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Failure Assessment on Effects of Pressure Cycle Induced Fatigue on Natural Gas Pipelines Hugo Filipe Barros de Oliveira Dias Thesis to obtain the Master of Science Degree in Materials Engineering Supervisor: Prof. PhD Alberto Eduardo Morão Cabral Ferro Co-supervisor: Eng. Carlos Alberto Pires Sousa Examination Committee: Chairperson: Prof. PhD Maria de Fátima Reis Vaz Supervisor: Prof. PhD Alberto Eduardo Morão Cabral Ferro Member of the Committee: Prof. PhD Pedro Miguel Gomes Abrunhosa Amaral November 2014
Transcript of Failure Assessment on Effects of Pressure Cycle Induced ... · PDF fileFailure Assessment on...
Failure Assessment on Effects of Pressure Cycle
Induced Fatigue on Natural Gas Pipelines
Hugo Filipe Barros de Oliveira Dias
Thesis to obtain the Master of Science Degree in
Materials Engineering
Supervisor: Prof. PhD Alberto Eduardo Morão Cabral Ferro
Co-supervisor: Eng. Carlos Alberto Pires Sousa
Examination Committee:
Chairperson: Prof. PhD Maria de Fátima Reis Vaz
Supervisor: Prof. PhD Alberto Eduardo Morão Cabral Ferro
Member of the Committee: Prof. PhD Pedro Miguel Gomes Abrunhosa Amaral
November 2014
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“Make big plans, aim high in hope and work…
let your watchword be order
and your beacon beauty”
Burnham
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Acknowledgments
Firstly, I would like to thank my parents for all the support through the years and for making
available resources for doing this work. Without them my education and growth as a person and
a professional would not been possible.
Secondly, I would like to acknowledge REN – Redes Energéticas Nacionais, in particular to
Chief Operating Officer, Engineer, João Conceição, for allowing me to take an academic
internship for concluding my Masters. Furthermore, at REN-Gasodutos, I would like to express
my gratitude to my co-supervisor Engineer Carlos Pires Sousa for the reception within the
company and for making resources available to me, as I needed them. Moreover, I would like to
recognize all people that were in a way connected with this work, namely, the Area Managers
Rui Marmota, Paulo Ferreira and Ferreira Marques and Engineers David Gil, João Marrazes
and João Teixeira Santos.
Thirdly, I would like to recognize my supervisor PhD Alberto Ferro to put up with me since my
second year in the University, and for the assistance and care through the work. Also, I would
like to acknowledge PhD Ricardo Baptista for his help in this work. Without his advices, several
results present in this work would not be possible.
Finally, I would like to express my deeply gratitude to all my friends from Instituto Superior
Técnico and other places for the friendship and for helping me to have great times.
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Resumo
A probabilidade de falha de uma estrutura pode ser minimizada através de uma avaliação de
integridade que permita adoptar correctamente as acções mitigadoras e preventivas
necessárias. O objectivo desta dissertação é avaliar se os gasodutos de transporte de gás
natural estão sujeitos ao perigo de falha devido ao agravamento de defeitos graças à fadiga
causada por ciclos de pressão. Estes ciclos de pressão podem ser originados pela alteração da
filosofia de injecção de gás natural na rede no Terminal de Gás Natural Liquefeito, em Sines,
tendo como objectivo a redução de custos maximizando as emissões nos períodos de tarifa
reduzida. Os ciclos de pressão foram simulados no software SIMONE e os valores resultantes
utilizados em ensaios de fadiga, na avaliação de integridade baseada nas normas BS 7910 e
API 579 e modelação numérica através do software Abaqus/CAE.
Os resultados obtidos confirmaram que os gasodutos não têm perigo de falhar devido a fadiga
provocada pelos ciclos de pressão, em situações em que não haja intervenção de terceiros. Os
tempos estimados de falha rondariam os 150 a 200 anos.
Foi também realizado um estudo probabilístico para prever a falha de um gasoduto com um
defeito (semi-elipse), cuja probabilidade de fractura foi aproximadamente 7 × 10−4.
Palavras-chave: Fadiga; FEM; Fitness-for-Purpose; Gasoduto; Ciclo de Pressão; Aço
X70; XFEM
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Abstract
The probability of pipeline failure can be minimized if structural integrity is assessed and
necessary prevention and mitigation measures appropriately taken.The goal of this work is to
evaluate if natural gas pipelines are subjected to failure when cracks are activated by pressure
cycle induced fatigue. Pressure cycles can be originated by modification of the natural gas send
out philosophy in the liquefied natural gas terminal, in Sines, aiming for a operation cost
reduction boosting emissions on low tariff periods. Send out cycles were simulated with
software SIMONE and the resulting values were used in fatigue tests, in the integrity
assessment studies through procedures BS 7910 and API RP 579 and in numerical modelling
of crack growth with software Abaqus/CAE.
The results obtained confirmed that natural gas pipelines do not have danger to fail under
pressure cycle induced fatigue, with high amplitudes whenever third party activities are not
involved. Predicted times to failure ranged from 150 to 200 years.
A probabilistic study was also carried out in order to predict the failure of a pipeline with one
defect (semi-ellipse), whose probability of failure was found to be around 7 × 10−4.
Keywords: Fatigue; FEM; Fitness-for-Purpose; Pipeline; Pressure Cycle; X70 Steel;
XFEM
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Index
Acknowledgments ......................................................................................................................... iv
Resumo ......................................................................................................................................... v
Abstract ......................................................................................................................................... vi
Index ............................................................................................................................................. vii
List of Figures ............................................................................................................................ ix
List of Tables ............................................................................................................................. xi
Abbreviations ................................................................................................................................ xii
List of Symbols ............................................................................................................................ xiii
Chapter 1
Introduction .................................................................................................................................... 1
1.1 Context ................................................................................................................................ 1
1.2 Objective and Scope ........................................................................................................... 2
1.3 Thesis Outline ..................................................................................................................... 3
Chapter 2
Overview ........................................................................................................................................ 4
2.1 Portuguese Natural Gas System ......................................................................................... 4
2.1.1 Natural Gas Transmission Network ............................................................................. 5
2.1.2 Underground Gas Storage ........................................................................................... 6
2.1.3 Liquefied Natural Gas Terminal.................................................................................... 7
Chapter 3
Fundamental Concepts ................................................................................................................. 8
3.1 Review on Fracture Mechanics ........................................................................................... 8
3.1.1 Linear Elastic Fracture Mechanics ............................................................................... 9
3.1.1 Elastic-Plastic Fracture Mechanics ............................................................................ 10
3.2 Reviews on Fatigue Failure ............................................................................................... 11
3.3 Concepts of Pipeline Mechanics ....................................................................................... 15
3.4 Developments of high strength steels for pipelines .......................................................... 16
Chapter 4
Pressure Cycle Simulation .......................................................................................................... 18
viii
4.1 Introduction ........................................................................................................................ 18
4.2 SIMONE Simulation .......................................................................................................... 18
4.3 Conclusions ....................................................................................................................... 22
Chapter 5
Experimental Testing and Results............................................................................................... 23
5.1 Introduction ........................................................................................................................ 23
5.2 Mechanical characterization .............................................................................................. 23
5.3 Fatigue characterization .................................................................................................... 25
5.4 Conclusions ....................................................................................................................... 28
Chapter 6
Numerical Modelling .................................................................................................................... 29
6.1 Introduction ........................................................................................................................ 29
6.1.1 The Finite Element Method ........................................................................................ 29
6.1.2 XFEM framework ........................................................................................................ 31
6.2 Models and Results ........................................................................................................... 34
6.2.1 𝑲 and 𝑱 Estimation Values ......................................................................................... 34
6.2.2 𝑱-Based Failure Assessment Diagram ....................................................................... 37
6.4 Conclusions ....................................................................................................................... 40
Chapter 7
Integrity Assessment and Structural Reliability ........................................................................... 41
7.1 Introduction ........................................................................................................................ 41
7.1.1 Empirical Methods ...................................................................................................... 41
7.1.2 Fitness-for-Purpose Approach for Integrity Assessment ........................................... 42
7.1.3 Structural Reliability .................................................................................................... 45
7.2 Models and Results ........................................................................................................... 47
7.2.1 Fitness-for-Purpose for Integrity Assessment ............................................................ 49
7.2.2 Structural Reliability .................................................................................................... 55
7.3 Conclusions ....................................................................................................................... 57
Chapter 8
Final Remarks and Future Work ................................................................................................. 59
8.1 Final Remarks ................................................................................................................... 59
ix
8.2 Future Work ....................................................................................................................... 60
References .............................................................................................................................. 61
Appendix
I – Natural Gas Transmission Network ................................................................................... 67
II – Pressure cycle profiles and gas flow for different scenarios ............................................. 68
III – API 5L X70 Steel Euro Pipe Certificate ............................................................................ 70
IV – Assessment Procedure to Evaluate a Pipeline with Crack-Like Flaws ........................... 71
V – Methodology for Crack Growth Analysis ........................................................................... 73
List of Figures
Figure 1-1 – Causes of failure of Natural Gas pipelines around the world, from 2000 to 2012. [2]
[3] ................................................................................................................................................... 2
Figure 2-1 – LNG Terminal at Sines. [5] ....................................................................................... 7
Figure 2-2 – Comparison of the use of NG and LNG, through the years. [5] ............................... 7
Figure 3-1 – Effect of fracture toughness on the governing failure mechanism. [10] ................... 8
Figure 3-2 – a) Real and ideal crack tension behavior. b) Stress field around the crack. [13] ..... 9
Figure 3-3 – a) A 2D contour integral and b) a 2D closed contour integral. [14] ........................ 10
Figure 3-4 – Contour integral for general three dimensions crack front. [14] ............................. 11
Figure 3-5 - The damage tolerance approach to design. [10] ..................................................... 12
Figure 3-6 – (a) S-N curve with fatigue limit. [15] (b) Clam Shell fatigue crack surface. [15] ..... 12
Figure 3-7 – Random Load Spectrum. [9] ................................................................................... 13
Figure 3-8 – Crack length increase with number of cycles. [15] ................................................. 14
Figure 3-9 – Different regions of the 𝝏𝒂𝝏𝑵 vs ∆𝑲 plot. [17] ........................................................ 15
Figure 3-10 – Pipeline Stresses under Internal Pressure. [18] ................................................... 15
Figure 3-11 - Evolution of line pipe steel grades. [20] ................................................................. 16
Figure 4-1 – Gas Flow during a week for the Scenario 1 (highest nomination) and 2 (lowest
nomination). ................................................................................................................................. 19
Figure 4-2 – Scenario 1: Pressure Cycle Profiles, during a week. .............................................. 19
Figure 4-3 – Scenario 2: Pressure Cycle Profiles, during a week. .............................................. 20
Figure 4-4 –Pressure Range for: (a) Scenario 1 (b) Scenario 2. ................................................ 21
Figure 4-5 –Pressure Range for real-time profiles. ..................................................................... 21
Figure 5-1 – Steps to obtain specimens. [22] [23] ....................................................................... 23
Figure 5-2 – Stress-strain curve: a) Longitudinal Direction; b) Radial/Transverse direction....... 24
x
Figure 5-3 – Schematically representation of the compact specimen. [24] ................................ 25
Figure 5-4 – Detail of the camera attached to the machine (Left). Crack propagation (Right). .. 26
Figure 5-5 – Crack length vs. Number of cycles. ........................................................................ 26
Figure 5-6 – Fatigue crack growth rate: a) Specimen 1; b) Specimen 2. ................................... 26
Figure 5-7 – Details from the specimen after the fatigue failure. ................................................ 27
Figure 5-8 – Stages I and II of fatigue crack propagation. [25] ................................................... 27
Figure 6-1 – A body with a crack with a fixed boundary subjected to a load. [10] ...................... 29
Figure 6-2 – (a) Mesh with a crack. (b) Mesh without a crack. The circle numbers are the
element numbers. [29] ................................................................................................................. 32
Figure 6-3 – (a) An arbitrary crack in a mesh. (b) Local coordinate axes for two crack tips. [27]33
Figure 6-4 – Scenario 1: (a) Schematic representation (b) ABAQUS® models (FEM-Contour
Integral and XFEM) ..................................................................................................................... 34
Figure 6-5 – Scenario 2: (a) Schematic representation (b) ABAQUS® models (FEM-Contour
Integral and XFEM) ..................................................................................................................... 35
Figure 6-6 – Single Edge Notched Testing simulated with: (a) FEM (b) XFEM. ......................... 35
Figure 6-7 – Scenario 1: 𝑲 and 𝑱 parameters as a function of the Load. Values are for 𝒂 =
𝟐𝒎𝒎. ........................................................................................................................................... 36
Figure 6-8 – Scenario 1: 𝑲 and 𝑱 parameters as a function of the crack length. Values are for
P= 𝟏𝟓𝟎 𝑴𝑷𝒂. .............................................................................................................................. 36
Figure 6-9 – Center-cracked Tensile Plate simulated with XFEM. ............................................. 37
Figure 6-10 – Scenario 2: 𝑲 and 𝑱 parameters as a function of the: (a) Load. (b) Crack Length.
Values are for 𝒂 = 𝟐 𝒎𝒎 and for 𝑷 = 𝟏𝟓𝟎𝑴𝑷𝒂. ........................................................................ 37
Figure 6-11 – (a) Quadratic curve-fit to the J results in the elastic range. (b) Infer the elastic J
trend using the curve fit. .............................................................................................................. 38
Figure 6-12 – Finding the intersection of the Jtotal/Jelastic ratio and the result curve. .................... 38
Figure 6-13 – 𝑱-Based Failure Assessment Diagram. ................................................................. 39
Figure 7-1 – Failure Stress for cracked pipelines. ....................................................................... 41
Figure 7-2 – Schematically comparison between fracture condition differences in two
geometrical configurations, representing the concept of transferability. [32] .............................. 42
Figure 7-3 – Fracture Toughness on Geometric Shape relationship. [33] .................................. 43
Figure 7-4 – FAD Diagram defining regions of safeness for the structure. [17] .......................... 44
Figure 7-5 – Possible flaws in pipe: Axial oriented surface flaws ((a) Internal (c) External);
Circumferential oriented surface flaw ((b) Internal (d) External) and (e) Through-Wall flaw in a
pipeline. [17] [35] ......................................................................................................................... 50
Figure 7-6 – Failure Assessment Diagram (BS7910): (a) Level 1; (b) Level 2. .......................... 51
xi
Figure 7-7 – Failure Assessment Diagram (BS 7910) - Level 1 Assessment (a) Internal flaws (b)
External Flaws. ............................................................................................................................ 52
Figure 7-8 - – Failure Assessment Diagram (BS 7910) - Level 2 Assessment (a) Internal flaws
(b) External Flaws ....................................................................................................................... 53
Figure 7-9 – Leak before Breakage analysis for points that are unsafe for Level 2 Assessment.
..................................................................................................................................................... 53
Figure 7-10 –Failure Assessment Diagram (BS7910) – Fatigue Assessment (a) Level 1 (b)
Level 2. ........................................................................................................................................ 54
Figure 7-11 - Leak before Breakage analysis. ............................................................................ 54
Figure 7-12 – Remaining Life in-Service in function with the crack depth. ................................. 55
Figure 7-13 – API 579 Level 2 Assessment for growing crack. .................................................. 55
Figure 7-14 – Probability of Detection of a defect. ...................................................................... 56
Figure 7-15 – Probability of Failure over the years. .................................................................... 57
Figure 7-16 – Different FAD curves using different procedures. ................................................. 58
Figure A-1 – Gas Flow during February 26th to March 4
th, 2011. ................................................ 68
Figure A-2 – Gas Flow during September 21st to September 27
th, 2013. ................................... 68
Figure A-3 – Gas Flow during March 22nd
to March 28th, 2014. ................................................. 68
Figure A-4 – Pressure Cycle Profiles, during February 26th to March 4
th, 2011. ........................ 69
Figure A-5 – Pressure Cycle Profiles, during September 21st to September 27
th, 2013. ............ 69
Figure A-6 - Pressure Cycle Profiles, during March 22nd
to March 28th, 2014. ........................... 69
List of Tables
Table 2-1– Available capacity for commercial purposes of relevant points. [5] ............................ 6
Table 3-1 – Mechanical Properties for some API 5L Steel Grades. [21] .................................... 17
Table 4-1 – Total LNG Terminal gas nominations for two scenario studies. .............................. 18
Table 4-2 – Description of real-time profiles. .............................................................................. 20
Table 5-1 – Specimen Dimensions for Tensile Testing. ............................................................. 24
Table 5-2 – Results obtained from the tensile testing. ................................................................ 24
Table 5-3 – Specimen Dimensions for Fatigue Crack Growth Testing. ...................................... 25
Table 5-4 – Fatigue Crack Propagation Test results................................................................... 27
Table 7-1 – Trunckline L12000 Pipeline dimensions for different classes. ................................. 48
Table 7-2 – Flaw characterization. [35] [17] ................................................................................ 49
Table 7-3 – Remaining life in-service of the case 2 scenario. .................................................... 53
Table 7-4 – Input parameters for POF analysis. ......................................................................... 56
xii
Abbreviations
API American Petroleum Institute SMYS Specified Minimum Yield Strength
ASME American Society of Mechanical
Engineers SSY small scale yielding
ASTM American Society of Testing and
Materials, now ASTM International TMCP Thermo Mechanical Controlled Process
BSI British Standards Institute TSO Transmission System Operator
EPFM Elastic Plastic Fracture Mechanics UGS Underground Gas Storage
ERSE Energy Services Regulatory
Authority XFEM Extended Finite Element Method
FAD Failure Assessment Diagram
FEA Finite Element Analysis
FEM Finite Element Method
FFP Fitness-for-Purpose
FORM First Order Reliability Method
GRMS Gas Regulation and Metring Station
HRR Hutchinson, Rice and Rosegreen
IST Instituto Superior Técnico
LEFM Linear Elastic Fracture Mechanics
LNG Liquefied Natural Gas
MCS Monte-Carlo Simulation
NG Natural Gas
NGTN Natural Gas Transmission Network
OPEX Operating Expenditure
PFM Probabilistic Fracture Mechanics
PIMS Pipeline Integrity Management
System
POD Probability of Detection
PSF Partial Safety Factor
REN Redes Energéticas Nacionais
SCADA Supervisory Control and Data
Acquisition
POF Probability of Failure
SINTAP Structural Integrity Assessment
Procedures for European Industry
SMTS Specified Minimum Tensile
Strength
xiii
List of Symbols
𝑩 Specimen thickness 𝒂 Crack depth
𝑪 Paris’s law constant 𝒂𝒊 Initial crack depth
𝑫 Outer diameter of the pie 𝒂𝒄 Critical crack depth
𝑬 Young’s modulus 𝒂𝒇 Crack depth at failure
𝑭 Reference stress geometric factor 𝒄 Half of the crack length
𝑱 J-Integral 𝒎 Paris’s Law material constant
𝑲 Stress intensity factor 𝒏 Outward normal to Γ
𝐾𝑒𝑓 Effective stress intensity factor 𝒏𝑹𝑶 Ramberg-Osgood strain hardening
coefficient
𝑲𝑰 Stress intensity factor at mode I 𝒒 Notch sensitivity factor
𝑲𝑰𝑰 Stress intensity factor at mode II 𝒓 Crack tip radius
𝑲𝑰𝑪 Fracture toughness 𝒕 Thickness
𝑲𝒓 Toughness ratio 𝚪 Arbitrary path Enclosing the Crack Tip
𝑲𝒕𝒉 Threshold value for the Stress
intensity factor 𝚫𝑲 Stress intensity factor range
𝑳 Length of the pipe 𝚫𝝈 Stress range
𝑳𝒓 Load ratio 𝚽 Probability density function
𝑳𝒓𝒑 Primary load ratio 𝜶𝑹𝑶 Ramberg-Osgood constant
𝐿𝑟𝑚𝑎𝑥 Maximum cutoff value 𝜷
Minimum distance to the limit state
funciton
𝑴 Folia’s factor 𝜺 True strain
𝑵 Number of cycles 𝜺𝑯 Hoop strain
𝑵𝒇 Fatigue life 𝜺𝑳 Longitudinal strain
𝑷 Internal pressure 𝜺𝒓𝒆𝒇 Reference strain
𝑷𝒇 Probability of failure 𝝈 True stress
𝑹 Outer radius of the pipe 𝝈𝒇 Failure stress
𝑺𝒓 Load ratio 𝝈𝑯 Hoop stress
𝑾 Compact specimen parameter 𝝈𝑳 Longitudinal stress
𝑾𝒔 Strain energy 𝝈𝒓𝒆𝒇 Reference stress
𝒀 Geometrical shape factor 𝝈𝒖 Ultimate tensile stress
xiv
𝝈𝒕𝒉 Fatigue limit stress
𝝈𝒚 Yield Stress
𝝈𝜽𝜽 Opening stress ahead of the crack
𝝈∞ Far-field applied axial stress
�̅� Flow stress
𝝔 Paris law’s integration constant
𝜽 Angle of propagation
𝝂 Poisson’s ratio
𝝏𝒂
𝝏𝑵 Fatigue crack growth rate
(𝒓, 𝜽) Polar co-ordinate system, origin
located at the crack tip
1
Chapter 1
Introduction
1.1 Context
Natural gas (NG) is poised to capture a larger share of the world’s energy demand. Although
NG has been a part of the energy landscape since the Industrial Revolution, what is new and
changing is the new role of this unique resource in the global energy mix. NG is shifting from a
regional and often marginal fuel to becoming a focal point of global energy supply and demand.
