Materials Sciences and Applications, 2012, 3, 398-407
http://dx.doi.org/10.4236/msa.2012.36057 Published Online June 2012 (http://www.SciRP.org/journal/msa)
The Transformation of the Heterogeneous Materials under
the Fatigue Deformation
S. Kh. Shamirzaev, J. K. Ziyovaddinov, Sh. B. Karimov
Physical Technical Institute of Uzbek Academy of Sciences, Tashkent, Republic of Uzbekistan.
Received February 24th, 2012; revised March 24th, 2012; accepted April 23th, 2012
ABSTRACT
The objects of our paper are aluminum alloy samples (AASs) contained the different amount of Cu, Mn, Mg, Si and Li.
We are modeling the features of microstructure of potential relief of an AAS and studying its transformation under both
imposed fatigue deformation and wetted by liquid metals (Ga; or Hg; Li; In). We illustrate the main ideas by using only
the “time series” allied with effective internal friction 1
eff
Q

of an AAS. AASs like B-95 or 7075 are heterogeneous
materials for which the more energy can be absorbed by selected micro-regions of a tested sample. So micro-crack in
the space of AAS and alarm state of AAS arises. Each micro-region will to contribute the (the internal friction
belong to k-th micro-region) to the effective internal friction—
1
k
Q
1
k
Q1
eff
Q

accordance with fit statistic k
g
. We find a
number of micro-regions—L and series k
g
& from the experimental data like as the internal friction
k
Q


1
eff
Q
versus both the number of cycles—N and the deformation—е. Series k
g
&


1,2,3,,
k
Qk L present the micro-
structures of AASs. In this paper also is presented the original technology to forecast fatigue damage of an AAS. Here
the fatigue sensitive element (FSE) used. We made multiphase heterogeneous mixtures (MHMs) which contents a vari-
able volume of initial components. It is selected MHMs are using for produce FSEs. The present paper is aimed to es-
tablish the correlation of the FSEs microstructures changes and corresponding changes of the aluminum alloy micro-
structures at imposing the same spectra deformation on both of them. A change of FSEs microstructure investigated by
using their effective electrical resistance data.
eff
R
Keywords: Amplitude-Dependent Internal Friction; Fatigue; Cracking Process; Alarm State; Fatigue Sensitive Element
1. Introduction
The microstructure of an AAS is reflected on the micro-
structure of its potential relief that is originated by both a
residual deformation and an imposed fatigue deformation.
In local regions of polycrystalline alloy undergoes fa-
tigue loads, a wide spectrum of strongly exited states
arises [1,2]. These states can not be described by tradi-
tional methods of a perturbation theory. With the help of
mechanics methods of damage one can study only the
growth of macroscopic cracks using empirical—formula
dependencies describing the growth of a crack.
The various impurities in Aluminum implemented the
various resistances to fatigue of an AASs. There is not a
common low permits one in advance to determine both
what kind and haw much of microstructures will be si-
multaneously belong to AAS after a number cycles of
loads.
The main objective of this paper is to present the ex-
perimental method for estimating the effective output
parameters of AASs and their change under both the im-
posed fatigue deformation and the wetted by liquid met-
als. The output data of AASs depend on the microstruc-
tures they are possessed of. For example, effective inter-
nal friction—1
eff
Q

of the AAS is formed as a sum of
microstructures’ internal friction— with fit statistics
—
1
k
Q
k
g
:
1
1
L
effk k
k
QgQ
1




; ;
1
1
L
k
k
g




1,2, 3,,kL
Damages accumulated at the initial stage of fatigue
process change local parameters of the AASs [2-4]. The
micro—structures are irreversibly changed if sufficiently
high deformation is imposed on AASs. These processes
become more intensive and more intricate under wetted
by lick of liquid metals such as Gallium—Ga or Mercury
—Hg, in this case the AAS become very brittle and re-
duce their lifetime to zero [5]. As the number of cycle’s
increases AASs’ microstructures eventually begin to
make change. As a result the alarm state of an AAS
arises. Monitoring of the AASs’ alarm states has to been

