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Acta Materialia 84 (2015) 110–123
www.elsevier.com/locate/actamat
Mechanisms of subgrain coarsening and its effect on the mechanical
properties of carbon-supersaturated nanocrystalline hypereutectoid steel
Y.J. Li,a, A. Kostka,a P. Choi,a S. Goto,a,b D. Ponge,a R. Kirchheimc and D. Raabea,*
⇑
a
Max-Planck Institut für Eisenforschung, Max-Planck-Str. 1, D-40237 Düsseldorf, Germany
Department of Materials Science and Engineering, Faculty of Engineering and Resource Science,
Akita University, Tegata Gakuencho, Akita 010-8502, Japan
c
Institut für Materialphysik, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1,
D-37077 Göttingen, Germany
b
Received 3 August 2014; revised 10 October 2014; accepted 12 October 2014
Abstract—Carbon-supersaturated nanocrystalline hypereutectoid steels with a tensile strength of 6.35 GPa were produced from severely cold-drawn
pearlite. The nanocrystalline material undergoes softening upon annealing at temperatures between 200 and 450 C. The ductility in terms of elongation to failure exhibits a non-monotonic dependence on temperature. Here, the microstructural mechanisms responsible for changes in the mechanical properties were studied using transmission electron microscopy (TEM), TEM-based automated scanning nanobeam diffraction and atom probe
tomography (APT). TEM and APT investigations of the nanocrystalline hypereutectoid steel show subgrain coarsening upon annealing, which leads
to strength reduction following a Hall–Petch law. APT analyzes of the Mn distribution near subgrain boundaries and in the cementite give strong
evidence of capillary-driven subgrain coarsening occurring through subgrain boundary migration. The pronounced deterioration of ductility after
annealing at temperatures above 350 C is attributed to the formation of cementite at subgrain boundaries. The overall segregation of carbon atoms
at ferrite subgrain boundaries gives the nanocrystalline material excellent thermal stability upon annealing.
Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Cold-drawn pearlitic steel; Nanocrystalline steels; Strength softening; Annealing; Subgrain coarsening
1. Introduction
Cold-drawn pearlitic steel wires are important engineering materials for a variety of applications such as automobile tire cords, suspension bridge and power cables, piano
strings, and springs due to their ultrahigh strength. In
1995 it was reported that severe cold-drawing of pearlite
yields a tensile strength of 5 GPa [1]. In the following
years the tensile strength of cold-drawn pearlitic steel
wires has been increased to 6.35 GPa [2] and very recently
even up to 7 GPa [3]. The extraordinary strength has
made the materials attractive not only for engineering
applications but also for studying basic relationships
between structure and mechanical properties of nanoscaled alloys. During the past 50 years great efforts have
been made to understand the microstructural evolution
and its effect on strength upon cold drawing [3–9]. The
most frequently reported finding is deformation-induced
cementite decomposition [10–19] and its “unexpected”
consequence on strain hardening, i.e. the decomposition
of the hard phase—cementite—surprisingly does not
⇑ Corresponding
authors. Tel.: +49 211 6792853; fax: +49 211
6792333; e-mail addresses: y.li@mpie.de; d.raabe@mpie.de
adversely affect the material’s strength. On the contrary,
the tensile strength continuously increases upon cold
drawing [3,4,20], even when the cementite has been significantly dissolved [3,18,19]. It is worth noting that the
mechanism of deformation-induced cementite decomposition is still under dispute. Different from the assumption
that the decomposition takes place upon cold drawing,
due to the interaction between dislocations and carbon
[3,18,19], Takahashi et al. [21] suggested that it mainly
occurs upon low-temperature aging after cold drawing.
With the development of characterization techniques such
as Mössbauer spectroscopy [10], field ion microscopy
(FIM) [11,15,22–25] and atom probe tomography (APT)
[12–16,18,19] a deeper understanding of the mechanisms
of cementite decomposition and their effects on microstructure and strength has been achieved. Among these
characterization techniques APT is able to provide nanoand atomic-scale information on the carbon distribution
in both cementite and ferrite with high compositional
accuracy and statistical significance [2,19]. Recently, Li
et al. [3] observed that above a true drawing strain of
4.19 the original lamellar ferrite/cementite structure in a
hypereutectoid steel wire is gradually replaced by a 2-D
nanoscaled ferrite subgrain structure upon further drawing. The dissolved carbon atoms were found to be
http://dx.doi.org/10.1016/j.actamat.2014.10.027
1359-6462/Ó 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
segregated at ferrite subgrain boundaries (SGBs), suppressing dynamic recovery and thus stabilizing the dislocation structure. Hence, the heavily deformed wires are no
longer hypereutectoid pearlitic steels but carbon-supersaturated nanocrystalline hypereutectoid steels. At a true
drawing strain of 6.52 the subgrain size has been reduced
to below 10 nm, which provides a tensile strength of up to
7 GPa [3].
In many engineering applications such as suspension
bridges and power cables cold-drawn hypereutectoid steel
wires are subjected to hot-dip galvanization or blueing (a
heat treatment to simulate the hot-dip galvanized process,
up to 550 C for 15 min after cold drawing) to improve
their anti-corrosion property [26,27]. Such processes may
reduce the tensile strength because the temperature during
galvanizing can approach 500 C [26,27]. Thus, it is essential to study the thermal stability of heavily cold-drawn
pearlite as well as the microstructural mechanisms associated with strength reduction during annealing. The strength
reduction of cold-drawn pearlite during annealing has been
reported in Refs. [21,26–28,30]. Some results obtained by
microstructural investigations using TEM and APT can
be found in Refs. [13,26,28–30]. It is known that for the
same heat-treatment condition the annealed microstructure
of a material strongly depends on its microstructure prior
to annealing. For cold-drawn pearlitic steels this prior
microstructure, depending on the drawing strain d , can
be either a heterophase-dominated lamellar structure at
low strains or a nanosized carbon-supersaturated ferrite
subgrain-dominated dislocation structure at extremely high
strains [3]. The materials investigated in the abovementioned studies were mainly subjected to relatively low
drawing strain, where the lamellar structure still prevails.
