Bridge suspender steel wire micro-corrosion fatigue life prediction method and system

Abstract

The application belongs to the technical field of bridge structure safety, and discloses a bridge suspender steel wire fretting corrosion fatigue life prediction method and system, which comprises the following steps: obtaining steel wire initial parameters, establishing a steel wire fretting corrosion wear model through step-by-step iterative calculation based on Hertz contact theory and considering the stress non-uniform distribution and contact angle of the steel wire, and outputting the fretting corrosion wear depth and fretting corrosion wear rate of each analysis step; analyzing the wear notch stress concentration and multi-axial stress state of the steel wire based on the fracture mechanics theory, constructing a steel wire multi-axial corrosion fatigue crack propagation rate model, and outputting the crack propagation rate; adopting an equivalent initial crack method, comparing the fretting corrosion wear rate with the crack propagation rate through period-by-period iteration, carrying out a competition analysis of cracks and wear, dividing a fretting corrosion wear dominant stage and a multi-axial corrosion fatigue dominant stage, respectively solving the life of the two stages, and summing up the two stages to obtain 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 crack are a dynamic process of interaction and competition. In the early stage of degradation, the wear rate may be high, and the initial small cracks can be "worn off", at this time wear is the dominant damage mechanism; with the progress of wear, the contact geometry changes, the contact stress decreases, and the wear rate slows down, while the notch formed by wear causes stress concentration, inducing and accelerating crack propagation, making crack propagation gradually become the dominant damage mechanism. The existing technology fails to establish a theoretical model that can describe this competitive relationship, resulting in an inability to accurately predict the life of the hanger wire under the coupling effect of fatigue, corrosion, and fretting wear.

[0006] Therefore, there is an urgent need to propose a life prediction method that can integrate the contact wear, environmental corrosion, and multi-axial fatigue of bridge hanger wires during service, and scientifically describe the competition and evolution process of wear and crack, to solve the deficiencies of the existing technology and provide theoretical support for accurate and safe evaluation and scientific operation decision of bridge hanger wires. SUMMARY

[0007] The present application provides a bridge hanger wire fretting corrosion fatigue life prediction method and system, aiming to provide a bridge hanger wire fretting corrosion fatigue life prediction method that can couple contact wear, environmental corrosion, and multi-axial fatigue effects, and consider the competition mechanism of wear and crack.

[0008] In a first aspect, the present application provides a bridge hanger wire fretting corrosion fatigue life prediction method, comprising the following steps:

[0009] Step 1, establishing a wire fretting corrosion wear model: obtaining the geometric parameters, material mechanical property parameters, fretting contact parameters, and corrosion environment parameters of the wire, based on the Hertz contact theory, combining the contact angle between the wires and the stress non-uniform distribution caused by the wear notch, establishing a step-by-step iterative analysis model of the wire fretting corrosion wear depth, and calculating the fretting corrosion wear rate of each analysis step based on the step-by-step iterative analysis model;

[0010] Step 2, constructing a wire multi-axial corrosion fatigue crack propagation rate model: based on the theory of fracture mechanics, 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 wire during service, constructing a multi-axial stress intensity model, and then obtaining a multi-axial corrosion fatigue crack propagation rate model of the wire, and calculating the crack propagation rate of each analysis step based on the multi-axial corrosion fatigue crack propagation rate model;

[0011] 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 of each analysis step, carrying out a competition analysis of crack and wear of the steel wire, and dividing a fretting corrosion wear dominant stage and a multi-axial corrosion fatigue dominant stage, with the time when the crack propagation rate first exceeds the fretting corrosion wear rate as the boundary; calculating and outputting the life of the fretting corrosion wear dominant stage, and the life of the multi-axial corrosion fatigue dominant stage, summing the lives of the two stages to obtain and output the total fretting corrosion fatigue life of the steel wire.

[0012] As an optional implementation form of the first aspect of the application, the specific calculation method of step 1 for establishing the fretting corrosion wear model of the steel wire comprises: obtaining the wear volume based on the Hertz contact theory and the relationship between the normal load , the slip distance , the Brinell hardness of the material and the wear coefficient : ; performing differential calculation on the wear volume , and introducing the wear contact area of the steel wire to obtain the calculation formula of the wear depth increment of the steel wire: ; and further obtaining the calculation model of the wear depth of the steel wire; based on the calculation model of the wear depth of the steel wire, combining the contact angle β between the steel wires, and by modifying the wear contact area , the wear depth calculation model considering the contact angle modification of the steel wire is obtained; based on the wear depth calculation model considering the contact angle modification, the stress distribution coefficient K tti determined by the wear notch geometry is further introduced to obtain the wear depth calculation model of the steel wire considering the contact angle and the non-uniform distribution of stress; a step-by-step iterative calculation method is adopted, and the preset cycle number is taken as the analysis step, the wear depth, the contact area and the stress distribution coefficient of the steel wire are updated in each analysis step, the wear depth increment of the current analysis step is calculated, and the wear depth increment is converted into the wear rate.

