1 Copyright © 2014 by ASME
THERMAL AND MECHANICAL FATIGUE LOADING – MECHANISMS OF CRACK INITIATION AND CRACK GROWTH
Stefan Utz Institute for Materials Testing, Materials Science and Strength of Materials (IMWF) University of Stuttgart
Pfaffenwaldring 32, 70569 Stuttgart, Germany
Ewa Soppa, Christopher Kohler, Xaver Schuler, Horst Silcher
Materials Testing Institute (MPA) University of Stuttgart Pfaffenwaldring 32, 70569 Stuttgart, Germany
ABSTRACT The present contribution is focused on the experimental
investigations and numerical simulations of the deformation
behaviour and crack development in the austenitic stainless
steel X6CrNiNb18-10 (AISI–347) under thermal and
mechanical cyclic loading in HCF and LCF regimes. The main
objective of this research is the understanding of the basic
mechanisms of fatigue damage and development of simulation
methods, which can be applied further in safety evaluations of
nuclear power plant components. In this context the modelling
of crack initiation and crack growth inside the material structure
induced by varying thermal or mechanical loads are of
particular interest. The mechanisms of crack initiation depend
among other things on the art of loading, microstructure,
material properties and temperature. The Nb-stabilized
austenitic stainless steel in the solution-annealed condition was
chosen for the investigations. Experiments with two kinds of
cyclic loading – pure thermal and pure mechanical – were
carried out and simulated.
The fatigue behaviour of the steel X6CrNiNb18-10 under
thermal loading was studied within the framework of the joint
research project [1]. Interrupted thermal cyclic tests in the
temperature range of 150 °C to 300 °C combined with non-
destructive residual stress measurements (XRD) and various
microscopic investigations, e.g. in SEM, were used to study the
effects of thermal cyclic loading on the material. This thermal
cyclic loading leads to thermal induced stresses and strains. As
a result intrusions and extrusions appear inside the grains (at the
surface), at which micro-cracks arise and evolve to a dominant
crack. Finally, these micro-cracks cause continuous and
significant decrease of residual stresses.
The fatigue behaviour of the steel X6CrNiNb18-10 under
mechanical loading at room temperature was studied in the
framework of the research project [2]. With a combination of
interrupted LCF tests and EBSD measurements the deformation
induced transformation of a fcc austenite into a bcc ’-
martensite was observed in different stages of the specimen
lifetime. The plastic zones develop at the crack tips, in which
stress and strain amplitudes are much higher than the nominal
loading, and enable martensitic transformation in the
surrounding of the crack tip. The consequence of this is that
cracks grow in the “martensitic tunnels”. The short and long
crack growth behaviours of the steel X6CrNiNb18-10 under
mechanical loading at room temperature and T = 288 °C were
studied for different loading parameters. Moreover, the R-ratio
was modified in order to study the effect of crack closure at the
crack tip for long cracks.
Several FE-models of specimens with different geometries
and microstructures were created and cyclically loaded
according to the experimental boundary conditions. A plastic
constitutive law based on a Chaboche type model was
implemented as a user subroutine in the FE software ABAQUS.
The corresponding material parameters were identified using
uniaxial LCF tests of X6CrNiNb18-10 with different strain
amplitudes and at different temperatures. These calculations
aimed in the estimation of stress and strain distributions in the
critical areas in which the crack initiation was expected.
INTRODUCTION A large number of components in nuclear power plants are
exposed to cyclic loading for which fatigue failure must be
excluded. The evidence of sufficient fatigue safety margins is
based on fatigue analyses. The determination of the fatigue
lifetime rests on the assumption that certain damage events
accumulate in a linear manner over time. The damage state,
therefore, is described indirectly as a function of equivalent
stress or strain amplitude versus crack initiation curve. This
Proceedings of the ASME 2014 Pressure Vessels & Piping Conference PVP2014
July 20-24, 2014, Anaheim, California, USA
PVP2014-28411
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2 Copyright © 2014 by ASME
solution is often a pragmatic approximation for engineering
applications, but it does not explain the mechanisms underlying
fatigue and crack formation on the microscopic level.
