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International Journal of Mechanical Engineering and Technology (IJMET)
Volume 10, Issue 03, March 2019, pp. 1606–1614, Article ID: IJMET_10_03_161
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
QUANTITATIVE ASSESSMENT OF THE
EFFECTIVENESS OF HARDENING
MECHANISMS FOR CARBON AND LOW-
ALLOY STEELS WITH DIFFERENT
STRUCTURAL STATES
Kanaev A.T
"Kazakh Agro-Technical University named after S.Seifullin", Kazakhstan, Astana
Topolyansky P.A
LLC "Plasmacentre", Russian Federation, Saint Petersburg
Biizhanov S.K.
"Kazakh Agro-Technical University named after S.Seifullin", Kazakhstan, Astana
ABSTRACT
The aim of the work is a quantitative approximate assessment of the contribution of
various hardening mechanisms for carbon and low alloy steels according to their
chemical composition and parameters of a thin metallographic structure. It is generally
accepted that the work is of scientific and practical interest, since, as is known, there is
currently no theory that satisfactorily describes hardening mechanisms, especially for
new promising hardening methods (combined hardening methods, combined heat
treatment methods, plasma, laser processing, etc.). There are only approximations that
describe the existing hardening mechanisms, which do not provide a rigorous
quantitative assessment of the yield strength of steels with different structural states.
In this paper, by analyzing the literature data and our own experimental studies (on
chemical composition and structure parameters), the approximate contribution of
various hardening mechanisms to the yield strength of carbon, wheel and low-alloy
steels was quantified. The assessment is not strict, based on a number of assumptions.
It was established that for hot-rolled steel (St5ps) [1] the greatest contribution to
the yield strength is made by solid-solution and grain-boundary hardening (37.3% and
33.3%), in low-alloy steel 16G2AF [2], along with these components of hardening,
dispersion hardening plays a noticeable role (21.5%). It is shown that the combined
heat-strain treatment of St.5ps steel leads to an increase in dislocation hardening up to
32% due to an increase in the density of dislocations and the preservation of most of
the dislocations in rolled metal during accelerated cooling of hot-deformed austenite.
In wheeled steel, thermally treated by traditional technology (intermittent hardening
and tempering), the main contribution to strength is the grain-boundary and dislocation
Kanaev A.T., Topolyansky P.A., Biizhanov S.K.
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hardening (~ 33%). In the same steel, subjected to surface plasma hardening, due to the
strong grinding of the structure and formation of the nano-structured phase
components, strength indices increase significantly (42%).
Key words: hardening mechanisms, yield strength, deformation-heat treatment,
accelerated cooling, surface plasma quenching, nanostructured phase components,
grain size
Cite this Article: Kanaev A.T., Topolyansky P.A., Biizhanov S.K., Quantitative
Assessment of the Effectiveness of Hardening Mechanisms for Carbon and Low-Alloy
Steels with Different Structural States, International Journal of Mechanical
Engineering and Technology 10(3), 2019, pp. 1606–1614.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3
1. INTRODUCTION
The methodological basis of the research is the idea of the existence of a deep connection
between the structure and the physicomechanical and operational properties of metallic
materials. The entire previous groundwork in this scientific field is an illustration of the central
principle of materials science, according to which the behavior of materials is always
determined by their structure [1-3].
It is known that one of the main problems of modern metallurgy is the establishment of
quantitative connection between the structure and properties of alloys. To solve this problem,
it is necessary to identify the role and contribution of the existing mechanisms of hardening in
the constructive strength of steels subjected to different heat treatment, and therefore having
different structure [4-6]. Therefore, it is of theoretical and practical interest to quantify the
contribution to the yield strength of individual hardening mechanisms for carbon, wheel and
low alloy steels, widely used in construction and railway engineering.
2. RESEARCH MATERIALS AND METHODS
The main characteristics of carbon and low-alloy steels, which determine their structural
strength, are the yield strength and tendency to brittle fracture [11–13].
