Behavior, Failure Analysis, and Effectiveness of Mechanical Stress Improvement Process in Residual Stress Relaxations in Butt-Welded Austenitic Piping Using a Numerical Simulation Approach

doi:10.21203/rs.3.rs-3989175/v1

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Behavior, Failure Analysis, and Effectiveness of Mechanical Stress Improvement Process in Residual Stress Relaxations in Butt-Welded Austenitic Piping Using a Numerical Simulation Approach

https://doi.org/10.21203/rs.3.rs-3989175/v1

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published 30 Oct, 2024

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The utilization of the Mechanical Stress Improvement Process (MSIP) is a widely employed technique to improve the behavior and the failure analysis in nuclear power plants. Its purpose is to effectively prevent stress corrosion cracking by eliminating residual tensile stresses present in weldments. This approach serves to impede the formation of cracks and decelerate the advancement of existing failures in piping systems. Consequently, favorable compressive stresses are created along the inner surface of the pipe near the weld, including molten and heat-affected metal zones. To assess the efficacy of MSIP in reducing stress concentrations and enhancing structural integrity, multiple cases were evaluated via numerical simulations in this study. Moreover, the dimensions and placement of the MSIP tool were discussed, with the optimal position and width of the clamp being determined to be 30 mm from the weld line (WL) and 75 mm, respectively. The results of this study indicate that the WL region manifests significantly high compressive stresses, which gradually diminish within a 10 mm distance on each side of the WL.

MSIP

Stress corrosion cracking

Butt-welded piping

Numerical simulations

Austenitic stainless steel

The investigation of methods to enhance the state of residual stresses is an area of research that has its origins several decades ago. These tensions possess the potential to significantly influence the structural strength and functionality of important constituents, particularly within the domain of nuclear power plants and high-pressure systems, rendering them a matter of utmost significance. Throughout time, researchers and engineers have placed significant emphasis on comprehending, managing, and reducing these residual stresses, thereby emphasizing their importance in ensuring the safety and reliability of these systems.

The exploration of methods to enhance the state of residual stresses is an area of research that traces its roots back several decades. In its early stages, pioneering studies such as Tanaka and Umemoto's [1] groundbreaking work, presented in the 1980 seminar and countermeasures for Boiling Water Reactor (BWR) Pipe Cracking, shed light on the potential for improving residual stress conditions through the application of induction heating. This work laid the groundwork for subsequent research endeavors focused on controlling residual stresses in welded structures. As analytical tools and computational techniques continued to evolve, researchers like Brust and Kanninen [2] delved deeper into the analysis of residual stresses in materials, with a particular emphasis on girth-welded stainless-steel pipes. It was in the year 1981 that this study marked a pivotal moment in the field, as it emphasized the utmost importance of comprehending the distribution and magnitude of these stresses. Building upon this foundation, the work of Rybicki and McGuire [3] further highlighted the role of induction heating conditions in controlling residual stresses, thereby providing valuable insights into optimizing the induction heating process to achieve desired outcomes.

As time progressed, a diverse range of strategies emerged intending to modify and alleviate residual stresses. Studies such as Shimizu et al.'s investigation into residual stresses in girth butt-welded pipes [4], as well as Goldak et al. [5] introduction of a novel finite element model for welding heat sources, served as exemplars of the growing body of knowledge and innovative solutions within this field. These studies not only showcased the advancements in understanding residual stresses but also provided practical approaches to address them.The critical necessity of effectively managing residual stresses within nuclear power plant components prompted investigations such as Porowski et al. utilization of the MSIP to mitigate stress corrosion cracking [6]. The commencement of the expedition occurred in the year 1990, when Failure Analysis Associates embarked on their seminal work titled "PRAISE Enhancements to Include General Strain Hardening Exponents and Mid-Life Residual Stress and Water Chemistry Changes" [7]. This remarkable study, which was prepared for Lawrence Livermore National Laboratory in California, delved deep into the complexities surrounding strain hardening exponents and mid-life residual stress, within the context of evolving water chemistry. Moving forward, the journey takes us to the year 1997, when Schmidt et al. [8] embarked on pioneering research, presenting alternative methods for post-weld treatment of austenitic pipe welds in order to enhance the operational safety of BWR plants. This research introduced a new dimension to the practical application of residual stress management within the nuclear power sector, highlighting the continuous pursuit of safer and more dependable energy production.Taking this a step further, Voß (2001) delved into the investigation of relevant influencing variables on numerical welding simulations, thereby emphasizing the crucial role of computational tools in comprehending welding processes [9]. This work expanded the horizons of knowledge in the field and shed light on the significance of employing advanced techniques to gain a deeper understanding of welding phenomena.