Especially the role of the materials microstructure in the
fatigue process remains in this approach unexplained. The
knowledge of these correlations is, however, necessary when
setting up of the optimal microstructure ensuring longer lifetime
is intended.
NOMENCLATURE 3D three-dimensional
a0 notch length
da crack length increment
B thickness of the miniature C(T) specimen
BMBF German Federal Ministry of Education & Research
BMWi German Federal Ministry of Economics & Technology
C fitting parameter (Paris law)
C tensor of the elastic moduli
C(T) compact tension
EBSD electron backscatter diffraction
f flow rule
fcc face centered cubic
FE finite element
FIB focused ion beam
HCF high cycle fatigue
J2 second invariant
K, K stress intensity factor
LCF low cycle fatigue
n fitting parameter (Paris law)
dN short cycle interval
Nb niobium
NbC niobium carbides
p accumulated plastic strain
R isotropic hardening; load ratio
R strain ratio
RT room temperature
SEM scanning electron microscope
TEM transmission electron microscope
UMAT user-defined material model
W width of the miniature C(T) specimen
X kinematic hardening
XRD x-ray diffraction
th thermal expansion coefficient
total strain
el elastic strain
pl
plastic strain
th
thermal strain
stress tensor
MATERIAL Nb-stabilized austenitic stainless steel X6CrNiNb18-10
with chemical composition (balance Fe) as presented in Table 1
was used in this work.
Table 1: Chemical composition of the X6CrNiNb18-10 steel (in weight %, from melt analysis) [3,4]. 1st line: material used for thermal loading; 2nd line: material used for mechanical loading.
C Si Mn P S Cr Ni Nb Ta
0.023 0.340 1.860 0.019 0.002 18.10 10.10 0.450 ---
0.043 0.410 1.900 0.019 0.002 17.15 10.30 0.660 0.008
The material used for fatigue tests under thermal loading
was forged, solution-annealed at T = 1020 °C for 150 minutes
and water-quenched to room temperature [3]. Due to a strong
microstructural inhomogeneity (hardness, grain size) in a rod
cross-section – from the surface area to the centre – the rod was
solution-annealed again at T = 1030 °C for 90 minutes and
quenched with liquid nitrogen.
The material used for fatigue tests under mechanical
loading was manufactured by melting metallurgy, casting and
forming process with subsequent solution heat treatment at
T = 1050 °C for 10 minutes and was water-quenched to room
temperature [4].
The resulting microstructures consist in both materials of
austenitic grains with several twins, some isolated δ-ferrite
grains and finely distributed NbC located along the grain
boundaries, dislocations and lattice imperfections inside the
grains, see Fig. 1.
(a) (b)
Fig. 1: Microstructure of the X6CrNiNb18-10 steel: (a) material used
for thermal loading; (b) material used for mechanical loading.
The growth of large NbC often results in NbC depletion at
the grain boundaries. Two classes of NbC size distributions,
with the average values of:
fine fraction – 45 nm and 33 nm
coarse fraction – 228 nm and 410 nm respectively,
were found in an undeformed state of X6CrNiNb18-10 steel
using replica and thin foils.
MECHANICAL CYCLING LOADING Unnotched cylindrical specimens with polished lateral
surfaces were uniaxially loaded (LCF) in air at room
temperature with different total strain amplitudes between
0.25 % and 1.5 %, R = 1 with a strain rate of 0.1 % s-1
until
initiation of macroscopic crack of approximately 1 mm (visible
with the naked eye) or stress reduction of 10 %, see Fig. 2.
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3 Copyright © 2014 by ASME
Fig. 2: Stress curves (min., max.) recorded during the LCF-tests for
total strain amplitudes between 0.25 % and 1.5 %.
The total length of the specimen was adapted to the
vacuum chamber in SEM and allowed a non-destructive
microscopic analysis in the breaks between two loadings steps.
For this purpose two narrow flat bands (3 mm 20 mm),
symmetrically placed on the specimen lateral surface, were
grounded and electrolytically polished before loading. An
interrupted LCF test [5] combined with the EBSD technique
was performed on a cylindrical specimen in air at room
temperature with a total strain amplitude of 1.5 % and R = 1.