The Transformation of the Heterogeneous Materials under the Fatigue Deformation 399
developed. It is one of the main object of this paper.
New experimental techniques of k
g
and 1
k
Q

were
developed. The series k
g
& present the micro-
structures of polycrystalline Aluminum Alloys [4]. The
analysis of both new materials’ micro-structures as well
as existing materials’ micro–structures by novel methods
was made.
1
k
Q
2. The Ways of Realization
After imposing a limited number of cycles of fatigue
deformation that change the AASs’ microstructures, the
test cycle of deformation with selected value of ampli-
tude are imposed on the AASs’.
The

1
eff
Q

 (
 -value of imposed deformation) curve,
that was automatically recorded within test cycles of de-
formation, permits one to bring out the forthcoming
structures of AAS and its features, that will take place at
the near future cycles of imposed deformation. Reitera-
tion of these processes also for 1
eff
Q

 (—effec-
tive internal friction of AAS wetted by liquid metals—
Hg, Ga, In or Li) curve gives one the chance to do the
monitoring of the AASs microstructures change.
1
eff
Q
3. Internal Friction
Generally on a fatigue curve the numbers of cycles
are within 107 to 109. If an AAS is wetted by liquid
gallium—Ga, tends to sharp decrease with the ad-
vance of cracking process. It is known [5] that a quantity
of Ga leads to embitterment of AAS and decrease its
durability under Strain because of cracking processes.
The study of micro cracks, related with selected points
on surface of a test sample, is essential circumstance for
understanding the nature of fatigue. Another essential
circumstance is the study of sample’s internal friction
SN
N
Q
N


1
AAS.
But there are ample samples of construction alloys’


1
Q

 curves, that meet difficulties under the quantita-
tive comparison with the theory of dislocation damping.
This theory was developed for the homogeneous media.
The Aluminum Alloys are structurally heterogeneous. So
there are overstrained micro regions with high speed
evolution of damage processes. Those micro regions are
transformed under the load and verged towards to unsta-
ble state. They store mechanical energy due to both the
phonon mechanism [7] and a structural change which
one can notice before micro-cracking processes.
4. Experimental Installation
The two-component oscillator (sample and piezoceram-
ics), having an Eigen-frequency of about 18 kHz, was
used by Mason [8] for study the amplitude dependent
decrement on the vibration Strain amplitude. High level
of computer engineering was used by Mills D. and Brat-
ina W. J, [9], Kardashov B.K. et al. [10], Schenck H. et
al [11] for studying the effect of the oscillation amplitude
and temperature on the amplitude-dependent internal
friction


1
Q

. We also are using the two-component
oscillator (ZrTiPb-19 piezoceramics and the wetted by
liquid Ga on the AAS) having an Eigen-frequency of
about 20 kHz, for studying the effect of the oscillation
amplitude and cracking processes on the amplitude-de-
pendent internal friction

1
Q

 (see Figure 1).
The fatigue element (FE) is small weight (no more
than 5 g) and has film geometry. They are produced by
thermal vacuum evaporation of the charge onto the
polyamide support. The charge consists of a finely dis-
persed mixture of various initial components, e.g., a mix-
ture of granular Bi2–xTe3+x and Sb2–yTe3+y with carbonyl
iron [12].


. The internal friction relates to a number of
structure-dependent phenomena which permit to judge
about fine details of the real structure of a condensed
hard matter. For some samples

1
Q

 curves possess
a hysteretic dependence, which after Granato and Lucke
[6] can be related with moving and damping of hesitating
dislocation segments in the selected local regions of an
An ample number of grains do not take part in fatigue
process of both an AAS and a FE. In parallel with growth
of the number of strong deformed grains in AAS as well
as in FE, there are also the ample number of grains pos-
sessing their original state. The simple model of selected
FE describes these situations are given in [1,2]. Here is
Figure 1. Shape and ge ometrical dime nsions of the Aluminum Alloy Sample. A drop of liquid Ga w as imposed on this patter n.
After 12 hours this drop became a slur, as pictured at the Figure 1. (1) ZrTiPb-19—oscillator; (2) ZrTiPb-19—receiver; (3)
atigue element of the fatigue sensor. f

