.2 Creep Fatigue Crack Growth
Creep fatigue crack growth testing was performed on C(T) specimens according to the
testing standard, ASTM E-2760 [76]. The specimen dimension and material condition
for all the specimens are detailed in Table 3.4. Seven specimens were tested, one from
100
the new material P91-A was identified as CT-A, four from the ex-service material P91-B
were identified as CT-B and two from the ex-service material P91-C were identified as
CT-C1 and CT-C2. Note that test specimens CT-C1 and CT-C2 contributed to a larger
ASTM organised round robin project, as detailed in [3, 70]. CT-C1 and CT-C2 were
fatigue pre-cracking to an initial crack length to width ratio, 0 /a W ~ 0.4 at room
temperature, whereas CT-A and CT-B were electrical discharge machining (EDM)
notched with a wire diameter of 0.25 mm. All C(T) specimens were then side grooved
by 10% of the specimen thickness on each side.
The CFCG test loading condition, initial crack length, 0a , final crack length, fa , and
time to failure, ft , are detailed in Table 5.1. It should be noted that CT-B4 specimen
was tested in high temperature fatigue condition with 10 Hz frequency thus giving the
shortest time to failure. Due to the limited number of specimens, CT-C1 and CT-C2
were only tested at the same hold time whilst CT-B1 to CT-B3 were tested at hold
times of 600s, 60s and 30s. All CFCG tests were just stopped before fracture, thus time
to failure, ft , indicates the CFCG test duration. All C(T) specimens were subsequently
broken open at room temperature by high frequency fatigue loading. The initial crack
length, 0a , and final crack length, fa were then calculated using Eqn (3.2) by
averaging 9 measurements along the crack front [76].
Table 5.1 Test loading condition and durations
Specimen T ht P 0( )K a 0a 0a /W fa ft fN
ID (°C) (h) (kN) MPa.m1/2 (mm) (mm) (h) (cycle)
CT-A 620 600 15.0 22.5 22.5 0.5 30.5 1125 6750
CT-B1 600 600 13.0 22.6 25.0 0.5 28.7 311 1865
CT-B2 600 60 12.0 20.9 25.0 0.5 30.2 167 9105
CT-B3 600 30 12.0 20.9 25.0 0.5 30.5 133 13333
CT-B4 600 0 13.0 22.6 25.0 0.5 29.1 0.34 12316
CT-C1 625 600 7.5 20.5 20.8 0.4 27.9 408 2450
CT-C2 625 600 9.0 25.9 21.8 0.4 27.9 240 1438
101
5.2.1 Load Line Displacement
The load line displacements, LLD as a function of time normalised by the test duration
is shown in Figure 5.1 for all specimens tested. The x-axis was normalised so that each
curve could be observed clearly. In Figure 5.1, the initial loading up displacement was
excluded and the displacements after the loading up are presented. It can be seen in
Figure 5.1 that the new material, CT-A which was tested at K of 22.5 MPa.m1/2 and
temperature of 620°C had significantly longer test duration (see Table 5.1) than the ex-
service material (CT-B1). A large LLD prior to test completion may be due to the high
test load and temperature. Considering the hold time effect (30 to 600s), the test CT-B3
which was tested at 30s hold time, has the shortest time to failure (see Table 5.1).
5.2.2 Crack Growth Behaviour
Figure 5.2 shows the crack extension, a against the number of cycles normalised by
the number of cycles to failure, N/Nf. Note that the number of cycles is dependent on
the point where the test was interrupted, which corresponds to a point of significant
acceleration in crack growth rate. In Figure 5.2, all tests generally show crack growth
from initial loading and large crack extension (Δa) towards the end of the test
completion. Note that the test CT-B4 which was tested in fatigue only conditions at a
high frequency had very short test duration, as expected. Comparing the frequency and
hold time effect for the ex-service material at 600°C, the test duration becomes shorter
as the frequency increases (see Table 5.1).
102
Figure 5.1 Load line displacement versus normalised time.
Figure 5.2 Crack extension versus normalised number of cycles.
0.0
1.0
2.0
3.0
4.0
5.0
0.0 0.2 0.4 0.6 0.8 1.0
LL
D(m
m)
t/tf
CT-A CT-B1
CT-B2 CT-B3
CT-C1 CT-C2
0.0
2.0
4.0
6.0
8.0
10.0
0.0 0.2 0.4 0.6 0.8 1.0
Δa (
mm
)
N/Nf
CT-A CT-B1
CT-B2 CT-B3
CT-B4 CT-C1
CT-C2
103
5.3 Analysis of CFCG
The CFCG behaviour can be characterized using stress intensity factor range, K , and
creep fracture mechanic parameter C*. The NSW model could be used to predict the
creep crack initiation and creep-fatigue crack growth behaviour although it is usually
valid for CCG tests. The next sections present the CFCG analysis using the fracture
mechanic parameters and the CFCG prediction using the NSW model.
5.3.1 CFCG Correlation with Stress Intensity Factor Range
The stress intensity factor range can be used to characterise the CFCG behaviour
though it is strictly valid only for linear elastic behaviour, but it can be used as an
approximation if the plastic and creep zone size near the crack tip is limited. A material
with stress intensity factor as the controlling crack growth parameter is referred to as
creep brittle material.
The crack growth per cycle, da dN was plotted with the stress intensity factor range
for all the tests data in Figure 5.3. In general it can be seen that the crack growth per
cycle increased as the hold time increased. In order to investigate the effect of various
frequencies of CFCG data from [96-98] have been included in Figure 5.4. The dashed
and dotted line illustrates the regression fit made to the data with a frequency less than
0.002 Hz and between 0.01 and 1 Hz. At frequencies >0.01Hz, the CFCG behaviour
inclined to that of high cycle fatigue crack growth and data for all temperatures
considered fall close to each other. At lower frequencies, the crack growth rate
progressively increased with decreasing frequency and increase in temperature due to
a significant creep contribution. There is no clear unique relation obtained between
crack growth rate and K .This may be due to the fact that K does not account for the
creep fatigue crack tip field that may exist during the hold times. Hence the
characterisation of the CFCG rate with the steady state creep parameter, C* is
considered next.
104
Figure 5.3 Crack growth percycle da dN vs K for CFCG test data
Figure 5.4 Comparison of crack growth rate at various frequencies with available
literature data
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+01 1.E+02
da/
dN
(m
m/c
ycle
)
ΔK (MPa√m)
CT-A CT-B1 CT-B2 CT-B3
CT-B4 CT-C1 CT-C2
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+01 1.0E+02
da/d
N(m
m/c
ycle
)
ΔK (MPa√m)
CT-M-1
CT-FX-1
CT-B5,th=60s,T=600C,P=12kN
CT-B6,th=30sT=600C, P=12kN
CT-A-1
CT-A-2
ASTM T=625, th=600s, 7.5kN
ASTM T=625, th=600s, P=9kN
CFCG Ali,T=625,f=0.001
CFCG Ali,T=625,f=0.01
CFCG Ali, T=625,f=1.0
CFCGmagdalena, T=600, th=60min
FCG magdalena,T=600, f=0.5Hz
FCG,Gra T=600C, f=0.05 Hz
FCG test data, f=10Hz,P=13kN
T(°C) f(Hz) Kmax(MPa√m)
CT-A 620 0.0017 25.02
CT-B1 600 0.0017 25.11
CT-B2 600 0.015 23.18
CT-B3 600 0.027 23.18
CT-C1 625 0.0017 22.82
CT-C2 625 0.0017 28.83
Ref 625 0.0017 -
Ref 625 0.0017 -
Ref 625 0.0010 10.2
Ref 625 0.01 10.3
Ref 625 1.0 9.7
Ref 600 0.00027 -
Ref 600 0.5 -
Ref 600 0.05 -
CT-B4 600 10 25.11
CFCG
FCG
105
5.3.2 Crack Growth Correlation with C* parameter
CFCG may be described by creep fracture mechanic parameter, C*. The C*
parameter has been used to analyse creep crack growth where a steady state creep
deformation and damage has been developed at a crack tip. In CFCG, during the hold
time, creep deformation and damage may be developed, thus C* may be suitable to
describe the crack growth behaviour. The validity criteria for the use of C* as specified
in ASTM E1457 [54] was applied to the CFCG experimental data. The criteria are
described in Section 3.6.9.2.
The crack growth rates for CFCG test data have been correlated with the C* parameter
as shown in Figure 5.5 The best fit line to the CFCG data has been constructed as
denoted by the mean CFCG data in Figure 5.5. The P91 CCG scatter band at 580°C to
625°C [85] is also included. In [85], Maleki has developed the scatter band for P91
steel including parent and weld material. The data were collected from various sources
such as in reference [86, 99] provides an overall scatter band with an upper and lower
limit. The power law constant for these lines are given in Table 5.2. It can be seen that
there is a wide variation in the Grade P91 steel CCG data scatter band.
It is apparent that the CFCG data fall into the same scatter band as the static CCG,
however the CFCG data generally falls towards the upper bound of the static CCG data.
There is also some indication that an increase in temperature results in a high crack
growth rate as expected. CFCG rate in test data is on average an order of magnitude
higher than the mean line fitted to CCG data for a given value of C*. It is suggested for
components subjected to CFCG loading where the creep process control , that cyclic
crack growth rate can be predicted from static creep data using the creep fracture
mechanics parameter C*.
106
Figure 5.5 Correlation of creep fatigue crack growth data with C*
Table 5.2 Grade P91 CCG parameter [85]
CCG parameter Upper band Mean Lower band
D 17.2 4.5 2.3
0.7 0.7 0.8
Under steady state conditions, the CCG behaviour of a power-law creeping material
can be described by the NSW prediction model which is based on the experimental
uniaxial creep rupture properties. The NSW model could be used to predict the CFCG
for the low frequency cyclic loading condition with a hold time in which crack growth
may be dominated by creep process. In this section an approximate NSW (NSWA)
model has been employed to predict the CFCG behaviour.
The low frequency CFCG data has been correlated with C* parameter and compared
with the NSW model prediction as shown in Figure 5.6. In this figure, available
literature data on CFCG and CCG have been included for the temperature range of
600 to 625°C [85, 96, 98]. The P91 CCG scatter band at temperature ranging from
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01
da/d
t(m
m/h
)
C* (MPam/h)
CT-A CT-B1
CT-B2 CT-B3
CT-C1 CT-C2
CCG Data band (580°C- 625°C)
Mean (CCG) data
Mean (CFCG) data
107
580°C to 625°C [85] was also included. The mean CFCG and mean CCG are
presented with dash line as shown in Figure 5.6.
A power law exponent, n of 8.2 was used in the NSWA model. The creep failure strain
used for NSWA model in Eqn (2.59) is 30% which was based on average value of axial
measurement. The multiaxial creep ductility at the crack tip in NSWA model is taken to
be uniaxial creep ductility f for plane stress condition, and 30f and 10f for
strain condition [53]. It can be seen that in Figure 5.6, the plane strain condition with
30f resulted a cracking rate 4 times larger than 10f . Thus, the plane strain
condition with a factor of 10 is more appropriate to predict the CFCG data.
In Figure 5.6, it is clear that the CFCG test data are bounded by the plane stress and
plane strain prediction of approximate NSW model (NSWA).Using a factor 10f for
plane strain condition, it is observed in Figure 5.6 that most data especially the slower
rate longer term data generally fall below the NSWA plane strain prediction. For the
short term data, the plane stress predictions are shown for the fast rate tests. It is noted
that the NSW parameter used in Figure 5.5 are nominal for temperature range from
600 to 625°C. However in reality they are dependent on creep exponent and creep
ductility which may vary with material condition and temperature. Also the material
degradation due to long term services as well as low stresses tends to reduce failure
strain and cracking rates generally increases.
It is shown in Figure 4.13 and 4.14 that the creep ductility of the ex-service material
reduces in long term (low stress) tests which may be due to thermal aging effects. Thus
with the use of lower failure strain to reflect the long term behaviour the NSW model
should result in conservative prediction of crack growth rate. This is particularly
relevant for long term low C* predictions where material degradation may exhibit lower
creep ductility both due to material degradation and due to the failure strain sensitivity
to stress.
108
Figure 5.6 Correlation of creep fatigue crack growth data, CCG data band and
predictive NSWA model by using axialf
5.3.3 Creep Crack Initiation
The crack propagation can be caused by creep, fatigue or the interaction between two
mechanisms under creep fatigue loading. The crack growth is usually assumed to be
due to creep, hence the initiation time, ti is defined as the time for crack extension
a = 0.2 mm. In the CFCG, the crack growth is assumed to be due to creep, hence
the initiation time, ti can be predicted by NSW CCI prediction .In the initiation time
model, it is assumed that the crack grows from the time of first loading.
