the influence of welding current, voltage, and travel speed. The analysis focuses on peak temperature, out-of-plane

distortion, and elastic stress indicators derived from a linear thermo-elastic formulation. The results indicate that

welding current predominantly governs peak temperature, while travel speed has the strongest influence on thermal

gradients and distortion behavior; voltage exhibits a secondary but non-negligible effect on heat distribution. Simulated

thermal and deformation trends are benchmarked against published experimental and numerical studies on comparable

structural steels and show consistent qualitative behavior. Owing to the absence of plasticity, temperature-dependent

material properties, and direct experimental validation, stress results are interpreted solely as qualitative indicators

rather than physically realistic residual stresses. The study provides a structured thermo-elastic FEM and design-of-

SMAW numerical studies, offering practical insight into parameter screening for thermal and distortion control in

Keywords: Finite Element Method (FEM); Goldak’s double ellipsoidal model; SMAW; Solid Mechanics; Thermal

distribution.

1. Introduction. - Welding is one of the most widely used fabrication processes for permanently joining metallic

components in structural, pressure vessel, shipbuilding, and repair applications. In fusion welding processes, the joint

is formed by localized melting of the base (parent) material with or without the addition of a consumable filler metal,

followed by solidification to create a welded joint or weldment [1], [2]. The selection of welding consumables is

typically guided by compatibility with the parent materials in order to achieve acceptable metallurgical integrity and

workpiece, generating the heat required for melting the base metal and filler material. The decomposition of the flux

coating produces shielding gases and slag, which protect the molten weld pool from atmospheric contamination such

as oxygen and hydrogen, thereby reducing defects such as porosity and cracking [2–4]. A schematic representation of

the SMAW process and its associated heat source modeling framework is shown in Fig. 1. The figure illustrates the

interaction between the welding arc, consumable electrode, base metals, and the implementation of the moving heat

source within the finite element domain.

In recent decades, finite element modeling (FEM) has emerged as a powerful tool for analyzing welding processes,

offering detailed insight into transient temperature fields, deformation behavior, and stress development that are

difficult to measure experimentally. Numerous studies have investigated the effects of welding parameters on similar

and dissimilar materials using both experimental and numerical approaches.

Table I summarizes representative experimental and numerical studies investigating the influence of welding

parameters on thermal, mechanical, and metallurgical responses for various arc welding processes and materials [4–

40].

Across these studies, welding current is consistently reported as the dominant parameter governing heat input, with

higher currents leading to increased peak temperatures, deeper penetration, and enhanced hardness or tensile strength

in carbon and structural steels [4, 14, 18–24, 33]. Welding voltage primarily influences arc stability and bead geometry,

indirectly affecting thermal distribution and residual stress development [3, 17, 20]. In contrast, welding travel speed

is repeatedly shown to act as a controlling parameter for heat input density, where increased speed reduces peak

However, a careful examination of the existing literature reveals two important gaps. First, while extensive work exists

on SMAW of carbon steels, stainless steels, and aluminum alloys, numerical investigations focusing specifically on

dissimilar structural steel combinations remain limited. Second, although response surface methodologies (RSM) and

design of experiments (DOE) techniques have been successfully applied to welding processes, their integration with

three-dimensional transient thermo-mechanical FEM for SMAW remains relatively underexplored, particularly for

dissimilar steel joints.

which include S355J2+N and ASTM A572 Gr.50 structural steel plates. The filler material has been assumed to be one

of the base metals i.e., S355J2+N. Table II shows the material properties and chemical composition of metals. The

material properties were adopted from published literature and standard material databases commonly used in

numerical welding simulations [36], [37], [40]. The thermal conductivity and specific heat capacity were adopted from

the standard steel material library available in COMSOL Multiphysics and commonly used literature sources. At the

same time, density values were taken from experimentally reported ranges for the selected steels. In the present study,

all thermal and mechanical properties were assumed to be temperature-independent. This simplification was adopted

to focus on the comparative influence of welding parameters on thermal distribution and deformation, while

maintaining reasonable computational efficiency. Although temperature-dependent properties are known to influence

residual stress development, their inclusion was beyond the scope of the current thermo-elastic framework.

0.030

1.03

0.40

The joint geometry of the dissimilar metals is shown in Figure 2. As per ISO-9692, the joint preparation of structural

steel plates was carried out on AutoCAD 2021 and 3D design was made on SolidWorks 2016.

