EVALUATION OF HARDENING OF PLASTICALLY DEFORMED STEELS
P.V. Yasniy, V.B. Hlado, P.O. Maruschak and D.Ya. Baran
Ivan Pul’uj Ternopil State Technical University, Ruska 56 str., Ternopil, Ukraine
[email protected]
ABSTRACT
Analysis of cracks revealed on the surface of a continuous caster roll made it possible to identify them as low-cycle fatigue
cracks. During the low-cycle fatigue, a cyclic deformation of steel occurs, which results in the ultimate hardening of the
material with the maximum increase in the microhardness and density of dislocations within the low-angle boundaries [1].
Later on, due to the exhaustion of the material plasticity, the formation of microcracks and growth of the main crack
through the whole of its section occur. It is known that the ultimate hardening of the material under cyclic loading with onesided accumulation of strains and under static loading has the same value [1]. Hardening under plastic deformation is
associated with changes in the types of the material dislocation substructures that are responsible for the fracture
resistance.
The interrelation between the dislocation density and hardness and microhardness characteristics makes it possible to
evaluate the material degradation under operating conditions [2, 3].
The aim of this work is to study the effect of tensile plastic deformation on the variation in the microstructural parameters
of steels 15Kh13МF and 25Kh1М1F and also to establish a correlation relationship between the hardness, microhardness
and density of dislocations, as well as the value of the material plastic strain.
Materials and Investigation Procedure
Specimens of 5 × 6 × 30 mm in size were cut out along the axial direction from a bimetallic body of a roll produced by
centrifugal casting with alternate flowing of the layers. Steel 25Kh1М1F was used as a load-bearing layer of the roll and
steel 15Kh13МF as a protective layer. Chemical composition and mechanical properties of these steels at the
0
temperatures of +20 and +600 С are presented in Tables 1 and 2.
Table 1. Chemical composition of steels 15Kh13МF and 25Kh1М1F, %
Steel
15Kh13МF
25Kh1М1F
С
0.15
0.23-0.29
Mn
0.6
0.40-0.70
Si
0.65
0.17-0.37
V
0.150.30
Mo
0.60-0.80
Ni
0.30
Cr
12.2
1.50-1.80
S
0.019
≤ 0.025
Table 2. Mechanical properties of steels 15Kh13МF and 25Kh1М1F
Steel
T, 0C
E, МPа
15Kh13МF
20
600
1.81 ⋅10 5
1.31 ⋅10 5
25Kh1М1F
20
600
2.06 ⋅ 10 5
1.42 ⋅ 10 5
σ YS , МPа
338
242
σUS , МPа
456
334
δ 5 ,%
6.0
24.2
ψ ,%
509
321
718
369
21.7
21.0
47.6
64.5
4.8
56.6
Specimens were subjected to uniaxial tension loading at a temperature of +6000С. Tests were performed on a STM-100type servo-hydraulic machine equipped with an IBM computer. The longitudinal strain of the specimen and force were
measured during the experiment.
The specimen microstructure was studied on a TEM-125K-type transmission electron microscope using the thin-foil
method. Objects for microstructural studies were cut out from specimens in the longitudinal direction. The final thinning of
the objects was achieved by the method of jet electrolytic polishing of foils in the electrolyte composed of 10% of НСlO4
+90% of CH3COOH at a voltage of 140 V and current of 90 мА. According to the analysis of microdiffraction patterns, the
change in the dislocation density within the low-angle boundaries under conditions of tensile deformation was calculated.
At least 25-30 microdiffraction patterns were analyzed for each of the points. For the objects cut out of neck areas of the
~ was calculated according to the formula:
specimens fractured under tension, the actual necking ψ
~ = ln( F / F )
ψ
0
k
(1)
where F0 , Fk are the initial and current cross-section areas, respectively.
Since the great majority of dislocations are concentrated within the subgrains of the dislocation structure, the dislocation
density was calculated within the low-angle boundaries of the steels under investigation. The dislocation density with the
Burgers b within the subboundaries of the dislocation structure was calculated from the mean size between the
subboundaries d and the angle of their disorientation θ [4]:
ρ гр =
Kθ
,
bd
(2)
where К is the coefficient that depends on the shape of subgrains.
The angle of disorientation of the low-angle boundary θ was calculated on the basis of the analysis of microdiffraction
patterns according to the relationship:
θ=
∆r
R hkl
,
(3)
where ∆r is the length of the trail, or the distance between the reflections (hkl); Rhkl is the distance of the reflection (hkl)
from the central one.
The quantitative estimation of the material hardening after plastic deformation was made using the method of hardness
and microhardness, whereas the nonuniformity of the material hardening (nonhomogeneity) was determined using the
method of the statistical processing of the results of measuring the microhardness. The hardness was measured using a
Super Rockwell instrument with the indentation load of 150 N, and microhardness was measured using the PTM-3 type
device with the indentation load of 1 N and hold of 15 s.