Assuming that the transition time is exceeded [52], the creep crack initiation has been
analysed in terms of C* parameter. Figure 5.7 shows the measured initiation time, ti
correlation with C* for the crack extension Δa=0.2mm and the predictive NSWA CCI
model. As can be seen in Figure 5.7 the initiation time in the CFCG/CCG test data is
inversely related to the C* when the graph is plotted in logarithmic scale. The CCG
data [96] was included in the Figure 5.7 to compare the initiation time with CFCG tests
data. Due to the data scatter no trend can be inferred to the CCG and CFCG data.
In the CFCG, the crack growth is assumed to be due to creep, hence the initiation time,
ti can be predicted by NSW CCI prediction. The predictions of initiation time in
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01
da/d
t(m
m/h
)
C* (MPam/h)
CFCG ,CT-FX-1,T=600C, th=600s,f=0.0017
CFCG,CT-B5,th=60s,T=600C
CFCG,CT-B6th=30s, t=600C, P=12kN
CFCG,CT-A-1,T=625C,th=600s,f=0.0017
CFCG CT-A-2,T=625C,th=600s,f=0.0017
CFCG,CT-M-1,T=620C,th=600s,f=0.0017
CFCG Ali,T=625,,f=0.001
CFCG Ali,T=625,f=0.01Hz
CFCG Mag T=600,th=60 min
CCG, Ali, T=625 f=0
CCG,maleki ExPT=600C
CCG,Maleki ,ExP3,T=600C
CCG,MagT=600C
T(°C) f(Hz) Kmax (MPa√m)
CT-B1 600 0.0017 25.02
CT-B2 600 0.015 23.18
CT-B3 600 0.027 23.18
CT-C1 625 0.0017 22.82
CT-C2 625 0.0017 28.83
CT-A 620 0.0017 25.11
Ref 625 0.001 8.1
Ref 625 0.01 10.3
Ref 600 0.00027 -
Ref 600
Ref 600
Ref 600
Ref 600
CF
CG
CCG
CCG Data band (580°C-625°C)
NSWA- PE (εf /10)
NSWA- PS (εf )
εf =30%
Mean (CFCG) data
Mean (CCG) data
NSWA- PE
(εf /30)
109
Eqn (2.61) are provided by the lower bound (LB) and upper bound (UB) under plane
strain and plane stress condition, respectively as shown in Figure 5.7. The axial
measurement is employed in the NSW calculation. It can be seen in Figure 5.7 that the
experimental data fell between the plane stress and plane strain upper bound
prediction of NSWA model regardless of the frequency value. Based on steady state
crack growth rate, the plane stress and plane strain NSWA model provided a
reasonable estimate on the creep initiation time. Though this model is strictly valid for
static CCG only, the conservative assumption that the crack grows from time zero and
under steady state conditions appears to have accounted for the acceleration in crack
growth due to fatigue for these conditions.
Figure 5.7 Correlation of creep crack initiation and predictive model using axial
measurement a) NSW-MOD model and b) NSWA model
1.0E-02
1.0E-01
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01
t i (h
)
C*(MPa.m/h)
CT-A CT-B1
CT-B2 CT-B3
CT-C2 CCG data
εf = 30%
n=8.24
NSWA-PS-LB
NSWA- PE-LB
NSWA-PS-UB
NSWA-PE-UB(b)
110
5.4 Creep-Fatigue Interaction
The focus on the analysis is based on identifying the creep/fatigue interaction and the
effect of the material degradation on the subsequent creep and fatigue life. A linear
cumulative rule has been used to predict the interaction effect of CFCG behaviour.
The frequency dependence on creep fatigue interaction has been examined by plotting
the crack growth rate per cycle versus frequency, using Eqn (2.69) in Figure 5.8. The
fatigue and creep constants in Eqn (2.69) are given in Table 5.3. The CFCG test data
showed by a solid square symbol in Figure 5.8 were calculated using Eqn (2.69) by
taking a fixed K = 25 MPa√m in Figure 5.4 which correspond to values of K that fall
in the Paris law FCG region. An available CFCG/CCG test data in reference [96] has
been included in Figure 5.8 at similar K value.
At high frequencies where fatigue process control, the first term in Eqn (2.69) tend to
zero and totalda dN tends to become pure fatigue. The horizontal line in Figure 5.8
was constructed from the CT-B4 test by identifying the pure fatigue level from the
da/dN curve at a fixed K = 25 MPa√m in Figure 5.4 Note that the CT-B4 test was
performed in high frequency fatigue at 10 Hz where the fatigue dominant appears.
At low frequencies, time dependent creep mechanism dominates and the second term
in Eqn (2.69) is negligible. Hence, as the frequency tends to zero, totalda dN in
Eqn (2.69) becomes inversely proportional to the frequency and a slope of -1 is seen
when da dN is plotted against frequency on logarithmic scale. Assuming that the static
creep data can be considered as a very low frequency cyclic test, the creep crack
growth data [85] was included in the Figure 5.8.
In Figure 5.8, the CCG data point is plotted by identifying the mean cracking rate
da dt from the static CCG data band in Figure 5.6 at a fixed value of
*C =1.0x10-4 MPa.mh-1 which approximately corresponds to K = 25 MPa√m for the
fatigue test. A best fit line denoted as static CCG was constructed with a slope of -1 for
the mean CCG data as shown in Figure 5.8 using Eqn (2.69). It is expected as
frequency tends to zero the data should tend to the static CCG data limit.
111
The average CFCG data point in Figure 5.8 is estimated by taking mean cracking rate
da dt for mean CFCG data in Figure 5.6 at a fixed value of *C =1.0x10-4 MPa.m/h
and inserted into Eqn (2.68). The best dotted line (cyclic CFCG) has been constructed
with a slope of -1 to the mean CFCG data which suggest a higher cracking rate
compared to the static CCG tests as shown in Figure 5.8.
In addition, NSWA plane strain (NSWA PE) line is constructed in the same fashion
using the upper bound NSWA line in Figure 5.6 by identifying NSWA PE cracking rate
da dt at a fixed value of *C =1.0x10-4 MPa.mh-1. It should be noted in Figure 5.8 that
a scatter band is shown for each data point indicating a level of uncertainty in the data.
However the overall trend in Figure 5.8 is clear.
The interaction diagram in Figure 5.8 shows that the cyclic ex-service steel cracking at
low frequencies exhibits about a factor of four times the cracking rate of the mean CCG
static data and that the NSW line predicts a higher conservative upper bound. At the
same times the only interaction with the fatigue horizontal line is at the crossing points
where both cracking rates are similar. The shift to the right of the interaction region
indicated an increase in fatigue dominance and constraint. It should be noted that the
increase in cracking rate corresponds with reduced creep ductlities that are found in
ex-service steel and in creep/fatigue tests as predicted by the NSW model shown as
the upper bound in Figure 5.8.
At high frequencies, fatigue is the dominant mechanism and the crack growth per cycle
is insensitive to frequency, as shown by the horizontal line whereas at low frequencies,
creep is expected to dominate leading to intergranular fracture. At intermediate
frequencies (0.001Hz < f < 0.01Hz) creep processes are significant and mixed
intergranular and transgranular fracture is expected. As explained in [19] both types of
processes are likely to develop intermittently through or around individual grains.
Hence, at intermediate frequencies when one mechanism becomes arrested locally,
the other may take over to allow cracking to progress at a rate equal to the sum of
individual rates [19].
It can be inferred that the interaction point can be shifted from static CCG towards
cyclic FCG. The additional shift from the left to the right could be due to other factors
which increase constraint in an inherent way. Therefore material degradation and
112
embrittlement in ex-service conditions, low stresses and reduced failure ductilities will
all tend to increase the cracking rate. The NSW model in Figure 5.8 could be used to
bound these effects.
Table 5.3 Fatigue and creep constant
Fatigue [96] Creep [85]
p D
1.5×10-8 3.57 6.5 0.7
Figure 5.8 Frequency dependence of crack growth per cycle showing increase in
cracking rate for cyclic tests in the low frequency creep dominated region (ex-service
material)
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E-05 1.0E-04 1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01
da/d
N(m
m/c
ycle
)
Frequency (Hz)
CFCG test data
FCG,f=10Hz,T=600C
Ali, Delta 30
Ave CFCG data
Speicher 60mins
Static CCG Shervin
NSW PE
-1
High FCG
Interaction in constraint and intreaction point shift from static CCG towards cyclic FCG
CFCG Test data
FCG Test data
CCG/CFCG data [8]
Average CFCG test data
CFCG data [11]
CCG data [20]
NSWA PE
113
5.5 Fractography
Prior to breaking open the specimen a 3 mm slice was extracted from the mid
thickness of the sample to examine the fracture path. Figure 5.9 (a) to (c) shows an
optical microscopy of the fracture paths of samples CT-B, CT-C1 and CT-A,
respectively. The crack path in the ex-service material sample CT-B (Figure 5.9) is
relatively straight fronted, with a number of small branches from the main crack. In
Figure 5.9(b) the cracking behaviour of CT-C1 ex-service material, the initial fatigue
pre-crack is relatively straight; however in the CFCG region the crack grows at an
angle. However for the new material CT-A (Figure 5.9(c)), a large crack opening
displacement is observed, which is consistent with Figure 5.1, and the crack shows
some discontinuous branching, signifying that the crack growth is creep dominated.
High magnification images of CT-B1 (Figure 5.9(a)) showing the region (i) and (ii) are
presented in Figure 5.10. As shown in Figure 5.10(a), the secondary crack deviates
from the main crack and the cracks are surrounded by the creep cavities. Figure 5.10(b)
shows the main crack propagating accompanying by the creep voids near the main
cracks.
In order to investigate the effect of frequency on CFCG, the fracture surface of creep
fatigue crack growth region has been examined in more detail using the scanning
electron microscope (SEM). Figure 5.11 (a) to (d) shows the CFCG region for
frequencies of 0.0017 Hz, 0.0015 Hz, 0.027 Hz and 10 Hz. Although the surfaces were
oxidised the figures highlight the important cracking features that confirm the effect of
frequency on the mode of cracking at elevated temperatures. The SEM image of CFCG
region in Figure 5.11(a) is evidently intergranular indicating the creep dominance. The
cracking mode become trans-granular as the frequency becomes higher and the
fracture surfaces become more flat in appearance, Figure 5.11 (b) to (d).
114
Figure 5.9 Cracking behaviour a) CT-B; b) CT-C1 ; c) CT-A
115
Figure 5.10 High magnification images of CT-B region (a) i and (b) ii, showing cracks
and cavities near the crack
116
Figure 5.11 Fracture surface of CT-A and SEM images of fracture surface on the creep
fatigue crack growth region at different frequencies a) 0.0017 Hz (CT-B1) b) 0.015 Hz
(CT-B2), c) 0.027 Hz (CT-B3) and d) 10Hz (CT-B4)
117
5.6 Discussion
A linear cumulative damage rule can still predict the creep/fatigue interaction results
regardless of the degradation of the steel under ex-service conditions. This confirms
the approach taken by the codes of practice at least for short term tests. However, it is
clear that the mean CFCG rates for ex-service steels are faster by a factor of 4
compared to the mean CCG data. This can be attributed to the reduction in failure
strain observed in creep/fatigue tests as well as the reduced failure strains in ex-
service steels. Effectively it confirms the NSW plane strain predictions when creep
dominates under creep/fatigue conditions which identifies a reduction in failure strain
with an increase in constraint.
Unavailability of long term tests (> 10,000h) at low stresses and long dwell periods may
pose additional problems under creep control due to state of stress where lower creep
ductilities and high multiaxial stress state prevail. It is found that for low stress, low
ductility and increase in constraint under plane strain predictions of crack growth rate
data using the NSW creep crack growth model can conservatively bound the
experimental data at long terms which is more appropriate prediction for components
operational times.
High cracking rate in long term prediction may be attributed to the material degradation
in the ex-service material. This can be explained in term of microstructural evolution in
P91 steel where high dislocation density and sub grain coarsening may contribute to
the loss of ductility of the material. It is also suggested that low ductility and high
constraint are most likely to be prone to cracking and that the material service condition
could lead to the reduction in ductility.
The other factor of increasing in crack growth rates and subsequently decreasing in life
is due to the fatigue oxidation interaction process. The oxidation could not be
distinguished in the present investigation because the CFCG testing is not performed in
a vacuum. Since the testing is conducted in air, the role of environment cannot be
excluded. However if the oxidation reduces creep ductility, it will also be expected to
give enhanced crack growth rates.
