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The crack driving mechanisms in a coarse grained nickel-base superalloy RR1000 when subjected to in- and out of phase thermo mechanical fatigue are investigated. It is found that the difference in fatigue crack growth rate between these two load conditions is accounted for by the different mechanical conditions at the crack tip region, rather than oxidation effects. This is based on digital image correlation and finite element analyses of the mechanical strain field at the crack tip, which demonstrate that in phase leads to larger crack tip deformation and crack opening. Notably, it is demonstrated that in- and out of phase crack growth rates coincide when correlated to the crack tip opening displacement.
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International Journal of Fatigue
journal homepage: www.elsevier.com/locate/ijfatigue
On the mechanistic dierence between in-phase and out-of-phase thermo-
mechanical fatigue crack growth
V. Norman
a,
, S. Stekovic
a
, J. Jones
b
, M. Whittaker
b
, B. Grant
c
a
Division of Engineering Materials, Department of Management and Engineering, Linköping University, SE-58183 Linköping, Sweden
b
Institute of Structural Materials, Swansea University, Swansea SA1 8EN, UK
c
Rolls-Royce plc, Derby DE24 8BJ, UK
ARTICLE INFO
Keywords:
Aerospace
Superalloys
Thermomechanical fatigue
Crack growth rate
Crack opening
ABSTRACT
The crack driving mechanisms in a coarse grained nickel-base superalloy RR1000 when subjected to in- and out
of phase thermo mechanical fatigue are investigated. It is found that the dierence in fatigue crack growth rate
between these two load conditions is accounted for by the dierent mechanical conditions at the crack tip
region, rather than oxidation eects. This is based on digital image correlation and nite element analyses of the
mechanical strain eld at the crack tip, which demonstrate that in phase leads to larger crack tip deformation
and crack opening. Notably, it is demonstrated that in- and out of phase crack growth rates coincide when
correlated to the crack tip opening displacement.
1. Introduction
In recent years, there has been an increased awareness of the en-
vironmental impact of air travel. Therefore, it is of vital strategic im-
portance to the aviation industry to reduce aero engine emissions,
which is driven by the EUs Aviation Vision 2020 along with industrial
competition [1].
A signicant portion of these improvements are expected to come
from new engine designs in term of gas turbine eciency. Such an
increase in eciency of the gas turbine is usually achieved either by
weight reductions or by increasing the combustion temperature as a
result of fuel being burnt at temperatures approaching the stoichio-
metric value [2]. In either case, the material choice is of critical im-
portance. Eectively, the modern criteria for selecting materials include
requirements on high temperature fatigue and creep capabilities, as
well as requirements on suitable environmental and corrosion resistant
properties, which in the present context typically results in the em-
ployment of nickel base superalloys. The motivation of these strict
criteria is that the gas turbine operation cycle imposes harsh alternating
mechanical and thermal loads on the material during start up, take o,
descent and shut down. Such thermo mechanical conditions have the
potential to cause local stresses to peak at temperatures far below the
ight cycle maximum, resulting in the nucleation and propagation of
cracks; a phenomenon known as thermo mechanical fatigue (TMF).
In essence, TMF is a complex failure mechanism, caused by
combined thermal and mechanical load cycles [3], but is not a novel
phenomenon. Rather, it is well acknowledged to be the primary life
limiting aspect for many engineering components exposed to elevated
temperatures, such as parts in the combustion chamber, along with
turbine blades and discs [4,5]. More precisely, the TMF process can be
divided into an initiation and propagation stage, where this investiga-
tion addresses the latter. Only a very limited number of investigations
have been conducted involving TMF crack growth experiments on
nickel base superalloys, however, it has been established that the crack
growth rate is highly dependent on the phase angle between the
thermal and mechanical cycle, e.g. in (IP) and out of phase (OP) cycling
[68]. This introduces new perspectives regarding the general crack
growth mechanism in fatigue at elevated temperatures, which have
been extensively studied in the past based on isothermal fatigue and
dwell fatigue experiments [927]. In particular, based on crack growth
experiments in air and vacuum [917], the general conclusion is that
oxygen plays a signicant role, possibly through one of a number of
proposed mechanisms [16]. On top of this, some authors have argued
that inelastic creep deformation and stress relaxation at the crack tip
may inuence the growth rate [7,11,12,14,15,19,20]. However, it is
not yet known whether these mechanisms are able to account for the
dierences seen between IP and OP TMF crack growth experiments.
In view of the above investigations, three dierent kinds of me-
chanisms which potentially may account for the dierence in OP and
IP, are identied. Firstly, (i) it is suggested that crack closure eects
https://doi.org/10.1016/j.ijfatigue.2020.105528
Received 1 November 2019; Received in revised form 31 January 2020; Accepted 1 February 2020
Corresponding author.
E-mail address: viktor.norman@liu.se (V. Norman).
International Journal of Fatigue 135 (2020) 105528
Available online 08 February 2020
0142-1123/ © 2020 Published by Elsevier Ltd.
T
may inuence the crack growth rate depending on the thermo me-
chanical phase angle. For instance, recent studies [8,2830] have de-
monstrated that variations in crack growth rate caused by altering the
load ratio and temperature cycle are accounted for by compensating the
stress intensity factor range or the cyclic J integral with respect to crack
closure. Secondly, (ii) it is also expected that the dierent phase angles
may induce dierent stress strain states in the crack tip, which may
both explicitly and implicitly aect crack growth. For instance, dif-
ferent amount of inelastic crack tip deformation may occur depending
on whether the cycle is OP or IP. Conversely, implicit eects such as the
relation between the stress strain state at the crack tip and the diusion
of oxygen are also possible [9,10,16,31]. Accordingly, as the third and
nal category, (iii) it is also likely that aspects related to the material
structure may account for the eect of phase angle, including the
mentioned environment material interaction and potential crack tip
phase transformations [11,32]. In other words, any potential material
related weakening or toughening at the crack tip, dependent or in-
dependent of the atmosphere.
Even though fatigue crack growth mechanisms in nickel base su-
peralloys under isothermal conditions have been extensively in-
vestigated in the past, there is at present a very limited understanding
of the governing mechanisms under thermo mechanical load condi-
tions, which is necessary for the ecient development of next genera-
tion gas turbine materials. Accordingly, the objective of this in-
vestigation is to render a better understanding of the mechanisms
responsible for causing the dierence in crack growth rate between IP
and OP TMF load conditions. This is done by performing IP and OP TMF
crack growth tests on a coarse grained nickel base superalloy RR1000,
for which the potential mechanisms, including crack closure, crack tip
deformation and oxidation eects, are investigated by in situ digital
image correlation (DIC) and metallographic studies of interrupted tests.
In this way, the mechanisms are identied and their contribution as-
sessed by comparison of the IP and OP case. This has given new insights
regarding general aspect of crack growth at elevated temperatures re-
levant for both isothermal and thermo mechanical load conditions.
2. Experimental and computational methods
2.1. Materials
RR1000 is a superalloy developed by Rolls Royce plc and is mainly
used for discs in the rotative aero engine hot sections because of its
excellent high temperature mechanical properties. The ne grained
RR1000 has at least 25 °C increase in temperature capability over 720Li
and an equivalent crack growth behaviour to coarse grained Waspaloy
[33]. However, the need for increased engine eciency and lower
emissions has been driving towards higher pressure ratios and higher
operation temperatures. Therefore, a coarse grained RR1000 has been
developed to improve creep performance and fatigue crack growth re-
sistance of these components [34].
Coarse grained RR1000 is processed by a powder metallurgy route
and strengthened by
N
iA
l
3type gamma prime precipitates. The nominal
chemical composition in wt% and details about the processing as well
as the heat treatment of the alloy are given in reference [14]. The mi-
crostructure typically consists of grain sizes of ASTM 7 3 (32125 μ
m
).
Apart from the gamma matrix and main strengthening secondary and
tertiary gamma prime phases, the material also contains a dispersed sub
micron phases such as MC carbides and
M
B
3
2
borides. Both gamma
prime precipitates are distributed intergranularly with particle sizes
ranging from 1 μ
m
to 5 nm depending on the heat treatment and
cooling rates [35,36].
2.2. Measurement of fatigue crack growth rates under thermo mechanical
fatigue load conditions
The purpose with this test procedure is to assess the fatigue crack
growth rate when subjected to thermo mechanical cycling, in contrast
to standard fatigue crack growth tests during which the temperature is
constant. As similar to conventional thermo mechanical fatigue (TMF)
testing [3], the temperature varies with the same periodicity as the
applied mechanical load with a given phase angle such as for instance 0
or 180 degrees, often denoted as in phase (IP) and out of phase (OP),
respectively. As a consequence of the varying temperature, a distinction
between the dierent causes of deformation in the tests specimen must
be made, typically as
Fig. 1. (a) The single edge notched and (b) corner crack specimen geometry used for the TMF crack growth experiments.
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
2
=+εt ε t ε t() () (
)
ethmech
(1)
where
ε
e
is the actual strain measured by an extensometer,
ε
th
is the
thermal strain, i.e. the thermal expansion which varies with the tem-
perature, and εmech is the mechanical strain whose origin is solely the
applied force.
