A safety evaluation and design method for ship longitudinal weld structure

Abstract

The present application relates to the technical field of mechanical structure strength evaluation and structure design, and provides a safety evaluation and design method for a ship longitudinal weld structure, comprising determining a damage key position; using a nondestructive testing method to detect the minimum detectable crack size in the ship longitudinal weld structure; performing regularization and normalization processing on the detected crack; calculating the stress intensity factor amplitude corresponding to the current crack; judging whether the crack will expand in combination with the fatigue crack propagation threshold value predicted by the Zhu-Xuan model; based on the nondestructive testing result and the three-dimensional crack propagation analysis model, establishing a crack propagation digital twin; comparing the safety and reliability of different weld structure forms, size parameters and process schemes according to the crack propagation prediction result and the residual life evaluation result of the crack propagation digital twin under different structure schemes, to realize the optimization design of the ship longitudinal weld structure.

Description

A Safety Assessment and Design Method for Welded Longitudinal Frame Structures of Ships Technical Field

[0001] This invention relates to the technical field of mechanical structure strength assessment and structural design, and in particular to a method for safety assessment and design of welded longitudinal girder structures for ships. Background Technology

[0002] The welded longitudinal girder structure is a critical load-bearing component of large ships, and its integrity directly determines the overall longitudinal strength, stability, and service safety of the hull. However, due to the characteristics of welding manufacturing, various defects are inevitably introduced. Under long-term exposure to alternating loads in the marine environment, these defects are prone to develop into fatigue cracks, leading to structural fracture and seriously threatening the ship's navigational safety. Simply increasing the strength of the base material cannot effectively improve the strength of the welded joints of the longitudinal girder; on the contrary, it makes the welded areas more sensitive to initial defects. Therefore, accurate safety assessment and design for defective welded areas of the longitudinal girder are crucial.

[0003] Traditional SN curve assessment methods have significant limitations: firstly, their applicability is largely limited to steels with yield strengths below 400 MPa (Guideline for Fatigue Strength of Ship Structures 2015); secondly, this method cannot effectively consider the influence of complex factors such as load ratio and load sequence, leading to conservative fatigue life predictions and an inability to quantitatively assess the remaining life of cracked structures. Fracture mechanics-based assessment methods, however, do not restrict material strength grades. By assuming initial defects in the material, they transform the fatigue problem into a crack propagation process study. This not only reveals the crack initiation and propagation mechanisms from a mechanical perspective but also allows for accurate assessment of the remaining life of cracked components. However, this advantageous method is currently not used for the safety assessment of welded longitudinal girder structures in large ships, and corresponding design methods also lack.

[0004] Most existing studies on crack propagation are based on two-dimensional fracture mechanics theory. Although there has been some progress in stress ratio effect analysis, in practical applications, too much simplification is adopted, and excessive reliance is placed on empirical formulas in the code to calculate stress intensity factor and fatigue load spectrum, resulting in insufficient reliability of the results.

[0005] Therefore, there is an urgent need to design a safety assessment and design method for welded longitudinal girder structures of ships, which can meet the major needs of safety assessment and design of welded longitudinal girder structures of large ships and form a complete damage tolerance analysis and evaluation system. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for safety assessment and design of welded longitudinal girder structures for ships, comprising:

[0007] S1: Identify critical damage sites and identify welded longitudinal girder structures of ships that are sensitive to cracks and may lead to catastrophic failure;

[0008] S2: Use non-destructive testing (NDT) methods to detect the smallest detectable crack size in the welded structure of the ship's longitudinal girder;

[0009] S3: Regularize and normalize the detected cracks to unify the crack morphology characterization standards;

[0010] S4: Calculate the stress intensity factor amplitude corresponding to the current crack;

[0011] S5: Combine the fatigue crack propagation threshold value predicted by the Zhu-Xuan model to determine whether the crack will propagate. If the crack is determined not to propagate, then use the structural stress method to assess the service life of the welded longitudinal girder structure of the defective ship. If it is determined that the crack will propagate, calculate the remaining lifetime before the crack expands from its initial size to the critical instability size.

[0012] S6: Based on the non-destructive testing results and the three-dimensional crack propagation analysis model, establish a digital twin of crack propagation to realize the dynamic mapping and evolution prediction of crack state, and determine the inspection interval accordingly, and formulate inspection outline and subsequent safety precautions.

[0013] S7: Based on the crack propagation prediction results and remaining life assessment results of the crack propagation digital twin under different structural schemes, compare the safety and reliability of different welding structure forms, dimensional parameters and process schemes to achieve optimized design of the ship's longitudinal girder welding structure.

[0014] Furthermore, the non-destructive testing includes ultrasonic testing, magnetic particle testing, penetrant testing, X-ray testing, eddy current testing, and visual inspection.

[0015] Furthermore, the specific processing of regularization and normalization in step S3 is as follows:

[0016] For a single defect, the damage tolerance method based on fracture mechanics equates defects of different shapes to crack-like defects; irregular defects located on the surface of the structure are equated to semi-elliptical surface cracks, and the size of the original surface defect is equated to the major and minor semi-axes of the semi-elliptical crack; irregular defects deeply embedded in the structure are equated to deeply embedded elliptical cracks, and the size of the original internal defect is equated to the major and minor semi-axes of the elliptical crack.

[0017] For multiple defects, the interaction between each defect and its neighboring defects is evaluated using the original defect size, including:

[0018] (31) Determine the proximity of each internal defect to the surface. If a single subsurface defect meets the surface interaction criterion (distance between the defect and the surface) ,in If the depth of the defect itself is considered, then the underground defect is reclassified as a surface defect.

[0019] (32) Using the original size of each defect, assess the proximity of the defect to its neighboring defects. If two or more defects meet the proximity rules of the corresponding specification, then the multiple defects are equivalent to a single defect for analysis, and the combined defect is no longer evaluated in interaction with other defects.

[0020] Furthermore, the proximity rule includes:

[0021] ASME Standard: Minimum Spacing Between Two Defects in the Thickness Direction Not exceeding half the thickness of the larger defect, i.e. { , },in , Let be the thickness of the two defects;

[0022] RCC-MRx specification: Minimum spacing between two defects in the thickness direction The thickness should not exceed half the sum of the thicknesses of the two defects. Minimum distance between two defects in the width direction The width of the two defects shall not exceed half the sum of their widths. ,in, The width of the two defects;

[0023] BS 7910 specification: Minimum spacing between two defects in the thickness direction The thickness should not exceed half the sum of the thicknesses of the two defects. Minimum distance between two defects in the width direction The size of the defect shall not exceed that of the smaller of the two defects. { , };

[0024] GB / T 19624-2019 Standard: Spacing between two defects The size of the defect shall not exceed that of the smaller of the two defects. { , },in , These are the dimensions of the two defects.

[0025] Furthermore, the specific steps for calculating the stress intensity factor amplitude corresponding to the current crack in step S4 are as follows:

[0026] (41) Based on the regularized and normalized crack, structural geometry and material properties, establish a three-dimensional finite element global model, divide the crack propagation zone, apply boundary conditions and loads, and output the global model with boundary conditions and the crack propagation zone mesh.

[0027] (42) The global model uses FRANC3D to simulate and analyze the dynamic propagation behavior of the crack, identifies the geometric features of the crack front and discretizes them into sampling points, and outputs the coordinates of the discrete points of the crack front and the initial stress field distribution data.

[0028] (43) Determine the crack propagation direction of the three-dimensional model. Based on the curve of the crack tip, define a plane orthogonal to the tangent direction at each discrete point of the crack tip. Establish a polar coordinate system with the crack tip as the origin and use the maximum circumferential stress criterion to determine the propagation angle of the discrete point of the crack tip.

[0029] (44) Calculate the stress intensity factor amplitude based on crack geometry and fracture mechanics formula.

