Thermo-Mechanical Coupling Analysis of the Sealing Structure Stress of LNG Cryogenic Hose Fittings

: A cryogenic hose is used to transport liquefied natural gas at sea, where flexible fittings are sealed by corrugated lining and end flange welding. However, the extreme cryogenic temperatures of the conveyed fluid introduce substantial challenges to the integrity of the fitting seals’ structure during the LNG transfer process. In order to study the sealing performance of the fitting under LNG conveying conditions, this paper was based on the general finite element software ABAQUS 6.11 to carry out a thermo-mechanical coupling analysis of the end sealing stress. This paper also established a sealing performance analysis model of the corrugated fitting welding area under the fitting action of LNG load and internal pressure load. A sensitivity analysis was conducted on the influence of weld clearance, blunt edge size, and weld residual height on the weld stress of a fitting ring. The results show that, under the combined action of the medium internal pressure and cryogenic load, the size design of the weld area significantly affects the sealing performance of the fitting, among which the equivalent force of the weld clearance butt sealing area has the greatest impact. Moreover, it was found that a pressure of 5 MPa was 2 mm when the weld clearance was 2 mm, and the average stress at the weld was 53.68 MPa. Further, considering the synergistic influence of the blunt edge size, the weld clearance was 3 mm, the stress was minimal when the blunt side size was 4 mm, and the average stress was 17.42 MPa. These research results can serve as a reference for the design and analysis of the sealing structure of non-adhesive inner corrugated cryogenic hose fittings.


