evaluation of high pressure components of fuel injection systems using speckle interferometry

8/14/2019 Evaluation of High Pressure Components of Fuel Injection Systems Using Speckle Interferometry

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Evaluation of High Pressure Components

of Fuel Injection Systems

Using Speckle Interferometry

Der Technischen Fakultt derUniversitt Erlangen-Nrnberg

zur Erlangung des Grades

DOKTOR-INGENIEUR

vorgelegt von

Adis Basara

Erlangen, 2007


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Als Dissertation genehmigt

von der Technischen Fakultt der

Universitt Erlangen-Nrnberg

Tag der Einreichung: 19. Januar 2007

Tag der Promotion: 22. Mai 2007

Dekan: Prof. Dr.-Ing. Alfred Leipertz

Berichterstatter: Prof. Dr.-Ing. Eberhard Schlcker

Prof. Dr. rer. nat. Hal Mughrabi


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To my beloved parents


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Preface

Every accomplishment starts with a dream. My dream came to be true and possible

at the moment when I was awarded with a financial support by the Bavarian State

Ministry of Sciences, Research and the Arts for my research work. In this aspiration,

the Institute for Process Technology and Machinery at the Friedrich-Alexander

University of Erlangen-Nuremberg in Germany, who have hosted me during my four

years research stay, also played an important role. During this unforgettable time I

spent at the Institute, it became my second home and the staff of the Institute my

enlarged family. The present thesis arose from my occupational activities as aresearch assistant at the Institute. In order to conduct this long-term effort

successfully, numerous individuals helped me in one way or another with their

support and encouragement. Before laying out the thesis I would like to acknowledge

my indebtedness to them.

First and foremost, I express my deepest thanks and appreciation to my supervisor,

Prof. Dr. Eberhard Schlcker, for offering me an interesting research topic and giving

me the opportunity to finish it under his guidance. His creative ideas, valuable

criticism, many helpful discussions, irreplaceable encouragement and friendlyapproach contributed profoundly to the completion of the present work. I must

acknowledge also that through his collegial cooperation work he was mainly

responsible for the extremely friendly relationships and very warm working

atmosphere at the Institute.

Special gratitude is offered to Prof. Dr. rer. nat. Hal Mughrabi for preparing the

second review of this thesis. His engagement, interest, keen perception and useful

suggestions contributed to the improvement of various parts of the thesis.

Furthermore, I wish to express my sincere acknowledgements to the staff ofDANTEC Dynamics GmbH, Ulm, and of MAN Nutzfahrzeuge AG, Nuremberg, for

close cooperation in working together. Special thanks go to Dr. Thorsten Siebert and

Dr. Gerhard Mischorr for providing valuable comments, constructive ideas and many

helpful discussions during the different phases of my work.

Also, I am immensely grateful to the administration and technical staff of the Institute

and to research coworkers and students. All these made my time at the Institute

amazingly inspiring and enjoyable. Among them, I address particular thanks to

Dr. Lder Depmeier, Werner Polster and Renate Hirsekorn for their friendship thatwas far beyond that of working colleagues.


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My residence in Erlangen would not have been so rewarding without my colleagues

and friends: Kenan Nalbanti, Dr. Fahrudin Avdi, Dr. Ibrahim Hadi, Dr. Muris

Torlak, Dr. Armin Teskeredi, Dr. Samir Muzaferija, Tajib Vereget, Dr. Naser Sahiti,

Hamid Pintol, Bari Atec, Concepcion Encinas Bermdez, Jose Joaqun Sainz

Fernndez, Abdellah Lemouedda, Firas Affes, Badam Vijay Kumar, Dr. Axel Fronek,

Dr. Urlich Klapp, Dr. David Bolz, Dr. Uwe Seiffert, Jan Leilich, Oliver Schade, Stefan

Blendinger, Nicolas Alt, Robert Schatz, Andrej Ruschel, Tim Predel and Hans Bhrer.

Thank you very much for good time we spent together and for always being there for

me.

Finally, special recognition and deep thanks go to my sister and my brother for their

commitment and encouragement. But most of all, I am greatly indebted to my

beloved parents, who are the most meritorious persons and to whom I owe so much

for their enormous sacrifices and consistent support in every part of my life.

Erlangen, January 2007 Adis Basara


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Abstract

The modern high pressure fuel injection systems installed in engines provide a highly

efficient combustion process accompanied by low emissions of exhaust gases andan impressive level of dynamic response. The design and development of

mechanical components for such systems pose a great challenge, since they have to

operate under extremely high fluctuating pressures (e.g. up to 2000 bar) for a long

lifetime (more than 1000 injections per minute). The permanent change between a

higher and a lower pressure causes a cyclic stress in the material that leads to a

fatigue of material until a failure of the component occurs.

In cases where a good capability for high loading and an enhanced lifetime of

components are required, the components are usually autofrettaged in a productionprocess. An autofrettage process is a manufacturing procedure wherein beneficial

residual stresses are introduced into a component in order to improve the loading

capability as well as the lifetime of the component. Although the first deliberate

application of the autofrettage principle dates back to the beginning of the twentieth

century, the autofrettage process and its effects on high pressure components still

remain mostly unknown. The research work summarized in this thesis is a

contribution towards a better understanding of the autofrettage phenomenon.

Speckle interferometry, as a full-field laser optical measuring technique, was the toolselected to be used for that research purpose.

Evaluation of the effects of an autofrettage process on components with complex

geometry is not possible using analytical solutions and is restricted when numerical

methods are used owing to their strong dependence on material data. Limitations of

conventional measuring methods are another reason why these effects are still

unknown. One of the intentions of the present work was the utilization of the potential

of speckle interferometry for the evaluation of autofrettage process effects in high

pressure components, especially those having complex geometries. Experimentaltesting indicated that speckle interferometry, compared with conventional measuring

techniques, offers great potential for that purpose. Full-field measurements over the

outer surface of the component using speckle interferometry allowed the detection of

strain gradients. By analysis of the strain gradients measured on the outer surface,

the spreading of plastic deformation inside a component having a complex geometry

can be evaluated (e.g. autofrettage in a bend of a fuel line).

Another important part of this work was an investigation of the influence of the

pressure holding time on stress-strain generation during the autofrettage process.This influence has not been considered until now. It is the state of the art that

components in an industrial series production are held at the autofrettage pressure


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for several seconds. In doing so, it is assumed that a required stress-strain pattern

was generated. However, the results of the experimental investigation outlined here

revealed that completion of the plastic deformation caused by the autofrettage

process requires a much longer period of time, owing to the time-dependent nature of

the plastic deformation in the inner layers of a fuel line.

Experimental investigation indicated that fuel lines should be autofrettaged at some

higher pressure for a short period of time instead of keeping them for a longer period

at the pressure determined by the analytical calculation. In this way, a desirable

stress-strain state can be generated during the time required to maintain a profitable

series production ( stholding 10< ). The results of investigation showed also that

speckle interferometry offers great potential for localization of cracks in a fuel line wall

by analysis of the strain maps measured on the outer surface of the fuel line.

An additional objective of this work was the utilization of speckle interferometry as aquality control tool in a series production of fuel lines. In the past, the quality of

components was not evaluated in an industrial series production due to the

limitations of conventional measuring techniques. This may explain the frequent

damage to and unexpected failures of the existing fuel injection components under

nominal loads in recent years. Speckle interferometry matches todays industrial

demands, providing fast and reliable measurements without operating costs and with

significantly less effort than conventional measuring techniques. In the present work,

the potential of the particular Q-100 speckle interferometry measuring system forapplication in the reception control of semi-finished tubes and in the final control of

autofrettaged fuel lines was investigated. Furthermore, a concept for monitoring of

the autofrettage process in a series production of fuel lines was developed. In this

concept, quality inspection of fuel lines and control of the residual stress-strain

generation were based on the use of the Q-100 speckle interferometry measuring

system.