The yield strength, assessing the strength of steel, is determined by the well-known ratio of
Hall-Petch, which for the conditions of tension has the form:
𝜎𝑇= 𝜎𝑖+ 𝑘𝑦∙ 𝑑−1
2 (1)
where 𝜎𝑖 - friction tension of the crystal lattice during the motion of dislocations inside the
grains;
ky - coefficient characterizing the contribution of grains to the hardening;
d - diameter of the grain.
From formula (1) it follows that the strength of steel is inversely proportional to the square
root of the grain size (σT of the material increases with decreasing grain size). Lattice friction
tension
𝜎𝑖= 𝜎0+𝛥𝜎𝑇𝐵 + 𝜎𝑃+ 𝜎𝐷+ 𝜎𝐷𝑖. (2)
In this equation, 𝜎𝑖 is the sum of 𝜎0 - friction tension of the α-Fe lattice, increasing the
strength of solid solutions during doping - 𝛥𝜎𝑇𝐵, hardening due to the formation of perlite -
𝛥𝜎𝑃, deformation - 𝛥𝜎𝐷 and dispersion - 𝛥𝜎𝐷𝑖 hardening. In [13], it was shown that the
influence of all the listed hardening mechanisms on the yield strength is linearly additive, i.e.
they can be summed up. Therefore, the yield strength of the investigated structural steels (St5ps,
wheel steel grade 2 and low alloyed steel 16G2AF) can be considered as the sum of the terms
Quantitative Assessment of the Effectiveness of Hardening Mechanisms for Carbon and Low-
Alloy Steels with Different Structural States Control of Semi-Active Suspension
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in equation (2). The share of the contribution of individual hardening factors (equations 1 and
2) to the total yield strength of steel is not the same, and it depends on the type of alloying
elements and the degree of doping, the presence and dispersion of hardening phases, applied
deformation-thermal, plasma treatment and other factors.
Note that the tendency of steel to brittle fracture is estimated from the temperature of
transition from a viscous to a brittle state, which is defined as the ratio of the area of a viscous
fracture to the initial design section. The lower the temperature of the transition from a viscous
to a brittle state, the more reliable the material is, therefore, the more often they tend to apply a
material whose transition temperature is below the operating temperature, and this temperature
significantly depends on the grain size [14,15].
Based on the well-known hardening mechanisms described by equation (2), we analyzed
the effectiveness of various hardening mechanisms for carbon, wheel and low-alloyed steels
used in construction and railway transport, which differ not only in chemical composition, but
also in heat treatment [16-18].
The value of individual hardening factors and their contribution to the total yield strength
of these steels were determined by the known empirical formulas. The necessary for the
calculation coefficients are taken from the literature data [8,19]. In this case, the calculated
values of the yield strength of the investigated steels were compared with experimental data
according to GOST 5781, GOST 10884, GOST 19281 and GOST 10791.
Determination of structure parameters (content of perlite in steel, diameter of ferritic grains,
size and volume of the carbonitride phase fraction, etc.) to quantify the yield strength by
quantitative metallographic methods using a Neophot 21 research horizontal microscope and
Jeol JEM 2100 electron microscope. As the diameter of ferritic grains (d), we used the average
length of a straight line segment that intersects the grain in the plane of the thin section [20-22].
The volumetric fraction of dispersed particles (f) and their diameter (D) in low-alloy steel
16G2AF was determined by the method of electronic photography of thin foil, and the
interpartial distance (l) - by a known ratio
𝑙 = 𝐷 ∙ (𝑃 6
⁄𝑓)1
2.
The share of the pearlite component was determined by the Rosevale method, according to
which the areas of the structural components are calculated from the lengths of the straight
segments that fell on each of the structural components in accordance with the Cavalieri
principle [23].
