Variable amplitude fatigue in offshore structures Steven...

Steven De Tender

Variable amplitude fatigue in offshore structures

Academic year 2015-2016Faculty of Engineering and ArchitectureChair: Prof. dr. ir. Jan MelkebeekDepartment of Electrical Energy, Systems and Automation

Master of Science in Electromechanical EngineeringMaster's dissertation submitted in order to obtain the academic degree of

Counsellor: Ir. Nahuel MiconeSupervisor: Prof. dr. ir. Wim De Waele

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Steven De Tender

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Confidential up to and including 01/01/2018

Important

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to Ghent University or third parties. It is strictly forbidden to publish, cite or make public in any way this

master dissertation or any part thereof without the express written permission of Ghent University. Under

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The stipulations above are in force until the embargo date.

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Preface

“Research consists in seeing what everyone else has seen, but thinking what no one else has thought.”

- Albert Szent Gyorgyi

Variable amplitude fatigue in offshore structures is an important research topic that is more and more

studied. Green energy gains increasing importance in the current society and offshore wind turbines

are one of the most important solutions. Nowadays offshore structures are often designed based on

constant amplitude fatigue research, which can either over- or underestimate the real lifetime of

structures. It was therefore investigated in this thesis what the actual effect of variable loading

conditions is on the lifetime of structures. All material that is obtained in this thesis is innovative and

allows Labo Soete to perform further investigation to this topic. The knowledge gained in this thesis

was partly used by Olivier Rogge and Michiel Depoortere, to investigate the influence of corrosion on

fatigue. Both works can be used in the future to determine the effect of corrosion on variable

amplitude fatigue.

I want to thank my counsellor ir. Nahuel Micone and my promotor prof. dr. ir. Wim De Waele for the

professional guidance during my thesis. Their knowledge and support was crucial to obtain a good and

professional result.

This thesis was based on the master dissertation of Niels Laseure and Ingmar Schepens. I want to thank

them for the effort they put in building the foundation of my work and for their help when it was

necessary.

Special thanks to Olivier Rogge and Michiel Depoortere. Sharing lunch every afternoon with a moment

of laughter and working together at certain moments brightened the days at the lab. As I spent so

many time at the lab, I also want to thank the technicians for the help they gave when it was necessary.

Finally, I want to thank “Meetnet Vlaamse Banken” and Carlos Van Cauwenberghe for the delivered

wave data of the North Sea. Their input made it possible to perform tests based on a realistic load

spectrum.

"The author gives permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In the case of any other use, the copyright terms have to be respected, in particular with regard to the obligation to state expressly the source when quoting results from this master dissertation." 23/05/2016

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Steven De Tender

Variable amplitude fatigue in offshore structures Steven De Tender Supervisor: Prof. dr. ir. Wim De Waele Counsellor: Ir. Nahuel Micone Master's dissertation submitted in order to obtain the academic degree of Master of Science in Electromechanical Engineering Department of Electrical Energy, Systems and Automation Chair: Prof. dr. ir. Jan Melkebeek Faculty of Engineering and Architecture Academic year 2015-2016

Abstract

Fatigue is a well-known failure phenomenon which is and has been extensively studied. Even though,

most of the research is done to constant amplitude fatigue. Fatigue life of a structure is then

determined based on a linear rule, calculating the sum of the constant amplitude life. Therefore

variable amplitude effects are not taken into account, which might lead to under- or over-conservative

designs. This thesis investigates the influence of variable amplitude loading on the lifetime of a

structure. Based on wave data from the North Sea, realistic loading conditions are obtained, which are

then used for testing. To have an idea of the possible increase/decrease of lifetime, the obtained result

from a linear rule has to be determined for comparison. Therefore, the Paris law curve is determined

for the two materials that are used in this thesis. While gathering this data, multiple instrumentation

techniques were investigated. To perform all tests, a dedicated LabVIEW program was developed to

control the test setup.

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Steven De Tender

Supervisor(s): Nahuel Micone, Wim De Waele

Abstract Fatigue is a well-known failure

phenomenon which has been and still is

extensively studied. Often structures are designed

according to the safe-life principle so no crack

initiation occurs. Nowadays there is a high

emphasis on cost-efficiency, and one might rather

opt for a fail-safe design. Therefore a certain

amount of crack growth can be allowed in

structures, but then a good knowledge of stresses

and related crack growth rates is needed. To this

end, extensive studies are done to obtain a

material’s Paris law curve. Based on a linear rule,

crack growth for a variable amplitude load

spectrum is calculated using crack growth rates

from this Paris law curve. This however does not

account for variable amplitude effects such as

retardation and acceleration. The purpose of this

thesis is to investigate the

retardation/acceleration and the influence on the

overall lifetime of a structure.

Keywords Paris law curve, Variable amplitude

effects, fatigue

I. Introduction

The thesis is split up in two main parts. The first part

describes the Paris law curves and the way these are

obtained for two materials, which are offshore

grades NV F460 and NV F500 further denoted as

material A and B. Together with the determination

of these curves, different instrumentation techniques

are tested and evaluated for use in fatigue tests. As

this instrumentation research became a major part of

the thesis, it will be extensively discussed in one of

the next paragraphs.

The second part consists of the investigation of the

offshore variable amplitude loading on the lifetime

of a structure. The loads applied on the structure are

obtained from a JONSWAP analysis based on wave

data obtained from ‘Meetnet Vlaamse Banken’.

II. Test setup

As was mentioned above, the first part of the thesis

reports on the determination of the Paris law curves

of material A and B. To perform the tests necessary

to reach this goal, a dedicated LabVIEW program

was developed. Besides, different instrumentation

techniques were implemented to measure the crack

growth during the tests. The next paragraph will

discuss the used instrumentation techniques and the

main conclusions of the results gained with these

techniques in more detail. All tests were performed

with a stress ratio of R = 0.1 and a frequency of 10

Hz.

III. Instrumentation

The most important instrumentation technique that

was used is a clip gauge for the determination of

crack mouth opening displacement (CMOD). With

the compliance equations available in standard

ASTM E647 [1] this can be directly linked to a

certain crack length. This instrumentation technique

was used as an online control method for the crack

growth. Based on this output, the LabVIEW program

decided whether a new ΔK value had to be tested in

a K-decreasing or K-increasing test (see next

paragraph).

Direct current potential drop (DCPD) is used as a

second measurement technique. A constant current

is sent through the specimen and as the resistance of

the specimen increases when the uncracked ligament

of the specimen becomes smaller, the measured

voltage also increases. This voltage can be linked to

a certain crack length.

The strain gauge is used as a third measurement

technique. A strain gauge is applied to the back face

of the specimen. A crack length can be obtained

using a back-face compliance equation. The use of

this method was not as successful as the other two

techniques. As will be seen in the results in the

thesis, the shape of the reported crack growth curves

(see next paragraph) is similar to the other two

methods, but the scale however is different. It is

therefore suggested that the back-face compliance

equation should be adapted.

The fourth technique that was investigated is the use

of beachmarks. Changing the R ratio during testing

for a short period of time leads to a visual mark (dark

line) on the fracture face. Measuring the distance

between different beachmarks allows a post-mortem

validation of crack growth values measured with

other measurement methods. The results found for

this technique are very promising. With respect to

conventional methods based on a cyclic control of

the beachmark length, it was chosen to apply a

beachmark over a fixed crack length. Specifically,

this means that the beachmark stress ratio will be

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Steven De Tender

applied until a certain crack growth is reached.

Doing this ensures the good visibility for all applied

loads at any moment in the test. Figure 1 shows an

example of a specimen and the clear beachmarks.

Figure 1: Example of applied beachmarks

The fifth technique that was applied was digital

image correlation (DIC). However, as this was not

worked out in as much detail as the other four

techniques, it will not be further discussed in this

abstract.

IV. Paris law curve

A Paris law curve consists of three main parts: the

initiation phase (I), the stable propagation phase (II)

and the critical propagation phase (III). This is

illustrated in figure 2. The initiation phase has as a

lower limit called the threshold stress intensity factor

range (defined below). The stable propagation phase

starts and ends when the crack growth rate becomes

linear (in a double logarithmic diagram) with respect

to stress intensity factor range. The critical

propagation phase starts when there is crack growth

rate acceleration [1].

Figure 2: Paris law curve

A Paris law curve is typically determined with a K-

decreasing and K-increasing procedure for region I

and II respectively. Based on the measured a/W-N

curve (figure 3), the Paris law curve can be

constructed by determining the crack growth rates

(da/dN) and their corresponding stress intensity

factor ranges (ΔK). This stress intensity factor range

depends on the applied load, the crack size and

geometrical parameters of the used test specimen.

Figure 3: a/W-N curve

The Paris law curves of both materials were

determined with both the clip gauge and DCPD

measurement technique. As illustration, the Paris

law curve of material A determined with both

methods is shown in figure 4. It is clear that both

techniques give an excellent correlation, but as can

be seen the clip gauge technique gives the most

uniform result.

Figure 4: Paris law curve for material A based on

clip gauge and potential drop measurements

V. Variable amplitude effects

The actual goal of the thesis was to determine the

influence of a variable amplitude load spectrum on

the fatigue life of a structure. To have a realistic

loading spectrum, wave data in the North Sea was

obtained from ‘Meetnet Vlaamse Banken’. Based on

this wave data, the load spectrum on an ‘equivalent

monopile structure’ was determined. Based on this

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investigation, distinct ΔK blocks were determined

and used in multiple test procedures.

Three distinct procedures were tested: low to high

stress intensity (L-H), low to high to low stress

intensity (L-H-L) and semi-random stress intensity

tests. These tests were then presented in both a/W-N

and da/dN-N curves. This last curve plots the change

in crack growth rate over number of cycles. When

there is for instance retardation, the da/dN values

will slowly grow from a lower value, back to their

original crack growth rate as determined in the Paris

law curve of the material.

The L-H tests arranged the ΔK values from the

lowest to the highest values, determining the

influence of a preceding lower ΔK value. It was

found that there was a small retardation effect for

material A and no or almost no effect for material B.

For the L-H-L tests, it was found that the H-L part of

the test caused a significant amount of retardation. A

dedicated L-H-L test was performed with a large

transition between ΔK values. In the H-L part the

transition was so severe that total crack arrest

occurred. This clearly shows that an ordered variable

amplitude spectrum will always give rise to a longer

lifetime than predicted by a linear rule.

For the final semi-random tests the obtained ΔK

blocks from the wave data analysis were scrambled

in a semi-random order. The crack growth results

also showed a significant amount of retardation and

that certain block transitions resulted in total crack

arrest.

Finally, the random fatigue life corresponding to the

performed tests was calculated based on a formula

found in literature. The result was in line with the

findings of the experiments, as an even bigger

retardation was predicted for a random loading

spectrum.

Based on these results, it is suggested that with a

positive stress ratio, variable amplitude fatigue gives

rise to an overall retardation.

Acknowledgements

The author would like to acknowledge his counsellor

ir. Nahuel Micone and his promotor prof. dr. ir. Wim

De Waele for the professional guidance during my

thesis. Their knowledge and support was crucial to

obtain a good and professional result.

VI. References

[1] Micone, N., De Waele, W. (2015). Comparison

of Fatigue Design Codes with Focus on Offshore

Structures. In International Conference on Ocean,

Offshore and Artic Engineering. Canada, May 31 -

June 5. Ghent University, Soete Laboratory: ASME.

[2] Standard test method for measurement of fatigue

crack growth rates, ASTM E647. ASTM

International, West Conshohocken, USA, 2013.

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Table of contents

Preface ............................................................................................................................ III

Extended abstract ............................................................................................................. V

List of symbols ................................................................................................................. XI

1 Introduction ........................................................................................................................ 1

1.1 Problem statement .................................................................................................................. 1

1.2 Variable amplitude fatigue ...................................................................................................... 1

1.3 Random load histories versus ordered variable amplitude and constant amplitude spectra 2

1.4 Offshore load spectrum ........................................................................................................... 5

1.5 Support structures ................................................................................................................... 6

1.6 Spectrum processing ............................................................................................................... 7

1.7 Randomize signal ..................................................................................................................... 7

1.8 Stress ratio ............................................................................................................................... 8

1.9 Preview .................................................................................................................................... 8

2 Test setup: instrumentation ............................................................................................. 11

2.1 Introduction ........................................................................................................................... 11

2.2 Test setup .............................................................................................................................. 12

2.2.1 General test setup ......................................................................................................... 12

2.2.2 LabVIEW instrumentation test control .......................................................................... 13

2.2.2.1 Calibration ................................................................................................................. 13

2.2.2.2 Test condition ............................................................................................................ 15

2.2.2.3 Save data ................................................................................................................... 17

2.2.2.4 Visualisation .............................................................................................................. 18

3 Instrumentation research ................................................................................................. 21

3.1 Outline ................................................................................................................................... 21

3.2 Experimental procedure ........................................................................................................ 21

3.2.1 Material ......................................................................................................................... 21

3.2.2 Geometry ....................................................................................................................... 22

3.3 Clip gauge .............................................................................................................................. 23

3.3.1 General .......................................................................................................................... 23

3.3.2 Test results .................................................................................................................... 24

3.4 Potential drop ........................................................................................................................ 26

3.4.1 General .......................................................................................................................... 26

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3.4.2 Test results .................................................................................................................... 26

3.5 Strain gauge ........................................................................................................................... 28

3.5.1 General .......................................................................................................................... 28

3.5.2 Test results .................................................................................................................... 28

3.6 Beachmarking ........................................................................................................................ 30

3.6.1 General .......................................................................................................................... 30

3.6.2 Test results .................................................................................................................... 30

3.7 Digital Image Correlation ....................................................................................................... 33

3.8 Paris law curve ....................................................................................................................... 34

3.8.1 Clip gauge results........................................................................................................... 34

3.8.2 Potential drop results .................................................................................................... 36

4 Offshore load spectrum .................................................................................................... 39

4.1 Tripod – monopile analysis .................................................................................................... 40

4.1.1 Outline ........................................................................................................................... 40

4.1.2 Geometry ....................................................................................................................... 41

4.1.3 Maximum stress intensity factor ................................................................................... 41

4.2 Wave data analysis ................................................................................................................ 42

5 Variable amplitude fatigue: block loads ........................................................................... 47

5.1 Outline ................................................................................................................................... 47

5.2 LabVIEW test control ............................................................................................................. 47

5.2.1 Test condition ................................................................................................................ 47

5.2.2 Visualisation .................................................................................................................. 48

5.3 Test procedure and results .................................................................................................... 49

5.3.1 Low to high sequences .................................................................................................. 49

5.3.1.1 Procedure .................................................................................................................. 49

5.3.1.2 Test results ................................................................................................................ 51

5.3.2 Low to high to low sequences ....................................................................................... 54

5.3.2.1 Procedure .................................................................................................................. 54

5.3.2.2 Test results ................................................................................................................ 57

5.3.3 Semi-random procedure ............................................................................................... 62

5.3.3.1 Procedure .................................................................................................................. 63

5.3.3.2 Test results ................................................................................................................ 66

5.3.4 Discussion ...................................................................................................................... 69

6 Conclusions and future work ............................................................................................ 71

6.1 Instrumentation and Paris law curve .................................................................................... 71

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Steven De Tender

6.2 Variable amplitude loading ................................................................................................... 72

7 References ........................................................................................................................ 75

Appendix A: SCAD paper

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List of symbols

a crack length

a0 initial crack length

ar reference crack length

Δa crack growth interval

a/W relative crack length

B Specimen thickness

C Paris law constant

CMOD Crack mouth opening displacement

d internal diameter

D Outer diameter

da/dN crack growth rate

DCPD Direct current potential drop

DIC Digital Image Correlation

E Young’s modulus

E(x) Expected value

ESE(T) Excentrically-loaded single edge cracked tension

f frequency

h Mean water level

H Wave height

Hs Significant wave height

INST Instrumentation tests

JONSWAP Joint North Sea Wave Project

Kc Elastic fracture toughness

Kmax Maximum stress intensity factor

Kmin Minimum stress intensity factor

ΔK Stress intensity factor range

l Distance between slender piles

L-H low – high procedure

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L-H-L low – high – low procedure

m Paris law power

M bending moment

Material A NV F460

Material B NV F500

N Number of cycles

P Force

Pmax Maximum force

Pmin Minimum force

ΔP Force range

R Stress ratio

T Wave period

TP Peak period

u Wave speed

V Voltage

Vr Reference voltage

W Specimen width

Wb Bending resistance moment

Y0 Welded pin distance

ε Strain

ρ Autocorrelation

σ2 Variance

σmin minimum stress

σmax minimum stress

σUTS Ultimate tensile strength

σy Yield strength

μ Mean value

Introduction 1


1 Introduction

1.1 Problem statement

Fatigue is one of the major failure mechanisms in engineering structures. When designing structures

for fatigue, most of the times a linear rule based on constant amplitude material behaviour is used for

lifetime predictions. In reality however, materials behave differently because of variable amplitude

interaction effects which will be discussed lower. This difference in material behaviour might result

either in under- or over-conservative lifetime predictions. The first case is of course the most

dangerous one and is certainly unwanted. Some conservatism in a design is of course always wanted

for safety considerations, but an overly conservative design results in too high costs. This shows the

importance of determining the real material behaviour under realistic loading conditions.

First an offshore load spectrum on a wind turbine situated in the North Sea will be analysed. This

spectrum is obtained by using the JONSWAP spectrum, which was specifically developed for the North

Sea. From this analysis a wave distribution is obtained, this is then combined with a wave and current

load into a random load spectrum. An ordered block load spectrum can be obtained with the rainflow

counting method. This spectrum can be assumed as being equivalent with the random spectrum and

easily analysed. While doing so, according to literature [1,2,3], different variable amplitude effects will

occur, which are discussed below.

There is a difference between the retardation/acceleration effect (see next paragraph) of a random

spectrum and an ordered block load spectrum. It might be difficult to test a random spectrum in

practice and this is why testing both a completely ordered spectrum and a semi-random spectrum with

a certain “randomness” might be interesting. This randomness will be evaluated with an

autocorrelation value of the signal, which gives the cross-correlation between two successive peaks.

Also constant amplitude tests at the mean stress of the blocks tested will be included. Comparison will

be made between constant amplitude tests, ordered block tests, semi-random spectrum tests and a

calculated random fatigue life. The formula for this calculated fatigue life is found in literature and

used to confirm certain hypotheses.

1.2 Variable amplitude fatigue

When spectra are organized and block loads or single/sequential under-/overloads are used, a clear

interaction effect is observed [1,4]. Applying overloads results in a retardation of the fatigue crack

growth rate. There are several explanations for this. The first states that because of a plastic zone

ahead of the crack tip, compressive residual stresses are present when an overload was applied.

Combination of the applied stress and the residual stresses gives a lower resulting stress at the crack

tip. The second theory is often described as plasticity-induced crack closure. Due to the increased load,

the plastic wake around the crack tip is enlarged. This causes the stress at which the crack is re-opened

in the subsequent cycles to be substantially larger. The third explanation considers the crack tip to

blunt out under an overload. Additional cycles succeeding the overload are needed to create a sharp

crack tip again, which also gives rise to a retardation.

