Article citation information:
Vakulenko, I.A., Vakulenko, L., Bolotova, D., Kurt, B., Asgarov,
H., Çölova, Ö. Influence
structure on the plasticity of carbon steel of the railway wheel rim in
operation. Scientific Journal of Silesian
University of Technology. Series Transport. 2022, 115, 183-192. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2022.115.13.
Igor Alex VAKULENKO[1],
Leonid VAKULENKO[2],
Dariy BOLOTOVA[3],
Bulent KURT[4],
Hangardash ASGAROV[5],
Ömer ÇÖLOVA[6]
INFLUENCE STRUCTURE ON THE PLASTICITY OF CARBON STEEL OF THE RAILWAY
WHEEL RIM IN OPERATION
Summary. When
simulating the operating conditions of the rim of a railway wheel, an analysis
of change in the structural state from the possible degree of plastic
deformation and the heating temperature of steel near the rolling surface was
carried out. The development processes of spheroidization
and coalescence of cementite during heating of the cold-worked steel change its
ability to strain hardening. Substructure changes during heating to
temperatures of 500-550°C deformed steel are
accompanied by a simultaneous decrease in its ability to strain hardening and
the level of plasticity. When heated above 500-550°C,
the development of ferrite recrystallization processes provides a gradual
transition of the metal from substructure hardening to hardening from grain boundaries
with large angles of disorientation. It is shown that regardless of the nature
of the main structural element, the ability of steel to strain hardening and
the level of plasticity after heating are related by a proportional
relationship.
Keywords: carbon
steel, strain hardening, plastic deformation, temperature, cementite, ferrite
1. INTRODUCTION
In
the process of interaction of the railway wheel with the rail, the metal along
the rolling surface is subjected not only to significant plastic deformations
with a high degree of non-uniformity of distribution but also to significant
thermal effects. Analysis of known experimental data [1-3] indicates
differences in the kinetics of structural changes during the operation of
railway wheels, after thermal strengthening to different levels (Figure 1a). For a thin layer by the rim of the railway wheels, the
development processes of strain hardening during rolling are accompanied by a
different rate of accumulation of defects in the crystal structure in the phase
components of the carbon steel [4,5]. Considering that the structure of the
steel of the wheel consists of grains of ferrite and pearlite colonies (Figure 1b), the development of strain hardening processes in them,
with a simultaneous temperature effect during deceleration of the rolling
stock, can change the complex of properties of steel to a wide range. For
ferrite regions, the differences in the crystallographic slip systems between
adjacent grains, the frequency of the boundaries encountered [4], and the
formation of dislocation cellular structures form the basis for the increase of
the strength of the metal after cold plastic deformation. The presence of
dispersed carbide particles of various sizes and morphology (Figure 1b) in the steel structure is an additional obstacle to
moving dislocations. In proportion to the decrease in distance between the
cementite particles, an increase in the resistance of the metal to deformation
is achieved [6,7].
a
b
Fig. 1. Structure of the steel of the rim railway
wheel after accelerated cooling to a temperature of 650˚C:
(a) near the rolling surface; (b) at a distance of 25 mm.
Magnification is: (a) 800; (b) 1000
In
comparison with known mechanisms of strain hardening in large plastic
deformations, the development of this phenomenon in the area of the initiation
of plastic flow deserves some attention. In this case, it is of certain
theoretical and practical interest to trace the relationship between the
evolution of the structure and the development of strain hardening processes in
deformed carbon steels with different structural states. The aim is to assess
the effect of the structure of carbon steel on the strain hardening parameters
in the area of nucleation and propagation of plastic deformation.
2. MATERIAL AND
METHODS
The
material for this study was the carbon steel of a railway wheel (0.61% C) and
the concentration of the rest of the chemical elements was within the
requirements of regulatory documents. Samples of cylindrical shape, 3 mm in
diameter, after obtaining the required structural state in steel, were tested
with tension, as shown in the deformation diagram. The steel was examined after
two treatments. The quenching for martensite,
tempering at 650°C, plastic deformation by
drawing on 30, 60, and 80% (I), and isothermal decomposition of austenite at 550°C, plastic deformation of 30 and 80% (II). After
(I) and (II), the steel final annealing at 400-680°C.