Effect of Plastic Deformation on the Changes in the Dislocation Structure of the Material
Steel 15Kh13МF of the protective layer belongs to ferritic-martensitic steels. The microstructure of steel 15Kh13МF is a
lath dislocation martensite (Figure 1а), which also contains a great part of the ferrite, “massive” inclusions and carbide
precipitate (Figure 1b) and dispersed precipitate (Figure 1c). The presence of the extinction contours on the electronicmicroscopic pictures (Figure 1а,b,d) is indicative of the presence of dislocations of the same sign that cause a local
bending of the foil [5]. Breakdowns in the extinction contour lines (Figure 1d) testify to jump-like changes in the local
orientation of the crystal lattice [6]. Martensitic areas of the structure are the dislocation lath martensite wherein “massive”
inclusions, carbide precipitate and dispersed precipitate are observed. Parallel laths of martensite form the martensite
plates. The plated structure is characterized by a system of parallel laths of various sizes.The angle of disorientation
between the neighboring laths of the martensite in a plastically nondeformed material determined by the microdiffraction
о
method is roughly 3 .
Inside the martensite laths, a high density of dislocations takes place. These dislocations being taken individually hardly
differ and have a spotty contrast. The areas of the martensite laths with a lower dislocation density appear brighter in the
photographs. At a high magnification ( × 80000), Figure 1c shows the area of the dislocation structure with a spotty
contrast and dispersed precipitate. Here, the image contrast due to dislocations is difficult to differ from that due to
dispersed precipitate. Such contrast that is responsible for a blurred image of dislocation lines is likely to be due to the
presence of the considerable concentration of impurity atmospheres on dislocations. Thus, the peculiar features of the
image are indicative not only of the considerable density of dislocations but also of their essential pinning by impurity
atmospheres and the processes of redistribution of alloying elements as well, which results in the formation of precipitates.
The presence in the ferrite of carbide inclusions that are the effective barriers on the way of dislocation movement also
affects the mechanical properties of steel 15Kh13МF (Figure 1b).
Thus, the mechanical properties of steel 15Kh13МF in the initial state are conditioned by the presence of dislocation
boundaries of the lath martensite, a considerable density of dislocations in plates, pinning of dislocations by impurity
elements and dispersed precipitates, blocking of dislocation movement by inclusions.
After tensile deformation, certain changes in the morphology of the dislocation structure were detected, which consist in
the increase of the nonparallel alignment of dislocation subboundaries and decrease in the distance between the
subboundaries (Figure 1d). The martensite grain size reduction and increase in the fragmentation of laths of the
dislocation martensite were revealed. The presence of numerous reflections and their blurring in the microdiffraction
pattern are indicative of the decrease in the distance between low-angle boundaries (Figure 1f). An increase in the width
and angle of disorientation of diffraction reflections with respect to the central reflection was observed, which is indicative
of the disorientation of subboudaries of the ferritic-martensitic structure and laths of the dislocation martensite as
~ ), the angular disorientation
compared to the initial state of the material. With an increase in the plastic strain (necking ψ
between diffraction reflections increases and accordingly the dislocation density within the low-angle boundaries
increases.
~ =0.30, the formation of microcracks and micropores was observed near inclusions due to separation of the
At high ψ
inclusion from the matrix or as a result of breakdown of inclusions, which are the result of the accumulation of the limiting
dislocation density and exhaustion of the material plasticity (Figure 1 e).
а
b
c
d
e
f
Figure 1. Microstructure of steel 15Kh13МF: а) dislocation martensite ( × 30000 magnification; b) carbide precipitates in
the ferrite ( × 60000 magnification); c) dispersed precipitates in the ferrite ( × 80000 magnification); d) plastically deformed
martensite ( × 30000 magnification); e) microcracks and pores ( × 40000 magnification); f) microdiffraction.
Since the dislocation density increases in the process of plastic deformation and inclusions are effective barriers on the
way of dislocation movement, the dislocation density in local volumes reaches the boundary value, which results in the
separation of inclusions from the matrix or the breakdown of inclusions and formation of microcracks and pores.
Steel 25Kh1М1F of the load-bearing layer belongs to steels of the ferritic-pearlitic class. Electron-microscopic studies of a
nondeformed material revealed the presence of the structurally free ferrite, pearlitic colonies situated in different parts of
ferritic grains (Figure 2а) and carbide іnclusions of an elongated and globular shape (Figure 2b). The presence of the
cementite was identified from the analysis of diffraction patterns (the cementite reflections are identified in Figure 2c). The
dislocation microstructure of steel 25Kh1М1F in its initial state has a network and partially cellular dislocation structure.
