Bridge suspender steel wire fretting corrosion fatigue life prediction method and system

Abstract

The invention belongs to the technical field of bridge structure safety, and discloses a bridge suspender steel wire fretting corrosion fatigue life prediction method and system, and the method comprises the steps: obtaining the initial parameters of a steel wire, considering the stress non-uniform distribution and contact angle of the steel wire based on the Hertz contact theory, and carrying out the step-by-step iterative calculation, a steel wire fretting corrosion wear model is established, and the fretting corrosion wear depth and the fretting corrosion wear rate of each analysis step length are output; based on the fracture mechanics theory, the wear notch stress concentration and the multi-axis stress state of the steel wire are analyzed, a steel wire multi-axis corrosion fatigue crack propagation rate model is constructed, and the crack propagation rate is output; an equivalent initial crack method is adopted, the fretting corrosion wear rate and the crack growth rate are compared through cycle-by-cycle iteration, competition analysis of cracks and wear is carried out, a fretting corrosion wear dominant stage and a multi-axis corrosion fatigue dominant stage are divided, the service lives of the two stages are solved respectively, and the service life of the multi-axis corrosion fatigue dominant stage is calculated. The sum of the two is the total fretting corrosion fatigue life of the steel wire.

Description

Technical Field

[0001] This invention relates to the field of bridge structural safety technology, and in particular to a method and system for predicting the fatigue life of bridge hanger steel wires due to fretting corrosion. Background Technology

[0002] As key load-bearing components of suspension bridges and through-arch bridges, bridge suspenders endure the combined effects of vehicle loads, structural weight, and environmental erosion over extended periods. Their service safety directly determines the reliability and durability of the overall bridge structure. During long-term service, in addition to corrosion damage caused by atmospheric erosion, the steel wires within the bundles or strands that make up the suspenders experience repeated, minute relative slippage under periodically varying vehicle loads. This phenomenon is known as fretting. Fretting leads to scratching damage on the contact surfaces of the wires, i.e., fretting wear. Therefore, the deterioration of the suspender wires is actually the result of the coupled effects of fatigue, corrosion, and fretting wear; this complex damage mechanism is called fretting corrosion fatigue.

[0003] Currently, fatigue life prediction methods for suspension rod steel wires are mainly divided into two categories. The first category is based on stress-life (or strain-life) methods, which primarily rely on the stress-life curve of the material under specific conditions. S - N Life estimation is performed using curves and linear or nonlinear damage accumulation criteria (such as Miner's rule). These methods are relatively simple to calculate and widely used in engineering, but they are essentially empirical or semi-empirical methods based on experimental data. They lack a clear analysis of the physical mechanism of damage evolution and cannot accurately reflect the complex influence of factors such as corrosion and wear on the fatigue damage process.

[0004] The second category is based on fracture mechanics. This method divides life prediction into two stages: crack initiation and crack propagation. It mainly predicts the number of cycles required for a crack to propagate from its initial size to its critical size by establishing a fatigue crack propagation rate model (such as the Paris formula). However, most existing corrosion fatigue life prediction methods based on fracture mechanics only consider the accelerating effect of the corrosive environment on crack propagation, and rarely consider the influence of contact friction damage between steel wires (i.e., fretting wear). In the field of mechanical engineering, although there are some analytical methods for fretting damage, such as the critical plane method based on multiaxial stress analysis, the continuous damage mechanics method, the fretting characteristic parameter method, and the Crossland parameter method based on stress invariants, these methods are usually independent of crack propagation analysis and fail to effectively handle the interaction between wear and cracks.

[0005] In fact, fretting wear and fatigue cracking are an interactive and competitive dynamic process. In the early stages of deterioration, the wear rate may be high, capable of "wearing away" nascent microcracks; at this point, wear is the dominant damage mechanism. As wear progresses, the contact geometry changes, contact stress decreases, and the wear rate slows down. The notches created by wear then cause stress concentration, inducing and accelerating crack propagation, making crack propagation the dominant damage mechanism. Current technology has failed to establish a theoretical model that can describe this competitive relationship, resulting in the inability to accurately predict the lifespan of the hanger wire under the coupled effects of fatigue, corrosion, and fretting wear.

[0006] Therefore, there is an urgent need to propose a life prediction method that can integrate multiple factors such as contact wear, environmental corrosion, and multiaxial fatigue during the service process of bridge suspender wires, and can scientifically describe the competitive evolution process of wear and cracks, so as to solve the shortcomings of existing technologies and provide theoretical support for accurate safety assessment and scientific operation and maintenance decision-making of bridge suspender wires. Summary of the Invention

[0007] This invention proposes a method and system for predicting the fatigue life of bridge suspender steel wires due to fretting corrosion. The aim is to provide a method for predicting the fatigue life of bridge suspender steel wires due to fretting corrosion that can couple contact wear, environmental corrosion and multiaxial fatigue effects, and consider the competition mechanism between wear and cracks.

