Method for predicting welding residual stress distribution of pressure equipment based on structural constraint

Abstract

The application discloses a kind of based on structural restraint's pressure-bearing equipment welding residual stress distribution prediction method, belong to welding residual stress distribution prediction technical field.The method includes steps: S1, obtains the welding residual stress distribution data of pressure-bearing equipment flat plate workpiece under different parameters;S2, extract the longitudinal residual stress distribution data along the direction perpendicular to weld and thickness direction, qualitatively analyze the influence law of each main parameter on longitudinal residual stress distribution;S3, establish the residual stress distribution prediction model suitable for the flat plate workpiece of pressure-bearing equipment along the direction perpendicular to weld and thickness direction;S4, the residual stress distribution prediction model of pressure-bearing equipment flat plate workpiece along the direction perpendicular to weld and along thickness direction is corrected with bending constraint;S5, residual stress is predicted to actual pressure-bearing equipment flat plate workpiece or cylindrical workpiece using the corrected prediction model.The application can carry out high-precision prediction to thick-walled pressure-bearing equipment welding residual stress distribution.

Description

Technical Field

[0001] This invention relates to the field of welding residual stress distribution prediction technology, and specifically to a method for predicting welding residual stress distribution in pressure-bearing equipment based on structural constraints. Background Technology

[0002] Welding residual stress refers to the internal stress remaining due to the constraint of structural welding deformation. It can exacerbate creep damage, induce fatigue failure, and promote stress corrosion cracking, seriously threatening the service safety of pressure equipment. As pressure equipment develops towards larger sizes and higher constraints, the problem of welding residual stress becomes increasingly prominent. The main reasons are: larger structural dimensions lead to huge welding heat inputs and complex thermal cycling processes; multi-layer, multi-pass welding processes cause repeated superposition and coupling of stress fields; and high structural constraints prevent the free release of stress, resulting in extremely high levels and complex distributions of residual stress. Therefore, accurately understanding the distribution of welding residual stress in large pressure equipment is of great significance for optimizing welding processes, assessing structural safety, predicting equipment lifespan, and guiding in-service equipment inspection and maintenance.

[0003] Currently, existing methods for analyzing and predicting residual stress in welding of pressure equipment can be mainly divided into three categories: experimental measurement methods, numerical simulation methods, and empirical formula methods. Current research on predicting residual stress in welding of thick-walled pressure equipment, both domestically and internationally, focuses on experimental testing and numerical simulation methods. Experimental methods include physical detection techniques such as blind hole method, contour method, indentation method, X-ray diffraction, and neutron diffraction, measuring at specific points on actual welded parts or simulated samples to directly obtain residual stress values. However, experimental methods may damage the workpiece, or are limited to surface detection, and are mostly discrete point measurements, making it difficult to comprehensively and continuously obtain the complete residual stress field of the entire component. Numerical simulation methods, by establishing a thermo-mechanical coupling model, comprehensively consider multiple physical field factors such as welding heat input, material nonlinearity, and phase transformation effects. They can more accurately simulate the residual stress distribution under complex geometric and technological conditions and have become the mainstream method for analyzing and predicting welding residual stress. However, for large pressure equipment, which has a large diameter, thick walls, many welds, and strong structural constraints, the finite element method is complex to model, has high calculation costs, and requires a high level of professional background from users, thus limiting its rapid application in engineering sites.

[0004] To address the shortcomings of experimental measurement and numerical simulation methods, scholars have proposed empirical formula methods to achieve rapid and accurate prediction of residual stress. For example, the "Corrected Estimation Formula for Longitudinal Residual Stress in Flat Plate Welded Joints" proposes a longitudinal residual stress distribution model along the direction perpendicular to the weld for welded joints of medium and thin plates, considering the effects of welding parameters, the number of weld passes, and the heat flow distribution coefficient of the plate. However, this formula is not very applicable to thick and extra-thick plates, and it does not consider the unique geometric constraints and wall thickness constraints of pressure equipment. Furthermore, it cannot be applied to thick-walled cylindrical components of pressure equipment, limiting its engineering application. Especially for large cylindrical workpieces of pressure equipment, the welding residual stress is affected by a complex coupling of multiple factors, including welding heat input, welding speed, number of weld passes, joint type, material properties, structural dimensions, and structural constraints. It cannot be expressed by a single parameter or a directly related parameter; only a qualitative correlation can be established. For this reason, existing empirical methods are mostly simplified models that reduce or ignore the influence of some factors. Therefore, they are mostly applicable to simple flat workpieces, but not to thick-walled pressure equipment cylindrical workpieces with high structural rigidity, difficult deformation, and strong structural restraint. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention proposes a method for predicting the distribution of welding residual stress in pressure-bearing equipment based on structural constraints.

[0006] The present invention specifically adopts the following technical solution:

[0007] A method for predicting the welding residual stress distribution of pressure-bearing equipment based on structural constraints, comprising the following steps:

[0008] S1. Obtain the welding residual stress distribution data of the flat plate workpiece of the pressure equipment under different structural parameters, welding parameters, and material property parameters using finite element simulation or experimental measurement methods;

[0009] S2. Extract longitudinal residual stress distribution data along the direction perpendicular to the weld and the thickness direction from the residual stress distribution data obtained in step S1, and preprocess the longitudinal residual stress distribution data along the thickness direction. At the same time, qualitatively analyze the influence of each main parameter on the longitudinal residual stress distribution.