The utilization of the MSIP gained prominence during this period, as demonstrated by Ray et al. (2003)[10] groundbreaking work on using MSIP to prevent and mitigate primary water stress corrosion cracking in reactor vessel piping. This research highlighted the effectiveness of MSIP as a valuable tool in maintaining the integrity of nuclear power plant infrastructure, particularly in mitigating the deleterious effects of stress corrosion cracking.Over subsequent years, the exploration of techniques for managing residual stresses continued to expand. Hussnain and Siddique (2005) [11] ventured into numerical simulations of mechanical stress relieving, to reduce intergranular stress corrosion cracking in multi-pass Gas Tungsten Arc girth-welded pipe flange joints. On a parallel trajectory, Hurrell et al. (2006) [12] conducted a comprehensive review of various methods for mitigating residual stresses, specifically focusing on their application in the context of nuclear power plants. In the year 2007, Todinov [13] explored generic solutions for reducing the likelihood of overstress and wear-out failures. This exploration opened up new avenues of research and offered potential strategies for mitigating failures caused by excessive stress and wear. The subsequent year, 2008, stands as a critical juncture in this narrative, as Fredette et al.[14] undertook an analytical evaluation of the efficacy of the MSIP in pressurized water reactor primary cooling piping. Their work delved into the practical implications of utilizing MSIP, providing valuable insights for its application in critical infrastructure.As we continue on this scientific odyssey, Anderson et al. technical letter report in 2008[15] presents an analysis of ultrasonic data gathered from piping cracks at the Ignalina Nuclear Power Plant, both before and after the application of the MSIP. This meticulous examination of real-world data underscores the tangible benefits of utilizing MSIP in ensuring the safety of nuclear power plants.The thread of inquiry weaves further as Fredette and Scott (2009) [16] evaluate the effectiveness of the MSIP as a mitigation strategy for primary water stress corrosion cracking in pressurized water reactors, highlighting the profound implications of stress corrosion on reactor safety. Ehrnstén's contribution in 2012 [17] opened a new chapter in our understanding of corrosion and stress corrosion cracking in austenitic stainless steels. This insight into the material aspects of residual stress management adds a critical dimension to the discourse.

The following year, Ford et al. (2012) [18] delved into the intricate realm of intergranular stress corrosion cracking (IGSCC) in BWRs, unraveling the complexities of this specific form of corrosion within the nuclear domain. Transitioning into 2012, Aoike and Tsuruki's research [19]presents the development of the Residual Stress Improvement Method for Small-Diameter Butt-Welding Pipe, demonstrating the practical application of stress improvement techniques in small-scale, intricate welding scenarios.Sullivan and Anderson's assessment in 2013 of the MSIP for mitigating primary water stress corrosion cracking in nickel alloy butt welds within piping systems approved for leak-before-break signifies an ongoing commitment to nuclear safety [20]. The storyline progresses into 2014 with Bolognesi and their associates shedding light on the modeling and characterization of residual stresses in material processing, presenting a holistic perspective on residual stresses across various manufacturing processes [21]. The tale unfolds further as Facco et al. (2017) venture into the realm of finite element analysis, exploring the effect of the MSIP on weld residual stress and flaw growth in a thick-walled pressurizer safety nozzle [22].

As we navigate through the rich history of residual stress management, it becomes evident that decoupling the role of stress and corrosion is pivotal in understanding the interplay of these factors. Badwe et al. (2018) present this decoupling in the context of intergranular cracking of noble-metal alloys, pushing the boundaries of our comprehension in this domain [23]. Our odyssey through the intricate landscape of residual stress management is not confined to the past but extends into the present day. Liu et al. (2021) delve into the mitigation of residual stress and deformation induced by Tungsten Inert Gas (TIG) welding in thin-walled pipes through external constraints, showcasing the contemporary relevance of welding techniques [24]. Yang (2021) [25] offers a glimpse into recent advances in predicting weld residual stress and distortion, underlining the role of predictive modeling in this evolving field.The most recent addition to our narrative, Guo et al. (2022) [26] explores the effect of post-weld heat treatment on microstructure and corrosion behavior in weld overlay cladding materials, accentuating the importance of material-specific approaches in managing residual stresses.

In [27] Zeghida et al.(2022) delve into the effect of induction heating stress remedies on piping reliability, reaffirming the continued relevance of induction heating in addressing residual stresses. Drawing from prior investigations where a numerical simulation for Induction Heating Stress Improvement (IHSI) was conducted, a notable advantage of MSIP becomes apparent: its ability to be applied directly to pipes even during active service. This stands in contrast to the IHSI, which due to its thermal nature necessitates operational pauses. On the other hand, for a nominal pipe thickness of 5.5 mm or less, it is assumed that it is difficult to improve residual stress by applying IHSI because the temperature difference that can be applied is small due to the thin pipe thickness. However, it has been reported that the residual stress on the inner surface near the butt weld may exceed 300 MPa even in small-diameter pipes [28]. This delineation underscores MSIP's enhanced adaptability and efficiency in real-world scenarios.

