Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading
An approach has been developed that allows assessing inelastic phenomena in a material based on the parameter of the phase shift angle distribution between the stress and strain, which is measured in local zones on the surface of the investigated material. The distribution of the phase shift angle v...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
2009
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| Назва видання: | Проблемы прочности |
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| Цитувати: | Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading / G.G. Pisarenko, A.V. Voinalovich, A.N. Mailo // Проблемы прочности. — 2009. — № 1. — С. 141-146. — Бібліогр.: 11назв. — англ. |
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irk-123456789-484642013-08-20T06:26:47Z Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading Pisarenko, G.G. Voinalovich, A.V. Mailo, A.N. Научно-технический раздел An approach has been developed that allows assessing inelastic phenomena in a material based on the parameter of the phase shift angle distribution between the stress and strain, which is measured in local zones on the surface of the investigated material. The distribution of the phase shift angle variance in the service life range investigated allows tracing the kinetics of the discrete phenomena of inelasticity in the material studied. Разработан подход, позволяющий оценить явление неупругости в материале. Подход базируется на параметре угла фазового сдвига между напряжением и деформацией, измеряемого в локальных зонах на поверхности исследуемого материала. Распределение дисперсии угла фазового сдвига в рассматриваемом диапазоне долговечности позволяет описать кинетику развития дискретной неупругости в исследуемом материале. 2009 Article Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading / G.G. Pisarenko, A.V. Voinalovich, A.N. Mailo // Проблемы прочности. — 2009. — № 1. — С. 141-146. — Бібліогр.: 11назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48464 539.4 en Проблемы прочности Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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Научно-технический раздел Научно-технический раздел |
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Научно-технический раздел Научно-технический раздел Pisarenko, G.G. Voinalovich, A.V. Mailo, A.N. Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading Проблемы прочности |
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An approach has been developed that allows assessing inelastic phenomena in a material based on the parameter of the phase shift angle distribution between the stress and strain, which is measured in local zones on the surface of the investigated material. The distribution of the phase shift angle variance in the service life range investigated allows tracing the kinetics of the discrete phenomena of inelasticity in the material studied. |
| format |
Article |
| author |
Pisarenko, G.G. Voinalovich, A.V. Mailo, A.N. |
| author_facet |
Pisarenko, G.G. Voinalovich, A.V. Mailo, A.N. |
| author_sort |
Pisarenko, G.G. |
| title |
Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading |
| title_short |
Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading |
| title_full |
Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading |
| title_fullStr |
Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading |
| title_full_unstemmed |
Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading |
| title_sort |
evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading |
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Інститут проблем міцності ім. Г.С. Писаренко НАН України |
| publishDate |
2009 |
| topic_facet |
Научно-технический раздел |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/48464 |
| citation_txt |
Evolution of discrete phenomena of inelasticity in aluminum alloy under cyclic loading / G.G. Pisarenko, A.V. Voinalovich, A.N. Mailo // Проблемы прочности. — 2009. — № 1. — С. 141-146. — Бібліогр.: 11назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
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| first_indexed |
2025-07-04T08:58:58Z |
| last_indexed |
2025-07-04T08:58:58Z |
| _version_ |
1836706210204614656 |
| fulltext |
UDC 539.4
Evolution of Discrete Phenomena of Inelasticity in Aluminum Alloy
under Cyclic Loading
G. G. P isarenko , A. V. V oinalovich, an d A. N. M ailo
Pisarenko Institute of Problems of Strength, National Academy of Sciences of Ukraine,
Kiev, Ukraine
An approach has been developed that allows assessing inelastic phenomena in a material based on
the parameter o f the phase shift angle distribution between the stress and strain, which is measured
in local zones on the surface o f the investigated material. The distribution o f the phase shift angle
variance in the service life range investigated allows tracing the kinetics o f the discrete phenomena
o f inelasticity in the material studied.
K e y w o r d s : inelasticity, high-cycle fatigue, damageability, hardening, softening.
In tro d u c tio n . Investigations on the dynamics o f the discrete phenom ena of
structure evolution in local volumes o f the m aterial under cyclic deformation are
aimed at determining the relationship between these phenom ena and changes in
the material m echanical properties, and describing the laws o f damageability
within its lifetime range prior to the initiation o f the m ain crack. Contemporary
works on physical metallurgy consider the process o f m aterial deformation and
fracture as a dynam ically non-linear system, w hich is connected w ith the
environm ent by means o f the information exchange [1]. In order to describe the
changes in the m aterial structure in quantitative terms w ith a view to assess its
system characteristics at various stages o f damage accumulation, mathematical
approaches are used, which include m ultifractal param eterization o f the structure
[2, 3]. Special attention is paid to the near-surface layer o f the m etal as the place
o f fracture initiation, with the emphasis in m ost cases [4] on the difference in the
rates o f self-organization o f m icro- and m esostructures (self-sim ilarity and
hierarchical nature o f the processes) in the near-surface layers and internal
volumes.
