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7/27/2019 Creep Fatigue Experiments Modelling
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Service-type creep-fatigue experiments with cruciform
specimens and modelling of deformation
A. Samir, A. Simon, A. Scholz, C. Berger *
Institute of Materials Technology, Darmstadt University of Technology, Grafenstrasse 2, 64283 Darmstadt, Germany
Received in revised form 11 August 2005; accepted 31 August 2005
Available online 13 December 2005
Abstract
Advanced material models for the application to component life prediction require multiaxial experiments. A biaxial testing system forcruciform test pieces has been established in order to provide data for creep, creep-fatigue and thermomechanical fatigue (TMF)
experiments. For this purpose a cruciform specimen was developed with the aid of Finite element calculation and the specimen design was
optimised for tension and compression load. The testing system is suitable for strain (displacement) and load control mode. A key feature
deals with the opportunity to perform thermomechanical experiments. Further, a constitutive material model is introduced which is
implemented as a user subroutine for Finite element applications. The constitutive material model of type Chaboche considers both
isotropic as well as kinematic hardening and isotropic damage. Identification of material parameters is achieved by a combination of
Neural networks and subsequent Nelder–Mead Method.
q 2005 Elsevier Ltd. All rights reserved.
Keywords: Cruciform testing system; Creep-fatigue; Thermomechanical fatigue; Heat resistant steel; Constitutive material model; Neural networks; Finite element
1. Introduction
The lifetime of high temperature components normally
depends on variable loading conditions. This is due to start-up
phases, constant load phases and shut-down phases. Tempera-
ture transients, constant or variable pressure in pressurised
systems and constant or variable speed of rotors produce a
large variety of combined static and variable loading situations.
Temperature transients cause strain cycling with variable
thermal (secondary) stresses at the heated surface of turbine
components. In addition, pressure loading and, at rotors,
centrifugal loading leads to quasistatic (primary) stresses
(Fig. 1). As a consequence, creep-fatigue can be the critical
loading condition.
Generally, multiaxial stresses and strains in high tempera-
ture components cannot be described by uniaxial data. Life
prediction concepts either of conventional type or of advanced
type require suitable multiaxial experiments for verification
purposes. Additionally to tension/torsion or internal pressure
experiments developed in the past, experiments with cruciformtest pieces are of high interest.
A biaxial cruciform TMF testing system was developed
in cooperation of IfW Darmstadt and INSTRON Ltd [1–3].
Experiments on heat resistant steels and on nickel base
alloys were performed in order to demonstrate its capability.
This testing system consists of a high-stiffness loading
frame and incorporates four servohydraulic actuators with a
maximum force capacity of 250 kN, positioned on two
orthogonally arranged axes (Fig. 2). Beneficial is that the
actuators are equipped with hydrostatic bearings. Strain is
measured by a special high temperature biaxial extens-
ometer, developed in cooperation with SANDNER—Mes-
stechnik GmbH. Key features of this cruciform testtechnique are homogeneous stress–strain field (Fig. 3) as
well as plain crack distribution in the test zone (Fig. 4). The
equivalent plastic strain 3p,eq in Fig. 3 is calculated with the
equation
3p;eq :Z
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2
3Ep$Ep
r (1)
whereby Ep is referred to as plastic strain tensor. A wide
field of biaxial strain ratios f3Z3 y / 3 x between K1 up to C1
(3 y%3 x) is adjustable and allows the experimental simulation
of in-phase as well as out-of-phase loading. Both, load
control mode as well as strain (displacement) control mode
International Journal of Fatigue 28 (2006) 643–651
www.elsevier.com/locate/ijfatigue
0142-1123/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijfatigue.2005.08.010
* Corresponding author.
E-mail address: berger@mpa-ifw.tu-darmstadt.de (C. Berger).
