Experimental and numerical analysis of temperature distributions in SA 387 pressure vessel steel during submerged arc welding

Nomenclature

a, b

geometric parameter of double ellipsoid

c

specific heat

c _f, c _r

dimensions of the front and rear semi-ellipsoidal heat source

f _f, f _r

fractions of heat flux deposited, corresponding to the front and rear quadrants

h

convection coefficient of heat transfer

I

current applied to weld

k _x , k _y

thermal conductivity in x and y directions

q _in

rate of internal heat generation

q _out

rate of latent heat generation

t

time

T

temperature

T _∞

ambient temperature

TC _n

thermocouple location at n

Q

heat input

V

voltage applied to weld

ε

emissivity, engineering strain

η

efficiency of the welding process

ρ

density

σ

Stefan–Boltzmann constant, stress

1 Introduction

The design and manufacturing of pressure vessels for high-temperature applications are of paramount importance in ensuring the safety and reliability of industrial processes. These vessels play a critical role in containing substances under extreme thermal conditions, where any structural failure could lead to catastrophic consequences. Precision in design and adherence to rigorous manufacturing standards are essential to prevent material degradation, maintain structural integrity, and guarantee the longevity of these vessels, safeguarding both industrial operations and human safety.

SA 387 Grade 11 Class 2, a steel grade designed for use in pressure vessels under elevated temperature conditions, finds extensive application across various industrial sectors. Its effectiveness is particularly pronounced in the oil, gas, and petrochemical industries, where it excels in storing liquids and gases at elevated temperatures. The elevated chromium levels in this material confer remarkable resistance to both corrosion and oxidation, a vital attribute in applications involving sour gases [1]. In a multitude of industries, the SA 387 GR.11 CL.2 Plate is the preferred choice for elevated temperature service due to its capability to endure high operational temperatures at 600°C. This plate’s high chromium content imparts outstanding resistance to oxidation and corrosion, making it indispensable for sour gas applications. Its precise manufacturing techniques within the industry result in a product endowed with exceptional qualities, making it a staple in global industries across diverse applications. These qualities encompass impressive tensile strength, robustness, precise dimensional accuracy, impeccable surface finishes, weldability, extended service life, flexibility, durability, and the ability to withstand substantial loads. Furthermore, it exhibits full resistance to pitting, crevice corrosion, and stress corrosion cracking [2]. The chemical composition and the mechanical properties of the steel SA387 are given in Tables 1 and 2, respectively.

Submerged arc welding (SAW) is a widely employed process for coalescing metals through the application of electric arcs and the use of granular flux to shield the arc. SAW is particularly prevalent in heavy fabrication industries, although its limited mobility necessitates a relatively fixed workstation setup. The process involves the continuous deposition of flux to protect the arc and the workpiece, with the flux often serving to augment alloying elements introduced by the filler wire. SAW holds immense significance in the fabrication of pressure vessels.

This specialized welding technique involves immersing the welding arc and the joint in a granular flux, creating a controlled environment that offers several crucial advantages for pressure vessel construction. These are listed in the following.

1.6 Code and standard compliance

Many pressure vessels are designed and constructed to adhere to rigorous industry codes and standards, such as the ASME Boiler and Pressure Vessel Code. SAW has a reputation for consistently producing high-quality welds and facilitates compliance with these regulations, ensuring that the vessels meet safety and performance requirements.

The described process operates within inherent constraints on mobility, encompassing several key elements. First, movement along the weld line is essential, requiring the welding head, gun, nozzle, and associated components to traverse either longitudinally or radially, often with the workpiece positioned flat or horizontally. Additionally, flux application and delivery occur from a fixed location, representing a critical aspect of the operation. Figure 1 offers a schematic representation and an explanatory overview of the process. The figure illustrates a single arc and provides a cutout view displaying the completed weld.

Figure 1

Schematic representation of the SAW process.

