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On the microstructural evolution in a 10% Cr martensitic steel during interrupted low cycle fatigue testing at
650 C
N. Dudovaa,, R. Mishneva,b, R. Kaibysheva,b
a Laboratory for Mechanical Properties of Nanostructured Materials and Superalloys, Belgorod State National
Research University, 308015, Pobeda 85, Belgorod, Russia
b Laboratory of Advanced Steels for Agricultural Machinery, Russian State Agrarian University–Moscow
Timiryazev Agricultural Academy, 127550 Moscow, Russia
Abstract
The correlation between cyclic softening and microstructural evolution using the interrupted low cycle fatigue
(LCF) tests with a low strain amplitude of ±0.2% at 650 C in a 10% Cr steel was studied. Cyclic softening was
analyzed in terms of the friction and back stresses caused by short-range and long-range obstacles, respectively.
Softening was mainly attributed to a decrease in the friction stress due to the dislocation annihilation. Whereas the
back stress remained more stable due to additional precipitation on the lath boundaries, despite the intense lath
widening caused by the disappearance of lath boundaries.
Keywords: Martensitic steel; Low cycle fatigue; Cyclic softening; Dislocation structure; Precipitates.
1. Introduction
High-chromium martensitic/ferritic steels are used at elevated temperatures and applied stresses in the fossil
power plant industry [1,2]. These steels remain as the main materials for power units with ultrasupercritical
conditions with the operation temperature up to 650 C due to their high creep resistance in combination with
smaller thermal expansion and larger thermal conductivity compared to austenitic steels and nickel-based alloys [3].
Non-equilibrium hierarchical structure provides the creep resistance of high-chromium martensitic steels.
Normalized and tempered steels have the so-called tempered martensite lath structure (TMLS) consisting of prior
austenite grains (PAGs), packets, blocks and laths with a high density of free dislocations [4,5,6]. The M23C6
carbides and M(C,N) carbonitrides are located at boundaries of structural elements and homogeneously in the
Corresponding author.
E-mail addresses: dudova@bsu.edu.ru (N. Dudova), mishnev@bsu.edu.ru (R. Mishnev),
rustam_kaibyshev@bsu.edu.ru (R. Kaibyshev)
ferritic matrix, respectively. These precipitates impede dislocation movement and migration of lath boundaries [7,8].
Under aging or creep conditions, the Laves phase particles (Fe2(W,Mo)) precipitate [9,10]. The creep strength of
these steels depends on the resistance of the TMLS to transformation into the subgrain structure.
In addition to the main requirement to creep resistance, high-chromium steels should exhibit high fatigue
resistance. The components of steam turbines are often subjected to cyclic thermal stresses during start-up and shut-
down or during temperature transients. Therefore, degradation of microstructure under such loading conditions
occurs due to interaction between creep and fatigue processes in the low cycle fatigue (LCF) regime [11].
It is well known that high-chromium martensitic steels exhibit cyclic softening behavior under cyclic loading
at both room and elevated temperatures [12-18]. Many studies have shown that softening is attributed to the
decrease in free dislocation density, coarsening of martensitic laths and transformation of lath structure into
dislocation cell and subgrain structure, coarsening of precipitates [12-18]. It should be noted that most
microstructure examinations have been studied in fatigue fractured specimens, whereas the detailed microstructure
evolution during the interrupted LCF tests has been considered in a limited number of works [19,20,21].
New 9–12% Cr heat-resistant martensitic steels alloyed by the increased B (80–150 ppm) and decreased N
(30–100 ppm) contents exhibit improved creep resistance [22-29]. This effective way to enhance the creep
resistance was suggested by researchers at the National Institute for Materials Science (NIMS) in Japan [11]. The
predicted long-term creep rupture strength of these steels at 650 C for 100,000 h can attain 80-110 MPa [29]. The
numerous studies revealed that a high B content at a low N content effectively increases the coarsening resistance of
M23C6 carbides during creep at high temperatures [4,6,24-29]. Boron enriches M23C6 carbides located near the PAG
boundaries, which increases their coarsening resistance during creep. For example, the 10% Cr steel with 0.008% B
and 0.003%N [25,26] demonstrates an extremely high long-term creep strength of 110 MPa at 650 C for 100,000 h
due to superior stability of TMLS under creep condition.
Previous study of microstructure evolution during LCF in the 10% Cr steel was carried out at 600 C [21]. It
was found that during the first half-life, the lath structure retains at both low (±0.2%) and high (±0.6%) strain
amplitude. But at the same time, a pronounced decrease in the dislocation density and lath widening led to the
approximately 4 times higher rate of microhardness decrease during the first half-life than during the second half-
life. During the second half-life, transformation of the lath boundaries to the subboundaries was completed at
cycling with high strain amplitude. At low strain amplitude, the lath structure which was formed at half-life cycles
retained during the second half of testing up to failure.
On the other hand, the microstructure evolution at higher temperature of 650 C is of interest as this is the
operative temperature for the new generation martensitic steels used in A-USC power plants. Recently, it has been
found that the 10%Cr steel demonstrates unusual LCF behavior as compared with that at 600 C and lower
temperatures [17,21,30-32]. Namely, 1) the stress serrations were found on the plastic strain portion of the hysteresis
loops; 2) the positive temperature dependence of the cyclic strain hardening exponent n and the cyclic strength
coefficient K in the Morrow equation and the 4-fold decrease in the fatigue ductility coefficient
f in the Basquin-
Manson-Coffin relationship with temperature increase from 600 to 650 C. It was suggested that these features are
associated with dynamic strain aging effect on the cyclic behavior.
The aim of the present work is to study the evolution of microstructure in the 10% Cr steel during the
interrupted low cycle fatigue tests at 650 C with a low strain amplitude. Specific attention will be paid to the
changes in the lath boundaries, dislocation structure, dispersion of precipitates, and their effect on the cyclic
softening.
2. Experimental Procedure
A 10% Cr steel with the chemical composition (in wt. %) of 0.1% С, 0.06% Si, 0.1% Mn, 10.0% Cr, 0.17% Ni,
0.7% Mo, 0.05% Nb, 0.2% V, 0.003% N, 0.008% B, 2.0% W, 3.0% Co, 0.002% Ti, 0.006% Cu, 0.01% Al and Fe-
balance was examined. The steel was given a normalizing treatment at 1060 C for 30 min followed by air-cooling
and final tempering at 770 C for 3 h.