Introduction
The floating liquefied natural gas (FLNG) production, storage, and offloading unit (FLNG) is a type of floating production unit used for the development of offshore natural gas fields.It is used to extract, treat, liquefy, store, load, and unload natural gas [1].FLNG is also used in conjunction with LNG vessels to facilitate LNG transportation.Two methods are available for handling and transporting LNG: the tandem LNG unloading method, which can be utilized in deep-sea areas with harsh sea conditions; and the side-by-side LNG unloading method, which uses suspended cryogenic pipe and is primarily used in offshore areas with reasonably good sea conditions.The commonly used methods of LNG transportation are shown in Figure 1.It is applicable in deep-water environments with unfavorable sea conditions [2].
layer in non-bonded cryogenic flexible pipes [6].Their primary purpose is to bear internal pressure and serve as a sealing medium.In a pipeline system, bellows primarily support bending, lateral, and axial loads.Figure 2 depicts a bellow that is common in such a system.The equipment for a cryogenic flexible pipe and its supporting fittings is specially designed based on the pipe's operating conditions.A typical non-adhesive, internal corrugated, cryogenic flexible-pipe junction structure is depicted in Figure 3.It consisted of a metal bellow, a flange welded fitting, and the application of a welding principle to achieve the desired sealing effect.The fitting is to be installed at room temperature, and, while part of the tensile bending stress may be applied during the installation process, the bolt preload force will primarily affect the installation.The safety of the welded region is critical for the sealing reliability of the fitting because liquefied natural gas transportation is primarily affected by the pressure effect of the low-temperature medium in the pipe and the combined effect of temperature.The LNG cryogenic flexible pipe satisfies safety standards, adapts to a range of unique operating conditions, is highly flexible, robust against corrosion, and performs exceptionally well in heat insulation [3,4].Its applications in deep-sea liquefied natural gas extraction and transportation seem promising [5].Bellows are typically used as the lining layer in non-bonded cryogenic flexible pipes [6].Their primary purpose is to bear internal pressure and serve as a sealing medium.In a pipeline system, bellows primarily support bending, lateral, and axial loads.Figure 2 depicts a bellow that is common in such a system.The LNG cryogenic flexible pipe satisfies safety standards, adapts to a range of unique operating conditions, is highly flexible, robust against corrosion, and performs exceptionally well in heat insulation [3,4].Its applications in deep-sea liquefied natural gas extraction and transportation seem promising [5].Bellows are typically used as the lining layer in non-bonded cryogenic flexible pipes [6].Their primary purpose is to bear internal pressure and serve as a sealing medium.In a pipeline system, bellows primarily support bending, lateral, and axial loads.Figure 2 depicts a bellow that is common in such a system.The equipment for a cryogenic flexible pipe and its supporting fittings is specially designed based on the pipe's operating conditions.A typical non-adhesive, internal corrugated, cryogenic flexible-pipe junction structure is depicted in Figure 3.It consisted of a metal bellow, a flange welded fitting, and the application of a welding principle to achieve the desired sealing effect.The fitting is to be installed at room temperature, and, while part of the tensile bending stress may be applied during the installation process, the bolt preload force will primarily affect the installation.The safety of the welded region is critical for the sealing reliability of the fitting because liquefied natural gas transportation is primarily affected by the pressure effect of the low-temperature medium in the pipe and the combined effect of temperature.The equipment for a cryogenic flexible pipe and its supporting fittings is specially designed based on the pipe's operating conditions.A typical non-adhesive, internal corrugated, cryogenic flexible-pipe junction structure is depicted in Figure 3.It consisted of a metal bellow, a flange welded fitting, and the application of a welding principle to achieve the desired sealing effect.The fitting is to be installed at room temperature, and, while part of the tensile bending stress may be applied during the installation process, the bolt preload force will primarily affect the installation.The safety of the welded region is critical for the sealing reliability of the fitting because liquefied natural gas transportation is primarily affected by the pressure effect of the low-temperature medium in the pipe and the combined effect of temperature.Snedden presented bellows as regular corrugated tubes with excellent bending characteristics.In addition, they are extensively applied as expansion fittings in pipeline systems [8].Krovvidi proposed a design method for bellows that is suitable for high-temperature applications, with an operating temperature of 550 °C.The preliminary design of bellows below the temperature range was completed according to the EIMA standard, and the failure modes such as fatigue, in-plane instability, and in-column instability of the bellows were solved [9].Lei proposed a J integral estimation method for a crack located in the middle of a weld with a mismatch in mechanical properties from the surrounding base material [10].Souza described the development of a framework based on the EPRI crack-driven scheme.This framework was combined with the welding groove simplification program and the equivalent stress-strain relationship to evaluate the structural integrity of dissimilar girth welds in composite pipes and liners subjected to high-level bending loads.The framework is suitable for various pipe geometries, crack configurations, weld grooves, and weld strength mismatch levels.The EPRI estimation scheme for homogeneous pipes under bending is within the framework of ESSRM.The unique stress-strain curve describes the mechanical response of mismatched structures, including the effects of mismatched welding bevel geometry and welding strength [11].Ronda presented results of this numerical simulation for two simple welding benchmark problems, which were formulated for two thick plates [12].Xu J.J. established a thermal-metallurgical-mechanical (TMM) model for a finite element analysis of ultra-high strength steel laser welding.The solid-phase transformation model of austenitizing was improved by introducing the correlation coefficient of the heating rate.Seven cases (Case 1-5) considering different SSPT correlation effects and different austenitizing models (Case 5-7) were selected for welding stress simulation to study the stress evolution mechanism during welding.These effects include the changes in yield strength, thermal expansion coefficient, volumetric strain, and plastic strain, which are all caused by SSPT.The results show that each effect can significantly change the stress evolution process and the magnitude and sign of the final stress [13].Based on the Johnson-Cook material law and Johnson-Cook failure model, Yu M. established a three-dimensional finite element model of the thermal-mechanical coupling of friction stir welding in an ABAQUS environment.The temperature variation law of 7050 aluminum alloy friction stir welding in the three stages of impact, stay, and movement, as well as the influence of heat conduction on the back welding plate, were studied.The results showed that the temperature distribution on the cross-section of the plate was almost symmetrical, and the temperature curve of the nugget zone was V-shaped after the sudden drop stage.In the dwell stage, the friction heat was transmitted around and the plate was preheated.During the motion stage, the heat gradually accumulated until a quasi-stable temperature field was formed [14].In summary, the above research mainly studied the mechanical properties, the structural Snedden presented bellows as regular corrugated tubes with excellent bending characteristics.In addition, they are extensively applied as expansion fittings in pipeline systems [8].Krovvidi proposed a design method for bellows that is suitable for hightemperature applications, with an operating temperature of 550 • C. The preliminary design of bellows below the temperature range was completed according to the EIMA standard, and the failure modes such as fatigue, in-plane instability, and in-column instability of the bellows were solved [9].Lei proposed a J integral estimation method for a crack located in the middle of a weld with a mismatch in mechanical properties from the surrounding base material [10].Souza described the development of a framework based on the EPRI crackdriven scheme.This framework was combined with the welding groove simplification program and the equivalent stress-strain relationship to evaluate the structural integrity of dissimilar girth welds in composite pipes and liners subjected to high-level bending loads.The framework is suitable for various pipe geometries, crack configurations, weld grooves, and weld strength mismatch levels.The EPRI estimation scheme for homogeneous pipes under bending is within the framework of ESSRM.The unique stress-strain curve describes the mechanical response of mismatched structures, including the effects of mismatched welding bevel geometry and welding strength [11].Ronda presented results of this numerical simulation for two simple welding benchmark problems, which were formulated for two thick plates [12].Xu J.J. established a thermal-metallurgical-mechanical (TMM) model for a finite element analysis of ultra-high strength steel laser welding.The solid-phase transformation model of austenitizing was improved by introducing the correlation coefficient of the heating rate.Seven cases (Case 1-5) considering different SSPT correlation effects and different austenitizing models (Case 5-7) were selected for welding stress simulation to study the stress evolution mechanism during welding.These effects include the changes in yield strength, thermal expansion coefficient, volumetric strain, and plastic strain, which are all caused by SSPT.The results show that each effect can significantly change the stress evolution process and the magnitude and sign of the final stress [13].Based on the Johnson-Cook material law and Johnson-Cook failure model, Yu M. established a three-dimensional finite element model of the thermal-mechanical coupling of friction stir welding in an ABAQUS environment.The temperature variation law of 7050 aluminum alloy friction stir welding in the three stages of impact, stay, and movement, as well as the influence of heat conduction on the back welding plate, were studied.The results showed that the temperature distribution on the cross-section of the plate was almost symmetrical, and the temperature curve of the nugget zone was V-shaped after the sudden drop stage.In the dwell stage, the friction heat was transmitted around and the plate was preheated.During the motion stage, the heat gradually accumulated until a quasi-stable temperature field was formed [14].In summary, the above research mainly studied the mechanical properties, the structural optimization design of bellows, and the sealing performance of welded sealing elements in extreme environments through analysis, but it lacked a sealing performance analysis of the bellow fittings under low-temperature fluid transportation conditions.Therefore, based on the general finite element software ABAQUS [15], this paper carries out a sequentially coupled thermal stress analysis, as well as establishes a numerical analysis model of the sealing performance of the welded area of a non-bonded, inner-corrugated, ultra-low temperature flexible pipe fitting under the combined action of normal temperature internal pressure load and LNG low-temperature load and internal pressure.The welded area's equivalent force was analyzed as a measure of the sealing structure of the key indicators of a pressure-bearing capacity [16], and a sensitivity analysis was conducted for the weld clearance size of the blunt edge size of the three factors on the weld equivalent force [17].A sensitivity study of the weld clearance, blunt edge size, and weld height on the equivalent force of the weld area was conducted, and the studied weld equivalent force was employed as a key index to quantify the sealing structure's capacity to withstand pressure [18].The research results can provide reference for the design and analysis of the sealing structure of corrugated LNG hose fittings.
However, there are few existing studies on LNG cryogenic hoses, especially on the failure behavior of the sealing region between a hose and fitting.Moreover, there is a lack of understanding regarding the failure criteria and mechanical properties of LNG hose fittings.This study concentrates on the mechanical properties of a weld area under LNG temperature conditions.We evaluated the distribution of stress in the important area by employing the thermo-mechanical coupling method.This enabled us to discover the crucial design parameters that affect the fitting's ability to resist pressure.By conducting parameter analysis, the sealing performance of the hose fittings was improved.This provided valuable insights for the development of high-performance LNG hose fittings and ensured the safe operation of LNG transfer.