The observations were often performed under relatively
short and not sufficiently systematic annealing conditions.
In this sense, the strength–microstructure relationships during annealing of cold-drawn pearlite have not yet been systematically studied, especially for wires with extremely high
drawing strains.
Here we study the microstructure–property relationships
of annealed carbon-supersaturated nanocrystalline hypereutectoid (0.98 wt.% C) steels produced from severely
cold-drawn pearlite by a true strain d of 6.0. This initial
microstructure prior to annealing is significantly different
from the materials studied in previous papers in which heterophase boundaries are still dominant [13,21,26–30]. The
present work focuses mainly on the evolution of the nanoscaled subgrain structure in ferrite during annealing. More
specifically, first, systematic investigations have been performed on the evolution of the nanosized ferrite subgrain
structure during annealing. Second, quantitative analyzes
of the subgrain structures in terms of area fractions of
low-angle and high-angle grain boundaries have been performed as a function of the annealing temperature T a using
scanning nanobeam diffraction and the software ASTAR
[31]. Third, subgrain coarsening is for the first time experimentally studied at the atomic scale and understood
through triple-junction-controlled migration of subgrain
boundaries. Finally, the effect of T a on the ductility of
annealed wires is also studied. The relationship between
tensile strength and ferrite subgrain size can be described
by a Hall–Petch law. On the basis of these investigations
the effects of microstructural evolution on the mechanical
properties of the carbon-supersaturated nanocrystalline
steel upon annealing are discussed.
111
2. Experimental
2.1. Material and processing
The original pearlitic steel wires subjected to heavy cold
drawing were of hypereutectoid composition (Fe–0.98C–
0.31Mn–0.20Si–0.20Cr–0.01Cu–0.006P–0.007S in wt.% or
Fe–4.40C–0.30Mn–0.39Si–0.21Cr–0.003Cu–0.01P–0.01S in
at.%), and were provided by Suzuki Metal Industry Co.
Ltd. Before cold drawing the wires were austenitized at
950 C for 80 s followed by pearlitic transformation in a
lead bath at 580 C for 20 s and subsequent quenching in
water. After this treatment specimens were subjected to
cold drawing up to a true drawing strain of d ¼ 6:0. The
cold-drawn wire is characterized by a nanoscale ferrite subgrain structure associated with strong yet incomplete chemical decomposition of the cementite. The nanosized
subgrains exhibit a two-dimensional columnar morphology
which is elongated along the drawing direction. The
subgrain size in the transverse cross-section (perpendicular
to the wire axis) of the wire is 10 nm [3]. The carbonsupersaturated nanocrystalline steel samples were annealed
for 30 min between 150 and 450 C in 50 C intervals. Short
time annealing for 2 min was also performed at several
selected temperatures.
2.2. Mechanical testing
The tensile strength of the annealed samples was measured at room temperature with a Dia Stron LEX 810
device at an initial strain rate of _ 0 ¼ 1:16 10ÿ3 sÿ1 . The
true tensile strain is determined by ¼ ln l0 þDl
, where l0
l0
and Dl are the initial gauge length and the length change
of the wires, respectively. The wire tensile elongation was
measured by subtracting the machine elongation from the
total length change. The true tensile stress is determined
by r ¼ SF0 expðÞ, where F is the force and S 0 the initial
cross-section of the wires.
2.3. Characterization techniques
A JEOL JEM-2200FS operated at 200 kV was applied
to investigate the as-annealed samples in both TEM and
scanning TEM (STEM) modes. Crystallographic orientation and phase mapping were performed by nanobeam diffraction in scanning mode using a transmission electron
microscope equipped with a NanoMEGAS ASTAR system
[31]. The scanning was conducted at 0.5 nm spot and
1.25 nm step size.
APT investigations were performed using a local electrode atom probe (LEAP 3000X HRe, Cameca Instruments) in voltage mode at 70 K, a pulse fraction of 15%,
a pulse repetition rate of 200 kHz, and a detection rate of
0.005 atoms per pulse. Readers are referred to our previous
works [2,19] regarding the detailed analyzes of APT data
including chemical identification and 3-D reconstruction.
Samples for both TEM and APT were prepared using a
dual-beam focused-ion-beam (FIB) (FEI Helios NanoLab
600TM). TEM investigations were performed on the
cross-sections of wires. APT samples were prepared with
their tips perpendicular to the wire axis according to the
procedure described in Ref. [32] in order to reduce the local
magnification effect [17,33] and to probe as many ferrite
subgrains as possible.
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A subgrain is here defined in this context as a grain
without differentiating between low-angle (LAGBs) and
high-angle grain boundaries (HAGBs). Its size d Sub was
measured through the line intercept method based on the
APT and ASTAR data.
3. Results
3.1. Changes of strength and ductility upon annealing
Fig. 1(a) displays true tensile stress–strain curves of
annealed cold-drawn wires at various T a for 30 min. For
each annealing condition three specimens were measured
up to the point of fracture. The obtained average ultimate
tensile strengths rUTS are presented as a function of T a in
Fig. 1(b), where data with lower drawing strains taken from
the literature [21,26–28,30] are also plotted for comparison.