The Transformation of the Heterogeneous Materials under the Fatigue Deformation
400
also next sufficient conclusion: For all kinds of imposed
deformation (extension-compression; bending variations
with different coefficients of asymmetry; various spectra
of imposed deformations), at which the output parame-
ters (electric resistance n for FE and internal friction
for AAS) of materials are recorded in equal time (
 )
intervals, the next recurrent relations take place:
R
1
n
Q





11 nnnnn
R ORBRB 
  n
M (1)





111
11
nnn nn
QOQbQb 

 
n
m
g
q

(1а)
Here: n is the electric resistance of FE measured
under the same state of the environment; n is the ordinal
number of measurement (); g is the maxi-
mum number of the measurement performed; n is the
loading operator transferring the FE resistance from Rn-th
state to Rn+1-th state;
 is a complicated parameter to
characterize the type of imposed deformation; the “time
series” is composed of experimental data of the types:
R
1, 2,3,,n
O
12 11
,,, ,, ,,
nnn
RRRR RR

; (2)
 

 
 
21
1
111 1
1
11
,,, ,
,,
nn
nq
eff eff eff eff
eff eff
QQQ Q
QQ


 



,
(2a)
After imposing a limit number of cycles of fatigue de-
formation, that changes both the AA’s structure and the
FE’s structure, the test cycles of deformation with se-
lected value of amplitudes are imposed on the sample.
The 1 Q

 (—internal friction of AAS and
 —
value of imposed deformation) curve, that was automati-
cally recorded within test cycles of deformation, permits
one to bring out the forthcoming structures of AAS and
its features, that will take place at the near future cycles
of imposed deformation. Reiteration of these processes
gives one the chance to do the monitoring of fatigue fea-
tures of different Aluminum Alloys Samples as well as of
FEs (See [4]).
1
Q
5. The General Model
To gain a greater insight into why the

1
Q

 depend-
encies have the form as in Figure 2 (or Figure 3, before
B point), assume that for every overstrained micro-re-
gions the next




if
if
k
k
kk
Gm
QGm










 (3)
formulae takes place; k

varies in value. A scale factor
—


Gm is the same for each micro-region of the se-
lected AAS and depends on the degree of asymmetry—
of the imposed cyclic deformation. m
Each micro-region will be able to contribute to the
1
eff
Q

 accordance with statistic k
g
[2]:
 
1
1
L
kk
k
QgQ
1





; . (4)
1
1
L
k
k
g





1,,
k
QmN 

m
—Variation of internal friction of a k-th
micro-region depends on the amplitude-  and degree of
asymmetry- of the imposed cyclic deformation.
is a number of cycles; -number of micro-regions. For
the sake of convenience, assume that
N
L


m
1
max g
QM

and introduce the next value k
Z
:




kkg
Z
GmM m   ; (5)

1,2, 3,,kL
k
Z
and k
g
can be found from experimental data,
Figure 2 (or Figure 3, before the B point), and formulae
(4). Proceed as follows:

 
 
1
1
1
1
11 1
12
1
112 212
23
if 0
1
if
1
if , and so on.
L
k
k
QGgG
QGgGg
QGgGgGgg
 

 

 





 



  


(6)
Figure 2. Relative internal friction of Aluminum Alloy Sample (B-95) versus the relative imposed deformation.

The Transformation of the Heterogeneous Materials under the Fatigue Deformation 401
Notice that 12
L

   and

vary in each of
interval of


1
,
kk

. Let us take a derivative of


1
Q


with respect to  in each of Equation (6) equalities. Then
each subsequent equality can be subtracted from the pre-
ceding one. As a result one finds all quantities of k
g
,
k

, as well as ; and
L

Gm

g
M
m. Figure 4 pre-
sents the states of AAS after various numbers of cycles
and value of the imposed deformation. Information en-
tropy : S

1
L
k
k
SgLng

 
k
(7)
It is measure of the amount of disorder (different states)
in AAS states. This model also admits control of the
structural mutations in AAS and FE after N cycles of an
imposed regular deformation [4].
The same procedure was used on to the 1 Q



(or
, Q–1-wetted by liquid gallium-Ga internal fric-
tion of AASs) dependencies. Information entropy for this
situation . As a result, one can in advance to
bring out the forthcoming structures of FE&AAS and its
1
QN