[0013] As an optional implementation form of the first aspect of the application, the wear depth calculation model considering the contact angle modification of the steel wire has the specific calculation method that: the contact area of two mutually perpendicular steel wires is calculated; according to the included angle β between the axes of the two steel wires, the contact area of the steel wire considering the contact angle modification is calculated: ; the modified 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: .

[0014] 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.

[0015] 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.

[0016] 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 : ; ; .

[0017] 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 of crack and wear, when n the total load cycle number is N t = n · N , N represents the load cycle number, and when the crack propagation rate first exceeds the wear rate, the load cycle number at this moment 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: ; in the formula, l e is the critical crack length of the steel wire fracture, and the 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 and the corrosion fatigue crack propagation life N 2 are added to obtain the fretting corrosion fatigue total life N 总 : .

[0018] In a second aspect, the embodiments of the present application provide a bridge suspender steel wire fretting corrosion fatigue life prediction system, comprising:

[0019] a steel wire fretting corrosion wear calculation module, configured to acquire geometric parameters, material mechanical property parameters, fretting contact parameters and corrosion environment parameters of the steel wire, based on the Hertz contact theory, combined with the contact angle between the steel wires and the stress non-uniform distribution caused by the wear notch, a step-by-step iterative analysis model of the steel wire fretting corrosion wear depth is established, and the fretting corrosion wear rate of each analysis step is calculated based on the step-by-step iterative analysis model;

[0020] a steel wire crack propagation calculation module, configured to establish a stress intensity correction model taking into account the stress concentration of the wear notch based on the fracture mechanics theory, and combined with the tensile-shear multi-axial stress state of the steel wire in service, a multi-axial stress intensity model is constructed, and then a multi-axial corrosion fatigue crack propagation rate model of the steel wire is obtained, and the crack propagation rate of each analysis step is calculated based on the multi-axial corrosion fatigue crack propagation rate model;

[0021] The steel wire fretting corrosion fatigue life calculation module is used for calculating an equivalent initial crack length, carrying out a competition analysis of a crack and wear of a steel wire by iteratively comparing a fretting corrosion wear rate and a crack propagation rate through each analysis step, dividing a fretting corrosion wear dominant stage and a multi-axial corrosion fatigue dominant stage by taking a moment when the crack propagation rate first exceeds the fretting corrosion wear rate as a boundary, calculating and outputting a life of the fretting corrosion wear dominant stage, and a life of the multi-axial corrosion fatigue dominant stage, summing the lives of the two stages to obtain and output a total fretting corrosion fatigue life of the steel wire.

[0022] In a third aspect, an electronic device is provided, which includes a processor, a memory, and a program or instructions stored in the memory and executable on the processor, and the program or instructions, when executed by the processor, implement the steps of the method of the first aspect.

[0023] In a fourth aspect, a readable storage medium is provided, which stores a program or instructions, and the program or instructions, when executed by a processor, implement the steps of the method of the first aspect.

[0024] Compared with the prior art, the present application has the following beneficial effects:

[0025] 1. Multi-factor coupling, more accurate prediction: the present application couples and analyzes multiple source factors such as contact wear, environmental corrosion, and multi-axial fatigue of the bridge suspender steel wire during service, constructs a damage evolution model closer to engineering practice, and improves the accuracy of life prediction.

[0026] 2. Innovative competition mechanism, clear physical meaning: an innovative competition analysis mechanism of wear and crack is proposed, the entire fatigue life of the steel wire is divided into two stages of wear dominant and crack propagation dominant, the transition process of the damage mechanism is clearly described, and the physical meaning is clear.

[0027] 3. Strong model applicability, comprehensive consideration of working conditions: the wear model of the present application considers the contact angle of the steel wire of the steel strand, the semi-parallel wire bundle and other different forms of suspender, and the stress non-uniform distribution caused by the wear notch; the crack propagation model considers the stress concentration of the wear notch and the tensile-shear multi-axial stress state, and the model has stronger applicability.