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are available. A redirection between both modes is
arbitrarily possible. A further advantage of biaxial tests on
cruciform specimens is, contrary to tests with thin-walled
tubes, the widely decrease of buckling danger when high
loads are applied in compression direction. Another
advantage is the safety aspect when occurrence of failure
is expected or aimed. Extensive safety precautions are not
necessary for cruciform specimen tests but for other biaxial
testing systems like tube under internal pressure or rotating
disc. Furthermore, crack initiation and crack growth are
observable over the test zone with a diameter of 15 mm,
thickness 2 mm (Fig. 4).
2. Biaxial experiments
Investigations by Ohnami [4] have demonstrated the large
influence of loading ratio on number of cycles to crack
initiation. Pure fatigue tests on a 1%Cr-steel show a factor of
Fig. 1. Load conditions at a turbine rotor.
Fig. 2. Biaxial testing system with four hydraulic actuators (a), cruciform specimen with orthogonal extensometer (b) and (c), gauge lengthZ13 mm in A and B
directions.
Fig. 3. Scheme of the cruciform specimen (a) and elastic-plastic Finite element calculation showing equivalent plastic strain 3p,eq distribution (b) maximum
deformation in the test zone.
A. Samir et al. / International Journal of Fatigue 28 (2006) 643–651644
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10 in life between biaxial strain ratio F3ZK1 and F
3ZC1
(Fig. 5(a), solid lines).Long-term service-type creep-fatigue experiments on a
1%CrMoNiV rotor steel (Table 1) with four hold times (cycle
period t p) are performed on the cruciform testing system [5].
Experiments run under strain controlled mode with long hold
times. The strain ratio is given to F3Z0.5 and F
3Z1. The
measured load–strain hysteresis loops demonstrate the high
quality of control of small displacements (Fig. 6). Cyclic
softening at 525 8C can be observed as expected (Fig. 6(c) and
(d)). Crack is initiated in the test zone perpendicular to the axis
B outside of strain gauge at N z400.
An example of a biaxial experiment with F3Z0.5
demonstrates the influence of the biaxial strain ratio on the
load–strain behaviour (Fig. 7). It was proved in load control
mode as well as in strain control mode that the stability of the
centre of the specimen is given with a maximum deflection of
G1.5 mm.
A total of five biaxial service-type creep-fatigue experi-ments were performed on the 1%CrMoNiV rotor steel
(Fig. 5(a)) with relevant test durations up to about 2000 h.
As a first result at strain ratio F3Z1 a clear influence of
superimposed creep at hold times of factor 2 can be
observed. Secondly, a strain ratio of F3Z0.5 leads to an
increase of number of cycles to crack initiation N i of factor
1.5. This result confirms the pure fatigue biaxial experiment
results [4].
Further, biaxial strain controlled experiments lead to a
reduction of number of cycles to crack initiation N i up to factor
3 compared to uniaxial service-type creep-fatigue experiments
(Fig. 5(b)) [11]. On the one hand, an increase of total strainrange leads to a larger difference of N i values. But on the other
hand, increasing hold time has a more significant influence.
The advanced TMF test technique is demonstrated in Fig. 8
exemplarily. To achieve a desired mechanical strain com-
ponent, the temperature induced thermal expansion strain is
measured. Hereby free expansion of specimen is allowed due
to load control mode. Then the thermal expansion coefficient
automatically obtained by the system is used for active
compensation of the thermal strain during the TMF test.
There is no need of manual calculations.
Fig. 4. Example of surface cracks initiated in the test zone at biaxial fatigue
testing, 12%Cr-steel, T Z500 8C.
Fig. 5. Influence of biaxial strain ratio F3
on the number of cycles to crack initiation N i at fatigue testing, 1%CrMoV, T Z550 8C [4] and first results of long term
service-type creep-fatigue experiments (F3Z1.0 and F
3Z0.5), d3 /dt Z0.06%/min, 1%CrMoNiV, T Z525 8C (a), comparison with uniaxial experiments (b) and the
shape of the service-type cycle (c). t p, periodic time; t i, time to crack initiation corresponding to a crack depth of about 0.2 mm.
