Mechanical Behaviour of Lined Pipe - A Hilberink

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A. Hilberink

Mechanical Behaviour of Lined Pipe


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Mechanical Behaviour

of Lined Pipe

Proefschrift

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben,

voorzitter van het College voor Promoties

in het openbaar te verdedigen

op maandag 19 december 2011 om 10.00 uur

door

Annemiek HILBERINK

Ingenieur in Mechanical Engineering

geboren te Wieringemeer


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Dit proefschrift is goedgekeurd door de promotoren:

Prof. ir. F.S.K. Bijlaard

Prof.dr.ir. L.J. Sluys

Samenstelling promotiecommissie:

Rector Magnificus voorzitter

Prof. ir. F.S.K. Bijlaard Technische Universiteit Delft , promotor

Prof.dr.ir. L.J. Sluys Technische Universiteit Delft , promotor

Prof.dr.ir. M.L. Kaminski Technische Universiteit Delft

Prof. dr. ir. W. de Waele Universiteit Gent, Belgi

Ir. A.M. Gresnigt Technische Universiteit Delft

Dr. S.A. Karamanos University of Thessaly, Griekenland

D. Haldane Heriot-Watt University Edinburgh, Verenigd Koninkrijk

ISBN 978-94-6186-012-5

Cover design: J. Niermeijer

Layout: Grafisch bureau Grapefish

Printing: Sieca Repro, Delft, The Netherlands

Copyright 2011 by A. Hilberink

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or trans-

mitted in any form or any means, electronic, mechanical, photocopying, recording or otherwise, without

prior written permission of the autor.


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Mechanical Behaviour

of Lined Pipe

A. Hilberink


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This research was funded by:

Delft University of Technology

Heerema Marine Contractors

Kuroki Tube and Pipe Co. Ltd.

Agentschap NL, Maritiem Innovatie Platform


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V

Table of Contents

Acknowledgement VII

Summary IX

Nomenclature XISymbols XI

Subscripts XII

Abbreviations XIII

1. Introduction 11.1 Tendencies in the Offshore Oil and Gas Industry 1

1.2 Offshore Installation 21.3 Lined Pipe 4

1.4 Research on the Mechanical Behaviour of Lined Pipe 5

1.5 Research Objective 5

1.6 Research Approach and Thesis Outline 6

1.7 Conventions 9

2. Tight Fit Pipe 112.1 Manufacturing Process of Tight Fit Pipe 13

2.2 Geometry of Tight Fit Pipes 15

2.3 Stress-Strain Curves of Tight Fit Pipes 162.4 Radial Contact Stress in Tight Fit Pipes 19

2.5 Conclusions 24

3. Axial Compression of Single Walled Pipe 253.1 Introduction 25

3.2 Analytical Results 26

3.3 Numerical Results 30

3.4 Numerical Nonlinear Results Compared with Analyt ical Results 41

3.5 Numerical Parameter Study 42

3.6 Numerical Nonlinear Results Compared with Experimental Results 473.7 Conclusions 51

4.0 Axial Compression of Lined Pipe 554.1 Introduction 55

4.2 Numerical Results 56

4.3 Comparing Numerical Results of Lined Pipe with Single Walled Liner 64

4.4 Numerical Parameter Study 65

4.5 Conclusions 72

5. Pure Bending of Single Walled Pipe 755.1 Introduction 75


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VI

5.2 Numerical Uniform Ovalisat ion Model of Single Walled Liner 77

5.3 Numerical Model of Full Length Single Walled Liner in Pure Bending 81

5.4 Verification of Numerical Results for Single Walled Liner in Pure Bending 89

5.5 Numerical Parameter Study for Single Walled Liner 91

5.6 Numerical Uniform Ovalisat ion Model of Single Walled Outer Pipe 94

5.7 Numerical Model of Full Length Single Walled Outer Pipe in Pure Bending 95

5.8 Benchmark Results for Single Walled Outer Pipe 100

5.9 Numerical Results Single Walled Liner and Outer Pipe Compared 102

5.10 Conclusions 104

6. Full Scale Four Point Bend Tests on Lined Pipe 1076.1 Introduction 107

6.2 Experiments 107

6.3 Conclusions 138

7. Numerical Model Pure Bending of Lined pipe 141

7.1 Introduction 1417.2 Numerical Uniform Ovalisat ion Model of Lined Pipe 143

7.3 Numerical Model of Full Length Lined Pipe in Pure Bending 146

7.4 Numerical Results Lined Pipe and Single Walled Pipes Compared 156

7.5 Numerical and Experimental Results Lined Pipe Compared 158

7.6 Numerical Parameter Study for Full Length Lined Pipe in Pure Bending 175

7.7 Conclusions 195

8. Reeling of Lined Pipe 1978.1 Introduction 197

8.2 Reeling Experiments 1988.3 Comparing Reeling with Pure Bending Results 200

8.4 Conclusions 206

9 Conclusions and Recommendations 2079.1 Conclusions 207

9.2 Recommendations 210

References 213

List of Publications 219

Appendix A Stress-Strain Curves TFP 221

Appendix B Influence of Specimen Length on Residual Compressive Stress Test Results 225

Samenvatting 231

Curriculum Vitae 233


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VII

Acknowledgement

Many people and institutions have contributed directly and indirectly to this thesis. I would like to take

the opportunity to highlight some of them. First of all I would like to thank Eelke Focke for her inspirationand enthusiasm without which I would never have started this research. I would like to thank Professor

Frans Bijlaard and Professor Jan Meek for giving me the opportunity to start this PhD research. Especially,

I would like to express my gratitude to Professor Bert Sluys for embracing this research and always giv-

ing me the feedback I needed. I would like to thank Nol Gresnigt for his intractability, which led to lively

and fruitful discussions. Furthermore, I would like to thank Anton de Koning, Dr. Nakasugi and Mr. Fujita

from Kuroki Tube and Pipe for their contributions to this project. I would like to acknowledge Rien van de

Ruijtenbeek for his valuable input during the progress meetings.

Frank Lange I would like to thank for creating the environment that allowed me to work on this academicresearch within Heerema Marine Contractors, but above all for his confidence, continuous support and

personal coaching. Erwan Karjadi I would like to thank him for his endless patience, especially at those

moments I lost mine. Thomas Balder I would like to thank for his support; he made me enjoy program-

ming. My colleagues from the Innovation Department created a pleasant working atmosphere. Without

the dedication of the IS department at Heerema Marine Contractors my PhD would have taken me sig-

nificantly longer. I hope the results of this project are as valuable for HMC, as the execution phase of the

project was for me.

I would like to thank all people that contributed to the bend test program. Especially I would like to

express my appreciation to Heather Gower, I enjoyed working together, and hope we will work together

again in the near future. I would like to acknowledge John Hermsen, Arjen van Rhijn, Cees van Beek and

all other people in the Stevin laboratory for their commitment. Furthermore, I would like to express my

gratitude to Martin Kik of Heerema Vlissingen as well as all the people at Pipeline Technique Limited for

their flexibility and the high quality of work delivered.

I am thankful to the members of the Offshore Engineering Department at Delft University of Technology

that made me always feel at home despite my limited presence.

Finally I would like to thank my friends and family for their support throughout this PhD research. Joep,

without your dedication, support and confidence I would never have been able to combine finalising this

PhD research with a job and our new family life, while enjoying. You make things possible for me. And little

curious Tiemen, you make me see how interesting all normal things in life are.


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VIII


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IX

Summary

Mechanical Behaviour of Lined Pipe Annemiek Hilberink

With the expected continuous volume growth of recovered corrosive hydrocarbons over the com-

ing decennia under influence of the increasing worlds primary energy demand and the accompanying

expected volume growth of corrosive hydrocarbons, the need for corrosion mitigation grows. Mechani-

cally bonded lined pipe is a cost efficient option which guarantees high corrosion resistance over a long

lifetime. Mechanically bonded lined pipe is a type of double walled pipe, consisting of a carbon steel load

bearing outer pipe that provides structural capacity and a corrosion resistant liner, mechanically fitted

inside the outer pipe, protecting the carbon steel outer pipe from the transported corrosive product.

Installing lined pipe by means of the reeling installation method seems to be an attractive combination,

because it provides the opportunity of eliminating the demanding welds from the critical time offshore

and instead preparing them onshore. However, reeling of lined pipe is not yet proven technology. From

previous research it is known that lined pipe undergoing high plastic strains during reeling, exhibits liner

wrinkling and extensive ovalisation.