To demonstrate the effectiveness of MSIP in reducing stress concentrations and improving structural integrity, this paper provides backgrounds and numerical simulations concerning welding and MSIP. Multiple cases for the numerical simulations were utilized to assess the impact of MSIP on stress corrosion cracking in butt-welded austenitic piping.

2.1. Background

In tube welding, understanding and manipulating the parameters is critical to achieving a precise and strong joint. According to Table 1, our welding process was performed at a moderate speed of 0.003 m/s to ensure an accurate joint between the pipe sections. In addition, there is an electric current of 100 A, combined with a voltage of 12.5 V. An efficiency of 0.8 indicates the efficiency of energy conversion during the welding process and indicates a well-optimized system.

Table 1

Welding parameter.
Parameter	Speed	Current	Voltage	Efficiency
Value	0.003 m/s	100 A	12.5 V	0.8

During the welding process, a non-uniform thermal field was created surrounding the weld, which might cause residual stress to develop in welded structures. To determine the thermal field, transient thermal analysis with the required boundary conditions was used. The 3D transient state heat conduction Equation, which is provided below, governs the transient thermal analysis of the welding process.

$$\frac{\partial }{{\partial x}}\left( {{K_x}\frac{{\partial T}}{{\partial x}}} \right)+\frac{\partial }{{\partial y}}\left( {{K_y}\frac{{\partial T}}{{\partial y}}} \right)+\frac{\partial }{{\partial z}}\left( {Kz\frac{{\partial T}}{{\partial z}}} \right)+Q=\rho {C_P}\left( {\frac{{\partial T}}{{\partial t}} - v\frac{{\partial T}}{{\partial x}}} \right)$$

Where, ${C_P}$ = Specific heat, $J.k{g^{ - 1}}.K$; $\rho =$ Mass density, $kg.m{m^{ - 3}}$; $Q=$ Internal heat generation, $W.m{m^{ - 3}}$; $v=$ Relative speed of heat source $mm.{s^{ - 1}}$. The rate of heat rejection resulting from convection and radiation has been taken into account when solving the transient thermal analysis. Eq. (2) defines the convection and radiation boundary conditions.

$${K_x}\frac{{\partial T}}{{\partial x}}{n_x}+{K_y}\frac{{\partial T}}{{\partial y}}{n_y}+{K_z}\frac{{\partial T}}{{\partial z}}{n_z}+{q_r}+{h_c}\left( {T - {T_\infty }} \right)+\sigma \varepsilon F\left( {{T^4} - T_{r}^{4}} \right)=0$$

Where, ${h_c}=$heat transfer coefficient (convection), $W.{m^{ - 2}}.K$; $k=$ Thermal conductivity, $W.{m^{ - 1}}.K$; $q=$ heatflux, W.${m^{ - 1}}$; $\sigma =$Stefan-Boltzmann constant, $5.68 \times {10^{ - 8}}~W.{m^{ - 2}}.{K^4}$; $F=$ configuration factor; and ${n_x}$, ${n_y}$and ${n_z}$are the direction cosines of the boundary.

The Goldak warm temperature delivery model is important for proper welding simulations, in particular, withinside the context of the finite element Method (FEM). Unlike traditional models, Goldak's double ellipsoid design closely resembles actual heat distribution during welding (see Fig. 1). This three-dimensional model can be adapted to different processes and helps to predict metallurgical transformations and optimize weld quality. Its precision ensures structural integrity and improves the overall safety and efficiency of welding. Looking at the dimensions of the heat source in the figure, we see a front length of 5 mm and a rear length that is 15 mm longer, with a uniform width of 5 mm. The marked 3 mm depth demonstrates the penetrating ability of our heat source and strikes a balance between surface fusion and depth integrity. Taken together, these parameters ensure an efficient and precise welding process that promotes high-quality tubular joints that are essential for the intended applications. The equations below state the double ellipsoid heat source model, which best describes the heat source for arc welding:

For the front heat source [5]:

$$Q\left( {x,~y,~z,~t} \right)=\frac{{6\sqrt 3 {f_f}{Q_w}}}{{{a_f}bc\pi \sqrt \pi }}{e^{ - 3{x^{'2}}/{a_f}^{2}}}{e^{ - 3{y^{'2}}/{b^2}}}{e^{ - 3{z^{'2}}/{c^2}}}$$

For the rear heat source[5]:

$$Q\left( {x,~y,~z,~t} \right)=\frac{{6\sqrt 3 {f_r}{Q_w}}}{{{a_r}bc\pi \sqrt \pi }}{e^{ - 3{x^{'2}}/{a_r}^{2}}}{e^{ - 3{y^{'2}}/{b^2}}}{e^{ - 3{z^{'2}}/{c^2}}}$$

Where x, y, and z are the welded pipe's local coordinates, ${f_f}$ and ${f_r}$ are parameters that indicate the proportion of heat deposited in the front and rear portions, respectively. Note that ${f_f}$ + ${f_r}$ = 2.0.

