Scripta Materialia 52 (2005) 1223–1228
www.actamat-journals.com
Residual stresses in cold drawn pearlitic rods
J.M. Atienza
a
a,*
, J. Ruiz-Hervias a, M.L. Martinez-Perez b, F.J. Mompean b,
M. Garcia-Hernandez b, M. Elices a
Departamento de Ciencia de Materiales, UPM, E.T.S.I. Caminos, Canales y Puertos, c/Profesor Aranguren s/n, E-28040 Madrid, Spain
b
ICMM, CSIC, Campus de Cantoblanco, E-28049 Madrid, Spain
Received 4 January 2005; received in revised form 24 February 2005; accepted 3 March 2005
Available online 28 March 2005
Abstract
Residual stress profiles in the three principal directions in a cold-drawn pearlitic rod were calculated by a three-dimensional finite
element simulation and measured by synchrotron X-ray diffraction. It has been shown that anisotropy of cold-drawn pearlite has to
be considered for accurate simulations of residual stresses of steel wires.
Ó 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Keywords: Residual stresses; Cold drawing; Pearlitic steel; Finite element analysis; Synchrotron radiation
1. Introduction
Cold drawn pearlitic steel wires have a wide range of
structural applications: as reinforcements in prestressed
concrete and in tyres, but also as cables in deeper mine
shafts and off-shore petroleum production [1]. Wire
drawing involves the reduction of the wire section by
successive passes through a set of conical dies. Residual
stresses (tensile at the wire surface [2]) are generated as a
consequence of the inhomogeneous plastic deformation
associated to the process. It has been shown that residual stresses may influence the mechanical behavior of
the wires and their durability by reducing service life
in stress corrosion cracking [3] or fatigue [4]. Also,
Stobbs et al. [5] and Wilson et al. [6] studied the influence of internal stresses on the Bauschinger effect in
cold-drawn patented wires. In the case of prestressed
concrete rods, the authors have demonstrated that residual stresses reduce the elastic limit [7] and increase the
losses in stress relaxation tests [8]. This, in turn, may
make the material unsuitable for pre-stressing stan*
Corresponding author. Tel.: +34 91 3366 683; fax: +34 91 3366 680.
E-mail address: jmatienza@mater.upm.es (J.M. Atienza).
dards. Hence, it is very important to know the distribution of residual stresses generated by cold drawing and
to understand the mechanisms to modify them. This
way any negative effects could be prevented.
Residual stresses in cold drawn pearlitic wires are
both complicated to model [2,9], because of its anisotropy, and difficult to measure by diffraction [10–12],
due to the presence of cementite. To the authorsÕ knowledge there is not any work where the macroresidual
stress profiles across the section of the wire calculated
by numerical methods and measured by experimental
techniques are compared.
Heavily cold-drawn pearlitic steels are a nanocomposite of alternating ferrite (a-Fe) and cementite
(Fe3C) lamellae. The non-destructive measurement of
residual stresses by diffraction techniques in the cementite phase is still a challenging task, as shown in recent
studies [13–15]. In addition to the relatively low volume
fraction of Fe3C, its orthorhombic structure spreads the
scattering intensity into a large number of Bragg
reflections.
Several works [16–18] have shown that, at the end of
the drawing process, the mechanical behaviour of cold
drawn pearlitic wires is clearly anisotropic, due basically
1359-6462/$ - see front matter Ó 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
doi:10.1016/j.scriptamat.2005.03.003
J.M. Atienza et al. / Scripta Materialia 52 (2005) 1223–1228
to the progressive alignment of the cementite lamella in
the drawing direction and the development of a h1 1 0i
fiber texture in the ferrite phase. The effect of anisotropy
can be important for the deformation and the forces involved in the drawing process, and also for the final
residual stress profile [19]. However, until now, simulations of drawing process were based on the assumption
that the material was isotropic and von Mises yield criterion was used in the finite element models [2,9]. For
drawn pearlite, the use of a micromechanical based
approximation to represent anisotropy is difficult, because the mechanical behaviour of cementite and the
interaction between ferrite and cementite to obtain the
yield locus of pearlite are still far from established.
In this work, residual stresses generated by cold
drawing in a pearlitic steel rod have been determined.
A three-dimensional (3D) finite element simulation has
been developed to reproduce the fabrication process
and to calculate the final residual stress profile [20]. As
a first approximation, the Hill yield criterion has been
chosen to represent the anisotropy of drawn pearlite.