The structural studies of metal were carried out using electron and light
microscopes. The structure of the steel after treatment (I) and (II) is
illustrated in Figures 2a and b. The dislocation
density was estimated using X-ray structural analysis techniques by measuring
[8] the width of a line of the X-ray interference (211) (B211). The bearing elongation of the
sample was used as parameter ductility of the steels under study. The strain
hardening characteristics were determined from the analysis of tension curves
plotted in logarithmic coordinates. Strain curves were obtained by tension
samples on an Instron type testing machine, at a
strain rate of 10-3 s-1. To assess the effect of strain
hardening, methods of analysis of strain curves are used. In appearance, the
deformation curves of metallic materials can be divided into two types: with a
section of intermittent flow A-C
(Figure 2c) and without it (Figure 2d). Plastic deformation, accompanied by degenerated
sections A-C, changes the curve.
Various analytical dependencies are used to describe the patterns of change in
the deformation curves. One of them is the Ludwik
ratio [9]:
σ = σ₀+K·εm,
(1)
where σ0 -
stress of irreversible motion of dislocations [10], K constant, m - exponent.
To determine σ₀, K and m, the deformation
curve is plotted in logarithmic coordinates (Figures 2c
and d). The value of σ₀ is determined from the
extrapolation area of uniform strain hardening (CD) to zero plastic deformation (sector BC Figure 2d) [7]. In the absence area of
A-C on the deformation curve, the
limit of elasticity of the carbon steel was accepted as σ0.
Point D on the curve by the
deformation scale (εn) corresponds to
moment formation in a dislocation cell of the structure. The values K are the stress when ε =1. There
is no consensus on the physical meaning of K.
The specified characteristic is called the coefficient of plasticity [11], less
often strength [7], etc. The exponent m
is defined as a tangent of inclination angle α (Figure 2c) by the ratio (1):
m = Δlg
(σ-σ₀)/Δε
(2)
At
the same time, exponent m is not
sensitive to the structural changes of the metal during plastic deformation in
the CD section.
a
b
c
d
Fig. 2. Structure of the carbon steel after final
annealing at 650°C by: (a) – (I); (b)
– (II). Strain curve in the logarithmic coordinates with a
sector of the discontinuous deformation:
(c) – (A-C); (d) – without it. Magnification is
4000 x 2
3. RESULTS
AND DISCUSSION
During the
operation of a railway wheel, a thin layer of carbon steel close to the rolling
surface undergoes significant plastic deformation with a high degree of uneven
distribution. When decelerating the rolling stock, deformed metal of the wheel
can be heated up to high temperatures at the beginning of the phase
transformations. Based on the development of polygonization
and recrystallization processes in the ferrite [12, 13], spheroidization
and coalescence of cementite particles [1], after treatments (I) and (II), the
structural state of cold-deformed metal will change qualitatively. The observed
changes in the nature of strain hardening of the metal will determine
conditions for the formation of damage to the rolling surface of railway
wheels. The morphology and uniformity distribution of cementite particles in
steel have a significant effect on the nature of the development of the strain
hardening processes. The formation of certain unevenness at the distribution of
cementite during the isothermal decomposition of austenite in the temperature
range of pearlite transformation, after plastic deformation, and annealing is
inherited by the steel structure (Figure 2b). A more
detailed study of the structure reveals significant differences in the sizes of
neighboring ferrite grains of carbon steel. Considering the dependence of the
development processes of strain hardening on the size factor steel structure,
in the indicated micro volumes one should expect different values parameters of
the strain hardening of the metal. For
carbon steel generally, the level density defects of crystalline lattice
after annealing and stress of starting and moving of dislocations can determine the nature of the development of the metal strain
hardening processes. With an increase in annealing temperature, the
accumulated density of the crystal structure defects and, first, dislocations,
decreases (Figure 3a). The stress of irreversible
moving of dislocations decreases similarly (Figure 3b).
