A weight function method for calculating the surface crack stress intensity factor of a pipe girth weld

Abstract

This invention discloses a weighted function method for calculating the stress intensity factor of surface cracks in circumferential welds of pipelines. The method involves constructing a point load weighted function for calculating the stress intensity factor of surface cracks in circumferential welds of pipeline structures; establishing a finite element model of the pipeline structure containing surface cracks in the circumferential weld; calculating a reference solution for the stress intensity factor under a reference load based on the M-integral method; solving for the weight coefficients of the calculation points at the leading edge of the surface crack in the point load weighted function; establishing a weight coefficient prediction model through optimization of a backpropagation neural network using a genetic algorithm; and performing a double integral operation on the product of the point load weighted function and the stress distribution load on the surface crack of the circumferential weld to calculate the stress intensity factor. This invention solves the problems of existing methods being only applicable to cases where the stress distribution load varies unidirectionally along the crack depth, and being unsuitable for stress distributions that vary bidirectionally along both crack depth and crack length, which are common in actual structures, as well as increasing computational cost and reducing computational accuracy.

Description

Technical Field

[0001] This invention relates to the field of fracture mechanics and damage tolerance design for oil and gas pipelines, and particularly to a weighting function method for calculating the stress intensity factor of surface cracks in pipeline circumferential welds. Background Technology

[0002] With the development of the offshore oil and gas resource development industry, pipelines have become one of the main modes of offshore oil and gas transportation. Compared with onshore oil and gas pipelines, offshore oil and gas pipelines operate in harsher environments, bear more complex loads, and are more difficult to maintain. Oil and gas pipelines are typical welded structures, and initial defects inevitably occur near the circumferential weld. Under the alternating loads of the marine environment, these initial defects in the stress concentration area of ​​the circumferential weld are prone to transform into semi-elliptical surface cracks that continue to propagate, ultimately leading to pipeline structural fracture failure or even catastrophic accidents. Therefore, the circumferential weld is the weakest link in the entire pipeline structure, requiring damage-tolerant design methods to assess the service safety of structures containing cracks. This method is based on linear elastic fracture mechanics, using the stress intensity factor at the crack tip as the core parameter for assessing pipeline fracture failure. Therefore, the rapid and accurate calculation of the surface crack stress intensity factor of the circumferential weld is crucial for assessing the integrity and safety of offshore oil and gas pipeline structures.

[0003] Currently, commonly used methods for calculating the stress intensity factor of surface cracks in engineering can be divided into empirical formula methods, finite element methods, and weighted function methods. For oil and gas pipelines, Appendix 9B of API 579-1 "Fitness for Service" provides empirical formulas for the stress intensity factor of circumferential surface cracks on the outer wall of the pipeline. However, its applicability is limited to simple loading conditions and cannot consider the influence of weld shape and residual welding stress. The finite element method can be used to calculate the stress intensity factor of surface cracks in different structural forms under complex stress distribution loads. However, due to the requirements of different crack shapes and sizes, high-quality meshes need to be generated at the crack tip, which faces the problems of large modeling workload and low computational efficiency. The weighted function method is a semi-numerical and semi-analytical method for calculating the stress intensity factor. The expression of the weight function is only related to the geometric parameters of the crack body. Once the weight function is determined, the stress intensity factor of the crack body under arbitrary loads can be calculated by solving the integral of the product of the weight function and the stress distribution on the crack surface.

[0004] Among existing weighting function methods, the general weighting function proposed by Glinka is the most widely used and has been adopted by several damage tolerance design software programs (such as AFGROW and DARWIN). However, the general weighting function is only applicable to cases where the stress distribution load varies unidirectionally along the crack depth, and it is not applicable to the stress distribution that often occurs in actual structures, where the stress distribution varies bidirectionally along both the crack depth and crack length. Orynyak and Wang proposed different point load weighting function formulas to calculate the stress intensity factor of elliptical buried cracks under bidirectional stress distribution loads. Patent publication number CN 112989659 B discloses a method for establishing a surface crack intensity factor database based on the point load weighting function method. This method extends Orynyak's point load weighting function formula to the problem of semi-elliptical surface cracks on flat plates by adding a correction term. The stress intensity factor under three reference loads is obtained through finite element calculation as a reference solution, and the three weighting coefficients in the weighting function formula are solved. However, the introduction of multiple weighting coefficients inevitably increases the computational cost and reduces the computational accuracy, affecting the reliability of subsequent calculations. Summary of the Invention