[0008] In a first aspect, the present invention provides a method for predicting the fatigue life of fretting corrosion of steel wire in bridge hangers, comprising the following steps: Step 1: Establish a fretting corrosion wear model for steel wires: Obtain the geometric parameters, material mechanical property parameters, fretting contact parameters, and corrosion environment parameters of the steel wires. Based on Hertzian contact theory, and combined with the contact angle between the steel wires and the non-uniform stress distribution caused by the wear gap, establish a stepwise iterative analysis model for the fretting corrosion wear depth of the steel wires, and calculate the fretting corrosion wear rate for each analysis step based on the stepwise iterative analysis model. Step 2: Construct a multiaxial corrosion fatigue crack propagation rate model for steel wire: Based on fracture mechanics theory, establish a stress intensity correction model that takes into account the stress concentration of wear notches, and combine it with the tensile-shear multiaxial stress state of the steel wire during service to construct a multiaxial stress intensity model, thereby obtaining a multiaxial corrosion fatigue crack propagation rate model for the steel wire, and calculate the crack propagation rate for each analysis step based on the multiaxial corrosion fatigue crack propagation rate model. Step 3: Predict the fretting corrosion fatigue life of the steel wire: Calculate the equivalent initial crack length, and conduct a competitive analysis of the fretting corrosion wear rate and the crack propagation rate by iteratively comparing the fretting corrosion wear rate and the crack propagation rate through step-by-step analysis. The moment when the crack propagation rate first exceeds the fretting corrosion wear rate is used as the boundary to divide the fretting corrosion wear-dominant stage and the multiaxial corrosion fatigue-dominant stage. Calculate and output the life of the fretting corrosion wear-dominant stage and the life of the multiaxial corrosion fatigue-dominant stage. Sum the lifespans of the two stages to obtain and output the total fretting corrosion fatigue life of the steel wire.

[0009] As an optional implementation of the first aspect of this application, the specific calculation method for establishing the fretting corrosion wear model of the steel wire in step 1 includes: obtaining the wear volume based on Hertzian contact theory. With normal load Sliding distance Brinell hardness of materials and wear coefficient Relationship: ; for wear volume Differential calculations are performed, and the wear contact area of ​​the steel wire is introduced. The incremental depth of fretting corrosion wear of steel wire was obtained. The calculation formula: ; thereby obtaining the depth of fretting corrosion wear on the steel wire. The calculation model is based on the fretting corrosion wear depth of the steel wire. The calculation model, combined with the contact angle β between the steel wires, corrects the wear contact area. A fretting corrosion wear depth calculation model considering the correction of the steel wire contact angle is obtained; based on the wear depth calculation model with contact angle correction, a stress distribution coefficient determined by the geometry of the wear notch is further introduced. K tti A calculation model for the fretting corrosion wear depth of steel wire that simultaneously considers contact angle and non-uniform stress distribution is obtained. A step-by-step iterative calculation method is adopted, with a preset number of cycles as the analysis step size. In each analysis step size, the fretting corrosion wear depth, contact area and stress distribution coefficient of the steel wire are updated, and the increment of fretting corrosion wear depth in the current analysis step size is calculated and converted into fretting corrosion wear rate.

[0010] As an optional embodiment of the first aspect of this application, the specific calculation method of the fretting corrosion wear depth calculation model considering the correction of the steel wire contact angle is as follows: calculate the contact area of ​​two mutually perpendicular steel wires. ; Calculate the contact area after considering the correction for the contact angle of the steel wires, based on the included angle β between the axes of the two steel wires. : The corrected contact area Substituting into the fretting corrosion wear depth calculation model, we obtain the fretting corrosion wear depth calculation model considering the correction of the steel wire contact angle: The calculation model for the fretting corrosion wear depth of steel wire, which simultaneously considers contact angle and non-uniform stress distribution, is specifically calculated as follows: based on the ratio of the minor axis to the major axis of the wear notch... R s The ratio of the depth of the wear notch to the length of the semi-shaft. R d Calculate the stress concentration factor at each point of the wear notch. K ti Regarding the stress concentration factor K ti After normalization, the stress distribution coefficients at each point are obtained. K tti : ;in, The maximum value of the stress concentration factor of the wear notch; the stress distribution factor K tti By introducing the contact angle correction model for calculating the fretting corrosion wear depth, the final formula for calculating the fretting corrosion wear depth is obtained: .

[0011] As an optional implementation of the first aspect of this application, the specific calculation method for step 2, which constructs the multiaxial corrosion fatigue crack propagation rate model of the steel wire, is as follows: A stress intensity correction model considering stress concentration at the wear notch is established, based on the depth of the wear notch. and maximum stress concentration factor The stress intensity under uniaxial tensile stress conditions is corrected; the stress intensity correction model is then applied to the stress intensity under tensile stress-driven Mode I. K I and shear stress driven mode II stress intensity K II The calculation; based on the ratio of the material's shear fatigue limit to its uniaxial fatigue limit, ductile and brittle materials are distinguished, and their corresponding fatigue characteristic parameters and equivalent coefficients are calculated respectively; based on the critical plane method, combined with the above... K I , K II Based on fatigue characteristic parameters and equivalent coefficients, the multiaxial equivalent stress strength under tension-shear-material property action is calculated. The multiaxial equivalent stress intensity Substituting into the crack propagation rate model, we obtain the multiaxial corrosion fatigue crack propagation rate model for the steel wire: Where C and m are material parameters, determined by fitting the fatigue crack rate curves of materials under different corrosion environments; Where is the crack length and N is the number of load cycles. Δ represents the increment of multiaxial equivalent stress intensity. K th This represents the fatigue crack propagation threshold value.

[0012] As an optional embodiment of the first aspect of this application, the specific method for establishing the stress intensity correction model considering the stress concentration of the wear notch is as follows: using an asymptotic interpolation method, the stress intensity considering the stress concentration of the notch under uniaxial tensile stress is obtained. The calculation formula: In the formula, is the geometric correction factor for the crack. The nominal stress amplitude, The length of the crack. The depth of the wear notch. The maximum stress concentration factor of the wear notch; the calculation formula is... It is applied to calculate the stress intensity KI of Mode I driven by tensile stress and the stress intensity KII of Mode II driven by shear stress, thereby introducing the effect of stress concentration at wear notches into the calculation of multiaxial stress intensity.