The research work outlined in this thesis revealed that speckle interferometry offers

great potential for the evaluation of autofrettage process effects in high pressurecomponents and it matches todays industrial demands for an employment as a

quality control tool in the series production of fuel lines.


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Contents

Preface ....................................................................................................................... i

Abstract.................................................................................................................... iii

Contents....................................................................................................................v

Chapter 1

Introduction and Aim of the Work........................................................................... 1

Chapter 2

Evaluation of High Pressure Components:

Literature Survey and State of the Art.................................................................... 6

2.1 High Pressure Technology Today and Perspectives for the Future................................. 6

2.2 Application of High Pressure in the Fuel Injection System of a Diesel Engine................. 8

2.2.1 Role and Importance of High Pressure in a Combustion System............................... 8

2.2.2 Development of Diesel Fuel Injection Systems and Emission Control Legislation..10

2.2.3 Requirements on High Pressure Components......................................................... 14

2.3 Theory of Thick-Walled Tube ........................................................................................ 17

2.3.1 Elastic Thick-Walled Tube....................................................................................... 17

2.3.1.1 Stress Distribution in an Elastic Thick-Walled Tube ........................................ 18

2.3.1.2 Strain Distribution in an Elastic Thick-Walled Tube ......................................... 20

2.3.2 Criteria of Elastic Breakdown .................................................................................. 21

2.3.3 Elastic-Plastic Thick-Walled Tube ........................................................................... 23

2.3.3.1 Partially Autofrettaged Thick-Walled Tube ...................................................... 25

2.3.3.1.1 Stress Distribution in a Partially Autofrettaged Thick-Walled Tube ...... 27

2.3.3.1.2 Strain Distribution in a Partially Autofrettaged Thick-Walled Tube ....... 30

2.3.3.2 Completely Autofrettaged Thick-Walled Tube................................................. 31

2.3.3.2.1 Stress Distribution in a Completely Autofrettaged Thick-Walled Tube.. 32

2.3.3.2.2 Strain Distribution in a Completely Autofrettaged Thick-Walled Tube.. 34

2.4 Residual Stress Effects on the Operating Performance of Autofrettaged Components.. 35

2.5 Challenges and Problems in Autofrettage Process Evaluation...................................... 41

Chapter 3

Experimental Test Facility and Measuring Techniques...................................... 45

3.1 Experimental Test Facility............................................................................................. 45

3.2 Data Acquisition and Data Processing .......................................................................... 47

3.3 Strain Measurements Using Strain Gauges .................................................................. 50

3.4 Strain Evaluation Using Speckle Interferometry ............................................................ 52

3.4.1 Measurement of Surface Displacement................................................................... 54

3.4.1.1 Determination of Phase Change ..................................................................... 563.4.1.2 Physical Relationship Between Phase Change and Surface Displacement .... 58

3.4.1.3 Principle of Phase Offset Evaluation ............................................................... 61


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3.4.2 Measurement of Surface Shape .............................................................................. 63

3.4.3 Evaluation of Stresses and Strains.......................................................................... 66

3.4.4 Accuracy of the Q-100 Speckle Interferometry Measuring System.......................... 68

Chapter 4

Evaluation of Fuel Lines Using Speckle Interferometry......................................70

4.1 Application Potential of the Q-100 Measuring System for Evaluation of Fuel Lines....... 70

4.1.1 Applied Approaches ................................................................................................ 72

4.1.1.1 Analytical Calculations .................................................................................... 73

4.1.1.2 Finite Element Computations.......................................................................... 73

4.1.1.3 Strain Gauge Measurements .......................................................................... 75

4.1.1.4 Speckle Interferometry Measurements............................................................ 76

4.1.2 Experimental Procedure .......................................................................................... 77

4.1.3 Results, Discussion and Conclusions...................................................................... 81

4.1.3.1 Results of Investigations on the 30 x 10 Tube................................................. 81

4.1.3.2 Results of Investigations on the 6 x 2 Tube..................................................... 84

4.1.3.3 Concluding Remarks....................................................................................... 89

4.2 Determination of the Yield Strength............................................................................... 91

4.2.1 Selected Fuel Line and Sealing Principle Employed................................................ 92

4.2.2 Experimental Procedure and Evaluation of Results ................................................. 93

4.2.3 Results, Discussion and Conclusions...................................................................... 95

4.3 Effective Autofrettage Pressure Determination.............................................................. 99

4.3.1 Selected Fuel Lines, Experimental Procedure and Principle of Results

Evaluation ............................................................................................................. 101

4.3.2 Sealing Principle Employed................................................................................... 102

4.3.3 Results of Investigation and Concluding Remarks................................................. 103

4.4 Evaluation of the Autofrettage Process Effects in Components with Complex

Geometries ................................................................................................................. 108

Chapter 5

Influence of the Pressure Holding Time on Strain Generation.........................114

5.1 Introduction................................................................................................................. 114

5.2 Selected Fuel Lines and Sealing Principle Employed.................................................. 116

5.3 Experimental Procedure and Principle of Results Evaluation ...................................... 1175.4 Results and Discussion............................................................................................... 118

5.4.1 Results of Investigations........................................................................................ 118

5.4.2 General Discussion of the Results......................................................................... 125

5.4.3 Interdependence Between Autofrettage Pressure, Holding Time and Generated

Strain State ........................................................................................................... 129

5.4.4 Determination of Optimal Autofrettage Process Parameters for Series

Production............................................................................................................. 133

5.4.5 Detection of Internal Cracks by Speckle Interferometry Strain Measurements on

the Outer Surface.................................................................................................. 1365.5 Concluding Remarks................................................................................................... 149


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Chapter 6

Concept for Production Quality Control of Fuel Lines ..................................... 151

6.1 Review of Measuring Methods for Stress-Strain Evaluation........................................ 152

6.2 Testing of Non-Contact Applicability of the Q-100 SI Measuring System .................... 157

6.2.1 Easily Removable Holder for the Purpose of Non-Contact Application of the

Optical Sensor on the 30 x 10 Tube ...................................................................... 1576.2.2 Light-Contact Application of the Optical Sensor on the 8 x 2.2 Fuel Line............... 161

6.3 Concept for Quality Inspection of Fuel Lines in Series Production .............................. 165

6.3.1 Concept Description.............................................................................................. 165

6.3.1.1 RMC Module................................................................................................. 166

6.3.1.2 PSA Module.................................................................................................. 166

6.3.1.3 NAVC Module............................................................................................... 166

6.3.1.3.1 FILE CONVERTER Submodule ........................................................ 167

6.3.1.3.2 MEAN VALUE Submodule ................................................................ 167

6.3.1.3.3 DATABASE Submodule .................................................................... 1696.3.1.3.4 ANALYTICAL CALCULATIONS Submodule ..................................... 170

6.3.1.3.5 COMPARISON CONDITIONS Submodule........................................ 171

6.3.2 System for Industrial Application ........................................................................... 171

6.4 Concept for Control of Strain Generation in Series Production of Fuel Lines............... 171

6.4.1 Concept Description.............................................................................................. 171

6.4.2 Barriers to Implemenation of the Concept ............................................................. 175

Chapter 7

Summary, Conclusions and Outlook.................................................................. 177

7.1 Potential of Speckle Interferometry for Evaluation of High Pressure Components....... 177

7.2 Evaluation of the Autofrettage Process Effects in Components with Complex

Geometries ................................................................................................................. 178

7.3 Influence of the Pressure Holding Time on Strain Generation During the Autofrettage

Process....................................................................................................................... 179

7.4 Speckle Interferometry as a Quality Control Tool in the Series Production of

Fuel Lines ................................................................................................................... 181

Nomenclature ....................................................................................................... 182References............................................................................................................187

Inhalt......................................................................................................................199

Einleitung und Zielsetzung.................................................................................. 202

Zusammenfassung, Schlussfolgerung und Ausblick ....................................... 207

Lebenslauf ............................................................................................................ 213


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Chapter 1

Introduction and Aim of the Work

High pressure is a proven tool for the realization of a number of industrial processes,

for the production and development of new products and for the implementation of

specific production procedures. The motivation for the use of high pressure

technology is based on the great potential and benefit in improving the quality of

existing processes and products from both economic and environmental viewpoints.