A. Samir et al. / International Journal of Fatigue 28 (2006) 643–651 645
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3. Constitutive material model and parameter identification
Results of experiments with cruciform specimens can be
employed in combination with Finite element (FE) simulations
in order to verify various material models. FE simulations were
performed with ABAQUS whereby a constitutive material
model is implemented in user-defined subroutine UMAT.
Here, the underlying constitutive material model (Table 2)
describes a elasto-viscoplastic behaviour for small defor-
mations and was introduced by Tsakmakis [6]. A key feature is
the combination of effective stress with a generalised energyequivalence principle. An undamaged fictitious material is
described by means of effective variables ( ~T; ~E; ~x, etc. Table 2
rows 1–14) which are the basis of the constitutive material
model. The structure of this model can be attributed to
Chaboche and Lemaitre [12]. A damage variable D is defined
with an approach proposed by Lemaitre [7] additionally to
another set of variables (T,E,x, etc.) for the damaged real
material. The known behaviour of the undamaged fictitious
material is then mapped to the unknown behaviour of the real
material with damage. This step is done by substitution of the
effective variables using relations, which implicate the damage
variable D (Table 2 row 15). The yield function of the real
material is given by Table 2 row 16 and the damage is
described by the evolution equation in row 17.
In this material model m and l are elasticity parameters and
h and m the viscosity parameters. At kinematic hardening, c is
responsible for generation and b for limitation of hardening, p
and w are the parameters for static recovery. Analogously, in
the isotropic hardening the parameters g, b, p and u have the
functionalities as mentioned by kinematic hardening. The
material parameters for isotropic hardening k 0 (stress-valued)
and r 0 (strain-valued) are addressed to the original material.
For the evolution of damage two parameters a1 and q areresponsible. The parameters m and l (corresponding to n and E )
as well as k 0 and r 0 are given for 1%CrMoNiV steel at
T Z525 8C. The remaining parameters must be determined
with a proper method.
Within the current research work on creep-fatigue [5], the
material parameters of the constitutive model were determined
by a two-step approach with a combination of the Neural
networks method and the optimisation method by Nelder–
Mead (Figs. 9–12). The Neural networks method is already
established in similar non-linear problems [9] and can deliver a
‘global’ solution. The method by Nelder–Mead [10] is a direct
search method without the need of numerical or analytical
Table 1
Chemical composition and heat treatment of 1%CrMoNiV
C Si Mn P S Cr Mo Ni V Al Cu Sn
1%CrMoNiV 0.28 0.20 0.74 0.007 0.008 1.09 0.82 0.69 0.36 0.003 0.21 0.012
Manufacturing Segment of a rotor diameter 400 mm!6000 mm, forged
Heat treatment Austenitisation 5 h 950 8C/oil 50, then/air till 300 8CC1st tempering 10 h 700 8C/airC2nd tempering 10 h 710–720 8C/air
0.00 0.25 0.50 0.75 1.00 1.25 1.50
–0.6
–0.4
–0.2
0.0
0.2
0.4
th4
=0.075h
th3
=0.15h
th2
=0.7h
th1
=0.075haxis A
axis B
s t r a i n [ % ]
time [h]
axis A
axis B
–0.6 –0.4 –0.2 0.0 0.2 0.4
–100
–50
0
50
100
400
200
N=1
l o a d [ k N ]
strain [%]
–0.6 –0.4 –0.2 0.0 0.2 0.4
strain [%]
0 100 200 300 400
–100
–50
0
50
100
Fmin
Fm
Fmax
axis Aaxis B l o
a d [ k N ]
–100
–50
0
50
100
l o a d [ k N ]
number of cycles N
(d)
(a) (b)
(c)
Fig. 6. Biaxial strain cycle (identical signals for axis A and B) on cruciform specimen, d3 /dt Z0.06%/min, cycle period t pz1.3 h, hold times t h1.4, total hold time
1.0 h (a), hysteresis loops measured at N Z N i /2 (b), load–strain hysteresis loops (c) and cyclic softening behaviour, maximum load F max, mean load F m and minimum
load F min (d), N iz400, t iz530 h, 1%CrMoNiV steel, T Z525 8C.