[0013] As an optional embodiment of the first aspect of this application, the specific method for distinguishing ductile and brittle materials based on the ratio of the material's shear fatigue limit to its uniaxial fatigue limit, and calculating the corresponding fatigue characteristic parameters and equivalent coefficients respectively, is as follows: Calculate the material property parameter z: In the formula, This represents the material's shear fatigue limit. The material's uniaxial fatigue limit is given; when z ≤ 1, it is classified as a ductile material, and the characteristic angle γ and fatigue characteristic parameters are calculated. and equivalent coefficient B : ; ; When z > 1, it is determined to be a brittle material, and the characteristic angle γ and fatigue characteristic parameters are calculated. and equivalent coefficient B : ; ; .

[0014] As an optional implementation of the first aspect of this application, the specific calculation method for step 3, predicting the fatigue life of the steel wire under fretting corrosion, is as follows: based on the fatigue crack propagation threshold value Δ K th Nominal stress amplitude Δ s and the geometric correction factor for cracks Y Calculate the equivalent initial crack length l0; In the competition analysis between cracks and wear, when... n The step-by-step analysis corresponds to the total number of load cycles. N t = n · N N represents the number of load cycles, and the number of load cycles at which the crack propagation rate first exceeds the wear rate is calculated. N t The dominant life of fretting corrosion wear of steel wire is denoted as N 1. The corrosion fatigue crack propagation life of the steel wire is calculated by integrating the multiaxial corrosion fatigue crack propagation rate model. N 2: In the formula, l e The critical crack length at which the steel wire breaks, the critical crack length l e Based on material fracture toughness K e The critical stress intensity was calculated; the dominant lifespan of the fretting corrosion wear was determined. N 1 and the corrosion fatigue crack propagation life N The two values ​​are added together to obtain the total fretting corrosion fatigue life of the steel wire. N 总 : .

[0015] Secondly, embodiments of this application provide a system for predicting the fatigue life of bridge hanger steel wires due to fretting corrosion, comprising: The steel wire fretting corrosion wear calculation module is used to obtain the geometric parameters, material mechanical property parameters, fretting contact parameters and corrosion environment parameters of the steel wire. Based on Hertz contact theory, combined with the contact angle between the steel wires and the non-uniform stress distribution caused by the wear gap, a stepwise iterative analysis model for the fretting corrosion wear depth of the steel wire is established, and the fretting corrosion wear rate of each analysis step is calculated based on the stepwise iterative analysis model. The steel wire crack propagation calculation module is used to establish a stress intensity correction model that takes into account the stress concentration of wear notches based on fracture mechanics theory, and to construct a multiaxial stress intensity model by combining the tensile-shear multiaxial stress state of the steel wire during service, thereby obtaining a multiaxial corrosion fatigue crack propagation rate model of the steel wire, and calculating the crack propagation rate of each analysis step based on the multiaxial corrosion fatigue crack propagation rate model. The steel wire fretting corrosion fatigue life calculation module is used to calculate the equivalent initial crack length. By iteratively comparing the fretting corrosion wear rate and the crack propagation rate at each analysis step, it conducts a competition analysis between the steel wire crack and wear. Taking the moment when the crack propagation rate first exceeds the fretting corrosion wear rate as the boundary, it divides the fretting corrosion wear-dominant stage and the multiaxial corrosion fatigue-dominant stage. It calculates and outputs the life of the fretting corrosion wear-dominant stage and the life of the multiaxial corrosion fatigue-dominant stage. The lifespans of the two stages are summed to obtain and output the total fretting corrosion fatigue life of the steel wire.

[0016] Thirdly, embodiments of this application provide an electronic device, which includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the steps of the method described in the first aspect.

[0017] Fourthly, embodiments of this application provide a readable storage medium on which a program or instructions are stored, which, when executed by a processor, implement the steps of the method described in the first aspect.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. Multi-factor coupling for more accurate prediction: This invention couples and analyzes multiple factors such as contact wear, environmental corrosion, and multiaxial fatigue of bridge suspender steel wires during service, and constructs a damage evolution model that is closer to engineering practice, thereby improving the accuracy of life prediction.

[0019] 2. Innovative competition mechanism with clear physical significance: It innovatively proposes a competition analysis mechanism between wear and cracks, dividing the entire fatigue life of the steel wire into two stages: wear-dominated and crack propagation-dominated. It clearly describes the transformation process of the damage mechanism and has clear physical significance.

[0020] 3. The model has strong applicability and considers all working conditions: The wear model of this invention considers the wire contact angle of different types of suspension rods such as steel strands and semi-parallel wire bundles, as well as the non-uniform stress distribution caused by wear notches; the crack propagation model considers the stress concentration of wear notches and the tensile and shear multiaxial stress state, making the model more applicable.

[0021] 4. Simplified calculation, balancing accuracy and efficiency: The equivalent initial crack method is adopted, which equates the complex crack initiation and short crack propagation stages to an initial crack, simplifying the analysis process and significantly improving calculation efficiency while ensuring prediction accuracy. Attached Figure Description

[0022] Figure 1 This is a flowchart of a method for predicting the fatigue life of bridge hanger steel wire under fretting corrosion according to an embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the competition between fretting corrosion wear and multiaxial corrosion fatigue cracks in the steel wire in an embodiment of the present invention. Figure 3 This is a schematic diagram of a bridge hanger steel wire fretting corrosion fatigue life prediction system provided in an embodiment of the present invention. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0025] Example 1 Please see Figure 1 This is a flowchart illustrating a method for predicting the fatigue life of fretting corrosion of steel wire in bridge hangers, provided by an embodiment of the present invention. The method may include the following steps: Step 1: Establish a fretting corrosion wear model for steel wires: Obtain the geometric parameters, material mechanical property parameters, fretting contact parameters, and corrosion environment parameters of the steel wires. Based on Hertzian contact theory, and combined with the contact angle between the steel wires and the non-uniform stress distribution caused by the wear gap, establish a stepwise iterative analysis model for the fretting corrosion wear depth of the steel wires, and calculate the fretting corrosion wear rate for each analysis step based on the stepwise iterative analysis model.