[0005] This invention provides a weighting function method for calculating the stress intensity factor of surface cracks in pipe circumferential welds, thereby overcoming the aforementioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A weighting function method for calculating the stress intensity factor of surface cracks in a pipe circumferential weld includes the following steps:

[0008] S1: For pipeline structures containing surface cracks in circumferential welds, a point load weighting function is constructed, which includes undetermined weighting coefficients for calculation points at the leading edge of the surface cracks in the circumferential weld. The stress intensity factor calculation model for the surface cracks in the circumferential weld is obtained based on the point load weighting function as follows:

[0009]

[0010]

[0011] In the formula: s This represents the shortest distance from the point of application of the load P on the crack surface to the crack tip; This represents the distance from the point of application of the load P on the crack surface to the point where the stress intensity factor is calculated at the crack tip. The straight-line distance; ξ Indicates the calculation point of the stress intensity factor at the crack tip. The horizontal distance to the origin O of the local coordinate system of the crack; h This represents the horizontal distance from point C on the surface of the crack tip to the origin O of the local coordinate system of the crack. a Indicates the depth of surface cracks; cIndicates the half-width of a surface crack; T Indicates pipe thickness; Indicates the inner radius of the pipe; θ Indicates the weld toe transition angle; r Indicates the radius of curvature of the weld toe; ρ This represents the distance from the point P on the crack surface where the load is applied to the origin O of the local coordinate system of the crack. This represents the distance from point Q on the crack tip to the origin O of the local coordinate system of the crack; Indicates the calculation point of the crack front. The undetermined weighting coefficients are the same as the six dimensionless parameters. , , , , , Related functions; This represents the normalized distance at the crack tip, indicating the position of point P' at the crack tip. Indicates the surface crack shape ratio; This represents the ratio of crack depth to pipe wall thickness. This represents the ratio of the pipe wall thickness to the inner wall radius. This represents the ratio of the weld toe curvature radius to the pipe wall thickness. Indicates the crack leading edge Stress intensity factor at point; This represents the stress distribution on the crack surface. The point load weighting function represents the crack front under a unit point load applied at points P on the crack surface at x and y. Stress intensity factor at the location; S The area of ​​the entire crack surface;

[0012] S2: Based on the pipe structure containing surface cracks in the circumferential weld, a finite element model is established and meshed. At the same time, a stress distribution perpendicular to the crack surface is applied as the load boundary condition of the finite element model to obtain a finite element model with load boundaries.

[0013] S3: Based on the finite element model with load boundaries, calculate the stress intensity factor at each point on the crack front edge of the circumferential weld surface under the reference load condition, and use it as the reference solution for the stress intensity factor.

[0014] S4: Based on the stress intensity factor reference solution and the stress intensity factor calculation model, solve for the undetermined weight coefficients of the calculation points at the crack front edge of the circumferential weld surface in the point load weight function, and obtain the sample weight coefficient solution.

[0015] S5: Establish a dataset by using the dimensionless parameters as input variables and the sample weight coefficient solutions as output targets; optimize the backpropagation neural network based on the genetic algorithm, and construct a weight coefficient prediction model based on the dataset;

[0016] S6: Based on the weighted coefficient prediction model, the corresponding weighted coefficient solution is obtained by inputting the dimensionless parameters of the target, and then the point load weight function is obtained; the product of the point load weight function and the stress distribution load on the surface crack of the circumferential weld is double integrally calculated to realize the calculation of the stress intensity factor at each point on the crack front edge of the circumferential weld of the pipeline structure.

[0017] Furthermore, S2 specifically includes the following steps:

[0018] S21: Using ABAQUS finite element software, a finite element model of the circumferential welded pipe structure was established based on the three dimensionless parameters involved in the circumferential welded pipe.