When a single underload is applied, the main idea is that an acceleration effect will take place [1]. This

can again be explained with the residual stress concept, only now tensile residual stresses are present

at the crack tip. The effect however will be less pronounced than for the case of retardation [1,5]. As

Introduction 2

Steven De Tender

denoted in [5] there are a lot of parameters which influence the amount of retardation/acceleration,

such as the overload amplitude with respect to the main amplitude, the R-ratio, etc.

The previous paragraph only deals with single or multiple under-/overloads. The moment sequential

underloads are applied, it is still uncertain what the main load interaction effect will be [1]. For

overloads it is believed that in these cases also retardation will occur [1]. According to [3] the

retardation effect in these situations is even higher than for a single overload. Especially when block

loads are applied there is no general theory of what the effect will be on the fatigue life. There are

many possible combinations that can be investigated, the conclusions of most of the interesting cases

made in [1,3] are summarized in figure 1.

Of course in real life, there are no ordered spectra. Even if the spectrum is close to an ordered one,

there will always be random deviations. That is why random load histories also have to be considered.

Figure 1: Interaction effects dependent on load type [3]

1.3 Random load histories versus ordered variable amplitude and

constant amplitude spectra

In [6] sequential and random load spectra (figure 2) are compared with each other and with constant

amplitude fatigue. It was found that random loading is more damaging than sequential loading. For

this specific case the lifetime of the tested specimens was 1.3 times greater with the sequential

spectrum than with the random spectrum. It was also concluded that most of the specimens tested

under random loading were inside the lower and upper bound of the S-N curve estimated with

constant amplitude tests (both strip specimens and full scale test specimens were used). This suggests

that Miner’s rule is reasonably accurate for estimating variable amplitude fatigue damage.

Introduction 3


Figure 2: Loading patterns used for variable amplitude testing: sequential loading (left) and random loading (right) [6]

More or less the same study is reported in [4]. As in [6], it is also concluded that a random load history

gives more or less the same fatigue life as a constant amplitude signal with a comparable average stress

level. The explanation according to this paper is that both acceleration and retardation are balanced

due to the random nature of the signal. This however contradicts the conclusion that the effect of

retardation is more pronounced than acceleration [1,5]. For a more ordered variable amplitude signal,

specifically a sequential load with only one wave (or sequence) is used (figure 3). It is concluded that

the crack growth rate is substantially lower than for the random spectrum and the constant amplitude

signal. This is the same conclusion as in [6], and might be explained with the higher influence of

retardation [1,5].

Figure 3: Nominal stress cycles of the two types of variable amplitude loads applied ( (a) ‘random’ load; (b) ‘wave’ load) [4]

[7] shows that the investigation of a random signal is non-trivial. As every structural application has a

different load spectrum acting on it, there is not one kind of random spectrum. In this paper, different

variable amplitude sequences are studied. Sequences with a constant maximum amplitude, constant

minimum amplitude and constant mean amplitude are used. For all three tests positive R ratios and

positive stresses were applied. Figure 4 shows the comparison of three variable amplitude sequences

with a constant amplitude S-N curve. Sequence A has a constant maximum stress, but a varying

minimum stress and thus R ratio. In the same way, sequence B has a constant mean stress and

sequence C a constant minimum stress. All three sequences give different results with respect to each

other and the constant amplitude result. For sequences A and B, Miner’s rule is non-conservative, for

sequence C Miner’s rule is very conservative. One can conclude from this research that the validity of

Miner’s rule depends on the spectrum imposed on the test specimens.

Introduction 4

Steven De Tender

Figure 4: Comparison of the variable amplitude test results (Sequences A, B and C) with the constant amplitude S-N curve [7]

Random loading was investigated for constructional steels in [8]. Steels for offshore applications,

highway bridges and chimneys are considered. The specific investigation of the offshore constructions

is described more extensively in [9]. To investigate material behaviour under random loading, tests on

both tubular joints and plate specimens were performed. A fracture mechanics approach is considered,

to compare the outcome with the experimental results. Besides this, the definition of an irregularity

factor is used. This is defined as the number of positive-going mean value intersections of the signal

divided by the number of maxima of the load history. A narrow band loading (which is a narrow range

of load amplitudes) will have an irregularity close to unity. But a broad-banded spectrum will have a

factor closer to 0. According to the research a typical load history of a fixed offshore structure has an

irregularity factor between 0.6 to 0.8.

For the purposes of this thesis, there are two main important conclusions from this investigation. The

first is that for a narrow signal, the Miner’s sum will be quite close to 1 and thus the Miner’s rule theory

is more or less applicable in its original form. The more broad-banded (lower irregularity) the signal,

the lower the Miner’s sum upon failure becomes. It is suggested that with a rather broad-banded signal

a value around 1/3-1/2 for the Miner’s sum should be used, to obtain a conservative design.

The second conclusion is that there is a difference in severity of variable amplitude loading dependent

of the stress ratio. For load histories which are more or less equal in tension/compression, the variable

amplitude fatigue life is generally shorter than the constant amplitude life with an equivalent stress

range. On the other hand, for specimens primarily loaded in tension, the constant and variable

amplitude fatigue life was quite similar.

Besides these two conclusions, it is also stated that with lower equivalent stress levels, but equivalent

spectrum distribution, a higher Miner’s sum is found. This can be explained because of a lower crack

growth acceleration at lower stress levels.

In [10] Agerskov and Nielsen specifically studied the case of highway bridges. They compared two

different strain gauge measurements corresponding to one week’s traffic loading on a bridge.

Introduction 5


Experimentally and analytically a corresponding Miner’s sum of 0.5-1 was found for a signal that has a

stress ratio that is more or less equal to -1. It is mentioned however that for an R ratio of around -0.2,

they actually found Miner’s sums of 1.2-1.8. With a fracture mechanics approach on the other hand

values around 0.8-0.9 were retrieved. This is justified by arguing that the actual Miner’s sum is more

or less around the calculated value as, according to the authors, the actual found experimental results

were not completely valid. They stated that the correlation (mentioned below) of the signal was not

random enough and the obtained S-N curve was not completely valid.

Care should be taken with these kinds of interpretations, but there can be multiple reasons for this

difference in analytical and experimental results. One possibility might be that because of the more

ordered nature of the signal, more retardation occurs (as denoted in [6,7]) and the test results were

actually valid. Another reason might be that because almost only tensional stresses are applied, as was

mentioned in [8], the spectrum will be less severe than a tension/compression signal. Or finally, the

justifications made in [10] might be correct.

It can be concluded from the discussion above, that there is no general theory yet with respect to the

effect of a random load spectrum. Care should be taken with redistribution and simplifications applied

to any random load history.

1.4 Offshore load spectrum

As mentioned in the introduction, the main goal is to investigate a variable amplitude load spectrum

on a wind turbine in the North Sea. An offshore structure is subjected to wave loads, currents and wind

loads. The wave loads at the water level result from the wind. At the bottom there is an influence of

the currents, but as these act on the bottom of the structure, the bending moment from these forces

will be much smaller than from the wind and wave loads. These forces could be included for

completeness, but this would make the analysis a lot more difficult and are therefore neglected.

Wave spectra representative for the North Sea are provided by the JONSWAP spectrum [2]. With the

JONSWAP spectrum wave behaviour can be defined by means of only two parameters: the significant

wave height Hs and the peak period Tp. Tp is the period in a wave signal which contains the highest

energy and Hs is the mean of the largest 1/3rd waves that are statistically able to occur.

According to [2], after using the JONSWAP spectrum and determining the wave profile, the wave speed

can be calculated by means of the linear wave theory. Certain assumptions have to be complied with

in order to allow the theory to be used. These can be found in [2] and for our applications it can be

assumed that they are valid. The velocity can then be calculated according to:

𝑢(𝑧, 𝑡) =𝜋𝐻

𝑇 cosh (

2𝜋(𝑧 + ℎ)𝐿 )

sinh (2𝜋ℎ𝐿 )

cos (2𝜋𝑡

𝑇)

H is the wave height, T is the wave period, L is the wave length, h is the mean water level, t is time and

z is the height measured from the seabed. In the linear wave theory a constant wave height H is

assumed. In this analysis the wave data found from the JONSWAP spectrum will be used as a variable

height and thus varying wave velocities will be calculated. The value of the mean water level has to be

determined based on the application (height of the structure in sea). The parameters used in the linear

wave theory and the visualisation of a wave profile are shown in figure 5.

Introduction 6

Steven De Tender

Figure 5: Illustration of the parameters used in the linear wave theory and the wave velocity [2]

The final goal is to determine a load spectrum, and for this Morison’s formula will be used [2]. This

formula calculates a force using the velocity and acceleration determined with the linear wave theory.

Besides these two parameters, the use of a slender monopile structure with diameter D has to be

assumed. For this assumption to be valid, the slender pile hypothesis should be sound. Two criteria

have to be met for this:

1. The diameter should be small enough in comparison to the wave length, specifically: 𝐷 <

0.05𝐿

2. In case two slender piles are close to each other, this formula is only valid if the distance 𝑙

between them is large enough: 𝑙 > 3𝐷

Combination of the three theories gives a wave load spectrum, but as mentioned above wind loads

play an important role as well. How these will be implemented is explained in chapter 4.

1.5 Support structures

The ambition of this thesis is to investigate the fatigue behaviour of offshore structures and the load

spectrum applied on them. To do so, geometrical details are needed as is denoted in the previous

paragraph. These geometrical details are structure dependent, and thus it has to be specified which

structure is used. According to [11] a jacket structure is the most popular solution used in offshore

industry (figure 6, left). These are used for both shallow and deep waters and for numerous application

fields. When specifically looking at wind turbines, the application field nowadays is restricted to

shallower waters. In this case also monopiles (figure 6, right) are often used, and in [11] the use of a

tripod structure (figure 6, middle) is suggested as well. Multiple other support structures are used, but

the analysis will be restricted to these three options. Of course when using one of these options, care

has to be taken that the conditions denoted in the offshore load spectrum part are met.

Introduction 7


Figure 6: Schematic representation of a monopole, tripod and jacket structure [12]

1.6 Spectrum processing

In [3] it is already mentioned, that using a spectrum in its random form is not always feasible. That is

why researchers created test programs that are representative but more feasible to apply and analyse.

The rainflow counting method can be applied, as described in [13], to process the load history in such

a way that a more ordered spectrum is obtained. This is a widely used algorithm in many different

sectors. When an ordered spectrum is available, multiple operations can be performed to make the

spectrum more representative for the real one again. A MATLAB toolbox (WAFO) is available online.

1.7 Randomize signal

After ordering the load history, for instance in ascending or descending order, and the amount of

blocks is reduced to a value that keeps the testing time feasible, tests can be performed. To apply this

spectrum in a more realistic way, the spectrum can be relocated in such a way that it gets more

random, but still feasible to program into the software. To identify the “randomness” of a signal, an

autocorrelation function can be used [14]. Autocorrelation defines the cross correlation of a signal with

itself.

𝜌𝑘(𝑋) =𝐸[(𝑥𝑖 − 𝜇)(𝑥𝑖+𝑘 − 𝜇)

𝜎²

𝜇 and 𝜎² are the respective mean and variance of X, k is the lag period and E(x) is the expected value

of x. We take a lag period of 1 cycle, as we are interested in the cross correlation of successive cycles.

According to [14], if a spectrum is very long or applied repeatedly, we can simplify the autocorrelation

as being equal to

𝜌1(𝑋) = 𝑛∑ 𝑥𝑖𝑥𝑖+1 − (∑ 𝑥𝑖)²

𝑛𝑖=1

𝑛𝑖=1

𝑛∑ 𝑥𝑖2 −𝑛

𝑖=1 (∑ 𝑥𝑖)²𝑛𝑖=1

The autocorrelation can be determined between successive peaks, valleys or absolute values of the

difference between extrema. Dependent on the application or by testing in an empirical way it can be

chosen which one is the best choice. This concept can then be used to determine how random an

applied spectrum is.

Eventually this concept can be used to make a spectrum that is not random, but not completely

ordered and thus feasible but more realistic. The concept of randomness is very interesting to know

Introduction 8

Steven De Tender

how realistic the applied spectrum is. Because, as mentioned above, a random spectrum gives a

different behaviour than an ordered spectrum.

As completely random tests are not part of this thesis, the random life will be estimated based on an

equation found from literature. [15] denotes that the random crack growth rate can be determined

according to the Forman equation:

𝑑𝑎

𝑑𝑁𝑟𝑚𝑠=

𝐶∆𝐾𝑟𝑚𝑠𝑚

(1 − 𝑅𝑟𝑚𝑠)𝐾𝑐 − ∆𝐾𝑟𝑚𝑠

With C and m the Paris law curve constants of the stable propagation phase (see chapter 2 and 3), Rrms

the root mean squared stress ratio (constant 0.1 for the tests discussed in the thesis), Kc the elastic

fracture toughness [MPa*√m] and ΔKrms [MPa*√m] is the root mean square of the applied ΔK blocks.

Based on the crack growth, the lifetime can then be estimated.

1.8 Stress ratio

Most offshore spectra have a load history with almost the same tension/compression behaviour [8].

This means that the stress ratio R≈-1, with R = σmin/σmax a commonly used unit in describing load

characteristics in fatigue. However, in the thesis all tests will be performed with a stress ratio equal to

0.1, which is an often used ratio in aircraft industry for instance [13]. As ESE(T) specimens are used for

testing, only tensional stresses can be applied to the specimen. As was already mentioned above, a

different stress ratio gives a different behaviour of the material under both constant and variable

amplitude. As a stress ratio of R=0.1 is more severe than R=-1, using a different stress ratio for the tests

is conservative.

The effect of the stress ratio in variable amplitude conditions is more difficult to describe and interpret.

Care has to be taken according to [8], as the relation between constant amplitude and variable

amplitude fatigue depends on the stress ratio.

1.9 Preview

The rest of the thesis consists of two main parts. One part describes different kinds of instrumentation

and how they can be used to measure the crack growth in a test specimen. Together with an

instrumentation comparison, the goal of these tests is to determine the Paris law curve of two

materials that will be used throughout the thesis. To accomplish all of this, a dedicated LabVIEW

program was developed. How the program works and how to use it, together with some general

information about the test setup is discussed in chapter 2. The test results for the different kinds of

instrumentation are then presented in chapter 3.

The second part of the thesis focusses on the effect of variable amplitude loads on lifetime of a

structure. This research is presented in a framework considering offshore structures in the North Sea.

To make this possible, chapter 4 determines ΔK block loads based on wave data from the North Sea

and literature describing offshore loading conditions on structures.

To be able to perform tests considering this matter, the developed LabVIEW program discussed in

chapter 2 is altered in such a way that it is possible to do different types of block load tests. The blocks

found in chapter 4 will be combined in a L-H, L-H-L and semi-random sequence. Based on these results

and the random fatigue life formula, the effect of variable amplitude fatigue loading will be

determined.

Introduction 9


Chapter 6 summarizes the most important conclusions and specifies the future work that can be

performed based on the obtained results.

Introduction 10

Steven De Tender

Test setup: instrumentation 11


2 Test setup: instrumentation

2.1 Introduction

Fatigue can be investigated in different ways. In practice, the S-N curve approach is the most popular

to represent material characteristics. In this kind of diagram, a certain lifetime (as number of cycles) is

specified for every different constant amplitude stress level. Some applications however, might require

that a certain amount of crack growth is allowed, to make them cost efficient. In this case a Paris law

curve is often used to define the crack growth rate (da/dN) as a function of stress intensity factor range

(ΔK) [16,17]. As shown in figure 7 (right), crack growth rate is described as the increment in crack

growth per increment in cycles (da/dN). The Paris law curve can therefore be directly derived from the

a/W-N curve (figure 7 left) and the corresponding ΔK value for each part of the curve. The a/W-N curve

is obtained by plotting the relative crack depth (a/W) versus the number of cycles (N) [17].

The Paris law curve of a typical steel consists of three parts: the initiation phase (I), the stable

propagation phase (II) and the critical propagation phase (III). The initiation phase has as a lower limit

called the threshold stress intensity factor range (defined below). The stable propagation phase starts

and ends when the crack growth rate becomes linear (in a double logarithmic diagram) with respect

to stress intensity factor range. The critical propagation phase starts when there is crack growth rate

acceleration [16].

Figure 7: a/W-N curve (left) with K-decreasing (black) and K-increasing (blue), Paris law curve (right)

To be able to obtain the Paris law curve of a material, a dedicated LabVIEW program is developed. It

makes it possible to perform a complete test procedure according to ASTM E647 ([18]) delivering the

Paris law curve of a material with a single specimen. A standard test to do so, consists of a precracking,

K-decreasing and K-increasing procedure. Three different modules are available in the program for

each of these parts. To be aware of the most important criteria a test has to conform to according to

standard, a short overview is given.

The standard recommends a minimum precrack length based on geometrical parameters and a

maximum precrack growth rate (da/dN < 10-5 mm/cycle). The threshold region is determined with a K-

decreasing method. ΔK values are decreased until a crack growth rate lower than 10-7 mm/cycle is


Steven De Tender

reached; this is region I in the right part of figure 1 and the black part in the left figure. When going

from precracking to K-decreasing it is important to stay under the maximum stress intensity factor of

the precracking stage. Besides there should be sufficient crack growth (Δa) per block such that there

are as limited transient effects between blocks as possible. To determine the stable propagation phase,

a K-increasing procedure is used. ΔK blocks are increased up to the end of the stable propagation

phase, this is shown as region II in the right part of figure 1 and as the blue part of the left figure. Again

a significant Δa should be used per ΔK block to keep transient effects as low as possible and to have

da/dN values which are as stable as possible. For every different ΔK block in both the K-decreasing and

increasing modules multiple average da/dN measurements should be taken over a certain crack extent

to have redundancy in the measurements.

Besides obtaining the Paris law curve of the material, the program makes it possible to determine crack

growth (rates) with multiple kinds of instrumentation. The fundamental instrumentation technique for

this program however is a clip gauge. The clip gauge measures the crack growth and based on a wanted

stress intensity factor range, the desired force range is determined. This also means that the program

is based on the principle of ΔK control, which makes it possible to determine the range of points that

are desired to determine the Paris law curve beforehand.

Besides, the other instrumentation techniques investigated and used are strain gauges, direct current

potential drop (DCPD), digital image correlation (DIC) and beachmarking. In addition to the clip gauge,

the program is able to be controlled based on the strain gauge readings. For DIC, a camera is triggered

automatically at certain specified events. The obtained photos are post-processed after the test is

finished. The application of beachmarks is also programmed, together with the choice when and for

which crack length the beachmark has to be applied. With respect to the conventional way of applying

a beachmark, based on a specified amount of cycles, it has been chosen to apply beachmarks with a

specified length, based on the clip gauge control. This makes sure that every beach mark for whatever

ΔK level is clearly visible. For potential drop a separate program was used. All discussed

instrumentation techniques and the specific way they work are discussed in more detail in the next

chapter.