From the uppermost region extending down to the weld interface, the composition consists of distinct layers. At the uppermost layer lies the residual flux, which remains unconsumed during the welding process, serving solely to provide comprehensive coverage over the underlying weld zone. Directly beneath this protective blanket of flux lies the solidified slag, resulting from the fusion of the flux layer during the welding operation. Finally, the actual weld is situated below the slag layer. It is noteworthy to observe the precise positioning of the welding head, the flux feed hopper, and the direction of the welding operation. The power supply and electrode wire are seamlessly guided through the welding head, while the flux is effectively dispensed through the dedicated hopper mechanism [3].

In summary, SAW is of supreme importance in the fabrication of pressure vessels due to its ability to deliver high-quality, efficient, and reliable welds. Its capacity to maintain weld integrity, reduce defects, and adhere to industry standards makes it an indispensable welding technique for ensuring the safety and functionality of pressure vessels across various critical applications.

This study delves into the transient thermal characteristics of SA387-Gr.11-Cl.2 steel during SAW and investigates their temporal evolution. Some recent numerical and experimental efforts have been attempted [4–35], and Sepe et al. reviewed some of these findings in their work [36]. Temperature distribution can provide information about residual stress that may lead to material failures under unexpected operational conditions. To obtain accurate temperature distribution, one has to perform experiments that are time consuming and costly. To authors’ knowledge, the finite-element analysis (FEA) procedure has been applied for the first time using Goldak’s double ellipsoidal method on SA 387 steel. For this matter, an ANSYS Parametric Design Language (APDL) code is written to incorporate Goldak’s formulation. One can utilize the findings of this research without undergoing costly experiments. The current research presents a combination of meticulous experimental measurements and a developed numerical FEA characterizing the thermal behavior of SAW joints in this critical material. It addresses well the nonlinearity of complex thermal dynamics inherent to this material during the welding process. Numerical finite element (FE) simulations of temperature distributions, incorporating a 3D Goldak’s double ellipsoid heat source model integrated into the general-purpose FE software ANSYS, facilitated by a custom-developed code in APDL language. Subsequently, experimental measurements are conducted with various thermocouples (TC) strategically positioned on the specimen, enabling a comprehensive comparison between experimental and numerical data.

2 Materials and methods

In our experimental investigation, we utilized ASME SA 387 Grade 11 Class 2 steel as the base material. This steel grade is commonly employed in applications requiring resistance to elevated temperatures, notably within industries such as oil, gas, and petrochemicals. Two plates, both composed of the aforementioned material, were subjected to welding. The specimen dimensions measured 100 mm in length, 100 mm in width, and 8 mm in thickness, as depicted in Figure 2.

Figure 2

Workpiece dimensions.

Single-pass SAW was performed on a fully automatic welding machine, with welding parameters such as current, voltage, root gap, welding time, and welding speed carefully controlled. To identify the optimal current value, we conducted experiments with current as the variable, while maintaining voltage, welding speed, and the length of stick-out at constant values. Initial experiments involved a series of trial-and-error tests with varying current values, specifically 430, 530, 560, and 600 A. Subsequently, the most suitable current value for welding was determined to be 600 A. To determine the most suitable current value, a series of experiments were conducted with varying current levels. The selected welding parameters for the experiments are detailed in Table 3.

Sample parts were initially cut using a plasma-cutting machine and subsequently subjected to thorough cleaning through grounding. Before welding, a preheating process was applied to the area adjacent to the weld zone, maintaining it within a specified temperature range referred to as the preheating temperature. This temperature varies based on factors such as the chemical composition of the base metal, heat input, hydrogen diffusion, and base plate thickness. Typically, the preheating temperature range for SA387 GR 11 Class 2 steels falls between 150 and 200°C [37,38]. Preheating was accomplished using a localized heat treatment unit and electrical resistances. To prevent any unintended movement of metals during the welding process, the parent metal was securely clamped, and welding backing plates were affixed at the beginning and end of the component, as depicted in Figure 3.