The development of novel and more sustainable processes and products for futuregenerations is another interesting aspect. Thus, the application of elevated pressures

is permanently extending and gaining in popularity.

An example of the beneficial application of high pressure is the fuel injection system

of internal combustion engines. Here, the physico-hydrodynamic effect of the high

pressure is utilized whereby its energy is converted into the kinetic energy of the

fluid. This is the so-called atomization process, in which bulk liquid fuel is injected

under high pressure and converted into small droplets. The higher the injection

pressure, the finer is the spray created. The creation of a fine spray with smalldroplets is very important for the proper and effective realization of the combustion

process. The modern high pressure fuel injection systems installed in engines

provide a highly efficient combustion process accompanied by low emissions of

exhaust gases and an impressive level of dynamic response.

The fuel injection systems of diesel engines require significantly higher operating

pressures when compared to the systems of gasoline engines. This is due to the

higher air compression ratio of a diesel engine, to the higher viscosity of a diesel fuel,

and to the difference in thermodynamic behaviour and the difference in the workingprinciple of a diesel engine. The design and development of mechanical components

for such systems are therefore more complex.

A characteristic feature of any high pressure process is exhibiting absolutely artificial

environments far beyond those existing in nature. The operating pressures in such

processes are in the range from 100 to 10000 bar and can be of a static or fluctuating

nature. High pressure components are required to maintain these conditions for a

long lifetime. Owing to the extremely high pressures, the material of components is

usually stressed even statically up to its strength limit. However, it is common for the


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components to be stressed by a fluctuating internal pressure under the operating

conditions, what affects the material even more.

For example, mechanical components of the fuel injection system (Fig. 1.1) are

stressed with extremely high fluctuating pressure amplitudes for a long time (more

than 1000 injections per minute). This permanent change between a higher and a

lower pressure causes a cyclic stress in the material, which leads to a fatigue of the

material until mechanical failure of the component occurs. The fatigue strength of the

component exposed to the fluctuating load is generally lower than the yield strength

and it decreases as the number of loading cycles increases. Mechanical components

of the fuel injection system (e.g. fuel lines, fuel rail, high pressure pump and injectors)

have to withstand a nearly infinite number of loading cycles in their lifetime without

failure. In order to achieve this, the loading of the components is limited by a certain

maximal allowed fluctuating internal pressure. Therefore, it presents a major

challenge to design and to develop the components that have to be suitable for safe

operation under such extremely fluctuating pressure amplitudes for a long lifetime.

Figure 1.1. Mechanical components of a common rail fuel injection system of a diesel

engine (adapted from [115]).

In cases where a good capability for high loading and an enhanced lifetime of

components are required, the components are usually autofrettaged in series

production. An autofrettage process is a manufacturing procedure wherein the

component is subjected to a static internal pressure far beyond the intended

operating pressure in order to induce a partially yield of the component. After a short

period of time, the component is unloaded and the required permanent plastic


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deformation is reached. The plastic deformation is accompanied by the generation of

residual stresses in the component. The objective of the autofrettage process is to

obtain a favourable residual stress pattern in a manufacturing process which brings

beneficial effects under the operating conditions. By application of the autofrettage

process, the static loading capability of components can be increased due to the

strain hardening effect which takes place during the process. Furthermore, the

residual stress pattern generated reduces crack initiation, retards the fatigue crack

growth rate and consequently increases the fatigue limit of the component [31, 77,

87].

In order to achieve a favourable residual stress pattern which gives the beneficial

effects under the operating conditions, it is important to conduct the autofrettage

process appropriately. The generation of unfavourable residual stresses through the

process could have detrimental consequences for the performance of the

component. For the purpose of the safe and reliable application of the autofrettage

process, thereby decreasing the risk of damage and unexpected failures of

components under nominal loads, there is a requirement for a measuring method

that permits an evaluation of the stress-strain state within components.

The research work summarized in this thesis is a contribution towards a better

understanding of the effects of the autofrettage process on high pressure

components of fuel injection systems. Speckle interferometry, as a full-field laser

optical measuring technique, was the tool selected for this research purpose. The

first objective of the work was to test the application potential of the particular Q-100

speckle interferometry measuring system for evaluation of high pressure

components.

Until now, the effects of the autofrettage process on high pressure components are

mostly unknown. An analytical solution exists in the literature [43, 46, 55, 56, 60, 79,

88] for very simple geometries such as a smooth tube and was derived under certain

assumptions (elastic-perfectly plastic, homogeneous isotropic and incompressible

material behaviour). Only a limited prediction of the residual stress generation

through the process could be obtained by the use of such solution, since real

materials are mostly not isotropic, not incompressible and in most cases do not

behave as expected from idealized models of material response. The present work

involves investigations performed on fuel lines which, due to the cold-working

manufacturing procedure, indicate orthotropic material behaviour.

Analytical solutions for components with complex geometries have been proposed

only for the simple case of cross-bored tube [21, 39, 40, 63, 78]. Numerical methods,

which overcome disadvantages and deficiencies of the analytical solutions, are these

days used more intensively for the evaluation of the autofrettage process in

components with complex geometries. Some results of such numerical investigations


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performed in recent decades can be found in the literature [18, 31, 87, 95, 96].

However, the main problem with numerical methods is the strong dependency on the

material data, which are not always available in an industrial series production.

Therefore, the use of the advantages of speckle interferometry as a full-field

measuring technique for stress-strain evaluation in components having complex

geometries was a further goal of this work. The results obtained indicated that using

speckle interferometry it is possible to develop 3D stress-strain maps along the

complete component surface. This is very important in order to have a better

understanding of the autofrettage process effects on stress-strain generation within,

e.g., the complete fuel line.

Another important part of this work was an investigation of the influence of the

pressure holding time on stress-strain generation during the autofrettage process.

The influence of the pressure holding time on the final effects of the autofrettage

process has not been considered until now; this influence was studied experimentally

for the first time in this work. The industrial production of components relies either on

a limited analytical steady solution or on simple numerical computations using steady

models which do not consider the influence of the holding time on the plastic

deformation process. It is the state of the art that the components are held at the

pressure for only a few seconds (approximately 3 to 10 s) during the autofrettage

process. In doing so, it is assumed that a required stress-strain pattern was

generated. However, the results of the experimental investigations outlined in this

work revealed that completion of the plastic deformation caused by the autofrettageprocess requires a much longer period.

An additional objective of this thesis was the utilization of speckle interferometry as a

quality control tool in a series production of fuel lines. Mechanical components of fuel

injection systems nowadays are autofrettaged in series production. Since there was

no proper measuring method which could be used as a quality control tool in such

series production, the generation of the stress-strain pattern during the autofrettage

process and the quality of components have not been evaluated until now. The whole

procedure of the design, development, process planning and manufacture ofcomponents relies on analytical calculations and numerical computations. These

methods cannot give information about the component quality and therefore the

knowledge about the effective residual stresses generated during the autofrettage

process was mostly poor. In addition, the methods cannot consider the influence of

other parameters such as geometric and metallurgical imperfections, the influence of

previous manufacturing processes or even disturbances through the process itself.

These can also affect the final quality of the autofrettaged components. All this can

explain the frequent damage to and unexpected failures of the existing fuel injectionsystem components under nominal loads in recent years.