118
It is clear that further detailed testing is needed to confirm the prediction lines in Figure
5.8, however the present finding can confirm that firstly the linear cumulative damage is
sufficiently accurate for lifing assessment as long as s appropriate low dwell cyclic test
data are available for the material. Secondly, with an appropriate ductility such as for
P91, the NSW model can conveniently predict the upper bound cracking rate under
creep-fatigue condition.
5.7 Summary
The creep fatigue crack growth behaviour of P91 steel in new and ex-service
material conditions has been examined.
The crack growth data was characterized using fracture mechanics parameters
ΔK and C*. The results showed that at high frequency (> 0.01 Hz), the CFCG
behaviour tend to that of high cycle fatigue crack growth and is best correlated
with the ΔK parameter whereas at lower frequencies, creep mechanisms have
been found to dominant and best correlated with the C* parameter.
The correlation between crack growth rate and C* parameter, shows that most
of the CFCG tested at 600°C to 625°C fall within the CCG P91 scatter band
data for this temperature range.
Based on steady state crack growth rate, the plane stress and plane strain
NSWA model provides a reasonable estimate of the creep initiation time.
An interaction diagram based on a linear cumulative damage rule has been
proposed to predict the creep-fatigue interaction results regardless the
degradation of the steel under ex-service condition. It is shown that the mean
CFCG rates for ex-service steels are faster by a factor of 4 compared to the
mean CCG data.
The present finding can confirm that firstly the linear cumulative damage is
sufficiently accurate for lifing assessment as long as appropriate low dwell
cyclic tests are available for the material. Secondly, with an appropriate ductility,
the NSW model can conveniently predict the upper bound cracking rate under
creep-fatigue condition.
Fractographic assessment has been performed to confirm the experimental
findings. An intergranular fracture surface was observed for all CFCG tests
examined with a frequency of less than 0.002Hz indicating that the fracture
process is creep dominant.
119
Chapter 6
Finite Element Simulation of
Notched Bar
6.1 Introduction
Most components are generally subjected to multiaxial stress state. The most
convenient method of introducing multiaxial stress states in laboratory test is to subject
notched specimens to an axial tensile load [75]. The effect of multiaxility can be
investigated by changing the notch geometries. A notch imposes constraint to creep
deformation and creep damage may result from the formation, growth and coalescence
of cavities leading to creep rupture. Therefore it is important to be able to predict
accurately the extent of creep damage and rupture life under multiaxial stress condition.
The strengthening effect the presence of notch can be observed in P91 material [32,
100, 101]. Eggeler [100] studied the notch on creep behaviour of P91 steel and
observed strengthening in the steel. The strengthening effect was found to decrease
with the decrease in applied stress and increase in rupture life. Other materials show
similar effects are Nimonic 80A [102], 2.25Cr-1Mo[103] and Cr-Mo-V [104].
A finite element (FE) analysis may provide a suitable tool to give a more detailed
analysis for the creep deformation and damage accumulation prior to failure under
multiaxial creep conditions. Finite element analysis can be used to predict the
multiaxial stress state and the rupture of notched bar creep specimens. The influence
of multiaxial stress state can be studied by varying the notch geometries.
FE analysis coupled with continuum damage mechanics has been extensively used for
creep damage and rupture life prediction under multiaxial stress state. For example
Kachanov Robotnov model [32, 105-109], Spindler model [110] and Cock and Ashby
model [104, 111]. In this work, FE analysis has been performed to predict the creep
rupture life under multiaxial condition based on the Cocks and Ashby model. This
method has been widely used in creep crack growth prediction [112-114].
120
In this chapter, finite element analyses were carried out to study the influence of notch
geometry on the stress distribution across the notch throat during the creep exposure.
Damage evolution can be simulated and rupture life can be predicted from the finite
element analysis. The predictions from the FE models are compared with experimental
data for the material.
6.2 Material model
The tensile and creep deformation behaviour of new and ex-service material has been
previously described in Chapter 5. The tensile properties have been obtained from the
experimental data. In the FE analysis, the tensile properties tested at 600ºC as shown
Figure 4.2 were employed.
Creep properties of ex-service material were obtained from experimental data as
discussed in Chapter 4. The value of minimum and average creep strain rate may vary
over the wide range of stress as shown in Figure 4.10 and 4.11, respectively. The use
of average creep strain rate may account for all the three creep regions and the final
fracture. The creep properties based on low stress and high stress region were
tabulated in Table 4.6. Creep ductility of P91 material has shown a wide scatter over
the wide range of stress as shown in Figure 4.16. The estimated creep ductility of 30%
and 12% have been used in the FE analysis as the upper and lower bound value,
respectively.
6.3 Finite Element Model
6.3.1 Finite Element Meshes
Finite element analyses were performed on a two dimensional axisymmetric (2D)
model of notched bar specimen using ABAQUS v6.12. One quarter of the specimen
was modelled taking into advantage the symmetry of the specimens as shown in
Figure 6.1. The specimen is modelled using four node axisymmetric elements with
reduce integration (CAX4R). The mesh sensitivity analysis has been performed on
three different mesh densities. The more refined mesh had an influential on the
predicted rupture time. Therefore, the most refined mesh with the total number of
nodes, 16803 and the total number of element, 16434 were used. The model was
meshed in two major sections with a finer mesh around the notch root. An illustration of
121
the type of the mesh in the local notch region that was employed is shown
Figure 6.2.The smallest element size ahead of the notch root is 0.02 mm x 0.03 mm.
The boundary condition was applied as shown in Figure 6.1 where the nodes along the
bottom face were restrained in the y-direction. The uniform stress was applied along
the top face of the model such that the desired net section stress across the throat is
achieved.
(a) (b)
Figure 6.1 Schematic of notched bar specimen a) whole specimen b) details of notch
throat
122
(a) (b)
Figure 6.2 FE Mesh a) Blunt notch b) Medium Notch
6.3.2 Creep Damage Model
A ductility exhaustion method is employed to calculate the creep damage during the FE
analysis. A damage parameter, ω is established such that 0 1 and failure occurs
when ω=1. The rate of damage accumulated is defined as the ratio of the creep
strain rate to the multiaxial creep ductility and is given by:
*
c
f
(6.1)
where c is the equivalent (Mises) creep strain rate and *
f is the multiaxial creep
ductility. The total damage at any time is the integral of the damage rate and can be
expressed as
0
tdt (6.2)
In order to account the creep ductility on the multiaxial stress states, the Cocks and
Ashby model [35] has been employed. In the model, the stress triaxiality is defined by
the ratio of the mean stress and equivalent stress and the ratio of uniaxial and
multiaxial creep ductility is defined by Eqn (2.36). This equation was implemented in
the ABAQUS code using user subroutine USDFLD.
123
6.3.3 Creep Damage Simulation
The creep damage simulation is similar that seen in [113, 115] where the damage is
simulated by reducing an elements load carrying capacity when the damage parameter,
ω attains its critical value. This is achieved by specified the stress at the element gauss
point to experience elastic perfectly plastic behaviour with a yield stress of 1 MPa. This
setting was set using user defined field (USDFLD) subroutine in ABAQUS where the
damage of each element is also evaluated. The USDFLD subroutine was also used to
switch the values A and n depending on the normalized value. When the damage at
the centroid of the element attains ω=1.0 then the element is considered fully damaged.
The analyses were run until terminated by the program when the numerical difficulties
were encountered.
6.4 Notched Bar Simulation Result
6.4.1 Stress Distribution
In the notched bar analysis, the stress distributions across the notch throat are non-
uniform. It is therefore necessary to evaluate the stress distribution across the notch
throat as a function of normalised distance from the notch root. Figure 6.3 to 6.5 show
the distribution of von-Mises stress, maximum principal stress and hydrostatic stress,
respectively across the notch throat from the initial loading until steady state life as a
function of normalized distance from the notch root, r/a. The normalised distance is
shown from the centre of the specimen where r/a=0 is at the centre and r/a=1 is at the
notch root.
From Figure 6.3 it can be seen that after loading during the creep exposure the von-
Mises stress is highest at the notch root for both notch type. As the creep deformation
takes places, stress redistribute across the notch throat was found to change with
creep exposure and approach stationary state. The stress redistributes and achieve it
steady state after 42 h of creep exposure. At the centre of the notch, r/a=0, the von
Mises stress was significantly lower than that of 0.2% proof stress of P91 material
(287 MPa). At the notch root r/a=1, the von Mises stress is still lower than the 0.2%
proof stress, suggesting that the localized plastic deformation at the notch root does
not contribute in the stress distribution across the notch throat from the beginning of
creep loading for this material [32].
124
It is also seen in Figure 6.3 (a) and (b) that the von-Mises stress is lower than that of
the net stress for both notch acuity at steady state life which may indicate the notch
strengthening effect, as observed experimentally.
The distribution of maximum principal stress across the notch throat for blunt and
medium notch is shown in Figure 6.4 (a) and (b), respectively. As shown in
Figure 6.4 (a) after reaching steady state life, the maximum principal stress distribution
shows a maximum value at r/a~0.6 which is more than the net stress for a blunt notch
type. For medium notch specimen (Figure 6.4(b)), the peak of maximum principal
stress occurred closer to the notch root. The hydrostatic stress distribution across the
notch throat for blunt and medium notch are shown in Figure 6.5 (a) and (b),
respectively. The hydrostatic stress distribution shows similar behaviour to that of the
maximum principal stress. The hydrostatic stress remained below the net stress for
both notches.
One of the factors that influence creep rupture behaviour under multi axial stress state
is triaxiality. Triaxiality is defined as the ratio of hydrostatic stress and the von Mises
stress. Figure 6.6 shows the variation of triaxiality across the notch throat for blunt and
medium notch. It can be seen in Figure 6.6 that the triaxiality is maximum at notch
throat distance of r/a=0.5 for blunt notch whereas the triaxiality is maximum near the
notch root i.e r/a=0.8 for medium notch. The medium notch has a maximum value of
triaxiality nearly twice of the blunt notch. For both notch types, the triaxiality across the
notch throat is significantly higher than that for a uniaxial test specimen ( m e =1/3).
125
Figure 6.3 Von Mises stress distribution for blunt and medium notch at
net stress 187=MPa
50.0
100.0
150.0
200.0
250.0
300.0
0 0.2 0.4 0.6 0.8 1
σ e(M
Pa
)
r/a
a) Blunt notch
0 after loading
0.001tf
0.5tf
0 h after loading
0.001tr
0.5tr
50.0
100.0
150.0
200.0
250.0
300.0
0 0.2 0.4 0.6 0.8 1
σ e(M
Pa)
r/a
b) Medium notch
0h after loading
0.001tf
0.5tf
0 h after loading
0.001tr
0.5tr
126
Figure 6.4 Maximum principal stress distribution for blunt and medium notch net stress
= 187 MPa
100.0
150.0
200.0
250.0
300.0
350.0
0 0.2 0.4 0.6 0.8 1
σ1(M
Pa
)
r/a
a) Blunt notch
0 after loading
0.001tf
0.5tf
0 h after loading
0.001tr
0.5tr
50.0
100.0
150.0
200.0
250.0
300.0
0 0.2 0.4 0.6 0.8 1
σ 1(M
Pa)
r/a
b) Medium notch
0h after loading
0.001tf
0.5tf
0 h after loading
0.001tr
0.5tr
127
Figure 6.5 Hydrostatic stress distribution for blunt and medium notch bar at net stress =
187 MPa
50.0
75.0
100.0
125.0
150.0
0 0.2 0.4 0.6 0.8 1
σm(M
Pa
)
r/a
a) Blunt notch
0h after loading
0.001tf
0.5tf
0 h after loading
0.001tr
0.5tr
50.0
100.0
150.0
200.0
0 0.2 0.4 0.6 0.8 1
σ m(M
Pa)
r/a
b) Medium notch
0h after loading
0.001tf
0.5tf
0 h after loading
0.001tr
0.5tr
128
Figure 6.6 Variation of triaxility across the notch throat for blunt and medium notch at
t = 0.5tr
6.4.2 Axial Displacement
The experimental axial displacement for a blunt and medium notched are compared
with finite element prediction as shown in Figure 6.7(a) and (b), respectively. As shown
in Figure 6.7, the finite element results predict a higher axial displacement than that of
experimental displacement due to the use of average creep strain rate properties which
account all three creep regions. Although not shown here, similar behaviour was
predicted for all displacement experimental result at different net stresses. The time to
rupture predicted by FE was taken when few elements reaches ω=1.0.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.2 0.4 0.6 0.8 1
σ m/σ
e
r/a
Blunt notch
Medium notch
129
Figure 6.7 Comparison of FE prediction with test data for a) blunt notch b) medium
notch
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 500 1000 1500 2000
Dis
pla
cem
ent (
mm
)
Time (h)
Test data
FE Prediction
σnet =187 MPaBlunt notch
(a)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 100 200 300 400 500
Dis
pla
cem
en
t (
mm
)
Time (h)
Medium Notch
Test data
FE Prediction
σnet =226 MPa
(b)
130
6.4.3 Creep Damage
In order to evaluate the creep damage accumulation, a ductility exhaustion approach
has been used in the FE analysis by employing Cocks and Ashby damage model. The
damage calculated when the element attains ω=1.0. The predicted time to rupture was
taken when few elements reach ω=1.0. Two dimensional contour plots of creep
damage across the notch throat for blunt and medium notch are shown in Figure 6.8
and 6.9, respectively. The blunt notch shows the most uniform widespread of damage
and the medium notch shows the most localised damage. It is observed that that the
maximum damage first occurs near the notch root and shifted toward the notch
subsurface as it reached steady state as shown in Figure 6.8. In Figure 6.9, the
location of damage starts at the notch root from the beginning until the time to failure
which is similar to the micrograph seen in the specimen (Figure 4.34). The most severe
region of damage is seen along the notch throat for both type of notch.
