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\begin{document}

\title{Numerical evaluation of temperature fields and residual stresses in butt
weld joints and comparison with experimental measurements}



\author[1]{Raffaele Sepe}%
\author[2]{Alessandro De Luca}%
\author[2]{Alessandro Greco}%
\author[3]{Enrico Armentani}%
\affil[1]{University of Salerno Department of Industrial Engineering}%
\affil[2]{University of Campania Luigi Vanvitelli Department of Engineering}%
\affil[3]{University of Naples Federico II Department of Chemical Engineering Materials and Industrial Production}%


\vspace{-1em}



  
  \date{June 16, 2024}


\begingroup
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\selectlanguage{english}
\begin{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.%
\end{abstract}%



\sloppy


Numerical evaluation of temperature fields and residual stresses in butt
weld joints and comparison with experimental measurements

\par\null

Raffaele Sepe\textsuperscript{1,*}, Alessandro De
Luca\textsuperscript{2}, Alessandro Greco\textsuperscript{2}, Enrico
Armentani\textsuperscript{3}

\textsuperscript{1)}Dept. of Industrial Engineering, University of
Salerno, Via Giovanni Paolo II, 132 - 84084 -- Fisciano (SA) - Italy

\textsuperscript{2)}Dept. of Engineering, University of Campania ``Luigi
Vanvitelli'' Via Roma, 29 -- 81031 Aversa (CE), Italy

\textsuperscript{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-mail\emph{rsepe@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

\emph{h\textsubscript{c}} temperature dependent convective film
coefficient

\emph{k} thermal conductivity

\emph{m\textsubscript{seam}} mass of half welding bead

\emph{n\textsubscript{component}} number of components of whole half
welding bead

\emph{q\textsubscript{latent}} latent heat per mass unit

\({\dot{q}}_{n}\) heat flux

\emph{t\textsubscript{weld}} 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

\emph{v} the welding speed

\emph{vol\textsubscript{component}} volume of the single component

\emph{vol\textsubscript{seam}} volume of half welding bead

\emph{C} specific heat

C\textsubscript{eq} equivalent carbon content

{[}\emph{C\textsuperscript{th}} {]} thermal stiffness

{[}\emph{D\textsuperscript{ep}} {]} total stiffness matrix

{[}\emph{D\textsuperscript{e}} {]} elastic stiffness matrix

{[}\emph{D\textsuperscript{p}} {]} plastic stiffness matrix

\emph{E} Young Modulus

\emph{G} Tangential modulus

\emph{H} temperature dependent film coefficient

\emph{I} welding current

\emph{L\textsubscript{component}} length of the single component

\emph{L\textsubscript{seam}} length of welding bead

\emph{Q} heat input

\emph{Q\textsubscript{component}} energy to be applied to the single
components

\emph{Q\textsubscript{latent}} latent heat

\emph{Q\textsubscript{real}} energy supplied to the entire half welding
seam

\emph{Q\textsubscript{sensible}} sensible heat

\emph{T\textsubscript{az}} absolute zero of the thermal scale used for
this work (Celsius degrees)

\emph{T\textsubscript{r}} temperature of the environment transferring by
radiation

\emph{T\textsubscript{s}} solidus temperature

\emph{T(x, y, z, t)} temperatures distribution of the welded plate

\emph{T\textsubscript{0}} initial temperature

\emph{T\textsubscript{[?]}} temperature of the environment transferring
heat by convection

\emph{V} voltage

\selectlanguage{greek}\emph{ε} \selectlanguage{english}surface emissivity

\selectlanguage{greek}\emph{η} \selectlanguage{english}arc efficiency

\selectlanguage{greek}\emph{ν} \selectlanguage{english}Poisson ratio

\selectlanguage{greek}\emph{ρ} \selectlanguage{english}density

\selectlanguage{greek}\emph{σ} \selectlanguage{english}Stefan-Boltzmann constant

\selectlanguage{greek}\emph{σ\textsubscript{r}}\selectlanguage{english} tensile strength

\selectlanguage{greek}\emph{σ\textsubscript{s}}\selectlanguage{english} 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 Gunnort\textsuperscript{1} or Connor\textsuperscript{2}. 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.\textsuperscript{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.\textsuperscript{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 Makerle\textsuperscript{7} and by Dong\textsuperscript{8}.

