A method for evaluating the residual strength of multi-scale fiber-reinforced flexible tubes under tensile and bending loads

Abstract

This invention discloses a multi-scale method for assessing the residual strength of fiber-reinforced flexible pipes under tensile and bending loads, belonging to the field of strength assessment technology for composite material structures in marine engineering. The method includes: extracting fiber distribution characteristics using digital image processing based on scanning electron microscopy images; constructing a two-dimensional Reverse Velocity (RVE) geometric model of the fiber-reinforced structure with hygrothermal degradation using the Monte Carlo method to predict macroscopic elastic parameters; and developing a VUMAT user-defined material subroutine with dynamic damage based on Fortran, embedding damage initiation and evolution failure criteria for the fiber-reinforced structure, and simulating the nonlinear coupled evolution process of multiple damage modes, including fiber fracture, matrix cracking, and interface debonding. This invention constructs a multi-scale analysis framework of "material-damage-response" by coupling microscopic material composition, mesoscopic damage model, and macroscopic pipe structure analysis, solving the problem of the lack of multi-scale damage coupling analysis in traditional methods under complex loads, and improving the accuracy of residual strength assessment of pipes under tensile-bending combined loads.

Description

Technical Field

[0001] This invention relates to the field of strength assessment technology for composite material structures in marine engineering, specifically a method for assessing the residual strength of multi-scale fiber-reinforced flexible tubes under tensile and bending loads. Background Technology

[0002] As offshore oil and gas resource development moves into deeper waters, fiber-reinforced flexible pipes have become key equipment due to their advantages such as lightweight, high strength, corrosion resistance, and good flexibility. These pipes employ a multi-layered composite structure with complex cross-sectional configurations and significant anisotropy. Under complex static tensile and bending loads in the deep sea, their mechanical behavior and failure mechanisms are extremely complex, necessitating the development of multi-scale analysis methods that integrate the "micro-meso-macro" levels.

[0003] Current analytical methods suffer from the following main shortcomings: First, at the level of microscopic material parameter prediction, traditional empirical formulas are based on the assumption of idealized uniform fiber arrangement, which makes it difficult to accurately characterize the real random distribution and interface microscopic features under high fiber content, resulting in large prediction errors of macroscopic elastic parameters. Second, at the level of damage analysis, commonly used failure criteria (such as the maximum stress criterion) have poor adaptability to the nonlinear coupling effects of various damage modes such as fiber, matrix, and interface debonding, limiting the accuracy of failure prediction. Finally, at the level of multi-scale coupling, existing studies are mostly based on uniaxial loads and have failed to effectively construct the evolution and transmission chain of damage from microscopic to macroscopic under complex tension-bending combined loads, resulting in insufficient reliability of residual strength assessment of pipelines under actual working conditions. To address these issues, a multi-scale fiber-reinforced flexible pipe residual strength assessment method under tension-bending loads is proposed. Summary of the Invention

[0004] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for evaluating the residual strength of multi-scale fiber-reinforced flexible tubes under tensile and bending loads, comprising the following steps:

[0005] Step 1: Based on scanning electron microscope images, fiber distribution features are extracted using digital image processing. Combined with the Monte Carlo random algorithm, a two-dimensional representative volume element geometric model that reflects the true microscopic randomness is constructed. In this model, a time-varying function based on the theory of wet heat aging is introduced to correct the matrix and interface properties. Finally, periodic boundary conditions and homogenization theory are applied to predict the macroscopic equivalent elastic parameters of the composite material under service environment through finite element calculation.

[0006] Step 2: Based on the material parameters obtained in Step 1, an ABAQUS user material subroutine is developed using the Fortran language. An improved three-dimensional Hashin and Hou failure criteria are embedded as damage initiation criteria. The Murakami-Ohno damage theory is used to define a stiffness nonlinear degradation model. Constitutive relations that can simulate the multi-mode damage coupling evolution of fiber fracture, matrix cracking and interface debonding are constructed, forming a multi-scale framework that connects microscopic material properties and macroscopic structural analysis.

[0007] Step 3: Establish a macroscopic finite element model of the fiber-reinforced flexible tube, assign the material properties and damage constitutive model defined in Step 1 and Step 2 to the fiber reinforcement layer, apply static axial tensile loads and bending moments with different proportions to the model, and perform nonlinear explicit dynamic analysis. The simulation reveals the complete mechanism of damage from microscopic initiation to macroscopic expansion and eventual failure under the synergistic effect of specific tensile-bending loads.

[0008] Step 4: Adjust the load ratio of tensile load and bending moment through the system, perform multiple sets of failure simulations as described in Step 3, record the ultimate tensile force and ultimate bending moment values ​​when the pipeline experiences macroscopic failure under each load ratio, form a series of failure data points, fit these data points in the tensile-bending moment two-dimensional plane, and generate a two-dimensional failure envelope that characterizes the strength limit of the pipeline under static tensile-bending combined load.

[0009] Step 5: Collect time-series data of environmental loads such as waves and currents in the target sea area and preprocess them; use hydrodynamic analysis software to establish an overall model of the flexible pipe system and perform in-situ static analysis; identify the dangerous sections of the pipe through simulation and extract the variation curves of axial tensile force and bending moment borne by the section throughout the entire analysis time period as the actual working condition load input.

[0010] Step 6: Map the actual load time history curve obtained in Step 5 onto the two-dimensional failure envelope diagram established in Step 4 to form the load path; for each load point at any time, calculate the shortest Euclidean distance from it to the failure envelope; based on this distance, define a normalized safety margin function to evaluate the real-time safety status and remaining strength of the pipeline throughout its service life.

[0011] Preferably, in step 1, the process of constructing the RVE model containing the time-varying function of hygrothermal degradation is as follows:

[0012] Based on scanning electron microscope (SEM) images, digital image processing techniques were used to extract fiber distribution, pore morphology, and interface features of fiber-reinforced flexible tubes in the target region. The output included a fiber distribution histogram, center coordinate dataset, orientation angular frequency distribution, and statistical features of pore characteristic parameters. Gaussian filtering was used to eliminate image noise, and threshold segmentation using the Otsu method was performed to obtain binary fiber / matrix images. Hough transform was combined to identify fiber geometric features, realizing the digital and quantitative extraction of microstructural features and providing high-fidelity statistical input for subsequent modeling.

[0013] Based on the extracted statistical features, the Monte Carlo random point projection algorithm is used to generate fiber center coordinates that satisfy the minimum spacing criterion. A two-dimensional RVE geometric model with random distribution characteristics is then built using Python scripts to drive Abaqus. This model is a two-dimensional representative volume element geometric model, which can realistically reflect the microscopic non-uniformity and randomness of the material.