[0019] The three dimensionless parameters involved in the circumferential welded pipe are: , , :

[0020]

[0021] S22: Using FRANC3D software, based on the fact that the surface crack involves two dimensionless parameters, the surface crack of the circumferential weld is inserted into the finite element model of the circumferential weld pipe structure.

[0022] The surface cracks involve two dimensionless parameters. , :

[0023]

[0024] S23: Mesh the finite element model obtained in S22 and apply a uniformly distributed stress perpendicular to the crack surface. As load boundary conditions for the finite element model, obtain the finite element model with load boundaries.

[0025] Furthermore, S3 specifically includes the following steps:

[0026] S31: Based on the aforementioned finite element model with load boundaries, the following steps are taken using FRANC3D software. M Integral method to obtain information about cracks M Integration value;

[0027] S32: According to M The integral value, combined with the material's elastic modulus and Poisson's ratio, yields the stress intensity factor at the crack front edge of the pipe circumferential weld surface. K for:

[0028]

[0029] In the formula: E Indicates the elastic modulus of a material; υ Indicates the Poisson's ratio of the material; Indicates intermediate parameters; M This indicates the information obtained from step S31. M Integration value;

[0030] S33: Stress distribution is adopted As a reference load, and with the normalized distance of the crack leading edge on the surface of the pipe circumferential weld as... The stress intensity factor is calculated at equal intervals within the range. By executing S31 to S32, the stress intensity factor at each point on the crack leading edge of the circumferential weld surface under the reference load condition is calculated and used as the reference solution for the stress intensity factor.

[0031] Furthermore, S4 specifically includes the following steps:

[0032] S41: The strategy for constructing the weight coefficients is as follows:

[0033] S411: The integrated stress intensity factor calculation model is as follows:

[0034]

[0035] S412: Stress distribution When used as a reference load condition, two numerical integration results are obtained for the integrated stress intensity factor calculation model. for:

[0036]

[0037]

[0038] S413: Based on the numerical integration results Combined with stress intensity factor reference solution Obtain the calculation point of the stress intensity factor at the crack front. The weighting coefficients of the point load weighting function are:

[0039]

[0040] S42: By discretizing the entire crack surface into a mesh, repeat step S41 to solve for the weight coefficients of each calculation point at the crack leading edge of the circumferential weld surface in the point load weight function, and obtain the weight coefficient solution.

[0041] Furthermore, S5 specifically includes the following steps:

[0042] S51: The dimensionless parameter , , , , , As input variables, the weight coefficients are solved Establish a dataset as the output target;

[0043] S52: Use the input variables as input to the backpropagation neural network and the output target as output to the backpropagation neural network. Train the backpropagation neural network using the dataset.

[0044] Meanwhile, the weights and biases of the backpropagation neural network are optimized based on the genetic algorithm to obtain the optimal combination of weights and biases of the backpropagation neural network, thereby obtaining the weight coefficient prediction model.

[0045] Beneficial Effects: This invention provides a weighted function method for calculating the stress intensity factor of surface cracks in pipe circumferential welds. Based on the point load weighted function theory, this invention establishes a quantitative relationship between weighting coefficients and pipe shape and size, local shape and size of the circumferential weld, and shape and size of the surface crack. It constructs a point load weighted function that considers six dimensionless parameters at the calculation points of the crack leading edge on the circumferential weld surface. This fully considers the influence of factors such as the location of the crack leading edge, the crack shape, the pipe shape, and the local shape of the circumferential weld on the stress intensity factor of the pipe circumferential weld surface crack. Compared with the general weighted function method, this invention is suitable for calculating the stress intensity factor of the crack leading edge on the surface of pipe circumferential welds under arbitrary stress distribution load conditions. By performing numerical integration on the product of the point load weighted function and the stress distribution load on the crack surface, the stress intensity factor of surface cracks in complex three-dimensional structures such as circumferential welded pipes can be calculated quickly and accurately. Compared with the traditional finite element method, this invention does not require re-meshing for finite element calculations when the crack shape and size change, and there is no need to generate a high-quality mesh at the crack tip. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart illustrating the weighting function method for calculating the surface crack stress intensity factor of a pipe circumferential weld according to the present invention.