[0028] 4. Simplified calculation, taking into account accuracy and efficiency: the equivalent initial crack method is adopted to equivalent the complex crack initiation and short crack propagation stage to an initial crack, which simplifies the analysis process, significantly improves the calculation efficiency on the premise of ensuring the prediction accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1is a flow chart of a bridge suspender steel wire fretting corrosion fatigue life prediction method according to an embodiment of the present application;

[0030] Figure 2 is a competition analysis schematic diagram of fretting corrosion wear and multi-axial corrosion fatigue cracks of a steel wire according to an embodiment of the present application;

[0031] Figure 3 is a structural schematic diagram of a bridge suspender steel wire fretting corrosion fatigue life prediction system according to an embodiment of the present application. DETAILED DESCRIPTION

[0032] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0033] The terms "first", "second", and the like in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described herein. In addition, "and / or" in the specification and claims indicates at least one of the connected objects, and the character " / ", generally indicates that the front and rear associated objects are in a "or" relationship. In the description of the present application, the meaning of "multiple" is two or more, unless otherwise explicitly specified.

[0034] Embodiment 1

[0035] Please refer to Figure 1 is a flow chart of a bridge suspender steel wire fretting corrosion fatigue life prediction method according to an embodiment of the present application. The method can include the following steps:

[0036] Step 1, establishing a steel wire fretting corrosion wear model: obtaining the 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.

[0037] (1-1) Initial conditions and basic mechanical model

[0038] According to the Hertz contact theory, the surface of the material can be assumed to be composed of a large number of semi-spherical micro-convex bodies, and material wear occurs at the top of the semi-spherical micro-convex bodies. When the stress of the cross section of the semi-spherical micro-convex body reaches the yield limit of the material, the micro-convex body will wear off, and the mathematical expression is:

[0039]

[0040] In the formula, F is the normal force; n is the number of semi-spherical micro-convex bodies; r is the radius of the semi-spherical micro-convex body; s x is the yield strength of the material.

[0041] During the friction process, the displacement of the material sliding friction is proportional to the size of the radius of the semi-spherical micro-convex body. When the sliding distance is S , the number of worn micro-convex bodies is S / 2 r times the number of single convex sphere wear:

[0042]

[0043] In the formula, V s is the wear volume when the sliding distance S ; S is the sliding distance; V is the volume of a single semi-spherical micro-convex body, and the calculation formula is:

[0044]

[0045] Combining formula (3) and formula (2), we get:

[0046]

[0047] Combining formula (1) and formula (4), we get the wear amount V s and the normal load F . In addition, in order to eliminate the interference of external experimental conditions and realize the quantitative description of the inherent wear characteristics of the material, the wear coefficient k is introduced in the formula to represent the wear behavior under different wear mechanisms, and the calculation formula is as follows:

[0048]

[0049] In the formula, the wear coefficient k is related to the material and the environment, and the contact friction performance of the material under different corrosion environments can be measured and quantified. The wear coefficient kThe influence of corrosion environment on the contact friction performance of steel wire is considered.

[0050] In addition to the yield strength of the material, the Brinell hardness of the material can also characterize the wear resistance of the material. The yield strength of the material s x The Brinell hardness of the material H There is a relationship as follows:

[0051]

[0052] In the formula, the Brinell hardness of the material H Determined from the standard GB / T 1172-1999 "Black metal hardness and strength conversion value".

[0053] Combined with formula (5) and formula (6), the wear volume of the steel wire is obtained as follows: V s Relationship with mechanical parameters:

[0054]

[0055] The wear depth is a key indicator for evaluating the wear amount of the material. The wear depth of the steel wire is calculated by differentiating formula (7) as follows:

[0056]

[0057]

[0058]

[0059] In the formula, A is the wear contact area of the steel wire; The wear depth of the steel wire is calculated by integrating formula (10) as follows:

[0060]

[0061] Fretting fatigue can cause wear of the surface material of the steel wire, forming an approximately elliptical wear trace, and the calculation formula of the contact area of the steel wire is as follows:

[0062]

[0063] (1-2) Considering the correction model of fretting corrosion wear depth of steel wire contact angle

[0064] The above model (formula (11)) is suitable for calculating the fretting corrosion wear depth of two steel wires in a mutual vertical contact state, but the contact conditions of the bridge suspender steel wires in actual engineering are relatively complex, and different contact angles exist, such as steel strand and semi-parallel steel wire bundle. At present, there is no reference for the wear depth calculation model under different contact angles.

