Method and device for predicting corrosion-multi-axial fatigue life of sling

Abstract

The invention relates to a sling corrosion-multi-axial fatigue life prediction method and device. The prediction method comprises the following steps: S10, acquiring key mechanical parameters of a sling under a predetermined load; s20, establishing a layered slip finite element model of the sling based on a layered slip theory, and solving the fatigue stress amplitude of each layer of steel wire of the sling; s30, the minimum fracture life and the corresponding steel wires are determined, and the accumulated damage degree of the remaining steel wires under the minimum fracture life is evaluated; s40, updating the layered slippage finite element model of the remaining steel wires, and determining the corrosion-multi-axial fatigue life of the sling; and S50, acquiring the corrosion-multi-axial fatigue life of the sling in multiple life cycles, and analyzing the probability distribution characteristics of the corrosion-multi-axial fatigue life of the sling. The performance evolution and failure process of the sling under the coupling action of the corrosion environment and the complex stress state can be simulated, and a reference basis is provided for service state evaluation and maintenance decision making of the sling.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering, and in particular relates to a method and device for predicting the corrosion-multiaxial fatigue life of suspension cables. Background Technology

[0002] The critical need for a strong transportation network is driving the development of bridges towards ultra-long spans. Cable-stayed bridges (especially suspension bridges), due to their advantages such as high spanning capacity, aesthetic appeal, and ease of construction, are widely used to cross obstacles such as rivers, lakes, seas, mountains, and canyons. As a crucial force-transmitting component of suspension and arch bridges, the reliability of the suspension cables significantly impacts the normal operation of the entire bridge. With increasingly complex bridge service conditions, the outer sheath of the suspension cables is highly susceptible to deterioration due to both internal factors (quality of raw materials and the proportions of their components) and external factors (manufacturing, installation, and service environment), resulting in direct exposure of the cable wires to the external environment. Corrosive gases and rainwater from the external environment erode the cable body, and under the coupled effect of alternating loads such as vehicles and wind, the cable wires may break. However, the timing and location of the breakage are difficult to determine, drastically increasing the service risk of the suspension cables. Analysis of suspension cable defects reveals that the main cause of performance degradation or failure is the coupling effect of corrosion and fatigue. The frequent cable breakage accidents and replacements in bridges both domestically and internationally indicate that research in the areas of suspension cable condition assessment and life prediction is still insufficient.

[0003] In the field of corrosion fatigue life prediction for structural components, existing research mainly revolves around probabilistic assessment methods and multi-factor coupled analysis. For example, CN110020497A proposes a probabilistic assessment method for the fatigue life of suspension cables in service bridges. By introducing stress redistribution and pitting effects, combined with a steel wire crack propagation model and correlation coefficients, it achieves an assessment of the overall life of the suspension cables. CN115046916A constructs a probabilistic distribution model for the corrosion fatigue life of high-strength steel wires, providing a probabilistic guarantee for reliability assessment. Meanwhile, some methods focus on life prediction based on actual monitoring data. For instance, CN114580234A establishes a suspension cable fatigue life prediction model based on measured bridge traffic volume data; while CN114943108A further comprehensively considers multiple load effects and future traffic flow information, achieving intelligent prediction of the fatigue life of suspension cables for dual-purpose road and rail suspension bridges. These methods share the common goal of integrating measured data, probabilistic analysis, or multi-factor simulation to improve the accuracy and reliability of corrosion fatigue life prediction.

[0004] The aforementioned fatigue life prediction methods for slings are mainly applicable to uniaxial tensile fatigue. However, slings are subjected to a combination of tension and bending during actual service, resulting in a complex multiaxial stress state. In practical engineering, the fatigue life of slings exhibits two stochastic characteristics: the first is the randomness of the load, meaning the loads borne by the sling (vehicle loads, wind loads, and other irregular loads) are random; the second is the randomness of the life prediction model itself, meaning the life under the same load is also random. Specifically, the randomness of life under load manifests as follows: even if experimental conditions are strictly controlled so that a sling is subjected to the exact same stress amplitude each time, its final fatigue life will fluctuate within a large range. This is because fatigue failure is essentially a process of accumulated damage within the material, a process inherently discrete. Existing fatigue life prediction methods mainly focus on the randomness of load action, but neglect the fact that the fatigue life of a structure under specific loads still exhibits randomness. Existing sling failure path analyses are mostly deterministic, failing to consider the dynamic evolution of external load conditions and the internal wire condition, such as wire breakage. This fails to reflect the deterioration process of sling performance and cannot provide real-time damage data. CN116050097A discloses a method and system for estimating the corrosion fatigue life of parallel wire cables. It simulates the fatigue life of each wire within the cable based on a wire corrosion fatigue life model and calculates the fatigue damage index for each wire. When a wire with a fatigue damage index greater than or equal to a first preset value appears in the cable, the wire breakage rate is obtained. The calculation stops when the breakage rate reaches a second preset value, and the corrosion fatigue life is then calculated. Although this literature considers the impact of stress redistribution within the cable when wires break during life estimation, it treats all wires within the cable as a parallel system. However, in reality, a sling is a composite system of multiple wires working collaboratively through contact and friction, rather than a single uniform rod.

