1. Introduction
The tube to tubesheet joints are extensively used in fabrication of critical nuclear reactor components such as end shield, shell and tube type heat exchanger, steam generator and condenser. These joints are crucial for separating fluids between the tube side and shell side, operating at different temperatures and pressures. Their integrity is vital for equipment availability, performance, and safety1,2).
As the nuclear reactor components increase in size and capacity, the number of tube-to-tubesheet joints grows, amplifying their importance. Failures in these joints can lead to significant economic losses, with documented cases over the last decade highlighting common failure mechanisms like fatigue and stress corrosion cracking (SCC)3,4). For example, Liu et al.5) reported shell and tube heat exchanger failures due to high residual stresses from resonant vibrations, promoting fatigue cracks. Usman and Nusair6) attributed the collapse of a heat exchanger, which failed after three and a half months, to thermal fatigue and localized heating. Ahmad et al.7) attributed the failure at the left-hand side of the heat recovery area tube to thermal fatigue in their investigation of boilers at the Kapar power station in Malaysia. Abdullah et al.8) identified SCC in a gas plant heat exchanger due to substandard workmanship in the tube-to-tubesheet welds.
The connection of tubes to tubesheet primarily involves welding, expansion, or a combination of both process9). Expansion methods include mechanical rolling, explosive expansion and hydraulic expansion10). When employing the expansion method, the tube-to-tubesheet joints must not only establish a secure seal between the tube side and shell side fluids but also possess the strength to endure axial loads-a topic that has undergone thorough investigation11-13). While welding is widely used joining technique for its cost-effectiveness and simplicity, it introduces challenges due to the residual stresses formed in the welded joint14,15). The concentrated heat input and substantial constraints imposed by the tubesheet during the welding process contribute to these stresses14,15). Various welding techniques, such as Tungsten Inert Gas (TIG), Shielded Metal Arc Welding (SMAW), Electron Beam Welding (EBW), and Laser Beam Welding (LBW), result in different heat inputs per unit area. Consequently, the residual stresses within the welded joints are highly sensitive to the specific welding method and the number of welding passes employed. The potential development of cracks during the service life of these joints is significantly influenced by these residual stresses16-18). Therefore, the longevity, reliability, and safety of these joints hinge on the meticulous selection of the welding process and its associated parameters. Careful consideration of these factors is essential to ensure optimal performance and durability of tube-to-tubesheet connections in various industrial applications.
In the construction of a power plant components, two categories (Category-1 and Category-2) of tube-to-tubesheet welds play a pivotal role19), as illustrated in Fig. 1. Category-1, depicted in Fig. 1(a), is crafted through a combination of welding and rolling procedures for non-class-1 nuclear components. These joints have notable drawbacks: they lack full penetration in welding, volumetric examination is impractical, and they are susceptible to crevice corrosion if contact pressure between the tube and tube sheet relaxes.
Fig. 1
Tube and tubesheet joint (a) Catergory-1 type combination of welding and rolling joint (b) Catergory-2 type full penetration weld joint
Category-2, showcased in Fig. 1(b), designed for typical class-1 Nuclear Power Plant (NPP) components like end shields, steam generators, heat exchangers etc. and addresses the shortcomings of Category-1 joints20). These are full penetration welded joints between the tube and tubesheet, allowing for volumetric ultrasonic examination. Furthermore, the design eliminates crevices, making these joints resistant to crevice corrosion. Owing to these advantages, Category-2 joints are applied in class-1 NPP components such as the construction of end shields for pressure tube type nuclear reactor21,22).
The fabrication process for class-1 NPP components with tube-to-tubesheet joints involves welding a large number of tubes to a thick tubesheet. Traditionally, these joints are welded from the tube Inner Diameter (ID) side using a semi-automated TIG welding process. Non-destructive examinations (NDE) are also conducted from the ID side. The welding process comprises multiple weld passes, with liquid penetrant examinations (LPE) performed after each pass23). This meticulous procedure is repeated for all joints, consuming a significant amount of process time. Due to the fabrication occurring in multiple passes, radiographic examination of these joints is not feasible. Therefore, after the completion of welding, volumetric ultrasonic examination is carried out in both radial and longitudinal directions to ensure the integrity of the joints23).
The manufacturing time of these class-1 NPP components can be substantially reduced by employing a single-pass welding process like EBW and LBW. This streamlined approach not only accelerates the fabrication process but also presents several additional advantages. The single-pass EBW and LBW process eliminates the need for edge preparation, contributing to a more seamless and efficient workflow. Moreover, the adoption of a single-pass welding process opens up the possibility for both radiography and ultrasonic examination of the joint. This dual examination capability enhances the quality control measures, ensuring the integrity of the weld. Additionally, the reduced chances of defects in single-pass welding as compared to multiple-pass welding contribute to the overall reliability and durability of the joints.
The utilization of single-pass EBW and LBW in tube- to-tubesheet joints is anticipated to reduce residual stresses and the Heat Affected Zone (HAZ) due to lower heat input. However, there is a notable gap in the existing literature concerning a comprehensive comparison between multipass TIG welding and single-pass Electron Beam (EB)/Laser Beam (LB) welding. This study aims to fill this void by examining the relative decrease in residual stresses, HAZ, and distortion.