A. Samir et al. / International Journal of Fatigue 28 (2006) 643–651646
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gradients and leads only to a ‘local’ solution. This method is
commonly referred to as unconstrained non-linear optimis-
ation. In the first step Neural Network identifies a parameter
vector close to the global solution within a parameter interval.
This result is used subsequently in the second step as an initial
parameter vector in the Nelder–Mead method for furtherimprovement of the solution.
In order to identify the parameters of the subjected
model for 1%CrMoNiV steel by means of Neural networks
(Fig. 9), 1D calculations depending on parameter variations
were performed. In Fig. 11(a) and (b) examples of such
simulations are depicted. These simulated data serve as
training patterns. Herefrom the Neural Network learns the
behaviour of the material model dependant on parameter
variation. Each pattern (s,3)i reflects a unique parameter
vector Pi (Fig. 9). Values of the parameters are randomly
selected in a properly defined interval whereas only one
material parameter is changed per parameter vector. Afterthe Neural Network is trained with these data patterns (s,3)itogether with their assigned parameter vectors Pi, it is able
to build a relationship between the shape of the patterns and
the material parameters.
At the end of the first step of the parameter identification
approach the results of a special experiment (Fig. 10) are used
to obtain the parameter vector Pid. This special uniaxial
experiment was performed on cylindrical specimen (diameter
10 mm) with a long period time t pz36 h and with long hold
times at different strain levels whereby the cycle is repeated
twice with exponential increasing strain rates at the slopes
(Fig. 10(a)). The first cycle is performed with a strain rate of
(d3 /dt )1Z0.06%/min and the two subsequent cycles followed
with (d3 /dt )2Z0.6%/min and (d3 /dt )3Z6%/min.
The idea of this approach is to identify the parameters l, m,
k 0, h, m,. of the material model with the knowledge of only
one special creep-fatigue experiment. As a result a unique
vector of parameters PidZ(l, m, k 0, h, m,., q) is going to beidentified which enables the material model to describe all
relevant effects of the real material.
This first set of parameters is improved in the second step by
Nelder–Mead method. Here, the decisive value is the least-
squares of distances between the hysteresis loops simulated by
material model and the experimental one at certain nodes. The
second step delivers by means of the initial parameter vector
0.00 0.25 0.50 0.75 1.00 1.25 1.50
time [h]
0.00 0.25 0.50 0.75 1.00 1.25 1.50
time [h]
– 0.6 – 0.4 – 0.2 0.0 0.2 0.4
strain [%]
– 100
–
50
0
50
100
l o a d [ k N ]
(b)
– 0.6
– 0.4
– 0.2
0.0
0.2
0.4
s t r a i n [ % ]
(a)
– 100
– 50
0
50
100
l o a d [ k N ]
(c)
– 100
– 50
0
50
100
l o a d [ k N ]
(d)
axis Aaxis B
axis Aaxis B
axis Aaxis B
0 200 400 600
Fmin
Fm
Fmax
axis A
axis B
number of cycles N
Fig. 7. Details of the biaxial experiment on cruciform specimen with biaxial strain ratio F3Z0.5, hold times see Fig. 6(a), strain vs. time curves for axis A and B (a),
load vs. time (b), hysteresis loops measured at cycle N Z1 (c) and cyclic softening behaviour, maximum load F max, mean load F m and minimum load F min (d),
N iz625, t iz830 h, d3 /dt Z0.06%/min, 1%CrMoNiV steel, T Z525 8C.
– 40
0
40
18 20 22t [min]
F [kN] axis A
axis B
300
400
18 20 22
T [°C] temperature
– 0.1
0.0
0.1
18 20 22
ε [%]axis A
axis B
(c)
(a)
(b)
Fig. 8. TMF cycles at biaxial testing under strain control with cruciform
specimen (a), in-phase cycles at axis A and out-of-phase cycles at axis B (b) and
measured load at both axis (c). The thermal strain is compensated automatically
after it has been measured at zero load conditions.
