Residual stresses in as-welded joints: finite element modeling and
neutron diffraction stress measurements
C. Acevedo
1,a
, J.M. Drezet
2,b
, J.-P. Lefebvre
3
, L. D'Alvise
3,c
and A.
Nussbaumer
1
1
ICOM Steel Structures Laboratory, ECOLE POLYTECHNIQUE FEDERALE DE LAUSANNE
(EPFL), Lausanne, Switzerland
2
LSMX Computational Materials Laboratory, ECOLE POLYTECHNIQUE FEDERALE DE
LAUSANNE (EPFL), Lausanne, Switzerland
3
CENAERO Excellence in Simulation Technologies for Aeronautics, Gosselies, Belgium
a
claire.acevedo@a3.epfl.ch,
b
jean-marie.drezet@epfl.ch,
c
laurent.dalvise@cenaero.be
Keywords: Welded joints, Residual strain and stress, Finite element analysis, Neutron diffraction
Abstract. This paper describes the numerical analysis method used to estimate welding induced resid-
ual stresses in K-shape tubular bridge joints. The knowledge of residual stress distribution is required
to design the geometry of K-joints loaded under fatigue stresses. Numerical simulations are focused
on the arc welding MAG process, generally used to weld joints in bridge construction. Thermo-
mechanical analyses are performed in 3D using two finite element codes: ABAQUS
®
and MORFEO
®
.
ABAQUS has the advantage to offer large analysis capabilities (nonlinear, transient, dynamic, etc.)
whereas MORFEO is more dedicated to welding processes and offers the possibility to analyze crack
propagation under fatigue loads. Computed residual stresses in the region surrounding the weld are
compared with measured residual stresses in order to estimate the ability of the codes to reproduce
these stresses. Position, orientation and magnitude of the highest residual stress components are dis-
cussed.
Introduction
Residual stresses created by thermal induced deformations during welding are particularly high in the
surface surrounding the weld. Combined with applied cyclic loadings, they influence the fatigue crack
propagation (onset, rate and shape) [1, 2]. This study evaluates residual stresses in order to control and
optimize the design of K-joints geometry.
Finite element simulations made in this paper are focused on the welding process of S355 steel.
An uncoupled formulation is used; the transient thermal analysis is followed by an elasto-plastic me-
chanical analysis. These simulations provide the 3D residual stress distribution along the weld. The
calculated residual stresses are compared with previously measured residual stresses in order to eval-
uate the accuracy of numerical models.
Presentation of the finite element analysis
A three dimensional thermo-mechanical finite element analysis is performed in order to simulate the
stress generation during welding. In the case of a mild steel such as the S355 steel, it has been shown
by [3] that phase transformations have a small effect on residual stresses generation, therefore phase
transformations are not considered in this analysis.
An uncoupled approach is used to solve, first, the 3D transient temperature field and, then, the
displacement field using the temperature field as input data.
Thermal analysis. The thermal analysis is based on transient non-linear heat conduction formu-
lation (Eq. 1).
Key Engineering Materials Vols. 488-489 (2012) pp 335-338
Online available since 2011/Sep/21 at www.scientific.net
© (2012) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/KEM.488-489.335
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ρ C
eq
∂T
∂t
= ∇
T
D∇T + s (1)
where ρ is the material density [kg/mm
3
], C
eq
is the specific heat C combined with the latent heat L
induced by melting [J/(kg.
◦
C)], T is the temperature [
◦
C], t is the time [s], D is the thermal conductivity
tensor reduced to one coefficient k for isotropic case [W/(mm.
◦
C))] and s is the volumetric heat source
[W/mm
3
].
The temperature-dependent thermal properties k, C and ρ are taken from the EN 1993-1-2:2005(E)
for mild steel. The conductivity value is increased to three times its value at the solidus temperature
[4, 5] to take into account the convection flow in the weld pool and kept constant at T ≥ T
solidus
. The
latent heat L induced by fusion/solidification between solidus and liquidus temperatures (1465-1544
◦
C for S355 steel) is considered using a value of 247000 J/(kg.
◦
C) [6]. Heat losses by radiation and
convection (boundary conditions) are considered on all surfaces.
The 7-passes welding, generating the K-joint weld, is simulated as a single pass with an equivalent
heat source. Each pass is made in four steps (half weld at the right brace toe, half weld at the left brace
toe and the two symmetrical half welds). This heat source is composed of a volumetric flux moving
along the weld path at a speed of 5.5 mm/s. The characteristics of the heat source are determined so
that the computed size of the weld pool matches the one measured on a macrograph. In ABAQUS, the
heat source is a sphere with a radius r = 15mm, in MORFEO, this is a truncated circular cone model
with a radius r
1
= 15 mm for its first base, r
2
= 9.3 mm for its second base and a height h= 15 mm.
To merge the seven weld passes into one equivalent pass, it is recommended by [7] to keep the total
heat input of the seven weld passes, Q = 41500 W. Metal deposition of the MAG arc welding is not
considered, the finite elements representing the weld are present in the model from the beginning.
Figure 1 depicts the 53966 nodes and 48549 elements used to model the K-joint composed of two
braces (diameter 88.9 mm, thickness 8 mm) welded onto a chord member (diameter 168.3 mm, thick-
ness 20 mm). The heat source traveling around the weld is also shown. 8-node brick linear elements
for heat transfer are chosen for the thermal analysis.
Mechanical analysis. The mechanical analysis is based on an elastic-plastic material behaviour
with a linear isotropic work hardening ignoring rate-dependent (creep) effects at high temperatures.
