Method of low-cycle fatigue test results processing
There is considered the method of proceeding during elaboration of low-cycle fatigue test results of metals. Presented method enables to determine the material data in various periods of fatigue life. The results obtained with the use of proposed method allow taking into account during fatigue life...
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Фізико-механічний інститут ім. Г.В. Карпенка НАН України
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| Cite this: | Method of low-cycle fatigue test results processing/ S. Mroziński, A. Lipski // Фізико-хімічна механіка матеріалів. — 2012. — Т. 48, № 1. — С. 79-82. — Бібліогр.: 5 назв. — англ. |
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Mroziński, S. Lipski, A. 2018-06-19T20:05:18Z 2018-06-19T20:05:18Z 2012 Method of low-cycle fatigue test results processing/ S. Mroziński, A. Lipski // Фізико-хімічна механіка матеріалів. — 2012. — Т. 48, № 1. — С. 79-82. — Бібліогр.: 5 назв. — англ. 0430-6252 https://nasplib.isofts.kiev.ua/handle/123456789/139186 There is considered the method of proceeding during elaboration of low-cycle fatigue test results of metals. Presented method enables to determine the material data in various periods of fatigue life. The results obtained with the use of proposed method allow taking into account during fatigue life calculations as the visible changes of cyclic properties of material. The above is of special importance in the case of material characterized by the absence of stabilization period. Подано новий метод аналізу результатів мaлoциклoвих випробувань металів на втому, який дає змогу визначити характеристики матеріалів на різних стадіях втоми. Отримані дані можуть бути використані для розрахунків втомної довговічності елементів конструкцій. Представлен новый метод анализа результатов мaлoциклoвых испытаний металлов на усталость, который позволяет определить характеристики материалов на разных стадиях усталости. Полученные данные могут быть использованы для расчета усталостной долговечности элементов конструкций. This paper was realized in the framework of the grant no. 1215/B/T02/2011/40 funded by Ministry of Science and Higher Education in 2011-2013. en Фізико-механічний інститут ім. Г.В. Карпенка НАН України Фізико-хімічна механіка матеріалів Method of low-cycle fatigue test results processing Эффективный метод обработки результатов испытаний на малоцикловую усталость Ефективний метод обробки результатів випробувань на малоциклову втом Article published earlier |
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Method of low-cycle fatigue test results processing |
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Method of low-cycle fatigue test results processing Mroziński, S. Lipski, A. |
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Method of low-cycle fatigue test results processing |
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Method of low-cycle fatigue test results processing |
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Method of low-cycle fatigue test results processing |
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Method of low-cycle fatigue test results processing |
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method of low-cycle fatigue test results processing |
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Mroziński, S. Lipski, A. |
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Mroziński, S. Lipski, A. |
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2012 |
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English |
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Фізико-хімічна механіка матеріалів |
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Фізико-механічний інститут ім. Г.В. Карпенка НАН України |
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Эффективный метод обработки результатов испытаний на малоцикловую усталость Ефективний метод обробки результатів випробувань на малоциклову втом |
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There is considered the method of proceeding during elaboration of low-cycle fatigue test results of metals. Presented method enables to determine the material data in various periods of fatigue life. The results obtained with the use of proposed method allow taking into account during fatigue life calculations as the visible changes of cyclic properties of material. The above is of special importance in the case of material characterized by the absence of stabilization period.
Подано новий метод аналізу результатів мaлoциклoвих випробувань металів на втому, який дає змогу визначити характеристики матеріалів на різних стадіях втоми. Отримані дані можуть бути використані для розрахунків втомної довговічності елементів конструкцій.
Представлен новый метод анализа результатов мaлoциклoвых испытаний металлов на усталость, который позволяет определить характеристики материалов на разных стадиях усталости. Полученные данные могут быть использованы для расчета усталостной долговечности элементов конструкций.
