Prediction method for microcrack propagation rate of underground engineering component considering surface modification

Abstract

The application discloses a kind of underground engineering component micro crack propagation rate prediction method considering surface modification, it is related to underground mine structure health monitoring, fracture mechanics evaluation technical field.The method introduces surface elastic model, constructs the surface modification characteristic length of including residual compressive stress strengthening factor and roughness weakening factor ， Calibration critical characteristic length, according to the size relationship of both, automatically determine micro crack to be surface opening type or subsurface shear type;Combined with the basic solution of modified contact stress and micro coupling equivalent stress amplitude, the crack propagation rate and residual fatigue life are calculated.The present application eliminates the traditional contact stress singularity, realizes the accurate prediction of micro crack propagation rate, crack development trend and residual fatigue life of underground component with surface modification layer, and is suitable for health monitoring and protection of key load-bearing components such as deep mine anchor rod, segment bolt, etc., which can provide a theoretical basis for component surface modification process optimization and micro damage prevention and control.

Description

Technical Field

[0001] This invention relates to the fields of underground mine structural health monitoring, fracture mechanics assessment, and surface modification mechanical analysis. Specifically, it relates to a method for predicting the fretting crack propagation rate of underground engineering components considering surface modification, and further to a method for quantitatively predicting the fretting crack propagation rate and remaining life of underground engineering components with surface modification layers by combining the fundamental solution of surface elasticity, fretting contact theory, and fatigue fracture theory. Background Technology

[0002] Prefabricated components and connection nodes in underground engineering projects such as tunnels, integrated utility tunnels, mine roadways, and deep foundation pits are subjected to complex loads over long periods, including surrounding rock creep, alternating ground pressure, construction blasting, and traffic vibrations. Under the coupled action of concentrated normal force, interfacial shear force, and alternating ground stress, the contact surfaces of these components undergo micron-level reciprocating slippage, resulting in a typical fretting phenomenon. During this fretting process, microcracks are prone to initiation at the contact edge areas; under the synergistic corrosive effects of groundwater and corrosive ions, these cracks continue to propagate, potentially leading to major safety accidents such as component cracking, structural leakage, or even support instability. To improve the wear resistance, slip resistance, and fatigue resistance of the component contact surfaces, surface modification treatment technologies are commonly used in engineering, such as surface rolling strengthening, modified coating spraying, carburizing treatment, and sandblasting hardening, forming a modified layer on the component surface with mechanical properties different from the substrate. The modified layer possesses relatively independent surface elasticity and surface stiffness, which can significantly alter the surface stress distribution under concentrated force, eliminate stress singularities in traditional elastic solutions, and thus affect interfacial shear stress, fretting slip amplitude, and the initiation and propagation behavior of fretting cracks.

[0003] However, existing fretting crack prediction technologies for underground engineering still have the following shortcomings: First, existing calculation models for the characteristic length of surface modification only introduce the single parameter of the shear modulus of the modified layer and the matrix, without considering the strengthening effect of residual compressive stress on the surface introduced by the plastic deformation of the rolling process, and ignoring the weakening effect of local stress concentration caused by the surface roughness of the fretting contact interface; a single elastic parameter cannot characterize the coupling effect of multiple factors such as rolling strengthening, rough fretting contact, and interface shear stiffness. The modified characteristic length calculated by this model deviates significantly from the actual fretting crack propagation behavior of underground engineering components, resulting in low accuracy in crack propagation rate prediction. Second, the traditional Flamant plane concentrated force fundamental solution does not consider the surface elastic effect of the surface modification layer, resulting in stress singularity. This causes the calculated contact stress and shear stress to deviate from the actual stress state of the component, affecting the accuracy of subsequent crack prediction. Third, existing fretting crack prediction models are mostly based only on the mechanical parameters of the matrix material, without establishing a quantitative coupling relationship between surface modification parameters, contact stress, fretting slip, and crack propagation, making them unsuitable for engineering components with modified surfaces. Fourth, existing methods rely heavily on empirical values ​​and conventional fatigue models, resulting in low prediction accuracy and difficulty in effectively guiding the optimization of surface modification processes and structural operation and maintenance decisions.