[0065] In order to more accurately calculate the actual wear condition of the bridge steel wire, the above model (formula (11)) is expanded into a wear depth correction calculation model that can consider different contact angles between the steel wires. The change of the contact angle of the steel wire directly affects the size of the contact ellipse area, the contact surface of two vertical steel wires is in an elliptical shape, and as the contact angle decreases, the contact area correspondingly increases, thereby causing the contact stress to decrease and the wear rate to decrease.

[0066] Under the same wear depth, for two steel wires with a contact angle of β The contact area of the two steel wires can be expressed as:

[0067]

[0068] wherein, β is the included angle between the axes of the two steel wires; A is the contact area of the two mutually perpendicular steel wires; A w is the contact area of the two mutually perpendicular steel wires; and

[0069] The fretting corrosion wear depth calculation model considering the correction of the contact angle of the steel wire is as follows:

[0070]

[0071] (1-3) Fretting corrosion wear depth model considering both the contact angle of the steel wire and the non-uniform distribution of stress

[0072] Because there is significant stress concentration at the wear notch position of the steel wire, the fatigue crack of the steel wire is prone to initiation and propagation at the wear notch area, thereby accelerating the accumulation of fatigue damage of the steel wire and accelerating the fatigue fracture of the steel wire. Therefore, in order to analyze the crack initiation and propagation at the wear notch position, it is necessary to clearly understand the stress distribution around the wear notch.

[0073] In the actual contact process of the steel wire, the stress distribution of the contact surface is closely related to the geometric shape of the wear notch. The stress concentration factor calculation formula considering the length, width and depth of the wear notch is as follows:

[0074]

[0075] wherein,K ti is the stress concentration factor of the stress point; R s is the ratio of the short axis to the long axis of the wear notch; R d is the ratio of the depth to the long semi-axis of the wear notch; f R s is the correlation coefficient. f , R s and R d The calculation formula is as follows:

[0076]

[0077]

[0078]

[0079] wherein, is the wear depth; b is the short semi-axis of the wear notch; c is the long semi-axis of the wear notch;

[0080] is the stress distribution coefficient of the stress point, which is obtained by normalizing the stress concentration factor of the stress point considering the influence of the stress distribution of the wire wear notch on the growth of the wire wear notch: K tti

[0081]

[0082] wherein, K tmax is the maximum value of the stress concentration factor of the wear notch.

[0083] Combined with formula (14) and formula (19), the wire fretting corrosion wear depth calculation formula considering the contact angle and stress distribution non-uniformity is obtained:

[0084]

[0085] (1-4) Wire fretting corrosion wear depth and fretting corrosion wear rate step-by-step iterative analysis model

[0086] Formula (20) represents the depth of each point in the wire wear notch when the slip distance is S The wire fretting corrosion wear displacement amplitude is s and experiences a complete fretting corrosion wear cycle (i.e. N =1), and the wear depth calculation can be expressed as: ​​

[0087]

[0088] 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:

[0089]

[0090]

[0091] 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.

[0092] 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.

[0093] (2-1) Stress intensity correction model considering the stress concentration effect of wear notch

[0094] 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:

[0095]

[0096] 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.

[0097] Based on the formula (24), the stress intensity Δ under the uniaxial tensile stress condition considering the stress concentration of the wear notch can be obtained by using the progressive interpolation method K n The calculation formula is as follows:

[0098]

[0099] In the formula, K tmax is the maximum stress concentration coefficient of the wear notch, is the depth of the wear notch.

[0100] (2-2) Multiaxial stress intensity model considering the influence of wear notch stress concentration

[0101] During the service of the bridge suspender wire, the suspender is subjected to the coupling effect of axial tension and transverse vibration, and is in a tensile-shear multiaxial stress state, and the crack propagation contains both mode I (tension stress driven crack propagation) and mode II (shear stress driven crack propagation). The existing suspender wire fatigue crack analysis mainly considers mode I crack, ignores the accelerating effect of shear stress and wear notch stress concentration on crack propagation, which will lead to conservative life prediction results. Based on fracture mechanics, this section considers the stress concentration effect caused by wire wear notch, and develops a multiaxial stress intensity model of wire.

[0102] Based on formula (25), the stress intensity Δ considering the stress concentration of the wear notch and driven by tensile stress K I The calculation formula is as follows:

[0103]

[0104] The stress intensity Δ considering the stress concentration of the wear notch and driven by shear stress K II The calculation formula is as follows:

[0105]

[0106] Formula (26) and formula (27) consider the influence of wire fretting corrosion wear notch stress concentration on wire multiaxial stress intensity.