The main objective of this study is to investigate the possibility of installing lined pipe by means of the

reeling installation method. Initially, the interaction of the lined pipe with the reel is not taken into

account and pure bending of the lined pipe is investigated. After the behaviour of the isolated lined pipe

in pure bending is fully understood, the interaction with the reel can be added to the process. In dealing

with the main research objective, the following questions were posed:

1. What variables do influence the mechanical behaviour of lined pipe in pure bending leading to a limit

state?

2. What is the sensitivity of the identified variables on this behaviour, in particular the onset of wrinkling

and the growth of the wrinkles during further bending?

In order to be able to determine what variables influence the mechanical behaviour of lined pipe and

to identify their sensitivity on this behaviour, first the mechanical behaviour of lined pipe needed to be

understood. A combination of numerical models and full scale four point bend tests were used to reach

the objective. Full scale four point bend tests were executed in order to compare the numerical results

with the test result and to investigate the influence of several test conditions and pipe characteris-

tics. With numerical modelling, the two different failure modes exhibited by elastic-plastic cylinders, i.e.

ovalisation for thick elastic-plastic cylinders and wrinkling for thinner elastic-plastic cylinders, were first

investigated separately before allowing them to interact. This approach has proven valuable by giving a

lot of insight and confidence in the final numerical models. The cascade of events exhibited by the lined

pipe in pure bending was fully understood. Liner wrinkling appeared to be the main failure mode of lined

pipe during bending.


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X

Comparison of the numerical results of the lined pipe with those of the single walled liner showed that

confinement of the liner in the outer pipe results in a significant increase of the liners maximum moment

capacity and corresponding curvature.

The sensitivity of the wrinkling behaviour of the confined liner in pure bending for several geometric,

material and contact parameters was examined by means of a parameter study in which the maximummoments and corresponding curvatures have been used. Reeling of lined pipe becomes technically fea-

sible when the reel radius exceeds the bending radius at which liner wrinkling initiates. Adjusting the

lined pipe to an existing reel system is likely to be a more economic option than building a new reel for

each lined pipe. From the parameter study it was found that the curvature at which the onset of liner

wrinkling occurs as well as the curvature at which the lined pipe reaches its maximum moment capacity

can be influenced with geometric and contact parameters of the lined pipe. Material parameters do not

have a significant influence on the curvature, until the ratio of the liner over outer pipe strength exceeds

a certain limit, above which the relatively strong liner causes the outer pipe to fail at lower curvature. As

a result, the lined pipe can be tuned for reeling with an existing reel system by means of the followingparameters, in order of decreasing effectiveness:

- Increasing liner thickness;

- Increasing relative outer pipe thickness with respect to liner pipe thickness while keeping the radius

over thickness ratio of the liner constant;

- Increasing friction between liner and outer pipe;

- Increasing radial contact stress between liner and outer pipe, i.e. the compressive hoop stress in the

liner, and

- Increasing tensile axial stress in liner.

The above results were obtained from the lined pipe analysis in pure bending. The main difference between

pure bending and reeling is that in addition to the constant moment applied during pure bending, a tensile

and distributed load is applied to the lined pipe. From a comparison of the numerical results of the lined

pipe in pure bending with the results of reeling experiments it was concluded that pure bending models

result in a non-conservative and thus not safe approximation for reeling. In order to be able to obtain

accurate results for reeling, cyclic bending should be included in the numerical model with for example

the reel on one side and the aligner on the other side in correspondence with regularly used reeling rigs

as well as a more accurate material model in order to account for anisotropy and hardening of the pipe

material.


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XI

Nomenclature

Symbols

Letters

a Moment arm [mm]

C Circumference [mm]

D Diameter [mm]

d Displacement [mm]

E Youngs modulus of elasticity [Mpa]

f Ovalisation [mm]F Force, load [N]

H Height [mm]

L Length [mm]

M Bending moment [Nm]

N Number [-]

p Pressure [Mpa]

R Radius [mm]

t Wall thickness [mm]

T Temperature [K]

u Displacement [mm]

V Shear force [Mpa]

X Radial position [mm]

Y Tangential position [0]

Z Axial position [mm]

Greek symbols

Difference, change

Infinitesimal small difference, derivative

Strain [-]

Angle [rad]

Curvature [-/m]

Poisson ratio [-]

Stress [Mpa]

Friction coefficient [-]

Rotation [rad]

Damping factor [-]


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XII

Subscripts

Position

cont Contact surface between liner and outer pipe

curv Curvature metercyl Hydraulic cylinder

elem Element

friction Friction

hw Half wave

lastnode Last node, i.e. node at cylinder end

liner Liner

local Local

outer Outer pipe

out Outsidereel Reel

roi Region of interest

snug Snug-fit, i.e. initially no radial contact stress nor a gap present

TFP Tight Fit Pipe

w Wave, wrinkle

Direction

avg Average

axial Axial direction; longitudinal direction

b Bending

circ Circumferential

cont Contact

hoop Hoop direction; circumferential direction

long Longitudinal

mean Mean

Mises Von Mises

radial Radial direction

S Secant

T Tangent

x Radial direction

y Tangential direction

z Axial direction


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XIII

Time step

i Initial

0.01 0.01% proof, i.e. at 0.01% permanent deformation

0.2 0.2% proof, i.e. at 0.2% permanent deformation

ult Ultimate

Magnitude

avg Average value

compr Compressive

cr Critical

global Global

max Maximum valuemean Mean value

meas Measured

min Minimum value

nom Nominal

pl Plastic

tension Tensile

yield Yield

Abbreviations

CRA Corrosion resistant alloy

ERW Electric resistance welded

FEM Finite Element Model

NDT Non-destructive testing

RCS Residual compressive stress test

roi Region of interest

RP Reference point

SMLS Seamless

TFP Tight Fit Pipe


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XIV


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1 Introduction

1. Introduction

1.1 Tendencies in the Offshore Oil and Gas Industry

The worlds primary energy consumption is expected to increase from the current 11.5tonnes of oil equivalent to over 16 billion in 2030, due to population and income growth,a growth of about 40% [Dudley, 2011]. Gas and non-fossil fuels only slowly gain shareat the expense of coal and oil, due to long asset lifetimes, the main driver of this changebeing the reduction of greenhouse emissions. The production of the three fossil fuels isexpected to keep growing, still having an important share of 75% on the total energyconsumption in 2030 as illustrated in Figure 1.1.

* Including biofuels

Figure 1.1 World commercial energy use [Dudley, 2011]

The contribution of natural gas is expected to increase significantly in the coming years. Apart from the

discovery of large reserves in Russia and Iran over the past few years, the potential economic develop-

ment of unconventional gas has increased the proven reserves considerably. The number of gas develop-

ments offshore is increasing significantly, in particular with the increased use of LNG, enabling global

transportation. Investments are expected in long export pipelines, and floating LNG plants, which further

increase the requirement for infield gas pipelines [Westwood, 2011; Evans, 2011].

Major oil producing fields are depleting fast, pushing the oil and gas industry towards more difficult res-

ervoirs. The offshore industry develops towards deepwater, harsher environments such as the Arctic,

and fields with more difficult reservoir characteristics, for example high sulphur content, high pressure,

high temperature, i.e. corrosive hydrocarbons, and/or high viscosity [Westwood, 2011]. Developments

of smaller fields often not justifying an own platform and developments in areas with limited existing

infrastructure, require long pipeline tiebacks to shore or to existing platforms.


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2 Chapter 1

Deepwater production will double in the coming five years until 2015, requiring large investments in sub-

sea infrastructure expecting to exceed US$ 850 billion. The search for more cost efficient methods and

materials has high priority in the industry, because development costs have more than doubled over the

past decade [Westwood, 2011].

1.2 Offshore Installation

With the oil recovery moving towards more harsh environments, pipeline installation is becoming ever

more challenging. During installation pipelines are exposed to loading conditions that are often govern-

ing for their design. In this section the most commonly used installation methods are discussed shortly,

together with the possible limit states [Kyriakides, 2007].

