A method for predicting low-cycle fatigue life of steel cable under tension based on field strength method

Abstract

To address the insufficient accuracy of existing methods in determining the life of steel cables under tensile loads, this invention proposes a method for predicting the low-cycle fatigue life of steel cables based on the field strength method. The method includes the following steps: 1) determining the critical locations of the steel cable under tensile conditions through finite element simulation; 2) constructing a mapping relationship between the total strain amplitude and the low-cycle fatigue life, i.e., a prediction model for the low-cycle fatigue life of the steel cable; 3) establishing a strain field strength model for the steel cable; 4) obtaining relevant data based on the finite element simulation results and substituting it into the strain field strength model to obtain the strain field strength; 5) estimating fatigue parameters and substituting them, along with the strain field strength, into the prediction model to obtain the low-cycle fatigue life of the steel cable. This invention introduces the field strength method, transforming the discrete three-dimensional stress field under multi-wire interaction into a strain field strength that represents the overall damage level of the region, overcoming the insufficient prediction accuracy of traditional numerical methods and existing point-based local stress-strain methods.

Description

Technical Field

[0001] This invention belongs to the field of steel cable fatigue life prediction, and relates to the prediction of fatigue life of steel cables subjected to tensile loads. By comprehensively considering factors such as the cable's geometry, mechanical response, critical locations, stress-strain distribution, and material fatigue characteristics, and combining the field strength method and fatigue damage accumulation theory, a high-precision and efficient method for predicting the low-cycle fatigue life of steel cables is proposed. Background Technology

[0002] Steel cables are widely used in industries such as aviation, aerospace, shipbuilding, and mining, and their failure often leads to serious safety accidents. When subjected to severe tensile loads, steel cables are prone to fatigue damage due to stress concentration, and may even experience sudden fracture. However, due to their complex geometry and manufacturing processes, resulting in significant variations in material and structural properties, accurate prediction of their fatigue life is difficult. Accurate prediction of the fatigue life of steel cables is crucial for ensuring the safe operation of equipment.

[0003] Currently, the main methods for predicting the fatigue life of steel cables include experimental methods, empirical formula methods, and numerical simulation methods.

[0004] The experimental method simulates actual working conditions through experiments. Although the results are intuitive, it is time-consuming, costly, and difficult to cover all complex load conditions.

[0005] The empirical formula method derives the life formula based on a simplified model, but ignores the uneven stress distribution caused by processes such as cold drawing and pressing during the steel cable forming process, resulting in limited prediction accuracy.

[0006] Numerical simulation is currently widely used, and this method can accurately simulate its mechanical response under tensile load. The literature "Xiong Weihong, Xiang Xiaodong, Yu Qing. Estimation of fatigue life of steel wire rope for bridge crane based on local stress-strain method [J]. Mechanical Science and Technology, 2015, 34(1): 47-50" proposes to use the local stress-strain method based on "point" combined with the Manson-Coffin formula to predict the fatigue life of steel wire rope. However, when the local stress-strain method based on "point" is applied to steel cables subjected to strong tensile loads, the following problems exist: (1) This method only focuses on the mechanical response of a single most dangerous point and ignores the overall influence of the gradient change of stress and strain in the damaged area on fatigue accumulation. This neglect of the "field" effect may lead to the prediction results being conservative or risky, and cannot reflect the overall behavior of the damaged area. (2) This method does not fully consider the dynamic change of contact stress between steel wires and the spatial distribution characteristics of the damaged area under the complex secondary helical structure of the steel cable, and it is difficult to accurately characterize the three-dimensional stress-strain field under the interaction of multiple wires, resulting in deviations in the identification of dangerous areas. (3) This method has not been adapted to the low-cycle fatigue characteristics under tensile load, and it is difficult to accurately reflect the life decay law under high strain cycle, thus limiting its applicability.

[0007] Therefore, in order to solve the problem of insufficient accuracy of existing methods in solving the life of steel cables under large strain tensile loads, it is urgent to establish a method for predicting the low-cycle fatigue life of steel cables with higher prediction accuracy, so as to provide methodological support for the optimal design and safety assessment of steel cables. Summary of the Invention

[0008] To address the issue of insufficient accuracy in existing methods for determining the life of steel cables under tensile loads, this invention proposes a method for predicting the low-cycle fatigue life of steel cables based on the field strength method.

[0009] The inventive concept of this invention is:

[0010] Faced with the problem of inaccurate predictions of wire rope life, the industry's traditional approach is to continuously refine the finite element mesh, attempting to find a more precise "maximum extreme point" on the contact surface. However, due to the extremely discrete microscopic contact within the wire rope, finite element calculations inevitably encounter "stress singularities": the finer the mesh, the greater the contact strain, causing the theoretical life to approach zero, and the computational load is extremely large, making errors prone to occur. Faced with this problem of increasingly incorrect calculations, technicians often can only attribute the errors to materials or processes, or make corrections using empirical formulas.

[0011] Through in-depth analysis of the microscopic mechanical behavior of steel wire ropes, the inventors of this invention discovered that premature failure of steel wire ropes is not fundamentally determined by a "mathematically extreme point," but rather by the overall "microscopic damage zone with a certain spatial volume" caused by fretting friction under multi-axial stress conditions between multiple bodies within the steel wire rope. Therefore, the root cause of inaccurate predictions lies in the failure of traditional "single-point damage mechanics" in discontinuous multi-body contact structures. It is necessary to introduce a macro-microscopic combined "volume damage theory (i.e., field strength method)" to use regional integral equivalents to mitigate the stress singularities at the contact points.

[0012] However, when a steel wire rope is under tension, the dozens or even hundreds of internal wires undergo complex spatial secondary helical relative slippage, constituting a complex multibody contact nonlinear problem. In engineering practice, simply solving for the local extrema of the contact interface and ensuring the convergence of the finite element method already consumes enormous computational resources. There is a prevailing bias in the industry that introducing additional spatial-dimensional "field strength calculus" calculations and extracting large amounts of mesh data for post-processing in such a large and complex discrete contact model would be extremely time-consuming and labor-intensive, making it difficult to implement. Therefore, the industry has long been limited to the "local strain method."

[0013] To overcome the aforementioned technical difficulties, this invention does not simply adopt the field strength method. Instead, it reconstructs a large number of underlying algorithms based on the discrete characteristics of steel wire ropes and proposes a unique data extraction and filtering mechanism, making the application of the field strength method feasible in engineering practice.