It can be seen that the tensile strength at room temperature
increases with d so that the strength of the current material
lies well above the literature data. With increasing annealing temperature all curves share a common feature, namely
the strength starts to decrease beyond a critical temperature. Similar to pure metals the critical annealing temperature increases with decreasing d . For highly prestrained
wires with d ¼ 6:0 the strength reduction occurs at
T a > 150 C with a steep negative slope. In contrast, for
slightly prestrained wires with d ¼ 1:7 [26] and 1.9 [27]
there is nearly no strength reduction up to 400 C.
Fig. 1(c) shows that the annealing temperature has a
non-monotonic influence on the ductility of the current
material. At T a < 350 C the ductility increases with the
annealing temperature, which is similar to pure metals
upon annealing, where the materials regain work-hardening
capability due to the recovery of deformation-induced
defects such as dislocations and subgrain boundaries. The
deterioration of ductility above 350 C may be related to
the reprecipitation and growth of cementite particles at
subgrain boundaries during annealing. This issue will be
further discussed in Section 4.4 based on APT
observations.
3.2. TEM investigations of the evolution of nanosized ferrite
subgrain structure with annealing temperature
Fig. 2 shows the STEM images in the transverse crosssection of annealed nanocrystalline hypereutectoid steel
wires observed at various T a for 2 and 30 min. After lowtemperature annealing at 150 C for 30 min the microstructure does not differ much from the as-cold-drawn state. The
typical curled grain morphology in connection with the formation of a [0 1 1] fiber texture [34] evolved during cold
drawing [2,13,15,35] still prevails (Fig. 2(a)). The remaining
strong strain contrast hinders the identification of the nanosized ferrite subgrain structure by STEM. When annealed
at 250 C for 30 min (Fig. 2(b)) the ribbon-shaped structure
becomes clearer. Neighboring lamellae consisting of ferrite
subgrains with blurred boundaries can be distinguished
from each other. In addition, a slight increase in the interlamellar spacing, which equals the transverse crosssectional subgrain size [3], can be observed. At 350 C for
2 min (Fig. 2(c)) the ribbon-shaped structure becomes less
pronounced. Several isolated subgrains with clear boundaries can be recognized. When extending the annealing time
to 30 min the whole subgrain structure becomes more distinctly visible (Fig. 2(d)). Each individual ferrite subgrain
can be clearly distinguished (Fig. 2(d)). In addition, slight
subgrain coarsening takes place. Upon annealing at
400 C (Fig. 2(e)) and 450 C (Fig. 2(f)) for 30 min significant subgrain coarsening occurs; however, the subgrain size
is still below 100 nm.
Fig. 3 shows the ferrite subgrain structures observed by
TEM at higher magnifications on as-annealed samples for
T a 350 C. Subgrains have coarsened significantly as
compared to the as-drawn state. Zooming in on the regions
highlighted with white squares reveals individual dislocations between neighboring subgrains (marked by red
arrows), which prevail even at the highest annealing temperature of 450 . These observations suggest that a large
volume fraction of LAGBs still exists after annealing.
Further quantitative measurements of the misorientation angle h of subgrain boundaries and phase identification are performed by nanobeam diffraction in scanning
mode using the ASTAR system [36]. Fig. 4 shows phase
mappings of the wires annealed under various conditions.
Green and black lines are LAGBS (3 6 h 15 ) and
HAGBs (h > 15 ), respectively. The boundaries with
h 3 are neglected due to orientation resolution. The
results show that the two major microstructural features
developed during severe cold drawing [2,3] prevail in the
annealed samples. First, the columnar subgrain morphology still exists since no overlap of subgrain boundaries is
observed in the transverse cross-section of the wires. Second, the initial lamellar structure has been replaced by
nanoscaled ferrite subgrain structures with cementite particles located at subgrain boundaries and triple junctions.
The presence of a large density of LAGBs in the ferrite is
confirmed by the ASTAR orientation maps. Annealing at
250 C for 30 min yields a fraction of LAGBs of 40% and
a subgrain size of 16 1:7 nm (Fig. 4(a)). At 450 C the
fraction of LAGBs decreases to 15% and the subgrain size
coarsens to 53 10 nm (Fig. 4(d)).
Cementite particles in the samples annealed at low temperatures were additionally investigated by means of
high-resolution TEM (HRTEM). Fig. 5(a) and (b) show
evidence of the presence of crystalline cementite after
low-temperature annealing at 250 C for 30 min and
350 C for 2 min, respectively. The carbon content of the
cementite particles has been further analyzed by APT
measurements.
The fast Fourier transform analysis shown in Fig. 5(b)
reveals stacking faults in the cementite. Since stacking
faults are usually introduced by plastic deformation of
cementite [37–39], the stacking faults observed here in the
annealed sample are probably inherited from the cementite
that remained after cold drawing. This result suggests that
part of the remaining cementite may still maintain its crystalline structure after cold drawing.
3.3. APT investigations of the evolution of the nanosized
ferrite subgrain structure as a function of the annealing
temperature
Fig. 6 shows APT results in transverse cross-sectional
views of the heavily cold drawn induced carbon-supersaturated nanocrystalline steel annealed at various conditions.
Only carbon atoms (red dots) are displayed. Regions identified by green-colored isoconcentration surfaces are
Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
113
Fig. 1. (a) True tensile stress–strain curves of annealed nanocrystalline hypereutectoid steel wires at different annealing temperatures T a for 30 min.