Figure 1.2 Schematic representation of S-lay pipeline installation and associated pipeline loadings

[Kyriakides, 2007]

The first installation method to be discussed is S-lay, referring to the shape in which the pipeline is sus-

pended from the vessel to the seabed as illustrated in Figure 1.2. During S-lay pipe joints are welded to

the free end of the pipeline, after which the welds are inspected and coated in a linearly arranged series

of stations onboard. The welded pipe joints leave the vessel at the stern, held by tensioners and supported

by the stinger with which the overbend radius is controlled. A too short stinger or too small bending

radius, might lead to excessive bending of the pipe, leading to buckling and fracture, possibly resulting

in flooding of the pipeline. After the pipeline leaves the stinger, it straightens and in the sagbend bends

in the opposite direction. The bending radius in the sagbend is controlled by the tension exerted by the

vessel. Excessive bending due to movement of the vessel in combination with the external water pres-

sure might result in local buckling and collapse. In general plastic deformation in overbend and sagbend

is avoided, and lay tension is minimised to avoid extensive ovalisation and additional installation costs.

The S-lay installation method is characterised by its high production rate, up to 6.5 km/day. It is most

suitable in shallow and intermediate water depths, because larger water depths require a longer stinger.

The second installation method is J-lay where the pipeline leaves the vessel nearly vertical and is laid

down on the seabed via the sagbend as shown in Figure 1.3. During J-lay pre-welded multiple joint sec-1.3. During J-lay pre-welded multiple joint sec-. During J-lay pre-welded multiple joint sec-

tions are raised into the tower and then welded to the free end of the pipeline, after which the weld is

inspected and coated in a single station. The welded pipe joints are then lowered while the vessel moves


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3 Introduction

forward, laying down a corresponding length of pipeline to the seabed. Excessive bending due to move-

ment of the vessel in combination with the external water pressure might result in local buckling and

collapse. The production rate for the J-lay installation method, up to 3.2 km/day, is somewhat lower than

for S-lay, but it is suitable for deeper waters due to the shorter suspended pipeline length resulting in a

reduced required lay tension.

Figure 1.3 Schematic representation of J-lay pipeline installation and associated pipeline loadings

[Kyriakides, 2007]

The last installation method to be discussed is the reel-lay installation method. Onshore, long lengths

of pipeline are welded together. After inspection of the welds and coating, the pipeline is spooled onto a

large diameter reel, generally mounted on the installation vessel. After spooling the pipeline onto the reel,

the vessel sails to the installation site and starts installing by gradually unspooling the pipeline as illus-

trated in Figure 1.4. Eliminating most of the pipeline fabrication processes offshore and instead executing

them onshore, results in significant reductions in installation time and costs. Reeling is the most efficient

installation method, reaching laying rates up to 3.5 km/hour.

Figure 1.4 Schematic representation of Reel-lay pipeline installation [Kyriakides, 2007]


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4 Chapter 1

However, during the reeling process the pipeline is plastically deformed, experiencing strains in the order

of 2%. The impact of the reeling installation method on the integrity of the pipeline becomes clear from

the mechanics during the process, which can best be described following the moment-curvature (M-)

diagram of a pipeline subjected to reeling, as given in Figure 1.5. During the reeling process, the following

stages can be distinguished:

1. Spooling on;2. Unspooling, and

3. Straightening.

During spooling on, the end of the pipeline is attached to the reel, a holdback tension is applied and

the reel is rotated slowly. The pipeline is plastically deformed until it follows the reel radius (0-1). Dur-

ing unspooling the pipe straightens due to the tension, experiencing reverse bending, as it is pulled of

the reel to the aligner (1-2). On the aligner, the pipeline is bent to a fixed curvature before entering the

aligner (2-3). As the pipeline moves from the aligner to the straightener, the pipeline straightens (3-4)

and is reverse bent in the straightener (4-5), so that after unloading (5-0) it ends up at zero moment andcurvature.

Figure 1.5 Moment-curvature response of pipeline during reeling installation

The multiple bending cycles during the reeling process induce ovalisat ion of the pipe cross section, reduc-

ing the resistance of the pipe against external pressure and local buckling. Additionally, extensive plastic

deformation results in some permanent elongation and changes in the material properties.

1.3 Lined Pipe

Together with the volume of recovered corrosive hydrocarbons increasing, the need for corrosion mitiga-

tion grows. When the hydrocarbons are only mild corrosive, carbon steel pipelines can be applied. In many

cases a corrosion allowance suffices, or otherwise addition of corrosion inhibitors or a plastic coating.

However, when corrosivity of the hydrocarbons increases and long term corrosion resistance needs to be


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5 Introduction

guaranteed, these mitigation methods do not longer suffice. Corrosion resistant alloy pipelines provide a

more suitable solution in these cases. Solid corrosion resistant alloy pipelines are very expensive.

A more cost efficient option are double walled pipes, consisting of a carbon steel load bearing outer pipe,

that provides the structural capacity, and a corrosion resistant alloy liner, protecting the carbon steel

outer pipe against the transported corrosive hydrocarbons. Two types of double walled pipes exist:- Metallurgically bonded; clad pipe, and

- Mechanically bonded; lined pipe

In comparison with clad pipe, lined pipe has the advantage that it is less expensive and has a shorter lead

time. Several manufacturing processes for the production of lined pipe exist. Lined pipes are manufac-

tured in joints of 12m length. At the ends of the joint, the liner and outer pipe are generally sealed with a

clad girth weld, which allows for NDT and cutbacks during welding offshore. A more detailed discussion

on the manufacturing process will follow in section 2.1.

1.4 Research on the Mechanical Behaviour of Lined Pipe

Over the last years, the behaviour of lined pipe during bending and reeling has gained interest as a re-

search topic. In 2002, Heerema Marine Contractors started a research project in cooperation with Delft

University of Technology and Kuroki Tube and Pipe to investigate the influence of reeling installation on

liner wrinkling and pipe ovalisation [Focke, 2007]. Axial compression tests and full scale reeling tests of

the spooling-on process were performed on TFP, in order to investigate liner wrinkling. This resulted in

a significant increase in knowledge on the behaviour of TFP during spooling-on [Focke, 2005a; 2005b;

2006; 2007; 2007a]. It was found that lined pipe undergoing high plastic strains during reeling, exhibits

liner wrinkling and extensive ovalisation. Det Norske Veritas initiated a Joint Industry Project called Lined

and Clad Pipeline Materials in 2005 which still continues. This project will result in a design guideline with

updated requirements for the design and fabrication of lined and clad pipelines [DNV, 2007; Johnsrud,

2009].In 2007 HMC and Delft University of Technology started the current research with the objective

to further investigate the influence of relevant variables on the mechanical behaviour of lined pipe during

bending, in particular the onset of wrinkling and the growth of the wrinkles during further bending. In

2010 both Statoil [Endal, 2010] and Technip [Howard, 2010] patented the application of internal over-

pressure during reeling to minimise wrinkling. Very recently, Technip has published a paper describing their

development program to design and qualify mechanically lined pipes for reeling based on the use of lined

pipe with appropriately chosen liner thickness without the use of internal pressure [Tkaczyk, 2011a]. A

patent covering the results of this development program has been applied for [Tkaczyk, 2011b]. A numeri-

cal analysis on the buckling of lined pipes under bending and external pressure is described by Vasilikis

and Karamanos [Vasilikis, 2011].

1.5 Research Objective

Installing lined pipe by means of the reeling installation method seems to be an attractive combination,

because it provides the opportunity of eliminating the demanding welds from the critical time offshore


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6 Chapter 1

and instead preparing them onshore. However, reeling of lined pipe is not yet proven technology. From

previous research [Focke, 2007] it is known that lined pipe undergoing high plastic strains during reeling,

exhibits liner wrinkling and extensive ovalisation. However, the mechanisms leading to these limit states

were not fully understood.

Local buckling of the outer pipe and thus of the integral lined pipe should be limited because of the fol-lowing reasons [Focke, 2007]:

- The lined pipe installed on the seabed needs to have sufficient resistance against the external water

pressure.

- A local buckle present after installation might increase during operation, for example in overspans.

Excessive local buckles will obstruct the flow of hydrocarbons and a pig from passing through the

pipe.

- Local buckling of the integral lined pipe might lead to fracture in the liner material. Once a through

wall crack is present in the liner, the corrosion resistance is no longer guaranteed. Additionally, in case

of a sudden pressure drop an overpressure might occur in between the liner and the outer pipe leadingto collapse of the liner.

Liner wrinkling should be limited because of the following reasons [Focke, 2007]:

- Wrinkles present in a production line might grow and shrink under the influence of fluctuations in

operation pressure, causing crack initiation.

- The presence of excessive liner wrinkles will obstruct the flow of hydrocarbons and a pig from passing

through the pipe.

