Method of the shortcut estimation of rails reliability by the fatigue strength criterion
The diagram of damage of structural steels under bending and contact loading has been constructed. The criterion of the critical state of steels is proposed, which corresponds to the formation of incipient surface cracks in the rolling friction zone. The methods of shortcut estimation of the damaged...
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Інститут проблем міцності ім. Г.С. Писаренко НАН України
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| Zitieren: | Method of the shortcut estimation of rails reliability by the fatigue strength criterion / L.A. Sosnovskii, N.A. Makhutov, V.I. Matviatsov, A.A. Kebikov // Проблемы прочности. — 2009. — № 1. — С. 88-94. — Бібліогр.:8 назв. — англ. |
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irk-123456789-484712013-08-20T06:59:35Z Method of the shortcut estimation of rails reliability by the fatigue strength criterion Sosnovskii, L.A. Makhutov, N.A. Matviatsov, V.I. Kebikov, A.A. Научно-технический раздел The diagram of damage of structural steels under bending and contact loading has been constructed. The criterion of the critical state of steels is proposed, which corresponds to the formation of incipient surface cracks in the rolling friction zone. The methods of shortcut estimation of the damaged state of railway rails, which provide prediction of their reliability and life under service conditions, are proposed. A set of experimental studies is made with objectives to justify the proposed diagram, criterion and methods. Описана процедура построения диаграммы повреждаемости конструкционных сталей при нагружении изгибной и контактной нагрузками. Предложены критерий критического состояния для сталей, который соответствует условию формирования поверхностных трещин в зоне трения качения, и методы ускоренной оценки поврежденного состояния железнодорожных рельсов, позволяющие прогнозировать их надежность и долговечность при эксплуатационном нагружении. Выполнена серия экспериментов, что дает возможность обосновать предложенные диаграмму, критерий и методы. 2009 Article Method of the shortcut estimation of rails reliability by the fatigue strength criterion / L.A. Sosnovskii, N.A. Makhutov, V.I. Matviatsov, A.A. Kebikov // Проблемы прочности. — 2009. — № 1. — С. 88-94. — Бібліогр.:8 назв. — англ. 0556-171X http://dspace.nbuv.gov.ua/handle/123456789/48471 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 Sosnovskii, L.A. Makhutov, N.A. Matviatsov, V.I. Kebikov, A.A. Method of the shortcut estimation of rails reliability by the fatigue strength criterion Проблемы прочности |
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The diagram of damage of structural steels under bending and contact loading has been constructed. The criterion of the critical state of steels is proposed, which corresponds to the formation of incipient surface cracks in the rolling friction zone. The methods of shortcut estimation of the damaged state of railway rails, which provide prediction of their reliability and life under service conditions, are proposed. A set of experimental studies is made with objectives to justify the proposed diagram, criterion and methods. |
| format |
Article |
| author |
Sosnovskii, L.A. Makhutov, N.A. Matviatsov, V.I. Kebikov, A.A. |
| author_facet |
Sosnovskii, L.A. Makhutov, N.A. Matviatsov, V.I. Kebikov, A.A. |
| author_sort |
Sosnovskii, L.A. |
| title |
Method of the shortcut estimation of rails reliability by the fatigue strength criterion |
| title_short |
Method of the shortcut estimation of rails reliability by the fatigue strength criterion |
| title_full |
Method of the shortcut estimation of rails reliability by the fatigue strength criterion |
| title_fullStr |
Method of the shortcut estimation of rails reliability by the fatigue strength criterion |
| title_full_unstemmed |
Method of the shortcut estimation of rails reliability by the fatigue strength criterion |
| title_sort |
method of the shortcut estimation of rails reliability by the fatigue strength criterion |
| publisher |
Інститут проблем міцності ім. Г.С. Писаренко НАН України |
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2009 |
| topic_facet |
Научно-технический раздел |