[0026] (1-1) Initial conditions and basic mechanical model According to Hertzian contact theory, the material surface can be assumed to be composed of a large number of hemispherical micro-protrusions, and material wear occurs at the tips of these hemispherical micro-protrusions. When the stress in the cross-section of a hemispherical micro-protrusion reaches the yield limit of the material, the micro-protrusion will wear off, and its mathematical expression is: In the formula, F Normal force;n The number of hemispherical micro-convexities; r The radius of the hemispherical micro-convex body; s x This represents the yield strength of the material.

[0027] During friction, the displacement of the material due to sliding friction is directly proportional to the radius of the hemispherical micro-protrusion. When the sliding distance is... S At that time, the number of worn micro-protrusions is equal to the number of worn single convex balls. S / 2 r Times: In the formula, V s Sliding distance S Wear volume during the process; S This is the sliding distance; V The volume of a single hemispherical micro-convex body is calculated using the following formula: Combining equation (3) and equation (2), we get: Combining equations (1) and (4), the wear amount is obtained. V s With normal load F The relationship is given. Furthermore, to eliminate interference from external experimental conditions and achieve a quantitative description of the inherent wear characteristics of materials, a wear coefficient is introduced into the formula. k To characterize wear behavior under different wear mechanisms, the calculation formula is as follows: In the formula, the wear coefficient k It is related to both material and environment, and can be used to measure and quantify the contact friction properties of materials under different corrosive environments, including the wear coefficient. k The influence of corrosive environments on the contact friction performance of steel wires was taken into account.

[0028] Besides yield strength, Brinell hardness can also characterize a material's wear resistance. Yield strength s x Brinell hardness H The following relationship exists: In the formula, Brinell hardness H Determine the value from the standard GB / T 1172-1999 "Conversion Values ​​of Hardness and Strength of Ferrous Metals".

[0029] Combining equations (5) and (6), the wear volume is obtained. V sRelationship with mechanical parameters: Wear depth is a key indicator for evaluating the amount of wear on a material. Differential calculation of equation (7) yields the following formula for calculating the increment of fretting corrosion wear depth on the steel wire: In the formula, A This represents the wear contact area of ​​the steel wire; Let be the fretting corrosion wear depth of the steel wire. Taking the indefinite integral of equation (10), the fretting corrosion wear depth of the steel wire can be obtained: Fretting fatigue causes wear on the surface material of the steel wire, forming approximately elliptical wear marks. The formula for calculating the contact area of ​​the steel wire is as follows: (1-2) Correction model for fretting corrosion wear depth considering wire contact angle The above model (Equation (11)) is applicable to calculating the fretting corrosion wear depth of two steel wires in a mutually perpendicular contact state. However, in actual engineering, the contact conditions of bridge suspender steel wires are more complex, with different contact angles, such as steel strands and semi-parallel steel wire bundles. At present, there is still no reference model for calculating wear depth under different contact angles.

[0030] To more accurately calculate the actual wear of bridge steel wires, this invention extends the above model (Equation (11)) into a wear depth correction calculation model that can consider different contact angles between steel wires. The change in the contact angle of the steel wires directly affects the size of the contact ellipse area. The contact surface of two perpendicular steel wires is elliptical. As the contact angle decreases, the contact area increases accordingly, which in turn leads to a decrease in contact stress and a decrease in wear rate.

[0031] For the same wear depth, for a contact angle of... β The contact area between two steel wires can be expressed as: in, β The angle between the axes of the two steel wires; A The contact area of ​​two perpendicular steel wires; A w To account for the contact area after the steel wire contact angle is corrected. Equation (13) takes into account the different contact angles between the steel wires of the bridge hanger and is applicable to the contact conditions of steel wires of various bridge hangers, such as steel strands and semi-parallel steel wire bundles.

[0032] The calculation model for fretting corrosion wear depth considering the correction for the steel wire contact angle is as follows: (1-3) A fretting corrosion wear depth model that takes into account both the wire contact angle and the non-uniform stress distribution Because of the significant stress concentration at the wear notch location, fatigue cracks in the steel wire are prone to initiation and propagation in this area, thus accelerating the accumulation of fatigue damage and ultimately, the wire's fatigue fracture. Therefore, analyzing crack initiation and propagation at the wear notch location requires clarifying the stress distribution around the notch.

[0033] During actual contact between steel wires, the stress distribution on the contact surface is closely related to the geometry of the wear notch. The formula for calculating the stress concentration factor considering the length, width, and depth of the wear notch is: in, K ti The stress concentration factor at each stress point; R s This is the ratio of the minor axis to the major axis of the wear notch; R d This is the ratio of the depth of the wear notch to the length of the semi-shaft; f for R s The correlation coefficient. f , R s and R d The calculation formula is as follows: in, This refers to the wear depth. b The short half-shaft with a wear notch; c The long half-shaft with a wear notch; To account for the impact of stress distribution at the wear notch on the growth of the wear notch, the concentration factor at each of the above points is adjusted. K tti After normalization, the stress distribution coefficients at each point are obtained: in, K tmax This represents the maximum stress concentration factor of the wear notch.