It is shown in [5, 6] that the process o f plastic deformation taking place at a
microlevel under cyclic loading is characterized by regular stage-like nature. The
results o f the investigations o f inelasticity variation within the high-cycle fatigue
region [7-9] show that traditional concepts o f the scattered damage progressing in
stages in metals and alloys at a m acrolevel can be extended by taking into account
the scale level o f the analysis o f inelastic processes o f m aterial deformation w hich
reveal stochastic peculiarities at the m icrostructural level. This approach is of
current importance considering the fact that the characteristics o f inelastic
processes in the material that were obtained on the basis o f the integral assessment
do not reflect the discrete character o f the m aterial damageability under cyclic
deformation [10].
The aim o f this work is to investigate the kinetics o f the discrete phenomena
o f inelasticity in the aluminum alloy under cyclic deformation in the high-cycle
fatigue region.
© G. G. PISARENKO, A. V. VOINALOVICH, A. N. MAILO, 2009
ISSN 0556-171X. Проблемы прочности, 2009, № 1 141
G. G. Pisarenko, A. V. Voinalovich, and A. N. Mailo
E x p erim en ta l M ethods. Changes in inelasticity were investigated during
fatigue tests o f cylindrical specimens w ith 7.5 mm diameter under axial tension-
compression on a m agnetostrictive setup w ith the loading frequency o f 20 kHzо
and a symmetrical cycle. Cyclic loading o f up to 5 • 10 cycles was applied at that
enabling to assess the kinetics o f discrete m anifestations o f inelasticity in the
studied alloy before the initiation o f the m ain crack. This paper presents the
results o f investigations o f the kinetics o f inelasticity in the aluminum alloy with
due account o f the frequency characteristics o f the phase shift distribution
between the stress and strain which is m easured in local volumes o f the m aterial
(for grain clusters) on the working surface o f the specimen using the method
described in [9].
The kinetics o f the m aterial inelasticity was evaluated taking into account the
changes in the value o f the generalized energy dissipation param eter at a steady
stress state initiated in the zone o f contact interaction between the gauge and the
specimen surface. The changes in the generalized param eter were attributed to the
evolution o f the material m icrostructure in the specimen surface zone studied.
Upon term ination o f certain stages o f the fatigue tests, statistically representative
samples o f the values o f the energy dissipation param eter corresponding to a
certain specimen loading time were obtained for each stage individually. Kinetic
dependencies o f the measured param eter were analyzed taking into account
relative variance o f the param eter values reflecting the discrete character o f the
inelasticity changes in the process o f cyclic loading.
E x p erim en ta l R esults. The kinetics o f the m aterial inelasticity was
investigated on the specimens made o f aluminum alloy. For each o f the three
cyclic stress levels applied, the kinetic damage accumulation curves were plotted
in the coordinate system, where the X-axis shows the num ber o f the load cycles
and the F-axis shows the relative variance o f the generalized inelasticity parameter
(Fig. 1). The non-monotonous character o f the curves w ith irregular alternation o f
the maxim a and m inim a demonstrates the stochastic regularity representative o f a
stationary random process o f structural evolution o f a non-uniform dissipative
system w hich is the material under study. These regularities include:
(i) a decrease in the frequency o f the maxim a and m inim a occurrence on the
kinetic damage accumulation curves plotted for low amplitudes o f cyclic stresses;
(ii) an increase in the amplitude values o f the generalized inelasticity
param eter as the m aterial exhausts its plasticity at the stages o f specimen
nonlocalized damage.
As seen from the curves in Fig. 1, the energy dissipation decreases during the
initial period o f loading which is evidenced by the material hardening [5]
resulting from the ordering o f microstructure, redistribution o f local overstressed
zones throughout the specimen volume, and hom ogenization o f the material [6].
During local assessment, this process is characterized by a decrease in the
norm alized value o f the variance, as compared to that for the m aterial in the initial
state, and corresponds to the cyclic hardening o f the alloy on the initial part o f the
generalized fatigue curve during the integral assessment o f the material inelasticity
characteristic [11].
A t the initial stage o f loading, the presented curves show lowering o f the
kinetic characteristic to some m inim um value that m ay be connected w ith the
142 ISSN 0556-171X. Проблемы прочности, 2009, N 1
Evolution o f Discrete Phenomena o f Inelasticity
material hardening (the aluminum alloy studied belongs to the cyclically hardening
materials). On the curves given in Fig. 1, the point corresponding to such an
extremum is designated by digit 1. W ith an increase in the cyclic stress amplitude
in the course o f fatigue tests, a more intensive accumulation o f damages takes
place in the alloy structure w ithin one load cycle, which is evidenced by the
displacement o f the first extremum point towards the sm aller num ber o f the
operating cycles.
N, cycles
c
Fig. 1. Kinetic diagrams of the generalized parameter of local inelasticity for different cyclic stress
amplitudes [(a) o a = 83.4 MPa; (b) o a = 73 MPa; (c) oa = 65.3 MPa].
The authors o f [10] present their interpretation o f the discrete events of
structural evolution o f a fatigued polycrystalline m aterial sim ilar to those
considered in this paper, and revealed by the kinetic characteristics o f m icro
hardness o f alloy D16T subjected to cyclic deformation at a stress o f 159 MPa.