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http://dspace.nbuv.gov.ua/handle/123456789/48471 |
| citation_txt |
Method of the shortcut estimation of rails reliability by the fatigue strength criterion / L.A. Sosnovskii, N.A. Makhutov, V.I. Matviatsov, A.A. Kebikov // Проблемы прочности. — 2009. — № 1. — С. 88-94. — Бібліогр.:8 назв. — англ. |
| series |
Проблемы прочности |
| work_keys_str_mv |
AT sosnovskiila methodoftheshortcutestimationofrailsreliabilitybythefatiguestrengthcriterion AT makhutovna methodoftheshortcutestimationofrailsreliabilitybythefatiguestrengthcriterion AT matviatsovvi methodoftheshortcutestimationofrailsreliabilitybythefatiguestrengthcriterion AT kebikovaa methodoftheshortcutestimationofrailsreliabilitybythefatiguestrengthcriterion |
| first_indexed |
2025-07-04T08:59:31Z |
| last_indexed |
2025-07-04T08:59:31Z |
| _version_ |
1836706244151214080 |
| fulltext |
UDC 539.4
Method of the Shortcut Estimation of Rails Reliability by the Fatigue
Strength Criterion
L. A. Sosnovskii,a N. A. M ak h u to v ,b V. I. M atv iatsov ,c and A. A. K ebikovc
a S&P Group Tribofatigue Ltd., Gomel, Belarus
b Blagonravov Institute of Machine Science, Russian Academy of Sciences, Moscow,
Russia
c Belarusian State University of Transport, Gomel, Belarus
The diagram o f damage o f structural steels under bending and contact loading has been
constructed. The criterion o f the critical state o f steels is proposed, which corresponds to the
formation o f incipient surface cracks in the rolling friction zone. The methods o f shortcut
estimation o f the damaged state o f railway rails, which provide prediction o f their reliability and
life under service conditions, are proposed. A set o f experimental studies is made with objectives to
justify the proposed diagram, criterion and methods.
K e y w o r d s : structural steel, fatigue resistance, strength, hardness, critical state,
damage state, estimation methods, railway rail.
Calculation and experimental methods have found wide use in estimating the
m echanical fatigue resistance o f materials and structural components. The general
convention is that the endurance limit a _ is calculated in terms o f some
m echanical characteristics that are determined by simple experimental tests.
Numerous theoretical and experimental works [1-3] deal w ith study o f the
interrelation between various m echanical characteristics o f steels.
Only few works [e.g., 4, 5] discuss the relationships between the contact
fatigue limit (for pure rolling friction) and the m echanical characteristics o f steels.
However, such relationships have not gained further generalization, which would
make it possible to predict both the damaged and the critical states o f steels in
terms o f the fatigue resistance criterion.
The service defects o f rails were analyzed in m any works [6 , 7, etc.].
However, up to now the substantiated methods o f estimation o f the mechanical
state and the damage o f rails in operation are practically not available.
Therefore, our aim was to develop the criterion and the methods o f estimation
o f the damaged state o f structural steels, including railway rails under operating
conditions.
A generalized analysis o f a wide range o f experimental data [1-7], which is
supplemented w ith the results on steel tests for railway rails and wheels [8] has
been performed. As a result, the state diagram o f damage o f structural (carbon
and alloyed) steels has been constructed, which characterized the relations
between the endurance limits under contact loading (p f ) and bending ( a _ 1)
conditions, the tensile strength limit (a b ), Brinell hardness (HB) and Vickers
hardness (H V ) (Fig. 1). The investigated steels varied by chemical composition
and structural states obtained by the respective heat treatment. The above-
© L. A. SOSNOVSKII, N. A. MAKHUTOV, V. I. MATVIATSOV, A. A. KEBIKOV, 2009
88 ISSN 0556-171X. Проблемы прочности, 2009, № 1
Method o f the Shortcut Estimation o f Rails Reliability
0 100 200 300 400 500 600 HV
Fig. 1. The diagram of damage of structural steels.
mentioned relationships for the ring scheme in Fig. 1 have been experimentally
determined and are described by the following relations
P f = 3.12HB, o _ 1 = 0 .5 ab , o b = 3.5HB,
a _ 1 = 1 .6 H V (o _ 1 < 500 M Pa), ( 1)
o _ 1 = 2.68HV _ 0.0025HV2 _ 93.3 (o _ 1 > 400 M Pa).