[0014] The data extraction and filtering mechanism proposed in this invention is as follows: First, the dangerous part is extracted and the area near the dangerous part is meshed. The dangerous part and the mesh-refined area are defined as the fatigue danger zone. A damage area with a radius equal to the field diameter is established with the centroid of the mesh element with the largest equivalent strain point in the fatigue danger zone as the center. Then, the node coordinates of each element are exported through the complex contact interface, and the centroid position of each independent element is obtained through coordinate calculation. Next, a local coordinate system is established with the centroid of the element with the largest strain as the origin. Based on the spatial straight-line distance between the centroid of each element and the origin, the system is traversed and filtered to eliminate invalid gaps. Finally, the strain field strength of the damaged area is obtained by weighted integration calculation using the steel cable strain field strength model that considers the failure function and the weight function (a weight function that combines distance and angle).

[0015] Based on the above inventive concept, the technical solution adopted by the present invention to solve its technical problem is as follows:

[0016] A method for predicting the low-cycle fatigue life of steel cables based on the field strength method, characterized by the following steps:

[0017] Step 1: Determine the critical locations of the steel cable under tensile load through finite element simulation;

[0018] Step 2: The Morrow correction method is used to correct the elastic strain components in the Manson-Coffin formula to obtain the low-cycle fatigue life prediction model for steel cables.

[0019] Step 3: Establish a strain field strength model for calculating cable life. This strain field strength model considers the damage region, failure function, and weighting function. The failure function value is the Von Mises equivalent strain. The weighting function is a weighting function that considers the damage gradient, orientation angle, and distance, and is used to characterize the contribution weight of each point in the damage region to the strain field strength of the damage region.

[0020] Step 4: Calculate the strain field intensity in the damaged area;

[0021] The dangerous area and its vicinity are defined as the fatigue danger zone. After refining the local mesh in the fatigue danger zone, finite element simulation is performed again to obtain finite element simulation data. The centroid of the mesh element with the largest equivalent strain point in the finite element simulation data is identified as the fatigue danger point. Based on the preset field diameter, the damage area is determined with the fatigue danger point as the center. Mesh elements with the centroid located in the damage area are selected, and the required parameter values ​​are extracted from the finite element simulation data and substituted into the strain field strength model of the steel cable to calculate the strain field strength of the damage area.

[0022] Step 5: Calculate the low-cycle fatigue life of the steel cable;

[0023] Obtain the values ​​of the remaining parameters in the low-cycle fatigue life prediction model of the steel cable, except for the total strain amplitude. Then, substitute the strain field strength calculated in step 4 into the total strain amplitude along with the remaining parameter values ​​into the low-cycle fatigue life prediction model of the steel cable to obtain the low-cycle fatigue life of the steel cable.

[0024] Furthermore, the hazardous locations in step 1 are identified through cross-validation using the maximum response criterion and the gradient mutation criterion: the maximum response criterion identifies the region with the maximum equivalent strain or maximum contact stress as the primary candidate hazardous region; the gradient mutation criterion identifies the region with a significant abrupt change in stress gradient or strain gradient as the potential hazardous region; a comprehensive verification analysis is performed on the primary and potential hazardous regions to determine the hazardous locations for fatigue failure.

[0025] Furthermore, in step 1, when performing finite element simulation, one-sixth of the twist pitch of the three-dimensional geometric model of the steel cable is used for finite element simulation.

[0026] Furthermore, the low-cycle fatigue life prediction model for steel cables established in step 2 is as follows:

[0027]

[0028] In the formula, For average stress, ; and These represent the local maximum and minimum stress values ​​at the fatigue-prone areas, respectively. The total strain amplitude, For elastic strain components, For plastic strain components, The fatigue strength coefficient, The fatigue ductility coefficient, denoted as F, where c is the fatigue strength index, E is the fatigue ductility index, E is the elastic modulus of the steel cable material, and N is the fatigue life.

[0029] Furthermore, the strain field strength model of the steel cable established in step 3 is as follows:

[0030]

[0031] In the formula, The strain field strength in the damaged area, Let V represent the volume of the damaged region Ω. For the destruction function, The weight function; ; θ is the distance between a point within the damage region Ω and the fatigue hazard point; θ is the angle between the line connecting the fatigue hazard point and a point within the damage region Ω and the horizontal direction.

[0032] Furthermore, the method for determining the field diameter in step 4 is as follows: extract the stress gradient curve along the normal of the fatigue danger point, and take the distance from the point where the rate of change of the stress gradient decreases to a point where it tends to be stable as the field diameter.

[0033] Furthermore, the field diameter is taken in the range of 0.5mm-0.8mm, or 0.3-0.8 times the diameter of the steel wire in the dangerous part.

[0034] Furthermore, in step 5, when the steel cable is made of conventional metal, the values ​​of the parameters other than the total strain amplitude in the low-cycle fatigue life prediction model of the steel cable are obtained based on the material static parameter estimation method; when the steel cable is made of non-metallic material, composite material or atypical metal with special microstructure, the values ​​of the parameters other than the total strain amplitude in the low-cycle fatigue life prediction model of the steel cable are obtained by experimental method or empirical estimation model.

[0035] Furthermore, in step 4, when refining the local mesh in the fatigue danger zone, the length of the refined section is 5 to 8 times the diameter of the steel wire at the corresponding dangerous part of the steel cable.

[0036] The beneficial effects of this invention are:

[0037] 1. This invention first constructs a three-dimensional finite element model of the steel cable and analyzes and determines the critical parts of the steel cable under tensile load through finite element simulation. Second, based on the finite element simulation, the stress and strain field data of the critical area are obtained, and the mapping relationship between the total strain amplitude and low-cycle fatigue life is constructed by combining the material fatigue characteristic parameters, that is, the low-cycle fatigue life prediction model of the steel cable. Next, the low-cycle fatigue damage characteristics of the steel cable under tensile load are clarified, and the strain field strength method is selected with strain as the control variable to establish a steel cable strain field strength model including the damage area, failure function, and weight function. Third, based on the finite element simulation results, the strain, volume, and centroid coordinate data of the critical area are obtained, and the strain field strength is obtained using the steel cable strain field strength model. Finally, the low-cycle fatigue life prediction model of the steel cable is adopted, and combined with the fatigue parameter estimation method based on the ultimate tensile strength and elastic modulus, the low-cycle fatigue life of the steel cable is obtained. This invention introduces a macro-micro combined "volume damage theory (i.e., field strength method)," which scientifically transforms the discrete three-dimensional stress field under multi-wire interaction into a macroscopic equivalent parameter (i.e., strain field strength) that can represent the overall damage level of the region. This overcomes the shortcomings of traditional numerical methods in predicting low-cycle fatigue life, which cannot consider the mutual influence of the damaged area. It also overcomes the problems of existing "point"-based local stress-strain methods, which neglect the "field" effect of the damaged area, are difficult to accurately characterize the three-dimensional stress-strain field of multi-wire interaction, and have insufficient adaptability to low-cycle fatigue characteristics. This invention can provide reliable technical support for subsequent structural optimization design, maintenance strategy formulation, and safe life assessment of steel cables.

