E-Journal of Advanced Maintenance Vol.9-3 (2017) 152-163
Japan Society of Maintenology

LCF and HCF of Austenitic Stainless Steels – ND-Monitoring of Physical
Properties to predict the SN Curve due to The PHYBAL Procedure for
Lifetime Determination
Gerd DOBMANN
Chair of Nondestructive Testing and Quality Assurance, Saar-University, Campus Dudweiler,
Saarbrücken, 66125, Germany
ABSTRACTThe need to reliably perform a fatigue life assessment is obvious, if we have the ageing infrastructure in our
power plants in view. Concerning components manufactured in austenitic stainless steel, in Germany, in PWR,
we do not have in the primary circuit, as main cooling line (MCL), an austenitic component. The German designis based on pipes, made from the same steel grade as the reactor pressure vessel (RPV) – but cladded on the
inner side by austenitic stainless steel. Therefore, Germany, for instance, has not the NDT inspection problems,
other countries have, with the dissimilar metal weld between RPV nozzle and MCL. However, the surge line
and the pressurizer spray line are fully made from austenitic stainless steel and they are exposed tothermomechanical fatigue. Concerning their fatigue behavior over lifetime of a NPP, many open questions still
exist. The paper describes fatigue experiments, monitoring the material in the servo-hydraulic fatigue machine
and the development of the PHYBAL procedure for physically based life evaluation. This new technology, incontrast to the standardized SN-Curve evaluation, only asks for a small number of specimens. In case of ahomogeneous material, only three tests, 1 incremental step test and 2 constant amplitude tests, are required forthe estimation of a complete S-N-fatigue curve by calculation.
KEYWORDS

ARTICLE INFORMATION

LCF, HCF, austenitic stainless steel, phase transformation, Villari effect,
GMR sensor, PHYBALArticle history:
Received 7 November 2016
Accepted 29 May 2017

1.

Introduction

The first, who systematically investigated the lifetime behavior of railway wheel axles undercyclic loading was August Wöhler (1819-1914) and the diagram discussing the cycle number tofailure of a set of nominal equal specimens (a number of 7 and more) fatigued at the same nominal
loading conditions has also been named according to him as the ‘Wöhler-curve’ being also named as
S-N-curve (S-stress, N-cycle number) in the international terminology [1] (Figure 1). A typical
S-N-curve is shown in Figure 2.

ISSN-1883-9894/10 © 2010 – JSM and the authors. All rights reserved.

152

Figure 1: August Wöhler [1]Figure 2: The S-N-curve

As the microstructure of real materials cannot be considered homogeneous there is a stochastic
scattering in the failure cycle number, which is becoming larger with decreasing applied stress. The
numbers of cycling are discussed in a logarithmic scale. A fatigue life is called ‘low cycle fatigue’(LCF) when the cycle number to failure NF is below 105 cycles, ‘high cycle fatigue’ (HCF) if NF is
above but below 107 and ‘very high cycle fatigue’ when even being above. Experiments are
performed under stress- or strain-controlled conditions. Parameters influencing such experiments aretemperature, cycling frequency, mean stress or mean strain, respectively, described by the stress- or
strain-ratio. Within the PHYBAL approach described below a separation is made between constant
amplitude tests (CAT) and load increase tests (LIT) the latter being a multiple step test with a constant
stepwise load increase.
In LCF and partially also HCF tests the specimen under test starts very early to change its surface
roughness by developing extrusions and intrusions due to dislocation slip bands reaching the surface
followed by micro crack development and ending in surface-breaking macro cracking.
Key elements in structural design are the material selection for an assumed service load (staticload and cyclic loads), the ultimate strength and the fatigue strength (continuous amplitude tests andrandom/stochastic loads) and the ductility. A component’s geometry, especially notches, and thestress conditions, including residual stresses are of important influence on lifetime.

2.

Basic Steps into NDT for Fatigue

Fraunhofer IZFP started in 1998 with first investigations to develop NDT technology tocharacterize fatigue damage. It was the beginning of a very fruitful cooperation with the Institute forMaterials Science and Engineering at Kaiserslautern University at the time and up to 2014 under theleadership of Dietmar Eifler.