[0014] In the two-dimensional RVE geometric model, a time-varying function of humid heat aging based on Fick's diffusion law and Arrhenius equation is introduced. Considering the moisture concentration gradient, temperature cycling and interfacial hydrolysis effect, the properties of the matrix and interface are modified to improve the degradation. The macroscopic equivalent elastic parameters of the composite material under specific deep-sea temperature and humidity spectrum service environment are predicted. The time-varying macroscopic material properties considering the long-term effects of deep-sea humid heat environment are obtained, and the accuracy of life assessment is improved.

[0015] Preferably, the process of predicting the macroscopic equivalent elastic parameters of the composite material under service conditions is as follows:

[0016] Periodic boundary conditions were applied to the two-dimensional RVE geometric model, and a unit macroscopic strain field was applied sequentially. The microscopic stress response was solved by the finite element method. Based on the periodic boundary and unit strain field loading, the accurate theoretical derivation of the macroscopic equivalent properties of the material was realized.

[0017] The average stress tensor under each strain field was calculated using the volume averaging method. Combined with the generalized Hooke's law inversion, the macroscopic equivalent elastic parameters of the composite material were obtained. Specifically, these parameters include the elastic modulus along the fiber direction, the elastic modulus perpendicular to the fiber direction, the in-plane Poisson's ratio, the out-of-plane Poisson's ratio, the in-plane shear modulus and the out-of-plane shear modulus, the tensile and compressive strength along the fiber direction, the tensile and compressive strength perpendicular to the fiber direction, and the in-plane shear strength. Based on the volume averaging and Hooke's law inversion, comprehensive and high-precision macroscopic equivalent material parameters and strength envelopes were obtained.

[0018] By embedding the damp heat aging factor into the material constitutive relation, and solving the boundary value problem of coupled diffusion-mechanical response, the material parameters at different service time points are dynamically predicted, and the degradation curve of material properties with service years is output, providing time-varying input for subsequent multi-scale analysis. By embedding the time-varying aging factor, the dynamic degradation prediction of material properties with service time is realized.

[0019] Preferably, in step 2, the process of writing a VUMAT subroutine containing dynamic impairments based on Fortran is as follows:

[0020] Abaqus secondary development was carried out using Fortran language, and the VUMAT subroutine was written to implement the stress update algorithm in the explicit analysis solver. An improved Hashin-Hou three-dimensional failure criterion was embedded in the VUMAT subroutine as the damage initiation criterion. This criterion contains four independent damage judgment modules: fiber tensile damage, fiber compressive damage, matrix tensile damage and matrix compressive damage, which effectively distinguishes and independently determines the damage initiation point of the fiber and matrix under different stress states.

[0021] When any damage mode meets the initial conditions, the Murakami-Ohno damage theory is used to activate the corresponding static damage variable and enter the damage evolution stage. At the same time, the damage variable accumulates independently according to the number of cycles and stress amplitude. When the accumulated damage reaches the preset damage threshold, the gradual degradation of material properties is triggered. The degree of reduction of each stiffness component is controlled by the damage variable to simulate the nonlinear accumulation process of damage under tension-bending load, realize the development of the constitutive model of fiber composite material, and simulate the nonlinear evolution process of damage by controlling the reduction of stiffness components through damage variables.

[0022] A multi-scale data interface was established, and the VUMAT subroutine was linked with the two-dimensional RVE geometric model and the composite structure damage evolution model to form a multi-scale analysis framework that coordinates micro-scale, meso-scale, and macro-scale analysis.

[0023] Preferably, in step 3, the process of elucidating the failure mechanism of fiber-reinforced flexible tubes under combined tensile load and bending moment load is as follows:

[0024] The VUMAT subroutine is integrated into the ABAQUS explicit solver. Based on the real-time damage variable, the material stiffness matrix is ​​dynamically degraded. Through the collaborative update of the composite structure damage evolution model and the macroscopic damage model, combined with the adaptive mesh refinement strategy, the damage initiation and evolution behavior is captured. The entire path of defect damage from microscopic initiation to macroscopic expansion under tensile load-bending moment is simulated, and the damage failure mechanism under the combined action of tension and bending moment is elucidated.

[0025] By adjusting the load ratio under multiple working conditions to generate a failure envelope, the strength limit boundary of the tensile and bending moment combination at different time points is characterized. Based on the dynamic load spectrum, the damage evolution of the pipeline under tension-bending coupled load is simulated, and the damage modes of fiber fracture, matrix cracking and interface debonding are identified.

[0026] Preferably, in step 4, the process of generating the two-dimensional failure envelope under tensile and bending loads is as follows:

[0027] By adjusting the amplitude ratio and phase relationship between the axial tensile load and the time-varying bending moment, the system sets up a variety of tension-bending combination conditions and constructs a two-dimensional failure envelope with the tensile load as the horizontal axis and the bending moment as the vertical axis, which is the tensile load-bending moment failure envelope, reflecting the ultimate strength boundary of the structure under static load combination.

[0028] Extending along the time dimension generates a two-dimensional failure envelope that reflects the relationship between time, load, and strength. At any given moment, the region below the two-dimensional failure envelope represents the load combination that ensures structural safety, while the two-dimensional failure envelope itself serves as the strength limit boundary at that moment, used for safety boundary assessment under dynamic conditions.

[0029] Preferably, in step 5, the process of extracting the time-varying curves of tensile load and bending moment in the dangerous area of ​​the pipeline is as follows:

[0030] Based on long-term monitoring and numerical simulation results of the target sea area, we collected time-series data of dynamic loads in the actual marine environment, including wave loads, eddy-induced vibrations and current-induced bending moments. We then performed time synchronization alignment and filtering on these data to construct a standardized dynamic load time-series file suitable for pipeline structure analysis. This file serves as the input condition for subsequent multi-scale simulations, achieving standardized integration of dynamic loads and improving the reliability and applicability of simulation inputs.

[0031] A finite element model of the flexible pipe is constructed based on hydrodynamic analysis software. The motion of the floating body, the geometric configuration of the pipe and the marine environmental load are comprehensively analyzed. Boundary conditions and material parameters are set to form a complete simulation platform suitable for static analysis, ensuring that the model is consistent with the actual engineering conditions and improving the reliability and applicability of the simulation.

[0032] Dynamic load time series data is embedded into the macroscopic pipeline finite element model through the user subroutine interface. The time-varying curves of tensile load and bending moment are output in real time at the monitoring points corresponding to the danger zone, forming a time-varying dataset that reflects the change law of internal force of the structure under actual marine dynamic load. This provides load input for subsequent failure envelope construction and safety margin assessment, realizes dynamic load mapping and real-time response output, and supports accurate strength assessment of the structure under real sea conditions.