[0030] Furthermore, the steps for solving the extended angle in step (43) are as follows:

[0031] Within a local plane, assuming a plane strain state (applicable to points inside the crack tip, far from the free surface), the expression for the circumferential stress at the tip of a type I crack is as follows:

[0032]

[0033] in, This represents the type I stress intensity factor at this discrete point;

[0034] It is a dimensionless function that is dependent on angles and is obtained by transforming the stress components under plane strain.

[0035] The radial distance from the crack tip to the field point;

[0036] It is an angle in polar coordinates. The direction corresponding to the normal to the original crack surface;

[0037] According to the maximum circumferential stress criterion, the crack propagation angle is consistent with the direction of the maximum circumferential stress, therefore... Regarding angles Find the first-order partial derivative and set it to 0, that is:

[0038]

[0039] Regarding formula (1) Differentiate the equation, substitute it into formula (2) to obtain the angle equation, and solve the equation to obtain the angle equation. Take the maximum value ,Should That is, the crack propagation angle at that discrete point. .

[0040] Furthermore, in step (44), the stress intensity factor amplitude The formula for calculation is:

[0041]

[0042] In the formula, It is the external load acting on the crack. It is the size of the crack. It is a geometric factor related to the crack propagation angle, and it usually needs to be calculated based on factors such as crack shape and loading method.

[0043] Furthermore, if the three-dimensional finite element model is large in scale, the boundary displacement / stress data of the crack propagation zone can be extracted to generate a local fine sub-model. The sub-model can then be imported into FRANC3D to improve the efficiency of crack propagation analysis.

[0044] Before conducting simulations, it is necessary to identify the key factors affecting the dynamic propagation of cracks, including crack geometry parameters, load conditions, and location environment parameters.

[0045] The crack geometry parameters include:

[0046] The smaller the angle between the crack and the direction of force, the greater the stress intensity factor. For example, the stress intensity factor of a hole edge crack is the largest at 30°, the propagation rate is the fastest, and the remaining life of the structure is the shortest; while a 90° perpendicular crack is the most stable.

[0047] The larger the aspect ratio of the crack shape, the more likely the surface crack is to flatten; buried cracks tend to be more circular, affecting their initiation life.

[0048] The load conditions include:

[0049] Stress level and stress intensity factor increase linearly with load. Under high stress, cracks propagate directly through the crack; under low stress, multi-path bifurcation may be triggered.

[0050] For different load types, under variable amplitude loads, the crack propagation rate is significantly higher than under constant amplitude loads, and the prediction model needs to be modified in conjunction with the formula.

[0051] The location environment parameters include:

[0052] The stress intensity factor increases and then decreases with crack depth, with the peak value appearing near the contact patch, where the risk of propagation is highest.

[0053] Stress gradients accelerate crack propagation in stress concentration areas such as hole edges and welds. For example, the stress intensity factor of a crack at the edge of a hole in aircraft skin increases sharply as it propagates to the edge of the hole.

[0054] Furthermore, the basis for determining whether the crack will propagate in step S5 is as follows:

[0055] When the crack propagation rate is less than 10 -7 When the crack propagation rate reaches 10 mm / cycle, it is considered that the fatigue crack will no longer propagate, therefore the crack propagation rate is set to 10. -7 Stress intensity factor amplitude corresponding to mm / cycle As the fatigue crack propagation threshold under this condition When the stress intensity factor amplitude Greater than the fatigue crack propagation threshold At that time, it was believed that the crack would enter the propagation stage;

[0056] Stress intensity factor amplitude It is a function of structural geometry, stress range, and instantaneous crack size, and its calculation formula is:

[0057]

[0058] In the formula, This refers to the stress amplitude. When the shape factor is used, for surface defects When near surface or internal defects ; The crack size;

[0059] When the stress intensity factor amplitude Equal to the fatigue crack propagation threshold value When the threshold value is obtained, the critical defect expansion size is determined. ;

[0060]

[0061] Fatigue crack propagation threshold values ​​under different stress ratios Obtained from the Zhu-Xuan model, the model is shown in equation (6):

[0062]

[0063] In the formula, and Size and stress ratio The relationships are as follows: , ; Stress ratio; , To be relative to stress ratio Relevant material constants;

[0064] Substituting the fatigue crack propagation threshold values ​​obtained in formula (6) for different stress ratios into formula (5), we can deduce the critical defect propagation size for different stress ratios. When the defect size If the crack is cracked under normal conditions, it will propagate; otherwise, it will not.

[0065] Furthermore, in step S5, when it is determined that the crack will not propagate, the structural stress method is used to assess the service life of the welded longitudinal girder structure of the defective ship. The formula for calculation is:

[0066]

[0067] In the formula, and This is an experimental constant;

[0068] For the first The equivalent structural stress variation range for each cycle is calculated using the following formula:

[0069]

[0070] in, For the first The range of nominal stress variation for each cycle; The thickness of the welded component; This is a material constant, determined by long crack propagation test data, and is generally taken as 3.6; For bending moment of inertia; For the first Multiaxial stress correction factor for each cycle; for SI units, thickness t, stress variation range, and equivalent structural stress variation range. The units are mm, MPa, and , respectively. For imperial units, thickness (t) and stress variation range Range of equivalent structural stress The units are respectively taken as in, , .

[0071] Furthermore, in step S5, when it is determined that the crack will propagate, the following calculations are performed:

[0072] When stress intensity factor Greater than fracture toughness At this point, the crack enters the unstable propagation stage, and when the stress intensity factor... Less than or equal to fracture toughness When calculating the remaining lifetime before the crack expands from its initial size to the critical instability size;

[0073] The fatigue crack propagation rate formula can be used to determine the fatigue crack propagation life of a component. Under constant amplitude cyclic loading, the Paris formula can be directly integralized to obtain:

[0074]

[0075] In the formula, For crack size from Expand to The required number of stress cycles, For crack propagation to The number of loops at time, if Given the initial crack length, then ; For crack propagation to The number of stress cycles at that time; , These are material constants;

[0076] By combining equations (4) and (9), we can obtain:

[0077]

[0078] Under finite life conditions, in equation (10) = constant, meaning that fatigue failure and SN curve have a corresponding relationship;

[0079] From equation (5), the fatigue stress amplitude at crack initiation can be obtained. :

[0080]

[0081] Find the point corresponding to the fatigue stress amplitude on the SN curve, read the lifetime, and obtain the remaining lifetime before the crack expands from the initial size to the critical size.

[0082] Furthermore, the specific steps of step S6 are as follows:

[0083] (61) Constructing an initial crack propagation digital twin

[0084] Based on the design drawings, material performance parameters and initial non-destructive testing results of the target structure, a crack propagation digital twin corresponding one-to-one with the physical structure is constructed. The digital twin includes a physical entity layer, a virtual model layer, a data interaction layer and an application layer.

[0085] The physical entity layer obtains the size, location, and morphological parameters of the initial crack in the target structure through non-destructive testing, and simultaneously collects structural geometric parameters and material mechanical property parameters (including fracture toughness). Fatigue crack propagation coefficient and index Elastic modulus Poisson's ratio (Residual stress distribution), and deploy a sensor network to collect real-time load and environmental parameters to form an initial data set;

[0086] The virtual model layer is based on the initial data set, constructs a three-dimensional finite element crack propagation analysis model with initial cracks, embeds crack propagation criteria adapted to the working conditions (Paris formula is used for conventional fatigue conditions, Walker formula or Forman formula is used for variable amplitude load conditions), and completes model parameter initialization and calibration through material test data to ensure the consistency between the initial state of the virtual model and the physical entity.

[0087] The data interaction layer establishes an IoT communication interface to realize real-time data transmission, format conversion, and multi-source data fusion between the physical entity layer and the virtual model layer. The application layer is used to realize crack state visualization, evolution prediction, and engineering decision output.

[0088] (62) Virtual-real mapping of crack state and digital twin update

[0089] Regularly perform non-destructive testing on the target physical structure to obtain the real-time size, location and morphological parameters of the crack, including crack length, depth, opening width, orientation, tip curvature and branching. Denoise and standardize the test data to generate a standardized crack state parameter set.