Model of the Fitting Seal Structure
The fitting sealing structure experiences temperature stress σ due to the presence of an internal and external temperature difference, which impacts the sealing performance.Since the piping system would now be operating under the worst circumstances, it is important to take temperature stress on the fitting welding seal into account.Leakage will occur concurrently if the fitting transmission medium's internal medium pressure exceeds the weld's strength [19].The critical failure stress P c and the medium pressure P for the seal at the critical failure stress are the engineering definitions of the least stress to ensure the seal.
Additionally, for welded seals, ensuring that the stress at the weld is less than the allowable stress of the welding material is one of the basic principles in the design of a welding structure.This ensures that the welded fitting will not be damaged or failed due to excessive stress during use.In the welded fitting, the weld is a key area, which is under the influence of various stresses, such as tension, shear, torsion, etc.The stress of the weld depends on the load applied during the welding process, the geometry of the welded fitting, the use of the environment, and other factors; the welding material has the characteristics of allowable stress, which is the maximum stress that the material can withstand.It is usually determined based on the yield strength of the material.Allowable stress is a key parameter in engineering design, which considers the safety and reliability of materials.In the design of a welded structure, it is necessary to analyze the stress at the weld.This includes determining the various stress components of the weld, such as axial tension, transverse shear, normal stress, etc. [20][21][22].The average stress at the weld needs to be lower than the allowable stress of the weld metal in order to prevent the strength of the weld from being compromised, that is where σ ave is the average stress at the weld (MPa); σ T is the temperature stress at the weld (MPa); P is the liquefied natural gas pressure (MPa); and [σ] is the permissible tensile stress of the weld material (MPa).
Through an analysis of the loads on the fitting under working conditions, the stress on the seal weld of the fitting under working conditions was captured, as depicted in Figure 4.The fitting was subjected to liquefied natural gas pressure, and, concurrently, the temperature stress at the weld was created by the existence of a temperature difference between the inner and outer walls [23,24].These two types of loads interacted to affect the fitting's sealing performance.
J. Mar.Sci.Eng.2024, 12, x FOR PEER REVIEW 5 of 17 be lower than the allowable stress of the weld metal in order to prevent the strength of the weld from being compromised, that is where σave is the average stress at the weld (MPa); σT is the temperature stress at the weld (MPa); P is the liquefied natural gas pressure (MPa); and [σ] is the permissible tensile stress of the weld material (MPa).
Through an analysis of the loads on the fitting under working conditions, the stress on the seal weld of the fitting under working conditions was captured, as depicted in Figure 4.The fitting was subjected to liquefied natural gas pressure, and, concurrently, the temperature stress at the weld was created by the existence of a temperature difference between the inner and outer walls [23,24].These two types of loads interacted to affect the fitting's sealing performance.To summarize, by combining Equations ( 1) and ( 2), the welded sealing of the corrugated LNG hose fittings will experience leakage if the strength at the weld is insufficient.In addition, the theory of the critical failure of sealing states that the fitting sealing performance is determined by analyzing the equivalent stress at the von Mises at the weld and the minimum stress at the sealing place, which determines whether or not to realize the sealing.The performance of the seal is determined by the welding stress; if the average welding stress is less than the material permitted stress, structural safety is ensured, and if it is larger than the critical failure pressure, the seal is effective [25,26].This is represented by the following: The strength of the weld controls the sealing performance of corrugated fittings; thus, the impact of the weld parameters on the sealing performance of the junction was investigated.A crucial aspect of the weld is depicted in Figure 5, where the bevel angle was established at 60° based on the GB/T 985.1-2008 specification [27].The specification gave a bevel angle of 60° for the base metal thickness between 5 and 40 mm.The welding strength was affected by the numerical adjustments made to the welding clearance, blunt edge size, and residual height of the weld.Using the force-heat coupling analysis approach, ABAQUS software was used to examine the sealing performance of the weld under fitting working conditions.Additionally, the sensitivity analysis of the three welding parameters was conducted to find the most sensitive parameter that influences the To summarize, by combining Equations ( 1) and ( 2), the welded sealing of the corrugated LNG hose fittings will experience leakage if the strength at the weld is insufficient.In addition, the theory of the critical failure of sealing states that the fitting sealing performance is determined by analyzing the equivalent stress at the von Mises at the weld and the minimum stress at the sealing place, which determines whether or not to realize the sealing.The performance of the seal is determined by the welding stress; if the average welding stress is less than the material permitted stress, structural safety is ensured, and if it is larger than the critical failure pressure, the seal is effective [25,26].This is represented by the following: The strength of the weld controls the sealing performance of corrugated fittings; thus, the impact of the weld parameters on the sealing performance of the junction was investigated.A crucial aspect of the weld is depicted in Figure 5, where the bevel angle was established at 60 • based on the GB/T 985.1-2008 specification [27].The specification gave a bevel angle of 60 • for the base metal thickness between 5 and 40 mm.The welding strength was affected by the numerical adjustments made to the welding clearance, blunt edge size, and residual height of the weld.Using the force-heat coupling analysis approach, ABAQUS software was used to examine the sealing performance of the weld under fitting working conditions.Additionally, the sensitivity analysis of the three welding parameters was conducted to find the most sensitive parameter that influences the strength of the weld.The stress value of the weld was calculated using limiting element analysis, which compared the size of the stress generated by the three key parameters.
strength of the weld.The stress value of the weld was calculated using limiting element analysis, which compared the size of the stress generated by the three key parameters.

Model Size
The fastening ring, two reverse spiral winding armor layers, the inner ring, the fitting flange, and the corrugated liner, in that order, are the fittings that connect the outer layer to the inner layer.We established a full three-dimensional finite element model of the fitting using ABAQUS 6.11 software.Figure 6 displays the geometric model of the fitting sealing structure.

Material Parameters
In order to make the fitting meet the requirements of use, it is necessary to select the materials of each layer of the fitting.Material selection is an important part of fitting design.The selection of appropriate materials may significantly improve the overall bearing performance of the fitting.In the selection of materials, the low temperature resistance, mechanical properties, and corrosion resistance of the materials should be considered first.By comparing the strength, toughness, plasticity, linear expansion coefficient, and corrosion resistance of the mainstream materials 'stainless steel (304,316,321, etc.) and 9Ni steel used in LNG pipelines, the advantages and disadvantages of the performance were analyzed and compared.In this study, 316L was selected as the main material of the fitting and A022 was used as the welding material.The sealing form of the welding seal was determined.At the same time, because the main material of the fitting was 316L (KaiBang Steel Co., Ltd., Jiangsu, China), the welding material was A022 (Hangguang weld material

Numerical Analysis of the Fitting Seal Structure 2.2.1. Model Size
The fastening ring, two reverse spiral winding armor layers, the inner ring, the fitting flange, and the corrugated liner, in that order, are the fittings that connect the outer layer to the inner layer.We established a full three-dimensional finite element model of the fitting using ABAQUS 6.11 software.Figure 6 displays the geometric model of the fitting sealing structure.
strength of the weld.The stress value of the weld was calculated using limiting ele analysis, which compared the size of the stress generated by the three key paramete

Model Size
The fastening ring, two reverse spiral winding armor layers, the inner ring, the flange, and the corrugated liner, in that order, are the fittings that connect the outer to the inner layer.We established a full three-dimensional finite element model of t ting using ABAQUS 6.11 software.Figure 6 displays the geometric model of the sealing structure.