As the meta-stable austenitic stainless steels 1.4541 (X6 CrNiTi 1810) and 1.4550 (X6CrNiNb 1810) are well introduced in power stations and plant constructions, because of theircorrosion resistance and high toughness, the evaluation of early fatigue damage and thus theresidual life is a task of enormous practical relevance. However, these types of steel form
martensite due to quasistatic and cyclic deformation by a phase transformation from the fcc
-phase to the bcc ’-martensite phase. Secondary hardening observed at room temperature iscaused by continuously increasing martensite formation; the terminology “secondary hardening”
reflects the fact that, from the beginning, with increasing load cycle number the material
reacts, at first, with increasing uncontrolled plastic strain amplitude a,p (cyclic softening),
and then, with decreasing plastic strain amplitude (cyclic strengthening or hardening).
An accelerated martensite formation leads to shortened life times in cyclic deformation
experiments. At room temperature, crack initiation mainly takes place in martensitic regions (besides

153slip bands in the austenite phase) and these often starting at carbo-nitrides. Increasing martensite
formation is an indicator for increasing material damage, subsequent to cyclic loading. The detectionof martensite in austenitic components can be seen as a hint to local plastic deformation and thus local
damage.
Due to the magneto-elastic effect the martensitic phase develops under the exposition in thegeomagnetic field of the earth and as a consequence specimens/components develop localized
ferromagnetic properties, which can be detected by sensitive magnetic probes. In the above named
cooperation two Ph.D. studies were initiated [2, 3] that have touched upon this topic in different ways.
Table 1 shows the chemical composition and Figure 3 presents the fatigue specimen with circularcross-section geometry
Table 1 Chemical composition in weight%
Element

C

N

S

Mn

P

S

Cr

Mo

Ni

Ti

Charge F

0.05

0.002

0.4

1.09

0.024

0.005

17.81

0.27

9.3

0.3

Charge K

0.03

0.006

0.45

1.72

0.022

0.014

17.31

0.28

10.18

0.16

Figure 3: Fatigue specimen geometry

Most of the fatigue tests [2] were performed under stress control and mean-stress-free conditions(R = -1) at room temperature and 320°C in a servo-hydraulic machine. The standard monitoring
technique applied, is to measure the uncontrolled plastic strain amplitude a,p through direct
measurement by using strain gages, or indirect calculation from physical parameters being measured(see chapter 3 and 4). Figures 4 and 5 document this in case of fatigue tests performed at room
temperature and 300°C respectively.
At room temperature constant amplitude tests were performed at stress amplitudes between 300
and 400 MPa at increments of 20 MPa and at 300 °C experiments were performed at stress amplitudes
between 240 and 290 MPa respectively. A very different behavior can be observed for those twodifferent temperature regimes as can be seen from Figures 4 and 5.

154

Plastic
Plastic strain
Strain

X 6 CrNiTi 18 10

Load cycles

Figure 4: Cyclic deformation curve at room temperature

Plastic strain
Plastic
StrainLoad cycles
Load cycles

X 6 CrNiTi 18 10

Figure 5: Cyclic deformation curve at 300°C

The secondary hardening observed at room temperature (Figure 4) is not observed at 300 °C(Figure 5). However, martensite is developing at 300 °C too, but to a much lower content. This was
the reason to why SQUID (Superconducting Quantum Interference Devices) sensors have been
considered in the NDT evaluation, which at that time had been just developed as high-temperature
super-conducting ceramic sensors [4] beside Giant Magneto Resistors [5].

155

HCF-I (room t emperat ure)HCF-II (T=300°C)

4.0
M agnet ic Flux Densit y [µT]

3.5
3.0
2.5
1.0

0.5

0.0

1E-4

1E-3

0.01

X 6 CrNiTi 18 10

0.1
N/N

max

1

10

100

[% ]

Figure 6: SQUID magnetometer measurements at tablet-specimens, cutting the fatigue specimens after
different load cycles

The GMR sensor system is based [3] on an integrated circuit (IC) in which 4 GMR are integrated
as a Wheatston bridge circuit, 2 of them being magnetically shielded while the other 2 were not. The
IC can be used as a magnetometer to measure absolutely the magnetic field or as a receiver sensor inan eddy current transmitter-receiver experiment. As transmitter a small joke-type u-shaped joke isapplied which senses the gauge length of the fatigue specimen with a 1mm lift-off. The IC is as sensor
integrated between the two pole-shoes of the little joke. Figure 7 shows the GMR sensor and the clip
gage (strain measurement) in the measurement position.