The main objective of this study is to investigate the possibility of installing lined pipe by means of the

reeling installation method. Initially, interaction of the lined pipe with the reel is not taken into account

while pure bending of the lined pipe is investigated. After the behaviour of the isolated lined pipe in pure

bending is fully understood, the interaction with the reel can be added to the process. In dealing with the

main research objective, the following questions are posed:

1. What variables do influence the mechanical behaviour of lined pipe in pure bending leading to a limit

state?

2. What is the sensitivity of the wrinkling behaviour to the identified variables, in particular the onset

of wrinkling and the growth of the wrinkles during further bending?

Based on the obtained knowledge, the parameters that influence the mechanical behaviour of lined pipe

in pure bending leading to a limit state can be quantified, enabling safe and economic design of lined pipe

for installation.

1.6 Research Approach and Thesis Outline

The research approach is based on the two different failure modes exhibited by elastic-plastic cylinders

under pure bending [Kyriakides, 1987; Reddy, B.D., 1979]:

- Thick elastic-plastic cylinders ( smaller than about 40 for steel) exhibit a moment maximum due


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7 Introduction

to uniform ovalisation, after which ovalisation localises. This is generally referred to as the natural

limit load due to the Brazier effect.

- Thinner elastic-plastic cylinders exhibit wrinkling and shell-type buckling leading to localised col-

lapse, which can precede the natural limit load of the Brazier effect as described for the thick cylin-

ders above. In these cases wavy deformations at the compression side of the cylinder develop, which

grow under increasing bending moment and curvature and then localise in a local kink. This in con-trast with thin elastic cylinders ( larger than about 120 for steel) that may buckle in the elastic

region and develop wrinkles and shell-type buckling even earlier, which can evolve into axisymmetric

or even diamond shaped shell buckling modes.

Depending on the diameter-to-thickness ratio of the pipe either one of these mechanisms will occur, or

the two mechanisms will interact, resulting in final failure of the cylinder having a specific shape of local

buckling as illustrated in Figure 1.6 and Figure 1.7 [Corona, 1988; Kyriakides, 1992; Corona, 2006]. Based

on the diameter-to-thickness ratio of liner and outer pipe, 100 and 22 respectively, the two mechanisms

are expected to interact in the lined pipe.

Figure 1.6 Local buckling of a thick walled elastic-plastic cylinder (SS-304 ) [Kyriakides, 2007]

Figure 1.7 Local wrinkling of a thin walled elastic-plastic cylinder (Al 6061-T6 ) [Kyriakides, 2007]

In order to be able to determine what variables influence the mechanical behaviour of lined pipe and

to identify their sensitivity to this behaviour, first the mechanical behaviour of lined pipe needs to be

understood. The research approach, as illustrated in Figure 1.8, is to first investigate the two different

failure modes exhibited by elastic-plastic cylinders separately, i.e. liner wrinkling and ovalisation, before

allowing them to interact. Investigation of the failure modes is based on finite element modelling in the

software package Abaqus/Standard. The liner wrinkling failure mode is investigated separately with axial


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8 Chapter 1

compression models, while models with unit length subjected to pure bending have been developed to

investigate the ovalisation failure mode separately. Subsequently three dimensional full length models

are developed in which the pipes are subjected to pure bending, and the two possible failure modes may

interact. The failure mechanisms in the lined pipe can be better understood by investigating pure bending

than by reeling, because in pure bending the lined pipe can be observed isolated, excluding the interaction

between lined pipe and reel.

Before starting the failure mode investigation, the characteristics of Tight Fit Pipe (TFP), a type of lined

pipe will be discussed in Chapter 2, starting with a description of the manufacturing process. The rest of

the chapter includes descriptions and results of the tests with which the characteristics of the TFPs that

were subjected to four point bend tests were determined.

For investigation of liner wrinkling, the single walled liner and the liner confined in the outer pipe have

been modelled in axial compression. The buckling behaviour of the single walled liner under axial com-

pression is discussed in Chapter 3. Additionally, the model outcomes are compared with test resultsfrom Focke [2007]. In Chapter 4 the buckling behaviour of the liner confined in the outer pipe under axial

compression is discussed. Both chapters include a parameter study to determine the influence of several

geometric and material parameters as well as friction on liner wrinkling.

The buckling behaviour of the single walled liner and outer pipe in pure bending is discussed in Chapter 5.

For determination of the limit load due to ovalisation, models with unit length subjected to pure bending

have been developed. Three dimensional full length models are developed in which the pipes are subjected

to pure bending, and the two possible failure modes may interact. The numerical results are compared

with the outcomes of empirical formulas. A parameter study is performed on the full length single walled

liner model to determine the influence of several geometric and material parameters on liner wrinkling.

The full scale four point bend tests that were executed on a number of eight TFPs are described in Chapter

6, and the test results are presented. In Chapter 7 the wrinkling behaviour of the confined liner as part

of the lined pipe in pure bending is discussed. The numerical results are compared with the test results.

Additionally, a parameter study is performed to determine the influence of the geometric, material and

contact parameters on the mechanical behaviour of lined pipe in pure bending. With this parameter study

the variables that do influence the mechanical behaviour of lined pipe in pure bending are determined, as

well as their sensitivity to this behaviour, in particular the onset of wrinkling and the growth of wrinkles

during further bending.

As a final step, numerical pure bending results are compared with reeling test results in Chapter 8 in order

to determine the influence of reeling on the mechanical behaviour of lined pipe.


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9 Introduction

Figure 1.8 Research approach and thesis outline, showing the relationship between chapters

1.7 Conventions

1.7.1 Geometry and coordinate system

The cylinder geometry and coordinate system used for the liner and the outer pipe are given in Figure 1.9.

In this figure denotes the radius, and denote the length and thickness of the cylinder, respectively.

The in-plane positions in circumferential and axial direction of a typical point are denoted by and ,

whereas the radial position is referred to as . The corresponding displacements and rotations are denoted

by and . The liner may have an initial geometric imperfection , that is assumed to be stress-free and

positive inward.


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10 Chapter 1

Figure 1 .9 Shell geometry and coordinate system Figure 1 .10 Deformed geometry for calcu-

lating ovalisation

1.7.2 Parameter definition

For describing buckling behaviour of the liner under axial compression, the following parameters are used:

- The global axial strain, , which is calculated over a certain length of the cylinder as the quotient

of the displacement over the initial length:

- The axial stress, , is extracted at the cylinder end, or the end of the region of interest, where

the load is applied.

In correspondence with Murphey and Langner [Murphey, 1985], the geometric parameters curvature and

global bending strain will be used to describe the critical bending behaviour of the cylinders. The small

difference between the global bending strain and the actual local strain is not accounted for. The buckling

behaviour of the liner under bending is described with the following parameters:

- The global bending curvature, which is calculated over a certain length of the cylinder as the quo-

tient of the rotation over the initial length:

- The global bending strain, , which is calculated as the product of the bending curvature and the

outer radius of the cylinder:

- The global bending moment, , is measured at the cylinder end, where the load is applied.

- Ovalisation, , is measured in the deformed pipe geometry as illustrated in Figure 1.10 at discrete

positions along the cylinder:


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11 Tight Fit Pipe

2. Tight Fit Pipe

An increasingly applied solution for the transportation of corrosive hydrocarbons is lined

pipe. Lined pipe consists of a carbon steel load bearing outer pipe that provides thestructural capacity and a corrosion resistant alloy (CRA) liner, protecting the carbonsteel outer pipe from the transported corrosive product. The liner is mechanically fittedinside the outer pipe. The following manufacturing processes are known to be used forthe fabrication of lined pipe:- Hydraulic expansion of the full pipe length;- Hydraulic expansion in steps along the pipe length;- Thermo-hydraulic expansion of the full pipe length, and- Forming of welded plates.

The thermo-hydraulic expansion process is used by Kuroki Tube and Pipe for the fabrication of TFP, a type

of lined pipe. This is the only expansion process resulting in a mechanical fit when using liner materials

with higher E-moduli such as duplex. A detailed description of this manufacturing process is given in sec-

tion 2.1.

A number of twelve TFPs were provided by Kuroki Tube and Pipe for this research. An overview of the

tested pipes characterised by their material properties, geometric properties and residual hoop stress, the

treatments before testing as well as the tests performed are included in Table 2.1 and Table 2.2.

After explanation of the manufacturing process of TFP, the procedures for obtaining the geometric char-

acteristics of the TFP are discussed. Complete descript ions of the procedures and all results of the tensile

tests and residual compressive stress tests are included in [Kolstein, 2010]. This chapter includes an

analysis of the results. The bend tests are discussed separately in Chapter 6.