This work aims to bridge the literature gap by conducting two three-dimensional thermo-mechanically coupled Finite Element (FE) analyses using FE based software. The focus is on comparing multi-pass TIG welding and single-pass EB/LB welding, with heat input values sourced from literature. As a case study, the comparison has been carried out for tube-to-tubesheet joints in end shields of the Advanced Heavy Water Reactor (AHWR)24), a class-1 NPP component. These end shields are made of SS304L material and contain full penetration weld joints of tubes (168 mm outer diameter and 10 mm thickness) with an 80 mm thickness tubesheet. The same material SS304L has been considered in this current analysis.
The results obtained from this analysis will contribute to characterizing the operational advantages and reliability of tube-to-tubesheet joints fabricated using these two welding techniques, shedding light on their potential benefits in terms of residual stresses, HAZ, and distortion.
1.1 Summary of Previous Finite Element Modelling Approaches
Numerous studies have employed FE analysis techniques to characterize the distribution of residual stresses, HAZ, and distortion in welded joints. For example, Xu and Wang25) conducted an investigation into the residual stress of tube-to-tubesheet welded joints using a two-dimensional (2D) axisymmetric FE model. They observed that an increase in preheating temperature resulted in a decrease in the peak residual stress of tube-to-tubesheet welded joints, while axial and hoop stresses increased with the gap between the tube and tube hole. Additionally, the peak von-Mises stress was identified near the interface between the surface welding layer and base metals. Bhadra et al.26) explored the residual stress distribution in CO2 laser butt welding joints of AISI 304 steel, employing a three-dimensional (3D) FE model. Their findings indicated that transverse and longitudinal residual stresses were tensile in the weld and HAZ, transitioning to compressive stresses away from the weld. Furthermore, the transverse maximum stress was notably lower than the longitudinal maximum stress.
Suman and Biswas27,28) conducted a study investigating the impact of welding layer and preheating on the residual stress of creep strength-enhanced ferritic steel butt welding joints using a 3D FE model. Their observations revealed that a single-pass weld exhibited a stable variation of residual stress along the weld thickness, surpassing the performance of a multi-pass weld. Additionally, preheating was found to reduce the maximum longitudinal stress of the HAZ by 90%. In a different study, Al-Badour et al.29) utilized a 3D thermo-mechanical FE model to predict residual stress in tube-to-tubesheet welded joints for friction stir seal welding. The results indicated that the radial residual stress was compressive at the tube-ligament interface, enhancing the overall properties of tube-to-tubesheet welded joints. Dong et al.30) conducted a parametric analysis of residual stress for pipe girth welds in BS 7910 using the FE model. They proposed a shell theory-based estimation scheme to elucidate the improved estimation of the residual stress profile, addressing deficiencies observed in BS 7910 and API 579.
Xu and Zhao31) conducted a study to analyze the impact of welding, operating temperature, and operating pressure on the thermo-mechanical stress of tube-to-tubesheet welded joints, employing the FE model. Their findings revealed a significant influence of welding residual stress on thermo-mechanical stress, with the generation of local stress concentrations in tube-to-tubesheet welded joints. In a separate investigation, Han et al.32) explored the residual stress in elliptical tube-to-tubesheet welded joints for the phthalic anhydride switch condenser using the FE model. The study identified the maximum residual stress in the weld along the direction of the long axis, with the peak residual stress occurring at the location of 180° in the elliptical joints. Wan et al.14) assessed the weld residual stress of tube-to-tubesheet welded joints through a 3D FE model. Their analysis revealed that the maximum tensile residual stress appeared in the weld, primarily induced by cosmetic welding. Furthermore, duplex welding was found to decrease the residual stress of the weld root and surface.
All the aforementioned studies on FE welding simulations of tube-to-tubesheet joints have predominantly concentrated on the analysis of category-1 type tube-to- tubesheet joints. Additionally, the author is not aware of any previous research that has conducted a comparative analysis of welding processes for tube-to-tubesheet joints or performed FE analysis of welding processes for category-2 type welded joints. This study aims to bridge this gap by specifically addressing and exploring the welding processes associated with category-2 type tube-to-tubesheet joints. Subsequent sections will delve into the FE modeling, results, and conclusions.
2. Finite Element Modelling
This section provides an overview of the theory and methodology utilized in finite element modelling for the single/multi pass welding process of tube to tubesheet joint. FE analysis of weld joint involves solving a coupled thermo-mechanical problem. In this work welding simulations are carried out using the FE software33).
2.1 Geometry
The illustrated geometrical configuration of the tube and tubesheet is depicted in Fig. 2. This joint exhibit a tube with an outer diameter of 168 mm and a thickness of 10 mm, welded to a tubesheet with a thickness of 80 mm through a full penetration welded joint. These specific dimensions have been selected for analysis due to their similarity to those employed in AHWR24) end shield.