[0004] In view of this, it is urgent to combine the Gurtin-Murdoch surface elasticity theory, the fundamental solution of the concentrated force of planar surface modification, the micro-dynamic model and the fatigue crack propagation theory to construct a micro-motion crack prediction method applicable to underground components with surface modification layers. This method has important theoretical value and engineering application prospects. Summary of the Invention

[0005] In view of the technical problems existing in the background art, the present invention provides a method for predicting the fretting crack propagation rate of underground engineering components considering surface modification. It introduces the basic solution of the concentrated force of planar surface modification to correct the contact stress field, and establishes a full-chain quantitative calculation model of surface modification parameters, interface contact stress, fretting slip amplitude, equivalent stress amplitude and crack propagation rate. This enables accurate prediction of the fretting crack propagation rate, crack development trend and remaining fatigue life of underground components with surface modification layers. At the same time, it can provide a theoretical basis for optimizing the surface modification process parameters of components and preventing fretting damage. It is applicable to the health monitoring and protection of key load-bearing components such as anchor bolts and segment bolts in deep mines.

[0006] In a first aspect, embodiments of the present invention provide a method for predicting the propagation rate of microcracks in underground engineering components considering surface modification, comprising the following steps: S1. Parameter Acquisition and Calibration: On-site measurement of working parameters, correction and calibration of mechanical parameters of the matrix and surface modification layer, and calibration of interface and fatigue parameters are carried out on the underground engineering micro-motion-prone components after surface modification treatment; and the surface modification characteristic length and critical surface modification characteristic length are calculated based on the mechanical parameters. S2. Solution of contact stress field: Based on the mechanical model of the surface modified layer, the fundamental solution of the plane surface modified concentrated force is used to calculate the normal stress and polar coordinate radial stress of the component contact surface, and obtain the true contact stress distribution under the action of the modified layer. S3. Calculation of interface micro-motion parameters: The interface friction force is calculated by combining the normal stress of the contact surface with the friction model, the average shear stress of the interface is solved, and the interface micro-motion slip amplitude is calculated according to the slip theory. S4. Determination of fretting crack initiation mode: Compare the surface modification characteristic length with the critical surface modification characteristic length to determine the initiation location and cracking mode of fretting cracks, and select the corresponding fretting fatigue constant; S5. Calculation of micro-motion coupled mechanical parameters: Couple the far-field alternating ground stress with the interface shear stress to obtain the comprehensive equivalent stress amplitude. Combine the geometric shape correction coefficient and the instantaneous crack length to solve the stress intensity factor amplitude at the crack tip. S6. Crack propagation rate calculation: Substitute the stress intensity factor amplitude and the fretting fatigue constant of the corresponding mode into the Paris formula adapted to the fretting condition to calculate the crack propagation rate under the current load cycle. S7. Calculation of remaining fatigue life: Using the initial crack length as the lower limit of integration and the critical failure crack length as the upper limit of integration, the crack propagation rate is integrated to obtain the remaining fatigue life of the component. S8. Graded Early Warning and Output: Based on the crack propagation rate and / or remaining fatigue life, graded early warning is issued, differentiated treatment plans are formulated, and an evaluation report is output.

[0007] As a further improvement of the present invention, in step S4, when the surface modification characteristic length is less than or equal to the critical surface modification characteristic length, it is determined that the maximum shear stress is located on the surface of the component, and the crack is initiated in a surface opening mode, and the first set of fretting fatigue parameters is selected; when the surface modification characteristic length is greater than or equal to the critical surface modification characteristic length, it is determined that the maximum shear stress migrates to the subsurface of the component, and the crack is initiated in a subsurface shear mode, and the second set of fretting fatigue parameters is selected.

[0008] As a further improvement of the present invention, the calculation process of the surface modification characteristic length is as follows: Based on the ratio of the matrix shear modulus to the surface modification layer shear modulus, the ideal surface modification characteristic length is determined; a strengthening correction is introduced by the residual compressive stress in the surface layer to obtain the surface modification characteristic length after residual stress correction; a weakening correction is introduced by the surface roughness to obtain the final surface modification characteristic length; the calculation formula is as follows: ; in, β The characteristic length of surface modification. β 0 For the ideal surface modification feature length, sres This represents residual compressive stress on the surface. R q The root mean square roughness of the surface. k 1 The residual stress fitting coefficients are... k 2 The surface roughness fitting coefficient is... s s To provide force dimension parameters, l 0 This is a parameter with length dimensions.