[0034] Combining equations (14) and (19), we obtain the formula for calculating the fretting corrosion wear depth of steel wire that simultaneously considers the contact angle and the unevenness of stress distribution: (1-4) Iterative analysis model of fretting corrosion wear depth and fretting corrosion wear rate of steel wire Equation (20) characterizes the slip distance as S The depth of each point in the wear notch of the steel wire at that time, and the amplitude of the fretting corrosion wear displacement of the steel wire. s And it undergoes a complete fretting corrosion wear cycle (i.e. N =1), and its wear depth can be calculated as follows: Fretting corrosion wear of steel wire is a material wear degradation process that occurs over time or with increasing load cycles. Therefore, for any given number of wear cycles... N To analyze step size (e.g.) N =100 times), using a step-by-step iterative calculation method, the following formulas are obtained for the increment of fretting corrosion wear depth and the wear depth of the steel wire: in, and The first i Second and third i -1 analysis step length for fretting corrosion wear depth. Initial wear depth. This can be considered as a micro-defect or micro-crack on the material surface. The initial wear depth of the steel wire... Substituting into equation (14), the wear depth of the steel wire during the fretting corrosion wear process at the first analysis step can be calculated. In each subsequent analysis step, the parameters such as the fretting corrosion wear depth, contact area, and stress distribution coefficient of the steel wire are updated. By iterating step by step, the fretting corrosion wear depth and fretting corrosion wear increment of the steel wire at each analysis step can be calculated.

[0035] Step 2: Construct a multiaxial corrosion fatigue crack propagation rate model for steel wire: Based on fracture mechanics theory, establish a stress intensity correction model that takes into account the stress concentration of wear notches, and combine it with the tensile-shear multiaxial stress state of the steel wire during service to construct a multiaxial stress intensity model, thereby obtaining a multiaxial corrosion fatigue crack propagation rate model for the steel wire, and calculate the crack propagation rate for each analysis step based on the multiaxial corrosion fatigue crack propagation rate model.

[0036] (2-1) Stress intensity correction model considering the stress concentration effect of wear notch Based on fracture mechanics theory, the fatigue crack propagation rate is a function of stress intensity. Under uniaxial tensile stress conditions, the stress intensity Δ... K The calculation formula is as follows: In the formula, Y Δ is the geometric correction factor for the crack; s This is the nominal stress amplitude; l The crack length is given.

[0037] Based on equation (24), the stress intensity Δ considering the stress concentration at the notch under uniaxial tensile stress can be obtained by using the asymptotic interpolation method. K n The calculation formula is as follows: In the formula, K tmax The maximum stress concentration factor of the wear notch. This represents the depth of the wear notch.

[0038] (2-2) Multiaxial stress intensity model considering the stress concentration effect of wear notch During service, bridge suspender wires are subjected to a coupling effect of axial tension and lateral vibration, resulting in a multiaxial stress state of tension and shear. Crack propagation includes both Mode I (tensile stress-driven crack propagation) and Mode II (shear stress-driven crack propagation). Existing fatigue crack analyses of suspender wires mainly consider Mode I cracks, neglecting the accelerating effect of shear stress and wear notch stress concentration on crack propagation, which leads to conservative life prediction results. This section, based on fracture mechanics, considers the stress concentration effect caused by wire wear notches and develops a multiaxial stress strength model for the wire.

[0039] Based on equation (25), the stress intensity driven by tensile stress and considering the stress concentration at the wear notch. K I The calculation formula is as follows: Stress intensity driven by shear stress and considering stress concentration at wear notches K II The calculation formula is as follows: Equations (26) and (27) take into account the influence of stress concentration at the fretting corrosion wear notch on the multiaxial stress strength of the steel wire.

[0040] Crack propagation is closely related to material properties. Ductile and brittle materials exhibit drastically different crack propagation directions, rates, and failure mechanisms under multiaxial stress. Introducing material property parameters... z The calculation formula is as follows: In the formula: t -1This refers to the material's shear fatigue limit. f -1 This represents the uniaxial fatigue limit of the material.

[0041] For ductile materials (z≤1), the crack propagation direction is closely related to the stress field distribution and needs to be determined by the characteristic angle. c Quantifying the anisotropy of crack propagation. Characteristic angle. c Characteristic angle reflects the angle between the crack propagation direction and the tensile stress axis in ductile materials under multiaxial stress. A larger value indicates a more significant influence of shear stress on the crack propagation direction. c The formula for calculation is: It is a key material parameter in the fatigue limit criterion, used to quantify the fatigue characteristics of materials under multiaxial loading, and its equivalent coefficient. B Used to integrate dual-mode stress intensity, with settings differentiated according to material type. For ductile materials, , B The formula for calculation is: For brittle materials ( z >1), the crack propagation mechanism of brittle materials differs significantly from that of ductile materials. Internal defects in brittle materials are primarily cleavage fracture, the crack propagation direction is dominated by tensile stress, shear stress has a weak influence on crack propagation, and crack propagation does not exhibit significant anisotropy, thus requiring no correction using characteristic angles. Therefore, characteristic angles... c The calculation formula is: Fatigue characteristic parameters of brittle materials and equivalent coefficient B Material property parameters can be used directly. z The equivalent contribution of shear stress is characterized by the following formula: Based on the critical plane method, the multiaxial stress intensity under tension-shear-material property action is calculated as follows: In the formula, K 1 ，K 2 and K H It is a load parameter with the same dimensions as stress intensity; i It is the orientation of the plane of maximum normal stress amplitude at the far field. Equation (35) takes into account the influence of the multiaxial stress intensity of the steel wire on the fatigue crack propagation performance of the steel wire.

[0042] K 1 、K 2. K H , i The calculation formulas are as follows: (2-3) Multiaxial corrosion fatigue crack propagation rate model for steel wire Combining the classic crack propagation rate model and equation (35), the multiaxial corrosion fatigue rate model d of steel wire l / d N It can be represented as follows: In the formula, C , m For material parameters, Δ represents the increment of multiaxial equivalent stress intensity. K th This represents the fatigue crack propagation threshold value, which is determined by fitting the fatigue crack rate curve of the material under different corrosive environments, thus taking into account the influence of the corrosive environment on the fatigue crack propagation performance of the steel wire.