[0005] In summary, existing prediction methods mostly focus on single-scale or static factors, making it difficult to simultaneously characterize the randomness of cable fatigue life, the time-varying nature of external loads, and the dynamic evolution of internal wire damage. Therefore, developing a corrosion-multiaxial fatigue life prediction method that can integrate the above-mentioned multi-dimensional and dynamic evolution characteristics has become a key problem that urgently needs to be solved in this field. Summary of the Invention

[0006] In view of the shortcomings of the existing technology, the present invention provides a method for predicting the corrosion-multiaxial fatigue life of slings. This method can comprehensively, accurately and efficiently simulate the performance evolution and failure process of slings under the coupled action of corrosive environment and complex stress state, realize the prediction of sling life and reliability assessment, and provide a reference for the service status assessment and maintenance decision of slings.

[0007] To achieve the above objectives, the present invention is specifically implemented as follows:

[0008] A method for predicting corrosion-multiaxial fatigue life of suspension cables includes the following steps:

[0009] S10, Obtain the key mechanical parameters of the sling under a predetermined load, including the maximum axial stress of the sling. and minimum value and the relative displacement of the slings ;

[0010] S20. Based on the layered slip theory, a layered slip finite element model of the sling is established. The key mechanical parameters are applied to the layered slip finite element model to simulate the multiaxial fatigue of the sling under the combined action of tension and bending, and to solve the fatigue stress amplitude of each layer of steel wire in the sling.

[0011] S30, under multiaxial fatigue conditions, based on the corrosion fatigue life probability model of steel wire, according to the fatigue stress amplitude, each steel wire in each layer of steel wire is randomly assigned a corrosion-multiaxial fatigue life, the minimum fracture life and its corresponding steel wire are determined, and the cumulative damage degree of the remaining steel wires under the minimum fracture life is evaluated.

[0012] S40, update the layered slip finite element model of the remaining steel wires, and repeat S20 and S30 until the sling reaches the predetermined wire breakage rate, thereby determining the corrosion-multiaxial fatigue life of the sling;

[0013] S50, repeat S20, S30 and S40 to obtain the corrosion-multiaxial fatigue life of the sling over multiple life cycles, and analyze the probability distribution characteristics of the corrosion-multiaxial fatigue life of the sling.

[0014] In some embodiments, S10, obtaining the key mechanical parameters of the sling under a predetermined load includes:

[0015] S111, Based on the bridge design drawings, establish a three-dimensional finite element model of the bridge;

[0016] S112, Calculate the axial stress value of the suspender cable under dead load. Simultaneously, transient dynamic analysis was performed to obtain the axial stress time history of the sling and the relative displacement time history at both ends of the sling;

[0017] S113, Select the maximum value of the time history of the relative displacement between the two ends of the sling as the relative displacement of the sling. Maximum axial stress of the sling and minimum value Calculate using the following formula:

[0018] ;

[0019] ;

[0020] In the formula, This represents the axial stress value of the sling under constant load. This represents the equivalent stress amplitude of the axial stress time history of the suspender cable under moving load.

[0021] In some embodiments, S20, establishing a layered slip finite element model of the suspender based on layered slip theory includes:

[0022] S211, treating the same layer of wires in the sling as a whole, the sling... The steel wire is simplified to Layered beam element;

[0023] S212, set each layer of beam unit to a rectangular section, and keep the cross-sectional area and bending stiffness of each layer of beam unit consistent with the original steel wire layer;

[0024] S213 uses spring units to simulate the interaction forces between different layers of steel wire.

[0025] In some embodiments, in S20, the key mechanical parameters are applied to the layered slip finite element model to simulate multiaxial fatigue of the sling under combined tension and bending, and the fatigue stress amplitude of each layer of steel wire in the sling is solved, including:

[0026] S221, the maximum axial stress of the sling and minimum value Relative displacement of slings The maximum axial stress of the sling was calculated by applying the layered slip finite element model to the sling. and relative displacement Stress in each wire layer of the sling under combined action and the minimum axial stress of the sling and relative displacement Stress in each wire layer of the sling under combined action ;

[0027] S222, fatigue stress amplitude of each steel wire layer of the sling Calculate using the following formula:

[0028] ;

[0029] In the formula, Number the number of suspension cable layers. , This refers to the number of cable layers.

[0030] In some embodiments, the corrosion fatigue life probability model is expressed as:

[0031] ;

[0032] In the formula, For steel wire under stress amplitude The corrosion fatigue life under the action is described by the Weibull distribution function. Here are the shape parameters of the Weibull distribution. For specified stress amplitude The function represents the characteristic parameters of the Weibull distribution.

[0033] In some embodiments, S30, determining the minimum fracture life and its corresponding steel wire includes:

[0034] S311, inside the sling The steel wires are considered as a parallel model to obtain the fatigue stress amplitude of each layer of steel wires in the sling. , Number the steel wire layers;

[0035] S312, the fatigue stress amplitude Substitute the model into the steel wire corrosion fatigue life probability model, and randomly generate the fatigue stress amplitude of each steel wire. Fracture life during operation , Number the steel wire;

[0036] S313, fracture life Minimum lifespan As The steel wire under fatigue stress amplitude The minimum fracture life under action, the minimum life value The corresponding steel wire is designated as the first broken steel wire.