[0038] 2. Considering the drawbacks of excessive computation and difficulty in convergence when performing ultra-dense meshing and finite element analysis on the entire three-dimensional geometric model of the steel cable, this invention employs a two-stage meshing and finite element analysis: In step 1, the three-dimensional geometric model of the steel cable is meshed, and the critical areas are identified using finite element simulation; in step 4, since only simulation data from the fatigue critical area is needed, only the critical areas and their surrounding regions are locally meshed. This method, which first uses low-density or normal-density meshing to macroscopically determine the critical areas and then locally refines the mesh with high-density meshing to improve the accuracy of simulation calculations, balances the accuracy of finite element simulation results and computational efficiency, and also avoids the situation where stress singularity calculations become increasingly incorrect due to the traditional method of overall mesh refinement. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the boundary conditions and loads of a steel cable under tensile conditions.

[0040] Figure 2 This is a schematic diagram of the coupling constraints at both ends of the steel cable.

[0041] Figure 3 It is a strain field strength model for steel cables.

[0042] Figure 4 This is a three-dimensional structural diagram of the damaged area.

[0043] Figure 5 This is a cross-sectional schematic diagram of the side strand of the triangular strand steel cable in an embodiment of the present invention.

[0044] Figure 6 This is a three-dimensional geometric model of the triangular strand steel cable in this embodiment of the invention.

[0045] Figure 7 This refers to the coupling constraint at both ends of the triangular strand steel cable in this embodiment of the invention.

[0046] Figure 8 These are the boundary conditions and loads under the tensile condition of the triangular strand steel cable in the embodiments of the present invention.

[0047] Figure 9 This is a three-dimensional finite element model obtained by meshing the three-dimensional geometric model of the triangular strand steel cable in this embodiment of the invention.

[0048] Figure 10 These are the dangerous parts identified in the embodiments of the present invention under the tension condition of the triangular strand steel cable.

[0049] Figure 11 This is a diagram showing the reinforcement of the wire mesh in dangerous areas. Detailed Implementation

[0050] The present invention will be further described below with reference to the accompanying drawings.

[0051] The proposed method for predicting the low-cycle fatigue life of steel cables based on the field strength method not only considers the most dangerous point, but also obtains a strain field strength value that can represent the overall damage level of the region by integrating the three-dimensional strain field of the entire damaged area of ​​the dangerous part, thereby achieving accurate life prediction.

[0052] Reference Figure 1 The present invention proposes a method for predicting the low-cycle fatigue life of steel cables based on the field strength method, which specifically includes the following steps:

[0053] Step 1: Identify the dangerous parts of the steel cable;

[0054] Step 1.1: Establish a three-dimensional geometric model of the steel cable;

[0055] A parametric modeling method is used to establish a three-dimensional geometric model of any strand in the whole rope: First, the characteristics of the secondary helical structure of the steel cable are analyzed, and the centroid equations of each steel wire and the core in any strand of the whole rope are established; then, based on the centroid equations, spline curves of the centroids of each steel wire and the core in the strand are generated using 3D modeling software. These spline curves can accurately represent the complex three-dimensional spatial trajectory of a single steel wire and the core in the whole rope; subsequently, the three-dimensional geometric model of the strand is generated by sweeping along the spline curves of the corresponding centroids of each steel wire and the core according to their cross-sectional shape; and then, the three-dimensional geometric model of the strand is generated using 3D modeling software. The "sweep" function in the software uses the two-dimensional cross-sectional shape of each wire as the outline and the spline curve of the centroid line of each wire as the sweep path, extending the two-dimensional cross-section of each wire along the spline curve of its centroid line to generate a three-dimensional solid geometric model of each wire. Similarly, the "sweep" function in the 3D modeling software uses the two-dimensional cross-sectional shape of the rope core as the outline and the spline curve of the rope core's centroid line as the sweep path, extending the two-dimensional cross-section of the rope core along the spline curve of its centroid line to generate a three-dimensional solid geometric model of the rope core. The three-dimensional geometric models of each wire and the rope core together constitute the three-dimensional geometric model of the strand.

[0056] The three-dimensional geometric model of the strand is imported into finite element analysis software. The software's array function is then used to assemble the three-dimensional geometric model of the strand into a three-dimensional geometric model of the steel cable (the complete three-dimensional geometric model of the cable). Preferably, one-sixth of the lay length of the three-dimensional geometric model of the steel cable can be used for finite element analysis to balance computational accuracy and efficiency. The material parameters of the steel wires, strand core, and rope core in the steel cable can be input into the actual three-dimensional geometric model of the steel cable.

[0057] Step 1.2: Set the operating conditions and boundary conditions;

[0058] When a steel cable is subjected to tensile load, its boundary conditions and constraints are as follows:

[0059] One end is subject to a fixed constraint, constraining all degrees of freedom; the other end employs a kinematic coupling constraint, coupling the other end of the cable (whole rope) to a reference point, through which an axial tensile force is applied to the cable. The boundary conditions of the cable under tension are as follows: Figure 1 As shown, the coupling constraints at both ends of the steel cable are as follows: Figure 2 As shown.

[0060] Step 1.3: Mesh generation and solver settings;

[0061] The three-dimensional geometric model of the steel cable (whole rope) established in step 1.1 (or one-sixth of the lay length of the three-dimensional geometric model of the steel cable) is meshed using C3D8R hexahedral elements (a type of reduced integration element). These C3D8R hexahedral elements effectively avoid shear locking, which is easily caused by fully integrated elements, when dealing with large deformation bending and highly nonlinear contact problems between wires under tension conditions. This ensures computational accuracy while improving computational efficiency in large discrete contact calculations. When meshing, the number of mesh types per wire should be determined based on the required computational accuracy and the wire diameter. Preferably, the number of mesh types in the circumferential direction of a single wire cross-section should not be less than 8. Along the wire generatrix direction, the mesh size can be 0.5 to 5 times the wire diameter. The overall mesh size should be designed to balance computational accuracy and efficiency.