[0090] Based on the structural reference coordinate system, the above-mentioned standardized crack state parameter set is accurately mapped to the virtual model layer of the crack propagation digital twin, replacing the crack geometric parameters in the original virtual model, and performing local mesh reconstruction (using singular element refinement) on the crack tip region to ensure the accuracy of stress intensity factor calculation.

[0091] By integrating the dynamic load spectrum (processed by rainflow counting) and environmental parameters (temperature, humidity, and concentration of corrosive media) collected by real-time sensors, the boundary conditions and material performance parameters of the virtual model are corrected (including corrections for residual stress relaxation and corrosion-induced fracture toughness degradation), and the three-dimensional finite element crack propagation model is updated simultaneously.

[0092] By verifying the consistency between the virtual and real states, the stress field at the crack tip calculated by the updated virtual model is compared with the measured strain data of the physical structure. If the deviation exceeds the allowable threshold in the engineering, the model parameters are iteratively adjusted until the deviation meets the requirements, thus completing the dynamic update of the digital twin.

[0093] (63) Reassessment based on the crack state of the updated digital twin

[0094] Using the updated three-dimensional finite element crack propagation model and combined with the future load prediction spectrum, the current crack propagation rate is calculated and the crack propagation path is predicted (by combining the stress concentration distribution of the structure to determine whether it extends to the critical load-bearing area).

[0095] The remaining life prediction value is obtained by iteratively calculating the number of cycles required for the crack to propagate from its current size to the critical instability size (crack tip stress intensity factor K ≥ fracture toughness K1C);

[0096] (64) Engineering decision-making and iterative optimization of digital twins

[0097] Based on the evaluation results of crack propagation path, remaining life and remaining strength, the optimal inspection interval is dynamically determined to ensure that the inspection interval is less than 1 / 3 of the remaining life and to avoid unstable fracture between two inspections.

[0098] Develop a detailed inspection outline, specifying key inspection areas (crack tips and predicted propagation paths, stress concentration areas), inspection methods (high-precision methods such as ultrasonic phased array and X-ray tomography), and inspection accuracy requirements (crack size measurement error ≤3%).

[0099] For different safety risk levels (divided into low, medium, high, and extremely dangerous levels based on remaining life, remaining strength, and crack propagation rate), corresponding safety precautions should be formulated.

[0100] The present invention has the following beneficial effects:

[0101] (1) This invention addresses the challenges of complexity, accuracy, and real-time performance in the safety assessment of ship welded structures. It uses three-dimensional finite element technology to analyze fatigue crack propagation and combines it with life assessment technology based on fracture mechanics to construct a digital twin of crack propagation, thereby achieving closed-loop updates between detection data, crack evolution, and life prediction.

[0102] (2) The damage tolerance design method for welded longitudinal girder structures proposed in this invention has the advantages of high accuracy, real-time quantitative prediction of crack propagation life and guidance of structural design. Compared with the cumulative damage method based on the traditional SN curve and linear cumulative damage criterion, this invention fully considers the influence of the stress state at the crack tip on the remaining life of the structure, and is more suitable for welded structures with a large number of initial defects. It has important scientific significance and application value for the design and construction of large ship structures.

[0103] (3) The present invention adopts more accurate three-dimensional finite element simulation technology, combined with fatigue crack propagation theory, to realistically simulate complex welding nodes, which will significantly improve the accuracy of crack propagation analysis and provide a reliable basis for welding structure design.

[0104] (4) Based on the non-destructive testing results and the three-dimensional crack propagation analysis model, the present invention constructs a crack propagation digital twin to realize the dynamic mapping and evolution prediction of crack state, thereby determining a reasonable inspection interval; and by formulating an inspection outline and subsequent safety precautions, a closed-loop update mechanism of detection data-crack evolution-life prediction is formed to continuously iterate and improve the digital twin. Attached Figure Description

[0105] Figure 1 is a schematic diagram of the safety assessment and design process of the present invention.

[0106] Figure 2 is a simplified schematic diagram of common defects in this invention.

[0107] Figure 3 is a schematic diagram of the process for calculating the stress intensity factor amplitude corresponding to the current crack in this invention.

[0108] Figure 4 is a schematic diagram of extracting the fatigue crack propagation sub-model from the three-dimensional finite element global model in this invention.

[0109] Figure 5 is a schematic diagram of the relationship between fatigue crack propagation and instability propagation.

[0110] Figure 6 is a schematic diagram of the fatigue crack propagation rate and SN curve in this invention.

[0111] Figure 7 is an equivalent simplified diagram of the initial defects of the longitudinal girder welded structure in the embodiment.

[0112] Figure 8 is a schematic diagram of the crack geometry in FRANC3D.

[0113] Figure 9 is a schematic diagram of the crack tip and crack propagation path in FRANC3D.

[0114] Figure 10 shows the variation curve of the type I stress intensity factor.

[0115] Figure 11 is a schematic diagram comparing the simulated and experimental values ​​of fatigue crack propagation life.

[0116] Figure 12 is a curve showing the fitting of the finite element simulation values ​​for crack propagation. Detailed Implementation

[0117] The technical solution of the present invention will be further described in detail below with reference to specific embodiments. However, these embodiments are not intended to limit the present invention. Any similar structures and similar variations of the present invention should be included in the protection scope of the present invention. The commas in the present invention all indicate the relationship between and. The English letters in the present invention are case-sensitive.

[0118] As shown in Figure 1, this invention provides a safety assessment and design method for welded longitudinal girder structures of ships, including...

[0119] S1: Identify critical damage sites and identify welded longitudinal girder structures of ships that are sensitive to cracks and may lead to catastrophic failure;

[0120] S2: The minimum detectable crack size in the welded structure of the ship's longitudinal girder is detected using non-destructive testing (NDT) methods; the NDT includes ultrasonic testing, magnetic particle testing, penetrant testing, radiographic testing, eddy current testing, and visual inspection.

[0121] S3: The detected cracks are regularized and normalized to unify the crack morphology characterization standards; the specific processing is as follows:

[0122] As shown in Figure 2, for a single defect, the damage tolerance method based on fracture mechanics equates defects of different shapes to crack-like defects; irregular defects located on the surface of the structure are equated to semi-elliptical surface cracks, and the size of the original surface defect is equated to the major and minor axes of the semi-elliptical crack; irregular defects deeply embedded inside the structure are equated to deeply embedded elliptical cracks, and the size of the original internal defect is equated to the major and minor axes of the elliptical crack.

[0123] For multiple defects, the interaction between each defect and its neighboring defects is evaluated using the original defect size, including:

[0124] (31) Determine the proximity of each internal defect to the surface. If a single subsurface defect meets the surface interaction criterion (distance between the defect and the surface) ,in If the depth of the defect itself is considered, then the underground defect is reclassified as a surface defect.

[0125] (32) Using the original size of each defect, assess the proximity of the defect to its neighboring defects. If two or more defects meet the proximity rules of the corresponding specification, then the multiple defects are equivalent to a single defect for analysis, and the combined defect is no longer evaluated in interaction with other defects.

[0126] The proximity rules include:

[0127] ASME Standard: Minimum Spacing Between Two Defects in the Thickness Direction Not exceeding half the thickness of the larger defect, i.e. { , },in , Let be the thickness of the two defects;

[0128] RCC-MRx specification: Minimum spacing between two defects in the thickness direction The thickness should not exceed half the sum of the thicknesses of the two defects. Minimum distance between two defects in the width direction The width of the two defects shall not exceed half the sum of their widths. ,in, The width of the two defects;

[0129] BS 7910 specification: Minimum spacing between two defects in the thickness direction The thickness should not exceed half the sum of the thicknesses of the two defects. Minimum distance between two defects in the width direction The size of the defect shall not exceed that of the smaller of the two defects. { , };

[0130] GB / T 19624-2019 Standard: Spacing between two defects The size of the defect shall not exceed that of the smaller of the two defects. { , },in , These are the dimensions of the two defects.