2.2 Material Properties
This analysis incorporates temperature-dependent thermo-physical properties for both base and weld metals. The AHWR end shields are made up of SS304L material, thus the same material has been considered under the current analysis24). In the simulations involving multi-pass welding, the material properties of the filler material are assumed to be identical to those of the base metal. Fig. 3 illustrates the variation of thermal properties, encompassing specific heat, thermal conductivity, and density. Additionally, Fig. 4 and Fig. 5 showcase the variation of mechanical properties, including Young’s Modulus, Yield Strength, Coefficient of Thermal Expansion, and true stress-strain curves.
For stainless steel, the melting temperature is considered to be the average between the solidus temperature (1400°C) and the liquidus temperature (1455°C), resulting in a value of 1428°C. The latent heat of fusion for stainless steel is 268 kJ/kg.
2.3 Meshing
Finite element simulations were conducted using linear 3D elements to model the tubesheet, tube, and welds. These elements were selected for their robust performance in non-linear finite element simulations. In the weld region, a very fine mesh with a 1mm size was employed, while coarser elements were used farther from the welds. The finite element meshing is visually represented in Fig. 6 for single-pass welding simulations and Fig. 7 for multi pass welding simulations.
In Fig. 7, a 45° V-groove was incorporated into the multi-pass welding simulations. This V-groove was subsequently filled with five different bead sizes, each representing the material deposited in five distinct multi-pass welding processes. These elements were modelled using an element birth and death technique. Initially, all elements of the bead were inactive (“dead”). Activation, or element birth, occurred when the temperature of the element reached the melting point of the material. This comprehensive modelling approach allows for an accurate representation of residual stresses in multi-pass welding processes.
The multi-pass welding process simulation requires individual welding simulations for each bead deposition. For this particular investigation, five welding simulations are necessary for each deposited bead. To enhance computational efficiency, a quarter symmetric model has been employed for the welding process simulation. Fig. 7 depicts the quarter symmetric model used in the welding process.
2.4 Thermal Analysis
The thermal analysis of the welding process involves solving a coupled thermo-metallurgical equation, represented by equation (1).
In this equation, T stands for temperature, t for time, P for phase proportion, while i and j are indexes of phases. Lij (T) denotes the latent heat for the transformation from phase i to phase j, and Aij signifies the portion of phase i transformed to phase j in a unit of time. Additionally, ρi (T), λi (T), and Ci (T) represent the mass density, thermal conductivity, and specific heat, respectively, for phase i.
In the current analysis, there are primarily two phases considered: the base metal and a fictive phase. The fictive phase is initially assigned to the weld beads at the start of the welding simulation. These elements are initially deactivated. However, when the temperature of these elements surpasses the melting point of the alloy, they become activated. It’s important to note that in the single-pass EB/LB welding simulations, which represent an autogenous welding process, no fictive phase is present.
In welding processes, the generation of heat input is governed by intricate physical phenomena. Accurately modelling this heat input source is crucial for correctly predicting residual stresses in welding. Therefore, in finite element-based welding simulations, weld heat input models are employed to accurately depict heat generation using simplified mathematical models. In this approach, the heat input is defined through analytical input power distribution models, denoted as q (x, y, z, t) (W/m3). This defined heat input is then utilized to compute temperature distributions. Here, x, y, and z represent coordinates within a Cartesian coordinate system, and t denotes time. The total analytical power input can be described by equation (2):
Where, Ω is the heat source region.
In this work, the single-pass welding processes has been modelled with a conical heat source with gaussian radial distribution and linear axial distribution using equations (3) and (4):
Q0 is the source intensity (W/m3), r0 (m) and ri(m) are the radius of cone at its upper and lower end, and H (m) represents as the height of the cone r(z) represents the radius of the cone at any intermediate location z. These values are represented schematically in Fig. 8(a).
Q0 is related to input power P by equation (5),
Here, η represents the efficiency of power conversion. In the case of EB welding, this term represents the loss of kinetic energy of electrons during their transition to heat energy. In the case of laser welding, this term depends on the absorption coefficient of the material.
Thus, the numerical simulations of the EB welding process requires estimation of following heat source parameters - input power (P), upper and lower radius of the heat source - (ri, r0), depth of the conical heat source (H). In addition, welding speed (Vw) is required as it affects the heat input per unit length. These parameters are estimated from prior experimental results on EBW/LBW of stainless-steel pipes/plates. The details of the same are explained in Section (2.5).
This study utilizes the Goldak double ellipsoidal heat source model34) to simulate the multipass TIG welding process. This model accurately represents the heat power density generated by an electric arc during welding. The mathematical representation of Goldak’s heat source involves two half ellipsoids connected along a symmetry axis, described by equations (6) and (7):
Here, af, ar, b, and c represent the dimensions of the semi-ellipsoid axes. Coefficients ff and fr (ff + fr = 2) denote energy distribution in the front and back of the heat source, satisfying the conditions Qf (x,y,z) and Qr (x, y, z). Fig. 8(b) illustrates the schematic of the Goldak’s heat source model.
Similar to previous case, numerical simulations using the Goldak heat source model necessitate the estimation of specific parameters: Input power (P), dependent on heat input per unit length (q) and welding velocity (Vw), and heat source distribution parameters-af, ar, b, and c. These parameters are estimated from prior experimental studies conducted on multipass TIG welding, as elucidated in Section (2.6).