[0062] The solver uses an explicit dynamic algorithm, and the solution time is set according to the actual loading conditions, generally greater than or equal to 0.3s. This solution time is sufficient to completely simulate the entire load application process and capture the maximum stress and strain response of the structure. Geometric nonlinearity and contact adaptive functions are enabled to ensure no contact penetration between steel wires.

[0063] Step 1.4: Identification of hazardous areas;

[0064] After completing the construction of the three-dimensional geometric model of the steel cable, boundary conditions, mesh generation, and solver settings, the calculation task can be submitted for finite element analysis to obtain the solution results. Stress and strain field data of the three-dimensional finite element model of the steel cable are extracted from the solution results. Stress and strain contour maps are plotted based on the stress and strain field data. Based on the critical location identification criteria and combined with the stress and strain contour maps, a comprehensive analysis can be performed to determine the fatigue failure risk locations of the steel cable.

[0065] The criteria for identifying hazardous areas are as follows:

[0066] (1) Maximum response criterion: The area where the maximum equivalent strain or maximum contact stress occurs is the primary candidate hazardous area.

[0067] (2) Gradient mutation criterion: Areas where stress gradient or strain gradient changes significantly are considered potentially dangerous areas.

[0068] By conducting a comprehensive verification analysis of the two types of dangerous areas mentioned above, the true source of crack initiation can be determined, and this true source is the finally identified location of fatigue failure.

[0069] Based on the above criteria for identifying dangerous parts, the most vulnerable parts for fatigue can be identified, providing key input for subsequent analysis.

[0070] Because the contact between dozens or even hundreds of steel wires inside a steel cable is extremely complex when it is under tension, numerical stress singularities are easily generated in finite element calculations. If the maximum response criterion is used alone to find the extreme point to determine the danger zone, misjudgment is likely to occur. Therefore, this invention introduces the gradient mutation criterion for cross-validation when identifying dangerous parts. Together, the two constitute the scope of investigation for judging the true source of fatigue.

[0071] Step 2: Establish a low-cycle fatigue life prediction model for steel cables;

[0072] The fatigue life of materials is typically evaluated using the S-N curve, which reflects the relationship between stress (S) and fatigue life (N), or the strain curve, which reflects the relationship between stress (S) and fatigue life (N). The relationship between fatigue life N curve.

[0073] When a material is under low-cycle fatigue, it is usually through The curve represents the relationship between load and life, and the total strain amplitude can be expressed using the Manson-Coffin formula. Relationship with fatigue life N:

[0074] (2-1)

[0075] In the formula, The total strain amplitude, For elastic strain components, For plastic strain components, The fatigue strength coefficient, The fatigue ductility coefficient, is the fatigue strength index, c is the fatigue ductility index, and E is the elastic modulus of the steel cable material.

[0076] The Manson-Coffin formula in equation (2-1) above is only applicable to symmetrical cyclic conditions where the stress ratio R = -1 and the average stress is zero. However, in actual operation of steel cables, asymmetrical loads will generate non-zero average stress, among which tensile average stress will significantly shorten fatigue life. Therefore, this invention modifies the Manson-Coffin formula in equation (2-1) to obtain a low-cycle fatigue life prediction model for steel cables.

[0077] This invention employs the Morrow correction method to correct the elastic strain components in the Manson-Coffin formula to reflect the mean stress. The resulting accelerated damage effect. The Morrow correction method assumes that the mean stress... This is equivalent to reducing the fatigue strength limit of the material. Therefore, after modifying formula (2-1), we obtain a low-cycle fatigue life prediction model for steel cables that accurately reflects the influence of mean stress and is applicable to low-cycle fatigue conditions:

[0078] (2-2)

[0079] The average stress in the formula Represented as:

[0080] (2-3)

[0081] In the formula, R is the stress ratio, and ; and These are the local maximum and minimum stress values ​​at the fatigue-prone locations, extracted from the finite element solution results.

[0082] With the above correction, the term representing the elastic strain amplitude in equation (2-1) is... Adjusted to This means that, under the same total strain amplitude Below, compared to R=-1, when The number of cycles that the material can withstand. It will decrease. Therefore, equation (2-2) will reduce the average stress. The influence of this was incorporated into the low-cycle fatigue life prediction model for steel cables, making it applicable to a wider range of asymmetric loading conditions.

[0083] It should be noted that the total strain amplitude in the above formula is usually taken from the extreme value of the single-point strain at the fatigue hazard point in traditional single-point fatigue life prediction. However, due to the complex multibody nonlinear contact inside the steel cable, the extreme value of the single-point strain is easily distorted by numerical singularities. Based on the principle of equivalent physical driving force, this invention uses the "strain field strength" obtained by spatial weighted integration, which can characterize the overall damage level of the entire damage area, to equivalently replace the "total strain amplitude" in the low-cycle fatigue life prediction model of the steel cable in subsequent steps to solve for the life, thereby eliminating the influence of mesh singularities and scientifically introducing the strain gradient effect.

[0084] Step 3: Establish a strain field strength model for the steel cable;

[0085] Based on the field strength method, when a component is in a low-cycle fatigue state, it will undergo elastoplastic deformation. At this time, the stress response tends to be stable, and the field strength is calculated using strain as the fatigue control parameter.

[0086] This invention addresses the low-cycle fatigue condition of steel cables caused by tensile loads; therefore, the cable life calculation requires the use of a cable strain field strength model. This model treats fatigue damage as a regional behavior rather than a single-point behavior. Figure 3 As shown, this step first theoretically assumes a critical fatigue point P (its specific spatial location will be determined in subsequent step 4 using high-precision finite element simulation data), and defines a damage region Ω near the theoretical critical fatigue point P. This damage region has the critical fatigue point P as its geometric center and a field diameter R... * Let r be the radius of the hemispherical spatial region defined by the radius Ω, and represent the spatial distance between any point Q within the damaged region Ω and the fatigue hazard point P. By performing a weighted integral on the strain field within the damaged region Ω, the complex strain distribution of the entire damaged region Ω is transformed into a single equivalent strain parameter, namely, the "strain field strength". This strain field strength value represents the overall damage level of the entire damaged region Ω and can be used for subsequent fatigue life calculations.

[0087] The strain field strength model of steel cable can be expressed as:

[0088] (3-1)

[0089] In the formula, The strain field strength in the damaged area, Let V represent the volume of the damaged region Ω. For the destruction function, The weight function.

[0090] The following provides a detailed introduction.