LCF tests were carried out at 650 C under fully reversed tension-compression loading conditions with
constant total strain amplitude on cylindrical specimens with a gauge length of 18 mm and a diameter of 5 mm using
an Instron 8801 testing machine. The ratio of minimum strain to maximum strain was -1 and the frequency was 0.5
Hz, which corresponded to the strain rate of 3×10-3 s-1. The low total strain amplitude was
ac = ±0.2%, where elastic
strain component was higher than plastic one [31,32]. The strain was measured using an extensometer located in
direct contact with the gage part of specimen. First, two LCF tests up to failure were carried out with number of
cycles of 4884 and 5459. These tests were stopped when the stress amplitude decreased by more than 20% over the
last 50 cycles. Then, the interrupted at different stages LCF tests were carried out using the subsequent specimens,
one specimen per one level. The interruptions were made at the steady-state stage (after 5 cycles), at cyclic softening
stage after ~Nf/4 cycles (1250 cycles) and ~Nf/2 cycles (2500 cycles). The interrupted tests were stopped after a full
loop closing cycles using the Instron LCF 3 Software. Stress-strain hysteresis loops were recorded continuously to
determine the cycle-dependent changes in the stress and plastic strain amplitude. The microhardness was determined
using a Wilson Wolpert 402 MVD hardness tester under a load of 300 g on the mechanically polished samples with
an accuracy of 4%.
The microstructure was examined using the Z-contrast technique with a Quanta 600FEG scanning electron
microscope (SEM) equipped with an electron backscatter diffraction (EBSD) pattern analyzer incorporating an
orientation imaging microscopy (OIM) system and a JEOL JEM-2100 transmission electron microscope (TEM).
TEM foils were prepared by double-jet electro-polishing using a solution of 10% perchloric acid in glacial acetic
acid. OIM images were obtained with a step size of 120 to 170 nm and subjected to a cleanup procedure,
establishing a minimal confidence index of approximately 0.1 and a minimal number of points per grain of 8. High-
and low-angle boundaries (HABs and LABs) were defined to have a misorientation of 15º and 2º θ 15º and
depicted in the OIM maps using black and white lines, respectively. In order to evaluate the distribution of strain or
the stored energy in TMLS, the kernel average misorientation (KAM) values were obtained from OIM images. The
transverse lath/subgrain sizes were measured on the TEM micrographs by the linear intercept method, counting all
the clear visible (sub)boundaries. The dislocation densities were estimated by counting the individual dislocations in
the (sub)grain/lath interiors per unit area on at least six arbitrarily selected typical TEM images for each data point.
The particle size and aspect ratio were estimated from the SEM micrographs, counting at least 150 particles for each
data point. The particle sizes were also estimated from the TEM micrographs. The occupancy of precipitates on the
PAG and lath boundaries (in %) was estimated on the SEM micrographs as (particle projection length / boundary
projection length) x100%. The number density of precipitates on the PAG and lath boundaries was estimated on the
SEM micrographs as the number of particles per boundary area, which is the product of the boundary length (in m)
and the thickness of the foil (0.1 m). The equilibrium volume fractions of phases were calculated by version 5 of
the Thermo-Calc software using the TCFE7 database entering the BCC A2, FCC A1, M23C6 and Laves phase C14
equilibrium phases for the actual steel composition.
3. Results
3.1. Fatigue behavior
The cyclic stress response of the 10% Cr steel at 650 C and
ac = ±0.2% is shown in Fig. 1. Three stages can
be distinguished on the stress amplitude (
/2) versus the cycle number curve plotted on the linear scale (Fig. 1a).
At stage I, from 1 to ~Nf/4 (~1250) cycles, rapid cyclic softening occurred. At stage II, from ~Nf/4 to ~ 0.85 Nf
cycles, the steel exhibited a continuous linear decrease in the stress with an increase in the number of cycles. Stage
III, from ~ 0.85 Nf cycles to failure, corresponded to the initiation and propagation of macroscopic cracks that
resulted in a rapid reduction of the stress level untill the specimen failure. The stress drop between linear regression
and stress at failure comprised approximately 10%.
Figure 1b shows the same (
/2) vs. N curve plotted on the semilogarithmic scale. A short steady-state stage
during the first 10 cycles can be distinguished. Then, the stress continuously decreased at the cyclic softening stage
up to failure. The cyclic softening coefficient, d(
/2)/dlgN, was approximately 27. Compared with the LCF
behavior at a lower temperature of 600 C and the same
ac = ±0.2% [21], the cyclic softening stage at 650 C is
characterized by a slightly higher (by 20%) coefficient (at 600 C,
/lgNf = 22).
For the microstructural characterization, the subsequent LCF tests were interrupted at the steady-state stage
(after 5 cycles), at the onset of stage II after ~Nf/4 (1250) cycles and at stable stage II after ~ Nf/2 (2500) cycles.
Fig. 1. Cyclic stress response curves of the 10% Cr steel at 650 °C,
ac = ± 0.2% plotted on the linear scale (a) and
semilogarithmic scale (b). Symbols indicate the interrupted fatigue tests for microstructural characterization.
Figure 2 demonstrates the change in hysteresis loop with the number of reversals (1; 5; ~Nf/4 (1250); and
~Nf/2 (2500) cycles). For the first cycle, the value of the peak tensile stress (+
a ) was almost the same as the peak
compression stress (
a) (Table 1). At subsequent cycles, the +
a values exceeded the
a values. The relative
difference between +
a and
a, estimated as ((+
a
a)/+
a)100%, increased from approximately 6% to 9%
with an increase in the number of reversals from 5 to ~Nf/2 (Fig. 2a). So, the hysteresis loops were not fully
symmetrical. The tensile stress amplitude at the 5th cycle was slightly higher than at the first cycle due to cyclic
hardening. During the following testing, the tensile stress amplitude remarkably decreased due to cyclic softening.
Fig. 2. Stress-strain hysteresis loops of the 10% Cr steel for cycles ranging from the first to half-life at 650 C,
ac =
± 0.2% (a). Effect of number of cycles on the plastic strain amplitude (b).
Narrow hysteresis loops indicate for the dominance of the elastic component
ap in the total strain amplitude
ac. At
the first and 5th cycles, the
ap was the same (±0.0293%) that comprised 14.65% from the
ac. By the end of stage I,
i.e. at the ~Nf/4 cycle, widening of loop evidenced for the significant increase in the
ap (by 2 times) to 28.2%.
Nevertheless, by the last cycle before abrupt drop of the stress,
ap remained non-dominant and was less than 35%
(Fig. 2b, Table 1). The ~Nf/2 and ~Nf/4 points were characterized by similar stress and plastic strain amplitudes.
Table 1. Change in the LCF data of the 10% Cr steel with the number of cycles at 650 C,
ac = ± 0.2%.
Number of cycle
ap, %
Relative fraction
of
ap in
ac, %
Peak tensile
stress, +
a,
MPa
Peak
compression
stress,
a,
MPa
100
)(
a
aa
,
%
1
0.0293
14.65
279.31
284.79
1.9
5
0.0293
14.65
293.72
277.13
5.6
~Nf/4 (1250)
0.0564
28.2
242.94
222.53
8.4
~Nf/2 (2500)
0.0631
31.55
233.12
212.60
8.8
Nf
0.0673
33.65
183.44
184.27
0.5
3.2. Microhardness evolution under LCF at 650
C
The as-tempered 10% Cr steel exhibited a microhardness of 250.7 HV (Fig. 3). Cyclic deformation up to
failure led to a decrease in microhardness by 9.3%. It should be noted that a significant part of the reduction (6%)
occurred during stage I of testing. The microhardness of the specimen interrupted after the 1250 cycle was 236 HV.