[0010] S3. Based on the residual stress distribution data along the vertical weld direction and thickness direction extracted in step S2, and the influence law of each main parameter on the longitudinal residual stress distribution along the vertical weld direction and thickness direction, establish a prediction model for residual stress distribution along the vertical weld direction and thickness direction suitable for flat workpieces of pressure equipment.

[0011] S4. Based on the structural parameters, welding parameters, and material property parameters set in step S1, the residual stress distribution data of the cylindrical workpiece of the pressure equipment is obtained by using finite element simulation or experimental measurement. Based on the limit method, assuming that the cylinder with an infinite radius of curvature is a flat plate, the residual stress distribution prediction models of the flat workpiece of the pressure equipment along the direction perpendicular to the weld and along the thickness direction obtained in step S3 are respectively modified by bending constraints to obtain residual stress distribution prediction models along the direction perpendicular to the weld and residual stress distribution prediction models along the thickness direction applicable to flat and cylindrical workpieces of the pressure equipment.

[0012] S5. Using the residual stress distribution prediction model along the vertical weld direction and the residual stress distribution prediction model along the thickness direction established in step S4, the residual stress of the actual pressure-bearing equipment flat plate workpiece or cylindrical workpiece is predicted.

[0013] Furthermore, the structural parameters in step S1 mainly include wall thickness and weld bevel form, and the welding parameters mainly include heat input energy, welding speed and number of weld passes. For finite element simulation, the material property parameters mainly include yield strength conductivity, density, elasticity, plasticity, coefficient of thermal expansion and specific heat capacity; for experimental measurement methods, the material property parameter mainly is yield strength.

[0014] Furthermore, in step S2, the longitudinal residual stress data along the thickness direction needs to be preprocessed by normalizing the thickness.

[0015] Furthermore, the residual stress distribution prediction model for the flat workpiece of the pressure-bearing equipment along the direction perpendicular to the weld seam established in step S3 is as follows:

[0016] ;

[0017] ;

[0018] ;

[0019] In the formula, This refers to the longitudinal residual stress along the direction perpendicular to the weld. For yield strength, It is half the width of the tensile stress zone. The distance from the center of the weld. The thickness of the flat workpiece in the pressure-bearing equipment. The base thickness is 40mm. This represents the total number of weld passes. For the first Effective heat input power of each weld bead For the first The welding speed of the first weld bead. This is the compressive stress correction factor. This is the bevel coefficient. This is a correction factor for the low-stress zone at the weld center, used to control the degree of stress reduction in this zone. This is the width coefficient of the low-stress zone at the weld center, controlling the influence width of the low-stress zone; specifically, for medium-thin plates of 4~20mm, For plates with a thickness of 20~60mm, , For extra-thick plates of 60~120mm, , For X-type bevels, the bevel correction factor is... Take 1; for V-groove, Take 1.5; for U-shaped bevels and double U-shaped bevels, Take 2.

[0020] Furthermore, the residual stress distribution prediction model along the thickness direction of the flat workpiece of the pressure-bearing equipment established in step S3 is as follows:

[0021] ;

[0022] In the formula, This represents the longitudinal residual stress along the thickness direction. For yield strength, The distance from the center of the weld. The thickness of the flat workpiece in the pressure-bearing equipment. The intersection point of the first and second function prediction curves. This is the intersection point of the second and third segment function prediction curves.

[0023] Furthermore, the correction process in step S4 is as follows:

[0024] S41. Using finite element simulation or experimental measurement, obtain the welding residual stress distribution data of cylindrical workpieces of pressure equipment with different diameter-to-thickness ratios under the structural parameters, welding parameters, and material property parameters set in step S1, and extract the longitudinal residual stress distribution data along the direction perpendicular to the weld and along the thickness direction respectively.

[0025] S42. Introduce the diameter-to-thickness ratio to analyze the influence of cylindrical bending constraints on the circumferential residual stress distribution along the vertical weld direction and along the thickness direction. Based on the limit method, assume that the cylindrical workpiece with an infinite radius of curvature is a flat plate. Modify the residual stress distribution prediction model of the pressure equipment flat workpiece along the vertical weld direction and the thickness direction obtained in step S3 by bending constraints. Obtain the residual stress distribution prediction model along the vertical weld direction and the residual stress distribution prediction model along the thickness direction applicable to the pressure equipment flat and cylindrical workpieces.

[0026] Furthermore, the residual stress distribution prediction model along the perpendicular weld direction for plate and cylindrical workpieces of pressure equipment, obtained in step S4 after bending constraint correction, is as follows:

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] In the formula, The corrected longitudinal / circumferential residual stress along the direction perpendicular to the weld. It is half the width of the corrected tensile stress zone. The inner diameter of the cylindrical workpiece in the pressure equipment. The aspect ratio is the diameter to the thickness. This is the correction factor for the width of the plastic zone of the circumferential weld. This is the correction factor for the stress amplitude of the circumferential weld. and The coefficients are obtained by fitting using the least squares method.