NG will increasingly complement wind and other renewable energy sources, particularly in
power generation acting as a solid back up for these sources intermittence. It is anticipated that
gas will grow by more than a third over its current global consumption by 2025 [1]. Gas growth
is accelerating, in part, because the infrastructure networks that connect supply and demand
are becoming more diverse and expanding around the world but mainly boosted by new supply
options like shale gas. NG requires networks to link sources of production to the various
locations where it will be used. Liquefied Natural Gas (LNG) plays an important role by linking
overseas producers and consumers and also as security of supply by offering several choices
of suppliers. One defining characteristic of pipeline networks is that they become more valuable
with size as more entities join the network. These characteristics facilitate the development of
adjacent networks, uncovering hidden opportunities to create value as new links are
established. Thus, the NG pipeline industry is starting to implement comprehensive integrity
management practices to meet the demands of new regulatory imperatives and public interests.
These new demands require formal integrity management planning programs to be developed
and applied where pipeline failures could affect “High Consequence Areas”. A formal integrity
management plan, in particular, the so called Pipeline Integrity Management System (PIMS)
incorporates some process for identifying threats to pipeline’s integrity. Once such threats are
identified, the pipeline operator shall characterize the degree of risk associated with the threat
as a means of prioritizing responses, identify suitable methods to assess the presence of the
threat, and develop appropriate mitigations. Interest has arisen regarding fatigue as one such
possible integrity threat. Figure 1-1 shows other possible threats regarding pipeline failure
around the world. Yet, just a small part is due to induced fatigue as the use of pressure cycling
operation to improve energy efficiency is far from being applied. Moreover, as the need for
energy increases and the natural gas market rises in flexibility, the need for optimizing and
reduction of costs plays a big role in every decision. Any innovation regarding efficiency needs
to be supported with a structural integrity assessment, especially if it involves changes in
nominal flow conditions required, in order to ensure network life cycle, public safety and
environmental protection. Catastrophic failure of any structure can be avoided if structural
integrity is assessed and necessary safety protocols are developed accordingly.
2
Figure 1-1 – Causes of failure of Natural Gas pipelines around the world, from 2000 to 2012. [2] [3]
Therefore, the structural integrity of pipelines commences with good design and construction
practices, which will eliminate most of the potential failure modes. Additionally, as pipelines can
operate in hostile environments they are constantly threatened by defects and damage that
occur in-service. These in-service defects are the major cause of pipeline failures; therefore to
understand and control structural integrity, in -service defects must be understood and
controlled.
1.2 Objective and Scope
Natural Gas is mostly transported in pipelines. The larger of these pipelines are called
transmission pipelines. In the Portuguese Natural Gas System, there are two main entries, one
in Campo Maior, through the Maghreb-Europe Gas Pipeline, with a fix capacity contract with the
Algerian supplier and another via LNG Terminal in Sines. To provide a more energy efficient
process, aiming for energy reduction in both cost and environmental, certain changes have to
be made in the Terminal. One of them can be adjusting the consumption profile of NG injected
in the network. This can be done by the rational use of the rotating equipment, not only for
promoting a system operation at maximum efficiency but also for avoiding successive starts and
stops from the equipment, is the focal point for the adequacy of periods of higher flow rate
emission of NG for the Natural Gas National Transmission Network (NGTN). It also promotes a
usage of high power consumption equipment in periods whose electricity tariff is lower. These
adjustment of the injection profile in the network, could lead to mechanical problems, in
particular fatigue, as the pressure cycle will be higher in the material. There are little to none
information about pressure cycle induced fatigue in NG pipelines, especially because generally
these failures happen where the pressure cycle is not significant or by other damages, as
shown in Figure 1-1. The study is going to be focus on the trunckline 12000 that goes from
Sines to Setubal. This line is the chosen location because in Sines, is where it is located the
LNG Terminal and major cycle impacts will occur over the line immediately downstream. Due to
the fact that the NG that enters through the Maghreb-Europe Gas Pipeline is a fix capacity
contract, it is in the LNG Terminal that a more efficient process can occur. Therefore this study
23%
5%
5%
3%
3%
8% 7%
1%
15%
3%
24%
6% Damage by OthersWeldsConstructionJointsPipelineOthersValve FittingOverpressureExternal CorrosionInternal CorrosionThird Party ActivitiesNatural Hazards
3
aims to evaluate the degree of exposure to failure from defects that could grow by pressure
cycle induced fatigue. Moreover, the work has the following goals:
Modelling the fatigue crack growth using finite element analysis (FEA);
Assessing the integrity of the structure by the means of Failure Assessment Diagram
(FAD) methods;
Producing recommendations to implement the proposed changes.
The expectation is that such assessments will identify growing defects due to fatigue so that
they can be repaired or removed before they reach sizes that will cause failures at normal
operating stress levels.
1.3 Thesis Outline
In chapter 1, it is expressed the goals of this thesis and where it is inserted. In chapter 2, the
Natural Gas National System is described from its assets and areas. Chapter 3 reviews fracture
mechanics concepts, in particular concepts of Linear Elastic Fracture Mechanics (LEFM),
Elastic Plastic Fracture Mechanics (EPFM) and Fatigue Failure.
Pressure Cycle Profiles were simulated and they are described in chapter 4. Due to the fact that
the change of nominal flow condition will induce fatigue in the structure, several methods were
conducted in order to infer the behaviour of the structure. Chapter 5 is reserved for laboratory
tests and analysis of its results. Specimens were subjected tensile and fatigue crack growth
tests. Numerical Modelling using a Finite Element Analysis software ABAQUS® is used to
predict some parameters (𝐾 and 𝐽) and the failure of the pipeline in chapter 6, using both
contour integral techniques and Extended Finite Element Method (XFEM). Integrity Assessment
and Structural Reliability are evaluated in chapter 7. Procedures for assessing the Fitness-For-
Purpose (FFP) have developed since the late 1960's and two of the most commonly used are
the recommended practice for assessing fitness-for-service published by the American
Petroleum Institute (API) in API RP 579 and the guidance for the assessment of defects metallic
structures published by British Standards Institute (BSI) in BS 7910. Both methods imply the
use of the Failure Assessment Diagram method to evaluate if a structure is in risk of collapse or
if the structure is safe. On the other hand, in order to infer how long a pipe can remain in-
service, probability of failure of a component with crack-like flaws was calculated, using
analytical, First-Order Reliability Methods (FORM) and Monte-Carlo Simulation (MCS).
This thesis ends with chapter 8 containing a summary that gives an overview of the main
concepts covered in preceding chapters of the document, as well, discussing the results
obtained by the different methods applied and future work to be done.
4
Chapter 2
Overview
This chapter tries to make an overview of the Portuguese Natural Gas System, mostly the
Natural Gas Transmission Network, the Underground Gas Storage (UGS) and the LNG
Terminal, in order to put this work on the context of REN.
2.1 Portuguese Natural Gas System
NG transmission pipeline are designed, built and operated to well established standards and
laws, because NG can pose a significant hazard to surrounding population and environment.
The combination of good design, materials and operating practices has ensured that
transmission pipelines have a good safety record. Besides safety and compliance with codes
and legislation, pipelines must ensure security of supply, delivering its products in a continuous
manner, to satisfy the shippers and the end users and also ensure cost effectiveness.
REN Gasodutos is one of the companies which are part of the REN Group [5] and it is the
single Portuguese Transmission System Operator (TSO) [4], whereby it is responsible for the
operation of the high pressure transmission system. REN Gasodutos is also responsible for
performing the Global Technical Management of the National Natural Gas Transmission
System, as Gas System Manager [5]. REN Gasodutos seeks to integrate the operation of the
different infrastructures of the Portuguese Natural Gas System, while ensuring public service
obligations related to security of supply, in terms of monitoring the establishment and
maintenance of security gas reserves by commercialization companies, as well as providing
open, transparent and non-discriminatory third party access to NG infrastructures. The
preparation of an integrated proposal for the development planning of the Portuguese Natural
Gas System and its corresponding submission to the National Energy Directorate, which occurs
every three years, is also an important task of the Gas System Manager.
As a TSO, REN Gasodutos is responsible for monitoring the balance between NG demand and
supply, and checking it against available, in order to ensure an efficient and cost-effective use of
NG infrastructures. A checking mechanism has been implemented, linking scheduling and
assignment processes, with a view to ensure the overall feasibility of the system. From a
technical perspective, REN Gasodutos offers the market all available capacity over a given
period of time, by managing pressure levels as well as performing residual system balancing
between intakes and offtakes, in order to maintain the transmission system's integrity, while
providing a reliable service to shippers.
The natural gas activities listed below are subject to economic regulation by the National
Regulator Agency (NRA/ERSE) [4]:
Natural gas high-pressure transmission network – through REN Gasodutos;
5
Overall technical management of the Portuguese Natural Gas System – through REN
Gasodutos;
Reception, storage and regasification of LNG – through REN Atlântico;
Underground gas storage – through REN Armazenagem;
Supplier switching management process – through REN Gasodutos.
These companies have been public service concession holders since 2006 with a licence for a
period of 40 years [4]. REN's natural gas infrastructures include the Natural Gas Transmission
Network, the LNG Terminal in Sines and the Underground Gas Storage facilities (5 caverns and
1 gas station) in Carriço. Furthermore, there is currently in progress a project for the
implementation of a compression station to be implemented in Carregado [6].
2.1.1 Natural Gas Transmission Network
REN Gasodutos operates the NGTN, feeding, at high pressure, a set of consumers with
different consumption needs. Among the various consumers are included Combined Cycle
Power Plants, Distribution Network Operators and Industrial clients. The NGTN is
geographically developed around two main trunk axes:
The main trunk line running from South to North from the Sines LNG Terminal to
Valença do Minho, which provides the supply of natural gas to the country's most
densely populated areas. There are three important branch lines connected with this
main trunk line, namely the pipeline that supplies the region of Lisbon, the pipeline that
interconnects the transmission system with the underground storage facilities of Carriço
and the pipeline that supplies gas to the central region of the country up to Viseu and
Mangualde.
The transmission line between the central point of the main trunckline, located in the
region of Leiria-Pombal and Campo Maior, at the eastern border between Portugal and
Spain. It also branches off to the underground storage facilities of Carriço, as well as an
important branch line connected with this transmission line, namely the pipeline that
supplies gas to the interior region of the country up to Guarda.
There are two Interconnection Points between the Portuguese and the Spanish Gas Systems,
namely Campo Maior/Badajoz in eastern Portugal, and Valença do Minho/Tuy in the northern
point of the main trunk line.
The different NGTN lines are divided by lots, comprising a main pipeline with many ramifications
associated, called branch lines. At the end of 2013, the NGTN consisted of the following
infrastructures [7]:
1 375 km of high-pressure gas pipelines;
65 junction stations for pipeline branching;
46 block valve stations;
5 industrial consumer junction station;
6
84 gas pressure regulating and metering stations;
2 custody transfer stations.
Supervised from a state-of-the-art National Dispatch Centre, using redundant fibre-optic
technology telecommunication systems, the NGTN connects the gas pipeline stations with the
LNG Terminal and the UGS facility at Carriço. All systems are equipped with digital
communication, especially with regard to the monitoring and registering of network input and
output flows. This allows for the best practices to be adopted both in relation to information
quality and supervision response. Most of the lines of NGTN are piggable1, however there are
currently 8 branch lines non-piggable due to physical impossibility of the infrastructure. Those
lines have been inspected by indirect assessment by analysing the data from cathodic
protection and other inspection methods, particularly by guided wave technology. As far as
capacities per day, the NGTN sends out over 700 GWh per day of natural gas to the system, as
observed in Table 2-1.
Table 2-1– Available capacity for commercial purposes of relevant points. [5]
Available Capacity for Commercial Purposes of Relevant Points
𝑮𝑾𝒉 per day
𝑴𝒎𝟑(𝒏)
per day
Input
Sines (LNG Terminal) 193 16.20
Carriço (UGS - withdrawal) 85 7.10
Campo Maior 134 11.30
Valença do Minho 40 3.40
Output
Sines (LNG Terminal) 143 12.0
Carriço (UGS - injection) 24 2.00
Campo Maior 70 5.90
Valença do Minho 25 2.10
Outputs by GRMS (total) 707 59.40
2.1.2 Underground Gas Storage
The UGS facilities include the gas station and the gas caverns. The gas station comprises
several process sections that are used according to the operation mode of the facilities:
In injection mode: reception of natural gas from the pipeline, metering and
compression into the caverns;
In withdrawal mode: pressure reduction of the gas coming from the caverns,
dehydration, metering and delivery into the pipeline.
1 Pigging refers to the practice of using devices known as pigs to perform cleaning, inspecting and
maintenance operations on a pipeline. This is done without stopping the flow of the product in the pipeline
7
The gas caverns are built via a controlled leaching process of the existing salt dome formation
at the average depth of 1200 metres [5]. Currently there are five caverns in operation. The five
operational gas caverns have a combined storage capacity of 3.155 𝐺𝑊ℎ (around 265 𝑀𝑚3) [4].
The gas station has a nominal injection capacity of 110000 𝑚3(𝑛)/ℎ and a nominal withdrawal
capacity of 300 000 𝑚3(𝑛)/ℎ [4]. Expansion of the infrastructure of NG underground storage is
currently under way and additional caverns are scheduled to come on stream in the future.
2.1.3 Liquefied Natural Gas Terminal
The LNG Terminal is operated by REN Atlântico and is located in the industrial area of Sines
port. The Terminal receives methane carriers from different LNG liquefaction plants around the
world and stores the unloaded LNG in cryogenic tanks, from where it is pumped through open-
rack vaporizers and sent out into the natural gas transmission system.
Figure 2-1 – LNG Terminal at Sines. [5]
The facilities can receive and dock ships with capacities ranging from 35 000 to 210 000 𝑚3 of
LNG, corresponding to 240 to 1 450 𝐺𝑊ℎ, respectively [5]. There are two storage tanks that
have a combined storage capacity of 240 000 𝑚3of LNG and a third one that have 150 000
𝑚3of storage capacity. These tanks make possible the NG injection capacity into the NGTN of
190 𝐺𝑊ℎ/𝑑𝑎𝑦 to 380 𝐺𝑊ℎ/𝑑𝑎𝑦 [5].
Figure 2-2 – Comparison of the use of NG and LNG, through the years. [5]
0
10
20
30
40
50
60
70
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
Tw
h
NG LNG
8
Chapter 3
Fundamental Concepts
Fracture mechanics denotes the applied mechanics framework needed for characterizing the
behaviour of cracked components under applied loads. Its objective is to characterize the local
deformation around a crack tip, in order to predict how crack will affect the components
behaviour. [8] The fracture process is related with nonlinear deformation, as the zone where the
fracture process takes place, is the region around the crack tip where dislocation motions occur.
The zone size is characterized by the number of grain sizes for brittle fracture or by either
inclusion or second phase particle spacing for ductile fracture. Different theories have been
advanced to describe the fracture process in order to developed predictive capabilities, like
Linear Elastic Fracture Mechanics, Elastic-Plastic Fracture Mechanics. [12] The main goal of
this chapter it is to do a quick theoretical review of some concepts that are going to be used
through the work, mainly, 𝐽-integral, stress intensity factor and fatigue failure.
3.1 Review on Fracture Mechanics
For engineering materials, such as metals, there are two primary modes of fracture, brittle and
ductile. In the first one, the cracks spread very rapidly with little or no plastic deformation.
Ductile fracture on the other hand has three stages, void nucleation, growth and coalescence. In
this mode, the crack moves slowly and is accompanied by a large amount of plastic
deformation. The crack will not grow unless the applied load is increased.
Figure 3-1 – Effect of fracture toughness on the governing failure mechanism. [10]
Consider a cracked plate that is loaded to failure. Figure 3-1 is a schematic plot of failure stress
in function of the fracture toughness (𝐾𝐼𝑐). For low toughness materials, brittle fracture is the
governing failure mechanism, and critical stress varies linearly with 𝐾𝐼𝑐. At high toughness
values, LEFM is no longer valid, and failure is governed by the flow properties of the material. At
intermediate toughness levels, there is a transition between brittle fracture under linear elastic
conditions and ductile overload. Nonlinear fracture mechanics bridges the gap between LEFM
and collapse [10].
