Comparison of fatigue characteristics for some selected structural materials under bending and torsion
The paper presents a review of the multiaxial fatigue criteria including a ratio of normal and shear stresses. The paper also contains fatigue characteristics for bending and torsion of some selected constructional materials. The ratio of normal stresses to shear stresses was determined for the defi...
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irk-123456789-1391592018-06-20T03:11:33Z Comparison of fatigue characteristics for some selected structural materials under bending and torsion Kurek, М. Łagoda, Т. The paper presents a review of the multiaxial fatigue criteria including a ratio of normal and shear stresses. The paper also contains fatigue characteristics for bending and torsion of some selected constructional materials. The ratio of normal stresses to shear stresses was determined for the defined number of cycles Nf in the range 5⋅10⁴÷2⋅10⁶. Moreover, from the performed analysis of fatigue equations and the relative difference R it appears that materials can be divided into groups for which it is possible or it is not possible to apply the constant value of the considered ratio in the criteria including this ratio. Подано огляд критеріїв багатовісної втоми, які охоплюють співвідношення нормальних та зсувних напружень. Розглянуто втомні характеристики деяких вибраних конструкційних матеріалів за згину та закруту. Визначено співвідношення нормальних до зсувних напружень для певної кількості циклів Nf у діапазоні 5⋅10⁴÷2⋅10⁶. Із результатів аналізу втомних характеристик та відносної зміни R виявлено, що матеріали можна поділити на дві групи, для яких доцільно чи недоцільно застосувати стале значення розглянутого в критерії співвідношення. Дан обзор критериев многоосной усталости, которые включают соотношения нормальных и напряжений сдвига. Рассмотрены усталостные характеристики некоторых избранных конструкционных материалов при изгибе и кручении. Определено соотношение нормальных и напряжений сдвига для определенного числа циклов Nf в диапазоне 5⋅10⁴÷2⋅10⁶. Из результатов анализа усталостных характеристик и относительной разницы R установлено, что материалы можно разделить на две группы, для которых возможно или невозможно применить постоянное значение рассмотренного в критерии соотношения. 2011 Article Comparison of fatigue characteristics for some selected structural materials under bending and torsion / M. Kurek, T. Łagoda // Фізико-хімічна механіка матеріалів. — 2011. — Т. 47, № 3. — С. 59-67. — Бібліогр.: 22 назв. — англ. 0430-6252 http://dspace.nbuv.gov.ua/handle/123456789/139159 en Фізико-хімічна механіка матеріалів Фізико-механічний інститут ім. Г.В. Карпенка НАН України |
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The paper presents a review of the multiaxial fatigue criteria including a ratio of normal and shear stresses. The paper also contains fatigue characteristics for bending and torsion of some selected constructional materials. The ratio of normal stresses to shear stresses was determined for the defined number of cycles Nf in the range 5⋅10⁴÷2⋅10⁶. Moreover, from the performed analysis of fatigue equations and the relative difference R it appears that materials can be divided into groups for which it is possible or it is not possible to apply the constant value of the considered ratio in the criteria including this ratio. |
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Kurek, М. Łagoda, Т. |
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Kurek, М. Łagoda, Т. Comparison of fatigue characteristics for some selected structural materials under bending and torsion Фізико-хімічна механіка матеріалів |
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Kurek, М. Łagoda, Т. |
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Kurek, М. |
| title |
Comparison of fatigue characteristics for some selected structural materials under bending and torsion |
| title_short |
Comparison of fatigue characteristics for some selected structural materials under bending and torsion |
| title_full |
Comparison of fatigue characteristics for some selected structural materials under bending and torsion |
| title_fullStr |
Comparison of fatigue characteristics for some selected structural materials under bending and torsion |
| title_full_unstemmed |
Comparison of fatigue characteristics for some selected structural materials under bending and torsion |
| title_sort |
comparison of fatigue characteristics for some selected structural materials under bending and torsion |
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Фізико-механічний інститут ім. Г.В. Карпенка НАН України |
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2011 |
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| citation_txt |