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0430-6252 |
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https://nasplib.isofts.kiev.ua/handle/123456789/139186 |
| citation_txt |
Method of low-cycle fatigue test results processing/ S. Mroziński, A. Lipski // Фізико-хімічна механіка матеріалів. — 2012. — Т. 48, № 1. — С. 79-82. — Бібліогр.: 5 назв. — англ. |
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| fulltext |
79
Ô³çèêî-õ³ì³÷íà ìåõàí³êà ìàòåð³àë³â. – 2012. – ¹ 1. – Physicochemical Mechanics of Materials
METHOD OF LOW-CYCLE FATIGUE TEST RESULTS PROCESSING
S. MROZIŃSKI , A. LIPSKI
University of Technology and Life Sciences, Bydgoszcz, Poland
There is considered the method of proceeding during elaboration of low-cycle fatigue test
results of metals. Presented method enables to determine the material data in various
periods of fatigue life. The results obtained with the use of proposed method allow taking
into account during fatigue life calculations as the visible changes of cyclic properties of
material. The above is of special importance in the case of material characterized by the
absence of stabilization period.
Keywords: low-cycle fatigue, mechanical properties.
In the method of fatigue life calculations, which is based on local strain and stress,
analysis [1] the material data determined in fatigue tests in the low-cycle fatigue area
are used. The test realization and elaboration of the results correspond to ASTM E 606-04:
Standard Practice for Strain-Controlled Fatigue Testing. According to the directions in
this document the low-cycle properties of metals are determined on the base of con-
stant – amplitude test on several (five minimum) levels of controlled stress or strain
[2]. On each strain or stress level at least three fatigue tests are performed. During each
fatigue test for the selected loading cycles momentary values of loading force and strain
of the specimen are recorded. Recorded stress and strain values enable to carry out the
analysis of the basic hysteresis loop parameters and to define relations between them.
One of the two characteristics evaluated on the base of the performed fatigue tests
is the diagram of cyclic strain describing the relation between plastic strain amplitude
εap and stress amplitude σa. It is assumed that there is the exponential relation between
these parameters from the stabilization period. In the bilogarithmic coordinate system
this relation is described with the Morrow equation [3]
lg lg lga apK n′ ′σ = + ε , (1)
where K′ is exponent of the diagram, n′ is directional coefficient of the diagram (coeffi-
cient of hardening). The n′ and K′ parameters of equation (1) are the basic material data
used during fatigue life calculations. There are no doubts about the presented method
of results elaboration in the case of cyclically stable materials. They are obvious, ho-
wever, in the case of materials characterized by the changes of cyclic properties they
do not reveal the period of stabilization.
In the papers on low-cycle fatigue tests of metals [4] it can be found that the
period of stabilization of metals and their alloys is very short or even it is absent [5].
For such materials the necessary hysteresis loop parameters (σa and εap) are obtained
from the period which corresponds to the half-life n/N = 0.5, where N is fatigue life on
the given loading level until failure, n = 0.5N.
The method of the determination of hysteresis loop parameters, in the case when
there is no stabilization period, is presented in Fig. 1. Schematically the example of the
changes of diagrams of one of the parameters (σa), which can be found in equation (1)
is shown for five values of total strain εac.
Corresponding author: S. MROZIŃSKI, e-mail: Stanislaw.Mrozinski @utp.edu.pl
80
It results from the course of σa
changes that the material undergoes
visible weakening. Points marked with
a circle on individual stress diagrams
indicate the fatigue half-life (0.5n/N) at
each level of total strain εac. The values
of n′ and K′ parameters obtained as the
result of coordinates approximation of
these points with the equation (1) de-
scribe only the momentary cyclic pro-
perties of the material from the life pe-
riod n/N = 0.5. During fatigue life calcu-
lations they are informally approxima-
ted for the whole range of fatigue life.
Such an approach in determination of
material data can be one of the reasons
of the calculations and test results diversification for many metals and their alloys [5].