Over the last years, several destructive and non-destructive techniques
have been developed to experimentally evaluate the residual
stresses.\textsuperscript{9-16} Among these techniques, the most used
ones are the non-destructive ultrasonic techniques, used for example by
Satymbau and Ramachandrani\textsuperscript{9}, the non-destructive
neutron\textsuperscript{12,13} and X-ray\textsuperscript{14} diffraction
techniques and the destructive hole drilling technique, used by
Schajer\textsuperscript{16}. 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 al\textsuperscript{17} 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.\textsuperscript{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 Chang\textsuperscript{18,19} 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
al\textsuperscript{23-25}, 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.\textsuperscript{26} Kermanpur et
al\textsuperscript{27}investigated 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
al\textsuperscript{28,29} 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 al\textsuperscript{30} 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
al\textsuperscript{31} focused their investigation on butt welded
joints. Finally, Tsirkas\textsuperscript{32}, 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
Mazumder\textsuperscript{33}proposed a 3D transient FE model for
simulating a Gas Metal Arc Welding (GMAW) process. Tsirkas et
al\textsuperscript{34}, 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 al\textsuperscript{35}investigated 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 al\textsuperscript{36} 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 al\textsuperscript{37,38} 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 al\textsuperscript{39}, 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 Vila\selectlanguage{ngerman}ça et
al\textsuperscript{40}, while Binda et al\textsuperscript{41} 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
model\textsuperscript{42,43} 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.\textsuperscript{44}

In this study a novel FE model, based on the ``element birth and death''
technique, has been developed by means of ABAQUS\textsuperscript{®} 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,\ldots{}). 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
model\textsuperscript{17,27,32,33,34,44}, 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.\textsuperscript{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.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

Figure 1 Dimensional details of plates and boundary conditions used
during the welding process in the experimental test.

Table 1 Chemical composition (wt\%) of S275JR steel.\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
C & Mn & P\textsubscript{max} & S\textsubscript{max} &
C\textsubscript{eqmax}\tabularnewline
\midrule
\endhead
0.12\selectlanguage{ngerman}÷0.18 & 0.3\selectlanguage{ngerman}÷0.6 & 0.04 & 0.05 & 0.28\tabularnewline
\bottomrule
\end{longtable}

Table 2 Mechanical properties of the base materials at room temperature.\selectlanguage{english}
\begin{longtable}[]{@{}llllll@{}}
\toprule
Material & \selectlanguage{greek}\emph{σ\textsubscript{s}}\selectlanguage{english} {[}MPa{]} &
\selectlanguage{greek}\emph{σ\textsubscript{r}}\selectlanguage{english} {[}MPa{]} & \emph{E} {[}GPa{]} & \emph{G}
{[}GPa{]} & \selectlanguage{greek}\emph{ν}\selectlanguage{english}\tabularnewline
\midrule
\endhead
S275JR & 275 & 430 & 210 & 89.8 & 0.3\tabularnewline
\bottomrule
\end{longtable}

In order to assess the reliability of the proposed FE model and, in
particular, the validity of the thermal simulations results, six\emph{K}
-type thermocouples have been arranged at different distances (Figures
2A and 2B) from the weld beads in order to monitor the temperatures
distribution: two thermocouples, TC1 and TC2, at a quarter region of the
plate and at the mid-plane level (\emph{y} = 62 mm,\emph{z} = 4 mm), the
remaining, TC3, TC4, TC5 and TC6 have been fixed at the middle region of
the plate and at the mid-plane level (\emph{y} = 124 mm, \emph{z} =4
mm). To record the values of temperatures, a personal computer with a
PCI 6221 DAQ (Data AcQuisition) card of National Instrument and
LabView\selectlanguage{ngerman}\textsuperscript{®} 2018 software have been used. Moreover,
during the welding process, both voltage and current have been measured
using a voltmeter and an ammeter, respectively, both connected to the
weld circuit.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

Figure 2 Layout of thermocouples A; thermocouples installed B;
distortion of the welding joint measured by means CMM C.

An arc efficiency, \selectlanguage{greek}\emph{η,} \selectlanguage{english}of 0.82 for SMAW\textsuperscript{45} has
been considered; therefore, the heat input per mm of weld
length,\emph{Q} , can be calculated using the equation (1);

\selectlanguage{greek}\emph{Q = ηVI/v}\selectlanguage{english} (1)

where \selectlanguage{greek}\emph{η} \selectlanguage{english}is arc efficiency; \emph{V,} the voltage; \emph{I,} the
current and \emph{v,} the welding speed. The values of \emph{Q} are also
reported in Table 3.

Table 3 Welding parameters.\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
\begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Pass\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Efficiency \selectlanguage{greek}\emph{η}\selectlanguage{english}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Wire diameter {[}mm{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Current \emph{I} {[}A{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Voltage \emph{V} {[}V{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
Travel speed \emph{v} {[}mm/s{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\emph{Q} {[}J/mm{]}\strut
\end{minipage} & \begin{minipage}[b]{0.12\columnwidth}\raggedright\strut
\[{\dot{u}}^{{}^{\prime\prime\prime}}\] {[}W/mm\textsuperscript{3}{]}\strut
\end{minipage}\tabularnewline
\midrule
\endhead
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
0.82\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
3.2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
108\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
29.5\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1.56\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
1674.7\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
62.372\strut
\end{minipage}\tabularnewline
\begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
98\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
26.0\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
2.166\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
964.62\strut
\end{minipage} & \begin{minipage}[t]{0.10\columnwidth}\raggedright\strut
23.829\strut
\end{minipage}\tabularnewline
\bottomrule
\end{longtable}

In order to assess the reliability of the proposed FE model to evaluate
the welding distortion, the \emph{u\textsubscript{z}} (Figure 2C)
displacements of the plate have been measured at some locations of the
joints, by means of a Coordinate Measuring Machine (CMM).