This relatively high loading amplitude was chosen in order to
ensure a moderate number of loading cycles necessary to cause
specimen fracture.
By EBSD the distribution of grain orientations on the
specimen surface and identification of deformation induced ’-
martensite in the austenitic matrix were performed. The
resolution of the standard scans was 1 µm, additional scans of
interesting details were recorded with higher resolution.
In addition to LCF tests, miniature C(T) specimens with the
thickness B = 3.2 mm, the width W = 16 mm and a half round
notch with the length of a0 = 3.84 mm (see Fig. 3a;
DIN EN ISO 12737) were manufactured and cyclically loaded
in HCF regime in air at room temperature. The dimensions of
these specimens allowed a non-destructive investigation in SEM
and a new ex situ loading after break. The notch area of the
C(T) specimen, in which the crack initiation was expected, was
observed by light microscope and recorded at different stages of
the specimen lifetime during the test. The crack length
increments da after short cycle intervals dN were measured with
a special software and evaluated as a function of the crack
length and location of microstructural barriers (grain
boundaries, grain orientation) for different loading parameters,
see Fig. 3.
The EBSD measurements were performed on specimens
before loading and in the same areas after loading at different
stages of the specimen lifetime. The EBSD scans showed
microstructural changes leading to martensitic transformation
and initiation of fatigue cracks.
(a) (b)
(c) (d)
Fig. 3: (a) Miniature C(T) specimen; (b, c) Crack growth in the
notch; (d) Crack growth velocity as a function of the crack length measured in the miniature C(T) specimen of X6CrNiNb18-10 under
cyclic loading with the upper force of 900 N, R = 0.1.
In cylindrical specimens the crack formation was observed
in the interface between austenite and ’-martensite or in fully
martensitic areas. Martensitic transformation took place there
before the first crack emerges [5]. In C(T) specimens the crack
path is enforced through the specimen geometry.
As soon as the crack emerges, martensitic transformation at
the crack tip takes place. This permanent phase transformation
at the crack tip forms a kind of "martensitic tunnel" in which the
crack grows, see Fig. 4. The thickness of the martensitic layer
depends on the grain orientation and can be locally very thin
and thereby difficult to detect.
(a) grain orientations in
austenite
(b) phase distribution:
green - austenite, red - ’-
martensite
Fig. 4: Crack propagation in the “martensitic tunnel” in the
miniature C(T) specimen loaded with an upper force of 900 N, R = 0.1: (a) distribution of the grain orientation in austenite; (b) phase distribution: green - austenite, red - ’-martensite.
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LONG CRACKS Several tests were carried out with standard C(T)
specimens to determine the crack growth behavior of long
cracks and the threshold value, where no further crack growth
occurs. The load ratio R = min load / max load was varied from
0.1 to 0.7. As an example for all tests, the specimens of
X6CrNiNb18-10 loaded with R = 0.1 is shown in Fig. 5.
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1 10 100 1000
da/d
N [
mm
/LW
]
K [MPam]
Paris-ParametersC = 7*10-10
n = 3,7
Erdogan-Ratw.-ParametersC* = 2,5*10-6, n* = 3,0Kc = 250 MPamK0 = 3,5 MPam
ASME XI, airR=0,1C = 2,43 *10-9
n = 3,3
Fig. 5: Crack growth behavior of a C(T) specimen of
X6CrNiNb18-10, R = 0.1, air condition, room temperature.
The experimental K-values vary between 5 MPa m and
50 MPa m . The approximation according to Paris law [6] of
the linear data range
da / dN = C∙Kn (1)
leads to fitting parameters of 7∙10-10
for C an 3.7 for n. The
parameters from ASME XI [7] for austenitic materials are
2.43*10-9
for C and 3.3 for n, so that both curves intersect each
other. For higher K-values the ASME XI-equation predicts
lower crack growth rates then experimentally determined.
Another approximation was carried out using the Erdogan-
Ratwami-equation [8]:
da/dN = C∙(K-K0) / ((1-R)KC –K) (2)
This equation fits the whole range of cyclic crack growth
between threshold value and collapse. The fitting is quite good
in the linear range of cyclic crack growth, but not conservative
in the range of low K-values. For K-values higher than
50 MPa m no crack growth data could be determined
because of the specimen’s plastification. These results can be
regarded as valid for all other R-ratios investigated.