The welding heat source's power is ${Q_w}$. Calculations can be made based on the welding current, arc voltage, and arc efficiency. It is assumed that the TIG welding technique has an arc efficiency η of 80%. Parameters that can affect the characteristics of the welding heat source are ${a_f}$, ${a_r}$, b, and c. Under the welding requirements, the heat source's specifications can be changed to produce the necessary melted zone.

As illustrated in Fig. 2, our simulation incorporated one cylinder with a wallthickness of 3 mm, a length of 300 mm, and an outer diameter of 306 mm.

Incorporated within Fig. 3 are the boundary conditions for welding simulations that inherently encompass both thermal and mechanical factors. The thermal component of the solution encompasses free convection and radiation emanating from the material. To predict deformation and stress with precision, mechanical boundary conditions are a necessary prerequisite.

In the context of the static mechanical analysis, thermal loads are modeled as equivalent to body force. To determine structural analysis inputs, a specific course of action derived from the previous transient thermal study was utilized. Subsequently, the resulting stresses and strains were computed based on incremental stress-strain relationships, as described in Eq. (5).

$$d\varepsilon =d{\varepsilon ^l}+d{\varepsilon ^p}+d{\varepsilon ^T}$$

Where, $d\varepsilon =$ total strain; $d{\varepsilon ^l},d{\varepsilon ^p}{\text{~}}and{\text{~}}d{\varepsilon ^T}$ are the elastic strain, plastic strain, and thermal stress, respectively. In the field of welding, the selection of steel employed can exert a considerable influence on both the welding outcome and the ultimate longevity of the manufactured item. Within the realm of our simulation, we have opted to employ stainless steel (AISI 304) in the context of welding applications, owing to its distinctive attributes and attendant advantages. The AISI 304 alloy is a widely employed stainless steel alloy that encompasses both chromium and nickel, granting it substantial resistance towards rust, corrosion, and staining. Such a combination of traits renders it an exceptional choice for welding applications that necessitate elevated strength, durability, and resilience against harsh environments. Furthermore, the low carbon content of AISI 304 enhances its resistance to sensitization and ensures its exceptional weldability. The material properties of AISI 304 were sourced from [9], and Fig. 4 and Table 2 provide the material properties and their temperature dependence.

Table 2

Material Properties and Their Dependence on Temperature [9].
Temperature [°C]	Thermal conductivity [N/(s. K)]	Specific heatcapacity$\left[ {m{m^2}/\left( {{s^2}.^\circ C} \right)} \right]$	Expansion coefficient [1/°C]	Young’s modulus [GPa]
20	15.7	$5.1 \times {10^8}$	$1.6 \times {10^{ - 5}}$	200
100	16.8	$5.25 \times {10^8}$	$1.7 \times {10^{ - 5}}$	195
200	17	$5.41 \times {10^8}$	$1.8 \times {10^{ - 5}}$	190
400	21	$5.72 \times {10^8}$	$1.9 \times {10^{ - 5}}$	180
600	23.5	$6.04 \times {10^8}$	$2 \times {10^{ - 5}}$	150
800	26.5	$6.3 \times {10^8}$	$2.05 \times {10^{ - 5}}$	128
1000	29.2	$6.48 \times {10^8}$	$2.12 \times {10^{ - 5}}$	70
1200	32.2	$6.73 \times {10^8}$	$2.2 \times {10^{ - 5}}$	15
1400	35.1	$6.91 \times {10^8}$	$7 \times {10^{ - 6}}$	10
1500	36.2	$7 \times {10^8}$	$0.1 \times {10^{ - 6}}$	2

2.2. Simulation

A simulation was conducted to analyze the transient stress occurring during the welding process through the development of a three-dimensional FEM using Simufact-welding. Initially, thermal analysis was conducted to determine the temperature histories, which were subsequently applied to the mechanical model through the indirect coupling method to simulate the transient stress. To reduce computational costs, only half of the symmetrical weldments from the weld center line were selected for the simulation model. This selection resulted in the meshing of a total of 120250 nodes and 120249 elements for the surface model summary and, 121144 nodes and 59844 elements for the volume model summary. Due to the drastic changes in the weld metal during the actual welding process, a finer mesh with a length of 1 mm was utilized in the FEM for the weld zone, while the element size gradually increased from the weld center line to the pipe's edge. Figure 5 depicts the finite element mesh.

3.1. Concept and operating

In the domain of engineering and materials science, it is utterly imperative to ensure the structural soundness of components while simultaneously mitigating the potential for stress-induced failure [12]. Specifically, welded constructions are particularly susceptible to residual tensile stresses, which can trigger IGSCC and negatively impact their dependability [16]. Through a more profound comprehension of the intricate relationship between tensile stresses, material sensitivity, and environmental factors, experts have been able to better grasp how these three elements all contribute to the development of IGSCC [23]. As a consequence, a collection of remedial techniques has emerged as critical solutions to combat the IGSCC quandary. These include stress improvement (SI) methods [26], modified welding technologies [2], the use of new materials [17], and careful regulation of the chemical composition of the weld water [18]. Among the SI techniques, the functioning and principles of which are elucidated in Fig. 6; MSIP holds a distinctive position.