This chapter explains the general structural of the program and some specific parts that are important

either for the Paris law curve tests or the instrumentation application. Together with the program, the

general test setup and the interaction with the program is briefly discussed.

2.2 Test setup

2.2.1 General test setup

The test setup consists of a hydraulic MTS810 servo-hydraulic system equipped with a load cell of 100

kN capacity. For simple constant amplitude or variable amplitude force control tests, the machine can

be controlled with the so-called ‘FlexTest’-system. When however tests are being controlled online

based on clip gauge data and with ΔK control, a more sophisticated control system is needed. The

interested reader is referred to [2] for more detailed information of how this ‘FlexTest’ software works

and how it can be used for simple tests.

The LabVIEW program is designed to externally control the MTS system. This is done through an

external server and a data acquisition card from National Instruments. The current program is based

on the original design of Laseure and Schepens [2]. Different parts of the program are unaltered. So is

the communication between the MTS system, LabVIEW, the external server, the data acquisition card



and the load cell. The specifications of how this communication is practically implemented are also

discussed in [2].

2.2.2 LabVIEW instrumentation test control

As was mentioned above, the program used to control the tests is based on the original design of

Laseure and Schepens. Therefore certain basic parts of the program that were not altered will not be

further discussed. In the next paragraph, the improved program will be compared with the previous

version, explaining the new possibilities.

2.2.2.1 Calibration

The user interface consists of four different tabs: calibration, test condition, save and visualisation. The

calibration tab is shown in figures 8 and 9 for the new and old version respectively. This part specifies

some basic inputs necessary for the good working of the program. The calibration of MTS and DAQ are

both inputs to guarantee a good communication between different modules, for which the reader is

referred to [2].

The specimen calibration on the one hand asks for certain basic constant properties of the specimen

and on the other hand specifies certain variable properties. The Young’s modulus (E [GPa]), specimen

thickness (B [mm]), specimen width (W [mm]) and the notch length ([mm]) are constant throughout

the test and necessary for calculations inside the program. a0 [mm] is the initial crack length from

which a certain test starts. As the test is clip gauge or strain gauge controlled, the needed load range

is calculated based on the gauge output. However when starting up the program, the clip gauge/strain

gauge has to stabilise before it is able to control the test. Therefore the initial required forces are

calculated based on the parameter a0. The mounting offset is a parameter that can be adjusted based

on the preload applied on the specimen. This makes sure that the actual applied load takes into

account the preload and like this the theoretically wanted load can be applied as accurate as possible.

The clip gauge calibration tab is based on a methodology explained in [2]. A blade micrometre is used

to measure the CMOD. In parallel the voltage is also measured. By doing so at different steps (of 1 mm

e.g.), a linear relation is obtained between clip gauge voltage and CMOD. The slope (A) and the offset

(B) are then used to convert the clip gauge voltage to CMOD, which is eventually used to calculate

crack growth. The clip gauge factor is a constant factor between the voltage readings in the MTS

software and the LabVIEW output.

The strain gauge calibration is performed with a COND-SGA-D conditioner from SENSY. Making the

initial offset and determining a second calibration point with a shunt resistor, a linear relation is

obtained between strain and strain gauge voltage. From the obtained strain, the crack growth can be

calculated. The offset and ratio that are added at the bottom of the strain gauge tab, are there because

of some problems with the crack growth calculation. As will be shown in chapter 3, the formula used

to calculate crack growth from the obtained strain did not give the expected results and therefore the

offset and ratio was used trying to modify the calibration and crack growth equation. This will be

discussed in more detail in chapter 3.

The ON/OFF button starts and stops the test when pressed. The test can be either controlled by the

clip gauge or by external command (when for instance testing something in the program), by pressing

the ‘Ext.Cmd’ button. The external command controls the test based on the initial input of a0 and will

thus not update the crack growth based on clip gauge data.


Steven De Tender

As shown there is a possibility to use DIC which, as was explained in the introduction, makes it possible

to use a connected camera automatically to take photographs at specified moments. In the tests

described in chapter 3, this is done every block change for the K-decreasing as well as for the K-

increasing procedure. When the DIC button is pressed, the program will send a signal to the data

acquisition card every block change for a specific amount of cycles. In this time-lapse, there can be

opted for different possibilities, e.g. continuously taking photos as long as the signal is sent.

Finally, as was mentioned before, there is the opportunity of switching between clip gauge and strain

gauge control.

Figure 8: User interface, calibration tab from instrumentation test program

Figure 9: User interface, calibration tab from previous program



2.2.2.2 Test condition

The major part of the calibration tab has stayed the same, besides the adaptation of the strain gauge

calibration, the input of a0, the possibility to use DIC and an external command. Important to mention

is that the previous program was based on force control, while the improved version has ΔK control.

This will become more clear later on in this paragraph. The choice for ΔK control was mostly based on

the fact that in this way, points with constant crack growth rate in the Paris law curve can be

determined. Besides it makes the program and results more stable and easier to control. Different ΔK

values can be chosen and multiple average da/dN points are measured per ΔK block. As the philosophy

behind the program has changed so much, only the improved program will be discussed from here on.

Figure 10 show the test condition tab in the user interface. The general test conditions specify some

basic things that have to be considered by the user. The initial Kmax [MPa*√m] at which the program

has to start either the K-decreasing or K-increasing procedure. The stress ratio R and the frequency f

that are equal to 0.1 and 10 Hz respectively for all test results presented in chapter 3. The start regime

can be equal to 0, 1 or 2 (as is clarified in the visualisation tab, figure 12), with 0 the precracking stage,

1 the K-decreasing procedure and 2 the K-increasing procedure. In the precracking stage it is

programmed that the crack growth rate cannot exceed the value obliged by standard.

It is programmed that an automatic transition can occur from stage 0 to 1 and from 1 to 2. To go from

the precracking stage to the K-decreasing procedure, the crack length has to become larger than the

value given by the user in ‘Start Kdecr’. The transition from K-decreasing to K-increasing is

automatically performed when the threshold limit of 10-7 mm/cycle is achieved for two da/dN

measurements. It might however be preferable to perform the two tests separately. It is therefore

possible to start immediately in stage 1 or 2 if wanted. If one wants to start in stage 1, a value higher

than 10-7 has to be filled in in the initial da/dN line in the general test conditions tab. Otherwise the

program recognizes a value lower than the threshold limit twice and will jump to stage 2. This

procedure is not necessary when a K-increasing test has to be performed immediately.

Figure 10: User interface, test condition tab from instrumentation test program


Steven De Tender

Finally, inside the general test conditions the user has to specify the amount of da/dN points wanted

per ΔK block. Multiple crack growth rate measurements should be done per block as this ensures a

redundant measurement. It is advised to use 4 or 5 da/dN measurements per block.

In the block transition tab, the transition values are specified for a block change and the change of the

Δa per reported da/dN point. Of course for both the increasing and decreasing method, ΔK blocks have

to change to obtain different measurements and a complete Paris law curve. All da/dN measurements

per block have a constant crack length. Every block change however, this crack length is decreased or

increased for respectively the decreasing and increasing method. In case of the K-increasing procedure

this is done because crack growth becomes so fast that a larger Δa is needed to assure a stable da/dN

measurement. For the K-decreasing the Δa is lowered because da/dN values become so small that it is

too time-consuming to obtain certain crack growth.

These transitions are based on fixed rules and are specified by the user. The Δa for the first block has

to be reported together with an initial increment, which will be multiplied with the ΔK value of the

previous block when going to the next one. The first block will start with the initially specified Δa, after

which this value will be updated every block change. Dependent if it is a K-decreasing or increasing

procedure, the following respective rules are used:

∆𝑎𝑛𝑒𝑤 = ∆𝑎𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 −∆𝑎𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠

𝑓𝑎𝑐𝑡𝑜𝑟∆𝑎,𝐾𝑑𝑒𝑐𝑟

∆𝑎𝑛𝑒𝑤 = ∆𝑎𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 +∆𝑎𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠

𝑓𝑎𝑐𝑡𝑜𝑟∆𝑎,𝐾𝑖𝑛𝑐𝑟

where the two factors are specified by the user in the block transition tab. For the increment (denoted

as i in the formulas below), a similar procedure is performed. The formulas for respectively the K-

decreasing and increasing method are given below.

𝑖𝑛𝑒𝑤 = 𝑖𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 +(1 − 𝑖𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠)

𝑓𝑎𝑐𝑡𝑜𝑟𝑖,𝐾𝑑𝑒𝑐𝑟

𝑖𝑛𝑒𝑤 = 𝑖𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 −(𝑖𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 − 1)

𝑓𝑎𝑐𝑡𝑜𝑟𝑖,𝐾𝑖𝑛𝑐𝑟

where logically the increment is a value lower than 1 for the K-decreasing procedure and higher than

1 for the K-increasing method. A mechanism has been provided to be able to decrease the steps

between blocks for both the K-decreasing and increasing method. However this is not obliged by the

standard, which only recommends steps lower than 10% per block. It is however advantageous for the

results that at the end of the K-decreasing procedure the steps become short enough to have a good

idea of the threshold behaviour of the material. Similar for the K-increasing it is useful to have lower

increments such that ΔK does not reach too high values too fast, which would result in specimen

failure.

The last part of the test condition is the beachmark part. In here it can be selected whether beachmarks

are wanted or not. Besides that option, there are three variables that can be changed to obtain a good

beachmark procedure. The first one is the stress ratio. Beachmarking was already briefly investigated

by Laseure and Schepens [2] who found that a stress ratio R=0.64 is the least interfering stress ratio

when determining crack growth rates for the Paris law curve with a stress ratio R=0.1. Therefore this

value is always used when beachmarks are applied in chapter 3.



Instead of specifying a number of beachmark cycles, it is opted in the program to perform a beachmark

for a certain crack length which can be chosen by the user. Based on the experience of the presented

results in chapter 3, 0.15 mm was found to be a good value to have a clear beachmark, even though it

does not take too long to be applied with the lower ΔK values. Because of the lower crack growth rates

with a higher stress ratio, the choice was made not to perform any beachmarks in the K-decreasing

procedure, as this would be too time consuming.

The amount of beachmarks can be specified by indicating the amount of block changes after which a

beachmark has to be applied. For example, 5 block changes as input means that the 6th, 11th, 16th…

block there will be beachmarks. A beachmark is applied every 2nd da/dN measurement of a selected

ΔK block.

Finally it is important to mention that due to instrumentation inertia, when a sudden block change

occurs, the values of clip or strain gauge are not trustable for a short amount of cycles. Therefore the

program has a built in mechanism that takes over the test for a certain amount of cycles, such that the

clip or strain gauge can stabilise. After they have stabilised, the clip or strain gauge are back in control

of the test.

2.2.2.3 Save data

The save tab makes it possible for the user to specify the location to save the test data (figure 11). This

test data is saved as a TDMS file that can be converted to a dataset in software packages such as

MATLAB. The physical parameters that are saved are:

1. Pmax [kN]

2. Pmin [kN]

3. CMODmax [mm]

4. CMODmin [mm]

5. N [-]

6. da/dN [mm/cycle]

7. ΔK [MPa*√m]

8. a/W clip gauge [mm]

9. a/W strain gauge [mm]

10. strain [-]

Figure 11: User interface, save tab from instrumentation test program


Steven De Tender

2.2.2.4 Visualisation

The tab visualisation (figure 12) shows the most important online measurements. The external

command that was already mentioned is shown when it is being used in the graph in the upper left

corner (1). When the signal to take photos for the DIC measurement is sent through to the camera,

the green indicator lights up (2). The current situation (3) is shown: precracking (regime 0), K-

decreasing (regime 1) or K-increasing (regime 2). The gain (4) is a value that is described in [2] based

on the feedback loop as already mentioned. The current increment and Δa (dependent on the case)

are shown (5) to be able to confirm when the crack growth rate measurement is finished and a next

one is started. This is based on the value of ‘sum delta a’ (6), which gives the online crack growth from

the start of the new da/dN measurement on. If this value becomes equal to the wanted Δa for that

block stage, a da/dN point is calculated and reported. This value is shown (7) and stays constant until

a next measurement is performed. To have an idea of the currently determined da/dN value, da/dN2

(8) gives the average crack growth rate from the start of the new da/dN measurement on. This is based

on the ‘sum delta a’ value and the number of cycles since a new crack growth rate measurement was

started.

The total amount of cycles is specified in the cycle count (9). Next to this the number of cycles of the

precrack (10) is shown, together with the number of cycles in a certain block stage (11). When there is

a ΔK block change, the cycles block stage will go back to 0. The step number (12) gives the number of

ΔK blocks that are already measured and the da/dN point indicator (12) gives the number of da/dN

points that are already measured in this step. This makes it possible for the user to know the test

progression at any moment.

‘Sum delta a’ that controls the da/dN measurements and the block changes can be either based on

clip gauge (13) or strain gauge (14) input. For both clip gauge and strain gauge, the voltage is given

from which respectively the CMOD and strain can be calculated. From these values the program

automatically calculates the relative crack growth which is then also shown in the user interface. This

makes it possible for the user to check whether the clip and strain gauge give trustable results with

respect to each other and other instrumentation techniques.

Figure 12: User interface, visualisation tab from instrumentation test program

1

2

3

5

6

7 8

4

14 13

15 15 15

16 16 17

9

10

11

12



The three charts on top (15) show the signals from the load cell, clip gauge and strain gauge. This allows

the user to check whether the signal is a constant sine wave or if something is wrong. The two charts

below (16) give the a/W-N charts for both clip and strain gauge to check the short term behaviour of

the instrumentation.

Finally, the measured maximum and minimum load values are shown with respect to the desired Pmax

(17). This can be checked together with the values shown by the MTS software to be sure that the

correct loads are applied to the specimen. Besides, the current ΔK and the final wanted ΔK in the

precrack stage are shown.


Steven De Tender

Instrumentation research 21


3 Instrumentation research

3.1 Outline

Previous chapter discussed about the capabilities of the developed LabVIEW program and how to use

it. In this chapter, the test results that were obtained with this program will be shown and discussed.

As mentioned, five different techniques to determine crack growth and thus crack growth rate are

used: clip gauge, direct current potential drop (DCPD), strain gauge, digital image correlation (DIC) and

beachmarking. The use of clip gauge and strain gauge is quite common in fatigue testing. The

difference with other approaches is that an online clip gauge/strain gauge controlled test is used based

on ΔK control. This makes it possible to online monitor the crack growth rate and therefore the crack

length. Based on this principle, tests can be completely planned beforehand by indirectly controlling

the crack length. This makes it for instance possible to specify a beachmark length, to be sure the

beachmark is perfectly visible for every ΔK value.

Direct current potential drop (DCPD) is a technique with some major advantages with respect to

conventional measurement techniques. DCPD is a method that is more and more used in fatigue

applications, because of its flexibility in terms of geometry and environments [19, 20]. It has therefore

a wide range of possible applications. The technique is introduced in this chapter and compared with

the results of both clip and strain gauge.

DIC is frequently used in quasi-static tests, but not common for fatigue tests. In [2] the DIC technology

was used during fatigue tests, but no good correlation was achieved. The same kind of analysis will be

performed here, even though with a few adjustments with respect to the analysis done in [2]. The

preliminary results that were found, are also shown in this chapter.

Beachmarking is a visual method that makes it possible to determine the crack growth in a test

specimen post-mortem. As already mentioned above, it is possible with the LabVIEW program to

control the crack length of a beachmark and therefore be sure of its visibility.

All tests discussed in this chapter were carried out in laboratory conditions, with a stress ratio R=0.1

and frequency f=10 Hz. Multiple tests were done throughout the thesis with multiple purposes. All

instrumentation tests are denoted as ‘INST00x’ following with either a or b to indicate the material

type. Dependent on the test, they can consist of a K-decreasing part, a K-increasing part or both. The

purpose of these tests was twofold. On the one hand to determine the Paris law curve of the used

materials. On the other hand to compare different instrumentation techniques.

This chapter discusses the different kinds of instrumentation one by one. The techniques are compared

with respect to each other based on the a/W-N curves of two tests (one for each material). At the end

of the chapter, the Paris law curves obtained from the different tests are presented. The chapter starts

with an experimental procedure specifying the used material and geometry. The test setup and the

way the load is applied to the specimen are already discussed in chapter 2 and will therefore not be

discussed here.

3.2 Experimental procedure

3.2.1 Material

Two different materials, described in [21], are used and analysed throughout the thesis. As is done

there, they will be called material A and B. Material A is similar to an offshore grade NV F460 and


Steven De Tender

material B to NV F500, which are both HSLA steels. Table 1 denotes the microstructural properties of

the materials and table 2 gives the mechanical properties.

Table 1

Material C Mn Si P S Cu Ni Cr Mo

NV F460 (A)

[%] 0.08 1.24 0.24 0.01 0.001 0.05 0.21 0.05 0.005

NV F500 (B)

[%] 0.11 1.35 0.22 0.01 0.001 0.15 0.16 0.09 0.07

Table 2

Material σy [MPa] σuts [MPa]

NV F460 (A)

560 635

NV F500 (B)

630 680

3.2.2 Geometry

The tests and test results discussed in the thesis are determined with an ESE(T) specimen. Figure 13

and 14 show the ESE(T) specimens and the used dimensions for material A and B respectively. The

stress intensity factor range is proportional to the load range, depends on the crack length and the

type of geometry. The specific formula of ΔK [MPa*√m] for an ESE(T) specimen (which can be found in

[18]) is:

∆𝐾 = [∆𝑃/(𝐵√𝑊)]𝐹

With ΔP [N] the load range, B [mm] the specimen thickness, W [mm] the specimen width and F [-] a

factor depending on the relative crack length, for which the exact formula can be found in [18].

Figure 13: ESE(T) specimen material A



Figure 14: ESE(T) specimen material B

3.3 Clip gauge

3.3.1 General

The clip gauge is mounted in a machined crack mouth of the specimen (figure 15 (1)). With the

compliance equations (available in [18]) the measured CMOD can be directly linked to a certain crack

length. The clip gauge used is an Epsilon clip-on-gauge, model 3541-005M-100M-LT with 5.00 mm

gauge length which can travel from -1.00 to 10.00 mm.

For an ESE(T) specimen, the crack length can be calculated using the expressions for front-face

compliance:

𝑎𝑊⁄ = 𝑀0 +𝑀1𝑈 +𝑀2𝑈

2 +𝑀3𝑈3 +𝑀4𝑈

4 +𝑀5𝑈5

𝑈 = [(𝐸𝐵𝑣0∆𝑃

)

12+ 1]

−1

With E [GPa] the Young’s modulus, B [mm] the specimen thickness, v0 [mm] the CMOD and ΔP [kN]

the load range. M0, M1, M2, M3, M4 and M5 are constants that can be found in [18].

All clip gauge results were visually confirmed by means of a small microscopic camera. The specimens

were marked with lines with a predetermined distance to be able to track the crack length as is shown

in figure 15 (7). The visual confirmation is performed at the start and end of every test as prescribed

by the standard and is shown in the test results below.