THERMAL CYCLIC LOADING To study the effects of thermal cyclic loading on the
material, interrupted thermal cyclic tests in the temperature
range of ~160 °C to 300 °C were used. For this purpose a
special type of specimen (Fig. 6) was developed to realize high
frequent (HCF) thermal cyclic loading. These specimens had a
concave shape (so-called “calotte”) that results in a minimum
wall thickness of 1 mm. The concave shape was machined on
both sides with high precision by the use of die sinking. The
dimension of these specimens enabled various microscopic
investigations, e.g. in SEM, and non-destructive residual stress
measurements (XRD) on a polished specimen surface.
30
Fig. 6: Specimen with a concave shape (“calotte”) on both sides.
The parameters of the thermal cyclic tests performed at the
Materials Testing Institute (MPA) University of Stuttgart are
shown in Table 2.
Table 2: Parameters of the thermal cyclic tests.
temperature
range
temperature
difference
heating
rate
cooling
rate
~ 160 °C to 300 °C ~ 140 K ~ 90 K/s ~ 75 K/s
~ 210 °C to 270 °C ~ 70 K ~ 60 K/s ~ 75 K/s
Well-defined and repeatable stress and strain conditions as
well as temperature states were realized with the test device
shown in Fig. 7.
(a)
(b)
Fig. 7: Test device for thermal cyclic loading:
(a) schematic figure; (b) real test device.
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The specimen (1) was heated inductively (2) and cooled by
pressurized air (3) on the same side. No additional external
mechanical load was applied during the thermal cyclic tests.
Two pyrometers (4a) and (4b) measured the local surface
temperature continuously on both sides in the center of the
specimen. These temperatures were almost identical because of
the small wall thickness in the center of the specimen.
The measured surface temperature of the thermal cyclic test
in the range of ~160 °C to 300 °C and also in the range of
~210 °C to 270 °C is shown for the first 500 seconds in Fig. 8a
and in detail in Fig. 8b.
After heating-up from room temperature to maximum
temperature (270 °C and 300 °C, respectively) with reduced
generator power, the temperature holding stage (120 seconds)
and afterwards the thermal cycling (heating with full generator
power and alternating cooling) are readily identifiable.
(a)
0 100 200 300 400 500
0
50
100
150
200
250
300
350
150 - 300 °C
200 - 270 °C
tem
pe
ratu
re / °
C
time / s
(b)
250 255 260 265 270
0
50
100
150
200
250
300
350
150 - 300 °C
200 - 270 °C
tem
pe
ratu
re / °
C
time / s
Fig. 8: Measured surface temperatures (pyrometer) in the center of
the specimen: (a) overview; (b) detail while thermal cycling.
The temperature profile during thermal cyclic loading on
the specimen surface was studied by the use of additional
temperature measurements with an infrared camera. The time-
dependent and also the position-dependent variations of the
temperature profile are illustrated in Fig. 9.
It is obvious that there exists an almost uniform radial
temperature profile concentrically around the center of the
spherical cap. This behavior was observed during heating-up
(Fig. 9a) as well as at the cooling valley (Fig. 9b).
Extensive preliminary tests with a thermocouple were
performed at different temperatures to calibrate the non-contact
temperature measurements (infrared camera and pyrometer) on
the metallic shiny surface.
100°C
300°C
200°C
(a) (b)
(c) (d)
Fig. 9: Surface temperatures measured at certain points in time
(thermal cycling in the range of ~160 °C to 300 °C): temperature profile (a) while heating up for the first time; (b) at the beginning of the temperature holding stage; (c) at the end of the
temperature holding stage; (d) at the cooling valley.
The resulting strains at the specimen surface were
measured additionally with the non-contact and material
independent measuring system ARAMIS [9]. This optical
measuring system consists of a digital image correlation
technique. ARAMIS can be used for measuring 2D and 3D
deformations and strains at components and specimens. The
measurement takes place with a high time and position
resolution and also with a very high precision.