9
3.1.1 Linear Elastic Fracture Mechanics
Modern fracture mechanics was originated by Griffith studies in the 1920s when he successfully
showed that fracture in glass occurs when the strain energy release resulting from crack growth
is greater than the surface energy. [11] In 1948, Irwin extended Griffith’s strain energy release
rate criterion to include metals by accounting for the energy absorbed during plastic flow around
the flaw. [12] By 1960, the fundamental principles of linear elastic fracture mechanics were in
place. LEFM is used to predict material failure when response to the load is elastic and the
fracture response is brittle. LEFM uses the strain energy release rate, 𝒢, or the stress intensity
factor, 𝐾, as a fracture criterion [10].
Considering a homogeneous linear-elastic material, Irwin derived expressions which describes
the stress distribution in the region in front of the crack of a plate in tensile loading. These
expressions are shown below.
𝜎𝑥 =𝐾𝐼
√2𝜋𝑟[𝑐𝑜𝑠
𝜃
2(1 − 𝑠𝑒𝑛
𝜃
2𝑠𝑒𝑛
3𝜃
2)] (3.1)
𝜎𝑦 =
𝐾𝐼
√2𝜋𝑟[𝑐𝑜𝑠
𝜃
2(1 + 𝑠𝑒𝑛
𝜃
2𝑠𝑒𝑛
3𝜃
2)]
(3.2)
𝜏𝑥𝑦 =
𝐾𝐼
√2𝜋𝑟[𝑠𝑒𝑛
𝜃
2𝑐𝑜𝑠
𝜃
2𝑐𝑜𝑠
3𝜃
2]
(3.3)
These equations describe the stress concentration in the crack tip region in function of the
toughness. However, they represent a singularity for 𝑟 = 0 where 𝜎 → ∞. As the 𝑟 is getting
smaller, the local stress increases, reaching the yield strength of the material.
Figure 3-2 – a) Real and ideal crack tension behavior. b) Stress field around the crack. [13]
This situation leaves the crack tip inside a region of plastically deformed material, where stress
relived and linear solutions are not the most acceptable. Several models were purpose to
correct the effect of the plasticized zone. All of them considered a bigger effective length of the
crack than the true crack length, as a form of minimized the effect of the plastic zone in the
stress field and in the elastic unloading. Though, these models have limited application due to
the fact that the plastic zone radius must be inside the region of the solid where the elastic
a) b)
10
solutions are valid. Finally, LEFM is especially adequate to fragile failure, where the response of
the material is mostly linear-elastic until the instability.
3.1.1 Elastic-Plastic Fracture Mechanics
Elastic-Plastic Fracture Mechanics is an alternative developed for the study of the behaviour of
non-linear materials and exhibit considerable plasticity in the crack tip of a flaw, i.e., materials
under large-scale or general yielding conditions. EPFM had its beginnings in 1961, when Wells
noticed that initially sharp cracks in high toughness materials were blunted by plastic
deformation. Wells proposed the use of the distance between the crack faces at the deformed
tip to measure fracture toughness [10]. The stretch between the crack faces at the blunted tip is
known as the crack tip opening displacement. In 1968 Rice developed another EPFM
parameter called the J-integral. It describes the elastic-plastic deformation around the crack tip
to be nonlinear elastic. The J-integral was shown to be equivalent to 𝒢 for linear elastic
deformation and to the crack tip opening displacement for elastic-plastic deformation. During the
same year, Hutchinson Rice, and Rosengreen showed that J was also a nonlinear stress
intensity parameter, for materials whose mechanical behaviour is described by the Ramberg-
Osgood equation [10].
휀
휀𝑦
=𝜎
𝜎𝑦
+ 𝛼𝑅𝑂 (𝜎
𝜎𝑦
)
𝑛𝑅𝑂
(3.4)
The J-integral can be used as an elastic-plastic or fully plastic crack growth fracture parameter,
much like 𝐾 is used as an elastic fracture parameter.
Figure 3-3 – a) A 2D contour integral and b) a 2D closed contour integral. [14]
J-Integral characterizes the stress field and its fracture conditions in the neighbourhood of the
crack. For virtual crack advance in the plane of a three dimensions fracture, the energy release
rate is given by:
𝐽 = lim
Γ→0∫ 𝑛 ∙ 𝐻 ∙ 𝑞 ∙ 𝜕ΓΓ
(3.52)
where Γ is the contour around the crack tip, 𝜕Γ is the arc increment on Γ, 𝑛 is the outward
normal to Γ, 𝑞 is the unit vector in the virtual crack extension direction. 𝐻 is defined according to:
𝐻 = 𝑊𝐼 − 𝜎
𝑑𝑢
𝑑𝑥
(3.63)
(b) (a)
11
The strain energy can be defined as:
𝑊𝑠 = ∫ 𝜎𝑖𝑗𝜕휀𝑖𝑗
𝜀
0
(3.74)
The two dimensions J-Integral can be extended to a three dimensional crack front where the J
is defined point wise with respect to a parametric variable along the crack front.
In three dimensions, the energy release for a unit segment of crack advance over a finite
segment of the crack front ,𝐽, is defined as:
𝐽 = −∫ [𝐻
𝜕�̅�
𝜕𝑥+ (𝑓 ∙
𝜕𝑢
𝜕𝑥) ∙ �̅�] 𝜕𝑉
𝑉
(3.85)
Figure 3-4 – Contour integral for general three dimensions crack front. [14]
3.2 Reviews on Fatigue Failure
Fracture mechanics often plays a role in life prediction of components that are subject to time
dependent crack growth mechanisms such as fatigue. The rate of cracking can be correlated
with fracture mechanics parameters such as the stress-intensity factor, and the critical crack
size for failure can be computed if the fracture toughness is known. Damage tolerance, as its
name suggests, entails allowing subcritical flaws to remain in a structure. Repairing flawed
material or scrapping a flawed structure is expensive and is often unnecessary. Fracture
mechanics provides a rational basis for establishing flaw tolerance limits. Consider a flaw in a
structure that grows with time (e.g., a fatigue crack) as illustrated schematically in Figure 3-5.
The initial crack size is inferred from nondestructive examination, and the critical crack size is
computed from the applied stress and fracture toughness.
12
Normally, an allowable flaw size would be defined by dividing the critical size by a safety factor.
The predicted service life of the structure can then be inferred by calculating the time required
for the flaw to grow from its initial size to the maximum allowable size. Fatigue is a process of
structural degradation caused by fluctuations of stress cycles. Stresses are typically amplified
locally by structural discontinuities, geometric notches, surface irregularities, defects, or
metallurgical non-homogeneities. Fatigue may occur in three sequential stages, the formation of
a crack, called initiation, the stable incremental enlargement of the crack in service, called
propagation and the rapid instable fracture. Initiation of fatigue occurs at microstructure-scale
nucleation sites within the material such as inclusions, pores, or soft grained regions, or as they
become generated through micro void coalescence by the straining process. The presence of
macro-scale stress concentrators enhances crack nucleation as the process of progressive
localized permanent structural change occurring in material subjected to conditions which
produce fluctuating stresses and strains at some point or points.
The fatigue behavior of a material is generally described by the Wöhler curve or S-N curve,
which plots the stress amplitude against the number of cycles to failure. For materials with a
fatigue limit, the S-N curve will advance towards a horizontal asymptote at the level 𝜎 = 𝜎𝑡ℎ.
When a fatigue limit does not exist, the fatigue strength or endurance limit is defined as the
value for failure after a specified high – typically 106 number of cycles [10]. The initiation
Figure 3-5 - The damage tolerance approach to design. [10]
Figure 3-6 – (a) S-N curve with fatigue limit. [15] (b) Clam Shell fatigue crack surface. [15]
(a) (b)
13
process described above causes the formation of a crack in otherwise sound, un-cracked metal.
As load cycles accumulate, initiation is followed by propagation or enlargement of the crack in
service. Fatigue fracture surfaces frequently exhibit prominent concentric features, such as
those shown in Figure 3-6 (b) [9]. The crack surface shows two distinct markings on two
different scales. At a macroscopic scale, so-called clamshell markings also called beach marks
can be seen. They are the result of irregularities in the growth of the fatigue crack, due to
changes in loading conditions. Propagation necessarily concerns a crack that is already
present, so it is most useful to consider propagation in terms of parameters related to fracture
mechanics. The crack-tip stress intensity is an expression of the theoretical stress at the tip of a
crack, derived from LEFM.
𝐾 = 𝑌𝜎√𝜋𝑎 (3.9)
where 𝑌 is the geometry factor and 𝑎 the crack length. The geometry factor accounts for the
crack’s configuration and its orientation in the plate. The geometry factor may change as the
flaw enlarges. The service stresses fluctuate over a range, ∆σ, so the fluctuation in stress-
intensity is:
Δ𝐾 = 𝑌Δ𝜎√𝜋𝑎 (3.10)
A typical operating pressure spectrum for a natural gas pipeline may look something like what is
shown in Figure 3-76 (b). Typically the largest cyclical component is seasonal, which means it
occurs once per year. The pressure signal is stochastic, meaning it consists of an apparently
random mix of signal amplitudes. [15]
Although the load spectrum is already much more realistic than the harmonic loading with
constant frequency and amplitude, practical loading is mostly random. Prediction of fatigue life
is only possible after this random load is transferred into a harmonic load spectrum, with known
frequencies and amplitudes. Several experiments have shown that the crack length is an
exponential function of the number of cycles [9]. This means that crack growth is very slow until
the final stage of fatigue life, where a relative short number of cycles will result in fast crack
growth leading to failure. The initial fatigue crack length seems to be a very important parameter
for the fatigue life.
Figure 3-7 – Random Load Spectrum. [9]
14
For an initially undamaged material, it takes 𝑁𝑖 cycles to initiate a crack by dislocation
movement and void coalescence. The initial crack forms at this fatigue crack initiation life.
Moreover, in most cases it is so small that it cannot be detected. In this stage I, crack growth is
provoked by shear stresses and involves slip in a single crystallographic slip plane. After 𝑁𝑖
cycles, in stage II of crack growth, crack propagation is faster and it is provoked by tensile
stresses and involves plastic slip on multiple slip planes at the crack tip, resulting in striations.
The crack growth is now much faster and after 𝑁𝑓, its length is 𝑎𝑓 and after a few cycles 𝑎𝑐 is
reached and failure occurs. For higher stress amplitudes, the crack growth will be faster.
𝑁𝑟
𝑁𝑓
= 1 −𝑁
𝑁𝑓
(3.11)
To predict the fatigue life of structures, crack growth models have been proposed, which relate
𝜕𝑎
𝜕𝑁 to stress amplitude or maximum stress, which can be expressed by the stress intensity
factor, where stresses are low. Microstructural models relate the crack grow rate to
microstructural parameters, such as the distance between striations. The Paris Law is the
simplest fatigue crack growth law [13]. The equation has the form:
𝜕𝑎
𝜕𝑁= 𝐶(∆𝐾)𝑚 (3.12)
where 𝐶 and 𝑚 are material constants, ∆𝐾 the stress intensity factor range and 𝜕𝑎
𝜕𝑁 the fatigue
crack growth rate. In this model, the crack growth rate is independent of the stress ratio and, if
∆𝐾 > ∆𝐾𝑡ℎ,, crack growth occurs.
For low and high values of ∆𝐾, Paris law does not describe accurately the crack growth rate.
For ∆𝐾 ≈ 𝐾𝑡ℎ, the lower limit, a crack grows extremely slowly, hampered by the roughness of
the crack faces. For still smaller values of ∆𝐾, the crack growth is extremely small but not
completely zero. For high values of ∆𝐾, crack growth is much faster than predicted by the Paris
law. Paris law can be integrated analytically, where it increases from 𝑎𝑖 to 𝑎𝑓 and 𝑁 goes from
𝑁𝑖to 𝑁𝑓. The result 𝑁𝑓− 𝑁𝑖can be represented as a function of 𝑎𝑓 with 𝑎𝑖 as parameter or vice
versa. The fatigue life is reached, when the crack length becomes critical.
Figure 3-8 – Crack length increase with number of cycles. [15]
15
𝑁𝑓 − 𝑁𝑖 =∆𝜎−𝑚
Β𝑚𝐶(√𝜋)𝑚
(1 −𝑚2
)𝑎
𝑓
(1−𝑚2
)[1 − (
𝑎𝑖
𝑎𝑓
)
(1−𝑚2
)
] (3.13)
where 𝛽 and 𝑚 are material constant, ∆𝜎 is the stress range, 𝑎𝑖 is the crack initial length and 𝑎𝑓
is the crack final length (when the structure fails).
Figure 3-9 – Different regions of the 𝝏𝒂 𝝏𝑵⁄ vs ∆𝑲 plot. [17]
The final stage of fatigue crack growth occurs when the crack-growth rate accelerates under the
influence of ductile tearing or cleavage and the crack grows to such size that failure can occur
at the next applied load cycle.
3.3 Concepts of Pipeline Mechanics
Pipelines must be able to withstand a variety of loads. However, buried pipelines are essentially
restrained elements, as the displacement of the pipe is restricted by the soil around it. [18]
Thus, for buried pipelines, the major stress is caused by the internal pressure and this hoop
stress is usually the major design consideration.
Typically for calculation purposes pipelines are considered to be in a bi-axial state called plane
stress. The active stresses considered are shown in Figure 3-10 .The hoop stress, 𝜎𝐻, acts
Figure 3-10 – Pipeline Stresses under Internal Pressure. [18]
16
around the circumference of the pipe and the longitudinal stress, 𝜎𝐿, is directed along the long
axis of the pipe. In general, there is a third stress, a shear stress, which could be acting on the
edges of the above unit section, but this is not normally significant and is usually neglected in
calculations of transmission pipelines. Pipelines with diameter to wall thickness ratios greater
than 20, typical of transmission pipelines, are considered “thin-walled” as the distribution of
normal stress perpendicular to the surface is essentially uniform throughout the wall thickness.
[15] For isotropic materials, the relationship between stress and strain under plane stress
conditions is expressed as:
(휀𝐻
휀𝐿) =
1
𝐸[
1 −𝜈−𝜈 1
] (𝜎𝐻
𝜎𝐿) (3.14)
The hoop stress is the normal stress on a longitudinal plane through the pipe centreline
resulting from internal forces resisting the gas pressure force, and it goes as:
𝜎𝐻 =𝑃𝐷
2𝑡 (3.15)
where 𝑃 is the internal pressure, 𝐷 the outer diameter of the pipe and 𝑡 the wall thickness of the
pipeline.
3.4 Developments of high strength steels for pipelines
In order to improve transportation capacity, the demand for large diameter pipes lead to
fabrication of steels with higher strength accompanied with sufficient toughness and ductility,
even when operating in harsh environments. High Strength Steels used in pipelines follow API
5L – Specifications for Line Pipe and they vary from API 5L Grade A25 to API 5L Grade X120.
They possess highly refined grain and high cleanliness and are characterized by the low
sulphur content and reduced amount of detrimental second phases such as oxides, inclusions
and pearlite.
Figure 3-11 - Evolution of line pipe steel grades. [20]
17
The determining factor responsible for mechanical property improvement for currently used high
strength steels relies in the Thermo Mechanical Controlled Processing (TMCP) routes followed
by accelerated cooling [20]. High strength steels are designed to provide better mechanical
properties and/or greater strain capacity to sustain imposed plastic deformation. In fact, higher
strength line pipe steels tend to have lower uniform elongation, resulting in a lower
deformability. This is obviously an opposite trend regarding to what is desired for high strength
pipelines. Also for strain-based design applications must have sufficient toughness and high
deformability as well as higher strain hardening. This means a lower yield to tensile ratio and a
higher uniform elongation [16]. The chemical composition of high strength steel may vary
depending on what mechanical property requirements are needed. Generally, they have
manganese content up to 2.0 wt% in combination with very low carbon content (< 0.10 wt% C)
and minor additions of alloying elements such as niobium, vanadium, titanium, molybdenum
and boron, allowing pressures till 20 𝑀𝑃𝑎. [20] The main function of the alloying additions is
strengthening of the ferrite through grain refinement, solid solution and precipitation hardening.
Solid solution hardening is closely related to the alloy element content, whilst precipitation
hardening and grain refinement depend on the interaction between chemical composition and
TMCP. Thus, each individual element coupled with the cooling rate will determine the type and
volume fraction of phases that will form in given steel processed under given conditions. Table
3-1 shows some properties of the different API 5L Steel Grades, normally used on pipelines.
Table 3-1 – Mechanical Properties for some API 5L Steel Grades. [21]
Steel Grade SMYS (MPa) SMTS (MPa) Yield to Tensile Ratio Elongation min. (%)
A 210 331 0.63 28
B 245 413 0.59 23
X42 290 413 0.70 23
X56 390 490 0.80 20
X70 485 570 0.85 17
X80 552 620 0.89 16
X100 690 760 0.91 14
From the table, it is possible to infer that the values of yield strength and tensile strength
increase as the steel grade increases, the minimum uniform elongation of the material is
reduced as the grade gets higher and the Yield to Tensile Ratio increases as the steel grade
increases, as well.
18
Chapter 4
Pressure Cycle Simulation
4.1 Introduction
In this chapter, different emission profiles to be injected to the network, according to a certain
value of nomination2, will be simulated. The aim is to have high amplitudes in order to evidence
a more pronounced pressure cycle, so creating a more favourable fatigue failure.
While companies do their best to estimate demand for NG, it is nearly impossible to predict the
exact quantity a given facility will consume. Pipelines and utilities require industrial companies
to utilize nomination and balancing programs to manage gas flow and minimize operational
imbalances. The concept of physical quantity of gas starts to take place.
The LNG Terminal operation is highly conditioned on the needs of the NG Portuguese system,
especially those conducted by the electricity market and LNG global market. This constraint has
not allowed a proper rationalization of distribution. Moreover, the low nominations, especially on
weekends, make the daily NG optimization profile difficult for the Dispatching Centre.
4.2 SIMONE Simulation
For the purpose of the study, two scenarios of nominations were chosen. The first one it is
expected to induce pressure cycle profiles with large amplitudes and the second with low
amplitudes. These two cases are trying to emulate the reality. The nomination values are
divided by days (as notice in
Table 4-1) and they are divided by hours, as shown in Figure 4-1.
Table 4-1 – Total LNG Terminal gas nominations for two scenario studies.
Periods Scenario 1 Scenario 2
Saturday (𝒎𝟑(𝒏)) 2 808 000 2 808 000
Sunday 𝒎𝟑(𝒏)) 3 918 000 3 918 000
Monday to Friday 𝒎𝟑(𝒏)) 12 240 000 5 180 000
There are considered only two entries of NG in the network, namely, through Campo Maior
(from Maghreb-Europe Gas Pipeline) and through the LNG Terminal. The other two entries
presented in section 2, through Valença do Minho and UGS, are not considered due to the fact
that Valença do Minho has a limited capacity and the flow rates are really low, and for
simplification purposes, there is no injection or withdraw from UGS.