From the analysis of the relationship between them (Figure 3c),
it follows that the initial stages of propagation of the plastic deformation
(the stress range from B to A, Figure 2c)
depend to a greater extent on the density of dislocations preserved after
annealing of the metal, with by practically no influence from the remnants subboundaries of the cold-deformed metal. As the degree of
plastic deformation increases and increase in density of dislocations, a change
in their mobility will determine the nature of the development of the strain
hardening processes and the associated level of steel plasticity. Compared to the uneven distribution of
cementite particles, where it is rather difficult to separate substructure
hardening from the influence of the grain boundaries with large disorientation
angles, was used processing to obtain the structure of the ultra-fine ferrite
grains (Figure 2a). In this case, the uniform
arrangement of cementite particles after tempering the hardened steel excludes
the development of cementite spheroidization and its
influence on the development of polygonization and
recrystallization of ferrite during annealing of deformed steel. Moreover, the
practically absent coalescence of cementite particles during annealing of
plastically deformed steel excludes the possible location of the carbide phase
inside ferrite grains (Figure 2a). Heating of cold-deformed carbon steels with structure
(I) (Figure 4) is accompanied by changing of plastic properties, and a similar
nature is observed for steel with structure (II) (Figure 3). Analysis of the
fine-crystalline structure during annealing of cold-deformed carbon steel with
the structure type (Figure 2a), after treatment (I),
testifies to an almost monotonic decrease in the density of crystal structure
defects introduced by deformation (Figure 4a). In
comparison with practically identical character of changes in B211 and σ0
(Figures 3 and 4), some differences are found. One explanation for the non-monotonic
decrease in B211 and σ0
with annealing temperature (Figure 3) is the development processes of the spheroidization of cementite plates and coalescence of
carbide particles during annealing of deformed steel (treatment II). The
observed character relation σ0 ~ f(B211)
(Figure 3c) is a consequence effect of spheroidization and coalescence of cementite on the
development dislocation recombination processes during annealing of plastically
deformed metal. Simultaneously, with the
presence of a certain amount of structurally free ferrite in the structure of
steel with 0.61% C, a change in morphology at the carbide phase and the
coalescence of cementite particles during annealing should inevitably lead to
significant changes in the average distance between cementite particles. In
steel, after treatment (I), during annealing, the development of coalescence
has a much smaller effect on the change in the average diameter of cementite
particles and the distance between them. Therefore, differences in the
development of dislocation annihilation processes during metal annealing after
treatments (I) and (II) will have a corresponding effect on the formation of
nuclei and subsequent development of ferrite recrystallization. Hence, during
treatment (I), the development of ferrite polygonization
and recrystallization processes is limited by the space of former subgrains, while the distance between cementite particles
remains practically unchanged. Thus, the effect of density defects of the
crystal structure from plastic deformation on the value of σ0 has the
form of equidistantly spaced curves (Figure 4c). Even
greater differences are found when comparing the nature of the change of the
strain hardening index versus the annealing temperature. Comparative analysis
dependence of m on the annealing
temperature indicates qualitative differences for the investigated steel
treatments. Indeed, if for treatment (II), an extreme nature of the dependence
is observed (Figure 5a), then for treatment (I) when
heated from 400 to 550°C, the value of m remains practically unchanged (Figure 6a) and only then does it begin to increase from the
annealing temperature. The extreme nature of the change in m (Figure 5а)
indicates a change in the main element of the structure in carbon steel after
tempering. So, for temperatures from 400 to 550°C,
the strain hardening of steel is determined by the parameters of the
substructure, and for temperatures ranging from 550-600°C,
the increasing role of ferrite grain boundaries with large angles of
disorientation (Figure 2b). Indeed, as follows from
[10], in ferrite after plastic deformation and heating to temperatures of 400-450°C, one can observe the first signs of the
development of recrystallization processes, and at temperatures of 500-550°C, their already noticeable acceleration.