[0033] Furthermore, the residual stress distribution prediction model along the thickness direction for flat and cylindrical workpieces of pressure equipment obtained after bending correction in step S4 is as follows:

[0034] ;

[0035] In the formula, The corrected longitudinal / circumferential residual stress along the direction perpendicular to the weld. The intersection point of the first and second function prediction curves. This is the intersection point of the second and third segment function prediction curves.

[0036] The present invention has the following beneficial effects:

[0037] (1) The prediction model established by this invention systematically considers the influence of structural constraints such as thick / extra-thick plates, bevel form and bending on the distribution of residual stress, so that the prediction model can accurately reflect the complex three-dimensional stress state unique to thick-walled pressure vessels, realize high-precision prediction of the welding residual stress distribution of thick-walled pressure equipment, provide key design basis for the manufacturing of thick-walled pressure equipment, and help provide theoretical guidance for welding process and post-weld heat treatment process to control residual stress from the source, improve the safety and reliability of equipment, and reduce the risk of failure of pressure equipment;

[0038] (2) The prediction model established by this invention is a parameterized empirical function, which transforms the complex welding mechanics problem into a functional relationship between the input parameters and the output results. Compared with the finite element simulation method, it has the advantages of high computational efficiency, fast speed and low cost, which meets the needs of rapid evaluation and iterative optimization of welding process in engineering field and greatly shortens the welding process design cycle. Attached Figure Description

[0039] Figure 1 This is a flowchart of the prediction method of the present invention;

[0040] Figure 2 The present invention relates to a residual stress distribution cloud map obtained from finite element simulation of a flat workpiece in a pressure-bearing device;

[0041] Figure 3 This is a schematic diagram comparing the model prediction results and finite element simulation results of the longitudinal residual stress distribution of the flat workpiece of the pressure-bearing equipment along the direction perpendicular to the weld in Embodiment 1 of the present invention.

[0042] Figure 4 This is a schematic diagram comparing the model prediction results and finite element simulation results of the longitudinal residual stress distribution along the thickness direction of the flat plate workpiece of the pressure-bearing equipment in Embodiment 1 of the present invention.

[0043] Figure 5 This is a schematic diagram comparing the model prediction results and finite element simulation results of the circumferential residual stress distribution of the cylindrical workpiece of the pressure equipment along the direction perpendicular to the weld in Embodiment 2 of the present invention.

[0044] Figure 6 This is a schematic diagram comparing the model prediction results and finite element simulation results of the circumferential residual stress distribution along the thickness direction of the actual pressure-bearing cylindrical workpiece in Embodiment 2 of the present invention. Detailed Implementation

[0045] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and specific examples.

[0046] Reference Figure 1This invention provides a method for predicting the welding residual stress distribution of pressure-bearing equipment based on structural constraints, which is used to calculate and predict the welding residual stress distribution of large pressure-bearing equipment. The specific steps are as follows.

[0047] S1. Obtain welding residual stress distribution data of flat plate workpieces of pressure equipment under different structural parameters, welding parameters, and material property parameters using finite element simulation or experimental measurement methods.

[0048] In this step, the structural parameters mainly include wall thickness and weld bevel form, and the welding parameters mainly include welding heat input, welding speed and number of weld beads. For the finite element simulation method, the material property parameters mainly include conductivity, density, elasticity, plasticity, expansion and specific heat capacity. For the experimental measurement method, the material property parameter mainly is yield strength, and the welding residual stress distribution data of the pressure equipment plate workpiece under different structural parameters, welding parameters and material property parameters are obtained through finite element simulation and / or through neutron diffraction experiments and profilometry experiments.

[0049] In this specific embodiment, the welding residual stress distribution data is mainly obtained through finite element simulation. The finite element simulation process is as follows:

[0050] (1) Establish a two-dimensional or three-dimensional structural model of the flat plate workpiece of the pressure equipment in the ABAQUS finite element software, and introduce the welding heat source model and related elastic-plastic constitutive model to obtain the finite element thermo-mechanical coupling model of the workpiece of the pressure equipment.

[0051] (2) Welding heat input is applied through the welding heat source model to simulate the welding process of the workpiece of the pressure equipment. The temperature field distribution and residual stress field distribution are obtained through thermo-mechanical coupling calculation.

[0052] (3) Design different combinations of structural parameters, welding parameters and material property parameters, and obtain different welding residual stress distribution data by changing the simulation parameters of the model in step (1).

[0053] In step (1) above, when the established finite element model is a two-dimensional model, the welding heat source model is a two-dimensional ramp heat input model; when the finite element model is a three-dimensional model, the welding heat source model is a three-dimensional double ellipsoidal heat source model. In addition, the three-dimensional model has a huge computational load in the above finite element simulation process, so the two-dimensional model is the main model and the three-dimensional model is the auxiliary model.