Figure 3

Clamping of the workpiece and setup of the SAW process.

Before initiating the SAW process, the test plate pair was firmly attached using gas tungsten arc welding (GTAW) from both upper and lower sections to prevent sample displacement during welding. For tack welding and weld-backing-plate placement, the GTAW process was executed using an Esab Origo Tig 3001i TIG welding machine with a power source of 300 A. A filler metal ER80S-B2 with a 2.4 mm diameter was employed for the GTAW process. The gas composition consisted of 99.997% argon, delivered at a flow rate ranging from 11 to 16 L·min⁻¹. The SAW welding machine used in the experiments is shown in Figure 4.

Figure 4

SAW machine utilized in the experiments.

Backing material, situated at the root of a weld joint, serves the purpose of supporting molten weld metal and facilitating complete joint penetration. To protect the bottom surface of the workpiece from damage, a ceramic protector was affixed to it. SAW was performed utilizing a 1,000 A constant potential power source, specifically the Miller Sub arc DC 1000. A filler metal with a 3.2 mm diameter, conforming to AWS A5.23: F8P2-EB2-B2, was used, along with Esab Flux 10.62 agglomerated fluoride-basic flux [39]. The chemical composition of the filler metal is detailed in Table 4.

Temperature data were recorded using K-type TC wires, which are composed of chrome/nickel aluminum TC wire insulated with high-temperature glass braid. These measurements were facilitated by a Honeywell eZtrend paperless recorder equipped with six directly connected analog inputs. To ensure accurate measurements, the TC wires were affixed directly to the workpiece using a “TC Attachment Unit.” Five TCs were strategically placed for temperature measurement, with their corresponding attachment points depicted in Figure 5, while the geometric specifics are provided in Figure 6.

Figure 5

TCs attached to the workpiece.

Figure 6

Geometric data of TC measurement points.

Among these, TC1, TC4, and TC5 were situated 15 mm away from the weld centerline of the weld joint, while TC2 and TC3 were positioned 10 mm in the x-direction away from TC1. The specific coordinates for the placement of these TCs are referenced from the chosen coordinate system, which was centered at the midpoint of the part.

Access to the recorded data stored in the Digital Honeywell Recorder was facilitated with the Pro version of TrendViewer, an application developed by Honeywell. These data were then conveniently made accessible in MS Excel format for analysis and subsequent processing.

2.1 Numerical model development for FEM

In the domain of arc welding, the distribution of temperature plays a pivotal role in influencing residual stress, distortion, and the strength of a welded structure, thereby affecting the overall quality of the resultant structure. Consequently, understanding the temperature evolution during welding has become a crucial research focus in recent decades. The utilization of mathematical models to predict welding temperatures has gained prominence, given the often prohibitively expensive nature of experimental predictions. Among the various mathematical models, numerical modeling, specifically FEA, has emerged as the preferred industry method for simulating and monitoring welding processes due to its computational efficiency and speed [40].

In this study, we developed an FEA model using ANSYS 2020 R2, incorporating the Goldak double ellipsoidal heat source model to predict the thermal cycle of SAW accurately. The primary objective of this research is to create an FEA model capable of reliably predicting the SAW thermal cycle with high accuracy compared to experimental results. The numerical simulation of the welding process was conducted through transient thermal analysis within ANSYS 2020 R2. The Goldak double ellipsoidal formulation was coded using the APDL to simulate characteristics of the SAW process applied to high-temperature resistive, anti-corrosive pressure vessel steel.

In the preprocessing phase of FEA, the material properties essential for accurate modeling can be categorized into two groups: thermal properties and physical properties of SA 387 GR 11 Class 2 steel [40]. Thermal properties include thermal conductivity (W·m⁻¹·°C) and specific heat (J·kg⁻¹·°C), while physical properties encompass density (kg·m⁻³), Young’s modulus (GPa), and thermal expansion (W·m⁻¹·°C), as shown in Table 5. It is important to note that these material properties were assumed to vary with temperature during the heating and cooling cycles. When data were not available, an extrapolation procedure was utilized.