Material Parameters
In order to make the fitting meet the requirements of use, it is necessary to sele materials of each layer of the fitting.Material selection is an important part of fittin sign.The selection of appropriate materials may significantly improve the overall be performance of the fitting.In the selection of materials, the low temperature resis mechanical properties, and corrosion resistance of the materials should be consi first.By comparing the strength, toughness, plasticity, linear expansion coefficien corrosion resistance of the mainstream materials 'stainless steel (304,316,321, etc.) an steel used in LNG pipelines, the advantages and disadvantages of the performance analyzed and compared.In this study, 316L was selected as the main material of the and A022 was used as the welding material.The sealing form of the welding sea determined.At the same time, because the main material of the fitting was 316L (Ka Steel Co., Ltd., Jiangsu, China), the welding material was A022 (Hangguang weld ma

Material Parameters
In order to make the fitting meet the requirements of use, it is necessary to select the materials of each layer of the fitting.Material selection is an important part of fitting design.The selection of appropriate materials may significantly improve the overall bearing performance of the fitting.In the selection of materials, the low temperature resistance, mechanical properties, and corrosion resistance of the materials should be considered first.By comparing the strength, toughness, plasticity, linear expansion coefficient, and corrosion resistance of the mainstream materials 'stainless steel (304,316,321, etc.) and 9Ni steel used in LNG pipelines, the advantages and disadvantages of the performance were analyzed and compared.In this study, 316L was selected as the main material of the fitting and A022 was used as the welding material.The sealing form of the welding seal was determined.At the same time, because the main material of the fitting was 316L (KaiBang Steel Co., Ltd., Jiangsu, China), the welding material was A022 (Hangguang weld material Co., Ltd., Shanghai, China).A022 is an ultra-low carbon Cr18Ni12Mo2 stainless steel electrode with a titanium-calcium coating.The carbon content of the deposited metal is ≤0.04%.It has good heat resistance, corrosion resistance, crack resistance, and stomatal resistance.It has good operating process performance.The coating is resistant to red and has good strength.
Considering the small variation of the elastic modulus of metallic materials in the calculated temperature range, the use of an ideal elastic-plastic material model in ABAQUS ensures the accuracy of the calculation while reducing the computational cost.The material parameters are demonstrated in Table 1.

Mesh Division
The three-dimensional hexahedral heat transfer unit DC3D8 was employed in the thermal analysis.This element can better adapt to complex geometries and non-uniform meshes, thereby providing more accurate temperature field distribution.The hourglass control mode was not enabled, and one could obtain the fitting's results for temperature distribution.The fitting's stress distribution will be obtained by changing the unit to C3D8R for the ensuing static analysis.This element can be used for linear and complex nonlinear analyses involving contact, as well as elastoplastic and large deformation, and it has high computational efficiency.At the same time, hourglass control is enabled to control the numerical stability of the C3D8R unit to ensure the accuracy and reliability of the model.The mesh division is shown in Figure 7.
ABAQUS ensures the accuracy of the calculation while reducing the computational cost.The material parameters are demonstrated in Table 1.

Mesh Division
The three-dimensional hexahedral heat transfer unit DC3D8 was employed in the thermal analysis.This element can better adapt to complex geometries and non-uniform meshes, thereby providing more accurate temperature field distribution.The hourglass control mode was not enabled, and one could obtain the fitting's results for temperature distribution.The fitting's stress distribution will be obtained by changing the unit to C3D8R for the ensuing static analysis.This element can be used for linear and complex nonlinear analyses involving contact, as well as elastoplastic and large deformation, and it has high computational efficiency.At the same time, hourglass control is enabled to control the numerical stability of the C3D8R unit to ensure the accuracy and reliability of the model.The mesh division is shown in Figure 7.
In order to ensure the accuracy of the results, it is necessary to ensure the coordination of mesh quality and displacement when dividing the cross-section geometric model so as to avoid the occurrence of long and narrow elements.At the same time, the convergence of the number and density of meshes was also discussed.When the mesh is refined 2 times, the change in mechanical performance analysis results does not exceed 5%, which proves that the mesh shown in Figure 7 met the requirements of engineering analysis.Therefore, this mesh was used in the subsequent finite element analysis.

Load and Boundary Conditions
In the process of thermal analysis, the temperature-displacement coupling analysis step (steady state) was adopted, the time length was set at 1, the automatic increment and maximum increment step were 1000, the initial increment step was 0.01, the minimum increment step was 10 −7 , and the maximum increment step was 1.The thermal analysis process required that the surface heat exchange conditions be set, and the heat dissipation In order to ensure the accuracy of the results, it is necessary to ensure the coordination of mesh quality and displacement when dividing the cross-section geometric model so as to avoid the occurrence of long and narrow elements.At the same time, the convergence of the number and density of meshes was also discussed.When the mesh is refined 2 times, the change in mechanical performance analysis results does not exceed 5%, which proves that the mesh shown in Figure 7 met the requirements of engineering analysis.Therefore, this mesh was used in the subsequent finite element analysis.