In the welding process, the heat input by the welding torch primarily contributes to melting the base material and filler material. A portion of the heat is conducted away from the welding location through metal conduction, while the remaining heat is dissipated to the environment through convection and radiation. This study comprehensively considers all these heat transfer mechanisms. The ambient temperature is assumed to be 30°C, and the heat loss to the environment is simulated through thermal analysis until the temperature of the weld region reaches 30°C.
In actual scenarios, the typical dimensions of a tube sheet for pressure tube type advanced heavy water nuclear reactor is around 8000 mm. However, for numerical simulations in this study, a tube sheet of dimensions 900x900 mm is utilized. Given the substantial size of the tubesheet and the consequent high rate of heat conduction at the four lateral surfaces, adjustments are made by modifying the convection heat transfer coefficient to 135 W/m2K. This modification ensures the accurate consideration of heat loss through conduction. Similarly, the heat loss by conduction from the other end of the tube is accounted for by adjusting the heat transfer coefficient to 27.5 W/m2K.
2.5 Estimation of Heat Source Parameters of EB/LB Welding for SS304L material.
In this section, the explanations for estimating various parameters necessary for simulating EB/LB welding using conical heat source model are provided. In EB welding, the effective power (P) is determined by equation (8):
Here, Ib represents beam current, Vacc stands for accelerating voltage, and η signifies the efficiency of energy conversion from the kinetic energy of electrons to thermal energy. The value of η is typically in the range of 80-95%35,36). In this study an average value of 90% is used. This effective power, P, is also related to the heat input per unit length (q) and the welding velocity (Vw) through equation (9):
For this study, a moderate welding velocity (Vw) of 1000 mm/min is utilized. The heat input per unit length (q) is estimated using equation (10) from Kar et al.37).They established this correlation based on numerous EB welding experiments on SS304LN material. The equation (10) relates the heat input per unit length of weld (q) to a given weld penetration (H):
Utilizing this relation, the heat input per unit length required for 10mm penetration in SS304L material is estimated at 294 J/mm. Experimental values of heat input per unit length for a penetration of around 10 mm varies from 214 J/mm to 428 J/mm36,37) as it also depends upon the weld width. Therefore, an average value of q equal to 321 J/mm is used in these studies.
Based on the input effective power (P) and welding velocity (Vw), the cross-sectional area of the weld zone (Fm) can be obtained by equation (11)36),
In above equation, ηt represents thermal efficiency, indicating the proportion of input heat energy used in melting the material. For SS304L material, the thermal efficiency varies from 46% to 63% for a weld penetration of 10mm36,38). In this study, an average value of 55% is utilized.
Sm represents the heat capacity corresponding to the melting temperature (J/m3), calculated by equation (12):
Where, r represents metal density(kg/m3); C represents specific heat capacity of metal (J/(kg·K); DTm = Tm - To increase from the initial temperature (To) to the melting point (Tm); Lm - specific heat of fusion(J/kg). Sm equals 8.915×109 J/m3, derived from the given para- meters.
Additionally, the cross-sectional area of the weld pool (Fm) can be determined by the average weld width (B) and depth of penetration (H) using equation (13):
The average weld width (B) is calculated by equation (14)36),
where dt represents beam diameter (m); dt = 2r0 (upper radius of the conical heat source).
Solving Equations (9, 11 & 12), The upper radius of the conical heat source, r0 can be calculated and is represented by equation (15):
Using aforementioned values of ηt, P, Sm,Vw & H, ro ≈ 0.7mm
In previous studies, Chiumenti39) and Dhinakaran40) adopted a parabolic function to represent the power source density in beam welding, gradually decreasing to zero at the maximum penetration (H) of the weld. They conducted numerical modelling of the welding process using this parabolic heat source and validated their results by comparing them with temperature measurements obtained from experimental welding trials. However, in this study, a conical heat source is being simulated. Consequently, the inner radius of the conical heat source, denoted as ri, is established by equating the volume of the conical heat source to that of the previously used parabolic heat source. According to this assumption, ri = 0.68r0 is derived, leading to the utilization of ri = 0.47mm for this particular study. Table 1 provides a comprehensive compilation of all the parameters required for simulating the EB/LB welding process, as discussed in the preceding paragraphs.
Table 1
Heat source parameters used for simulation of EB/LB welding
2.6 Estimation of Heat Source Parameters of TIG Welding
In this section, the explanations for estimating various parameters necessary for simulating TIG welding using Goldak’s heat source model are provided. The welding speed in Category-1 type tube-to-tube sheet TIG welding typically ranges between 64-85 mm/min8). Comparatively, in plate TIG welding, the speeds typically range around 130-450 mm/min41,42). These speeds are notably lower than those observed in EB/LB welding due to the relatively lower heat input density in TIG welding. For this study, welding simulations are conducted using an average welding velocity of 100 mm/min to represent the tube-to-tubesheet welding process.
The average heat input per unit length per pass in multipass TIG welding falls within the range of 787-1480 J/mm8,42). For this study, simulations are conducted using an average value of 1000 J/mm. Additionally, previously validated heat source parameters42) - af /ar = 0.25, ff = 1.2, fr = 0.8, and η = 85% - are utilized in simulations. The parameters b & c are contingent upon weld bead dimensions and were adjusted for each simulation pass to closely align the dimensions of the heat source with those of the weld bead. Table 2 presents a comprehensive compilation of all the parameters necessary for simulating the multipass TIG welding process.