[0048] Figure 2 This is a schematic diagram showing the configuration of crack size on the surface of the pipe circumferential weld in this embodiment;

[0049] Figure 3 This is a schematic diagram of the load weight function parameters for the surface crack points of the pipe circumferential weld in this embodiment;

[0050] Figure 4 This is a schematic diagram of the finite element model of the surface crack of the pipe circumferential weld in this embodiment;

[0051] Figure 5 This is a schematic diagram of the global numerical integration mesh of the crack surface in this embodiment. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] This embodiment provides a weighting function method for calculating the stress intensity factor of surface cracks in pipe circumferential welds, such as... Figure 1 As shown, the specific steps include:

[0054] S1: For the three-dimensional crack problem in an arbitrary elastic body, the formula for calculating the stress intensity factor based on the point load weighting function is as follows:

[0055] (1)

[0056] In the formula: This represents the stress intensity factor at point P' at the crack tip. The stress distribution on the crack surface is represented by the point load weighting function. This represents the stress intensity factor at the crack tip P' under the condition that a unit point load is applied at point P on the crack surface at (x,y). S This represents the area of ​​the entire crack surface.

[0057] like Figure 2 As shown, the geometric characteristics of surface cracks in the circumferential welds of offshore oil and gas pipelines are complex, involving multiple geometric parameters, including the pipeline wall thickness. T Pipe inner wall radius Weld toe transition angle θ Weld toe curvature radius r Surface crack depth a and surface crack half width c ;like Figure 3As shown, for a pipeline structure containing surface cracks in the circumferential weld, a point load weight function is constructed, which includes undetermined weight coefficients for the calculation points at the leading edge of the surface crack in the circumferential weld, to obtain a calculation model for the stress intensity factor of the surface crack in the pipeline circumferential weld. The expression of the point load weight function is as follows:

[0058] (2)

[0059] In the formula: s This represents the shortest distance from the point of application of the load P on the crack surface to the crack tip; This represents the distance from the point of application of the load P on the crack surface to the point where the stress intensity factor is calculated at the crack tip. The straight-line distance; ξ Indicates the calculation point of the stress intensity factor at the crack tip. The horizontal distance to the origin O of the local coordinate system of the crack; h This represents the horizontal distance from point C on the surface of the crack tip to the origin O of the local coordinate system of the crack. a Indicates the depth of surface cracks; c Indicates the half-width of a surface crack; T Indicates pipe thickness; Indicates the inner radius of the pipe; θ Indicates the weld toe transition angle; r Indicates the radius of curvature of the weld toe; ρ This represents the distance from the point P on the crack surface where the load is applied to the origin O of the local coordinate system of the crack. This represents the distance from point Q on the crack tip to the origin O of the local coordinate system of the crack; Indicates the calculation point of the crack front. The undetermined weighting coefficients are the same as the six dimensionless parameters. , , , , , Related functions; This represents the normalized distance at the crack tip, indicating the position of point P' at the crack tip. Indicates the surface crack shape ratio; This represents the ratio of crack depth to pipe wall thickness. This represents the ratio of the pipe wall thickness to the inner wall radius. This represents the ratio of the weld toe curvature radius to the pipe wall thickness.

[0060] When the crack leading edge position parameter ( ), crack shape parameters ( and Pipe shape parameters () ) and local shape parameters of the circumferential weld ( and When taking different values, the weighting coefficient Things will change, therefore, by establishing and , , , , and The quantitative relationship between them, the proposed point load weight function, i.e. formula (2), can take into account the influence of various factors such as the location of the surface crack leading edge, the shape of the surface crack, the shape of the pipeline and the local shape of the circumferential weld on the stress intensity factor of the surface crack of the pipeline circumferential weld.

[0061] S2: Based on the pipe structure containing surface cracks in the circumferential weld, a finite element model is established and meshed. At the same time, a stress distribution perpendicular to the crack surface is applied as the load boundary condition of the finite element model to obtain a finite element model with load boundaries.