1.374S
features that will take place at the near future cycles of
imposed deformation.
High level of computer engineering was used by us to
study the effect of the cracking processes, caused by liq-
uid metals, on the amplitude-dependent internal friction


1
Q

. The rate of sample mechanical irregularity was
found to be different for the different time after wetted
by liquid Ga.
In Figures 5 and 6 are presented the internal friction
Q–1 of Aluminum Alloy Samples versus of both the
—cycles and the
N

—deformations imposed on AASs
(D16-T). At the Figure 7 and Figure 8 are presented the
е
f
f changes under simple and complicated mode of
loads.
R
6. The Original Technology to Forecast
Fatigue Damage of an Aluminum Alloy
We shall consider both the fatigue curve of AA (Figure
9) and the equal change resistance curve (E—n curve
for selected values of


0n
rRRR 0 ) of SEs (Figure
Figure 3. Relative internal friction of Aluminum Alloy’s Sample (B-95) wetted by liquid gallium-Ga, versus the relative im-
posed deformation. This curve reflected the cracking process, beginning from B point. At the C point sample fractured.
Figure 4. The state (g & Zk) of Aluminum Alloy in the end (see point A on Figure 2) of the direct “road”. Information entropy
for this state S = 0.950. The full diagram (g & Zk) is inserted the greasy zero points of which are presented on the main figure.

The Transformation of the Heterogeneous Materials under the Fatigue Deformation
402
Figure 5. Internal friction Q–1 of Aluminum Alloy’s Sample (D16-T) versus N cycles of the imposed deformation coresponding
both 32 kg/mm2 (1) and 26 kg/mm2 (2) loads. The asymmetry coefficient is unity (m = 1).
Figure 6. Internal friction Q–1 of Aluminum Alloy’s Sample (D16-T) versus imposed deformation. (1) After imposed 5 × 104
cycles of 25 kg/mm2 load; (2) After imposed 5 × 106 cycles of 25 kg/mm2 load.
10) were obtained at the same conditions of imposed
spectrum of deformation.
Our description is very close to one, which was given
n [13]. The difference is in the next. Instead of to select i

The Transformation of the Heterogeneous Materials under the Fatigue Deformation 403
Figure 7. Reff of SE versus N (sample mode of loads).
Figure 8. Reff of SE versus N (complicated mode of loads).
the SE’s which ECRC is the “same” as investigated
metal, we introduce the alarm state of an Aluminum Al-
loy Sample (AAS), it gives us the opportunity to escape
the analysis of mechanical amplifier [13].

The Transformation of the Heterogeneous Materials under the Fatigue Deformation
404
Figure 9. Fatigue curve of an Aluminum Alloy (D16-T) sample.
Figure 10. Equal change of resistance curve for SE, rigidly installed on the sample of Aluminum Alloy.
Figure 10 shows the equal change of resistance curves
(ECRCs) of FEs rigidly installed at the sample of AA.
The rate of spectrum of deformation is the value E:


12
e
ф
Ee
 
2
0
1
ф
e
ф
eфre tt
d


 (8)
e(t)-value of imposed deformation; t-time; ф-equal
time interval at which the resistance’s n were meas-
ured. Figure 11 shows е
R
f
f versus n for difference
value of
R
E. From these curves one can compose the
Figure 12.
Figure 13 shows the operative curve for an AAS and

The Transformation of the Heterogeneous Materials under the Fatigue Deformation 405
Figure 11. Sensitive elements r-n dependence for different value of <E>.
Figure 12. Crossing the Fatigue Curve with equal change of resistance curves forms the Alarm Curve for Aluminum Alloy’s
Sample.
to be suit for it the Alarm curve. A crossing point of
these curves is the service AAS failure. One can adaptive
forecast this point using the series Equation (2) and for-
mula Equation (1) [14].
Just bellow we present the methodical example (Me)
helping to understand the main idea. (See Figure 14, or
Figure 1 Me ÷ Figure 4 Me). At the Figure 1 Me there
are two operative curve, which, for the simplicity, made
as linear. The first have energy equal E1, the second have
energy E2 (E2 > E1). The second Figure 2 Me is the
same as Figure 1 Me. But instead of arbitrary fixed sec-
nd line there one have a failure line. At the Figure 3 Me o

The Transformation of the Heterogeneous Materials under the Fatigue Deformation
406
Figure 13. Alarm curve for Aluminum Alloy’s Sample and operative curve for sensitive elements, rigidly installed onto this
Aluminum Alloy’s Sample .
Figure 14. Methodical examples.