[0131] S4: Calculate the stress intensity factor amplitude corresponding to the current crack. The specific steps are as follows:

[0132] As shown in Figure 3, (41) based on the crack, structural geometry and material properties after regularization and normalization, a three-dimensional finite element global model is established using ABAQUS, the crack propagation zone is divided, boundary conditions and loads are applied, and the global model with boundary conditions and the crack propagation zone mesh are output.

[0133] (42) The global model uses FRANC3D to simulate and analyze the dynamic propagation behavior of the crack, identifies the geometric features of the crack front and discretizes them into sampling points, and outputs the coordinates of the discrete points of the crack front and the initial stress field distribution data.

[0134] (43) Determine the crack propagation direction of the three-dimensional model. Using the curve of the crack tip as a reference, define a plane orthogonal to the tangent direction at each discrete point of the crack tip. Establish a polar coordinate system with the crack tip as the origin. Use the maximum circumferential stress criterion to determine the propagation angle of the discrete points of the crack tip. The solution steps are as follows:

[0135] Within a local plane, assuming a plane strain state (applicable to points inside the crack tip, far from the free surface), the expression for the circumferential stress at the tip of a type I crack is as follows:

[0136]

[0137] in, This represents the type I stress intensity factor at this discrete point;

[0138] It is a dimensionless function that is dependent on angles and is obtained by transforming the stress components under plane strain.

[0139] The radial distance from the crack tip to the field point;

[0140] It is an angle in polar coordinates. The direction corresponding to the normal to the original crack surface;

[0141] According to the maximum circumferential stress criterion, the crack propagation angle is consistent with the direction of the maximum circumferential stress, therefore... Regarding angles Find the first-order partial derivative and set it to 0, that is:

[0142]

[0143] Regarding formula (1) Differentiate the equation, substitute it into formula (2) to obtain the angle equation, and solve the equation to obtain the angle equation. Take the maximum value ,Should That is, the crack propagation angle at that discrete point. .

[0144] (44) Calculate the stress intensity factor amplitude based on crack geometry and fracture mechanics formulas. The formula for its calculation is:

[0145]

[0146] In the formula, It is the external load acting on the crack. It is the size of the crack. It is a geometric factor related to the crack propagation angle, and it usually needs to be calculated based on factors such as crack shape and loading method.

[0147] In addition, if the three-dimensional finite element model is large in scale, the boundary displacement / stress data of the crack propagation zone can be extracted to generate a local fine sub-model, as shown in Figure 4. The sub-model can then be imported into FRANC3D to improve the efficiency of crack propagation analysis.

[0148] Before conducting simulations, it is necessary to identify the key factors affecting the dynamic propagation of cracks, including crack geometry parameters, load conditions, and location environment parameters.

[0149] The crack geometry parameters include:

[0150] The smaller the angle between the crack and the direction of force, the greater the stress intensity factor. For example, the stress intensity factor of a hole edge crack is the largest at 30°, the propagation rate is the fastest, and the remaining life of the structure is the shortest; while a 90° perpendicular crack is the most stable.

[0151] The larger the aspect ratio of the crack shape, the more likely the surface crack is to flatten; buried cracks tend to be more circular, affecting their initiation life.

[0152] The load conditions include:

[0153] Stress level and stress intensity factor increase linearly with load. Under high stress, cracks propagate directly through the crack; under low stress, multi-path bifurcation may be triggered.

[0154] For different load types, under variable amplitude loads, the crack propagation rate is significantly higher than under constant amplitude loads, and the prediction model needs to be modified in conjunction with the formula.

[0155] The location environment parameters include:

[0156] The stress intensity factor increases and then decreases with crack depth, with the peak value appearing near the contact patch, where the risk of propagation is highest.

[0157] Stress gradients accelerate crack propagation in stress concentration areas such as hole edges and welds. For example, the stress intensity factor of a crack at the edge of a hole in aircraft skin increases sharply as it propagates to the edge of the hole.

[0158] S5: Combine the fatigue crack propagation threshold value predicted by the Zhu-Xuan model to determine whether the crack will propagate. If the crack is determined not to propagate, then use the structural stress method to assess the service life of the welded longitudinal girder structure of the defective ship. If it is determined that the crack will propagate, calculate the remaining lifetime before the crack expands from its initial size to the critical instability size.

[0159] The criteria for determining whether a crack will propagate are:

[0160] When the crack propagation rate is less than 10 -7 When the crack propagation rate reaches 10 mm / cycle, it is considered that the fatigue crack will no longer propagate, therefore the crack propagation rate is set to 10. -7 Stress intensity factor amplitude corresponding to mm / cycle As the fatigue crack propagation threshold under this condition When the stress intensity factor amplitude Greater than the fatigue crack propagation threshold At that time, it was believed that the crack would enter the propagation stage;

[0161] Stress intensity factor amplitude It is a function of structural geometry, stress range, and instantaneous crack size, and its calculation formula is:

[0162]

[0163] In the formula, This refers to the stress amplitude. When the shape factor is used, for surface defects When near surface or internal defects ; The crack size;

[0164] When the stress intensity factor amplitude Equal to the fatigue crack propagation threshold value When the threshold value is obtained, the critical defect expansion size is determined. ;

[0165]

[0166] Fatigue crack propagation threshold values ​​under different stress ratios Obtained from the Zhu-Xuan model, the model is shown in equation (6):

[0167]

[0168] In the formula, and The relationship between the magnitude and the stress ratio R is as follows: , ; Stress ratio; , To be relative to stress ratio Relevant material constants;

[0169] Substituting the fatigue crack propagation threshold values ​​obtained in formula (6) for different stress ratios into formula (5), we can deduce the critical defect propagation size for different stress ratios. When the defect size If the crack is cracked under normal conditions, it will propagate; otherwise, it will not.

[0170] When it is determined that the crack will not propagate, the structural stress method is used to assess the service life of the welded longitudinal girder structure of a defective ship. The formula for calculation is:

[0171]

[0172] In the formula, and This is an experimental constant;

[0173] For the first The equivalent structural stress variation range for each cycle is calculated using the following formula:

[0174]

[0175] in, For the first The range of nominal stress variation for each cycle; The thickness of the welded component; This is a material constant, determined by long crack propagation test data, and is generally taken as 3.6; For bending moment of inertia; For the first Multiaxial stress correction factor for each cycle; for SI units, thickness t, stress variation range, and equivalent structural stress variation range. The units are mm, MPa, and , respectively. For imperial units, thickness (t) and stress variation range Range of equivalent structural stress The units are respectively taken as in, , .

[0176] When it is determined that the crack will propagate, the following calculations are performed:

[0177] When stress intensity factor Greater than fracture toughness At this point, the crack enters the unstable propagation stage;

[0178] As shown in Figure 5, when the stress intensity factor amplitude Greater than the fatigue crack propagation threshold When the threshold value is obtained, the critical defect expansion size is determined. When the stress intensity factor equal to fracture toughness The critical size for instability propagation is obtained at this time. When the stress intensity factor Less than or equal to fracture toughness When, that is, less than the critical size for instability propagation. Calculate the remaining lifetime before the crack expands from its initial size to the critical instability size under the given conditions;

[0179] The fatigue crack propagation rate formula can be used to determine the fatigue crack propagation life of a component. Under constant amplitude cyclic loading, the Paris formula can be directly integralized to obtain:

[0180]

[0181] In the formula, For crack size from Expand to The required number of stress cycles, For crack propagation to The number of loops at time, if Given the initial crack length, then ; For crack propagation to The number of stress cycles at that time; , These are material constants;

[0182] By combining equations (4) and (9), we can obtain:

[0183]

[0184] Under finite life conditions, in equation (10) =constant, meaning there is a corresponding relationship between fatigue failure and the SN curve; as shown in Figure 6, the left horizontal axis of the figure is the logarithm of the stress intensity factor range. The vertical axis represents the logarithm of the crack propagation rate. ,when (When the threshold stress intensity factor range is specified), →0, the crack hardly propagates. At that time, the crack propagation rate and Satisfying the Paris formula, when Increase to near the material's fracture toughness hour, A sharp increase occurs as cracks propagate rapidly until fracture, at which point the lifespan contribution is minimal. The right side of the graph shows the horizontal axis as the logarithm of the number of cycles. The vertical axis represents the logarithm of the stress range. This reflects the macroscopic relationship between stress range and fatigue life: the slanted line represents the stress range. With the number of loops Increase and decrease, the slope of the sloping line is This stage corresponds to the "stable propagation zone" in the diagram: the crack grows from its initial size... Initially, the crack steadily propagates under cyclic stress until it reaches a critical size; its lifespan is determined by the cumulative number of crack propagations. In the horizontal segment, when the stress range is below the fatigue limit... At this point, the material can withstand an unlimited number of cycles without fatigue fracture.