[0091] 1) Damaged area

[0092] The geometric model of the damaged region Ω is as follows Figure 4 As shown, the damage region Ω is a region centered on the fatigue hazard point P with a field diameter R. * A hemispherical region with radius R represents the area that significantly influences the fatigue behavior at fatigue hazard point P. * The magnitude of R is determined by the stress-strain gradient near the fatigue critical point P. Specifically, it is determined by extracting the stress gradient curve along the normal to the fatigue critical point P, and taking the distance from which the rate of change of the stress gradient decreases to a point where it tends to stabilize as the field diameter R. * For the secondary helical structure steel cable involved in this invention, the field diameter R * The recommended value range is 0.5mm-0.8mm, or 0.3-0.8 times the diameter of the steel wire in the dangerous part as the field diameter R. * .

[0093] Regarding the judgment and explanation of the above-mentioned stress gradient change rate decreasing to a point of equilibrium: In the fatigue field strength method theory, the field diameter R...* The essence of stress concentration is defining the spatial extent of its influence. Mathematically, the stress gradient curve along the normal direction of the fatigue hazard point P is a decay curve. A plateau point is where the first derivative of the decay curve approaches zero or reaches a very small convergence threshold. In mechanical physics, this indicates that the location has moved away from the region of intense stress gradients caused by geometric discontinuities or contact compression, and entered a region with relatively uniform stress distribution. For those skilled in computational mechanics and fatigue analysis, the inflection points or plateau segments of the gradient curve can be used to identify characteristic parameters.

[0094] 2) Destruction function

[0095] Destructive function This reflects the influence of strain and material properties on local fatigue strength. It transforms the complex strain state at any point within the damage region Ω into a single numerical value, indicating the risk level at which strain at that point leads to component failure. Since the steel wire in the cable is an elasto-plastic metallic material, the Von Mises equivalent strain criterion is chosen when applying the field strength method to solve for the fatigue life of the cable. The failure function of the cable... The calculation formula is:

[0096] (3-2)

[0097] In the formula, The strain tensor representing a point contains the strain components of that point in three orthogonal spatial directions in a Cartesian coordinate system; subscripts and For strain tensor index; The equivalent strain of Von Mises can be extracted from the finite element simulation results; , , These are the first, second, and third principal strains, which can be extracted from the finite element simulation results.

[0098] 3) Weighting function

[0099] weight function The weighting function represents the contribution of the strain state at each point within the damage region Ω to the crack initiation at the fatigue hazard point P. As the distance from the fatigue hazard point P increases, the weighting function... Gradually decays. For isotropic materials, the weighting function... It depends only on the geometry of the damaged region; while the weighting function of anisotropic materials It is also affected by the elastic properties of the material. Based on the actual situation and influencing factors of the steel cable, the effects of damage zone gradient, orientation angle, and distance need to be considered. Since the material is anisotropic metallic, the weighting function of the steel cable... for:

[0100] (3-3)

[0101] Where r represents the distance between a point Q within the damaged region Ω and the fatigue hazard point P; θ is the angle between the line connecting the fatigue hazard point P and the point Q within the damaged region Ω and the 0° horizontal direction, such as... Figure 4 As shown; λ is a coefficient related to the stress gradient. When the cable is under low-cycle fatigue, λ is expressed as:

[0102] (3-4)

[0103] In the formula, This represents the maximum strain value at the critical location.

[0104] In summary, based on the above analysis, the contribution weights of each point to the total damage were obtained, laying the foundation for the subsequent solution of the strain field strength.

[0105] Step 4: Calculate the strain field strength;

[0106] The strain field strength of the cable at the critical location was calculated using the strain field strength model established in step 3. To determine the strain, volume, and centroid coordinates of each mesh element in the critical area of ​​the steel cable, it is necessary to ascertain the following: Mesh element strain and volume can be directly obtained from the finite element simulation software. By selecting the mesh element within the critical area using the "query value" function, the Von Mises strain value (as the failure function value) and volume value for each mesh element can be obtained. The centroid coordinates of the mesh elements cannot be directly queried; however, they can be obtained by querying the finite element solution file, obtaining the coordinates of the eight nodes of any mesh element, and then exporting them to a data file. For any given mesh element, the coordinates of its eight nodes are iterated, and each sum is divided by the number of nodes (8) to obtain the centroid coordinates of that mesh element. This centroid coordinate file can then be exported. Based on this, the subsequent strain field strength can be calculated using programming.

[0107] The method for solving the strain field strength is as follows:

[0108] First, the critical areas of the steel cable and their vicinity, as determined in Step 1, are locally meshed to create a refined set of elements that incorporate stress / strain gradient characteristics. These critical areas and the mesh-refined regions are defined as fatigue hazard zones. The length of the mesh-refined section should be 5 to 8 times the diameter of the wire at the corresponding critical area. Finite element simulations are then performed again on the refined model, and the simulation data is extracted.

[0109] Subsequently, based on the position coordinates of the eight nodes in each grid cell of the fatigue hazard zone, the centroid coordinates of each grid cell in the fatigue hazard zone are calculated and imported into the data file.

[0110] Then, the volume, Von Mises strain value (as the failure function value), and centroid coordinates of each mesh element in the fatigue critical zone are extracted from the re-finite element solution results; the field diameter R is defined. * The mesh element with the maximum equivalent strain point within the entire fatigue hazard zone is retrieved and identified. The centroid of this mesh element is identified as the fatigue hazard point P. A local coordinate system is established with the centroid of fatigue hazard point P as the origin, and a circle with a radius equal to the field diameter R is defined with this centroid as the center. * The sphere is used as the damaged area Ω.

[0111] Next, based on the distance between the centroid and the center of the circle for each grid cell, determine whether the centroid of each grid cell is within the damage region Ω defined in the previous step. If the distance d between the centroid and the center of the circle for a certain grid cell is less than or equal to the field diameter R... * If the centroid is within the damage region Ω, then it means that the centroid is within the damage region Ω. For mesh elements whose centroid is within the damage region Ω, calculate the distance r between the centroid and the center of the circle, and the angle θ between the line connecting the centroid and the center of the circle and the 0° horizontal direction.

[0112] Finally, the volume of each grid element with the centroid in the damaged region Ω, the Von Mises strain value (as the failure function value), the distance r between the centroid and the center of the circle, and the angle θ between the line connecting the centroid and the center of the circle and the 0° direction are substituted into the strain field strength model of the steel cable shown in formula (3-1), and the strain field strength of the damaged region Ω is calculated by weighted integration. .