2.2.1. Specimen geometry
For the aforementioned purpose, the specimens used were notched
in order to initiate a starting crack following a pre cracking procedure
explained below. The specimen geometry is displayed in Fig. 1a. The
grip section of the specimen was cylindrical with a diameter of 12 mm
while the middle section had an approximately rectangular cross sec-
tion with a thickness of 3 mm and a width of 12 mm. Nominally, the
notch had a radius of 1 mm and a notch depth of 3.0 mm. The speci-
mens were manufactured through turning and wire electrical discharge
machining, without application of any additional surface nishing
process.
2.2.2. Pre cracking procedure
A pre cracking procedure was conducted to initiate and propagate a
starting crack to a reasonable length. Due to lack of experience, the pre
cracking procedure was varied for the rst specimens until an optimised
procedure regarding minimal duration and applied stress, was estab-
lished. For this reason, the procedure was not the same for most of the
specimens. The load parameters and notch geometry employed for
crack initiation are displayed in Table 1. Subsequent propagation to
reach a reasonable starting crack length was done in a stepwise manner
reducing the maximum stress with steps of 30 MPa in order to propa-
gate through any eventual plastic zone caused by the previous max-
imum stress value. Regarding the test initiated at
σ
max
= 210 MPa and
R=1(
S
and
S5
in Table 1), these were subsequently propagated at
240 MPa, and then again at 210 MPa with R = 0 for the same reason
prior to the actual test. At the end of the pre cracking procedure for
each specimen, the crack had a length of about one millimetre. It should
also be noted that one of the tests,
S
4
was initiated and propagated
using the same temperature cycle as the actual test with the purpose of
investigating the eect of a TMF initiated starting crack as similar to
what is expected in a real component. Furthermore, the second test
S
2
was carried out with an alternative notch appearance, which however,
did not decrease the duration of the pre crack procedure.
2.2.3. Test procedure
After having reached the desired starting crack length, the crack
growth tests were conducted in both a IP and OP conguration, with a
temperature cycle between 400 and 750 °C. The total cycle time was
70 s divided into 35 s ramp up and down in temperature with a tri-
angular wave shape. The mechanical load consisted of a prescribed
stress with the same periodicity as the above cycle and a load ratio R
equal to zero. A total number of ve crack growth test were conducted
as presented in Table 1.
2.2.4. Test set up
All tests and pre crack operations were conducted in an Instron
8801 servo hydraulic test machine equipped with an induction heating
system including a cylindrical copper coil with its centre axis coinciding
with the specimen centre axis. To even out the temperature distribution
and assist cooling, compressed air ow directed towards the specimen
through three nozzles was used, positioned circumferentially with equal
angular spacing and the same distance to the specimen, as well as at the
same vertical position as the notch. All tests were controlled and
monitored using a dedicated TMF software developed by Instron, which
automatically performs a pre test procedure, involving thermal stabi-
lisation, thermal strain measurement and validation. In addition, an
elastic modulus measurement program included in the software was run
prior to the test on each specimen, measuring the elastic modulus at
dierent constant temperatures using load cycles of
±
20 MPa, hence
safely within the elastic range of the material. The strain was measured
using an Instron extensometer 2632-055 with a gauge length
L
e
of
12.5 mm and the temperature was measured using a N type thermo-
couple spot welded in the centre of the side surface of the specimen,
slightly beneath the expected crack path. After each test, it was veried
that the thermocouple did not interfere with the crack path.
Before the start of the test series, a thermal proling procedure was
conducted in order to evaluate the temperature distribution on the
specimen. For this purpose, a dummy specimen was tested to which six
dierent N type thermocouples were attached at six dierent locations;
three on each side evenly distributed along the axial centre line of the
specimen. By monitoring the temperature at each thermocouple, the
coil and air nozzles were adjusted in order to achieve a temperature
dierence less than 10 °C throughout the selected temperature cycle, as
recommended by the TMF standard [3]. Evidently, the chosen cong-
uration of the coil and air nozzles was not changed during the sub-
sequent test series.
2.2.5. Crack length measurement method
The crack length as a function of number of cycles was determined
using the compliance method in accordance with previous investiga-
tions involving the same or similar specimen geometry [29,37,38]. The
method is based on the correlation between the crack length and the
compliance or stiness of the specimen, which is acquired from nite
element simulations of the employed specimen geometry. The method
is outlined in detail in [38] and is only briey reproduced here.
Anite element model representing the specimen was set up using
Abaqus CAE version 6.12 with the nominal specimen dimensions
mentioned above, see Fig. 1a. The specimen has two symmetry planes
which can be exploited, therefore only one quarter of the specimen was
included in the model. In addition to the symmetry boundary condi-
tions, uniaxial and monotonic traction was prescribed on the cross
section situated at the grips by restricting the node displacement on this
plane to be uniform with a non zero component only in the tensile
direction using a coupling equation to a dummy node [39]. The pre-
scribed stress ramp going up to 200 MPa was then implemented by
assigning an isolated force, whose magnitude is compensated by the
cross sectional area, to the dummy node. Regarding the material
properties, they were only assigned as elastic with data originating from
a tensile test program conducted on the considered materials by Rolls
Royce plc. In total, the model consisted of roughly 6000 brick elements
employed with reduced integration and an approximate size of 200 μ
m
in the gauge length volume.
Starting from the above described model, a plane crack was added
by suppressing the symmetry condition over the surface at which the
Table 1
Information regarding the conducted crack growth tests and the associated pre
cracking procedure.
Name Test Crack initiation Notch geometry
400750 °C 25 °C
R=0 20Hz
S1
σ
ma
x
= 250 MPa R = 0
IP
σ
ma
x
= 300 MPa
S2
σ
ma
x
= 210 MPa R = 0
IP
σ
ma
x
= 300 MPa
S3
σ
ma
x
= 210 MPa R = 1
OP
σ
ma
x
= 210 MPa
S4
σ
ma
x
= 210 MPa 400750 °C
IP R = 1
σ
ma
x
= 240 MPa
S5
σ
ma
x
= 210 MPa R = 1
IP
σ
ma
x
= 210 MPa
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
3
crack extension was anticipated. Accordingly, a set of dierent models
were set up, each having a plane crack of dierent extension ranging
from 0.5 to 5 mm measured from the notch root. Around the crack tip,
the mesh was rened to a spider web conguration with decreasing
element size closer to the crack tip reaching the smallest size of 10 μ
m
.
The brick elements of the innermost ring were collapsed into wedge
elements whose crack tip nodes were tied. In order to simulate the
experiments, the stiness of each such model was then assessed as the
slope of the applied stress at the dummy node and the strain, evaluated
as the node displacement at the point where the extensometer arm is
placed divided by the gauge length. The result of this procedure is
displayed in Fig. 2a, where the stiness normalised to the zero crack
length stiness is plotted against the prescribed crack extension, in-
cluding a polynomial t.
Experimentally, the stiness was evaluated in every load cycle as
the slope of the stress and mechanical strain curve at the turning point
of maximum stress over an interval of 8095% of the maximum stress
value. This interval corresponds to a temperature interval of 680 to 730
°C over which the elastic modulus of the material varies negligibly. The
un cracked stiness used to normalised the experimental stiness value
was taken from the initial stiness measurement, performed prior to pre
cracking, see Section 2.2.4, at the average temperature corresponding
to the above stress range. Subsequently, using the polynomial expres-
sion given by the FE modelling, the stiness was converted into a crack
length and then dierentiated to obtain the crack growth rate.
2.2.6. Stress intensity factor assessment method
Regarding crack growth, a conventional procedure is to relate the
crack growth rate to the mode I stress intensity factor, here denoted as
K
I
, which is a parameter dependent on the applied stress and crack
length as
=
K
σYaπa()
Imax (2)
where
σ
max
is the nominal stress applied to the specimen and
Ya(
)
is a
geometrical factor dependent on the crack length a.
The geometrical factor Yof this particular load geometry was as-
sessed using the same set of nite element models as described above.
Based on Eq. (2), the geometrical factor was computed as
̃
̃
=Ya K
σπa
() I
max (3)
where
̃
K
I
is the stress intensity factor of the nite element model
evaluated as the average stress intensity factor along the whole crack
front,
̃
σ
max
is the applied stress of 200 MPa and ais the crack length
implemented in the model as mentioned above, Section 2.2.5.By
varying the crack length over the set of nite element models, a func-
tional dependence of Ywas acquired, see Fig. 2b, which was tted using
a polynomial expression as similar to the stiness curve.
As will be seen in this investigation, crack closure has an important
inuence on the crack growth behaviour. For this reason, the eective
stress intensity factor is computed and correlated to the crack growth
rate, with the purpose of compensating for crack closure [40]. This
parameter is obtained as
=−
K
σ πa()
Ieff max op,(4)
where
σ
max
is the nominal stress and
σ
o
p
is the crack opening stress
which can be measured experimentally, see Sections 2.3 and 2.5,Yis
the geometrical factor and athe crack length.
2.2.7. Additional thermo mechanical fatigue crack growth tests of corner
cracked specimens
In order to validate the TMF crack growth experiments, additional
tests performed using a dierent laboratory set up, but with the same
test parameters, were included in the investigation. For these tests, a
corner cracked specimen design with a rectangular cross section was
employed, see Fig. 1b. The test piece gauge length had a 7 × 7 mm
square cross section and 20 mm length, with a 0.35 mm ± 0.01 mm
single edge notch machined using a diamond edge saw blade at one
corner.