The MSIP technique exudes a remarkable ability to generate compressive stresses at the weldment mechanically. This is achieved by the deployment of a hydraulic mechanical clamp, which contracts the pipe on one side of the weldment, as depicted in Fig. 7.

In Fig. 8, the fundamental principles of the MSIP are meticulously illustrated, offering a step-by-step visualization of this intricate method. The first panel, labeled (a), depicts the application of pressure onto the pipe, causing it to contract (where a: represents clamping placement on the welded pipes and b: represents the width of the clamps). This contraction serves as a precursor to the permanent deformation visualized in panel (b), which provides a schematic representation of the post-MSIP structural changes. Finally, panel (c) delves into the underlying mechanics of the process, showcasing how compression is generated in both axial and hoop directions. Together, these panels provide a cohesive and in-depth overview of the MSIP, elucidating the mechanics and outcomes at each pivotal stage.

It is noteworthy that the pipe is only squeezed locally in the direct proximity of the circumferential weld, but not at the weld itself, as depicted in Fig. 8a. The plastic zone, which spans throughout the weldment region, is facilitated by the contraction of the pipe and the position of the tool. The contracted ring exerts a radially inward force on the pipe and the weld, as shown in Fig. 8b. The deformation compatibility along the pipe, illustrated in Fig. 8c, necessitates a concave axial profile of the pipe in the weld root region. The outcome of this process is the generation of residual compressive stresses at the inner pipe surface in both the axial and hoop directions, respectively. The extent of contraction required for stress redistribution is dependent on the joint geometry and materials. Typically, the required change in pipe circumference before and after the process remains in the range of 0.5 to 0.8%. The pipe contraction at the weldment is only about 0.2 to 0.3%. It is important to note that the maximum contraction is limited by the tool design, which incorporates spacers and shims. Since the process is displacement-controlled, prior knowledge of actual material strength is not a prerequisite for establishing process parameters. The verification of MSIP for each application is achieved by merely measuring the circumferential pipe contraction (Fig. 9).

3.2. Simulation

A FEM with three dimensions was created using Simufact-welding to replicate the momentary tension during the MSIP process. To gain an understanding of the factors involved in MSIP, the following actions were taken: Firstly, the initial step involved the presentation of results obtained from the mechanical model after the welding simulation. Secondly, clamps were introduced to the welded pipes (as illustrated in Fig. 10). Thirdly, a known clamp width of 'b' was applied (as depicted in Fig. 11). Fourthly, the distance 'a' was manipulated (as shown in Fig. 11). Subsequently, step two was repeated with varying values of 'b' (75, 100, and 125 mm). Finally, the resulting stress was recorded for further analysis.

Figure 12 showcases an intricate 3D finite element mesh model that encapsulates the structural details of welded pipes in conjunction with the MSIP tools.

This high-fidelity representation serves to highlight the complexities involved in the interaction between the welded structures and the MSIP apparatus. The mesh aids in providing a granular view of stress distribution, potential deformation regions, and the probable impact zones of the MSIP tools on the welded pipes. Such a detailed visualization is instrumental in understanding the mechanical behavior of the system, ensuring that the application of the MSIP tools is both precise and effective in optimizing the mechanical properties of the welded joints.

4.1 Results analysis after welding

Welding introduces a myriad of stresses within materials due to localized heating and subsequent cooling. These thermal stresses arise from differential expansion and contraction caused by temperature gradients. After welding, the remaining locked-in stresses, termed residual stresses, are often highest within the weld bead and its adjacent heat-affected zone (HAZ) as shown in Fig. 13, The HAZ, being a transition between the molten weld pool and the unaffected base material, undergoes a distinct thermomechanical evolution, making it particularly susceptible to these stresses. Understanding and managing these stresses is crucial, as they can impact the structural integrity, performance, and longevity of the welded component.

This study gives a thorough investigation of the inner and outer surfaces of a pipe's axial residual stress distributions. To illustrate the conclusions, two Figures, namely Fig. 14a and Fig. 14b, have been used. Figure 14a depicts the distribution of axial residual stress on the interior, while Fig. 14b shows the distribution of axial residual stress on the exterior. By observing Fig. 14b, it is evident that the WL region exhibits significantly high compressive stresses. However, these compressive stresses gradually diminish and vanish to zero within a 15 mm distance of the WL. Beyond this critical region, an intriguing phenomenon occurs, where the stress state transitions from compressive to tensile. Further away from the WL, at a distance of approximately 70 mm, these low-magnitude tensile stresses converge towards zero once again. On the other hand, when focusing on the inner surface of the cylinder, Fig. 14a reveals a distinctive pattern. Near the WL, high tensile stresses are observed, which subsequently reverse their nature and transform into compressive residual stresses at a distance of 15 mm. These compressive stresses then steadily increase, reaching a nearly constant value of zero when measured at a distance of 70 mm from the WL. The comprehensive examination of these axial residual stress distributions provides valuable insights into the behavior and characteristics of stresses in the examined pipe system.