A. Samir et al. / International Journal of Fatigue 28 (2006) 643–651 647
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Pid an optimised parameter vector Pid,opt representing the
creep-fatigue properties of the investigated steel 1%CrMoNiVat T Z525 8C.
As a result of this two-step approach a satisfactory
recalculation of the uniaxial experiment (Fig. 10) was obtained
(Fig. 11(c)).
Alternatively to the one special experiment, a parameter
identification procedure was established in order to use
knowledge from several conventional experiments, which
are usually available in an integrated approach. These
experiments are addressed to tensile tests, fatigue tests and
creep-fatigue tests at different strain rates and finally creep
tests. T he idea is to use these experimental data
simultaneously at the parameter identification procedure.
Unfortunately, this more complex and time-consuming
procedure leads to unsatisfactory results. Future efforts are
necessary to improve this way. In general, the parameter
identification procedure has to be optimised in the sense of
industrial applicability and saving of time.
4. Finite element simulation and verification
The verification process of the constitutive material
model and the determined material parameters from the
two-step approach (Fig. 11(c)) follows the flowchart shown
in Fig. 12. A Finite element model of the cruciform
specimen subjected to the service-type creep-fatigue loading
conditions is used to produce a data basis comparable to
experimental results.As mentioned above, the verification experiments on the
cruciform specimen are performed in strain control mode
(Fig. 12(a)). The strain is controlled in the test zone of the
specimen (Fig. 12(b)) and the result of the experiment is the
measured curve of load vs. time (Fig. 12(c)). At Finite element
simulation (Fig. 12(d)) it is not possible to use a strain signal as
boundary conditions. Hence, the load vs. time curve measured
Fig. 9. The procedure of parameter identification by Neural Network: training
step with patterns produced by parameter variation followed by material model
simulations (1) and identification step with experimental data (2).
Table 2
Summary of the constitutive material model basing on Chaboche and extended by Tsakmakis [6], damage law by Lemaitre [7]
Equation Description Material parameters
1 ~EZ ~EeC~Ep Additive decomposition of the strain tensor in elastic and plastic parts
2 ~TZC½ ~EeZ2m ~EeClðtr ~EeÞ1 Generalised elasticity law (Hookean law) m, l
3 ~xZc ~Y
~ RZgð~r C ~r 0ÞRelations of stresses to strains of kinematic and isotropic hardening as
internal variables
r 0
4 ^ f ðf Þð ~T; ~xÞ :Z
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi32ð ~TK~xÞ D$ð ~TK~xÞ D
q Equivalent stress definition, ( f ) means fictitious material
5 F ðf Þð ~T; ~x; ~ RÞ :Z^ f
ðf Þð ~T; ~xÞK ~ RKk 0Yield function for fictitious material k 0
6 F ðf Þð ~T; ~x; ~ RÞO0 Yield condition
7 _~s :ZhF im
hRate of the accumulated plastic strain h, m
8 _~EpZ32
ð ~TK~xÞ D^ f
_~s Rate of the plastic strain tensor
9 _~YZ _~EpKb_~s ~YK pjjc ~YjjwK1 ~Y Rate of kinematic hardening strain with dynamic and static recovery c, b, p, w
10 _~r Z _~sKb~r _~sKpðg~r Þu Rate of isotropic hardening strain with dynamic and static recovery g, b, p, u
11 ~T$ _~EK_jR0 Dissipation inequality to ensure the thermodynamical consistence