[0062] Specifically, the following steps are included:

[0063] S21: As Figure 4 As shown, the finite element model of the circumferential welded pipe structure was established using ABAQUS finite element software based on the three dimensionless parameters involved in the circumferential welded pipe.

[0064] The three dimensionless parameters involved in the circumferential welded pipe are: , , :

[0065] (3)

[0066] In this embodiment, 80 different finite element models of circumferential welded pipe structures were created, and the inp file of each finite element model of circumferential welded pipe structure was exported.

[0067] S22: Import the finite element model inp file of the circumferential welded pipe structure using FRANC3D software. Based on the fact that the surface crack involves two dimensionless parameters, insert the circumferential welded surface crack into the finite element model of the circumferential welded pipe structure.

[0068] The surface cracks involve two dimensionless parameters. , :

[0069] (4)

[0070] For each finite element model of the pipeline structure, 25 different semi-elliptical surface cracks were sequentially inserted;

[0071] S23: Mesh the finite element model obtained in S22, and simultaneously apply a uniformly distributed stress perpendicular to the crack surface. As the load boundary conditions for the finite element model, a finite element model with load boundaries is obtained. Specifically, the stress distribution on the crack surface is defined using the Loads / Crack Face Pressure Traction function. As the load boundary condition, uniformly distributed stress is chosen. As a reference load boundary condition, where It can be any positive number.

[0072] S3: Based on the finite element model with load boundaries, calculate the stress intensity factor at each point on the crack front edge of the circumferential weld surface under the reference load condition, and use it as the reference solution for the stress intensity factor.

[0073] Specifically, the following steps are included:

[0074] S31: Based on the aforementioned finite element model with load boundaries, the Cracks / Compute SIFs function in FRANC3D software is used to select... M Integral method to obtain information about cracks M Integration value;

[0075] The M The expression for integration is:

[0076] (5)

[0077] In the formula: W Represents strain energy density; x The vector representing the position of the integration point; n Represents the unit outward normal vector; T This represents the surface force at the integral curve; u Represents the displacement vector; l Indicates the length of the contour line surrounding the crack tip;

[0078] S32: For type I cracks, according to M The integral value, combined with the material's elastic modulus and Poisson's ratio, yields the stress intensity factor at the crack front edge of the pipe circumferential weld surface. K for:

[0079] (6)

[0080] In the formula: E Indicates the elastic modulus of a material; υ Indicates the Poisson's ratio of the material; Indicates intermediate parameters; M This indicates the information obtained from step S31. M Integral value; For points on the surface of the crack tip, the state is plane stress, while for other points on the crack tip, the state is plane strain;

[0081] S33: Stress distribution is adopted As a reference load, and with the normalized distance of the crack leading edge on the surface of the pipe circumferential weld as... Values ​​are taken at equal intervals within the range. Stress intensity factors at each point on the crack front edge of the circumferential weld surface under reference load conditions are calculated by executing S31 to S32, and these are used as the reference solution for stress intensity factors. In this embodiment, for 2000 cases (80×25) of circumferential weld surface cracks in pipeline structures, the normalized distance of the crack front edge is used. Ten points are taken at equal intervals within the range of 0.0 to 1.0, and the stress intensity factor of each point at the crack front is extracted as a reference solution.

[0082] S4: Based on the stress intensity factor reference solution and the stress intensity factor calculation model, solve for the undetermined weight coefficients of the calculation points at the crack front edge of the circumferential weld surface in the point load weight function, and obtain the sample weight coefficient solution.