[0037] In some embodiments, S30 further includes determining the minimum fracture life and its corresponding steel wire:

[0038] S321, Update the layered slip finite element model of the sling, remove the first... The broken steel wire, the remaining The steel wires are considered as a parallel model to obtain the fatigue stress amplitude of each layer of steel wires in the sling. ;

[0039] S322, the fatigue stress amplitude Substituting the corrosion fatigue life probability model of the steel wire, the values ​​of each steel wire under fatigue stress alone are randomly generated. Fracture life during operation ;

[0040] S323, according to the previous steel wires Fatigue stress amplitude experienced during wheel load cycles to and the corresponding actual number of loops to Calculate the cumulative damage of each wire. ;

[0041] S324, based on the accumulated damage Calculate the fatigue stress amplitude of each steel wire at the current time. The number of cycles that can be withstood under the influence ;

[0042] S325, determine the total number of iterations. Minimum lifespan The minimum lifespan The corresponding steel wire is the first A broken steel wire.

[0043] In some embodiments, the cumulative damage of the individual wires Represented as:

[0044] ;

[0045] Each steel wire under the current fatigue stress amplitude The number of cycles that can be withstood under the influence Represented as:

[0046] .

[0047] In some embodiments, when the steel wire occurs In cases where the sling fails immediately after the secondary fracture, the corrosion-multiaxial fatigue life of the sling is considered. Represented as:

[0048] .

[0049] In some embodiments, the method further includes performing time-varying reliability analysis on the sling, wherein the time-varying reliability index is expressed as:

[0050] ;

[0051] In the formula, The lifespan of the sling at which it reaches the failure wire breakage rate is described by a normal distribution function. The sling broke The lifespan of the steel wire is described using a normal distribution function. , The mean and standard deviation of the corrosion-multiaxial fatigue life of the slings; , The sling broke Mean and standard deviation of the lifespan of the steel wire.

[0052] The present invention also provides a device for predicting the corrosion-multiaxial fatigue life of slings, comprising:

[0053] The parameter acquisition module is used to acquire key mechanical parameters of the sling under a predetermined load, including the maximum axial stress of the sling. and minimum value and the relative displacement of the slings ;

[0054] The finite element simulation module is used to simulate multiaxial fatigue of slings under combined tension and bending based on the layered slip finite element model of the sling, and to solve the fatigue stress amplitude of each layer of steel wires in the sling; it is also used to determine the minimum fracture life and its corresponding steel wire based on the corrosion fatigue life probability model of the steel wire, and to evaluate the cumulative damage of the remaining steel wires at the minimum fracture life; and it is used to determine the corrosion-multiaxial fatigue life of the sling.

[0055] The analysis module is used to obtain the corrosion-multiaxial fatigue life of the sling over multiple life cycles and analyze the probability distribution characteristics of the corrosion-multiaxial fatigue life of the sling.

[0056] The advantages of this invention compared to existing technologies are: This invention provides a method for predicting the corrosion-multiaxial fatigue life of slings, taking into account the complex stress states experienced by slings during actual service, and can more accurately simulate the performance evolution of slings. Specifically:

[0057] (1) Efficiency and results are balanced: By establishing a layered sliding finite element model of the sling, the stress state of the steel wire inside the sling can be simulated efficiently and accurately, which improves the efficiency of simulation analysis and ensures the accuracy of simulation results.

[0058] (2) Effectively simulates the complex multiaxial stress state of the suspender under tension and bending: Existing fatigue life prediction methods for bridge suspenders are mainly applicable to uniaxial tensile fatigue. This invention applies axial tensile stress to the suspender while applying relative displacement at both ends to simulate the bending of the suspender. Combined with the layered slip finite element model, it accurately simulates the complex multiaxial stress state of the suspender under the combined tension and bending action.

[0059] (3) Accurate characterization of the randomness of fatigue life in cable corrosion: This invention considers the randomness of fatigue life through a probability model of steel wire corrosion fatigue life, and predicts the fracture life of the steel wire based on probability. The life distribution is basically consistent with the actual situation. (Refer to...) Figure 6The lifespan of slings is not a fixed value, but rather exhibits a clear probability distribution. The probability density function (PDF) curve peaks at 2-3 million cycles, indicating that the sling lifespan is most likely concentrated in this range, while the cumulative distribution function (CDF) curve clearly shows the cumulative failure probability that the lifespan does not exceed a certain value. The steel wire corrosion fatigue life probability model used in this invention can effectively characterize this randomness, making the lifespan prediction result no longer a single value, but a probability distribution that better conforms to engineering reality, providing a quantitative basis for assessing the failure risk of slings at different service cycles.

[0060] (4) Dynamic evaluation of sling reliability evolution: The parallel sling wire model provided by the present invention takes into account the dynamic evolution of service conditions, and can realize the real-time update of wire performance status and damage accumulation. Figure 8 The paper demonstrates the dynamic process of the reliability index of slings decreasing with increasing cycle count, exhibiting different numbers of steel wires. It clearly shows that the more steel wires (187 vs. 90), the slower the reliability index decreases under the same cycle count, indicating a stronger ability to maintain a safe state. This demonstrates that the present invention, through a coupled model, can simulate the entire performance degradation process of slings under long-term loads, achieving dynamic prediction of reliability indicators. This allows engineers to anticipate the future safety status of slings, providing forward-looking guidance for preventative maintenance decisions.