A graphical representation of temperature distributions along and in the vicinity of the WL has been obtained (Fig. 15). The simulation observations reveal that the maximum temperature of 1500°C was recorded directly above the WL, followed by a gradual decrease in temperature with increasing distance from the WL. Temperature measurements were conducted at a consistent distance of 150 mm of the WL, encompassing the region commonly referred to as the HAZ. The HAZ is recognized as the zone where thermal gradients induce significant changes in the material's microstructure and mechanical properties (HAZ is about 30 mm from WL). Figure 16 delineates the nuanced temperature distribution across the wallthickness, capturing the variances noted at designated measurement positions. The temperature graph vividly highlights a steep thermal gradient from the centerline to a distance of 50 mm. At the centerline, we observe the pinnacle of the temperature gradient, where the heat reaches its zenith at 1500°C. However, as we traverse from the centerline to 20 mm, there's a dramatic reduction, plummeting to a markedly cooler 230°C. Beyond this, from the 20mm mark up to 50mm, the temperature descent is less gradual, dwindling only to 70°C. This gradient illustrates the intense concentration of heat at the core and its sharp dispersal in the initial radial outward journey, followed by a tempered decline as we move further away. Such a thermal profile is pivotal for deciphering the material's heat behavior, aiding in optimizing processes related to material treatments, and understanding potential stress implications. By analyzing the temperature profiles within the HAZ (see Figs. 15 and 16), valuable insights can be gained regarding the thermal behavior and potential implications on the structural integrity of the welded pipes.

4.2 Results analysis after MSIP

The positioning of clamping is a crucial factor in ensuring the uniformity of shrinkage caused by MSIP and the prevention of any deformation or harm to the pipes. Figure 11 provides a lucid depiction of the recommended clamping placement on the welded pipes. The positioning of clamping is determined based on the dimensions and configuration of the pipes, as well as the location of the welds. a₁, a₂, a₃, a₄, a₅and a₆ denote the distance from the WL and are equivalent to 0, 15, 20, 25, 30, and 40 mm correspondingly, while b₁, b₂, and b₃ represent the width of the clamps employed and are equal to 75, 100, and 125 mm accordingly. MSIP is a technique that is widely used in BWR power plants to prevent stress corrosion cracking. It works by eliminating the residual tensile stresses present in weldments, which are areas where two pieces of metal are joined together by welding. By eliminating these stresses, MSIP prevents cracks and slows the progression of existing failures in piping systems. The technique involves introducing a slight permanent shrinkage in a section of pipe near the weld. This causes plastic deformation, which redistributes the stresses originally present in the weld material and creates favorable compressive stresses along the inner surface of the pipe near the weld, including molten and heat-affected metal zones.

Figure 17 provides a comprehensive visualization of axial residual stress across different stages of the MSIP. One of the critical parameters is the precise displacement of the clamp within the pipe. The clamp advances at a velocity of 0.1mm/s. The plots artfully chart the progression of these stresses, starting from their initial state before the application of MSIP (After welding), through the transient changes that occur during the MSIP and specifically at the time 50% of the MSIP is completed, the clamp has moved a distance of 0.75mm. Progressing further, upon reaching 75% completion of the MSIP, the clamp has fully realized its designated displacement, arriving at the 1mm mark, and culminating in the final stress distribution post-MSIP The 100% completion indicates the final phase, post which the clamp is removed, marking the end of the MSIP. This sequential portrayal allows for a clear comparison, revealing the efficacy of the MSIP in mitigating unwanted residual stresses. By juxtaposing these stages, one can glean insights into the transformative capacity of MSIP, understanding how it acts to optimize and stabilize the stress distribution, thereby enhancing the mechanical integrity of the material.

Figure 18 presents a meticulous depiction of the effective plastic strain variations across distinct phases of the MSIP. The plots capture the evolution of these strains, starting with their baseline configuration before the MSIP initiation (after welding) where the maximum value of the plastic strain was about 0.86, transitioning through the dynamic alterations observed during the MSIP (after 50% and 75% of MSIP) Where the value began to decline and reached to 0.51 and 0.34 respectively, and in the post-MSIP residual state (after 100% of MSIP) the maximum plastic strain value is approximately zero. Observing the transformations from one stage to the next offers invaluable insights into how MSIP functions to enhance material properties, ensuring that plastic deformations are kept within desired limits and contributing to the overall structural integrity of the material.