The TMF crack growth testing of this specimen type was undertaken
using two dierent heating methods. The rst set up comprised of an
Instron 100 kN servo hydraulic test frame, utilising a Zwick CUBAS
control system. A Trueheat 10 kW induction heating system was utilised
to deliver rapid heating rates through a 4 mm diameter copper tube non
uniform multi turn longitudinal eld helical coil with an approximate
external diameter of 60 mm. Rapid cooling rates were enabled through
forced air cooling using four Meech pneumatic air ampliers with their
output control through proportional solenoid valves. Temperature
feedback was provided through a 0.2 mm diameter N type thermo-
couple, spot welded at the centre of the 20 mm gauge length on an
opposing face to the starter notch.
The second set up consisted of a Instron 100 kN servo-electric test
frame together with a DARTEC control system. A second generation
radiant lamp furnace (RLF) was designed in collaboration with Severn
Thermal Solutions Ltd to generate rapid heating rates similar to that of
an induction coil. The 12 kW RLF was a standard split body design with
each half containing three horizontally mounted lamps. Three in-
dependently controllable heating zones allowed the accurate tempera-
ture control and proling, whist built in internal compressed air cooling
delivered the rapid cooling rates required by the complex TMF wave-
forms. Again temperature feedback was provided through a 0.2 mm
diameter N type thermocouple, spot welded at the centre of the 20 mm
gauge length on an opposing face to the starter notch.
A Dirlik control system interfaced together with the set ups de-
scribed above was employed to record crack length against number of
cycles readings through pulsing a 10 A signal and utilising the direct
current potential drop technique. The crack length was converted into
crack growth rate data by using the incremental polynomial method, as
described in the ASTM 647 appendixes, standard test method for
measurement of fatigue crack growth rates [41].
Similar to the single edge notched specimen described above, rig-
orous thermal proling was undertaken using six 0.2 mm diameter N
Fig. 2. Estimated dependence of the (a) normalised stiness and (b) the geometrical factor Y on the crack length from the conducted FE simulations. Note that
denition of crack length here does not include the notch depth.
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
4
Type thermocouples. These thermocouples were spot weld at the centre
gauge location on each of the four rectangular specimen faces to realise
the radial heating gradient. A further two thermocouples were spot
welded 5 mm above and below a centre thermocouple to generate axial
temperature distributions. Similarly to as described in Section 2.2.4, the
authors employed the stringent temperature limits imposed by the
governing TMF strain control standard [3].
The test parameters employed were the same as for the single edge
notched specimen, namely a triangle waveform with =
R
0over a 400
750 °C temperature range with heating and cooling rates at 10 °C/s.
However, due to the dierence in the geometry of the specimens, a peak
stress of 500 MPa were employed in order to have similar value in stress
intensity factors. Regarding pre cracking, it was performed at room
temperature using sinusoidal wave with =
R
0.
1
, starting with propa-
gation at 600 MPa and 4 Hz, then 550 MPa and 2 Hz and nally at
500 MPa and 1 Hz, in order to reach the starting crack length gently
thereby avoiding the introduction of any residual plastic strain ahead of
the crack tip. The same pre cracking procedure was used for all tested
corner cracked specimens.
2.3. Crack closure stress measurement method based on specimen stiness
Crack closure stress is vaguely dened as the nominal stress at
which the crack is closed and has been demonstrated to inuence the
TMF crack growth rate [8,28,29]. The eect of crack closure is easily
demonstrated by looking at the cyclic stress strain data in which the
stiness value signicantly changes depending on whether the crack
faces are in mechanical contact or not. Based on this feature, the crack
closure stress was determined in the present study following a sug-
gested procedure outlined by Palmert et al. [8].
Accordingly, the crack closure stress was assessed in terms of the
ratio between the stiness of an arbitrary cracked conguration Cand
the stiness of the un cracked reference conguration
C
0
, where both
stiness variables depend on the instantaneous temperature and nom-
inal stress. By this denition,
CC/
0
supposedly becomes unity when the
crack is completely closed, since the stiness is expected to be the same
then as for an un cracked specimen, while less than unity when the
crack is open. For mathematical convenience, the stiness ratio is
transformed by the following operation
=
=
DCC
CC
1/
1/|
σσ
0
0max (5)
where =
CC/|
σσ0max is the value of the stiness ratio at the instant of
maximum nominal stress. In this way, the newly derived crack closure
factor Dis zero when completely closed, and unity when completely
open. Note that this interpretation presupposes that the crack is com-
pletely open at maximum nominal stress, which however is expected to
be true for all tests conducted in this investigation. The variation in
factor Dwill clearly be inuenced by the continuous separation of the
crack faces when loaded, since the amount of partial crack closure re-
lates to the specimen stiness. Accordingly, the crack faces at the crack
tip will be the last to separate and it is therefore motivated to associate
crack closure event with the nominal stress applied when the factor Dis
very close to unity. For this reason, crack closure stress dened as the
nominal stress at which Dexceeds 0.9 in this investigation, as suggested
by Palmert et al. [8].
Experimentally, crack closure was only assessed for the single edge
notched specimen. The stiness Cwas determined at twenty stress
values regularly distributed over the loading branch of the hysteresis
loop, as the slope of the stress strain curve over an interval of ±7.5% of
the maximum stress of the cycle. The temperature variation over this
interval is 50 °C, over which the variation in elastic modulus is negli-
gibly small. The reference stiness
C
0
was taken from the initial sti-
ness measurement, performed prior to pre cracking, see Section 2.2.4,
at the average temperature corresponding to the above stress range.
2.4. Metallographic analysis of interrupted tests
A metallographic investigation was conducted on the specimens
subjected to the OP and IP condition described above, namely specimen
S
3
and
S5
in Table 1 respectively, which were interrupted at the same
crack length of 4.2 mm. The specimens were then cut in order to re-
trieve the rectangular middle section, which in turn were cut with a
cutting plane perpendicular to the crack face and parallel with the
width dimension. In this way, the crack tips were studied both at the
side surface of the specimen and on a plane in the centre of the notch,
i.e. at half the thickness. The metallographic surfaces were then ground
and polished using a standard program for nickel base superalloys.
The microscope equipment used were an optical microscope and a
scanning electron microscope (SEM). The former was a Nikon Optiphot
optical microscope and the latter a HITACHI SU-70 eld emission gun
SEM, equipped with a solid state 4 quadrant backscattered electron
detector, using 8 and 10 kV acceleration voltage and a working distance
of about 9 mm. Furthermore, energy-dispersive X-ray spectroscopy
(EDS) was performed at 20 kV at a working distance of 15 mm.
2.5. Image analysis of the crack tip region
In this investigation, the deformation eld ahead of the crack tip in
the single edge notched specimen was measured using digital image
correlation (DIC) in order to acquire a better understanding of how IP
and OP loading aect the mechanical conditions at the crack tip region.
For the same purpose, the displacement eld was further used to assess
the crack tip opening displacement.
The images were captured using a Nikon UBS29 QXC F camera
mounted at a lateral viewpoint of the specimen. The images were of a
size of 2592 × 1944 pixels and captured at a magnication of about
40×. The camera was positioned to view the notch from a lateral di-
rection and images were captured every 35 s, i.e. twice every cycle at
the instant of maximum and minimum stress. Only for a few occasions,
images were captured more frequently at a frequency of 1 Hz, namely
when the crack length was about 3 and 4.2 mm. No articially added
speckle pattern was utilised since the natural surface roughness was
enough to acquire accurate correlation in the DIC analyses. Even so,
surface oxidation was not an problem since the time between correlated
images was less than required to produce signicant changes in the
appearance of the specimen surface. Furthermore, the view of the
specimen was constantly illuminated using high power LED spots
comparable to 150 W halogen light sources in order to eliminate the
disturbance from the black body radiation of the specimen. An open
source matlab based DIC code written by Eberl et al. at the John
Hopkins University and distributed by mathworks [42], was used for
the image correlation with a subset pixel size of 31 × 31 pixels.
For all conducted DIC analyses, the reference image was selected as
the image taken at minimum load, i.e. zero applied stress, at the same
load cycle as the analysed image of interest. For this reason, the dis-
placement elds presented in this investigation are always with respect
to the deformation state at zero nominal load, which is not necessarily a
state of zero residual deformations.
Within the DIC software, the obtained displacement eld was
smoothed, using a Gaussian distribution of weights with a Gaussian
kernel size of 31 control points and three smoothing passes. The
smoothed displacement eld was then subsequently dierentiated in
order to obtain the strain eld. Furthermore, by assuming homo-
geneous temperature in the region of interest, the mechanical strain
was acquired using Eq. (1),i.e. by subtraction of the thermal strain
measured in the TMF pre test procedure.
The crack tip opening displacement (CTOD) was calculated by post
processing of the DIC analyses similar to the method presented by Vasco
Olmo et al. [43]. More precisely, CTOD was dened as the dis-
continuous jump in the eld of the displacement component of the
tensile direction (y-direction), at an x-position along the crack 10 μ
m
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
5
from the crack tip location at the instant of maximum nominal stress.