Table 2
Heat source parameters used for simulation of TIG welding
2.7 Mechanical Analysis
The nodal temperature profiles are acquired through thermal analysis, following the procedure outlined in section (2.4). These temperature-time histories for each node, corresponding to each welding pass, serve as inputs for the mechanical analysis, facilitating the determination of residual stresses and distortion arising from the welding process. In the mechanical analysis, rigid body motions were restricted by providing minimum degrees of freedom, achieved by fixing the four corner nodes of the tube sheet.
In the mechanical analysis of welding, the careful selection of material models and input parameters significantly impacts the accurate prediction of weld distortion and residual stresses. Various studies have delved into the influence of material models on the residual stresses produced during welding processes. Comparisons among different material models-such as perfectly plastic43), kinematic hardening43,44), isotropic hardening43,44), and mixed hardening material models43,45)-have been conducted against residual stress measurements obtained from experimental studies. The findings indicate noteworthy disparities between the residual stresses predicted by FE simulations employing perfectly plastic and kinematic hardening material models, as opposed to those derived from experimental measurements. However, both mixed hardening and isotropic hardening material models demonstrate closer agreement between the predicted residual stress values and experimental measurements. In the present study mechanical analysis has been carried out using an isotropic hardening material model. Temperature dependent material properties have been considered in analysis as per the details explained in Section (2.2).
The current mechanical analysis is conducted within a Lagrangian framework utilizing a large strain formulation. The mechanical analysis, specifically in the elasticplastic range, adheres to classical equilibrium laws expressed by equation (16),
Here, ∇represents the gradient operator, σ represents stress components, and b represents body force. The relationship between stresses and strains is defined by equation (17),
Where, [D] and εe are stiffness and elastic strain vectors respectively. The elastic strain vectors are derived from equation (18),
Here, εpl, εth, and ε denote plastic strain, thermal strain, and total strain vectors, respectively. The strain components εvol (volumetric strain), εphase (strain due to phase change), and εtrp (strain due to transformation plasticity) represent the strain components associated with phase transformation at the solid phase and solid-liquid phase changes. In the context of SS304L material, the strain components εphase and εtrp are negligible, as this material primarily remains in the FCC phase until reaching its melting temperature.
The comparison between components welded using five-pass TIG welding and single-pass EB/LB welding involves analysing the weld and HAZ dimensions and residual stresses resulting from these welding processes. Residual stresses within the weld, HAZ, and base metal were assessed at two distinct temperatures: Room Temperature (RT) at 30°C and Operating Temperature (OT) at 100°C. The obtained residual stresses were then categorized according to the procedures outlined in the ASME Boiler and Pressure Vessel Code (B& PVC) Section III NB and Section VIII Div II, classifying them into Membrane, Bending, and Peak Stress categories. Multiple Stress Classification Lines (SCLs) were established at varying distances from the weld, both within the tube and across the tubesheet. This comparison aims to elucidate differences in residual stress profiles resulting from these distinct welding methods.
2.8 Validation of Numerical Simulations
To validate the accuracy of the numerical simulations, an experiment was conducted on EB welding by joining two 12 mm thick plates made of austenitic stainless-steel type 304L. Temperature measurements during the welding were performed using K-type thermocouples placed at distances of 3 mm, 2 mm, and 4 mm from the weld centerline. The temperature profiles recorded at these thermocouple locations are illustrated in Fig. 9. After welding, the plate was sectioned across its thickness and subjected to chemical etching to reveal the weld pool size, which is shown in Fig. 10(a).
Fig. 9
Experimental and numerical temperature profiles at various locations with respect to weld center line
Fig. 10
Comparison of weld pool sizes (a) Experiment; (b) Temperature contour plots using numerical simulation
The numerical simulation of the plate weld joint was performed using the conical heat source model, with input parameters selected following the procedure in Section 2.5. Temperature profiles at the thermocouple locations were obtained from the simulations and compared to the experimentally measured profiles, as shown in Fig. 9. The weld pool sizes from the simulations, determined based on regions with temperatures above 1428°C (the melting point), are also shown in Fig. 10(b). The numerical results closely match the experimental results for both temperature profiles and weld pool size, validating the numerical analysis procedure.
Serindag et al.46) prepared a multi-pass TIG weld joint using 10 mm thick stainless-steel type 316L plates, observing weld widths of 3.5 mm at the weld root, 5.5 mm at the weld middle, and 10 mm at the weld top after accounting for the removal of the root gap. In our case, as shown in Fig. 11(b), weld widths of 3.16 mm at the weld root, 5.65 mm at the weld middle, and 8.76 mm at the weld top were obtained. The weld pool size from the numerical simulation closely matches the results observed by46), once the root gap effect is removed. This validates the accuracy of the numerical simulation and the welding heat source input parameters used for the multi-pass TIG welding analysis, as detailed in Section 2.6.