Figure 6.10 shows the evolution of damage for both notch acuities for the
net stress = 187 MPa. Damage evolutions across the notch are shown at 0.25 tr, 0.5 tr
and tr. It can be seen that the damage accumulation at each element across the notch
throat increases over time. It can also been seen that the point at which damage first
occurs is closer to the notch root for the medium notch than for the blunt notch. This is
expected given that the maximum triaxial stress state is closer to the notch surface for
the medium notch than for the blunt notch. A similar behaviour has been reported for
P92 steel [116] where an increase in notch acuity result the damage location to move
closer to notch root.
131
Figure 6.8 Creep damage contour for blunt notched at net stress = 187 MPa
Figure 6.9 Creep damage contour for medium notched at net stress = 187 MPa
132
Figure 6.10 Damage evolution across the notch throat at net stress of 187 MPa for a)
blunt notch and b) medium notch
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.2 0.4 0.6 0.8 1
Da
ma
ge
,ω
r/a
a) Blunt notch
tf=1797h
0.5tf
0.25tf
tr=1777 h
0.5tr
0.25tr
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 0.2 0.4 0.6 0.8 1
Da
ma
ge
,ω
r/a
b) Medium notch
tf=2837
0.5tfh
0.25tf
tr=2837 h
0.5tr
0.25tr
133
6.4.4 Prediction of Rupture Time
In this work, the predictions of rupture time were based on FE analysis coupled with
Cocks and Ashby model. The rupture times were predicted when the few elements
attains the damage, ω =1. It is shown that the prediction of the rupture time using
Cocks and Ashby model in Eqn (2.36) is strongly dependent on the creep ductility. In
order to predict the rupture time, the lower and upper bound creep ductility of 30% and
12%, respectively have been used in the FE.
Figure 6.11(a) and (b) shows of prediction of rupture time plot with net stress for blunt
and medium notch, respectively. The uniaxial and notched bar test data were also
plotted in the same figures. It can be seen in both figures, the rupture life of notched
specimens are higher than that of uniaxial specimens indicating the notch
strengthening effect as observed experimentally. It is expected that with increasing
notch acuity the rupture life increased hence the notch strengthening enhanced.
The Cock and Ashby model has been used to predict the rupture life by using the lower
and upper bound creep ductility of 30% and 12%. It can be seen in the Figure 6.11(a)
that for the blunt notch, lower bound creep ductility (0.12) predicts the rupture life better
than upper bound creep ductility (0.30). The prediction of the long term rupture life for
blunt notch specimen seem to coincide with the uniaxial data which may indicate that at
long term test data the blunt notch may exhibit similar behaviour to that of uniaxial
specimen. For medium notched in Figure 6.11(b), the upper bound creep ductility
predicts the rupture life better than the lower bound creep ductility. At the same net
stress, the medium notches always have the longer predicted lifetime than the blunt
notch.
134
Figure 6.11 FE Prediction of rupture life using f =0.30% and 0.12% for a) blunt notch
and b) medium notch
50
500
10 100 1,000 10,000
Ne
t str
ess (
MP
a)
Time to rupture (h)
Test data ( P91-B-Blunt notch)
Test data ( P91-B-Uniaxial)
Series10
Series11
a) Blunt notch
FE Prediction (εf =0.30)
FE Prediction (εf =0.12)
Fit to unixial data
50
500
10 100 1,000 10,000
Ne
t st
ress
(M
Pa
)
Time to rupture (h)
Test data (P91-B- Medium notch)
Test data (P91-B-Uniaxial)
FE Prediction
FE Prediction
b) Medium notch
FE Prediction (εf =0.30)
FE Prediction (εf =0.12)
Fit to unixial data
135
6.5 Discussion
The von Mises, maximum principal and hydrostatic stress distribution has been plotted
a function of normalised distance from the notch root across the notch throat. The von
Mises stress was lower than that of 0.2% proof stress of P91 material (287 MPa) at
the notch root r/a=1, suggesting that the localized plastic deformation at the notch root
does not contribute in the stress distribution across the notch throat from the beginning
of creep loading for this material [32]. The von Mises stress distribution of blunt
notched specimen was more uniform than that of medium notch specimen. It is widely
reported that von Mises stress controls the creep deformation and creep cavity
nucleation process, maximum principal stress controls the stress directed diffusion
controlled intergranular cavity growth and hydrostatic stress controls the continuum
cavity growth [33]. The presence relatively uniform von Mises stress across the notch
plane is expected to produce more or less uniform trangranular creep cavity nucleation
across the notch plane [33]. Similar behaviour was reported for P91 steel [32].
The creep damage for blunt and medium notch has been evaluated using a ductility
exhaustion approach. The blunt notch shows the most uniform widespread of damage
and the medium notch shows the most localised damage. It is observed that the
maximum damage first occurs near the notch root and shifted toward the notch
subsurface for blunt notch. For the medium notch, the location of damage starts at the
notch root from the beginning until the time to failure which is similar to the micrograph
seen in the medium notch specimen (Figure 4.34). This is expected given that the
maximum triaxial stress state is closer to the notch surface for the medium notch than
for the blunt notch. A similar behaviour has been reported for P92 steel [116] where an
increase in notch acuity result the damage location to move closer to notch root.
The predictions of rupture time were based on FE analysis with Cocks and Ashby
model where the rupture times were predicted when the few elements attains the
damage, ω =1. The Cock and Ashby model has been used to predict the rupture life by
using the lower and upper bound creep ductility of 30% and 12%. For the blunt notch
lower bound creep ductility (0.12) predicts the rupture life better than upper bound
creep ductility (0.30). For medium notch, the upper bound creep ductility predicts the
rupture life better than the lower bound creep ductility.
136
6.6 Summary and Conclusion
The FE analyses have been performed on P91 material for blunt and medium
notched bar.
A ductility exhaustion model has been used within the FE model by employing
the Cocks and Asbhy model.
The stress distribution for blunt notched specimens showed more uniform
distribution compared to medium notched specimen. The von Mises stress is
lower than the net stress for both notch acuity which indicates the notch
strengthening effect as observed experimentally.
As defined in the Cocks and model, the triaxiality contributes to the creep
rupture behaviour under multiaxial stess state. It is shown that the triaxiality is
maximum at notch throat distance of r/a = 0.5 for blunt notch whereas the
triaxility is maximum near the notch root, i.e r/a=0.8 for medium notch. The
medium notch has a maximum of triaxiality nearly twice of the blunt notch.
Creep damage evolution has shown that the blunt notch shows the most
uniform widespread of damage and the medium notch show most localised
damage
Creep ductility of 12% and 30% predicts the rupture life well for blunt and
medium notched bar, respectively.
137
Chapter 7
Influence of Prior Creep Strain on
Tensile Response and Low Cycle
Fatigue Behaviour
7.1 Introduction
In order to improve plant efficiency, conventional power plants which have been in
service for a long-term period are now required to operate flexibly. The flexible
operations and in-service history effects can often lead to creep and fatigue interaction
which may shorten the components life. Thus it is important to evaluate the creep and
fatigue interaction in the life assessment of power plant components [117, 118].
The main aim of this research is to examine the influence of prior creep strain/damage
on subsequent tensile response and low cycle fatigue (LCF) behaviour of service
exposed P91 steel. Previous research usually considered combined creep-fatigue tests
where the specimens were held at constant stress or strain at a period of time (hold
time) [62, 64, 119-121]. This would impose a relatively short hold time of the creep
process and may not be an accurate measure for the predictability of the effects of
prior creep and fatigue portion of the tests. The creep-fatigue tests with a relatively
short hold time in stress control do not produce extensively larger creep strain than
corresponding relaxation tests but the ‘creep damage’ attained is mainly strain, not
creep cavitation damage in the grain boundaries that causes intergranular fracture and
reduces material ductility. The extrapolation to the more ‘long- term’ type of creep
damage is thus questionable [119].
In this work, rather than introducing the creep damage during the hold time, the creep
damage was introduced prior to LCF testing. The creep damage was introduced by
performing the uniaxial creep testing at 600°C and interrupting the test at the desired
creep strain level. By this approach, the material which was subjected to prior creep
138
strain in addition to ex-service condition may have severe conditions and was most
likely to simulate realistic conditions in the power plant components.
Prior deformation including inelastic deformation and pre- straining is known to improve
the material performance [71, 122] for some materials. The influence of prior creep
strain on low cycle fatigue tests at elevated temperature were investigated on CrMoV
[72], 316H [123], and P91[73] material. It was shown that for CrMoV steel the fatigue
life increases for the crept sample under 175 MPa at 575°C [72]. For P91 material, the
influence of prior creep strain on subsequent fatigue had been investigated by
Takahashi [73]. Two samples were crept at 600°C under 140 MPa for 500h and 1000h.
Subsequently fatigue tests were performed at a strain range of 0.5%, strain rate of
0.1%s-1 and load ratio, R of -1. It was observed that as fatigue reduces, the creep life
increases.
Following previous work [71-73, 123] and limited research on P91, this research aims
to examine the influence of prior creep strain on tensile and low cycle fatigue behaviour.
The prior creep strain has been introduced into the material under ex-service
conditions at elevated temperature by interrupting the uniaxial creep tests on uniaxial
creep samples at 600ºC. In this chapter, the process of introducing creep damage into
the material is explained in detail and tensile and low cycle fatigue tests results are
presented. In order to examine the effect of prior creep strain, the test results are
compared for the material with and without prior creep strain.
7.2 Global Creep Damage Tests and Results
As mentioned in Chapter 3, the interrupted creep tests were performed on three
different specimens, namely standard 8mm diameter uniaxial creep specimen, large
18mm uniaxial creep specimen and notched bar specimen with net diameter of 12 mm.
All the interrupted creep tests were performed at 600ºC under the net stress of 150
MPa. The results of all interrupted creep tests are explained in the next section.
7.2.1 Global Creep Tests on Standard Specimen
Creep strain was uniformly introduced into the material by performing uniaxial creep
tests and interrupting them at various levels of creep strain. All creep tests were
performed on standard 8mm uniaxial creep specimens at 600ºC under 150 MPa. As
139
shown in Chapter 2, the creep test performed under such conditions ruptured around
800h. This condition is favourable for interrupting the creep test at various creep strain
levels since introducing the creep strain on each specimen is time consuming. The
material used in the interrupted creep testing was the new (P91-A) and ex-service
material (P91-B) as detailed in Chapter 3. The interrupted creep specimens are
denoted as ACD1 to ACD4 and BCD1 to BCD4 for new and ex-service material,
respectively. Tensile tests were subsequently performed at room temperature on these
specimens.
7.2.1.1 Creep Deformation
Eight uniaxial creep tests were performed at 150 MPa and 600°C.They were
interrupted at different levels of creep strain. The creep strain variation was plotted in
Figure 7.1 and 7.2 for new and ex-service material, respectively. In Figure 7.1, uniaxial
creep rupture test denoted as UCD which was tested under same stress and
temperature until rupture is included. As can be seen in Figure 7.1, BCD1 was
interrupted in the middle of the tertiary creep region and necking behaviour was clearly
seen on the specimen. BCD2 and BCD4 were interrupted approximately at the onset of
secondary and tertiary region, respectively. The interrupted creep strain on each
specimen was monitored during the test and measured after the test. The creep
deformation in UCD showed acceleration in the secondary and tertiary region, thus
exhibiting obvious necking on the specimen until rupture. Generally, similar creep
deformation behaviour can be seen for most specimens early on but variability seen in
secondary region.
Similar creep deformation behaviour can be seen in Figure 7.2 for the new material.