The experimental results summarized there account for the complexity o f the
revealed dependence o f the series o f macrohardness peaks on the num ber of
operating cycles characterizing this complexity by different level o f stability
against the influence o f cyclic deformation regimes shown by certain alloy
components (Al, Cu, Mg). The kinetic characteristics presented in Fig. 1 are their
analogues expressed by changes in the dissipative properties.
According to the conclusions concerning the behavior o f a dissipative system
in fatigue as presented in [11], the m aterial hardening process is governed by
certain laws. First o f all, this process is characterized by the discreteness o f the
m aterial hardening events w ith subsequent softening that occur periodically and
ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1 143
G. G. Pisarenko, A. V. Voinalovich, and A. N. Mailo
whose behavior is close to that described in [10]. According to the aforementioned,
the first event o f significant manifestation o f the changes in the properties o f the
fatigued polycrystalline m aterial (bifurcation o f dissipative structure) occurs
when the m aterial reaches the state o f ultimate plasticity [7] and is a random
quantity. Its position on the lifetime scale corresponds to the periodicity o f the
series o f the m aterial hardening-softening events succeeding each other to
fracture. Their position corresponds to the material capacity to resist fatigue in
accordance w ith the law described using the series o f Ivanova [11]:
N i
N
= A 1/ n
i+1
where A is a dimensionless universal constant o f fracture, N t is the num ber of
cycles corresponding to the ith extremum, and n = 1, 2, 4, 8, ... . According to
[11], the constant A characterizes the energy state o f the m aterial local volume
by analogy with the process o f melting. This constant is believed to be practically
independent o f the modifications in the metal chemical composition at room
tem perature and, therefore, its value was taken to be A ^ 0.22 for aluminum
alloys.
On the diagrams in Fig. 1, the calculated series is shown on a conventional
horizontal line by solid symbols and is compared to the experimental values of
the m inim a on the curves. The results o f comparison are listed in Table 1.
T a b l e 1
Comparison of the Recurrent Series Value with the Experimental Values
of the First Extremum on the Kinetic Curves of Damageability
a a , MPa 83.4 73.0 65.3
N 1calc , cycles 2.01-106 4.50-106 3.81-106
N lexp , cycles 1.51 • 106 4.00 • 106 5.60-106
0 ,% 26.0 7.1 31.9
In Table 1: a a is the amplitude o f cyclic stresses, N 1caic is the num ber of
1expcycles corresponding to the first calculated m em ber o f the recurrent series, N
is the num ber o f cycles corresponding to the first extremum on the curve, and 6
is the conformity error between the first extremum on the curve and the calculated
num ber o f cycles.
The task o f the calculation was to find the first value o f the num ber of
operating cycles which corresponds to the first point o f bifurcation. To do so, the
num ber o f cycles corresponding to the first m inim um on the curve was taken as
such in the first approximation. Next, the whole series was calculated for this
value. By comparing the obtained estimated life values o f the series and the
experimental ones, a standard error was determined which was used to specify the
accuracy o f the estimated life value. The calculation continued until the minimal
generalized error 6 between the estimated and experimental values was reached.
Comparison o f the num ber o f cycles corresponding to the hardening extrema on
144 ISSN 0556-171X. npoôëeMbi npounocmu, 2009, N 1
Evolution o f Discrete Phenomena o f Inelasticity
the kinetic diagram (Fig. 1) in the service life range to m acrocrack initiation and
the members o f the recurrent series calculated from the above formula is shown in
Fig. 2.
The graphs show a good agreement between the experimental data and the
calculated results. Therefore, the appearance o f the extrema on the kinetic curves,
which are similar to those shown in Fig. 1, may adequately reflect the kinetics o f
structural changes in the material o f an elastic-plastic body under conditions o f
non-localized fatigue damage.
N i , cycles N i > cycles
N j , cycles N i , cycles
a b
N t, cycles
N i, cycles
c
Fig. 2. Correspondence of the experimental values of the extrema to the members of the calculated
recurrent series [(a) a a = 83.4 MPa; (b) a a = 73 MPa; (c) a a = 65.3 MPa].
The developed m ethodology allows assessing the kinetics o f changes in the
material properties under conditions o f cyclic deformation by the parameters o f
distribution o f the generalized param eter o f inelasticity m easured locally on the
surface o f the material under study.
C o n c l u s i o n s
1. Local nonuniformity o f the material inelastic properties is a structure-
dependent characteristic o f damageability o f a structural material in fatigue.
2. A satisfactory agreement between the estimated values in the series o f
bifurcation points under cyclic loading and the hardening extrema on the curves
6 8
o f inelasticity distribution in the service life range from 10 to 10 cycles has
been obtained for an aluminum alloy.
ISSN 0556-171X. npoôneMu npouuocmu, 2009, № 1 145
G. G. Pisarenko, A. V. Voinalovich, and A. N. Mailo
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Received 11. 06. 2008
146 ISSN 0556-171X. npo6neMbi npouHocmu, 2009, № 1
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