Figure 7: GMR and Clip gage in measurement condition

In Figure 8 the GMR eddy current transfer-impedance is discussed (blue color) and comparedwith the plastic strain amplitude (red color). Depending on the content of martensite, the eddy current
impedance obviously becomes sensitive such that the secondary hardening due to the martensite canbe seen. As the martensite has enhanced dislocation density, electrical conductivity as well as
magnetic permeability will be reduced, furthermore, the compressive residual stresses in themartensite phases change the permeability to lower values. However, a certain threshold must be
passed, such that the effect becomes visible for stresses a ≥ 380 MPa.
In Figure 9, we can learn that the GMR transfer impedance follows exactly the time behavior of
the strain, but indicates with the increased off-set the continuous development of martensite, i.e. an

156

800

X6 CrNiTi 18 10
GMR-Wirbelstrommessung
One-step-test
X6
CrNiTi 18 10
R = -1, room temperature
Einstufenversuche,
R = -1, RT
Eddy current impedance

400 MPa2
3 
apa,p10][

GMR-ImpedanzZGMR
ZGMR[a.u.]
GMR-Impedance[arb.
Units]

increase of magnetization in the specimen, which was documented by the SQUID magnetometermeasurements too (Figure 6).
1000
3

600

380 MPa400

1330 MPa

200

300MPa0101

X 6 CrNiTi 18 10103
Lastspielzahl
Loadcycles

105

107

0

Figure 8: Online monitoring of fatigue tests at room temperature with the GMR, one step tests

2

GMR eddy current impedance
GMR-Wirbelstrommessung
multiple-steploading, loading mix
mehrstufige
Belastung

ZGMR
-3

600

a,p 10 ]GMR-Impedanz ZGMR [a.u.]

800

1

400

a,p
200

0
0

X 6 CrNiTi 18 1051,210Lastspielzahl
Load cycles

02,4105

Figure 9: Multi-step loading with a stochastic loading mix, room temperature experiment

3.

The Basis of PHYBALWhen Dietmar Eifler became professor in Essen, he took over the thermometric measurement
technique from his predecessor, Professor H. Harig [6], but then further developed the monitoring
technique by implementing additional electrical resistance measurements in the servo-hydraulictesting machine. The schematic of this setup is shown in Figure 10 and cyclic deformation curves
based on strain (a), temperature (b) and electrical resistance measurements (c) are given in Figure 11.
To reliably perform the temperature measurement, the clamping of the fatigue specimens has to157

be thermostatically controlled by external cooling. By doing this, a continuous heat flow from thespecimen into the clamping is guaranteed. The resistance measurement is realized by high precision inthe µ regime. It should also be mentioned here, that H. J. Bassler [2] begun to perform online
monitoring of temperature as well as strain and compared the results with the development of themagnetic phase in cyclic deformation curves when applying load increase tests. It was the beginningof the PHYBAL approach development and the integration of magnetic measurements.

Figure 10: Thermometric, electric resistance and strain measurements

158

Figure 11: Cyclic deformation curves based on a) strain, b) temperature, c) resistance4.

The PHYBAL Procedure [7, 8]

At least as long as a material can be fairly considered to be homogeneous the physically-based
life calculation PHYBAL can replace the standard Wöhler test by one load increase test (LIT) and two

159

constant amplitude tests (CAT). The LIT is performed to estimate the endurance level (if this can beconsidered to exist at all) and to select appropriate amplitudes for the two CATs. The LIT starts(Figure 12a) at a stress amplitude a, start, which is stepwise increased by a (20 MPa) after a defined
number of cycles N (9000) until failure, being a range after which stabilization in the plastic strain
development (hardening and/or softening) can be considered. Besides the stress amplitude a, thepossible measurable physical properties (plastic strain amplitude a,p, change in temperature T,change in electrical resistance R) have been indicated in Figure 12b. Also the impedance obtained
through the GMR sensor as a result of the magnetic field can be plotted versus the number of cycles
N.

