in
st
iao
gin
ch D
et,
School of Materials Science and Engineering, Chongqing University, Chongqing 400030, People’s Republic of China
� 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
divided by fine and closely spaced cementite and ferrite
lamellae extending almost parallel to the drawing direction.
The thickness of these lamellae can be as fine as 10–20 and
1–2 nm for the ferrite and cementite lamellae, respectively.
Studies of deformation mechanisms and microstructure in
drawn pearlitic wires date back to the 1960s and 1970s,
⇑ Corresponding author at: Danish–Chinese Center for Nanometals,
Materials Research Division, Risø National Laboratory for Sustainable
Energy, Danmarks Tekniske Universitet, DK-4000 Roskilde, Denmark.
Tel.: +45 46775859.
E-mail address: xzha@risoe.dtu.dk (X. Zhang).
Available online at www.sciencedirect.com
Acta Materialia 59 (2011) 3422–34
Keywords: Microstructure; Strengthening mechanisms; Pearlitic steel wire
1. Introduction
Cold-drawn high-carbon steel wires of approximately
eutectoid composition have the highest strength of all steel
products, up to 5–6 GPa. They have wide industrial appli-
cations, including cables for suspension bridges, steel cords
for automobile tyres and springs. The high strength is also
of interest in new applications, for example where steel
wires may be used as reinforcement in windmill wings for
cleaner energy production. Technological interest has led
to numerous scientific studies over the years of the struc-
tures and properties [1–3]. However, with the advancement
of microscopical techniques, also encompassing the devel-
opment of atom probe field ion microscopy [4,5], new
opportunities have been created which have led to the pres-
ent study, which focuses on the strengthening mechanisms
which cause the exceptional high strength. These mecha-
nisms occur in a structure with nanoscale dimensions sub-
Received 11 January 2011; received in revised form 8 February 2011; accepted 10 February 2011
Available online 17 March 2011
Abstract
Strengthening mechanisms and strength–structure relationships have been analyzed in a cold-drawn pearlitic steel with a structural
scale in the nanometer range and a flow stress of about 3.5 GPa. The wires have been drawn up to a strain of 3.7 and the structures
analyzed and quantified by transmission electron microscopy and high resolution electron microscopy. The mechanical properties have
been determined by tensile testing. It is found that the interlamellar spacing and the thickness of the cementite lamellae are reduced in
accordance with the changes in wire diameter up to a strain of 2.5. At a higher strain enhanced thinning of the cementite lamellae points
to decomposition of the cementite and carbon enrichment of the ferrite lamellae. Dislocations are stored in the interior of the ferrite
lamellae and their density increases to about 2 � 1016 m�2. A high dislocation density is also observed at the ferrite/cementite interface.
Three strengthening mechanisms have been analyzed: (i) boundary strengthening, (ii) dislocation strengthening and (iii) solid solution
hardening. The individual and combined contributions, based on an assumption of linear additivity, of these mechanisms to the wire
strength have been estimated. Good agreement has been found between the estimated and the measured flow stresses, which is followed
up by a discussion of structure and strengthening mechanisms with a view to extrapolation to larger strains, finer structures and larger
stresses.
Microstructure and strengthen
pearlitic
Xiaodan Zhang a,b,⇑, Andy Godfrey a, X
aAdvanced Materials Laboratory, Department of Materials Science and En
bDanish–Chinese Center for Nanometals, Materials Resear
Danmarks Tekniske Universit
c
1359-6454/$36.00 � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All
doi:10.1016/j.actamat.2011.02.017
g mechanisms in cold-drawn
eel wire
xu Huang b, Niels Hansen b, Qing Liu c
eering, Tsinghua University, Tsinghua 100084, People’s Republic of China
ivision, Risø National Laboratory for Sustainable Energy,
DK-4000 Roskilde, Denmark
www.elsevier.com/locate/actamat
30
rights reserved.
and seminal papers have been published by Embury and
Fisher [1] and Langford [2]. These authors primarily
related the high strength to the close spacing between the
cementite lamellae (or fragments) on the assumption that
the cementite acts as a barrier to dislocation glide, as do
grain boundaries in polycrystalline iron. They therefore
introduced the Hall–Petch relationship and related the flow
stress of the wires to the reciprocal square root of the
spacing between the cementite lamellae (the interlamellar
spacing or ILS). It was found by transmission electron
microscopy (TEM) examination that this spacing decreases
in accordance with the reduction in wire diameter and a
relationship between the flow stress (r) and the strain (e)
also including Kikuchi diffraction analysis and spot
indexing by collecting nanobeam diffraction patterns by
field emission gun (FEG-)TEM. The wires have been
drawn up to a strain of 3.7 giving a flow stress around
3.7 GPa. It is found that all three mechanisms contribute
significantly to the wire strength and that their sum agrees
well with the measured flow stress. This agreement leads to
a more general discussion of strengthening mechanisms in
nanoscale structures.
