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.