2 A request for a physical quantity of gas under a specific purchase, sales or transportation agreement or
for all contracts at a specific point.
19
Figure 4-1 – Gas Flow during a week for the Scenario 1 (highest nomination) and 2 (lowest nomination).
It is observed above, that the biggest gas flow entry variations are through the LNG Terminal.
This situation happens due to the fact that the work has the goal to study the influence of the
gas flow variations in the trunckline closest to the Terminal (L12000). However, due to fix
contract capacities, other locations have to be taking in account, namely, Tapada (L4000),
Bidoeira (L2500) and Frielas (L1209). Also, these are considered the most mechanically
requested locations after Sines (L12000). The gas flow values are the inputs to the software
SIMONE 3 for simulating the pressure cycle profiles within the pipelines. The maximum
projected working pressure (84 bar) and the minimum pressure in every single distribution point
in the network (50 bar) were used as boundaries conditions. Moreover, a static initial state was
used in order to have the first iteration for the simulation to start. This is also beneficial because,
it allows for a better comparison between results and different nominations, i.e., it was set an
initial value for the send out pressure in the Terminal in order to create conditions where all
cases could be compared.
Figure 4-2 – Scenario 1: Pressure Cycle Profiles, during a week.
3 SIMONE (SIMulation and Optimization of Networks) is the Europe leading integrated standard software
package in simulating and optimizing gas flows in pipeline systems. It is developed by the SIMONE
Research Group with the collaboration and cooperation of German company LIWACOM
Informationstechnik GmbH. This software allows real-time functions and SCADA integration interface.
0,00E+00
2,00E+05
4,00E+05
6,00E+05
8,00E+05
1,00E+06
Sat
urd
ay (
00
:00
:00
) S
atu
rday
(0
3:0
0:0
0)
Sat
urd
ay (
06
:00
:00
) S
atu
rday
(0
9:0
0:0
0)
Sat
urd
ay (
12
:00
:00
) S
atu
rday
(1
5:0
0:0
0)
Sat
urd
ay (
18
:00
:00
) S
atu
rday
(2
1:0
0:0
0)
Su
nd
ay (
00
:00
:00
) S
un
day
(0
3:0
0:0
0)
Su
nd
ay (
06
:00
:00
) S
un
day
(0
9:0
0:0
0)
Su
nd
ay12
:00
:00
) S
un
day
(1
5:0
0:0
0)
Su
nd
ay (
18
:00
:00
) S
un
day
(2
1:0
0:0
0)
Mo
nday
(0
0:0
0:0
0)
Mo
nday
(0
3:0
0:0
0)
Mo
nday
(0
6:0
0:0
0)
Mo
nday
(0
9:0
0:0
0)
Mo
nday
(1
2:0
0:0
0)
Mo
nday
(1
5:0
0:0
0)
Mo
nday
(1
8:0
0:0
0)
Mo
nday
(2
1:0
0:0
0)
Tues
day
(0
0:0
0:0
0)
Tues
day
(0
3:0
0:0
0)
Tu
esd
ay (
06
:00
:00
) T
ues
day
(0
9:0
0:0
0)
Tu
esd
ay (
12
:00
:00
) T
ues
day
(1
5:0
0:0
0)
Tu
esd
ay (
18
:00
:00
) T
ues
day
(2
1:0
0:0
0)
Wed
nes
day
(0
0:0
0:0
0)
Wed
nes
day
(0
3:0
0:0
0)
Wed
nes
day
(0
6:0
0:0
0)
Wed
nes
day
(0
9:0
0:0
0)
Wed
nes
day
(1
2:0
0:0
0)
Wed
nes
day
(1
5:0
0:0
0)
Wed
nes
day
(1
8:0
0:0
0)
Wed
nes
day
(2
1:0
0:0
0)
Thru
sday
(0
0:0
0:0
0)
Th
rusd
ay (
03
:00
:00
) T
hru
sday
(0
6:0
0:0
0)
Th
rusd
ay (
09
:00
:00
) T
hru
sday
(1
2:0
0:0
0)
Th
rusd
ay (
15
:00
:00
) T
hru
sday
(1
8:0
0:0
0)
Th
rusd
ay (
21
:00
:00
) F
rid
ay (
00
:00
:00
) F
rid
ay (
03
:00
:00
) F
rid
ay (
06
:00
:00
) F
rid
ay (
09
:00
:00
) F
rid
ay (
12
:00
:00
) F
rid
ay (
15
:00
:00
) F
rid
ay (
18
:00
:00
) F
rid
ay (
21
:00
:00
)
Gas
Flo
w (m
3 (n))
Scenario 1 - LNG TerminalScenario 1 - Campo MaiorScneraio 2 - LNG TerminalScneraio 2 - Campo Maior
5,00
6,00
7,00
8,00
9,00
Sat
urd
ay (
00:0
0:0
0)
Sat
urd
ay (
03:0
0:0
0)
Sat
urd
ay (
06:0
0:0
0)
Sat
urd
ay (
09:0
0:0
0)
Sat
urd
ay (
12:0
0:0
0)
Sat
urd
ay (
15:0
0:0
0)
Sat
urd
ay (
18:0
0:0
0)
Sat
urd
ay (
21:0
0:0
0)
Sun
day
(00
:00:
00)
Sun
day
(03
:00:
00)
Sun
day
(0
6:00
:00
)
Sun
day
(09
:00:
00)
Sun
day
12:0
0:00
)
Sun
day
(15
:00:
00)
Sun
day
(18
:00:
00)
Sun
day
(21
:00:
00)
Mo
nday
(00
:00:
00)
Mo
nday
(03
:00:
00)
Mo
nday
(06
:00:
00)
Mo
nday
(09
:00:
00)
Mo
nday
(12
:00:
00)
Mo
nday
(15
:00:
00)
Mo
nday
(18
:00:
00)
Mo
nday
(21
:00:
00)
Tue
sday
(0
0:0
0:0
0)
Tue
sday
(0
3:0
0:0
0)
Tu
esd
ay (
06:
00:0
0)
Tu
esd
ay (
09:
00:0
0)
Tu
esd
ay (
12:0
0:00
)
Tu
esd
ay (
15:0
0:00
)
Tu
esd
ay (
18:0
0:00
)
Tu
esd
ay (
21:0
0:00
)
Wed
nes
day
(00
:00:
00)
Wed
nes
day
(03
:00:
00)
Wed
nes
day
(06
:00:
00)
Wed
nes
day
(09
:00:
00)
Wed
nes
day
(12
:00:
00)
Wed
nes
day
(15
:00:
00)
Wed
nes
day
(18
:00:
00)
Wed
nes
day
(21
:00:
00)
Thru
sday
(00
:00:
00)
Th
rusd
ay (
03:0
0:00
)
Th
rusd
ay (
06:0
0:00
)
Th
rusd
ay (
09:0
0:00
)
Th
rusd
ay (
12:0
0:00
)
Th
rusd
ay (
15:0
0:00
)
Th
rusd
ay (
18:0
0:00
)
Th
rusd
ay (
21:0
0:00
)
Fri
day
(0
0:00
:00)
Fri
day
(03
:00:
00)
Fri
day
(06
:00:
00)
Fri
day
(09
:00:
00)
Fri
day
(12
:00:
00)
Fri
day
(15
:00:
00)
Fri
day
(18
:00:
00)
Fri
day
(21
:00:
00)
Pre
sure
(M
Pa)
SINES TAPADA
BIDOEIRA FRIELAS
20
Figure 4-3 – Scenario 2: Pressure Cycle Profiles, during a week.
As expected, the highest variations are present in Sines for both scenarios. Also, these two
scenarios were compared with typical real life profiles. These profiles were chosen to cover all
behaviours that happen every day in the network. A small description of them is shown in Table
4-2 and the Gas Flow and Pressure Profile can be shown in Appendix II.
Table 4-2 – Description of real-time profiles.
Week Dates Nomination (GWh) Description
1 February 26
th to
March 4th, 2011
>100
This week reflects a time of high consumption
of NG, where the off take of the two main
entries was high, especially from the Terminal.
2
September 21st
to September
27th, 2013
70-80
This week is an example of a typical week
where the NG that is inputted in the network
comes from Campo Maior as the main entry
but the LNG market is also favourable for the
LNG Terminal off take.
3
March 22nd
to
March 28th,
2014
20-30
This week reflects the ‘actual’ situation of the
NGTN system. The consumption of the
network is low. Due to the fix contract capacity
from the Maghreb-Europe Pipeline, the NG
that comes through that entry almost can fulfil
all needs of the Market. The LNG Terminal is
running in low yield s and everything that it is
send off from it, it is consumed in Chaparral4.
4 Delivery points where several companies are located like Repsol YPF – Petrochemicals, E.D.P.Thermal
Power Plant, SELL – Gasoline Blending, Petrogal – Oil Refinery, and others.This delivery point is located 7
km from the LNG Terminal.
5,00
6,00
7,00
8,00
9,00
Sat
urd
ay (
00
:00
:00
)
Sat
urd
ay (
03
:00
:00
)
Sat
urd
ay (
06
:00
:00
)
Sat
urd
ay (
09
:00
:00
)
Sat
urd
ay (
12
:00
:00
)
Sat
urd
ay (
15
:00
:00
)
Sat
urd
ay (
18
:00
:00
)
Sat
urd
ay (
21
:00
:00
)
Su
nd
ay (
00
:00
:00
)
Su
nd
ay (
03
:00
:00
)
Su
nd
ay (
06
:00
:00
)
Su
nd
ay (
09
:00
:00
)
Su
nd
ay12
:00
:00
)
Su
nd
ay (
15
:00
:00
)
Su
nd
ay (
18
:00
:00
)
Su
nd
ay (
21
:00
:00
)
Mo
nday
(0
0:0
0:0
0)
Mo
nday
(0
3:0
0:0
0)
Mo
nday
(0
6:0
0:0
0)
Mo
nday
(0
9:0
0:0
0)
Mo
nday
(1
2:0
0:0
0)
Mo
nday
(1
5:0
0:0
0)
Mo
nday
(1
8:0
0:0
0)
Mo
nday
(2
1:0
0:0
0)
Tues
day
(0
0:0
0:0
0)
Tues
day
(0
3:0
0:0
0)
Tu
esd
ay (
06
:00
:00
)
Tu
esd
ay (
09
:00
:00
)
Tu
esd
ay (
12
:00
:00
)
Tu
esd
ay (
15
:00
:00
)
Tu
esd
ay (
18
:00
:00
)
Tu
esd
ay (
21
:00
:00
)
Wed
nes
day
(0
0:0
0:0
0)
Wed
nes
day
(0
3:0
0:0
0)
Wed
nes
day
(0
6:0
0:0
0)
Wed
nes
day
(0
9:0
0:0
0)
Wed
nes
day
(1
2:0
0:0
0)
Wed
nes
day
(1
5:0
0:0
0)
Wed
nes
day
(1
8:0
0:0
0)
Wed
nes
day
(2
1:0
0:0
0)
Thru
sday
(0
0:0
0:0
0)
Th
rusd
ay (
03
:00
:00
)
Th
rusd
ay (
06
:00
:00
)
Th
rusd
ay (
09
:00
:00
)
Th
rusd
ay (
12
:00
:00
)
Th
rusd
ay (
15
:00
:00
)
Th
rusd
ay (
18
:00
:00
)
Th
rusd
ay (
21
:00
:00
)
Fri
day
(0
0:0
0:0
0)
Fri
day
(0
3:0
0:0
0)
Fri
day
(0
6:0
0:0
0)
Fri
day
(0
9:0
0:0
0)
Fri
day
(1
2:0
0:0
0)
Fri
day
(1
5:0
0:0
0)
Fri
day
(1
8:0
0:0
0)
Fri
day
(2
1:0
0:0
0)
Pre
sure
(M
Pa)
SINES TAPADA BIDOEIRA FRIELAS
21
Even the more aggressive scenario (Week 1 - February 26th to March 4
th, 2011) has lower
pressure range amplitudes than the scenario 1. For this reason, and because the goal of the
study is to try to make an assessment of the worst case possible that could happen to the
pipeline, the scenario 1 is going to be chosen for doing the fatigue testing, integrity assessment
and for modelling the crack propagation, as the worst case scenario that can happen. This can
be observed in Figure 4-4 and Figure 4-5.
Figure 4-4 –Pressure Range for: (a) Scenario 1 (b) Scenario 2.
Figure 4-5 –Pressure Range for real-time profiles.
0
5
10
15
20
Nu
mb
er
of
Cyc
les
pe
r w
ee
k
Pressure Range (MPa)
2500.PI002 4000.PI002
1209.PI102 12800.PI002
0
5
10
15
20
Nu
mb
er
of
Cyc
les
pe
r w
ee
k
Pressure Range (MPa)
2500.PI002
4000.PI002
1209.PI102
12800.PI002
(a) (b)
0
5
10
15
20
0<ΔP<5 5<ΔP<10
Nu
mb
er
of
Cyc
les
Pressure Range (bar)
BIDOEIRA2500.PI002
TAPADA 4000.PI002
SINES 12800.PI002
FRIELAS 1209.PI102
0
5
10
15
20
0<ΔP<5 5<ΔP<10 10<ΔP<15
Nu
mb
er
of
Cyc
les
Pressure Range (bar)
BIDOEIRA 2500.PI002
TAPADA 4000.PI002
SINES 12800.PI002
FRIELAS 1209.PI102
0
5
10
15
20
Nu
mb
er
of
Cyc
les
Pressure Range (bar)
BIDOEIRA 2500.PI002
TAPADA 4000.PI002
SINES 12800.PI002
FRIELAS 1209.PI102
(a)
(b)
(c)
Legend:
(a) March 22nd
to March 28th, 2014
(b) September 21st to September 27
th,
2013
(c) February 26th to March 4
th, 2011
22
4.3 Conclusions
Nowadays, the fix capacity contract with the Algerian supplier is almost enough to supply the
NGTN. However, as the economy increases (as expected), the need for more NG to be injected
to the network is going to happen. In this situation, a flexible LNT Terminal is the answer to fulfil
all distribution points at a lower rate, than the one of the fix contract. For the organization, an
optimized profile emission leading to a more energy efficient process, aiming for energy
reduction in both cost and environmental is essential. These profiles would reflect high
amplitudes each cycle, therefore, subjecting the pipeline to a higher exposure of fatigue, as
these fluctuations would vary the hoop stress level in the pipeline. The LNG Terminal has
several equipment that can rationally use, as they can follow a rotation program within the
company. This leads not only for promoting a system operation at maximum efficiency but also
for avoiding successive starts and stops from the equipment, is the focal point for the adequacy
of periods of higher flow rate emission of NG for the NGTN. Two nomination scenarios were
considered to create pressure cycle profiles within the pipe. Scenario 1 proposed the highest
amplitudes of both. The results obtained were focused on Sines and the line L12000 due to the
fact that it is the closest to the Terminal, so it would be the most mechanically request point in
the network. These scenarios allowed to understand that it would be possible to save power
and cost by day using optimized emission profiles, by sending out the maximum gas flow during
the times of the day that the electricity tariffs are lower and using minimum injection rates,
during the times when the electricity tariffs are higher. For the LNG Terminal, it would
correspond on a cost saving per year of 5-10% in operating expenditure (OPEX).
23
Chapter 5
Experimental Testing and Results
5.1 Introduction
This chapter describes the laboratory activities carried out to mechanically characterize and to
determine the fatigue resistance characteristics of the material. The experimental results will be
used in modelling and in the applied integrity assessment methods, in order to determine the
integrity of a pipeline in the presence of pressure cycle induced fatigue.
Test specimens were cut from an 28 inch (711.1 millimetres) steel pipe, 12.9 millimetres thick.
This component had already been in-service in trunkline L03000 close to Monforte, Portugal
and it is made of API 5L grade X70 steel from EUROPIPE (Certificate can be observed in
Appendix III). In order to obtain specimens for all experimental activities, the component went
through the following steps, as represented in Figure 5-1:
1. Removing the high density polyethylene (HDPE) coating from the outside;
2. Remove the sprayed epoxy resin from the inside;
3. Flattening the surface;
4. Extract specimens for the different experiments.
Figure 5-1 – Steps to obtain specimens. [22] [23]
5.2 Mechanical characterization
Due to the dimensions and geometry of the piece, it was difficult to extract cylindrical
specimens. So, flat specimens were obtained instead. These specimens were extracted from
two different directions of the piece and their dimensions are shown in Table 5-1. Tensile testing
was carried out in the laboratories of the Escola Superior de Tecnologia of the Instituto
Politécnico de Setubal. An Instron 1432 machine, with a load cell of 100 𝑘𝑁 and with a
crosshead speed of 0.20 𝑚𝑚/𝑚𝑖𝑛 was used. The elongation was measured by the means of a
24
extensometer that was connected to the specimen. No standard was followed in order to do this
test.
Table 5-1 – Specimen Dimensions for Tensile Testing.
Thickness (mm) Width (mm) Height (mm)
Longitudional 5.20 15.18 50.00
Radial / Transverse 4.77 15.04 50.00
Raw experimental data were extracted to an excel sheet in order to be analysed. Stress-strain
curves, obtained from the recorded data, are shown in Figure 5-2.
Figure 5-2 – Stress-strain curve: a) Longitudinal Direction; b) Radial/Transverse direction.
Table 5-2 resumes the important stress and strain experimental data points and ratios. The
standard API 5L – Specification for Line Pipe, define minimum values for mechanical resistance
for different steel grades, in the rolling direction. For the API 5L Grade X70 steel, the standard
define a specified minimum yield strength (SMYS) of 485 𝑀𝑃𝑎 and a tensile strength (SMTS)
of 570 𝑀𝑃𝑎, as seen in Table 3-1.
Table 5-2 – Results obtained from the tensile testing.
Properties Direction
Longitudinal Radial / Transverse
Young’s Modulus (GPa) 207 207
Yield Strength (MPa) 513 551
Ultimate Tensile Strength (MPa) 582 676
Yield-to-Tensile Ratio 0.88 0.84
Uniform Elongation (%) 7.00 8.51
0
100
200
300
400
500
600
700
0 0,1 0,2 0,3
Stre
ss (
MP
a)
Strain
EngineeringCurve
True Curve
0
100
200
300
400
500
600
700
800
0 0,1 0,2 0,3
Stre
ss (
MP
a)
Strain
EngineeringCurve
True Curve
a) b)
25
The results obtained are in accordance with the standard API 5 L and with the certificate of the
pipe. It can be also perceived that in the radial / transverse direction, the values are higher than
the longitudinal direction. This difference occurs due to the fact that the radial direction is the
rolling direction when the steel plates are being fabricated, and the process induces strength
mechanisms in the steel, making the results in this direction higher than the longitudinal
direction.
5.3 Fatigue characterization
For fatigue characterization, compact specimen were used (Figure 5-3) and their dimensions
are shown in Figure 5-3 – Schematically representation of the compact specimen.
