Numerical evaluation of
temperature fields and residual stresses in butt weld joints and
comparison with experimental measurements
Raffaele Sepe1,*, Alessandro De
Luca2, Alessandro Greco2, Enrico
Armentani3
1)Dept. of Industrial Engineering, University of
Salerno, Via Giovanni Paolo II, 132 - 84084 – Fisciano (SA) - Italy
2)Dept. of Engineering, University of Campania “Luigi
Vanvitelli” Via Roma, 29 – 81031 Aversa (CE), Italy
3)Dept. of Chemical, Materials and Production
Engineering, University of Naples “Federico II” P.le V. Tecchio, 80 –
80125 Naples, Italy
Corresponding author: Raffaele Sepe, e-mailrsepe@unisa.it
Abstract
This paper presents a novel numerical model, based on the Finite Element
(FE) method, for the simulation of a welding process aimed to make a
two-passes V-groove butt joint. Specifically, a particular attention has
been paid on the prediction of the residual stresses and distortions
caused by the welding process. At this purpose, an elasto-plastic
temperature dependent material model and the “element birth and death”
technique, for the simulation of the weld filler supply over the time,
have been considered within this paper.
The main advancement with respect to the State of the Art herein
proposed concerns the development of a modelling technique able to
simulate the plates interaction during the welding operation when an
only plate is modelled, taking advantage of the symmetry of the joint;
this phenomenon is usually neglected in such type of prediction models
because of their complexity.
Problems arising in the development of this modelling technique have
been widely described and solved herein: transient thermal field
generated by the welding process introduces several deformations inside
the plates, leading to their interaction, never faced in literature.
Moreover, the heat amount is
supplied to the finite elements as volumetric generation of the internal
energy, allowing overcoming the time-consuming calibration phase needed
to use the Goldak’s model, commonly adopted in literature.
The proposed FE modelling technique has been established against an
experimental test, with regard to the temperatures field and to the
joint distortion. Predicted results showed a good agreement with
experimental ones. Finally, the residual stresses distribution in the
joint has been evaluated.
Keywords: Residual stress, Welding, FEM, Butt weld joint, Element
“birth and death” technique.
Nomenclature
hc temperature dependent convective film
coefficient
k thermal conductivity
mseam mass of half welding bead
ncomponent number of components of whole half
welding bead
qlatent latent heat per mass unit
\({\dot{q}}_{n}\) heat flux
tweld time necessary to travel a distance equals
to the length of the single component
\({\dot{u}}^{{}^{\prime\prime\prime}}\) volumetric generation of the internal energy
v the welding speed
volcomponent volume of the single component
volseam volume of half welding bead
C specific heat
Ceq equivalent carbon content
[Cth ] thermal stiffness
[Dep ] total stiffness matrix
[De ] elastic stiffness matrix
[Dp ] plastic stiffness matrix
E Young Modulus
G Tangential modulus
H temperature dependent film coefficient
I welding current
Lcomponent length of the single component
Lseam length of welding bead
Q heat input
Qcomponent energy to be applied to the single
components
Qlatent latent heat
Qreal energy supplied to the entire half welding
seam
Qsensible sensible heat
Taz absolute zero of the thermal scale used for
this work (Celsius degrees)
Tr temperature of the environment transferring by
radiation
Ts solidus temperature
T(x, y, z, t) temperatures distribution of the welded plate
T0 initial temperature
T∞ temperature of the environment transferring
heat by convection
V voltage
ε surface emissivity
η arc efficiency
ν Poisson ratio
ρ density
σ Stefan-Boltzmann constant
σr tensile strength
σs yield stress
DBEM Dual Boundary Elements Method
CMM Coordinate Measuring Machine
FEM Finite Element Method
FZ Fusion Zone
GMAW Gas Metal Arc Welding
HAZ Heat Affected Zone
MIG Metal Inert Gas
SMAW Shielded Metal Arc Welding
Introduction
Welding is among the most relevant joining techniques used in the
structural field and it is particularly attractive for the transport
field such as aerospace, automotive and rail, thanks to the advantages
it offers in terms of weight saving, monolithic structures, design
flexibility and costs. Notwithstanding such benefits, several issues
could arise and compromise the efficiency and the performance of the
structure. Specifically, defects, residual stresses, porosities, cracks
propagation facilitation, distortions and the consequent misalignments
of the joint can affect the monoliths due to the thermal cycles involved
during the process, as widely described in several books by some authors
such as Gunnort1 or Connor2. The
highly localized transient heat and the strongly non-linear temperature
fields, characterizing the thermal cycles, combined with the subsequent
non-uniform cooling phase, cause plastic deformations in both the Fusion
Zone (FZ) and the Heat Affected Zone (HAZ), as a result of the
non-uniform thermal expansion and contraction of the
metal.3 Hence, at the end of the welding process, the
structure will be characterized by residual stresses that, combined with
the in-service loading conditions, could reduce the structural
performance, cause assembly issues, and influence the fatigue and
buckling strength.4-6 Therefore, the measurement of
the residual stress-strain state of welded components supports the
designers in the development of more efficient structures.