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Figure 15: Illustration of instrumented ESE(T) specimen (material A)

3.3.2 Test results

Throughout this chapter, instrumentation techniques will be compared by means of two combined K-

decreasing and K-increasing tests, one for both material A and B. In this paragraph, the two tests are

compared with a visual observation performed with a small microscopic camera. The results are shown

in figure 16 and 17. A single specimen was used for both the K-decreasing and K-increasing test. For

the K-decreasing procedure, it is clear that while decreasing the ΔK values, the crack growth per

number of cycles becomes smaller. This results in lower crack growth rates and thus the lower region

of the Paris law curve (paragraph 3.8).

For the K-increasing procedure, the ΔK values are increased, which results in a higher crack growth

rate. For both tests there are clear ‘flat’ regions in the K-increasing region. These are caused by the

application of beachmarks to the specimen, which slows down the crack growth rate significantly. The

results of the beachmarks are discussed in more detail in paragraph 3.6.

It is clear that the clip gauge has an excellent correlation with the actual crack growth based on the

visual measurements. This both for material A and B as can be seen in figure 16 and 17.



Figure 16: a/W-N curve from a combined K-decreasing and K-increasing procedure, material A INST003a

Figure 17: a/W-N curve from a combined K-decreasing and K-increasing procedure, material B, INST004b


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3.4 Potential drop

3.4.1 General

Direct current potential drop (DCPD) is used as a second measurement technique. A constant current

is sent through the specimen and as the resistance of the specimen increases when the uncracked

ligament of the specimen becomes smaller, the measured voltage also increases. This voltage can be

linked to a certain crack length with the formula (which can be found in [18]):

𝑎 =𝑊

𝜋𝐶𝑜𝑠−1

(

Cosh (𝜋𝑊𝑌0)

𝐶𝑜𝑠ℎ(𝑉𝑉𝑟𝐶𝑜𝑠ℎ−1(

𝐶𝑜𝑠ℎ (𝜋𝑊𝑌0)

𝐶𝑜𝑠 (𝜋𝑊𝑎𝑟)

))

)

with a [mm] the crack length, W [mm] the specimen width, Y0 [mm] the distance between

measurement pins (see next paragraph), V [V] the measured voltage, ar [mm] a reference crack size

from another measurement method and Vr [V] the corresponding voltage for this reference crack

length.

The direct current power source used was an auto ranging Farnell AP60-150 set at 35 Amperes. The

measurement instrument used was a nanovolt meter Agilent 34420 with a continuous integrating

measurement method (Multi-slope III A-D converter) and a –D Linearity of 0.00008% of reading

+0.00005% of range. Figure 15 shows the test setup as was already discussed in paragraph 3.3. Besides

the clip gauge, the potential drop connections are also shown here. At the bottom and the top (3 and

4) the current is introduced and connected to earth. 5 and 6 are measurement pins, used to measure

the potential difference over the crack mouth. 7 denotes the reference pins, which measure a

reference potential difference to filter out environmental effects, such as temperature changes.

3.4.2 Test results

In this paragraph, the potential drop results are compared to the clip gauge data together with the

visual confirmation. Later on in paragraph 3.8, when the Paris law curve of the two materials is

presented, the Paris law curve obtained with potential drop is compared to the one with clip gauge

data. In this paragraph, a/W-N curves are used to make an instrumentation comparison. Figures 18

and 19 show the results for both material A and B for the same test as was shown in paragraph 3.3.

Both methods have an excellent correlation, except for a small deviation in the initial part of the K-

decreasing and increasing procedure for both materials.

At the start of both K-decreasing and K-increasing there is a small deviation between both methods.

As was mentioned before, clip gauge results were checked visually multiple times (based on the

reference lines in figure 15) and this had a good correlation with the actual crack length for both tests

(K-decreasing and K-increasing). Therefore it can be concluded that the potential drop had a small

deviation at the start of each test. As the potential drop calculation is based on an input of the initial

voltage for a certain crack growth, the correlation can be a bit deviated. For the rest of the K-decreasing

procedure the potential drop readings are close to perfect.

For the K-increasing procedure, the DCPD also has a small deviation at the end of the test for material

A. This was something that was observed with some other tests as well. Besides the initial voltage and

crack growth also the initial pin distance (paragraph 3.3) is an input of the potential drop equation.



Therefore the correlation at larger crack growth rates might be less accurate as the pin distance

becomes larger. But as can be seen from figure 18, these are minor deviations that mostly occur at

very high crack growth rates and at the end of the specimen. The two instrumentation techniques give

a very good a/W-N curve overall for both materials.

Figure 18: a/W-N curve, comparing DCPD measurements and clip gauge output (material A, INST003a)

Figure 19: a/W-N curve, comparing DCPD measurements with clip gauge output (material B, INST004b)


Steven De Tender

3.5 Strain gauge

3.5.1 General

The strain gauge is used as a third measurement technique. A strain gauge is applied to the back face

of the specimen. When the specimen deforms, the electrical resistance of the gauge changes. This

resistance difference is measured through a Wheatstone bridge, from which an output voltage is

obtained. This voltage can then be calibrated to a strain value with the use of a COND-SGA-D

conditioner from SENSY. This strain value is then used in the back face compliance equation, which is

represented in the standard [18] for an ESE(T) specimen:

𝑎𝑊⁄ = 𝑁0 +𝑁1(log(𝐴)) + 𝑁2(log(𝐴))

2 +𝑁3(log(𝐴))3 +𝑁4(log(𝐴))

4

𝐴 =−𝜀

𝛥𝑃𝐵𝑊𝐸

With ε [-] strain, ΔP [kN] the load range, B [mm] the specimen thickness, W [mm] the specimen width

and E [GPa] the Young’s modulus.

The strain gauges used for the tests are from Tokyo Sokki Kenkyujo, type FLA-3-1 with a gauge

resistance of 120±0,3Ω (at 23°C). The working range is -20°C to 80°C. A temperature compensation is

achieved using the thermal expansion coefficient of steel (11.10-6/°C). The compensation range is

+10°C to 80°C. The gauge length and width is 3 and 1,7 mm respectively, the gauge base length and

base width is 8,8 and 3,5 mm respectively. The size of this strain gauge makes it suitable for use on the

back face of the ESE(T) specimens of both NV F460 and NV F500. The gauge is mounted at the back of

the specimen, which is indicated in figure 15. It is important that in the mounting process it is checked

that the strain gauge is applied in the centre of the specimen to increase the accuracy.

3.5.2 Test results

The previous two tests are again used in this paragraph to judge the operation of the strain gauge. The

strain gauge output is compared to the clip gauge and DCPD measurements in figure 20 and 21. It is

clear that the strain gauge does not operate as expected from these two graphs. For both materials,

the crack growth rate is much too low for the K-decreasing procedure. For the second test, the

difference between the strain gauge reading and the other measurement techniques even

accumulates up to 2 mm at the end of the test. For the K-increasing part, the crack growth rate

measured by the strain gauge is too high in comparison with the other measurement techniques.

This difference was already noticed in previous tests. As a solution it was tried to use a constant factor

(ratio) to alter the calibration in such a way that correct outputs were obtained (using the other

techniques as a reference). The use of this ratio was already mentioned in chapter 2, when discussing

the strain gauge calibration (paragraph 2.2.2.1). This factor did however not give good results for an

entire test. Observation showed that a different factor is needed for different ΔK intervals. The same

factor was applied for the discussed tests and this shows good results for ΔK values in between 15-30

MPa*√m, which is a range that is used in the initial part of the K-increasing tests shown below. For

values below this range the crack growth rate was too low (K-decreasing procedure), for values above

the range the crack growth rate was too high.

Based on the results above, the validity of the used equation might be questioned, as there is a clear

ΔK dependence in the error observed. This observation is not a certainty however as their might be

other possible causes for the problem. It is clear however from the reported results that the shape of



the curves is correct. The detected problem can be denoted to a problem in the processing of the

output voltage rather than to the use or mounting procedure.

Besides the observed deviation from the real crack growth, which is believed to be ΔK dependent,

there is also a stress ratio dependency of the strain gauge. It was observed with trial tests that when a

beachmark was applied (and the stress ratio was increased to R = 0.64), the crack length reported by

the strain gauge suddenly increased to a very high value. When the stress ratio was decreased to 0.1

again, the strain gauge returned to its original value plus the extra crack growth. To deal with this,

another factor was applied to the output of the strain gauge the moment the beachmark was applied.

As can be seen from the figures below, this approach worked very well. Therefore it might be

concluded that when forces are suddenly or slowly changed during a fatigue test, this influences the

strain gauge output in such a way that the results become invalid.

Figure 20: a/W-N curve, comparing strain gauge measurements with clip gauge and DCPD output (material A, INST003a)


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Figure 21: a/W-N curve, comparing strain gauge measurements with clip gauge and DCPD output (material B, INST004b)

3.6 Beachmarking

3.6.1 General

As was mentioned in the introduction, beachmarking is a method that can be used to validate the crack

growth reported by other measurement methods. To do this, the specimen was broken after the test

to visually inspect the two sides of the fatigue crack. If the beachmark is applied in a correct way, it is

visually observable. The crack length up to the beachmark can be measured and compared to a

calculated crack length. This will be done in the next paragraph in comparison to the clip gauge results.

As highlighted in chapter 2, experimental experience showed that 0.15 mm is a good value for the

beachmark length. This is long enough to be perfectly visible, but not too long to be too time-

consuming. The stress ratio R=0.64 that is used for the beachmarking is obtained from the analysis

performed in [2]. It was chosen to carry out beachmarks in the K-increasing part of the test only, as

beachmarks in a K-decreasing test would take too much time.

3.6.2 Test results

For material A, the same test that is discussed above is shown in figure 22. To show more detail in the

curve, only the K-increasing procedure is plotted. Figure 23 shows the two broken parts of the used

specimen for this test. Using the scale next to the two parts, it is possible to calculate the crack length.

Determining the crack length from the back side of the specimen on, the relative crack length of the

three beachmarks is close to: 35.5 mm, 40.25 mm and 47.75 mm. The distinct line in the beginning of

the specimen crack surface is caused by the transition from K-decreasing to K-increasing procedure.

Even though this was done gradually, this has some impact on the crack surface. Dividing the relative

crack lengths by the specimen width (60 mm) gives their respective a/W values. Using the known



amount of cycles when the beachmarks were applied, their respective points in an a/W-N curve are

determined. It is clear that the beachmark results give a very good correlation with the clip gauge data

(and thus also with the DCPD results).

Figure 22: a/W-N curve for a K-increasing procedure, showing three beachmarks (material A, INST003a)

Figure 23: Specimen INST003a post-mortem fatigue crack surface

Notch

Beachmark 1

Beachmark 3

Beachmark 2


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Figure 24 shows the result for material B, which is the same test as discussed above for this material.

Again only the K-increasing part of the test is shown. Figure 25 shows the post-mortem broken

specimen of this test. The relative crack lengths belonging to the beachmarks are: 25.5 and 30 mm for

this specimen. Again there is a distinct line in the beginning of the test which is caused by the transition

of K-decreasing to K-increasing test. When the relative crack length is divided by the specimen width

(40 mm), the result can be plotted in an a/W-N curve (figure 24). There is a deviation between

beachmark and clip gauge result in comparison with the test for material A, but still the result is

excellent.

The specimen in figure 23 has a gold-like appearance. This is caused by putting it in an oven for a few

hours, as this might increase the visibility of the beachmarks. However, when comparing to figure 25,

the visibility of the beachmarks is maybe a little bit better, even though there is no significant

improvement. For this specimen, the left part was also put in the oven for a smaller amount of time

however, such that the surface does not corrode too much. As already concluded from figure 23, there

is no clear improvement in the visibility of the beachmarks by subjecting the specimen to a high

temperature for a few hours.

Finally, it can be observed that the crack front for the specimen of material A is more uniform than

that of material B. Due to the lower thickness of the specimen of material B, it might be more prone

to the occurrence of ‘crack tunneling’ [22]. At the sides of the specimen there is a lower stress

triaxiality, which causes the crack to grow slower at the sides, which results in a non-uniform crack

front. If it would be too severe, the solution is to side groove the specimen. Even though the

phenomenon is observed, it is not that severe to opt for that solution if necessary.

Figure 24: a/W-N curve for a K-increasing procedure, showing three beachmarks (material B, INST004b)



Figure 25: Specimen INST004b post-mortem fatigue crack surface

3.7 Digital Image Correlation

As already mentioned in chapter 2, the LabVIEW program has the internal possibility to trigger a

camera to take pictures. The photographs are then post-processed using the MATLAB program made

in [2]. Photographs are taken during the test without stopping it as this lowers the quality of the tests.

Besides, the specimen is not opened with a high force (as was done in [2]), as this influences the

eventual outcome. The methodology thus has been adapted in such a way that it is applicable online

during testing.

The results that were obtained were however not good. Figure 26 shows a dedicated test performed

to evaluate the good working of the DIC measurement technique. The clip gauge value was observed

to work excellent in this test and can therefore be used as a reference. It is clear that the middle part

of the test is the best, but even though the overall correlation of the DIC technique with the real crack

growth is not good.

A possible solution for this problem might be to take multiple photos at every block transition. The

photographs that give an impossible crack length result can then be neglected. The eventual result can

then be for instance the mean value of the found results. For all tests reported in this thesis multiple

photographs were taken per transition, however the approach was not yet tried. This is a first

suggestion as a future improvement for this topic.

A second possibility to improve the outcome is to zoom in closer on the uncracked ligament. The

photographs taken with the camera are of high quality and this might therefore result in an easier

crack tip detection.

Notch

Beachmark 1

Beachmark 2


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Figure 26: Instrumentation test comparing clip gauge results with the DIC measurement technique

3.8 Paris law curve

3.8.1 Clip gauge results

Figure 27 shows the averaged Paris law curve of material A. 4 tests are shown and it is clear that all

tests have a very good correlation. INST003a was the test shown in the instrumentation comparison

above. INST001a and INST002a are two tests that were added to the Paris law curve for redundancy.

INST004a was an instrumentation test specifically performed to determine the threshold behaviour of

the material. Even though there are no da/dN points recorded underneath that one assumed by the

code to be considered as threshold (10-7 mm/cycle), the lowest point obtained is 1.26*10-7 mm/cycle

crack growth for ΔK=4.96 MPa*√m. This clearly shows that the threshold of the material is close to a

ΔK of 5 MPa*√m. A typical HSLA steel has according to [23] indeed, for a stress ratio of 0.1, a ΔKthreshold

of around 4-6 MPa*√m.

In the threshold region it was also observed during the tests that there is more scatter in the da/dN

values for the same ΔK value. One can also observe that the highest region of the stable propagation

phase has some scatter as well. This can be explained as these high ΔK values are really close to the

unstable propagation phase. Therefore it can be concluded that the stable propagation phase ranges

between ΔK values of 9-55 MPa*√m.



Figure 27: Paris law curve material A

Figure 28: Paris law curve material B

Figure 28 shows the result of 4 tests for material B. INST004b is the test discussed above in the

instrumentation comparison. As it is immediately clear that there is more scatter for this material than


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for material A, it was decided to add 3 tests in the Paris law curve for redundancy: INST001b, INST002b

and INST003b. The K-decreasing part of INST004b was also a dedicated test to obtain the threshold

point. However, for this material the point obtained closest to the threshold is not as low as with

material A, but still the curve gives a good idea of the threshold behaviour. For a ΔK of 5.71 MPa*√m

a crack growth rate of 4.63*10-7 mm/cycle was obtained. As with material A, the threshold will thus be

very close to a ΔK of 5 MPa*√m.

Another observation is that the stable propagation phase with this material is a bit longer, with ΔK

values ranging from 9 to 70 MPa*√m. This can be explained by the higher strength of material B with

respect to material A. The crack growth rate of material B is similar to that of material A close to the

threshold region up to ΔK values of 10-15 MPa*√m. Above this level, crack growth rates of material B

become significantly larger for the same ΔK values. So even though the material is stronger and reaches

higher stress intensity factor ranges, the crack grows faster under the same loading conditions. A

possible explanation for this different material behaviour might be the different microstructure.

Material A has a ferritic structure, while material B has a bainitic one. Therefore it might be less

resistant to crack growth. Another possible explanation can be the different stress strain behaviour as

described in [21]. Material A has more strain hardening when it is plastically deformed. More energy

is therefore needed for the crack tip to propagate, as there is plastic deformation every cycle. This

might explain the slower crack growth rate for material A. Both of these explanations are however just

suggestions and cannot be confirmed.

All test results of both materials were visually confirmed at the start and end of the test as prescribed

by the standard. This visual confirmation was shown for some tests in a/W-N curves before when

comparing the different kinds of instrumentation.

The stable propagation phase of a Paris law curve can be described according to the following formula:

𝑑𝑎

𝑑𝑁= 𝐶∆𝐾𝑚

These constants were determined for tests INST003a and INST004b for material A and B respectively,

with as result:

𝑑𝑎

𝑑𝑁= 2.7 ∗ 10−9∆𝐾3.167

𝑑𝑎

𝑑𝑁= 6 ∗ 10−10∆𝐾3.8757

It has to be stressed that these results were determined for da/dN values in mm/cycle.

3.8.2 Potential drop results

In the following, the Paris law curves obtained from the DCPD results are shown. It is of course only

logical that these are more or less the same, as the same a/W-N curves were obtained from the tests.

Figures 29 and 30 show the results for test INST003a and INST004b respectively. To obtain the results

for the Paris law curve of the potential drop, the entire crack length was divided by the entire number

of cycles for one ΔK block, while for the clip gauge data 4 or 5 points were obtained automatically by

the LabVIEW program. From these points, the bad data is discarded and the good measurements are

averaged and used for the Paris law curve. These deviations might for instance be caused by material

behaviour, sudden environmental changes… This explains why the Paris law curve of the clip gauge is

more uniform than the one of the DCPD technique. Besides, the clip gauge is controlling the test and

will therefore report when, according to its own data, the needed crack growth is achieved.



As was already observed previously, the result of material B is prone to more noise. A possible reason

for this is due to the lower thickness. As was already mentioned, this causes the crack to be less

uniform. This might cause some deviation between clip gauge and potential drop results in some

measurements, as they measure crack growth in a completely different way.

From the two figures below, it can be concluded that the Paris law can be determined by the potential

drop technique as well. The same analysis could be done for the strain gauge, but as there is already a

big difference between the a/W-N curves with respect to the other measurement techniques, this is

not evaluated in this work. It can however be concluded that by using the program discussed in chapter

2, an entire Paris law curve can be obtained with a single specimen based on different measurement

techniques.

Figure 29: Paris law curve INST003a obtained from DCPD (red) and clip gauge (black) readings


Steven De Tender

Figure 30: Paris law curve INST004b obtained from DCPD (red) and clip gauge (black) readings

Offshore load spectrum 39


4 Offshore load spectrum

Different supporting structures are used for offshore wind turbines. The reason that a specific

structure is used depends on the application and its variables, for instance: water level, sea bed

conditions, price, load spectrum… [24]. Only 3 kinds of supporting structures will be considered in this

chapter: tripod, monopile and jacket structures. Worldwide, monopiles are the most commonly used

offshore wind support structures. However in the North Sea, jacket structures are often used. For

instance at the Thornton bank, C-power installed a wind turbine farm supported by jacket structures

(figure 31). Tripod structures are known and used in the oil & gas industry, but according to [24] only

one offshore wind project has made use of the technology in 2012. As its use is not yet common,

research is going on. [25] gives a finite element analysis of a tripod supporting structure in the

Mediterranean sea.