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In order to avoid this and to provide safe and reliable application of the autofrettage

process, the applicability of the Q-100 speckle interferometry measuring system in

the reception control of semi-finished tubes and in the final control of autofrettaged

fuel lines was investigated and is outlined here. Furthermore, a concept for the

quality inspection of fuel lines in series production and a concept for the control of the

residual stress generation during the autofrettage process were developed and

addressed in the present work.


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Chapter 2

Evaluation of High Pressure Components:

Literature Survey and State of the Art

2.1 High Pressure Technology Today and Perspectives

for the Future

Although the roots of high pressure science can be traced back over many centuries,

the practical application of high pressure in industry dates back to the beginning of

the twentieth century. Basic research and scientific studies carried out by pioneers of

high pressure science have been the key for the implementation of the technology on

a commercial scale. A great advance was also made through the continuing

development of other fundamental sciences (materials science, chemistry,

thermodynamics, heat and mass transfer, fluid dynamics, etc.) over the course of

time.

High pressure nowadays is a proven tool for the realization of a number of industrial

processes, for the production and development of new products and for the

implementation of specific production procedures. The motivation for the use of high

pressure technology is based on the great potential and benefit in improving the

quality of the existing processes and products from both economic and

environmental viewpoints. The development of novel and more sustainable

processes and products for future generations is another interesting aspect.

The application of elevated pressures is continuously extending and gaining

popularity. Hence it is evident that high pressure as a tool in industry will play an

even more important role in the future. Possible areas of immediate interest lie in

energy storage and conversion devices (e.g. use of hydrogen as a fuel, new coal to

oil or gas conversion systems, search for new oil and mineral deposits at greater

depths or in off-shore locations [99]), the food industry (e.g. pasteurization and

sterilization of various foodstuffs, crystallization of fats), the polymer industry,

pharmacy [109], medicine [109], microbiology [109], biotechnology (e.g. bio diesel

production technology, proteins) and so on.

Table 2.1 provides a survey of the application of high pressure technology todayregarding the methods used and pressure levels applied [10, 100].


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Table 2.1. Applications of the high pressure in industry (adapted from [10,100]).

METHOD PRESSURE [bar] PRODUCT OR APPLICATION

Solid-state reaction > 125000 Synthetic diamondsProduction of synthetic polymers up to 5500 Low-density polyethylene

up to 3450 Ethylene vinyl chloride

up to 965 Tetrafluoroethylene (Teflon)

up to 260 High-density polyethylene and polypropylene

Catalytic chemical synthesis 20 - 700 Ammonia, propionic acid, acetic acid,

butanediol, fats, oils, margarine, fatty acids,

urea (fertilizers), methanol and hydrocarbons

Hydrogeneration 100 - 300 Edible oils, hydrogasification, hydrocracking,

desulfurization, catalytic cracking,

naphtha hydroforming, coal liquefaction,

fatty alcohols, 1-6 hexanediol, 1-4 butanediol,hexamethylenediamine and C4 to C15 products

Wet (air) oxidation 100 - 400 Organic waste elimination (water treatment sludge,

herbicides, pesticides, used oils, paper industry, pulp

industry, olive oil industry and petrochemical industry)

Extraction of products with supercritical 80 - 300 Decaffeinated coffee and tea, spices, hops, herbs,

fluids (e.g. water, CO2) vegetable oils, aromas, essences, colours, drugs,

tobacco, perfumes and plant-protective agents

Micronization with supercritical fluids 80 - 300 Fine particles and powders from various products

(e.g. CO2) (cosmetic, perfume and pharmaceutical industries)

Dyeing with supercritical fluids and 80 - 300 Dyeing of fabrics, wood

cell structure treatment with impregnation and tobacco impregnationsupercritical fluids (e.g. CO2)

Leaching of ores 100 - 300 Aluminium (from bauxite), technical gases

(N2, O2, H2, He) and gas liquefaction

Oil and gas production 100 - 400 Drying, inhibition, desulfurization and odorization

Separation of isotopes up to 300 Heavy water

Fluid conveying (transport) 100 - 200 Pipeline transport of ores and coal

Polymer processing 100 -400 Polymer spinning, polymer filtration and polymer extrusion

High-performance liquid chromatography 100 - 700 Analytical chemistry and chemical production

Kinetic fluid (jet) energy with water up to 4000 Jet cutting

up to 2000 Jet cleaning

up to 600 Jet treatment of fabricsKinetic fluid energy (homogenization, up to 1500 Foodstuffs (milk, baby food, yogurts, ice-cream),

emulsification, dispersion, cell-cracking) pharmaceutical products, cosmetics (tooth paste,

lotions, creams), chemical products and bio-products

Potential (pressure) fluid energy up to 10000 Autofrettage

up to 5000 Hydroforming

up to 4000 Isostatic pressing (sintered parts)

Spray drying up to 1000 Fine powders of various products

Fuel injection up to 2000 Diesel engine

Thermal power generation 100 - 250 Steam power plants

Potential (pressure) energy effects up to 10000 Pasteurization, sterilization, pascalization,

on organic products coagulation, gelatation ofvarious foodstuffs and other bio-products


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As shown in the table, the operating pressures in the processes are up to 10000 bar

and can be of either static or fluctuating nature. High pressure components are

required to maintain these conditions for a long lifetime. Owing to the extremely high

pressures, the material of components is usually stressed even statically up to its

strength limit. However, it is common that the components are stressed by a

fluctuating internal pressure under the operating conditions, which affects the

material even more. The constant change between a higher and a lower pressure

causes cyclic stress in the material that leads to a reduction of the material strength

since fatigue of the material occurs. Therefore, it is a major challenge to design and

to develop components that have to be suitable for safe operation under such

extremely fluctuating pressure amplitudes for a long lifetime.

The attention of this thesis is focused on the problems in the design and

development of high pressure components for the fuel injection systems of a diesel

engine.

2.2 Application of High Pressure in the Fuel Injection

System of a Diesel Engine

2.2.1 Role and Importance of High Pressure in a Combustion

System

The combustion process that takes place inside an engine is essentially dependent

on the way in which the combustion components (air and fuel) are supplied into a

chamber, on the quality of the prepared mixture charge and on the ignition

conditions. The proper realization of these individual steps affects the combustion

process and determines the quality of the combustion system itself (i.e. combustion

efficiency, fuel consumption, exhaust gas emissions, combustion noise).

In the course of time, different types of systems for the supply of components and the

preparation of mixture in internal combustion engines [92, 93] have been developed.Almost all modern engine concepts use the principle of injection of a liquid fuel under

pressure into air. This is the so-called atomization process, in which bulk liquid is

converted into small droplets (Fig. 2.1). The liquid fuel is forced under high pressure

through the orifice of a nozzle, what causes a creation of a liquid sheet outside the

nozzle in the first instance. This sheet becomes unstable at a certain distance from

the nozzle and breaks up into ligaments due to the interaction between the external

aerodynamic forces of the surrounding air and the internal surface forces of the liquid

fuel. Further interaction between these forces causes instability of the ligaments and

the creation of droplets.


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Creation of a sheet byforcing a liquid through

a nozzle orifice

Waves appearing due to

the instability of the sheet

Sheet breaks upinto ligaments

Instability of ligamentscauses the creation of droplets

Figure 2.1. Principle of droplet formation as a result of the interaction between the

external aerodynamic forces of the surrounding air and the internal forces of a liquid

due to the surface tension (adapted from [82]).

The fuel injection systems of diesel engines addressed in this thesis requiresignificantly higher operating pressures (up to 2200 bar) than the systems of gasoline

engines (up to 200 bar). This is due to the higher air compression ratio of a diesel

engine, to the higher viscosity of a diesel fuel, and to the difference in thermodynamic

behaviour and the working principle of a diesel engine.