(b) Maximum tensile stress vs. annealing temperature; data taken from the literature with different initial drawing strains and annealing times ta
[2,21,26–28,30] for comparison. (c) Influence of annealing temperature on the elongation to failure derived from (a).
cementite, as will be confirmed later. The nanoscaled subgrain structure with carbon segregating at subgrain boundaries was inherited from the as-cold-drawn state. The
subgrain size d sub increases with increasing T a and ta , which
is consistent both with the STEM observations and the
ASTAR measurements. The influence of the annealing temperatures on the carbon concentrations in ferrite and
cementite is quantified by using proximity histograms
across ferrite–cementite interfaces. The results in Fig. 7
show that carbon has reached the stoichiometric concentration of 25 at.% in the cementite formed in the as-annealed
states already at 250 C for 30 min. Correspondingly, the
carbon concentration in ferrite decreases with the annealing
temperature, indicating that more carbon atoms partition
from ferrite into cementite with increasing T a , and thus
the volume fraction of cementite increases. The stoichiometric carbon concentration inside cementite together with
its crystalline structure (revealed in Fig. 5) identify the
regions enclosed by the isoconcentration surfaces in
Fig. 6 as crystalline cementite.
In comparison to carbon the concentration of Mn in
both ferrite and cementite is strongly temperature dependent. Up to annealing at 350 C for 2 min a homogeneous
distribution of Mn throughout both the ferrite and cementite phases, as a consequence of mechanical alloying during
cold drawing [40], is detected. When extending ta to 30 min,
slight partitioning of Mn into cementite adjacent to ferrite–
cementite interfaces can be observed (see blue curve in
Fig. 7). Further enhancing T a leads to stronger partitioning
of Mn into the cementite. However, it is worth noting that
even after annealing at the highest T a of 450 C studied
here, the incoming flux of Mn from the ferrite cannot be
accommodated throughout the cementite. We attribute this
saturation behavior to a kinetic freezing effect (smaller diffusion coefficient in cementite than in ferrite) as reported in
Refs. [2,40]. Regarding the detailed distributions of other
alloying elements, such as Si and Cr, readers are referred
to Refs. [21,40].
Fig. 8 shows the distribution of Mn (green dots) in the
samples annealed at T a 350 C. The distribution of Fe
(blue dots) is also displayed as a reference. Fe is observed
to be homogeneously distributed in ferrite for all annealing
conditions. After annealing at 350 C for 2 min, a similarly
homogeneous distribution of Mn is observed throughout
the whole detected volume, including ferrite and cementite,
as also seen from the concentration profile in Fig. 7 (pink
line). After annealing at 400 C for 2 min some Mndepleted zones appear near subgrain boundaries, as indicated by arrows in Fig. 8(b). After annealing for 30 min
at the same temperature the Mn-depleted zones with a
width of 10–20 nm become significant (see arrows in
Fig. 8(c)). In addition, the Mn-depleted zones do not symmetrically appear on both sides but only on one side of the
subgrain boundaries. It is worth noting that the observation of a continuous distribution of Fe (without any depletion near the subgrain boundaries) rules out the possibility
of attributing the non-symmetrical Mn-depleted zones to
lens artifacts associated with the APT measurements [41–
45]. A possible explanation of this phenomenon will be discussed in Section 4.2.
Fig. 9 displays the ultimate strength of annealed samples, rUTS , as a function of the reciprocal of the square root
of the subgrain size d Sub of the as-annealed states (red symbols). This relationship is referred to as the Hall–Petch relation. In the context of heavily cold-drawn pearlite wires the
Hall–Petch relationship has been commonly used to
describe the strength increase in terms of the gradual reduction in the average lamellar spacing between the ferrite and
the cementite [4]. The internal heterophase interfaces
impede dislocation movement and multiplication and hence
strengthen the material. The data for the same wires in the
as-cold-drawn state [3] are also displayed for comparison
(black symbols). Surprisingly, the rUTS –d ÿ0:5
Sub relationship
for as-annealed wires also obeys a Hall–Petch law with a
slope k HP of 621 MPa lm0:5 . Moreover, the k HP -value for
the annealed materials is slightly smaller than that for the
as-cold-drawn materials, i.e. the annealed materials are
stronger than the cold-drawn wires for the same subgrain
size. The k HP value, which is affected by the carbon concentration at the grain boundary, has been reported to be in
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Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
Fig. 2. STEM images of heat-treated nanocrystalline hypereutectoid steel wires in transverse cross-sections showing evolution and coarsening of the
nanosized subgrain structures during annealing.
the range between 315 and 760 MPa lm0:5 [46–50]. While
the ferrite grain size investigated in the literature was
in the micrometer range [46–50], it is interesting to observe
that the current value observed in the nanocrystalline steel
also falls in the reported range.
4. Discussion
As mentioned in Section 1, the microstructures prior to
annealing are strongly dependent on the drawing strain d .
They differ from each other not only in the defect density
and interlamellar spacing, but also in the morphology
and the volume fractions of the phase constituents. For
the wires with low and moderate drawing strains lamellar
structures are still dominant despite the cementite decomposition [13,21,26–30]. For the present case with extremely
high drawing strain of 6.0 a significant decomposition of
cementite has occurred and the original lamellar structure
has been replaced by a carbon-supersaturated ferrite subgrain structure [3]. Furthermore, once the ferrite subgrain
structure becomes dominant it controls the strength of
materials not only during further cold drawing [3] but also
upon annealing. As shown in Section 3, ferrite subgrain
coarsening is evidently a major reason for the strength
reduction upon annealing. Thus, we will focus in the following on understanding the mechanisms of subgrain
coarsening and its influence on the mechanical properties.
The unexpected phenomenon of the observed ductility deterioration with increasing T a is also briefly discussed.