Table 5-3. The standard ASTM E647 – Measure of Fatigue Crack Growth Rates was followed
for carrying out the tests.
Figure 5-3 – Schematically representation of the compact specimen. [24]
Table 5-3 – Specimen Dimensions for Fatigue Crack Growth Testing.
Dimensions Specimen 1 Specimen 2 Specimen 3
W (mm) 32.29 32.09 32.13
B (mm) 8.24 8.27 8.28
A camera was attached to the Universal Testing Machine (Instom 1432) in order to record crack
propagation and a frequency of 12 𝐻𝑧. Pictures were treated after in order to infer the fatigue
crack growth rate with the increase of the number of cycles. The results for specimen 3 are not
presented due to the fact that they were not valid according to the Standard. The results are
presented in Figure 5-5, Figure 5-6 and in Table 5-4.
26
Figure 5-4 – Detail of the camera attached to the machine (Left). Crack propagation (Right).
Figure 5-5 – Crack length vs. Number of cycles.
Figure 5-6 – Fatigue crack growth rate: a) Specimen 1; b) Specimen 2.
Table 5-4 resumes the most important results of the tests. The surfaces of the cracked
specimens were observed on a stereoscope. The specimens fail for over 55 000 cycles. The
values of the threshold of the stress intensity factor, which determinates whether a crack is able
to propagate, are a fairly high value. However, once the amplitude of the applied load is larger
than the threshold value, the crack grows at an extremely fast rate, imposing a great threat to
the pipeline integrity. Details of the resulting surface failure are shown on Figure 5-7.
0,009
0,012
0,015
0,018
0,00E+00 1,50E+04 3,00E+04 4,50E+04 6,00E+04
Cra
ck le
ngt
h (
m)
Number of cycles
Specimen 1 Specimen 2
a b
c
)
d
)
1,00E-08
1,00E-07
1,00E-06
1,00E-05
15 20 25 30
∂a/∂
N (
m/c
ycle
)
ΔK (MPa∙m1/2)
1,00E-08
1,00E-07
1,00E-06
1,00E-05
15 20 25 30
∂a/∂
N (
m/c
ycle
)
ΔK (MPa∙m1/2) a) b)
27
Table 5-4 – Fatigue Crack Propagation Test results.
Specimen Material
parameter, 𝑪
Material
parameter, 𝒎
Number of
cycles to fail ∆𝑲𝒕𝒉 (𝑴𝑷𝒂)
𝟏 4 × 10−13 3.94 63161 21.92
𝟐 4 × 10−12 3.28 55800 19.52
Figure 5-7 – Details from the specimen after the fatigue failure.
It is noticeable three main regions, crack initiation (stage I), fatigue crack propagation (stage II)
and then an area where the final fracture occurs (stage III).
Figure 5-8 – Stages I and II of fatigue crack propagation. [25]
Crack Initiation
Fatigue Crack
Propagation
Fast Fracture
28
In the first region, the fatigue crack propagates along high shear stress planes (45 degrees), as
it can be seen schematically in Figure 5-8, as the crack propagates until it is decelerated by a
microstructural barrier such as grain boundaries, which cannot accommodate the initial crack
growth direction. This kind of steel has a lot of microstructural barriers due to grain refinement in
the TMCP. The smooth region observed in Figure 5-7 is the region where stage II takes place
(region where Paris Law is acceptable), as the crack propagation develops in a more linear
way. This situation happens when 𝐾 increases as a consequence of crack growth and slips
starts to develop in different planes close to the crack tip. While it is noticeable that stage I is
orientated 45 degrees in relation to the applied load, propagation in stage II is perpendicular to
the load direction. Because it was not possible to use a scanning electron microscope, it was
not possible to see the presence of surfaces ripples (striations). Their formation is due to
successive blunting and re-sharpening of the crack tip. Finally, when observing Figure 5-7 it is
possible to see a region of total unstable crack growth as 𝐾 approaches 𝐾𝐼𝐶 . The “beach marks”
can be seen, as well, as a result of successive arrests or decrease in the rate of fatigue crack
growth due to a temporary load drop, or due to an overload that introduces a compressive e
residual stresses field ahead of the crack tip. The final fracture presents a fibrous and irregular
aspect, as the fracture, in this case, is ductile.
5.4 Conclusions
The results obtained in the tensile test shows that the pipe fulfils the minimum requirements of
the API 5L Standard, as both yield and tensile strength are higher than the minimum specified
values. As far as the fatigue tests are concerned, the specimens fail for over 55 000 cycles. The values
of the threshold of the stress intensity factor, which determinates whether a crack is able to
propagate, are a fairly high value. However, once the amplitude of the applied load is larger
than the threshold value, the crack grows at an extremely fast rate, imposing a great threat to
the pipeline integrity. The Paris’s law parameters obtained compared with other works are
slightly higher. [22] This behaviour might be explained by the high frequency used during the
tests.
29
Chapter 6
Numerical Modelling
6.1 Introduction
This chapter has the goal to represent models in finite element commercial software of a
pipeline with a crack, in order to evaluate 𝐾 and 𝐽 parameters to be used on integrity
assessment and to validate the experimental results, as well. The FEA is widely recognize as a
good tool to solve fracture mechanics problems and the usage of Abaqus/CAE5 as a finite
element analysis software is due to the fact that it allows the implementation of XFEM for
evaluating fracture mechanics parameters.
6.1.1 The Finite Element Method
Consider the domain Ω in Figure 6-1. The domain is bounded by the boundary Λ that consists of
four sets; Λ𝑡 with a prescribed traction 𝑡̅, Λ𝑢 with prescribed displacements and two traction-free
crack surfaces 𝐴𝑐+ and 𝐴𝑐
− [26].
Figure 6-1 – A body with a crack with a fixed boundary subjected to a load. [10]
The equilibrium equations and boundary conditions are (for contact-free crack surfaces) [27]:
∇ ∙ 𝜎 + 𝑏 = 0 in Ω (6.1)
𝜎 ∙ 𝑛 = 𝑡̅ on Λ𝑡 (6.2)
𝜎 ∙ 𝑛 = 0 on 𝐴𝑐+ (6.3)
𝜎 ∙ 𝑛 = 0 on 𝐴𝑐− (6.4)
𝑢 = 𝑢𝑝𝑟𝑒𝑠𝑠 on Λ𝑢 (6.5)
5 SIMULIA Abaqus FEA (formely ABAQUS) is a software suite for finite element analysis and computer-
aided engineering, from Dassault Systemes. There are five core products on Abaqus product suite,
Abaqus/CAE, Abaqus/Standard, Abaqus/Explicit, Abaqus/CFD and Abaqus/Electromagnetic. Abaqus/CAE
or Complete Abaqus Envirnment, is used to model and analysis of mechanical components and pre-
processing assemblies and visualizing the finite element analysis result.
30
And the corresponding weak form 6is
∫ 𝜎: (∇𝛿𝜈)Ω
= ∫ 𝑡̅Λ𝑡
∙ 𝛿𝜈𝑑Γ + ∫ 𝑏 ∙ 𝛿𝜈𝑑ΩΛ
(6.6)
which holds for arbitrary test functions 𝛿𝜈. Although the weak formulation has always the same
form, the element quality 7depends on the constitutive relations, as well of the selected shape
forms. Respecting the elasticity theory, tension obeys:
[ 𝜎𝑥𝑥𝜎𝑦𝑦
𝜎𝑧𝑧
𝜎𝑥𝑦
𝜎𝑥𝑧
𝜎𝑦𝑧]
= 𝐷
[ 휀𝑥𝑥휀𝑦𝑦
휀𝑧𝑧
2휀𝑥𝑦
2휀𝑥𝑧
2휀𝑦𝑧]
(6.7)
Being 𝐷 given by
𝐷 =𝐸(1 − 𝜈)
(1 + 𝜈)(1 − 𝜈)
)1(2
2100000
0)1(2
210000
00)1(2
21000
000111
0001
11
00011
1
(6.8)
Where 𝜎𝑖𝑗 and 휀𝑖𝑗 are the tension and strain components. In the finite elemento method, the
actual continuum or body of solid is represented by an assemblage of subdivisions called
elements. These elements are regarded as interconnected at specified joints called nodes or
nodal points. The nodes are usually placed on the boundaries where adjacent elements are
considered to be connected. It is necessary to assume that the variation of field variable inside
a finite element can be approximated by a simple function because the actual variation of the
field variable, such as displacement, stress, pressure or velocity, inside a continuum is not
known. These approximated functions, which are also called interpolation models, are
characterized as the values of the field variables at the nodes. When field equations, such as
6 A week form states the condition that the solution must satisfy in an integral sense, wherea a strong form
of the governing equations along with boundary conditions states the conditions at every point over a
domain that a solution must satisfy.
7 Element quality is always relative, as the local parametric coordinate system is assumed for each
element type and how well physical coordinate systems, both element and global, match the parametric
dictates element quality.
31
equilibrium equations, for the whole continuum are created, the new unknowns become the
nodal values of the field variables. However, the nodal values of the field variable can become
known values by solving the field equations, which are generally composed of matrix equations.
Once these are known, the field variable throughout the assemblage of elements is clarified by
the approximated functions. This orderly step-by-step process is always followed for the solution
of a general continuum problem in the same manner as in Abaqus/CAE [27].
Although FEM can be used to compute fracture mechanics parameters such as K and the J-
integral, it is currently not possible to directly carry out automatic crack growth simulation in
finite element software such as Abaqus/CAE [8]. The region around the crack front has to be
continuously re-meshed and a ring of rosette-like elements has to be constructed around the
crack tip in order to compute J-integral and to predict the crack propagation angle. Automatic
crack propagation is only available under certain conditions for finite element software where
crack propagation path is pre-defined. The extended finite element method surpasses
disadvantages associated with the meshing of crack surfaces existing FEM.
6.1.2 XFEM framework
The extended finite element method is an extension of the conventional finite element method
based on the concept of partition of unity [26], i.e. the sum of the shape functions must be unity.
It was developed by Ted Belytschko and collaborators in 1999. Using the partition of unity
concept, XFEM adds a priori knowledge about the solution in the finite element space and
makes it possible to model discontinuities and singularities independently of the mesh. This
makes it a very attractive method to simulate crack propagation since it is not necessary to
update the mesh to match the current geometry of the discontinuity and the crack can
propagate in a solution-dependent path. In XFEM, enrichment functions connected to additional
degrees of freedom are added to the finite element approximation in the region where the crack
is located in the mesh to include the discontinuities and singularities. These enrichment
functions consist of the asymptotic crack tip functions that capture the singularity at the crack tip
and a discontinuous function that represent the gap between the crack surfaces [28].
To explain how the discontinuous functions are added to the FE approximation, a simple two-
dimensional crack is illustrated [20]. Consider the case of a crack in a mesh with four elements,
where the crack is placed on the element boundary, seen in Figure 6-2. The finite element
approximation for the mesh is
𝑢ℎ(𝑥) = ∑ 𝜙𝑖(𝑥)𝑢𝑖
10
𝑖=1
(6.9)
where 𝜙𝑖 is the shape function for node 𝑖, 𝑢𝑖 is the displacement vector at node 𝑖 and 𝑥 is the
position vector. Define 𝑘 and 𝑙 as
𝑘 =
𝑢9 + 𝑢10
2, 𝑙 =
𝑢9 − 𝑢10
2
(6.10)
32
i.e. 𝑘 lie in between 𝑢9 and 𝑢10 and 𝑙 is half the distance between 𝑢9 and 𝑢10.
Figure 6-2 – (a) Mesh with a crack. (b) Mesh without a crack. The circle numbers are the element numbers. [29]
Now, 𝑢9 and 𝑢10 can be expressed in terms of 𝑘 and 𝑙 as
𝑢9 = 𝑘 + 𝑙, 𝑢10 = 𝑘 − 𝑙 (6.11)
Adding these expressions into equation (6.9) yields
𝑢ℎ(𝑥) = ∑ 𝜙𝑖𝑢𝑖 + 𝑘(𝜙9 + 𝜙10) + 𝑙
8
𝑖=1
(𝜙9 + 𝜙10)𝐻(𝑥) (6.12)
where the discontinuous sign/jump function 𝐻(𝑥) is introduced as
𝐻(𝑥) = {1, 𝑥 > 0
−1, 𝑥 < 0
(6.13)
Now, 𝜙9 + 𝜙10 can be replaced by 𝜙11 and 𝑘 by 𝑢11 and the finite element approximation can be
expressed as
𝑢ℎ(𝑥) = ∑ 𝜙𝑖(𝑥)𝑢𝑖 + 𝜙11𝑢11
8
𝑖=1
+ 𝑙𝜙11𝐻(𝑥) (6.14)
The first two parts on the right-hand side are the standard finite element approximation, and the
third part is the additional discontinuous jump enrichment. Equation (6.14) shows that the finite
element approximation of a crack in a mesh, as in Figure 6-2, may be interpreted as a mesh
without a crack and an additional discontinuous enrichment.
Discontinuous asymptotic crack tip functions are added to the nodes that surround the crack tip
[26], as illustrated in Figure 6-3 to capture the singularity. If the tip does not end at an element
boundary, the crack tip functions also describe the discontinuity over the crack surfaces in the
element containing the crack tip. Thus, in total, there are two types of enrichments, the
asymptotic crack tip functions to describe the crack tip and the jump function to describe the
rest of the crack. The nodes are enriched with the jump function when their supports are fully
intersected by a crack whereas the element nodes surrounding the crack tip are enriched with
the crack tip functions. The circled nodes are enriched with the jump function and the squared
ones are enriched with the crack tip functions.
33
Figure 6-3 – (a) An arbitrary crack in a mesh. (b) Local coordinate axes for two crack tips. [27]
The total formulation of XFEM can now be derived. Let all the nodes in the mesh be defined by
the set 𝑆, the nodes surrounding the crack tip by the set 𝑆𝑐 and the nodes whose supports are
cut by the crack (excluding the nodes in 𝑆𝑐) be defined by 𝑆ℎ. The finite element approximation
now reads
𝑢ℎ(𝑥) = ∑ 𝜙𝐼(𝑥)
𝐼∈𝑆
[𝑢𝐼 + 𝐻(𝑥)𝑎𝐼 + ∑𝜓𝑖(𝑥)𝑏𝐼𝑖
4
𝑖=1
] (6.15)
where 𝑢𝐼 is the nodal displacement vector, the 𝑎𝐼 nodal enriched degree of freedom vector that
with the jump function 𝐻(𝑥) represent the gap between the crack surfaces and 𝑏𝐼𝑖 the nodal
enriched degree of freedom vector that with the crack tip functions 𝜓𝑖(𝑥) represent the crack tip
singularity.
6.1.2.1 Crack growth propagation
Various criteria have been proposed to predict the angle at which a crack will propagate, which
include the maximum tangential stress criterion, the maximum principal stress criterion, the
maximum energy release rate criterion, the minimum elastic energy density criterion and T-
criterion [30]. The crack propagation angles predicted by these criteria are slightly different but
all have the implication that 𝐾𝐼𝐼 = 0 at the crack tip as the crack extends. The maximum
tangential stress criterion is chosen for the current study due to be one of the most criterions
used on XFEM studies [27]. The stress field around the crack tip of a homogeneous, isotropic
linear elastic material can be expressed as:
𝜎𝜃𝜃 =
1
√2𝜋𝑟𝑐𝑜𝑠
1
2𝜃 (𝐾𝐼𝑐𝑜𝑠2
1
2𝜃 −
3
2𝐾𝐼𝐼𝑠𝑖𝑛𝜃)
(6.17)
where 𝜃 and 𝑟 are polar coordinates centered at the crack tip in the plane orthogonal to the
crack front. The crack propagation direction can be obtained using the condition 𝜕𝜎𝜃𝜃
𝜕𝜃= 0:
𝜃 = 𝑐𝑜𝑠−1 (
3𝐾𝐼𝐼2 + √𝐾𝐼
4 + 8𝐾𝐼2𝐾𝐼𝐼
2
𝐾𝐼2 + 9𝐾𝐼𝐼
2 ) (6.17)
34
Where the crack propagation angle is measured with respect to the crack plane and 𝜃 = 0
represents the crack propagation in the ‘straight-ahead’ direction.
6.1.2.2 Crack growth magnitude
Two common approaches have been used when modeling quasi-static crack growth within the
XFEM framework. The first approach is to assume a constant crack growth increment [26] and
simply update the crack geometry in a constant manner. The crack growth increment commonly
used in literature is 0.1. The second option is to use an external criteria to predict the increment
of crack growth. Paris Law [16] is used in our case where we can find the increment of crack
growth to take the form given below where C is the Paris Law constant, m is the Paris Law
exponent, N is the number of elapsed cycles. The mixed mode correction for Paris Law [31]
takes the form:
Δ𝑎 = 𝐶𝑁 (√𝐾𝐼
4 + 8𝐾𝐼𝐼24)
𝑚
(6.17)
6.2 Models and Results
6.2.1 𝑲 and 𝑱 Estimation Values
In order to obtain mechanical properties to ensure that the laboratory results and the integrity
assessments procedures are similar, two scenarios were modelled with Abaqus/CAE. In first
one the defect is placed prependicular to the direction of the pipe. So the longitudional stresses
are the most critical stresses. In the second scenario, the defect is placed along the direction of
the pipe, thus hoop stresses are the critical stresses.
Figure 6-4 – Scenario 1: (a) Schematic representation (b) ABAQUS® models (FEM-Contour Integral and XFEM)
𝑟
𝜎𝐿 𝜎𝐿
𝜎𝐿 2𝜋𝑟 𝜎𝐿
2𝑎
𝑊
XFEM Model
FEM Model
(a) (b)
35
Figure 6-5 – Scenario 2: (a) Schematic representation (b) ABAQUS® models (FEM-Contour Integral and XFEM)
In scenario 1 (Figure 6-4), the pipeline can be aproximated to a single edge notched tensile
plate (SENT), in order to be exported to Abaqus/CAE models and in scenario 2 (Figure 6-5), to
a center-cracked tensile plate (CCT) – Scenario 2 (Figure 6-5).
The numerical calculation of 𝐽 and 𝐾 (Mode I) was carried out. The results were obtained using
XFEM and Contour Integral techniques. For both cases, the numbers of contours were 5. This
parameter controls the number of element rings around the crack tip that construct the contour
domains for the contour integral calculation. The contour integral calculation is the most
important aspect in stationary crack analysis since it gives the measure to assess critical crack
size.
Figure 6-6 – Single Edge Notched Testing simulated with: (a) FEM (b) XFEM.
The stress intensity factors in Abaqus/CAE are calculated along the crack front for a finite
number of positions, so called contour integral evaluation points. These points are chosen
XFEM Model
(a) (b)
𝜎𝐻
𝜎𝐻 𝑟
𝜎𝐻
2𝜋𝑟
𝜎𝐻
2𝑎
𝑊
FEM Model
(b
(a)
36
automatically by Abaqus/CAE where the crack front intersects the element boundaries. Several
contour integral calculations are performed at each evaluation point for all specified element
rings. The elements surrounding the crack tip element constitute the first partial contour domain.