[0185] From equation (5), the fatigue stress amplitude at crack initiation can be obtained. :

[0186]

[0187] Find the point corresponding to the fatigue stress amplitude on the SN curve, read the lifetime, and obtain the remaining lifetime before the crack expands from the initial size to the critical size.

[0188] S6: Based on non-destructive testing results and a three-dimensional finite element crack propagation analysis model, establish a digital twin of crack propagation to achieve dynamic mapping and evolution prediction of crack states. Based on this, determine inspection intervals, formulate inspection outlines and subsequent safety precautions. Specific steps are as follows:

[0189] (61) Constructing an initial crack propagation digital twin

[0190] Based on the design drawings, material performance parameters and initial non-destructive testing results of the target structure, a crack propagation digital twin corresponding one-to-one with the physical structure is constructed. The digital twin includes a physical entity layer, a virtual model layer, a data interaction layer and an application layer.

[0191] The physical entity layer obtains the size, location, and morphological parameters of the initial crack in the target structure through non-destructive testing, and simultaneously collects structural geometric parameters and material mechanical property parameters (including fracture toughness). Fatigue crack propagation coefficient and index Elastic modulus Poisson's ratio (Residual stress distribution), and deploy a sensor network to collect real-time load and environmental parameters to form an initial data set;

[0192] The virtual model layer is based on the initial data set, constructs a three-dimensional finite element crack propagation analysis model with initial cracks, embeds crack propagation criteria adapted to the working conditions (Paris formula is used for conventional fatigue conditions, Walker formula or Forman formula is used for variable amplitude load conditions), and completes model parameter initialization and calibration through material test data to ensure the consistency between the initial state of the virtual model and the physical entity.

[0193] The data interaction layer establishes an IoT communication interface to realize real-time data transmission, format conversion, and multi-source data fusion between the physical entity layer and the virtual model layer. The application layer is used to realize crack state visualization, evolution prediction, and engineering decision output.

[0194] (62) Virtual-real mapping of crack state and digital twin update

[0195] Regularly perform non-destructive testing on the target physical structure to obtain the real-time size, location and morphological parameters of the crack, including crack length, depth, opening width, orientation, tip curvature and branching. Denoise and standardize the test data to generate a standardized crack state parameter set.

[0196] Based on the structural reference coordinate system, the above-mentioned standardized crack state parameter set is accurately mapped to the virtual model layer of the crack propagation digital twin, replacing the crack geometric parameters in the original virtual model, and performing local mesh reconstruction (using singular element refinement) on the crack tip region to ensure the accuracy of stress intensity factor calculation.

[0197] By integrating the dynamic load spectrum (processed by rainflow counting) and environmental parameters (temperature, humidity, and concentration of corrosive media) collected by real-time sensors, the boundary conditions and material performance parameters of the virtual model are corrected (including corrections for residual stress relaxation and corrosion-induced fracture toughness degradation), and the three-dimensional finite element crack propagation model is updated simultaneously.

[0198] By verifying the consistency between the virtual and real states, the stress field at the crack tip calculated by the updated virtual model is compared with the measured strain data of the physical structure. If the deviation exceeds the allowable threshold in the engineering, the model parameters are iteratively adjusted until the deviation meets the requirements, thus completing the dynamic update of the digital twin.

[0199] (63) Reassessment based on the crack state of the updated digital twin

[0200] Using the updated three-dimensional finite element crack propagation model and combined with the future load prediction spectrum, the current crack propagation rate is calculated and the crack propagation path is predicted (by combining the stress concentration distribution of the structure to determine whether it extends to the critical load-bearing area).

[0201] Iterative calculations are performed to determine the crack propagation from its current size to the critical instability size (crack tip stress intensity factor). ≥ Fracture toughness The required number of cycles is used to obtain the predicted remaining lifetime.

[0202] (64) Engineering decision-making and iterative optimization of digital twins

[0203] Based on the evaluation results of crack propagation path, remaining life and remaining strength, the optimal inspection interval is dynamically determined to ensure that the inspection interval is less than 1 / 3 of the remaining life and to avoid unstable fracture between two inspections.

[0204] Develop a detailed inspection outline, specifying key inspection areas (crack tips and predicted propagation paths, stress concentration areas), inspection methods (high-precision methods such as ultrasonic phased array and X-ray tomography), and inspection accuracy requirements (crack size measurement error ≤3%).

[0205] For different safety risk levels (divided into four levels: low, medium, high, and extremely dangerous based on remaining life, remaining strength, and crack propagation rate), corresponding safety precautions are formulated. In low-risk conditions, the inspection interval is extended; in medium- and high-risk conditions, load reduction and local reinforcement measures are adopted; and in extremely dangerous conditions, the machine is immediately shut down for maintenance.

[0206] By accumulating multiple batches of nondestructive testing data, model prediction results, and physical structure operation data, and optimizing model parameters and data fusion algorithms, a closed-loop iterative mechanism of "detection-update-evaluation-decision-verification" is formed to continuously improve the prediction accuracy and adaptability of digital twins.

[0207] S7: Based on the crack propagation prediction results and remaining life assessment results of the crack propagation digital twin under different structural schemes, compare the safety and reliability of different welding structure forms, dimensional parameters and process schemes to achieve optimized design of the ship's longitudinal girder welding structure.

[0208] To verify this invention, a damage tolerance assessment was conducted on a cracked welded structure of the longitudinal girder of a large container ship. The specific method is as follows:

[0209] S1: Identify the critical damage locations and identify the welded longitudinal girder structures of the ship that are sensitive to cracks and may lead to catastrophic failure; the critical damage locations are selected from the fatigue-prone locations recommended by the China Classification Society's "Guideline for Fatigue Strength of Ship Structures 2015": the connection node (junction) between the bilge longitudinal girder and the transverse bulkhead; the node model is 1500 mm long, 400 mm wide, and 800 mm high; the transverse bulkhead and outer bottom plate are 10 mm thick, the longitudinal girder is made of HP200×9 bulb flat steel (panel width 28 mm), the reinforcing rib size is 150×10, and the connection between the longitudinal girder and the panel adopts a soft heel and soft toe design;

[0210] S2: The minimum detectable crack size in the connection node (junction) between the longitudinal rib and the transverse bulkhead was detected by non-destructive testing (NDT). A single initial main crack was detected on the longitudinal rib panel, located in the center of the bulb flat steel panel, 2 mm from the weld toe end, with a length of 3 mm along the free surface, a maximum depth of 1 mm, and an angle of 0°.

[0211] S3: Regularize and normalize the detected cracks to unify the crack morphology characterization standards;

[0212] The defect is simplified to a semi-elliptical surface crack, with an initial crack depth. Half-length Defect projection length Corresponding to the major axis of the ellipse, depth The equivalent crack location corresponding to the minor axis of the ellipse is shown in Figure 7.

[0213] S4: Calculate the stress intensity factor amplitude corresponding to the current crack.