[0113] In summary, by extracting the required strain values, volume, nodal coordinates, and other information from the finite element solution results obtained in the above steps, the field strength integral can be calculated, ultimately yielding the strain field strength value characterizing the overall damage level of the damaged region Ω. The strain field strength value Equivalent to the total strain amplitude in the low-cycle fatigue life prediction model of the steel cable established in step 2. .

[0114] Step 5: Calculate the low-cycle fatigue life of the steel cable;

[0115] In step 2 above, for the asymmetric stress cyclic conditions experienced by the steel cable during actual operation, the Manson-Coffin formula modified by the Morrow correction method, i.e., equation (2-2), is used as the prediction model for the low-cycle fatigue life of the steel cable. For the remaining parameters in the prediction model for the low-cycle fatigue life of the steel cable, this invention adopts a method for estimating fatigue parameters based on material static parameters. This method can establish a quantitative relationship between the tensile properties of the material and the cyclic fatigue parameters.

[0116] It should be clearly stated that the formulas for estimating fatigue parameters based on material static parameters have specific applicable ranges. These empirical formulas are mainly applicable to most conventional metallic materials, especially medium- and high-strength structural steels like those used in the steel cables of this invention, which exhibit typical elastoplastic behavior. For non-metallic materials, composite materials, or atypical metals with special microstructures, direct application is not recommended. Instead, experimental methods or publicly available empirical estimation models for specific materials can be used to obtain fatigue parameters. Given that the steel cable material meets the above applicable range, and that obtaining direct data through numerous low-cycle fatigue tests is difficult in practical engineering, this estimation method effectively balances computational efficiency and prediction accuracy.

[0117] Specifically as follows:

[0118] First, obtain the parameter values:

[0119] Both the fatigue strength index b and the fatigue ductility index c are material fatigue characteristic constants closely related to the material of the steel cable. They can be obtained by consulting the fatigue characteristic handbook of the metal material used in the steel cable, or determined by fitting the symmetrical cyclic fatigue test data of standard specimens.

[0120] fatigue strength coefficient Based on tensile strength Estimate:

[0121] (5-1)

[0122] fatigue ductility coefficient Based on tensile strength And estimation of elastic modulus E:

[0123] (5-2)

[0124] Among them, tensile strength The elastic modulus E can be obtained from the tensile test of the steel cable material.

[0125] Subsequently, the maximum stress was obtained using finite element analysis. and minimum stress Substituting into formula (2-3), the average stress is calculated. ;

[0126] Finally, the fatigue strength index b, fatigue ductility index c, and average stress were compared. Fatigue strength coefficient Fatigue ductility coefficient Elastic modulus E, strain field strength obtained by integration in step 4 As the total strain amplitude Substituting these equations into the low-cycle fatigue life prediction model for steel cables shown in equation (2-2), and solving the equations using the iterative method, the low-cycle fatigue life of the steel cable under tensile load can be obtained. .

[0127] Example:

[0128] This embodiment uses the example of predicting the low-cycle fatigue life of a right-hand twisted triangular strand steel cable of model 6V×34-FC under a tensile load of 381kN for detailed explanation.

[0129] Reference Figure 5 The geometric parameters of the strands are as follows: the lay length of the main strand of the steel cable is L = 255 mm, the lay length of the side strands is L' = 250 mm, the diameter of the steel cable is 36 mm, and the side strands have 34 wires, divided into core wire, inner layer wire, middle layer wire, and outer layer wire. Specifically, each side strand has 1 core wire, 9 inner layer wires, 12 middle layer wires, and 12 outer layer wires. The core diameter is D = 14 mm, the core diameter of the side strand is d1 = 1.25 mm, the inner layer wire diameter is d2 = 1.25 mm, the middle layer wire diameter is d3 = 1.6 mm, and the outer layer wire diameter is d4 = 2.3 mm. The elastic modulus of the wire material is... MPa, yield strength is 1800MPa, Poisson's ratio is 0.3; the elastic modulus of the polyethylene rope core is 8000MPa, Poisson's ratio is 0.4.

[0130] Based on the method of the present invention, the method for predicting the low-cycle fatigue life of steel cables in this embodiment specifically includes the following steps:

[0131] Step 1: Identify the dangerous parts of the steel cable;

[0132] Step 1.1: Construct a three-dimensional geometric model of the steel cable;

[0133] Taking the right-handed, clockwise twisted triangular strand steel cable of model 6V×34-FC as the research object, a three-dimensional geometric model was constructed using parametric modeling method:

[0134] The centroid spline curves of each steel wire are generated using UGNX. Based on the centroid spline curves, a three-dimensional geometric model of a single steel wire is generated by sweeping. The core and side strands of the rope are modeled separately.

[0135] Save the three-dimensional geometric model generated in the previous step as a .x_t format, import it into ABAQUS, and assemble 6 strands of rope with the rope core as the central axis through the array function to form a three-dimensional geometric model of the triangular strand steel cable (the three-dimensional geometric model of the whole rope).

[0136] For finite element analysis, one-sixth of the lay length (approximately 42.5 mm) of the length of the three-dimensional geometric model along the triangular strand steel cable is used to balance computational accuracy and efficiency. Figure 6As shown.

[0137] Step 1.2: Set the operating conditions and boundary conditions;

[0138] To accurately simulate the mechanical response of a steel cable under tension, this embodiment uses a boundary condition with one end fixed and the other end subjected to a load for finite element analysis.

[0139] First, establish coupling reference points RP-1 and RP-2 at the center positions on both sides of the steel cable core. Then, use motion coupling constraints to couple and constrain each wire section at both ends to the reference points. The coupling constraints are as follows: Figure 7 As shown.

[0140] Next, after completing the coupling constraints on the two end sections, the section containing the coupling reference point RP-1 was set as a completely fixed end, and constraints were applied to all six degrees of freedom (UX / UY / UZ / UR1 / UR2 / UR3). The section containing the coupling reference point RP-2 was set as a free end, with only its axial torsional degree of freedom UR3 constrained, and an axial tensile load of 381 kN was applied at the coupling reference point RP-2. To avoid sudden increases in tensile load causing model distortion, the amplitude curve of the tensile load was set to increase linearly with the analysis and solution time. The boundary conditions under the tensile condition are as follows: Figure 8 As shown.

[0141] Step 1.3: Mesh generation and solver selection;

[0142] In the ABAQUS mesh generation module, the triangular strand steel cable model was seeded and meshed. Each wire in the model is an independent entity, therefore, each wire needs to be seeded individually. The seed number for the wire end face and the surface generatrix was set to 12 and 100, respectively. An advanced algorithm was used to generate the mesh, which offers high computational accuracy and strong convergence when handling highly nonlinear contact problems. During mesh generation, the inner strands and core wires of the triangular strand steel cable were fitted with C3D8R hexahedral elements featuring reduced integral algorithm and hourglass control. The mesh generation results are shown below. Figure 9 As shown, the total number of grid cells is 406,400 and the total number of nodes is 556,308.