[0009] As a further improvement of the present invention, the critical surface modification characteristic length is obtained by standard specimen fretting fatigue test. The calibration rules include: preparing multiple sets of standard specimens with only the surface modification intensity changed and the other parameters being the same; performing fretting fatigue loading on each set of specimens and observing the crack initiation position; fitting the surface modification characteristic length corresponding to the surface / subsurface transformation at the crack initiation position as the critical surface modification characteristic length.

[0010] As a further improvement to the present invention, it also includes: S9. Surface modification process reverse optimization: Preset the target remaining fatigue life of the component, reverse the calculation process of step S7, and solve the optimal value of the surface modification characteristic length required to meet the target life. Based on this, output the control range of the shear modulus or modification thickness of the surface modification layer as a quantitative basis for surface modification process optimization.

[0011] As a further improvement of the present invention, in step S1, the field working condition parameters include: the concentrated force of the contact surface normal of the component, the far-field alternating stress amplitude, the contact characteristic length, the actual contact area and the initial crack length, and the critical failure crack length is determined. Interface and fatigue parameters include: interface friction coefficient, fretting coupling correction coefficient, geometry correction coefficient, and fretting fatigue constant; The mechanical parameters of the matrix and the surface modified layer include: shear modulus of the component matrix, shear modulus of the surface modified layer, residual stress of the surface layer, root mean square roughness of the surface, residual stress influence coefficient and surface roughness influence coefficient.

[0012] As a further improvement of the present invention, in step S2, the mechanical model of the surface modification layer is the Gurtin–Murdoch surface elastic model, and the modified fundamental solution is the modified fundamental solution of the concentrated force on the surface of a planar semi-infinite body. In step S3, the friction model is the Coulomb friction model, and the slip theory is the elastic slip theory.

[0013] As a further improvement of the present invention, in step S5, the comprehensive equivalent stress amplitude is obtained by superimposing the far-field alternating geostress amplitude and the interface average shear stress corrected by the micro-motion coupling correction coefficient, and the calculation formula is as follows: ; in, The comprehensive equivalent stress amplitude is given by α, which is the micro-motion coupling correction coefficient, Δσ, which is the far-field alternating geostress amplitude, and τ, which is the average shear stress at the interface.

[0014] As a further improvement of the present invention, in step S8, the graded early warning includes: dividing the working state of the component into a safe zone, a warning zone and a dangerous zone according to the crack propagation rate and / or the remaining fatigue life; the differentiated treatment plan includes: maintaining routine monitoring in the safe zone, increasing the detection frequency and assessing the integrity of the surface modification layer in the warning zone, and immediately carrying out reinforcement, crack repair or interface retreatment in the dangerous zone.

[0015] Secondly, embodiments of the present invention provide a system for predicting the fretting crack propagation rate of underground engineering components considering surface modification, which is used to execute the above-mentioned method for predicting the fretting crack propagation rate of underground engineering components considering surface modification, including: The parameter acquisition and calibration module is used to acquire the geometric parameters, load parameters, material mechanical parameters, surface modification parameters, and fretting fatigue parameters of deep mine fretting-prone components that have undergone surface modification treatment, and to calculate the surface modification characteristic length and calibrate the critical surface modification characteristic length. The contact stress field solution module is used to calculate the normal stress and polar coordinate radial stress of the contact surface of the component based on the corrected fundamental solution of the surface modification concentrated force. The interface micro-motion parameter calculation module is used to calculate the interface friction force, the average interface shear stress, and the micro-motion slip amplitude based on the normal stress of the contact surface. The crack initiation mode determination module is used to compare the surface modification feature length with the critical surface modification feature length, determine the initiation location of fretting cracks, and select the corresponding fretting fatigue constant. The coupling calculation module is used to couple the far-field alternating ground stress with the micro-motion interface shear stress to obtain the comprehensive equivalent stress amplitude and calculate the stress intensity factor amplitude at the crack tip. The crack propagation and life calculation module is used to calculate the crack propagation rate based on the Paris formula and obtain the remaining fatigue life through integration. The graded early warning and output module is used to provide graded early warnings based on crack propagation rate and remaining fatigue life, and output an evaluation report. The process reverse optimization module is used to preset the target remaining fatigue life, reverse iteratively solve for the optimal value of the surface modification feature length required to meet the target life, and output the control range of the shear modulus or modification thickness of the surface modification layer.