3. Results & Discussions
This section presents the outcomes derived from the finite element analysis of the tube-to-tube-sheet weld joint, following the methodology outlined in Section 2. The analysis focuses on several aspects, including the maximum temperature contour for weld pool size, temperature-time history to assess sensitization tendency, comparison of weld and HAZ dimensions, residual stresses, and distortion of both the single-pass EB/LB welding and five-pass TIG welding processes.
3.1 Temperature Contour and HAZ
The finite element analysis of the tube-to-tube-sheet weld joint was performed for both the single-pass EB/LB welding and five-pass TIG welding processes as per the procedure described in Section 2.4. The analysis was conducted until the temperature of the welded region reached around room temperature i.e., 30°C. The maximum temperature attained during the welding simulation period at regions near the tube-to-tubesheet joint is shown in Fig. 11 for both single-pass EB/LB and five-pass TIG welding. In this figure, the tube cross-section, from the Inner Diameter (ID) to the Outer Diameter (OD), indicated in gray, reaches temperatures above 1428°C, i.e., melting temperature, and thus represents the weld pool.
It was observed that the weld pool size is smaller in single-pass EB/LB welding compared to the five-pass TIG welding. The weld pool width at the tube-to-tubesheet joint ID is 2.2 mm wider in EB/LB welding, while it measures 8.76 mm in the case of five-pass TIG welding. This difference is attributed to the higher heat input and lower power density in TIG welding compared to EB/LB welding.
The HAZ resulting from both single-pass EB/LB welding and five-pass TIG welding processes at room temperature and operating temperature is illustrated in Fig. 12. In this figure, the HAZ is delineated by the temperature contour region between the lower critical temperature, 723°C, and the melting temperature, 1428°C. It’s noteworthy that the HAZ in single-pass EB/LB welding is 73% smaller compared to five-pass TIG welding, both at room and operating temperatures.
3.2 Temperature Time History
In both single-pass EB/LB welding and five-pass TIG welding processes, understanding the relationship between time, temperature, and sensitization is crucial for ensuring the integrity and longevity of welded components, particularly in materials like austenitic stainless steel. Time and temperature play pivotal roles in determining the degree of sensitization, which refers to the precipitation of chromium carbides at grain boundaries, rendering the material susceptible to intergranular corrosion. During welding, the HAZ experiences a transient thermal cycle, with temperatures typically reaching a peak and then gradually cooling. The temperature-time history at two locations (Point A and B indicated in Fig. 11) were obtained for both single-pass EB/LB welding and five-pass TIG welding. In Fig. 11, point A represents the weld center, while Point B is located at a distance of 2.5 mm from the weld center. Point B is chosen to ensure it falls within the HAZ for multi-pass TIG welding at the weld root surface. The same distance was used for comparison with single-pass EB/LB welding. The temperature-time history at weld center (point-A) is depicted in Fig. 13, while Fig. 14 illustrates the temperature-time history at Point B.
Fig. 13
Comparison of temperature profile for single-pass EB/LB welding and five-pass TIG welding at weld centre (Point A)
Fig. 14
Comparison of temperature profile for single-pass EB/LB welding and five-pass TIG welding in HAZ (Point B)
The peak temperature during welding is higher for single-pass EB/LB welding compared to five-pass TIG welding. In single-pass EB/LB welding, the exposure time is relatively short-lived compared to five-pass TIG welding, where five welding passes can result in prolonged exposure to elevated temperatures. This extended exposure in five-pass TIG welding can increase the likelihood of sensitization, as the material spends more time within the critical temperature range of 450-800°C. Sensitization tendency also depends on the total heat input during welding. The higher heat input during TIG welding increases the risk of sensitization due to slower cooling rates, leading to longer residence times in the critical temperature range. Consequently, the risk of sensitization is higher in TIG welding compared to single-pass EB/LB welding.
Wiednig et al.47) reported that toughness in the fusion zone also increases during EB welding and their findings clearly show that EBW joints have sufficient toughness and are superior then flux-cored metal active gas welding. Rapid cooling in EB/LB welding minimizes the risk of sensitization in stainless steel 304L, which is beneficial in preventing intergranular corrosion. However, rapid cooling introduces several concerns related to mechanical property degradation. One significant issue is the potential for increased hardness47). Rapid cooling can lead to the formation of microstructures that are harder and less ductile47,48). The high cooling rates also causes the localized thermal expansion and contraction leads to high residual stresses and deformation. However, single-pass EB/LB welding generates smaller overall residual stresses and deformation compared to multi-pass TIG welding due to the lower heat input, as shown in Figs. 15 and 24. As a result, the likelihood of cracking is reduced in EB weld joints.