The following cyclic loading up to ~Nf/2 cycles resulted in a continuous decrease in microhardness to 230 HV, i.e.
by 3%. At the second half-life, the microhardness decreased insignificantly (by 1%) to 227.5 HV.
Fig. 3. Effect of number of cycles
at 650 C,
ac = ± 0.2% on the
microhardness of the 10% Cr
steel.
3.3. Microstructure evolution under LCF at 650
C
3.3.1. Evolution of tempered martensite lath structure and dispersion of precipitates
Before the LCF testing, the as-tempered 10% Cr steel had a typical lath structure (Figs. 4a, 5a). It was
described in detail prevoiusly [17,21,25,26,30-32]. An average size of PAGs was 35 m, an average lath width was
380 nm; and the dislocation density within the lath interiors was 1.7×1014 m-2. The M23C6 carbides with an average
size of about 70 nm were densely located at HABs of PAGs, packets, and lath boundaries, although some lath
boundaries were almost free of these carbides. MX carbonitrides (mainly Nb(C,N)) with a size of 30 nm were
uniformly distributed within the martensite laths.
The SEM and TEM micrographs (Figs. 4, 5) show gradual changes in the lath structure and dispersion of
precipitates during LCF at 650 C,
ac = ± 0.2%. The lath structure was mainly retained up to failure, although the
mean lath width gradually increased and the dislocation density in the lath interiors decreased, both by
approximately 40% (Fig. 6). The dislocation density noticeably reduced during the first 5 cycles (by 13%), whereas
a smaller decrease (by approximately 7-8%) occured at each of the following interrupted steps (Fig. 6a). In contrast,
the mean lath width increased insignificantly during the first 5 cycles (by ~8%). While a noticeable part of the lath
widening occurred in the first quarter of LCF testing (by ~30%) (Fig. 6b).
Fig. 4. SEM and TEM micrographs of the 10% Cr steel in the as-tempered condition (a) and after fatigue tests at
650 C,
ac = ± 0.2% interrupted after 5 cycles (b), 1250 cycles (c), 2500 cycles (d) and after fatigue failure (e).
Fig. 5. SEM micrographs obtained in
Z-contrast of the 10% Cr steel in the
as-tempered condition (a) and after
fatigue tests at 650 C,
ac = ± 0.2%
interrupted after 5 cycles (b), 1250
cycles (c), 2500 cycles (d) and after
fatigue failure (e).
Fig. 6. Change in the dislocation
density (a) and lath width (b),
estimated from TEM micrographs,
during LCF testing at 650 C,
ac = ±
0.2%.
The distribution of precipitates noticeably changed under cyclic deformation. Before the LCF testing, the
М23С6 carbides located along the PAG boundaries were somewhat larger than along the lath boundaries. This is
confirmed by a wider distribution hystogram of the particle size (Fig. 7a) and a larger average size of particles (Fig.
8a) located along the PAG boundaries (73 nm) as compared to the lath boundary particles (66 nm). Moreover, the
PAG boundaries were more occupied by precipitates (~50% of the boundary projection length) than the lath
boundaries (~25%) (Fig. 8b). And the number density of precipitates (number of precipitates per boundary area) on
the PAG boundaries was higher (~ 0.7 m-2) than on the lath boundaries (~ 0.4 m-2) (Fig. 8c). It should be noted
that a significant part of boundary precipitates had an elongated shape along the boundaries. The aspect ratio
averaged ~1.8 and ~2 for the precipitates along the PAG and lath boundaries, respectively, and could attain a high
value of up to 5 (Fig. 9a).
Fig. 7. Particle size distributions along the PAG and lath/subgrain boundaries in the 10% Cr steel in the as-tempered
condition (a) and after fatigue tests at 650 C,
ac = ± 0.2% interrupted after 5 cycles (b), 1250 cycles (c), 2500
cycles (d) and after fatigue failure (e). Data were estimated from SEM micrographs.
Fig. 8. Change in the characteristics
of precipitate distribution along the
PAG and lath boundaries in the 10%
Cr steel during LCF testing at 650
C,
ac = ± 0.2%: a) the mean particle
size; b) the occupancy of precipitates
on the boundaries; c) the number
density of precipitates. Data were
estimated from SEM micrographs.
Fig. 9. Distributions of aspect ratio of particles located along the PAG and lath/subgrain boundaries in the
10% Cr steel in the as-tempered condition (a) and after fatigue tests at 650 C,
ac = ± 0.2% interrupted after 5 cycles
(b), 1250 cycles (c), 2500 cycles (d) and after fatigue failure (e). Data were estimated from SEM micrographs.
It seems that after 5 cycles of deformation, the microstructure was similar to the as-tempered structure. The
boundaries of PAGs and laths were decorated by fine precipitates. The average sizes of these particles increased to
91 and 72 nm, respectively; growth was approximately 25% and 9% (Figs. 5b, 7b, 8a). The particles became more
rounded in shape already after 5 cycles. The aspect ratio distributions of precipitates on the PAG and lath boundaries
become narrower, and their peaks shifted to the lower values (Fig. 9b). This led to a decrease in the average aspect
ratio by ~25% to ~1.4 and ~1.6 for the precipitates along the PAG and lath boundaries, respectively.
The following cyclic deformation up to ~Nf/4 and even up to failure, Nf, did not change the mean size of
precipitates located along the PAG boundaries as well as along the lath boundaries (Fig. 8a). However, after ~Nf/4
cycles, it was found that the occupancy of precipitates on the boundaries began to increase (Fig. 8b). The boundaries
had become more filled with precipitates (Fig. 5c). A large number of small rounded particles were observed,
especially, along the lath and block boundaries. The number density of precipitates also tended to increase (Fig. 8c).
It can be suggested that additional precipitation occurred during cyclic deformation.
After ~Nf/2 cycles, coarse subgrains were revealed in some regions of packets and blocks (Fig. 5d). The size
of such subgrains could attain 2...5 m. The low density of precipitates was typical for these coarse subgrains.
Precipitates in the subgrain interiors had the rounded shape, mainly. The number density and occupancy of
precipitates on the PAG and lath boundaries continuously increased with an increase in the number of cycles until
failure (Fig. 8b,c).
After failure, the microstructure was characterized as a lath structure (with the mean size of lath width of 560
nm) with individual coarse subgrains and blocks up to several micrometers in size (Figs. 4e, 5e). The precipitates on
the PAG and lath boundaries were fine and densely distributed (Figs. 5e, 7e, 8). In coarse subgrains and blocks, the
precipitates were rarely observed.