[0054] The two-dimensional slope heat input model is as follows:

[0055] (1);

[0056] (2);

[0057] (3);

[0058] The three-dimensional double ellipsoidal heat source model is as follows:

[0059] (4);

[0060] Simultaneously, a conversion formula for total net linear energy was established to realize the conversion of welding parameters between two-dimensional and three-dimensional slope heat input models, so as to facilitate a comparison of the welding heat input energy and welding speed provided by the two-dimensional slope heat input model and the three-dimensional double ellipsoidal heat source model from the same dimension; the above conversion formula for total net linear energy is as follows:

[0061] (5);

[0062] In the formula, The serial number indicates the number of the sequence. weld bead, This represents the total number of weld passes. For the first The voltage of each weld bead, measured in volts (V). For the first The current for each weld bead, measured in amperes (A). For the first Thermal efficiency of the weld bead, in % For the first The distributed heat flux of the weld bead, expressed in J / (m²). 3 . s), For the first The volume of a single weld bead, expressed in meters (m). 3 ; For the first The welding speed of each weld bead, expressed in m / s; For the first Net linear energy of a weld bead, expressed in J / m; For the first The effective heat input power of each weld bead, measured in W; For the first The cross-sectional area of ​​the weld bead, in m². 2 ; For the first The time of heat input per unit length affected by each weld bead, measured in seconds.

[0063] In step (3) above, when designing different combinations of structural parameters, welding parameters, and material property parameters, the parameters can be adjusted by controlling the variable method, and finally the welding residual stress distribution data of several pressure equipment plate workpieces under different structural parameters, welding parameters, and material property parameters can be obtained.

[0064] S2. Extract longitudinal residual stress distribution data along the direction perpendicular to the weld and the thickness direction from the residual stress distribution data obtained in step S1, and preprocess the longitudinal residual stress distribution data along the thickness direction. At the same time, qualitatively analyze the influence of each parameter on the longitudinal residual stress distribution along the direction perpendicular to the weld and the thickness direction.

[0065] Specifically, the welding residual stress distribution data obtained through finite element simulation in step S1 above is actually a residual stress distribution cloud map, such as... Figure 2 The diagram shows the residual stress distribution cloud map of a pressure equipment workpiece with a wall thickness of 55mm under a certain parameter combination. Each node on the residual stress distribution cloud map includes the coordinate position (X, Y) and the residual stress value (transverse residual stress, longitudinal residual stress, and normal residual stress).

[0066] Based on this, to facilitate data analysis, analysis paths were selected along the vertical weld direction and the thickness direction to extract corresponding longitudinal residual stress data and construct a dataset. The analysis path along the vertical weld direction is a path extending from the center of the weld inside the pressure equipment workpiece as the origin, extending towards both sides of the weld. The analysis path along the thickness direction is a path extending along the thickness direction from the center of the weld surface of the pressure equipment workpiece as the origin. Furthermore, for the longitudinal residual stress data extracted along the thickness direction analysis path, due to varying thicknesses, the thickness coordinates need to be normalized, that is, the thickness of different pressure equipment workpieces is normalized to the range of 0 to 1.

[0067] The longitudinal residual stress distribution data extracted along the analysis path perpendicular to the weld and the longitudinal residual stress data extracted along the analysis path along the thickness after normalization are classified and organized to obtain a dataset of longitudinal residual stress distribution along the vertical weld and a dataset of longitudinal residual stress distribution along the thickness with a unified reference system and capable of visual comparison. Then, the influence of each parameter on the residual stress distribution is qualitatively analyzed, and the main parameters affecting the residual stress distribution are selected.

[0068] Qualitative analysis of the extracted residual stress data revealed that welding process and material properties primarily affect the magnitude of residual stress, while wall thickness and weld bevel form mainly control the spatial distribution of residual stress. This is because wall thickness and weld bevel form generate structural constraints, altering the degree of restraint and local stiffness.

[0069] S3. Based on the residual stress distribution data along the vertical weld direction and thickness direction extracted in step S2, and the influence law of each main parameter on the longitudinal residual stress distribution along the vertical weld direction and thickness direction, establish prediction models for residual stress distribution along the vertical weld direction and thickness direction suitable for flat workpieces of pressure equipment.

[0070] The process of establishing the residual stress distribution prediction model for the flat workpiece of the pressure equipment along the vertical weld direction is as follows: First, based on the influence law of each main parameter on the longitudinal residual stress distribution along the vertical weld direction as qualitatively analyzed in step S2, a basis function that conforms to the residual stress distribution trend is selected, and the error between the basis function and the actual residual stress distribution curve is evaluated. Based on the error and the influence law of each main parameter on the residual stress distribution, the basis function is corrected. Then, based on the residual stress distribution data along the vertical weld direction extracted in step S2, the correction coefficient is fitted using the least squares method to obtain the residual stress distribution prediction model along the vertical weld direction applicable to the flat workpiece of the pressure equipment.