The discontinuous jump in displacement was assessed by tting a step
function, namely the error function as
=+ −
f
yaberfcyd() · [·( )]
(6)
where abc,, and dare tting constants, to the displacement component
prole in the y-direction along y-position y. From the tted parameters,
CTOD was hence dened as b2, since the total step height of the error
function is 2. This procedure was performed over a range of x-positions
along the crack, yielding a crack opening prole along the crack, from
which the value at a 10 μ
m
distance from the crack tip was determined.
Due to the diculty to accurately identify the crack tip location by
visual inspection systematically, a special criteria was employed to
assess the pixel coordinates of the crack tip in the images. Since the y-
coordinate of the crack is conveniently assessed by the above t, i.e. as
the dparameter [43], the real diculty was to assess the x-coordinate.
To this end, this location was dened as the x-position along the crack
at which the slope of the tted step function, i.e. =
=bc|
df
dy yπ
02, falls
below a critical value taken as 0.1. This criteria is well motivated since
a too low value of the slope indicates that there is no discontinuity in
the displacement eld. The particular value of 0.1 was chosen based on
agreement with manual inspections of crack tips in images.
In addition, based on the measured CTOD, the crack closure stress
was measured as the stress at which the CTOD exceeds 1 μ
m
. To in-
crease the reliability of this measurement, the average stress CTOD
curve over three subsequent cycles was considered. The reason for
taking this particular value was simply that it roughly corresponded to
the minimum detectable opening in view of the scatter over these three
cycles. The crack opening stress was only assessed at crack length of
three millimetres in all tests, which were used as a representative value
for the whole tests.
2.6. Modelling of the deformation behaviour at the crack tip
As a complement to the DIC measurement, nite element (FE)
modelling of the displacement eld around the crack tip in the single
edge notched specimen was performed. The intention with this work
was to complement the DIC measurements as well as acquire more
detailed information about the local strain ahead of the crack tip and
the crack opening.
To this end, the same specimen model as used for the compliance
method and stress intensity factor computation was employed, except
for higher degree of mesh renement at the crack tip corresponding to a
smallest element size of 5 μ
m
at the crack tip. However, rather than
restricting the behaviour to purely elastic, the material was given an
ideal plastic von Mises behaviour [39]. Hence, the eective von Mises
stress at yield, as well as the elastic modulus, was assessed as the
temperature dependent mechanical properties acquired from a series of
tensile tests at dierent temperatures performed by Rolls Royce plc.
This is a simplied approach but is motivated in view of the low rate of
hardening seen in tensile tests and the ensuing results in agreement
with experimental data as demonstrated later in Section 3.2. Moreover,
the employed temperature dependent thermal expansion coecients
were calculated from the thermal strain measured in the TMF pre test
procedure.
The boundary conditions were applied in the same way as when
performing the compliance method described in Section 2.2. Similarly,
the same set of dierent models were set up, each having a plane crack
of dierent extension ranging from 0.5 to 5 mm measured from the
notch root. However, in order to represent the cyclic history associated
with the cyclic loading in the experiments, each model was cycled
between zero and 210 MPa over three cycles. The load values were
chosen to be the same as in the experiments, i.e. specimen
S
3
and
S5
in
Table 1. Additional cycles did not have any further signicant eect
due to the ideal plastic material behaviour. Moreover, time dependent
uniform temperature elds were applied with the same cyclic variations
and magnitudes as in the experimental OP and IP cycling, i.e. between
400 °C and 750 °C.
In order to have consistency with the DIC analyses, the strain elds
acquired from the FE simulations were taken with reference to the
deformation state at zero nominal load of the same cycle, using avail-
able tools in Abaqus [39]. Furthermore, the computed thermal strain
was subtracted from this strain eld output, in agreement with Eq. (1),
in order to acquire the mechanical strain eld. A denition of CTOD
consistent with the DIC post processing was also employed, namely as
the interpolated node displacement in the y-direction at the position of
10 μ
m
from the crack tip location at the instant of maximum nominal
stress.
3. Results and discussion
3.1. Investigation of the eect of crack closure
In a wide context, crack closure has been demonstrated to aect the
fatigue crack growth rate in metallic materials [40,44]. Regrading the
present material type and load condition, the origin to crack closure has
been attributed to a number of phenomena including plasticity
[8,20,45,46], roughness [21] and oxide induced [7,12] crack closure.
However, without particular knowledge of the exact closure me-
chanism, recent studies [8,2830] have demonstrated that variations in
crack growth rate caused by altering the load ratio and temperature
cycle are accounted for by compensating the stress intensity factor
range or the cyclic J-integral with respect to crack closure, i.e. Eq. (4) in
Section 2.2. For this reason, the eect of crack closure is investigated in
the present study to see whether it may explain the distinction between
in-phase (IP) and out-of-phase (OP) cycling.
Experimental determination of crack closure is however a subject of
controversy. In this investigation, two methods were employed, namely
by direct visual observation supported by digital image correlation
(DIC) and a method based on the measurement of the compliance
variation caused by crack closure, both explained in Sections 2.5 and
2.2 respectively. For the latter method, the compliance variation over a
given load cycle is converted to an opening parameter D, which by its
denition attains zero when completely closed and unity when com-
pletely open. Accordingly, the crack opening stress
σ
o
p
can then be
dened as a critical value of D, here selected as 0.9, see Section 2.3.
Fig. 3 compares the outcome when using the two dierent methods
to assess the degree of crack closure. In Fig. 3a, the crack tip opening
displacement (CTOD) measured using DIC is plotted as a function of
stress for one OP cycle and an IP cycle which occurred at a crack length
of about 3 mm in both cases. For the same OP and IP cycle, the crack
opening parameter Dis plotted as a function of stress in Fig. 3b. In the
former gure, crack opening is interpreted as the instant when CTOD
exceeds a limit value, chosen as 1 μ
m
, and in the former, when the
opening parameter exceeds 0.9, as motivated in Sections 2.5 and 2.2
respectively.
Interestingly, it is indicated that the two methods do not yield
consistent values of the crack opening stress
σ
o
p
. While the compliance
method results in a signicant dierence in crack opening stress be-
tween OP and IP, the DIC method asserts that the values are adjacent
and underestimated. The reason for this is mainly believed to be that
the critical value of the opening parameter 0.9, is not strict enough.
However, due to limitations of accuracy of measurement of the spe-
cimen compliance, it is meaningless to select a higher value, e.g. 0.95,
since such small deviation from unity is comparable in magnitude to the
measurement error of the opening parameter. Nevertheless, the DIC
method is argued to be more reliable since the method is based on the
local deformation events at the crack tip, rather than a macroscopic
variable such as the specimen compliance.
Using the crack opening stress acquired using the DIC method,
thermo mechanical faitgue (TMF) crack growth rate is correlated with
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
6
respect to the stress intensity factor and the eective stress intensity
factor for which crack closure is compensated as described in Section
2.2.6, see Fig. 4. Surprisingly, the variations seen in the IP tests of the
single edge notched (SEN) specimen in Fig. 4a are eliminated by
compensating for crack closure. A similar observation was made in the
investigation by Palmert et al. [8] in which isothermal and IP crack
growth tests with various load ratios and durations of dwell on a single
crystal nickel base alloy, collapsed into a single curve when adjusted for
crack closure. In contrast, the variation of growth rates seen in here is
likely to originate from the dierence in the pre cracking procedure, in
view of the low amount of variation seen for the corner crack (CC)
specimen for which the pre crack procedure was not varied. Thus, it is
concluded that the pre cracking procedure, i.e. the choice of load ratio
and whether the pre crack cycling is thermo mechanical or conducted at
room temperature, does not explicitly aect the crack propagation rate.
Rather, it has an implicit eect which is entirely accounted for by the
inuence of crack closure on fatigue crack propagation.
It is noted that for test conducted with the same pre-crack proce-
dure, the crack opening stress is lower in OP than in IP, see Fig. 3a. This
is in line with a recent study of a temperature dependent yield strip
model intended for TMF crack growth [45], which has indicated that
crack closure is more pronounced in IP compared to OP. However, it is
not evident why the dierence in pre-cracking procedure has such a
signicant eect on the crack opening level. It is suggested that the
dierent pre cracking procedures, see Table 1, have caused dierent
amount of residual plastic deformation in the notch which plausibly
could aect the degree of subsequent crack closure. Unfortunately, no
detailed information about the residual strain eld is available, hence
this proposition cannot be conrmed at present.
Looking at the crack growth behaviour of both specimen types in
Fig. 4, it is seen that IP loading results in a distinctly higher crack
growth rate compared to OP loading. This is expected since in IP the
crack is exposed to the maximum load at the same instant of maximum
temperature, during which the material is less prone to withstand high
stresses and oxidation eects. Furthermore, based the results of the SEN
specimen, it is concluded that crack closure eect is of importance in
assessing the fatigue crack growth rate. However, it does not single
handedly account for the distinction between growth rates in OP and IP
loading.
3.2. Analysis of the crack tip deformation behaviour
A general aspect which may account for the dierences between in-
phase (IP) and out-of-phase (OP) load conditions, is the stress-strain
state in the region ahead of the crack tip. Some authors have for in-
stance argued that inelastic creep deformation at the crack tip may
potentially contribute to increased crack growth rates in nickel base
superalloys [7,11,12,14,15,19,20,47]. Furthermore, it is also expected
that the crack tip stress strain state aects the diusion of oxygen
[9,10,16,31],whose presence has been demonstrated to severely aect
the fatigue crack growth rate based on crack growth test under air and
vacuum conditions [917]. Thus, even in the absence of sustained loads
and an oxidising atmosphere, dierent thermo mechanical cycles may
impose dierent crack tip stress strain states due to the temperature-
dependence of the mechanical constitutive behaviour of the material.