[0083] Specifically, the following steps are included:

[0084] S41: The strategy for constructing the weight coefficients is as follows:

[0085] S411: The integrated stress intensity factor calculation model involves substituting the proposed point load weight function, i.e., formula (2), into formula (1) to obtain the stress distribution load. The formula for calculating the stress intensity factor at the crack tip P' under the given conditions is:

[0086] (7)

[0087] S412: Stress distribution When used as a reference load condition, two numerical integration results are obtained for the integrated stress intensity factor calculation model. for:

[0088] (8)

[0089] (9)

[0090] S413: Based on the numerical integration results Combined with stress intensity factor reference solution Obtain the calculation point of the stress intensity factor at the crack front. The weighting coefficients of the point load weighting function are:

[0091] (10)

[0092] In the formula: This is the reference solution for the surface crack stress intensity factor calculated in step S3;

[0093] S42: By discretizing the entire crack surface into a mesh, repeat step S41 to solve for the weighting coefficients of each calculated point at the crack front edge of the circumferential weld surface in the point load weighting function, and obtain the weighting coefficient solution. Specifically, as follows... Figure 5 The crack surface is discretized into a mesh, and the Gauss-Legendre method is used to numerically integrate equations (8) and (9), yielding the results. and The value of the stress intensity factor reference solution; Numerical integration results and Substituting into formula (10), the weighting coefficients of each point at the crack leading edge on the surface of the circumferential weld are obtained. ;

[0094] In this embodiment, by repeating step S4, the weight coefficients of each point at the crack front edge under different pipe shape and size and surface crack shape and size conditions of the circumferential weld are solved, with a total of 20,000 different samples.

[0095] S5: Establish a dataset by using the dimensionless parameters as input variables and the sample weight coefficient solutions as output targets; optimize the backpropagation neural network based on the genetic algorithm, and construct a weight coefficient prediction model based on the dataset;

[0096] Specifically, the following steps are included:

[0097] S51: The dimensionless parameter , , , , , As input variables, the weight coefficients are solved Establish a dataset as the output target;

[0098] S52: A backpropagation neural network is established, mainly composed of an input layer, hidden layers, and an output layer. Prediction performance is evaluated by selecting neural networks with different numbers of hidden layers and neurons to ensure the model's accuracy and generalization ability. The input variables are used as the input to the backpropagation neural network, and the output target is used as its output. The backpropagation neural network is trained using a dataset.

[0099] Simultaneously, MATLAB software is used to optimize the weights and biases of the backpropagation neural network based on a genetic algorithm to obtain the optimal combination of weights and biases. In this embodiment, in view of the problems of slow convergence speed and easy getting trapped in local optima in the training process of the backpropagation neural network, a genetic algorithm with global search capability is selected to optimize the weights and biases of the backpropagation neural network, thereby improving the convergence speed and prediction accuracy of the backpropagation neural network, and thus establishing a weight coefficient prediction model.

[0100] S6: Based on the weighted coefficient prediction model, the corresponding weighted coefficient solution is obtained by inputting the dimensionless parameters of the target, and then the point load weight function is obtained; the product of the point load weight function and the stress distribution load on the surface crack of the circumferential weld is double integrally calculated to realize the calculation of the stress intensity factor at each point on the crack front edge of the circumferential weld of the pipeline structure.

[0101] Specifically, for a pipe structure with surface cracks in a circumferential weld of a given size, when the dimensionless parameter... , and The value of is within the range of formula (3), and and When the value of is within the range of formula (4), the position of any point P' at the crack front edge is normalized according to the distance. Characterization is performed; the weighted coefficient prediction model established in step S5 is used to... , , , , and As input variables, the weighting coefficients of any point P' at the crack tip are obtained. The entire crack surface is meshed using a pre-programmed stress intensity factor calculation program, and the stress distribution load acting on the crack surface is input. With weighting coefficients The Gauss-Legendre method is used to numerically integrate formula (7), which can quickly calculate the stress intensity factor at each point on the crack front edge of the pipe circumferential weld surface under a given stress distribution load.

[0102] To facilitate understanding of the technical solution of the method described in this embodiment, a detailed explanation is provided through the following specific embodiments.

[0103] Taking a certain offshore oil and gas pipeline as an example, the pipeline material uses an inner wall radius of... R i The pipe wall thickness is 160mm. T It is 21mm X80 pipeline steel, with a weld toe transition angle. θ The radius of curvature of the weld toe is 5°.r It is 1.00mm.