Comparison of fatigue characteristics for some selected structural materials under bending and torsion / M. Kurek, T. Łagoda // Фізико-хімічна механіка матеріалів. — 2011. — Т. 47, № 3. — С. 59-67. — Бібліогр.: 22 назв. — англ. |
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Фізико-хімічна механіка матеріалів |
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AT kurekm comparisonoffatiguecharacteristicsforsomeselectedstructuralmaterialsunderbendingandtorsion AT łagodat comparisonoffatiguecharacteristicsforsomeselectedstructuralmaterialsunderbendingandtorsion |
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| fulltext |
59
Ô³çèêî-õ³ì³÷íà ìåõàí³êà ìàòåð³àë³â. – 2011. – ¹ 3. – Physicochemical Mechanics of Materials
COMPARISON OF FATIGUE CHARACTERISTICS FOR SOME SELEC-
TED STRUCTURAL MATERIALS UNDER BENDING AND TORSION
M. KUREK, T. ŁAGODA
Opole University of Technology, Poland
The paper presents a review of the multiaxial fatigue criteria including a ratio of normal
and shear stresses. The paper also contains fatigue characteristics for bending and torsion
of some selected constructional materials. The ratio of normal stresses to shear stresses
was determined for the defined number of cycles Nf in the range 5⋅104÷2⋅106. Moreover,
from the performed analysis of fatigue equations and the relative difference R it appears
that materials can be divided into groups for which it is possible or it is not possible to
apply the constant value of the considered ratio in the criteria including this ratio.
Keywords: fatigue characteristics, normal and shear stresses, constructional materials.
Most machines, devices and structures must be characterized by a very high life
and reliability. However, determination of fatigue life is often difficult because it can-
not be done with one equation. Numerical calculations allow to predict behavior of
machine elements and structures under service loadings [1–21]. At present fatigue life is
usually determined with analytic methods and computer simulations. This paper
presents relations between the fatigue strength of some selected materials under pure
bending and pure torsion, namely determination of the ratio of normal stresses to shear
stresses. Many fatigue stress criteria include this ratio in their equations. In the criteria
proposed by Tresca and Huber–Mises–Hencky assume 2 and 3 as values of this ratio,
respectively.
The main aim of this paper is to determine relations between the fatigue life under
bending and torsion for some chosen constructional materials. Next, the materials with
no parallelism of characteristics for pure bending and pure torsion are determined. A
model of fatigue life determination for such materials will be presented in future
papers.
Criteria of multiaxial fatigue. A multiaxial fatigue criterion must include a sub-
stitute quantity allowing to compare multiaxial and uniaxial loadings. Owing to that,
we are able to evaluate the influence of various complex loadings on fatigue life. If
cyclic behaviour of the material under simple loadings is known, it is possible to assess
influence of complex loadings on fatigue life. Even the oldest criteria of fatigue life
determination include the following ratio
1 /af afB = σ τ . (1)
Such relationship is the criterion proposed by Gough and Pollard [7], pioneers of
research work on bending and torsion. Relationships were modified by Nisihara and
Kawamoto in 1941 [15]. Gough’s criterion can be applied only for in-phase loadings.
The further modification by Lee [9] includes phase shifts. In [12] you can find a general
form of the multiaxial fatigue criterion for the high-cycle range. The equation assumes
that fatigue damage is caused by a linear combination of normal and shear stresses on
Corresponding author: M. KUREK, e-mail: m.kurek@doktorant.po.edu.pl
60
the critical plane. Findley [6] proposed the criterion based on observation of the planes
of fatigue crack initiation in steels and aluminium alloys. Another criterion including
the ratio σaf /τaf is the relationship presented by Stanfield, Guest and Stulen-Cummings
[18]. In [21], Zenner and Lui presented the criterion where the equivalent stress was
determined from the combination of the mean normal stresses σa and shear stresses τa.
In [3], Carpinteri and Spagnoli presented a proposal based on the experimental
criterion formulated by Gough. Achtelik [19] proposed the criterion for description of
fatigue strength under loading by synchronously variable torsional and bending
moments.
The basic relations between normal and static stresses allow to analyze bending
and torsion and obtain new forms of the multiaxial fatigue criterion. Ogonowski [11]
proposed the expression for elastic-plastic materials
1 1( ) max{ ( )} (2 ) ( )eg s
t
t B t B tη ησ = τ + − σ . (2)
This criterion is applied when the critical plane is influenced by shear stresses.