Figure 31: Jacket offshore wind turbine support structure, used at the Thornton bank in the North Sea (©C-Power nv [26])

The goal of this chapter is to define a set of ΔK blocks that might be expected in offshore supporting

structures. The procedure begins with a finite element analysis of a tripod structure [25]. From this,

the maximum calculated stress value is combined with the information reported in [27], where an

equivalent monopile structure based on the tripod from [25] is considered. Based on these works a


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maximum stress intensity factor applied to the structure can be determined. The second source is

wave data from the North Sea [28], which is analysed with the approach explained in paragraph 4 from

chapter 1. Like this the loads on a standard monopile structure in the North Sea can be determined.

Combined with the knowledge of [25] these forces can be converted in ΔK values based on [29].

Together with information of C-power regarding maximum stresses in offshore structures and the

known maximum force from the tripod analysis, a realistic random load spectrum can be determined.

4.1 Tripod – monopile analysis

4.1.1 Outline

Offshore structures are in practice subjected to variable amplitude loading from wind, waves and

current. [25] gives the finite element optimization of a tripod support structure for an offshore wind

turbine in the Mediterranean sea. Both wind and wave loads are estimated for this specific location.

Currents however will be neglected, as will be done throughout the whole dissertation. The optimized

geometry is shown together with the forces in figure 32.

Figure 32: Overall dimensions and main data of a tripod support structure [25]]

Since obtaining the stress field of a jacket structure is not an easy task, the assumption of an equivalent

monopile structure will be used, based on [27]. The equivalent monopile structure is then loaded with

the same forces as shown in figure 32. It has the same length but a different volume, diameter and

thickness.

As mentioned in paragraph 2.2.1, two different materials are used and analysed throughout the thesis,

They are called material A and B (specifications can be found in tables 1 and 2 in chapter 3). For the



theoretical derivation of the blocks, material A (NVF460) will be used. A similar derivation is performed

for material B even though.

4.1.2 Geometry

To determine the geometry of an equivalent monopile, certain assumptions have to be made. We will

use the same height (140 m) as the tripod in the paper ([25]) and a volume of 90 m³ will be assumed.

The maximum stress that is allowed to occur in the structure depends on the yield strength of the used

material and the degree of safety. Based on information from C-power, a typical ‘utilization’ (max.

allowed stress / yield strength) is 0.85. This conforms with [25] where the maximum allowed stress is

300 MPa and the used material is S355 steel, which has a yield strength of 355 MPa (utilization = 0.845).

To have a similar maximum stress level within a different material, the same utilization should be used.

As material A has as yield strength 520 MPa, the maximum stress is 442 MPa. From the forces in figure

32 an equivalent maximum bending moment at the base of the structure can be calculated. With

normal loads negligible, the maximum stress is equal to the maximum bending moment divided by the

bending resistance moment:

𝜎𝑚𝑎𝑥 = 𝑀𝑚𝑎𝑥/𝑊𝑏

The bending resistance moment of the monopile (hollow cylinder [30]) can be calculated as:

𝑊𝑏 =𝜋(𝐷4 − 𝑑4)

32𝐷

Finally, using the geometrical relation between volume, diameter and thickness (𝑉 =𝜋ℎ

4(𝐷2 − 𝑑2)),

three equations are obtained for three unknowns. Solving these equations for the diameter and

thickness gives only one physically meaningful equation. Table 3 shows the results for both material A

and B. As said the same analysis was done for material B, but instead of choosing the volume and

calculating the corresponding diameter, the same diameter as for material A was assumed initially.

Material B has a higher yield strength and can thus resist the same forces with a lower thickness. For

a constant diameter, this means that the volume also decreases.

Table 3

Material σmax [MPa] Mmax [kN*m] Wb [m³] V [m³] h [m] D [m] t [mm]

NV F460 (A)

476 580000 1.22 90 140 8.27 24.65

NV F500 (B)

535.5 580000 1.08 76 140 8.27 20.91

4.1.3 Maximum stress intensity factor

Based on the geometry and maximum stress on the structure, the maximum occurring stress intensity

factor range on the structure can be found. To determine this a certain notch geometry has to be

assumed. As is done in [31] an external circumferential surface crack is assumed (figure 33), for which

KI,max can be calculated as:

𝐾𝐼,𝑚𝑎𝑥 = √𝜋𝑎𝑐 (∑𝜎𝑖𝑓𝑖 (𝑎

𝐵,𝑎

2𝑐,𝐵

𝑟𝑖) + 𝜎𝑏𝑔𝑓𝑏𝑔 (

𝑎

𝐵,𝑎

2𝑐,𝐵

𝑟𝑖)

3

𝑖=0

)


Steven De Tender

With 𝜎𝑖 axisymmetric stress components, 𝜎𝑏𝑔 the maximum bending stress on the outer wall of the

structure and fi, fbg are geometrical functions that are tabulated in [29]. These functions depend on the

notch depth (a), width (2c), thickness (B), tube radius (ri) and the position of the notch where the stress

intensity factor has to be determined. This can be either the deepest point of the notch, or the

intersection of the notch with the free surface, which are A and B respectively in figure 33. Besides the

notch geometry, the crack depth ac also determines the maximum stress intensity factor. An

assumption has to be made for this crack depth to determine the maximum stress intensity factor.

Figure 33: External circumferential surface crack [29]

In this case, the axisymmetric stresses are negligible with respect to the bending stresses. fi and fbg

have the same order of magnitude, therefore the equation for KI,max can be reduced to:

𝐾𝐼,𝑚𝑎𝑥 = √𝜋𝑎 (𝜎𝑏𝑔𝑓𝑏𝑔 (𝑎

𝐵,𝑎

2𝑐,𝐵

𝑟𝑖) )

When the stress intensity factor at point A is determined, which is the most severe case, the solutions

for both material A and B are shown in table 4. The crack depth was chosen in such a way that

maximally 1/3rd of the remaining thickness was cracked.

Table 4

Material a/t anotch [mm]

a/2c ri [m] B/ri fbg ac [mm] KI,max

[MPa*√m]

NV F460 (A)

0.276 6.80 0.5 4.11 0.0060 0.6688 15.45 65.12

NV F500 (B)

0.276 5.77 0.5 8.27 0.0051 0.6689 13.91 68.09

4.2 Wave data analysis

To determine common loads on structures in the North Sea, data was obtained from “Meetnet Vlaamse Banken Hydrometeo” of the “Vlaamse Hydrografie” [28]. This data can then be analysed with the procedures developed in [2] which were discussed in paragraph 1.4. An interface has been made available by Laseure and Schepens, which makes it possible to determine loads on a structure (shown in figure 34), based on the significant wave height, peak period, water level and pile diameter.



Figure 34: Interface to determine loads on structures [2]

The significant wave height is defined as the mean height of the 1/3rd highest waves. The peak period is the period in a wave signal that contains the highest energy. These are two parameters that are available in the wave data obtained from [28]. The data was obtained in the North Sea, the difference with the already reported Tp and Hs in [2] is that these values were obtained for the coastal region. As offshore structures are positioned deeper in the sea, this gives a more correct idea of the real loads on an offshore construction. To determine the mean water level, it is assumed that the structure is positioned at the Thorntonbank (where the wind turbines of C-power are installed). [32] shows that the mean water level can be assumed to be 10-15 m. The pile diameter was already determined in paragraph 2.1.2. The used wave data was obtained within the last 10 years, from 2005 to 2007, 2008 to 2009 and 2011

to 2013. All wave data was used together and to determine different loads on the structure, different

cases were considered. First and for all, the mean, minimum and maximum peak period and significant

wave height were determined, which are tabulated in table 5. Both the actual values as their belonging

Tp/Hs values are reported.

Table 5

Hs,mean [m] Tp,mean [s] Hs,min [m] Tp,min [s] Hs,max [m] Tp,max [s]

Value

1,04 5.47 0.157 1.72 5.43 32

Related Tp/Hs

5.47 1.04 4.35 0.309 8.53 0.401


Steven De Tender

Besides these values, several cases were considered in the data to get the most occurring and most

severe cases out of it and to get a broad idea of the loads applied to the structures. All cases and their

corresponding loads for material A and B are shown in tables 6 and 7 respectively (where for each case

the percentage of points in the dataset that meet the case is shown). The main goal of the analysis is

to determine different ΔK blocks, which can then be used in variable amplitude tests. To determine

these ΔK values, the wave loads based on the significant wave height and peak period are determined

with the mentioned interface. Besides wave loads, an offshore structure is also subjected to wind and

current loads. Current loads can be neglected as they are smaller than wave and wind loads and their

resultant bending moment is very small. Wind loads however cannot be neglected as they cause a

large bending moment in the structure. As wave loads originate from wind, it is common sense to

assume that a higher wave load corresponds to a higher wind load. To obtain an idea of the

corresponding wind load to the wave load acquired from the interface, the same correlation is used as

was observed in the loads in figure 32 [25] (where the different bending moment is taken into account).

Based on this reasoning, the total load on the structure can be determined. If again the normal loads

are neglected and only the bending moment is considered, KI can be easily determined, as it was done

in paragraph 2.1.3. In table 6 the ΔK value that is found for each case is presented.

Based on the Paris-law curve of both materials, some of the obtained blocks close to the threshold

region can be discarded. For material A all blocks are discarded up to ΔK = 6.44 MPa*√m. Due to the

proximity of this value to the threshold, it was chosen not to take it into account in the analysis. For

material B, ΔK blocks are discarded up to ΔK = 3.23 MPa*√m. A ΔK value of 7.18 Mpa*√m is close to

the threshold, but has a crack growth rate that is yet high enough to take it into account. The stress

intensity factor ranges of both materials will then be used to investigate variable amplitude load effects

in the next chapter.

Table 6: ΔK blocks material A

Cases Fwater [kN] Fwind [kN] σbg [MPa] ΔK [MPa*√m]

Hs,max 2000 1919 242.63 32.17

Tp,max 25 23.99 3.03 0.40

Hs,min 50 47.97 6.07 0.80

Tp,min 125 119.93 15.16 2.01

Hs and Tp mean 400 383.78 48.53 6.44

Hs < 1 m (60%) 180 172.70 21.84 2.90

Hs > 1 m ; Tp > 5 s (25%)

610 585.27 74.00 9.81

Hs > 1 m ; 3 s< Tp < 5 s (7.5%)

500 479.72 60.65 8.04

Hs > 2 m ; Tp > 5 s (4%)

900 863.51 109.18 14.47

0.5% highest Hs 1400 1343.24 169.84 22.52



Table 7: ΔK blocks material B

Cases Fwater [kN] Fwind [kN] σbg [MPa] ΔK [MPa*√m]

Hs,max 2000 1919 285.55 35.93

Tp,max 25 23.99 3.57 0.44

Hs,min 50 47.97 7.14 0.89

Tp,min 125 119.93 17.84 2.24

Hs and Tp mean 400 383.78 57.11 7.18

Hs < 1 m (60%) 180 172.70 25.70 3.23

Hs > 1 m ; Tp > 5 s (25%)

610 585.27 87.09 10.96

Hs > 1 m ; 3 s< Tp < 5 s (7.5%)

500 479.72 71.38 8.98

Hs > 2 m ; Tp > 5 s (4%)

900 863.51 128.50 16.17

0.5% highest Hs 1400 1343.24 199.89 25.15


Steven De Tender

Variable amplitude fatigue: block loads 47


5 Variable amplitude fatigue: block loads

5.1 Outline

The second main part of the thesis consists of an investigation related to variable amplitude loading

and its effects on the lifetime of a structure. Chapter 1 already discussed the influence of an ordered

spectrum with respect to constant amplitude and randomly distributed amplitude fatigue. According

to this study an ordered spectrum had a higher fatigue life than a randomly distributed spectrum (for

sequential loads). Besides, it was found that for tests only loaded in tension, the variable amplitude

and constant amplitude fatigue life was more or less similar. A last observation is that for block loading,

there was no real general theory whether acceleration or retardation will occur.

The previous chapter determined for both NV F460 (material A) and NV F500 (material B) a series of

equivalent stress intensity factor ranges for offshore conditions. These ΔK blocks can then be used in

different test procedures to determine the effect of block loading on the lifetime.

The first tested procedure is a L-H sequence (all blocks were ordered from low to high). The second

procedure that is evaluated is a L-H-L sequence (going from low to high and back to low ΔK values).

The third and last series of tests is dedicated to the so-called semi-random tests. These tests combine

different ΔK values in a non-ordered way, trying to achieve a result in between an ordered and random

spectrum.

This chapter discusses the different test sequences and the results obtained from these tests. All

results obtained in this chapter will be compared to the discussed literature. To be able to perform

these tests however, the discussed LabVIEW program in chapter 2 was adapted in such a way that

block load tests can be performed. Before going into detail on the test procedure and results, this

adapted LabVIEW program will be discussed.

5.2 LabVIEW test control

As in the program discussed in chapter 2, the user interface is split up in 4 different tabs. The calibration

and save tab are exactly the same as in the previous program. The reader is referred to chapter 2 for

a detailed explanation of how both parts work. The test condition has of course completely changed

for this program and therefore the visualisation has also changed a little bit. Both test condition and

visualisation are discussed in a separate paragraph.

5.2.1 Test condition

The main idea behind this altered program is simpler than described in chapter 2. As shown in figure

35, the left part of the user interface consists of the possibility to define 15 different ΔK blocks and

their belonging crack length. Based on the regime these blocks are used in different ways for different

procedures. There are 3 different regime possibilities: precracking (0), ordered sequence (1) and

random sequence (2). The start regime can be specified as 0, 1 or 2. If 0 is chosen, the regime choice

specifies which regime is wanted after the ‘end precrack’ crack length is reached. If case 1 or 2 is chosen

as start regime, the regime choice and start regime should have the same value.

If regime 1 is chosen, the program will start with ΔK block 1. When the desired Δa1 is reached the

procedure will jump to ΔK2 and so on. A block transition is performed when the needed crack length is

achieved. This crack length is split-up based on the block specifications. Ppb small is the parts per block

for ΔK blocks lower than the ΔK value specified in DK trans ppb. Ppb big is the value for blocks with a


Steven De Tender

higher ΔK value than this DK trans. The parts per block divides the Δa value in the specified amount of

parts and performs a da/dN measurement per Δa part. It is internally programmed that when the #

blocks is reached, for the next block the ΔK value will fall back to 0 MPa*√m. A last thing to specify is

that when regime 1 is used, with or without 0 as start regime, Kmax0 should be the same as ΔK1. Like

this the test will always start with the correct ΔK value.

Figure 35: User interface, test condition tab from block loading test program

If regime 2 is chosen, the program will scramble a fixed amount of blocks in a random way. At this

moment, this is done in such a way that the first 3 ΔK blocks are used 5 times in a randomly scrambled

order. The specified Δa is divided by 5, which is then the Δa per block used for this ΔK value. Again

multiple crack growth rate values are evaluated based on the same logic explained for regime 1.

What is still lacking is a programme alternative where based on the input of #blocks and #sub-blocks

all possible variations and procedures can be chosen. Right now the only possible configuration is fixed

to 3 blocks that are split up in 5 sub-blocks, it might thus be a future improvement to allow for more

configurations. Besides, the logic behind this random program is still crack growth based and not based

on a specific amount of cycles per block. Efforts were done to make such kind of program with a cycle

based control, however this was not successful. It will be briefly discussed in the part of the test results

why this might be a useful improvement.

It is worth mentioning that for both regime 1 and 2 all possible instrumentation techniques are still

available except for beachmarking as this is not useful in this program. All tests presented in this

chapter are performed with clip gauge control. It can still be chosen to perform a strain gauge

controlled test and DIC photographs could be taken after every block change.

5.2.2 Visualisation

The visualisation part of the program has not changed much with respect to the program discussed in

chapter 2. As can be seen in figure 36, a few parts of the user interface are deleted with respect to the

user interface shown in figure 13. Besides, three indicators are added: # wanted points 1 and 2 (1) and

an array that specifies the order of the scrambled blocks in regime 2 (2). This makes it possible for the

user to check the block distribution obtained from the randomization performed in the program. The

amount of wanted points are the da/dN measurements performed per block. Based on the ppb rules,



this can be either the value of ppb small or ppb big. This gives the user the possibility to check the

progress of the test as the number of da/dN points measured is also indicated.

The purpose of the program was to test the L-H and L-H-L sequences with regime 1 of the program.

The semi-random tests would be performed with regime 2. Because of some problems with the logics

behind regime 2, it was opted to perform all tests based on regime 1. This problem and a solution will

be explained in more detail in paragraph 5.4 when discussing the semi-random tests.

Figure 36: User interface, visualisation tab from block loading test program

5.3 Test procedure and results

In this paragraph, the blocks presented in chapter 4 will be ordered in different ways. The purpose of

these tests is to determine the different lifetime for all tests together with retardation/acceleration

effects that might occur. Comparing the different tests, conclusions will be made about the influence

of variable amplitude loading in comparison with random loading. Finally, the lifetime of these block

load tests will be compared with the calculated fatigue life based on linear rules (as was discussed in

chapter 1).

All test results presented in this paragraph are accompanied of clip gauge, potential drop and DIC

measurements. The strain gauge was applied for some tests, but as this technique is not yet working

as it should it was chosen not to show it in the results. As was done for the tests in chapter 3, all test

results were visually confirmed in the beginning and end stages.

5.3.1 Low to high sequences

5.3.1.1 Procedure

For this procedure all ΔK values found from the wave data are used, going from the lowest value to

the highest one. Figure 37 and table 8 show the configuration for material A. Besides the ΔK values,

the crack length used per block is specified. To avoid any problems with the clamping and test setup,

it is attempted to keep the maximum loads under 10 kN. To accomplish this, the test has to start with

an extended crack length for this material. Therefore a precrack is applied with a ΔK = 15 MPa*√m.

1 2


Steven De Tender

When the crack length is almost reached, the precrack ΔK values are lowered by 10% every 0.1 mm

crack growth, until a ΔK value close to 8 MPa*√m is reached.

The crack lengths are chosen to limit the test time on the one hand and on the other hand to have

crack lengths that allow for sufficiently stable da/dN measurements. For this and all successive tests,

the number of da/dN points measured per ΔK block is chosen with the ppb small and big, as was

discussed in the previous paragraph of the LabVIEW program. Overall, the number of measurements

per block is small (2 to 4) for the smaller ΔK values. A minimum Δa value (0.02 mm to 0.03 mm) is

needed to obtain a sufficiently stable measurement. As the crack growth rate is small for these ΔK

values, the amount of points is kept low to keep the test time limited. For this test 3 points are

measured for the 2 lowest blocks and 20 points for the highest ones. The da/dN value that is reported

per ΔK block in table 8 is the estimated value based on the Paris law curve of the material. With this

information the test time can be estimated, without being able to include acceleration/retardation

effects of course. With all this information it is possible to plan an entire test beforehand.