[0107] Crack propagation is closely related to material properties. The crack propagation direction, rate and failure mechanism of ductile materials and brittle materials under multiaxial stress are completely different. By introducing the material property parameter z The calculation formula is as follows:

[0108]

[0109] In the formula, t-1 This refers to the material's shear fatigue limit. f -1 This represents the uniaxial fatigue limit of the material.

[0110] 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. g Quantifying the anisotropy of crack propagation. Characteristic angle. g 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. g The formula for calculation is:

[0111]

[0112] 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:

[0113]

[0114]

[0115] 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... g The calculation formula is:

[0116]

[0117] 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:

[0118]

[0119]

[0120] Based on the critical plane method, the multiaxial stress intensity under tension-shear-material property action is calculated as follows:

[0121]

[0122] where, K 1 ，K 2and K H is a load parameter with the same dimension as stress intensity; t is the maximum normal stress amplitude plane orientation at far field. Equation (35) considers the effect of multi-axial stress intensity on the fatigue crack growth behavior of steel wire.

[0123] K 1 、K 2, K H , t The calculation equations are as follows, respectively:

[0124]

[0125]

[0126]

[0127]

[0128] (2-3) Multi-axial corrosion fatigue crack growth rate model of steel wire

[0129] Combining the classic crack growth rate model and equation (35), the multi-axial corrosion fatigue rate model d l / d N of steel wire can be expressed as follows:

[0130]

[0131] where, C , m is a material parameter, represents the increment of multi-axial equivalent stress intensity, Δ K th represents the fatigue crack growth threshold value, which is determined according to the fitting of the material fatigue crack rate curve under different corrosion environments, that is, the effect of corrosion environment on the fatigue crack growth behavior of steel wire is considered.

[0132] 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.

[0133] (3-1) Equivalent initial crack method and competition analysis between wear and crack

[0134] 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.

[0135] Equivalent initial crack length l The calculation formula for 0 is as follows:

[0136]

[0137] In the formula, Δ K th 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.

[0138] 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.

[0139] With step size N Taking 100 cycles as an example, the competitive discrimination formula for steel wire cracking and wear is as follows:

[0140]

[0141] In the formula, For wear rate, dl / d N The crack propagation rate is da / dt. When the wear rate is greater than the crack propagation rate, wear is dominant, and when the wear rate is less than the crack propagation rate, crack propagation is dominant.

[0142] (3-2) Prediction of fretting corrosion fatigue life of steel wire

[0143] In the above gradual analysis of the competition between cracks and wear of the steel wire, when the number of load cycles experienced by the steel wire is n times of gradual analysis (i.e. N t = n · N and the crack growth rate just exceeds the wear rate, the number of load cycles experienced by the steel wire at this time is N t , which is the life value of the fretting corrosion wear dominant of the steel wire N 1.

[0144] When the crack growth rate of the steel wire exceeds the wear rate, the corrosion fatigue crack propagation life of the steel wire N 2 can be calculated as follows:

[0145]

[0146] In the formula, l 0 is the equivalent initial crack length; l e is the critical crack length of the steel wire fracture, and its calculation formula is as follows:

[0147]

[0148]

[0149] In the formula, K e is the material fracture toughness, which represents the performance of the material to resist crack unstable propagation.

[0150] In summary, the fretting corrosion fatigue life of the steel wire N 总 is the sum of the lives of the two stages of wear and crack propagation, that is,

[0151]

[0152] Example 2

[0153] Please refer to Figure 3 , which shows the structure of a bridge boom steel wire fretting corrosion fatigue life prediction system according to the second embodiment of the present application. The system includes the following key modules:

[0154] The steel wire fretting corrosion wear calculation module 100 is configured to acquire geometric parameters, material mechanical property parameters, fretting contact parameters and corrosion environment parameters of the steel wire, establish a step-by-step iterative analysis model of the fretting corrosion wear depth of the steel wire based on the Hertz contact theory, in combination with a contact angle between the steel wires and stress non-uniform distribution caused by the wear notch, and calculate a fretting corrosion wear rate of each analysis step based on the step-by-step iterative analysis model;

[0155] The steel wire crack propagation calculation module 200 is configured to establish a stress intensity correction model taking into account stress concentration of the wear notch based on the fracture mechanics theory, construct a multi-axial stress intensity model in combination with a tensile-shearing multi-axial stress state of the steel wire during service, further obtain a multi-axial corrosion fatigue crack propagation rate model of the steel wire, and calculate a crack propagation rate of each analysis step based on the multi-axial corrosion fatigue crack propagation rate model.