[0071] The specific correction process is as follows: For the longitudinal residual stress distribution data along the direction perpendicular to the weld, when the workpiece of the pressure equipment is a medium-thin plate (4~20mm), its maximum tensile residual stress is mainly in the central area of ​​the weld, using a general empirical model (basis function). This indicates the residual stress variation trend of medium and thin plates; however, the maximum tensile residual stress of thick or extra-thick plates is not limited to the weld center. Influenced by triaxial stress state and work hardening, the maximum tensile stress near the surface of thick or extra-thick plates is usually slightly higher than the yield strength. Specifically, when the plate workpiece of the pressure equipment is a 20-50mm thick plate, the maximum tensile residual stress in the center region of the workpiece is close to the yield strength; when the plate workpiece of the pressure equipment is an extra-thick plate exceeding 60mm, the maximum tensile stress in the center region of the workpiece is as low as half of the yield strength, and even a compressive stress zone appears at the weld center. The general empirical model shows significant deviation or failure when applied to thick plate structures. Therefore, based on the residual stress distribution data obtained from experiments and / or simulations, and in conjunction with GB / T 15574-2016 "Classification of Steel Products", 60mm is used as the dividing point. Based on medium and thin plates, two different coefficient correction strategies are adopted for thick plates (20mm-60mm) and extra-thick plates (≥60mm). To address the phenomenon of low-stress zones appearing in the center of the sheet material, an exponential decay function correction term is introduced. This correction is only applicable to Playing a role in the vicinity, when As the value moves away from zero, the absolute value of this correction term rapidly approaches zero. Furthermore, the low-stress zone differs for medium-thin plates, thick plates, and extra-thick plates; it is almost non-existent in thin plates, while the low-stress zone is very pronounced in extra-thick plates. Therefore, a correction factor for the low-stress zone at the weld center is introduced into this correction term. and the width coefficient of the low stress zone at the center of the weld This represents the stress reduction magnitude and the width of the low-stress zone formed in the weld center region. Meanwhile, for compressive stress, the change becomes more pronounced and wider with increasing plate thickness; therefore, a compressive stress correction factor is further introduced. Make corrections, and and The relationship is linear. Furthermore, the weld groove shape also affects the residual stress distribution, especially the half-width of the tensile stress zone in the welded joint. Therefore, a groove coefficient is introduced into the half-width of the tensile stress zone. Characterize its impact.

[0072] After the above corrections, the prediction model for the residual stress distribution of the flat workpiece of the pressure equipment along the direction perpendicular to the weld is as follows:

[0073] (6);

[0074] (7);

[0075] (8);

[0076] Applying the above-mentioned residual stress distribution prediction model along the direction perpendicular to the weld to engineering practice can... The expression is modified to:

[0077] (9);

[0078] In the formula, The longitudinal residual stress is expressed in Pa along the direction perpendicular to the weld. Yield strength, in Pa; It is half the width of the tensile stress zone, in meters (m). This is the distance from the center of the weld, in meters. The thickness of the flat plate workpiece in the pressure equipment is expressed in meters (m). The base thickness is 40mm, which is 0.04m. This represents the total number of weld passes. For the first The effective heat input power of each weld bead, measured in W; For the first The welding speed of each weld bead, expressed in m / s; This is a dimensionless correction factor for compressive stress. The bevel coefficient is dimensionless. This is a correction factor for the low-stress zone at the center of the weld, used to control the degree of stress reduction in the low-stress zone at the center of the weld. It is dimensionless. This is the width coefficient of the low-stress zone at the weld center, controlling the influence width of the low-stress zone, with units in meters; specifically, for medium-thin plates (4~20mm). For thick plates (20~60mm). , For extra-thick plates (60~120mm). , For bevel X, the bevel correction factor is... Take 1; for V-groove, Take 1.5; for U-shaped bevels and double U-shaped bevels, Take 2.

[0079] The process of establishing the residual stress distribution prediction model along the thickness direction of the aforementioned pressure-bearing equipment flat workpiece is as follows: Based on the influence law of each main parameter on the longitudinal residual stress distribution along the thickness direction analyzed in step S2, the pressure-bearing equipment workpiece exhibits a clear trend of low stress in the middle region and high stress in the two side regions. The residual stress distribution data along the thickness direction in step S2 can be divided into three segments according to the stress distribution trend. Nonlinear least squares fitting is performed on each segment to obtain three quadratic functions, and the intersection point is taken as the segmentation point to obtain the residual stress distribution prediction model along the thickness direction applicable to the pressure-bearing equipment flat workpiece. That is:

[0080] (10);

[0081] In the formula, The longitudinal residual stress is expressed in Pa. Yield strength, in Pa; This is the distance from the center of the weld, in meters. The thickness of the flat plate workpiece in the pressure equipment is expressed in meters (m). The intersection point of the first and second function prediction curves. This is the intersection point of the second and third segment function prediction curves.

[0082] S4. Based on the structural parameters, welding parameters, and material property parameters set in step S1, obtain the welding residual stress distribution data of the cylindrical workpiece of the pressure equipment using finite element simulation or experimental measurement methods; and based on the limit method assuming that the cylinder with an infinite radius of curvature is a flat plate, perform bending constraint correction on the residual stress distribution prediction model of the flat workpiece of the pressure equipment along the direction perpendicular to the weld and the thickness direction obtained in step S3, respectively, to obtain the residual stress distribution prediction model along the direction perpendicular to the weld and the residual stress distribution prediction model along the thickness direction applicable to flat and cylindrical workpieces of the pressure equipment.