[0143] Due to the complex geometry of the triangular strand steel cable and the intricate contact interactions between the wires, coupled with significant deformation during service, this constitutes a complex nonlinear contact problem. Therefore, an explicit solver is more suitable. The solution time is set to 0.3 seconds. Because of the large deformation of the steel cable in the simulation analysis, the geometric nonlinearity switch needs to be enabled.

[0144] Step 1.4: Identification of hazardous areas;

[0145] After obtaining the solution results from the finite element method, the location of the wire bearing the maximum stress and strain load in the cable is determined, i.e., the critical load area of ​​the cable, located in the inner layer of the triangular strand near the main rope core. The finite element analysis results are as follows: Figure 10 As shown.

[0146] Step 2: Establish a low-cycle fatigue life prediction model for steel cables;

[0147] In this embodiment, for a 6V×34-FC triangular strand steel cable subjected to a high tensile impact load of 381kN, since its internal steel wires have entered the elastoplastic deformation stage and the plastic strain component is dominant, a strain-based low-cycle fatigue analysis method is adopted. Simultaneously, considering that the triangular strand steel cable is subjected to asymmetric cyclic loads during service, the influence of mean stress on fatigue life must be corrected.

[0148] In practice, the fatigue damage characteristics of the steel cable are characterized using the Morrow-modified Manson-Coffin equation, and the strain amplitude is established. A quantitative relationship model between fatigue life N and cable fatigue life prediction model:

[0149]

[0150] This completes the detailed construction of the low-cycle fatigue life prediction model for steel cables in this embodiment. The model will be directly called for life calculation in subsequent steps.

[0151] Step 3: Establish a strain field strength model for the steel cable;

[0152] In this embodiment, according to step 3 of the aforementioned technical solution, the strain field strength is calculated using the cable strain field strength model shown in formula (3-1), the failure function is set as the Von Mises equivalent strain of formula (3-2), and the weight function adopts a function form that considers distance and gradient, i.e., formula (3-3).

[0153] Considering the diameter d4=2.3mm of the outer layer steel wire of the side strand of this type of triangular strand steel cable and its stress gradient distribution characteristics, in this embodiment, the field diameter R of the damaged area is selected. * The value is 0.8 mm. This value falls within the acceptable range for the field diameter and can effectively cover areas with drastic stress gradient changes around the critical point. Damage area. It is then defined as having the danger point P as the center of the sphere, with a radius equal to the field diameter R. * A hemispherical region;

[0154] The definitions and calculation principles of the remaining parameters are completely consistent with those described in step 3 of the aforementioned technical solution, and will not be repeated here.

[0155] Step 4: Calculate the strain field strength;

[0156] First, based on the hazardous areas identified in step 1, the triangular strand steel wire was locally meshed to improve computational accuracy. The specific steps were as follows: In the finite element software, the component corresponding to the hazardous area steel wire was selected. A segment containing the maximum strain point on the wire path was cut using the "Split Edge: Specify Parameters by Position" function, with a length 6 times the wire diameter. The "Split Geometry: Define Cutting Plane" function was used to separate the analysis segment from the rest of the wire using a plane perpendicular to the wire axis. Mesh refinement was performed only on this analysis segment. The global approximate mesh size for the analysis segment was set to 0.1 mm, the number of wire cross-section types to be 12, and the number of side generatrix types to be 100. C3D8R hexahedral elements were used for mesh generation, while the remaining parts maintained a sparse mesh to balance computational efficiency. After refinement, the mesh was as follows: Figure 11 As shown.

[0157] Next, strain field data of the hazardous area were exported using finite element software, specifically including:

[0158] Element strain: In the finite element post-processing module, select the densified hazardous area element, extract the VonMises equivalent strain value of each element through the "Query Value" function, and export it to an Excel file;

[0159] Element volume: Similarly, query the volume parameters of each element in the hazardous area and export them to an Excel file;

[0160] Node coordinates: Obtain the coordinates of 8 nodes (Def.Coords) of all grid cells in the encrypted area using the "Query Value" function of the .odb file, export them to an Excel file, and store the node coordinates of each grid cell in association with the cell number.

[0161] Subsequently, the centroid coordinates of the mesh elements are calculated. Based on the exported node coordinates, the centroid coordinates of each element are calculated, and the steps are as follows:

[0162] In Excel, iterate through the coordinates of the 8 nodes in each cell using the formula.

[0163]

[0164] Similarly, calculate the centroid coordinates of the unit cell. ;

[0165] The grid cell number, centroid coordinates, strain values, and volume parameters are integrated into a structured data table to establish a grid cell information database.

[0166] Finally, the strain field strength is calculated using programming, as follows:

[0167] Define parameters and set the field diameter R.* =0.8mm, import the grid cell information database;

[0168] Determine the reference point, retrieve the grid cell with the largest equivalent strain point in the danger zone, and establish a local coordinate system with the centroid of the grid cell as the origin;

[0169] Damage domain filtering involves traversing all mesh elements and calculating the straight-line distance between the centroid of each mesh element and the origin. Filter out The damage domain is composed of mesh elements. ;

[0170] The weight function is calculated by determining the distance for each grid cell within the damage domain according to the formula. (Distance between the centroid of the mesh cell and the origin) and the included angle (The angle between the line and the x-axis), substitute into the weighting function formula:

[0171] When in a low-cycle fatigue state

[0172]

[0173] weight function

[0174] Field strength integration, strain field strength calculated according to the strain field strength model of steel cable. :

[0175]

[0176] The program outputs the strain field strength values ​​and the distribution of strain contribution percentages for each grid element within the damage domain, saving the results as a .txt file. The strain contribution percentage for each grid element refers to the specific share contributed by a particular grid element when the total strain field strength is obtained through final integration.

[0177] Through the above steps, with the point of maximum equivalent strain as the center point and the field diameter as R, * For a hemisphere with a diameter of 0.8 mm, the weight of each mesh element at the point of maximum equivalent strain is calculated, yielding the field strength and strain under a tensile load of 381 kN on the steel cable. =0.00923.