[0104] Using ABAQUS and FRANC3D software, different crack shape ratios were created. a / c Depth ratio a / T Weld toe transition angle θ and weld toe curvature radius r A crack appeared on the surface of the circumferential weld of the pipe. Two stress distribution loads were applied to the crack surface as follows:

[0105]

[0106]

[0107] By combining the finite element calculation results under two stress distribution loading conditions K FE The weight function calculation results of the method described in this embodiment K WF Compare the results as shown in Tables 1 and 2:

[0108] Table 1: Stress Distribution Load Calculation results of stress intensity factor (unit: )

[0109]

[0110] Table 2: Stress Distribution Load Calculation results of stress intensity factor (unit: )

[0111]

[0112] The comparison shows that the method described in this embodiment has high calculation accuracy. Within the applicable size range, the error is within 5% for various high-order complex stress distribution loads, and the calculation efficiency can be improved by more than 40 times compared with the finite element method.

[0113] The method described in this embodiment constructs a point load weight function for calculating the stress intensity factor of surface cracks in circumferential welds of pipeline structures; establishes a finite element model of the pipeline structure containing surface cracks in the circumferential weld; calculates a reference solution for the stress intensity factor under a reference load based on the M-integral method; solves for the weight coefficients of the surface cracks in the circumferential weld; optimizes the backpropagation neural network using a genetic algorithm to establish a weight coefficient prediction model; and finally performs a double integral operation on the product of the point load weight function and the stress distribution load over the entire crack surface, thus quickly and accurately predicting the stress intensity factor of surface cracks in pipeline circumferential welds. The method described in this embodiment is applicable to the calculation of stress intensity factors of surface cracks in pipeline circumferential welds under arbitrary stress distribution loads, providing a basis for damage tolerance assessment of key nodes in oil and gas pipelines.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A weighting function method for calculating the stress intensity factor of surface cracks in pipe circumferential welds, characterized in that, Specifically, the following steps are included: S1: For pipeline structures containing surface cracks in circumferential welds, a point load weighting function is constructed, which includes undetermined weighting coefficients for calculation points at the leading edge of the surface cracks in the circumferential weld. The stress intensity factor calculation model for the surface cracks in the circumferential weld is obtained based on the point load weighting function as follows: In the formula: s This represents the shortest distance from the point of application of the load P on the crack surface to the crack tip; This represents the distance from the point of application of the load P on the crack surface to the point where the stress intensity factor is calculated at the crack tip. The straight-line distance; ξ Indicates the calculation point of the stress intensity factor at the crack tip. The horizontal distance to the origin O of the local coordinate system of the crack; h This represents the horizontal distance from point C on the surface of the crack tip to the origin O of the local coordinate system of the crack. a Indicates the depth of surface cracks; c Indicates the half-width of a surface crack; T Indicates pipe thickness; Indicates the inner radius of the pipe; θ Indicates the weld toe transition angle; r Indicates the radius of curvature of the weld toe; ρ This represents the distance from the point P on the crack surface where the load is applied to the origin O of the local coordinate system of the crack. This represents the distance from point Q on the crack tip to the origin O of the local coordinate system of the crack; Indicates the calculation point of the crack front. The undetermined weighting coefficients are the same as the six dimensionless parameters. , , , , , Related functions; This represents the normalized distance at the crack tip, indicating the position of point P' at the crack tip. Indicates the surface crack shape ratio; This represents the ratio of crack depth to pipe wall thickness. This represents the ratio of the pipe wall thickness to the inner wall radius. This represents the ratio of the weld toe curvature radius to the pipe wall thickness. Indicates the crack leading edge Stress intensity factor at the point; This represents the stress distribution on the crack surface. The point load weighting function represents the crack front under a unit point load applied at points P on the crack surface at x and y. Stress intensity factor at the location; S The area of ​​the entire crack surface; S2: Based on the pipe structure containing surface cracks in the circumferential weld, a finite element model is established and meshed. At the same time, a stress distribution perpendicular to the crack surface is applied as the load boundary condition of the finite element model to obtain a finite element model with load boundaries. S3: Based on the finite element model with load boundaries, calculate the stress intensity factor at each point on the crack front edge of the circumferential weld surface under the reference load condition, and use it as the reference solution for the stress intensity factor. S4: Based on the stress intensity factor reference solution and the stress intensity factor calculation model, solve for the undetermined weight coefficients of the calculation points at the crack front edge of the circumferential weld surface in the point load weight function, and obtain the sample weight coefficient solution. S5: Establish a dataset by using the dimensionless parameters as input variables and the sample weight coefficient solutions as output targets; optimize the backpropagation neural network based on the genetic algorithm, and construct a weight coefficient prediction model based on the dataset; S6: Based on the weighted coefficient prediction model, the corresponding weighted coefficient solution is obtained by inputting the dimensionless parameters of the target, and then the point load weight function is obtained; the product of the point load weight function and the stress distribution load on the surface crack of the circumferential weld is double integrally calculated to realize the calculation of the stress intensity factor at each point on the crack front edge of the circumferential weld of the pipeline structure.