[0043] Step 3: Predict the fretting corrosion fatigue life of the steel wire: Calculate the equivalent initial crack length, and conduct a competitive analysis of the fretting corrosion wear rate and the crack propagation rate by iteratively comparing the fretting corrosion wear rate and the crack propagation rate through step-by-step analysis. The moment when the crack propagation rate first exceeds the fretting corrosion wear rate is used as the boundary to divide the fretting corrosion wear-dominant stage and the multiaxial corrosion fatigue-dominant stage. Calculate and output the life of the fretting corrosion wear-dominant stage and the life of the multiaxial corrosion fatigue-dominant stage. Sum the lifespans of the two stages to obtain and output the total fretting corrosion fatigue life of the steel wire.

[0044] (3-1) Equivalent initial crack method and competition analysis between wear and crack Fatigue crack propagation in materials includes three stages: fatigue crack initiation, short-crack propagation, and long-crack propagation. Using the equivalent initial crack method, fatigue life prediction can be achieved solely through long-crack analysis, avoiding the complex analysis and modeling of crack initiation and short-crack propagation, thus significantly simplifying fatigue life prediction.

[0045] Equivalent initial crack length l The calculation formula for 0 is as follows: In the formula, Δ Kth Δ is the threshold value for fatigue crack propagation. s This is the nominal stress amplitude; Y is the geometric correction factor for the crack.

[0046] like Figure 2 As shown, fretting corrosion fatigue of steel wire is a process in which wear and cracking interact and compete with each other. In the initial stage of fretting corrosion fatigue of steel wire, the wear rate is greater than the crack initiation and propagation rate, leading to rapid material spalling and loss, eliminating any cracks that may have formed on the material contact surface. As time increases or the number of load cycles increases, the contact area between steel wires increases, the contact stress decreases, and the shear stress decreases. The wear rate of the steel wire decreases and gradually falls below the crack initiation and propagation rate, causing the crack to propagate continuously and eventually leading to the fracture of the steel wire. Therefore, in the fretting corrosion fatigue analysis of steel wire, it is necessary to conduct a stepwise discriminant analysis of the competitive process between cracking and wear.

[0047] With step size N Taking 100 cycles as an example, the competitive discrimination formula for steel wire cracking and wear is as follows: In the formula, For wear rate, d l / d N This represents the crack propagation rate. When the wear rate is greater than the crack propagation rate, wear dominates; when the wear rate is less than the crack propagation rate, crack propagation dominates.

[0048] (3-2) Predicting the fretting corrosion fatigue life of steel wire In the step-by-step analysis of the competition process between wire cracking and wear described above, when... n Stepwise analysis (i.e.) N t = n · N And when the crack growth rate just exceeds the wear rate, the number of load cycles experienced by the steel wire. N t This refers to the lifespan value dominated by fretting corrosion wear of the steel wire. N 1.

[0049] When the crack growth rate of a steel wire exceeds its wear rate, the corrosion fatigue crack propagation life of the steel wire is extended. N 2 can be calculated as follows: In the formula, l 0 equivalent initial crack length; l e The critical crack length for wire breakage is given by the following formula: In the formula, K e Fracture toughness is the material's ability to resist the unstable propagation of cracks.

[0050] In summary, the fretting corrosion fatigue life of steel wire N 总 The sum of the lifespans for the wear and crack propagation stages, i.e. Example 2 Please see Figure 3 The diagram shown is a structural schematic of a bridge hanger steel wire fretting corrosion fatigue life prediction system according to the second embodiment of this application. The system includes the following key modules: The steel wire fretting corrosion wear calculation module 100 is used to obtain the geometric parameters, material mechanical property parameters, fretting contact parameters and corrosion environment parameters of the steel wire. Based on Hertz contact theory, combined with the contact angle between the steel wires and the non-uniform stress distribution caused by the wear gap, a step-by-step iterative analysis model for the fretting corrosion wear depth of the steel wire is established, and the fretting corrosion wear rate of each analysis step is calculated based on the step-by-step iterative analysis model. The steel wire crack propagation calculation module 200 is used to establish a stress intensity correction model that takes into account the stress concentration of wear notches based on fracture mechanics theory, and to construct a multiaxial stress intensity model by combining the tensile-shear multiaxial stress state of the steel wire during service, thereby obtaining a multiaxial corrosion fatigue crack propagation rate model of the steel wire, and calculating the crack propagation rate of each analysis step based on the multiaxial corrosion fatigue crack propagation rate model. The steel wire fretting corrosion fatigue life calculation module 300 is used to calculate the equivalent initial crack length. By iteratively comparing the fretting corrosion wear rate and the crack propagation rate at each analysis step, it conducts a competition analysis between steel wire crack and wear. Taking the moment when the crack propagation rate first exceeds the fretting corrosion wear rate as the boundary, it divides the fretting corrosion wear dominant stage and the multiaxial corrosion fatigue dominant stage. It calculates and outputs the life of the fretting corrosion wear dominant stage and the life of the multiaxial corrosion fatigue dominant stage. It sums the lifespans of the two stages to obtain and output the total fretting corrosion fatigue life of the steel wire.

[0051] The bridge suspender steel wire fretting corrosion fatigue life prediction system in this application embodiment can be a device, or a component, integrated circuit, or chip in a terminal. The device can be a mobile electronic device or a non-mobile electronic device. For example, mobile electronic devices can be mobile phones, tablets, laptops, PDAs, in-vehicle electronic devices, wearable devices, ultra-mobile personal computers (UMPCs), netbooks, or personal digital assistants (PDAs), etc., while non-mobile electronic devices can be servers, network attached storage (NAS), personal computers (PCs), etc. This application embodiment does not specifically limit the specific implementation.