Figure 37: Block loading procedure L-H material A

Table 8

count Δa [mm] a/W ΔK [MPa*√m] da/dN

[mm/cycle]

1 0,1 0,565 8,04 1,99E-06

2 0,1 0,567 9,81 3,73E-06

3 1,0 0,568 14,47 1,28E-05

4 4,5 0,585 22,52 5,19E-05

5 4,3 0,660 32,17 1,60E-04

The procedure for material B is similar to the one discussed for material A. Even though, the necessary

(pre)crack length at the start of the test is not as high in order to keep the loads low enough. Besides,

it was chosen to start with a minimum ΔK block of 8.98 MPa*√m, since using a baseline of 7.18

MPa*√m would take lots of time, certainly in the initial stage. Two da/dN measurements are taken for

8,049,81

14,47

22,52

32,17

0

5

10

15

20

25

30

35

0,565 0,567 0,568 0,585 0,660

ΔK

a/W



the 2 lowest blocks and 10 for the highest ones. All other test specifications can be found in figure 38

and table 9.

Figure 38: Block loading procedure L-H material B

Table 9

count Δa [mm] a/W ΔK [MPa*√m] da/dN

[mm/cycle]

1 0,12 0,490 8,98 2,97E-06

2 0,16 0,493 10,96 6,43E-06

3 0,5 0,497 16,17 2,90E-05

4 3,5 0,510 25,15 1,61E-04

5 3 0,597 35,93 6,41E-04

5.3.1.2 Test results

In the discussion of the test results for the L-H procedure both a/W-N and da/dN-N curves are

presented. The a/W-N curve was already used in chapter 3 to discuss the results of the instrumentation

tests. A da/dN-N curve shows the crack growth rate evolution over the number of cycles. For a Paris

law curve test this would be useless, as every ΔK value should give the same da/dN value for every

measurement. This is the case as the transitions between blocks are lower than 10% and therefore no

retardation/acceleration should occur. In this case, block loads are applied with a difference higher

than 10% between their values. Therefore an interrupted evolution over time of the da/dN values

might be observed.

Figure 39 shows the a/W-N curve for material A for both clip gauge and potential drop. The transitions

between blocks are clearly observed for the transition of ΔK = 8.04 MPa*√m to 9.81 MPa*√m. These

transitions are less clear for the potential drop even though. This might be explained as the clip gauge

is directly influenced by the applied load of the hydraulic machine, while the potential drop measures

the current through the specimen and therefore the crack length. Even though it follows the same

8,9810,96

16,17

25,15

35,93

0

5

10

15

20

25

30

35

40

0,490 0,493 0,497 0,510 0,597

ΔK

a/W


Steven De Tender

crack growth behaviour, the transition is less sudden than with the clip gauge, which makes the

potential drop technique less sensitive to sudden transitions. Another possibility is that since the clip

gauge controls the test, it can track the block transitions easier.

Figure 39: a/W-N curve, L-H procedure material A showing clip gauge and potential drop results together with a visual confirmation

Figure 40: da/dN-N curve, clip gauge results of the L-H procedure of material A



Figure 40 shows the da/dN-N curve of the first test. All points represented are da/dN measurements

taken during the test for different ΔK blocks. These measurements are represented in a different colour

for each of their respective ΔK values. The horizontal dash-dotted lines in the figure give an indication

of the expected crack growth rate based on the Paris law curve of the material. Based on this

information, it can be concluded that a small amount of retardation occurs going from a lower ΔK value

to a higher one. Besides, it can be concluded from this test that the retardation is more pronounced

for lower ΔK values than for the higher ones. With ΔK = 32.17 MPa*√m there is even no retardation

observed.

Figure 41 shows the a/W-N curve of the L-H procedure of material B. Again transitions can be observed

for the highest blocks, even though it is not possible to observe the transition going from ΔK=8.04

MPa*√m to 9.81 MPa*√m. Again there is more noise and deviation in the potential drop signal than

with the clip gauge. It was observed for all tests that there was more noise in the results of material B

than material A. As already mentioned this extra noise might be caused by the smaller thickness of the

specimen.

Figure 42 shows the da/dN-N curve of the L-H procedure for material B. It is immediately clear from

this figure that there is more deviation between the reported crack growth rates in the Paris law curve

and the measured da/dN values. As there is no real trend in this difference, when taking into account

all ΔK blocks, this can be explained by the observed scatter in the Paris law curve of this material

(chapter 3, figure 28). Again, this extra scatter might be explained by the specimen geometry.

Another observation in this figure is that there is less retardation (if any) than observed for material A.

Only for a ΔK of 16.17 MPa*√m there might be some interaction effects.

Figure 41: a/W-N curve, L-H procedure material B showing clip gauge and potential drop results together with a visual confirmation


Steven De Tender

Figure 42: da/dN-N curve, clip gauge results of the L-H procedure of material B

Based on the reported da/dN values and those obtained from the Paris law curve, the observed retardation can be quantified. For material A the expected test time based on a linear rule can be calculated as:

𝑁𝑡𝑜𝑡𝑎𝑙 =∆𝑎1

𝑑𝑎/𝑑𝑁1+

∆𝑎2𝑑𝑎/𝑑𝑁2

+∆𝑎3

𝑑𝑎/𝑑𝑁3+

∆𝑎4𝑑𝑎/𝑑𝑁4

+∆𝑎5

𝑑𝑎/𝑑𝑁5

This gives an Ntotal of 269000 cycles. The real number of cycles observed in the test is equal to 287000

cycles. With respect to the linear rule there is 6.7% longer lifetime.

For material B the same analysis is performed, with as results 109000 cycles expected from the Paris

law crack growth rates and 143000 cycles for the real number of cycles. It should be noted that a large

part of this retardation is caused by the measurements obtained for a ΔK of 8.98 MPa*√m. As this is

the initial block, the deviation between the measured da/dN values and those reported in the Paris

law curve cannot be caused by retardation (but probably due to the scatter in the Paris law curve).

Therefore these points are left out of the lifetime calculation. The amount of cycles becomes 68600

and 67800 based on the linear rule and the real measurements respectively. As in the first block no

retardation can occur, we can conclude that the total difference between the two is due to scatter and

that overall there is no or almost no retardation or acceleration for this material.

5.3.2 Low to high to low sequences

5.3.2.1 Procedure

For these tests, ΔK blocks are first increased until the maximum value found from the wave data, after

which the stress intensity factor ranges are decreased down to the minimum value. The test

specifications for the first test of material A are presented in figure 43 and table 10. Two different tests



are performed for both materials. In this first test all values found from the wave data are used and

run through from low to high and back to low.

Again there was opted to keep the forces below 10 kN. To do so a similar precrack is needed as with

the L-H test of material A, starting with a ΔK value of 15 MPa*√m and when the crack was close enough

to the wanted a/W, ΔK values were gradually decreased up to a value close to 8.04 MPa*√m. 2 da/dN

measurements are taken for the 2 lowest ΔK values and 20 measurements for the 3 highest ones. Again

the test time can be estimated based on a linear rule and the reported da/dN values for every ΔK block

presented in table 10.

Figure 43: Block loading procedure L-H-L 1 material A

Table 10

count Δa [mm] a/W ΔK [MPa*√m] da/dN [mm/cycle]

1 0,067 0,565 8,04 1,99E-06

2 0,067 0,566 9,81 3,73E-06

3 0,8 0,567 14,47 1,28E-05

4 4,8 0,581 22,52 5,19E-05

5 1,8 0,661 32,17 1,60E-04

6 1,0 0,691 22,52 5,19E-05

7 0,4 0,707 14,47 1,28E-05

8 0,067 0,7139 9,81 3,73E-06

9 0,067 0,715017 8,04 1,99E-06

8,049,81

14,47

22,52

32,17

22,52

14,47

9,818,04

0

5

10

15

20

25

30

35

0,565 0,566 0,567 0,581 0,661 0,691 0,707 0,714 0,715

ΔK

a/W


Steven De Tender

In the second L-H-L test performed with material A only 3 ΔK values are used: 14.47, 32.17 and 14.47

MPa*√m. This test has been carried out to determine whether or not there is more

retardation/acceleration when the jump between blocks is much bigger. For this test, only the da/dN-

N curve will be shown as the a/W-N curve does not give any added value to the results.

For material B two similar tests are performed. The specifications of the first test are shown in figure

44 and table 11. Again it is opted to keep the forces low enough to not overload the clamping of the

specimen. It can be noticed that as with the L-H procedure for this material, the initial ΔK is again 8.98

MPa*√m to keep the test time limited. The lowest block is however added at the end of the test as can

be seen in figure 44. Again a gradual decrease of the ΔK values is performed up to the initial value of

the test. For the three lowest blocks (7.18, 8.98 and 10.96 MPa*√m) three da/dN measurements are

performed, for the higher blocks 10 measurements are taken.

The second test for this material also consists of three blocks: 16.17, 35.93 and 16.17 MPa*√m. Again

this test will show whether a bigger jump results in more retardation/acceleration. It is also chosen

only to show the da/dN-N curve for this test.

Figure 44: Block loading procedure L-H-L 1 material B

8,9810,96

16,17

25,15

35,93

25,15

16,17

10,968,98

7,18

0

5

10

15

20

25

30

35

40

0,488 0,491 0,495 0,507 0,587 0,647 0,690 0,702 0,706 0,709

ΔK

a/W



Table 11


1 0,12 0,488 8,98 2,97E-06

2 0,16 0,491 10,96 6,43E-06

3 0,5 0,495 16,17 2,90E-05

4 3,2 0,507 25,15 1,61E-04

5 2,4 0,587 35,93 6,41E-04

6 1,7 0,647 25,15 1,61E-04

7 0,5 0,690 16,17 2,90E-05

8 0,16 0,702 10,96 6,43E-06

9 0,12 0,706 8,98 2,97E-06

10 0,08 0,709 7,18 1,25E-06


For test L-H-L-1 of material A, figure 45 shows the a/W-N curve. As was discussed before, the test starts

with a value of 8.04 MPa*√m. The transition to 9.81 MPa*√m is not visible in this figure, but the other

transitions going from low to high are clearly visible. The transition from 32.17 to 22.52 MPa*√m,

which starts the H-L part of the test is indicated with an arrow in figure 43. It is clear that there are

retardation effects. For the next transition going to 14.47 MPa*√m these effects are even more

pronounced.

When going to 9.81 √m it is clear from the figure that after this transition there is (almost) no crack

growth anymore. It was observed that when the transition occurred, initially there was a very small

crack growth (≈0.005 mm). After that, complete crack arrest was observed. The test was left running

for more than 400 000 cycles after the transition and besides the initial crack growth there was no

crack growth observed anymore. The initial crack growth can be explained based on the distribution

of the compressive residual stresses imposed by the plastic zone. It might be that the initial part of the

crack tip has less crack closing residual stresses and a small crack growth is therefore still possible.

It is again clear from this figure that the transitions between blocks are much clearer with the clip

gauge output than with the potential drop measurements. A possible explanation was already given

above.


Steven De Tender

Figure 45: a/W-N curve, L-H-L-1 procedure material A showing clip gauge and potential drop results together with a visual confirmation

Figure 46 gives the da/dN-N curve of this material. It is clear that in the threshold region for the two

lowest ΔK values, there is more scatter in the crack growth and therefore in the da/dN measurements.

Again a small retardation effect is observed for the L-H part of the test when the transition from ΔK =

32.17 to 22.52 MPa*√m occurs. It is evident from the da/dN measurements that there is a significant

retardation effect (even larger than the one evidenced in the L-H test). Eventually for the last couple

of measurements, the crack growth rate goes back to its predicted value from the Paris law curve. The

transition to ΔK = 14.47 MPa*√m causes, relatively speaking, an even higher retardation effect.

Eventually the crack growth does not return to its normal value. When the transition to 9.81 MPa*√m

occurs, there was complete crack arrest. Even though there was a very small crack growth initially,

after 10000 to 20000 cycles no crack growth was observed and therefore it was decided not to present

the related da/dN, as this would also significantly decrease the clearness of the figure.

It can already be concluded from this test that there is a significant retardation effect going from high

to low ΔK blocks. The transitions can even be so severe that complete crack arrest can occur. As the

test was not left running for longer than 400000 cycles it cannot be concluded if this crack arrest is

infinite until a higher ΔK value is applied to start initiation again.



Figure 46: da/dN-N curve, clip gauge results of the L-H-L-1 procedure of material A

To determine whether crack arrest can occur for higher ΔK values as well, a second L-H-L test was

performed. The result for this test is shown in figure 47. For the transition of ΔK from 14.47 to 32.17

MPa*√m it can again be concluded that for higher ΔK values no or almost no retardation occurs. It

might even be considered that a small amount of acceleration occurs, but as the difference between

the measured values and the reported crack growth rate in the Paris law curve is so small, this cannot

be concluded. When going to a ΔK of 14.47 MPa*√m, complete crack arrest is observed. Again, initially

there was a very small crack growth which makes it possible to report a da/dN value. However after

10000 to 20000 cycles there was no crack growth observed anymore. The severity of this crack arrest

can be apprehended by comparing the obtained crack growth rate with 10-7 mm/cycle, which is the

value necessary to obtain the threshold region for the Paris law curve.


Steven De Tender

Figure 47: da/dN-N curve, clip gauge results of the L-H-L-2 procedure of material A

The a/W-N curve for the first L-H-L procedure of material B is shown in figure 48. The test started as

reported with a ΔK value of 8.98 MPa*√m. The transition to 10.96 MPa*√m is again difficult to see, but

the other transitions are clearly observed. The start of the H-L part is again indicated with an arrow in

the figure. A similar behaviour is observed for the two first transitions of the H-L regime, with more

retardation when going from 25.15 to 16.17 MPa*√m than from 35.93 to 25.15 MPa*√m. However,

when going to ΔK = 10.96 MPa*√m no crack arrest occurs. There is a significant amount of retardation

but the transition to 8.98 MPa*√m eventually occurs. The ΔK values are of course different for this

material, but for both materials this transition is a 33% decrease of the ΔK values. This shows that there

is a difference in material behaviour. And again, no crack arrest occurred for the transition to 7.18

MPa*√m. The different material behaviour might be explained by the bainitic microstructure of the

NV F500 material [21]. This might be a cause for less plasticity at the crack tip when a transition occurs

and therefore lower compressive residual stresses. Besides, as was already stated in chapter 3,

material A has more strain hardening when plastically deformed. Therefore more energy is needed for

the crack tip to propagate. This might explain its higher tendency for crack arrest than with material B.

It is difficult to observe the last transition in figure 48, but figure 49 shows the crack growth rate

behaviour in more detail. As was mentioned already, the initial behaviour of the material is very similar

to that of material A. But with the transition to 10.96 MPa*√m it is observed that even though the

crack growth rate dropped to a very low value, eventually the crack started growing again even though

it did not reach its normal crack growth rate before the next transition. For the other two blocks it is

observed that there is also a high amount of retardation and the crack growth rate stays significantly

below its predicted value, but still no crack arrest occurred. This clearly shows the different material

behaviour.



Figure 48: a/W-N curve, L-H-L-1 procedure material B showing clip gauge and potential drop results together with a visual confirmation

Figure 49: da/dN-N curve, clip gauge results of the L-H-L-1 procedure of material B

Even though there was no crack arrest observed in the L-H-L-1 test, it is clear from figure 50 that for a

transition from ΔK =35.93 to 16.17 MPa*√m crack arrest does occur. As was already observed with


Steven De Tender

material A, initially there was a very small amount of crack growth (≈0.005 mm) after which the crack

totally arrested. Even though the test only ran for 150000 cycles after the crack arrest occurred, it can

be concluded from this test that crack arrest occurs in this material for this transition.

Figure 50: da/dN-N curve, clip gauge results of the L-H-L-2 procedure of material B

Again the lifetime observed from the test will be compared with the lifetime obtained by using a linear

rule. It is however clear that when crack arrest occurs, a quantification of the retardation effect is

impossible. It can therefore already be concluded that an ordered block spectrum containing a H-L

regime will always have a much longer lifetime than is predicted with a linear rule. To be able to obtain

a quantification of the retardation only the non-arrested parts of the L-H-L-1 test will be used.

The amount of cycles for the test up to ΔK = 14.47 MPa*√m (in the H-L part) is predicted with a linear

rule to be 269000. The real amount of cycles recorded up to this moment is 380000. This shows that

even without taking into account the arrest there is already a 41.3 % longer lifetime.

For the L-H-L-1 test of material B, all blocks and their belonging da/dN measurements are taken in

account. The predicted lifetime is 242000 cycles, while the real value is 738000 cycles.

As the L-H-L-2 test for both materials resulted in a crack arrest it is useless to try to quantify the

retardation. It can however be concluded that for large transition factors between blocks, the imposed

compressive residual stresses at the crack tip usually result in crack arrest.

5.3.3 Semi-random procedure

The third and last type of test that was performed is a semi-random test. This is called semi-random

as it still consists of block loads, but these are now distributed in a more random way. The initial way

the test was planned, was to use the second regime from the LabVIEW program (paragraph 5.2) even

though the problem with using this program is that it is crack length controlled. When a transition from

for instance ΔK = 32.17 to 14.47 MPa*√m occurs, crack arrest will occur and the test will not be

finished. This clearly shows that this is not the best approach to perform a random test. Therefore it



was attempted to perform a semi-random test based on cycle control. This was however not achieved.

Therefore these tests are called semi-random as the block loads are distributed in a semi-random way

such that no crack arrest occurs before the end of the test. They are performed by using regime 1 of

the LabVIEW program, giving in the blocks manually.

In the a/W-N curve only the clip gauge output will be shown. This is done to enhance the visualisation,

as there are 14 block transitions in the entire test. Besides, as in the previous tests, the da/dN-N curve

is presented for both tests.

5.3.3.1 Procedure

The test procedure for material A is presented in figure 51 and table 12. The two lowest blocks are

discarded to keep the test time acceptable. In between the three highest blocks found from the wave

data, 2 intermediate values are chosen. The sequence of blocks consists of 3 blocks per ΔK value, that

are distributed in a semi-random way. The crack length at which the test is started is again taken high

enough to keep the loads on the clamping system as limited as possible. For the entire test 5 da/dN

measurements are taken for each ΔK block. Finally, the crack growth rates presented in table 12 are

again determined based on the Paris law curve obtained in chapter 3.