[0016] Beneficial effects: Compared with the prior art, the present invention has the following technical advantages: 1. Coupled with two core process / interface parameters: residual compressive stress from rolling and surface roughness. A positive reinforcement correction term for residual stress and a negative weakening correction term for roughness are constructed to establish a multi-physical quantity coupled surface modification characteristic length calculation model. The model can completely degenerate into a traditional model considering only shear modulus, exhibiting strong compatibility. It comprehensively characterizes the effective influence range of the modified layer under the combined effects of interfacial shear stiffness, rolling residual compressive stress reinforcement, and roughness fretting stress concentration, significantly improving the prediction accuracy of fretting crack propagation rate in underground components.

[0017] 2. Improved calculation accuracy by correcting stress singularity: The introduction of the Gurtin-Murdoch surface elasticity model and the fundamental solution of the concentrated force of the surface modification solves the problem of stress singularity in the traditional Flamant solution, accurately characterizes the stress homogenization effect of the surface modification layer, and the stress field calculation results are in high agreement with the actual engineering.

[0018] 3. The model has complete coupling and is suitable for modified components: A quantitative model of the entire chain of surface modification parameters, contact stress, fretting slip and crack propagation is established, which is specifically designed for underground components with surface modifications such as rolling, coating and hardening, filling the gap in existing technology.

[0019] 4. Combining theory and engineering, with a wide range of applications: It can be applied to various underground engineering structures with surface modified layers, such as precast tunnel segments, connecting bolts, support anchors, steel arch frames, foundation pit steel supports, and integrated pipe gallery splicing components, and has strong versatility.

[0020] 5. Dual guidance value: It can not only accurately predict the propagation rate and remaining life of fretting cracks, but also optimize process parameters such as shear modulus and thickness of the surface modification layer in reverse, thereby suppressing the initiation of fretting cracks from the source.

[0021] 6. High scalability: It can be directly connected to the on-site sensor monitoring system to realize automatic parameter acquisition and online model calculation, and is compatible with intelligent underground engineering health monitoring platform.

[0022] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and in order to make the above and other objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention are described below. Attached Figure Description

[0023] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0024] Figure 1 This is a flowchart illustrating the method for predicting the microcrack propagation rate of underground engineering components considering surface modification, provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of a planar semi-infinite body surface modification layer subjected to concentrated force, provided in an embodiment of the present invention. Figure 3 This is a schematic diagram illustrating the coupling relationship between contact stress, fretting slip, and crack propagation in a surface-modified component provided in an embodiment of the present invention. Detailed Implementation

[0025] The embodiments of the technical solution of the present invention will now be described in detail with reference to the accompanying drawings. These embodiments are merely illustrative of the technical solution of the present invention and are therefore intended to limit the scope of protection of the present invention.

[0026] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the invention, are intended to cover non-exclusive inclusion.

[0027] In the description of the embodiments of this invention, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly specifying the number, specific order, or primary and secondary relationship of the indicated technical features. In the description of the embodiments of this invention, "multiple" means two or more, unless otherwise explicitly defined.

[0028] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0029] In the description of the embodiments of this invention, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this document generally indicates that the preceding and following related objects have an "or" relationship.

[0030] To address the technical problems of existing technologies that fail to consider the elastic effect of surface modification, exhibit singularities in stress calculations, and lack sufficient accuracy in predicting fretting cracks, this invention provides a method for predicting the fretting crack propagation rate of underground engineering components that considers the surface modification (effect). This method introduces a correction to the contact stress field using the fundamental solution of the concentrated force of the planar surface modification layer, establishing a quantitative calculation model for the entire chain of surface modification parameters, interfacial contact stress, fretting slip amplitude, equivalent stress amplitude, and crack propagation rate. This enables accurate prediction of the fretting crack propagation rate, crack development trend, and remaining fatigue life of underground components with surface modification layers. Simultaneously, it provides a theoretical basis for optimizing surface modification process parameters and controlling fretting damage.