Table 5

Thermal properties of SA 387Gr 11 Cl.2 [41]

Temp.	Density	Thermal conductivity	Specific heat	Enthalpy
(°C)	(kg·m−3)	(W·m−1·°C)	(J·kg−1·°C)	(J·m−3 × 108)
20	7,750	41	470	0.1
100	7,750	40.6	487	3.6
200	7,750	40.1	529	7.2
300	7,750	38.7	564	11
400	7,750	36.8	605	15
500	7,750	34.8	666	19.8
600	7,750	32.8	760	25
700	7,750	29.1	1,008	30
800	7,750	27.5	803	37
900	7,750	24	650	45
1,000	7,750	20.1	650	50
1,100	7,750	15.8	650
1,200	7,750	11.1	650
1,300	7,750	6
2,500				90

Acquiring precise temperature-dependent material properties data from the literature proved to be challenging. Consequently, for this study, the material properties of SA 387 were adopted as provided by the ASME Boiler and Pressure Vessel Code, specifically ASME BPVC.II.D.M-2021. The SA 387 GR 11 Class 2 material in question is characterized as 1¼Cr–½Mo carbon–molybdenum steel.

A three-dimensional FE model was developed to address the engineering challenge at hand. The model focused on simulating SAW of single-sided single-pass butt joints, and it was created and analyzed using Space Claim 2020 R2 and ANSYS Mechanical Workbench. The model’s accuracy is contingent on parameters such as element size, node count, and time step size. Increasing the number of nodes not only enhances model precision but also extends the processing time.

In this thermal analysis, the chosen element type was SOLID90, as shown in Figure 7. SOLID90 represents an advanced iteration of the 3D eight-node thermal element, SOLID70. This element comprises 20 nodes, each with a single degree of freedom related to temperature. The use of 20-node elements with compatible temperature shapes is particularly well suited for modeling curved boundaries. Consequently, the 20-node thermal element finds applicability in both 3D steady state and transient thermal analyses. The FE model was composed of 358,743 nodes and 80,800 elements, with an element size of 0.001 m. The isometric view of the meshed model is shown in Figure 8.

Figure 7

Nodal representation of SOLID90 thermal element.

Figure 8

Isometric view of the meshed model.

Boundary conditions encompass a set of loadings, constraints, and contact conditions that define the simulation’s state in a particular design configuration. Before initiating transient thermal and static structural analyses, these boundary conditions must be systematically applied to the model through a sequence of experimental procedures. Within this set, several loading and constraint conditions are expressed mathematically. In thermal analysis, the boundary conditions involve aspects such as convection and specific heat flux, while static structural analysis incorporates forces, moments, and displacements [42].

Heat transfer mechanisms are indeed commonly categorized into three main modes: conduction, convection, and radiation, as shown in Figure 9. The heat flow at the weld joint plays a critical role in the melting process. A substantial amount of heat at the source is emitted through radiation from the high-temperature region’s surface and the melt pool’s surface. Simultaneously, a significant portion of the heat required for melting is conveyed to the material through processes of conduction and convection [43].

Figure 9

Heat transfer modes during the welding process.

In thermal analysis, the transient temperature field (T) within the welded component is a function of time and spatial coordinates (x, y). This field is governed by a non-linear heat transfer equation:

(1) ∂ ∂ x k x ∂ T ∂ x + ∂ ∂ y k y ∂ T ∂ y + q in + q lat = ρ c ∂ T ∂ t ,

where q _in represents the rate of internal heat generation, and q _lat denotes the rate of latent heat generation. The coefficients of thermal conduction in the x and y directions are represented as k _x and k _y , respectively. Additionally, c signifies the specific heat, and ρ represents the density of the plate material. In this model, we accounted for the latent heat released during phase transformations. As a result, an enthalpy formulation was adopted. Enthalpy encapsulates all the necessary data for calculating latent heat release, with the exception of thermal conductivity and density, as documented in previous research [44].