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12 Chapter 2

Table 2.1 Characteristics and performed tests on TFPs without a coating simulation cycle


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13 Tight Fit Pipe

Table 2.2 Characteristics and performed tests on TFPs with a coating simulation cycle

2.1 Manufacturing Process of Tight Fit Pipe

TFP is a double-walled pipe where a corrosion resistant alloy liner is mechanically fitted inside a car-

bon steel outer pipe through a thermo-hydraulic manufacturing process as illustrated in Figure 2.1. A

schematic representation of the stress and strain ( ) development in the hoop direction of the

liner during the different stages of the manufacturing process is given in Figure 2.2. The numbers in the

explanation of the different manufacturing stages, correspond with the numbers indicated in the figures.

(1) First the outer pipe is heated to a certain temperature inside an oven in which it remains throughout

the manufacturing process. Subsequently, the corrosion resistant alloy liner is inserted concentrically

into the heated outer pipe, while the liner temperature is kept low using cooling water. (2) Just after

insertion, the water pressure in the liner is increased and the liner is expanded first elastically and then

plastically. The liner comes in contact with the outer pipe. Further increase of the water pressure causes

the outer pipe to expand elastically together with the plastically expanding liner. (3) The liner tempera-


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14 Chapter 2

ture increases due to contact with the outer pipe. (4) Then, the water pressure is decreased, causing both

the outer pipe and the liner to shrink elastically, together forming the TFP. (5) Finally the oven is opened

and the TFP is cooled in the atmosphere [Focke, 2007].

At the end of the manufacturing process a residual compressive hoop stress is present in the liner and a

residual tensile hoop stress in the outer pipe, both illustrated in Figure 2.3. The resulting contact stressbetween the liner and the outer pipe provides the mechanical bond as can be seen in Figure 2.4. Further-

more, a residual compressive axial stress is present in the liner and a residual tensile axial stress in the

outer pipe, as illustrated in Figure 2.5.

Figure 2.1 Schematic representation of the TFP manufacturing process [Focke, 2007]

Figure 2.2 Liner hoop stress and strain during manufacturing process of TFP


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15 Tight Fit Pipe

Figure 2.3 Equilibrium of tensile hoop stress in

outer pipe and compressive hoop stress in liner[Focke, 2007]

Figure 2.4 The radial contact stress causes a

mechanical bond between the liner and outer pipe[Focke, 2007]

Figure 2.5 Equilibrium of tensile axial stress in outer pipe and compressive axial stress in liner

2.2 Geometry of Tight Fit Pipes

According to the standards, pipes can deviate from the nominal dimensions within specified tolerances.

The actual dimensions of the tested TFPs were measured as described in this section.

2.2.1 Thickness

The thickness of the liner and outer pipe could not be measured for the intact TFPs, because the ends

were seal welded. Therefore the thicknesses were measured from the residual compressive stress test

specimens at four equally spaced positions around the circumference with a mechanical calliper. The

thicknesses of the TFPs on which no residual compressive stress tests were performed, were measured

after testing when they were sectioned. The thicknesses and as included in Table 2.1 and

Table 2.2 are the average values of the four measurements.

For the numerical models, the conservative, nominal thicknesses were taken. When comparing the model

results with the bend test results, this underestimation should be accounted for.


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16 Chapter 2

2.2.2 Diameter

The measured outer diameters of the outer pipe as included in Table 2.1 and Table 2.2 are the

average of two values measured at each pipe end. The diameter was measured with a mechanical calliper

at two equally spaced positions around the circumference, in the same cross-sectional plane for both

pipe ends.

The pure bending numerical models will be validated based on the experimental bend test results of the

three TFPs without a coating simulation cycle. The outer diameters of the outer pipe used in the numeri-

cal models should therefore correspond with the actual bent TFPs and is set equal to the 324.7mm outer

pipe outer diameter of the two 14.3mm thick outer pipes. This value slightly overestimates the outer

diameter of the 17.5mm thick seamless outer pipe. When comparing the model results with the bend test

results, this overestimation should be accounted for.

2.3 Stress-Strain Curves of Tight Fit Pipes

Tensile tests are performed on liner and outer pipes of the TFPs to determine the stress-strain response,

after the coating simulation cycle when applicable.

2.3.1 Set up and procedure of tensile test

The tensile tests are performed according to [NNI, 2001]. Specimens were taken from liner and outer pipe

in both hoop and axial direction in order to determine the material characteristics in these two directions,

as illustrated in Figure 2.6 and Figure 2.7. For the ERW pipes, the tensile specimens were taken outside the

heat affected zone of the weld. The liner wall was insufficiently thick to take a full round specimen from

the hoop direction. Therefore, a specimen with a similar shape as the axial specimens was taken from the

liner in hoop direction, after which it was flattened.

Figure 2.6 Liner tensile specimens Figure 2.7 Outer pipe tensile specimens


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17 Tight Fit Pipe

Figure 2.8 and Figure 2.9 illustrate the test set up for the flattened liner hoop specimen and the round

outer pipe hoop specimen, respectively. The total elongation over the complete length of the specimen

was measured with the actuators of the tensile test machine. Additionally, an extensometer was placed

over the mid section of the specimen to measure local elongations where necking was expected to occur.

Necking did not always occur in this section, but then still the total elongation could be used to deter-

mine the stress-strain curve for the specimen.

Figure 2.8 Flat specimen in test arrangement Figure 2.9 Round specimen in test arrangement

The E-moduli resulting from the measured stress-strain curves during elastic deformation appeared to be

higher than what was expected from literature. This might be caused by some setting in the test arrange-

ment at the beginning of the test . It was decided to replace the resulting E-moduli with the values known

from literature, i.e. 205 GPa for X65 and 193 GPa for 316L. The relevant stresses and strains as obtained

from the tensile test results are included in Table 2.1 and Table 2.2.

2.3.2 Tensile test results of Tight Fit Pipes without coating simulation cycle

Pure bending numerical models will be compared with experimental bend test results of three TFPs with-

out a coating simulation cycle. The material response used in the numerical models should therefore

correspond with the actual bent TFPs. In Appendix A representative curves from the tensile tests are

selected. Figure 2.10 includes the selected representative curves, P01KA M90-K for the outer pipe, and

T13KB M99-K for the liner. From comparison of the tensile test results it was found valid to consider

the liner and outer pipe material to be isotropic. Furthermore, the outer pipe material acts significantly

stronger than the liner material.

In the numerical models the liner material consists of a linear elastic part, with a modulus of elasticity

of 193 GPa until the representative curve deviates from this slope, followed by a plastic part, in corre-

spondence with the representative stress-strain curve. The material curve for the outer pipe material is

constructed in the same way, with a modulus of elasticity of 205 GPa.


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18 Chapter 2

The representative outer pipe stress-strain curve matches the seamless pipes well, while it slightly over-

estimates the ERW outer pipe stress-strain curve. The numerical bend models can be validated directly

based on the bend tests on TFPs with 14.3mm and 17.5mm seamless outer pipes. When comparing the

model results with the bend test results of the TFP with the ERW outer pipe, the overestimation of the

outer pipe strength in the models should be accounted for.

The use of isotropic hardening and associative plasticity with a Mises yield surface in this research is

anticipated to give sufficiently accurate numerical results, because the lined pipe materials do not show

extensive hardening and the pipes are only bend ones in a single direction.

0 0.01 0.02 0.03 0.04 0.050

100

200

300

400

500

600

700

[-]

[MPa]

Representati ve tensile test curve

liner T13KB M99-KRepresentati ve tensile test curve

outer pipe P01KA M90-K

Figure 2.10 Representative true stress-strain curves for liner and outer pipe

2.3.3 Tensile test results of Tight Fit Pipes with a coating simulation cycle

In addition to the tensile tests on the TFPs without a coating simulation cycle, some more tests were

performed on a TFP that underwent a coating simulation cycle, during which it was fully heated at 2200C

before it was tested and bent. The results of these tests are included in Appendix A. In correspondence

with the results from the TFPs without a coating simulation cycle, it was found that the material behav-

iour of both the liner and the outer pipe is isotropic and that the outer pipe material acts significantly

stronger than the liner material.

2.3.4 Comparing tensile test results of Tight Fit Pipes without and with a coating simula-tion cycle

The stress-strain curves resulting for the liner and the outer pipe of the TFPs with a seamless, 17.5mm

thick outer pipe, of which one underwent a coating simulation cycle while the other did not, are given in

Figure 2.11.

The outer pipe material of the TFP (T12KA) that underwent a coating simulation cycle acts less strong

than the untreated TFP (T13KB), while the stress-strain curves of the liner material do correspond well.