The relative difference between the velocities of the liquid fuel jet and the air in a

chamber influences the atomization process. The higher the relative difference

between the velocities, the better is the atomization effect. Owing to the high air

compression ratio of a diesel engine, the density and temperature of air (i.e. therelative motion of air) in the chamber are relatively high and therefore a higher

velocity (i.e. pressure energy) of the injected fuel is required.

Another important reason for the high injection pressure in diesel engines is the high

resistance of a diesel fuel (i.e. high viscosity) to deform under action of shear

stresses caused by the fuel flowing through the nozzle orifice.

Finally, the time required to produce a combustible mixture of air and fuel vapour (i.e.

the time required for the generation of droplets by atomization, the vaporization of

droplets and mixing with the surrounding air) in diesel engines represents asignificant fraction of the total time (i.e. time period during power and exhaust

strokes) available for the completion of the combustion process. For this reason, the

generation of a finer spray with smaller droplets, which evaporate faster, is very

important for the proper realization of the combustion process. The residence time

that droplets spend in the chamber is limited. If droplets do not evaporate fully and do

not create a combustible mixture with the air within that period of time, burning of

them will not occur and a large amount of unburned hydrocarbons may be produced.

Consequently, the efficiency of the engine decreases while the fuel consumption andexhaust gas emissions increase.


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All the aforementioned reasons indicate the importance of high pressure in the

combustion system of internal combustion engines. The design and development of

the mechanical components for diesel fuel injection systems is more complex than

those for gasoline engines due to the significantly higher injection pressures in the

case of the diesel fuel injection systems.

2.2.2 Development of Diesel Fuel Injection Systems and Emission

Control Legislation

The development of diesel engines until today is the result, on the one hand, of

continuous inventions, the engagement of automotive manufacturer suppliers, the

readiness of investment and the strength of automotive manufacturers. On the other

hand, it is the result of the continuous introduction of emission control legalisation

which has the purpose of reducing the corresponding negative consequences of asignificant increase in traffic density in recent years on the environment.

Emission control legislation, which imposes mandatory limits on exhaust gas

emissions and defines the corresponding test procedures, has been adopted in all

industrialized countries. The CARB (California Air Resources Board) legislation is

valid in California, Maine, Massachusetts and New York, while the EPA

(Environmental Protection Agency) legislation applies to the remaining 49 states of

the USA, Canada, South America and Australia. In Europe, Asia, North and South

Africa, the EU (European Union) legislation is valid. Finally, the Japanese legislationimposes limits on exhaust gas emissions in Japan.

Like other legislation in the world, the EU legislation defines the limits of pollutants

(carbon monoxide, hydrocarbons, nitrogen oxides and particulates) and specifies the

corresponding test procedures for verifying compliance with the legislation depending

on the engine concept (gasoline or diesel) and according to the vehicle class (e.g.

passenger cars, light commercial vehicles, medium commercial vehicles, heavy

commercial vehicles and off-road vehicles). Figure 2.2 shows the development of the

EU legislation on exhaust gas emissions for light commercial vehicles over the

course of time.

As shown in the figure, each newly introduced legislation is progressively more

stringent, which continually places greater demands on the fuel injection systems in

the engine. Hence the limits of the conventional diesel fuel injection concepts (in-line

fuel injection pump system and distributor injection pump system) and the

requirements of the newly introduced emission control legislation, with which each

new vehicle model had to comply, have led to many inventions in the design of diesel

fuel injection systems during the last two decades. A great advance in the

improvement of diesel engine performances was made since 1994 with the


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development of new high pressure injection systems (unit injector system, unit pump

system and common rail system) which operate at pressures higher than 1300 bar.

Figure 2.2. Development of EU legislation for light commercial vehicles over the course

of time [90].

As mentioned before, one of the major challenges in the development of fuel injection

systems is the development of all mechanical components that have to be suitablefor operation under extremely high fluctuating pressures for a long lifetime. In

particular, the development of the fuel lines, the purpose of which is to deliver the fuel

between the components of the system, suffers considerable difficulties. The

geometry of the fuel line (inner diameter, wall thickness and bend radius), the

properties of available materials that can be cold drawn in manufacturing the semi-

finished tubes for such fuel lines, and the manufacturing treatment (e.g. autofrettage)

applied to the fuel lines define a maximum allowed pressure in the fuel injection

system. Other mechanical components of the system (e.g. injector, pump and fuel

rail) can withstand higher system pressures owing to the possibility of choosing from

diverse designs and manufacturing concepts (e.g. shrunk assembly, multiwall

assembly, autofrettage) and using different higher strength materials. Indeed, the

most frequent damage to and unexpected failures of fuel injection systems under

nominal loads over the past years have occurred on the fuel lines.

In a unit injector system, a high pressure pump and an injector form a single unit

which is fitted in one cylinder, Fig. 2.3a. Since there is no high pressure fuel line

between the pump and injector, a significantly higher fuel injection pressure could be

ensured (up to 2200 bar). In contrast, an injector-and-holder assembly with a high

pressure pump of a unit pump system(Fig. 2.3b) and a fuel rail with a high pressure


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pump and injectors of the common rail system (Fig. 2.3c) are connected by high

pressure fuel lines. According to the state of the art, the maximum injection pressure

in such concepts is therefore lower (up to 1800 bar today).

(a) (b)

(c)

Figure 2.3. Principle of operation of modern fuel injection systems of a diesel engine

(adapted from [93]): a) unit injector system, b) unit pump system, c) common rail system.

The unit injector system achieves the highest injection pressures of all diesel fuel

injection systems currently available. However, the maximum pressure in the

operation of the unit injector system and also in the operation of the unit pump

system is available only at higher engine speeds since the function of pressure

generation and the function of fuel injection are inseparable. A good torque curve

combined with low pollutant emission demands a high injection pressure when the


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engine operates under maximum load at lower speeds. A fuel injection system which

overcomes this problem is a common rail system. This fuel injection concept is more

intensively used today because it offers several advantages compared with the other

injection concepts.

The main advantage of the common rail fuel injection system in comparison with

other injection systems is its ability to separate the functions of pressure generation

and fuel injection. In this way, it is possible to vary the injection pressure and the

injection timing over a broad scale. Separation of the pressure generation and fuel

injection functions is achieved by first storing the fuel under high pressure in a fuel

rail and then delivering the fuel to the injectors only on demand. Thus, the injection

pressure is largely independent of engine speed or injected-fuel quantity, and is

generated and controlled by a high pressure pump. This ensures a more favourable

torque curve of the engine. Therefore, the system offers the greatest degree of

flexibility in the choice of fuel injection parameters. In addition, due to a significantly

higher level of adaptability in engine design, the common rail system can be applied

to a wide range of vehicle applications (10 to 1000 kW/cylinder).

Three generations of common rail systems have been developed since 1997. In the

first generation, the maximum injection pressure was 1350 bar for passenger cars

(1997) and 1400 bar for commercial vehicles (1999). The maximum injection

pressure in the second generation (2001 for passenger cars and 2002 for

commercial vehicles) was increased to 1600 bar. In the first and second generations,

the injection process was controlled by a magnetic solenoid on the injectors.

The injection pressure of 1600 bar remained the same in the third generation for

passenger cars (2003) wherein piezo inline injectors were employed to improve the

combustion process. Such an injection control method provides a more precise

metering of the amount of fuel injected, reduces the intervals between injections and

has the possibility to deliver a required fuel quantity into a large number of separate

injections for each combustion stroke. Since the magnetic injectors were still used in

the third generation of the common rail systems for commercial vehicles (2004), the

injection pressure was increased to 1800 bar in order to fulfil the EURO 3 legislation.

Sustained efforts for the optimization and improvement of the combustion process, in

order to comply with EURO 4 legislation, led to a requirement for a further increase in

injection pressure up to 2000 bar. Since the directives will become progressively

more stringent in the years ahead (e.g. EURO 5 legislation takes effect from 2008),

higher injection pressures of more than 2000 bar are expected.