The next partial contour domain contains the first domain and the next element ring directly
connected to the first contour domain. Each subsequent contour domain is built up by adding
the next element ring to the previous contour domain. Theoretically, the contour integral
calculation is independent of the size of the contour domain as long as the crack faces are
parallel. But, because of the approximation with a finite element solution, K and J for the
different element rings will vary and should converge as the domain is increased. Therefore the
first element ring was discarded in the analyses because of their large deviation. The results
can be observed below, for example, for a crack depth of 𝑎 = 2𝑚𝑚.
Figure 6-7 – Scenario 1: 𝑲 and 𝑱 parameters as a function of the Load. Values are for 𝒂 = 𝟐𝒎𝒎.
Figure 6-8 – Scenario 1: 𝑲 and 𝑱 parameters as a function of the crack length. Values are for P= 𝟏𝟓𝟎 𝑴𝑷𝒂.
Figure 6-9 shows the crack propagating through the model representing scenario 2 (CCT
simulation). The results can be observed in Figure 6-10. It is notice that the values obtained by
the second scenario are lower than those obtained for the first scenario (SENT simulation).
0,00E+00
5,00E+02
1,00E+03
1,50E+03
2,00E+03
2,50E+03
3,00E+03
0
5
10
15
20
25
30
35
40
45
0 50 100 150 200 250 300
J (k
Pa.
m)
KI (
MP
a.m
1/2
)
Load (MPa)
FEM (KI) XFEM (KI) Literature (KI)
FEM (J) XFEM (J)
0,00E+00
2,00E+04
4,00E+04
6,00E+04
8,00E+04
1,00E+05
1,20E+05
1,40E+05
1,60E+05
0
50
100
150
200
250
300
350
1 2 3 4 5
J (k
Pa.
m)
KI (
MP
a.m
1/2
)
Crack length (mm)
FEM (KI) XFEM (KI) Literature (KI)
FEM (J) XFEM (J)
37
Figure 6-9 – Center-cracked Tensile Plate simulated with XFEM.
Figure 6-10 – Scenario 2: 𝑲 and 𝑱 parameters as a function of the: (a) Load. (b) Crack Length. Values are for
𝒂 = 𝟐 𝒎𝒎 and for 𝑷 = 𝟏𝟓𝟎𝑴𝑷𝒂.
6.2.2 𝑱-Based Failure Assessment Diagram
From the values obtained, through Abaqus/CAE, an assessment based on 𝐽-integral will be
carried out, in order to know which ratios 𝑎/𝑊 put the structure in danger of failure, this is, how
long can a crack grow until the structure is in danger of failure/collapse. This assessment will be
done using values obtained by the SENT simulation. This choice reflects how the applied load is
risky for the structure and the values are higher when there is a crack placed on the edge,
which means, for the model proposed, cracks longitudinal to the applied load are far more risky
for a structure than those that the circumferential oriented. This observation is also confirmed
when doing the integrity assessment by the means of standards/recommended practices. The 𝐽-
0
1000
2000
3000
4000
5000
6000
0
10
20
30
40
50
60
70
80
90
100
1 2 3 4 5J
(kP
a.m
)
KI (
MP
a.m
1/2
)
Crack length (mm)
FEM (KI)
XFEM (KI)
Literature (KI)
FEM (J)
XFEM (J)
0
2000
4000
6000
8000
10000
0
10
20
30
40
50
60
70
80
0 100 200 300
J (k
Pa.
m)
KI (
MP
a.m
1/2
)
Load (MPa)
FEM (KI)
XFEM (KI)
Literature (KI)
FEM (J)
XFEM (J)
(a) (b)
38
based Failure Assessment Diagram can be started adjusting a curve to the results from the
Abaqus/CAE simulation. A quadratic curve fit is expected since 𝐽 is proportional to 𝐾 which is
linear in the elastic range. This situation can be observed in Figure 6-11. The elastic J trend is
computed using the curve-fit and compared to the several next 𝐽 curves to confirm that the
results are in the elastic range and that the curve-fit is valid. In a typical elastic-plastic analysis
without a crack, the initial load increments can be large since equilibrium convergence is
expected. However, for an elastic-plastic fracture analysis with a crack several small load
increments are needed at the beginning of the analysis to ensure that 𝐽 results will be in the
elastic range. The maximum load must be high enough to create yielding at the crack front,
which is usually a much higher than the operating or design load. The curve fit is used to
extrapolate and infer the elastic J trend for higher load increments (Figure 6-11).
Figure 6-11 – (a) Quadratic curve-fit to the J results in the elastic range. (b) Infer the elastic J trend using the
curve fit.
The nominal load value is obtained using the material specific FAD equation evaluated at 𝐿𝑟 =
1. When the material specific FAD curve equation is evaluated at 𝐿𝑟 = 1, it takes this form given
by:
𝐽𝑡𝑜𝑡𝑎𝑙
𝐽𝑒𝑙𝑎𝑠𝑡𝑖𝑐
|𝐿𝑟=1
= 1 +0.002𝐸
𝜎𝑦
+0.5
1 +0.002𝐸
𝜎𝑦
(7.26)
Figure 6-12 – Finding the intersection of the Jtotal/Jelastic ratio and the result curve.
y = 0,0286x2 R² = 1
0
1000
2000
3000
0 100 200 300
J (k
Pa.
m)
Load (MPa)
Curve fit
Computed J
0
10
20
30
40
50
60
70
80
0 200 400 600 800 1000
J (M
Pa.
m)
Load (MPa)
J totalJ elastic
(a) (b)
0
0,5
1
1,5
2
2,5
0 200 400 600 800 1000
Jto
tal/J
ela
sti
c
Load (MPa)
Material Specific Value = 2.04
𝜎𝑛𝑜𝑚𝑖𝑛𝑎𝑙 = 930.8 MPa
39
The reference stress geometric factor, F, is defined as the ratio of the yield strength to the
nominal stress obtained at 𝐿𝑟 = 1.
F =𝜎𝑦
𝜎𝑛𝑜𝑚𝑖𝑛𝑎𝑙|𝐿𝑟=1
(7.27)
The nominal load value is obtained from the intersection point in Figure 6-12 and it gives the
reference stress that satisfies the material specific FAD equation at 𝐿𝑟 = 1. The reference
stress and 𝐿𝑟 can be computed for analysis increment to obtain the analysis specific and
material specific values. The reference stress, at each load increment is given by:
𝜎𝑟𝑒𝑓 = F𝜎𝑖 (7.28)
The FAD curve is obtained by using:
L𝑟 =𝜎𝑟𝑒𝑓
𝜎𝑦
=F𝜎𝑖
𝜎𝑦
(7.29)
𝐾𝑟 = √𝐽𝑒𝑙𝑎𝑠𝑡𝑖𝑐
𝐽𝑡𝑜𝑡𝑎𝑙
(7.30)
Where 𝐽𝑡𝑜𝑡𝑎𝑙are the elastic-plastic analysis 𝐽 results, and the 𝐽𝑒𝑙𝑎𝑠𝑡𝑖𝑐values were obtained from
the curve-fit to the first few result increments in the elastic range. The maximum cutoff value is
given by:
𝐿𝑟𝑚𝑎𝑥 =
𝜎𝑦 + 𝜎𝑇
𝜎𝑦
(7.31)
The evaluation points are computed using the stress intensity from the elastic analysis and the
reference stress at the given load. 𝐿𝑟and 𝐾𝑟values are computed using the equations (7.2) and
(7.3). The J-based FAD can be shown below. The points are representative of the ratio 𝑎/𝑊,
which represents how much a structure is cracked.
Figure 6-13 – 𝑱-Based Failure Assessment Diagram.
0
0,4
0,8
1,2
1,6
0 0,2 0,4 0,6 0,8 1 1,2
Kr
Lr
a/W=17% a/W=33% a/W=50% a/W=67% a/W=83%
40
6.4 Conclusions
Fracture mechanics parameters, 𝐾 and 𝐽 values were obtained for two models, which tried to
emulate cracks in a structure that are parallel or perpendicular to the applied load. Two
techniques were used in order to obtain those values. Contour integral FEM is a technique well
accepted for fracture mechanics problems. However, in order to improve computational time
and to not be limited to the re-meshing of the model for each instance, XFEM was used as well.
It was noticeable that XFEM gives values for 𝐾 close to those obtained by contour integral FEM
or by the literature, in both SENT and CCT plates. However, comparing these representations,
the values are higher when there is a crack placed on the edge, which means, for the model
proposed, cracks longitudinal to the applied load are far more risky for a structure than those
that the circumferential oriented. This situation is also confirmed when integrity assessment is
done by the use of standards/ recommended practices. In terms of 𝐽 values, XFEM and contour
integral FEM values are in the same order of magnitude, although the second one as always
higher values than the first one. The same behaviour from the SENT and CCP plates is
observed when estimating 𝐽 as for K values. With those values, a J-based FAD was created to
predict the failure of a structure using the crack depth to thickness of the component ratio. Like
it was concluded and validated with the use of FFP practices, only ratio over 70% are suitable of
being in a “danger” zone. Note that mixed modes of failure were presented on the J-based
FAD.
41
Chapter 7
Integrity Assessment and Structural Reliability
7.1 Introduction
Pipelines have quality patterns that have to be ensured. However reception quality controls are
not enough to ensure the quality of the pipeline itself. During installation, mounting and
operation incidents can occur that originate defects. The goal of this chapter is to predict
wheatear the component must be repaired, replaced or remediate and to predict the remaining
life of the component, even with defects.
7.1.1 Empirical Methods
In 1960s, the Battelle Laboratories developed a failure criterion for crack like defects in thin-
walled pipelines, known as the NG18 equations. The failure stress (due to internal pressure)
takes the form of:
𝜎𝑓 = 𝜎 ∙1 −
𝑎𝑡
1 −𝑎𝑡(1𝑀
) (7.1)
where 𝜎 is the flow stress and 𝑀 is the Folias Factor. The flow stress is an empirical concept
that tries to represent, trough a single parameter, the strain hardening behaviour of an elastic-
plastic material. It is defined by:
𝜎 =𝜎𝑦 + 𝜎𝑢
2 (7.2)
The Folias Factor represents the stress concentration due to the formation of a perturberance in
the pipe wall in the bulging region, due to internal pressure and tries to quantify the
magnification of the stress at the crack tip.
Figure 7-1 – Failure Stress for cracked pipelines.
0
0,2
0,4
0,6
0,8
1
1,2
0 1 2 3 4 5 6 7 8 9 10
No
rmal
ize
d F
aillu
re S
tre
ss (𝜎𝑓/𝜎
)
Crack size (2c/(R∙t)1/2)
a/t=0.2 a/t=0.4 a/t=0.6 a/t=0.8
42
Figure 7-1 shows the normalized failure stress as a function of the normalized crack size, for
various ratio 𝑎/𝑡. This representation permits to evaluate allowed defects in the material in a
simply manner. Empirical methods are considered safes because they are based on
conservative premises. However their application to thin walled pipelines made of steels with
different yield to tensile ratios and in higher strength steels, like the X70, X85 or the X100, is
limited because experimental data is limited. Thus, propagation of cracks can occur due a
combination of plastic deformation and ductile failure and NG18 equations do not take that in
account.
7.1.2 Fitness-for-Purpose Approach for Integrity Assessment
Real scale fracture tests are extremely costly and difficult to carry out. Thus, small scaled
specimens are used, in laboratory to test fracture mechanics behaviour. This similarity of the
stress-strain field between the specimen and the real scale structure. This allows correlating
laboratory test results to cracked structures real conditions.
Figure 7-2 – Schematically comparison between fracture condition differences in two geometrical
configurations, representing the concept of transferability. [32]
Every testing standard to evaluate the fracture toughness of the material is elaborated to
provide a high degree of plastic constraint in the crack tip, in order to produce more
conservative values of toughness. Usually, thin wall tubular structures present a low level of
plastic constraint as the thin wall does not favour a plane strain state. Moreover, pressurized
tubes like pipelines are mainly subjected to bending momentums, which hampers the formation
of tri axel strain states. The struggle to transfer results from the laboratory to real scale
configurations is illustrated in Figure 7-3. This graph presents qualitatively the effect of plastic
constraint on the determined fracture toughness value for a specific geometrical configuration.
Thus, it is easy to understand that the failure behaviour of cracked structures depends heavily
on the shape and loading of the structure itself. To overcome these difficulties, the scientific
community, the industry and the regulatory organizations have joined efforts to develop
analytical methods and engineering procedures to assess the integrity of structures.
43
Figure 7-3 – Fracture Toughness on Geometric Shape relationship. [33]
Nowadays, it is consensus that every polycrystalline metallic structure contains defects, but
does not mean that they put the structure in risk of integrity [34]. The fitness-for-purpose
approach is based in fracture mechanics analysis and its objective is to evaluate the impact
caused by a defect in the performance of a certain structure [34]. A FPP approach presents a
tremendous economic potential. It is possible to define safe operation conditions and even
extend the structure’s life cycle. Natural gas, Petroleum and Nuclear industries motivated the
establishment of procedures for these approach. The most used are the BS7910 from British
Standard Institute [35], the API RP 579 from the American Petroleum Institute [17] and the R6
Procedure from the Nuclear Fuels & Co. from United Kingdom (former Central Electricity
Generating Board) [36]. None of these approaches embraces all evaluation techniques. In fact,
there is divergence in the results obtained by the different methods, as they use different
formulations. Even so, specific methods are used in specific areas. The R6 Procedure is used
more often in the electrical generation sector. The recommended practice API RP 579 is mostly
used in the chemical industry, and in the petroleum and gas industries the BS7910 approach is
the one most in focus.
7.1.2.1 Failure Assessment Diagram Method
Regions of safe and unsafe operation of the structure are defined in a 2D space. The vertical
axis is the toughness ratio, 𝐾𝑟, which is the ratio between the stress intensity factor applied and
the fracture toughness of the material (equation 7.3). The horizontal axis presents the stress
ratio, as the ratio between the applied stress and a reference stress (equation 7.4). When the
stress applied in equal to the reference stress, the structure starts to collapse plastically [36].
𝐾𝑟 =𝐾𝐼
𝐾𝐼𝐶
(7.3)
𝐿𝑟 =𝜎
𝜎𝑟𝑒𝑓
(7.4)
Two modes of failure are represented in this diagram; the vertical axis coincides with the total
fragile failure and the horizontal axis, with the likelihood of plastic collapse. In the transition
region between failure modes, there is a mixed elastic-plastic failure mode. The FAD appears
44
for the first time in the original R6 Procedure, as the interpolation curve for both mechanisms is
obtained by the strip yield model, purposed by Dugdale. This model proposes a solution for a
plain strain problem of a crack in an infinite plate with an elastic-plastic material subjected to
tensile stresses [36]. Considering the plasticity effect on the crack tip, an effective stress
intensity factor is defined as:
𝐾𝑒𝑓 = 𝜎𝑦√𝜋𝑎 [8
𝜋2ln 𝑠𝑒𝑐 (
𝜋𝜎
2𝜎𝑦
)]
−12⁄
(7.5)
For the model to be able to describe the failure of a structure while the stress applied
approaches its collapse stress, the yield strength must be replaced by the collapse stress in
equation 7.5. To obtain the FAD curve it is necessary to normalize the effective 𝐾 by the elastic
𝐾 (equation 7.6) and re-write equation 7.5 making its crack size independent, as observed in
equation 7.7.
𝐾𝐼 = 𝜎√𝜋𝑎 (7.6)
𝐾𝑒𝑓
𝐾𝐼
=𝜎𝑐
𝜎[8
𝜋2ln 𝑠𝑒𝑐 (
𝜋𝜎
2𝜎𝑐
)]
−12⁄
(7.7)
After simplifying the equation and resolve it for 𝐾𝑟 and 𝐿𝑟, the equation of the curve for the
diagram is:
𝐾𝑟 = 𝐿𝑟 [8
𝜋2ln 𝑠𝑒𝑐 (
𝜋𝐿𝑟
2)]
−12⁄
(7.8)
Figure 7-4 – FAD Diagram defining regions of safeness for the structure. [17]
Figure 7-4 shows a FAD proposed by the R6 procedure, defining regions of safe operation for a
structure. The evaluation procedure consists in determining the coordinates of a point (𝐿𝑟, 𝐾𝑟)
for the structure in study. Another advantage for using the FAD approach is the possibility to
evaluate the actual situation of the structure and to the locus of the failure, while the stress
applied or the defect present in the structure is increasing. This characteristic allows predicting
how far the failure has progressed and which is the dominant mode of failure or plastic
instability [36]. The conceptual simplicity of the FAD makes it useful and easy to apply.
However, the critical step is to obtain values for 𝐾𝑟 and 𝐿𝑟.Each procedure has its specific
formulation and the determination of some parameters is not trivial.
45
7.1.3 Structural Reliability
For structural reliability analysis assessment of a component failure, a deterministic description
is necessary. Instead, for statistical analysis is requires computing the Probability of Failure
(POF) from the scatter of the random input quantities. Probability Fracture Mechanics (PFM)
deals with the assessment of the reliability of structures containing crack-like defects in terms of
probabilities attributed to a certain failure event. It is well accepted that certain parameters
involved in fracture mechanics analysis are probabilistically distributed variables. Material
properties always exhibit scatter, crack sizes are statistical variables and loadings may also be
random [8]. Given the input variables 𝑥 = (𝑥1, 𝑥2, … , 𝑥𝑁) with defined Probability Density
Function (PDF), 𝑓(𝑥1)… 𝑓(𝑥𝑁), the POF is defined as:
P𝑓 = ∫ 𝑓𝑋1(𝑥1)
𝑔(𝑥1,…,𝑥𝑁≤0
⋯𝑓𝑋𝑁(𝑥𝑁)𝑑(𝑥1)⋯ 𝑑(𝑥𝑁) (7.9)
The failure function 𝑔(𝑥1, … , 𝑥𝑁) divides the domain of the variables into two parts:
{𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝐷𝑜𝑚𝑎𝑖𝑛 𝑔(𝑥1, … , 𝑥𝑁) ≤ 0
𝑆𝑎𝑓𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝑔(𝑥1, … , 𝑥𝑁) > 0
The integration has to be carried out over the failure domain 𝑔(𝑥1, … , 𝑥𝑁) ≤0. For simplicity,
variables are assumed to be stochastically independent for the POF calculation [37]. The failure
criterion is based on the Failure Assessment Diagram, whereas the limit state equation
𝑔(𝑥1, … , 𝑥𝑁) can be broken down into two separate functions, according to:
𝑔𝐹𝐴𝐷(𝑋) = (𝐾𝑟 − 𝜌)𝐾𝐼𝐶 − 𝐾𝐼 , &𝐿𝑟 ≤ 𝐿𝑟𝑚𝑎𝑥 (7.10)
𝑔𝐿𝑟𝑚𝑎𝑥(𝑋)𝐿𝑟
𝑚𝑎𝑥 − 𝐿𝑟 , &𝐿𝑟 > 𝐿𝑟𝑚𝑎𝑥 (7.11)
Most of the cases, the detection of defects in pipelines is carried out using intelligent pigs, as
part of the normal operation and maintenance program. During inspections, not all defects can
be identified due to the sensitivity of the equipment. The process of inspection and repair of a
pipeline at a given time interval will change the anticipated distribution of crack depths and
length because some of the detected cracks will be repaired. The exact distribution will depend
upon the repair strategy adopted, the frequency of inspection and the sensitivity of the pig. The
remaining cracks will not lead to failure but those missed by the inspection tool might cause gas
leakage of the pipeline. Probability of Detection (POD) is defined as:
P𝐷/𝑎 = 1 − 𝑒−𝜆𝑎 (7.12)
Hence, if the detectable depth of the pig follows the exponential distribution function, both the
average detectable size and the standard deviation equal to1/λ. Detected defects only represent
part of the overall defect population. The PDF of the undetected cracks is:
𝑓𝑈𝐷(𝑎) =
𝑃𝑁𝐷(𝑎)𝑓(𝑎)
∫ 𝑃𝑁𝐷(𝑎)𝑑𝑎∞
0
(7.13)
46
In the pipeline industry, it is customary to define the POF per kilometre length of pipeline [8].