The density of the dislocations of hardened steels was determined by X-ray analysis on the
form of diffraction lines, and in hot rolled steel the density of dislocations was quantified by
the translucent electron microscopy of thin foil [24, 25] (Table 1).
Note. Based on the experimental data, it was assumed that ~ 0.015 (C + N) was dissolved
in the ferrite, the rest of the carbon and nitrogen were bound into carbonitrides. The friction
tension of the α-iron lattice (Peierls-Nabarro tension) is estimated by the formula
𝜎0= 2 ∙ 10−4 ∙ 𝐺 (3)
where G is the shear modulus of iron. G = 84000 MPa.
The Peierls-Nabarro tension is the minimum tension necessary for the movement of a
dislocation in a crystal, and it is determined by the properties of the crystal lattice and
characterizes the friction forces in it. At alloying of metal there is an increase of friction forces,
i.e. alloying increases resistance of dislocations, due to interaction of dissolved atoms of
alloying elements with dislocation. In the first approximation, the Peierls-Nabarro tension can
be correlated with the yield strength of a single crystal metal. This value significantly depends
Kanaev A.T., Topolyansky P.A., Biizhanov S.K.
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on the content of impurities in the metal. Therefore, as the purity of the metal and the degree of
perfection of the crystals improved, it turned out to be an ever-smaller value of the yield strength
of single crystals. Taking into account the literature data in the calculation, the friction tension
of the α-Fe lattice is assumed to be ~ 30 MPa [8,26,27] (Table 2).
Table 1 Baseline data for the quantitative assessment of the yield strength of the investigated steels
№
Steel characteristics
Mark of the studied steels and their structural state
St5ps,
hot Rolled
St5ps,
deformation-heat
treatment
Grade 2 wheel
steel,
intermittent
hardening and
medium
tempering
Grade 2 wheel
steel,
surface plasma
hardening
16G2AF
Normalization
1
Content of alloying elements in α-
Fe, %:
Mn
Si
P
V
(C+ N)
Cr
Ni
Cu
0,65
0,11
0,04
-
0,015
-
-
-
0,65
0,11
0,04
-
0,015
-
-
-
0,80
0,40
0,033
-
0,015
0,25
0,23
-
0,80
0,40
0,033
-
0,015
0,25
0,23
0,10
1,5
0,45
0,035
0,11
0,015
-
-
-
2
Hardening phase (dispersed
particle)
-
-
-
-
V (С, N)
3
Perlite share, %
40
30
-
37,5
17
4
Grain size:
(number according to GOST 5639-
82),
d, MM
0,061
(5)
0,015
(9)
0,017
(9)
0,007
(11)
0,014
(9)
5
Volume fraction of dispersed
particles, f, %
-
-
-
-
0,096
6
Size of disperse particles, D, nm
-
-
-
-
30
7
Interpartial distance, λ, nm
-
-
-
-
765
8
The nature of the dislocation
structure (with a uniform
distribution of dislocations), ρ, cm-2
109
109
109
109
109
Table 2-Quantitative estimation of the yield strength of steels with different structural state
№
Indicators
Steel Grade
St5ps,
hot Rolled
St5ps,
deformation-heat
treatment
Grade 2 wheel
steel,
intermittent
hardening and
medium
tempering
Grade 2 wheel
steel,
surface plasma
hardening
16G2AF
Normalization
1
Lattice friction tension
30/11,8
30/6,3
30/5,7
30/4,3
30/6,1
2
Solid solution
hardening
95/37,3
95/20,2
171/32,8
175/25
115/23,5
3
Hardening, poured
with perlite
40/15,7
35/7,5
31,0/6,0
35/5,0
40/8,2
4
Dislocation hardening
5/2.0
150/32
120/23
170/23,6
5/1,0
5
Dispersion Hardening
-
-
-
-
105/21,4
6
Grain Boundary
Hardening
85/33,3
160/34
170/32,6
295/42
195/39,8
7
Calculated value of
yield strength
255
470
522
705
490
8
Experimental value of
the yield strength
285
440
585
790
440
Quantitative Assessment of the Effectiveness of Hardening Mechanisms for Carbon and Low-
Alloy Steels with Different Structural States Control of Semi-Active Suspension
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Note. In the numerator - the absolute value of hardening (MPa), in the denominator - the
proportion of hardening due to this mechanism, (in% of the calculated value of the yield
strength).