2. A weight function method for calculating the surface crack stress intensity factor of a pipe girth weld according to claim 1, characterized in that, S2 specifically includes the following steps: S21: Using ABAQUS finite element software, a finite element model of the circumferential welded pipe structure was established based on the three dimensionless parameters involved in the circumferential welded pipe. The three dimensionless parameters involved in the girth welded pipe are , , : S22: Using FRANC3D software, based on the fact that the surface crack involves two dimensionless parameters, the surface crack of the circumferential weld is inserted into the finite element model of the circumferential weld pipe structure. The surface crack involves two dimensionless parameters , : S23: meshing the finite element model acquired in S22 and applying uniform stress perpendicular to the crack surface As a load boundary condition of the finite element model, a finite element model having a load boundary is acquired.

3. The weighting function method for calculating the surface crack stress intensity factor of a pipe circumferential weld according to claim 2, characterized in that, S3 specifically includes the following steps: S31: Based on the aforementioned finite element model with load boundaries, the following steps are taken using FRANC3D software. M Integral method to obtain information about cracks M Integral value; S32: According to M The integral value, combined with the material's elastic modulus and Poisson's ratio, yields the stress intensity factor at the crack front edge of the pipe circumferential weld surface. K for: In the formula: E Indicates the elastic modulus of a material; υ Indicates the Poisson's ratio of the material; Indicates intermediate parameters; M This indicates the information obtained from step S31. M Integration value; S33: Stress distribution is adopted As a reference load, and with the normalized distance of the crack leading edge on the surface of the pipe circumferential weld as... The stress intensity factor is calculated at equal intervals within the range. By executing S31 to S32, the stress intensity factor at each point on the crack leading edge of the circumferential weld surface under the reference load condition is calculated and used as the reference solution for the stress intensity factor.

4. The weighting function method for calculating the surface crack stress intensity factor of a pipe circumferential weld according to claim 3, characterized in that, S4 specifically includes the following steps: S41: The strategy for solving the weight coefficients is as follows: S411: The integrated stress intensity factor calculation model is as follows: S412: Stress distribution When used as a reference load condition, two numerical integration results are obtained for the integrated stress intensity factor calculation model. for: S413: Based on the numerical integration results Combined with stress intensity factor reference solution Obtain the calculation point of the stress intensity factor at the crack front. The weighting coefficients of the point load weighting function are: S42: By discretizing the entire crack surface into a mesh, repeat step S41 to solve for the weight coefficients of each calculation point at the crack leading edge of the circumferential weld surface in the point load weight function, and obtain the weight coefficient solution.

5. A weight function method of calculating the surface crack stress intensity factor of a pipe girth weld according to claim 4, characterized in that, S5 specifically includes the following steps: S51: The dimensionless parameter , , , , , As input variables, the weight coefficients are solved Establish a dataset as the output target; S52: Use the input variables as input to the backpropagation neural network and the output target as output to the backpropagation neural network. Train the backpropagation neural network using the dataset. Meanwhile, the weights and biases of the backpropagation neural network are optimized based on the genetic algorithm to obtain the optimal combination of weights and biases of the backpropagation neural network, thereby obtaining the weight coefficient prediction model.

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