4.2.1 Effect of clamp position

Upon the successful conclusion of the welding process, we ventured into the realm of the MSIP technique. This intricate method involved the meticulous securing of a clamp with an unwavering width of 75 mm. Further explorations ensued, as we embarked on a journey to uncover the effect of varying distances between the clamp and the WL. Precisely, we delved into the positions of 0, 15, 20, 25, 30, and 40 mm from WL, unraveling a tapestry of intriguing insights. Figures 19 and 20 offer an in-depth analysis of the implications of different clamp placement positions on the distribution of residual stresses at the inner and outer surface of an axial section of the material respectively. The study meticulously examines positions set at 0, 15, 20, 25, 30, and 40 mm from the WL. The comparative visual representation reveals the intricate relationship between the clamp's position and the ensuing stress distribution. Notably, among the positions explored a placement at a = 30mm emerges as the optimal point, yielding the most desirable stress distribution profile. This finding accentuates the significance of precise clamp positioning, demonstrating its critical role in achieving mechanical stability and integrity within the welded region. These Figures serve as a guiding tool, underscoring the importance of strategic clamp placement for maximizing the efficacy of MSIP interventions.

In a continuous endeavor to validate and bolster the findings delineated in Figs. 19 and 20, Fig. 21 was meticulously crafted. This Figure delves into the intricate dynamics between varying clamp placement positions and the consequent residual stress distribution, focusing especially on the wall-thickness of the material. For clarity, the analyzed clamp positions are distinctly at 0, 15, 20, 25, 30, and 40 mm from the WL. For a clearer understanding, the figure has been bifurcated into two distinct sections: a) representing the clamp side at -10 mm from the WL and b) illustrating the opposite side at 10 mm from the WL. This differentiation is crucial in depicting how stresses vary on the clamp side versus the other side of the WL by changing the position of the clamp. Importantly, the results consistently point to the placement at a = 30 mm as being optimal, reaffirming the conclusions of Figs. 19 and 20.

Through this systematic approach in Fig. 21, the findings across the series are reinforced, underscoring the robustness and reliability of the presented results.

It is worth noting that the optimal dimension proved to be 30 mm from WL, where the tensile stresses in the inner surface transformed into compressive stresses, as depicted in Fig. 19.

In stark contrast, the otherdimensions failed to incite any significant change, the tensile stresses remained unchanged. The findings confirm the criticality of adopting an approach that ensures the complete exclusion of the MSIP method from the HAZ region.

4.2.2 Effect of clamp width

In Fig. 22, there's a striking visual representation of residual stress distribution, particularly post-welding and after the MSIP with varying clamp widths of 75, 100, and 125 mm. This distribution is artistically and scientifically represented through a color spectrum, allowing for an immediate and clear interpretation of stress concentrations and dispersions.What stands out prominently in Fig. 22 is the exemplary distribution achieved with the 75 mm clamp width. Compared to its wider counterparts, the 75 mm width exhibits a more balanced and harmonious stress distribution. The color gradients in this particular representation suggest a well-regulated and favorable stress landscape.

After the meticulous implementation of the MSIP on welded pipes, precisely stationed 30 mm from the WL, an enlightening panorama of results was unveiled, as vividly captured in Figs. 23 and 24. These figures, serving as the empirical bedrock, indicated an optimal clamp width of 75 mm, exhibiting unparalleled efficacy in optimizing stress distribution. In contrast, when the research ventured into wider clamps, specifically widths of 100 mm and 125 mm, a discernible disparity emerged. Intriguingly, these alternative widths registered suboptimal stress levels compared to the 75 mm width. Collectively, this data-driven exploration provides a holistic view of the role of clamp width in the MSIP, offering invaluable insights. These compelling revelations do not merely showcase the prowess of the MSIP technique in optimizing stress distributions but also underscore the intricate interplay between clamp width and the resultant stress profiles. In light of these findings, engineers and researchers are better equipped to make judicious decisions regarding clamp width selection, paving the way for enhanced mechanical resilience of welded pipes.

Figure 25 offers a holistic view of the stress landscape throughout two distinct regions: a) the clamp side, represented as -10 mm from the WL, and b) the opposing side, situated 10 mm from the WL. The widths under consideration remain consistent with the previous figures, encompassing 75, 100, and 125 mm. Notably, the visualization for the 75 mm width reaffirms its superior efficacy in optimizing stress distribution, which was initially observed in Figs. 23 and 24. The clear demarcation between the clamp side and the opposing side further enhances the understanding of how these clamp widths influence the stress distribution across the entire axial section. By offering Fig. 25 as a complementary analysis to Figs. 23 and 24, the study provides a robust, multi-faceted examination of the impact of clamp widths on residual stress distribution, fortifying the evidence for the optimized performance of the 75 mm width in the MSIP.