2. Finite element model

The numerical simulation of a welding process involves the investigation
of the thermo-mechanical response of the joint. This behaviour can be
simulated by a numerical method, by using an uncoupled approach
consisting of two consecutive analyses: the former, where the thermal
problem is solved independently on the joint mechanical response, under
a free-free configuration, to obtain the temperatures distribution; the
latter, consisting of a subsequent mechanical analysis, where the
temperatures history previously predicted at each node is used as
thermal load. Such uncoupled approach, which is well established in
literature for such type of analyses,\textsuperscript{17,22,34} allows
saving computational costs with respect to the coupled one, with a
comparable and an acceptable level of accuracy. All simulations have
been carried out by means of the finite element commercial code
ABAQUS\selectlanguage{ngerman}\textsuperscript{®} v. 6.14.

The same FE model has been used for both thermal and mechanical
analyses. Concerning the mesh, 8-nodes hexahedral 3D finite elements
have been used for both base and weld zones. More in detail, DC3D8
finite elements have been used for the thermal analysis, allowing
introducing the temperature as unique degree of freedom, and C3D8 finite
elements, characterized by the three translations as degrees of freedom,
has been used for the mechanical analysis. According to Figure 3, a
finer mesh has been developed for the chamfer region; a transition mesh
for the HAZ (Heat Affected Zone) region and a coarser mesh, with a
linear bias, for the other parts of the plate. As a result, FE model
counts a total of 11904 finite elements and 14175 nodes.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Figure 3 Finite element model.

Moreover, the simulation of the weld passes has been carried out
according to the element birth and death technique. Such technique
starts by the modelling of the whole weld bead (Figure 4A), by
separating it in 124 groups of finite elements (64 for each weld pass),
named in the following ``components'' (Figure 4B). Subsequently, all
elements are deactivated by multiplying their properties by a severe
reduction factor (e.g. 10\textsuperscript{-6}) in a way to exclude them
from the simulation. When the added material needs to be simulated in
order to virtually perform the welding process, it is not actually added
to the model, but it is progressively reactivated, component by
component: material properties of the finite elements belonging to the
weld seam return to their starting values, participating again to the
evolution of the joint material.

The model has been developed by taking advantage of the symmetry of the
joint geometry and of the use of the same material for all joint parts
(weld bead included). Under this condition, it is possible to simulate
the experimental test just by modelling one plate and a half seam.

Both thermal and mechanical analyses involve a first step, 1 \selectlanguage{ngerman}·
10\textsuperscript{-4} s long, during which all ``components''
simulating the whole weld seam are removed. Then, 62 couples of load
steps, corresponding to about 158.97 s, are alternatively set to
simulate the first weld pass (Figure 4B -- red elements). Each couple
consists of a first step, 1 · 10\textsuperscript{-4} s long, which
allows reactivating a single ``component''; a second step, which allows
simulating the thermal load on the previously reactivated ``component''
(the duration time, in this case, depends on the weld speed). Before
simulating the second pass, a load step, 108 s long, is set to simulate
the time dedicated to the first weld seam cleaning operations.
Afterwards, other two groups of 62 load steps, corresponding to about
114.5 s are set to simulate the second pass (Figure 4B -- blue elements)
according to the same modelling technique of the first pass. Finally, a
load step, 1886 s long, has been set to simulate the plate cooling phase
up to a temperature of about 60 °C. The FE analysis time increment is
automatically calculated by the software and a full Newton-Raphson
method is used to obtain the incremental calculation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

Figure 4 Representation of the ``components'' with indication of the two
groups of elements constituting the two passes A; i-th red components of
first pass, i-th blue components of second pass B.

Thermal analysis

The thermal analysis of the welding process is essentially a
mathematical solution of the differential problem based on the equation
of energy conservation:

\(\selectlanguage{greek}\text{ρC}\selectlanguage{english}\frac{\partial T}{\partial t}={\dot{u}}^{{}^{\prime\prime\prime}}+\frac{\partial}{\partial x}\left(k_{x}\frac{\partial T}{\partial x}\right)+\frac{\partial}{\partial y}\left(k_{y}\frac{\partial T}{\partial y}\right)+\frac{\partial}{\partial z}\left(k_{z}\frac{\partial T}{\partial z}\right)\), (2)

where the temperatures distribution \emph{T(x, y, z, t)} of the welded
plate is a function of both spatial and time coordinates; \selectlanguage{greek}\emph{ρ}
,\selectlanguage{english}\emph{C} and \emph{k} are the density, the specific heat and the
thermal conductivity of the material, respectively, and
\({\dot{u}}^{{}^{\prime\prime\prime}}\) is the change rate of internal energy per volume
unit. Eq. (2) is a non-linear differential equation since \selectlanguage{greek}\emph{ρ} ,
\selectlanguage{english}\emph{C} and \emph{k}depend on the temperature. Initial and boundary
conditions of the problem are respectively:

\(T\left(x,y,z;t=0\right)=T_{0}\), (3)

\({\dot{q}}_{n}\left(x,y,z;t\right)=-\left(k_{x}\frac{\partial T}{\partial x}n_{x}+k_{y}\frac{\partial T}{\partial y}n_{y}+k_{z}\frac{\partial T}{\partial z}n_{z}\right)\), (4)

where \emph{T\textsubscript{0}} = 23.5 \selectlanguage{ngerman}°C is the initial temperature of
the material; \({\dot{q}}_{n}\) is the heat flux at a generic boundary
having an outward local unit vector \(\hat{n}\left(x,y,z\right)\). In welding
problems, at external surfaces, the heat flux \({\dot{q}}_{n}\)may
consist of one or more of the following modes: convective heat loss,
radiative heat loss and boundary heat \(\dot{q_{0}}\). The latter has
been neglected in the proposed FE model. Convective and radiative heat
losses on the external surfaces of the welded plates are given
respectively by:

\({\dot{q}}_{\text{nc}}=h_{c}\left[T\left(x,y,z;t\right)-T_{\infty}\right]\), (5)

\({\dot{q}}_{\text{nr}}=\selectlanguage{greek}\text{εσ}\selectlanguage{english}\left\{\left[T\left(x,y,z;t\right)-T_{\text{az}}\right]^{4}-\left(T_{r}-T_{\text{az}}\right)^{4}\right\}=h_{r}\left[T\left(x,y,z;t\right)-T_{r}\right]\), (6)

where \emph{T\textsubscript{[?]}} and \emph{T\textsubscript{r}} are
respectively the temperatures of the environment transferring heat by
convection and radiation and they are usually equal to the room
temperature; \selectlanguage{greek}\emph{ε} \selectlanguage{english}is the surface emissivity; \selectlanguage{greek}\emph{σ} \selectlanguage{english}= 5.67 \selectlanguage{ngerman}·
10\textsuperscript{-8} W/m\textsuperscript{2}K\textsuperscript{4} is the
Stefan-Boltzmann constant; \emph{h\textsubscript{c}} is the temperature
dependent convective film coefficient and \emph{T\textsubscript{az}} =
-273.15 °C is the absolute zero of the thermal scale used for this work
(Celsius degrees). From Eq. (6) the radiative heat losses can be
expressed in the form of convective heat losses by means of temperature
dependent convective film coefficient \emph{h\textsubscript{r}} ,
therefore from Eq. (5) and (6) a unique temperature dependent film
coefficient, \emph{H,} can be considered:

\emph{H} = \emph{h\textsubscript{c}} + \emph{h\textsubscript{r}} . (7)

Particularly important in the thermal model is the heat input per
mm\emph{Q,} reported in Table 3. This is the energy supplied by the
welding machine per unit of length. In the proposed simulation a half of
this energy has been supplied to a half of the seam because one plate
only has been modelled. Therefore, energy supplied to the entire half
welding seam during the simulation is equal to:

\(Q_{\text{real}}=\frac{Q\bullet\ L_{\text{seam}}}{2}\ \), (8)

where: \emph{L\textsubscript{seam}} is the length of welding bead.

This energy can be subdivided into three parts:

\emph{sensible heat} : energy to heat the weld material from the initial
temperature (\emph{T\textsubscript{0}} ) to the solidus temperature
(\emph{T\textsubscript{s}} ):

\(Q_{\text{sensible}}=\text{vol}_{\text{seam}}\bullet\int_{T_{0}}^{T_{S}}\selectlanguage{greek}\text{ρ\ C\ dT}\selectlanguage{english}=m_{\text{seam}}\int_{T_{0}}^{T_{S}}\text{C\ dT}\), (9) where: \selectlanguage{greek}\emph{ρ} \selectlanguage{english}and \emph{C} are the density
and specific heat of the material respectively and
\emph{vol\textsubscript{seam}} and\emph{m\textsubscript{seam}} are the
volume and the mass of half welding bead;

\emph{latent heat} : energy due to phase transition from the solidus
temperature (\emph{T\textsubscript{S}} ) to the liquidus temperature
(\emph{T\textsubscript{L}} ):

\(Q_{\text{latent}}=m_{\text{seam}}\ \bullet q_{\text{latent}}\) , (10) where: \emph{m\textsubscript{seam}} is the
mass of half welding bead and\emph{q\textsubscript{latent}} is the
latent heat per mass unit;

the energy to further heat the weld material is equal to:

\(Q_{\text{body\ flux}}=Q_{\text{real}}-Q_{\text{sensible}}-Q_{\text{latent}}\), (11) while the energy to be applied to the single
components is:\(Q_{\text{component}}=\frac{Q_{\text{body\ flux}}}{n_{\text{component}}}\), (12) where:
\emph{n\textsubscript{component}} is the number of components of whole
half welding bead. This latter part of the energy acts as volumetric
generation of the internal energy \({\dot{u}}^{{}^{\prime\prime\prime}}\) (Table 3) and it
is computable by Eq. 13:\({\dot{u}}^{{}^{\prime\prime\prime}}=\frac{Q_{\text{component}}}{\text{vol}_{\text{component}}\ \bullet t_{\text{weld}}}=\frac{Q_{\text{body\ flux}}}{n_{\text{component}}}\bullet\ \frac{v}{\text{vol}_{\text{component}}\ \bullet L_{\text{component}}}=\frac{Q_{\text{body\ flux}}\ \bullet v}{\text{vol}_{\text{seam}}\bullet\ L_{\text{component}}}\), (13) where:
\emph{vol\textsubscript{component}} and\emph{L\textsubscript{component}}
are the volume and the length of the single component, respectively;
\emph{v} is the welding speed and\emph{t\textsubscript{weld}} is the
time necessary to travel a distance equals to the length of the single
component by Eq. (14);\(t_{\text{weld}}=\frac{L_{\text{component}}}{v}\ \). (14)

In the proposed FE model, the specific power \({\dot{u}}^{{}^{\prime\prime\prime}}\) has
been applied to each component during the
time\emph{t\textsubscript{weld}} as volumetric flux and it has been
applied by means of the law shown in Figure 5.

The load has been applied so that the area under the load curve is
constant and equals to \({\dot{u}}^{{}^{\prime\prime\prime}}\) at varying travel time
(\emph{t\textsubscript{weld}} ). Two ramps {[}with duration of 0.5\%
of\emph{t\textsubscript{weld}} {]}, to avoid the discontinuity during
the load application, and a little time offset of
2\selectlanguage{ngerman}·10\textsuperscript{-6}\emph{s} between two load curves have been
defined, in order to encourage the convergence of the solution. The
height of the trapezium\emph{h} is computable by Eq. (15):

\({\dot{u}}^{{}^{\prime\prime\prime}}=A_{\text{trapezium}}=\frac{\left(B+b\right)\bullet h}{2}=\frac{\left\{\left(1\bullet t_{\text{weld}}\right)+\left[\left(1-2\bullet 0.005\right)\ t_{\text{weld}}\right]\right\}\ \bullet h}{2}=\left(1-0.005\right)\bullet\ t_{\text{weld}}\ \bullet h\)(15)

and hence:

\(h=\frac{{\dot{u}}^{{}^{\prime\prime\prime}}}{\left(1-0.005\right)\bullet t_{\text{weld}}}\). (16)\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

Figure 5 Load curve.

Thermal boundary conditions, given by Eqs. (3) and (4), occur at all the
surfaces except the adiabatic plane at the longitudinal symmetry plane
of the final joint; in the same manner, for numerical simplicity, the
surfaces of the chamfer hollow have been considered adiabatic before
supplying the filler material.

Thermal properties dependent on temperature\textsuperscript{46,47} are
reported in Figure 6A. In order to take into account the transformation
phase in the thermal analysis, a latent heat per mass unit, a solidus
temperature and a liquidus temperature equals to 277000 J/kg, 1495 \selectlanguage{ngerman}°C,
1540 °C respectively, have been used, whereas the temperature dependent
heat loss coefficient \emph{H} , applied on the surfaces, is shown in
Figure 6B.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

Figure 6 Thermal properties of material dependent on temperature A;
variation of heat loss coefficient \emph{H} with temperature B;
mechanical properties of material dependent on temperature C; stress vs.
strain curves with temperature D.

Mechanical analysis

Temperature history achieved by the thermal analysis has been used in
the mechanical analysis as thermal loads. An elasto-plastic material
model, based on the von Mises yield criterion and isotropic strain
hardening rule, has been considered, including the effects of the
temperature on the material properties.

The stress-strain relations can be written as:

\(\left[\selectlanguage{greek}\text{dσ}\selectlanguage{english}\right]=\left[D^{\text{ep}}\right]\bullet\left[\selectlanguage{greek}\text{dε}\selectlanguage{english}\right]-[C^{\text{th}}]\bullet dT\), (17)

being:

\(\left[D^{\text{ep}}\right]=\left[D^{e}\right]+\left[D^{p}\right]\), (18)

where: {[}\emph{D\textsuperscript{ep}} {]} is the total stiffness
matrix; {[}\emph{D\textsuperscript{e}} {]} is the elastic stiffness
matrix; {[}\emph{D\textsuperscript{p}} {]} is the plastic stiffness
matrix and {[}\emph{C\textsuperscript{th}} {]} is the thermal stiffness

Moreover, as aforementioned, a particular attention must be paid on the
modelling of the symmetry boundary conditions. The transient thermal
field generated by the welding process introduces several deformations
inside the plates, leading to their interaction. Such interaction, which
increases as the plate length increases (due to their rotation), has
never been considered in the FE models proposed in
literature\textsuperscript{17,21,22,31,34,36}, by reducing this problem
to a simple application of the symmetric boundary conditions. This
results into too many approximations in the simulated residual
stress-strain state, especially for long plates.