A variation of temperature, obtained as the thermal analysis output, implies thermal strain. In a
thermo-elastic-plastic analysis, the generalised Hooke's law is expressed as follows (Eq. 2):
σ = Cϵ
el
= C(ϵ − ϵ
pl
− ϵ
th
) (2)
where C is the elasticity tensor. The temperature-dependent mechanical properties required to solve
the previous equation are the Young's modulus E [MPa] and the Poisson's ratio ν for the elastic part, the
yield stress f
y
[MPa] and the stress evolution as a function of the accumulated plastic strain f
y
+ Hp
(linear isotropic hardening assumption) for the plastic part and the thermal expansion coefficient α
[/
◦
C] for the thermal part.
The Young's modulus E is defined according to the EN 1993-1-2:2005(E) and the Poisson's ratio
ν, the thermal expansion coefficient α and the yield stress f
y
according to [8].
The mesh is identical to the one used for thermal analysis, but reduced integration is used for the
mechanical part in the ABAQUS model. Concerning boundary conditions, displacements are set to
zero at the chord right extremity, no traction or compression is applied.
Results and discussion
Residual strain measurements were conducted at the Institute Laue-Langevin (ILL) on a K-joint sam-
ple with a chord wall of 20 mm thick. This method enables to measure triaxial residual stresses non-
destructively deep inside the sample. The residual stresses calculated from these measurements are
336 Advances in Fracture and Damage Mechanics X
Fig. 1: On the left, temperature field from ABAQUS model during the movement of the torch. On
the right, cut view of transversal residual stresses from MORFEO showing a restraining effect in the
gap area between the braces (stress values in kPa).
compared in Fig. 2 with residual stresses resulting from numerical models. Stress distributions, along
a vertical line passing through the 20 mm chord wall thickness underneath the weld toe, are given in
the transverse direction (perpendicular to the weld), the longitudinal direction (parallel to the weld)
and the radial direction (in the radial direction of the tube). The same simulation was performed with
ABAQUS
®
[9] and MORFEO
®
[10] from Cenaero research center.
5
10
15
20
z
@mmD
-100
100
200
300
400
Transverse
Stresses
@MPaD
ILL data points
MORFEO model Weld toe Ga
ABAQUS model Weld toe Ga
5
10
15
20
z
@mmD
-100
100
200
300
Longitudinal
Stresses
@MPaD
ILL data points
MORFEO model Weld toe Ga
ABAQUS model Weld toe Ga
5
10
15
20
z
@mmD
-100
-50
50
100
150
200
Radial
Stresses
@MPaD
ILL data points
MORFEO model Weld toe Ga
ABAQUS model Weld toe Ga
Fig. 2: Comparison of transverse, longitudinal and radial residual stress distributions (ABAQUS,
MORFEO and experimental data) at the weld toe though the 20 mm chord wall thickness.
Key Engineering Materials Vols. 488-489 337
In Fig. 2, the results obtained numerically confirmed that transverse residual stresses are greater
than longitudinal ones, which are greater than radial ones. Figure 1b also gives the proof that a strong
restraining effect occurs between the braces keeping transversal residual stresses at a high value.
Figure 2 shows that the numerical distributions give the global magnitude of experimental residual
stresses and that the maximum values they reach are quite close to the experimental ones. However, the
transverse residual stress distribution obtained with ABAQUS is shifted to the right compared with the
experimental distribution. It means that transverse residual stresses should be compressive at 13 mm
depth but the models present tensile residual stresses through all the depth. MORFEO results predict
more accurately the transverse residual stress distributions whereas ABAQUS results fit better the
longitudinal stress distribution. The difference between both codes might be attributed to the different
heat source models.
Globally, numerical results are in an acceptable agreement with experimental results.
Conclusion
The numerical results, obtained using the ABAQUS and MORFEO codes, have shown to be globally
in good agreement with the experimental results obtained from neutron diffraction measurements.
Our simplified model proved its ability to reproduce the residual stress distribution in the region sur-
rounding the welds even though the peak values are not always well captured and the distribution is
sometimes shifted.
Numerical simulations have clearly confirmed the importance of transverse residual stresses and
the restraining effect occurring in the gap area. Transverse residual stresses are detrimental because
they will superimpose with applied fatigue stresses which are also predominantly transversally ori-
ented.
References
[1] T.R. Gurney: Fatigue of Welded Structures. Cambridge University Press (1979).
[2] K. Masubuchi: Analysis of welded structures. Pergamon Press (1980).
[3] P. Dong and J.K. Hong: Recommendations for determining residual stresses in fitness-for-service
assessment. Welding Research Council Bulletin Vol. 476 (2002).
[4] V.J. Papazoglou and K. Masubuchi: J. Press. Vess.-T. ASME Vol. 83-87 (1982), p. 119.
[5] J. Goldak, A. Chakravarti and M. Bibby: Metall. Trans. B Vol. 15B Numb. 2 (1984), p. 299.
[6] L.O. Raymond and J. Chipman: Trans. Met. Soc. AIME Vol. 239 (1967), p. 630.
[7] L.-E. Lindgren: J. Therm. Stresses 24 (2001), p. 141.
[8] P. Michaleris. Courses at the Pennsylvania State University (2011).
[9] ABAQUS: Analysis user's manual version 6.9 (Dassault Systèmes, 2009).
[10] MORFEO: v1.3 user manual (Cenaero, 2009).
338 Advances in Fracture and Damage Mechanics X