Load and Boundary Conditions
In the process of thermal analysis, the temperature-displacement coupling analysis step (steady state) was adopted, the time length was set at 1, the automatic increment and maximum increment step were 1000, the initial increment step was 0.01, the minimum increment step was 10 −7 , and the maximum increment step was 1.The thermal analysis process required that the surface heat exchange conditions be set, and the heat dissipation coefficient of the membrane layer was set to 0.01.This number describes the heat dissipation capacity of the membrane or membrane layer at a temperature gradient.A lower heat dissipation coefficient means that the membrane finds it relatively difficult to dissipate heat, while a higher heat dissipation coefficient means that the membrane has a better heat dissipation performance.The heat dissipation coefficient of the metal material is usually between 0.01 and 10, where the heat exchange between the layers of the fitting and the external environment needs to be reduced as much as possible; as such, the heat dissipation coefficient was 0.01.The temperature of the surroundings was set to 20 • C, and the contact between the fitting's layers was set with the thermal conductivity in the contact properties to 16 (mW/(mm• • C).The corrugated liner of the fitting's wall surface had its temperature boundary condition set to −163 • C. In the process of force analysis, the static general analysis step was used, the time length was set to 1, the automatic increment and maximum increment step were 1000, the initial increment step was 0.01, the minimum increment step was 10 −7 , and the maximum increment step was 1.As demonstrated in Figure 8, the load can be obtained from the fitting's stress distribution by changing the unit to C3D8R for the static universal analysis.The analysis results of thermal stress as the initial state of the internal pressure analysis, as well as the corrugated liner and the flange wall surface to apply 2 MPa internal pressure, can be used to verify the sealing performance.
tion capacity of the membrane or membrane layer at a temperature gradient.A lower heat dissipation coefficient means that the membrane finds it relatively difficult to dissipate heat, while a higher heat dissipation coefficient means that the membrane has a better heat dissipation performance.The heat dissipation coefficient of the metal material is usually between 0.01 and 10, where the heat exchange between the layers of the fitting and the external environment needs to be reduced as much as possible; as such, the heat dissipation coefficient was 0.01.The temperature of the surroundings was set to 20 °C, and the contact between the fitting's layers was set with the thermal conductivity in the contact properties to 16 (mW/(mm•°C).The corrugated liner of the fitting's wall surface had its temperature boundary condition set to −163 °C.In the process of force analysis, the static general analysis step was used, the time length was set to 1, the automatic increment and maximum increment step were 1000, the initial increment step was 0.01, the minimum increment step was 10 −7 , and the maximum increment step was 1.As demonstrated in Figure 8, the load can be obtained from the fitting's stress distribution by changing the unit to C3D8R for the static universal analysis.The analysis results of thermal stress as the initial state of the internal pressure analysis, as well as the corrugated liner and the flange wall surface to apply 2 MPa internal pressure, can be used to verify the sealing performance.

Welding Seal Performance Analysis
The finite element model of the fitting under the combined action of low temperature and internal pressure was calculated, and the overall temperature distribution of the fitting is shown in Figure 9. From Figure 10, it can be seen that the maximum surface temperature of the outer clasp of the fitting was −102 °C, and the temperature of the inner tube in direct contact with the LNG medium was −163 °C.Same as the medium temperature, the overall temperature of the fitting gradually increased from the inside to the outside.In the actual work, the fitting was, from 20 °C to −163 °C, liquefied natural gas, and the temperature change in the fitting was a process.Therefore, the changes in temperature and stress at the weld of the fitting were extracted, and the change in stress with the temperature was obtained.As shown in Figure 11, the average stress at the weld was analyzed with the change in temperature.With the decrease in the temperature at the weld, the stress at the weld increased gradually.When the temperature at the weld reached −163 °C, the average stress at the weld reached a maximum of 16 MPa.According to the sealing critical failure theory, the fitting met the minimum requirements for sealing; at the same time, because the average stress at the weld of the fitting is far less than the allowable strength of the weld material, there was no strength failure in the fitting sealing structure, so the fitting was sealed in the working state.

Welding Seal Performance Analysis
The finite element model of the fitting under the combined action of low temperature and internal pressure was calculated, and the overall temperature distribution of the fitting is shown in Figure 9. From Figure 10, it can be seen that the maximum surface temperature of the outer clasp of the fitting was −102 • C, and the temperature of the inner tube in direct contact with the LNG medium was −163 • C. Same as the medium temperature, the overall temperature of the fitting gradually increased from the inside to the outside.In the actual work, the fitting was, from 20 • C to −163 • C, liquefied natural gas, and the temperature change in the fitting was a process.Therefore, the changes in temperature and stress at the weld of the fitting were extracted, and the change in stress with the temperature was obtained.As shown in Figure 11, the average stress at the weld was analyzed with the change in temperature.With the decrease in the temperature at the weld, the stress at the weld increased gradually.When the temperature at the weld reached −163 • C, the average stress at the weld reached a maximum of 16 MPa.According to the sealing critical failure theory, the fitting met the minimum requirements for sealing; at the same time, because the average stress at the weld of the fitting is far less than the allowable strength of the weld material, there was no strength failure in the fitting sealing structure, so the fitting was sealed in the working state.
As illustrated in Figure 12, the weld and pressure contact with the maximum stress on the inside of the weld, i.e., the weld of the inner layer with an average stress of 5.11 MPa (for the fittings at room temperature and a 2 MPa pressure) were subjected to cryogenic conditions and pressure, and this conducted under the combined action of the model of the calculation results.This was performed rather than the fittings being subjected to the combined influence of cryogenic conditions and internal pressure; as such, the corrugated pipe stress model at the weld analysis showed that, under cryogenic and internal pressure conditions, the weld and pressure contact with the largest stress on the inside was 16 MPa for the weld internal measurement.This process was found to be 10.89MPa more than the results of the calculations that were performed at room temperature, thus demonstrating that temperature affects weld stress and that cryogenic conditions increase stress, which, in turn, affects sealing performance.As illustrated in Figure 12, the weld and pressure contact with the maximum stress on the inside of the weld, i.e., the weld of the inner layer with an average stress of 5.11 MPa (for the fittings at room temperature and a 2 MPa pressure) were subjected to cryogenic conditions and pressure, and this conducted under the combined action of the model of the calculation results.This was performed rather than the fittings being subjected to the combined influence of cryogenic conditions and internal pressure; as such, the corrugated pipe stress model at the weld analysis showed that, under cryogenic and internal pressure conditions, the weld and pressure contact with the largest stress on the inside was 16 MPa for the weld internal measurement.This process was found to be 10.89As illustrated in Figure 12, the weld and pressure contact with the maximum stress on the inside of the weld, i.e., the weld of the inner layer with an average stress of 5.11 MPa (for the fittings at room temperature and a 2 MPa pressure) were subjected to cryogenic conditions and pressure, and this conducted under the combined action of the model of the calculation results.This was performed rather than the fittings being subjected to the combined influence of cryogenic conditions and internal pressure; as such, the corrugated pipe stress model at the weld analysis showed that, under cryogenic and internal pressure conditions, the weld and pressure contact with the largest stress on the inside was 16 MPa for the weld internal measurement.This process was found to be 10.89MPa more than the results of the calculations that were performed at room temper thus demonstrating that temperature affects weld stress and that cryogenic conditio crease stress, which, in turn, affects sealing performance.The temperature differential between the inside and outside of the fitting stru causes temperature stress, which raises the tension at the weld and affects the fi ability to seal.When the medium internal pressure and the cryogenic load were together, the average stress on the inside of the weld was 16 MPa.The comparison results of the two model calculations revealed that the increase in the average stress weld in the bellows, which was 10.89 MPa, was the thermal stress that was generat The temperature differential between the inside and outside of the fitting structure causes temperature stress, which raises the tension at the weld and affects the fitting's ability to seal.When the medium internal pressure and the cryogenic load were acting together, the average stress on the inside of the weld was 16 MPa.The comparison of the results of the two model calculations revealed that the increase in the average stress at the weld in the bellows, which was 10.89 MPa, was the thermal stress that was generated by the temperature.The largest amount of stress was on the inside of the weld when the fitting was subjected to only 2 MPa pressure at room temperature.The research has revealed that the temperature of the fitting sealing impact is important, and that the cryogenic effect needs to be taken into account for the project as a whole.