In parallel, residual stresses have been experimentally
measured by synchrotron X-ray diffraction in ferrite
and cementite [21]. Stress profiles in the axial, hoop
and radial directions are compared.
2. Material
Straight bars (20 mm diameter and 6 m length) of
pearlitic steel were specially produced for this research
by Saarstahl AG (Völklingen, Germany). The aim of
using such a large diameter, instead of 5–7 mm diameter
as rods used in prestressed concrete, was to have a large
cross section that allows us to measure the residual
stress profile along the diameter by diffraction techniques. The bars were produced by hot rolling and aged
to reduce residual stresses to a minimum. The chemical
composition (in weight percentage) of the steel was:
0.75–0.8% C, 0.15–0.35% Si, 0.6–0.9% Mn, <0.025% P,
<0.025% S, 0.2–0.06% Al, resulting in approximately
11% Fe3C in volume. The rods were cold drawn in
one pass (in precisely controlled conditions) to a final
diameter of 18 mm (20% reduction in section). Die
geometry was precisely measured: final diameter d1 =
17.91 mm, bearing length lz = 6.36 mm (35.5% d1) and
the die inlet angle 2a = 15.36°. Residual stresses are very
sensitive to any processing after drawing (especially the
straightening process). To avoid any change in the residual stress pattern generated by drawing, bars were kept
straight during the whole process.
Conventional tensile tests were performed with a
universal testing machine to obtain the mechanical
properties of the wires before and after drawing. The
mechanical properties of the pearlitic wires (an average
of at least three tests) are shown in Fig. 1.
1200
Af
After drawing
1000
Before drawing
STRESS (MPa)
STRE
1224
800
600
400
200
0
0
2
4
6
8
10
12
STRAIN (%))
Fig. 1. Comparison between the stress–strain curves of the pearlitic
steel rod before and after drawing.
3. Numerical work
3.1. Finite element model
3.1.1. Numerical model: simulation of the drawing
process
A numerical model using the code ABAQUS [22] was
developed to study the residual macrostress state generated by drawing. The material was considered homogeneous and an elastoplastic law with strain hardening was
chosen to model the rod behaviour. The constitutive
equation employed as the initial data of the model is
the stress–strain curve of the pearlitic steel before drawing, measured in the laboratory. The drawing process
has been simulated by forcing the rod to pass through
the die and imposing the displacement of the front end
of the rod. The die has been modelled as an elastic material with the elastic modulus of tungsten carbide [20].
The contact between the rod and the die has been reproduced with a Coulomb friction coefficient which ranges
from 0.01 to 0.2 in industrial practice [23,24]. The friction coefficient was changed within this range and no
significant influence was found on the results. Residual
stresses are calculated at the end of the process, when
the whole rod has passed through the die. Starting and
final parts of the rod are not considered for this purpose.
More details are given elsewhere [20].
3.1.2. Anisotropy of cold drawn pearlitic wires
As a first approximation to represent the anisotropy
of drawn pearlite, the well known Hill yield criterion
has been chosen. The Hill criterion [22,25] is a simple
extension of the von Mises criterion and it can be expressed in Cartesian components by this way:
2
2
f ðrÞ ¼ ½Aðr22 r33 Þ þ Bðr33 r11 Þ þ Cðr11 r22 Þ
þ 2Dr223 þ 2F r231 þ 2Gr212 1=2
2
J.M. Atienza et al. / Scripta Materialia 52 (2005) 1223–1228
A ¼ ð1=R222 þ 1=R233 1=R211 Þ=2
D ¼ 3=ð2R223 Þ
B ¼ ð1=R233 þ 1=R211 1=R222 Þ=2
F ¼ 3=ð2R213 Þ
C ¼ ð1=R211 þ 1=R222 1=R233 Þ=2 G ¼ 3=ð2R212 Þ
Where Rij, called the tension ratios, can be defined by:
Rii ¼ rii =r0
Rij ¼ rij =s0
i 6¼ j
where rij are the yield stress in direction ij, r0 is the reference yield stress and s0 = r0/31/2.
By means of torsion tests, Gil Sevillano et al. [18]
showed that for a pearlitic wire before drawing, the relation between the tensile and shear stresses that produce
yielding is close to the value (31/2 = 1.73) predicted by
the von Mises criterion (yield criterion for isotropic
materials). However, Delrue et al. [16] has recently reported that this relation in the case of drawn wires for
tyre reinforcement is around 2.4 instead of 1.73. Also,
Gil Sevillano [17,18] studied the progressive alignment
of cementite lamellae to the drawing direction and
pointed out that the tensile strength increases when the
cementite lamella is oriented by drawing (more than
10% larger than the isotropic case).