[0061] (5) Accurately predict the life of the suspension cable and empower scientific maintenance decision-making: The layered sliding finite element model of the suspension cable provided by this invention can efficiently and accurately simulate the stress state of the steel wire inside the suspension cable; combined with the three-dimensional finite element model of the suspension bridge, the layered sliding model of the suspension cable, the parallel model of the suspension cable steel wire and the steel wire corrosion fatigue life probability model, it can simulate the entire process of performance degradation and failure of the suspension cable during service, realize the prediction of the life of the suspension cable and the reliability assessment, and provide a reference for the service status assessment and maintenance decision-making of the suspension cable. Attached Figure Description

[0062] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following description are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0063] The structures, proportions, sizes, etc. illustrated in this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed herein, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0064] Figure 1 This is a flowchart of a method for predicting the corrosion-multiaxial fatigue life of a suspension cable provided in an embodiment of the present invention;

[0065] Figure 2 This is a schematic diagram of a three-dimensional finite element model of a bridge provided in an embodiment of the present invention;

[0066] Figure 3 This is a schematic diagram of the layering of the sling wires provided in an embodiment of the present invention;

[0067] Figure 4 This is a schematic diagram of the layered sliding finite element model of the sling provided in an embodiment of the present invention;

[0068] Figure 5 This is a schematic diagram of the cross-section update of the finite element model of the layered sliding of the sling provided in an embodiment of the present invention;

[0069] Figure 6 This is a schematic diagram of the probability distribution of corrosion-multiaxial fatigue life of slings provided in an embodiment of the present invention;

[0070] Figure 7 This is a fitting graph showing the relationship between corrosion-multiaxial fatigue life of slings and the number and breakage rate of steel wires, provided in an embodiment of the present invention.

[0071] Figure 8 This is a fitting diagram of the relationship between the sling reliability index and the number of steel wires provided in the embodiments of the present invention;

[0072] Figure 9 This is a schematic diagram illustrating the principle of the cable corrosion-multiaxial fatigue life prediction method provided in an embodiment of the present invention;

[0073] Figure 10 This is a block diagram of the cable corrosion-multiaxial fatigue life prediction device provided in an embodiment of the present invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments and descriptions of the present invention are used to explain the present invention, but are not intended to limit the present invention.

[0075] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0076] It should be understood that the terms "comprising / including," "consisting of," or any other variations are intended to cover non-exclusive inclusion, such that a product, apparatus, process, or method that comprises a list of elements includes not only those elements but may also include, where necessary, other elements not expressly listed, or elements inherent to such a product, apparatus, process, or method. Without further limitation, an element defined by the phrases "comprising / including," "consisting of," does not exclude the presence of additional identical elements in the product, apparatus, process, or method that includes said element.

[0077] It should also be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device, component or structure referred to must have a specific orientation, be constructed or operated in a specific orientation, and should not be construed as a limitation of the present invention.

[0078] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0079] See Figure 1 As shown, according to an embodiment of the present invention, a method for predicting the corrosion-multiaxial fatigue life of a sling is provided. This method mainly includes: S10, obtaining the key mechanical parameters of the sling under a predetermined load, including the maximum axial stress of the sling. and minimum value and the relative displacement of the slings S20: Based on the layered slip theory, establish a layered slip finite element model of the sling, apply key mechanical parameters to the layered slip finite element model, simulate multiaxial fatigue of the sling under combined tension and bending, and solve for the fatigue stress amplitude of each layer of steel wires in the sling; S30: Under multiaxial fatigue conditions, based on the corrosion fatigue life probability model of the steel wires, randomly assign a corrosion-multiaxial fatigue life to each steel wire in each layer according to the fatigue stress amplitude, determine the minimum fracture life and its corresponding steel wire, and evaluate the cumulative damage degree of the remaining steel wires under the minimum fracture life; S40: Update the layered slip finite element model of the remaining steel wires, and repeat S20 and S30 until the sling reaches the predetermined wire breakage rate, thereby determining the corrosion-multiaxial fatigue life of the sling; S50: Repeat S20, S30 and S40 to obtain the corrosion-multiaxial fatigue life of the sling in multiple life cycles, and analyze the probability distribution characteristics of the corrosion-multiaxial fatigue life of the sling. It is easy to understand that the corrosion-multiaxial fatigue life of a sling is the failure life of the sling.

[0080] The following combines preferred implementation methods and Figure 9 The prediction principle shown provides a detailed explanation of each step of the method.

[0081] S10, Obtain the key mechanical parameters of the sling under a predetermined load, including the maximum axial stress of the sling. and minimum value and the relative displacement of the slings .

[0082] Specifically, in this embodiment of the invention, S10 can be carried out according to the following steps:

[0083] S111, Based on the bridge design drawings, establish a three-dimensional finite element model of the bridge, taking a suspension bridge as an example, such as... Figure 2 As shown.

[0084] In the three-dimensional finite element model of this suspension bridge, the main cable and suspenders are simulated using rod elements, while the stiffening girder truss members and the towers are simulated using beam elements.

[0085] S112, Calculate the axial stress value of the suspender cable under dead load. Simultaneously, transient dynamic analysis was performed to obtain the axial stress time history of the sling and the relative displacement time history at both ends of the sling.

[0086] Preferably, this embodiment employs the moving load method to apply vehicle motion for transient dynamic analysis; the equivalent stress amplitude of the axial stress time history of the suspension cable is calculated using the rainflow counting method and the Miner linear cumulative damage criterion. .