Weld Critical Parameter Impact Analysis
When welding, the size of the weld clearance has an impact on the weld's strength.The following process was used in this study: Set the internal pressure to 2 MPa and 5 MPa to compare the stress changes in the weld caused by the low-temperature load and the fitting action of the internal pressure.Then, respectively, set the weld clearance to 1 mm, 2 mm, 3 mm, and 4 mm.Set the weld residual height to 1 mm and the size of the blunt edges to 2 mm to avoid overlooking other significant factors.The quarter-fitting sealing model is to be established and calculated, and the overall stress distribution is to be obtained, as shown in Figure 13.The average stress change in the fitting with different weld clearance sizes and different internal pressures is then analyzed, as shown in Figure 14, where 2 MPa and 5 MPa are the internal pressures as the input to the load.The simultaneous simplification of calculations is possible.This is because the fitting is an axisymmetric structure, and the loaded condition is also an axisymmetric distribution.As Figure 13 illustrates, the stress distribution results derived from the fitting's quadratic model were correct and in line with the overall model's stress distribution results.The analysis of the weld clearance and average stress of the weld change law, as shown in Figure 14, demonstrated that the weld clearance had a greater impact on the weld value when the fitting was subjected to 2 MPa and 5 MPa pressures.As the clearance increased, the average stress at the weld increased and then decreased within the same pressure, with the 2 MPa pressure producing the highest average stress of weld clearance at 21.78 MPa, 5 MPa pressure, and 53.68 MPa weld.The average stress at the weld was 21.78 MPa  As Figure 13 illustrates, the stress distribution results derived from the fitting's quadratic model were correct and in line with the overall model's stress distribution results.The analysis of the weld clearance and average stress of the weld change law, as shown in Figure 14, demonstrated that the weld clearance had a greater impact on the weld value when the fitting was subjected to 2 MPa and 5 MPa pressures.As the clearance increased, the average stress at the weld increased and then decreased within the same pressure, with the 2 MPa pressure producing the highest average stress of weld clearance at 21.78 As Figure 13 illustrates, the stress distribution results derived from the fitting's quadratic model were correct and in line with the overall model's stress distribution results.The analysis of the weld clearance and average stress of the weld change law, as shown in Figure 14, demonstrated that the weld clearance had a greater impact on the weld value when the fitting was subjected to 2 MPa and 5 MPa pressures.As the clearance increased, the average stress at the weld increased and then decreased within the same pressure, with the 2 MPa pressure producing the highest average stress of weld clearance at 21.78 MPa, 5 MPa pressure, and 53.68 MPa weld.The average stress at the weld was 21.78 MPa at 2 MPa pressure and 53.68 MPa at 5 MPa pressure.And, with a 1 mm clearance and 2 MPa pressure, the minimum stress at the weld was 18.85 MPa; this differed from the calculated values of a 2 mm clearance by 3.93 MPa, or 20.85%.With a 5 MPa pressure and a 1 mm clearance, the minimum stress was 47.36 MPa, which differed by 6.32 MPa, or 13%.The sealing performance improved with increasing weld stress.The computed results indicated that a clearance of 2 mm is the ideal size.To compare the stress change in the weld under the combined effects of cryogenic load and internal pressure, the value of the blunt edge size was changed.The internal pressure was set to 2 MPa and 5 MPa, and the blunt edge size was, respectively, set to 2 mm, 3 mm, and 4 mm.To ensure that the influence of other critical factors was excluded, the weld clearance and weld residual height were kept constant at 1 mm. Figure 15 illustrates the analysis of the average stress changes at various blunt edge sizes and fitting internal pressures.
under the combined effects of cryogenic load and internal pressure, the value of the blunt edge size was changed.The internal pressure was set to 2 MPa and 5 MPa, and the blunt edge size was, respectively, set to 2 mm, 3 mm, and 4 mm.To ensure that the influence of other critical factors was excluded, the weld clearance and weld residual height were kept constant at 1 mm. Figure 15 illustrates the analysis of the average stress changes at various blunt edge sizes and fitting internal pressures.Figure 15 demonstrates that the average stress value of the weld was unaffected by the variations in the size of the blunt edge.The fitting was exposed to pressure values of 2 MPa and 5 MPa.As the size of the blunt edge increased, the maximum stress at the weld reduced.Under equal pressure conditions, the average stress was greatest at the blunt edge with a size of 2 mm.Specifically, at a pressure of 2 MPa, the average stress at the weld was 18.85 MPa.The average stress at the weld was determined to be 5 MPa based on the calculation findings.Additionally, the ideal passivated edge size was found to be 2 mm.
We established a finite element model of weld clearance fittings, as well as varied the weld margin height and compared the changes in the stress of the weld fittings under the fitting actions of low-temperature load and internal pressure.The internal pressure was set to 2 MPa and 5 MPa, and the weld margin height was, respectively, set to 0.5 mm, 1 mm, 1.5 mm, and 2 mm.These parameters will allow one to study the effect of weld margin height on fitting sealing performance.The blunt edge size was fixed at 1 mm, and the weld clearance was set at 1 mm to guarantee that the impact of the other crucial factors was eliminated.Figure 16 illustrates the analysis of the average stress variation that was conducted at various weld margin height sizes and fitting internal pressures.Figure 15 demonstrates that the average stress value of the weld was unaffected by the variations in the size of the blunt edge.The fitting was exposed to pressure values of 2 MPa and 5 MPa.As the size of the blunt edge increased, the maximum stress at the weld reduced.Under equal pressure conditions, the average stress was greatest at the blunt edge with a size of 2 mm.Specifically, at a pressure of 2 MPa, the average stress at the weld was 18.85 MPa.The average stress at the weld was determined to be 5 MPa based on the calculation findings.Additionally, the ideal passivated edge size was found to be 2 mm.
We established a finite element model of weld clearance fittings, as well as varied the weld margin height and compared the changes in the stress of the weld fittings under the fitting actions of low-temperature load and internal pressure.The internal pressure was set to 2 MPa and 5 MPa, and the weld margin height was, respectively, set to 0.5 mm, 1 mm, 1.5 mm, and 2 mm.These parameters will allow one to study the effect of weld margin height on fitting sealing performance.The blunt edge size was fixed at 1 mm, and the weld clearance was set at 1 mm to guarantee that the impact of the other crucial factors was eliminated.Figure 16 illustrates the analysis of the average stress variation that was conducted at various weld margin height sizes and fitting internal pressures.Figure 16 illustrates the analysis results of the weld height and weld average stress change rules for the fittings that were subjected to 2 MPa and 5 MPa pressures.At the same pressure, the average stress at the weld decreased as the weld height increased.At 0.5 mm, the average stress at the weld was highest at 2 MPa pressure, where it was 19.09 MPa, and at 5 MPa pressure, it was 47.90 MPa.The ideal weld height, thus, was 0.5 mm, based on the computation findings.
Overall, the three main parameters influenced the fitting sensitivity analysis, which compared the following: the pressure of 2 MPa and 5 MPa, the size of the clearance, the size of the obtuse edge, and the welding residual height.Figure 16 demonstrates that the average stress at the weld increased and then decreased with the size of the clearance.Similarly, Figures 14 and 15 show that the average stress at the weld decreased as the size of the obtuse edge and welding residual height increased.The alteration in mean stress indicated that the weld was under stress.The changes in clearance size had a direct impact on the weld area, the contact surface between the media, the pressure, and the temperature.Additionally, the changes in clearance size also affected the weld volume, weld area, weld size, and fitting weld stress, with the most significant impact being observed in the clearance size changes.At a pressure of 2 MPa, the highest average stress and the minimum average stress experienced a shift of 20.85%.This change had the greatest impact on the sealing performance of the fitting.The weld clearance was the primary factor that significantly affected the sealing performance due to the substantial impact of pressure and temperature on the tension of the weld.