12 jZ jeð ~EeÞC jðkinÞp ð ~YÞC j
ðisÞp ð~r Þ Free energy function, decomposition in a elastic part and two kinematic
and isotropic plastic parts
13 ~TZ vj
v ~Ee; ~xZ
vj
v ~Y; ~ RZ vj
v~r Derivatives of free energy function
14 jeðEeÞZ jðf Þe ð ~EeÞ
jðkinÞp ðYÞZ j
ðf ;kinÞp ð ~YÞ
jðisÞp ðr ÞZ j
ðf ;isÞp ð~r Þ
Generalised energy equivalence between real damaged and fictitiousundamaged material (Tsakmakis)
15 ~TZ T ffiffiffiffiffiffiffi1K D
p ; ~xZ x ffiffiffiffiffiffiffi1K D
p ; ~ RZ R ffiffiffiffiffiffiffi1K D
p
~EeZ ffiffiffiffiffiffiffiffiffiffiffi
1K Dp
Ee; ~YZ ffiffiffiffiffiffiffiffiffiffiffi
1K Dp
Y; ~r Z ffiffiffiffiffiffiffiffiffiffiffi
1K Dp
r
Correlations between values in damaged real material and effective values in
undamaged fictitious material (Tsakmakis)
16 F ðT; x; R; DÞZg^ f ðf Þð ~T; ~xÞKg ~ RKk 0
Yield function of the real material, nZ1 for metals n
gð DÞZ ð1K DÞ1 = 2Kn
17_ DZa1
Krvjv D
À Áð1K DÞq
_~sDamage rate definition by Lemaitre
a1, q
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in the experiment must be used instead whereby a strain vs.
time curve can be obtained from the solution (Fig. 12(e)). This
simulated strain curve can be compared with the measured
strain curve (Fig. 12(f)).
In order to get an overview about the applicability of the
material model service-type creep-fatigue experiments shown
in Fig. 5(a) were recalculated with one material parameter set
(Pid,opt). Acceptable results have been obtained for the
simulation of biaxial strain ratios F3Z1.0 and F
3Z0.5
(Fig. 13). These results are limited to first cycles. The
extension of the material model to life prediction is an ongoing
research work.
0 5 10 15 20 25 30 35 40 –800
–600
–400
–200
0
200
400
600
800
s t r e s s [ M P a ]
time [h]
–0.50 –0.25 0.00 0.25 0.50
strain [%]
–0.50 –0.25 0.00 0.25 0.50 –500
–250
0
250
500
ExperimentSimulation
s t r e s s [ M P a ]
strain [%]
(c)
(a)
–800
–600
–400
–200
0
200
400
600
800
s t r e s s [ M P a ]
(b)
Fig. 11. Visualisation of data patterns (150 curves) simulated by the material model for training of the Neural Network, stress vs. time (a), stress–strain loops (b),
comparison of uniaxial experiment with simulation of material model and parameters achieved in two steps by Neural Network method and Nelder–Mead
optimisation (c), 1%CrMoNiV steel, T Z525 8C, d3 /dt Z0.06%/min.
0 36 72 108 – 0.50
– 0.25
0.00
0.25
0.50(dε /dt)
1= 0.06 %/min
(dε /dt)2= 0.6 %/min
(dε /dt)3= 6.0 %/min
s t r a i n [ % ]
time [h]
0 10 20 30 40
s t r e s s [ M P a ]
time [h]
– 0.50 – 0.25 0.00 0.25 0.50 – 500
– 250
0
250
500
– 500
– 250
0
250
500
s t r e s s [ M P a ]
strain [%]
(c)(b)
(a)
Fig. 10. Results of the uniaxial parameter identification experiment, t pz36.4 h, with long hold times t hz3 h at different strain levels and strain rates, strain vs. time
(a), stress vs. time for (d3 /dt )1 (b) and the hysteresis loop (c) 1%CrMoNiV steel, T Z525 8C.
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Summarising, a satisfying description of deformation of first
cycles with this model has been achieved for uniaxial and
biaxial service-type creep-fatigue loading. For modelling of
life prediction under creep-fatigue until crack initiation it is
necessary to simulate all cycles. This requires very long
computing times producing large amounts of training patterns
by 1D simulations needed for the parameter identification.