Fig. 15
Tresca stress contour cross-sections near the tube-to-tubesheet joint (a) Single-pass EB/LB welding at RT, (b) Single-pass EB/LB welding at OT, (c) Five-pass TIG welding at RT, (d) Five-pass TIG welding at OT
Fig. 16
Comparison of hoop residual stress contour on both welding at RT (a) Single-pass EB/LB welding, (b) Five-pass TIG welding
Fig. 17
Comparison of axial residual stress contour on both welding at RT (a) Single-pass EB/LB welding, (b) Five-pass TIG welding
3.3 Comparison of Residual Stresses
During welding, the temperature near the weld area rises significantly, causing expansion of the metals. Subsequently, after welding, there is a rapid cooling of the base metal and weld pool due to heat transfer to the surrounding environment. As the temperature drops post-welding, residual stresses and shrinkage develops in the welded component. These residual stresses gradually increase as the metal cools to ambient temperature. Residual stresses are particularly pronounced in the weld pool and its immediate vicinity, with the maximum stresses typically occurring at the root of the weld. ASME Section III, which governs the design and construction of nuclear facility components, follows the Tresca theory due to its more conservative nature, predicting yielding at lower stress levels. Accordingly, the Tresca residual stress contour for single-pass EB/LB welding in the welded component after cooling to room temperature and operating temperature is depicted in Fig. 15(a-b), while those for five-pass TIG welding are shown in Fig. 15(c-d). Analysis of the residual stress contours reveals that stresses at the operating temperature are lower in both weld joints. Furthermore, it is evident that in single-pass EB/LB welding, residual stresses are concentrated near the weld region, whereas in five-pass TIG welding, the region affected by residual stresses is larger.
Calculating axial, hoop, and radial stress components in tube welding is crucial for assessing the structural integrity and performance of welded joints. These stress components provide valuable insights into the distribution of stresses within the welded structure, helping to identify potential areas of weakness or vulnerability. Axial stress, acting along the longitudinal axis of the tube, influences its overall stability and resistance to axial loading. Hoop stress, which acts circumferentially around the tube, is essential for evaluating its ability to withstand internal pressure and prevent rupture. Radial stress, perpendicular to both axial and hoop stresses, influences the tube’s resistance to deformation and its interaction with external forces. The comparison of hoop, axial, and radial residual stresses near the tube-to-tubesheet joint depicted in Fig. 16 through Fig. 18 for both single-pass and five-pass TIG welding.
The hoop residual stresses are concentrated near the tube-to-tubesheet weld joint and are predominantly tensile throughout the weld cross-section, as depicted in Fig. 16. However, the magnitude of hoop residual stress is higher in five-pass TIG welding compared to single-pass EB/LB welding. The axial residual stresses are observed to be tensile in nature at the tube ID and compressive at the tube OD, as depicted in Fig. 17. The axial residual stresses are notably higher in five-pass TIG welding compared to single-pass EB/LB welding. Additionally, the magnitude of radial residual stresses near the tube-to-tubesheet weld joint is found to be negligible compared to hoop and axial residual stresses, as shown in Fig. 18.
The residual stresses near the HAZ region of the tube-to-tubesheet joint are compared for both single-pass EB/LB welding and five-pass TIG welding, at both room and operating temperatures. For this comparison, a 5 mm distance from the weld centerline is selected. The comparison of hoop residual stresses is shown in Fig. 19, while axial residual stresses are shown in Fig. 20. It is observed that axial residual stresses (σz) are tensile at the tube ID and compressive at the tube OD. Hoop stresses (σθ) are tensile and have the highest magnitude among hoop, axial, and radial stresses. Additionally, for single-pass EB welding, both residual hoop stresses and axial stresses are smaller at operating temperature compared to room temperature. This demonstrates that the advantage of reduced residual stresses in single-pass EB/LB welding is also maintained at operating temperature.
3.4 Comparison of Membrane + Bending Stress Intensity
The residual stresses developed in tube-to-tubesheet during the welding are classified as secondary and peak stresses. Secondary stresses occur due to thermal gradients during welding, where the material expands and contracts while being constrained by surrounding areas, leading to self-limiting deformation or distortion. Peak stresses are highly localized, concentrated around the weld bead or HAZ, and can contribute to local failure mechanisms such as cracking or fatigue.
The design by analysis approach is employed for the code qualification of nuclear components. In this approach, all six components of normal and shear residual stresses are linearized into constant membrane, linear bending, and non-linearly varying peak stresses according to the procedures outlined in B&PVC Section III NB and Section VIII Div II. SCLs were established at varying distances from the weld, both within the tube and tubesheet, as indicated in Fig. 21. These SCLs are identified as Weld Center, T1, T2, T3, T4, T5 in the tube, and B1, B2, L1 in the tubesheet.
The principal stresses (σ1, σ2 and σ3) of membrane plus bending stress at these SCLs were calculated by solving the stress invariant equation. Then, the equivalent stress intensity (σ1 - σ3) was calculated for comparison to elucidate differences in residual stress profiles resulting from these distinct welding methods. The maximum membrane plus bending stress intensity is plotted in Fig. 22 at RT and Fig. 23 at OT. The allowable stress is limited by the 3Sm criterion, as specified by ASME Section III.
The study revealed that employing single-pass EB/LB welding results in lower maximum membrane plus bending stress intensity at both RT and OT compared to five-pass TIG welding. At RT, it is approximately 32% lower at 5 mm and 60% lower at 20 mm distance from the weld center. Additionally, the maximum membrane plus bending stress intensity in the tube at a 5 mm distance from the weld center is 10% lower at RT compared to OT in single-pass EB/LB welding. Similarly, in five-pass TIG welding, it is 7% lower at RT compared to OT.