The strains on the surface measured with ARAMIS for
thermal cycling in the range of ~160 °C to 300 °C are presented
in Fig. 10.
Fig. 10: Strains measured with ARAMIS for thermal cycling in the range of ~160 °C to 300 °C.
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The measured strain in the x-direction (horizontal) over the
time is shown in the upper left. In the upper right the measured
strain in the x-direction (horizontal) is presented over a
fictitious horizontal (blue) and vertical (red) cut through the
center of the specimen at the cooling valley (minimum surface
temperature). The minimum of the measured strain is in the
center of the specimen, too. In the lower the left and right
camera snapshot of the optical measurement system ARAMIS
was superimposed with the color scale of the measured strain in
the x-direction (horizontal). Areas with no calculated results are
turned off.
The results of the measured strains in the x-direction
(horizontal) and y-direction (vertical) over the time in the center
of the spherical cap are presented in Fig. 11 with the measured
temperature.
The measured strains in horizontal (x) and vertical (y)
directions increase throughout the first heating up to maximum
temperature (red). During the thermal cycling, the measured
strains alternate with a small phase shift relating to the
measured temperature.
(a)
(b)
Fig. 11: Strains measured with the optical 3D deformation analysis system ARAMIS compared with measured surface temperature in
the center of the spherical cap: (a) overview; (b) detail while thermal cycling.
MICROSTRUCTURE AFTER THERMAL CYCLING The effects of thermal cyclic loading on the material were
studied by the use of interrupted thermal cyclic tests in the
temperature range of ~160 °C to 300 °C and ~210 °C to 270 °C
respectively. For this purpose, various microscopic investi-
gations, e.g. in SEM, and XRD measurements were carried out.
The surface-microstructure in the center of the spherical
cap at initial conditions and after thermal cyclic loading in the
range of ~160 °C to 300 °C is presented in Fig. 12. Significant
surface modifications and several microcracks were detected.
As a remark, the hardness indentations were used as position
marks ensuring to analyze the same position at all times and did
not affect the investigation results.
(a) (b)
Fig. 12: Surface-microstructure: (a) initial conditions;
(b) after thermal cyclic loading of 12’500 cycles (~160 °C to 300 °C).
Parallel line patterns with different orientation from grain
to grain did arise inside several grains. Figure 13 illustrates that
these parallel line patterns are slip bands with characteristic
extrusions and intrusions.
(a) (b)
Fig. 13: Surface-microstructure after 12’500 thermal cyclic loadings
between ~160 °C to 300 °C: (a) parallel line patterns; (b) detail (extrusions, intrusions).
These surface effects were investigated by means of the
FIB method exemplarily down to a depth of ~20 µm at several
positions in the center of the spherical cap, see Fig. 14.
(a) (b)
Fig. 14: FIB-investigation of extrusions and intrusions after 22’000
thermal cyclic loadings in the range of ~160 °C to 300 °C: (a) overview; (b) detail with subgrain structure.
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At some of these parallel extrusions and intrusions
microcracks initiate and arise into the specimen depth and along
the parallel direction, as shown in Fig. 15.
(a) (b)
Fig .15: FIB-investigation of microcracks after 22’000 thermal
cyclic loadings (~160 °C to 300 °C) at different positions: (a) microcrack; (b) initiation of microcracks.
Some of these microcracks evolve to a dominant crack in
the course of progressive thermal cyclic loading. Figure 16
shows one side of the crack and its corresponding crack tip.
(a) (b)
Fig. 16: Dominant crack in the center of the spherical cap after
22’000 thermal cyclic loadings in the range of ~160 °C to 300 °C: (a) one side of the dominant crack; (b) detail of the crack tip.
Furthermore, these microcracks cause a significant and
continuous decrease of residual stresses in the center of the
spherical cap. The scatter bands of residual stresses measured
by XRD in the course of progressive thermal cyclic loading in
the range of ~160 °C to 300 °C are illustrated in Fig. 17. Almost
no residual stresses were detectable after occurrence of the
dominant crack.