The 2D model was designed keeping in view the recommended root gap, root face, material thickness, and bevel angle.

(Figures II(a) and II(b)) shows that the geometry consists of a root gap of 3 mm, a root face of 3 mm, and an included

Gaussian distribution of power density and offers versatility to both deep and shallow penetration welds. The heat

Likewise, for the rear quadrant:

where, x, y, and z are the local spatial coordinates.

where V is the Voltage (V), I is the current (A), and η is the thermal efficiency (%).

The product of the voltage (V), current (I), and thermal efficiency (η), is typically 80% for SMAW, which means that

power provided by the welding source is 80% converted to the thermal energy required for welding. ν is the welding

The thermal analysis of the 3D model involves the most important factor known to be the conservation of energy.

The governing equation related to transient heat transfer analysis in welding is denoted by (Equation [3]) [47].

vector, Q is the internal rate of heat generation, x, y, and z are the coordinates in the reference system, and t is time.

It is assumed that there will be radiation losses from the outer surface of the plates by both, convection, and

radiation. The heat losses will be prominent around and in the weldment via radiation whereas the area away from

the weld zone will experience heat loss through convection [48], [49]. Hence, a combined heat transfer coefficient is

The parameters in the 3D double ellipsoidal model are given in the following Table III and the welding parameters in

Table IV. Goldak’s double ellipsoidal 3D heat source model is validated with the experimental results obtained by

Christensen et al [50].

2.3 Design of Experiments (DOE). - The excessive current and voltage during the welding process may induce stresses

numerical simulation. So, the simulation tool for analysis and optimization of SMAW process parameters is to be used.

Therefore, a 3D simulation of weld geometry with modules coupled (Heat transfer with Solid Mechanics) in COMSOL

Multiphysics 5.5 simulation software is built for the present study.

The Box-Behnken Design (BBD) is a form of response surface methodology (RSM) that requires at least three levels

to run a single experiment. In this study, the three-level-three-factor BBD technique was applied to obtain the best

combination of welding variables for the sound quality of the weld [52], [53], [54], [55], [56]. Table V represents the

chosen welding variables along with their levels.

0

0.003

responses, consistent with the use of log-transformed linear models [61–64].

The low R² value for Td indicates that a first-order log-linear model is insufficient to fully capture deformation

behaviour, which is influenced by geometric stiffness and boundary effects beyond primary process parameters. The

ANOVA results indicate that welding current exhibits the strongest statistical influence on T_max, as evidenced by

the lowest p-value, followed by welding speed and voltage. For Td, the p-values are comparatively higher, indicating

weaker explanatory power. This aligns with the sensitivity considerations described widely in welding DOE literature

interpreted as parametric trends rather than optimized welding conditions.

3.2 Thermal Response. - Figures 10(a) and 10(b) illustrate the maximum temperature variation along the weld line (x-

axis) and through the depth (z-axis). The temperature rises rapidly once the arc initiates, reaches a peak sufficient for melting

and fusion, and fluctuates slightly along the x-direction due to the evolving heat-sink effect of the surrounding base metal.

Along the z-axis, the temperature decreases with depth as heat is conducted away from the active fusion zone. These thermal

cycles govern melting, fusion, and the subsequent development of distortion.

The thermal expansion and contraction associated with the heating and cooling cycle induce elastic strain fields, which

are represented by the elastic von Mises indicator (Res_Str). As discussed earlier, this quantity does not represent true

residual stress but provides a qualitative map of regions experiencing higher thermo-elastic loading during welding.

Distortion (Td) reflects the cumulative effect of these elastic strains and the steep temperature gradients in the joint.

Minimizing weld volume, optimizing heat input, and controlling inter-pass timing are common methods for reducing

reproduced the characteristic features of SMAW thermal behaviour reported in the literature.

Figure IV shows the transient thermal distribution as the heat source travels along the weld line. The predicted peak

temperatures exceed the melting range of the steel (~1425–1500 °C), followed by rapid cooling once the heat source

moves forward. This behaviour is consistent with established SMAW thermal cycles, where peak temperatures remain

concentrated in the fusion zone and decrease sharply within a few millimeters of the weld centreline [44–46], [48–50].