2. Experimental
Five samples at five cold-drawing strains covering the
X. Zhang et al. / Acta Materialia 59 (2011) 3422–3430 3423
was formulated [1]:
r ¼ r0 þ k1 expðe=4Þ ð1Þ
where r0 is the friction stress of the ferrite and k1 is a con-
stant which can be derived from the Hall–Petch slope. This
equation is a good approximation of the evolution in flow
stress with increasing drawing strain, as has been shown in
many studies [1,6–8]. An illustration is given in Fig. 1.
However, this figure also shows significant deviation from
a linear relationship, especially at large strains, which
points to other strengthening mechanisms in addition to
the barrier resistance of cementite. Such mechanisms could
be legion, as the wire structure is complex, but this paper
will focus on dislocation strengthening and solid solution
hardening. Our approach follows that of previous studies
where strengthening of drawn pearlitic wires has been con-
sidered as the additive effect of more than one microstruc-
tural mechanism [1,6–11]. The reason is that it has been
observed that a dislocation structure with a high density
of dislocations evolves in the ferrite lamellae [12] and that
these lamellae can be enriched by carbon in solution, espe-
cially at high strains at which the cementite lamellae start
to decompose [7,13–18]. It follows that the following three
strengthening mechanisms will be analyzed: (i) barrier or
boundary strengthening; (ii) dislocation strengthening;
(iii) solid solution hardening.
The analysis will be based on characterization of
structural morphology and structural parameters by
TEM and high resolution electron microscopy (HREM)
Fig. 1. Summary of mechanical data relating the flow stress to the
drawing strain.
different strain hardening stages in Fig. 1 of high strength,
near-eutectoid composition steel with a carbon content
of 0.8 wt.% (supplied by NV Bekaert SA (Zwevegem,
Belgium) Technology Center Laboratory) were investigated.
These samples represent intermediate steps of the manufac-
turing process from the as-patented wire (1.26 mm) to the
final drawn filament (0.2 mm). The sample details are listed
in Table 1.
The structural analysis based on the ferrite and cement-
ite phases will focus on the evolution of structural param-
eters during wire drawing. They are the ILS, the thickness
of cementite and dislocation configurations and density
in the ferrite lamellae. Standard grinding and electro-
polishing (10% perchloric acid in ethanol) procedures were
used to prepare specimens for investigationa by scanning
electron microscopy (SEM) and TEM. The wires were
examined in the longitudinal section. For the SEM obser-
vations specimens were additionally etched in 4% Nital.
The ILS and cementite thickness were measured by
TEM, taking care to ensure edge-on conditions to deter-
mine the cementite thickness. Additionally, the ILS of
wires deformed to low strains (e < 1.51) was measured by
SEM using the method of Gensamer et al. [19]. For each
sample data were collected from 30 measurements on ran-
domly chosen areas. Dislocation configurations and densi-
ties were examined using a JEOL 2000FX TEM at 200 kV
and a JEOL 3000 FEG–TEM at 300 kV.
The stress–strain curves have been determined directly
on as-received drawn wires using standard tensile tests
Fig. 2. True stress–true strain curves for the wires.
Table 1
Summary of wire samples used in this study.
Sample
1 2 3 4 5
Diameter (mm) 1.26 0.899 0.591 0.332 0.2
Strain 0.00 0.68 1.51 2.67 3.68
3424 X. Zhang et al. / Acta Materia
for wires. The strain rate was 2.5 � 10�3 s�1 and the 0.2%
proof stress is taken as the flow stress. The ultimate tensile
stress (UTS) and total elongation have also been deter-
mined (see Table 2). The stress–strain curves for the drawn
wires are shown in Fig. 2, together with the curve for the
initial pearlitic sample. None of the specimens show a yield
point and parabolic hardening has been observed up to the
UTS.