Synergistic Effect Sensitivity Analysis
The dimensions of the weld seam and blunt edge were configured at 1 mm, 2 mm, 3 mm, and 4 mm, thereby resulting in a total of 12 possible combinations.In order to study the impact of temperature on the weld sealing law, the height of the weld residue was standardized to 1 mm, thereby eliminating the influence of the remaining weld material.The single-factor sensitivity study clearly showed that, when the load is adjusted to 2 MPa, the average stress change rule at the weld can be understood more easily when analyzing fittings with different clearances and blunt edge diameters, as depicted in Figure 17. Figure 16 illustrates the analysis results of the weld height and weld average stress change rules for the fittings that were subjected to 2 MPa and 5 MPa pressures.At the same pressure, the average stress at the weld decreased as the weld height increased.At 0.5 mm, the average stress at the weld was highest at 2 MPa pressure, where it was 19.09 MPa, and at 5 MPa pressure, it was 47.90 MPa.The ideal weld height, thus, was 0.5 mm, based on the computation findings.
Overall, the three main parameters influenced the fitting sensitivity analysis, which compared the following: the pressure of 2 MPa and 5 MPa, the size of the clearance, the size of the obtuse edge, and the welding residual height.Figure 16 demonstrates that the average stress at the weld increased and then decreased with the size of the clearance.Similarly, Figures 14 and 15 show that the average stress at the weld decreased as the size of the obtuse edge and welding residual height increased.The alteration in mean stress indicated that the weld was under stress.The changes in clearance size had a direct impact on the weld area, the contact surface between the media, the pressure, and the temperature.Additionally, the changes in clearance size also affected the weld volume, weld area, weld size, and fitting weld stress, with the most significant impact being observed in the clearance size changes.At a pressure of 2 MPa, the highest average stress and the minimum average stress experienced a shift of 20.85%.This change had the greatest impact on the sealing performance of the fitting.The weld clearance was the primary factor that significantly affected the sealing performance due to the substantial impact of pressure and temperature on the tension of the weld.

Synergistic Effect Sensitivity Analysis
The dimensions of the weld seam and blunt edge were configured at 1 mm, 2 mm, 3 mm, and 4 mm, thereby resulting in a total of 12 possible combinations.In order to study the impact of temperature on the weld sealing law, the height of the weld residue was standardized to 1 mm, thereby eliminating the influence of the remaining weld material.The single-factor sensitivity study clearly showed that, when the load is adjusted to 2 MPa, the average stress change rule at the weld can be understood more easily when analyzing fittings with different clearances and blunt edge diameters, as depicted in Figure 17. Figure 17 shows the maximum stress, which was 21.78 MPa and occurred when the fitting weld clearance was 2 mm and the blunt edge size was 2 mm.On the other hand, when the fitting weld clearance was 3 mm and the blunt edge size was 4 mm, the average stress decreased by 25% to 17.42 MPa.The results indicate that alterations in the fitting weld clearance and obtuse edge size have an impact on the dimensions of the fitting weld volume.Furthermore, the stress of the fitting undergoes considerable changes when subjected to temperature load, but the size of the obtuse edge remains constant.From the observed variations in the stress size, it can be deduced that the effectiveness of the fitting's seal is greatly influenced by alterations in the weld clearance.This parameter is the most susceptible to modifications in the fitting's welding sealing parameter.