[0033] Preferably, in step 6, the process of calculating the safety margin under the actual operating load point of the fiber-reinforced flexible tube is as follows:

[0034] The pre-processed dynamic load spectrum of the marine environment is mapped to the tensile-bending two-dimensional load space to form a load point sequence that varies with time. Axial tensile force and time-varying bending moment loads are applied synchronously according to the time step to generate the motion trajectory of the load point in the tensile load-bending moment plane. This is used to characterize the dynamic force path of the pipeline during actual service, realize the continuous visualization of dynamic load in two-dimensional space, and intuitively reflect the evolution of the pipeline force path over time.

[0035] Extract the constructed tensile-bending failure envelope (two-dimensional failure envelope), and use the minimum distance algorithm to calculate the shortest Euclidean distance from each point on the load point trajectory to the current envelope in real time. Quantify the instantaneous proximity of the load point to the strength boundary under the combined action of tensile load and bending moment, realize the real-time distance quantification between the load point and the strength boundary, and accurately judge the degree of structural approach to failure at each moment.

[0036] Based on the minimum distance calculation results, a normalized safety margin assessment function is defined to convert the distance value into a dimensionless safety index. Combined with a preset safety threshold, it determines in real time whether the load point is within the safe area of ​​the envelope, and outputs a continuous safety margin time history curve and early warning status. This provides a quantitative basis for structural integrity assessment and operation and maintenance decisions, provides a continuous safety status curve and automatic early warning, and supports data-based intelligent operation and maintenance and risk management.

[0037] This invention provides a method for evaluating the residual strength of multi-scale fiber-reinforced flexible tubes under tensile and bending loads. It has the following beneficial effects:

[0038] (I) The method for evaluating the residual strength of multi-scale fiber-reinforced flexible tubes under tensile and bending loads combines digital image processing and Monte Carlo random modeling to create a two-dimensional RVE geometric model that truly reflects the microscopic features such as fiber distribution and porosity. This fundamentally overcomes the shortcomings of traditional empirical formulas based on the idealized assumptions of fiber-reinforced flexible tubes, significantly improving the prediction accuracy of macroscopic equivalent material parameters and achieving a precise mapping from microstructure to macroscopic performance.

[0039] (II) This method for assessing the residual strength of fiber-reinforced flexible tubes under tensile and bending loads utilizes scanning electron microscopy (SEM) images to digitally extract microscopic features such as fiber distribution and diameter. A parametric RVE model conforming to real statistical characteristics is established, and combined with periodic boundary conditions and homogenization theory, it achieves accurate prediction of the macroscopic elastic parameters of composite materials, replacing traditional empirical formulas based on idealized assumptions. Secondly, it breaks through the incremental damage analysis technology of composite materials developed using a secondary VUMAT subroutine. A user material subroutine required for the ABAQUS explicit solver is developed using Fortran language, embedding the three-dimensional Hashin and Hou theory failure criteria and the Murakami-Ohno tensor damage theory (a nonlinear stiffness degradation model). This accurately simulates the nonlinear coupling evolution process of various damage modes, such as fiber fracture, matrix cracking, and interface debonding, under complex loads. Thirdly, it overcomes the key technologies for multi-scale coupled analysis of fiber-reinforced flexible tubes under complex loads. Through a multi-scale data transfer interface, the material parameters obtained from the microscopic RVE model, the incremental damage model defined at the mesoscale, and the macroscopic pipe structure analysis are coupled, forming a high-precision prediction method for the residual strength of fiber-reinforced flexible tubes under complex deep-water conditions. Attached Figure Description

[0040] Figure 1 This is a schematic diagram illustrating the workflow of a method for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to the present invention.

[0041] Figure 2 This is a schematic diagram of the process for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to the present invention. Detailed Implementation

[0042] 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, and 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.

[0043] Example 1, please refer to Figure 1 , Figure 2 This invention provides a technical solution: a method for evaluating the residual strength of multi-scale fiber-reinforced flexible tubes under tensile and bending loads, comprising the following steps:

[0044] Step 1: Based on scanning electron microscope (SEM) images, digital image processing is used to extract fiber distribution features. A two-dimensional Reinforced Vessel (RVE) geometric model of the fiber-reinforced structure with hygrothermal degradation is constructed using the Monte Carlo method to predict macroscopic elastic parameters. Based on SEM images, digital image processing techniques are used to extract fiber distribution, pore morphology, and interface features of the fiber-reinforced flexible tube in the target region. The output includes a fiber distribution histogram, center coordinate dataset, orientation angular frequency distribution, and statistical features of pore characteristic parameters. Gaussian filtering is used to eliminate image noise, and threshold segmentation using the Otsu method is performed to obtain binary fiber / matrix images. Hough transform is then used to identify fiber geometric features, achieving digital and quantitative extraction of microstructural features. This provides high-fidelity statistical input for subsequent modeling. Based on the extracted statistical features... The system employs a Monte Carlo random point projection algorithm to generate fiber center coordinates that satisfy the minimum spacing criterion. A two-dimensional Relative Volume Unit (RVE) geometric model with random distribution characteristics is then built using a Python script-driven Abaqus system. This model, a two-dimensional representative volume element geometric model, accurately reflects the microscopic non-uniformity and randomness of the material. A time-varying function based on Fick's diffusion law and the Arrhenius equation is introduced into the two-dimensional RVE geometric model. Considering moisture concentration gradients, temperature cycling, and interfacial hydrolysis effects, the degradation correction of matrix and interfacial properties is applied. This predicts the macroscopic equivalent elastic parameters of the composite material under specific deep-sea temperature and humidity spectrum service environments, obtaining time-varying macroscopic material properties considering the long-term effects of deep-sea humid and hot environments, thus improving the accuracy of lifespan assessment.

[0045] The specific work involved: acquiring cross-sectional images of the fiber-reinforced flexible tube in the target area using a Zeiss GeminiSEM 300 scanning electron microscope with a resolution of 2048×1536 pixels and an operating voltage of 10kV. Image preprocessing was performed using the OpenCV library in Python: Gaussian filtering was used for smoothing and noise reduction, and the Otsu method was used to automatically determine the grayscale threshold. The image was segmented into binary images of the fiber phase and the matrix phase. Based on this, Hough transform was applied to detect fiber contours, extracting the center coordinates, equivalent diameter, major-minor axis ratio, and fiber orientation angle for each fiber. Statistical features were then output, including a fiber distribution histogram (diameter distribution range of 5~15μm, step size 1μm), orientation angular frequency distribution (statistically calculated at 5° intervals), pore area ratio, and average pore size. Based on the extracted statistical features, a Monte Carlo random point-dropping algorithm was implemented using Python scripts to generate fiber center coordinates. The minimum fiber spacing threshold was set to 1.2 times the average fiber diameter to ensure no fiber overlap and that the distribution conformed to the characteristics of real samples. This was achieved using Abaqus Scripting. Using the Abaqus / CAE 2023 interface, a 2D RVE geometric model with dimensions of 100μm × 100μm was established, with the fiber volume fraction controlled within the range of 45% to 60%. When assigning material properties, a time-varying function considering damp heat aging was introduced, specifically in the following form:

[0046] ;

[0047] in, The time-varying elastic modulus of the matrix material under humid and hot aging conditions. The initial elastic modulus of the matrix is ​​taken as 3.5 GPa. Service time (unit: years) For reference time (taken as 10 years). The aging degradation coefficient (values ​​range from 0.02 to 0.05, depending on the material formulation) is used. The interface properties are modified in a similar manner to simulate the influence of the high temperature, high pressure and humid environment of the deep sea on the material properties. Periodic boundary conditions are applied to the two-dimensional RVE geometric model in Abaqus. The displacement coordination between adjacent boundaries is achieved through nodal constraint equations. Six sets of unit macroscopic strain fields are applied in sequence. Finite element analysis is performed using CPS4R plane strain elements to extract the microscopic stress field distribution. Then, the average stress tensor under each strain field is calculated based on the volume average method. The macroscopic equivalent elastic parameters of the composite material are obtained by inversion using the generalized Hooke's law, including: elastic modulus along the fiber direction, transverse elastic modulus, in-plane Poisson's ratio, in-plane shear modulus, and tensile strength and compressive strength along the fiber direction.

[0048] Furthermore, the process of predicting the macroscopic equivalent elastic parameters of composite materials under service conditions is as follows: Periodic boundary conditions are applied to the two-dimensional RVE geometric model, followed by sequential application of a unit macroscopic strain field. The microscopic stress response is solved using the finite element method. Based on the periodic boundary conditions and unit strain field loading, a precise theoretical derivation of the material's macroscopic equivalent properties is achieved. The average stress tensor under each strain field is calculated using the volume averaging method. Combined with the generalized Hooke's law, the macroscopic equivalent elastic parameters of the composite material are obtained through inversion. Specifically, these parameters include the elastic modulus along the fiber direction, the elastic modulus perpendicular to the fiber direction, the in-plane Poisson's ratio, the out-of-plane Poisson's ratio, and the in-plane shear rate. Based on volume averaging and Hooke's law inversion, comprehensive and high-precision macroscopic equivalent material parameters and strength envelopes were obtained, including modulus, out-of-plane shear modulus, tensile and compressive strength in the fiber direction, tensile and compressive strength perpendicular to the fiber direction, and in-plane shear strength. The hygrothermal aging factor was embedded into the material constitutive relation. By solving the boundary value problem of coupled diffusion-mechanical response, the material parameters at different service time points were dynamically predicted, and the degradation curve of material properties with service years was output, providing time-varying input for subsequent multi-scale analysis. By embedding the time-varying aging factor, the dynamic degradation prediction of material properties with service time was realized.

[0049] The specific work involves: after obtaining a two-dimensional Restricted Velocity (RVE) geometric model containing random fiber distribution, establishing displacement constraint equations between opposite nodes of the two-dimensional RVE geometric model to form periodic boundary conditions, ensuring the deformation compatibility of the microstructure in macroscopic homogenization analysis. Then, six independent unit macroscopic strain fields are sequentially applied to the two-dimensional RVE geometric model, corresponding to the three normal strain and shear strain components in the plane. Simulation calculations are performed using CPS4R plane strain elements in Abaqus finite element software, with element sizes controlled below 2 micrometers to ensure the accuracy of fiber-matrix interface stress calculation. Each strain field is applied through a separate static analysis step, and the microscopic stress field distribution data after stable convergence is extracted. Based on the microscopic stress response under each strain field, the average stress tensor is calculated using the volume averaging method. Specifically, the stress field over the entire two-dimensional RVE geometric model is integrally averaged to obtain the macroscopic stress components corresponding to each strain field. Combined with the generalized Hooke's law, the composite stress tensor is inverted by solving a system of linear equations. The macroscopic elastic parameters of the material, calculated as follows: elastic modulus along the fiber direction (typical value 120-150 GPa), transverse elastic modulus (8-12 GPa), in-plane Poisson's ratio (0.25-0.35), and in-plane shear modulus (4-7 GPa). Simultaneously, by introducing the maximum stress criterion, strength parameters are extracted from microscopic failure analysis, including fiber-direction tensile strength (1800-2400 MPa), compressive strength (1000-1500 MPa), transverse tensile strength (40-80 MPa), and in-plane shear strength (60-100 MPa). All parameters are calibrated based on actual material test data, meeting the accuracy requirements for engineering applications. A time-varying function of hygrothermal aging is embedded in the material constitutive relation. This function, based on the Arrhenius equation and combined with Fick's second law, couples the moisture concentration field, temperature field, and time variable to quantitatively describe the matrix plasticization, interfacial hydrolysis, and performance degradation caused by moisture penetration. Its expression is: ,in, This indicates the material performance parameters that change over time under humid and hot aging conditions. These are the initial performance parameters. The aging rate coefficient is related to temperature and humidity (range: 0.01-0.05 / year). For service time, The aging index is set to 0.5-1.0. The time-varying function of damp heat aging is then integrated into the material property definition module to dynamically reduce the elastic modulus, shear modulus and interfacial strength. By setting different service time nodes, the material performance degradation curve is predicted and the time-varying material parameter matrix is ​​output.

[0050] Step 2: Based on the macroscopic elastic parameters obtained from the RVE geometric model, a VUMAT subroutine containing the damaged fiber-reinforced structure is written in Fortran. This subroutine embeds the damage evolution model of the fiber-reinforced flexible tube, forming a multi-scale analysis framework. Abaqus secondary development is performed using Fortran to write the VUMAT subroutine. A stress update algorithm is implemented in the explicit analysis solver, and an improved Hashin-Hou three-dimensional failure criterion is embedded in the VUMAT subroutine as the damage initiation criterion. This criterion includes four independent damage judgment modules: fiber tensile damage, fiber compressive damage, matrix tensile damage, and matrix compressive damage. This effectively distinguishes and independently determines the damage initiation points of the fiber and matrix under different stress states. When any damage mode meets the initiation condition, the Murakami-Ohno damage theory is used to activate the corresponding static damage variable and enter the damage evolution stage. Simultaneously, the damage variable accumulates independently based on the number of cycles and stress amplitude. When the accumulated damage reaches a preset damage threshold, it triggers the material property... Progressive degradation is achieved by controlling the reduction of each stiffness component through damage variables, simulating the nonlinear accumulation process of damage under tensile-bending loads, and realizing the development of a constitutive model for fiber composite materials. By controlling the reduction of stiffness components through damage variables, the nonlinear evolution process of damage is simulated. A multi-scale data interface is established, and the VUMAT subroutine is linked with the two-dimensional RVE geometric model and the composite structure damage evolution model to form a multi-scale analysis framework that coordinates micro-, meso-, and macro-scale. Through the data interface, the VUMAT subroutine can read the time-varying material parameters output by the two-dimensional RVE geometric model in real time and map them to the material properties of the macro-scale finite element model, realizing the dynamic updating of material properties with service time and humid and hot environment. At the same time, the real-time damage variables in the VUMAT subroutine and the damage driving force parameters in the composite structure damage evolution model exchange data bidirectionally, forming a collaborative updating mechanism for meso-scale damage initiation and macro-scale damage evolution, ensuring the physical consistency of the multi-scale damage evolution process, and improving the accuracy and reliability of residual strength assessment of composite materials under complex tensile-bending loads.