3. Results
3.1. Morphology and structural parameters
The evolution of the cementite morphology as a func-
tion of the drawing strain has been reported in a previous
paper [20]. In agreement with previous findings [21], it was
found that the cementite plates align with increasing strain
to the extent that about 97% are realigned parallel to the
drawing direction when the drawing strain reached 1.5 with
an angular spread of 30�. The reduction in thickness of the
ferrite lamellae (F) and thickness of the cementite lamellae
(T) have been measured and related to the drawing strain,
shown in Fig. 3 and Table 3. On the assumption that T is
reduced in accordance with the wire diameter, T can be
related to the true strain, which is expressed as:
e ¼ lnðA0=AÞor lnðD0=DÞ2 ð2Þ
where A0 and D0 relate to the cross-sectional area and the
diameter of the initial wire and A and D refer to those of
a drawn wire. T can then be expressed by the relationship
[1]:
T ¼ T 0 expð�e=2Þ ð3Þ
where T0 is the original thickness of about 19 nm. The cal-
culated value for T is plotted in Fig. 3, illustrating good
correspondence between the measured and calculated val-
ues of T. In addition to measuring T, the ILS has been
determined as a function of strain (see Fig. 3b). It can be
Area reduction (%) 0 49 78 93 98
seen that there is good agreement between the measured
and the calculated ILS, in support of the assumption leading
Table 2
UTS and elongation of wire samples used in this study.
Strain
0.00 1.51 2.67 3.68
UTS (MPa) 1386 1904 2674 3640
Total elongation (%) 9.0 2.7 1.9 2.1
to Eq. (1), namely that this spacing decreases in accordance
with the reduction in wire diameter. In the low strain part
of the curve (up to approximately e = 1.5) it is recognized
that there are a number of complications with such an
analysis. These include the fact that the wire center is likely
to deform by plane strain rather than an axisymmetric
deformation mode (as indicated by the characteristic curling
seen in the transverse sections of drawn wires [22]) and also
the fact that significant reorientation of the pearlitic struc-
ture takes place as the microstructure evolves towards one
where the ferrite and cementite lamellae are parallel to the
drawing axis [23,24]. It is believed that these factors are
reflected in the larger scatter seen in thickness measure-
ments at the lowest investigated strain (e = 0.68). Overall,
however, cementite evolution (and ILS) follows the predic-
tion from the assumption of simple axisymmetric deforma-
tion. However, for a strain above 3 the calculated thickness
of cementite is 2.9 nm, whereas the measured thickness is
about 2.1 nm. This difference points to a decomposition
of about 30 wt.% cementite with about 1.1 at.% carbon
enriching the ferrite based on the original concentration
of 3.63 at.% (0.8 wt.%) carbon.
3.2. Dislocation configuration and density
The mechanical properties of deformed metals are dom-
inated by dislocation storage, and the dislocation density in
the ferrite lamella is an important factor in understanding
the strain hardening and its contribution to the flow stress
of drawn pearlitic steel wires. Since little systematic data is
available this study has focused on the storage of disloca-
tions and their configurations in the ferrite lamellae as
observed by TEM. However, at very large strains where
the fineness of the ferrite lamellae makes it difficult to
quantify the dislocation density the density at a strain of
3.68 has been determined in the JEOL 3000 microscope
in high resolution mode.
Fig. 4 shows the dislocations in the ferrite lamellae
in the initial structure, with a dislocation density of
7.5 � 1013 m�2. The random dislocation lines can be
observed as a result of the phase transformation. Disloca-
tion configurations in the ferrite lamellae parallel to the
drawing direction at a strain of 0.68 are shown in
Fig. 5. Most of the dislocations are spread in the ferrite
lamellae, with the two ends of the line located at the
steps in the ferrite/cementite boundaries. Calculation of
the dislocation density gives a value of 7 � 1014 m�2,
which is in accordance with the results of crystallographic
orientation measurements [12]. Fig. 6 shows a TEM
micrograph and a sketch of the dislocation configuration
in the ferrite lamellae at a strain of 2.67. Note that the
dislocations in the ferrite lamellae are distributed very
regularly with a spacing of 10–20 nm. Calculation of
the dislocation density gives a value of 8.8 � 1015 m�2.
The TEM and HREM investigations of the wire at a
lia 59 (2011) 3422–3430
strain of 3.68 show that the dislocation density is
2 � 1016 m�2.
teria
X. Zhang et al. / Acta Ma
3.3. Structural heterogeneities
The observation of morphological changes and the
detailed analysis show that the structural evolution is not
homogeneous during wire drawing, At small and medium
strains the cementite reorients, a process which involves
shear banding and grain curling [2,21,22,25,26]. Such heter-
ogeneities change the structural morphology but may also
affect the density and arrangement of dislocations in the
ferrite lamellae. However, the characterization of such het-
erogeneities is for further research, as it will require a fairly
detailed characterization of microstructural parameters at
Fig. 3. (a) Thickness of the cementite lamellae and (b) ILS vs. drawing strain
cementite lamellae of the same area at a strain of 0.6. The thickness of the c
reduction in thickness of the cementite lamellae and ILS, assuming that they d
also given in (a) and (b). The error bars represent the standard deviation for
Table 3
ILS and thickness of ferrite (F) and cementite (T).