[0031] This invention introduces the Gurtin–Murdoch surface elasticity theory into the micro-motion contact problem of macroscopic engineering components, constructing a fundamental solution for the concentrated force correction of surface modification on a planar semi-infinite body. This fundamentally eliminates the stress singularity of the traditional Flamant solution and accurately characterizes the stress homogenization effect of the surface modification layer. A dimensionless surface modification characteristic length is constructed, explicitly coupling the positive strengthening effect of residual compressive stress with the negative weakening effect of surface roughness. A critical threshold, the critical surface modification characteristic length, is introduced as a boundary criterion for crack initiation modes, enabling quantitative determination of surface-opening and subsurface shear-type initiation and adaptation of fracture mechanics parameters. A computational model is established, encompassing surface modification parameters, contact stress field, interface micro-motion parameters, crack initiation modes, coupled equivalent stress and stress intensity factor, crack propagation rate, and remaining life. Based on the target remaining life, the optimal surface modification characteristic length is solved through inverse iteration, outputting the range of process parameter control.

[0032] Please see Figure 1 As shown, this invention provides a method for predicting the fretting crack propagation rate of underground engineering components considering surface modification (effect). The method uses the Gurtin–Murdoch surface elasticity model to describe the mechanical behavior of the surface modification layer, and combines the fundamental solution of the concentrated force correction for a planar semi-infinite body surface, the Coulomb friction model, the fretting slip model, the coupled equivalent stress model, and the Paris fatigue crack propagation formula to construct an overall calculation system. The specific process is as follows: S1, Parameter Acquisition and Full Parameter Calibration For downhole components prone to fretting after surface modification treatment, parameter measurements and laboratory calibration were performed in three categories: S11, Actual measured parameters of on-site operating conditions Measured concentrated force along the normal line of the contact surface of the component Far-field alternating geostress amplitude Contact characteristic length Actual contact area The initial crack length on the component surface is measured using ultrasonic testing or microscopic observation. Determine the critical failure crack length according to the component design standards. .

[0033] S12, Correction and Calibration of Mechanical Parameters of Substrate and Surface Modification Layer The shear modulus of the component matrix material was determined through indoor testing and mechanical experiments. Shear modulus of surface modified layer Surface residual stress was obtained by X-ray diffraction residual stress testing. s res The root mean square roughness of the surface was obtained by white light interferometry. R q Fretting fatigue tests were conducted on control specimens with different rolling pressures and residual stress levels to obtain the residual stress fitting coefficients. k 1 By testing the modification depth using standard samples with different surface roughnesses, the surface roughness fitting coefficients were obtained. k 2 ; The final calculation of the surface modification feature length β .

[0034] Using standard specimens with the same matrix and surface modification process as the target component, comparative tests of gradient modification strength fretting fatigue were conducted to observe the critical point of crack initiation location transformation and to obtain the critical surface modification characteristic length through fitting and calibration. β r The parameters are stored in the parameter library for S4 crack mode determination.

[0035] The basic model is defined as follows: the computational model is a plane strain semi-infinite body. For the component base area, The interface of the modified layer on the component surface; a concentrated normal force acts at the origin of the interface. (N / m), Tangential Concentration (N / m); polar coordinates Rectangular coordinates Jointly describe the stress field.

[0036] Correction of surface modification characteristic parameters: Traditional ideals for characterizing the mechanical differences between the modified layer and the matrix; existing models define the modification characteristic length solely based on the ratio of the shear modulus of the modified layer to the matrix. ; In the formula: β 0 The ideal surface modification feature length is dimensionless. G S The shear modulus of the surface-modified layer is given in Pa. G Let be the shear modulus of the matrix material of the component, in Pa.