[0051] The specific work involved: Secondary development of Abaqus using Fortran, developing the VUMAT subroutine suitable for explicit analysis. The core of the VUMAT subroutine is the implementation of the stress update algorithm. By reading the strain increment at each integration point, the stress tensor is calculated based on the current material state, and the state variables are updated. Then, an iterative framework based on elastic prediction and damage correction is adopted, integrating an improved Hashin-Hou three-dimensional failure criterion as the static damage initiation criterion. This decomposes the failure behavior of composite materials into four independent physical modes: fiber tensile damage (criterion: longitudinal tensile stress exceeds fiber tensile strength, typical value 2200 MPa), fiber compressive damage (based on the comparison of longitudinal compressive stress and fiber compressive strength, typical value 1300 MPa), matrix tensile damage (controlled by transverse tensile stress and matrix tensile strength, typical value 60 MPa), and matrix compressive damage (dependent on the interaction of transverse compressive stress and shear strength). Each mode has an independent damage activation flag and threshold to ensure accurate identification of damage initiation under different stress states.

[0052] For determining the initiation of damage, the Hashin criterion is used to determine fiber tensile and compressive damage, and the Hou criterion is used to determine matrix tensile and compressive damage. The corresponding criteria are shown in the following formulas:

[0053] Fiber tensile failure ( ):

[0054] ;

[0055] Fiber compression failure ( ):

[0056] ;

[0057] Matrix tensile failure ( ):

[0058] ;

[0059] Matrix compression failure ( ):

[0060] ;

[0061] In the formula: , , , , These represent the stresses in the material along directions 11, 12, 13, 22, and 23. , , , These are the failure criterion values ​​that describe the damage caused by fiber tension, fiber compression, matrix tension, and matrix compression, respectively. , , , These are the tensile and compressive strengths of unidirectional laminates along the fiber direction and the transverse tensile and compressive strengths. and These are longitudinal shear strength and transverse shear strength, respectively. is a coefficient used to describe the degree of influence of shear stress on fiber tensile failure.

[0062] Regarding the damage evolution determination process, damage begins when any damage initiation criterion is met. Continued loading will reduce the material's stiffness, and the material enters the damage evolution stage. According to Murakami Ohno's damage theory, the damage variables under each damage mode are represented as follows:

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] In the formula: Let be the damage variable, representing the th The damage level of each damage mode is initially set to 0, indicating that no damage has occurred to the material. During loading, damage begins when the material meets the failure criterion. As the value gradually increases from 0, the material stiffness gradually decreases. When the value is increased to 1, the element completely fails, and the stiffness degenerates to 0. These are the current equivalent displacement, the equivalent displacement at the onset of damage, and the equivalent displacement at the final failure, respectively, for different failure modes. The failure criterion value calculated for damage initiation determination; The fracture energy of the material; The equivalent stress at eventual failure; This is the equivalent displacement at the point of final failure; The element characteristic length is used to eliminate mesh dependence in finite element simulation and ensure the conservation of fracture energy.

[0068] Once any failure mode satisfies the initial conditions of the Hashin-Hou criterion, the VUMAT subroutine automatically activates the evolution module based on the Murakami-Ohno damage theory. By introducing a second-order damage tensor, it describes the stiffness degradation behavior of anisotropic materials. For each damage mode, an independent static damage variable is defined. The damage variable is updated independently according to the Miner criterion and co-influences the reduction of the elastic matrix during the stress update process. It is also updated according to the evolution law controlled by the energy release rate. During the stress update process, the reduced elastic matrix is ​​calculated in real time according to the current damage state. The evolution of the damage variable and the stiffness reduction are carried out independently at each integration point. The convergence of the global calculation is ensured by an explicit time integration scheme. Finally, it accurately simulates the nonlinear accumulation, interaction and expansion process of various damage modes such as fiber fracture, matrix cracking and interface debonding in composite materials under tension-bending coupled load.

[0069] Step 3: Simulate the damage initiation and evolution failure of fiber-reinforced flexible pipes under tensile and bending moments, elucidate the failure mechanism of fiber-reinforced flexible pipes under tensile load-bending moment combined load, integrate the VUMAT subroutine into the ABAQUS explicit solver, dynamically degrade the material stiffness matrix based on real-time damage variables, capture damage initiation and evolution behavior through the collaborative updating of composite structure damage evolution model and macroscopic damage model, and combine adaptive mesh refinement strategy, simulate the entire path of defect damage from mesoscopic initiation to macroscopic expansion under tensile load-bending moment, elucidate the damage failure mechanism under the combined action of tension and bending moment, generate time-varying two-dimensional failure envelope by adjusting the load ratio of multiple working conditions, characterize the strength limit boundary of tensile and bending moment combination at different time points, simulate the damage evolution of the pipeline under tensile-bending coupled load based on dynamic load spectrum, and identify the damage modes of fiber fracture, matrix cracking and interface debonding;

[0070] Step 4: By adjusting the load ratio of different tensile load-bending moment conditions, a two-dimensional failure envelope under tensile-bending load is generated. By adjusting the amplitude ratio and phase relationship between the axial tensile load and the time-varying bending moment, the system sets multiple tensile load-bending moment combination conditions and constructs a two-dimensional failure envelope with tensile load as the horizontal axis and bending moment as the vertical axis, which is the tensile-bending failure envelope. This reflects the ultimate strength boundary of the structure under static load combination. Extending along the time dimension, a two-dimensional failure envelope reflecting the time-load-strength relationship is generated. In the two-dimensional failure envelope at any time, the area below the two-dimensional failure envelope represents the load combination that ensures structural safety, and the two-dimensional failure envelope itself is the ultimate strength boundary at that time, used for safety boundary assessment under dynamic conditions.