Further, the value of the density of dislocations, according to B211, decreases by 1,5 - 2 times [14]. When the temperature rises to 550-600°C,
an acceleration of the development recrystallization processes is
observed in ferrite. Although ferrite volumes in which recrystallization is
completed are insignificant and the structure as a whole remains dispersed, the
regions free of dislocations are already found [10,15]. An increase in the
proportion of such metal volumes is accompanied by an increase in the number of
grain boundaries with large disorientation angles (Figures 2b).
Consequently, decrease volumes of ferrite with subgrain
boundaries and m starts to grow with
a temperature in heating. After the completion of recrystallization and the
beginning growth of the ferrite grains, an increase in the strain hardening
coefficient of steel is observed (Figure 5a). In this
case, there is a transition from the substructure hardening of the metal to the
effect of ferrite grain boundaries on the plastic properties (Figure 5b). The practically absent
increase relative elongation of annealing temperatures up to 550°C (Figure 5b) is
primarily due to the retention of subboundaries in
ferrite after plastic deformation. Given that an increase characteristic of
strain hardening provides an increase in the stable propagation of the plastic
deformation, an increase in m should
be accompanied by an increase in the plasticity of the metal. Indeed, as
follows from the analysis of the ratio δ~f(m), for steel with the structural state (II), an increase in the
strain hardening coefficient is accompanied by an increase in the relative
elongation (Figure 5c). In this case, the provision
of an increase in m, regardless of
the mechanism, strain hardening (from the presence of subboundaries
or boundaries of ferrite grains) is accompanied by an unambiguous increase
value of δ. Moreover, a detailed analysis of the δ - m ratio reveals division into regions,
which correspond to substructure hardening (curves 1 and 3) and hardening from
ferrite grain boundaries (curves 2 and 4). Thus, regardless of the strain
hardening mechanism, the increase in m
contributes to an increase in the ductility of the steel. Considering the
dependence of the development strain hardening processes on the structural
state of steel, a similar relationship should be expected for processing (I).
The nature of the influence degree of plastic deformation and the annealing
temperature on m, δ and the
relationship between them for treatment (I) is shown in Figure 6. A comparative
analysis of the ratios (Figures 5 and 6) indicates a qualitative similarity
only for certain characteristics. If for the strain hardening coefficient as a
whole, the extreme character remains, and for the relative elongation it is
similar to an exponential dependence on the annealing temperature, then the
construction of the relationship between them indicates significant differences
in the behavior of the metal with structures after treatments (I) and (II).
Therefore, when annealing cold-deformed steel with structure (II), first spheroidization and then coalescence of cementite particles
have a known effect on the substructure and development of ferrite recrystallization
(Figure 2b). Compared to a deformation of 30%, when
δ during annealing to 550°C does not exceed
6% (Figure 5b), an increased dislocation density
after deformation of 80% promotes to a greater extent the development of
dislocation redistribution processes and increased plasticity of the metal. In
steel with structure (I), substructure changes and the development of ferrite
recrystallization are mainly limited to the distance between cementite
particles, which practically does not change upon annealing.
a
b
с
Fig. 3. The change of: (a) - B211;
(b) - σ0; and (c) - the ratio
between both of them on the dependence on plastic deformation (1- 30; 2 -
80%) and annealing temperature in the treatment (II) of the carbon steel
a
b
c
Fig. 4.
The change of: (a) - B211; (b) - σ0 and (c) - the ratio between both of them
on the dependence on plastic deformation (1- 30; 2 – 60, 3 - 80%)
and annealing temperature in the treatment (I) of the carbon steel
Thus, the sizes of the subgrains during
annealing and the ferrite grains during recrystallization should be limited by
the distance between cementite particles (Figure 2a).