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2.2.3 Requirements on High Pressure Components

All mechanical components employed in the aforementioned high pressure injection

concepts (pump, injector, fuel rail and fuel line) are exposed to extremely high

fluctuating pressures under the operating conditions. As an example, a typical

pressure-time pattern of the internal pressure fluctuation in a fuel line during engine

operation is presented in Fig. 2.4. The fluctuation between a higher MAXp and a lower

pressure level MINp results in cyclic stress in the fuel line material (fluctuating

changes between a higher MAX and a lower stress MIN ) with the same time-

dependent course. As shown, these changes have very high frequency (up to 10

cycles per 100 ms) under the operating conditions.

1750

1800

1850

1650

1700

1600

15500.15 0.20 0.25 0.30

Time, t [s]

Internalpressure,pin[bar]

p

pMEAN

pMAX

pMIN

Fuel line: 6 x 1.75 Material: St 30

Figure 2.4. Typical pressure-time pattern (fluctuation of the internal pressure in a fuel

line during engine operation).

Such cyclic stress leads to a reduction in material strength since fatigue of the

material occurs. The failure of a component due to the fatigue of the material startswithout warning, as is the case with static material failure (i.e. no obvious elongation

or necking). The fatigue failure starts with some discontinuities in the material of the

component, such as a sharp reentrant angle, notches and grooves of different

shapes, a tool or punch mark, or flaws and defects in the material itself. The stress in

these regions is larger than in the surrounding material and local yielding may occur,

even though the bulk of the material is stressed well below the yield strength. During

the first few cycles of a plastic flow in these regions, the atoms on each side of the

slip plane form new bonds without losing strength. Under continued cycling,

microscopic cracks are generated along the slip planes. Once such a crack has been

initiated, the stress concentration at the end of the crack promotes further growth,


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and the crack develops as the cycling continues. Finally, when the crack length

reaches a critical dimension, one additional cycle causes complete failure.

It is well known that the fatigue strength of a component subjected to a cyclic load is

generally lower than the yield strength of the component material and decreases as

the number of cycles increases (Fig. 2.5). The fatigue limit is the stress level below

which the component can withstand an infinite number of cycles without failure.

NFS

NFSNumber of cycles to failure, N [-]

Stress,[

N/mm2]

NFL

NFL

Reyield strength of material

fatigue strength at specifiednumber of cycles NFS

fatigue limit

Figure 2.5. Plot of stress-cycle ( - N) fatigue data.

Since the mechanical components of the fuel injection system are stressed withextremely high fluctuating pressure amplitudes for a long time (more than 1000

injections per minute), the material of the components is usually stressed up to its

strength limit (i.e. fatigue limit). The requirements for a further increase in injection

pressure in order to improve the combustion process and to comply with always more

stringent emission control legislation therefore involve considerable difficulties in the

design of the mechanical components of the fuel injection systems.

In cases where a good capability for high loading and enhanced lifetime of

components at the desired fatigue limit are required, the components are usuallyautofrettaged in a manufacturing process. It is the state of the art that the mechanical

components of the fuel injection systems nowadays are autofrettaged in series

production. The objective of the autofrettage process is to obtain a favourable

residual stress pattern in a manufacturing process which brings beneficial effects

under the operating conditions. By application of the autofrettage process, the static

loading capability of components could be increased. Furthermore, the residual

stress pattern generated reduces crack initiation, retards the fatigue crack growth

rate and consequently increases the fatigue limit of the component.


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This work addresses investigations of high pressure fuel lines which fail more

frequently than other components of fuel injection systems under nominal operating

conditions and whose development is more complex. As an example, a set of such

fuel lines for a common rail system of a six-cylinder engine is shown in Fig. 2.6.

Figure 2.6. Set of high pressure fuel lines for a common rail system of a six-cylinder engine.

The priority in the development of fuel lines is to minimize their length and to increase

their inner diameter. Shorter lines having a larger inner diameter provide better

injection performance. The inner diameter is related to throttling loss and

compression effects, which are reflected in the injected fuel quantity. Furthermore,the fuel line length influences speed-sensitivity the rate of discharge.

Another important point in the development of fuel lines is, as already mentioned, the

interdependencies and trade-offs between the geometry of the fuel line (inner

diameter, wall thickness and bend radius), the material properties, the autofrettage

treatment employed and the maximum system pressure. A thick fuel line cannot be

sharp bent. However, the fuel lines have to be routed in the predefined grooves of an

engine with a defined bend radius. In this way, a given bend radius determines the

maximum inner diameter and maximum wall thickness of the fuel line. A limited fuelline wall thickness for certain material properties and the corresponding autofrettage

treatment further define the maximum allowable stress in a material and, thus, the

maximum system pressure.

A very narrow range of available materials that can be cold drawn in a manufacturing

of semi-finished tubes for such fuel lines additionally complicates the development of

fuel lines. This is because the available materials are already utilized up to their

strength limits and cannot follow the requirements of always more stringent emission

control legislation. Therefore, an autofrettage treatment nowadays plays an importantrole in increasing of a capability for high loading of fuel lines.


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The influences of the fuel line geometry, the properties of the fuel line material, the

autofrettage treatment used and the operating pressure on the stress-strain state

within the fuel line wall can be calculated by using the proposed analytical solution

which is briefly outlined in the following section.

2.3 Theory of Thick-Walled Tube

High pressure components have been made with many different shapes, but a

cylindrical shape is used more than any other. Virtually every pressure apparatus has

at least some parts which are cylindrical in cross-section, and almost all pipes are of

that shape. The standard theoretical analysis of high pressure cylindrical components

divides them into two groups, the theory of a thin-walled and the theory of a thick-

walled tube. The theory of a thin-walled tube, i.e. a tube with a very small wall

thickness in comparison with the other dimensions, makes the assumptions that thetangential stress distribution is constant across the wall and that the stresses in the

radial direction are negligible. In contrast, the theory of a thick-walled tube, i.e. a tube

with a wall ratio 16.1= inout rrk [59], considers the non-uniform tangential stress

distribution across the tube wall and takes the radial stresses into account. This

thesis addresses the theory of a thick-walled tube whereas the wall ratio in the case

of the mechanical components of the fuel injection systems (e.g. cylindrical parts of

the pump and injector, fuel rail and fuel lines) is higher than 2.

An analytical solution of a thick-walled tube in the literature is classified in two

specific cases: an elastic thick-walled tube (the material of the tube exposed to

pressure behaves elastically) and an elastic-plastic thick-walled tube (the tube is

partially or completely overstrained, i.e. autofrettaged).

2.3.1 Elastic Thick-Walled Tube

The problem of determining the stresses and strains in an elastic thick-walled tube

was first solved by the French scientists Lam and Clapeyron [60] in 1833 (Eq. 2.1).In order to formulate the relations for an elastic thick-walled tube, the following

assumptions are made:

the material is homogeneous and linearly elastic isotropic,

displacements and strains are small (infinitesimal),

the tube is free from internal stress before the pressure is applied,

the tube is geometrically perfect and

the applied internal pressure ( inp ) is uniformly distributed over the inner surface.

In the analysis, an elastic thick-walled tube, having an inner radius inr and an outer

radius outr (Fig. 2.7), subjected to an internal pressure inp is considered. Summing


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forces acting at the control element in the tangential, radial and axial directions,

assuming that axial symmetry exists (stresses are independent of ; it follows that

0== zr ), and by simplifying that plane stress conditions prevail ( 0== zrz )

give the equation of equilibrium for the control element exposed to the two-

dimensional state of stresses:

( ) ( ) 02

sin2 =

+++

ddrddrrddr rrr (2.1)

If small quantities of high order are neglected, the above equation can be reduced to

0=dr

dr rr

(2.2)

rin rout

pin

r

r+dr

d

dr

r

Figure 2.7. Static equilibrium of a control element located at a radial distance from

the axis of an elastic thick-walled tube.