3.3.2. Evolution of low-angle and high-angle boundaries (EBSD)
The evolution of low-angle (LABs) and high-angle (HABs) boundaries during LCF testing was studied on
OIM images obtained by the EBSD technique (Fig. 10). Under cyclic loading until failure, the number fraction of
LABs with a misorientation of 2-15 noticeably decreased (by ~ 30%), whereas the number fraction of HABs
increased (Figs. 10a2-e2, 11a, Table 2). This resulted in a slight increase in the average misorientation angle by
approximately 7. It should be noted that a remarkable decrease in the number fraction of LABs (by ~20%) occurred
already during the first 5 cycles (Fig. 11a, Table 2).
As well as the number fraction increased, the density of LABs (length of boundaries per unit area) gradually
decreased with the number of cycles (Fig. 11d). At the same time, the density of HABs changed insignificantly. This
fact indicates that the fraction of LABs decreased as a result of the dissapearance of a part of LABs during cyclic
deformation.
Among LABs, the 2 boundaries were most susceptible to changes. Thus, after failure, the number fraction of
the 2 LABs was 2 times less relative to all boundaries and by ~40% less relative to all LABs (Table 2, Fig. 11b,c).
The density of all LABs decreased by ~ 2×105 m-1 during the LCF test, and the half of this decrease was due to the
2 boundaries (~1×105 m-1) (Fig. 11d, Table 2). Boundary maps in Fig. 10(a4-e4) demonstrate the gradual
dissapearance of the 2 boundaries (these boundaries are colored red).
The distribution hystograms of LAB misorientation (Fig. 10a3-e3) show that the number fraction of the 5-7
LABs and 10-15 LABs increased with number of cycles (Fig. 11c). However, their number fraction relative to all
LABs and HABs did not change (Fig. 11b). Moreover, the density of the 5-7 LABs slightly decreased, and the
density of the 10-15 LABs did not change significantly (Fig. 11d).
Therefore, the EBSD analysis of boundaries revealed the dissapearance of LABs, especially, the 2
boundaries during LCF testing. Then, the evolution of the lath boundaries and dislocation structure during cyclic
deformation were studied by TEM of foils.
Fig. 10. OIM images (a1-e1) with corresponding distributions of misorientation angle of all boundaries (a2-
e2) and LABs (a3-e3), and maps showing the 2-3 LABs (in red colour) and HABs (a4-e4) of the 10% Cr steel in
the as-tempered condition (a) and after fatigue tests at 650 C,
ac = ± 0.2% interrupted after 5 cycles (b), 1250
cycles (c), 2500 cycles (d) and after fatigue failure (e).
Table 2. Change in the boundary parameters of the 10% Cr steel with the number of cycles at 650 C,
ac = ± 0.2%.
Parameter
As-tempered
5 cycles
~Nf/4 (1250)
~Nf/2 (2500)
Nf
Number fraction of boundaries, %
HABs
41.1
52.3
50.7
52.9
54.8
LABs
58.9
47.7
49.3
47.1
45.2
2LABs
16.8
12.2
12.2
11.1
9.2
5-7 LABs
14.1
12.7
13.5
14.1
14.2
10-15 LABs
2.9
2.8
3.3
3.1
4.1
Number fraction of boundaries relative to all LABs, %
2LAB, %
28.5
25.6
24.7
23.6
20.4
5-7 LABs
23.9
26.5
27.4
30.0
31.4
10-15 LABs
4.9
5.9
6.7
5.6
9.0
Density of boundaries, ×105 m-1
HABs
4.83
5.95
5.28
5.23
5.99
LABs
6.91
5.44
5.14
4.66
4.94
2 LABs
1.97
1.39
1.27
1.10
1.01
5-7 LABs
2.43
1.99
1.91
1.88
2.10
10-15 LABs
0.34
0.32
0.35
0.31
0.45
Fig. 11. Change in the number fraction
(a,b,c) and density (d) of boundaries in
the 10% Cr steel during LCF testing at
650 C,
ac = ± 0.2%. Data were
estimated from OIM maps.
3.3.3. Evolution of dislocation structure
After the first 5 cycles, compared to the as-tempered microstructure, the dislocation tangles were formed in
most of the laths (Fig. 12a). The carbides located along the lath boundaries and fine MX carbonitrides in the matrix
impeded the movement of dislocations in the lath interiors (Fig. 12b). Gliding dislocations were aligned into pile-
ups (Fig. 12c). Lattice dislocations during glide could annihilate with dislocations of the opposite sign. Therefore,
the dislocation density in the lath interiors, estimated by TEM, noticeably decreased (by about 13%) (Fig. 6a).
The onset of partial dissappearance of dislocation subboundaries was revealed (Fig. 12a). Thus, in Fig. 12a
the knitting-out dislocations from lath/subgrain boundaries can be seen. They could appear due to the reaction of
moving dislocations and dislocations belonging to lath/subgrain boundaries. This led to annihilation and extracting
of subboundary dislocations. It should be noted that the sections of lath boundaries without precipitates were more
succeptible to dissolution, whereas the boundaries with dense chains of precipitates were stable (Fig. 12a).
The mean size of carbides located on the lath boundaries was ~ 71 nm, and most of particles had the size in
the range 50…75 nm (Fig. 13a), which corresponds to the mean size and size distribution estimated from SEM
micrographs (Fig. 7b2).
Fig. 12. TEM micrographs of the
10% Cr steel after 5 cycles of LCF
testing at 650 C,
ac = ± 0.2%
showing: a) dislocation tangles in
the lath interiors; b) carbides
impede dislocation movement; c)
alignment of gliding dislocations
into pile-ups and pinning of
dislocations by fine MX
carbonitrides.
Fig. 13. Particle size distributions along the lath boundaries in the 10% Cr steel in the as-tempered condition
(a) and after fatigue tests at 650 C,
ac = ± 0.2% interrupted after 5 cycles (b), 1250 cycles (c), 2500 cycles (d) and
after fatigue failure (e). Data were estimated from TEM micrographs.
After ~Nf/4 (1250) cycles, dislocation cells with wide dislocation walls and new subgrains with a decreased
dislocation density were observed (Fig. 14a). Coarse subgrains were formed in the regions without densely
distributed carbides. Continuous dissolution of subboundaries by knitting reactions occurred. The lath boundaries,
free from densely distributed carbides, rapidly disappeared at stage I. At the same time, lath boundaries with dense
chains of precipitates remained, although some of their regions also began to disappear (Fig. 14a). The precipitates
located at the places of the former lath boundaries became more rounded in shape, in contrast to the elongated
precipitates in the as-tempered state. The interaction of gliding dislocations with dislocations of tangles or pile-ups
led to the formation of new subboundaries (Fig. 14b).
After ~Nf/2 (2500) cycles, a noticeable number of the lath boundaries disappeared. This is evidenced by the
numerous precipitates located at the previous lath boundaries (Fig. 15a). This led to formation of wide laths or
coarse subgrains. The precipatates located inside the wide laths or subgrains had a rounded shape, mainly, and the
distance between these precipitates was similar to or larger than the size of particles. The mean size of the lath
boundary precipitates in the absence of boundaries decreased to ~ 50 nm after ~Nf/4 and ~Nf/2 cycles. It can be
suggested that these carbides changed their shape due to partial dissolution. Those lath boundaries which contained
the chains of densely located elongated precipitates, remained stable (Fig. 15b).