4.1. Dislocation annihilation and rearrangement
Severely cold drawing the pearlitic steel wires yields a
ribbon-shaped ferrite structure containing nanosized
subgrains, whose boundaries along the longer edges of
the ribbons have high misorientation angles, which can
still be recognized after annealing at 250 C for 30 min
Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
115
Fig. 3. TEM images of heat-treated nanocrystalline hypereutectoid steel wires in transverse cross-sections revealing the nanosized ferrite subgrain
structures. Images at high magnification show dislocation arrays forming low-angle grain boundaries (marked by red arrows). (For interpretation of
the references to color in this figure legend, the reader is referred to the web version of this article.)
(Fig. 4(a)). In connection with the formation of a strong
½0 1 1 wire texture [3,34,51,52], the subgrain boundaries
connecting the neighboring longer edges of the ribbons
should be mainly of tilt type with low misorientation angles
[53]. The STEM investigation indicates that 40% of subgrain boundaries are LAGBs after annealing at 250 C
for 30 min. If the magnitude of the misorientation angles
between all boundaries are disregarded, the subgrains exhibit equiaxed morphology in the cross-section of the wire [3].
The HAGBs in severely deformed materials, due to their
strong interactions with dislocations and the high internal
stresses, are generally believed to be in a non-equilibrium
state, yielding very high lattice distortions in their vicinity.
When the grain size is reduced down to several tens of
nanometers, the distortion zone can extend into the grain
interiors [54]. This strong distortion makes an identification
of the grain boundaries by TEM methods difficult.
After annealing at 150 C for 30 min no reduction in
strength is observed (Fig. 1(b)). After annealing at 250 C
for 30 min, the material strength is somewhat reduced,
but still remains at a level around 5.5 GPa, indicating that
no significant microstructural changes occurred. It is also
noticed that the carbon concentration in ferrite after
annealing at this temperature is distinctly higher than the
values measured at higher temperatures (Fig. 7 top). This
result is consistent with the observation of a small size
and low volume fraction of cementite as shown in
Figs. 4(a) and 6(a), meaning that a considerable formation,
i.e. reprecipitation, of cementite at the expense of solute
carbon atoms in the ferrite did not happen. The main
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Fig. 4. Phase maps obtained via scanning nanobeam TEM diffraction (ASTAR) for heat-treated nanocrystalline hypereutectoid steel wires in the
transverse cross-section. Green and black lines are for subgrain boundaries with misorientation angles of 3–15 and 15–62:8 , respectively. (For
interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. TEM images showing crystalline cementite after annealing at (a) 250 C for 30 min and (b) 350 C for 2 min. Fast Fourier transform (FFT)
analyzes reveal the presence of stacking faults inside of the cementite.
microstructural change upon annealing at a temperature
below 250 C for 30 min is thus attributed to partial annihilation of dislocations in the cell walls and near subgrain
boundaries, where dislocations of opposite sign can recombine and disappear. The remaining dislocations of the same
sign rearrange into low-energy configurations by forming
new subgrain boundaries or by being integrated into existing LAGBs. This process results in a partial relaxation of
the non-equilibrium structure of the existing HAGBs and
a reduction of internal elastic stresses so that the visibility
of the subgrain boundaries inside the curled lamellae is
improved (Fig. 2(b)). On the other hand, the relaxation
of non-equilibrium grain boundaries may induce a
strengthening effect by limiting dislocation emission (see
Section 4.3 for a further discussion), which compensates
the softening effect due to dislocation annihilation so that
the materials’ strength does not significantly decrease.
The slight increase in subgrain size is considered mainly
due to the rearrangement of dislocations.
Above annealing temperatures of 350 C subgrain coarsening becomes the major microstructural phenomenon. In
the next section, the mechanism of subgrain coarsening will
be further discussed.
4.2. Boundary migration induced subgrain coarsening
Subgrain coarsening may occur through coalescence of
the neighboring subgrains [55] or migration of boundaries
Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
117
Fig. 6. 3-D carbon atom maps of heat-treated nanocrystalline hypereutectoid steel wires in transverse cross-section views. The isoconcentration
surfaces for 7 at.% C are shown in green. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of
this article.)
[56–59]. The latter process is commonly assumed to be the
major underlying mechanism of subgrain coarsening. Before
discussing mechanisms of subgrain coarsening in the current
microstructure, we recall the main features observed in association with the depletion of Mn near some of the subgrain
boundaries (Fig. 8). First, the depletion area is asymmetrical
around the subgrain boundaries; second, the degree of depletion is thermally activated, since it is stronger the higher the
annealing temperature and the longer the annealing time.
Annealing at 400 C for 30 min yields Mn depletion zones
of 10 ÿ 20 nm in width around the subgrain boundaries.
This phenomenon can hardly be explained by segregation
of Mn at subgrain boundaries through bulk diffusion. The
Mn diffusion
pffiffiffiffiffiffiffiffidistance in the ferrite matrix can be estimated
as x ¼ 6 D t. Taking the bulk diffusivity DMn
¼ 2:4
a
10ÿ23 m2 sÿ1 [60] at 400 C and an annealing time of 30 min
results in a diffusion distance of about 0.5 nm, which is far
below the observed value of 10 ÿ 20 nm. In addition, even
if the long diffusion distance could be achieved by bulk diffusion, symmetrical Mn-depleted zones would have formed on
both sides of the subgrain boundaries. Therefore, we propose
that the observed asymmetric Mn-depleted zones are the
result of migration of subgrain boundaries, which sweep
and accumulate Mn atoms into the boundaries during migration. Due to the low diffusivity in ferrite the Mn atoms behind
the swept zones cannot readily redistribute into the depleted
zones to recover a local chemical equilibrium, i.e. the zones
behind the moving subgrain boundaries remain depleted in
Mn. This mechanism suggests a grain boundary migration
related non-equilibrium segregation process that leads to
an enrichment of Mn atoms at moving ferrite subgrain
boundaries.