The ACD1 and ACD4 were interrupted at the beginning of secondary and tertiary creep
region whilst the ACD2 and ACD3 were interrupted in the secondary creep region. It
should be noted that it is difficult to maintain similar creep deformation behaviour as
utmost care was taken to monitor the test. The interrupted creep strain on each
specimen was monitored during the test and measured after the test. The value of
interrupted creep strain and time are given in Table 7.1.
140
Figure 7.1 Creep deformation for interrupted creep tests for ex-service material.
Figure 7.2 Creep deformation for interrupted creep tests for new material.
0.0
2.0
4.0
6.0
8.0
10.0
0 100 200 300 400 500
Cre
ep
str
ain
(%
)
Time (h)
UCD
BCD1
BCD2
BCD3
BCD4
600°C
0.0
2.0
4.0
6.0
8.0
10.0
0 100 200 300 400 500
Cre
ep s
train
(%
)
Time (h)
ACD1
ACD2
ACD3
ACD4
600°C
141
Table 7.1 Variation of interrupted creep strain and time, creep strain rate and the creep
strain fraction for the new and ex-service material
Specimen ID in t (%) intt (h) min (h-1) int f
BCD1 6.7 475 8.00 x 10-5
0.27
BCD2 4.5 316 9.30 x 10-5
0.18
BCD3 2.5 201 8.00 x 10-5
0.10
BCD4 1.4 68 - 0.06
ACD1 6.2 477 8.20 x 10-5 0.25
ACD2 3.6 306 8.75 x 10-5 0.15
ACD3 3.3 206 9.30 x 10-5 0.13
ACD4 1.0 68 - 0.04
7.2.1.2 Creep Strain Rate
The variation of creep strain rate against time was plotted in Figure 7.3 and 7.4 for ex-
service and new material, respectively. The minimum creep strain rate was calculated
from Figure 7.1 and 7.2 for ex-service and new material, respectively and summarised
in Table 7.1. For all tests, the minimum creep strain rate was evaluated in a steady
state region of the creep curve except for ACD4 and BCD4 which were interrupted at
the primary region. It is shown in Table 7.1 that the minimum creep strain rate for all
the tests have similar value. The minimum creep strain rate for UCD is 1.50 x 10-4 h-1
was larger than all other tests due to the accelerated creep deformation in the
secondary creep region.
The creep strain fraction is shown in Table 7.1 where the final creep strain to rupture
was taken from the specimen UCD as shown in Figure 7.1. The final creep strain to
rupture was 24.5 mm. The use of creep strain fraction may provide an appropriate
measure of the prior creep strain.
142
Figure 7.3 Creep strain variation against time for ex-service material
Figure 7.4 Creep strain variation against time for new material
0.0E+00
1.0E-04
2.0E-04
3.0E-04
4.0E-04
5.0E-04
0 100 200 300 400 500
Str
ain
rate
(h-1
)
Time (h)
BCD1
BCD2
BCD3
BCD4
0.0E+00
1.0E-04
2.0E-04
3.0E-04
4.0E-04
5.0E-04
0 100 200 300 400 500
Str
ain
ra
te (h
-1)
Time (h)
ACD1
ACD2
ACD3
ACD4
143
7.2.2 Global Creep Tests on Large Uniaxial Specimen
In order to investigate the prior creep strain on low cycle fatigue behaviour, uniaxial
creep tests were performed on 18 mm diameter uniaxial creep specimens and
interrupted at 4 to 6% of creep strain. All the interrupted creep tests were performed at
600°C and 150 MPa. The large uniaxial creep specimens were then re-machined into
the LCF specimen with a diameter of 7 mm and gauge length of 15 mm. The LCF
specimens were polished to remove the surface region where cracking might occur.
The material used was ex-service material, P91-B.
The variation of creep strain against time is shown in Figure 7.5. The prior creep strain
specimens were denoted as GD1 to GD6. The creep rupture specimen denoted as GD
is also included in Figure 7.5. The creep rupture strain for GD specimen is 41.3% and
the reduction of area is 87%. It was observed that the GD3 and GD5 exhibited necking
on the specimens. Similar behaviour can be seen in all the specimens in the primary
creep region but slight deviation can be seen toward the end of the test, especially for
GD6.
7.2.3 Global Creep Tests on Large Notched Bar Specimen
Prior creep strain was introduced in two large notched bar specimens having a net
cross section diameter of 12 mm to introduce as much as creep strain on the localized
area of the notch. As shown in Chapter 4, section 8.2, the use of notched bar specimen
particularly the blunt notch showed that the creep damage was concentrated at the
centre of the notch throat. The interrupted creep tests were performed at 600°C under
the net stress of 150 MPa. Figure 7.6 shows the displacement for the two notched
specimens. As shown in Figure 7.6, the global creep tests for both notched specimens
were interrupted approximately at 1100 h, however the displacement for GN1 is larger
than GN2.
144
Figure 7.5 Variation of creep strain against time for large specimens.
Figure 7.6 Variation of displacement against time for large notched bar specimens.
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
0 100 200 300 400 500 600
Cre
ep
S
tra
in (
%)
Time (h)
σ = 150 MPa T = 600°C
GD
GD1
GD2
GD3
GD4
GD5
GD6
0.00
0.05
0.10
0.15
0.20
0.25
0 200 400 600 800 1000 1200
Dis
pla
cem
en
t (m
m)
Time (h)
GN1
GN2
σnet = 150MPaT = 600°C
145
7.3 Tensile Tests and Results
Tensile tests were performed on interrupted creep specimen to examine the influence
of prior creep strain on plastic behaviour. For comparison, the tensile tests were also
performed on new material (without prior creep strain). In addition, a thermally aged
specimen was also included in order to investigate the effect of thermal aging on the
material. The aged specimen was tested in an isothermal condition at 600ºC for 1200h.
All the tensile tests were performed under a constant strain rate of 0.001s-1 at room
temperature.
7.3.1 Tensile Response
Figure 7.7 to 7.8 shows the engineering stress strain and true stress strain response,
respectively for the new material with and without prior creep strain.It can be seen in
Figure 7.7 that the engineering stress strain behaviour for the prior creep specimen
show significant changes compared to the one without prior creep strain. For the prior
creep strained specimens, the ACD1 which had the highest creep strain showed the
lowest tensile curve whilst the ACD4 which had the lowest creep strain showed the
highest tensile curve. ACD2 and ACD3 which both had prior creep strain of 3.61% and
3.28% respectively exhibited almost similar tensile curve. Similar tensile behaviour can
be seen in the true strain curve as shown in Figure 7.8.
Figure 7.9 and 7.10 shows the engineering stress strain and true stress strain,
respectively for ex-service material with and without prior creep strain. The thermally
aged specimen is also plotted in the same figures. It can be seen in Figure 7.9 that the
tensile deformation up to 0.2 strains are almost the same for thermally aged specimen
and material without prior creep. This may indicate that there is no effect of thermal
aging on the tensile deformation. Similar observations have been made in [124] where
the effect of aging on tensile stress can be neglected. In [124], the aging conditions
were 3700h, 7110h and 16870h at 600ºC. It can be also seen in Figure 7.9 that there
are significant changes in the stress strain response for prior creep specimens as
compared to the one without prior creep strain. These changes however are not
significant in the specimens with different levels of creep strain. From Figure 7.7 to
7.10, it may indicate that the prior creep strain has reduced the tensile curve for new
and ex-service materials.
146
Figure 7.7 Engineering stress strain curve for new material with and without prior creep
strain
Figure 7.8 True stress strain curve for new material with and without prior creep strain
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
σen
g(M
Pa)
εeng (mm/mm)
ACD1
ACD2
ACD3
ACD4
Without prior creep strain
0
100
200
300
400
500
600
700
800
900
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
σtr
ue
(MP
a)
εtrue (mm/mm)
ACD1
ACD2
ACD3
ACD4
Without prior creep strain
147
Figure 7.9 Engineering stress strain curve for ex-service material with and without prior
creep strain
Figure 7.10 True stress strain curve for ex-service material with and without prior creep
strain
0
100
200
300
400
500
600
700
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
σen
g(M
Pa
)
εeng (mm/mm)
No prior creep strain
Thermal Aged
BCD1
BCD2
BCD3
BCD4
0
100
200
300
400
500
600
700
800
900
0 0.05 0.1 0.15 0.2 0.25 0.3
σtr
ue(M
Pa)
εtrue (mm/mm)
No prior creep strain
Thermal Aged
BCD1
BCD2
BCD3
BCD4
148
7.3.2 Influence of Prior Creep Strain on Tensile Response
In order to examine the influence of prior creep strain on new and ex-service material,
the stress strain responses are compared for both materials at various level of creep
strain as shown in Figure 7.11(a) to (e). Note that ACD1 to ACD4 are referred to as
new material and BCD1 to BCD4 are referred to as ex-service material. The stress
strain responses in Figure 7.11(a) to (d) were compared to the similar prior creep strain
at 6-7%, 4-5%, 3% and 1%, respectively. It can be seen in Figure 7.11(a) that at 6-7%
creep strain, the stress strain curves are similar to each other. Similar behaviour can
also be seen in stress Figure 7.11(b), whereby there was only slight increase of tensile
curve for the new material. In Figure 7.11 (c), (d) and (e) it was observed that the
tensile ductility is larger for new material than the ex-service material. The tensile curve
for creep stain at 1% (Figure 7.11 (d)) shows significant difference than the tensile
curve in new material for the same prior creep strain. This may be due to less time
(~50 h) was required to activate the creep phenomena, hence higher YS and UTS was
achieved compared to the other prior creep specimens. Generally it can be inferred
that the stress strain response for prior creep strain for new material exhibit higher
tensile strength than the prior creep strain on ex-service material.
Variations of 0.2% proof stress and ultimate tensile strength are shown in Figure 7.12
for ex-service and new material. The x-axis in Figure 7.12 is the creep strain fraction as
given in Table 7.1. It can be seen that for both materials the 0.2% proof stress and
ultimate tensile strength reduces as a result of creep pre-straining compared to the
material without prior creep strain. Generally, it can be observed in Figure 7.12 that the
0.2% proof stress and ultimate tensile strength for new material are always higher than
that of ex-service material. The reduction of 0.2% proof stress in the prior creep
specimens may be attributed to microstructural evolution which occurred during the
creep prestraining at 600°C. The microstructural evolution in terms of decrease in
dislocation density and sub grain and carbide coarsening with increasing creep
exposure has been reported for P91 steel [14, 125].
Variations of tensile strain and total strain at failure for all tests are given in Figure 7.13
for the new and ex-service material. The total strain at failure was calculated by adding
the tensile strain at failure and the interrupted creep strain. The total strain and tensile
strain at failure increases by 15% from the zero (no prior creep strain) to 0.05 creep
strain fraction for the ex-service material. In general, it can be observed that the tensile
strain and total strain at failure increases as the creep strain ratio increases.
149
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
σen
g(M
Pa)
εeng (mm/mm)
BCD1
ACD1
Prior Creep Strain: 6-7%
(a)
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
σen
g(M
Pa)
εeng (mm/mm)
BCD2
ACD2
Prior Creep Strain: 4-5%
(b)
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
σen
g(M
Pa)
εeng (mm/mm)
BCD3
ACD3
Prior Creep Strain: 3%
(c)
150
Figure 7.11 Comparison of stress strain curve behaviour of ex-service and new
material at different levels of prior creep strain a) 6-7% b) 5% c) 3% d) 1% e) without
prior creep strain
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
σen
g(M
Pa)
εeng (mm/mm)
BCD4
ACD4
Prior Creep Strain: 1%
(d)
0
100
200
300
400
500
600
700
0 0.1 0.2 0.3 0.4
σen
g(M
Pa)
εeng (mm/mm)
Ex-service material
New material
Without Prior Creep Strain
(e)
151
Figure 7.12 Variation of tensile properties for different level of creep strain for new and
ex-service material
Figure 7.13 Variation of tensile tensile strain at failure and total strain for new and ex-
service material.
300
350
400
450
500
550
600
650
700
750
800
0.0 0.1 0.2 0.3
σ (M
Pa
)
εint/εf
UTS new
UTS ex
YS new
YS ex
UTS new materialUTS ex-service material
σ0.2 new material
σ0.2 ex-service material
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
0.0 0.1 0.2 0.3
ε en
g (%
)
εint/εf
ef new
ef EX
total new
total ex
Tensile strain at failure for new material
Tensile strain at failure for ex-serviced material
Total strain at failure for new material
Total strain at failure for ex-serviced material
152
7.4 Low Cycle Fatigue Test and Result
Low cycle fatigue testing has been performed on material with and without prior creep
strain. Five specimens denoted as LCF1 to LCF5 are referred to as ex-service material
without prior creep strain and the other 6 specimens denoted as GD1 to GD6 are
referred to as ex-service with prior creep strain. Two specimens denoted as GN1 and
GN2 were also prior creep strained on the notched bar specimens to impose as much
as creep strain on the localized area of the notch. The introduction of the prior creep
strain has been explained in Section 7.2.2 and 7.2.3.