[0071] The specific work involves: based on mesoscale damage theory, introducing the finite element method to construct a damage evolution model for composite structures, accurately describing the initiation and propagation behavior of micro-damage in fiber-reinforced composite materials. The composite structure damage evolution model uses damage variables... (Values ​​range from 0 to 1, where 0 represents intact material and 1 represents complete material failure) are used as key characterization parameters. Governing equations are established using the energy functional minimization principle. In the ABAQUS finite element software platform, a damage solution module is implemented through secondary development using the user subroutine VUMAT. Model parameters in the composite structure damage evolution model are set, covering fracture energy density, damage length parameter, damage degradation function, and driving force threshold. Simultaneously, the damage evolution time step is controlled within the range of 0.001-0.01s to ensure computational stability, and the iteration convergence tolerance is set to 1×10⁻⁶. -6 It accurately captures the initiation and initial expansion of microscopic damage modes such as matrix cracking and fiber-matrix interface debonding; combined with an adaptive mesh refinement strategy, it automatically refines the mesh in the potential damage expansion area to improve the accuracy of damage path capture and reduce mesh sensitivity.

[0072] Step 5: Collect actual marine environmental load spectrum, perform overall static load analysis on the flexible pipe, and extract time-varying curves of tensile load and bending moment in the dangerous area of ​​the pipe;

[0073] Step 6: Based on the tensile-bending failure envelope and combined with the time-varying curve of marine environmental load, calculate the safety margin of the fiber-reinforced flexible tube under the actual working load point.

[0074] Example 2, as Figure 1 , Figure 2As shown, based on Example 1, the present invention provides a technical solution: In step 5, the process of extracting the time-varying curves of tensile load and bending moment in the dangerous area of ​​the pipeline is as follows: Based on the long-term monitoring and numerical simulation results of the target sea area, the actual marine environment dynamic load time series data containing wave load and current-induced bending moment are collected, and time synchronization alignment and filtering are performed on them to construct a standardized dynamic load time series file suitable for pipeline structure analysis. This file serves as the input condition for subsequent multi-scale simulation, realizing the standardized integration of complex loads and improving the reliability and applicability of simulation input. Based on hydrodynamic analysis software, a flexible pipe overall finite element model is constructed. The floating body motion, pipeline geometry and marine environment load are comprehensively analyzed, and boundary conditions and material parameters are set to form a complete simulation platform suitable for static analysis. The dynamic load time series data is embedded into the macroscopic pipeline finite element model through the user subroutine interface. The time-varying curves of tensile load and bending moment are output in real time at the dangerous point, forming a time-varying dataset that reflects the change law of internal force of the structure under the action of actual marine dynamic load. This provides load input for subsequent failure envelope construction and safety margin assessment, realizing load dynamic mapping and real-time response output, and supporting accurate strength assessment of the structure under real sea conditions.

[0075] The specific work involves: based on long-term monitoring and numerical simulation of the target sea area, preprocessing the collected wave load and current-induced bending moment data; using MATLAB scripts to time-align the multi-source load time series data to ensure that each load component has a unified time reference; setting the sampling interval to 0.1 seconds to meet the frequency requirements of pipeline dynamic response analysis; and using a Butterworth low-pass filter to smooth the raw data with a cutoff frequency set to 5Hz to filter out high-frequency noise and retain the main load components. The processed data is stored in a standardized format as a text file, including timestamps, axial forces, lateral shear forces, and bending moment components. The total data duration is no less than 3 hours, covering at least 100 typical wave cycles, providing a realistic and reliable dynamic load input for subsequent multi-scale simulations. An overall finite element model of the flexible pipe is established using OrcaFlex hydrodynamic analysis software, encompassing pipeline geometric parameters and material properties. Under static and external environmental conditions, a steady-state load of 1.5 times the operating tension is applied under hydrostatic pressure conditions. Under extreme sea conditions, a 100-year return period wave load is applied according to the DNVGL-RP-F109 standard. The internal force results of the pipeline's critical sections (such as contact points and suspension points) under design conditions are extracted through static analysis. The preprocessed dynamic load time series file is embedded into the macroscopic pipeline finite element model through an Abaqus user subroutine. Critical points are set in the pipeline's critical areas. Load data is read in real time through a Fortran subroutine. In each analysis step (time step 0.001s), the corresponding axial tensile force and time-varying bending moment are applied to the reference point at the pipeline end. During the simulation, the monitoring points output the time-varying curves of tensile load and bending moment. This time-varying dataset reflects the internal force response law of the pipeline under actual marine dynamic loads, providing an accurate load input basis for subsequent construction of the failure envelope and calculation of safety margin.

[0076] Furthermore, the process of identifying and extracting the maximum tensile load and bending moment of the pipeline's critical sections under design conditions is as follows: Based on the established overall finite element model of the flexible pipe, the dynamics of the floating body, the pipeline configuration, and the external environmental loads are comprehensively analyzed to perform static load analysis. The maximum tensile load and bending moment of the pipeline's critical sections under design conditions are identified and extracted. Static load analysis is performed under three design conditions: hydrostatic pressure, maximum tension, and extreme sea state. The structural response of the pipeline under various loads is calculated, and its stress state and deformation characteristics are evaluated. This provides multi-condition data for the identification of critical sections, enhancing the comprehensiveness and accuracy of the assessment. Based on the analysis results, key critical sections of the pipeline, such as contact points and suspension points, are identified. The maximum tensile load and bending moment of each section under design conditions are extracted to form static strength assessment benchmark values. This provides load input for subsequent multi-scale structural strength analysis and failure envelope verification, establishing a static load benchmark to support dynamic strength and envelope verification analysis.

[0077] The specific work content is as follows: A finite element model of the flexible pipe is constructed using OrcaFlex software. Pipe geometric parameters are defined based on the actual engineering design documents, and material properties are assigned to each layer according to the composite material layup structure. An anisotropic constitutive model is used for the fiber reinforcement layer, while isotropic models are used for the inner liner and outer protective layer. The model comprehensively considers the pipe's buoyancy, seawater density, buoyancy module distribution, and nonlinear bending stiffness. By setting the pipe ends as a tensioner end and a seabed anchoring end, the actual laying and in-situ states are simulated. Regarding environmental loads, based on D... The NVGL-RP-F109 standard inputs include a 100-year return period wave spectrum, near-surface current profiles with surface velocities, and time history data considering the six-degree-of-freedom motion of the floating body, ensuring that the simulation platform is consistent with actual engineering in terms of geometry, materials, boundary conditions, and environmental conditions. In the established overall finite element model of the flexible pipe, static load analysis is performed under hydrostatic pressure, maximum operating tension, and extreme sea state conditions. Under hydrostatic pressure, the hydrostatic pressure after pipe installation and 1.2 times the pipe's wet weight are applied as axial pretension. Under maximum operating tension... Under normal operating conditions, design working tension (30%-50% of the minimum tensile strength of the pipeline) and corresponding internal pressure are applied according to API 17J specifications. For extreme sea state conditions, once-in-a-century wave and current loads are applied according to DNV GL-ST-F201 specifications, considering additional bending moments caused by buoy displacement. A nonlinear static solver is used to calculate the axial force, bending moment, shear force distribution, and deformation patterns of the pipeline under each operating condition. The overall stress level, local curvature changes, and end constraint reactions of the pipeline are assessed, identifying areas of stress concentration and significant deformation, thus providing a basis for subsequent critical section determination. The system provides quantitative data support; based on the static analysis results, it identifies several critical sections of the pipeline with the most significant internal forces and deformations under various working conditions, including the seabed contact point, the ship end suspension point (suspension area), and the section with the maximum bending moment in the middle. According to the DNVGL-RP-F105 standard, it extracts the extreme values ​​of internal forces of each section under the most unfavorable load combination. The extreme values ​​of the loads are used as the benchmark input for the static strength assessment of the pipeline, and are used for load verification and failure envelope construction in subsequent multi-scale structural strength analysis to ensure that the simulated load conditions cover the envelope range of the actual engineering design.