In fact, as many researchers investigated on these issues, there is an
extensive literature concerning the evaluation techniques of the
residual stresses in welded joints. Wide literature reviews have been
proposed by Makerle7 and by Dong8.
Over the last years, several destructive and non-destructive techniques
have been developed to experimentally evaluate the residual
stresses.9-16 Among these techniques, the most used
ones are the non-destructive ultrasonic techniques, used for example by
Satymbau and Ramachandrani9, the non-destructive
neutron12,13 and X-ray14 diffraction
techniques and the destructive hole drilling technique, used by
Schajer16. However, these techniques show several
limits such as the inaccuracies affecting the measures and the high
costs. Current computational methods allow overcoming these limitations
by simulating the welding processes and determining the stress-strain
state; among these, Finite Element (FE) method appears to be the most
suitable.
During the last decades, several scientific articles proposed FE models
able to simulate complex welding processes. Typically, due to the
coexistence of thermal and mechanical phenomena, the development of
numerical models for welding structures can be very challenging; so,
several strategies could be applied.
A comparison between the modelling strategies based on FE method has
been proposed by Mollicone et al17 in 2006, while
Lindgren, in 2001, presented a detailed review about the state of art
related to the FE modelling and to the simulation of the welding
processes in three articles.18-20 Among the many
developed techniques, the so-called “element birth and death” is one
of the most used. Briefly, it starts by the modelling of the entire weld
seam. Subsequently, the finite elements of the seam are deactivated and
progressively reactivated only when the heat is supplied, as explained
in detail in section 2. The literature presents various researches based
on the use of such simulation technique, for different welding
processes.
Teng and Chang18,19 used the element birth and death
technique for simulating the welding process for butt joints made of
carbon steel. They used the X-ray diffraction technique for validating
the numerical results. Based on the same technique, Armentani et
al23-25, in three consecutive studies between 2006 and
2007, simulated the welding processes for butt welded joints by varying
such properties as the weld filler and the thermal material properties.
In 2014, the same FE model was established against some
experiments.26 Kermanpur et al27investigated on butt welded joints, for pipe applications, by using the
element birth and death approach. They validated the numerical model
against some experimental tests and performed a further sensitivity
analysis by changing the arc efficiency and the heat source values in
input. Subsequently, Sepe et al28,29 used the same
technique for simulating the welding processes of two butt welded
joints, made of similar and dissimilar materials, respectively.
More recently, Modal et al30 in 2017 investigated on
the residual stresses in a multi-pass welded T-joint by using a FE
model, based on the element birth and death technique, validated by
comparing numerical and experimental results. Hashemzadeh et
al31 focused their investigation on butt welded
joints. Finally, Tsirkas32, in 2018, proposed and
validated an element birth and death technique-based model for
simulating a laser welding process for aircraft components made of
aluminium.