8 % 15 % 38 % 63 % 100 %
-100
0
100
200
300
400
resid
ua
l str
ess (
sca
tte
r b
an
d)
[MP
a]
lifetime [-]
Fig. 17: Scatter bands of residual stresses measured by XRD in the
course of progressive thermal cyclic loading (~160 °C to 300 °C).
SIMULATIONS A plastic constitutive law of Chaboche type [10], which is
defined by the following equations, has been used for the finite
element simulations.
elεCσCCσ ::: 1 (3)
0)()(2 kpRJf Xσ (4)
)(2
3
2 Xσ
Xσε
Jppl (5)
3
1i
iXX (6)
TCdT
dCppC
i
iiii
pl
ii XXεX )(
3
2 (7)
p
iiiiiep
)()( (8)
pRQbR )( (9)
where σ is the stress tensor, C is the tensor of the elastic
moduli, 2J is the second invariant, f is the flow rule, R is the
isotropic hardening, and X is the kinematic hardening. The
elastic strain elε is given by
plthel εεεε , where ε is
the total strain and )(th
th
refΤΤα 1ε is the thermal strain
with the thermal expansion coefficient th . plε is the plastic
strain and p is the accumulated plastic strain. k , iC , i ,
i , i ,b und Q are material parameters.
This plastic constitutive model has been implemented as a
user subroutine in the FE software ABAQUS. An implicit
numerical integration scheme using the backward Euler method
has been employed.
The material parameters have been determined using
uniaxial, isothermal LCF tests of the material X6CrNiNb18-10.
The LCF tests were conducted at different temperatures (room
temperature, 200 °C and 350 °C) and with different total strain
amplitudes (strain controlled) [1].
For the identification of the parameters the LCF tests have
been simulated with the plastic constitutive law where the
parameters have been varied until the sum of the squares of the
differences of the computed and measured stresses were
minimized. The parameters as a function of the temperature are
obtained by interpolating the parameters at room temperature,
200 °C and 350 °C.
SIMULATION OF THERMAL CYCLIC LOADING The 3D finite element model was created on a scale of 1:1
with ~8’500 linear brick elements (type DC3D8 elements for
thermal and type C3D8 elements for mechanical simulation)
and ~9’000 nodes. No symmetry simplifications could be used
because of heating and cooling from only one side of the
specimen (no symmetry in the section plane xy).
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Furthermore, the inductor was a torus with a small gap at
the bottom side caused by production (no symmetry in the
section plane xz).
Figure 18 illustrates the meshed 3D finite element model
with mechanical boundary conditions at the bottom side and the
real specimen.
(a) (b)
Fig. 18: Specimen (“calotte”): (a) meshed 3D finite element model
with mechanical boundary conditions; (b) real specimen.
The experimental thermal cycling tests were analyzed by
means of 3D finite element calculations (FE-simulations).
Therefore, extensive numerical investigations with user
subroutines were carried out to reproduce the real behavior of
the specimen.
The surface temperatures (temperature profile) at heating
peak measured with infrared camera (Fig. 19a) are compared
with the thermal FE-simulation with ABAQUS (Fig. 19b), for
instance. The good qualitative and quantitative match is
distinctly and visibly.
100°C
300°C
200°C
(a) (b)
Fig. 19: Surface temperatures at heating peak: (a) measured with
infrared camera; (b) simulated with ABAQUS.
The numerically calculated, time-dependent and
inhomogeneous temperature fields were assigned to the mesh of
the 3D finite element model (mapping). These temperature
fields result in thermally induced stresses and strains. The used
material model (plastic constitutive law of Chaboche type) for
the mechanical finite element simulations is described above.
Necessary mechanical material properties, e.g.
temperature-dependent Young’s modulus or thermal expansion,
were determined experimentally or taken from Mangold [11].
Some results of the mechanical 3D finite element
simulation in the center of the spherical cap for thermal cycling
in the range of ~160 °C to 300 °C, are presented in Fig. 20.
The calculated strains in horizontal (x) and vertical (y)
direction increase throughout the first heating up to maximum
temperature (red). During the thermal cycling, the calculated
strains alternate with a small phase shift relating to the
temperature. Altogether, the FE-simulation displayed the
identified effects of the real specimen (see Fig. 11).