This is an important aspect which must be claried in order to fully
distinguish IP and OP load conditions.
Using digital image correlation (DIC) technique, the above pre-
sumption is armed, see Fig. 5a and b. The gure shows the me-
chanical strain eld ahead of the crack tip at maximum applied stress of
210 MPa at one OP and one IP cycle which occurred at a crack length of
about 3 mm. Even though the dierences are small, the IP cycle is seen
to impose a higher mechanical straining in the crack tip region. This is
further supported by the conducted nite element (FE) simulations
Fig. 3. (a) Crack tip opening displacement (CTOD) and (b) opening parameter Dderived from the specimen compliance, as a function of applied stress for one IP and
one OP cycle at a crack length of about 3 mm in both cases. The test parameters were 400750 °C,
=
R
0
and =σ21
0
max MPa, and the tested specimens were
S3
and
S5
, presented in Table 1, for the OP and IP test respectively. In (a), the average, maximum and minimum value of CTOD over three subsequent load cycle.s are
displayed.
Fig. 4. Fatigue crack growth rate as a function of (a) stress-intensity factor and (b) eective stress intensity factor in the single edge notched (SEN) and corner cracked
(CC) specimen subjected to OP and IP TMF loading with 400750 °C and
=
R
0
. All conducted TMF test are included, however they are only dierentiated if the test is
OP or IP. The SEN specimen tested in IP have been subjected to dierent pre-crack procedures, as presented in Table 1. The eective stress intensity factor is
calculated according to Eq. (4) for which the stress opening stress is acquired using the DIC method, see Section 2.5.
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
7
presented in Fig. 5c and d, which manifest a similar appearance in the
mechanical strain eld, as well as a small dierence between the OP
and IP cycle. Thus, there is consistent theoretical and experimental
support to argue that IP cycling results in higher deformation at the
crack tip region compared to OP cycling.
It should be remembered that the FE model in Figs. 5c and d does
not incorporate the eect of crack closure. Thus, the FE simulations
only reect the dierence originating from the eect of a phase shift in
the temperature cycle, without the eventual inuence of crack closure.
Consequently, strain localisation at the crack tip occurs at all stress
levels in the FE model, even though it is not intuitively expected in
reality for stress levels below the crack opening stress. On the other
hand, crack closure occurs almost concurrently in the considered OP
and IP cycle, see Fig. 3a. Therefore, the dierence seen in Fig. 5a and b
is mainly associated with the eect of the temperature cycle on the
thermo mechanical constitutive behaviour.
The dierence in mechanical straining between IP and OP in ab-
sence of crack closure, is attributed to the temperature dependence of
the yield strength. Clearly, the material is at maximum temperature at
maximum stress, during which the yield strength is lower compared to
at minimum temperature. As a result, the crack tip is subjected to a
higher degree of inelastic deformation in contrast to an OP cycle, for
which inelastic deformation is better resisted thanks to the higher yield
strength at lower temperatures.
A larger crack tip deformation in the IP case is also reected in the
measurement of the crack tip opening displacement (CTOD), see
Fig. 3a, in which CTOD is shown to be larger in IP compared to OP for
the same applied stress and crack length. This is further illustrated in
Fig. 6a, in which CTOD measured by DIC is plotted as function of crack
length. Eectively, the crack tip opens up more at maximum stress in IP
compared to OP for the major part of the tests.
In Fig. 6a, CTOD acquired from the FE simulations is included as
well, which demonstrates the overestimation of the experimentally
measured values. The discrepancy is again argued to be due to the
absence of crack closure in the FE model. To compensate for this, an
alternative denition of CTOD is attempted in which CTOD is assessed
as
=−
==
δδ δ||
FE σσ FE σσ
max o
p
(7)
where
δ
FE
is the closure-free CTOD computed in the FE model,
σ
max
is
the maximum stress of the cycle and
σ
o
p
is the crack opening stress
determined using DIC. This expression is a simple empirical estimate
similar to the proposition given by Donahue et al. [48], and accounts
for the eect of crack closure on CTOD by considering the crack
opening relative to the value at the crack opening stress
σ
o
p
. Based on
this measure, improved agreement with experimentally measured va-
lues is obtained, see Fig. 6b, even though CTOD in OP is still over-
estimated, which much likely is due to the absence of hardening be-
haviour in the FE model. Nevertheless, both experiments and the FE
simulations indicate that IP loading results in higher crack tip opening
compared to OP, also when the eect of crack closure is included.
Based on the above observation, it is well motivated to suggest that
the higher crack growth rate in IP, as demonstrated in Fig. 4b, may
originate from more severe mechanical load conditions at the crack tip
region. To validate this proposition, it is argued that CTOD is a suitable
parameter to relate to crack tip deformation, since theoretically, a
Fig. 5. Mechanical strain eld in the tensile
direction measured using DIC in (a) an OP
and (b) IP cycle, as well as simulated by nite
element (FE) analysis, (c) and (d) for the OP
and IP cycle respectively. The mechanical
strain is measured at the maximum cyclic
stress with reference to the minimum cycle
stress of zero MPa at the cycle corresponding
to a crack length of 3 mm in both the ex-
periments and FE simulations. The test para-
meters were 400750 °C,
=
R
0
and
=σ21
0
max MPa, and the studied specimens
were
S3
and
S5
, presented in Table 1, for the
OP and IP test respectively. In (a) and (b), the
mechanical strain eld at maximum stress is
averaged over three subsequent cycles during
which the movement of the crack tip location,
as marked out by the circle, is negligible. To
ease the distinction between the gures, level
curves corresponding to the uniaxial yield
strain, which is about 0.5% over the tem-
perature range 400750 °C, and 0.75%, i.e.
=≅εσE/0.5
yy y
% in black and =ε0.75
yy %in
red, are included. (For interpretation of the
references to color in this gure legend, the
reader is referred to the web version of this article.)
Fig. 6. Crack tip opening displacement
(CTOD) as a function of crack length
measured by DIC and modelled using FE
and Eq. (7). In (a) the experimentally
measured CTOD is compared with CTOD
measured in the FE directly, see Section
2.6, while in (b), the measured CTOD is
compared to the estimate given by Eq. (7).
The test parameters were 400750 °C,
=
R
0
and =σ21
0
max MPa, and the tested
specimens were
S3
and
S5
, presented in
Table 1, for the OP and IP test respectively.
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
8
higher CTOD can only be accommodated through higher straining of
the region ahead of the crack tip. The argument is also supported by the
investigation by Eckmann and Schweizer [20], in which damage evo-
lution ahead of the crack is correlated with the crack mouth opening,
which is similar parameter related to how much a crack is open.
Accepting this premise, the correlation between crack growth rate
and CTOD is made as similar to previous investigations [38,4850], see
Fig. 7. Intriguingly, this correlation demonstrates the approaching of
the IP and OP curves compared to Fig. 4b, which suggests that the fa-
tigue crack growth rate in OP and IP are similar when compared at
equivalent mechanical conditions at the crack tip. In other words, the
crack growth rate seems to be dominated by the amount of crack tip
deformation and opening which is caused during a given cycle, in-
cluding the eects of crack closure and the constitutive behaviour of the
material.
The above demonstration suggests that oxidation plays a minor role
in distinguishing the mechanisms of crack growth in OP and IP loading,
in contrast to previous suggestions regarding isothermal dwell fatigue
[18] and TMF conditions [6,7]. However, as discussed in the next
section, oxygen is known to accelerate the crack growth rate at elevated
temperatures. Therefore, it is emphasised that crack growth is not in-
dependent of an oxidising atmosphere. Rather, it is proposed that the
dierence in the eect of oxygen between IP and OP loading is small for
the tested material, as further discussed in the next section.
3.3. Metallographic investigation of the crack tip region
The results of the previous sections suggest that the eective in-
phase (IP) and out of phase (OP) TMF crack growth in RR1000 is mainly
controlled by the deformation caused at the crack tip. On the other
hand, many investigators have pointed out that crack tip oxidation
clearly inuences the crack growth rate at constant elevated tempera-
ture for nickel base superalloys. In particular, it has been convincingly
demonstrated that the eect of oxygen accelerates the isothermal crack
growth rate by performing tests at dierent partial pressures of oxygen
[917], including investigations on RR1000 [11,14,16]. Furthermore,
grain boundary oxidation ahead of the crack tip has been reported in
Inconel 718 [19], as well as in RR1000 [14,22,23], under sustained
load conditions. Clearly, there is a potential inuence of material re-
lated aspects, such as the inuence of the microstructure and oxidation
at the high stressed crack tip region, which requires attention in view of
the results of the previous sections.
Fig. 8 displays the cross sectional appearance of the primary crack
tip in the centre of the specimen, i.e. middle position of the crack front,
for the OP and IP test interrupted at a crack length of roughly 4.2 mm in
both specimens. The gure also includes energy dispersive X ray
spectroscopy (EDS) results of the same area with respect the chemical
presence of oxygen. Clearly, oxygen is present in the crack as expected
in both the OP and IP specimen. However, the analysis, including the
visual inspection of the SEM images, does not indicate a signicant
distinction regarding the role of oxides between the two crack tips.