Other modelling and simulation techniques have been developed and
applied for welding processes. Choi and Mazumder33proposed a 3D transient FE model for simulating a Gas Metal Arc Welding
(GMAW) process. Tsirkas et al34, in 2003, proposed a
3D FE model for simulating a laser welding process, considering also the
metallurgical transformations, by using a nonlinear heat transfer
analysis, based on a keyhole formation model, and a coupled transient
thermo-mechanical analysis. Similarly, Cho et al35investigated on the residual stresses in a butt-welded joint and
validated the FE model by means of experimental tests based on the hole
drilling technique. Gary et al36 carried out a thermal
FE simulation of a butt joint developed by a Metal Inert Gas (MIG)
welding process and studied the influence of the welding parameters on
the temperature fields. Citarella et al37,38 developed
a Dual Boundary Elements Method (DBEM) based model and a coupled
FEM/DBEM for investigating the influence of the residual stresses on the
cracks propagation in friction stir welded aluminium butt joint. Other
simulation techniques are based on analytical models, as proposed by
Mochizuki et al39, that evaluate the residual stresses
in a pipe butt welded joint and validate the model by means of a neutron
diffraction experimental test. Similarly, another analytical model for
friction stir welding has been proposed by Vilaça et
al40, while Binda et al41 proposed a
semi-empirical model, based on analytical solving approach, for
simulating a laser welding process and evaluating the temperature
fields.
Almost all of the aforementioned simulation models use the Goldak’s
model42,43 to solve the thermal and the mechanical
equations, considering either the double-ellipsoid heat source model or
the Gaussian heat source model. Nevertheless, Goldak’s model requires an
extremely accurate calibration phase before proceeding with the
simulation of the entire process. This calibration is based on
experimental measurements and requires several control cycles,
representing a time consuming process.44
In this study a novel FE model, based on the “element birth and death”
technique, has been developed by means of ABAQUS® v.
6.14 code for the simulation of a welding process that can be applied
for several types of joints (e.g. butt joint, T-joint,…). Among
the main proposed elements of novelty, the modelling of the heat input
has to be mentioned. The heat amount is supplied to the finite elements
as volumetric generation of the internal energy. Such technique does not
require any calibration phase as for Goldak’s
model17,27,32,33,34,44, so the modelling time is
significantly reduced.
A two-passes V-groove butt welded joint, involving two plates
characterized by the same material and geometry, has been investigated
herein. Taking advantage of the joint symmetry, the FE model has been
developed by modelling an only plate and a half seam to reduce the
computational costs. Concerning the mechanical analysis, a new modelling
strategy is proposed. It consists in simulating the interaction between
the two joint counterparts, never considered in the FE models presented
in literature.17,21,22,31,34,36
In order to assess the reliability of the proposed numerical procedure,
numerical results have been compared with those provided by an
experimental test, herein presented. For such purpose, temperatures
distribution has been measured during the welding process by using some
thermocouples placed at different locations nearby the weld bead;
welding distortions have been subsequently measured by means of a
Coordinate Measuring Machine (CMM). A very good agreement has been
achieved, demonstrating the efficiency of the proposed model.
1. Materials and methods
Two carbon steel plates of size 248 mm x 125 mm (thickness of 8 mm)
which form a single V-groove joint between them (Figure 1A) have been
welded by using the Shielded Metal Arc Welding (SMAW) process. The
material of the plates is a structural low carbon steel S275JR. The
typical chemical composition of the material used in the experimental
test and the mechanical properties at room temperature are reported in
Tables 1 and 2, respectively. The welding process has been carried out
through two passes and a time gap of 108 between the successive passes
has been addressed to remove the slag formed during the first pass. The
welding parameters, related to each pass, are reported in Table 3. Both
weld passes have been carried out at uniform speed and under room
conditions using a 2.5 mm diameter flux-coated SMAW electrode ESAB OK
48.50 (AWS E 7018). The weld bead sequence is shown in Figure 1B and the
start point (A) and the end point (B) of each welding pass are shown in
Figure 1C. The plates have been simply placed on the work table shown in
Figure 1D. In this arrangement, the most parts of the top and bottom
surface areas of the plates are exposed to the environmental conditions.