Further, the FE simulation of every cycle using the user-
defined subroutine UMAT is also time consuming. Therefore,
an extrapolation method is required to reduce the computation
time to a reasonable level. A suitable way already applied in
constitutive material modelling is to extrapolate the entire setof the internal variables after few cycles [13]. The extrapol-
ation procedure is repeated periodically and after every
iteration few equilibrium cycles are computed again. By this
method the calculation time can be reduced by a factor between
10 up to 1000. Currently, further efforts are being made in order
to prepare such methods for industrial application.
At present, the two subsequent cycles with higher strain
rates (d3 /dt )2Z0.6%/min and (d3 /dt )3Z6%/min (Fig. 10(a))
are not discussed in parameter identification process. Further,
improvements for modelling of deformation and life prediction
are to be expected due to a consideration of rate dependency of
the material behaviour.
5. Concluding remarks
Research activities are focussed on the development of
advanced life prediction methods in order to improve
economic performance of power plants. To achieve this
aim, high temperature creep and creep-fatigue experiments
on heat resistant steels and nickel base alloys have been
performed under biaxial loading with a new advanced
cruciform testing technique. Modelling of deformation
extended for the 2D/3D case is established and lifing
including damage calculation is in progress to create a
useful tool for industrial applications.First results of modelling work of deformation on a
1%CrMoNiV steel demonstrates the potential of advanced
methods for parameter identification. Further efforts are
necessary in order to improve such methods by suitable
extrapolation methods for direct industrial application.
Acknowledgements
Thanks are due to the Deutsche Forschungsgemeinschaft
(No BE 1890, 16-1), the Forschungsvereinigung der Arbeits-
gemeinschaft der Eisen und Metall verarbeitenden Industrie
e.V. (AVIF-No A166) and the FKM Forschungskuratorium
0.0 0.5 1.0 1.5-0.6
-0.3
0.0
0.3
0.6
Experiment
s t r a i n [ % ]
time [h]
0.0 0.5 1.0 1.5-80
-40
0
40
80
Experiment
l o a d [ k N ]
time [h]
0.0 0.5 1.0 1.5-0.6
-0.3
0.0
0.3
0.6
Simulation
s t r a i n [ % ]
time [h]
0.0 0.5 1.0 1.5-0.6
-0.3
0.0
0.3
0.6
ExperimentSimulation
s t r a i n [ % ]
time [h]
testing system,material
FEM simulation,material model, parameters
comparison
0.0 0.5 1.0 1.5-0.6
-0.3
0.0
0.3
0.6
Experiment
s t r a i n [ % ]
time [h]0.0 0.5 1.0 1.5-0.6
-0.3
0.0
0.3
0.6
Experiment
s t r a i n [ % ]
time [h]
0.0 0.5 1.0 1.5-80
-40
0
40
80
Experiment
l o a d [ k N ]
time [h]0.0 0.5 1.0 1.5
-80
-40
0
40
80
Experiment
l o a d [ k N ]
time [h]
0.0 0.5 1.0 1.5-0.6
-0.3
0.0
0.3
0.6
Simulation
s t r a i n [ % ]
time [h]0.0 0.5 1.0 1.5
-0.6
-0.3
0.0
0.3
0.6
Simulation
s t r a i n [ % ]
time [h]
0.0 0.5 1.0 1.5-0.6
-0.3
0.0
0.3
0.6
ExperimentSimulation
s t r a i n [ % ]
time [h]
testing system,material
testing system,material
FEM simulation,material model, parameters
FEM simulation,material model, parameters
comparison
(a) (b)
(c)
(d)(e)
(f)
Fig. 12. Flowchart of the verification method of the material model with material parameters, comparison of Finite element results to experimental data.
A. Samir et al. / International Journal of Fatigue 28 (2006) 643–651650
7/27/2019 Creep Fatigue Experiments Modelling
http://slidepdf.com/reader/full/creep-fatigue-experiments-modelling 9/9
Maschinenbau e.V. (FKM-No 052510) for financial support
and the working groups of German Power Plant Industry for
accompaniment.