Heat transfer during welding involves the initial application of the heat source to the welded component, followed by cooling through a combination of convection and radiation. In this analysis, we did not consider forced convection. The heat flux on the surfaces of the welded plate due to convection and radiation is expressed by the following equations:

(2) q con = h ( T − T ∞ ) ,

(3) q rad = ε σ ( T 4 − T ∞ 4 ) ,

where T _∞ represents the ambient temperature, and T signifies the boundary temperature exposed to the environment. The Stefan–Boltzmann constant, denoted as σ (5.67 × 10⁸ W·m⁻²·°C⁻⁴), and ε, which represents emissivity, were included in the equations. The convection coefficient was defined as h = 100 W·m⁻² for all surfaces of the plate, except for the top surface, which was considered insulated when the welding torch was directly above it. All analyses were conducted, taking into account the temperature-dependent thermal properties of the base metal. The model’s formulation was based on the following assumptions:

1. The initial temperature of the test plate was set at 150°C.

2. The ambient temperature of the weldments was maintained at 20°C.

3. Thermal properties of the material, such as specific heat, enthalpy, and conductivity, are temperature-dependent, as shown in Table 5.

4. Physical properties of the material, including elastic modulus and thermal expansion, are temperature-dependent.

5. Density is a constant value of 7,750 kg·m⁻³.

6. The convection heat transfer coefficient was set at 10 W·m⁻²·°C, and for radiation, an emissivity value of 0.9 was used.

7. The top face and side surfaces of the welded part were taken as insulated. Heat losses due to radiation and convection were considered only for the bottom surface of the welded parts.

8. Forced convection was not taken into account.

9. Element birth and death were not considered.

Boundary conditions for transient thermal analysis are shown in Figure 10.

Figure 10

Boundary conditions for transient thermal analysis.

2.2 Moving heat source model

The modeling of a moving heat source represents an atypical transient thermal process. In our approach, the moving heat source is modeled using ANSYS 2020 R2 with APDL codes. The objective is to move the heat source continuously at minor increments while maintaining constant heat energy. During this dynamic process, the center of the heat source changes over time. This is achieved by modifying the parameters within the function that describes the heat source’s locations as a function of time. To develop the temperature distribution in our analysis, we employ Goldak’s double ellipsoidal heat source model, as depicted in Figure 11 [45]. This approach successfully represents the heat flux generated by the welding torch in SAW. A general FE solution scheme for heat transfer problems in the welding process is illustrated in Figure 12 [46], and accordingly, a transient temperature simulation has been performed by the authors to show numerical stability and experimental validation purposes [39].

Figure 11

Schematic diagram for Goldak’s double ellipsoid model [45].

Figure 12

Flow diagram for thermal FEM procedure [46].

The power density within our developed model is distributed throughout a volume, spanning both the front and rear quadrants of the heat source is

(4) q ( x , y , z ) = 6 × ( 3 ) × f × ɳ × Q a × b × c × π × π × exp − 3 x 2 a 2 − 3 y 2 b 2 − 3 z 2 c 2 .

The heat flux equation for the heat source model or welding arc in the front quadrant is expressed as follows:

(5) q ( x , y , z ) = 6 × ( 3 ) × f f × ɳ × Q a × b × c × π × π × exp − 3 x 2 a 2 − 3 y 2 b 2 − 3 z 2 c f 2 .