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Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
Fig. 7. Proximity histograms of C (top) and Mn (bottom) obtained from multiple interfaces (enclosed region > 6 nm) shown in Fig. 6 for as-annealed
wires at various annealing temperatures and times. (Inset) An enlarged image showing the C concentrations in the ferrite. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of this article.)
However, in the present case, strong segregation of Mn
at subgrain boundaries was not observed. Instead, accompanying the depletion of Mn near the subgrain boundaries,
the partitioning of Mn into the cementite becomes more
pronounced and the Mn concentration in the ferrite
decreases (Fig. 7 bottom). The apparent correlation
between these observations would suggest that the Mn
atoms are first accumulated at subgrain boundaries by
boundary migration, and then diffuse along the subgrain
boundaries into the cementite. It is known that Mn is a carbide-forming element and that its solubility in cementite is
much higher than that in ferrite at 400 C according to
ThermalCalc calculations [2,40]. Clearly, the difference in
solubility yields a thermodynamic driving force that promotes diffusion of Mn from ferrite into cementite. The only
question is how the partitioning process kinetically works.
Fig. 7 bottom shows that in the center of the cementite particles the Mn concentration approximately equals the value
measured inside the ferrite. This is due to the fact that the
Mn atoms originally remaining in the ferrite were automatically incorporated into the cementite particles upon
growth when the cementite was formed in paraequilibrium.
In the regions near the ferrite–cementite interface a much
higher concentration of Mn was built up inside the cementite. After annealing at 400 C for 30 min the Mn concentration in the cementite adjacent to the ferrite–cementite
interfaces is about 7 times that in ferrite (Fig. 7 bottom).
Recalling that the bulk diffusion distance at this annealing
condition is only about 0.5 nm, the sluggish bulk diffusion
cannot be the reason for the substantial partitioning of Mn
into cementite. Instead, it can only be attributed to fast
diffusion of Mn through subgrain boundaries and triple
junctions. In summary, the most likely mechanism for the
depletion of Mn near the subgrain boundaries and the partitioning of Mn into cementite is suggested to proceed in
terms of two processes: first, Mn atoms are captured at subgrain boundaries by boundary migration; second, the captured Mn atoms diffuse along the subgrain boundaries or
triple junctions into cementite. A similar sweeping mechanism has been proposed by Uray and Menyhárd to explain
the segregation of iron at grain boundaries and secondphase particles in tungsten [61]. However, their analysis
was performed on the basis of an indirect measurement
of electrical resistivity. The current work gives direct evidence of the existence of this mechanism at the atomic
scale.
The above discussion has demonstrated that Mn depletion near subgrain boundaries together with partitioning
of Mn into cementite can serve as an indicator for boundary migration. Fig. 10 schematically shows two typical
examples taken from Fig. 8(c). Fig. 10(a) shows three grains
sharing a triple junction line (perpendicular to the page in
3-D). As a convention the grain boundaries between neighboring grains Gi and Gj are defined as Gi–Gj. The Mndepleted zone exists in grain 1 and near the boundaries
G1–G2 and G1–G3, but not near the GB G2–G3. This
observation suggests that boundary G2–G3 did not move
during annealing, and boundaries G1–G2 and G1–G3
together with their respective triple junctions moved along
G2–G3. Consequently, the boundary G2–G3 becomes
shorter while grain G1 coarsens and grains G2 and G3
shrink. Similarly, the movement of the two triple junctions
Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
119
Fig. 9. Tensile strength vs. the reciprocal square root of the ferrite
subgrain size d Sub for heat-treated nanocrystalline hypereutectoid steel
wires produced by cold drawing at d ¼ 6 (red circles). Data for asdrawn wires [3] are shown for comparison. (For interpretation of the
references to color in this figure legend, the reader is referred to the
web version of this article.)
Fig. 8. Distributions of C (red), Fe (blue), and Mn (green) atoms in the
nanosized ferrite subgrain structures with carbon segregation and
spheroidized cementite at subgrain boundaries. Black arrows mark the
possible original locations of subgrain boundaries which migrate
during annealing. (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of this article.)
towards each other, shown in Fig. 10(b), leads to the coarsening of the grains G1 and G4, and the shrinkage of G2
and G3. Thus the Mn decoration and depletion patterns
indicate the movement of the grain boundaries in the current microstructure.
The segregation of Mn in cementite as shown in Fig. 7
bottom, together with the atom map shown in Fig. 8, indicate that only slight boundary migration occurs upon
annealing at 350 C for 2 min. Above this condition the
boundary migration becomes stronger with higher temperature. However, even at the highest investigated temperature of 450 C the annealed subgrain size remains below
100 nm. This is believed to be mainly due to the effect of
solute segregation at subgrain boundaries, which significantly reduces the grain boundary energy and thus the
Fig. 10. (a and b) Subgrain structures schematically superimposed on
selected areas taken from the left part and middle part of Fig. 8,
respectively. White areas mark Mn-depleted regions and yellow full
circles represent triple junctions among grains labeled with G1–G4.
Arrows indicate the migration direction of the triple junctions. (For
interpretation of the references to color in this figure legend, the reader
is referred to the web version of this article.)
driving force for coarsening [62,63]. An additional limiting
factor of grain coarsening in the current nanostructured
material may be due to a drag effect associated with the triple junction lines. Traditionally, triple junctions are considered to have very high, even practically infinite, mobility
so that they have little influence on boundary migration.
120
Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
Fig. 11. Schematic diagrams showing the influence of (a) the annealing-induced changes in subgrain boundary character and (b) the
starting point on the Hall–Petch slope. T a is the annealing temperature. f HAGBs is the volume fraction of HABGs. Scd and Sa represent the
starting points for cold drawing and annealing, respectively. A and A0
represent the data for cold-drawn and as-annealed materials, respectively, which have the same subgrain size.
