Steven De Tender Variable amplitude fatigue in offshore structures Academic year 2015-2016 Faculty of Engineering and Architecture Chair: Prof. dr. ir. Jan Melkebeek Department of Electrical Energy, Systems and Automation Master of Science in Electromechanical Engineering Master's dissertation submitted in order to obtain the academic degree of Counsellor: Ir. Nahuel Micone Supervisor: Prof. dr. ir. Wim De Waele
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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
Confidentiality
Confidential up to and including 01/01/2018
Important
This master dissertation contains confidential information and/or confidential research results proprietary
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
no circumstance this master dissertation may be communicated to or put at the disposal of third parties.
Photocopying or duplicating it in any other way is strictly prohibited. Disregarding the confidential nature
of this master dissertation may cause irremediable damage to Ghent University.
The stipulations above are in force until the embargo date.
III
Variable amplitude fatigue in offshore structures
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.
V
Variable amplitude fatigue in offshore structures
Variable amplitude fatigue in offshore structures
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
VI
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
VII
Variable amplitude fatigue in offshore structures
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
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.
Offshore load spectrum 43
Variable amplitude fatigue in offshore structures
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
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
Variable amplitude fatigue: block loads 48
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,
Variable amplitude fatigue: block loads 49
Variable amplitude fatigue in offshore structures
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
Variable amplitude fatigue: block loads 50
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
Variable amplitude fatigue: block loads 51
Variable amplitude fatigue in offshore structures
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
Variable amplitude fatigue: block loads 52
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
Variable amplitude fatigue: block loads 53
Variable amplitude fatigue in offshore structures
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
Variable amplitude fatigue: block loads 54
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
Variable amplitude fatigue: block loads 55
Variable amplitude fatigue in offshore structures
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
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
Variable amplitude fatigue in offshore structures
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
Conclusions and future work 72
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
Conclusions and future work 73
Variable amplitude fatigue in offshore structures
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.
Conclusions and future work 74
Steven De Tender
References 75
Variable amplitude fatigue in offshore structures
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.
[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).
[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.
Appendix A: SCAD paper
Variable amplitude fatigue in offshore structures
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
Appendix A: SCAD paper
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,
Appendix A: SCAD paper
Variable amplitude fatigue in offshore structures
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].
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.
Appendix A: SCAD paper
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.
Appendix A: SCAD paper
Variable amplitude fatigue in offshore structures
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
Appendix A: SCAD paper
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.
Appendix A: SCAD paper
Variable amplitude fatigue in offshore structures
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.
Appendix A: SCAD paper
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