The lath boundaries could disappear or move. Fig. 15b shows the lath boundary free from precipitates that
migrated to the right. The precipitates at the place of almost disappeared lath boundary (Fig. 15c,d) were able to
interact with dislocations and pin them. So, along with fine MX carbonitrides, the M23C6 carbides located inside the
wide laths and subgrains impeded the dislocation motion. Dislocations pinned by particles were observed (Fig. 15).
During the second half of the LCF test, the lath structure mainly remained (Fig. 16). However, the size of
some coarse subgrains attained several micrometers. The lath and block boundaries were decorated by numerous
fine precipitates (dprec=65 nm) (Fig. 16a). The mean size of precipitates located at the previous lath boundaries
further decreased to 32 nm. The gradual dissolution of these precipitates eventually led to the fact that the interiors
of coarse subgrains were mostly free of precipitates (Fig. 16b).
Fig. 14. TEM micrographs of the 10% Cr steel after
1250 cycles (~Nf/4) of LCF testing at 650 C,
ac = ±
0.2% showing: a) stable lath boundaries with densely
distributed precipitates and onset of their dissolution; b)
new subboundary formation.
Fig. 15. TEM micrographs of the 10% Cr steel after
2500 cycles (~Nf/2) of LCF testing at 650 C,
ac = ±
0.2% showing: a) numerous precipitates at the previous
lath boundaries and interaction of dislocations with
precipitates; b) stable lath boundaries with densely
distributed precipitates, and migrating lath boundary free
of particles.
Fig. 16. TEM micrographs of the 10% Cr steel after LCF failure test at 650 C,
ac = ± 0.2% showing: a) fine
precipitates on the lath boundaries; b) coarse subgrains free of precipitates.
Therefore, lath and subgrain boundaries disappeared by knitting-out of dislocations belonging to the
boundaries and their subsequent annihilation with lattice dislocations. Lath and subgrain boundaries with dense
chains of precipitates were sufficiently resistant against disappearance compared to boundaries without precipitates
or boundaries with rounded and isolated precipitates. TEM observations are in accordance with the SEM results,
according to which the precipitates remained small in size (Fig. 13), and the number density of precipitates on the
lath boundaries increased with the number of cycles. Carbides on the places of the former lath boundaries tended to
dissolve. Both homogeneously distributed MX particles and lath boundary precipitates impeded the dislocation
movement and provided the formation of dislocation tangles and nets. Under LCF at a low strain amplitude of ±
0.2% at 650 C, the TMLS of the 10% Cr steel evolved into a mixture of a lath structure and coarse subgrains.
3.3.4. Evolution of kernel average misorientation (KAM)
Additionally, evolution of kernel average misorientation (KAM) was studied. The KAM maps obtained by
EBSD technique are presented in Fig. 17(a1-e1) for the as-tempered and LCF tested specimens. KAM is defined as
the average misorientation between a kernel point and its neighboring points excluding those out of grain boundary,
which reflects the local lattice curvature [33].
Before the LCF tests, the 10% Cr steel was characterized by the relatively high mean KAM value of 0.66.
The KAM map shows that the green-colored high-stress regions dominated in the as-tempered structure, and they
were located in the vicinity of LABs. The peak of KAM value corresponds to the range 0.4-0.6 (Fig. 17a2).
Under the cyclic deformation, the green-colored regions continuously decreased, while the blue-colored
regions with less stress increased Fig. 17(b1-e1). After failure, a decrease in the mean KAM value from 0.66 to
0.51 comprised ~ 30% (Fig. 17f). After the 5th cycle, the mean KAM value decreased to 0.576, i.e. decreased by
~15%. This was due to a lower fraction of the KAM ≥0.6 and a higher fraction of the KAM in the range 0.2…0.6
(Fig. 17b2). The KAM distribution curve after ~Nf/4 cycles nearly corresponded to that after 5 cycles (Fig. 17g).
Whereas after ~Nf/2 cycles, it noticeably changed and the peak shifted to the range 0.2…0.4 (Fig. 17g). The
appearance of well-defined blue-colored regions with lower KAM values suggests that recovery processes occurred
in these regions (Fig. 17a1-e1).
It is known that KAM can serve as dislocation density indicators and is positively related to the density of
geometrically necessary dislocations within EBSD step size [34,35]. The dislocation density was calculated by
equation [36]:
hb
KAM
KAM
33
8
(1)
where
is the mean KAM value (in radians), h is the scanning step (170 nm), b is the Burgers vector (2.5 10-10 m).
The dislocation density values estimated by KAM value,
KAM, are presented in Table 3. They are
approximately 2.5 times higher than the density of lattice dislcations values calculated by TEM,
TEM, which can be
related to the mobile dislocations. Probably, this can be attributed to the fact that the misorientation <5 can be
associated with the geometrically necessary dislocations as well as LABs. And this can increase the dislocation
density, estimated by KAM value, as compared to the
TEM, calculated by counting the dislocations in the lath
interiors on TEM micrographs. Higher values of
KAM are in accordance with the work presented by Zhilyaev et al.
[36], where the
KAM values exceeded the values estimated from X-ray diffraction analysis.
Fig. 17. KAM maps with corresponding distributions of KAM values of the 10% Cr steel in the as-tempered
condition (a) and after fatigue tests at 650 C,
ac = ± 0.2% interrupted after 5 cycles (b), 1250 cycles (c), 2500
cycles (d) and after fatigue failure (e). Change in the average KAM (f) and the KAM distribution curve (g) during
LCF testing.
Table 3. Change in the dislocation density estimated by TEM and EBSD techniques during LCF test with the
number of cycles at 650 C,
ac = ± 0.2%.
As-tempered
5 cycles
~Nf/4 (1250)
~Nf/2 (2500)
Nf
KAM, degree
0.66
0.576
0.555
0.517
0.509
TEM, × 1014 m-2
1.7
1.5
1.4
1.3
1.2
КАМ, × 1014 m-2
4.2
3.6
3.5
3.3
3.2
The
KAM values gradually decreased during LCF similarly to the evolution of
TEM (Fig. 18). A noticeable
decrease of
КАМ occurred in the first 5 cycles (by ~16%), whereas in each of the following steps the dislocation
density decreased only by ~3…6%. Therefore, the reduce in the KAM value and corresponding dislocation density,
estimated by KAM value, is indicative for the decrease in the density of dislocation of the same sign. This
dislocation behavior is typical for cyclic deformation of material undergoing cyclic softening [33]. In contrast,
during simple tensile deformation, the
КАМ dislocation density significantly increases [33].
Fig. 18. Evolution of dislocation density estimated by KAM and TEM of the 10% Cr steel during LCF testing at 650
C,
ac = ± 0.2%.
Therefore, evolution of KAM maps revealed that the KAM value decreased in the vicinity of LABs, mainly.