As noted above, currently there is no theory that satisfactorily describes hardening
mechanisms, especially for new promising hardening methods, such as combining hot
deformation with subsequent hardening heat treatment, plasma hardening, etc. There are only
approximations describing the mechanisms of hardening, which do not give a rigorous
quantitative estimate of the yield strength. The remaining hardening factors
(𝛥𝜎𝑇𝐵,𝛥𝜎𝑃,𝛥𝜎𝐷,𝛥𝜎𝐷𝑖,𝛥𝜎3), besides the resistance of the lattice to the dislocation movement,
were taken into account using known formulas. At the same time, the principle of linear
additivity of hardening by individual mechanisms is used.
3. RESEARCH RESULTS AND DISCUSSION
In carbon steel St5ps (hot rolled state) the main components of hardening are solid-solution and
grain-boundary hardening, the share of which for this steel is 37.3% and 33.3%, respectively.
In absolute terms, the proportions of these terms are 95 MPa and 85 MPa. In steel St.5ps,
subjected to a combined deformation-heat treatment, deformational (dislocation) hardening
makes a significant contribution to the overall hardening. If the share of strain hardening in
St.5ps steel cooled in calm air from a rolling end temperature of 1050 °С (hot rolled state) is ~
5%, then in the same steel hardened according to the interrupted quenching scheme followed
by high self-tempering (heat-strengthened state) the deformation fraction hardening increases
to 32%. (absolute value 𝛥𝜎𝐷= 150 MPa). This is probably due to an increase in the density of
dislocations when combining hot rolling followed by immediate quenching and tempering. As
mentioned above, recrystallization processes are suppressed by quenching and a significant part
of the dislocations caused by hot rolling of austenite are fixed. At the same time, the dislocation
structure of hot-deformed austenite is inherited by martensite in the process of phase austenite-
martensitic transformation. In addition, during deformation-heat treatment, along with the
grinding of austenitic grain, the grinding of martensite crystals is achieved [28,29]. The
dominant hardening mechanism in wheel steel subjected to traditional heat treatment (according
to GOST 10791) is grain-boundary and solid-solution hardening, which are ~ 170 and 171 MPa,
respectively [30].
If we take into account that solid-solution hardening is due to the difference in the atomic
diameters of the matrix and the alloying element and their elastic moduli, then a high proportion
of solid-solution hardening in this steel can be explained by the resistance to moving
dislocations from dissolved Mn, Si and P atoms in α-Fe. The hardening coefficients of ferrite
with these elements are KMn=35, KSi=85, KP=690 [13].
In plasma-hardened wheel steel, the role of grain-boundary hardening (𝛥𝜎3=280 МПа) is
noticeable due to the strong grinding of grain size (d=0.007 mm) with the formation of
nanostructured elements of the phase components of the structure. As is known, when using
ultrahigh heating and cooling rates (~6000 ºС/s), which takes place with innovative plasma
technologies, a high complex of physic-mechanical properties of the processed materials is
created, unattainable with traditional heat treatment methods [31]. The possibility of creating a
nanostate of highly crushed (fragmented) structure and elements of nanocomposites in the
process of phase transformation is also shown in [32, 33], where it is noted that the physic-
mechanical properties of nanostructured steels (strength, ductility, toughness, crack resistance,
etc.) with the volume fraction of the nano-structural elements ~ 20-30% significantly surpass
the indicators of the corresponding materials received by traditional technologies.