LCF tests were conducted at room temperature in total strain control using the servo
hydraulic machine. A room temperature extensometer was used to measure the strain
during the testing. The LCF tests were performed at a strain range between 0.5% and
1.2% and a strain rate of 0.001s-1. The results were compared to the one with and
without prior creep strain and the fatigue behaviour was examined.
7.4.1 Cyclic Stress Response
The LCF tests were performed on the ex-service specimens with and without prior
creep strain. Figure 7.14 to 7.16 show the cyclic stress response of the steel for both
material conditions under different strain ranges. As can be seen in Figure 7.14 to 7.16
the stress amplitude decreases with increase in the number of cycles which indicates
that both material conditions exhibits cyclic softening. The cyclic softening is strongly
dependent on the strain ranges applied. It is noteworthy that the number of cycles to
softening increased with decrease in strain ranges. The cyclic softening is significant
when the applied strain ranges is low.
It can be seen in Figure 7.14 that at the highest strain range of 1.2% there was a slight
increase in the cyclic stress at the first cycle followed by the mild hardening of nearly
up to the initial 10-20 cycles. However at the lowest strain range of 0.5%, there was
drastic increase in the cyclic stress at the first cycle and followed by the cyclic softening
until fracture. For all strain ranges, the stress amplitude drop drastically towards the
end of the cycle. This may be due to the formation of macro-cracks and their
subsequent growth which reduced the load bearing ability of the specimen.
153
For the material with prior creep (Figure 7.15), at the highest strain range of 1.2%, mild
hardening occurred during the first cycle followed by the softening after about 10-20
cycles. At strain ranges below 1.2%, cyclic softening occurred during the first cycles
and steadily continued to soften until the failure. Similar behaviour can be seen in the
GN1 and GN2 specimens as shown in Figure 7.16 where cyclic softening exhibit during
the first cycle at a strain range of 0.8% and 0.5%. Detail comparison and explanation
on the influence of prior creep strain at a corresponding total strain range are explained
in the Section 7.4.4.
In order to compare the degree of softening at different strain range a softening
parameter, S is calculated based on following relationship [63, 121]:
1
1
100%halfa a
a
S
(7.1)
where 1a and half
a are the cyclic stress amplitude for the first and half cycle,
respectively. The degree of softening as a function of total strain ranges is plotted in
Figure 7.17. As seen in Figure 7.17, most of the test data shows that the softening
degree decreases with the increase in total strain range and the softening degree is
more pronounced in the material without prior creep strain.
154
Figure 7.14 Cyclic stress response for material without prior creep strain.
Figure 7.15 Cyclic stress response of prior creep specimens
250
300
350
400
450
500
550
1 10 100 1000 10000 100000
Str
ess
(M
Pa
)
Number of cycles
Without prior et=1.2%
Without prior et=0.8%
Without prior et=0.7%
Without prior et=0.5%
Δεt =1.2%
Δεt =0.8%
Δεt =0.7%
Δεt =0.5%
200
250
300
350
400
450
1 10 100 1000 10000 100000
Str
ess (
MP
a)
Number of cycles
Prior creep et=1.2%
Prior creep et=0.8%
Prior creep et=0.7%
Prior creep et=0.6%
Prior creep et=0.5%
Δεt =1.2%
Δεt =0.8%
Δεt =0.7%
Δεt =0.6%
Δεt =0.5%
155
Figure 7.16 Cyclic stress response or prior creep notched specimen
Figure 7.17 Dependence of the degree of softening on the total strain range.
200
250
300
350
400
450
500
1 10 100 1000 10000 100000
Str
ess
(M
Pa
)
Number of cycles
GN1 et=0.8%
GN2 et=0.5%
Δεt =0.8%
Δεt =0.5%
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1 1.2 1.4
De
gre
e o
f so
fte
nin
g, S
(%)
Strain range,Δεt (%)
Without prior creep (LCF specimen)
With prior creep (GD specimen)
With prior creep (GN specimen)
156
7.4.2 Determination of Cycle to Failure
The cyclic stress response in Figure 7.14 to 7.16 show that the material exhibits cyclic
softening behaviour at different strain ranges. The specimens that exhibit cyclic
softening behaviour consist of three stages namely softening, stabilization and failure
[126] as shown in Figure 7.18. As shown in Figure 7.18, in the first stage, the stress
decrease considerably before reaching a constant value during the second stage. The
second stage occupies the largest proportion of the cycles. At the final stage, the stress
level drop drastically leading to failure. In this subsection, the number of cycles in each
of the stages and the number of cycles to failure are described.
The definition of Nsta, Ntan and Nfinal are referred to the beginning of the constant rate
evolution of the peak stress level, the beginning of the stress drop in the third stage
and the number of cycle to failure, respectively [126]. Several failure criteria have been
proposed in ASTM standard [77] and British Standard BS7270:2006 [127] to define the
failure. The British Standard BS7270:2006 [127] states that the number of cycles is
defined as the maximum stress decreased by a prescribed percentage predicted by
extrapolation of the second stage stabilisation curve. A 10 % drop ( 10fN ) is considered
as a possible failure criterion in this study.
The final number of cycles, finalN ,represents the final number of cycles as the
machine stopped as recorded by the servo hydraulic machine as a result of the
machine setting to avoid the total fracture of the specimen that could damage the
machine. The value of defined number of cycles according to Figure 7.18 for all the
specimens tested are shown in Table 7.2.
157
Figure 7.18 Definition of Nsta,Ntan,Nf10 and Nfinal for the GD2 specimen tested at strain
range of 0.5%
Table 7.2 The values of Nsta,Ntan,Nf10 and Nfinal
Specimen
ID
Strain range
(%)
Nsta
(cycles)
Ntan
(cycles)
Nf10
(cycles)
Nfinal
(cycles)
LCF1 1.2 10 540 713 749
LCF2 0.5 20 25500 37155 37600
LCF4 0.8 10 3500 4440 4462
LCF5 0.6 10 10000 11005 11044
LCF6 0.7 10 7600 8325 8340
GD1 0.8 30 5400 7880 7963
GD2 0.5 10 38800 39200 39820
GD3 1.2 30 1500 2488 2772
GD4 0.6 10 6500 8180 8246
GD5 1.0 30 3150 3830 3846
GD6 0.7 10 1050 13800 14524
GN1 0.8 20 7500 8000 8529
GN2 0.5 20 25000 34400 37728
260
280
300
320
340
360
380
400
1 10 100 1000 10000 1000001000000
Ma
xim
um
Str
ess
(M
Pa
)
Number of cycles, N
Stage 1 Stage 2 Stage 3
10%
Nsta
Ntan
Nfinal
Nf10
158
7.4.3 Cyclic Stress Strain Response
The cyclic stress strain response obtained from the LCF testing is also known as a
hysteresis loop. Figure 7.19 (a) to (c) shows an example of the hysteresis loop
obtained during the LCF test for total strain range, t , of 0.8%,0.7% and 0.5%,
respectively. In Figure 7.19 (a) the cyclic stress response was plotted for first cycle, half
cycle and Nf10. It can be seen that the stress amplitude deceasing from the first cycle to
the final cycle indicating the cyclic softening behaviour. Note that the final cycle here is
referred to the number of cycle that reached 10% criterion. This cyclic softening
behaviour is more pronounced at lower strain ranges as shown in Figure 7.19(b) and
(c). At the end of the cycle, the compressive half loop shows irregularities shape which
reveals the appearance of the crack in the specimen.
As the fatigue design is concerned, the cyclic stress strain responses at the half life
cycle were taken as representative of the approximately stable behaviour observed
during the low cycle fatigue life. The cyclic stress strain response at the half life cycle
for the LCF and GD specimen are shown in Figure 7.20 and 7.21, respectively for all
the total strain ranges examined. From Figure 7.20 and 7.21, it can be seen that an
increase in total strain ranges resulted in increase in stress amplitude and plastic strain
amplitude. The relatively higher plastic strain magnitudes suggest that increasing the
total strain results in large plasticity which probably resulted in early crack nucleation
and propagation hence, the observed shorter LCF life. The half life cycle can be
represented by the power law relationship as given by Eqn (2.70). The cyclic strain
hardening coefficient, K and the cyclic strain hardening exponent, n are tabulated in
Table 7.3 .
159
Figure 7.19 Cyclic stress response for a) GD1 b) GD6A and c) GD2
-500
-400
-300
-200
-100
0
100
200
300
400
500
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Str
ess (
MP
a)
Strain (%)
GD1Δεt=0.8%
First cycle
Half cycle
Final cycle
N1
Nf10/2
Nf10
a)
-500
-400
-300
-200
-100
0
100
200
300
400
500
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
Str
ess (
MP
a)
Strain (%)
GD6Δεt=0.7%
First cycle
Half cycle
Final cycle
N1
Nf10/2
Nf10
b)
-500
-400
-300
-200
-100
0
100
200
300
400
500
-0.4 -0.2 0 0.2 0.4
Str
ess (
MP
a)
Strain (%)
GD2Δεt=0.5%
First cycle
Half cycle
Final cycle
N1
Nf10/2
Nf10
c)
160
Figure 7.20 Half life cycle for LCF specimens (without prior creep)
Figure 7.21 Half life cycle for GD specimens (with prior creep)
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess (
MP
a)
Strain (%)
Without prior creepHalf life cycle
et=1.2%
et=0.8%
et=0.7%
et=0.5%
Δεt =1.2%
Δεt =0.8%
Δεt =0.7%
Δεt =0.5%
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess (
MP
a)
Strain (%)
Prior creep Half life cycle
et=1.2%
et=0.8%
et=0.7%
et=0.5%
Δεt =1.2%
Δεt =0.8%
Δεt =0.7%
Δεt =0.5%
161
Table 7.3 Half life cycle stress strain properties for LCF and GD material
Material Condition K n
LCF 771.1 0.1
GD 1003.8 0.2
7.4.4 Influence of Prior Creep Strain on LCF behaviour
In order to investigate the influence of prior creep strain on LCF behaviour, the cyclic
stress and cyclic stress strain response are compared at a corresponding total strain
range. Figure 7.22 (a) to (e) shows the cyclic stress behaviour for the material with and
without prior creep strain at total strain range between 1.2% and 0.5%, respectively. As
can be seen from all the figures, at a corresponding strain range the stress amplitude
for material with prior creep strain is decreased by almost 8 to 10 times than that of
material without prior creep strain. This indicates that the material with prior creep
strain reduces its strength by means of material evolution during the creep test.
However, the degree of softening as plotted in Figure 7.17 has shown that softening is
more pronounced in the material without prior creep strained which may indicate that
the creep prestraining has small effect on the cyclic softening behaviour. The cyclic
softening is mainly attributed to the rearrangement of dislocation which offers less
resistance to deformation [128].
As for notch prior creep specimen (GN1 and GN2), the cyclic stress response (Figure
7.23 (a) and (b) ) shows an increase of stress amplitude by almost 4 times than that of
prior creep specimen (GD) for the first 100-200 cycles. The increased of stress
amplitude in GN specimen as compared to GD specimen may be due to the insufficient
creep strain introduced in the notch specimen.
In terms of fatigue life, it is observed that the fatigue life slightly increased by 1000 to
3000 cycles for prior creep material particularly at higher total strain range (0.7% to
1.2%) as shown in Figure 7.22 (a) to (c). For lower strain range, the fatigue life almost
similar for both material condition. It is noted that the fatigue life is defined by the 10%
drop of maximum stress as explained in Section 7.4.2 and the value is given in Table
7.2. For notch prior creep specimen (GN1), at total strain range 0.5%, the fatigue life is
almost similar to the material with and without prior creep strain as shown in Figure
7.23(a). At total strain range of 0.8% (Figure 7.23 (b)), the fatigue life for notch prior
162
creep specimen is larger than that of specimen without prior creep strain but similar to
the specimen with prior creep strain. This may inferred that creep prestraining
increased the fatigue life particularly at high strain range.
The cyclic stress strain behaviour at half cycle was compared for the material with and
without prior creep at the corresponding total strain range as shown in Figure 7.24 (a)
to (e). The half life cycle was considered for the comparison as it is the stabilized cycle
and important for design consideration. For all the total strain ranges examined, the
stress amplitude are always higher than the material without prior creep strain;
however the plastic strain remained similar. At lower strain ranges, the plastic strain
range seemed smaller for the material with no prior creep strain.