[0087] S113, Select the maximum value of the time history of the relative displacement between the two ends of the sling as the relative displacement of the sling. The maximum value of axial stress in the sling and minimum The value is calculated according to formulas (1) and (2).

[0088]

[0089] S20. Based on the layered slip theory, a layered slip finite element model of the suspender is established. Key mechanical parameters are applied to the layered slip finite element model to simulate the multiaxial fatigue of the suspender under the combined action of tension and bending, and the fatigue stress amplitude of each layer of steel wire in the suspender is solved.

[0090] Specifically, in the embodiments of the present invention, referring to Figures 3 to 4 S20 can be carried out in the following steps:

[0091] S211, treating the same layer of wires in the sling as a whole, the sling... The steel wire is simplified to Layered beam unit.

[0092] S212, set each layer of beam unit to a rectangular section, and keep the cross-sectional area and bending stiffness of each layer of beam unit consistent with the original steel wire layer.

[0093] S213 uses spring units to simulate the interaction forces between different layers of steel wire.

[0094] It is easy to understand that a sling's life cycle includes multiple fractures, meaning that within a sling's life cycle, multiple of its n internal steel wires will break.

[0095] Preferably, the fatigue stress amplitude of each steel wire layer during the first fracture is... You can obtain it by following these steps:

[0096] S221, the maximum axial stress of the sling and minimum value Relative displacement of slings The maximum axial stress of the sling was calculated by applying the layered slip finite element model to the sling. and relative displacement Stress in each wire layer of the sling under combined action ( Number the number of suspension cable layers. , (Number of cable layers), and minimum axial stress of the cable. and relative displacement Stress in each wire layer of the sling under combined action ;

[0097] It should be noted that in the finite element model of layered slip of the sling, the maximum value of the axial stress applied to the sling is... and minimum value The tension of the sling and the relative displacement applied to the sling were simulated. This simulates the bending of the sling; the maximum axial stress. (or minimum value) ) and relative displacement The combination simulates the combined tension and bending stress of the suspender cable, and the fatigue stress amplitude is calculated accordingly. It can effectively reflect the complex multiaxial stress state of the sling.

[0098] S222, fatigue stress amplitude of each steel wire layer of the sling Calculate according to formula (3).

[0099]

[0100] It is easy to understand that the fatigue stress amplitude of each wire layer at the k-th fracture is... The calculation method is the same as the fatigue stress amplitude of each wire layer of the suspender cable in the first fracture. The calculation is similar, that is:

[0101]

[0102] In the formula, Based on the maximum axial stress of the sling and relative displacement Stress in each wire layer of the sling under combined conditions; Minimum axial stress of the sling and relative displacement Stress in each wire layer of the sling under combined conditions; , All calculations are based on the finite element model of the sling after k-1 steel wires have broken.

[0103] S30, under multiaxial fatigue conditions, based on the corrosion fatigue life probability model of steel wire, randomly assigns corrosion-multiaxial fatigue life to each steel wire in each layer of steel wire according to the fatigue stress amplitude, determines the minimum fracture life and its corresponding steel wire, and evaluates the cumulative damage degree of the remaining steel wires under the minimum fracture life.

[0104] As a preferred embodiment, the corrosion fatigue life probability model of the steel wire is calculated according to equation (5).

[0105]

[0106] In the formula, For steel wire under stress amplitude The corrosion fatigue life under the action is described by the Weibull distribution function; The shape parameter of the Weibull distribution; For specified stress amplitude The function represents the characteristic parameters of the Weibull distribution.

[0107] Specifically, in this embodiment of the invention, the initial determination of the minimum fracture life and its corresponding steel wire can be carried out according to the following steps:

[0108] S311, inside the sling The steel wires are considered as a parallel model to obtain the fatigue stress amplitude of each layer of steel wires in the sling. , Number the steel wire layer.

[0109] It should be noted that the parallel model in this embodiment is specifically assumed to be: once a steel wire breaks, the entire steel wire fails, and the lifespan of each steel wire is independent and does not affect each other.

[0110] S312, the fatigue stress amplitude of each steel wire layer of the sling Substitute the steel wire corrosion fatigue life probability model into the random generation of the sling internal Corrosion of steel wire - multiaxial fatigue life ( Number the steel wire. );

[0111] S313 will reduce corrosion-multiaxial fatigue life. Minimum lifespan As The steel wire under fatigue stress amplitude The minimum fracture life under action, the minimum life value The corresponding steel wire is designated as the first broken steel wire.

[0112] It should be noted that, It can also be understood as the number of load cycles from the start of the sling bearing the load until the first wire breaks.

[0113] In the second random fracture simulation, the sling becomes The parallel connection model of the steel wires shows the fatigue stress amplitude of each layer of steel wires in the sling. Substitute the steel wire corrosion fatigue life probability model into the random generation of the sling internal Corrosion of steel wire - multiaxial fatigue life Corrosion-multiaxial fatigue life Also understood as The steel wire is only in the fatigue stress range Fracture life under load.