Subsequently, in proportion to the degree of deformation, increase stability of
the substructure upon annealing will lead to a shift in the moment of
accelerated development of dislocation annihilation towards higher temperatures
(Figure 6b). The above position is confirmed by the
nature of the influence of the degree of deformation and annealing temperature
on the value of δ for structure (I). For steel after deformation of 30%,
the observed monotonic increase in δ with an increase in annealing
temperature is gradually replaced by the completely brittle state of the metal
after deformation of 80% up to 550°C (curve 3,
Figure 6b). This is because subboundaries
in ferrite formed as plastic deformation cannot perform the functions places of
nucleation and annihilation of dislocations. Considering that the main number
of dislocations of cold-deformed metal is presented in form of subboundaries, the retention of their presence in the
structure up to a temperature of 550°C
significantly limits the participation of dislocations in maintaining
conditions for the propagation of plastic deformation. On other hand, in
proportion degree of plastic deformation, there is a shift onset of intensive
development of the steel softening processes towards high temperatures. Indeed,
if for a degree deformation of 30% beginning of an increase in steel ductility
is observed in the temperature order of 450°C,
for 60% - 500°C, then after 80% required heating
to temperatures of at least 600°C. Comparative
analysis with dependences of m and δ on the magnitude of deformation and annealing
temperature for the structural state (II) (Figure 5) indicates a less
pronounced effect degree of deformation on the temperature onset intense
softening of the metal. Moreover, the qualitatively different nature of the
mutual change between m and δ for structural states (I) and (II), is an additional
confirmation of the above explanations. Considering that the structural state
rim of the railway wheels is presented in the form of pearlite colonies in
different dispersion (Figure 1), the nature of the development\ processes of
structural transformations in a thin metal layer near the rolling surface
during wheel operation determines the conditions of the surface damage
formation. The process formation of surface damage to a railway wheel can be
represented as consisting of successively developed processes of structural
changes in the metal. Indeed, uneven plastic deformation along the rolling
surface and the subsequent heating of the metal during the deceleration of the
railway rolling stock leads to the formation of structures with different
morphology of cementite particles. In fact, the carbide phase is particles
ranging from remnants of cementite plates with incomplete spheroidization
process to globular particles, similar to the structural state (II). Subsequent
plastic deformation of a metal with such structures and inevitable heating
leads to the formation of structures similar to treatment (I). Based on this,
the formed structural heterogeneity in adjacent micro volumes of metal is one
of the reasons for the occurrence of damage to the rolling surface of railway
wheels during operation.
a
b
c
Fig. 5. The change of: (a) - m ; (b) - δ , on the dependence on plastic deformation (1 -
30;
2 - 80%) and annealing temperature in treatment (II) of the carbon steel.
The ratio between both of them: (c) - (3,4 - 30; 1,2 - 80%)
a
b
c
Fig. 6.
The change of: (a) - m ; (b) - δ
–; (c) - the ratio between
both of them on the dependence on plastic deformation (1- 30, 2 – 60, 3 -
80%) and annealing temperature in treatment (I) of the carbon steel
4.
CONCLUSIONS
1. The ratio of gradient of plastic deformation along the rolling
surface and heating up of temperatures onset of the phase transformations
determine the structural state of the steel in the rim of the railway wheel,
the ability to strain hardening, and achieve a level of plasticity.
2. When plastically deformed steel is heated to temperatures of 500-550ºC, the development of substructure hardening processes
is accompanied by a decrease in the ability of the steel to strain hardening
and the level of plasticity.
3. In proportion to the heating temperature of deformed steel
from 500-550ºC, a gradual transition from
substructure hardening to hardening in the boundaries of ferrite grains is
observed, contributing to an increase in strain hardening and plasticity.
4. Regardless of the nature of the main element of the structure,
the ability to strain hardening explains the change in the level of plasticity
of carbon steel on the rolling surface of railway wheels during operation.
References
1.