More in detail, when the first component is reactivated together with
its symmetric boundary conditions, the plate starts to rotate due to the
thermal loads, approaching, as a consequence, to the longitudinal
symmetry plane. By progressively reactivating the components, up to the
last components of the weld seam, the plate rotation may induce
components to find themselves significantly beyond the longitudinal
symmetry plane. Actually, such rotation is limited by the interaction of
the plate with its counterpart. All these considerations suggest
considering such phenomenon during the modelling, even if the modelling
involves both plates.

Moreover, the plate rotation may lead also to convergence issues,
especially as the plate length increases. The main reason of these
convergence issues can be addressed to the activation of the symmetric
constraints, which, under these conditions, would be applied to a more
deformed plate (with respect to the real test case), leading to an
increase of the residual stresses that can facilitate the lack of the
analysis convergence.

In order to take into account the interaction of both plates in the
proposed symmetric approach-based FE model, a row of finite elements
(green finite elements in Figure 7) has been placed along the left side
of the longitudinal symmetry plane (Figure 7A). This row of elements, of
the same length as the plate (248 mm), is made of 62 C3D8 finite
elements and 252 nodes; an arbitrary width (\emph{x} direction) and a
height \emph{(z} direction), slightly greater than the ``root face''
(Figure 1), simulates the interaction with the two plates, also in case
of out-of-plane displacements. The mechanical material properties of
these finite elements are the same of the plate. Concerning the boundary
conditions applied on this row of elements, nodes placed on the
interacting surface (face looking at the longitudinal symmetry plane)
have been fully constrained.

In addition, the interaction between the plate and the work table, shown
in Figure 1D, has been numerically replicated by modelling the work
table as a rigid plane and by modelling the interaction between the
plate and the rigid plane by means of a surface to surface contact
algorithm. Moreover, in order to completely constrain the rigid motion
of the plate, the translation along the \emph{y} and \emph{z} axes of
the node (\emph{x} = 0, \emph{y} = 0, \emph{z} = 0) of the seam and the
translation along the \emph{z} axis of the node (\emph{x} = 0, \emph{y}=
248, \emph{z} = 0) have been fixed.

The interaction between the modelled plate and the row of elements has
been defined through a surface to surface contact algorithm.
Specifically, at the first load step the interaction involves all
V-grove finite elements; subsequently, due to the progressive
reactivation of ``components'' of the first weld pass together with the
activation of the symmetric constraints along the \emph{x} direction
(Figure 7), the interaction and the green finite elements belonging to
the row of elements are removed progressively as well (Figure 7B),
because not more useful. It must be highlighted that the simulation
strategy does not increase significantly the computational costs.

The translational constraints along the \emph{x} direction are
progressively applied to the components nodes placed along the
longitudinal symmetric plane during the weld pass. This type of boundary
condition constrains also the rigid motion of the plate around
\emph{y}and \emph{z} directions.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

Figure 7 Row of elements (in green) simulating the left side plate A;
suppression of the elements of row activation of the symmetric
constraints along \emph{x} direction B.

Also the mechanical properties\textsuperscript{46,47} have been
considered temperature dependent (Figure 6C). Moreover, since the
structural analysis involves plastic deformation of the material, in
this work, the hardening material model with von Mises yield criterion
and the isotropic strain hardening rule have been assumed. The stress
vs. strain curves, as a function of the temperature, are shown in Figure
6D.

Moreover, in steels, martensite is formed from austenite containing
carbon atoms and, in view of the diffusionless nature of its formation,
it ideally inherits the carbon atoms of the parent austenite. Therefore,
while for some steel welded parts the solid-state austenite--martensite
transformation during cooling has a significant influence on the
residual stresses and distortion\textsuperscript{17,33,34,48,49,50,51},
especially when the equivalent carbon content is high, for others (low
equivalent carbon content), it may be neglected as well demonstrated by
Cho et al\textsuperscript{52} and Deng.\textsuperscript{53} According to
Cho et al\textsuperscript{52} and Deng\textsuperscript{53}, the
modelling of the transformation phase does not change the level of
accuracy of the FE model, in terms of residual stresses and distortions
prediction, when the welding process involves low carbon steels with low
equivalent carbon content (about C\textsubscript{eq} = 0.23\%), as the
steel used in this work. As a result, the solid-state transformation
phase has not been considered in the modelling.

In order to evaluate the influence of the interaction between the
plates, a second mechanical analysis has been carried out without
considering the row of finite elements placed along the left side of the
longitudinal symmetry plane (Figure 7) and by applying only the
translational constraints along the \emph{x} direction to simulate the
symmetry constraints.

3. Results and discussion

In this section, numerical results of the welding simulation are
presented and compared with experimental ones, in order to assess the
reliability of the used FE models.

3.1 Thermal analysis

The temperatures measured at six points by means of six thermocouples
have been compared with the respective predicted ones.