[0114] It's easy to understand, this The steel wire had already been subjected to fatigue stress before this. Under the influence of This is the next load cycle. As can be seen from S313, this... The steel wire under fatigue stress amplitude Corrosion-multiaxial fatigue life under action All are greater than the first minimum fracture life. So this The steel wire under fatigue stress amplitude Remaining lifespan under action Calculate according to formula (6):

[0115]

[0116] According to Miner's linear cumulative damage criterion, under fatigue stress amplitude Under the influence of Damage to each wire after one load cycle Calculate according to formula (7):

[0117]

[0118] this The steel wire continues to be under fatigue stress amplitude Number of cycles that can be withstood under the influence Calculate according to formula (8):

[0119]

[0120] Loop count Minimum lifespan ,for The steel wire under fatigue stress amplitude Under the influence of After one load cycle, continue at the fatigue stress amplitude Minimum fracture life under action, minimum life value The corresponding steel wire is the second broken steel wire. The number of load cycles from the breakage of the first wire to the breakage of the second wire in the sling.

[0121] And so on, the kth The confirmation and approval of the minimum fracture life and its corresponding steel wire shall be carried out in accordance with the following steps:

[0122] S321, Update the layered slip finite element model of the sling, remove the first... The broken steel wire, the remaining The steel wires are considered as a parallel model to obtain the fatigue stress amplitude of each layer of steel wires in the sling. .

[0123] S322, fatigue stress amplitude Substituting into the steel wire corrosion fatigue life probability model, the fatigue stress amplitude of each steel wire under only fatigue stress is randomly generated. Corrosion-multiaxial fatigue life during operation .

[0124] Easy to understand, corrosion-multiaxial fatigue life for The steel wire is only in the fatigue stress range Fracture life under action, but this The steel wire had already been subjected to fatigue stress before this. Under the influence of Second load cycle, under fatigue stress amplitude Under the influence of Subsequent load cycles, ..., at fatigue stress amplitude Under the influence of One load cycle, total Wheel load cycle.

[0125] S323, according to the previous steel wires Fatigue stress amplitude experienced during wheel load cycles to and the corresponding actual number of loops to Calculate the cumulative damage of each wire. .

[0126] Preferably, according to the Miner linear cumulative damage criterion, after undergoing Cumulative damage to each wire after wheel load cycle Calculate according to formula (9).

[0127] S324, based on cumulative damage Calculate the fatigue stress amplitude of each steel wire at the current time. The number of cycles that can be withstood under the influence .

[0128] Ideally, the number of cycles Calculate according to formula (10).

[0129]

[0130] S325, determine the total number of iterations. Minimum lifespan The minimum lifespan The corresponding steel wire is the first A broken steel wire.

[0131] Easy to understand, all loop counts Minimum lifespan ,for A steel wire after experiencing After the wheel load cycle, continue under fatigue stress amplitude Minimum fracture life under action, minimum life value The corresponding steel wire is the first The broken steel wire It was also understood that the sling was from the first The steel wire broke to the first The number of load cycles when the steel wire breaks.

[0132] S40 updates the layered slip finite element model of the remaining steel wires. S20 and S30 are executed repeatedly until the sling reaches the predetermined wire breakage rate, thereby determining the corrosion-multiaxial fatigue life of the sling.

[0133] Reference Figure 5 Taking the second determination of the minimum fracture life and its corresponding steel wire as an example, the layered slip finite element model of the sling is updated, the first fractured steel wire (represented by the dashed line in the figure) is removed, and the remaining wires are established. A finite element model of the layered slippage of the sling with steel wires, but the wire numbers remain unchanged.

[0134] Similarly, when the minimum fracture life and its corresponding steel wire are determined for the kth (k≥2) time, a total of k-1 broken steel wires are removed from the sling. The finite element model should be updated to a layered slip finite element model of the sling with n-k+1 remaining steel wires.

[0135] Step S30 has been explained in detail above and will not be repeated here.

[0136] Preferably, this embodiment uses the wire breakage rate as the final failure criterion for the sling. When the sling reaches a specified wire breakage rate... Time, i.e., the number of broken wires At this point, the entire sling fails, and the cycle ends.

[0137] The number of load cycles experienced by the sling from the start of bearing load until the wire breaks after k cycles is calculated according to formula (11):

[0138]

[0139] It's easy to understand that if a sling fails after k fractures, This refers to the corrosion-multiaxial fatigue life of the sling.

[0140] S50, repeat S20, S30 and S40 to obtain the corrosion-multiaxial fatigue life of the sling over multiple life cycles, and analyze the probability distribution characteristics of the corrosion-multiaxial fatigue life of the sling.

[0141] As mentioned in the background art, the fatigue life of slings exhibits two random characteristics, and this application focuses on simulating the random characteristics of the same sling under the same load.

[0142] In this embodiment, the corrosion-multiaxial fatigue life probability distribution of the sling is as follows: Figure 6 As shown, the sling life is not a fixed value, but exhibits a clear probability distribution. The probability density function (PDF) curve shows a peak at 2-3 million cycles, indicating that the sling life is most likely concentrated in this range, while the cumulative distribution function (CDF) curve clearly shows the cumulative failure probability that the life does not exceed a certain value.

[0143] Preferably, this embodiment also includes time-varying reliability assessment of the slings. The core function of time-varying reliability assessment is to elevate the safety status of the slings from a static and fuzzy judgment to a dynamic and quantifiable prediction and management. It achieves dynamic early warning of the remaining lifespan and safety risks of the structure by characterizing the evolution of reliability indicators as the service time (or load cycle count) gradually decreases. Based on this, time-varying reliability assessment can accurately support risk-based preventative maintenance decisions, optimize maintenance timing and resource allocation by setting reliability thresholds to predict maintenance windows, and ultimately provide crucial theoretical basis and decision support for service safety early warning, maintenance strategy formulation, and life-cycle cost optimization of bridge slings by quantifying the performance degradation process throughout the entire life cycle.