This could be due to intense knitting-out reaction between lattice dislocations and lath boundary dislocations. This
led to the partial disappearance of the lath and subgrain boundaries and formation of coarse subgrains.
4. Discussion
4.1. Microstructural evolution
The microstructural observation by SEM, TEM and EBSD techniques of the 10% Cr steel after interrupted
LCF tests at 650 C and a low strain amplitude
ac = ± 0.2% revealed two main changes typical of cyclically
softened materials such as the lath widening and decrease in the dislocation density [12-20]. The lath widening was
confirmed by an increase in the mean lath width, observed by TEM, and a simultaneous decrease in the number
fraction and density of LABs, estimated by the EBSD technique. A decrease in the dislocation density was shown
also by both TEM and EBSD techniques. Under cyclic loading, the dislocation glide leads to the annihilation of
lattice dislocations in the lath interiors. In addition, the dislocations belonging to the lath boundaries are knitted-out.
The subsequent annihilation of these dislocations and lattice dislocations results in a decrease in the dislocation
density and partial disappearance of lath boundaries. This is consistent with the results for the 9-12% Cr steels by
Fournier et al. [37], who reported the vanishing of dislocations from the LABs during fatigue loading. Knitting-out
of dislocations from the lath boundaries leading to their dissolution was observed by Chauchan et al. [38] in the 9Cr-
ODS steel, by Wang et al. [39] in the P92 steel, and by Roldan et al. [40] in the reduced activation martensitic
Eurofer97 steel. Dislocation annihilation starts from the regions around the lath and subgrain boundaries, which is in
line with the results of Gopinath et al. obtained on the P92 steel during LCF at 600 C [41]. The disappearance of
the lath boundaries was confirmed by a decrease in the number fraction and density of LABs, whereas the density of
HABs did not change significantly. The disappearance of the LABs during cyclic deformation is in accordance with
the works of Lukas et al. [42] on the 2.25Cr-1Mo steel, Kim and Weertman [43] and Sauzay et al. [44] on the
9Cr1Mo steel and Rae et al. [45] on the 12%Cr turbine steel.
It was found that the precipitates forming dense chains along the lath boundaries have a pinning effect and
provide the high resistance of the boundaries against dissolution. Whereas boundaries without precipitates or
boundaries with rounded and isolated precipitates disappear easily.
On the other hand, cyclic deformation sufficiently affects the morphology and distribution of precipitates. It
can leads to spheroidization of precipitates, especially, the precipitates that locate at the places of previous lath
boundaries. The lath boundary carbides in the absence of lath boundaries tended to become smaller and eventually
dissolve. Thus, their mean size gradually decreased from ~50 to ~30 nm and their aspect ratio decreased from 1.6 to
1.3 with an increase in number of cycles from ~Nf/4 (1250) to Nf. As a result, almost no particles were observed in
coarse subgrains.
The revealed spheroidization of precipitates is in accordance with the works [42,43,46,47]. Kim and
Weertman [43] and Shankar et al. [47] reported that some carbides became spherical in the modified 9Cr–1Mo
ferritic steel under LCF with hold time condition, as well as in a LCF test at 600 C with a strain amplitude of
0.6%. Wang et al. [46] revealed a change in carbide morphology from anisotropic to more rounded and coarser in
the low-alloy 0.29C-1.16Cr-1.29Mo-0.24V steel with bainitic microstructure during cyclic deformation at 550 C.
The authors of Ref. [46] suggested that cyclic deformation destroys the coherence of interfaces such as plate-shaped
V-rich carbides and provides an essentially infinite source of growth ledges. This changes the morphology to a more
rounded shape with minimal interface energy. A high concentration of point defects produced by cyclic deformation
accelerates the diffusional processes, which enhances Ostwald ripening [46].
It can be assumed the processes of Ostwald ripening lead to the dissolution of a part of small particles and the
coarsening of some large particles. Thus, the fraction of particles smaller than 50 nm decreased from ~24% to ~10%
or less, whereas the fraction of particles larger than 100 nm increased from ~7% to ~ 20% on the lath boundaries
and from ~14% to ~30…40% on the PAG boundaries (Fig. 7). Therefore, the coarsening of precipitates on the PAG
boundaries occurs more noticeably. Coarsening of carbides is typical for cyclically deformed steels [46,48].
On the other hand, the occupancy of precipitates on the boundaries and their number density increase
simalteneously, starting from the first cycles, in the studied 10% Cr steel. And the mean size of precipitates on the
PAG and lath boundaries increased by 25% and 9%, respectively, during the first cycles and then remained stable
(~91 and ~72 nm) until failure. It can be suggested that during the LCF test, additional strain-induced precipitation
of the M23C6 carbides occurred. According to the Thermo-Calc prediction, the mole fraction of the M23C6 phase at a
tempering temperature of 770 C is 2.33 mol.%, and at 650 C it slightly increases to 2.376 mol.%. Probably,
tempering for 3 h did not provide the complete precipitation of M23C6 carbide, and cyclic deformation induced
additional precipitation. Precipitation of M23C6 carbides has been reported for the 316L stainless steel during an
isothermal fatigue test at 600 C with a strain amplitude of ± 0.6% by Prasad Reddy et al., although it takes about 50
h for carbide precipitation during aging [49].
In contrast, SEM and TEM observations of foils of the 10% Cr steel studied did not reveal the Laves phase
particles (after ~Nf/4 cycles). As a thermally activated process, the Laves phase precipitation had not yet occurred,
or probably had only just begun. A more detailed examination of precipitates using extraction replicas will be
required. Absence of the Laves phase is in accordance with results of Ishii et al. [50], Hu et al. [51] and Jing et al.
[52], who reported that the Laves phase precipitation did not occur during a pure fatigue test due to its short-term
nature. Whereas this phase intensively precipitated during the creep-fatigue test [53], the fatigue test with tension
holding [50], the thermal fatigue test [54].
A pronounced interaction of dislocations with precipitates were observed. On the one hand, M23C6 carbides at
the lath boundaries were able to pin the dislocation motion along the laths. On the other hand, MX particles and
M23C6 carbides in the lath and subgrain interiors were able to impede dislocations, even those particles that became
spheroidized and isolated, due to their small size.
Cyclic softening is also attributed to the dislocation rearrangement and formation of low-energy structural
elements such as the dislocation cells and subgrains. Wide cell boundaries contains high dislocation density,
whereas cell and subgrain interiors have a low density of dislocations. Cell formation is typical for the cyclically
deformed martensitic steels is in accordance with the works [42,43,51,52]. It can be suggested that at elevated
testing temperature of 650 C, the recovery processes are affected by dislocation climb [55,56]. As it is known,
under cyclic deformation, climb is induced by the high concentration of vacancies produced by cyclic slip and
diffusion of vacancies toward dislocations [56].