Figure 12 a: Load Increase Test (LIT) with stress amplitude aFigure 12b: Measured Cyclic Deformation curves, a,p, T, R, or GMR impedance/magnetic field

The stress amplitude a from which the measured properties (the measurands: a.p, T, or R)
increase significantly non-linearly according a power law, defines a,LIT, the lower stress value for the
LIT. This stress level is around the endurance limit and, with the load steps to follow, even a closer
indication for the endurance limit may be given. The stress amplitude reached at specimen failure isindicated as f, LIT. The stress-controlled axially loaded LITs and CATs are performed on a
servo-hydraulic machine using triangular load-time functions and a load cycling frequency in the 5 Hz
range.
The power law per Morrow is assumed as model and can be used to describe the stress-strain160

curves as shown in Figure 12b obtained from the LIT and transferred to the CAT behavior. In theconventional terminology, it is valid, as a function of the strain amplitude (Equation (1)):

 a  K   a, p 

n

(1)

Here K’ is the cyclic hardening coefficient and n’ the cyclic hardening exponent. The hardening
exponent n’ is found as the logarithmic decrement of the power law shown in Figure 12b, so far themeasurand is a.p.
By generalizing the power law for physically measured properties other than plastic strain, being
called M here, one obtains (Equation (2)):

 a  K M  M 

nM

(2)

The generalized hardening coefficient is K M and the generalized cyclic hardening exponent is nM .
The generalized Basquin equation describes, similar as the power law in Equation (1) the relation
between the applied stress and the load cycle number (Equation (3))

 a   f ,M  2N f 

bM

(3)

 f ,M is the fatigue strength coefficient and bM the fatigue strength exponent respectively. Bothare unknown and must be determined by data evaluation. However, per Morrow’s law the bM can be
determined through the following relation:

bM 

nM
5nM 1(4)

The only residual finally unknown is  f ,M that can be determined from the CATs throughEquation (3).
The S-N-curve can then be calculated according to (Equation (5)):
1   bMN f  0.5 a   f ,M 

(5)Figure 13a shows the procedure for the calculation of the Wöhler curve from the two
experimental CAT data and 8 LIT-data in the, for instance as example, (a - R) half-logarithmic-plane. At first, we have only the 2 points of the CAT- data and the linearly fitted 8
LIT data points with the logarithmic decrement of 0.29. The next step is to transform the 6 LIT-data
points, to find in between the a, LIT and f, LIT values, into the linear-logarithmic fit with the 2
CAT-data-points. The solution for calculating is the simple linear mathematical theorem ofintercepting lines. By using this, the 6 old LIT data-points find in the plane new coordinates. The newlogarithmic decrement is found by linear data-fit, taking in account the 2 CAT point-coordinates aswell as the new LIT data-coordinates; it is 0.09. The fatigue strength coefficient, which is 650,
follows, according equation (3), from one of the CAT-data-evaluations. Figure 13b summarized thecomparison between the calculated approach and classical Wöhler curve approach. The agreement isfull sufficient.

161

Figure 13a: Transformation of the LIT data into the CAT data

Figure 13b: Agreement between measured Wöhler curve data and calculated ones

5.

Conclusions and Future Activities

The economic benefit of Wöhler curve calculation based on only 3 tests is tremendous. Testingtime and material cost reduce the overall cost in the range of 90% when compared to the conventional
Wöhler curve determination. However, the procedure needs validation and reliable qualification. The
confidence of industrial users has to be found in order to initialize a consensus towards a
standardization activity. In the case of strongly scattering materials further research maybe required
although the principle may still be valid. Ageing infrastructure integrity can be secured by such ashort term and reduced sampling process allowing sampling to be made from the ageing structure.
Sampling here is therefore only a weak ‘destructive’ measure or better a fairly simple replacement.
Especially with the magnetic data generated a strong access to the fatigue characterization of steels
can be provided.

162

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