The failure probability is valid for pipelines with exactly one crack of random size, as given in
equation 7.9. If there is more than one crack in the system and they are assumed to be
independent, the cumulative POF per km of pipe length can be obtained as:
P𝑓|𝑡𝑜𝑡𝑎𝑙 = 1 − (1 − 𝑃𝑓)𝑞 (7.14)
The actual number of cracks of flaws is normally unknown in advance. However, it can be
shown that the number of flaws per component is a Poisson-distributed random variable [19].
Therefore, the probability of having exactly 𝑞 cracks is given by:
P𝑞 =
𝑘𝑞
𝑞!𝑒𝑘
(7.15)
Thus, the cumulative POF per 𝑘𝑚 of pipe length for multiple cracks takes the form:
P𝑓|𝑡𝑜𝑡𝑎𝑙 = 1 − ∑𝑘𝑞
𝑞!𝑒𝑘(1 − 𝑃𝑓)
𝑞∞
𝑞=0
= 1 − 𝑒𝑘𝑃𝑓 ≈ 𝑘𝑃𝑓 (7.16)
The POF can be evaluated by numerical integration, the First Order/Second Order Reliability
Method (FORM/SORM), and by Monte-Carlo Simulation (MCS) [8]. The analytical method is
rarely used, as multi-dimensional integration becomes very difficult to solve if a system includes
more than three variables. The FORM/SORM is often used to account the uncertainty in limit
state models and it is widely used for evaluating 𝑃𝑓 in structure reliability analysis. Nevertheless,
when inspection programme of non-normal variables is involved, the predicted value becomes
unreliable and it is difficult to estimate the error. On the other hand, MCS is a simple and
reliable method for simulation of a complex system but it suffers from expensive computational
cost due to the large number of samples required when the POF is very low.
7.1.3.1 Analytical Method
If there are fewer than three variables, the analytical method may be used to calculate the POF.
By using numerical integration P𝑓 can be obtained. For example, if only crack length and crack
depth are modelled as random variables, equation (7.9) becomes:
P𝑓 = ∫ 𝑓(𝑎)𝑓(2𝑐)𝑔(𝑎,2𝑐)≤0
𝑑(𝑎)𝑑(2𝑐) (7.17)
Where 𝑓(𝑎), 𝑓(2𝑐) denote the PDF of the crack depth and the crack length, which are assumed
stochastically independent.
7.1.3.2 First/Second-Order Reliability Method
The FORM/SORM is a combination of both analytical and approximate methods [39]. Based
upon the reliability theory, a random event function can be approximated by a linearized form
about the design point in the standard normal space. In the probabilistic analysis, all variables
47
are treat as stochastic with independent mean values and standard deviations. The failure
probability P𝑓 can be obtained by:
P𝑓 = Φ(−β) = 1 − Φ(β) (7.19)
Where Φ(β) = ∫1
√2𝜋exp (
𝑢2
2) 𝑑𝑢
𝛽
−∞. Although FORM/SORM is easy to implement, in some cases,
the result converges very slowly or oscillates about one solution without convergence. Another
limitation of using FORM/SORM is that the random parameters and limit state functions must be
continuous [39].
7.1.3.3 Monte-Carlo Simulation
The MCS is a simple method based on the fact that the failure probability integral can be
regarded as a mean value in a stochastic process [37]. By generating a large number 𝐺 of
independent repetitions, the POF can be therefore estimated as the quotient of the failure 𝐺𝑓
counts, to the number of simulations performed in conjunction with the limit state formulations,
which is given as follows:
P𝑓 =𝐺
𝐺𝑓
(7.20)
In contrast to FORM/SORM, MCS allows the details of the physical failure mechanics to be
preserved without linearization of the failure surface. In addition, other non-normal variable
distributions can be readily accommodated in the analysis. Another big advantage of MCS is
that it always converges if the sample size is large enough.
However, the main disadvantage for the use of MCS is that it is not very efficient compared with
FORM/SORM. The major contribution to the POF are in a small part of the whole integration
interval but the MCS samples in a much large region, as the accuracy of MCS heavily depends
on the number of samples used in the simulation [37].
7.2 Models and Results
In order to evaluate the behaviour of the methods applied, several crack dimensions were
tested to represent the geometrical shape and size of the flaw, form an elliptical shape to a
circumferential shape, leading to three cases considered:
Case 1 - Theoretical points, considering two ratios:
𝑡/𝑅 = 0.1, representing thin-walled pipelines;
𝑡/𝑅 = 0.25, representing thick-walled pipelines.
Also, several crack depth to thickness ratios (𝑎/𝑡 = 0.1, 𝑎/𝑡 = 0.5 and 𝑎/𝑡 = 0.8,) were
considered, meaning that the crack is growing in the direction of the thickness. The ratio
𝑎/𝑡 = 0.8 is considered because several standards consider that the critical crack depth is 80%
of the thickness of the material component. [33] [16] [35] [34]
48
Case 2 – Larger acceptable defects resulting from hydraulic testing
In this case, no geometrical ratios are considered. Instead, the dimensions from Table 7-1 were
used. These values are representative of the truckline L12000. This pipeline is the closest to the
LNG Terminal, where the change of the gas send out will happen there.
Table 7-1 – Trunckline L12000 Pipeline dimensions for different classes.
External Diameter
(in.) Material Class
Wall Thickness
(mm)
Minimum testing Pressure on Plant
(MPa)
Crack Depth (mm)
20 API 5L
Grade X70
I 6.4 114.2 3.1
92.4 3.4
II 7.9 141 3.6
105 4.2
III 9.5 169.5 4.2
117.6 5.1
28 API 5L
Grade X70
I 8.7 110.9 3.8
92.4 4.3
II 11.1 141.5 4
105 5.5
III 12.7 161.9 5
117.6 6.1
32 API 5L
Grade X70
I 10.3 114.9 4.3
92.4 4.9
II 11.9 132.7 4.8
105 5.5
III 14.3 159.5 5.4
117.6 6.8
Table 7-1 also shows the crack depth resulting from on plant hydraulic testing. Pressure testing
has long been an industry-accepted method for validating the integrity of pipelines. This integrity
assessment method can be both a strength test and a leak test. Selection of this method shall
be appropriate for the threats being assessed. ASME B31.8 contains details on conducting
pressure tests for both post-construction testing and for subsequent testing after a pipeline has
been in service for a period of time. The Code specifies the test pressure to be attained and the
test duration in order to address defined threats.
Case 3 – Known crack dimension with remaining life assessment.
Whereas in Case 2, cracks were static, in this case, cracks will grow every time a fatigue load
cycle is completed. This evaluation reports only to Level 2 Assessment. According to Paris Law
(Equation 3.31):
Δa = C∆K𝑚 (7.22)
49
a𝑛+1 = a𝑛 + Δa (7.23)
Equivalent equations apply for the second axis of the semi-ellipse. Also, if equation 7.22 and
7.23 are combined:
Δa = C(Y∆σ√𝜋𝑎𝑖)𝑚 (7.24)
This equation is used to calculate the size increment of a specific defect when a certain stress
range is applied. The remaining life is also computed. For the Paris’s equation, the remaining
life is the following:
N𝑓 =2 (𝑎𝑐
2−𝑚2 − 𝑎𝑖
2−𝑚2 )
(2 − 𝑚) ∙ 𝐶 ∙ (𝑌∆𝜎√𝜋𝑎𝑖)𝑚
(7.25)
7.2.1 Fitness-for-Purpose for Integrity Assessment
As stated in section 7.1.2, the fitness-for-purpose approach is based in fracture mechanics and
has an objective to evaluate the impact caused by a defect in the performance in service of a
certain structure. Two procedures have been used, the API RP 579 and the BS 7910. Although
the first one in more used in chemical industries, some Fitness-in-Service approaches are used
with other standards (like ASME B31.8) in REN. The use of both procedures allows a better
understanding of the FFP approaches and to compare both results. Crack-like flaws are planar
flaws, which are predominantly characterized by a length and depth [17]. They may either be
embedded or surface breaking. Examples of real crack-like flaws include planar cracks, lack of
fusion and lack of penetration in welds, sharp groove due to localized corrosion, and branch
type cracks associated with environmental cracking [17]. Table 7-2 shows the approximations of
an ideal and an actual flaw.
Flaw characterization rules allow existing or postulated crack geometry to be modeled by a
geometrically simpler one in order to make the actual crack geometry more amenable to
fracture mechanics analysis. The rules used to characterize crack-like flaws are necessarily
conservative and intended to lead to idealized crack geometries that are more severe than the
actual crack geometry they represent. These characterization rules account for flaw shape,
orientation and interaction [35].
Table 7-2 – Flaw characterization. [35] [17]
Actual Ideal
Through-wall Flaw
50
Actual Ideal
Surface Flaw
Embedded Flaw
In this study, surface cracks (internal and external) oriented axially and circumferentially to the
pipe were considered. Through-wall cracks were also assessed for leakage-before-break
analysis. The schematic representations of the pipe with the cracks can be found below, on
Figure 7-5.
Figure 7-5 – Possible flaws in pipe: Axial oriented surface flaws ((a) Internal (c) External); Circumferential
oriented surface flaw ((b) Internal (d) External) and (e) Through-Wall flaw in a pipeline. [17] [35]
(a (b
(c (d
(e
51
The part through-wall depth of a flaw can be considerably more difficult to estimate than the
length. Either a default value or a value based on detailed measurements may be used for the
flaw depth in an assessment [35]. If no information is available about the depth of the flaw, a
conservative assumption is to consider that the flaw penetrates the wall (e.g.,𝑎 = 𝑡). In
pressurized components, an actual through-wall flaw would most likely lead to leakage, and
thus would not be acceptable in the long term. However, if it can be shown that a through- wall
flaw of a given length would not lead to brittle fracture or plastic collapse, then the component
should be acceptable for continued service with a part-through-wall flaw of that length [17].
Additional special considerations may be necessary for pressurized components containing a
fluid where a leak can result in auto refrigeration of the material near the crack tip, or other
dynamic effects. Flaw depths smaller than the full wall may be assumed if justified by service
experience with the type of cracking observed.
7.2.2.1 BS 7910 Procedure
The FFP assessment of this procedure was carried out concerning fracture mechanics by
loading and fatigue. Two levels of safeness were considered.
Case 1
The same points used in the empirical methods were used to validate the concept. The results
can be seen in Figure 7-6, for the two levels of safeness.
Figure 7-6 – Failure Assessment Diagram (BS7910): (a) Level 1; (b) Level 2.
The following conclusions can be obtained analysing the FAD:
Internal cracks are more dangerous for the structure than external cracks;
Considering the same cracks for thin and thick-walled pipelines, it is notice that thick-
walled have much more resistance to failure than the thin-walled pipes;
Axial cracks are more prone to failure than circumferential cracks;
0
0,4
0,8
1,2
0 0,2 0,4 0,6 0,8 1
Kr
Sr
t/Ri=0.1 (int/axi)
t/Ri=0.25 (int/axi)
t/Ri=0.03 (int/axi)
t/Ri=0.25 (int/circ)
t/Ri=0.03 (int/circ)
t/Ri=0.1 (ext/axi)
t/Ri=0.25 (ext/axi)
t/Ri=0.03 (ext/axi)
t/Ri=0.1 (ext/circ)
t/Ri=0.25 (ext/circ)
t/Ri=0.03 (ext/circ)
t/Ri=0.1 (t-wall)
t/Ri=0.25 (t-wall)
t/Ri=0.03 (t-wall)0
0,4
0,8
1,2
0 0,2 0,4 0,6 0,8 1 1,2
Kr
Lr
t/Ri=0.1 (int/axi)
t/Ri=0.25 (int/axi)
t/Ri=0.03 (int/axi)
t/Ri=0.25 (int/circ)
t/Ri=0.03 (int/circ)
t/Ri=0.1 (ext/axi)
t/Ri=0.25 (ext/axi)
t/Ri=0.03 (ext/axi)
t/Ri=0.1 (ext/circ)
t/Ri=0.25 (ext/circ)
t/Ri=0.03 (ext/circ)
t/Ri=0.1 (t-wall)
t/Ri=0.25 (t-wall)
t/Ri=0.03 (t-wall)
(a) (b)
52
Comparing the two levels, it is noticeable that Level 1 assessment is more conservative
than Level 2 as in the first level, more technical concepts are not applied, giving points
in the FAD that are less safer than level 2 assessment.
Case 2
This case uses values from Table 7-1, related with the larger acceptable defects for a pipeline
after the hydraulic test. The pipe dimensions considered are the same as the pipes used in
trunckline L12000. The results can be seen in Figure 7-7.
As referred, due to the conservatism of Level 1 Assessment, all points are observed in the
unsafe region of the FAD and the following conclusions can be made:
Circumferential cracks are more prone to brittle fracture than the cracks oriented axially;
The lower the class of the pipeline, less suitable is to plastic collapse;
The higher the diameter of the pipeline, more unsafe it is;
Mostly all points represented are in a region that both brittle fracture and plastic
collapse occurs.
Figure 7-7 – Failure Assessment Diagram (BS 7910) - Level 1 Assessment (a) Internal flaws (b) External Flaws.
Due to their unsafeness for Level 1, Level 2 Assessment was made, and it can be inferred that:
All points represented for internal cracks are in the safe region;
External cracks, oriented axially, are unsafe for higher diameters, meaning that is
needed to repair, remove or remediate the component with these cracks. A part from
these, it is possible to consider the crack as trough-walled ones and do a break before
leak analysis with these points (Figure 7-9). It is possible to see that all points are in the
safe zone. However, for the 32 inches pipes, representative points are really close to
the limit curve, meaning that special attention is needed using pipes with these types of
cracks.
0
0,5
1
1,5
2
0 0,2 0,4 0,6 0,8 1
Kr
Sr
(ext/axi) D20-CI
(ext/axi) D20-CII
(ext/axi) D20-CIII
(ext/axi) D28-CI
(ext/axi) D28-CII
(ext/axi) D28-CIII
(ext/axi) D32-CI
(ext/axi) D32-CII
(ext/axi) D32-CIII
(ext/circ) D20-CI
(ext/circ) D20-CII
(ext/circ) D20-CIII
(ext/circ) D28-CI
(ext/circ) D28-CII
(ext/circ) D28-CIII
(ext/circ) D32-CI
(ext/circ) D32-CII
(ext/circ) D32-CIII0
0,5
1
1,5
2
0 0,2 0,4 0,6 0,8 1
Kr
Sr
(int/axi) D20-CI
(int/axi) D20-CII
(int/axi) D20-CIII
(int/axi) D28-CI
(int/axi) D28-CII
(int/axi) D28-CIII
(int/axi) D32-CI
(int/axi) D32-CII
(int/axi) D32-CIII
(int/circ) D20-CI
(int/circ) D20-CII
(int/circ) D20-CIII
(int/circ) D28-CI
(int/circ) D28-CII
(int/circ) D28-CIII
(int/circ) D32-CI
(int/circ) D32-CII
(int/circ) D32-CIII
(a) (b)
53
Figure 7-8 - – Failure Assessment Diagram (BS 7910) - Level 2 Assessment (a) Internal flaws (b) External Flaws
Figure 7-9 – Leak before Breakage analysis for points that are unsafe for Level 2 Assessment.
Using Paris Law, it is possible to determine the remaining life of a structure with those type of
cracks. That information is shown in Table 7-3.
Table 7-3 – Remaining life in-service of the case 2 scenario.
External Diameter (in)
Class Wall Thickness
(mm) Crack Depth
(mm) Remaining years
in-service
20
I 6.4 3.4 50
II 7.9 4.2 42
III 9.5 5.1 39
28
I 8.7 4.3 49
II 11.1 5.5 43
III 12.7 6.1 42
32
I 10.3 4.9 49
II 11.9 5.5 47
III 14.3 6.8 41
0
0,2
0,4
0,6
0,8
1
1,2
0 0,2 0,4 0,6 0,8 1 1,2
Kr
Lr
(ext/axi) D20-CI
(ext/axi) D28-CI
(ext/axi) D28-CII
(ext/axi) D28-CIII
(ext/axi) D32-CI
(ext/axi) D32-CII
(ext/axi) D32-CIII
0
0,4
0,8
1,2
0 0,4 0,8 1,2
Kr
Lr
(int/axi) D20-CI(int/axi) D20-CII(int/axi) D20-CIII(int/axi) D28-CI(int/axi) D28-CII(int/axi) D28-CIII(int/axi) D32-CI(int/axi) D32-CII(int/axi) D32-CIII(int/circ) D20-CI(int/circ) D20-CII(int/circ) D20-CIII(int/circ) D28-CI(int/circ) D28-CII(int/circ) D28-CIII(int/circ) D32-CI(int/circ) D32-CII(int/circ) D32-CIII 0
0,4
0,8
1,2
0 0,4 0,8 1,2
Kr
Lr
(ext/axi) D20-CI(ext/axi) D20-CII(ext/axi) D20-CIII(ext/axi) D28-CI(ext/axi) D28-CII(ext/axi) D28-CIII(ext/axi) D32-CI(ext/axi) D32-CII(ext/axi) D32-CIII(ext/circ) D20-CI(ext/circ) D20-CII(ext/circ) D20-CIII(ext/circ) D28-CI(ext/circ) D28-CII(ext/circ) D28-CIII(ext/circ) D32-CI(ext/circ) D32-CII(ext/circ) D32-CIII
(a) (b)
54
Case 3
This last case is concerned with the growth of a crack with known dimension over the load
cycles. Starting with a crack depth of 0.1 𝑚𝑚, the assessment is carried out till the crack
reaches 6 𝑚𝑚. Figure 7-10 shows the results obtained, for the two assessment levels
considered. When the crack depth reaches certain value, the point is placed in the unsafe zone,
meaning that the structure has to be repaired, remediated or replace. A LFB analysis was made
for these points. The result was that crack depth above 4 𝑚𝑚 have a big probability of leakage
and/or, eventually, failure. An interesting observation is that internal cracks oriented axially fail
easier than external ones. The evaluation for the remaining life of the component was made
according to the previous results and, as it can be seen in Figure 7-12, the bigger the crack
depth, the lower is the remaining years in-service of the component.