[0037] This traditional ideal model only considers interfacial shear stiffness and does not account for the residual compressive stress on the surface caused by rolling plastic deformation. This residual compressive stress inhibits crack tip opening and expands the effective modification influence zone. Simultaneously, this model neglects the roughness of the fretting contact interface; micro-protrusions cause localized stress concentration, accelerating crack initiation and compressing the effective modification feature length. Based on the above traditional model, the following parameter corrections are made: 1. Introduce residual compressive stress strengthening correction The effective influence zone of residual compressive stress expansion modification is obtained by multiplying the reference length by the strengthening factor to obtain the characteristic length of surface modification modified by residual compressive stress strengthening. β σ : ; 2. By introducing surface roughness weakening correction, the final corrected surface modification feature length is obtained. β : ; In the formula: s s Force dimension, MPa; s res The surface residual compressive stress is MPa; without rolling reinforcement, the surface residual compressive stress is 0, which can be obtained through X-ray diffraction residual stress testing. R q The root mean square roughness of the surface is measured in mm. Under ideal working conditions, the surface is completely smooth without any bumps or depressions. R q A value of 0 can be obtained through white light interference optical roughness testing; l 0 The unit of measurement is length, mm; k 1 is the residual stress fitting coefficient, dimensionless, characterizing the sensitivity of residual compressive stress to the modified feature length; k 2is the surface roughness fitting coefficient, which is dimensionless and characterizes the sensitivity of surface roughness to the influence of modified feature length.

[0038] This invention introduces a critical surface modification characteristic length. β cr As the dividing threshold for the initiation mode of fretting cracks, it is dimensionless; among which, β cr It is only related to the component matrix material and the type of surface modification process, and is not affected by changes in field load, roughness, or residual stress. It is calibrated through fretting fatigue tests on standard specimens. The calibration rules are as follows: prepare multiple sets of standard specimens with only the modification strength changed and all other parameters completely identical; perform fretting fatigue loading on each set of specimens and observe the crack initiation location (surface / subsurface); fit the modification characteristic length corresponding to the change in crack initiation location, which is the material-specific critical threshold.

[0039] β cr The physical meaning is: β < β cr The effective range of the modified layer is insufficient, and the stress peak remains on the surface of the component. β > β cr The modified layer exhibits sufficient stress homogenization and residual compressive stress strengthening effects, with peak shear stress migrating to the subsurface.

[0040] S13, Interface and Fatigue Parameter Calibration The interfacial friction coefficient was determined by reciprocating sliding friction and wear tests based on the contact surface material and surface modification process. Through fretting fatigue control tests under different stress ratios, the coupling amplification effect of interfacial shear stress on far-field stress was fitted, and the fretting coupling correction coefficient was calibrated. α Based on the crack geometry of the component (surface semi-elliptical crack / through crack / corner crack), select the geometry correction factor with reference to fracture mechanics standards (such as GB / T 4161-2007 Metallic Materials Plane Strain Fracture Toughness KIC Test Method). Y By conducting fretting fatigue tests on standard specimens, the crack propagation rate under different stress intensity factors was measured, and the fretting fatigue constant of the material was obtained by fitting the Paris formula. C , m .

[0041] Among them, the propagation mechanisms of Mode I surface-opening cracks and Mode II subsurface shear cracks are fundamentally different: the former is mainly driven by crack opening and propagation under normal tensile stress, while the latter is mainly driven by shear slip propagation under interfacial shear stress. The stress field distribution at the crack tip is different, and the sensitivity of the fatigue propagation rate to the stress intensity factor is also different. Therefore, the material constants in the Paris formula are different. C , m They must be calibrated separately and cannot be mixed.

[0042] The calibration methods for the above two sets of fretting fatigue constants are as follows: (1) Mode I Surface opening fatigue constant C 1. m 1. Prepare standard specimens with pre-existing surface cracks and conduct graded loading tests under fretting fatigue conditions dominated by normal alternating loads. Monitor the crack length variation with the number of cycles using the DC potential method or the imprinting method, and calculate the crack propagation rate corresponding to different stress intensity factor amplitudes ΔK. According to the Paris formula Perform a double log-linear fit to obtain C 1. m 1; (2) Mode II Subsurface Shear Fatigue Constant C 2. m 2. Prepare double-sided notched shear specimens or compact shear specimens, and conduct tests under fretting fatigue conditions dominated by tangential alternating loads. Monitor crack propagation and fit the Paris equation to obtain... C 2. m 2.