(a)
(b)
Fig. 20: Strain profile compared with surface temperature in the
center of the spherical cap as a result of finite element simulation of thermal cycling in the range of ~160 °C to 300 °C with ABAQUS:
(a) overview; (b) detail while thermal cycling.
The measured strains (ARAMIS) at the specimen surface
are compared with the results of the 3D finite element
simulation for thermal cycling in the range of ~160 °C to
300 °C in Fig. 21. The measured and the numerically calculated
results in horizontal (x) direction are in good accordance.
0.0060.0050.0040.0030.0020.0010.000
-0.001-0.002-0.003-0.004-0.005
LE11
(a) (b)
Fig. 21: Strain distribution at maximum temperature for thermal
cycling in the range of ~160 °C to 300 °C: (a) ARAMIS measurement; (b) 3D finite element simulation.
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EVALUATION OF THE THERMAL FATIGUE LIFETIME To evaluate the fatigue lifetime of the specimen, an
approach of the equivalent strain range according to ASME
2011a, Section III, Division 1-NH (T-1413) [12] was used for a
representative thermal cycle (steady state) in the range of
~160 °C to 300 °C and ~210 °C to 270 °C. In this connection,
the fatigue lifetime assessment results from strain components.
Subsequently the numerically calculated lifetime in the center of
the specimen was compared with the experimentally observed
lifetime (crack).
The equivalent strain range is computed as follows [12]:
Step 1: Calculate all strain components for each point, i, in
time (xi, yi, zi, xyi, yzi, zxi,) for the complete cycle. When
conducting inelastic analysis, the stress and strain
concentration effects of local geometric discontinuities are
included in this step (…).
Step 2: Select a point when conditions are at an extreme
for the cycle, either maximum or minimum. Refer to this time
point by a subscript o.
Step 3: Calculate the history of the change in strain
components by subtracting the values at the time, o, from the
corresponding components at each point in time, i, during the
cycle.
∆xi = xi – x0 (10)
∆yi = yi – y0
etc;
Step 4: Calculate the equivalent strain range for each
point in time as:
2/1
222
2
22
.
2
3*12
2
zxiyzixyi
xizi
ziyiyixi
iequiv
(11)
where
v* = 0.5 when using the rules of T-1420
v* = 0.3 when using the rules of T-1430
Step 5: Define Δmax as the maximum value of the above
calculated equivalent strain ranges, Δequiv.i.
The above five step procedure may be used regardless of
whether principal strains change directions.
The maximum value of the equivalent strain range for
thermal cycling in the range of ~160 °C to 300 °C and ~210 °C
to 270 °C was calculated from mechanical 3D finite element
simulations assuming v* = 0.5. The distribution of the
maximum equivalent strain range shows Fig. 22.
The highest equivalent strain range appears in the center of
the specimen in each time. The maximum values are 0.76 %
(~160 °C to 300 °C) and 0.27 % (~210 °C to 270 °C). From this
it follows that the maximum equivalent strain amplitudes are
0.38 % (~160 °C to 300 °C) and 0.135 % (~210 °C to 270 °C).
(a) (b)
Fig. 22: Distribution of the maximum equivalent strain range calculated according to ASME for stabilized thermal cycles in the
range of: (a) ~160 °C to 300 °C; (b) ~210 °C to 270 °C.
The experimentally observed lifetime of the calotte was
defined as a through-thickness crack in the center of the calotte.
This lifetime was in the range of about 10’000 to 20’000 cycles
(for thermal cycling between ~160 °C to 300 °C) and in the
range of about 175’000 to 235’000 cycles (for thermal cycling
between ~210 °C to 270 °C).
Compared with pure mechanical and isothermal fatigue
tests [1], this is in a good accordance with a mechanical fatigue
lifetime of about 20’000 cycles (total strain amplitude of
0.38 %) and 200’000 cycles (total strain amplitude of 0.135 %),
see Fig. 23. Consequently, the fatigue lifetime of the analyzed
specimens under thermal cyclic loading (defined as a through-
thickness crack in the center of the calotte) is approximately
comparable to the fatigue lifetime at isothermal mechanical
loading (defined as a stress reduction of 5 %), but it tends to
result in minor lifetime.