After plastic deformation of the ferritic-pearlitic steel 25Kh1М1F, the changes in the dislocation structure were detected. At
~ =0.35, a entangle and network disoriented dislocation substructures were observed (Figure2d). A
the plastic strain ψ
cellular disoriented and partially fragmented dislocation structure (Figure2е, f) and a noticeable increase in the width of
~ =0.50.
diffraction reflections were typical of the values of the actual necking ψ
The increase in the plastic strain value is accompanied by a fragmentation of subgrains, a decrease in size and increase
~ =0.90, result in the formation of local areas of the completely
in the disorientation of structural blocks. Large strains, ψ
fragmented structure (Figure 2g), formation of stable configurations in the form of low-angle boundaries of considerable
disorientation, as evidenced by the presence of numerous reflections and their blurring on microdiffraction patterns.
~ =0.50, a break of the cementite precipitates due to cutting of the precipitate by dislocations was observed, with
At high ψ
no microcracs and micropores being formed (Figure 2h). It is evident that the break of the cementite precipitates has been
occurred as a result of accumulation of dislocation charges of the boundary value having the opposite signs from different
sides near the obstacle (precipitate) and annihilation of dislocation charges during the break (cutting) of the obstacle [7].
а
c
b
d
e
f
h
g
Figure 2. Мicrostructure of steel 25Kh1М1F: а) pearlitic colony ( × 20000) ; b) carbide precipitate in the ferrite ( × 30000); c)
microdiffraction (cementite reflections); d) network and partially cellular dislocation structure ( × 30000); e) cellular
dislocation structure ( × 30000); f) partially fragmented dislocation structure ( × 30000); g) fragmented dislocation structure
( × 30000); h) cutting of the precipitate by dislocations ( × 40000).
The dependence of the dislocation density within the low-angle boundaries of steels 15Kh13МF and 25Kh1М1F on the
~ of the specimens is given in Figure 3. For both of the steels, the dislocation density within the low-angle
actual necking ψ
boundaries increases linearly and does it more intensely under deformation of specimens from steel 15Kh13МF.
ρbd⋅10-14, m-2
5,5
5,0
4,5
4,0
3,5
3,0
1
2,5
2
2,0
1,5
0
0,2
0,4
0,6
0,8
1,0
ψ~
Figure 3. Dependence of the dislocation density within the low-angle boundaries of steels 25Kh1М1F (1) and
15Kh13МF (2) on the value of the actual necking of specimens
Evaluation of Hardening of Steels Using the Methods of Hardness (Microhardness)
The increase in the hardness of steels due to strain hardening is explained mainly by two reasons: the formation of the
intragranular substructure that fulfils the role of additional barriers and the increase in the disorientation of the boundaries
of the structure components existing in the initial state of the material. Plastic deformation causes an increase in the
number of dislocations in the material; the resistance to their migration increases. The engineering evaluation of the
hardening processes can be made using the method of hardness (microhardness) which also characterizes the
deformation capacity of the material. The data on the hardness (microhardness) measurements for steels 25Kh1М1F (1)
~ of specimens) are presented in Figure 4а and
and 15Kh13МF at various levels of plastic strain (the actual necking ψ
Figure 4b.
The obtained regularities of change in the hardness and microhardness with the actual necking of specimens can be
described by linear relationships. As is seen from Figure 4, with an increase in the plastic strain, the hardness and
microhardness of the steels increases, and in this case steel 15Kh13МF is hardened more intensely. This is likely to be
due to the difference in the dislocation structure of these steels. The microstructure of the ferritic-martensitic steel
15Kh13МF contributes to the pinning of dislocations and makes their movement difficult. Deformation of the ferriticpearlitic steel 25Kh1М1F, which is a structurally free ferrite with areas of sorbite, is accompanied by the fragmentation of
subgrains, decrease in size and increase in the disorientation of structural blocks. The above factors are responsible for
the increase of the hardness (microhardness) of structural elements and their boundaries that depends upon the
microstructure of each of the steels under study.
As is seen from Figure 3, at the same values of necking after tensile plastic deformation, the dislocation density in steel
15Kh13МF іs essentially higher and increases more intense as compared to steel 25Kh1М1F, which is responsible for
more intense hardening and the increase in the hardness and microhardness of steel 15Kh13МF. Here, as is evident from
Figure 3, the maximum plastic strain and dislocation density within the low-angle boundaries of steel 25Kh1М1F is higher
than that in steel 15Kh13МF, which is responsible for the enhanced strength and plasticity of this steel.