[0043] S2, Calculation of contact stress field using the fundamental solution of surface modification The fundamental solution corrected by concentrated force on the modified plane surface is used to calculate the normal stress at the contact surface of the component. Radial stress in polar coordinates This eliminates the stress singularity of traditional elastic solutions and yields the true contact stress distribution under the action of the modified layer.

[0044] The fundamental solution for the plane stress of the normal concentrated force under surface modification is calculated as follows.

[0045] Normal concentrated force on the surface of a planar semi-infinite body P The radial stress correction solution considering surface elasticity effects: ; Component surface ( y =0) Normal stress: ; In the formula: The radial stress is expressed in polar coordinates, in Pa. The normal stress is expressed in rectangular coordinates, in Pa. The distance from the calculation point to the origin of the load is in meters (m). Polar angle, rad; is the horizontal coordinate, in meters (m).

[0046] This modified solution eliminates the stress singularity of the traditional Flamant solution, and the stress in the near-surface region tends to a finite value, truly reflecting the stress homogenization effect of the surface modification layer.

[0047] S3, calculates the interfacial friction, shear stress, and fretting amplitude. Using the Coulomb friction model, the interfacial friction force is calculated from the normal stress at the contact surface. Further solve for the average shear stress at the interface. The amplitude of interfacial fretting slip is calculated based on the elastic slip theory. And determine whether the slip amplitude exceeds the critical value for fretting crack initiation.

[0048] The calculation of interface friction and fretting slip parameters is shown below.

[0049] 1. Interfacial friction: ; 2. Average interfacial shear stress: ; 3. Micro-slip amplitude: ; In the formula: The interfacial friction force is expressed in N. The coefficient of friction of the contact surface; This represents the actual contact area of ​​the component. ; The average shear stress at the interface is given in Pa. The amplitude of the interface micro-slip is in meters (m). The contact feature length is in meters (m). Let be the shear modulus of the component matrix, Pa.

[0050] S4, Determination of Micro-crack Initiation Mode Based on the surface modification characteristic lengthβ Critical surface modification characteristic length relative to matrix critical threshold β cr The comparison results determine the location of fretting crack initiation; when β ≤ β cr When the maximum shear stress is determined to be located on the component surface, the crack initiates with a surface-opening type (Mode I), and the first set of fretting fatigue constants is selected accordingly. C 1 , m 1 ;when β>β cr When the maximum shear stress migrates to the subsurface of the component, the crack initiates in a subsurface shear mode (Mode II), and the second set of fretting fatigue constants is selected accordingly. C 2 , m 2 .

[0051] S5, Calculate the mechanical parameters of the micro-motion coupling. By coupling the far-field alternating ground stress with the micro-motion interface shear stress, the comprehensive equivalent stress amplitude is obtained. By combining the geometric correction factor and the instantaneous crack length, the stress intensity factor amplitude at the crack tip is solved. .

[0052] The calculation of the equivalent stress amplitude and stress intensity factor amplitude of the micro-motion coupling is shown below.

[0053] 1. Micro-motion coupling equivalent stress amplitude, also known as comprehensive equivalent stress amplitude: ; 2. Crack tip stress intensity factor amplitude: ; In the formula: The equivalent stress amplitude of the micro-motion coupling, also known as the comprehensive equivalent stress amplitude, is expressed in Pa. The far-field alternating geostress amplitude is given in Pa. This is the micro-coupling correction coefficient; For the stress intensity factor amplitude, ; For structural geometry correction factors; The instantaneous crack length is in meters (m).

[0054] S6, Calculate the instantaneous propagation rate of the fretting crack. Substituting the stress intensity factor amplitude and the fretting fatigue constant into the Paris formula adapted to the fretting condition, the crack propagation rate under the current load cycle is calculated. .

[0055] S7, Integral calculation of the remaining fatigue life of the component With initial crack length The lower limit of integration and the critical failure crack length. As the upper limit of integration, the crack propagation rate formula is integrated to obtain the total number of load cycles from the current state to complete failure of the component, i.e., the remaining fatigue life. By combining the on-site load cycle frequency, the remaining actual service time of the component is calculated.

[0056] The crack propagation rate and remaining fatigue life are calculated as follows.