4.2.3 Effect of MSIP on the cracked structure

In the field of piping system maintenance and repair, the MSIP presents a potent technique for addressing stress-induced cracks. Our numerical simulations indicate that this method can effectively redistribute stress in uncracked piping systems, consequently diminishing the likelihood of crack onset. We introduced a circumferential crack with a depth of 1 mm beneath the WL. Following the simulated welding process, there was a marked opening of the crack. To enhance clarity in our visualization, we augmented the deformation factor six-fold, as delineated in Fig. 26.

Despite this initial widening post-welding in our simulation, we employed the MSIP method as a remedial strategy. The simulation showed that, by inducing compressive stresses via MSIP, it was possible to offset the tensile stresses that caused the crack to open, culminating in its closure, as evident in Fig. 27. This numerical investigation underscores both the preventive and corrective potential of MSIP in modeled piping systems. Following the results extracted from Figs. 26 and 27 the MSIP stands out as a pivotal innovation in the mitigation of stress-induced cracks within piping systems. Its multi-faceted capabilities encompass the creation of an optimized stress distribution that not only caters to the immediate vicinity of the weld but also radiates beneficial effects to the adjacent material. By systematically reducing residual stresses, MSIP invariably bolsters the overall structural integrity of the piping. Furthermore, the enhancement of the weld's mechanical properties is a testament to the holistic improvement introduced by the process. Beyond just repair, MSIP represents a proactive approach, potentially preempting stress concentrations that could culminate in cracks. This comprehensive suite of benefits renders MSIP not just as a solution but as a forward-thinking strategy for ensuring the longevity and reliability of piping systems.

This paper focuses on the benefits of using the MSIP procedure to prevent stress corrosion cracking in butt-welded austenitic piping. By placing the MSIP strategically outside the HAZ, it's possible to achieve desired mechanical stress improvements in specific areas. This results in a helpful stress distribution that reduces tensile residual stresses and introduces compressive stresses. This approach can work for both pipes that haven't cracked yet and those that have. It's a flexible solution for handling stress-induced cracks in piping. The MSIP technique has several advantages over traditional welding methods. Firstly, it enables the creation of compressive stresses in the weld and surrounding material, which can deter crack formation. Secondly, it can minimize the residual stresses that often emerge during welding, a factor linked to stress corrosion cracking. Lastly, the MSIP approach can enhance the mechanical properties of the weld and nearby material, boosting overall durability and resistance to corrosion. By applying MSIP early, the need for pipe replacement can be eliminated, inspection frequency can be reduced, and utility providers can save money.

Conflicts of Interest

The authors declare no conflict of interest.

Acknowledgments

The authors acknowledge the Ministry of Higher Education and Scientific Research, Algeria, for technical and financial support (Project code. A01L09UN410120200002).

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Behavior, Failure Analysis, and Effectiveness of Mechanical Stress Improvement Process in Residual Stress Relaxations in Butt-Welded Austenitic Piping Using a Numerical Simulation Approach

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Journal Publication

Version 1

Abstract

Figures

1. INTRODUCTION

2. WELDING PROCESS

2.1. Background

2.2. Simulation

3. MSIP PROCESS

3.1. Concept and operating

3.2. Simulation

4. RESULTS AND DISCUSSION

4.1 Results analysis after welding

4.2 Results analysis after MSIP

4.2.1 Effect of clamp position

4.2.2 Effect of clamp width

4.2.3 Effect of MSIP on the cracked structure

CONCLUSION

Declarations

Conflicts of Interest

Acknowledgments

References

Status:

Journal Publication

Version 1

Temperature [°C]	Thermal conductivity [N/(s. K)]	Specific heatcapacity\(\left[ {m{m^2}/\left( {{s^2}.^\circ C} \right)} \right]\)	Expansion coefficient [1/°C]	Young’s modulus [GPa]
20	15.7	\(5.1 \times {10^8}\)	\(1.6 \times {10^{ - 5}}\)	200
100	16.8	\(5.25 \times {10^8}\)	\(1.7 \times {10^{ - 5}}\)	195
200	17	\(5.41 \times {10^8}\)	\(1.8 \times {10^{ - 5}}\)	190
400	21	\(5.72 \times {10^8}\)	\(1.9 \times {10^{ - 5}}\)	180
600	23.5	\(6.04 \times {10^8}\)	\(2 \times {10^{ - 5}}\)	150
800	26.5	\(6.3 \times {10^8}\)	\(2.05 \times {10^{ - 5}}\)	128
1000	29.2	\(6.48 \times {10^8}\)	\(2.12 \times {10^{ - 5}}\)	70
1200	32.2	\(6.73 \times {10^8}\)	\(2.2 \times {10^{ - 5}}\)	15
1400	35.1	\(6.91 \times {10^8}\)	\(7 \times {10^{ - 6}}\)	10
1500	36.2	\(7 \times {10^8}\)	\(0.1 \times {10^{ - 6}}\)	2