[0083] Specifically, the correction process in step S4 of this embodiment is as follows:

[0084] S41. Based on the finite element structural model of the pressure equipment flat plate workpiece established in step S1, different diameter-to-thickness ratios are introduced. Using the control variable method as the principle, cylindrical workpieces with similar structural dimensions of circumferential weld joints are established. Alternatively, actual cylindrical workpieces of pressure equipment with different diameter-to-thickness ratios are taken. The residual stress distribution data of the cylindrical workpieces of pressure equipment with different diameter-to-thickness ratios under the structural parameters, welding parameters, and material property parameters set in step S1 are obtained using the finite element simulation method or experimental measurement method. The longitudinal residual stress distribution data along the direction perpendicular to the weld and along the thickness direction are extracted respectively.

[0085] S42. Introduce the diameter-to-thickness ratio to analyze the influence of the bending constraint on the circumferential residual stress distribution along the vertical weld direction and along the thickness direction of the cylinder. Based on the limit method, assume that the cylinder with an infinite radius of curvature is a flat plate. Modify the residual stress distribution prediction model along the vertical weld direction and along the thickness direction of the pressure equipment flat plate workpiece obtained in step S3 by bending constraint, quantify the influence of bending constraint, and obtain the residual stress distribution prediction model along the vertical weld direction and the longitudinal residual stress distribution prediction model along the thickness direction applicable to the pressure equipment flat plate and cylindrical workpiece.

[0086] In step S42 above, the influence of the cylinder bending constraint on the circumferential residual stress distribution along the direction perpendicular to the weld seam is analyzed. The analysis shows that when the diameter-to-thickness ratio is small, the high-pressure stress zone extensively covers the pipe wall surface. As the radius of curvature increases, the relative flexibility of the pipe wall increases significantly, and the radial restraint effect of the cylinder structure on weld shrinkage weakens. This flexibility allows the joint to release some strain energy through slight deformation, thus significantly reducing the peak level of residual stress. At this point, the stress distribution gradually flattens, tending towards the typical characteristics of a flat plate butt weld, no longer exhibiting the severe stress gradient between the core and surface in a small-diameter pipe. Furthermore, the thicker the cylinder wall, the greater the structural stiffness; at the same diameter-to-thickness ratio, the influence of bending constraint is less pronounced, and the distribution characteristics are closer to those of a flat plate. Specifically, when the diameter-to-thickness ratio is infinitely large, the welded joint locally approaches a plate of uniform thickness, and the influence of bending constraint can be ignored. In actual design, the minimum diameter-to-thickness ratio is around 1, at which point the influence of bending constraint on the welded joint structure reaches its maximum. This bending constraint directly affects the width of the plastic zone and the stress amplitude of the circumferential weld. Therefore, a correction factor for the plastic zone width of the circumferential weld is introduced. and the correction factor for stress amplitude of circumferential weld The model was modified. Furthermore, since the minimum diameter-to-thickness ratio is around 1, the correction factor for the plastic zone width of the circumferential weld is adjusted. and the correction factor for stress amplitude of circumferential weld Since the value is close to 0 but not quite 0, the plastic zone width correction coefficient is represented by an exponential function of deformation. and stress amplitude correction factor The changes.

[0087] After the above modifications, the residual stress distribution prediction model along the direction perpendicular to the weld seam for flat and cylindrical workpieces in pressure equipment is obtained as follows:

[0088] (11);

[0089] (12);

[0090] (13);

[0091] (14);

[0092] (15);

[0093] Applying the above-mentioned residual stress distribution prediction model along the direction perpendicular to the weld to engineering practice can... The expression is modified to:

[0094] (16);

[0095] In the formula, The corrected longitudinal / circumferential residual stress along the direction perpendicular to the weld, in Pa; This is half the width of the corrected tensile stress zone, in meters (m). The inner diameter of the cylindrical workpiece in the pressure equipment is expressed in meters (m). The aspect ratio is dimensionless; This is a dimensionless correction factor for the width of the plastic zone of the circumferential weld. This is a dimensionless correction factor for the stress amplitude of the circumferential weld. and The coefficients are obtained by least squares fitting, are dimensionless, and are obtained by fitting in this embodiment. The value is 0.1. It is 0.05.

[0096] In addition, the influence of the diameter-to-thickness ratio analysis on the circumferential residual stress distribution of the cylinder along the thickness direction in step S42 above is analyzed. The analysis shows that the apex of the high stress zone of the cylindrical workpiece is slightly higher than the yield strength of the material, and the valley point of the low stress zone is about the minimum stress value of the low stress zone. Therefore, based on the residual stress distribution prediction model along the thickness direction established in step S3, a correction term can be introduced into the constant term of the quadratic function to make corresponding curvature corrections in order to correct the stress values ​​of key points.

[0097] Therefore, in step S42 above, when modifying the prediction model established in step S3 using finite element data of residual stress along the thickness direction of the cylindrical workpiece of the pressure equipment, a correction term is specifically introduced into the constant term of the quadratic function for correction. By fitting the residual stress distribution curves under different diameter-to-thickness ratios, the characteristic constant in the correction term is determined, and the stress values ​​at the extreme points of the piecewise function are corrected. This yields a prediction model for the residual stress distribution along the thickness direction applicable to flat and cylindrical workpieces of pressure equipment, namely:

[0098] (17);

[0099] In the formula, The corrected longitudinal / circumferential residual stress along the direction perpendicular to the weld, in Pa; The intersection point of the first and second function prediction curves. This is the intersection point of the second and third segment function prediction curves.