[0144] In this embodiment, the time-varying reliability index of the sling is calculated according to formula (12):

[0145]

[0146] In the formula, The lifespan of the sling at which it reaches the failure wire breakage rate is described by a normal distribution function. The sling broke The lifespan of the steel wire is described using a normal distribution function. , The mean and standard deviation of the corrosion-multiaxial fatigue life of the slings; , The sling broke Mean and standard deviation of the lifespan of the steel wire.

[0147] The sling life analysis results in this embodiment are referenced. Figure 7At the same wire breakage rate (e.g., 20%), increasing the number of wires (from 90 to 187) has little impact on the average sling life, indicating that the number of wires has little effect on the average sling life. At the same number of wires (e.g., 90), increasing the wire breakage rate (from 5% to 30%) will increase the average sling life, but the sling life corresponding to the same number of broken wires (from 10% to 20% compared to from 20% to 30%) will decrease, indicating that the wire breakage rate gradually increases. This provides data support for determining critical maintenance timing and replacement standards.

[0148] The reliability analysis results of the sling in this embodiment are referenced. Figure 8 Increasing the number of steel wires (from 90 to 187) can improve the reliability of slings in the early stages of service, but the reliability declines faster, and they are more likely to fail at the end of their service life. This provides a direct basis for reliability-based design and the identification of high-risk slings.

[0149] Reference Figure 10 This embodiment also provides a cable corrosion-multiaxial fatigue life prediction device, including: a parameter acquisition module 100, a finite element simulation module 200, and an analysis module 300.

[0150] Specifically, the parameter acquisition module 100 is used to obtain the key mechanical parameters of the suspension cable under a predetermined load based on the three-dimensional finite element model of the bridge. Among these key mechanical parameters, the maximum value of the axial stress of the suspension cable is included. and minimum value and the relative displacement of the slings .

[0151] The finite element simulation module 200 is used to simulate the multiaxial fatigue of the sling under combined tension and bending based on the layered slip finite element model of the sling, and to solve the fatigue stress amplitude of each layer of steel wire in the sling; and to determine the minimum fracture life and its corresponding steel wire in the parallel steel wire model of the sling based on the corrosion fatigue life probability model of the steel wire, and to evaluate the cumulative damage of the remaining steel wire at the minimum fracture life; and to determine the corrosion-multiaxial fatigue life of the sling.

[0152] Analysis module 300 is used to obtain the corrosion-multiaxial fatigue life of the sling over multiple life cycles and analyze the probability distribution characteristics of the corrosion-multiaxial fatigue life of the sling.

[0153] It should be noted that this device is a device corresponding to the above prediction method. All implementation methods in the above prediction method embodiments are applicable to this embodiment and can achieve the same technical effect.

[0154] The device incorporates a probabilistic model of steel wire corrosion fatigue life, taking into account the stochastic characteristics of fatigue life. Based on probability, it predicts the fracture life of the steel wire, and the life distribution largely matches the actual situation. By combining a three-dimensional finite element model of a bridge, a layered slippage model of the suspender cable, a parallel connection model of the suspender cable wires, and a probabilistic model of steel wire corrosion fatigue life, the entire process of performance degradation and failure of the suspender cable during service can be simulated. This enables life prediction and reliability assessment of the suspender cable, providing a reference for service status assessment and maintenance decisions.

[0155] It will be readily understood by those skilled in the art that, without conflict, the above-mentioned preferred solutions can be freely combined and superimposed.

[0156] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sling corrosion-multi-axial fatigue life prediction method, characterized by, Includes the following steps: S10, Obtain the key mechanical parameters of the sling under a predetermined load, including the maximum axial stress of the sling. and minimum value and the relative displacement of the slings ; S20. Based on the layered slip theory, a layered slip finite element model of the sling is established. The key mechanical parameters are applied to the layered slip finite element model to simulate the multiaxial fatigue of the sling under the combined action of tension and bending, and to solve the fatigue stress amplitude of each layer of steel wire in the sling. S30, under multiaxial fatigue conditions, based on the corrosion fatigue life probability model of steel wire, according to the fatigue stress amplitude, each steel wire in each layer of steel wire is randomly assigned a corrosion-multiaxial fatigue life, the minimum fracture life and its corresponding steel wire are determined, and the cumulative damage degree of the remaining steel wires under the minimum fracture life is evaluated. S40, update the layered slip finite element model of the remaining steel wires, and repeat S20 and S30 until the sling reaches the predetermined wire breakage rate, thereby determining the corrosion-multiaxial fatigue life of the sling; S50, repeat S20, S30 and S40 to obtain the corrosion-multiaxial fatigue life of the sling over multiple life cycles, and analyze the probability distribution characteristics of the corrosion-multiaxial fatigue life of the sling.