The heat flux equation for the heat source model or welding arc in the rear quadrant is as follows:

(6) q ( x , y , z ) = 6 × ( 3 ) × f r × ɳ * Q a × b × c × π × π × exp − 3 x 2 a 2 − 3 y 2 b 2 − 3 z 2 c r 2 ,

where, a, b, c _f, and c _r represent the geometric parameters, where c _f and c _r denote the dimensions of the front and rear semi-ellipsoidal heat sources, and f _f and f _r represent the fractions of heat deposited, corresponding to the front and rear quadrants’ heat apportionment of the heat flux. It is important to note that f _f + f _r equals 2. Q represents the heat input, while x, y, and z are the coordinates of the heat flux. Additionally, η stands for the efficiency of the welding process [47].

The Goldak double-ellipsoidal model is employed to characterize the volumetric heat flux in arc-welding processes. This model is renowned for its widespread use and popularity in simulating arc-welding procedures. To implement the Goldak double ellipsoid model within the ANSYS environment, specific APDL commands are required.

f _f and f _r parameters are calculated using the following formulas:

(7) f f = 2 × c f c f + c r ,

(8) f r = 2 × c r c f + c r ,

(9) f f + f r = 2 .

In the experiment conducted for this study, the energy input rate Q (I = 600 A, V = 31 V, η = 0.8) and the welding speed were set at 15,000 W and 0.01 m·s⁻¹, respectively. Through an examination of the weld part and cross-section, as illustrated in Figures 12–15, heat source parameters were determined as follows: a = 10 mm, b = 8 mm, c _r = 10 mm, c _f = 30 mm (3 × c _r), f _f = 0.5, and f _r = 1.5.

Figure 13

Goldak’s double ellipsoidal parameters view on the test plate.

Figure 14

Goldak’s double ellipsoidal parameters: the view of bead width (value for parameter “a”).

All measured parameters for the double ellipsoidal model are presented in Table 6. These values were utilized in the development of the FEM code. Table 7 provides a summary of the welding parameters used in the SAW process, which are necessary inputs for the transient FE solution. Typical efficiency values for various welding processes are listed in Table 8, with SAW being reported as 91–99% [38]. However, during the numerical integration of FE iterations, the solutions exhibited divergence, indicating numerical instability. This challenge was resolved by reducing the efficiency to a level of η = 0.8, resulting in convergent solutions in the FE calculations. Numerical instability may arise due to high heat input. For this reason, we take 0.8 efficiency values in the calculations of heat input. Heat input is described by efficiency × voltage × current. Numerical results and experimental results give near values at this efficiency.

Table 6

Measured model parameters used in FEA (all dimensions are in mm)

a	b	c f	c r	f f	f r
10	8	10	30	0.5	1.5

Table 7

Welding parameters used in SAW

Power (A)	600
Voltage (V)	31
Heat input Q = I × V × ɳ (W)	15,000
Progression speed (mm·s−1)	10

Table 8

Efficiency ranges for various welding processes [38]

Welding process	ɳ
GTAW Ar, steel	25–75
GTAW He, Al	55–80
GTAW Ar, Al	22–46
SMAW steel	66–85%
GMAW Ar, steel	66–70
SAW steel	91–99

Figure 15

Goldak’s double ellipsoidal parameters view on test plate: a, c _r, and c _f.

3 Results and discussion

The primary objective of this study is to develop a 3D-FEA model capable of predicting the SAW thermal cycle with higher accuracy compared to experimental work. Transient temperature distribution analysis was conducted using ANSYS 2020 R2 software. The 3D FE model was executed on an Intel(R) Core(TM) i7-10750H CPU @ 2.60 GHz with 16 GB RAM. The analysis required approximately 20 h of CPU time. Predicted temperatures were then compared with temperatures obtained from experiments. In the experimental phase, temperature distribution was measured using chrome/nickel aluminum TCs with a diameter of 0.71 mm. Temperature history during the welding process was recorded using a Honeywell Eztrend temperature recorder, and the recorded temperature data were exported to Excel for analysis.