The relatively low temperatures and durations of the coating simulation cycle were not expected to have

any influence on the material properties. If it would have an influence, an effect on the chrome alloy of the

liner would be more likely than on the carbon steel of the outer pipe. The difference in strength of the two


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19 Tight Fit Pipe

carbon steel outer pipes was probably already present before the coating simulation cycle. This is con-

firmed by the fact that an equal stress difference is found between the material properties of the three

pipes without a coating simulation cycle as included in Appendix A. Furthermore, since the variability of

the material properties in seamless pipes is known to be high and the test specimens were taken from the

pipe at a certain location, the tensile test results might be different at other locations.

Figure 2.11 Nominal stress-strain curves for liner and outer pipe of 17.5mm and without a coating simula-

tion cycle compared

2.4 Radial Contact Stress in Tight Fit Pipes

As a result of the manufacturing process, a residual compressive hoop stress is present in the liner and

a residual tensile hoop stress in the outer pipe. The resulting radial contact stress between the liner and

the outer pipe provides the mechanical bond as was illustrated in Figure 2.4. This resulting radial contact

stress will be determined by means of residual compressive stress tests.


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20 Chapter 2

2.4.1 Set up and procedure of residual compressive stress test

Residual hoop stress tests are performed on 200mm long TFP specimens in correspondence with the

method as proposed in [API, 2009], to determine the residual compressive stress in the liner due to the

mechanical bond between liner and outer pipe. During these residual compressive stress tests, the outer

pipe is taken off the liner by saw-cutting it in longitudinal direction with a band saw as illustrated in

Figure 2.12.

Figure 2.12 Residual compressive stress test

The inside surface of the liner is equipped with three bi-axial strain gauges at half the specimen height at

600, 1800and 3000around the circumference, while the saw cut is located at 1200as illustrated in Figure

2.13. During saw cutting the outer pipe, the strain gauges measure the changes in hoop and axial strains

in the liner continuously.

Figure 2.13 Location of strain gauges and saw cut during residual compressive stress test

The measured strain changes equal the elastic strains that were present in the liner after the manufac-

turing process of the TFP. During the manufacturing process, the liner is plastically deformed and plastic

strains are present in the liner as a result. The difference between the measured strain changes and the

actual strains present in the liner as part of the TFP is illustrated schematically in Figure 2.14. The radial

contact stress between the liner and outer pipe is the result of the difference in elastic strains and can

thus be derived from the measured strain changes. In addition to the strain changes, the resulting gap

between the two saw cut surfaces was measured at half the outer pipe thickness.


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21 Tight Fit Pipe

Figure 2.14 Measured change in hoop strain

The residual stresses in hoop and axial direction that were present in the liner can be calculated from themeasured strain changes with the following equations:

where is the number of strain gauges.

Additionally, the radial contact stress that was present between liner and outer pipe can be retrieved with

the following equation:

In Appendix B, a discussion on the validity of the residual compressive stress test and its results is

included. As a result of this discussion it is considered valid to use the strain changes measured during the

residual compressive stress test as a first approximation for calculating the contact stress, hoop stresses,

and axial stresses originally present in the TFP.


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22 Chapter 2

2.4.2 Residual compressive stress test of Tight Fit Pipes without pretreatment

The strains measured during the residual compressive stress test for the TFP with the 14.3mm thick

seamless outer pipe are represented in Figure 2.15, as an example. This figure shows that the axial strains

decreased, while the hoop strains increased, i.e. that the liner shortened in length and increased in diam-

eter. The material needed for the increase in diameter was provided for by a decrease in length.

An overview of the measured strains for the TFPs tested is given in Table 2.1 and Table 2.2. The average

strains are based on two or three consistent measured strains. In case one strain showed significant

deviation from the remaining two, it is not included in the average strain.

Figure 2.15 Strain curves for liner and outer pipe of 14 .3mm seamless TFP P01KA in hoop and axial direction

2.4.3 Influence of preheating and hydrotesting on radial contact stress

To investigate the influence of preheating and hydrotesting on the residual compressive stress, speci-

mens of a TFP with a seamless 17.5mm thick outer pipe (T14KA), were given the following pretreatments

before they were subjected to the residual compressive stress test:

- Preheating at 1800C for 30 minutes;

- Preheating at 2500C for 30 minutes;

- Hydrotesting at an internal pressure of 150 bar for 10 minutes. These hydrotests were carried out on

1000mm long TFP pieces, which were closed with welded end caps. After hydrotesting the 1000mm

long pieces were cut into 200mm long specimens.

An overview of the measured strains for these pipe specimens is given in Table 2.3.

The influence of preheating can be determined by plotting the contact pressures against the preheating

temperatures. From Figure 2.16 it can be concluded that preheating had a negative effect on the contact

stress, and increase of the preheating temperature resulted in a further decrease of the contact stress.

The loss of contact stress due to preheating is caused by the thermal expansion coefficient of the liner

being higher than that of the outer pipe.


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23 Tight Fit Pipe

Table 2.3 Residual compressive stress results of TFPs with different heat treatments and hydrotests

Figure 2.16 Influence of preheating temperature on contact stress

Figure 2.17 Influence of hydrotest pressure on contact stresses from different preheating temperatures

From Figure 2.17, it unexpectedly shows that hydrotesting resulted in a further decrease of the contact

stress. Theoretically it is expected that a hydrotest introducing plastic deformation of the liner would

result in an increase of the contact stress due to the elastic radial retraction of the outer pipe being larger


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24 Chapter 2

than of the liner after pressure release. Test results in correspondence with this expectation are reported

by Wilmot [2011].

2.5 Conclusions

The geometric and material characteristics that will be used as the base case for the numerical models

simulating axial compression and pure bending of the single walled liner, single walled outer pipe and the

lined pipe, are included in Table 2.4.

Table 2.4. Material and geometric characteristics TFP used for base case pure bending numerical model

*) The yield stress for the liner cannot properly be defined, since the 316L material shows plasticity at very

low strains


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25 Axial Compression of Single Walled Pipe

3. Axial Compression of Single Walled Pipe

3.1 Introduction

The wrinkling behaviour of single walled cylinders under axial compression has been atopic of interest for many researchers. Much work has been done on elastic wrinkling;however, the liner investigated in this chapter wrinkles in the plastic range.

The main experimental data for plastic wrinkling of single walled elastic-plastic cylindrical shells under

axial compression quoted in literature are from Lee [1962] and Batterman [1965]. In addition to the

experiments, both authors compared the experimental results with analytical predictions. As mentioned

by Bardi [2006a], Lees comparison of the measured limit stresses with calculated bifurcation stressesis inappropriate because of the significant difference in strains at which bifurcation occurs. Additionally,

Bardi mentioned that Battermans conclusions based on his experiments are somewhat suspicious since

his experimental collapse stresses were influenced by length effects. However, these length effects do

not influence Battermans analytical predictions for infinitely long cylinders. In this chapter, Battermans

analytical predictions will be used.

Additional analytical works were published, starting with Bushnell [1976]. Bushnells Bosor-5 program

based on the finite difference energy method calculates plastic wrinkling and post buckling for a variety

of different cylindrical shells. Gellin [Gellin, 1979] also developed a model for the post buckling behaviour

of elastic-plastic axially loaded cylindrical shells. Amongst others, Tvergaard [1983a; 1983b] extended

this type of analysis by first allowing the axisymmetric wrinkles to localize and then modelling the transi-

tion to non-axisymmetric wrinkling modes.

A very comprehensive description of the behaviour of cylindrical shells under axial compression was given

by Bardi [2006a; 2006b]. This description is used as a guide to explain the cascade of events preced-

ing plastic collapse of the liner. Figure 3.1 shows a typical stress-strain response resulting from a

numerical model of a single walled liner under axial compression. Initially the liner deforms uniformly fol-

lowing the perfect response, until the so-called plastic bifurcation point is reached, as indicated in Figure

3.1, from which the liner response deviates from the perfect response. Axisymmetric wrinkling becomes

prevailing with increasing amplitude, eventually leading to the limit load as indicated in Figure 3.1. The

limit load can be considered as the limit state of the structure. Under displacement controlled loading

after passing the limit load, the load carrying capacity of the liner drops.


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26 Chapter 3

Figure 3.1 Typical stress-strain response of single walled liner under axial compression

In this thesis, the wrinkling behaviour of the numerical models is evaluated based on the stress and strain

at the resulting limit load, since the limit load can be better defined than the bifurcation point. However,

the analytical methods give expressions for the stress and strain at the bifurcation point. For the numeri-

cal models of the single walled liner, the bifurcation point is defined as the point where the stress differ-

ence between the liner response and the perfect solution exceeds 0.1%.