100
Hµ, 3000
MPa
HRB
90
2800
2600
80
2400
70
2200
60
2000
1800
50
0
0,1
0,2
0,3
0,4
ψ~
1600
0
0,3
0,6
0,9
1,2
ψ~
а)
b)
Figure 4. Dependence of the hardness (а) and microhardness (b) of steels 25Kh1М1F (1) and 15Kh13МF (2) upon the
actual necking of the specimens. (See the symbols in Figure 3).
Thus, the effect of the tensile plastic deformation of the steels under investigation at a microstructural level consists in the
increase of the density of dislocations within the low-angle boundaries, increase of disorientation of the subgrain structure,
decrease in the distance between the low-angle boundaries (structural element size reduction). The above factors give
rise to the distortion of the crystal lattice of the material and result in the formation of substructural barriers to dislocation
movement, which intensifies the process of metal hardening.
Interrelation between the Hardness (Microhardness) and Dislocation Density
Based on the analysis of the kinetics of material hardnening in uniaxial tension (Figures 3 and 4), the interrelation has
been established between the hardness (microhardness) and dislocation density within the low-angle boundaries (Figure
5). With the increase in the dislocation density, the hardness and microhardness increase and hardening of steels occurs.
The intensity of hardening is determined by the initial dislocation density in the material and its microstructure, which
determines the value of the hardness (microhardness) increment at various degrees of deformation.
In particular, steel 15Kh13МF is hardened more intensely than steel 25Kh1М1F. This is due to different energy consumed
by deformation, which is caused by the distinctions in transformation of dislocation substructures and exhaustion of the
material deforming capacity.
According to the experimental results obtained, the interrelation between the parameters of hardness (microhardness) and
the dislocation density within the low-angle boundaries can be described by a linear relationship:
H = H 0 + ∆H = H 0 + k∆ρ
(4)
where
H 0 = initial hardness (microhardness) of the material
∆H = increment of the material hardness (microhardness) after deformation
∆ρ = ρ k − ρ 0 = increment of the dislocation density in the material after deformation
ρ 0 = initial dislocation density in the material
ρ k = dislocation density in the material after plastic deformation
k = index that characterizes the intensity of hardening.
The values of the quantities of Equation (4) for steels 15Kh13МF and 25Kh1М1F are summarized in Table 3.
Thus, it is seen from Figure 5 а,b that the hardness (microhardness) of the deformed steels 15Kh13МF and 25Kh1М1F at
0
a test temperature of +600 С depends linearly on the dislocation density increment within the low-angle boundaries,
irrespective of the strain value.
HRB
92
Hµ,
MPa
88
2600
84
2400
80
2200
76
2000
72
68
64
1800
0
0,4
0,8
1,2
1,6
2,0
∆ρ⋅10-14, m-2
0
1
2
3
4
∆ρ⋅10-14, m-2
а)
b)
Figure 5. Dependence of the hardness (a) and microhardness (b) of steels 25Kh1М1F (1) and 15Kh13МF (2) upon the
dislocation density increment in the material after deformation (See the symbols in Figure 3)
Тable 3. Parameters of Equation (4)
Steel
ρ 0 ⋅10-14, m-2
k⋅1014
H0
H µ , МPа
HRB
15Kh13МF
2.10
2080
74
13.1/170*
25Kh1М1F
1.75
1750
68
4.07/235*
Note. The magnitudes of the coefficient for hardness are given in the numerator, whereas those for
•
microhardness are given in the denominator
Conclusions
0
1. The effect of the tensile plastic deformation at a temperature of +600 С on the microstructure, dislocation density within
the low-angle boundaries, hardness and microhardness of steels 15Kh13МF and 25Kh1М1F after deformation was
investigated. It has been revealed that with the increase in the plastic strain, the dislocation density within the low-angle
boundaries increases linearly together with the hardness and microhardness of the steels under study.
2. It has been found that in the ferritic-martensitic steel 15Kh13МF under conditions of plastic deformation, the out-ofparallelism increases and the distance between the subboundaries of the dislocation structure decreases, laths of the
dislocation martensite are divided and fragmented. After plastic deformation of the ferritic-pearlitic steel 25Kh1М1F, with
an increase in the strain, the network and partially cellular dislocation structure is transformed into the entangle and
cellular nondisoriented and the cellular disoriented and partially fragmented structure with the areas of the completely
fragmented dislocation structure being formed.
3. The linear dependence has been established between the hardness (microhardness) and the dislocation density within
the low-angle boundaries of the plastically deformed steels. At the same strains, the exhaustion of plasticity (hardening) of
steel 15Kh13МF occurs more intensely than in steel 25Kh1М1F. This is caused by the insufficient plasticity of laths of the
lath martensite that serve as additional barriers capable of retarding the movement of dislocations. The maximum plastic
strain and dislocation density within the low-angle boundaries in steel 25Kh1М1F are higher than in steel 15Kh13МF,
which is responsible for the better characteristics of strength and plasticity of that steel.
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