The basic regularity integrally described by the diagram is such: the increase
in the fatigue resistance o f structural steel attained by different hardening methods
occurs in accord with the growth o f its hardness (strength). The diagram has one
specific feature: the dependence o f o _ ^ o b ) is extreme: at o b ~ > 1400 M Pa the
limit o f bending hardness o _ 1 m anifest the initial growth w ith increasing steel
strength, but then has a tendency to decrease. This allows us to propose the
following set o f interrelated characteristics (Fig. 1, shaded) controlling the
transition o f structural steels to the critical state:
550 < o_c) < 650 M Pa,
• 1200< p fc) < 1300 M Pa, (2a)
380 < H B (c) < 420,
ISSN 0556-171X. npodxeMbi npounocmu, 2009, N9 1 89
L. A. Sosnovskii, N. A. Makhutov, V. I. Matviatsov, and A. A. Kebikov
400 < H V (c) < 440,
1 (c) (2b)1300 < obc) < 1500 MPa.
As applied to the behavior o f steel determined under operating conditions,
the diagram (Fig. 1) m ay have the following interpretation. I f the hardness
(strength limit) grows in operation, this testifies that the fatigue resistance
increases at a time. Such increase represents the process o f steel hardening under
operating conditions and proceeds until transition into the critical region occurs
for the dependence o _ i ( H V ) (shaded in Fig. 1). This is the region where the
surface damage starts. Thus, Fig. 1 can be considered as the state diagram o f steel
damage in terms o f bending and contact fatigue criteria and (2 ) as the criterion for
the critical state o f structural steels.
Figure 1 yields another important practical conclusion: the increase in steel
hardness by more than = 400 H V is ineffective for systems that are operating
under cyclic conditions, when bending and contact stresses are excited
simultaneously and in the only (dangerous) region, i.e., in contact mechanical
fatigue.
Since the m echanical state o f steel can be estimated by the total set o f the
considered m echanical characteristics presented in Eq.(2) and by any o f them, for
practical purposes it is recom m ended to use the methods o f estimation o f the
m echanical state o f steel that are based on m easuring o f Vickers hardness. The
hardness was investigated for the railway rails o f the M insk city subway. The
objects o f investigation were railroad rail pieces: 1) new ones that have not been
in use; 2) rails after operation time correponding to 300 mln ton gross, i.e.,
norm ative tonnage that characterizes the total operating time o f rails. Afterthe
latter is achieved, the rails should be replaced irrespective o f the fact whether their
serviceability is exhausted or not; 3) after operating time o f 210 m ln ton gross.
The scheme o f m easuring the Vickers hardness H V at the rolling surface o f a rail
is shown in Fig. 2. Over the surface section 40 X 90 mm in size 2500 points were
marked, at each o f which the Vickers hardness was determined.
For the used rails it is established that the surface layer o f metal in a wheel
rolling over a rail is deformed unevenly - the specific regions (Fig. 2) determined
by a sharp change in the hardness distribution fields are revealed. These zones are
nonuniform both in width and length o f the rail head.
Figure 3 shows the obtained data analyzed using the state diagram o f damage
o f structural steels (Fig. 1). The solid vertical straight line stands for the initial
state (before operation H V = 261). The dotted lines correspond to characteristic
deformation zones I, II, and I I I after operating tim e o f 300 mln ton gross. It is
seen that in zone II I (H V = 320) the critical state is far short o f being attained,
whereas that o f the m etal surface layer in zone I I (H V = 410) is consistent with
the start o f the critical state. But in zone I criterion (1) for the critical state is
exceeded (H V = 480 > H V (c)). However it should be noted that this zone
occupies a small section o f the rolling surface (up to 8%); hence, it can be
assumed that the used rails did not exhaust their serviceability.
