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: [email protected] (C. Berger).

http://www.elsevier.com/locate/ijfatigue

http://www.elsevier.com/locate/ijfatigue



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



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



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.




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.




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




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


strain [%]

(c)

(a)

–800

–600

–400

–200

0

200

400

600

800


(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


time [h]

– 0.50 – 0.25 0.00 0.25 0.50 – 500

– 250

0

250

500

– 500

– 250

0

250

500


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.




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


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


s t r a i n [ % ]

time [h]





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.




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 %





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.


Documents

Creep Fatigue Experiments Modelling