Figure 7.25 (a) and (b) compares the cyclic stress strain behaviour for the LCF, GD
and GN specimens at half life cycle for strain ranges of 0.5% and 0.8%.It can be seen
from the figure that the stress amplitude for LCF at half life cycle is higher than the GD
and GN specimen. The plastic strain amplitude for GN specimen was similar to other
specimens.
163
200
250
300
350
400
450
500
550
1 10 100 1000 10000 100000
Str
ess
(M
Pa
)
Number of cycles
LCF1_1.2
GD3_1.2
Δεt= 1.2%
(a)
200
250
300
350
400
450
500
550
1 10 100 1000 10000 100000
Str
ess (
MP
a)
Number of cycles
LCF4_0.8
GD1_0.8
Δεt= 0.8%
(b)
200
250
300
350
400
450
500
1 10 100 1000 10000 100000
Str
ess (
MP
a)
Number of cycles
GD6A_0.7
LCF_0.7
Δεt= 0.7%
(c)
164
Figure 7.22 Comparison of cyclic stress response of material with and without prior
creep strain at room temperature for strain ranges a) 1.2%, b) 1.0%, c) 0.8%, d) 0.6%
and e) 0.5%
200
250
300
350
400
450
500
1 10 100 1000 10000 100000
Str
ess (
MP
a)
Number of cycles
LCF6_0.6
GD4_0.6
Δεt= 0.6 %
(d)
200
250
300
350
400
450
500
1 100 10000 1000000
Str
ess
(M
Pa
)
Number of cycles
LCF2_0.5
GD2_0.5
Δεt= 0.5 %
(e)
165
Figure 7.23 Comparison of cyclic stress response of material with no creep damage
(LCF), with creep damage (GD) and with notched creep damage (GN) at rom
temperature for strain ranges a) 0.5% and b) 0.8%,
200
250
300
350
400
450
500
1 10 100 1000 10000 100000
Str
ess
(M
Pa)
Number of cycles
No prior creepPior creepNotch prior creep
Δεt= 0.5%
(a)
200
250
300
350
400
450
500
550
1 10 100 1000 10000 100000
Str
ess
(M
Pa)
Number of cycles
No prior creepPrior creepNotch prior creep
Δεt= 0.8%
(b)
166
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess (
MP
a)
Strain (%)
Half life cyclePrior creepNo prior creep
Δεt = 1.2%
(a)
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess (
MP
a)
Strain (%)
Half life cycle
Prior creep
No pior creep
Δεt = 0.8%
(b)
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess (
MP
a)
Strain (%)
Half life cycle
Prior creep
No prior creep
Δεt = 0.7%
(c)
167
Figure 7.24 Comparison of cyclic stress stain behaviour of material with and without
prior creep strain at strain ranges a) 1.2%, b) 1.0%, c) 0.8%, d) 0.6% and e) 0.5%
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess (
MP
a)
Strain (%)
Half lie cycle
Prior creep
No Prior creep
Δεt = 0.6%
(d)
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess (
MP
a)
Strain (%)
Half life cycle
Prior creep
No Prior creep
Δεt = 0.5%
(e)
168
Figure 7.25 Comparison of cyclic stress stain behaviour of material with no creep
damage (LCF), with creep damage (GD) and with notched creep damage (GN) at
strain ranges a) 0.5% and b) 0.8%.
-600
-400
-200
0
200
400
600
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
Str
ess (
MP
a)
Strain (%)
Half life cycle
No prior creep
Prior creep
Notch prior creep
Δεt = 0.5%
(a)
-600
-400
-200
0
200
400
600
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Str
ess
(M
Pa
)
Strain (%)
Half life cycle
No prior creep
Prior creep
Notch prior creep
(b)
Δεt = 0.8%
169
7.4.5 Life Prediction
7.4.5.1 Strain life relationship
The fatigue life plot was established based on power law relationship between elastic
and plastic strain amplitude with number strain reversal to failure 2Nf as given by:
2 2 2
pt e
(7.2)
where the first term on the right hand side is the elastic plastic strain amplitude and the
second term is the plastic strain amplitude. The elastic and plastic strain amplitude
relation to 2Nf is given by Basquin [67] and Coffin-Manson [68] [69] relationship. The
strain life relationship is given by
'
'2 22
b cftf f fN N
E
(7.3)
where 2t is the total strain amplitude, and 2Nf is the number of cycle to failure,
E is the elastic modulus, 'f is the fatigue strength coefficient, '
f is the fatigue
ductility coefficient, b and c are the fatigue strength exponent and fatigue ductility
exponent , respectively. The value of these constants and coefficient for Eqn (7.3)
established by least square analysis are summarized in Table 7.4. In general, c is in
range between -0.5 to -0.7 for ductile material and the present value fit well for the
material with prior creep at room temperature.
The Basquin and Coffin –Mansion plots for material without prior creep strain (LCF)
and material with prior creep strain (GD and GN) are plotted in Figure 7.26 and 7.27,
respectively. The elastic and plastic strain contribution to the total strain was dependent
on the applied total strain ranges during the LCF testing. It can be seen in both figures
that at the plastic strain were higher than the elastic strain at a larger total strain whilst
at lower total strain, the elastic strain showed dominant influence to the total strain
range. This indicates that the plastic deformation was significantly dominant at higher
strain level.
170
The intersection between elastic and plastic strain ranges, 2e and 2p , is
shown in both figures (Figure 7.26 and Figure 7.27). This intersection point is referred
as the transition life. It can be said that below the transition life, damage is dominated
by plasticity while at higher fatigue lives, elasticity dominates. The transition life for LCF
and GD and GN specimens at room temperature is 15000 cycles and 20000 cycles,
respectively.
Table 7.4 LCF parameter of material with and without prior creep
Material Condition ' /f E 'f b c
Without prior Creep 0.004 0.0456 -0.096 -0.343
With prior creep 0.008 0.3165 -0.146 -0.531
171
Figure 7.26 Basquin and Coffin –Mansion plots for material without prior creep strain
(LCF specimens)
Figure 7.27 Basquin and Coffin –Mansion plots for material with prior creep strain (GD
and GN specimens)
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06
Δε/
2(a
bs)
2Nf (cycle)
Total strain range
Plastic strain amplitude
Plastic stain Literature Data
Elastic strain
RT
2Nt
15000 cycles
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06
Δε /
2(a
bs)
2Nf (cycle)
Total strain amplitude
Plastic strain
Elastic strain
RT
2Nt
20000 cycles
172
7.4.6 Fracture behaviour
Upon the testing completion, the cracking behaviour and fracture surface were
examined. Figure 7.28 and 7.29 shows the cracking behaviour for specimens with prior
creep (GD and GN) and specimen without prior creep (LCF). It can be observed in both
figures that the LCF specimen exhibited severe cracking behaviour than the GD and
GN specimens. Most of the specimens show that the final fracture is at 45 degree to
the loading direction.
The fracture surface has been examined under the scanning electron microscope to
investigate the crack propagation behaviour and the failure mechanism. Figure 7.30
and 7.31 shows the SEM images of the fracture surface of GD4 and LCF5 which were
tested at the same strain range, i.e. 0.6%. In Figure 7.30 (a) and 7.31 (a), the fracture
surface consists of crack propagation zone and fracture zone. In both figures, it was
observed that the crack initiated from the surface of the specimen. Under the cyclic
loading, the fatigue cracks initiated from the surface and gradually propagated toward
the inner surface of the specimen as shown in Figure 7.30 (a) and Figure 7.31 (a).
Under high magnification resolution, the secondary cracks and the fatigue striations
were seen on the fracture surface as shown in Figure 7.30 (b) and Figure 7.31 (b). The
evidence of fatigue striation may indicate that the failure mechanism is purely a
transgranular fracture. In the specimens tested, the cracking behaviour and crack
propagation is similar for the specimen with and without prior creep strain.
As suggested in Figure 5.8 for creep crack growth rates where creep/fatigue is involved
the failure ductilities reduce considerably leading to shorter lives. The same argument
that is presented in the NSW model can linked to creep/fatigue at low frequencies
where creep dominates but fatigue helps reduce failure ductility (with no necking as in
Figure 7.28) leading to faster failure rates. Hence the NSWA upperbound using the
lower failure strains from uniaxial LCF tests can give more conservative predictions in
crack growth rates.
173
Figure 7.28 Cracking behaviour of GD and GN specimens a) GD3,t =1.2%,
(b) GD1,t =0.8 %, (c) GD6A,
t =0.7 %, (d) GD4,t =0.6 % (e) GD2,
t =0.5 %
(f) GN1,t =0.8 %(g) GN2,
t =0.5 %.
(a) (b) (c) (d)
(e) (f) (g)
174
Figure 7.29 Cracking behaviour of LCF specimens a) t =1.2%, (b)
t =0.8 %,
(c) t =0.7 %, (d)
t =0.6 % (e) t =0.5 %.
(a) (b) (c)
(d) (e)
175
Figure 7.30 SEM images of GD4 specimen (t =0.6 %) (a) Fracture surface
containing crack propagation and fracture zone, (b) and (c) high magnification of crack
propagation zone.
176
Figure 7.31 SEM images of LCF specimen (t =0.6 %)(a) Fracture surface containing
crack propagation and fracture zone, (b) and (c) high magnification of crack
propagation zone.
177
7.5 Discussion
Creep strain has been introduced into the material by performing uniaxial creep tests
and interrupting them at various levels of creep strain. All creep tests were performed
on three types of specimens at 600ºC under 150 MPa. Creep deformation curves for all
interrupted creep testing have shown similar behaviour which is appropriate for better
comparison. The creep strain fraction has been used to indicate the level of prior creep
strain.
The 0.2% proof stress and ultimate tensile strength decreases as a result of prior creep
strain at 600°C compared to the material without prior creep strain for both new and ex-
service material. This reduction is more pronounced as the creep strain fraction
increases. The reduction of 0.2% proof stress in the prior creep specimens may be
attributed to the microstructural evolution which occurred during the creep prestraining
at 600°C. The microstructural evolution in terms of coarsening of precipitates, decrease
in dislocation density and sub-grain coarsening with increasing creep exposure have
been reported for P91 steel [14, 125, 129]. Similar observation can be seen in [74],
where the material has been crept until failure and the tensile specimen has been
manufactured from the rupture samples.
The tensile deformation for ex-service material is almost similar for thermally aged
specimen and non-thermally aged specimen (without prior creep strain). This indicates
that there is no effect of thermal aging on the tensile deformation. Similar observations
can be seen in [124], where the effect of thermal aging on tensile behaviour can be
neglected. In [124], the aging conditions were 3700h, 7110h and 16870 at 600°C.
On the other hand, the tensile failure strain increases when the material was subjected
to prior creep strain. This may be related to the formation of intergranular damage on
the gain boundaries during the creep deformation. However, the increase of the tensile
strain at failure in Figure 7.13 may vary at different levels of prior creep strain. This may
be due to the similar creep mechanism in the secondary region where the damage may
start to initiate and the level of prior creep strain may not quantify the level of creep
damage. Furthermore, it was shown that the creep damage may be pronounced in the
tertiary region where the accelerated creep strain and necking occur in the specimens
[25, 79].
178
The low cycle fatigue testing has been performed on ex-service P91 material for both
prior and without prior creep strain, at room temperature. Generally, it is observed that
for the ex-service P91 material, both prior and without prior creep strain, particularly at
low strain ranges, the material showed a continuous softening till the onset of the final
drop. This type of softening is known to occur in the martensitic materials such as P91
[64-66, 130, 131] ,P92 [63], X10 [132]. The cyclic softening may be associated with the
microstructural evolution mainly due to the formation of cell structure, in line with former
researcher observation during the cyclic loading [120, 133] and the behaviour is more
pronounced at elevated temperature [63, 65, 133].
The cyclic stress strain behaviour has shown that the reduction of the maximum stress
at first, half and final cycle which confirms that the cyclic softening behaviour had
occurred. Another important aspect to be looked at where the fatigue design is
concerned is the plastic strain amplitude at half life cycles. The cyclic stress strain
responses at half cycles have shown that an increase in total strain ranges results in
increase in stress amplitude and plastic strain amplitude and a corresponding decrease
in fatigue life. The relatively higher plastic strain magnitudes suggest that increasing
the total strain results in large plasticity which probably causes early crack nucleation
and propagation hence, the observed shorter LCF life.
The influence of prior creep strain on low cycle fatigue has been analysed and
compared to the one without prior creep strain. It has been shown that at a
corresponding strain range the stress amplitude for material with prior creep strain is
decreased by almost 8 to 10 times than that of material without prior creep strain. This
indicates that the material with prior creep strain reduces its strength by means of
material evolution during the creep test. However, the degree of softening as plotted in
Figure 7.17 has shown that softening is more pronounced in the material without prior
creep strain which may indicate that the creep prestraining has small effect on the
cyclic softening behaviour. The cyclic softening is mainly attributed to the
rearrangement of dislocations which offers less resistance to deformation [128].