[0214] (41) Based on the regularized and normalized crack, structural geometry and material properties, a three-dimensional finite element global model was established using ABAQUS, the crack propagation zone was divided, boundary conditions and loads were applied, and the global model with boundary conditions and the crack propagation zone mesh were output. Through static calculation, it was found that the stress near the weld toe of the bulkhead was greater than that at the end away from the bulkhead. Therefore, this area was selected as the crack propagation zone to establish a sub-model.

[0215] (42) The sub-model uses FRANC3D to simulate and analyze the dynamic propagation behavior of the crack, identifies the geometric features of the crack front and discretizes them into sampling points, and outputs the coordinates of the discrete points of the crack front and the initial stress field distribution data.

[0216] (43) Determine the crack propagation direction of the three-dimensional model. Using the curve of the crack tip as a reference, define a plane orthogonal to the tangent direction at each discrete point of the crack tip. Establish a polar coordinate system with the crack tip as the origin. Use the maximum circumferential stress criterion to determine the propagation angle of the discrete points of the crack tip. The solution steps are as follows:

[0217] Within a local plane, assuming a plane strain state (applicable to points inside the crack tip, far from the free surface), the expression for the circumferential stress at the tip of a type I crack is as follows:

[0218]

[0219] in, This represents the type I stress intensity factor at this discrete point;

[0220] It is a dimensionless function that is dependent on angles and is obtained by transforming the stress components under plane strain.

[0221] The radial distance from the crack tip to the field point;

[0222] It is an angle in polar coordinates. The direction corresponding to the normal to the original crack surface;

[0223] According to the maximum circumferential stress criterion, the crack propagation angle is consistent with the direction of the maximum circumferential stress, therefore... Regarding angles Find the first-order partial derivative and set it to 0, that is:

[0224]

[0225] Regarding formula (1) Differentiate the equation, substitute it into formula (2) to obtain the angle equation, and solve the equation to obtain the angle equation. Take the maximum value ,Should That is, the crack propagation angle at that discrete point. .

[0226] (44) Calculate the stress intensity factor amplitude based on crack geometry and fracture mechanics formulas. The formula for its calculation is:

[0227]

[0228] In the formula, It is the external load acting on the crack. It is the size of the crack. It is a geometric factor related to the crack propagation angle. It usually needs to be calculated based on factors such as crack shape and loading method. The output of the crack propagation path (as shown in Figure 8-9), the variation curve of type I stress intensity factor (as shown in Figure 10), and the crack length-life relationship curve (as shown in Figure 11) are the results of the FRANC3D simulation.

[0229] S5: Combine the fatigue crack propagation threshold value predicted by the Zhu-Xuan model to determine whether the crack will propagate. If the crack is determined not to propagate, then use the structural stress method to assess the service life of the welded longitudinal girder structure of the defective ship. If it is determined that the crack will propagate, calculate the remaining lifetime before the crack expands from its initial size to the critical instability size.

[0230] When the stress intensity factor amplitude Equal to the fatigue crack propagation threshold value When the threshold value is obtained, the critical defect expansion size is determined. ;

[0231]

[0232] Fatigue crack propagation threshold values ​​under different stress ratios Obtained from the Zhu-Xuan model, the model is shown in equation (6):

[0233]

[0234] In the formula, and Size and stress ratio The relationships are as follows: , ; Stress ratio; , To be relative to stress ratio Relevant material constants;

[0235] Substituting the fatigue crack propagation threshold values ​​obtained in formula (6) for different stress ratios into formula (5), we can deduce the critical defect propagation size for different stress ratios. When the defect size If the crack is cracked under normal conditions, it will propagate; otherwise, it will not.

[0236] When it is determined that the crack will not propagate, the structural stress method is used to assess the service life of the welded longitudinal girder structure of a defective ship. The formula for calculation is:

[0237]

[0238] In the formula, and This is an experimental constant;

[0239] For the first The equivalent structural stress variation range for each cycle is calculated using the following formula:

[0240]

[0241] in, For the first The range of nominal stress variation for each cycle; The thickness of the welded component; This is a material constant, determined by long crack propagation test data, and is generally taken as 3.6; For bending moment of inertia; For the first Multiaxial stress correction factor for each cycle; for SI units, thickness t, stress variation range, and equivalent structural stress variation range. The units are mm, MPa, and , respectively. For imperial units, thickness (t) and stress variation range Range of equivalent structural stress The units are respectively taken as in, , .

[0242] When it is determined that the crack will propagate, the following calculations are performed:

[0243] When stress intensity factor Greater than fracture toughness At this point, the crack enters the unstable propagation stage;

[0244] The fatigue crack propagation rate formula can be used to determine the fatigue crack propagation life of a component. Under constant amplitude cyclic loading, the Paris formula can be directly integralized to obtain:

[0245]

[0246] To verify the reliability and accuracy of the damage tolerance assessment method for welded longitudinal girder structures of ships according to the present invention, this verification was carried out by comparing experimentally measured crack length-life data with simulated crack length-life data. The specific process and results are as follows:

[0247] First, a cubic polynomial fitting was performed on the crack length-life data obtained from the simulation to construct a continuous fitting curve for subsequent comparison and analysis with experimental data. The cubic polynomial formula used for fitting is:

[0248]

[0249] in, The length of the crack. This refers to the number of cycles (lifespan). The intercept is... , , These are the coefficients of the linear, quadratic, and cubic terms, respectively.

[0250] After fitting all simulation data points, the fitted curve and related parameters were obtained (as shown in Figure 12). Figure 12 uses cycles / cycles as the x-axis and crack length as the y-axis. The purple circle represents the discrete simulation value of "crack length - cycles" obtained through FRANC3D+ABAQUS co-simulation; the red curve is the above cubic polynomial fitting curve. The fitting parameters and goodness-of-fit index are as follows:

[0251] Fitting parameters: intercept coefficient of the first term coefficient of the quadratic term coefficient of the cubic term ;

[0252] The sum of squared residuals = 2.6884, indicating that the deviation between the fitted curve and the simulation data points is extremely small, verifying the reliability of the fitting results;

[0253] Coefficient of determination After adjustment This indicates that the cubic polynomial fitting curve has a very high degree of fit and can fully explain the variation pattern of the simulation data.

[0254] The fitted curve trend can be divided into two stages: ① In the early stage of the curve (40,000~80,000 cycles), the crack length increases slowly, corresponding to the stable propagation stage of fatigue cracks, during which the crack propagation rate is low; ② In the later stage of the curve (after 100,000 cycles), the crack length increases significantly, corresponding to the accelerated unstable propagation stage of fatigue cracks, at which point the crack approaches the critical size and the propagation rate rises sharply. This trend perfectly matches the typical evolution law of fatigue cracks from "stable propagation → accelerated instability," further confirming the rationality of the fitted model.

[0255] Substituting the experimentally measured crack length into the above fitting function, the simulated fitted lifetime for the corresponding crack length was calculated and compared with the experimentally measured lifetime. The results are shown in Table 1.

[0256] Table 1

[0257]

[0258] As shown in Table 1, the relative errors between all simulated lifespans and experimentally measured lifespans are controlled within the allowable engineering range of ±20%, with the maximum error being 11.39%, indicating a reasonable error level. The high fitting degree of the fitted curves and their consistency with the fatigue crack evolution law fully verify that the damage tolerance assessment method for welded longitudinal girder structures of ships in this invention has high reliability and accuracy.

[0259] S6: Based on non-destructive testing results and a three-dimensional finite element crack propagation analysis model, establish a digital twin of crack propagation to achieve dynamic mapping and evolution prediction of crack states. Based on this, determine inspection intervals, formulate inspection outlines and subsequent safety precautions. Specific steps are as follows:

[0260] (61) Constructing an initial crack propagation digital twin

[0261] Based on the design drawings, material performance parameters and initial non-destructive testing results of the target structure, a crack propagation digital twin corresponding one-to-one with the physical structure is constructed. The digital twin includes a physical entity layer, a virtual model layer, a data interaction layer and an application layer.