3.5 Comparison of Axial Deformation
During the welding process, the intense localized heat causes the material to expand and subsequently contract upon cooling. This thermal cycle can lead to distortions such as angular deformation, longitudinal bending, and buckling. These deformations can compromise the alignment and dimensional accuracy of the welded components, potentially leading to issues such as misalignment, improper fit-up, and even cracks or failures under operational stresses. Calculating deformation is essential to predict and mitigate these adverse effects, ensuring that the welded joints meet the required specifications and perform reliably under service conditions. Deformations in all three directions-axial, radial, and hoop were observed in the tube-to-tubesheet weld joint after the formation of the weld. The axial deformation in the single-pass EB/LB welding and five-pass TIG welding at both RT and OT is shown in Fig. 24. The axial deformation is found to be negative, indicating the shrinkage of material near the weld joint.
The maximum axial deformation near the tube-to-tubesheet joint is approximately -0.3 mm for single-pass EB/LB welding, while it reaches -2.2 mm for five-pass TIG welding. Overall, the deformation in single-pass EB welding is approximately 87% less compared to five-pass TIG welding. Additionally, axial deformation is in single-pass EB/LB is approximately 10% smaller at operating temperature compared to room temperature.
3.6 Discussions
The variations in stress distribution at different temperatures can significantly impact the long-term reliability and performance of tube-to-tubesheet joints in real operational conditions. In environments with fluctuating temperatures, differential expansion between the tube and tubesheet materials can lead to uneven stress distribution, particularly at the weld joints. Over time, this can result in localized stress concentrations, increasing the risk of fatigue failure or stress corrosion cracking. Additionally, HAZ experiences thermal cycling, which can exacerbate residual stresses and contribute to long-term degradation of the welds.
Single-pass EB/LB welding offer several benefits over conventional multi-pass welding methods. These techniques provide deep penetration in a single pass, making them ideal for welding thick sections without the need for multiple layers. This results in reduced residual stress and distortion due to the smaller heat-affected zone, minimized thermal cycling and lower likelihood of sensitization as discussed in section 3.1-3.5. The precise and concentrated heat input from EB/LB welding also improves weld quality by producing cleaner, more uniform welds with fewer impurities or defects. Additionally, these methods are faster, increasing production efficiency, and often require less post- weld treatment due to the reduced distortion and higher quality of the weld.
However, there are significant practical challenges in implementing EB/LB welding on an industrial scale. The specialized equipment, such as electron or laser beam welding machines, is expensive and requires substantial capital investment. EBW, in particular, requires a vacuum chamber, which limits its applicability and adds complexity. Both processes demand precise control over parameters like beam intensity and speed, necessitating highly skilled operators and advanced monitoring systems, which increase operational costs. Additionally, the need for specialized operator training and the limited accessibility of EBW for certain configurations and materials pose further obstacles. Despite these challenges, the long-term benefits of reduced residual stresses, improved weld quality, and faster processing make EB/LB welding highly valuable in critical applications, particularly in industries where precision and reliability are essential, such as the nuclear sector.
4. Conclusion
The coupled thermo-mechanical analysis was conducted to examine the residual stresses in the tube-to- tube-sheet weld joint formed by single-pass EB/LB welding or five-pass TIG welding. Single-pass EB/LB welding simulations utilized a 3D Gaussian heat source, while five-pass TIG welding simulations employed a double ellipsoidal heat source. The analysis included a comparison of weld pool shape, heat-affected zone, residual stresses and distortions in both the tube and tube sheet using both welding techniques at room temperature and operating temperature. The following conclusions were drawn from the numerical analysis:
1) The weld pool in the tube-to-tubesheet joint using single-pass EB/LB welding is approximately 72% smaller compared to five-pass TIG welding. Additionally, the HAZ in single-pass EB/LB welding is 73% smaller than in five-pass TIG welding, at both room temperature and operating temperatures.
2) The peak temperature at the weld center is around 3000°C in single-pass EB/LB welding, whereas it is approximately 1800°C in five-pass TIG welding. The residence time within the sensitization temperature range is much smaller in single-pass EB/LB welding compared to five-pass TIG welding. Consequently, the risk of sensitization is significantly lower in single-pass EB/ LB welding.
3) The analysis of the residual stress contours reveals that residual stresses in single-pass EB/LB welding are concentrated near the weld region, whereas in five-pass welding, the region affected by residual stresses is larger. The residual stresses diminish as the distance from the tube-to-tubesheet weld joint increases. Additionally, the residual stresses in single-pass EB/LB welding are smaller compared to five-pass TIG welding at both room temperature and operating temperature.
4) The residual stress intensity at room temperature is approximately 32% lower at a 5 mm distance and 60% lower at a 20 mm distance from the weld center in single-pass EB/LB welding compared to five-pass TIG welding. Similar reductions in residual stress intensity were observed at operating temperature as well.
5) The axial deformation in single-pass EB/LB is approximately 86% less as compared to five-passes TIG welding. The smaller deformation in single-pass EB/ LB allows the engineers to ensure proper alignment and fit-up of welded components.
6) Overall, the study concludes that single-pass EB/ LB welding offers advantages for tube-to-tubesheet weld joints due to its lower likelihood of sensitization, reduced heat-affected zone, diminished distortions, and lower residual stresses.
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