Figure 8 shows the temperature distributions at the middle section of
the plate along the transverse direction during the two passes, with the
welding arc located at the middle of the welding path. It is possible to
appreciate a good agreement between numerical and experimental results,
with the numerical curves that well estimate the experimental
measurements during both welding passes.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image8/image8}

\end{center}
\end{figure}

Figure 8 Temperature distributions at the middle section of the plate
along transversal direction during the first (A) and the second (B)
passes.

The experimental-numerical thermal histories are shown in Figure 9, for
the thermal cycles recorded in correspondence of the thermocouples TC1
and TC2, and in Figure 10 for thermal cycles recorded from thermocouples
from TC3 to TC6.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

Figure 9 Thermal histories in correspondence of thermocouples: A, TC1;
B, focus on TC1; C, TC2 and D, focus on TC2.

Figure 9 shows a good agreement between numerical and experimental
results as general trend. In order to better highlight the differences
between numerical and experimental curves, thermal histories curves at
TC1 and TC2 have been cut at a time of 550 s and reported in Figures 9B
and 9D, respectively. According to Figures 9A and 9B, the FE model
provides, in correspondence of TC1, a small over-estimation of about 23
\selectlanguage{ngerman}°C in the first peak value, corresponding to the first pass. This can be
due to a displacement of the thermocouple within the plate hole,
occurred during the first pass, leading to a not perfect contact between
the thermocouple and the plate. This difference cannot be found during
the second pass because the correct position of all thermocouples was
checked at the end of the first pass. Moreover, according to Figure 9B,
a time shift can be observed between numerical and experimental data.
Such disagreement can be attributed to the welding speed, not perfectly
constant along the whole weld seam, but, in proximity of thermocouple
TC1, faster than the value reported in Table 3. As matter of the fact,
the welding speed reported in Table 3 has been calculated as the ratio
of the time spent for the first pass to the length of the weld seam.

Figure 10 shows the comparison of the numerical results with the
experimental ones in correspondence of thermocouples located at the
middle section of the plate during the whole process. Also here, in
order to highlight the differences between numerical and experimental
results, curves have been cut at 550 s and reported in Figures 10B, 10D,
10F and 10H. Excluding the initial experimental values of the curves,
which are affected by high noise due to the electrical shock at the
beginning of the welding process, it can be stated that the experimental
results are in good agreement with the numerical ones. It can be
observed that the FE model provides a small over-estimation of about 17
°C in correspondence of the second peak, during the second pass, at TC3
(Figure 10B), while there are slight differences in the peak values
during the first pass at TC4 (Figure 10D) and TC6 (Figure 10H),
characterized by an under-estimation of the numerical results. However,
these differences are lower than about 5 \%.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

Figure 10 Thermal histories in correspondence of thermocouples: A, TC3;
B, focus on TC3; C, TC4; D, focus on TC4; E, TC5; F, focus on TC5; G,
TC6 and H, focus on TC6.

Figures 11A and 11B show the temperature distributions during the first
and second passes at welding times of \emph{t} = 66.67 s and \emph{t} =
315 s respectively. The centre of the welding arc at these times is at
the position of \emph{x} = 0 mm and \emph{y} = 104 mm. As it can be seen
from the figures, the peaks of temperature around the welding arc, at
the two instants, are calculated to be about 2460 \selectlanguage{ngerman}°C and 2116 °C,
respectively, suggesting that the material is melted in the fusion zone.
High temperatures are present nearby the fusion zone (FZ), defining the
heat affected zone (HAZ).

During the first pass, the thermal gradients are very steep in the
proximity of the heat source, while they decrease during the second
pass; furthermore, near the welding line, the distance between the
isotherms increases as the cooling rate decreases and the welding pool
also presents a very small area in front of the welding arc.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

Figure 11 Temperature distributions {[}\selectlanguage{ngerman}°C{]} during: A, I pass at
time\emph{t} = 66.67 s and B, II pass at time \emph{t} = 315 s.

Figure 12 compares the experimental and the predicted FZ and HAZ. As
shown in this figure, the geometry and shape of both weld seam and HAZ
are well numerically replicated. As matter of the fact, the HAZ can be
defined as the section reaching a temperature higher than 727 °C during
the welding process.\textsuperscript{54}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}

Figure 12 Numerical-experimental comparison of HAZ, during the first (A)
and the second pass (B).

By comparing the numerical results with the experimental ones, it is
possible to state that the used methodology is suitable to predict very
accurately the temperatures distribution in the welded joint, without
the need to perform a tuning process to opportunely calibrate the heat
source.\textsuperscript{17,27,32,33,34,44}

3.2 Mechanical analysis

The longitudinal residual stresses\selectlanguage{greek}\emph{σ\textsubscript{y}}\selectlanguage{english} , induced
from the longitudinal expansion and contraction of the material during
the welding process, along the\emph{x} -direction at the midsection
(\emph{y} = 124 mm, \emph{z} = 4 mm) are shown in Figure 13A (line with
marker). The self-equilibrium of the weldment is such that the tensile
and compressive residual stresses are present at the weld seam and away
from the welding line respectively. High tensile residual stresses are
present in correspondence of the zones nearby the Welding Centre Line
(WCL), due to the contraction resistance of the material as the cooling
phase begins. Then, they decreased to zero, as the distance from the
(WCL) increases, becoming compressive for the zones far from the weld
seam. The transversal residual stresses \selectlanguage{greek}\emph{σ\textsubscript{x}}\selectlanguage{english} along
the\emph{x} -direction in the midsection (\emph{y} = 124 mm, \emph{z} =
4 mm) are shown in Figure 13B. Tensile residual stresses are present in
correspondence of the zones nearby the (WCL). Subsequently, they
decreased as the distance from the (WCL) increased, up to 0, almost.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image13/image13}