[0052] The bridge hanger wire fretting corrosion fatigue life prediction system in this application embodiment can be a device with an operating system. This operating system can be Android, iOS, or other possible operating systems; this application embodiment does not specifically limit it.

[0053] This application provides a bridge hanger wire fretting corrosion fatigue life prediction system that can achieve... Figure 1 The various processes implemented in the method embodiment of the bridge hanger steel wire fretting corrosion fatigue life prediction method are not described in detail here to avoid repetition.

[0054] Optionally, embodiments of this application also provide an electronic device, including a processor, a memory, and a program or instructions stored in the memory and executable on the processor. When the program or instructions are executed by the processor, they implement the various processes of the above-described embodiment of the method for predicting the fatigue life of bridge suspender steel wire under fretting corrosion, and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0055] This application also provides a readable storage medium storing a program or instructions. When the program or instructions are executed by a processor, they implement the various processes of the above-described method for predicting the fatigue life of bridge suspender steel wire under fretting corrosion, and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0056] The processor is the processor in the electronic device described in the above embodiments. The readable storage medium includes computer-readable storage media, such as computer read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0057] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0058] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0059] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A method for predicting the fretting corrosion fatigue life of a bridge boom wire, characterized by, The method comprises the following steps: Step 1, establishing a steel wire fretting corrosion wear model: obtaining geometric parameters, material mechanical property parameters, fretting contact parameters and corrosion environment parameters of the steel wire, based on the Hertz contact theory, combining the contact angle between the steel wires and the stress non-uniform distribution caused by the wear notch, establishing a step-by-step iterative analysis model of the fretting corrosion wear depth of the steel wire, and calculating the fretting corrosion wear rate of each analysis step based on the step-by-step iterative analysis model; Step 2, constructing a steel wire multi-axial corrosion fatigue crack propagation rate model: based on the fracture mechanics theory, establishing a stress intensity correction model considering the stress concentration of the wear notch, and combining the tensile-shear multi-axial stress state of the steel wire in service, constructing a multi-axial stress intensity model, and then obtaining a multi-axial corrosion fatigue crack propagation rate model of the steel wire, and calculating the crack propagation rate of each analysis step based on the multi-axial corrosion fatigue crack propagation rate model; Step 3, predicting the fretting corrosion fatigue life of the steel wire: calculating the equivalent initial crack length, comparing the fretting corrosion wear rate and the crack propagation rate through iterative analysis step by step, carrying out the competition analysis of the crack and wear of the steel wire, and dividing the fretting corrosion wear dominant stage and the multi-axial corrosion fatigue dominant stage according to the time when the crack propagation rate first exceeds the fretting corrosion wear rate; calculating and outputting the life of the fretting corrosion wear dominant stage and the life of the multi-axial corrosion fatigue dominant stage, summing up the lives of the two stages to obtain and output the total fretting corrosion fatigue life of the steel wire.

2. The method of claim 1, wherein, The specific calculation method of the step 1 for establishing the steel wire fretting corrosion wear model comprises: Obtaining wear volume based on hertz contact theory Relationship with normal load , sliding distance , material brinell hardness and wear coefficient ​ ； Volume of wear The differential calculation is performed and the wear contact area of the steel wire is introduced The calculation formula of the steel wire fretting corrosion wear depth increment is obtained ​ ； Further, a calculation model of the fretting corrosion wear depth of the steel wire is obtained ​ Based on the calculation model of the micro-corrosion wear depth of the steel wire , combined with the contact angle β between the steel wires, the micro-corrosion wear depth calculation model considering the correction of the contact angle of the steel wire is obtained by correcting the wear contact area . The wear depth calculation model based on the contact angle correction is further introduced with a stress distribution coefficient determined by the wear notch geometry K tti to obtain a steel wire fretting corrosion wear depth calculation model considering the contact angle and stress non-uniform distribution simultaneously A step-by-step iterative calculation method is used, and a preset cycle number is used as an analysis step. In each analysis step, the fretting corrosion wear depth, contact area and stress distribution coefficient of the steel wire are updated, the fretting corrosion wear depth increment of the current analysis step is calculated, and the fretting corrosion wear rate is converted.

3. The method of claim 2, wherein, The specific calculation method of the fretting corrosion wear depth calculation model considering the contact angle correction of the steel wire is that: Calculating the contact area of two steel wires perpendicular to each other ; According to the included angle between the axes of the two steel wires β , the contact area is calculated taking into account the correction of the contact angle of the steel wires : ； The contact area is corrected Substituting the micro-corrosion wear depth calculation model, the micro-corrosion wear depth calculation model considering the correction of the contact angle of the steel wire is obtained: ； The specific calculation method of the fretting corrosion wear depth calculation model of the steel wire considering the contact angle and the stress non-uniform distribution is that: According to the ratio of the short axis to the long axis of the wear notch R s And the ratio of the depth of the wear notch to the long semi-axis R d The stress concentration coefficient of each point of the wear notch is calculated K ti ; The stress concentration coefficient K ti The stress distribution coefficient of each point is obtained by normalization K tti : ； wherein is the maximum value of the stress concentration factor for a wear notch; The stress distribution coefficient K tti The fretting corrosion wear depth calculation model with the contact angle correction is introduced, and the final fretting corrosion wear depth calculation formula is obtained: 。 4. The method of claim 1, wherein, The specific calculation method of the step 2 for constructing the steel wire multi-axial corrosion fatigue crack propagation rate model is that: A stress intensity correction model considering the stress concentration of the wear notch is established, and the stress intensity is corrected based on the depth of the wear notch and the maximum stress concentration coefficient under uniaxial tensile stress conditions; application of the stress intensity correction model to the calculation of mode I stress intensity K I and mode II stress intensity K II ​ Based on the ratio of the shear fatigue limit of the material to the uniaxial fatigue limit, the ductile material and the brittle material are distinguished, and the corresponding fatigue characteristic parameters and equivalent coefficients are calculated; Based on the critical plane method, combined with the K I , K II , fatigue characteristic parameters and equivalent coefficients, the multi-axial equivalent stress intensity under the action of tensile-shear-material characteristics is calculated K mix ; The multiaxial equivalent stress intensity K mix Substituting the crack propagation rate model, the multiaxial corrosion fatigue crack propagation rate model of the steel wire is obtained: ； wherein, C , m is a material parameter determined from the fatigue crack growth rate curve of the material under different corrosion environments; l is the crack length, N is the number of load cycles, denotes the increment of the multiaxial equivalent stress intensity, Δ The specific method for establishing the stress intensity correction model considering the stress concentration of the wear notch is that: th denotes the fatigue crack propagation threshold value.