These observations are in agreement with previous investigations of
fatigue crack tip oxidation in RR1000 subjected to sustained loads of
K
Imax,equal to 20
M
Pa m
during 10 min [51,52], and of K
Δ
equal to
17 and 30
M
Pa m
during one hour [18] at 700 °C in air, for which no
oxygen were identied ahead of the crack tip. On the other hand, longer
Fig. 7. Fatigue crack growth rate in the single edge notched specimen as a
function of CTOD measured using DIC, see Section 2.5, when subjected to TMF
cycling for which the test parameters were 400750 °C,
=
R
0
and
=σ21
0
max MPa.
Fig. 8. Backscattered scanning elec-
tron microscopy (SEM) images of the
primary crack tip at a crack length of
roughly 4.2 mm in the specimen sub-
jected to (a) OP and (b) IP, as well as
EDS analyses of the same areas with
respect to chemical presence of oxygen
in (c) OP and (d) IP. The SEM images
are captured using 10 kV acceleration
voltage, 9 mm working distance and
with 10 kmagnication.
V. Norman, et al. International Journal of Fatigue 135 (2020) 105528
9
dwell times have shown to yield traces of isolated oxides ahead of the
crack tip in RR1000 [14,22,23]. In the present study, the specimens
were only subjected to temperature in the range of 700750 °C during
10 s, coincident with maximum load only for the IP tests. Thus, in view
of the tested thermo mechanical load cycle of 70 s cycle period, it is not
unexpected that the time is insucient to cause signicant crack tip
oxidation. This point clearly favours the argument that the assistance of
oxidation does not account for the dierence between IP and OP crack
growth rates in RR1000, as suggested in the previous section.
On the other hand, the above argument is opposed by the observed
dierence in crack path morphology between OP and IP crack growth.
In agreement to what is often reported for nickel base superalloys
[6,7,24], the conducted IP tests tend to manifest intergranular growth
while OP is more transgranular, see Fig. 9, which is consistent with the
general observation of increased tendency for intergranular growth
with increasing temperatures [15,2527] and dwell times [14,15,53]
under isothermal conditions. More importantly, it is also reported that
the propensity of intergranular growth morphology decreases with
decreasing partial pressure of oxygen [9,11,12,14], which indicates a
dependency of the crack growth mechanism on the presence of oxygen.
Thus, based on the crack path morphology, the inuence of oxygen on
the distinction between IP an OP crack growth in RR1000 cannot be
completely ruled out at this point.
Another observable feature in Fig. 9 is the dierence in the caused
deformation in the wake of the growing crack. Based on the achieved
electron channelling contrast [18,54], the IP case demonstrates low
amount of deformation, except for the few grains which have failed
trangranularly, see Fig. 9b, whereas the OP case indicates severe de-
formation, see Fig. 9a. Thus, it appears as if plastic deformation asso-
ciated with the crack tip is accommodated by plastic deformation
within the grain in OP crack growth, while deformation in terms of
grain boundary sliding seems more justied in IP crack growth. By
some investigators [55,56], grain boundary sliding ahead of the crack
tip has been suggested to complement environmentally assisted inter-
granular cracking of nickel base superalloys. However, it has also re-
cently been demonstrated that grain boundary sliding occurs even
under vacuum, above 700 °C when subjected to tensile and creep load
conditions [5760]. Thus, this indicates that oxygen is not necessarily
needed to cause intergranular deformation at elevated temperatures.
Consequently, it is possible that the dierence in crack path mor-
phology between OP and IP is a result of changes in the deformation
behaviour of the microstructure between 400 °C and 750 °C, regardless
of the role of oxygen.
4. Conclusions
Based on the adjacent correlations of both IP and OP crack growth
rates to the crack tip opening displacement, and the observed ab-
sence of oxygen ahead of the crack tip, it is proposed that the
dierence between IP and OP TMF crack growth rate in coarse
grained RR1000 originates from the mechanical conditions at the
crack tip region, rather than environmental eects. This is supported
by digital image correlation analyses of the mechanical strain eld
at the crack tip, which demonstrate that IP cycling leads to larger
crack tip deformation compared to OP at the same crack length and
load parameters (
=
σ
210
max MPa, =
R
0and
T
= 400750 °C).
Moreover, nite element modelling suggests that the observed dif-
ferences in crack tip deformation and opening arise from the eect
of crack closure and the temperature dependence of the constitutive
behaviour of the material.
For the tested single edge notched specimen, crack closure assessed
in terms of a crack opening stress
σ
o
p
, is highly dependent of the pre
cracking procedure, i.e. the choice of load ratio and whether the pre
crack cycling is thermo mechanical or conducted at room tem-
perature. However, the eective crack growth rate adjusted for
crack closure, is independent of pre cracking procedure.
Declaration of Competing Interest
The authors declare that they have no known competing nancial
interests or personal relationships that could have appeared to inu-
ence the work reported in this paper.
Acknowledgement
This project has received funding from the European Unions
Horizon 2020 research and innovation programme and Joint
Undertaking Clean Sky 2 under grant agreement No. 686600.
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11
... These measurements of crack closure often rely on variables that are an indirect consequence of the phenomenon itself and therefore require a set of assumptions to characterise crack closure in isolation. Besides, measurements at the small region around the crack tip (in which crack closure is relevant) are very difficult to obtain and require specialised experimental techniques, such as digital image correlation [21,22]. Although providing close-up details of the evolution of strains at the crack tip, these sophisticated techniques cannot characterise crack closure through the thickness of the specimens and are, therefore, approximations [23]. ...
... In that work, the authors also show the importance of accounting for crack closure to explain crack growth for a similar alloy as the one discussed here. Their experimental methodology has been compared to estimations of crack closure using digital image correlation techniques in [21]. For this work, the same methodology has been adopted to evaluate crack closure experimentally, which will be summarised in the following paragraphs. ...
... In recent years, a lot of studies on TMF characteristics have been reported for several types of materials, such as 9% Cr steel [14][15][16][17], nickel-base alloys [18][19][20], titanium-aluminide alloys [21,22] etc. In addition, with the rapid development and broad application of 300 series austenitic stainless steel, the TMF behaviour of 300 series austenitic stainless steel has become a hot spot in the field of high-temperature structural integrity [23][24][25]. ...
Article
Thermomechanical fatigue tests were performed on austenitic stainless steel in the temperature range of 250-400 • C. Results show that the increase in strain amplitude reduces fatigue life and enhances the impact of phase angle. DSA is only observed in the tensile direction under out-of-phase while in the compression direction under other phase angles at a low strain amplitude. The slip bands with a high dislocation density enhance fatigue resistance, and dislocation tends to form cell structures at high strain amplitudes. Moreover, oxidation damage contributes a lot to the reduction of fatigue life at high strain amplitudes.
... Its dimensions basically follow the ASTM standard [14] with a thickness is 10 mm and a width is 40 mm. For the thermo-mechanical in-phase fatigue loading conditions, the single edge notched tension (SENT) specimens were employed [15]. The specimen geometry is displayed in Fig. 1b. ...
Article
The ambient and high-temperature fatigue crack growth behaviors in C(T) and SENT specimens of Ni-based superalloy for turbine disk application were studied in a wide interval of temperatures 25–750°C using a combination a electro- and servohydraulic test systems and fractographic investigations. The fatigue, creep-fatigue interaction and thermo-mechanical in-phase fatigue (TMF IP) crack growth tests are performed under isothermal and dynamic waveforms loading conditions. The interpretation of the experimental results is given in terms of the traditional stress intensity factors and C-integral as well as new normalized cyclic fracture diagrams. It is found that there are definite temperature-sensitive regions separate for harmonic fatigue and creep-fatigue interaction loading conditions in which the crack growth rate of Ni-based alloy increases sharply. Scanning electron microscopy in longitudinal sections containing cracks revealed the mechanisms responsible for fatigue crack initiation and growth. The couple effect of temperature ranging and isothermal and dynamic waveforms loading conditions on fatigue life was discussed.
... 曹 [82] 为了计算弹塑性体缺口根部非比例加载下的应力-应变响应,将多轴 [111][112][113] [114][115][116][117] [123][124][125] 和循环裂纹张开位移 [126,127] (1-86) ...