Strain
0.00 0.68 1.51 2.67 3.68
ILS (nm) 89 70 55 28 20
F (nm) 70 56 45 23 18
T (nm) 19 14 10 5 2
lia 59 (2011) 3422–3430 3425
different positions in the wire. The following analysis will
therefore be based on the assumption of a fibrous structure
where the ferrite and cementite lamellae are parallel to the
and TEM micrographs showing the (c) edge-on and (d) inclined state of
ementite lamellae was measured in the edge-on condition. The calculated
eform in accordance with the macroscopic changes in wire dimensions, is
the data at each strain. The data presented in the box is magnified.
Fig. 4. TEM micrograph of an undeformed sample showing the disloca-
tions in the ferrite lamellae with black arrows. The dislocation density is
7.5 � 1013 m�2.
eria
3426 X. Zhang et al. / Acta Mat
drawing direction and values for the interlamellar spacing
and the dislocation density will be the average values for
all structures. This averaging also allows the present data
to be compared with data reported in the literature.
4. Analysis of structure and strength
The relationship between microstructure and strength
will be analyzed on the basis of the structural observations
Fig. 5. (a) TEM micrograph of a sample deformed to a strain of 0.68 and
(b) a sketch of the dislocation structure in the ferrite lamellae. The
dislocation density is 7 � 1014 m�2.
Fig. 6. (a) TEM micrograph of a sample deformed to a strain of 2.67 and
(b) a sketch of the dislocation structure in the ferrite lamellae. The
dislocation density is 8.8 � 1015 m�2.
pointing to three strengthening mechanisms contributing to
the wire strength:
� boundary strengthening related to the distance between
the cementite lamellae (r(b));
� dislocation strengthening related to the dislocation den-
sity in the ferrite lamellae (r(q));
� solid solution hardening related to the carbon concen-
tration in the ferrite lamellae (r(ss)).
It is assumed that these strength contributions are line-
arly additive, thus the flow stress of the wire can be
expressed as:
rðeÞ ¼ r0 þ rðbÞ þ rðqÞ þ rðssÞ ð4Þ
where r(e) is the flow stress at a given drawing strain and r0
is the friction stress of pure ferrite. The contributions from
the three strengthening mechanisms will be analyzed
separately.
4.1. Boundary strengthening
The contribution of cementite lamellae to the strength is
estimated based on the Hall–Petch equation relating the
yield stress (ry) to the distance between barriers which
can act as obstacles to dislocation glide. This relationship
had been shown to be valid in the case of polycrystalline
metals where the barrier distance is equal to the grain size
[27]. In applying this equation to pearlite the barrier spac-
ing is taken to be equal to the mean free path of disloca-
tions, which is estimated to be twice the width of the
ferrite lamellae (d), i.e. [19].
ry ¼ r0 þ kð2dÞ�0:5 ð5Þ
Eq. (5) has in previous studies been shown to give a sat-
isfactory description of the relationship between wire
strength and barrier distance. Early examples are Embury
and Fisher [1], where the barriers are characterized as tan-
gled walls and cementite fragments, and Langford [2],
where the barriers are characterized as cementite lamellae.
In these studies values for the constants r0 = 40–70 MPa,
k = 0.62 [1] and k = 0.58–0.68 [2] were reported from mea-
surements over a wide strain range. In these studies it was
also noted [1,2] that these constants correspond to those
obtained for polycrystalline ferrite, indicating similar bar-
rier strengths for grain boundaries and for cementite
lamellae.
Eq. (5) is also applied in the present analysis. However,
as other strengthening mechanisms than barrier spacing
may be operative and as the contributions of such mecha-
nisms may depend on the drawing strain, Eq. (5) is applied
separately for corresponding values of stress (r0.2%) and
spacing on the assumption of a constant r0, which is taken
to be 60 MPa. Values for k are given in Table 4, showing a
significant increase in k with increasing strain, which to a
lia 59 (2011) 3422–3430
certain degree follows the relationship r � exp (0.25e) in
Fig. 1. This strain dependence of k points to contributions
decomposition of the cementite, which has been found
[16] to increase with increasing strain in the large strain
region. This contribution will be analyzed in the next
section.
4.3. Solid solution hardening
A contribution by solid solution hardening (r(ss)) is esti-
mated based on Eqs. (4) and (7) by taking k(e) = 0.31. The
results are given in Table 6. The value for r(ss) shows that
this contribution to the total flow stress is not important
for strains up to about 2.67. However, for e = 3.67 r(ss)
is significant. This contribution r(ss) = 478 MPa relates
to the observation of decomposition of about one-third
of the cementite, enriching the ferrite with a carbon con-
centration of 1.1 at.%. Based on literature values [32], the
Table 4
Hall
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