2.3.1.1 Stress Distribution in an Elastic Thick-Walled Tube

Differential equation (2.2) can be solved by adopting the strain-displacement

relations for elastic deformation of a thick-walled tube and by applying the boundary

conditions at the inner ( inrinr p= ) and outer ( 0=routr ) surfaces of the tube. The

solution gives the expressions for the tangential and radial stress components within

an elastic thick-walled tube subjected to an internal pressure (Fig. 2.8):


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1

1

2

2

+

=

in

out

outin

rr

rrp

(2.3)

1

1

2

2

=

in

out

outin

r

rr

rrp

(2.4)

In order to evaluate an axial stress component z (i.e. to extend this two-dimensional

into a three-dimensional analysis), it is necessary to know whether or not the whole

of the end forces are balanced by the axial stresses. If the pressure load in an axialdirection is taken wholly externally, i.e. a tube with open ends, then overall

equilibrium of an axial portion of the tube requires that

0=endsopenz (2.5)

0

1.25

1.00

0.75

0.50

0.25

-1.00

-0.75

-0.50

-0.25

-1.25

/pin

r

zpin0 1 2 3

Figure 2.8. Stress distribution across the wall of an elastic thick-walled tube ( 3=k )

subjected to an internal pressure.

If, however, the wall takes the whole of the end loads due to the internal pressure,

i.e. a tube with closed ends, then the axial stress can be expressed by


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12

=

in

out

inendsclosedz

rr

p

(2.6)

These equations indicate that the radial stress component ( r ) is alwayscompressive, whereas the tangential stress ( ) and axial stress ( z ) components

are always tensile. In addition, the tangential stress component is always larger than

other components and has a maximum at the inner surface of the tube. Furthermore,

the axial stress component is constant across the wall thickness.

It is important to emphasize here that by increasing the wall ratio ( inout rrk /= ) from

1.16 to about 3 results in a reduction in the tangential stress and axial stress

components at the inner surface of the tube while the radial stress component

remains constant, Fig. 2.9. A further increase in the ratio (from 3 to infinite) does not

significantly reduce the stresses at the inner surface of the tube and it is, therefore,

not economical.

Figure 2.9. Decrease in stresses at the inner surface of an elastic thick-walled tube as

a result of increasing the wall ratio inout rrk /= .

2.3.1.2 Strain Distribution in an Elastic Thick-Walled Tube

Since deformations and strains in an elastic thick-walled tube are relatively small(straight-line portion of a stress-strain diagram), the theory of infinitesimal strains is


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applied here. To express the relationship between the applied principal stresses and

the resulting principal strains, the influence of each stress on strain components

needs to be considered separately. Final stress-strain relations for the case of

homogeneous linearly elastic isotropic material stressed multiaxially can be

formulated by the generalized Hookes law:

( )[ ]zrE

+=1

(2.7)

( )[ ]zrrE

+=1

(2.8)

( )[ ]rzz E +=1

(2.9)

2.3.2 Criteria of Elastic Breakdown

As mentioned above, the maximum stress in a tube subjected to an internal pressure

is on the inner surface. If an internal pressure is high enough to stress the material

beyond its elastic limit ( eR ), yielding of the material (i.e. overstrain) will evidently first

appear at this location. The determination of a lowest value of an internal pressureinrin

p , , which causes yielding of the material at the inner surface of a tube with closed

ends, is the subject of this section. In the case of a tube with open ends, the axial

stress component should be zero ( 0=z ).

In order to define the conditions (i.e. critical stress situation) under which yielding of

the material at the inner surface starts, the behaviour of the material under these

conditions has to be known. However, the material properties (yield strength, tensile

strength, breaking strength, breaking elongation, etc.) available in the literature were

obtained by a uniaxial tensile test on a specimen of the material with defined

geometry and under defined test conditions [28, 29]. A comparison of the effect of a

multiaxial stress state in a thick-walled tube with the effect of a uniaxial stress state

found in a specimen (made of the same material as the tube) during a tensile test in

the laboratory is not directly possible. For this purpose, it is necessary to define the

equivalent stress which represents the complete three-dimensional stress situation in

the tube and which can be compared with the standard material data available in the

literature. In this way, the results of the standard uniaxial tensile test can be used to

predict yielding of the material when a tube is exposed to the three-dimensional


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stress state. This is known in the literature [19, 57, 74] as the criteria of elastic

breakdown and there are six most often used criteria.

Comparison and validation of different criteria with results obtained by experiments

on thick-walled tubes have been the topic of many studies [12, 14, 24, 37-39 72-75,

81]. The results obtained are presented in Fig. 2.10 and can be summarized as

follows. On the one hand, the maximum principal stress criterion, the maximum

principal strain criterion and the total strain energy criterion have significant

deviations in comparison with the results obtained by experiments. On the other

hand, the maximum shear stress criterion shows negligible deviations, whereas the

maximum distortion strain energy criterion best fits the results of experiments.

Figure 2.10. Comparison of different criteria with the experimental results

(adapted from [15]).

Therefore, the maximum shear stress criterion and the maximum distortion strainenergy criterion are the only applicable criteria in high pressure technology where

ductile materials are commonly employed. From the expression for equivalent stress

( e ) one can obtain the lowest value of the internal pressure ( inrinp , ) which causes

yielding of the material at the inner surface of a thick-walled tube with closed ends.

An expression for equivalent stress according to the maximum shear stress criterion

is given by Eq. (2.10):


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e

rrin

out

out

rinrrzre R

rr

rr

p

in

in

====>>=

=

1

222

2

,max (2.10)

Equation (2.11) expresses the equivalent stress according to the maximum distortion

strain energy criterion:

( ) ( ) ( )[ ] e

rrin

out

out

rinrrzze R

rr

rr

p

in

in

=++=

=

1

35,02

2

,

222

(2.11)

2.3.3 Elastic-Plastic Thick-Walled Tube

In order to obtain a favourable residual stress pattern that brings beneficial effects

under the operating conditions, many engineering components are loaded

significantly beyond their elastic limit in a manufacturing process. In this process, the

component is subjected to static internal pressure far beyond the intended operating

pressure in order to induce partial yielding of the component. After a short period of

time the pressure is released and the required permanent plastic deformation isreached within the inner yielded region. The outer elastic region of the component

attempts to return to its original state but is prevented from the inner region which

has been expanded due to the plastic deformation. As a result, a beneficial state of

residual stresses is introduced in the wall of the component: the outer elastic region

is maintained in a residual tension, while the inner deformed region is in a residual

compression, Fig. 2.11.

This procedure is known as an overstrain or autofrettage. The term autofrettage

comes from the French meaning self-hooping. The procedure can either be realizedby a hydraulic pressurization or can be caused mechanically by forcing an oversized

mandrel or swage through the bore. The objective of the autofrettage process is to

obtain a favourable residual stress pattern in a manufacturing process which

thereafter brings beneficial effects under the operating conditions. By application of

the autofrettage process, the static loading capability of components can be

increased due to the strain hardening effect which takes place during the process.

Furthermore, the residual stress pattern generated reduces crack initiation, retards

the fatigue crack growth rate, and consequently increases the fatigue limit of the

component [31, 77, 87].


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The permanent deformation of a thick-walled tube through this internal cold working

process has been known since the time when the Austrian general Uchatius

discovered the principle of strengthening the bronze barrels for artillery guns. The

earliest deliberate application of the autofrettage principle was at the beginning of the

twentieth century (suggested by French artillery designer Malaval - according to

Jacob [52], 1906) in the French gun-barrel industry. The procedure was then

gradually developed in the period between the two World Wars and is widely used

today, not only in the armament industry, but also in other industries such as the

chemical, the nuclear, the automotive, the artificial diamond industry, and most

recently even in the food industry.