Thesis
High temperature components, such as aero engine turbine disks, are usually subjected to the random multiaxial thermo-mechanical fatigue loading during service process. Therefore, it is of great theoretical and practical significance to investigate the damage mechanism and fatigue life prediction method for high temperature structure durability design. Based on the investigations of damage mechanism and deformation behavior of superalloys under the multiaxial thermo-mechanical fatigue loading, the variable amplitude multiaxial thermo-mechanical fatigue life prediction method of the material and structural level was proposed in this paper. Firstly, through the constant/variable amplitude uniaxial/multiaxial thermo-mechanical fatigue tests of Ni-based superalloy GH4169, the damage mechanism of the material was revealed under multiaxial thermo-mechanical fatigue loading. It is found that the tensile stress can cause creep voids between grains at high temperature, and shear stress can increase creep damage by tearing the voids. The continuous evolution process of creep voids can induce intergranular fracture, which can lead to the sharp decrease of failure life. It is also found that non-proportional additional hardening behavior can increase the stress response, which can increase the fatigue, creep and oxidation damages, and result in the failure life to be dramatically decreased. Secondly, based on the microstructure observation, the deformation behavior of the material is further investigated under multiaxial thermo-mechanical cyclic loading. Due to the temperature dependence of mechanical properties, the stress response of the material at low temperature is larger than that at high temperature, resulting in a mean stress biased towards low temperature under symmetrical strain loading. It is also found that the strengthening phases were elongated under dynamic strain aging, which can increase the pinning of dislocation motion and cause cyclic hardening. Thirdly, the path dependent ration factor and the non-proportional hardening coefficient were introduced in the kinematic hardening rule to consider the effect of non-proportional additional hardening on cyclic mechanical behavior, in which the rotation factor was used to characterize the path dependence of hardening degree. At the same time, the dynamic strain aging influence factor was introduced to consider the caused cyclic hardening behavior. Based on the above modification, a viscoplastic constitutive model considering non-proportional additional hardening and dynamic strain aging was proposed. The stress-strain data of multiaxial thermo-mechanical fatigue tests were used to verify the proposed model, and the prediction error is between -1.51% and 7.54%. Forthly, the relationship between pseudo stress increment and actual stress increment was proposed by analyzing stress-strain curves of the material and structure. Then, combined with the proposed viscoplastic constitutive model, the notch stress-strain evaluation method was proposed, which can consider the influence of temperature change on notch correction. The results of thermal-structural non-linear finite element analysis for fir tree structural specimen were used to verify the proposed method, and the prediction error ranges from -4.98% to 6.44%. Fifthly, a multiaxial thermo-mechanical cycle counting method considering temperature history was proposed to process loading history in real time. At the same time, based on the mechanism study, the multiaxial fatigue-oxidation-creep damage was characterized, especially considered the effect of non-proportional additional hardening on damage. Then, combined with the notch stress-strain evaluation method, the variable amplitude multiaxial thermo-mechanical fatigue life prediction method was proposed, which is suitable for the actual structure, and a multiaxial thermo-mechanical fatigue life prediction system was developed. The life results of constant/variable amplitude multiaxial thermo-mechanical fatigue tests were used to verify the proposed method, and the prediction errors were within a factor of 2. Finally, the turbine disk structure of an aero engine was analyzed by the proposed method. The turbine disk structure was simulated by thermal-structural non-linear finite element analysis based on secondary development, and the location of the dangerous point was determined. Then, the stress-strain history and temperature history of the dangerous point were extracted to evaluate the multiaxial fatigue-oxidation-creep damage at this point. It was found that the reason for the low life of the point may be that the larger tensile stress to cause more creep damage.
... The oxide layer can be formed on the surface of the structure exposed to the high temperature, and it can be further broken and peeled off during the deformation of the component [16][17][18][19]. It has been experimentally reported in [20,21] that the creep and oxidation mainly depend on high temperature exposure, applied stress and holding time, which means that the relative contribution of each fatigue, oxidation and creep can be changed with different service conditions [22][23][24]. In terms of the deformation behavior, the rate dependent viscous response can be activated by the creep in addition to the plastic deformation, resulting in stress relaxation during the stable operation phase at high temperature [25,26]. ...
Article
In this paper, a new life assessment framework is proposed based on the elastic-viscoplastic modeling and the damage behavior for the structural component under multiaxial non-proportional loading at high temperature. The viscoplastic constitutive model with the ability to capture the non-proportional hardening effect is used to obtain the stress-strain fields, in which a new method based on the rotation of strain axis is proposed to evaluate the notch rotation factor. The damage model, which can comprehensively capture the multiaxial fatigue-oxidation-creep behaviors, is used to assess the failure life. In addition, the proposed framework is evaluated by the life results under proportional and non-proportional fatigue loadings at 650°C, and the errors are found to be within a factor of 2.
Article
The presented methodology in this study is addressed to in-phase (IP) and out-of-phase (OOP) loading cycles in stationary and transient thermo-mechanical fields. The subject of the numerical and experimental study is a single edge notch tension (SENT) specimen produced from a high-temperature nickel-based alloy ХН73М. In order to determination a local thermo-mechanical stress-strain rate and displacement fields a new algorithm for the multi-physics numerical calculations developed and implemented incorporates Maxwell 3D, Fluent and Transient Structural modules of ANSYS 2021R1. The employment of proposed algorithm to represent the cyclic history associated with the TMF conditions in the experiments, multi-physics finite element (FE) modelling of the stress, strain and displacement fields in the SENT specimen was performed. Additionally, time dependent non-uniform temperature fields were determined with the same cyclic variations and magnitudes as in the experimental OOP and IP cycling. As a complement to the FEM computations, the infra-red thermography temperature distribution measurements was implemented for the TMF state in the experiments in the SENT specimen. The comparison multi-physics FE-analysis and direct measurements shown in the present study is intended to contribute to a better understanding of the different mechanisms driving TMF crack growth and the address the outstanding questions associated with basic methodology.
Article
The advanced aluminum–lithium alloy is used in aircrafts fuselage. Based on the combination of fatigue test and digital image correlation technique, the influence of pre-corrosion and in situ corrosion damage on the fatigue performance of 2198-T8 aluminum–lithium alloy was investigated. The integrated evolution process of fatigue crack and strain distribution fields of two types of the damaged sheets were captured and evaluated by the digital image correlation technique. The results reveal a declining tendency of in situ corrosion fatigue life with the rise of solution temperature, as well as the decrease of flow rate. But, at increasing the NaCl concentration, the fatigue life tends to decrease first and then increase. The observed fatigue behavior and related phenomena are directly associated with fracture morphology such as micro-cracks and corrosion pits. The analysis indicates a competition mechanism between fatigue and corrosion, the fatigue damage dominates the failure process under lower NaCl concentration on the contrary to the higher one that the corrosion damage is the dominant factor. Considering the effect of flow rate on the surface adhesion, the crack tends to initiate at the position of low flow rate. The simulation on the flow field presents an attractive similarity with experimental results.
Article
Investigating fatigue crack growth behavior of materials is crucial to the life design and safety evaluation of engineering structures. During the practical service condition, the temperature keeps changing, which cannot be studied by the traditional fatigue crack growth test method at constant temperature. In this study, we focus on constructing a new thermomechanical fatigue (TMF) crack propagation testing method, developing a thermal deformation compensation method, and proposing an equivalent compliance method suitable for variable temperature conditions based on ASTM E647 standard to measure the crack length. Furthermore, the load‐ and strain‐controlled TMF tests under different phase angles are carried out to prove the validity of the new method. A temperature compensation method for the variable temperature test is proposed. A modified compliance method for crack length measurement is developed. The thermomechanical fatigue (TMF) crack propagation testing method was standardized. Only the stress intensity factor range ΔK cannot be used to characterize the fatigue crack growth rate.
Article
In this article, machine learning is used to predict lifetime under isothermal low-cycle fatigue and thermo-mechanical fatigue loading, both of which represent the most complex loadings that couple creep, fatigue and oxidation damage. A uniaxial fatigue and fatigue-creep dataset, which was obtained for temperatures of between 300∘C and 600∘C for a low-alloy martensitic steel, is utilized in this study. Two different machine learning based approaches to lifetime prediction are demonstrated. The first approach is based only on a shallow neural network, whereas the second approach is proposed as a combination of a sequence learning based model - either long short-term memory network or gated recurrent unit - with the shallow neural network. A good correlation between the experiment and the prediction suggests that lifetime under complex thermo-mechanical loading can be reasonably predicted via the proposed machine learning based damage models.
Article
The exhaust nozzle, made of titanium, is the part of a jet engine where the final expansion of the hot gas from the turbine occurs and where the speed of the exhaust gas is further increased to create thrust. During the work, it is exposed to elevated temperatures and compressive and hoop stresses, which makes the cracks’ occurrence in the exhaust nozzle’s inner sleeve unavoidable, making repairs during maintenance necessary. In this study, crack growth in the repaired inner sleeve was analyzed. The aim of the study was to evaluate the fatigue life of the damaged inner sleeve when a new method of repair is applied and to compare obtained number of cycles with the number observed in the maintenance workshop after the old method of repair was used. Developing the numerical model and conducting simulations using the extended finite element method (XFEM) and finite element method (FEM), it was concluded that a new type of repair should be used to provide longer fatigue life of the damaged exhaust nozzle.
Article
Full-text available
Crack growth mechanisms for Alloy 617 at 800 °C were investigated in air with specific emphasis on the transition from cycle-dependent to time-dependent crack growth mechanisms in the creep-fatigue regime. Crack growth studies were conducted using compact tension samples, a load ratio of 0.5, and triangular 5 Hz, 0.33 Hz, and 0.05 Hz waveforms, a trapezoidal 0.05 Hz waveform with 17 s hold time, and sustained loading. Fatigue crack growth rates were relatively insensitive to changes in frequency and hold times in air up to ∆K ≈ 11.5 MPa√m for R = 0.5, i.e, Kmax = 23 MPa√m. Above this threshold, the onset of time dependent crack growth was observed via a creep void nucleation and coalescence mechanism for triangular and trapezoidal waveforms with a loading frequency of 0.05 Hz, and during sustained loading. An estimate of the threshold for stress assisted grain boundary oxidation (SAGBO) crack growth was calculated to be 23 MPa√m, and oxidized grain boundaries observed near the crack tip were mostly uncracked, suggesting the SAGBO threshold was not reached before the onset of the void nucleation mechanism. A comparison of results across all available studies suggests that a threshold-based transition from cycle- to time-dependent crack growth at 800 °C likely exists. However, the stress intensity factor does not maintain similitude to accurately define a threshold across studies. Thus, gaining an understanding of the crack tip stress states that define the various time dependent mechanisms should be considered in future work.