3.2 Analytical Results

As mentioned in the introduction, an analytical prediction of the critical stress, strain and half wave-

length at the bifurcation point is obtained according to Batterman [1965].

An analytical fit of the stress-strain curve as resulted from the tensile tests is required. The liner mate-

rial has a low proportionality limit and extended strain-hardening capability, characteristic for stainless

steel alloys as discussed by Rasmussen [Rasmussen, 2001]. As a consequence, nor the Ramberg-Osgood

expression nor the Needleman expression give representative fits. The following alternative analytical fit

developed for the stress-strain curves of stainless steel alloys based on the Ramberg-Osgood expression

[Rasmussen, 2001], is used:


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The derivation of the input parameters from a tensile test stress-strain curve is illustrated in Figure 3.2.

The characteristic values used to fit the representative material curve of the liner material with the alter-

native analytical Ramberg-Osgood expression are included Table 2.4. The resulting stress-strain response

of the fit is given in Figure 3.3, together with the representative tensile test curve of the liner material as

derived in section 2.3.2.

Figure 3.2 Definition of input parameters for alternative Ramberg-Osgood expression

Figure 3.3 Representative tensile test and alternative Ramberg-Osgood fit of liner compared


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28 Chapter 3

This stress-strain curve is used to derive the material moduli used by Batterman [1965] as illustrated

in Figure 3.4 as input for the analytical equations to determine the plastic critical wrinkling stress and

strain, as well as the critical half wavelength of the axisymmetric mode.

Figure 3.4 Definition of modulus of elasticity, tangent modulus and secant modulus

The theory according to Batterman [1965] provides the following analytical equations, based on the

J2-flow theory with isotropic hardening:

Similar expressions were obtained by Batterman for the J2-deformation theory.


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The resulting stress, strain and critical half wavelength values at the bifurcation points calculated

according to Batterman are included in Table 3.1 and plotted in Figure 3.5, together with the stress-strain

curves from the tensile test and the analytical fit according to the alternative Ramberg-Osgood expres-sion. It shows that flow theory gives results that bifurcate later than deformation theory.

Figure 3.5 Bifurcation stresses and strains according to Batterman

Table 3.1 Plastic bifurcation stress, strain and critical half wavelength according to Batterman

In literature extensive discussions on the proper choice of a plasticity theory for bifurcation buckling

can be found [Deerenberg, 1994]. From a physical perspective, flow theory is the correct theory to use.

However, for some bifurcation buckling problems of thin-walled metallic structures, such as axially com-

pressed cylindrical shells, the so-called plastic buckling paradox exists. It has been shown by vari-

ous authors [Bushnell, 1982; Blachut, 1996] that test results are in better agreement with deformation

theory than with flow theory, the latter resulting in unrealistically high bifurcation loads. For different

bifurcation buckling problems it was demonstrated that small imperfections bring the outcomes of the

J2-flow and deformation theories closely together [Tugcu, 1991]. Needleman and Tvergaard [Needleman,

1981; Tvergaard, 1983] showed in particular for axially compressed cylindrical shells that a plasticity

theory with a corner in the yield surface lowers the buckling stress in comparison with the flow theory.

Sewel [Sewel, 1972] anticipated that the precise truth involves a combination of anisotropy, yield surface

corners and imperfections. Summarising, no simple answer exists on what plasticity theory to use for a

buckling problem.


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30 Chapter 3

Since the main focus of this study is bending of lined pipe, for which the plastic buckling paradox does

not apply, flow theory with isotropic hardening will be used throughout the complete study. Flow the-

ory for axial compression resulted in high bifurcation loads, but the results were more consistent than

obtained with deformation theory. The bifurcation results for axial compression will be adjusted by intro-

ducing small geometric imperfections.

3.3 Numerical Results

3.3.1 Linear buckling analysis

Linear buckling analyses, i.e. eigenvalue analyses, are performed on different lengths of the liner to deter-

mine the critical half wavelength.

Model description of numerical linear buckling analysis

The geometry of the liner model as used for the linear buckling analyses is shown in Figure 3.6. Nosymmetry planes are used in the circumferential direction, to allow for all axisymmetric as well as non-

axisymmetric mode shapes to occur. The cylinder ends are constrained to a reference point at the centre

of the respective cylinder end, and , by means of a kinematic coupling in axial and tangential

direction, as illustrated in Figure 3.7. The applied boundary conditions fully constrain the reference point

at , while the reference point at is free in axial direction. A unit load is applied at the reference

point at , compressing the liner in axial direction.

Figure 3.6 Geometry and boundary conditions of

single walled liner, linear wrinkling model

Figure 3.7 Geometry including mesh and kinematic

couplings of single walled liner linear wrinkling

model

The mesh consists of three layers of C3D8R solid elements, which are 8-node linear bricks with reduced

integration and hourglass control. The number of elements in circumferential direction is kept constant at

240 elements. While varying the length of the liner, the number of elements in axial direction is adjusted

to keep the ratio between element length and width approximately constant at one.


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31 Axial Compression of Single Walled Pipe31

3.3.2 Results of numerical linear buckling analysis

From linear buckling analyses on different liner lengths, the first wrinkling mode shape of the liner is

axisymmetric for all lengths, similar to the enlarged linear mode shape as shown in Figure 3.8 for the liner

having a length of 106 mm.

Figure 3.8 Axisymmetric mode shape of liner with length of 106mm consisting of three half waves

With increasing liner length, the liner exhibits an increasing number of half waves . For example, in

a liner with a total length of 50mm only one half wave develops when performing an eigenvalue analysis,

while two half waves develop in a 51mm long liner. A liner with a total length of 86mm exhibits two half

waves and an 87mm long liner exhibits three half waves in an eigenvalue analysis. For each number of half

waves, a maximum and minimum total length for the cylinder is determined. By dividing the total cylinder

length by the number of half waves, the maximum and minimum half wave lengths can be determined

for each number of half waves. The maximum determined half wave lengths for the different numbers of

half waves together form the upper bound, whereas the minimum lengths form the lower bound. From

the upper and lower bound, the average critical half wavelength is calculated, as illustrated in Figure 3.9.

Figure 3.9 Critical half wavelength liner


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32 Chapter 3

The calculated average half wavelengths iterate towards the critical half wavelength, which follows from

Figure 3.9:

The linear eigenvalue buckling loads depicted in confirm that 35.35mm is the critical half wavelength.

Table 3.2 Linear eigenvalue buckling loads for different liner lengths

This numerically determined critical half wavelength approximates the analytical solution of Battermanbased on deformation theory while it is overestimated by the analytical solution of Batterman based

on flow theory, as included in Table 3.1. This result is in line with what would be expected based on the

plastic buckling paradox as discussed in section 3.2.

3.3.3 Model description of numerical nonlinear analysis

The geometry of the liner as used for the nonlinear investigation of the liner wrinkling behaviour under

axial compression is shown in Figure 3.10. In order to reduce calculation times, a quarter of the liner is

modelled with symmetric boundary conditions along the longitudinal edges.

Figure 3.10 Geometry and boundary conditions of single walled liner under axial compression

The constraints and boundary conditions at the cylinder ends are the same as described for the linear

wrinkling model. A displacement is prescribed at the reference point at , compressing the liner in axial

direction. The length of the liner model is set to 106 mm, three times the elastic critical half wavelength

as determined from the numerical linear buckling analyses in section 3.3.1. This absolute number of three

times the critical half wavelength results in a length closest to the specimen length of 100mm as tested


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by Focke [Focke,2007], which will be discussed in section 3.6. The mesh consists of C3D8R solid ele-

ments, which are 8-node linear bricks with reduced integration and hourglass control. Based on the mesh

sensitivity analysis as described later on in this section, the mesh consists of 120 circumferential, 30

longitudinal and three radial elements. The material properties of the liner are defined according to the

representative nominal isotropic stress-strain curve that resulted from the tensile tests as included in

section 2.3.

The axial stress is measured at the cylinder end where the load is applied. The global axial strain is calcu-

lated as the quotient of the displacement over the initial cylinder length.