2. The prediction method according to claim 1, characterized in that, In S10, the key mechanical parameters of the sling under the predetermined load include: S111, Based on the bridge design drawings, establish a three-dimensional finite element model of the bridge; S112, Calculate the axial stress value of the suspender cable under dead load. Simultaneously, transient dynamic analysis was performed to obtain the axial stress time history of the sling and the relative displacement time history at both ends of the sling; S113, Select the maximum value of the time history of the relative displacement between the two ends of the sling as the relative displacement of the sling. Maximum axial stress of the sling and minimum value Calculate using the following formula: ； ； In the formula, This represents the axial stress value of the sling under constant load. This represents the equivalent stress amplitude of the axial stress time history of the suspender cable under moving load.

3. The prediction method according to claim 1, characterized in that, In S20, the layered slip finite element model of the suspender cable, based on the layered slip theory, includes: S211, treating the same layer of wires in the sling as a whole, the sling... The steel wire is simplified to Layered beam element; S212, set each layer of beam unit to a rectangular section, and keep the cross-sectional area and bending stiffness of each layer of beam unit consistent with the original steel wire layer; S213 uses spring units to simulate the interaction forces between different layers of steel wire.

4. The prediction method according to claim 1, characterized in that, In S20, the key mechanical parameters are applied to the layered slip finite element model to simulate the multiaxial fatigue of the sling under combined tension and bending, and to solve for the fatigue stress amplitude of each layer of steel wire in the sling, including: S221, the maximum axial stress of the sling and minimum value Relative displacement of slings The maximum axial stress of the sling was calculated by applying the layered slip finite element model to the sling. and relative displacement Stress in each wire layer of the sling under combined action and the minimum axial stress of the sling and relative displacement Stress in each wire layer of the sling under combined action ; S222, fatigue stress amplitude of each steel wire layer of the sling Calculate using the following formula: ； In the formula, Number the number of suspension cable layers. , This refers to the number of cable layers.

5. The prediction method according to claim 1, characterized in that, The corrosion fatigue life probability model is expressed as follows: ； In the formula, For steel wire under stress amplitude The corrosion fatigue life under the action is described by the Weibull distribution function. Here are the shape parameters of the Weibull distribution. For specified stress amplitude The function represents the characteristic parameters of the Weibull distribution.

6. The prediction method according to claim 5, characterized in that, In S30, determining the minimum fracture life and its corresponding steel wire includes: S311, inside the sling The steel wires are considered as a parallel model to obtain the fatigue stress amplitude of each layer of steel wires in the sling. , Number the steel wire layers; S312, the fatigue stress amplitude Substitute the model into the steel wire corrosion fatigue life probability model, and randomly generate the fatigue stress amplitude of each steel wire. Fracture life during operation , Number the steel wire; S313, fracture life Minimum lifespan in As The steel wire under fatigue stress amplitude The minimum fracture life under action, the minimum life value The corresponding steel wire is designated as the first broken steel wire.

7. The prediction method according to claim 6, characterized in that, In S30, determining the minimum fracture life and its corresponding steel wire also includes: S321, Update the layered slip finite element model of the sling, remove the first... The broken steel wire, the remaining The steel wires are considered as a parallel model to obtain the fatigue stress amplitude of each layer of steel wires in the sling. ; S322, the fatigue stress amplitude Substituting the corrosion fatigue life probability model of the steel wire, the values ​​of each steel wire under fatigue stress alone are randomly generated. Fracture life during operation ; S323, according to the previous steel wires Fatigue stress amplitude experienced during wheel load cycles to and the corresponding actual number of loops to Calculate the cumulative damage of each wire. ; S324, based on the accumulated damage Calculate the fatigue stress amplitude of each steel wire at the current time. The number of cycles that can be withstood under the influence ; S325, determine the total number of iterations. Minimum lifespan in The minimum lifespan The corresponding steel wire is the first A broken steel wire.

8. The prediction method according to claim 7, characterized in that, The cumulative damage of each steel wire Represented as: ； Each steel wire under the current fatigue stress amplitude The number of cycles that can be withstood under the influence Represented as: ； as well as, In the steel wire In cases where the sling fails immediately after the secondary fracture, the corrosion-multiaxial fatigue life of the sling is considered. Represented as: 。 9. The prediction method according to claim 1, characterized in that, This also includes time-varying reliability analysis of the slings, with the time-varying reliability index expressed as: ； In the formula, The lifespan of the sling at which it reaches the failure wire breakage rate is described by a normal distribution function. The sling broke The lifespan of the steel wire is described using a normal distribution function. , The mean and standard deviation of the corrosion-multiaxial fatigue life of the slings; , The sling broke Mean and standard deviation of the lifespan of the steel wire.

10. A device for predicting the corrosion-multiaxial fatigue life of slings according to any one of claims 1 to 9, characterized in that, include: The parameter acquisition module is used to acquire key mechanical parameters of the sling under a predetermined load, including the maximum axial stress of the sling. and minimum value and the relative displacement of the slings ; The finite element simulation module is used to simulate the multiaxial fatigue of the sling under the combined action of tension and bending based on the layered slip finite element model of the sling, and to solve the fatigue stress amplitude of each layer of steel wire in the sling; And for determining the minimum fracture life and its corresponding steel wire based on the corrosion fatigue life probability model of the steel wire, and evaluating the cumulative damage of the remaining steel wire at the minimum fracture life; and for determining the corrosion-multiaxial fatigue life of the sling. The analysis module is used to obtain the corrosion-multiaxial fatigue life of the sling over multiple life cycles and analyze the probability distribution characteristics of the corrosion-multiaxial fatigue life of the sling.

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