Article
Full-text available
The loss of ductility in the high strength polycrystalline superalloy 720Li is studied in air between room temperature and 1000 C. Tensile ductility is influenced profoundly by the environment, leading to a pronounced minimum at 750 C. A relationship between tensile ductility and oxidation kinetics is identified. The physical factors responsible for the ductility dip are established using energy-dispersive X-ray spectroscopy, nanoscale secondary ion mass spectrometry and the analysis of electron back-scatter diffraction patterns. Embrittlement results from internal intergranular oxidation along the g-grain boundaries, and in particular, at incoherent interfaces of the primary g 0 precipitates with the matrix phase. These fail under local microstresses arising from the accumulation of dislocations during slip-assisted grain boundary sliding. Above 850 C, ductility is restored because the accumulation of dislo-cations at grain boundaries is no longer prevalent.
Chapter
Volume 19 is a resource for basic concepts, alloy property data, and the testing and analysis methods used to characterize fatigue and fracture behavior of structural materials. Contents include fatigue mechanisms, crack growth and testing; fatigue strength prediction and analysis; fracture mechanics, damage tolerance, and life assessment; environmental effects; and fatigue and fracture resistance of ferrous, nonferrous, and nonmetallic structural materials. Statistical aspects of fatigue data, the planning and evaluation of fatigue tests, and the characterization of fatigue mechanisms and crack growth are also covered. Practical applications and examples of fracture control in weldments, process piping, aircraft systems, and high-temperature crack growth and thermos-mechanical fatigue are also included. For information on the print version of Volume 19, ISBN 978-0-87170-385-9, follow this link.
Article
The fatigue crack growth (FCG) experiments for Ni-based powder metallurgy (PM) FGH97 superalloy were performed from RT to 800 °C in air. It has been found that the FCG life decreases in an accelerated manner with an increase in temperature in the service temperature range, and a sharp drop in FCG life was noticed at the inflection point temperature (Tc) of about 800 °C. The fractographic and microstructural analyses were carried out to investigate the primary reason for the phenomenon of observed sharp drop. The obtained results indicate that the fracture transforms from transgranular to intergranular mode during the crack propagation under elevated temperature, and the transition point of fracture mode (ΔKT) also declines rapidly with an increase in temperature. At 800 °C, ΔKT appears even from the crack starts to propagate, which is closely related to the significant decline of FCG life. Combined with the calculated apparent activation energies of FCG, it can be inferred that the sharp drop in FCG life is primarily attributed to the dynamic embrittlement induced weakening of grain boundary, which dominates in the intergranular FCG stage at 800 °C. Further, the evolution of the fracture mechanism governing the FCG process under the conditions of different temperatures and stress intensity factor range (ΔK) has been discussed. With an increase in temperature in the service temperature range, the dominant mechanism of the intergranular fractures transforms from stress assisted grain boundary oxidation to dynamic embrittlement, which results in the sharp decline of FCG life at Tc.
Article
Thermomechanical fatigue crack growth in a single crystal nickel base superalloy was studied. Tests were performed on single edge notched specimens, using in phase and out of phase thermomechanical fatigue cycling with temperature ranges of 100–750 °C and 100–850 °C and hold times at maximum temperature ranging from 10 s to 6 h. Isothermal testing at 100 °C, 750 °C and 850 °C was also performed using the same test setup. A compliance-based method is proposed to experimentally evaluate the crack opening stress and thereby estimate the effective stress intensity factor range ΔKeff for both isothermal and nonisothermal conditions. For in phase thermomechanical fatigue, the crack growth rate is increased if a hold time is applied at the maximum temperature. By using the compliance-based crack opening evaluation, this increase in crack growth rate was explained by an increase in the effective stress intensity factor range which accelerated the cycle dependent crack growth. No significant difference in crack growth rate vs ΔKeff was observed between in phase thermomechanical fatigue tests and isothermal tests at the maximum temperature. For out of phase thermomechanical fatigue, the crack growth rate was insensitive to the maximum temperature and also to the length of hold time at maximum temperature. The crack growth rate vs ΔKeff during out of phase thermomechanical fatigue was significantly higher than during isothermal fatigue at the minimum temperature, even though the advancement of the crack presumably occurs at the same temperature. Dissolution of γ′ precipitates and recrystallization at the crack tip during out of phase thermomechanical fatigue is suggested as a likely explanation for this difference in crack growth rate.
Article
Fatigue crack propagation tests under both isothermal and non-isothermal thermomechanical fatigue conditions have been performed on wrought Haynes 230, a ductile combustor material. A number of specimens were thermally aged by pre-straining and subsequent furnace exposure for 3000 h at 600 °C. The tests were performed both under load and strain control, between room temperature and 600 °C. The thermally aged notched specimens show a decrease in the crack initiation life, similar to results previously reported for smooth test specimens at room temperature. For the crack growth rates, the effects of thermal ageing were less pronounced than for crack initiation. Further, the tests have been simulated using the finite element method to calculate the crack driving force, where the plasticity induced crack closure is handled with a full history description. A temperature dependent linear kinematic hardening plasticity law has been adopted for describing the material behaviour between room temperature and 600 °C. A post-processing tool was used in which the plasticity induced crack opening level was calculated, followed by a calculation of the effective ΔJ range for each crack length. The adopted procedure yields good correlation between the different tests, under both isothermal and non-isothermal conditions.
Article
The complete fatigue process involving the growth of microstructurally small fatigue cracks prior to macrocrack initiation and the subsequent large crack propagation in notched compacted graphite iron, EN-GJV-400, specimens subjected to thermo-mechanical fatigue has been investigated. It is shown that microcracks are initiated at graphite tips within an extended volume at the notch which eventually leads to an abrupt microcrack coalescence event. As a macrocrack is generated in this way, the crack growth switches to conventional characteristics which is assessed in terms of elasto-plastic fracture mechanics parameters. Consequently, two important implications regarding lifetime assessment are identified; possible underestimation due to (i) how the stress is evaluated in view of the spacial distribution of microcracking and (ii) the crack retardation effect associated with the crack growth transition.
Article
In the current work an experimental study of the crack tip opening displacement (CTOD) is performed to evaluate the ability of this parameter to characterise fatigue crack growth. A methodology is developed to measure and to analyse the CTOD from experimental data. The vertical displacements measured by implementing Digital Image Correlation on growing fatigue cracks are used to measure the CTOD. Fatigue tests at R ratios of 0.1 and 0.6 were conducted on compact-tension specimens manufactured from commercially pure titanium. A sensitivity analysis was performed to explore the effect of the position selected behind the crack tip for the CTOD measurement. The analysis of a full loading cycle allowed identifying the elastic and plastic components of the CTOD. The plastic CTOD was found to be directly related to the plastic deformation at the crack tip. Moreover, a linear relationship between da/dN and the plastic CTOD for both tests was observed. Results show that the CTOD can be used as a viable alternative to ΔK in characterising fatigue crack propagation because the parameter considers fatigue threshold and crack shielding in an intrinsic way. This work is intended to contribute to a better understanding of the different mechanisms driving fatigue crack growth and the address the outstanding controversy associated with plasticity-induced fatigue crack closure.
Article
Effects of oxygen-related damage (i.e. oxidation and dynamic embrittlement) on fatigue crack propagation behavior in an advanced disc alloy have been assessed in air and vacuum under dwell-fatigue conditions at 725 °C. The enhanced fatigue crack propagation is closely related to oxygen-related damage at/ahead of the crack tip, which is determined by the testing environment, the dwell period and the crack propagation rate itself based on two dimensional (2D) observation of the crack tip in an optical microscope and scanning electron microscope. X-ray computed tomography has also been employed to examine the differences between three dimension (3D) crack morphology in air and vacuum conditions, and the crack features have been quantified in terms of crack opening displacements, secondary cracks and uncracked bridging ligaments. The results show that the fatigue crack propagation rate is related to the amount of secondary cracks, and the crack length increment in a loading cycle is related to the breaking/cracking of the uncracked bridging ligaments within the discontinuous cracking zone ahead of the crack tip as oxygen-related damage preferentially occurs in these highly deformed regions. By combination of 3D X-ray computed tomography and traditional 2D observation, a deeper understanding is provided of the mechanisms of oxygen-enhanced fatigue crack propagation behavior.
Article
The plastic crack tip opening displacement (CTODp) is considered to replace ΔK in the study of fatigue crack propagation. The cyclic plastic deformation of the 7050-T6 aluminium alloy was determined experimentally and modeled analytically. Then, a three-dimensional elastic–plastic numerical model which included crack growth was developed in order to predict the plastic CTOD for different loading conditions. In a parallel study, crack growth rates were determined experimentally in M(T) specimens with a thickness of 6 mm. A relation was subsequently established between da/dN and plastic CTOD for the 7050-T6 aluminium alloy, independent of stress ratio, showing that the CTOD is a viable alternative to ΔK in the analysis of fatigue crack propagation.