Figure 51: Semi-random block loading procedure material A

14,47

22,52

27

18

32,17

22,52

18

14,47

27

32,17

18

27

22,52

32,17

14,47

0

5

10

15

20

25

30

35

0,670 0,673 0,682 0,694 0,698 0,718 0,727 0,731 0,734 0,747 0,767 0,771 0,783 0,792 0,812

ΔK

a/W


Steven De Tender

Table 12

Count Δa [mm] a/W ΔK [MPa*√m] da/dN [mm/cycle]

1 0,2 0,670 14,47 1,28E-05

2 0,5 0,673 22,52 5,19E-05

3 0,75 0,682 27 9,21E-05

4 0,25 0,694 18 2,55E-05

5 1,2 0,698 32,17 1,60E-04

6 0,5 0,718 22,52 5,19E-05

7 0,25 0,727 18 2,55E-05

8 0,2 0,731 14,47 1,28E-05

9 0,75 0,734 27 9,21E-05

10 1,2 0,747 32,17 1,60E-04

11 0,25 0,767 18 2,55E-05

12 0,75 0,771 27 9,21E-05

13 0,5 0,783 22,52 5,19E-05

14 1,2 0,792 32,17 1,60E-04

15 0,2 0,812 14,47 1,28E-05

The test procedure for material B is represented in figure 52 and table 13. As was done for material A

as well, the lowest ΔK values found from the wave data are not used in this test. Between the three

highest ΔK values, 2 intermediate values are added again and all blocks are used three times in the

entire test. Similar as in the tests of material A the initial crack length is taken large enough to keep

the loads applied to the clamping low enough.



Figure 52: Semi-random block loading procedure material B

Table 13


1 0,25 0,515 16,17 2,90E-05

2 0,8 0,521 25,15 1,61E-04

3 1,2 0,541 30 3,18E-04

4 0,4 0,571 20,5 7,28E-05

5 1,5 0,581 35,93 6,41E-04

6 0,8 0,619 25,15 1,61E-04

7 0,4 0,639 20,5 7,28E-05

8 0,3 0,649 16,17 2,90E-05

9 1,2 0,656 30 3,18E-04

10 1,5 0,686 35,93 6,41E-04

11 0,4 0,724 20,5 7,28E-05

12 1,2 0,734 30 3,18E-04

13 0,8 0,764 25,15 1,61E-04

14 1,5 0,784 35,93 6,41E-04

15 0,3 0,821 16,17 2,90E-05

16,17

25,15

30

20,5

35,93

25,15

20,5

16,17

30

35,93

20,5

30

25,15

35,93

16,17

0

5

10

15

20

25

30

35

40

0,515 0,521 0,541 0,571 0,581 0,619 0,639 0,649 0,656 0,686 0,724 0,734 0,764 0,784 0,821

ΔK

a/W


Steven De Tender


Figure 53 shows the a/W-N curve of the semi-random procedure for material A. It is clear that in this

curve (almost) all transitions that were reported in the previous paragraph are visible. Even though it

is a useful graph to determine variable amplitude effects, the most interesting curve is definitely the

da/dN-N curve which is presented in figure 54. The first three blocks are a L-H sequence that shows no

or almost no retardation. The transition of ΔK from 27 to 18 MPa*√m results in a significant

retardation. The most interesting result however is the successive block of 32 MPa*√m, which does

not show any retardation/acceleration even though the crack growth rate of the previous block did

not yet reach its normal value. This can be either explained due to the large difference between the

blocks, or because there is no accumulating effect of retardation for these high ΔK values.

The next three blocks show clear retardation, easily explained due to H-L sequence. As the difference

between these three blocks is not that big, it might be that there is an extra retardation in the

successive blocks due to an accumulation effect starting from block 6 (where there was a large amount

of retardation due to the jump from 32.17 to 22.52 MPa*√m). Going from block 8 to 9 it does not seem

that there is a retardation effect, it even seems like there is a small acceleration in crack growth. Going

to the 10th block, this also seems to show a little acceleration with respect to its reported value in the

Paris law curve. This small accelerating effect is even more clear when going from the 11th block to the

12th (ΔK of 18 to 27 MPa*√m). Similarly going from block 13 to 14 the crack growth rate reported for

ΔK = 32.17 MPa*√m is higher than its normal value.

Finally it can be seen from figure 53 that the last transition from ΔK=32.17 to 14.47 MPa*√m resulted

in crack arrest. There is thus no influence of the preceding load history for this behaviour of the

material (which is similar as in test L-H-L-2). As was also reported in the previous tests, initially there

was a very small crack growth, after which total arrest was observed.

Figure 53: a/W-N curve, semi-random procedure material A showing clip gauge results together with a visual confirmation



Figure 54: da/dN-N curve, clip gauge results of the semi-random procedure of material A

Figures 55 and 56 show the a/W-N and da/dN-N curves of material B. The a/W-N curve of material B

is similar to that of material A. It also clearly shows that the final transition, going from ΔK = 35.93 to

16.17 MPa*√m results in total crack arrest. This thus also means that there is no influence of the

preceding load history for this behaviour.

In the da/dN-N curve it is clear that again the first three blocks show more or less no

retardation/acceleration. The transition to block 4 again results in retardation, which is not completely

gone with the last da/dN measurement. When going to ΔK = 35.93 MPa*√m however, instead of a

small acceleration as with material A, a clear retardation effect is observed. This shows that both

materials react in a completely different way to the retardation/acceleration accumulation.

Even though this effect was observed going from ΔK = 20.5 to 35.93 MPa*√m, this is not as severe as

in the case of the transition from block 8 to 9 (16.17 to 30 MPa*√m). Even though a small retardation

is also observed. This generality of this observation even becomes less credible as the transition from

16.17 to 30 MPa*√m (block 11 to 12) even gives a small acceleration. Therefore it cannot be concluded

whether there is an accumulating effect for this material or not. Even though there is some difference

in the material behaviour, as with the big material there is a small accelerating effect when going from

low to high and a preceding retardation effect.


Steven De Tender

Figure 55: a/W-N curve, semi-random procedure material B showing clip gauge results together with a visual confirmation

Figure 56: da/dN-N curve, clip gauge results of the semi-random procedure of material B

Again the difference in lifetime will be determined for this test. As there was total crack arrest at the

end of the test, the number of cycles will only be considered for the first 14 blocks. For the test of



material A, the predicted number of cycles is equal to 136000 cycles, while the actual number of cycles

is 382000 cycles. For material B the predicted lifetime with a linear rule is 68700 cycles and the actual

lifetime is 190000 cycles. This shows that the overall result of both materials is more or less in line,

even though there are some differences in material behaviour that were observed in this paragraph

and in the paragraph on the L-H-L tests. The overall result however is dominated by the large

retardation effect of the H-L parts that occur in the test.

5.3.4 Discussion

For all tests it can be concluded that in the H-L regime there is a small amount of retardation that

occurs for both materials. This effect is almost negligible with respect to the retardation observed for

the H-L part of the tests. In the L-H-L tests it was observed that in this H-L part retardation is significant

and even results in crack arrest in some transitions for material A. As was already stated before, the

reason for this different material behaviour might be the difference in microstructure of both

materials. Another possibility is the different stress strain behaviour of material A, that shows more

strain hardening. Therefore more energy has to be invested in every cycle and the material might be

more prone for crack retardation and arrest.

The semi-random tests showed an accumulation of retardation when the crack growth was not long

enough for the crack growth rate to return to its normal value. For material A it was observed that as

there was some retardation in the previous block, going from a higher to a lower block, it might result

in some acceleration. This effect is however almost negligible. Such behaviour was not observed for

material B. It is observed that these accelerating effects only occur when there is a substantial

accumulation of retardation in the lower blocks and it only occurs for the two highest blocks. It is not

yet clear what the explanation for this could be.

The main conclusion of this chapter is that for an ordered block spectrum the total lifetime is always

longer than predicted by a linear rule based on the crack growth rates reported in the Paris law curve.

This was also the case for a semi-random spectrum. This means that the application of a linear rule is

(over)conservative with respect to the ordered block spectra.

The autocorrelation values of all tests performed in this chapter are around 0.99. This shows that even

our semi-random test is too ordered with respect to a random spectrum. A solution to obtain a semi-

random spectrum with a lower autocorrelation value is to use cycle control instead of crack growth

control, as this makes it possible to have shorter block lengths and thus more variation. This shows

however that it is impossible to conclude something for a random spectrum with these tests. Even

though, based on these results it is probable that overall there will be retardation for a random

spectrum. As was already mentioned in the literature study, the variable amplitude effects are

different for different stress ratios. A different behaviour can be expected for stress ratios of R=-1. This

situation was not evaluated because of practical challenges. In any case, the used value (R = 0.1) is

normally accepted to be more damaging and therefore the chosen alternative should be on the

conservative side.

To have some idea of the lifetime for a random signal, the formula that was discussed in chapter 1 can

be used:

𝑑𝑎

𝑑𝑁𝑟𝑚𝑠=

𝐶∆𝐾𝑟𝑚𝑠𝑚

(1 − 𝑅𝑟𝑚𝑠)𝐾𝑐 − ∆𝐾𝑟𝑚𝑠

with C and m the Paris law curve constants found in chapter 3 for both materials, Rrms the overall stress

ratio (constant 0.1 for the tests discussed in the thesis), Kc the elastic fracture toughness [MPa*√m]


Steven De Tender

and ΔKrms [MPa*√m] is the root mean square of the applied ΔK blocks. The elastic fracture toughness

can be determined based on a formula specified in [33]:

(𝐾𝐼𝑐𝜎𝑦)

2

= 0.35𝐶𝑣𝜎𝑦+ 0.006

with KIc [MPa*√m] the elastic fracture toughness, σy [MPa] the yield stress and Cv [J] the Charpy V-

notch energy at -40°C. This last parameter can be found in [21] for both materials. The predicted values

of the elastic fracture toughness based on the formula are 240 and 269 MPa*√m for material A and B

respectively.

These values are used in the formula for the determination of the random crack growth rate. For the

L-H procedure of both material A and B, a random lifetime of 48 873 000 and 71 380 000 cycles is

predicted respectively. This is of course a very high value, but could actually be expected. Based on the

results that were found in this chapter, it is evident that when there is H-L transition in block loads,

there is a significant amount of retardation that might even result in crack arrest. This crack arrest

makes the lifetime of a structure much longer. It is therefore not that difficult to imagine that if in

reality there is crack arrest, a high enough load has to be achieved for multiple cycles for the crack

growth to initiate again. The results for the other tests are in line with this conclusion, but for

completeness, all predicted lifetimes are compared to the test results in table 14.

Table 14

LHa LHb LHL1a LHL1b SRa SRb

Linear rule 269000 68600 269000 242000 138000 68700

Test results 287000 67800 380000 738000 382000 190000

Random fatigue life

48870000 71380000 190430000 392450000 87050000 73320000

As mentioned above, the large difference between random and ordered block spectra might be

partially explained by the fact that in the lifetime of the ordered block loads crack arrest was not taken

in account. For instance the semi-random test of material A is reported as having 382000 cycles before

the test was finished. Actually it ran 800000 cycles and at that moment the crack was not even initiated.

This means that if no crack initiation occurs, the ordered block spectra might even predict a longer

lifetime than the random load spectra.

The results of this chapter also do not take into account the lowest ΔK values found from the wave

data. This shows that the actual lifetime of an offshore construction will be even larger than is

estimated based on these results. It might therefore be posed that designing a structure based on a

linear fatigue life calculation is overconservative.

Conclusions and future work 71


6 Conclusions and future work

6.1 Instrumentation and Paris law curve

Different kinds of instrumentation were used and optimised in this thesis. It can be concluded that the

clip gauge worked excellent when comparing it to visual measurements and with the post-mortem

analysis based on the beachmarks. This beachmarking technique is applied for multiple tests and was

found to be very successful. The application of a crack growth control instead of a cyclic control for this

technique makes it possible to obtain a clearly visible beachmark for every different ΔK value. It was

found from the results that a good value to work with is 0.15 mm. This keeps the test time acceptable

but also makes sure that the beachmark is clearly visible with the naked eye.

The second instrumentation technique that was used was the direct current potential drop. As can be

observed from all test results, this technique is also working well and usable to determine a Paris law

curve. Even though care has to be taken with the application of this technique for higher ΔK values. It

was observed during the tests that when going to higher stress intensity factor ranges, the potential

drop technique estimated the crack to be lower than it really was. A possible explanation for this , that

was already discussed in chapter 3, is the input of Y0 in the potential drop equation. For higher ΔK

values, the pin distance becomes larger as the vertical displacement is larger. Besides, these large ΔK

values were often reached for larger a/W values, were the vertical displacement and thus pin distance

is intrinsically larger. It was observed therefore that the initial input for the potential drop equation

does not always give the complete exact crack growth behaviour. Research to this topic might be an

interesting future improvement. The technique can then eventually be used to control the test instead

of using clip gauge control. To do so, the separate LabVIEW program for the DCPD application has to

be integrated in the program discussed in chapter 2.

The third instrumentation technique is the strain gauge. From chapter 3 it is clear that this technique

is not working as it should. It was observed that when using a correction factor in the compliance

equation, the crack growth could be predicted in a correct way for a certain ΔK range. However this

factor varied for different ΔK ranges. Therefore, it is believed that the used compliance equation is not

perfect for the ESE(T) specimen and that an extra ΔK dependent factor needs to be added. This

assumption is supported by investigating the general shape of the strain gauge output in the plots. It

is clear that this is similar to the clip gauge output, even though the crack growth is reported too small

for the K-decreasing part and too high for the K-increasing part of the tests in chapter 3. Investigating

this problem, by using a different equation, or using the output to add a certain ΔK dependent factor

to the equation might be an interesting topic to investigate in the future. It would then also be possible

to use the programmed strain gauge control for more harsh environments.

The fourth measurement technique is digital image correlation. As was explained in chapter 2, the

LabVIEW program makes it possible to automatically take pictures every block transition. These

photographs were then post-processed using the technique made available by Laseure and Schepens

[2]. This approach did however not give any useful results. A possible solution to this is to take multiple

pictures every block transition. Neglecting the pictures that give impossible results then might give a

good result. This was implemented in the LabVIEW program and the camera, but not yet tried. Another

possible solution for future research is to zoom in on the uncracked ligament.

Using all these techniques Paris law curves were obtained for both materials used in the thesis. Similar

threshold behaviour was observed with a ΔKthreshold of 5 MPa*√m. The stable propagation phase of both


Steven De Tender

materials is however slightly different. For the same ΔK values, the crack growth rate is larger for

material B with respect to the values in the Paris law curve of material A. This behaviour is observed

from ΔK values of 10-15 MPa*√m and more and might be allocated to the bainitic nature of material

B. Another possible explanation is the different stress strain behaviour of material A with respect to

material B. Material A has more strain hardening when it is plastically deformed. More energy is

therefore needed for the crack tip to propagate, as there is plastic deformation every cycle. This might

explain the slower crack growth rate for material A. Both of these explanations are however just

suggestions and cannot be confirmed. Besides material B seems to reach higher ΔK values in the stable

propagation phase than material A. Which can then be assigned to the higher strength of this material.

Both Paris law curves and the related formulas of the stable propagation regime are presented in

chapter 3.

6.2 Variable amplitude loading

Chapter 4 discussed the resulting block loads found from the wave data. Based on these results, test

procedures were defined in chapter 5. L-H, L-H-L and semi-random procedures were tested to

determine the influence of variable amplitude (retardation/acceleration) on the lifetime of a structure.

It was found that for all different procedures there was an overall retardation effect. A more significant

retardation effect was found for the H-L parts in the procedure as compared to the L-H regions. Except

for a small acceleration observed in the semi-random test caused by accumulative effects, no

acceleration was observed in any other tests. It is therefore not possible based on this one test to

conclude that acceleration occurs for stress ratios of R = 0.1. According to the formula found from

literature (paragraph 1.7) the random fatigue life was even larger than the values found from the

ordered block spectra. As was already denoted in chapter 5, this difference might be explained by not

taking into account the extra lifetime due to crack arrest for the ordered block procedures.

When comparing the experimental results with literature, it was found in [1,3] that there is more

retardation with multiple overloads. Even though there is no general theory of what will happen with

block loads, it is clear that a ‘block overload’ also results in retardation which is probably larger than

the retardation of a single or a few overloads.

As was mentioned in chapter 1, [4] and [6] pose that a random spectrum gives a more or less equal

lifetime as is calculated based on a linear damage rule. An ordered spectrum would be less damaging

according to these papers. Since stress ratios higher than 0 were also used, their conclusions should

be similar to the results of this thesis. It was indeed found that an ordered load spectrum gives a higher

lifetime. However, it is concluded from chapter 5 that a random load spectrum for a stress ratio of R =

0.1 also gives a much higher lifetime than the one predicted by a linear damage rule.

According to [7] the actual lifetime related to a random load spectrum differs for different spectra.

Therefore no simple overall conclusions can be made based on one random spectrum. This makes it

very difficult to compare the conclusions from chapter 5 with literature found in chapter 1. It can be

concluded that the experimental results that are retrieved should be interpreted with care. [9] clearly

indicates that a different stress ratio gives a completely different behaviour. It is however believed

from the results gathered in this thesis that for a positive stress ratio, there will always be overall

retardation for a random and an ordered load spectrum.

The use of the autocorrelation function to define a semi-random spectrum that is appropriate to

investigate the random loading behaviour, is an interesting topic to investigate in the future. As was

mentioned in chapter 5, efforts were done to make a cyclic controlled random test program. Like this,

different ΔK blocks can be applied in a much faster sequence which makes the applied spectrum more



random. Besides, it makes it possible to further investigate the accumulating effect of retardation and

crack arrest. Therefore it is suggested as a future improvement to adapt the program explained in

chapter 5 in such a way that cycle control is possible.


Steven De Tender

References 75


7 References

[1] Laseure, N., Schepens, I., Micone, N., De Waele, W. (2015) ‘Effects of variable amplitude loading on

fatigue life’, Sustainable Construction and Design, 6(3).

[2] Laseure, N., Schepens, I. (2015) ‘Fatigue of offshore structures subjected to variable amplitude

loading’, master dissertation at Ghent University.

[3] Micone, N., De Waele, W., Chhith, S. (2015) ‘Towards the Understanding of Variable Amplitude Fatigue’, Synergy, Gödöllő, Hungary, Octobre 12 – Octobre 15, 2015. Gödöllő, Hungary: Szent István University. Faculty of Mechanical Engineering.

[4] Maljaars, J., Pijpers, R., Slot, H. (2015) 'Load sequence effects in fatigue crack growth of thick-walled

welded C-Mn steel members', International Journal of Fatigue, 79(), pp. 10-24.

[5] Rushton, P.A., Taheri, F., Stredulinsky, D.C. (2007) 'Fatigue Response and Characterization of 350WT

Steel Under Semi-Random Loading', Journal of Pressure Vessel Technology, 129, pp. 525-534.

[6] Zhang, Y., Maddox, S.J., (2012). Fatigue testing of full-scale girth welded pipes under variable

amplitude loading. In Ocean, Offshore and Arctic Engineering. Rio de Janeiro, Brazil, 1-6 July . UK: TWI

Limited, Cambridge. Paper No.83054.

[7] Zhang, Y., Maddox, S.J. (2009) 'Investigation of fatigue damage to welded joints under variable

amplitude loading spectra', International journal of fatigue, 31, pp. 138-152.

[8] Agerskov, H. (2000) 'Fatigue in steel structures under random loading', Journal of Constructional

Steel Research, 53, pp. 283-305.