Such a conclusion has been supported by conducting com prehensive
experim ental studies o f the m icrostructure o f rail steel before and after use, by
90 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 1
Method o f the Shortcut Estimation o f Rails Reliability
Fig. 2. Typical distribution of hardness H V over the rolling surface of the rail head after operating
time of 300 (a) and 210 (b) mln ton gross [(1) mean hardness before use; (2) hardness distribution
after use].
analyzing the statistics o f rail failures, as well as by studying the anisotropy and
the character o f distribution o f material properties at the rolling surface o f rails.
The metallographic analysis o f the samples o f the rails before and after use
allows estimation o f the damaged state o f rail steel at the rolling surface in terms
o f the abundant defects and deformation level. The microstructure o f rail steel for
a new rail is shown in Fig. 3 in the left lower corner; for the largest deformation
region - zone I for a rail after having been used - in Fig. 3 in the upper right
corner. In the both cases the structure o f the core o f the samples is characterized
by the presence o f sorbite-like perlite, as well as o f separate zones o f fine-plate
perlite. A n embrilltled layer is seen in the surface layer o f zone I o f the rail
sample w ith operating tim e o f 300 mln ton gross. The density o f dislocations in
this layer is approximately 8-10 times higher than that in the bulk material. The
application o f the methods o f m etallographic analysis in this zone has permitted
revealing inclined cracks (Fig. 4a-c) formed under operating conditions.
Moreover, some internal cracks are observed, which are not exposed along the
surface and are oriented m ainly parallel to the surface (Fig. 4d). The depth of
occurrence o f cracks varies from 17 to 210 /im , the length - from 25 to 2000 ^m .
ISSN 0556-171X. npodxeMbi npounocmu, 2009, N 1 91
L. A. Sosnovskii, N. A. Makhutov, V. I. Matviatsov, and A. A. Kebikov
Fig. 3. Diagram of the mechanical state of rail steel after operating time of 300 mln ton gross.
In addition, the similar studies o f the rails w ith operating time o f 210 mln ton
gross are carried out. In this case, the m etallographic analysis has revealed no
operation damages similar to those shown in Fig. 4.
The analysis o f the data plotted in Figs. 1-4 leads to the general conclusion
that in operation there occurs spontaneous strengthening o f m aterial at the rolling
surface o f a rail. According to our data, the strength level estim ated by the
hardness growth increases with operating time in all zones and especially in
zone I (up to 1.5-2.0 times) In the latter case, approximately twofold increase in
the strength level is followed by transition to the strength reduction due to
development o f microcracks. It can be assumed that the critical state according to
(1) also corresponds to the above transition.
Thus, it has been confirmed by the metallographic analysis that the proposed
diagram o f the mechanical state o f steels permits one to correctly estimate the
damaged state o f rail steels under operating conditions as well as to predict the
onset o f the critical state.
The statistics and the character o f operation failures characterize the reliability
and serviceability o f railway rails. The accumulated specific failures o f rails
(pieces/km) - the failures pertained to the length o f the railway section were used
as the param eter for the serviceability o f rails under operating conditions.
Figure 5 presents the statistical results on rail failures in the line o f the M insk city
subway, whose length is 18.99 km, for 21 years o f operation after operating time
o f 315 m ln ton gross.
92 ISSN 0556-171X. npo6n.eMH npounocmu, 2009, N 1
Method o f the Shortcut Estimation o f Rails Reliability
Fig. 4. Incipient fatigue cracks found in zone I (operating time of 300 mln ton gross).
Coll ECt«( spe cific failv res, p i* ces/k 111
1
4.1S 1
3.4^
S.62
1
2.91
« a 1
■
2.3g 1A 1 failure
1 01
? 01 l . p
1
t.54|
1.70 ■" 1
rails wit 1 dangerous
[>.M
1.17 ailu res 1
0.58 0.69
0 47 0,47 a_s3. №2L 0.6? 0.69 )r74 0.80 ....... ....... .......
0.05 0.21 o;k> UJ2
y ear
p —
1
1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
14 42 70 98 126 155 186 220 237 275 315 359 403
tonnage, mln ton gross
Fig. 5. Collected specific failures of rails vs. operating time.