[0262] The physical entity layer obtains the size, location, and morphological parameters of the initial crack in the target structure through non-destructive testing, and simultaneously collects structural geometric parameters and material mechanical property parameters (including fracture toughness). Fatigue crack propagation coefficient and index Elastic modulus Poisson's ratio (Residual stress distribution), and deploy a sensor network to collect real-time load and environmental parameters to form an initial data set;

[0263] The virtual model layer is based on the initial data set, constructs a three-dimensional finite element crack propagation analysis model with initial cracks, embeds crack propagation criteria adapted to the working conditions (Paris formula is used for conventional fatigue conditions, Walker formula or Forman formula is used for variable amplitude load conditions), and completes model parameter initialization and calibration through material test data to ensure the consistency between the initial state of the virtual model and the physical entity.

[0264] The data interaction layer establishes an IoT communication interface to realize real-time data transmission, format conversion, and multi-source data fusion between the physical entity layer and the virtual model layer. The application layer is used to realize crack state visualization, evolution prediction, and engineering decision output.

[0265] (62) Virtual-real mapping of crack state and digital twin update

[0266] Regularly perform non-destructive testing on the target physical structure to obtain the real-time size, location and morphological parameters of the crack, including crack length, depth, opening width, orientation, tip curvature and branching. Denoise and standardize the test data to generate a standardized crack state parameter set.

[0267] Based on the structural reference coordinate system, the above-mentioned standardized crack state parameter set is accurately mapped to the virtual model layer of the crack propagation digital twin, replacing the crack geometric parameters in the original virtual model, and performing local mesh reconstruction (using singular element refinement) on the crack tip region to ensure the accuracy of stress intensity factor calculation.

[0268] By integrating the dynamic load spectrum (processed by rainflow counting) and environmental parameters (temperature, humidity, and concentration of corrosive media) collected by real-time sensors, the boundary conditions and material performance parameters of the virtual model are corrected (including corrections for residual stress relaxation and corrosion-induced fracture toughness degradation), and the three-dimensional finite element crack propagation model is updated simultaneously.

[0269] By verifying the consistency between the virtual and real states, the stress field at the crack tip calculated by the updated virtual model is compared with the measured strain data of the physical structure. If the deviation exceeds the allowable threshold in the engineering, the model parameters are iteratively adjusted until the deviation meets the requirements, thus completing the dynamic update of the digital twin.

[0270] (63) Reassessment based on the crack state of the updated digital twin

[0271] Using the updated three-dimensional finite element crack propagation model and combined with the future load prediction spectrum, the current crack propagation rate is calculated and the crack propagation path is predicted (by combining the stress concentration distribution of the structure to determine whether it extends to the critical load-bearing area).

[0272] Iterative calculations are performed to determine the crack propagation from its current size to the critical instability size (crack tip stress intensity factor). ≥ Fracture toughness The required number of cycles is used to obtain the predicted remaining lifetime.

[0273] (64) Engineering decision-making and iterative optimization of digital twins

[0274] Based on the evaluation results of crack propagation path, remaining life and remaining strength, the optimal inspection interval is dynamically determined to ensure that the inspection interval is less than 1 / 3 of the remaining life and to avoid unstable fracture between two inspections.

[0275] Develop a detailed inspection outline, specifying key inspection areas (crack tips and predicted propagation paths, stress concentration areas), inspection methods (high-precision methods such as ultrasonic phased array and X-ray tomography), and inspection accuracy requirements (crack size measurement error ≤3%).

[0276] For different safety risk levels (divided into four levels: low, medium, high, and extremely dangerous based on remaining life, remaining strength, and crack propagation rate), corresponding safety precautions are formulated. In low-risk conditions, the inspection interval is extended; in medium- and high-risk conditions, load reduction and local reinforcement measures are adopted; and in extremely dangerous conditions, the machine is immediately shut down for maintenance.

[0277] By accumulating multiple batches of nondestructive testing data, model prediction results, and physical structure operation data, and optimizing model parameters and data fusion algorithms, a closed-loop iterative mechanism of "detection-update-evaluation-decision-verification" is formed to continuously improve the prediction accuracy and adaptability of digital twins.

[0278] S7: Based on the crack propagation prediction results and remaining life assessment results of the crack propagation digital twin under different structural schemes, compare the safety and reliability of different welding structure forms, dimensional parameters and process schemes to achieve optimized design of the ship's longitudinal girder welding structure.

[0279] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

Claims

1. A method for safety assessment and design of welded longitudinal girder structures for ships, characterized in that, include: S1: Identify critical damage sites and identify welded longitudinal girder structures of ships that are sensitive to cracks and may lead to catastrophic failure; S2: Use non-destructive testing methods to detect the smallest detectable crack size in the welded structure of the longitudinal girder of a ship; S3: Regularize and normalize the detected cracks to unify the crack morphology characterization standards; S4: Calculate the stress intensity factor amplitude corresponding to the current crack; S5: Combine the fatigue crack propagation threshold value predicted by the Zhu-Xuan model to determine whether the crack will propagate. If the crack is determined not to propagate, the structural stress method is used to assess the service life of the welded longitudinal girder structure of the defective ship. ； If it is determined that the crack will propagate, calculate the remaining lifetime before the crack expands from its initial size to the critical instability size; S6: Based on the non-destructive testing results and the three-dimensional crack propagation analysis model, establish a digital twin of crack propagation to realize the dynamic mapping and evolution prediction of crack state, and determine the inspection interval accordingly, and formulate inspection outline and subsequent safety precautions. (61) Constructing an initial crack propagation digital twin: Based on the design drawings, material performance parameters, and initial non-destructive testing results of the target structure, a crack propagation digital twin corresponding one-to-one with the physical structure is constructed. The digital twin includes a physical entity layer, a virtual model layer, a data interaction layer, and an application layer. The physical entity layer obtains the size, location, and morphological parameters of the initial crack in the target structure through non-destructive testing, simultaneously collects structural geometric parameters and material mechanical performance parameters, and deploys a sensor network to collect real-time load and environmental parameters to form an initial data set. The virtual model layer constructs a three-dimensional finite element crack propagation analysis model containing the initial crack based on the initial data set, and embeds a crack propagation quasi-crack model adapted to the working conditions. Then, the model parameters are initialized and calibrated through material test data to ensure the consistency of the initial state of the virtual model and the physical entity; the data interaction layer builds an Internet of Things communication interface to realize real-time data transmission, format conversion and multi-source data fusion between the physical entity layer and the virtual model layer; the application layer is used to realize crack state visualization, evolution prediction and engineering decision output; (62) Virtual-real mapping of crack state and digital twin update: Regularly perform non-destructive testing on the target physical structure to obtain the real-time size, location and morphological parameters of the crack, including crack length, depth, opening width, direction, tip curvature and branching; denoise and standardize the test data to generate a standardized crack state parameter set; based on the structure Construct a reference coordinate system, accurately map the above-mentioned standardized crack state parameter set to the virtual model layer of the crack propagation digital twin, replace the crack geometric parameters in the original virtual model, and perform local mesh reconstruction on the crack tip region to ensure the accuracy of stress intensity factor calculation; integrate the dynamic load spectrum and environmental parameters collected by real-time sensors, correct the boundary conditions and material performance parameters of the virtual model, and update the three-dimensional finite element crack propagation model synchronously; through the consistency verification of virtual and real states, compare the stress field at the crack tip calculated by the updated virtual model with the measured strain data of the physical structure. If the deviation exceeds the allowable threshold of the project, iteratively adjust the model parameters until the deviation meets the requirements, and complete the dynamic update of the digital twin; (63) based on the updated data The crack state of the digital twin is reassessed by using the updated three-dimensional finite element crack propagation model and the future load prediction spectrum to calculate the current crack propagation rate and predict the crack propagation path; the number of cycles required for the crack to propagate from the current size to the critical instability size is iteratively calculated to obtain the remaining life prediction value; (64) Engineering decision making and digital twin iterative optimization: Based on the evaluation results of crack propagation path, remaining life and remaining strength, the optimal inspection interval is dynamically determined to ensure that the inspection interval is less than 1 / 3 of the remaining life and to avoid instability and fracture between two inspections; a detailed inspection outline is formulated to clarify the key inspection parts, inspection methods and inspection accuracy requirements; corresponding safety prevention measures are formulated for different safety risk levels;S7: Based on the crack propagation prediction results and remaining life assessment results of the crack propagation digital twin under different structural schemes, the safety and reliability of different welding structure forms, dimensional parameters, and process schemes are compared to achieve optimized design of the ship's longitudinal girder welding structure.

2. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 1, characterized in that, The non-destructive testing includes ultrasonic testing, magnetic particle testing, penetrant testing, X-ray testing, eddy current testing, and visual inspection.

3. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 1, characterized in that, The specific processing of regularization and normalization in step S3 is as follows: For a single defect, the damage tolerance method based on fracture mechanics is used to treat defects of different shapes as crack-like defects; irregular defects located on the surface of the structure are treated as semi-elliptical surface cracks, and irregular defects deeply buried inside the structure are treated as deeply buried elliptical cracks. For multiple defects, the interaction between each defect and its adjacent defects is evaluated using the original defect size, including: (31) determining the proximity of each internal defect to the surface, and if a single subsurface defect meets the surface interaction criteria, then the subsurface defect is reclassified as a surface defect; (32) Using the original size of each defect, assess the proximity of the defect to its neighboring defects. If two or more defects meet the proximity rules of the corresponding specification, then the multiple defects are equivalent to a single defect for analysis, and the combined defect is no longer evaluated in interaction with other defects.

4. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 3, characterized in that, The proximity rule includes: ASME standard: minimum distance between two defects in the thickness direction. Not exceeding half the thickness of the larger defect, i.e. { , },in , The thickness of the two defects; RCC-MRx specification: the minimum distance between the two defects in the thickness direction. The thickness should not exceed half the sum of the thicknesses of the two defects. Minimum distance between two defects in the width direction The width of the two defects shall not exceed half the sum of their widths. ,in, The width of the two defects; BS 7910 specification: minimum distance between two defects in the thickness direction. The thickness should not exceed half the sum of the thicknesses of the two defects. Minimum distance between two defects in the width direction The size of the defect shall not exceed that of the smaller of the two defects. { , GB / T 19624-2019 Standard: Spacing between two defects The size of the defect shall not exceed that of the smaller of the two defects. { , },in , These are the dimensions of the two defects.

5. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 1, characterized in that, The specific steps for calculating the stress intensity factor amplitude corresponding to the current crack in step S4 are as follows: (41) Based on the crack, structural geometry, and material properties after regularization and normalization, establish a three-dimensional finite element global model, divide the crack propagation zone, apply boundary conditions and loads, and output the global model with boundary conditions and the crack propagation zone mesh; (42) The global model performs simulation analysis on the dynamic propagation behavior of the crack through FRANC3D, identifies the geometric features of the crack front edge and discretizes them into sampling points, and outputs the coordinates of the discrete points of the crack front edge and the initial stress field distribution data; (43) Determine the crack propagation direction of the three-dimensional model, take the curve of the crack front edge as the reference, define a plane orthogonal to the tangent direction of each discrete point of the crack front edge, and establish a polar coordinate system with the crack tip as the origin, and use the maximum circumferential stress criterion to determine the propagation angle of the discrete points of the crack front edge; (44) Calculate the stress intensity factor amplitude based on the crack geometry and fracture mechanics formula.

6. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 5, characterized in that, The steps for solving the propagation angle in step (43) are as follows: In the local plane, assuming a plane strain state, the circumferential stress expression at the tip of a type I crack is: in, This represents the type I stress intensity factor at this discrete point; It is a dimensionless function that is dependent on angles and is obtained by transforming the stress components under plane strain. The radial distance from the crack tip to the field point; It is an angle in polar coordinates. The direction corresponds to the normal direction of the original crack surface; according to the maximum circumferential stress criterion, the crack propagation angle is consistent with the direction of the maximum circumferential stress, therefore... Regarding angles Find the first-order partial derivative and set it to 0, that is: Regarding formula (1) Differentiate the equation, substitute it into formula (2) to obtain the angle equation, and solve the equation to obtain the angle equation. Take the maximum value ,Should That is, the crack propagation angle at that discrete point. 。 7. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 5, characterized in that, Stress intensity factor amplitude in step (44) The formula for calculation is: In the formula, It is the external load acting on the crack. It is the size of the crack. It is a geometric factor related to the crack propagation angle.

8. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 5, characterized in that, If the scale of the three-dimensional finite element global model cannot be directly used for crack propagation calculation, the boundary displacement / stress data of the crack propagation zone is extracted to generate a local fine sub-model. The sub-model is then imported into FRANC3D to improve the efficiency of crack propagation analysis.

9. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 5, characterized in that, The criterion for determining whether a crack will propagate in step S5 is: when the crack propagation rate is less than 10... -7 When the crack propagation rate reaches 10 mm / cycle, it is considered that the fatigue crack will no longer propagate, therefore the crack propagation rate is set to 10. -7 Stress intensity factor amplitude corresponding to mm / cycle As the fatigue crack propagation threshold under this condition ； When the stress intensity factor amplitude Greater than the fatigue crack propagation threshold At that time, it was assumed that the crack would enter the propagation stage; stress intensity factor amplitude It is a function of structural geometry, stress range, and instantaneous crack size, and its calculation formula is: In the formula, This refers to the stress amplitude; For shape factor, The crack size; when the stress intensity factor amplitude... Equal to the fatigue crack propagation threshold value When the threshold value is obtained, the critical defect expansion size is determined. ； Fatigue crack propagation threshold values ​​under different stress ratios Obtained from the Zhu-Xuan model, the model is shown in equation (6): In the formula, and Size and stress ratio The relationships are as follows: 、 ； Stress ratio; 、 To be relative to stress ratio Relevant material constants; Substituting the fatigue crack propagation threshold values ​​obtained in formula (6) for different stress ratios into formula (5) to deduce the critical defect propagation size for different stress ratios. When the defect size If the crack is cracked under normal conditions, it will propagate; otherwise, it will not.

10. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 9, characterized in that, In step S5, if it is determined that the crack will not propagate, the life of the welded longitudinal girder structure of the defective ship is evaluated using the structural stress method. The formula for calculation is: In the formula, and This is an experimental constant; For the first The equivalent structural stress variation range for each cycle is calculated using the following formula: in, For the first The range of nominal stress variation for each cycle; The thickness of the welded component; This is a material constant, determined from long crack propagation test data; For bending moment of inertia; For the first Multiaxial stress correction factor for each cycle.

11. The safety assessment and design method for a welded longitudinal girder structure of a ship according to claim 9, characterized in that, In step S5, when it is determined that the crack will propagate, the following calculation is performed: when the stress intensity factor Greater than fracture toughness At this point, the crack enters the unstable propagation stage, and when the stress intensity factor... Less than or equal to fracture toughness When calculating the remaining life of the crack before it expands from its initial size to the critical instability size, the fatigue crack propagation life of the component can be determined using the fatigue crack propagation rate formula. Under constant amplitude cyclic loading, the Paris formula can be directly integralized to obtain: In the formula, For crack size from Expand to The required number of stress cycles, For crack propagation to The number of loops at time, if Given the initial crack length, then ； For crack propagation to The number of stress cycles at that time; ， Let be the material constant; by combining equations (4) and (9), we can obtain: Under finite life conditions, in equation (10) = constant, that is, fatigue failure and SN curve have a corresponding relationship; from equation (5), the fatigue stress amplitude at crack initiation can be obtained. ： Find the fatigue stress amplitude on the SN curve. At the corresponding point, read the lifetime to obtain the remaining lifetime before the crack expands from the initial size to the critical size.

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