Walat [21] proposed the criterion for materials of intermediate properties
(between brittle and elastic plastic).
1 14 3 3 2 3(3 2 4)( ) ( ) ( )
3( 3 1) 3( 3 1)eg s
B Bt t tη η
+ −
σ = σ + τ
± ±
. (3)
In this case the critical plane includes elements of covariance of normal and shear
stresses. Some of multiaxial fatigue criteria including a ratio of normal and shear
stresses are shown in Table 1.
Table 1. Some of multiaxial fatigue criteria including a ratio of normal
and shear stresses
Author Criterion
Gough and Pollard
2
2 af
aeq ab at
af
⎛ ⎞σ
⎜ ⎟σ = σ + ⋅ τ
⎜ ⎟τ⎝ ⎠
Nisihara and
Kawamoto
2 2 2 2
2 1 3 2af afa a a
af af af af af
⎡ ⎤ ⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞σ στ σ σ⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟+ − + − =⎢ ⎥ ⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟τ τ σ τ σ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦
Crossland
( )
( )
1/ 22 2 2
1 2 3 1 2 2 3 3 1
1 2 33 3 1
a a a a a a a a a
af
af
af
σ + σ + σ −σ σ − σ σ −σ σ =
⎛ ⎞τ
′ ′ ′⎜ ⎟= τ − − σ + σ + σ
⎜ ⎟σ⎝ ⎠
Findley 2 ,max max( ),aeq nn kσ = σ + τ 2
2
2 1
af
af
af
af
k
σ
−
τ
=
σ
−
τ
61
Lee
1/
1 af at
aeq ab
af ab
αα⎡ ⎤⎛ ⎞σ τ⎢ ⎥⎜ ⎟σ = σ + ⋅⎢ ⎥⎜ ⎟τ σ⎝ ⎠⎢ ⎥⎣ ⎦
Matake ,max max2 1af
aeq n
af
⎛ ⎞τ
⎜ ⎟τ = − σ + τ
⎜ ⎟σ⎝ ⎠
Lassere i Froustey ( )
2
22 2af
a a af F m
af
⎛ ⎞σ
⎜ ⎟σ + τ = σ −α σ
⎜ ⎟τ⎝ ⎠
Stulen i Cummings 1 31af
aeq a a
af
⎛ ⎞σ
⎜ ⎟σ = σ − − σ
⎜ ⎟τ⎝ ⎠
Carpinteri i Spagnoli
2
2 2
max
af
aeq a
af
⎛ ⎞σ
⎜ ⎟σ = σ + τ
⎜ ⎟τ⎝ ⎠
Zenner i Lui 2 2
aeq a aa bσ = σ + τ ,
2
1 3 4 ,
5
af
af
a
⎡ ⎤⎛ ⎞σ⎢ ⎥⎜ ⎟= −⎢ ⎥⎜ ⎟τ⎝ ⎠⎢ ⎥⎣ ⎦
2
1 6 2 .
5
af
af
b
⎡ ⎤⎛ ⎞σ⎢ ⎥⎜ ⎟= −⎢ ⎥⎜ ⎟τ⎝ ⎠⎢ ⎥⎣ ⎦
As for some materials, the coefficient k is stable, and the materials are characteri-
zed by parallelism of characteristics. In the case when
1( ) /f af afB N ≠ σ τ (4)
the solution of the algorithm for fatigue life assessment has not been found.
Comparison of fatigue characteristics for bending and torsion. The test results
in the high-cycle regime were approximated by the regression equation for bending
according to the ASTM recommendations 0 in the following form
log logf aN A Bσ τ= + σ ,
log Nf = Aσ + Bσ logσa . (5)
For torsion the regression equation takes the form
log Nf = Aτ + Bτ logτa , (6)
where Aσ, Bσ, Aτ, Bτ – coefficients of the regression equation for bending and torsion,
respectively.