As follows from the above data, for the rate o f rail failures, w hich is over the
recent years, on the average, 0.28 pieces/km, and for the m ean density o f freight
traffic, which is 22 m ln ton gross in the line per year, the attained rate o f failures
o f 5 pieces/km the rail tonnage will be ~ 410 m ln ton gross, i.e., the rails can
opeerate approximately for 4 years.
The perform ed studies o f the structure and the failure rate o f rails form a
sound base for the serviceability prediction o f rails in terms o f criterion (2).
ISSN 0556-171X. npodxeMbi npounocmu, 2009, N 1 93
L. A. Sosnovskii, N. A. Makhutov, V. I. Matviatsov, and A. A. Kebikov
To examine the m aterial properties at the rolling surface o f a rail, the shortcut
nondestructive control m ethod has been used to study the anisotropy factor. The
ratio d x /d y o f the diagonals o f pyram id imprints in the longitudinal and
transverse directions is proposed to be used as the anisotropy factor. It is found
that the value o f the anisotropy factor K a = d x /d y for material in the initial state
varies from 0.944 to 1.050, on the average, accounting for 0.997. Thus, it can be
stated that before operation the rail m aterial is practically isotropic.
The value o f the anisotropy coefficient K A for each o f the characteristic
deformation zones is different. Thus, for zone I it is, on the average, 0.965; for
zone I I - 0.978; for zone I I I - 0.982. In addition, for all characteristic deformation
zones it appears that usually d x < d y . A ll this points to the development (in the
process o f operation) o f the deformation anisotropy o f the material properties; this
regularity is known and is established by the non-destructive control methods in
the tensile or shock viscosity tests o f the samples cut in the longitudinal and
transverse directions.
The anisotropy o f the material properties at the rolling surface o f the rail
head is indicative o f the fact that as (2) forecasts, in zone I w ith the hardness
values higher than the critical ones the initial layer-by-layer damages o f m aterial
are expected to form. Such defects were seen in the analysis o f the m icro
deformations o f the rails, whose operating time was 300 m ln ton gross (Fig. 4).
Moreover, this supports the proposed criterion and the methods o f estimating the
damaged state o f railw ay rails.
The general conclusion is that the perform ed comprehensive experimental
investigations have substantiated the proposed diagram and the criterion o f the
critical state o f steels, as well as the methods o f estimating the damaged state of
rails under operating conditions.
1. R. B. Heywood, D e s ig n in g A g a in s t F a tig u e , Chapman & Hall Ltd., London
(1962).
2. V. T. Troshchenko and L. A. Sosnovskii, F a tig u e R e s is ta n c e o f M e ta ls a n d
A llo y s [in Russian], Naukova Dumka, Kiev (1987).
3. L. A. Sosnovskii, M e c h a n ic s o f F a tig u e F a ilu r e [in Russian], SPG Tribo-
fatigue Press, Gomel (1994).
4. A. F. Zolotarskii, T h erm a lly S h o r te n e d R a ils [in Russian], Transport, Moscow
(1976).
5. A. A. Susin, C h e m ic a l-T h e rm a l Im p re g n a tio n o f H ig h -S tr e s s e d P a r ts [in
Russian], Belorusskaya Navuka, M insk (1999).
6 . W. Harris, G u id e lin e s s to B e s t P r a c t i c e f o r H e a v y H a u l O p e ra tio n s : W h eel
a n d R a i l I n te r fa c e I s su se s , IHHA, Virginia Beach, USA (2001).
7. J. N. Beynon “Surface m etallurgy and rolling contact fatigue and w ear of
rail,” in: Proc. o f the 7th Int. Conf. on C o n ta c t M e c h a n ic s a n d W ea r o f
R a il /W h e e l S y s te m s (Brisbane, Australia, 2006), Brisbane (2006).
8 . N. A. M akhutov, L. A. Sosnovskii, and A. A. Kebikov, “M ethod of
estimating the m echanical state o f the material o f the rails after long service,”
Z a v o d . L a b ., D ia g n . M a te r . , 73, No. 4, 49-54 (2007).
Received 11. 08. 2008
94 ISSN 0556-171X. npo6neMbi nponuocmu, 2009, № 1
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