Conclusions
By conducting a theoretical analysis of the corrugated hose fitting welded seal structure, it was established that the sealing performance is determined by the stress of the welded seal.An analysis was conducted on the performance of the welded seal, where we specifically examined the effects of the different weld clearances, obtuse edge diameters, and weld residual heights on the sealing stresses.This study also investigated the parameter that had the most impact on the welded seals.The ABAQUS simulation program was utilized to determine the stress at the weld seam under the combined effects of static temperature load, cryogenic conditions, and internal pressure.The findings indicated the following: (1) Both the temperature load and the medium pressure have an impact on fittings.The use of a cryogenic medium induces the fittings to be in an operational state.There exists a temperature gradient between the interior and exterior, with the outer wall's temperature potentially reaching as low as −100 °C.As a result, the analysis of the sealing performance of the fittings must take into account the temperature component.(2) Compared to the static load model at room temperature, the fitting's sealing performance under a medium internal pressure and cryogenic load increased by 10.24 MPa to 25.3 MPa, with the temperature stress increasing.The weld stress was even.Cryogenics affect the fitting sealing and raise the equivalent stresses in the welded area due to thermal stresses.Figure 17 shows the maximum stress, which was 21.78 MPa and occurred when the fitting weld clearance was 2 mm and the blunt edge size was 2 mm.On the other hand, when the fitting weld clearance was 3 mm and the blunt edge size was 4 mm, the average stress decreased by 25% to 17.42 MPa.The results indicate that alterations in the fitting weld clearance and obtuse edge size have an impact on the dimensions of the fitting weld volume.Furthermore, the stress of the fitting undergoes considerable changes when subjected to temperature load, but the size of the obtuse edge remains constant.From the observed variations in the stress size, it can be deduced that the effectiveness of the fitting's seal is greatly influenced by alterations in the weld clearance.This parameter is the most susceptible to modifications in the fitting's welding sealing parameter.

Conclusions
By conducting a theoretical analysis of the corrugated hose fitting welded seal structure, it was established that the sealing performance is determined by the stress of the welded seal.An analysis was conducted on the performance of the welded seal, where we specifically examined the effects of the different weld clearances, obtuse edge diameters, and weld residual heights on the sealing stresses.This study also investigated the parameter that had the most impact on the welded seals.The ABAQUS simulation program was utilized to determine the stress at the weld seam under the combined effects of static temperature load, cryogenic conditions, and internal pressure.The findings indicated the following: (1) Both the temperature load and the medium pressure have an impact on fittings.The use of a cryogenic medium induces the fittings to be in an operational state.There exists a temperature gradient between the interior and exterior, with the outer wall's temperature potentially reaching as low as −100 • C. As a result, the analysis of the sealing performance of the fittings must take into account the temperature component.(2) Compared to the static load model at room temperature, the fitting's sealing performance under a medium internal pressure and cryogenic load increased by 10.24 MPa to 25.3 MPa, with the temperature stress increasing.The weld stress was even.Cryogenics affect the fitting sealing and raise the equivalent stresses in the welded area due to thermal stresses.
(3) This study found that a 2 mm weld clearance, 2 mm blunt edge size, and 0.5 mm weld residual height optimize the fitting sealing performance for the three most important

Figure 3 .
Figure 3. Schematic diagram of a typical fitting sealing structure.

Figure 3 .
Figure 3. Schematic diagram of a typical fitting sealing structure.

Figure 4 .
Figure 4. Force at the fitting seal weld.

Figure 4 .
Figure 4. Force at the fitting seal weld.

Figure 5 .
Figure 5. Critical geometric parameters of the weld.

Figure 6 .
Figure 6.Geometric model of the fitting sealing structure.

Figure 5 .
Figure 5. Critical geometric parameters of the weld.

Figure 5 .
Figure 5. Critical geometric parameters of the weld.

Figure 6 .
Figure 6.Geometric model of the fitting sealing structure.

Figure 6 .
Figure 6.Geometric model of the fitting sealing structure.

Figure 7 .
Figure 7.The mesh encryption that was conducted twice.

Figure 7 .
Figure 7.The mesh encryption that was conducted twice.

Figure 8 .
Figure 8. Location of the internal pressure load action.

Figure 8 .
Figure 8. Location of the internal pressure load action.

JFigure 9 .Figure 9 .Figure 9 .Figure 10 .
Figure 9. Temperature distribution of the fitting at −163 °C.(a) The overall temperature distribution of the fittings.(b) The fitting profile temperature distribution.

Figure 10 .
Figure 10.Average weld strains at various temperatures.(a) The stress of a 0 °C weld; (b) the stress of a −20 °C weld; (c) the stress of a −50 °C weld; (d) the stress of a −100 °C weld; and (e) the stress of a −163 °C weld.

Figure 11 .
Figure 11.Variation in the weld stress with temperature.

Figure 10 .Figure 10 .
Figure 10.Average weld strains at various temperatures.(a) The stress of a 0 • C weld; (b) the stress of a −20 • C weld; (c) the stress of a −50 • C weld; (d) the stress of a −100 • C weld; and (e) the stress of a −163 • C weld.

Figure 11 .
Figure 11.Variation in the weld stress with temperature.

Figure 11 .
Figure 11.Variation in the weld stress with temperature.

Figure 12 .
Figure 12.The equivalent force at the weld at different temperatures in 2 MPa pressure cond (a) The equivalent stresses at the weld at 20 ℃.(b) The equivalent stresses at the weld at −163

Figure 12 .
Figure 12.The equivalent force at the weld at different temperatures in 2 MPa pressure conditions.(a) The equivalent stresses at the weld at 20 °C.(b) The equivalent stresses at the weld at −163 • C.

J 17 Figure 13 .
Figure 13.The equivalent force for the finite element model of fittings.

Figure 14 .
Figure 14.Average stresses for the different weld clearance sizes at 2 MPa and 5 MPa internal pressure.

Figure 13 . 17 Figure 13 .
Figure 13.The equivalent force for the finite element model of fittings.

Figure 14 .
Figure 14.Average stresses for the different weld clearance sizes at 2 MPa and 5 MPa internal pressure.

Figure 14 .
Figure 14.Average stresses for the different weld clearance sizes at 2 MPa and 5 MPa internal pressure.

Figure 15 .
Figure 15.Average stresses for the different blunt edge size sizes at 2 MPa and 5 MPa internal pressures.

Figure 15 .
Figure 15.Average stresses for the different blunt edge size sizes at 2 MPa and 5 MPa internal pressures.

Figure 16 .
Figure 16.Average stresses for different weld height sizes at 2 MPa and 5 MPa internal pressures.

Figure 16 .
Figure 16.Average stresses for different weld height sizes at 2 MPa and 5 MPa internal pressures.

Figure 17 .
Figure 17.Average stresses for the different weld clearance and blunt edge size sizes at a 2 MPa internal pressure.

Figure 17 .
Figure 17.Average stresses for the different weld clearance and blunt edge size sizes at a 2 MPa internal pressure.