4.2. Evolution of the friction and back stresses
In order to consider the effect of microstructural evolution on the cyclic softening of the 10% Cr steel, the
evolution of the maximum tensile stress was analyzed in terms of friction and back stresses determined according to
the method of Cottrell [57]. As it is known, the flow stress to produce the plastic deformation during monotonic
tensile test is composed by two contributions [58]:
- the friction stress
F, which is caused by short-range obstacles such as the lattice friction, precipitated
particles, other dislocations and foreign atoms;
- the back stress
B, which is originated by long-range obstacles such as subgrain boundaries.
For cyclic stress, the friction and back stresses can be estimated from the hysteresis loops according to the
Cottrell method [57,59,60] as shown in Fig. 19. At the start of plastic deformation in the cycle, at the yield stress
Y,
the back stress generated in the preceding half cycle acts in the same direction as the stress. Thus, the yield stress is
the difference between the friction stress acting on the dislocations and the back stress [57,59,60]:
Y=
F -
B (2)
On the other hand, at the end of the forward cycle, at the peak stress
max, when the back stress has again
reached its maximum value, the stress is the sum instead of difference of the friction and back stress [57,59,60]:
max=
F +
B=
Y+2
B (3)
Therefore, the friction stress and the back stress can be determined as [57,59,60]:
F = (
max+
Y)/2 (4)
B = (
max-
Y)/2 (5)
Fig. 19. Scheme of the
Kuhlmann-Wilsdorf and Laird
technique for estimating the
back stress
B and the friction
stress
F from a fatigue
hysteresis loop [59].
A new method of stress partitioning was suggested by Fournier et al. for martensitic steels [61] and was
applied for different steels by Sisodia et al. [62]. This modified method takes into account the viscous stress at
elevated temperatures. However, for the cyclic tests of the 10% Cr steel with a low strain amplitude of 0.2%, the
viscous stress was negligible, as it can be seen on hysteresis loop for the 300th cycle – the linear part is observed
almost up to maximal stress level (Fig. 19). Therefore, the viscous stress can be ignored. The linear part on the
hysteresis loops was detected with the same slope of regression line, with the exception of the loops at the last
cycles. It is known that the Young’s modulus drops sharply due to propagation of macroscopic crack [61]. So, the
slope of regression line was slightly changed for detecting the linear part of some last hysteresis loops (at stage III,
after 4850 cycles).
Figure 20 shows the evolution of the peak tensile stress, the friction stress and the back stress. At stage I,
from 2 to ~1250 cycles (2 - ~0.25 Nf) of LCF test, rapid softening is accompanied by a noticeable decrease in the
friction stress from ~180 to ~140 MPa (by ~30%). A short-term stage from 1 to 10 cycles can be distinguished,
where the peak tensile stress increases from 275 to 294 MPa (by ~7%) or the stress amplitude remaines stable at
~285 MPa (Fig. 1b). At this stage, the back stress noticeably increases from ~110 to ~116 MPa (by ~5%). Further,
the back stress remains almost stable up to 100th cycle and then slightly decreases (Fig. 20b).
Fig. 20. Evolution of the peak tensile, friction and back stresses of the 10% Cr steel during LCF test at 650 C,
ac =
± 0.2%. The curves are plotted on the linear scale (a) and semilogarithmic scale (b).
At stage II, from ~1250 to ~4700 cycles (~0.25-~0.85 Nf), a continuous cyclic softening is associated with a
decrease in the friction stress and a less pronounced decrease in the back stress. The slope of the friction stress curve
is 2.7 times larger than that of the back stress curve (Fig. 20a).
At stage III, > ~4700 cycles (> ~0.85 Nf), rapid cyclic softening occurs, which correlates with a noticeable
decrease in the friction stress by ~23% and the back stress by ~ 13%. As it is known, rapid softening at this stage
occurs due to formation and development of crack in the specimen gauge length.
Since the friction stress is caused by short-range obstacles, its rapid decrease at stage I can be associated with
intense rearrangement and annihilation of free dislocations in the lath interiors. On the other hand, a more stable
back stress indicates the presence of stable long-range obstacles such as lath and subgrain boundaries. A slow
change in the back stress at stage II can evidence for the retention of the lath structure in the 10% Cr steel under
LCF at 650 C with a low strain amplitude.
These results are in accordance with the results obtained on the P92 steel at 600 C with a strain amplitude of
±0.2% [63,64]. Zhang et al. revealed a similar rapid decrease in the friction stress by about 40% at the initial stage
(0-0.22 Nf), whereas the back stress exerted by the lath and subgrain boundaries was almost stable [63,64]. In
contrast, an intense decrease in the back stress was revealed by Armas et al. [65] in the F82H modified steel with
tempered martensite structure at 450 C with a strain amplitude of ±0.3%. Intense transformation of the lath
structure into an equiaxed subgrain structure due to accelerated carbide coarsening provided a significant (about
50%) drop in the back stress over a short period of LCF test (0-0.14 Nf) [65].
4.3. Relation between the evolution of frictional and back stresses and microstructural parameters
Then, let us compare the change in the friction and back stresses and the microstructural parameters at stages
I and II of cyclic deformation. Figure 21 a and b shows a decrease in the friction and back stresses, σF/σFo and σB/σBo,
as a function of fatigue life fraction N/Nf according to relationships: σF/σFo = k1(N/Nf) and σB/σBo = k2(N/Nf), where k1
and k2 are the coefficients.
At stage I, a short-term hardening period during the first 10 cycles is accompanied with a decrease in the σF
by ~3% and an increase in the σB by ~5%. Rapid softening at the subsequent cycles at stage I (10-~0.25Nf) is
attributed to the decrease in the friction stress, the slope of the (σF/σFo vs N/Nf) curve is 0.87. At the same time, the
back stress exhibits the slope of 0.43. At stage II (~0.25-~0.85 Nf), the rate of decrease in the friction stress is
higher than that of the back stress (the slope is 0.16 and 0.11, respectively). During stage II, the friction stress
level decreases from 0.77σFo to 0.66σFo, whereas the back stress level decreases from 0.95σBo to 0.89σBo. Stage III (>
~0.85 Nf) is characterized by a high rate of decrease in both the friction and back stresses (the slope is 0.94 and
0.79, respectively).
Fig. 21. Change in the friction stress (a) and back stress (b), square root dislocation density (c), inverse lath width,
1/dlath (d), and number density of precipitates on lath boundaries (e) vs the fatigue life fraction N/Nf of the 10% Cr
steel at 650 C,
ac = ± 0.2%.
The friction stress is known to be caused by short-range obstacles such as dislocations, and the strengthening
from dislocations is given by [3]:
σdisl =α1MGb
(6)
where α1 is the material constant, M is the Taylor factor, G is the shear modulus, b is the Burgers vector,
is the
density of free dislocations in the matrix.
The gradual decrease in the square root dislocation density, estimated by TEM,
, (Fig. 21c) correlates
with a decrease in the friction stress (Fig. 21a). Thus, at the end of stage I, the level of friction stress of 0.77σFo is
accompanied with the level of 0.9
0
. At stage II, the rate of decreasing the
vs N/Nf curve is 0.14 that is
similar to the rate of decrease in the friction stress. Obviously, a decrease in the dislocation density is one of the
main factors that provide a rapid decrease in the friction stress at the first stage and a smoother decrease at the
second stage.