As is customary [Bardi, 2006b], the post buckling response is followed by introducing a small initial

imperfection corresponding with the critical mode shape as found from the linear eigenvalue analysis. The

critical mode shape is the mode for which the liner is most sensitive, although the cylinder might be even

more sensitive for combinations of mode shapes. A sinusoidal imperfection, consisting of three half waves

in correspondence with the linear wrinkling mode for this cylinder, was prescribed to the liner geometry.In reality pipes will never be perfect either, so introducing such a small imperfection can be justified.

3.3.4 Sensitivity for applied mesh of numerical nonlinear model

The liner mesh should result in acceptable computation time in combination with sufficiently accurate results.

In this section, the sensitivity of the numerical model for the applied mesh will be evaluated. This evaluation

is based on the stresses and strains at resulting limit load, since the limit load can be better defined than the

bifurcation point. In this subsection, the initial imperfection is given an amplitude of 10-2mm.

First of all, the number of elements in longitudinal and circumferential direction in the liner mesh is varied

while keeping the ratio between element length and width approximately constant at one. The results are

represented in Figure 3.11 and Figure 3.12.

Figure 3.11 Strain sensitivity of different meshes with the ratio between element length and width approxi-

mately constant at one


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34 Chapter 3

Figure 3.12 Stress sensitivity of different meshes with the ratio between element length and width approxi-

mately constant at one

Table 3.3 Influence of mesh refinements with the ratio between element length and width approximately

constant at one on stress and strain at limit load, relative to the finest solid mesh with 480 circumferential

and 60 elements in axial direction

From Table 3.3 it shows that the mesh with 240 elements is the coarsest mesh resulting in negligible dif-

ference in stress and strain at limit load compared with the finest mesh applied. Comparing the meshes

with 240 and 120 elements in circumferential direction in Table 3.3 shows that a 75% reduction in the

total number of elements results in a 0.5% increase in stress at limit load and a 6.7% increase in strain at

limit load.

For two meshes with 120 and 240 elements in circumferential direction, the influence of the aspect ratio

is studied. The results are given in Figure 3.13, Figure 3.14 and Table 3.4.


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Figure 3.13 Strain sensitivity of different meshes with 120 and 240 elements in circumferential direction

and different aspect ratios

The strain at limit load of the mesh with 240 circumferential and 30 elements in axial direction corre-

sponding with the strain of the finest mesh, as shown in Figure 3.13, might be caused by the fact that

the number of 30 elements in axial direction can be divided by the number of three half waves, and the

location of the maximum amplitude of the prescribed sinusoidal imperfection exactly coincides with one

of the mesh nodes. This makes it easier for the model to follow the mode shape. The influence of the

number of elements in axial direction compared to the number of half waves became more explicit when

modelling another lined pipe, as described in [Hilberink, 2010a].

Figure 3.14 Stress sensitivity of different meshes with 120 and 240 elements in circumferential direction

and different aspect ratios

Figure 3.13, Figure 3.14 and Table 3.4 confirm that a significant reduction in number of elements in circum-

ferential direction from 240 to 120 results in only a minor difference in stress and strain at limit load. In

general, it can be concluded that an increased number of elements in axial direction makes it easier for the


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36 Chapter 3

model to follow the mode shape, resulting in lower stress and strain at limit load. However an increased

number of elements results in an increase in computation time.

Table 3.4 Influence of mesh refinement with ratio between element length and width approximately one

on stress and strain at limit load, relative to finest solid mesh with 240 circumferential and 60 elements in

axial direction

The difference between the meshes with 240 and 120 elements in circumferential direction both hav-

ing 30 elements in axial direction on the stress-strain response, as shown in Figure 3.15, is considered

negligible.

Figure 3.15 Stress-strain response of meshes with 120 and 240 elements in circumferential direction and 30

elements in axial direction

Increasing the radial number of elements from three to seven, in the mesh with 120 circumferential and

30 elements in axial direction, results in a slightly lower strain for the limit load. The values in Table 3.5

confirm that the influence on the limit load and corresponding strain is small.


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Table 3.5 Influence of element type and number of elements over liner thickness for solid elements on stress

and strain at limit load, relative to finest solid mesh with 240 circumferential and 60 elements in axial

direction

In Figure 3.16 the stress-strain responses of the models consisting of C3D8R solid elements are compared

with the stress-strain response of a model meshed with S4R shell elements. The shell geometry is discre-

tised at a reference plane, in this case the mid-plane and the corresponding thickness is defined through

the section property definition. From Figure 3.16 it shows that the post buckling behaviour of the single

walled liner under axial compression is influenced by the type of element and number of solid element

layers over its thickness. Contrary, the resulting mode shapes as given in Figure 3.17 show less difference.However, from the perspective of the research objective, the mechanical behaviour up to the bifurcation

point and limit load is of main interest. Af ter passing the limit load, the load carrying capacity of the liner

drops prohibiting safe installation. From the values in Table 3.5 it can be concluded that element type and

number of elements in thickness direction do not have a significant influence on the limit load but do have

a significant influence on the post buckling response.

Figure 3.16 Stress-strain response of meshes with 120 circumferential, 30 elements in axial direction con-3.16 Stress-strain response of meshes with 120 circumferential, 30 elements in axial direction con-.16 Stress-strain response of meshes with 120 circumferential, 30 elements in axial direction con-16 Stress-strain response of meshes with 120 circumferential, 30 elements in axial direction con-6 Stress-strain response of meshes with 120 circumferential, 30 elements in axial direction con-

sisting of S4R and C3D8R elements with respectively three or seven elements in thickness direction


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38 Chapter 3

Figure 3.17 Resulting mode shapes at maximum strain of meshes with 120 circumferential, 30 ele-

ments in axial direction consisting of S4R and C3D8R elements with respectively three or seven elements in

thickness direction

The mesh with 120 elements in circumferential direction, 30 elements in axial direction and 3 elements

in thickness direction gives sufficiently accurate results in combination with an acceptable number of

elements and thus acceptable computation time. This mesh will be used in the remainder of this chapter.

3.3.5 Mechanical behaviour of liner under axial compression

Wrinkling behaviour

The wrinkling behaviour is described, following the solutions of the single walled liner with an initial

sinusoidal imperfection consisting of three half waves having an amplitude of 10 -2mm. The stress-strain

responses of the perfect single walled liner under axial compression and the single walled liner with an

initial imperfection amplitude of 10-2mm, both given the mesh with 120 elements in circumferential

direction, 30 elements in axial direction and 3 elements in thickness direction are shown in Figure 3.18.

The bifurcation point and limit load of the imperfect liner are indicated in the figure.

Figure 3.18 Stress-strain response of perfect single walled liner under axial compression and single walled

liner with initial imperfection amplitude 10-2mm


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Figure 3.19 Radial deformation development along the length of single walled liner under axial compression

with initial imperfection amplitude 10-2mm

Figure 3.19 includes the radial deformation of the axially compressed imperfect liner at subsequent strain

levels. In the beginning, the imperfect liner follows the material stress-strain response of the perfect

liner. The liner expands axisymmetric and uniform over the complete length in outward radial direction.

At the bifurcation point, indicated in Figure 3.18, the stress-strain response starts deviating from the

perfect liner solution and the liner deforms into an axisymmetric wrinkling mode in correspondence with

the critical axisymmetric mode shape consisting of three half waves. With the prescribed displacement

increasing, the amplitude of the wrinkles developing in the imperfect liner grow progressively, reducing

the stiffness of the liner and leading to a load maximum, the limit load indicated in Figure 3.18. After the

stress-strain response has passed the limit load, the load carrying capacity of the liner decreases and

the wrinkles grow excessively. This is in correspondence with the description according to Bardi [2006a;

2006b].

Imperfection amplitude

As mentioned during the model description, the post buckling response of the wrinkled cylinder can be

followed by introducing a small initial imperfection corresponding with the critical axisymmetric mode

shape [Bardi, 2006b] as found from the linear eigenvalue analysis. The high bifurcation values resulting

from using flow theory can be adjusted for by introducing small geometric imperfections. In this subsec-

tion the sensitivity of the numerical model for the initial imperfection will be evaluated.


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40 Chapter 3

Figure 3.20 Stress-strain response for different initial imperfection amplitudes

Table 3.6 Stresses and strains at bifurcation point for different initial imperfection amplitudes, relative toinitial imperfection amplitude 10-3mm

Table 3.7 Stresses and strains at limit load for different initial imperfection amplitudes, relative to initial

imperfection amplitude 10-3mm

The stress-strain curves resulting for several initial imperfection amplitudes are shown in Figure 3.20. The

stress and strain values at the bifurcation point as well as those at the limit

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Mechanical Behaviour of Lined Pipe - A Hilberink

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