The relations between the fatigue lives for pure bending and pure torsion of some
constructional materials were determined according to the test results presented in [6–
9, 14–16, 20]. In this paper, also the value of the following ratio was also determined
1
( )
( )
( )
a f
f
a f
N
B N
N
σ
=
τ
(7)
After transformation of equations (5) and (6) we have:
1 1log
1( ) 10
f
A AN
B B
fB N
σ τ
σ τ
⎛ ⎞− −
−⎜ ⎟
⎝ ⎠= (8)
Non-ferrous metal alloys. Brass CuZn40Pb2 [9] and aluminium alloys D-30 [15]
and AlCuMg1 [7] were considered. Chemical composition of the tested non-ferrous
62
metal alloys are shown in Table 2. Coefficients of the regression equation according to
Eqs. (5) and (6) for particular loading variants are shown in Table 3. Figs. 1 and 2 pre-
sent the fatigue curves for pure bending and pure torsion of CuZn40Pb2 and AlCuMg1.
Table 2. Chemical composition of the tested non-ferrous metal alloys
Material, % Mg Cu Pb Al Zn Mn Fe Si
CuZn40Pb2 [9] – 0.5...0.6 0.1...0.35 0.1 rest – – –
AlCu4Mg1 [8] 0.4...1.0 3.8...4.8 – rest 0.5 0.4...1.0 0.7 0.2...0.8
D-30 [16] 0.42 3.81 – rest – 0.44 0.38 0.35
Table 3. Coefficients of regression equations for non-ferrous metal alloys
Bending Torsion
Material
Aσ Bσ Aτ Bτ
CuZn40Pb2 [9] 19.977 –5.857 45.309 –17.172
AlCuMg1 [7] 21.806 –7.027 19.939 –6.868
D-30 [15] 30.538 –10.753 25.385 –9.174
Fig. 1. Fig. 2.
Fig. 1. Fatigue curves for pure bending and pure torsion for CuZn40Pb2:
1 – logNf = 19.997 – 5.857 logσa; 2 – logNf = 45.309 – 17.172 logτa.
Fig. 2. Fatigue curves for pure bending and pure torsion for AlCuMg1.
1 – logNf = 21.806 – 7.027 logσa; 2 – logNf = 19.939 – 6.868 logτa.
Fig. 3 shows a relation between the
ratio B1(Nf) and a number of cycles Nf for
non-ferrous metals.
The ratio B1(Nf) for both kinds of
duralumin is constant, and its value for
D-30 varies from 1.407 to 1.492, for
AlCu4Mg1 the ratio B1(Nf) takes the
values 1.642÷1.665. Stability of the ratio
of normal stresses to shear stresses allows
to apply a constant value of this ratio in
fatigue criteria including it in their
relationships. In the case of brass, the
ratio B1(Nf) was not constant, and it could
Fig. 3. Dependence of the ratio B1(Nf) on a
number of cycles Nf for non-ferrous metals.
1 – AlCuMg1; 2 – D-304; 3 – CuZn40Pb2.
63
be expected after analysis of fatigue curves (Figs. 1 and 2) and coefficients of the curve
slopes. As for brass, various values of B1(Nf) cause that it is not possible to apply a
constant value of the ratio in fatigue criteria where the ratio is included.
Then, stability of B1(Nf) was determined by calculation of the relative difference R
expressed as
4 6
1 1
4
1
[ (5 10 ) (2 10 )] 100%
(5 10 )
B BR
B
⋅ − ⋅
= ⋅
⋅
. (9)
Analysis of the considered constructional materials is based on the assumption
that a relative difference less than 10% qualifies the material as a material of the cons-
tant coefficient B1(Nf) in the given range of Nf.
Carbon steels. Iron-carbon alloys are unalloyed carbon steels because contents of
other elements does not exceed the limit values defined. Carbon steels have got diffe-
rent structures depending on carbon contents. Coefficients of the regression equation
for particular variants of loading are presented in Table 4.