Galina et al. [64] first proposed that triple junctions might
have finite mobility. Recently, molecular dynamics simulations performed by Upmanyu et al. [65] suggested that the
mobility of triple junctions in nanocrystalline materials can
be sufficiently small to determine the rate of grain boundary
migration. Gottstein et al. [66] theoretically studied the role
of triple junctions on grain growth in nanocrystalline materials. They demonstrated on nanocrystalline Pd that triple
junction drag could significantly slow down the growth of
Pd grains. In the present case, a drag effect of triple junctions on grain growth may also exist due to the nanoscaled
subgrain size. A third stabilizing effect on subgrain coarsening in the present case might be due to the formation of
cementite particles at subgrain boundaries and at triple
junctions, which renders further movement of boundaries
difficult.
4.3. Modified Hall–Petch relationship applied to the annealed
carbon-supersaturated nanocrystalline hypereutectoid steel
In our recent work [3] we reported that during cold
drawing of pearlite the ferrite–cementite lamellar structure
still prevails up to a strain range d 4:19. Above this
drawing strain the ferrite subgrain structure becomes dominant and dynamic recovery is strongly suppressed due to
segregation of carbon at nanosized ferrite subgrain boundaries. As a result, the subgrain size continuously decreases
upon further straining and the corresponding tensile
strength increases following a Hall–Petch relation (see
Fig. 9 and also Ref. [3]). After annealing it is interesting
to observe that the annealed material with its reduced
strength and coarser subgrain structure also follows a
Hall–Petch law (Fig. 9), indicating that subgrain coarsening
is the main reason for the strength reduction.
When comparing the strength–size relationships
recorded for annealed and cold-drawn materials, it is
noticed that the Hall–Petch slope k HP for the annealed
material is smaller than that of the deformed material
and the annealed material is stronger than the deformed
one for the same subgrain size. The explanation for this
phenomenon lies in the fact that the annealed microstructure is not only substantially different from the lamellar
structure that was still prevailing at low drawing strains,
consisting of parallel and alternating ferrite and cementite
layers, but also significantly deviating from the subgrain
structure formed at high drawing strains. During annealing
the cold-drawing induced ferrite subgrains further coarsen
and spheroidal cementite particles form. Clearly, the heattreatment process applied in the current study cannot bring
the heavily deformed microstructure back to the initial
structure through a reverse evolution by replacing the subgrain structure with a fine lamellar structure. Thus the variation of the tensile strength of specimens with annealed
and hence coarsened subgrain structure is not necessarily
expected to follow the same strength–size relationship as
the wires with a lamellar structure. One of the reasons that
renders the annealed samples mechanically stronger than
the cold-drawn wires can be attributed to the increase in
the subgrain boundary misorientation upon annealing, as
shown in Fig. 4. Thus, in comparison to the deformed wires
with the same subgrain size, the annealed structure contains
a higher density of HAGBs, which are more efficient obstacles than LAGBs at hindering the penetration of dislocations through the grain boundaries.
Another probably even more important reason may be
due to the relaxation of non-equilibrium grain boundaries
upon annealing. It is known that the strength of nanocrystalline materials is mainly controlled by grain boundaries,
whose strengthening effect is twofold. On one hand, they
act as effective obstacles against dislocation motion, leading
to a direct strengthening. On the other hand, they provide
additional dislocation sources because those sources, which
are usually operative in the grain interior of coarse-grained
materials, do not exist inside nanosized grains. During
annealing the relaxation of non-equilibrium grain boundaries may render dislocation sources less active or even
remove them from the grain boundaries. Consequently,
the applied external load has to be increased to enable
the emission of dislocations from grain boundaries. Thus,
for the same subgrain size, this additional strengthening
effect makes the annealed subgrain structure stronger than
the deformed subgrain structure where grain boundaries
remain at a higher energy level and the emission of dislocations is easier. The effect of relaxation of non-equilibrium
grain boundaries on the strength of materials upon annealing has been studied by molecular dynamics simulations
[67]. The authors reported that the relaxed grain boundaries are less prone to emit dislocations which enhances
the materials’ strength. Similar results on an annealingenhanced strengthening effect were reported by Valiev
et al. [68] in nanostructured Ti produced by high-pressure
torsion, by Wang et at. [69] in electrodeposited nanocrystalline Ni and by Huang et al. [70] in nanosized Al produced
by accumulative roll bonding.
Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
Fig. 11(a) schematically summarizes the above-discussed
strengthening effects due to the change in the grain boundary
character upon annealing. Curve r shows a “gedanken”
Hall–Petch relation of annealed materials that experience
only subgrain coarsening without any change in grain
boundary character. The superposition of the enhanced
obstacle effect of the grain boundaries on dislocation motion
by increasing the volume fraction of HAGBs f HAGBs (curve
s) and the enhanced difficulty of dislocation emission from
boundaries due to annealing induced-boundary relaxation
(curve t) not only improve the final strength of the annealed
material, but also reduce the Hall–Petch slope. At first sight
this explanation seems to be contradictory to the common
understanding that a higher strength of grain boundaries
usually yields a higher Hall–Petch slope. In fact, there is no
such interpretation conflict, though it should be noted that
the starting points of the two Hall–Petch curves are different,
as depicted below in Fig. 11(b). The starting point (Scd in
Fig. 11(b)) of the curve for the cold-drawn material (the
black line) corresponds to the original lamellar structure
prior to cold drawing. For the annealed material the curve
starts from the cold-drawn state (Sa , red line in Fig. 11(b)).