[9] Agerskov, H., Pedersen, N.T. (1992) 'Fatigue life of offshore steel structures under stochastic loading', Journal of structural engineering, 118(8), pp. 2101-2117.

[10] Agerskov, H., Nielsen, J.A. (1999) 'Fatigue in Steel Highway Bridges under Random Loading', Journal of structural engineering, 125(2), pp. 152-162.

[11] Cathie, D. (2012) Offshore pile design: International practice, Cathie Associates.

[12] Arnoudt, J., Triest, G. (2016) Early-stage Cost Estimation of Offshore Wind Farm Projects using Monte Carlo Simulation , Available at:http://www.slideshare.net/JoostArnoudt/presentation-evm-europe-2013 (Accessed: 22/05/2016).

[13] Roylance, D. (2001) Fatigue, Cambridge: Massachusetts Institute of Technology.

[14] Post, N.L. (2008) Reliability based design methodology incorporating residual strength prediction of structural fiber reinforced polymer composites under stochastic variable amplitude fatigue loading, Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University.

[15] S. M. Beden, S. Andhullah and A.K. Ariffin. (2009) ‘Review of fatigue crack propagation models for

metallic components’, European Journal of Scientific Research, 28(3), pp. 364-397.

[16] Micone, N., De Waele, W. (2015). Comparison of Fatigue Design Codes with Focus on Offshore Structures. In International Conference on Ocean, Offshore and Artic Engineering. Canada, May 31 - June 5, 2015. pp. 11

[17] Klysz, S., Leski, A. (2012) 'Good Practice for Fatigue Crack Growth Curves Description', in Belov, A. (ed.) Applied Fracture Mechanics. InTech, pp. 197-200.

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[18] Standard test method for measurement of fatigue crack growth rates, ASTM E647. ASTM International, West Conshohocken, USA, 2013.

[19] Černý, I (2004). “The use of DCPD method for measurement of growth of cracks in large components at normal and elevated temperatures”. Engineering Fracture Mechanics 71 (2004) 837–848.

[20] Jacobsson L, Persson S., Melin S. (2009).“SEM study of overload effects during fatigue crack growth using an image analyzing technique and potential drop measures”. Fatigue Fract Eng Mater Struct 33, 105–115.

[21] Micone, N. (2014) Internal report V4 : Material Characterization, Ghent University: Labo Soete.

[22] Hertelé, S. (2015) Course: Fracture Mechanics, Ghent University: Labo Soete.

[23] Khlefa A. Esaklul, William W. Gerberich and James P. Lucas, "Near-Threshold Behavior of HSLA Steels," in HSLA Steels-Technology & Applications. American Society for Metals, Metals Park OH, 1984, p 571.

[24] Miñambres, O.Y. (2012) Assessment of Current Offshore Wind Support Structures Concepts - Challenges and Technological Requirements by 2020 , Karlshochschule International University.

[25] Torcinaro, M., Petrini, F., Arangio, S. (2010) ‘Structural Offshore Wind Turbines Optimization’,

Earth and Space 2010: pp. 2130-2142.

[26] C-power (2015) Jackets, Available at: http://www.c-power.be/jackets (Accessed: 22/05/2016).

[27] Torcinaro, M., Petrini, F., Arangio, S. (2014) Structural Optimization of Offshore Wind Turbines, Available at: http://www.slideshare.net/StroNGER2012/4-structural-optimization-of-offshore-wind-turbines-petrini (Accessed: 15/02/2016).

[28] Thorntonbank Golfdata 2005 – 2013, Meetnet Vlaamse Banken, 18-02-2016.

[29] Fitnet MK7, Annex A: Stress intensity factor (SIF) solutions, 2006.

[30] Wittel, H., Muhs, D., Jannasch, D., Voβiek (2013) Roloff/Matek: Machineonderdelen Tabellenboek, 5 edn., Den Haag: Sdu Uitgevers.

[31] Loncke, K., (2012). Scheurpropagatie in buizen onderworpen aan vermoeiingsbelasting. Thesis. Gent: Ghent University / Universiteit Gent.

[32] Van den Eynde, D., Baeye, M., Brabant, R., Fettweis, M., Francken, F., Haerens, P., Mathys, M., Sas, M., Van Lancker, V. (2013) 'All quiet on the sea bottom front? Lessons from the morphodynamic monitoring', in Degraer, S., Brabant, R., Rumes, B. (ed.)Environmental impacts of offshore wind farms in the Belgian part of the North Sea: Learning from the past to optimise future monitoring programmes. Royal Belgian Institute of Natural Sciences, Operational Directorate Natural Environment, Marine Ecology and Management Section. 239 pp.

[33] Maropoulos, S., Ridley, N., Kechagias, J., Karagiannis, S. (2004) 'Fracture toughness evaluation of a H.S.L.A. steel', Engineering fracture mechanics, 71(12), pp. 1695-1704.



ONLINE FATIGUE CRACK GROWTH MONITORING WITH CLIP GAUGE

AND DIRECT CURRENT POTENTIAL DROP

S. De Tender, N. Micone and W. De Waele

Ghent University, Laboratory Soete, Belgium

Abstract: Fatigue is a well-known failure phenomenon which has been and still is extensively studied. Often structures are designed according to the safe-life principle so no crack initiation occurs. Nowadays there is a high emphasis on cost-efficiency, and one might rather opt for a fail-safe design. Therefore a certain amount of crack growth can be allowed in structures, but then a good knowledge of stresses and related crack growth rates is needed. To this end, extensive studies are done to obtain a material’s Paris law curve. Within the framework of research for offshore wind turbine constructions, tests were done to determine the crack growth rate of a high strength low alloy (HSLA) steel. A dedicated LabVIEW program was developed to be able to determine an entire Paris law curve with a single specimen, by controlling the stress intensity factor range

(ΔK). The program is controlled by the readings of a clip gauge, which make it possible to plan the amount

of crack growth per ΔK block and thus plan an entire test in advance. The potential drop technique was also

applied in order to obtain the Paris law curve. Clip gauge results were compared with direct current potential drop monitoring. This comparison was done by means of an a/W-N diagram and the resulting Paris law curves. The results show a very good correlation between both methods and with the visual confirmation.

Keywords: ΔK, da/dN, Paris law curve, a/W-N curve, clip gauge, DCPD, K-decreasing, K-increasing

1 NOMENCLATURE

da/dN crack growth rate mm/cycle

K stress intensity factor 𝑀𝑃𝑎 ∗ √𝑚

P Force N

Δa crack length mm

f frequency Hz

R stress ratio -

σy yield strength MPa

σuts Ultimate tensile strength MPa

B Specimen Thickness mm

W Specimen Width mm

E Young’s Modulus GPa

v0 Crack mouth opening mm

Displacement

V Voltage V

Y0 Measurement pin mm

distance


Steven De Tender

2 INTRODUCTION

Fatigue can be investigated in many different ways. In practice, the S-N curve approach is the most popular to represent material characteristics. In this kind of diagram, a certain lifetime is specified for every different constant amplitude stress level. Some applications however, might require that a certain amount of crack growth is allowed, to make them cost efficient. In this case a Paris law curve is often used to define the crack growth rate as a function of stress intensity factor range [1,2]. As shown in figure 1 (right), crack growth rate is described as the increment in crack growth per increment in cycles

(da/dN). The stress intensity factor range (ΔK) is proportional with the force range (ΔP), depends on

geometrical parameters of the used specimen and on the crack length. The curve of a typical steel consists of three parts: the initiation phase (I), the stable propagation phase (II) and the critical propagation phase (III). The initiation phase has as a lower limit the threshold stress intensity factor range (defined below). The stable propagation phase starts and ends when the crack growth rate becomes linear with respect to stress intensity factor range. The critical propagation phase starts when there is crack growth rate acceleration [1].

Another way of representing crack growth in a material is by plotting the relative crack depth (a/W) versus the number of cycles (see fig. 1 (left) [2]). This is an easy way of comparing different kinds of instrumentation and verifying their output with a visual confirmation.

Figure 57: a/W-N curve (left) with K-decreasing (black) and K-increasing (blue), Paris law curve (right)

ASTM E647 ([3]), which is the standard test method for measurement of fatigue crack growth rates, describes how the Paris law curve should be determined. The standard recommends a minimum precrack length based on geometrical parameters, and a maximum precrack growth rate (da/dN < 10-5

mm/cycle). The threshold region is determined with a K-decreasing method. ΔK values are decreased

until a crack growth rate lower than 10-7 mm/cycle is reached, this is region I in the right part of figure 1 and the black part in the left figure. When going from precracking to K-decreasing it is important to stay under the maximum stress intensity factor of the precracking stage. Besides there should be sufficient

crack growth (Δa) per block such that there are as limited transient effects between blocks as possible.

For determining the stable propagation phase, a K-increasing procedure is used. ΔK blocks are

increased up to the plastic region, which is shown as region II in the right part of figure 1 and as the blue

part of the left figure. Again a significant Δa should be used per ΔK block to keep transient effects as low

as possible and to have da/dN values which are as stable as possible.

The goal of the tests are on the one side to obtain a Paris law curve for a certain material based on a clip gauge controlled test. For every different ΔK block in both the K-decreasing and increasing modules

4 or 5 average da/dN measurements are taken over a certain crack extent. This crack growth is measured online by means of a clip gauge. These points are then set out in the Paris law diagram. On the other side clip gauge output is compared with direct current potential drop (DCPD) measurements and a visual confirmation. DCPD is a method that is more and more used in fatigue applications,



because of its flexibility for geometries and environments [4,5]. It has therefore a wide range of possible applications. The results of this technique are compared with the clip gauge measurement by means of both an a/W-N curve and their responding Paris law curves.

3 EXPERIMENTAL PROCEDURE

3.1 Material

The steel that is used is similar to an offshore grade NV F460, which is a typical HSLA steel. Table 1 denotes the microstructural properties of the material and table 2 gives the mechanical properties [6].

Table 15

Material C Mn Si P S Cu Ni Cr Mo

NV F460 [%] 0.08 1.24 0.24 0.01 0.001 0.05 0.21 0.05 0.005

Table 16

Material σy [MPa] σuts [MPa]

NV F460 520 603

3.2 Geometry

The stress intensity factor depends on the geometry and thus on the specimen type. The tests and test results discussed in this paper are determined with an ESE(T) specimen. Figure 2 shows this ESE(T) specimen and the used dimensions. The stress intensity factor range is proportional to the load range, depends on the crack length and the type of geometry. The specific formula of ΔK for an ESE(T)

specimen (which can be found in [3]) is:

∆𝐾 = [∆𝑃/(𝐵√𝑊)]𝐹

With ΔP the load range, B the specimen thickness (15 mm), W the specimen width (60 mm) and F a

factor depending on the crack length, for which the exact formula can be found in [3].

Figure 58: ESE(T) specimen

3.3 Instrumentation and testing procedure

For the tests described in the dissertation two instrumentation techniques are used to monitor crack growth. The first one is a clip gauge which is mounted in a machined crack mouth of the specimen (figure 3 (1)). Four strain gauges (two on each leg of the clip gauge) measure strain and thus compliance of the specimen, which is translated in a certain voltage through a Wheatstone bridge. The voltage is converted to a crack mouth opening displacement (CMOD) by calibrating the clip gauge. With the compliance equations (available in [3]) this can be directly linked to a certain crack length. The clip gauge used is a 3541-005M-100M-LT model with 5.00 mm gauge length which can travel from -1.00 to 10.00 mm.


Steven De Tender

For an ESE(T) specimen, the crack length can be calculated using the expressions for front-face compliance:

𝑎𝑊⁄ = 𝑀0 +𝑀1𝑈 +𝑀2𝑈

2 +𝑀3𝑈3 +𝑀4𝑈

4 +𝑀5𝑈5

𝑈 = [(𝐸𝐵𝑣0∆𝑃

)

12+ 1]

−1

With E the Young’s modulus, B the specimen thickness, v0 the CMOD and ΔP the load range. M0, M1,

M2, M3, M4 and M5 are constants that can be found in [3].

Direct current potential drop (DCPD) is used as a second measurement technique. A constant current is sent through the specimen and as the resistance of the specimen increases when the uncracked ligament of the specimen becomes smaller, the measured voltage also increases. This voltage can be linked to a certain crack length with the formula (which can be found in [3]):

𝑎 =𝑊

𝜋𝐶𝑜𝑠−1

(

Cosh (𝜋𝑊𝑌0)

𝐶𝑜𝑠ℎ (𝑉𝑉𝑟𝐶𝑜𝑠ℎ−1 (

𝐶𝑜𝑠ℎ (𝜋𝑊𝑌0)

𝐶𝑜𝑠 (𝜋𝑊𝑎𝑟)

))

)

With a the crack length, W the specimen width, Y0 the distance between measurement pins (see next paragraph), V the measured voltage, ar a reference crack size from another measurement method and Vr the corresponding voltage for this reference crack length.

The direct current power source used was an auto ranging Farnell AP60-150 set at 35 Amperes. The measurement instrument used was a nanovolt meter Agilent 34420 with a continuous integrating measurement method (Multi-slope III A-D converter) and a –D Linearity of 0.00008% of reading +0.00005% of range. Figure 4 shows the connections needed for potential drop. At the top and the bottom (2 and 3) the current is introduced and connected to earth. 4 and 5 are measurement pins, used to measure the potential difference over the crack mouth. 6 denotes the reference pins, which measure a reference potential difference to filter out environmental effects, such as temperature changes. 7 indicates reference lines that are used to visually confirm the crack length that is reported by the different instrumentation techniques.



Figure 59: Illustration of instrumented ESE(T) specimen. Crack growth is monitored by clip gauge and potential drop measurements.

3.4 a/W-N curve

The comparison of the two instrumentation methods mentioned can be done with either the Paris law curve or by means of an a/W-N curve. An a/W-N curve is shown in figure 4 where both K-decreasing and K-increasing are combined. Besides the two instrumentation techniques a visual confirmation is performed, where the most important points that were detected at the beginning and end of the test are shown (as recommended by standard [3]). Both methods have an excellent correlation, except for the last and initial part of the test where there is a small deviation between them.

At the start of both K-decreasing and K-increasing there is a small deviation between both methods. The clip gauge results were checked visually multiple times (based on the reference lines in figure 3) and this had a good correlation with the actual crack length for both tests (K-decreasing and K-increasing). This means that the potential drop underestimated the crack growth at the beginning of both tests. The potential drop calculation is based on an input of the initial voltage for a certain crack growth and therefore initially at the start-up of a test, the correlation can be a bit deviated. For the rest of the K-decreasing the potential drop readings are close to perfect. For the K-increasing, the DCPD also has a small deviation at the end. Besides the initial voltage and crack growth also the initial pin distance (paragraph 3.3) is an input of the potential drop equation. Therefore the correlation at larger crack growth rates might be less accurate as the pin distance becomes larger . But as can be seen from figure 4, these are minor deviations and the two instrumentation techniques give a very good a/W-N curve.

1

2

7

4

6

3

5


Steven De Tender

Figure 4: a/W-N curve with both K-decreasing and K-increasing parts determined using potential drop and clip gauge

3.5 Paris law curve

As was mentioned above, for both the K-decreasing and K-increasing method, a series of da/dN

measurements are taken per ΔK block. To obtain the value of da/dN the specified Δa is logically divided

by the amount of cycles needed to obtain this crack growth. Multiple da/dN values are saved per block in LabVIEW for redundancy, with a constant crack length for every measurement per block. Every block change this crack length is decreased/increased for respectively the decreasing and increasing method.

In case of the K-increasing this is done because crack growth becomes so fast that a larger Δa is needed

to assure a stable da/dN measurement. For the K-decreasing the Δa is lowered because da/dN values

become so small that it is too time-consuming to obtain certain crack growth.

The program makes it possible to obtain a Paris law curve with a single specimen, but of course multiple tests can be done for redundancy. The averaged results for both clip gauge and potential drop are shown in figure 4. In the stable propagation phase similar da/dN values for both DCPD and clip gauge are obtained. The standard requires a value lower than 10-7 mm/cycle crack growth to obtain the threshold stress intensity factor range, which takes a long time to obtain. Even though a few points in the neighbourhood were obtained and a clear trend is observed. This means that the threshold is around

5-6 𝑀𝑃𝑎 ∗ √𝑚. A typical HSLA steel according to [7] has indeed, for a stress ratio of 0.1, a ΔKthreshold of

around 4-6 𝑀𝑃𝑎 ∗ √𝑚 dependent on the material characteristics. The stable propagation phase is clearly

seen with both instrumentation techniques for ΔK values ranging from 10 to 50 𝑀𝑃𝑎 ∗ √𝑚.

It is clear that both methods have an excellent correlation. At both the threshold and the higher region of the curve, there is more deviation. The deviation at the end of the K-increasing test was already observed and discussed for the a/W-N curve as well. Based on these observations, the scatter for the

higher ΔK values can be explained. At the threshold it was observed that, in general, there was more

scatter in the crack growth rate. This might explain differences between instrumentation.



Figure 5: Paris law curve obtained from DCPD (red) and clip gauge (black) readings

4 CONCLUSIONS

In this work, a ΔK control test was performed in order to obtain the Paris law curve of an HSLA steel

making use of both clip gauge and DCPD instrumentation techniques. For this purpose, a self-developed LabVIEW program was used, that allows to control a test from the voltage readings of the clip gauge. It makes it possible to obtain an entire Paris law curve with only one specimen. In parallel, DCPD was used to correlate the measured voltage with the crack growth. A specimen was subjected to both a K-decreasing and K-increasing test. The resulting a/W-N and Paris law curve were plotted and used to compare the two instrumentation techniques. Based on these two curves, they show a good correlation with both each other and a visual confirmation. Even though there was a bit more scatter in the initial potential drop readings, it is a very promising method, which can eventually also be used as an online method to control a test.

5 REFERENCES

[1] Micone, N., De Waele, W. (2015). Comparison of Fatigue Design Codes with Focus on Offshore Structures. In International Conference on Ocean, Offshore and Artic Engineering. Canada, May 31 - June 5. Ghent University, Soete Laboratory: ASME.

[2] Klysz, S., Leski, A. (2012) 'Good Practice for Fatigue Crack Growth Curves Description', in Belov, A. (ed.) Applied Fracture Mechanics. InTech, pp. 197-200.

[3] Standard test method for measurement of fatigue crack growth rates, ASTM E647. ASTM International, West Conshohocken, USA, 2013.

[4] Černý, I (2004). “The use of DCPD method for measurement of growth of cracks in large components at normal and elevated temperatures”. Engineering Fracture Mechanics 71 (2004) 837–848.

[5] Jacobsson L, Persson S., Melin S. (2009).“SEM study of overload effects during fatigue crack growth using an image analyzing technique and potential drop measures”. Fatigue Fract Eng Mater Struct 33, 105–115.

[6] Micone, N. (2014) Internal report V4: Material Characterization, Ghent University: Labo Soete.


Steven De Tender

[7] Khlefa A. Esaklul, William W. Gerberich and James P. Lucas, "Near-Threshold Behavior of HSLA Steels," in HSLA Steels-Technology & Applications. American Society for Metals, Metals Park OH, 1984, p 571

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