[0178] Step 5: Calculate the low-cycle fatigue life of the steel cable;

[0179] In this embodiment, the material static parameters (elastic modulus E = 221 GPa, yield strength 1800 MPa) of the outer layer of the triangular strand steel cable are first substituted into the estimation formula shown in Table 1 to obtain the four key fatigue parameters required for the low-cycle fatigue life prediction model of the steel cable. The specific calculation results are: fatigue strength index b = -0.12, fatigue elongation index c = -0.62, and fatigue strength coefficient... fatigue ductility coefficient .

[0180] Table 1. Estimation formulas for relevant parameters in the low-cycle fatigue life prediction model of steel cables.

[0181]

[0182] Subsequently, the maximum and minimum stresses obtained from the finite element analysis were extracted, and the average stress was calculated. .

[0183] The four fatigue parameters and mean stress obtained above The strain field strength obtained from the integral in step 4 is substituted into the cable low-cycle fatigue life prediction model obtained by correcting the linear relationship of Morrow's elastic stress. From this, we can obtain:

[0184]

[0185] Finally, by solving the above equations, the fatigue life N of the dangerous part of the triangular strand steel cable under a tensile load of 381kN can be obtained as 171.15, that is, the fatigue life under this working condition is 171 cycles.

[0186] In summary, the proposed method for predicting the low-cycle fatigue life of steel cables based on the field strength method encompasses a complete closed loop, from refined modeling of the steel cable, identification of critical locations, extraction of strain field data, solving the field strength integral, to the final iterative calculation of life. By transforming the strain field gradient effect in the micro-region into a macro-level life prediction index, it effectively solves the problem of insufficient life prediction accuracy for low-cycle fatigue of steel cables under complex tensile loads.

Claims

1. A method for predicting low-cycle fatigue life of steel cable tension based on the field strength method, characterized in that, Including the following steps: Step 1: Determine the critical locations of the steel cable under tensile load through finite element simulation; Step 2: The Morrow correction method is used to correct the elastic strain components in the Manson-Coffin formula to obtain the low-cycle fatigue life prediction model for steel cables. Step 3: Establish a strain field strength model for calculating cable life. This strain field strength model considers the damage region, failure function, and weighting function. The failure function value is the Von Mises equivalent strain. The weighting function is a weighting function that considers the damage gradient, orientation angle, and distance, and is used to characterize the contribution weight of each point in the damage region to the strain field strength of the damage region. Step 4: Calculate the strain field intensity in the damaged area; The dangerous area and its vicinity are defined as the fatigue danger zone. After refining the local mesh in the fatigue danger zone, finite element simulation is performed again to obtain finite element simulation data. The centroid of the mesh element with the largest equivalent strain point in the finite element simulation data is identified as the fatigue danger point. Based on the preset field diameter, the damage area is determined with the fatigue danger point as the center. Mesh elements with the centroid located in the damage area are selected, and the required parameter values ​​are extracted from the finite element simulation data and substituted into the strain field strength model of the steel cable to calculate the strain field strength of the damage area. Step 5: Calculate the low-cycle fatigue life of the steel cable; Obtain the values ​​of the remaining parameters in the low-cycle fatigue life prediction model of the steel cable, except for the total strain amplitude. The strain field strength calculated in step 4 is equivalent to the total strain amplitude. Substitute these values ​​along with the remaining parameters into the low-cycle fatigue life prediction model of the steel cable to solve for the low-cycle fatigue life of the steel cable.

2. The method for predicting low-cycle fatigue life of steel cable tension based on the field strength method according to claim 1, characterized in that, The hazardous locations in step 1 are identified through cross-validation using the maximum response criterion and the gradient mutation criterion: the maximum response criterion identifies the area with the maximum equivalent strain or maximum contact stress as the primary candidate hazardous area; the gradient mutation criterion identifies the area with a significant abrupt change in stress gradient or strain gradient as the potential hazardous area; a comprehensive verification analysis is performed on the primary and potential hazardous areas to determine the hazardous locations for fatigue failure.

3. The method for predicting low-cycle fatigue life of steel cable tension based on the field strength method according to claim 1, characterized in that, In step 1, when performing finite element simulation, one-sixth of the twist pitch of the three-dimensional geometric model of the steel cable is used for finite element simulation.

4. The method for predicting low-cycle fatigue life of steel cable tension based on the field strength method according to claim 1, characterized in that, The low-cycle fatigue life prediction model for steel cables established in step 2 is as follows: In the formula, For average stress, ; and These represent the local maximum and minimum stress values ​​at the fatigue-prone areas, respectively. The total strain amplitude, For elastic strain components, For plastic strain components, The fatigue strength coefficient, The fatigue ductility coefficient, denoted as F, where c is the fatigue strength index, E is the fatigue ductility index, E is the elastic modulus of the steel cable material, and N is the fatigue life.

5. The method for predicting low-cycle fatigue life of steel cable tension based on the field strength method according to claim 1, characterized in that, The strain field strength model of the steel cable established in step 3 is as follows: In the formula, The strain field strength in the damaged area, Let V represent the volume of the damaged region Ω. For the destruction function, The weight function; ; The distance between a point within the damaged area Ω and the fatigue risk point; θ is the angle between the line connecting the fatigue hazard point and a point within the damage area Ω and the horizontal direction.

6. The method for predicting low-cycle fatigue life of steel cable tension based on the field strength method according to claim 1, characterized in that, The method for determining the field diameter in step 4 is as follows: extract the stress gradient curve along the normal of the fatigue danger point, and take the distance from the point where the rate of change of the stress gradient decreases to a point where it tends to be stable as the field diameter.

7. The method for predicting low-cycle fatigue life of steel cable tension based on the field strength method according to claim 6, characterized in that, The diameter of the wire should be between 0.5mm and 0.8mm, or 0.3 to 0.8 times the diameter of the wire in the dangerous part.

8. The method for predicting low-cycle fatigue life of steel cables based on the field strength method according to claim 1, characterized in that, In step 5, when the steel cable is made of conventional metal, the values ​​of the parameters other than the total strain amplitude in the low-cycle fatigue life prediction model of the steel cable are obtained based on the material static parameter estimation method; when the steel cable is made of non-metallic material, composite material or atypical metal with special microstructure, the values ​​of the parameters other than the total strain amplitude in the low-cycle fatigue life prediction model of the steel cable are obtained by experimental method or empirical estimation model.

9. The method for predicting low-cycle fatigue life of steel cable tension based on the field strength method according to claim 1, characterized in that, In step 4, when refining the local mesh in the fatigue danger zone, the length of the refined section is 5 to 8 times the diameter of the steel wire at the corresponding dangerous part of the steel cable.

Images