In this work, a UserÕs Subroutine in ABAQUS [22]
has been defined to change the R-values in the different
planar directions according to the progressive alignment
of cementite lamellae. For this purpose, the results of
Delrue and Gil Sevillano have been used. The wire before drawing has been considered isotropic and to obtain an idea of the anisotropic level of the final wire,
several hardness tests have been done in different directions. The results have shown that even just after one
drawing pass, the longitudinal direction is more than
10% harder than the transversal one. This result has
been taken into account in the finite element model.
3.2. Previous experimental validation
To validate the numerical model, it was necessary to
check that:
(i) the wire drawing process was correctly reproduced
(drawing simulation);
(ii) the mechanical properties of the drawn rod were
predicted (material simulation);
(iii) the residual stress state was properly calculated
(residual stresses simulation).
compared with the previous ones results found in the literature. The drawing force is probably the most studied
parameter in wire drawing. The most complete experimental research in this field was carried out by Wistreich
in 1955 and is cited in the majority of the subsequent
studies [26,27]. He measured the drawing force for a
given percentage of section reduction changing the
geometry of the die. It was shown that for every percentage of reduction there was a die angle for which the
drawing force was minimum. In the present study, the
conditions in which Wistreich made those tests were
reproduced with the numerical model (same material
properties, same friction coefficient). The influence of
the die angle in the drawing force at 20% and 30% of
section reduction was studied and the results were compared with the previous ones. It can be seen in Fig. 2
that the numerical results agree very well with the experimental measurements.
3.2.2. Material simulation (simulation of the tensile test
for the drawn wire)
To verify that the numerical model was able to predict the mechanical properties of the final wire, a tensile
test was simulated on the cold drawn wire. The results
from the simulation were compared with the experimental test shown in Fig. 1. The constitutive equation
employed as the initial data for the model was the
stress–strain curve of the pearlitic steel before drawing
(Fig. 1). Then the initial wire was drawn numerically
and after that, a tensile test was simulated on the drawn
wire. Boundary conditions were uniform displacements
at the ends of the bar, in order to simulate a tensile test
under displacement control. Fig. 3 shows a comparison
between the numerical results of tensile tests of the
drawn wire and the experimental stress–strain curve.
0.8
RELATIVE DRAWING FORCE
The parameters A, B, C, D, F and G in the Hill criterion
can be expressed as:
1225
Experimental 30% (W
(Wistreich)
Experimental
ri
20% (Wistreich)
Numerical 30%
Numerical 20%
0.7
0.6
0.5
0.4
0.3
0.2
0
2
4
6
8
10
12
14
16
DIE ANGLE (degrees)
3.2.1. Drawing simulation (experimental checking of
drawing force)
To check that the model reproduced the drawing process, the calculated results of the drawing force were
Fig. 2. Relative drawing force (drawing force/yield stress) as a
function of the die angle for two percentage of section reduction.
Comparison between the numerical results and the experiments of
Wistreich.
1226
J.M. Atienza et al. / Scripta Materialia 52 (2005) 1223–1228
tron and X-ray diffraction (Fig. 4). More details are
given in Ref. [20]. An excellent agreement between
numerical computations and experimental results was
obtained. This supports the validity of the numerical
model.
1200
STRESS (MPa)
1000
800
600
4. Experimental work
400
Wire before drawing
Drawn wire (experimental)
Drawn wire (numerical)
200
0
0
0.5
1.0
1.5
2.0
STRAIN (%)
Fig. 3. Comparison between the simulated and the experimental
tensile test for the cold drawn rod. The experimental stress–strain
curve before drawing was used as input to compute the stress–strain
curve of the drawn bar.
The agreement is very good, and this is especially
remarkable at the beginning of yielding. The influence
of residual stresses in this region was clearly shown by
the authors [7].
3.2.3. Residual stress simulation (experimental checking
for a single-phase material)
As a first step to understanding the generation of
residual stresses during cold drawing, a similar study
was performed in a single phase ferritic steel rod [20]
to check that the numerical model was able to predict
the residual stress state. A ferritic rod, 20 mm diameter,
was cold drawn under the same conditions described in
Section 2. The profile of residual stresses was calculated
with the finite element simulation and measured by neu-
Fig. 4. Comparison between axial residual stresses measured by
neutron and X-ray diffraction and numerical simulations in a cold
drawn single phase ferritic rod [20].