The basic aim of this paper is the analysis of the influence of the material damage
degree on the momentary parameters of equation (1). The additional aim is the evalua-
tion of the possibility of analytical description of material data in various periods of
fatigue life.
Test procedure. Tests were carried out with the use of specimens made of
AW2024 aluminium alloy (σu = 514 MPa, σy = 322 MPa). The specimens for the tests
were prepared according to
standard [1]. Shape and di-
mensions (in mm) of the spe-
cimen are presented in Fig. 2.
Tests were carried out at
five values of strain εac. Total
strain amplitude (εac = const)
was the controled parameter
during fatigue tests. Detailed
chart of the tests is presented in Table.
During fatigue tests for the selected loading cycles the momentary values of
loading and strain were recorded. As the criterion of the fatigue tests termination on
each value of strain εac there was accepted about 5% decreasing of the loading force in
the half-cycle of tension in relation to its value from period of saturation.
New method of tests results processing and its verification. The loading and
strain values recorded for the selected cycles of loading were processed in order do
determine the changes of the basic hysteresis loop parameters, namely εap and σa. Mo-
mentary stress in the specimen σ was determined by dividing the momentary value of
the loading by the cross-section area of the specimen. With the use of maximum (σmax)
and minimum (σmin) stress
values the value of stress
amplitude σa was evalua-
ted. Similar way of pro-
ceeding was accepted in
the case of plastic strain
amplitude εap determina-
tion. In Fig. 3 the example
of the diagrams of two
Fig. 1. Method of tests results processing
with the use of the classical method
(material without a stabilization period).
Fig. 2. Test specimen.
Table. Parameters of loading courses
Loading course Parameters
εac1 = 0.5%
εac2 = 0.65%
εac3 = 0.8%
εac4 = 1.0%
εac5 = 1.5%
f = 0.2 Hz
81
hysteresis loop parameters (εap and σa) in the function of loading cycles number is shown.
Fig. 3. Courses of changes of hysteresis loop parameters σa (a) and εap (b):
1 – εac = 0.5%; 2 – 0.65; 3 – 0.8; 4 – 1.0; 5 – 1.5%.
As it was expected the visible period of cyclic properties stabilization was not
observed. With the increase of the loading cycle number n the characteristic parameters
of hysteresis loop change. The stress amplitude σa increases (Fig. 3a) and at the same
time the plastic strain amplitude εap decreases (Fig. 3b). The changes of these loop pa-
rameters prove the cyclic hardening of aluminium alloy. Hardening increases with the
increase of the strain level εac.
In order to evaluate the influence of
fatigue damage degree on the equation (1)
parameters, a new method of the results
processing was applied. The essence of this
method is that during approximation of
hysteresis loop parameters (εap and σa)
with straight lines described with equation
(1) their values from various periods of
relative life n/N are used. This is shown
schematically in Fig. 4.
In Fig. 4 there the method of tests
results processing after separation of 10
periods of relative life n/N for each level of
loading are presented. These periods are
obtained with the use of the parallel lines
L1–L10, which indicate the periods of life in
which the values of the loop parameters εap and σa are determined.
Coefficients n′ and exponents K′ of equation (1) obtained in various periods of life
are analysed in the function of the relative life n/N. Examples of the obtained diagrams
are presented in Fig. 5. The values of the mentioned parameters obtained with the use
of the classical and proposed method are marked with circles.
On the base of obtained diagrams it can be found that values of n′ and K′ parame-
ters undergo changes and depend on the period of relative life n/N. Analysis of the re-
sults elaborated with the use of the classical method demonstrates that values of n′ and
K′ parameters determined in the half-life (n/N = 0.5) are not the mean values for the
whole area of life. Comparative analysis of the obtained results shows the scale of sim-
plification which is calculated by accepting the values of n′ and K′ parameters from one
period of fatigue life n/N = 0.5 as the results of elaboration. Equation (1) parameters
obtained during the tests can be presented in the form of the discrete diagram or conti-
nuous function. In Fig. 5 the example of the elaborated results approximation in 10 pe-
riods of life with the use of the continuous function by connecting the middles of each
period of life with a fine line is shown.