The FEM simulation results depicting the progression of temperature distributions at the top of the plate, where welding was performed along the welding center direction, are presented in Figures 16–20. These figures correspond to elapsed times of 3, 6, 10, 30, and 250 s, respectively.

Figure 16

Temperature distribution at the top face after 3 s.

Figure 17

Temperature distribution at the top face after 6 s.

Figure 18

Temperature distribution at the top face after 10 s.

Figure 19

Temperature distribution at the top face after 30 s.

Figure 20

Temperature distribution at the top face after 250 s.

To investigate the temperature profile through the thickness of the workpiece, a midsection at the weldline was targeted. Figures 21–23 show the temperature distributions after 6, 10, and 250 s, respectively.

Figure 21

Temperature distribution at the middle of the weld line after 6 s.

Figure 22

Temperature distribution at the middle of the weld line after 10 s.

Figure 23

Temperature distribution at the middle of the weld line after 250 s.

Figures 24 and 25 depict the top and bottom faces of the welded specimen, respectively. The welding direction, the TC locations, and the welding parameters are indicated on the top face.

Figure 24

Top face of the welded specimen.

Figure 25

Bottom face of the welded specimen.

The sample part was preheated to approximately 150°C before welding. At the start of welding, the temperatures of TCs (TC1, TC2, TC3, TC4, and TC5) were recorded as 129.4, 158.7, 157.2, 139, and 153.1°C, respectively. Before the welding started, the heating apparatus was removed from the workpiece, which resulted in some temperature drops on the part.

Each TC value obtained from experiments was compared with the corresponding node temperature in FEM, as shown in separate graphs in Figures 27–31.

Figure 26

Experimental data for temperature (vertical) vs time (horizontal) graph for each TC point.

Figure 27

Numerical FEM data for temperature (vertical) vs time (horizontal) graph corresponding to each TC location.

Figure 28

Comparison of temperature vs time history for the experimental and the FEM results at TC1.

Figure 29

Comparison of temperature vs time history for the experimental and the FEM results at TC2.

Figure 30

Comparison of temperature vs time history for the experimental and the FEM results at TC3.

Figure 31

Comparison of temperature vs time history for the experimental and the FEM results at TC4.

The experimental and FE (FEM) results for temperature history belonging to each of the five-TC locations are shown in Figures 26 and 27, respectively.

The temperature distribution recorded during the experimental work is compared with the results obtained from the FEA. Since a cumulative comparison graph involving ten curves (five for the experimental, and another five for the numerical results) would make the display cumbersome, individual comparisons are opted for each TC location. These comparisons are shown in Figures 28–32 for the TC points of TC1, TC2, TC3, TC4, and TC5, respectively. A strong correlation between the two sets of data is observed, confirming the capability of the numerical model in predicting temperature profiles during SAW of SA 387 Grade 11 Class 2 steel.

Figure 32

Comparison of temperature vs time history for the experimental and the FEM results at TC5.

Figures 26 and 27 illustrate the temperature variations over time for specific points. As the heat source approaches a point, its temperature increases, and as the heat source moves away, the temperature gradually decreases. Notably, at points 1, 4, and 5, located near the heat source, the temperatures are higher than those at points 2 and 3. Additionally, the temperature at point 2 is higher than that at point 3. Overall, a good agreement is observed between the predicted and experimental temperatures.

At point 1, as welding commenced, TC1 recorded a temperature of 129.4°C in the experimental work. The maximum temperature of 591.9°C was reached at 27 s, with the TC measuring the maximum value for the subsequent 4 s. According to the predicted temperature obtained from FEA at the node corresponding to TC1, the maximum temperature was 603.34°C at 20 s. This time difference is attributed to the response time of the recorder, which measures temperatures with a delay of 4–5 s. At 250 s, the temperature on the specimen was 435.3°C, while the predicted temperature by FEA was 382.17°C. Thus, for point 1, there is an observed difference of approximately 2% at the maximum temperature and approximately 13% at 250 s.