Table 4. Coefficients of regression equation for carbon steels
Bending Torsion
Material
Aσ Bσ Aτ Bτ
982 FA [16] 43.821 –14.925 49.333 –18.518
5695 [16] 46.383 –16.667 61.250 –25.000
0,1%C1 [16] 36.395 –12,346 35.918 –13.513
0,1%C2 [7] 48.276 –17.240 40.571 –15.873
0,4%C3 [7] 35.883 –11.778 65.702 –25.641
0,4%C [7] 96.926 –37.037 47.868 –18.868
0,9%C [7] 23.410 –6.944 21.071 –6.493
S20C [5] 20.846 –6.173 18.364 –6.061
SC450 [5] 49.741 –18.518 36.301 –13.699
S45C [5] 25.294 –7.936 25.807 –9.174
S45C-H [5] 34.555 –11.111 38.473 –13.513
S45C-DA [5] 40.225 –14.084 30.505 –10.989
Ck45 [15] 29.147 –9.200 55.995 –20.702
C40 [15] 48.262 –17.332 40.757 –15.170
1 – full specimen; 2 – holed specimen; 3 – normalized.
Fig. 4 shows the dependence of the ratio B1(Nf) on a number of cycles Nf for
carbon steels. In order to obtain readable graphs, the considered steels were divided
into two groups. Group 1 includes steels with the relative difference R less than 5%
(Fig. 4a). Group 2 contains steels with R greater than 5%.
Low-alloy steels. The test results obtained for steels S255 JO (former 18G2A) and
S355JOWP (former 10HNAP) were considered. Fig. 5 presents the dependence of the
ratio B1(Nf) on a number of cycles Nf for steels S255 JO and S355JOWP. From Fig. 5 it
results that in the case of steel S255 JO the ratio B1(Nf) is not constant in the range of a
number of cycles (5·104÷2·106). This conclusion can be proved by determination of the
relative difference for steel S255 JO (it is greater than 18%). The considered ratio is
constant for steel S355JOWP, where R does not exceed 5%. Finally, we can state that
64
in the case of low-alloy steels the ratio B1(Nf) in the given range of a number of cycles
can take similar or different values.
Fig. 4. Dependence of the ratio B1(Nf) on a number of cycles, Nf. a: R < 5%; 1 – steel S20C;
2 – steel 0.1% C full specimen; 3 – steel 0.1% C, holed specimen; 4 – steel 982FA;
5 – steel 0.9% C. b: R > 5%; 1 – steel S45C; 2 – steel 5695; 3 – steel 0.4% C normalized;
4 – steel 0.4% C; 5 – S45C-H; 6 – steel S45C-DA; 7 – steel SC450.
Medium-alloy steels. Table 5 contains coefficients of regression equations for
particular loading variants 16. Fig. 6 shows the dependence of changes of the ratio
k(Nf) on a number of cycles Nf
for nickel steels 3% Ni, 3...3.5% Ni, and chromium
steels CrV, 42CrMo4V.
Fig. 5. Fig. 6.
Fig. 5. Dependence of the ratio B1(Nf) on a number of cycles Nf for low-alloy steels.
1 – S355JOWP; 2 – S255 JO.
Fig. 6. Dependence of the ratio B1(Nf) on a number of cycles Nf for medium-alloy steels.
1 – 3% Ni; 2 – CrV; 3 – 3…3.5% Ni; 4 – 42CrMo4V.
Table 5. Coefficients of regression equations for medium-alloy steels
Bending Torsion
Material
Aσ Bσ Aτ Bτ
3%Ni [6] 37.825 –12.500 62.878 –24.390
3…3.5%Ni [6] 39.354 –12.658 44.219 –15.625
CrV [6] 55.418 –18.868 68.478 –25.840
42CrMo4V [6] 16.439 –4.286 33.663 –11.628
High-alloy steels. Coefficients of the regression equations for particular loading
variants are presented in Table 6.
65
Fig. 7 shows the dependence of a change of the ratio k(Nf) on a number of cycles Nf
for high-alloy steels. Similar problem concerning high-alloy steels was analyzed in [2].
Table 6. Coefficients of regression equation for high-alloy steels
Bending Torsion
Material
Aσ Bσ Aτ Bτ
NiCr [6] 76.923 –22.544 27.027 –80.538
30CrNiMo8 [5] 27.536 –8.049 69.578 –24.622
3.5% NiCr I [6] 156.600 –55.555 41.422 –14.080
3.5% NiCr I (hollowed) [6] 30.731 –9.259 213.000 –83.333
3.5% NiCr II [6] 55.200 –18.182 47.900 16.667
35NCD16 [12] 31.953 –10.030 44.510 –15.080
Cast irons. Cast iron is a casting
alloy of iron, carbon and other elements
containing from 2 to 3.6% of carbon in
form of cementite or graphite. The follo-
wing cast irons were subjected to tests
under bending and torsion: Silal, Nicro
Silal and IC2. Silal is an example of a
brittle material, and Nicro Silal is a com-
parably plastic cast iron. The cast irons
GGG40, GGG60 or GTS45 were con-
sidered under tension, compression and
torsion [7, 14]. Fig. 8 presents the
dependences of the ratio B1(Nf) on a
number of cycles Nf for some cast irons.