References
[1] Berger C. DFG-Vorhaben. Forder-Nr. BE 1890, 16-1; 2000–2002.
[2] Scholz A, Kirchner H, Hortig P, Granacher J, Berger C. Proceedings of
materials week, Munich; 2000.
[3] Berger C, Granacher J, Kollmann FG, Debusmann Ch. DFG SFB 298. TU
Darmstadt, Arbeits- und Ergebnisbericht; 1999. p. 107–25.[4] Itoh M, Sakane M, Ohnami M. High temperature multiaxial low cycle
fatigue of cruciform specimen. Trans ASME JEMT 1994;116(1):90–8.
[5] Berger C. AVIF-Forschungsvorhaben A166. IfW, TU-Darmstadt; 2002
bis 2004.
[6] Tsakmakis C, Reckwerth D. The principle of generalized energy
equivalence in continuum damage mechanics. In: Deformation and
failure in metallic materials. Berlin: Springer: 2003. p. 3 [ISBN: 3-540-
00848-9].
[7] Lemaitre J. A course on damage mechanics. 2nd ed. Berlin, New York:
Springer; 1996 [ISBN: 3-540-60980-6].
[9] Huber N, Tsakmakis Ch. A neural network tool for identifying the
material parameters of a finite deformation viscoplasticity model with
static recovery. Comput Method Appl Mech Eng 2001;191:353–84.
[10] Nelder JA, Mead R. A simplex method for function minimization.
Comput J 1965;7:308–13.
[11] Scholz A, Haase H, Berger C. Simulation of multi-stage creep fatigue
behaviour, In: Blom AF, editor. Fatigue 2002, Proceeding of the
eighth international fatigue congress, vol. 5/5; Stockholm, 2002. p.
3133–40
[12] Lemaitre J, Chaboche J-L. Mechanics of solid materials. 1990. [ISBN:
0-521-32853-5].
[13] Kiewel H, Aktaa J, Munz D. Application of an extrapolation method in
thermocyclic failure analysis. Comput Method Appl Mech Eng 2000;182:
55–71.
Φε=1.0, t
p= 1.33 h,
∆εx=∆ε
y=0.60 %
ExperimentSimulation
ExperimentSimulation
ExperimentSimulation
ExperimentSimulation
Φε=1.0, t
p= 3.53 h,
∆εx=∆ε
y=0.60 %
Φε=1.0, t
p= 1.23 h,
∆εx=∆ε
y=0.42 %
0 1 2 3 4
Φε=1.0, t
p= 3.43 h,
∆εx=∆ε
y=0.42 %
time [h]
0 1 2 3 4
time [h]
0.00 0.25 0.50 0.75 1.00 1.25 1.50 – 0.6
– 0.3
0.0
0.3
0.6
Experiment
axis A
axis B
Simulation
axis A
axis B
Φε=0.5, t
p= 1.33 h,
∆εx=0.60 %, ∆ε
y=0.30 %
s t r a i n [ % ]
time [h]
0.00 0.25 0.50 0.75 1.00 1.25 1.50
time [h]
0.00 0.25 0.50 0.75 1.00 1.25 1.50
time [h]
(e)
– 0.6
– 0.3
0.0
0.3
0.6
s t r a i n [ % ]
(c)
– 0.6
– 0.3
0.0
0.3
0.6
s t r a i n [ % ]
(a)
– 0.6
– 0.3
0.0
0.3
0.6
s t r a i n [ % ]
(d)
– 0.6
– 0.3
0.0
0.3
0.6
s t r a i n [ % ]
(b)
Fig. 13. Finite element simulation of biaxial service-type creep-fatigue experiments (Fig. 5(a)), comparison of strain vs. time curves from experiment (fist cycle) to
those of FE model calculated with the constitutive material model and the material parameters determined, F3Z1.0 (a)–(d) and F
3Z0.5 (e), 1%CrMoNiV steel, T Z
525 8C, d3 /dt Z0.06%/min.
A. Samir et al. / International Journal of Fatigue 28 (2006) 643–651 651
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