[0078] In step 6, the process of calculating the safety margin under the actual operating load points of the fiber-reinforced flexible pipe is as follows: The pre-processed dynamic load spectrum of the marine environment is mapped to a two-dimensional load space of tensile load and bending moment, forming a time-varying sequence of load points. Axial tensile load and bending moment are simultaneously applied according to the time step, generating the time-varying motion trajectory of the load points in the tensile-bending plane. This trajectory is used to characterize the dynamic force path of the pipeline during actual service, achieving continuous visualization of complex loads in two-dimensional space, intuitively reflecting the evolution of the pipeline's force path over time. The constructed tensile-bending failure envelope is extracted, and the minimum distance algorithm is used to calculate the distance to each point on the load point trajectory in real time. The shortest Euclidean distance of the current envelope is used to quantify its instantaneous proximity under tensile load-bending moment combined conditions, realizing real-time distance quantification between the load point and the strength boundary, accurately judging the degree of structural failure approach at each moment, and defining a normalized safety margin assessment function based on the minimum distance calculation result, converting the distance value into a dimensionless safety index, and combining it with a preset safety threshold to determine in real time whether the load point is within the safe area of ​​the envelope, outputting a continuous safety margin time history curve and early warning status, providing a quantitative basis for structural integrity assessment and operation and maintenance decisions, providing a continuous safety status curve and automatic early warning, and supporting data-based intelligent operation and maintenance and risk management;

[0079] The expression for calculating the shortest Euclidean distance is as follows:

[0080] ;

[0081] In the formula: For the load point The shortest Euclidean distance to the failure envelope; For the first The load point at time; For time step index; For the first Axial tension at any given moment; For the first Bending moment at any given moment; This represents the total number of discrete points on the failure envelope. For the first failure envelope Axial tensile force corresponding to each discrete point; For the first failure envelope The bending moment corresponding to each discrete point; Index of discrete points of the envelope;

[0082] The calculation expression for the normalized safety margin assessment function is as follows:

[0083] ;

[0084] In the formula: For the first Normalized safety margin at any given moment; For reference feature length;

[0085] The specific work involves mapping preprocessed marine environmental dynamic load spectrum data (time step of 0.1 seconds, total duration of no less than 3 hours, including axial force and bending moment components) onto a two-dimensional load space with tensile load as the horizontal axis and bending moment as the vertical axis. Based on the timestamps in the data, axial tensile force and time-varying bending moment are applied synchronously to the end reference point of the overall finite element model of the flexible pipe, achieving real-time coupled loading of dynamic loads. During the loading process, the current load state is recorded every 0.1 seconds, forming a load point sequence that changes over time. This sequence constitutes a continuous motion trajectory on the tension-bending plane, used to intuitively characterize the dynamic force path of the pipeline during actual service and reflect the comprehensive influence of environmental factors on the pipeline's stress. Based on the tension-bending failure envelope established through multi-scale simulation (characterizing the pipeline's strength limit under different tensile load-bending moment combinations), the minimum Euclidean distance algorithm is used to calculate in real time the shortest distance from each point on the load point trajectory to the current failure envelope. During the calculation, the failure envelope is discretized into a dense set of points (the distance between points is no greater than 10 kN·m). For each load point on the trajectory, the distance between it and all envelope points is calculated, and the minimum value is taken as the safe distance at that moment. This distance directly quantifies the instantaneous proximity of the current load combination to the structural strength boundary, providing continuous numerical basis for subsequent safety status judgment. Based on the calculated minimum safe distance values ​​at each moment, a normalized safety margin evaluation function is defined by combining the minimum safe distance and the reference characteristic length. The reference characteristic length is taken as 10% of the pipe's outer diameter. When the safety margin is ≥1.0, the load point is determined to be within the safe area of ​​the failure envelope. When 0 < safety margin <1.0, it is considered to be close to the critical state, and an early warning is initiated. When the safety margin is ≤0, it is determined to be beyond the strength limit. Continuous safety margin time history curves and early warning status at each moment are output in real time, forming a complete structural safety monitoring data stream, providing quantitative and dynamic basis for pipeline operation, maintenance, and risk decision-making.

[0086] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0087] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for evaluating the residual strength of multi-scale fiber-reinforced flexible tubes under tensile and bending loads, characterized in that, Includes the following steps: Step 1: Based on scanning electron microscope images, digital image processing is used to extract fiber distribution features. Combined with the Monte Carlo method, a two-dimensional RVE geometric model of fiber-reinforced structure with hygrothermal degradation is constructed to predict macroscopic elastic parameters. The process of constructing the RVE model containing the time-varying function of humid heat degradation is as follows: Based on scanning electron microscope images, digital image processing technology is used to extract fiber distribution, pore morphology and interface features of fiber-reinforced flexible tubes in the target area. The output includes statistical features such as fiber distribution histogram, center coordinate dataset, orientation angular frequency distribution and pore feature parameters. Among them, Gaussian filtering is used to eliminate image noise, and threshold segmentation is performed by Otsu's method to obtain fiber / matrix binary images. Hough transform is combined to identify fiber geometric features. Based on the extracted statistical features, the Monte Carlo random point projection algorithm is used to generate fiber center coordinates that satisfy the minimum spacing criterion, and a two-dimensional RVE geometric model with random distribution characteristics is built using a Python script to drive Abaqus. In the two-dimensional RVE geometric model, a time-varying function based on Fick's diffusion law and Arrhenius equation is introduced to correct the degradation of matrix and interface properties and predict the macroscopic equivalent elastic parameters of composite materials under service environment. Step 2: Based on the macroscopic elastic parameters obtained from the RVE geometric model, write the VUMAT subroutine for the damaged fiber-reinforced structure in Fortran language, embed the fiber-reinforced flexible tube damage evolution model, and form a multi-scale analysis framework. Step 3: Simulate the damage initiation and evolution of fiber-reinforced flexible tubes under tensile and bending moments to elucidate the failure mechanism of fiber-reinforced flexible tubes under combined tensile and bending loads. Step 4: By adjusting the load ratio of different tensile load-bending moment conditions, a two-dimensional failure envelope under the combined action of tensile load and bending moment is generated. Step 5: Collect actual marine environmental load spectrum, perform overall static load analysis on the flexible pipe, and extract time-varying curves of tensile load and bending moment in the dangerous area of ​​the pipe; Step 6: Based on the tensile-bending failure envelope and combined with the time-varying curve of marine environmental load, calculate the safety margin of the fiber-reinforced flexible tube under the actual working load point.