[0156] The steel wire fretting corrosion fatigue life calculation module 300 is configured to calculate an equivalent initial crack length, carry out a competition analysis of the crack and the wear of the steel wire by iteratively comparing the fretting corrosion wear rate and the crack propagation rate step by step, 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, calculate and output a life of the fretting corrosion wear dominant stage and a life of the multi-axial corrosion fatigue dominant stage, sum the lives of the two stages to obtain and output a total fretting corrosion fatigue life of the steel wire.

[0157] The bridge suspender steel wire fretting corrosion fatigue life prediction system in the embodiment of the present application can be a device, or a component, an integrated circuit or a chip in a terminal. The device can be a mobile electronic device, or a non-mobile electronic device. Exemplarily, the mobile electronic device can be a mobile phone, a tablet computer, a notebook computer, a palm computer, a vehicle-mounted electronic device, a wearable device, an Ultra-mobile Personal Computer (UMPC), a netbook or a Personal Digital Assistant (PDA), etc., and the non-mobile electronic device can be a server, a Network Attached Storage (NAS), a Personal Computer (PC), etc., and the embodiment of the present application is not limited in this regard.

[0158] The bridge suspender steel wire fretting corrosion fatigue life prediction system in the embodiment of the present application can be a device with an operating system. The operating system can be an Android operating system, an IOS operating system or other possible operating systems, and the embodiment of the present application is not limited in this regard.

[0159] The bridge suspender steel wire fretting corrosion fatigue life prediction system provided by the embodiment of the application can realize Figure 1 The processes of the bridge suspender steel wire fretting corrosion fatigue life prediction method in the method embodiment are not repeated here.

[0160] Optionally, the embodiment of the application further provides an electronic device, including a processor, a memory, a program or instructions stored on the memory and executable on the processor, which realizes the processes of the above-mentioned bridge suspender steel wire fretting corrosion fatigue life prediction method embodiment and achieves the same technical effects when executed by the processor, and the same technical effects are not repeated here.

[0161] The embodiment of the application further provides a readable storage medium, which stores a program or instructions, which realizes the processes of the above-mentioned bridge suspender steel wire fretting corrosion fatigue life prediction method embodiment and achieves the same technical effects when executed by the processor, and the same technical effects are not repeated here.

[0162] The processor is the processor in the electronic device in the above-mentioned embodiment. The readable storage medium includes a computer readable storage medium, such as a computer read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, etc.

[0163] It should be noted that in this document, the terms "comprising", "including", or any other variant thereof are intended to cover non-exclusive inclusions, so that processes, methods, articles or devices including a series of elements not only include those elements, but also include other elements not explicitly listed, or include elements inherent to such processes, methods, articles or devices. Without more limitations, the element defined by the statement "including a" does not exclude the presence of other identical elements in the process, method, article or device including the element. In addition, it should be pointed out that the scope of the methods and devices in the embodiments of the application is not limited to the order of functions shown or discussed, but can also include functions performed in a substantially simultaneous manner or in the opposite order, for example, the described method can be performed in an order different from that described, and various steps can also be added, omitted or combined. In addition, the features described with reference to certain examples can be combined in other examples.

[0164] Those skilled in the art can clearly understand the above-mentioned embodiment method can be realized by means of software and the necessary general hardware platform, of course, also can be through hardware, but many cases the former is the better embodiment. Based on such understanding, the technical solutions of the present application essentially or say the part of the contribution to the prior art can be embodied in the form of software products, the computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disc), including a number of instructions to make a terminal (may be a mobile phone, computer, server, air conditioner, or network equipment, etc.) executes the method described in various embodiments of the present application.

[0165] The embodiments of the present application are described above in combination with the drawings, but the present application is not limited to the above-mentioned specific embodiments, the above-mentioned specific embodiments are only illustrative, but not limited, those skilled in the art can make many forms without departing from the purpose of the present application and the scope protected by the claims under the inspiration of the present application, all belong to the protection of the present 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 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.

9. An electronic device, comprising: It 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 for predicting the fatigue life of fretting corrosion of bridge suspender steel wire as described in any one of claims 1-7.

10. A readable storage medium, characterized by, The readable storage medium stores a program or instructions, which, when executed by a processor, implement the steps of the method for predicting the fatigue life of bridge suspender steel wire fretting corrosion as described in any one of claims 1-7.

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