Figure 7-10 –Failure Assessment Diagram (BS7910) – Fatigue Assessment (a) Level 1 (b) Level 2.
Figure 7-11 - Leak before Breakage analysis.
0
0,2
0,4
0,6
0,8
1
1,2
0 0,2 0,4 0,6 0,8 1 1,2
Kr
Lr
Through-Wall
0
0,5
1
1,5
2
0 0,2 0,4 0,6 0,8 1
Kr
Sr
Int/axi
Int/Circ
Ext/Axi
Ext/Circ
0
0,5
1
1,5
2
0 0,4 0,8 1,2
Kr
Lr
Int/Axi
Int/Circ
Ext/Axi
Ext/Circ
(a) (b)
55
Figure 7-12 – Remaining Life in-Service in function with the crack depth.
7.2.2.2 API 579 Procedure
Case 3 was re-calculated according with the API RP 579 procedure, in order to study the
differences between both FFP predictions. The results obtained dispear a more conservative
predition. Pipes are more prone to fail than in the BS 7910 prediction. API RP 579 is a more
conservative procedure because it does not require so many material properties. It is not
needed to re-estimate the other cases due to the fact that all results would be higher than those
obtained with the BS 7910. Nevertheless, as before, axial oriented cracks are more unsafe than
circumferential flaws, and internal defects are riskier than external ones.
Figure 7-13 – API 579 Level 2 Assessment for growing crack.
7.2.2 Structural Reliability
This study will also be carry out for the dimensions of trunckline L12000 pipes, mostly for 28
inch pipelines due to the fact that they are the most used diameter in that line. The cracks to be
analysed are assumed to be longitudinal and circumferentially oriented as the maximum hoop
stress is normal to the orientation of the flaw, the cases where brittle fracture and fatigue failure
are most likely to occur.
0
100
200
300
400
500
600
700
0 0,001 0,002 0,003 0,004 0,005 0,006
Re
mai
nin
g Y
ear
s o
f Se
rvic
e
Crack Depth (m)
0
0,5
1
1,5
2
2,5
0 0,2 0,4 0,6 0,8 1 1,2
Kr
Lrp
Int/Axi
Ext/Axi
Int/Circ
56
Table 7-4 – Input parameters for POF analysis.
Parameter Average Standard Deviation
Distribution type
Pipe Diameter (𝒎𝒎) 711 0 Fixed
Thickness (𝒎𝒎) 11.1 0 Fixed
Initial Crack Depth (𝒎𝒎) 1.527 0.794 Log-normal
Initial Crack Length (𝒎𝒎) 11.136 5.068 Log-normal
Pressure (𝑴𝑷𝒂) 6.897 0.608 Normal
Fracture Toughness (𝑴𝑷𝒂 ∙ √𝒎) 84.195 37.869 Normal
Yield Strength (𝑴𝑷𝒂) 532.104 18.899 Normal
Tensile Strength (𝑴𝑷𝒂) 628.988 47.456 Normal
Analytically, the POF is equal to 7.29 × 10−4. For calculating the POD, the parameter 𝜆 can be
defined, assuming that; the minimum detectable depth for the pig is 0.2 𝑚𝑚 and the probability
of detecting a defect depth of 30% of the thickness is 90%.. Thus, 𝜆 takes the following value,
for each class:
P𝐷 = 1 − 𝑒−𝜆(𝐷𝑒−0.2)
⇒ 0.90 = 1 − 𝑒−𝜆(𝑡×0.3−0.2)
⇒ λ = −
ln(1 − 0.9)
𝑡 × 0.3 − 0.2
This also implies that the average detectable depth is 1/𝜆 + 0.2, in this case, 1.559 𝑚𝑚. Figure
7-14 shows the detection probability function for the 28 inches diameter pipe.
Figure 7-14 – Probability of Detection of a defect.
As observed, a higher value of crack depth leads to a higher probability of detection. The
behaviour is similar for 20 and 32 inch diameter pipes used in trunckline L12000.
0%
25%
50%
75%
100%
0 0,5 1 1,5 2 2,5 3
Pro
bab
ility
of
De
tect
ion
Crack depth (mm)
D28CID28CIID28CIII
57
If the same analysis is made for multiple cracks, the resulting POF is 7.26 × 10−3, considering
10 cracks per kilometre. In terms of POF over the years, it is clear that, there is going to be
bigger cracks with time so it is normal that the POF will increase, as seen in Figure 7-15.
Figure 7-15 – Probability of Failure over the years.
The POF with MCS is also computed. With this method, random numbers were generated to be
inside the limit state function. The POF given is 7.36 × 10−4. The result is in good agreement
with the analytical solution as the difference is below 2%. Also, using FORM, the POF is
7.31 × 10−4 with 𝛽 = 3.182.
7.3 Conclusions
Several FFP approaches were used in order to predict the behaviour of crack-like defect in
pipelines. The cracks were considered to be internal and external to the surface of the pipe.
Both BS 7910 and API 579 can be used to access defects, and as observed, the results on both
documents are different. Due to conservatism, Level 1 Assessment for BS 7910 and API RP
579 is not a reliable technique to infer if the structure is in danger of fail or not. However if used
in in-field inspection, it could be a great method to know, with few calculations, if the flaw is
going to be dangerous or not. From observing the graphs, it can be assumed that both
circumferential and axially oriented cracks have both fracture mechanisms but the first one is
brittle fracture dominant and the seconds is plastic collapse dominant. The FFP approaches
done confirm that the most critical flaws are the longitudinal interior cracks and they are the
ones that the manufactures have to be more careful and they cannot be repaired in-service. In
terms of fatigue, the remaining life for the pipes in trunckling L12000 according with the
maximum crack depth allowed are around 40 to 50 years until failure. However, it has to be
stated that these values are for initial cracks with a great amount of penetration in the wall
thickness and generally, the initial cracks are much smaller, leading to more than 200 years in-
service life. The results obtained by assess the structure by the BS 7910 and the API 579
procedures are similar, although in the second one presents points with higher safety factors,
resulting in more conservative values, i.e., points more prone to fail in the FAD. The FAD curve
itself change with the level of assessment that is made but especially with the procedure that it
is followed.
0%
25%
50%
75%
100%
0 20 40 60 80 100 120 140 160 180 200
Pro
bab
ility
of
failu
re
Number of Years
58
Figure 7-16 – Different FAD curves using different procedures.
Figure 7-16 shows different curves for different procedures and although all curves are similar,
some are more conservative than others. Note that the maximum Load ratio also is changing.
The structural reliability analysis was done, assuming a certain known crack distribution. POF is
strongly dependent on the distribution of the defects in the pipeline, in particular the crack
depth. Other properties like yield strength, tensile strength and fracture toughness affects the
value of the POF. The value of POF is relatively low and there were a good agreement between
the three methods applied (analytical, FORM and MCS). As supposed the bigger the crack,
higher the probability of detection of the same crack. However, the sensitivity depends on which
inspection tool is used, and this can be a focal point in order to prevent some cracks to
propagate catastrophically.
0
0,5
1
1,5
0 0,2 0,4 0,6 0,8 1 1,2
Kr
Lr
BS 7910 Level 1A BS 7910 Level 2A BS 7910 Level 2B
API 579 Level 1 API 579 Level 2 API 579 Level 3
SINTAP FITNET R6 Procedure
59
Chapter 8
Final Remarks and Future Work
8.1 Final Remarks
The service demand for products transported through pipelines are inherently non-stationary.
As a result, operating pressure levels vary from time to time. Variations in operating pressure
produce variations in the hoop stress level in the pipeline, and can thus cause metal fatigue that
could eventually lead to failure in service of the structure. Generally, the fatigue life of a properly
designed sound structure is quite long. Typically, millions of normal service-stress fluctuations
are required for a failure to occur. In a pipeline the number of very large stress cycles (i.e.,
pressure cycles) is usually on the order of tens to hundreds of cycles per year, so one might
expect that the potential for a pressure-cycle-induced fatigue failure in any pipeline would be
insignificant. However, those variations on pressure cycle do not mean high amplitudes each
cycle. The goal of this thesis is to infer the degree of exposure of a pipeline to fatigue induced
by high amplitude pressure cycles (20-30 bar). Nowadays, the fix capacity contract with the
Algerian gas supplier is almost enough to supply the NGTN. However, as the economy activity
increases (as expected), the need to inject NG in the network is going to occur. In this situation,
a flexible LNT Terminal is the answer to fulfil all distribution points at a lower rate, than the one
of the fix contract. For REN, an optimized profile emission leading to a more energy efficient
process, aiming for energy reduction in both cost and environmental impact is essential. The
LNG Terminal has several facilities that can be used rationally, as they can follow a rotation
program within the company. This leads not only to the promotion of operating at maximum
efficiency but also to avoid successive starts and stops of the equipment. This the focal point for
the adequacy management of periods of higher flow rate emission of NG to the NGTN.
Scenarios that create different pressure cycle profiles within the pipe were simulated. These
scenarios allow understanding that it would be possible to daily save power and cost using
optimized emission profiles. Sending out the maximum gas flow during hours of lower electricity
tariffs and using minimum injection rates, during day hours of higher electricity tariffs, induce a
5-10% cost saving per year in the LNG Terminal. The results obtained, through fatigue tests,
numerical modelling and integrity assessment using fitness-for-purpose approaches concluded
that, in normal operational conditions, the pipe would not fail due to pressure cycle induced
fatigue. The carried out approaches confirmed that the most critical flaws are longitudinal
interior cracks and those that manufactures must be more aware as they cannot be repaired in-
service. In terms of fatigue, the remnant life for the pipes in truckling L12000, according with the
maximum crack depth allowed, is around 40 to 50 years. This is a convenient observation as
the normal period of concession is 40 years. However, it must be stated that these values are
consider initial cracks with a great amount of penetration in the wall thickness and generally, the
initial cracks are much smaller, leading to more than 200 years in-service life. This matches
60
reality as pipelines with more than 100 years old are still operative, as stated before in England
and in The Netherlands). Structural reliability analysis was carried out, assuming a certain
known crack distribution. POF is strongly dependent on the distribution of the defects in the
pipeline, in particular the crack depth. Other properties like yield strength, tensile strength and
fracture toughness affects the value of the POF. The value of POF is relatively low and there
was good agreement between the three methods applied (analytical, FORM and MCS). As
predicted the bigger the crack, the higher the probability of detection of the same crack.
However, sensitivity depends on the inspection tool used, and this can be a focal point in order
to prevent some cracks to propagate catastrophically. Nevertheless, a structure like a pipeline
can have long usage time, as NG is not very corrosive for because before being injected in the
structure, certain corrosive elements, particularly Sulphur, are extracted from the fluid. In order
to guaranty the integrity, security, operability and increasing life of the NG transportation
system, a Pipeline Integrity Management System may be implemented as a part of a
methodology of Management Assets. Almost 90% of the assets cost of the NGTN are buried
pipelines, so it is necessary to obtain equilibrium between security, maintenance costs and
reliability. Implementing PIMS would benefit greatly REN. The main benefits are intangible and
are related with the decrease of the probability of failure and accidents in the infrastructure,
thus, reducing NG supply interruption, human related damages (injuries and death), damage in
third-party infrastructures, civilian responsibility, negative impact in the image of the company,
environmental impacts, OPEX costs and costs associated with the repair of the structure and
loss of NG.
8.2 Future Work
For future work, more tests should be made in order to have a better sample of results, resulting
in a more trustworthy study. Also, the study should be extended to off plane cracks (cracks that
are not perpendicular or parallel to the applied load) in order to understand the relationship
between crack propagation angle and the applied load. Modelling should be also carried out for
curved structures in order to confirm the results obtained by the FFP approaches. As far as
Structural Reliability is concerned, a more in-depth analysis of the POF should be carried out for
cases where other distributions of cracks are used, as well to validate the concept with the data
from intelligent ‘pigs’. Different inspection and repair criteria should be available in the
simulation whereby an optimal maintenance strategy can be obtained by comparing different
combinations of inspection and repair procedures. The simulation provides not only data on the
probability of failure but also the predicted number of repairs required over the pipeline life thus
providing data suitable for economic models of the pipeline management.
61
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67
Appendix
I – Natural Gas Transmission Network
68
II – Pressure cycle profiles and gas flow for different
scenarios
Gas Flow
Figure A-1 – Gas Flow during February 26th
to March 4th
, 2011.
Figure A-2 – Gas Flow during September 21st to September 27
th, 2013.
Figure A-3 – Gas Flow during March 22nd
to March 28th
, 2014.
0
200000
400000
600000
800000
26-02-…
26-02-…
26-02-…
26-02-…
26-02-…
27-02-…
27-02-…
27-02-…
27-02-…
27-02-…
28-02-…
28-02-…
28-02-…
28-02-…
28-02-…
01-03-…
01-03-…
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02-03-…
02-03-…
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02-03-…
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03-03-…
03-03-…
03-03-…
03-03-…
04-03-…
04-03-…
04-03-…
04-03-…
04-03-…
Gas
Flo
w (
m3 (
n))
AS_S CTS_7000_E TERMINAL_L2
0
100000
200000
300000
400000
500000
600000
21-09-2013
…
21-09-2013
…
21-09-2013
…
21-09-2013
…
21-09-2013
…
22-09-2013
…
22-09-2013
…
22-09-2013
…
22-09-2013
…
22-09-2013
…
23-09-2013
…
23-09-2013
…
23-09-2013
…
23-09-2013
…
23-09-2013
…
24-09-2013
…
24-09-2013
…
24-09-2013
…
24-09-2013
…
24-09-2013
…
25-09-2013
…
25-09-2013
…
25-09-2013
…
25-09-2013
…
26-09-2013
…
26-09-2013
…
26-09-2013
…
26-09-2013
…
26-09-2013
…
27-09-2013
…
27-09-2013
…
27-09-2013
…
27-09-2013
…
27-09-2013
…
Gas
Flo
w (
m3(n
)) AS_S CTS_7000_E TERMINAL_L2
0
100000
200000
300000
400000
500000
22-03-…
22-03-…
22-03-…
22-03-…
23-03-…
23-03-…
23-03-…
23-03-…
24-03-…
24-03-…
24-03-…
24-03-…
25-03-…
25-03-…
25-03-…
25-03-…
26-03-…
26-03-…
26-03-…
26-03-…
27-03-…
27-03-…
27-03-…
27-03-…
28-03-…
28-03-…
28-03-…
28-03-…
Gas
Flo
w (
m3 (
n))
AS_S CTS_7000_E TERMINAL_L2
69
Pressure Cycles
Figure A-4 – Pressure Cycle Profiles, during February 26th
to March 4th
, 2011.
Figure A-5 – Pressure Cycle Profiles, during September 21st to September 27
th, 2013.
Figure A-6 - Pressure Cycle Profiles, during March 22nd
to March 28th
, 2014.
5
5,5
6
6,5
7
7,5
8
26-02-2011
…
26-02-2011
…
26-02-2011
…
26-02-2011
…
26-02-2011
…
27-02-2011
…
27-02-2011
…
27-02-2011
…
27-02-2011
…
27-02-2011
…
28-02-2011
…
28-02-2011
…
28-02-2011
…
28-02-2011
…
28-02-2011
…
01-03-2011
…
01-03-2011
…
01-03-2011
…
01-03-2011
…
01-03-2011
…
02-03-2011
…
02-03-2011
…
02-03-2011
…
02-03-2011
…
03-03-2011
…
03-03-2011
…
03-03-2011
…
03-03-2011
…
03-03-2011
…
04-03-2011
…
04-03-2011
…
04-03-2011
…
04-03-2011
…
04-03-2011
…
Pre
ssu
re (
MP
a)
2500.PI002 4000.PI002 12800.PI002 1209.PI102
5
5,5
6
6,5
7
7,5
8
21-09-2013
…
21-09-2013
…
21-09-2013
…
21-09-2013
…
21-09-2013
…
22-09-2013
…
22-09-2013
…
22-09-2013
…
22-09-2013
…
22-09-2013
…
23-09-2013
…
23-09-2013
…
23-09-2013
…
23-09-2013
…
23-09-2013
…
24-09-2013
…
24-09-2013
…
24-09-2013
…
24-09-2013
…
24-09-2013
…
25-09-2013
…
25-09-2013
…
25-09-2013
…
25-09-2013
…
26-09-2013
…
26-09-2013
…
26-09-2013
…
26-09-2013
…
26-09-2013
…
27-09-2013
…
27-09-2013
…
27-09-2013
…
27-09-2013
…
27-09-2013
…
Pre
ssu
re (
MP
a) 2500.PI002 4000.PI002 12800.PI002 1209.PI102
5
5,5
6
6,5
7
7,5
8
22
-03
-20
14
…
22
-03
-20
14
…
22
-03
-20
14
…
22
-03
-20
14
…
22
-03
-20
14
…
22
-03
-20
14
…
23
-03
-20
14
…
23
-03
-20
14
…
23
-03
-20
14
…
23
-03
-20
14
…
23
-03
-20
14
…
23
-03
-20
14
…
24
-03
-20
14
…
24
-03
-20
14
…
24
-03
-20
14
…
24
-03
-20
14
…
24
-03
-20
14
…
24
-03
-20
14
…
25
-03
-20
14
…
25
-03
-20
14
…
25
-03
-20
14
…
25
-03
-20
14
…
25
-03
-20
14
…
25
-03
-20
14
…
26
-03
-20
14
…
26
-03
-20
14
…
26
-03
-20
14
…
26
-03
-20
14
…
26
-03
-20
14
…
26
-03
-20
14
…
27
-03
-20
14
…
27
-03
-20
14
…
27
-03
-20
14
…
27
-03
-20
14
…
27
-03
-20
14
…
27
-03
-20
14
…
28
-03
-20
14
…
28
-03
-20
14
…
28
-03
-20
14
…
28
-03
-20
14
…
28
-03
-20
14
…
28
-03
-20
14
…
Pre
ssu
re (
MP
a) 2500.PI002 4000.PI002 12800.PI002 1209.PI102
70
III – API 5L X70 Steel Euro Pipe Certificate
71
IV – Assessment Procedure to Evaluate a Pipeline with
Crack-Like Flaws
72
73
V – Methodology for Crack Growth Analysis