2. The method for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to claim 1, characterized in that: The process of predicting the macroscopic equivalent elastic parameters of the composite material under service conditions is as follows: Periodic boundary conditions are applied to the two-dimensional RVE geometric model, and a unit macroscopic strain field is applied sequentially. The microscopic stress response is then solved using the finite element method. The average stress tensor under each strain field was calculated using the volume averaging method. The macroscopic equivalent elastic parameters of the composite material were obtained by inversion using the generalized Hooke's law. Specifically, these parameters include the elastic modulus along the fiber direction, the elastic modulus perpendicular to the fiber direction, the in-plane Poisson's ratio, the out-of-plane Poisson's ratio, the in-plane shear modulus and the out-of-plane shear modulus, the tensile and compressive strength along the fiber direction, the tensile and compressive strength perpendicular to the fiber direction, and the in-plane shear strength. By embedding the damp heat aging factor into the material constitutive relation, and solving the boundary value problem of coupled diffusion-mechanical response, the material parameters at different service time points are dynamically predicted, and the degradation curve of material properties with service years is output.

3. The method for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to claim 1, characterized in that: In step 2, the process of writing a VUMAT subroutine with dynamic impairments based on Fortran is as follows: Abaqus secondary development was carried out using Fortran language, and the VUMAT subroutine was written to implement the stress update algorithm in the explicit analysis solver. An improved Hashin-Hou three-dimensional failure criterion was embedded in the VUMAT subroutine as the damage initiation criterion. This criterion contains four independent damage judgment modules: fiber tensile damage, fiber compressive damage, matrix tensile damage and matrix compressive damage. When any damage mode meets the initial conditions, the Murakami-Ohno damage theory is used to activate the corresponding static damage variable and enter the damage evolution stage. At the same time, the damage variable accumulates independently according to the number of cycles and stress amplitude. When the accumulated damage reaches the preset damage threshold, the gradual degradation of material properties is triggered. The degree of reduction of each stiffness component is controlled by the damage variable to simulate the nonlinear accumulation process of damage under tension-bending load. A multi-scale data interface was established, and the VUMAT subroutine was linked with the two-dimensional RVE geometric model and the composite structure damage evolution model to form a multi-scale analysis framework that coordinates micro-scale, meso-scale, and macro-scale analysis.

4. The method for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to claim 1, characterized in that: In step 3, the process of clarifying the failure mechanism of fiber-reinforced flexible tubes under combined tensile load and bending moment load is as follows: The VUMAT subroutine is integrated into the ABAQUS explicit solver. Based on the real-time damage variable, the material stiffness matrix is ​​dynamically degraded. Through the collaborative update of the composite structure damage evolution model and the macroscopic damage model, combined with the adaptive mesh refinement strategy, the damage initiation and evolution behavior is captured. The entire path of defect damage from microscopic initiation to macroscopic expansion under tensile load-bending moment is simulated, and the damage failure mechanism under the combined action of tension and bending moment is elucidated. By adjusting the load ratio under multiple working conditions to generate a failure envelope, the strength limit boundary of the tensile and bending moment combination at different time points is characterized. Based on the dynamic load spectrum, the damage evolution of the pipeline under tension-bending coupled load is simulated, and the damage modes of fiber fracture, matrix cracking and interface debonding are identified.

5. The method for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to claim 1, characterized in that: In step 4, the process of generating the two-dimensional failure envelope under tensile and bending loads is as follows: By adjusting the loading ratio between axial tensile load and time-varying bending moment, the system sets up various tensile load-bending moment combinations to construct a two-dimensional failure envelope with tensile load as the horizontal axis and bending moment as the vertical axis, which is the tensile-bending failure envelope. In the two-dimensional failure envelope at any given time, the region below the two-dimensional failure envelope represents the load combination that ensures structural safety, and the two-dimensional failure envelope is the strength limit boundary at that time, used for safety boundary assessment under dynamic conditions.

6. The method for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to claim 1, characterized in that: In step 5, the process of extracting the time-varying curves of tensile load and bending moment in the dangerous area of ​​the pipeline is as follows: Based on long-term monitoring and numerical simulation results of the target sea area, we collected time-series data of dynamic loads in the actual marine environment, including wave loads, eddy-induced vibrations and current-induced bending moments. We then performed time synchronization alignment and filtering on these data to construct a standardized dynamic load time-series file suitable for pipeline structure analysis. A finite element model of the flexible pipe is constructed based on hydrodynamic analysis software. The motion of the floating body, the geometric configuration of the pipe and the marine environmental load are comprehensively analyzed. Boundary conditions and material parameters are set to form a simulation platform suitable for static mechanical analysis. Dynamic load time series data is embedded into the macroscopic pipeline finite element model through the user subroutine interface, and the time-varying curves of tensile load and bending moment are output in real time at the danger point, forming time-varying datasets that reflect the tensile load and bending moment under the actual marine dynamic load.

7. The method for evaluating the residual strength of a multi-scale fiber-reinforced flexible tube under tensile and bending loads according to claim 1, characterized in that: In step 6, the process of calculating the safety margin of the fiber-reinforced flexible tube under the actual operating load point is as follows: The pre-processed dynamic load spectrum of the marine environment is mapped to the tensile-bending two-dimensional load space to form a time-varying load point sequence. Axial tensile force and time-varying bending moment loads are applied synchronously according to the time step to generate the motion trajectory of the load points in the tensile-bending plane, which is used to characterize the dynamic force path of the pipeline during actual service. Extract the constructed tensile-bending failure envelope, and use the minimum distance algorithm to calculate the shortest Euclidean distance from each point on the load point trajectory to the current failure envelope in real time, quantifying its instantaneous proximity under the combined action of tensile load and bending moment. Based on the minimum distance calculation results, a normalized safety margin assessment function is defined to convert the distance value into a dimensionless safety index. Combined with a preset safety threshold, it determines in real time whether the load point is within the safety area of ​​the failure envelope and outputs a continuous safety margin time history curve and early warning status.

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