If Scd is taken as the starting point for the annealed material,
the line going through Scd and A0 (gray line) exhibits a higher
slope than the dark line, which is consistent with our explanation that the strength of the grain boundaries of asannealed materials is higher than that in the cold-drawn
materials for the same grain size at A. However, considering
that the annealed microstructure (with progressively coarser
grain structure) is completely different from that of the original lamellar structure, a Hall–Petch plot starting from Scd is
not a suitable presentation format for the annealed material,
and thus is not shown in Fig. 9. In addition, with further
increasing annealing temperature, the occurrence of strong
recrystallization would lead to grain structures with completely different boundary properties compared to those of
both the recovered and cold-drawn states. Furthermore,
grain boundaries may become less important and the
strength can be mainly controlled by the dislocation activity
in the grain interiors. In this case, it is reasonable to infer that
the Hall–Petch relation may break down (see the curved red
dashed line) above a certain annealing temperature.
A third strengthening mechanism which appears after
annealing may be due to the formation of spheroidal
cementite particles. Both STEM and APT investigations
indicate that the cementite particles are predominantly
located at triple junctions and subgrain boundaries. A similar result was reported by Takahashi et al. [21] who suggested that the reprecipitated cementite are located along
the prior ferrite–cementite interfaces. The strengthening
effect of these particles may be mainly attributed to their
effect on hindering grain boundary migration rather than
their interaction with dislocations. However, this interaction may have a strong influence on the ductility of the
annealed material, as will be discussed below.
4.4. Non-monotonic change of ductility upon annealing
As shown in Fig. 1(c) the ductility of the annealed materials investigated under the selected annealing conditions
exhibits a non-monotonic dependence on temperature.
The ductility reaches a maximum after annealing at
350 C. Below 350 C it increases with the annealing temperature, which is similar to the usual annealing effect
121
observed on deformed coarse-grained materials, i.e. the
material becomes softer and more ductile. The same reasons also apply for the present case at T a < 350 C. As discussed above, the major microstructural changes occurring
under these annealing conditions are the reduction in dislocation density, slight subgrain coarsening and concomitant
relief of internal stresses. These combined effects partially
recover the work-hardening potential of the wires.
Above 350 C the ductility deteriorates with increasing
temperature. This result is somewhat surprising, because
the main microstructural changes occurring in this temperature range, namely subgrain coarsening and spheroidization of cementite, would tend to enhance the ductility.
Spheroidization processing of conventional materials (in
contrast to nanosized materials) usually results in a homogeneous dispersion of cementite particles throughout the
ferrite grains. This structure contains less total interface
area per unit volume in spheroidized compared to lamellar
pearlite and provides the material with a continuous ferrite
matrix. Thus, plastic deformation of ferrite is less constrained by cementite and the material behaves more ductile. However, for the present carbon-supersaturated
nanocrystalline steel the spheroidization of cementite, in
particular at the high annealing temperatures, does not necessarily reduce the specific surface area of the cementite. In
contrast, the reprecipitation and growth of new cementite
particles leads to an increase in the area fraction of interfaces between ferrite and cementite. Furthermore, the
increase of the subgrain size leads to a reduction of the volume fraction of the subgrain boundary area. This means
that the ratio of the surface area of cementite to the area
of subgrain boundary increases with increasing subgrain
size. Hence, the structure consisting of larger subgrains
contains a high fraction of the more brittle cementite particles at boundaries than that consisting of smaller grains.
The influence of grain size on microcracking of grain
boundary carbide was explained by Smith [71] in terms of
a dislocation–carbide interaction model. The approach suggests that larger grains are more susceptible to microcracking of grain boundary carbides than smaller grains because
more dislocations pile up inside the coarser grains, generating a higher stress concentration against the brittle grain
boundary carbide.
5. Conclusions
After annealing at temperatures between 250 and 450 C
for 30 min, the carbon-supersaturated nanocrystalline
hypereutectoid steel produced from severely cold-drawn
pearlite exhibits significant temperature-dependent changes
in microstructure, tensile strength and ductility. Based on
TEM and APT investigations conducted on various
annealed samples the mechanisms responsible for the
microstructural evolution and its effect on the mechanical
properties are discussed.
No strength reduction is observed for T a < 150 C.
Strength softening due to dislocation annihilation and rearrangement may be compensated by relaxation of nonequilibrium grain boundaries which limits dislocation
emission upon loading.
At annealing temperatures of T a > 250 C the tensile
strength decreases and the subgrain size increases with T a .
The variation in tensile strength with subgrain size follows
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Y.J. Li et al. / Acta Materialia 84 (2015) 110–123
a Hall–Petch relationship. Interestingly, the annealed wires
are stronger than the cold-drawn samples for the same subgrain size. This result is correlated with the increasing area
fraction of HAGBs and the relaxation of non-equilibrium
grain boundaries, which makes penetration of dislocations
through and emission of dislocations from grain boundaries more difficult, respectively.
The migration of triple junctions and subgrain boundaries is confirmed by APT mappings of the Mn distribution. It is evident that subgrain coarsening occurs through
the migration of subgrain boundaries. Segregation of C
atoms at the ferrite subgrain boundaries gives the nanoscaled subgrain structure excellent thermal stability.
The ductility increases first with increasing temperature
up to 350 C, then decreases with further increasing temperature. The deterioration of ductility is suggested to be associated with the formation and growth of cementite particles
at ferrite subgrain boundaries.
Acknowledgments
The authors thank Dr. H. Yarita, Suzuki Metal Industry Co.
Ltd., for providing the cold-drawn specimens. We are grateful to
the Deutsche Forschungsgemeinschaft for co-sponsoring some of
this research (SFB 602 and KI230/34–1).
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