Residual stress profiles across the section of colddrawn pearlitic steel rod specimens were determined for
both the ferrite and cementite phases. High-energy synchrotron radiation was employed for this purpose [21].
The experiments were carried out at the ID15A beamline
of the ESRF (Grenoble, France). Strain scanning was
performed along a complete rod radius and a half of
the opposite, with measuring steps of 0.75 mm. Stress
analysis was carried out by single peak fitting to the individual reflections. A pseudo-Voigt function was used for
analysis of the {1 1 0} reflection of the ferritic phase.
Strain scanning in the cementite phase was performed
using the {1 2 2} reflection. Due to the relative poorer statistics in the cementite peaks as compared to the ferrite
ones, the number of fitting parameters had to be reduced,
and a fit to a Gaussian function gives better results. The
strain for every {h k l} set of planes was obtained from
the variation in d-spacing. The stress-free lattice parameter for ferrite was measured from iron fillings and
for cementite it was calculated by assuming the self-equilibrium hypothesis. Details are given in Ref. [21].
5. Residual stresses in cold drawn pearlitic wires:
numerical and experimental results
Macrostress in the pearlitic material was determined
by the stress experimentally measured in every phase
(the results are given in Ref. [21]), weighted with the relative percentage of every phase (rule of mixtures, in this
case 90% ferrite and 10% cementite) [21]. The experimental results and finite element simulations for the
macro residual stresses are compared in Fig. 5. The axial
macro stresses are tensile at the rod surface and compressive at the center. The radial stresses are always
compressive becoming zero at the rod surface, as expected from the boundary conditions. Finally, the hoop
component is tensile at the rod surface and compressive
at the center. The calculated and measured stress profiles
verify the self-equilibrium hypothesis. Both, the experimental and simulated profiles show the same behavior
along the rod diameter, the larger differences being
at the rod center. Anyway the agreement between
experimental and numerical results is remarkable. The
presence of tensile stresses at the surface may be dangerous for the material, reducing the service life in stress
corrosion cracking and fatigue.
J.M. Atienza et al. / Scripta Materialia 52 (2005) 1223–1228
1227
they would be significant for the final wires, where the
anisotropy level would be higher.
6. Summary and conclusions
The residual stress state generated by cold drawing in
a pearlitic steel rod has been determined. To the authorsÕ
knowledge, this is the first time in which numerical and
experimental results are compared over the whole section of the rod for this kind of material. A 3D finite element model, using the code ABAQUS, has been
developed to reproduce the drawing process and to calculate the residual stresses. The anisotropy of drawn
pearlite has been incorporated by using the Hill criterion, as a first approximation to the problem. For the
experimental work, a pearlitic steel rod subjected to
one drawing pass under carefully controlled conditions
has been employed. Synchrotron X-ray diffraction has
been used to measure stress profiles in the axial, hoop
and radial directions of both phases (ferrite and
cementite).
Both the experimental and simulated profiles of residual stresses exhibit the same behaviour along the rod
diameter, showing that the drawing process generates
a residual stress state in the final wire with significant
tensile stresses at the surface in the axial but also in
the hoop directions. The agreement between experimental and numerical results is remarkable. It has been also
shown that even in the first steps of processing, anisotropy has to be considered for accurate simulations of
forming processes.
Acknowledgement
Fig. 5. Comparison between the residual macrostresses calculated
from the finite element simulation and those computed from the
synchrotron measurements. The results of the finite element simulation
without anisotropy are also shown.
The results of the finite element simulation without
anisotropy are also depicted in Fig. 5. It is shown that
taking into account the anisotropy does not change
the shape of the residual stress profiles, with tensile
stress at the surface and compressive stress at the center.
However, the model without anisotropy overestimates
the real values of residual stresses. These differences
are clear even after one drawing pass, so it seems that
The Spanish Ministry of Education is gratefully
acknowledged for supporting this research through the
project FEDER 2FD97-1513. The authors are very
grateful for the help of Mr. Javier del Rı́o, from Bekaert,
in the purchase and drawing of the material. They are
also indebted to Etienne Aernoudt and Paul van Houtte
for stimulating discussions.
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