5. The method of claim 4, wherein, The specific method for distinguishing the ductile material and the brittle material based on the ratio of the shear fatigue limit of the material to the uniaxial fatigue limit, and calculating the corresponding fatigue characteristic parameters and equivalent coefficients is that: The stress intensity factor formula of the stress concentration of the notch under the uniaxial tensile stress condition is obtained by using the progressive interpolation method : ； wherein is a geometric correction factor for the crack, is a nominal stress amplitude, is a crack length, is a depth of the wear notch, is a maximum stress concentration factor for the wear notch; The computational formula is applied to compute the mode I stress intensity driven by tensile stress K I and mode II stress intensity driven by shear stress K II so that the effect of wear notch stress concentration is introduced into the multiaxial stress intensity computation.

6. The method of claim 4, wherein, The material attribute parameter z is calculated: The specific calculation method of the step 3 for predicting the fretting corrosion fatigue life of the steel wire is that: ； wherein is the shear fatigue limit of the material, is the uniaxial fatigue limit of the material; When z≤1, it is determined as a ductile material, and a characteristic angle γ and a fatigue characteristic parameter are calculated and an equivalent coefficient B : ； ； ； When z > 1, it is determined as a brittle material, and a characteristic angle γ and a fatigue characteristic parameter are calculated and an equivalent coefficient B : ； ； 。 7. The method of claim 1, wherein, The specific calculation method of the step 3 for predicting the fretting corrosion fatigue life of the steel wire is that: Based on the fatigue crack growth threshold value ΔKth The specific calculation method of the step 3 for predicting the fretting corrosion fatigue life of the steel wire is that: th , the nominal stress amplitude Δσ ​ and the crack geometry correction factor Kc Y , the equivalent initial crack length a0 is calculated as l 0; In the competition analysis of crack and wear, when the step-by-step analysis is carried out n , the corresponding total load cycle number is N t = n · N , N represents the load cycle number, and the load cycle number at the moment when the crack propagation rate first exceeds the wear rate is N t denoted as the fretting corrosion wear dominant life of the steel wire N 1; By integrating the multi-axial corrosion fatigue crack propagation rate model, the corrosion fatigue crack propagation life of the steel wire is calculated N 2: ； wherein l e is the critical crack length for wire breakage, said critical crack length l e is calculated based on the material fracture toughness K e and the critical stress intensity The fretting corrosion wear dominant life N 1 is added to the corrosion fatigue crack propagation life N 2 to obtain the total fretting corrosion fatigue life of the steel wire N 总 : 。 8. A bridge boom wire fretting corrosion fatigue life prediction system, characterized by, ​ The steel wire fretting corrosion wear calculation module is configured to obtain geometric parameters, material mechanical property parameters, fretting contact parameters and corrosion environment parameters of the steel wire, and based on Hertz contact theory, in combination with a contact angle between the steel wires and stress non-uniform distribution caused by a wear notch, to establish a step-by-step iterative analysis model of fretting corrosion wear depth of the steel wire, and to calculate a fretting corrosion wear rate of each analysis step based on the step-by-step iterative analysis model; The steel wire crack propagation calculation module is configured to establish a stress intensity correction model taking into account stress concentration of the wear notch based on fracture mechanics theory, and in combination with a tensile-shear multi-axial stress state of the steel wire during service, to construct a multi-axial stress intensity model, and further to obtain a multi-axial corrosion fatigue crack propagation rate model of the steel wire, and to calculate a crack propagation rate of each analysis step based on the multi-axial corrosion fatigue crack propagation rate model; The steel wire fretting corrosion fatigue life calculation module is configured to calculate an equivalent initial crack length, to carry out a competition analysis of cracks and wear of the steel wire by iteratively comparing the fretting corrosion wear rate and the crack propagation rate at each analysis step, to divide a fretting corrosion wear dominant stage and a multi-axial corrosion fatigue dominant stage based on a time when the crack propagation rate first exceeds the fretting corrosion wear rate, to calculate and output a life of the fretting corrosion wear dominant stage and a life of the multi-axial corrosion fatigue dominant stage, and to sum the lives of the two stages to obtain and output a total fretting corrosion fatigue life of the steel wire.

9. An electronic device, comprising: The readable storage medium stores programs or instructions, which are executed by the processor to implement the steps of the bridge suspender steel wire fretting corrosion fatigue life prediction method according to any one of claims 1-7.

10. A readable storage medium, characterized by, The readable storage medium stores programs or instructions, which are executed by the processor to implement the steps of the bridge suspender steel wire fretting corrosion fatigue life prediction method according to any one of claims 1-7.

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