During the first 10 cycles, a slight decrease (~3%) in the friction stress is accompanied with the unchanged
low plastic strain amplitude at the level of 14.65% from the total strain amplitude (Fig. 2b, Table 1). It can be
suggested that unlocking of dislocations from solute atoms at the beginning of cyclic deformation can contribute to a
slight decrease in the friction stress with cyclic softening coefficient
F/lgN =9 (Fig. 20b). Then, the dislocation
movement and following their annihilation occur which provide a more remarkable decrease in the friction stress
with a doubled softening coefficient of 18 (Fig. 20b).
The back stress is known to be determined by long-range obstacles. The lath boundaries are the main long-
range obstacles in the TMLS of martensitic steels. The strengthening from the substructure is inversly proportional
to the lath width [3]:
σlath =α2Gb/dlath (7)
where α2 is the material constant.
At stage I, the inverse lath width (1/dlath) gradually decreases to the level of 0.92 and 0.77 relative to the
initial value (1/dlath 0) (Fig. 21d). At stage II, the rate of decrease in 1/dlath is relatively high (0.35). However, an
increase and the following weak decrease in the back stress, which provides their high values at 10, ~Nf/4 and ~Nf/2
cycles (Fig. 21b), does not correlate with a rapid decrease in the inverse lath width. This fact means that, although
the noticeable lath widening occurs at the first and second stages of LCF, the back stress decreases insignificantly.
The question is why?
The lath boundaries serve as the main long-range obstacles in the lath structure. They continue to be effective
obstacles, despite their partial disappearance. The microstructural observation revealed the additional precipitation
on PAG and lath boundaries. We suggest that the precipitates on the lath boundaries can also be considered as long-
range obstacles.
The strengthening from precipitates according to Orowan stress is given by [3]:
σprecip = 0.8 MGb / λ (8)
where λ is the interparticle spacing. Taken into account that the change in the mean particle size on the lath
boundaries was insignificant during the first 5 cycles (from 65.8 to approximately 72 nm) and this size was stable
during following deformation, it can be assumed that the interparticle size is inversly proportional to the number
density of particles per lath boundary area,
.
The number density of particles on the lath boundaries gradually increases to 1.15
0 and 1.38
0 during stage
I and slightly increases to 1.4
0 by ~Nf/2 cycle (Fig. 21e). Therefore, the precipitation strengthening increases both
at stages I and II due to an increase in the number density of precipitates and, accordingly, a decrease in the
interparticle spacing.
In turn, additional precipitation strengthening compensates for part of the softening due to the lath widening
and the disappearance of lath boundaries both at stages I and II of LCF. Dense chains of precipitates at the lath
boundaries impede the dislocation movement and make the boundaries more resistant against dissolution. This leads
to strengthening of lath boundaries which serve as long-range obstacles and cause the back stress. As a result, the
back stress does not decrease sufficiently.
Schematic microstructural evolution in the 10% Cr steel during cyclic deformation at 650 C and a low strain
amplitude of ± 0.2% is presented in Fig. 22. Lattice dislocations as short-range obstacles gradually annihilate after
their unlocking from solute atoms that leads to reducing the friction stress. Lath boundaries as long-range obstacles
partially disappear which results in the lath widening. The following dislocation rearrangement leads to the
formation of cells and subgrains with low density of dislocations in their interiors. Additional precipitation at the
lath boundaries during cyclic deformation along with retaining the small size of precipitates provides the stable back
stress. Thus, additional precipitation at lath boundaries affects positively the fatigue resistance of the 10% Cr steel,
because it compensates for disappearance of a part of lath boundaries that prevents a rapid decrease in the back
stress.
Fig. 22. Schematic evolution of dislocations (a) and lath boundaries and precipitates (b) during cyclic loadings at
low strain amplitude.
Nevertheless, under cyclic loading at 650 C with a low strain amplitude, starting from the first cycles,
noticeable changes in the dislocation density, lath boundaries and precipitation distribution occur in the 10% Cr
steel. These changes can cause the significant variation of behavior under creep conditions.
5. Conclusions
The correlation between the cyclic softening and microstructural evolution using the interrupted low cycle fatigue
(LCF) tests with a low strain amplitude of ±0.2% at elevated temperature of 650 C in a 10% Cr-2% W-0.7% Mo-
3% Co-0.05% Nb-0.2% V-0.008% B-0.003% N steel (all in wt.%) was studied. The main results are summarized as
follows:
1. During the first 10 cycles, the short-term steady-state stage is attributed to a slight increase in the back stress due
to additional precipitation on the lath boundaries, which compensate for the softening due to the lath widening
and a slight decrease in the friction stress due to dislocation unpinning from solute atoms.
2. At the subsequent cycling at stage I, from ~10 to ~0.25 Nf cycles, rapid softening is accompanied with a
significant decrease in the stress amplitude by 30%, a microhardness decrease by 6% and a twofold increase in
the plastic strain amplitude in the total strain amplitude. Rapid softening correlates with an intense decrease in
the friction stress, mainly, due to a decrease in the lattice dislocation density. The back stress remains high
because the additional precipitation compensates for the rapid lath widening and disappearance of lath
boundaries.
3. At stage II, from ~0.25Nf to ~0.85Nf cycles, continuous cyclic softening is mainly associated with a decrease in
the friction stress due to a decrease in the dislocation density, whereas the back stress remains almost stable due
to competing processes of lath widening and precipitation on the lath boundaries.
4. Lath and subgrain boundaries disappear during cyclic loading by knitting-out of dislocations belonging to
boundaries and their subsequent annihilation with lattice dislocations. Disappearance of lath boundaries was
confirmed by the simultaneous decrease in the number fraction and density of low-angle boundaries, estimated
by the EBSD technique. The lath structure eventually evolves into a mixture of lath structure and coarse
subgrains.
5. A decrease in the dislocation density was shown both by the density of lattice dislocations in the lath interiors,
estimated by TEM, and by the density of geometrically necessary dislocations, estimated by KAM. The latter are
approximately 2.5 times higher than the dislocation density values calculated by TEM.
6. Spheroidization and gradual dissolution of boundary carbides at the places of previous lath boundaries occurs
due to Ostwald ripening processes. The subsequent coarsening of precipitates occurs more noticeably on the
PAG boundaries than on the lath boundaries.
7. Additional precipitation was evidenced by the simultaneous increase in the occupancy of precipitates on the
PAG and lath boundaries and their number density, starting from the first cycles, whereas the mean size of
precipitates on the PAG and lath boundaries increased by 25% and 9%, respectively, during the first cycles and
then remained stable (~91 and ~72 nm) until failure.
Acknowledgments: This study was financially supported by the Russian Science Foundation grant No. 22-29-
00145, https://rscf.ru/en/project/22-29-00145/. The studies were carried out on the equipment of the Joint Scientific
Center for Technologies and Materials of Belgorod State National Research University.
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