[0100] S5. Using the residual stress distribution prediction model along the vertical weld direction and the residual stress distribution prediction model along the thickness direction established in step S4, the residual stress of the actual pressure-bearing equipment flat plate workpiece or cylindrical workpiece is predicted.

[0101] Example 1

[0102] Based on the above-established residual stress distribution prediction models for plate and cylindrical workpieces of pressure equipment along the vertical weld direction and along the thickness direction, namely formulas (11) and (17), the longitudinal residual stress distribution of actual plate workpieces of pressure equipment is predicted.

[0103] The actual pressure-bearing equipment plate workpiece is a 60mm thick plate with an X-shaped weld bevel. The material is 12Cr2Mo1R. The welding parameters are shown in Table 1 below. The number of weld passes is 60, and the yield strength is approximately 510MPa.

[0104] Table 1 Welding parameters for the flat plate workpiece of the pressure equipment in Example 1

[0105]

[0106] Using formula (11), the longitudinal residual stress distribution along the direction perpendicular to the weld was predicted for the actual pressure-bearing equipment plate workpiece, and the longitudinal residual stress distribution curve along the direction perpendicular to the weld was obtained as follows: Figure 3 As shown, the prediction results of the prediction model are basically consistent with the residual stress distribution obtained from the finite element simulation results, and compared with the two-dimensional finite element simulation data.

[0107] Using formula (17), the longitudinal residual stress distribution along the thickness direction of the actual pressure-bearing equipment plate workpiece is predicted, and the longitudinal residual stress distribution curve along the thickness direction is obtained as follows: Figure 4 As shown, the prediction results of the prediction model are basically consistent with the residual stress distribution obtained from the finite element simulation results, and compared with the two-dimensional finite element simulation data.

[0108] Example 2

[0109] Based on the above-established residual stress distribution prediction model for plate and cylindrical workpieces of pressure equipment along the vertical weld direction and along the thickness direction, namely formula (11) and formula (17), the circumferential residual stress distribution of actual cylindrical workpieces of pressure equipment is predicted.

[0110] The structural parameters of the cylindrical workpiece of the actual pressure equipment are as follows: wall thickness is 100mm, radius is 900mm, and the welding bevel is a double U-shaped bevel; the welding parameters are shown in Table 2 below, the number of welds is 65; the material is 12Cr2Mo1R steel, and the yield strength is approximately 510MPa.

[0111] Table 2 Welding parameters for the cylindrical workpiece of the pressure equipment in Example 2

[0112]

[0113] Using formula (11), the circumferential residual stress distribution along the direction perpendicular to the weld of the actual pressure-bearing cylindrical workpiece is predicted, and the circumferential residual stress distribution curve along the direction perpendicular to the weld is obtained as follows: Figure 5 As shown, the prediction results of the prediction model are basically consistent with the residual stress distribution obtained from the finite element simulation results, and compared with the two-dimensional finite element simulation data.

[0114] Using formula (17), the circumferential residual stress distribution along the thickness direction of the actual pressure-bearing cylindrical workpiece is predicted, and the circumferential residual stress distribution curve along the thickness direction is obtained as follows: Figure 6 As shown, the prediction results of the prediction model are basically consistent with the residual stress distribution obtained from the finite element simulation results, and compared with the two-dimensional finite element simulation data.

[0115] The prediction results of Examples 1 and 2 above demonstrate that the prediction model established by the present invention can be used to predict the residual stress distribution of welding workpieces in actual pressure-bearing equipment, providing theoretical guidance for engineering applications.

