Thermal and Mechanical Fatigue Loading: Mechanisms of ...

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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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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.



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.



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.



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.



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.



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).



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.



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



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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