Fig. 4. The way of tests results elaboration:
L1 = 0.1n/N; L2 = 0.2n/N; … , L10 = 1.0n/N;
1 – lgσa = lgK1 + n′1 lgεap;
2 – lgσa = lgK5 + n′5 lgεap;
3 – lgσa = lgK10 + n′10 lgεap; A – εap and σa
on level εac2 in various periods of n/N.
82
Fig. 5. Results of low-cycle tests elaboration with the use of the classical and new method:
a – values of K′ exponent (1 – K′ = const – classical method; 2 – K′ = f(n/N) – new method);
b – values of n′ coefficient (1 – n′ = const – classical method; 2 – n′ = f(n/N) – new method).
CONCLUSIONS
The values of n′ and K′ parameters of AW2024 aluminium alloy obtained as a re-
sult of the fatigue tests results processing with the use of the classical method (method
presented in standard [4]) describe only the momentary cyclic properties. As a result of
the observed alloy hardening with the increase of loading cycles number the hysteresis
loop parameters change (Fig. 3). The values of n′ and K′ parameters are not constant
and depend on the period of life for which they were determined. A new test method of
the results elaboration allows us to determine the values of n′ and K′ parameters in va-
rious periods of fatigue life. It can be important using n′ and K′ in fatigue life calcula-
tions of construction elements made of cyclically unstable metals (aluminium alloys,
copper, titanium etc). Material data obtained with the use of the new method of results
processing enable a designer to estimate the range of possible changes of cyclic proper-
ties. In the case of the crucial construction elements it allows us to carry out the veri-
fying calculations for the extreme values of these parameters. The condition of obtai-
ning a reliable description of changes of n′ and K′ parameters in the function of relative
life n/N with the use of new method is division of the whole area of life into suitable
number of partitions. When the number is high enough then it is possible to approxi-
mate obtained results with a continuous function. Results obtained in that form become
very handy in use and can be applied during fatigue life calculations when observed
changes of cyclic properties of the material are taken into account. Such an approach to
fatigue life calculations was presented among others in paper [5].
PЕЗЮМЕ. Подано новий метод аналізу результатів мaлoциклoвих випробувань ме-
талів на втому, який дає змогу визначити характеристики матеріалів на різних стадіях
втоми. Отримані дані можуть бути використані для розрахунків втомної довговічності
елементів конструкцій.
PЕЗЮМЕ. Представлен новый метод анализа результатов мaлoциклoвых испытаний
металлов на усталость, который позволяет определить характеристики материалов на раз-
ных стадиях усталости. Полученные данные могут быть использованы для расчета уста-
лостной долговечности элементов конструкций.
Aknowledgement. This paper was realized in the framework of the grant no.
1215/B/T02/2011/40 funded by Ministry of Science and Higher Education in 2011-2013.
1. Fatigue Testing and Analysis (Theory and Practice) / Y.-L. Lee, J. Pan, R. B. Hathaway,
M. E. Barkey. – Elsevier, 2005. – P. 103–236.
2. ASTM E 606-04 Standard Practice for Strain-Controlled Fatigue Testing. ASTM Int.
3. Morrow J. D. W. Internal Friction, Damping and Cyclic Plasticity: Cyclic Plastic Strain
Energy and Fatigue of Metals, ASMT STP-378. – Philadelphia, 1965. – P. 45–84.
4. Kocańda S. and Kocańda A. Low-cycle fatigue strength of metals. – Warszawa: PWN, 1989.
– 439 p. (in Polish).
5. Mroziński S. Stabilization of cyclic properties in metals and its influence on fatigue life //
Dissertations № 128. – Bydgoszcz: Wydawnictwо UTP, 2008. – P. 1–148. (in Polish)
Received 05.04.2011
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