Hollomon
J.H. 1945. “Tensile deformation“. J. Member AIME
162: 268-290.
2.
Morrison W.B.
1966. “The effect of grain size on the stress–strain relationship
in low-carbon steel”. Trans. Am.
Soc. Metals. 59: 824-846.
3.
Morrison W.B.
1971. “Effect of changes in temperature and strain rate on the double in
behavior of alpha-iron”. Met. Trans.
2: 331-332.
4.
Imamura J., H. Hayakawa, T. Taoka.
1971. “Contribution
of local strain rate at Luders band front to grain
size dependence of lower yield stress in iron”. Trans. Iron. Steel. Inst. of Japan. 11: 191-200.
5.
Ren C., W. Dan, Y. Xu, et.al. 2018. “Effect of
heterogeneous microstructures on the strain hardening behaviors of ferrite
– martensite dual phase steel”. Metals. 8: 824-841. DOI: https//doi.org/103390/met 8100824.
6.
Calado W.R., R. Barlosa. 2013. “Influence of carbon content and
deformation temperature on ultra-grain refinement of plain carbon steels by
means of torsion test”. ISIJ International 53 : 1-13. DOI. :
https//doi.org/102355/isijinternational.53.909.
7.
Cottrell A.H. 1963. “The relation between the
structure and mechanical properties of metals”. Symposium NPL. Teddington. P. 455-473.
8.
Guinier A. 1956. Theorie et Technique de la ragiocristallographie.
Dunod, Paris.
9.
Ludwik P. 1909. Elemente der technologischen mechanik.
Verlag von Julius Springer. Berlin.
10. Babich V.K.,
Yu.P. Gulj, I.E. Dolzhenkov. 1972. Deformation
aging of steel. Moskow: Metallurgiya.
11. Crist B.W., C.V. Smith. 1967. “Comparison of the Hall–Petch parameters of zone-refined iron determined by the
grain size and extrapolation methods”. Acta met. 15: 809-816.
12. Ohmori
Y., A.T. Davenport, R.W.K. Honeycombe. 1972. “Crystallography of
pearlite”. Trans. I.S.I.J. 13: 128-137.
13. Staker
M.R., D.L. Holt. 1972.
“The dislocation cell size and dislocation density in cooper deformed at
temperatures between 25 and 700OC”. Acta met.: 569-579.
14. Prnka
T. 1971. “Beitrag zur
theorie der streckgrenze ousscheilungs verfestigter niedriglegierter stahle”. Arch. Eisenhiittenw
42: 919-925.
Received 29.01.2022; accepted in
revised form 28.03.2022
Scientific Journal of Silesian University of Technology. Series
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[1] Ukrainian State University
Science and Technology, Lazaryan St.,2, Dnipro, Ukraine, 49010. Email: vakulenko_ihor@ukr.net.
ORCID: https://orcid.org/0000-0002-7353-1916
[2] Management of Prydniprovsk
Railway, Yavornytskyi Av., 107, Dnipro, Ukraine,
49054. Email: leon.vakulenko@gmail.com. ORCID: https://orcid.org/0000-0003-2616-740X
[3] Dnipro Lyceum of Railway Transport,
Universalna St., 7, Dnipro, Ukraine, 49024. Email: dasha.bolotova@i.ua.
ORCID: https://orcid.org/0000-0001-6947-3663
[4] Engineering and Architecture
Faculty Metallurgy and Materials Engineering Department, Nevsehir
University, Nevsehir, Turkey. Email:
bkurt74@gmail.com. ORCID: https://orcid.org/0000-0002-7245-6774
[5] Mechanical Engineering, Karabuk University, Karabük,
Turkey. Email: hangardasaskerov@karabuk.edu.tr. ORCID:
https://orcid.org/0000-0003-4771-3406
[6] Mechanical Engineering, Karabuk University, Karabük,
Turkey. Email: omercolova@gmail.com. ORCID: https://orcid.org/0000-0002-4107-4298