Plastic deformed region

Linear elastic region

pin=0

in, in out, out

in0

Re

out>0out>0

Re

Figure 2.11. Effect of an autofrettage principle.

For the purpose of stress-strain analysis, an elastic-plastic thick-walled tube

(Fig. 2.12) subjected to an internal pressure (in

p ) is considered. Also in this case a

two-dimensional stress state acting at the control element can be described by a

differential equation (2.2). Solutions of the equation for two different cases of an

elastic-plastic thick-walled tube (partially and completely autofrettaged) are

separately outlined here. To formulate those relations for an elastic-plastic thick-

walled tube, besides the assumptions made in the analysis of an elastic thick-walled

tube (Section 2.3.1), the following additional assumptions have to be made:

the material is incompressible (Poissons ratio in both the elastic and plastic

regions is assumed to be 5.0= ; this is not the case at least in an elastic region

where 3.0= , but under this assumption it is only possible to solve differential

equation (2.2) in the case of an elastic-plastic thick-walled tube),


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no longitudinal elongation of the tube, 0=z (this was verified in a precise test by

Davis [26] on the flow of the thick-walled tubes made of steel and copper),

elastic-perfectly plastic behaviour of material in the case of a partially

autofrettaged thick-walled tube,

rigid-perfect plastic behaviour of material in the case of a completely autofrettaged

thick-walled tube.

Plastic deformed region

Linear elastic region

rin

pinr

r+dr

d

dr

r

rout

rj

Figure 2.12. Cross-section of a partially autofrettaged thick-walled tube with static

equilibrium of the control element.

2.3.3.1 Partially Autofrettaged Thick-Walled Tube

The problem of determining the stresses and strains in a partially autofrettaged thick-walled tube was solved analytically at the beginning of the twentieth century. Two

analytical methods for a partially autofrettaged thick-walled tube are available in the

literature [15, 57, 59]:

method based on the maximum distortion strain energy criterion proposed by

Prager & Hodge in 1951 [88] and Jrgensonn in 1953 [56],

method based on the maximum shear stress criterion (Jung in 1958 [55]).

In the work published by Prager & Hodge, as a strength parameter the yield strength

in shear was used, F , whereas in the work of Jrgensonn the yield strength in

tension was used, eR . Both approaches give an identical solution since the


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maximum distortion strain energy criterion relates the yield strength in shear F and

the yield strength in tension eR by the relation 3eF R= . In fact, the applied

stress-strain calculations in the plastic and elastic regions of a pressurized tube date

from the work of Ndai in 1927 [79], while the residual stress-strain calculations date

from the work of Hencky in 1924 [46]. The aforementioned methods (Prager &Hodge, Jrgensonn and Jung) are simplified forms of calculations purposely

developed for the practice.

An analytical method, mostly used in practice, based on the maximum distortion

strain energy criterion will be presented in this thesis. The equations for the method

based on the maximum shear stress criterion (proposed by Jung) can be similarly

derived. The only difference between the methods is in the conversion factor 23

whereby equations derived on the basis of the maximum distortion strain energy

criterion should be multiplied by this factor in order to obtain equations based on themaximum shear stress criterion.

In the case of a partially autofrettaged thick-walled tube, it is assumed that the tube

yields up to a certain point defined by the radius jr and beyond that point it remains

linearly elastic. The distance jr is the distance from the tube axis to the boundary of

the plastic-elastic junction. The ratio of the covered plastic deformed wall thickness

portion to the total wall thickness gives the autofrettage degree:

[ ]%100

=

inout

injd

rr

rra (2.12)

Initial yielding of the material at the inner surface of an elastic thick-walled tube will

start when the internal pressure achieves

2

2

, 13 out

ineendsclosedrin

r

rRp

in (2.13)

for closed end conditions, i.e. 0z in Eq. (2.11), and

21

4

4

2

2

,3

113

+

out

in

out

ineendsopenrin

r

r

r

rRp

in (2.14)

for open end conditions, i.e. 0=z in Eq. (2.11).

The magnitude of the internal pressure which causes yielding of a tube with closed

ends up to a radius jr can be determined from a boundary condition whereby the


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27

magnitude of the radial stress component at the inner surface is equal to the negative

magnitude of the internal pressure (j

inrinrrprpar

p ,,, == ):

+

in

j

out

jerin

r

r

r

rRp

jln21

3

2

2

, (2.15)

The magnitude of the internal pressure which causes yielding of a tube with open

ends up to a radius jr is always smaller than in the case of a tube with closed ends.

For simplicity, Eq. (2.15) can also be used for a tube with open ends.

Equations for the stress distribution in the elastic and plastic regions, derived in the

following section, correspond to the closed end condition, which is a common case in

engineering practice. In the case of a tube with the open end condition, the axial

stress component should be zero ( 0=z ).

2.3.3.1.1 Stress Distribution in a Partially Autofrettaged Thick-Walled Tube

By applying the boundary conditions that the radial stress component at the outer

surface of a tube is zero ( 0== outrrr

) and that a tube yields up to the radius of the

plastic-elastic junction where the distortional energy density (Eq. 2.11) reaches a

value equal to the distortional energy density at yield in a uniaxial case,

( )3

2 er

R can be solved the differential equation (2.2) in the case of the

elastic region of a partially autofrettaged thick-walled tube. The solution gives

expressions for the tangential and radial stress components within the elastic region

of a partially autofrettaged thick-walled tube. According to the assumptions ( 0=z

and 5.0= ) that have been made in this analysis and by employing the Hookes law

equation, the axial stress component in the case of a tube with closed ends can be

obtained from the expression ( )rz += 5.0 .

Therefore, general expressions for the distribution of stresses across the elastic

region (er) of a partially autofrettaged thick-walled tube (pa ) are given by

+

+=

1

1

32

2

2

2

2

2

,,

in

out

out

j

out

jeerpa

rr

rr

pr

r

r

rR (2.16)


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28

+

=

1

1

32

2

2

2

2

2

,,

in

out

out

j

out

jeerpar

rr

rr

pr

r

r

rR (2.17)

=

1

1

322

2

,,

in

outout

jeerpaz

rr

pr

rR (2.18)

where inrin ppp j = , is the pressure difference between the autofrettage pressure

(jrin

p , ) which causes yielding of a tube up to the radius jr and an actual applied

internal pressure ( inp ).

pin,rj 01 2 3

1.25

1.00

0.75

0.50

0.25

-1.00

-0.75

-0.50

-0.25

-1.25

0

1.50

1.75

-1.50

-1.75

/R

e

e

z

r

pin=0 0 1 2 3

1.25

1.00

0.75

0.50

0.25

-1.00

-0.75

-0.50

-0.25

-1.25

0

1.50

1.75

-1.50

-1.75

/R

e

e

z

r

(a) (b)

Figure 2.13. a) Distribution of applied principal stresses across the wall of a partially

autofrettaged thick-walled tube ( 3=k , %30=da ) subjected to the internal pressure jrinp , .

b) Distribution of residual principal stresses across the wall of a partially autofrettaged

thick-walled tube ( 3=k , %30=da ) unloaded to a zero pressure.


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29

Applied principal stresses in the elastic region of a tube subjected to the autofrettage

pressure (Fig. 2.13a) could be described by only the first terms in Eqs. (2.16) to

(2.18) [56, 80] because in that case inrin pp j =, and 0=p . If a tube is unloaded after

an autofrettage process from the plastic-elastic state, it will be left with residual

stresses. The unloading process is purely elastic (an elastic-perfectly plastic

behaviour of material) and, therefore, the residual principal stresses [46] in the elastic

region (Fig. 2.13b) could be describe

evaluation of high pressure components of fuel injection systems using speckle interferometry

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