102
103
104
105
106
107
0,01
0,1
1
10
*) NA25
Source: IfW Darmstadt / MPA Universität Stuttgart
X6CrNiNb18-10 (1.4550)
Mechanical tests: strain controlled (R = -1)
Calotte: pure thermal load
15 (RT) [IfW]
15 (200°C) [IfW]
15 (350°C) [IfW]
106 (RT) [IfW]
106 (200°C) [IfW]
106 (200°C) [MPA] *)
106 (350°C) [IfW]
Calotte (150 - 300 °C)
Calotte (200 - 270 °C)
str
ain
am
plit
ud
e
a [%
]
lifetime [-]
Fig. 23: Comparison of isothermal mechanical fatigue tests and thermal cyclic tests (calotte).
0.00760.00750.00700.00650.00600.00550.0050
0.00400.00350.00300.0025
eq,max
0.00200.00150.00100.00050.0000
0.0045
0.00270.00240.00220.00200.00180.00160.0013
0.00090.00070.00040.0002
eq,max
0.0000
0.0011
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10 Copyright © 2014 by ASME
SUMMARY AND CONCLUSION In the austenitic stainless steel X6CrNiNb18-10 different
crack initiation mechanisms were observed under thermal cyclic
and mechanical cyclic loading.
In the material under thermal cyclic loading in the
temperature range of ~150 °C to 300 °C, inhomogeneous
temperature fields result in thermal induced stresses and strains,
that cause intrusions and extrusions inside the grains (at the
surface). The mobility of dislocation is strongly influenced by
temperature. Especially in fcc materials like austenite, the yield
stress decreases significantly with increasing temperature and
local shear bands with high strain concentrations in differently
oriented grains can be formed. In the course of progressive
thermal cyclic loading, micro cracks initiate and arise at some
of these parallel intrusions and extrusions and finally evolve to
a dominant crack. Crack formation and crack growth is attended
by a continuous and significant decrease of residual stresses.
In the material under mechanical cyclic loading at room
temperature, deformation induced martensitic transformation in
the austenitic matrix was observed. The bcc ’-martensite is
unlike its tetragonal variant ductile and soft. The volume
fraction of the transformed martensite depends on the loading
amplitude. Higher strain amplitude leads to a larger volume
fraction of martensite. The critical strain amplitude, that must
be exceeded in order to trigger the phase transformation, is
about 0.3 %. Additionally, a certain amount of accumulated
strain must be achieved in order to “prepare” the microstructure
for the transformation which is connected with volume
expansion of 2 %. In the cylindrical smooth specimens loaded
in LCF regime, the formation of martensite was observed before
crack initiation. Fatigue cracks arose in the phase boundaries
between austenite and martensite or in fully martensitic areas. In
the miniature C(T) specimens under cyclic loading the
formation of plastic zone near the notch was observed. At a
later point of loading, a fatigue crack emerged in the notch root.
At the crack tip, in which stress and strain amplitudes are much
higher than nominal loading, martensitic transformation takes
place and forms a kind of “martensitic tunnel” around the
growing crack.
This work aims at a deeper understanding of the basic
phenomena which are accompanying fatigue on the nano- and
micro-levels in the austenitic stainless steel X6CrNiNb18-10 at
thermal and mechanical loading in air. For this purpose
experiments and finite element simulations were performed.
From the understanding of the phenomena underlying
fatigue in the X6CrNiNb18-10 for different loading and
temperature conditions, the impact of the microstructure on the
crack formation and crack growth under cyclic loading can be
identified more reliably.
ACKNOWLEDGMENTS This work was performed with support of the German
Federal Ministry of Economics and Technology (BMWi) and
the German Federal Ministry of Education and Research
(BMBF) which is gratefully acknowledged.
Dipl.-Ing. D. Willer, Dipl.-Ing. P. Kopp, Dr.-Ing. K.
Berreth, Mrs. J. Hüter, Mr. R. Scheck and Mr. G. Pfeiffer (MPA
University of Stuttgart) are truthfully thanked for their
assistance in the experiments.
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