At point 2, when welding began, TC2 recorded a temperature of 158.7°C in the experimental work. The maximum temperature of 462.5°C was reached at 120 s, with the TC measuring the maximum value for the next 6 s. According to the predicted temperature obtained from FEA at the node corresponding to TC2, the maximum temperature was 452.43°C at 60 s. At 250 s, the temperature on the specimen was 422.6°C, while the predicted temperature by FEA was 381.8°C. Thus, for point 2, there is an observed difference of approximately 2% at the maximum temperature and approximately 10% at 250 s.

At point 3, when welding began, TC3 recorded a temperature of 157.2°C in the experimental work. The maximum temperature of 434.4°C was reached at 149 s, with the TC measuring the maximum value for the next 14 s. According to the predicted temperature obtained from FEA at the node corresponding to TC3, the maximum temperature was 423.94°C at 108 s. At 250 s, the temperature on the specimen was 410.0°C, while the predicted temperature by FEA was 381.49°C. Thus, for point 3, there is an observed difference of approximately 2.4% at the maximum temperature and approximately 7% at 250 s.

At point 4, when welding began, TC4 recorded a temperature of 139.0°C in the experimental work. The maximum temperature of 595.2°C was reached at 29 s, with the TC measuring the maximum value for the next 3 s. According to the predicted temperature obtained from FEA at the node corresponding to TC4, the maximum temperature was 606.58°C at 23 s. At 250 s, the temperature on the specimen was 425.1°C, while the predicted temperature by FEA was 400.09°C. Thus, for point 4, there is an observed difference of approximately 2% at the maximum temperature and approximately 10% at 250 s.

At point 5, when welding began, TC5 recorded a temperature of 153.1°C in the experimental work. The maximum temperature of 589.5°C was reached at 27 s, with the TC measuring the maximum value for the next 5 s. According to the predicted temperature obtained from FEA at the node corresponding to TC5, the maximum temperature was 599.25°C at 18 s. At 250 s, the temperature on the specimen was 446.2°C, while the predicted temperature by FEA was 380.89°C. Thus, for point 5, there is an observed difference of approximately 1% at the maximum temperature and approximately 15% at 250 s.

Table 9 exhibits the temperatures obtained from the experiments and the FE numerical solutions. It reveals inconsiderable deviations at the peak temperatures and minute differences at the end of the welding process.

Numerical FEA shows satisfactory results compared to experimental test results. Therefore, this model can be applied to predict thermal cycles for different welding parameters and materials. The effect of cooling rates on joint performance and residual stress determination can be investigated.

4 Conclusions

This study examines a comprehensive exploration of temperature distributions during SAW of SA 387-Gr.11-Cl.2 steel. We have successfully characterized the thermal behavior of SAW joints through a combination of meticulous experimental measurements and developed numerical FEA. For welding an 8 mm thick plate with one pass, the suitable parameters were found to be 600 A current, 31 V voltage, and 10 mm·s⁻¹ welding speed. The development of an FEA model using ANSYS software incorporated 3D Goldak’s double ellipsoidal moving heat source model. The parameters for energy input were determined from the experiments and were incorporated into the model. Temperature profiles at specific points revealed a strong correlation between numerical predictions and experimental measurements. Any deviations between the two sets of data at maximum temperatures and the end of the welding process were thoroughly discussed. An average variation of 1.88% at peak temperatures and 11.8% at completion time was observed between the results. The experimental cooling periods were found to be slower than predicted by FEA. The results showed the temperature distribution at various time steps, illustrating the transient nature of the welding process. The findings demonstrate the accuracy of the numerical model in predicting temperature profiles during welding, providing valuable insights for understanding the HAZ, optimizing welding parameters, and controlling the microstructure and mechanical properties of welded structures. In addition to this, this work may be further extended by exploring the effect of cooling rates on joint performance and residual stresses.