From Fig. 8a and values of the rela-
tive ratio R for the first group of cast
irons it appears that the ratio B1(Nf) can-
not be related to all the cast irons. In the
case of Nicro Silal and IC2 constant value of B1(Nf) can be seen, for Silal a value of the
relative difference R exceeds 10%. As for the second group of cast irons (Fig. 8b), we
can find constant B1(Nf), so it is possible to apply B1(Nf) for the given group of cast
irons. The values of the ratio B1(Nf) vary about 1. It results from properties of cast irons
which are brittle and non-ductile materials.
Fig. 8. Dependence of the ratio B1(Nf) on a number of cycles Nf.
a: R > 5%; 1 – IC2; 2 – Nicro Silal; 3 – Silal.
b: R < 5%; 1 – GTS 45; 2 – GGG 60; 3 – GGG 40.
Fig. 7. Dependence of the ratio k(Nf) on a
number of cycles Nf for high-alloy steels.
1 – 3.5% NiCr I (hollowed); 2 – 3.5% NiCr II;
3 – 30CrNiMo8; 4 – 3.5% NiCr I;
5 – 35NCD16; 6 – NiCr.
66
CONCLUSIONS
The conversion factors proposed by Tresca and Huber–Mises–Hencky are widely
used and related to all the constructional materials for determination of strength and
fatigue life of machines. In this paper the fatigue dependence B1(Nf) was determined
for some chosen materials. Analyzing the graphs and values of the relative difference
R, we can draw the following conclusions:
1. It is not possible to apply the ratio B1(Nf) for all considered non-ferrous metals.
In the case of brass, a value of the ratio B1(Nf) is not constant in the given range of a
number of cycles. The remaining non-ferrous metals can be characterized by the
constant ratio but its value is below the Tresca and HMH conversion factors.
2. In the case of carbon steels, a value of the ratio B1(Nf) is not constant but it varies
depending on chemical composition and the applied heat treatment. Carbon steels
characterized by the constant values of the ratio in the given range of a number of cycles
do not reach the Tresca conversion factor 2 and the HMH conversion factor 3 .
3. The ratio B1(Nf) is not constant for all the considered alloy steels. It depends on
the applied heat treatment and contents of alloy additions.
4. As for cast irons, the ratio B1(Nf) in the given range of a number of cycles Nf is
close to 1 and strongly differs from Tresca and HMH conversion factors, and is
characteristic for the Galileo hypothesis.
РЕЗЮМЕ. Подано огляд критеріїв багатовісної втоми, які охоплюють співвідношен-
ня нормальних та зсувних напружень. Розглянуто втомні характеристики деяких вибра-
них конструкційних матеріалів за згину та закруту. Визначено співвідношення нормаль-
них до зсувних напружень для певної кількості циклів Nf у діапазоні 5⋅104÷2⋅106. Із ре-
зультатів аналізу втомних характеристик та відносної зміни R виявлено, що матеріали
можна поділити на дві групи, для яких доцільно чи недоцільно застосувати стале значен-
ня розглянутого в критерії співвідношення.
РЕЗЮМЕ. Дан обзор критериев многоосной усталости, которые включают соотно-
шения нормальных и напряжений сдвига. Рассмотрены усталостные характеристики не-
которых избранных конструкционных материалов при изгибе и кручении. Определено со-
отношение нормальных и напряжений сдвига для определенного числа циклов Nf в диапа-
зоне 5⋅104÷2⋅106. Из результатов анализа усталостных характеристик и относительной раз-
ницы R установлено, что материалы можно разделить на две группы, для которых воз-
можно или невозможно применить постоянное значение рассмотренного в критерии соот-
ношения.
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Received 01.10.2009
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