The Transformation of the Heterogeneous Materials under the Fatigue Deformation 407
one can see fatigue curve for testing samples and a way
haw it may be getting from Figure 4 Me. On the Figure
4 Me, one can see haw to get the Alarm curve for testing
sample, using the data of Figure 4 Me and arbitrary fixed
first and second line from Figure 1 Me.
REFERENCES
[1] S. Shamirzaev, “Modelling a Fatigue Imperfection of
Structural Materials,” International Journal of Fatigue,
Vol. 24, No. 7, 2002, pp. 777-782.
doi:10.1016/S0142-1123(01)00192-X
[2] S. Shamirzaev, “Response of Mhfms at a Fast and a Slow
Operational Loads,” A Collection of Technical Papers of
the AIAA/ASME/ASCE/AHS/ASC Structures, Structural
Dynamics, and Materials Conference and Exhibit, St.
Louis, 12-15 April 1999, pp. 1717-1726.
[3] S. Shamirzaev and G. Shamirzaeva, “The Rheological
Model of Fatigue Damage of Cm,” Proceedings of the
13th International Congress on Rheology, Cambridge,
20-25 August 2000, pp. 377-379.
[4] S. Shamirzaev, S. Ganihanov and G. Shamirzaeva, “The
Monitoring of Fatigue Features of Cm for a Very High
Cycle of Loads,” Proceedings of the International Con-
ference on Fatigue in the Very High Cycle Regime, Vi-
enna, 2-4 July 2001, pp. 245-252.
[5] W. Rostoker, J. M. McCaughey and H. Markus, “Embrit-
tlement by Liqouid Metals,” Reinhold Publishing Corpo-
ration, New York, 1960.
[6] A. V. Granato and K. Lucke, “Theory of Mechanical
Damping Due to Dislocations,” Journal of Applied Phys-
ics, Vol. 27, 1956, pp. 583-593. doi:10.1063/1.1722436
[7] V. S. Kuksenko, V. I. Betechtin, V. S. Ryskin and A. I.
Slutsker, “Nucleation of Submicroscopic Cracks in Stressed
Solids,” International Journal of Fatigue, 1975, Vol. 11,
No. 5, 1975, pp. 829-840. doi:10.1007/BF00012900
[8] W. P Mason, “Physical Acoustics and the Properties of
Solids,” Journal of the Acoustical Society of America,
Vol. 28, No. 6, 1956, pp. 1197-1219.
doi:10.1121/1.1908593
[9] W. J. Bratina, “Physical Acoustics,” Academic Press, New
York, 1966.
[10] B. K. Kardashev, S. P. Nikanorov and O. A. Voinova,
“Amplitude Dependent Internal Friction in NaF Crystals
in the Temperature Range 295 to 4.2 K,” Physica Status
Solidi (a), Vol. 12, No. 2, 1972, pp. 375-379.
doi:10.1002/pssa.2210120204
[11] H. Schenck, E. Schmidtmann and H. Kettler, “Effect of
Strain Aging on Processes Occurring in Cyclic Loading
of Steel,” Arch Eisenhuettenw, Vol. 31, 1960, p. 659.
[12] S. Shamirzaev, “Mhms for Fatigue Gage,” Iron and Steel
Institute of Japan Proceedings of the 7th International
Conference, Steel Rolling ’98, Chibo, 9-11 November 1998,
pp. 844-849.
[13] V. T. Troshchenko and V. I. Boiko, “Fatigue Damage
Sensor and Substatiation of Its Application, Communi-
cations 1 and 2,” Problemi Prochnosti, Vol. 1, No. 187,
1985, pp. 3-14
[14] S. Shamirzaev, “The Theory of Output Parameters of a
Pressing Powder Mixture with Random Packaging Den-
sity,” Solid State Sciences, Vol. 6, No. 10, 2004, pp. 1125-
1129. doi:10.1016/j.solidstatesciences.2004.07.004