[0116] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for predicting the distribution of welding residual stress in pressure-bearing equipment based on structural constraints, characterized in that, Including the following steps: S1. Obtain the welding residual stress distribution data of the flat plate workpiece of the pressure equipment under different structural parameters, welding parameters, and material property parameters using finite element simulation or experimental measurement methods; S2. Extract longitudinal residual stress distribution data along the direction perpendicular to the weld and the thickness direction from the residual stress distribution data obtained in step S1, and preprocess the longitudinal residual stress distribution data along the thickness direction. At the same time, qualitatively analyze the influence of each main parameter on the longitudinal residual stress distribution. S3. Based on the longitudinal residual stress distribution data along the vertical weld direction and thickness direction extracted in step S2, and the influence law of each main parameter on the longitudinal residual stress distribution along the vertical weld direction and thickness direction, establish prediction models for residual stress distribution along the vertical weld direction and thickness direction suitable for flat workpieces of pressure equipment. S4. Based on the structural parameters, welding parameters, and material property parameters set in step S1, the residual stress distribution data of the cylindrical workpiece of the pressure equipment is obtained by using finite element simulation or experimental measurement. Based on the limit method, assuming that the cylinder with an infinite radius of curvature is a flat plate, the residual stress distribution prediction models of the flat workpiece of the pressure equipment along the direction perpendicular to the weld and along the thickness direction obtained in step S3 are respectively modified by bending constraints to obtain residual stress distribution prediction models along the direction perpendicular to the weld and residual stress distribution prediction models along the thickness direction applicable to flat and cylindrical workpieces of the pressure equipment. S5. Using the residual stress distribution prediction model along the vertical weld direction and the residual stress distribution prediction model along the thickness direction established in step S4, the residual stress of the actual pressure-bearing equipment flat plate workpiece or cylindrical workpiece is predicted. The residual stress distribution prediction model along the perpendicular weld direction for plate and cylindrical workpieces of pressure equipment, obtained after bending constraint correction in step S4, is as follows: ； ； ； ； ； In the formula, The corrected longitudinal / circumferential residual stress along the direction perpendicular to the weld. It is half the width of the corrected tensile stress zone. The inner diameter of the cylindrical workpiece in the pressure equipment. The aspect ratio is the diameter to the thickness. This is the correction factor for the width of the plastic zone of the circumferential weld. This is the correction factor for the stress amplitude of the circumferential weld. and The coefficients are obtained by fitting using the least squares method; For yield strength, The distance from the center of the weld. The thickness of the flat workpiece in the pressure-bearing equipment. The base thickness is 40mm. This represents the total number of weld passes. For the first Effective heat input power of each weld bead For the first The welding speed of the first weld bead. This is the compressive stress correction factor. This is the bevel coefficient. This is a correction factor for the low-stress zone at the weld center. This is the width coefficient of the low-stress zone at the weld center; for medium-thin plates of 4~20mm, ; For plates with a thickness of 20~60mm, , For extra-thick plates of 60~120mm, , ; For X-type bevels Take 1; for V-groove, Take 1.5; for U-shaped bevels and double U-shaped bevels, Take 2; The residual stress distribution prediction model along the thickness direction for flat and cylindrical workpieces in pressure-bearing equipment, obtained after bending correction in step S4, is as follows: ； In the formula, The corrected longitudinal / circumferential residual stress along the direction perpendicular to the weld. The intersection point of the first and second function prediction curves. This is the intersection point of the second and third segment function prediction curves.

2. The method for predicting the welding residual stress distribution of pressure-bearing equipment based on structural constraints according to claim 1, characterized in that, The structural parameters in step S1 mainly include wall thickness and weld bevel form, and the welding parameters mainly include heat input energy, welding speed and number of weld beads. For the finite element simulation method, the material property parameters mainly include yield strength, conductivity, density, elasticity, plasticity, coefficient of thermal expansion and specific heat capacity; for the experimental measurement method, the material property parameter mainly is yield strength.

3. The method for predicting the welding residual stress distribution of pressure-bearing equipment based on structural constraints according to claim 1, characterized in that, In step S2, the longitudinal residual stress data along the thickness direction needs to be preprocessed by normalizing the thickness.

4. The method for predicting the welding residual stress distribution of pressure-bearing equipment based on structural constraints according to claim 1, characterized in that, The residual stress distribution prediction model for the flat workpiece of the pressure-bearing equipment along the direction perpendicular to the weld seam, established in step S3, is as follows: ； ； ； In the formula, This refers to the longitudinal residual stress along the direction perpendicular to the weld. For yield strength, It is half the width of the tensile stress zone. The distance from the center of the weld. The thickness of the flat workpiece in the pressure-bearing equipment. The base thickness is 40mm. This represents the total number of weld passes. For the first Effective heat input power of each weld bead For the first The welding speed of the first weld bead. This is the compressive stress correction factor. This is the bevel coefficient. This is a correction factor for the low-stress zone at the weld center. This is the width coefficient of the low-stress zone at the weld center; for medium-thin plates of 4~20mm, ; For plates with a thickness of 20~60mm, , For extra-thick plates of 60~120mm, , ; For X-type bevels Take 1; for V-groove, Take 1.5; for U-shaped bevels and double U-shaped bevels, Take 2.

5. The method for predicting the welding residual stress distribution of pressure-bearing equipment based on structural constraints according to claim 4, characterized in that, The residual stress distribution prediction model along the thickness direction of the flat workpiece of the pressure-bearing equipment established in step S3 is as follows: ； In the formula, This represents the longitudinal residual stress along the thickness direction. For yield strength, The distance from the center of the weld. The thickness of the flat workpiece in the pressure-bearing equipment. The intersection point of the first and second function prediction curves. This is the intersection point of the second and third segment function prediction curves.

6. The method for predicting the welding residual stress distribution of pressure-bearing equipment based on structural constraints according to claim 5, characterized in that, The correction process in step S4 is as follows: S41. Use finite element simulation or experimental measurement to obtain the welding residual stress distribution data of cylindrical workpieces of pressure equipment with different diameter-to-thickness ratios under the structural parameters, welding parameters and material property parameters set in step S1, and extract the circumferential residual stress distribution data along the direction perpendicular to the weld and along the thickness direction respectively. S42. Introduce the diameter-to-thickness ratio to analyze the influence of cylindrical bending constraints on the circumferential residual stress distribution along the vertical weld direction and along the thickness direction. Based on the limit method, assume that the cylindrical workpiece with an infinite radius of curvature is a flat plate. Modify the residual stress distribution prediction model of the pressure equipment flat workpiece along the vertical weld direction and the thickness direction obtained in step S3 by bending constraints. Obtain the residual stress distribution prediction model along the vertical weld direction and the residual stress distribution prediction model along the thickness direction applicable to the pressure equipment flat and cylindrical workpieces.

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