In terms of fatigue life, the prior creep strain has increased the fatigue life by 1000 to
3000 cycles at high strain range i,e 0.7 to 1.2%. At lower strain range, both materials
exhibit similar fatigue life behaviour. Even when the strength of prior creep specimen
was reduced, it maintained its strength until the failure time. This may be associated
with the microstructural evolution during the LCF testing. This behaviour however may
179
be different at elevated temperature where the creep damage takes place and shorten
the fatigue life.
The cyclic stress response for the prior strained notched specimens (GN1 and GN2),
shows a high strength compared to the plain bar specimen with prior creep strain at
corresponding strain range. This may be due to the insufficient creep strain introduced
in the notch specimen. The fatigue life for notch prior creep specimen is larger than that
of specimen without prior creep strain but similar to the specimen with prior creep strain
at 0.8% strain range. This may be inferred that creep prestraining increased the fatigue
life particularly at high strain range.The strain life relationship showed that the
contribution of elastic and plastic strain to total strain was dependent on the applied
total strain level during the LCF testing. The plastic strain plays significant role at higher
strain level.
Fractographic assessment has been performed on the fracture surface using SEM. It
has been shown that the fracture surface consists of crack propagation zone and
fracture zone. The evidence of fatigue striation may indicate that the failure mechanism
is purely a transgranular fracture. In the specimens tested, the cracking behaviour and
crack propagation is similar for the specimen with and without prior creep strain.
7.6 Summary
The tensile deformation for without prior creep strain and thermally aged
material shows similar behaviour
Creep strain effects on tensile deformation is evident
LCF test have been performed at room temperature under strain controlled
condition at strain ranges of 0.5 to 1.2% for the material with and without prior
creep strain.
In general, P91 material exhibit cyclic softening at all examined strain ranges.
Mild hardening was exhibited during the initial cycles followed by continuous
softening in the material without prior creep damage.
Most of the test data shows that the softening degree decreases with the
increase in total strain range. However, the softening degree is more
pronounced in the material without prior creep strained which may indicate that
the creep straining has small effect on the cyclic softening behaviour
180
The cyclic stress strain response or hysteresis loop at half cycle have shown an
increase an increase in total strain amplitude resulted in increase in stress
amplitude and plastic strain amplitude. The relatively higher plastic strain
magnitudes suggest that increasing the total strain results in large plasticity
which probably resulted in early crack nucleation and propagation hence, the
observed shorter LCF life.
The stress amplitude for material with prior creep strain is always lower than the
material without prior creep damage. This indicate that the material with prior
creep damage reduce its strength by means of material degradation during the
creep test.
In term of fatigue life, the prior creep strain has increased the fatigue life by
1000 to 3000 cycles at high strain range i,e 0.7 to 1.2%. At lower strain range,
both materials exhibit similar fatigue life behaviour.
Hysteresis loop for prior creep material is lower than the one without prior creep
strain at all strain ranges. The half life cycle has been considered for the
comparison as it is the stabilized cycle and important for design consideration.
For all the total strain range examined, the stress amplitude is always higher
than the material without prior creep strain; however the plastic strain remains
similar. At lower strain range the plastic strain range seem smaller for the
material with no prior creep strain.
The Basquin and Coffin Mansions plot for material without prior creep strain
(LCF) and material with prior creep strain (GD and GN) have shown that the
plastic strain were higher than the elastic strain at a larger total strain whilst at
lower total strain, the elastic strain show dominant influence to the total strain
amplitude. The transition life for LCF and GD/GN specimen at room
temperature is 15000 cycles and 20000 cycles, respectively.
Fractography have shown that the LCF specimen exhibit severe cracking
behaviour than the GD and GN specimens. Most of the specimen shows that
the final fracture is at 45 degree to the loading direction. The fracture surface
consists of crack propagation zone and fracture zone. It is observed that under
the cyclic loading the fatigue cracks initiate from the surface and gradually
propagated toward the inner surface of the specimen.
The evident of fatigue striation may indicate the failure mechanism is purely a
transgranular fracture. In all specimens tested, the cracking behaviour and
crack propagation is similar for the specimen with and without prior creep strain.
181
Chapter 8
Discussion, Conclusion and
Future Work
8.1 Introduction
Uniaxial and notched bar creep tests have been conducted on the new and ex-service
material, respectively. The experimental data at short term tests has been analysed
and compared with available data at long test times ( up to 100,000 h tests) which
shows that at longer creep life (>10,000h) the creep strength reduced dramatically. The
reason for a marked drop in creep rupture strength can be explained in terms of
coarsening of the precipitate and microstructural evolution where the sub grain size
gradually increased and abruptly coarsened up to the creep failure [13].
It has been shown in Figure 4.13 and 4.14 that at longer creep life the creep ductility
reduce significantly. This degrading phenomenon can be regarded with creep
cavitation growth process. The reduction of creep ductility has been more pronounced
under multiaxial stress condition and also under LCF test conditions where creep still
dominates. The models based on cavity growth used to predict the influence of
multiaxiality showed that the Spindler and Cocks and Ashby models in reasonable
agreement with the test data at high triaxiality though the Cocks and Ashby model over
predict at low triaxiality.
A finite element analysis has been used to predict the notched bar under multiaxial
stress state. The use of blunt and medium notch has shown that increase in triaxiality
reduced the rupture life. The FE analysis coupled with damage model by Cocks and
Ashby model have shown that the damage initiates near the notch subsurface for
medium notch. This has been confirmed by metallographic assessment shown in
Figure 4.34 where the creep damage location is approximately 0.3 mm from the notch
surface.
The mechanism of notch strengthening in Figure 4.24 and Figure 4.25 can be analysed
by the creep damage model. From the ductility exhaustion damage model, it is known
182
that the creep damage is determined by both the accumulated equivalent creep strain
at a period of time and by the multiaxial creep ductility. The accumulated equivalent
creep strain depends on the equivalent creep strain rate, which is determined by the
equivalent stress, whereas the multiaxial creep ductility depends on the stress triaxiality.
Therefore, the distribution of equivalent stress and stress triaxiality around the notch
determine the creep damage and fracture in the notched bar specimens.
The creep fatigue crack growth has been examined and a linear cumulative rule has
been used to predict the creep fatigue interaction. By using this approach an interaction
diagram as shown in Figure 5.8 has been produced. At high frequency fatigue is the
dominant mechanism and the crack growth rate is insensitive to the frequencies. At low
frequencies, the time dependent creep mechanism is dominated and crack growth is
sensitive to the frequencies.
In the region where creep is dominant, the data have been plotted by identifying the
cracking rate in the static CCG data at a fixed value of C* which approximately
correspond to the stress intensity factor range in the steady state Paris law region. By
using this approach, the cyclic CFCG and NSWA plane strain data point have been
constructed in similar fashion. It has been shown that the cyclic ex-service steel
cracking rate exhibit about a factor of four times the cracking rate of the mean static
CCG data. This may suggest that the ex-service material degradation would contribute
to the higher cracking rate and this is reflected by the reduced failure ductilities
observed in ex-service tests. The NSWA plane strain data point give an upper-bound
prediction of cracking rate and is therefore higher compared to the static CCG and
cyclic CFCG data. This also indicates that the CFCG failure strain data would be lower
than CCG for new and ex-service data. The plane strain NSWA prediction corresponds
with the lower failure ductilities measured for long term tests. This could be explained
by Fig 5.8 that the long term prediction may exhibit lower creep ductility due to the
material degradation and due to sensitivity of failure strain to stress.
The unavailability of long term tests (> 10,000h) at low stresses and long dwell periods
may pose additional problems under creep control due to state of stress where lower
creep ductilities and high multiaxial stress state prevail. It is found that for low stress,
low ductility and increase in constraint under plane strain predictions of crack growth
rate data using the NSW creep crack growth model can conservatively bound the
183
experimental data at long terms which is more appropriate prediction for components
operational times.
Increasing the constraints by means of material degradation, embrittlement in ex-
service condition, low creep ductilities and low stresses as well as including a cyclic
component when creep still dominates may increase the cracking rate and therefore
the frequency (da/dN) interaction point in Figure 5.8 can be shifted from left to the right.
The shift of interaction from static CCG toward cyclic FCG can therefore be attributed
to an increase in constraint described by the NSW model.
The interaction diagram in Figure 5.8 have shown that the cracking rate for cyclic
CFCG data is higher than that of CCG data which may be due to the material
degradation and increasing constraint. Hence, it is imperative that the design of power
plant component must be higher than cyclic CCG data.
It is clear that further detailed testing is needed to confirm the prediction lines in
Figure 5.8, however the present finding can confirm that firstly the linear cumulative
damage is sufficiently accurate for life assessment as long as there is appropriate low
dwell cyclic tests data are available for the material. Secondly the NSW model can
conveniently predict the upper-bound cracking rate under both creep-fatigue conditions
and material degradation, both of which lead to reduce failure strains.
In order to examine the influence of prior creep strain on tensile response the prior
creep strain has been introduced into the ex-service material by interrupting the
uniaxial creep tests on the uniaxial creep specimens at 600°C. Subsequently the
tensile tests have been performed at room temperature. The results of these tests have
been analysed and compared to those material without prior creep strain. Tensile
deformation is almost similar for thermally aged specimens and the one without prior
creep strain as shown in Figure 7.7 which indicates that there is no effect of thermal
aging on the tensile deformation. Similar observation can be seen in [124], where the
effect of thermal aging can be neglected. The proof stress of material decreases as a
result of prior creep strain at 600°C compared to the material without prior creep strain
for both new and ex-service material. The reduction of 0.2% proof stress in the prior
creep specimens may be attributed to the microstructural degradation in terms of
coarsening of precipitate, decrease in dislocation density and sub-grain coarsening [14,
125].
184
On the other hand, the failure strain in Figure 7.7 is increased when the material was
subjected to prior creep strain. This may be related to the formation of intergranular
damage on the gain boundaries during the creep deformation. However the reduction
of the tensile strain at failure in Figure 7.13 may vary at different level of prior creep
strain. This may be due to the similar creep mechanism in the secondary region where
the damage may start to initiate and the level of prior creep strain may not quantify the
level of creep damage. Further it has been shown in [79] that the creep damage may
be pronounced in the tertiary region where the accelerated creep strain occurs and the
necking occurs in the specimen.
The low cycle fatigue testing has been performed on ex-service P91 material for both
prior and without prior creep strain, at room temperature. Both materials, with and
without prior creep strain generally showed cyclic softening. It has been shown at all
strain ranges examined, the stress amplitude for the material with prior creep strain is
always lower than the material without prior creep strain which may indicate the
degradation on the material’s strength during the prior creep test. The fatigue life has
increased considerably for prior creep strain material at high strain range but remained
unchanged at lower strain range.
The cyclic stress strain response has shown that an increase in total strain amplitude
resulted in increase in stress amplitude and plastic strain amplitude and a
corresponding decrease in fatigue life. The relatively higher plastic strain magnitudes
suggest that increasing the total strain results in large plasticity which probably resulted
in early crack nucleation and propagation hence, the observed shorter LCF life. The
strain life relationship showed that the contribution of elastic and plastic strain to total
strain was dependent on the applied total strain level during the LCF testing. The
plastic strain plays significant role at higher strain levels.
8.2 Future Work
For the future work, numerical modelling of the creep damage process to predict
uniaxial and multiaxial failure can be used and enhanced to take into account the
actual material properties of the damaged material. This model will be also be used to
show its relevance to component failure under creep/fatigue conditions.
185
The influence of prior creep strain has been examined as part of this research work.
The low cycle fatigue test at high temperature is suggested to be performed on the
prior creep strain material as it may simulate the real condition in power plant
component. In order to characterise the prior creep strain/damage, an advanced
microstructural assessment is suggested including transmission electron microscopy
(TEM) and electron backscatter diffraction (EBSD) technique.
Instead of prior creep strain, the influence of prior cyclic loading is important to predict
the remnant life of power plant components. The specimens may be subjected to prior
cyclic loading and subsequent creep may be determined. Further tests such as fracture
toughness and creep crack growth can be performed on the prior cyclic specimens.
As explained previously in Chapter 5, further CFCG testing needs to be performed with
lower strain ranges and better measurements of the final strains in order to confirm
findings and provide more confidence on the interaction diagram in Figure 5.8. CFCG
testing is suggested to be performed in order to investigate constraint effects by
varying frequency, specimen geometry and test times.
186
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