\end{center}
\end{figure}

Figure 13 Comparison of the longitudinal residual stresses
distribution\selectlanguage{greek}\emph{σy}\selectlanguage{english} (A) and the transversal residual stresses
distribution\selectlanguage{greek}\emph{σx}\selectlanguage{english} (B), along \emph{x} -direction at midsection
(\emph{y} = 250 mm, \emph{z} = 4 mm) achieved by the FE models
considering and not the plates interaction.

In Figure 14 the numerical displacements, \emph{u\textsubscript{z}} ,
predicted in correspondence of the path \emph{y} =248 mm, \emph{z} = 0
mm (green line of Figure 14A) and in corresponding of the path
\emph{x}=125 mm, \emph{z} = 0 mm (red line of Figure 14B), achieved by
imposing the temperatures distribution predicted by the thermal analysis
as thermal loads in the mechanical analysis, are compared with the
experimental ones measured by means of a Coordinate Measuring
Machine(CMM) shown in Figure 2C. According to Figure 14, the numerical
results are in good agreement with experimental ones; therefore, it is
possible to state that the numerical technique, used for the mechanical
analysis, can predict with a high level of accuracy the distortions in
the welded joint.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image14/image14}

\end{center}
\end{figure}

Figure 14 Comparison of the experimental distortions with those
predicted by the FE models considering and not the plates interaction:
A, along the path at \emph{y} = 248 mm and \emph{z} = 0 mm and B, along
the path at \emph{x} = 125 mm and \emph{z} = 0 mm.

As aforementioned, in order to appreciate the effects provided by the
modelling of the plates interaction during the welding process, the
predicted residual stresses and distortions have been compared with
those provided by the simulation performed by deactivating the plates
interaction (Figures 13 and 14).

According to Figure 13A, as expected, it can be noticed that the
longitudinal residual stresses distribution seems to be unaffected by
the plates interaction. As matter of the fact, plates have not been
constrained along the longitudinal direction. Contrary, the plates
interaction affects the transversal residual stresses distributions,
because of the plates rotation during the welding process. Residual
stresses appear to be slightly higher (Figure 13B) for the model that
does not consider the plates interaction and they are expected to
increase for longer plates, because of their rotation.

If the effects of the plates interaction on residual stresses
distribution may be considered negligible for the selected test case, a
similar consideration cannot be done in terms of distortions
distribution. According to Figure 14, the predicted distortions
distribution appears to be sensibly higher and far from the experimental
data for the FE model that does not consider the plates interaction. As
a result, the plates interaction plays a key-role in the modelling of
the welding process induced distortion.

5. conclusions

This paper presents a novel numerical model, based on the Finite Element
method, for the simulation of a welding process aimed to make a
two-passes V-groove butt weld joint. In order to evaluate the residual
stresses, a 3D non-linear thermo-mechanical analysis has been carried
out. The thermo-mechanical response of the joint has been simulated by
using an uncoupled approach. Specifically, the ``element birth and
death'' technique has been used to simulate the welding filler during
the welding process. The originality of the proposed technique has to be
found in the simulation of the interaction occurring between the two
plates during the welding process, never considered in literature when
the problem is faced through a symmetrical approach. As a result, it was
possible to predict more accurately the residual stresses affecting the
joint, caused by the thermal distortions which lead the plates to
rotate. The proposed modelling technique appears to be fundamental for
long plates, since the plates interaction becomes not negligible as the
plate length increases. Specifically, in order to save the computational
costs, only a plate and half seam have been modelled. As a result, in
order to simulate the plates interaction, a row of finite elements has
been placed along the left side of the longitudinal symmetry plane. This
approach allows predicting the residual stresses also for long joined
plates, which require a higher number of nodes and elements and,
consequently, a higher time analysis. A surface to surface contact
algorithm has been considered between the half seam and the finite
elements row.

Moreover, differently from the literature, the heat amount is supplied
to the finite elements as a volumetric generation of the internal
energy, allowing overcoming the time-consuming calibration phase
required by the Goldak's model, commonly adopted in literature.

The reliability of the FE model has been shown by assessing the
predicted results, in terms of temperatures distribution and joint
distortion, against the results provided by an experimental test.
Temperatures distribution has been measured during the welding process
by using six thermocouples placed at different locations nearby the weld
bead; welding distortions were measured by means of a Coordinate
Measuring Machine. A good agreement has been found between numerical and
experimental results, showing the effectiveness of the proposed FE
modelling technique.

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