[0057] Paris formula for crack propagation rate: ; Remaining fatigue life integral formula: ; In the formula: The crack propagation rate is m / cycle; C , m This is the material fretting fatigue test constant, or simply fretting fatigue constant. The specific value is selected according to the crack type. The remaining fatigue life of the component is the number of load cycles. Let the initial crack length be m; The critical failure crack length is in meters (m).

[0058] S8, Tiered Early Warning, Result Judgment and Report Output S81, presets three-level early warning thresholds, and divides the working state of the component into safe zone, warning zone and danger zone according to crack propagation rate and remaining fatigue life; S82, develop a graded treatment plan: maintain routine monitoring in the safe zone; increase the frequency of detection and assess the integrity of the surface modification layer in the warning zone; and immediately carry out disease treatment such as reinforcement, crack filling, and interface retreatment in the danger zone. S83 integrates all calculation parameters, stress results, slip parameters, crack propagation data, life prediction results, and treatment recommendations to output a formal assessment report.

[0059] S9, Reverse optimization of surface modification process Preset component target remaining fatigue life The calculation process in step S7 is reversed and iterated to solve for the surface modification feature length required to satisfy the target lifetime. β The optimal value is determined, and a recommended shear modulus for the surface modification layer is output accordingly. Gs The range of control over the thickness of the modified material can serve as a quantitative basis for optimizing the surface modification process of components.

[0060] The following is a typical example of a surface-rolled reinforced concrete segment joint in a deep metal mine. The contact surface of the segment undergoes surface modification treatment through rolling reinforcement. Over a long period of time, it is subjected to the cyclic vibration of underground transport trains and the coupling effect of alternating geostress in the surrounding rock, resulting in micron-level interface micro-motion. The complete prediction method provided by this invention is used to sequentially complete parameter calibration, stress field solution, micro-motion parameter calculation, crack initiation mode determination, crack propagation rate solution, remaining fatigue life integral calculation, and graded early warning. The surface rolling process parameters are then iteratively optimized in reverse. At the same time, a comparative verification is carried out with traditional prediction models to fully illustrate the implementation process and technical advantages of this invention.

[0061] Example 1 Please see Figure 1 to Figure 3 As shown, Embodiment 1 of the present invention provides a method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification (effect), comprising the following steps: Step S1, Parameter Acquisition and Full Parameter Calibration This embodiment completes parameter measurements and indoor test calibration in three categories: field working conditions, material modification, and interface fatigue. Simultaneously, it calibrates the critical surface modification characteristic length required for crack mode determination. β cr .

[0062] S11, Actual measured parameters of on-site operating conditions The measured concentrated force along the normal line of the segment joint is P = 8.5 × 10⁻⁶. 4 N / m, far-field alternating geostress amplitude Δ s =2.2MPa; contact characteristic length L=0.8m, actual contact area A c =0.65m 2 The initial crack length on the joint surface was detected using ultrasonic flaw detection. a 0 = 0.8 mm; the critical failure crack length is determined according to the mine support design specifications. a c =12mm.

[0063] S12, Calibration of mechanical parameters and critical threshold of matrix and surface modification layer Indoor mechanical tests determined the shear modulus of the concrete matrix to be G=15GPa, and the shear modulus of the rolled modified layer to be Gs=45GPa; X-ray diffraction residual stress testing was used to obtain the surface residual compressive stress. s res=-180MPa; Root mean square roughness of the surface obtained by white light interference optical roughness test. R q =0.02mm; Fretting fatigue control tests were conducted on multiple sets of standard specimens with different rolling pressures and roughnesses to obtain the residual stress fitting coefficient. k 1=0.72, surface roughness fitting coefficient k 2 = 0.45, substituting this into the correction formula, we obtain the comprehensive corrected surface modification characteristic length. β Standard strength specimens with gradient modification, using the same substrate and rolling process as the tube segments, were prepared. Fretting fatigue loading was conducted, and the critical point for crack initiation location transformation was observed. The specific critical surface modification characteristic length of this material was experimentally calibrated. β cr =0.15, which is used as the threshold for determining the crack mode in step S4.

[0064] S13, Interface and Dual-Mode Fretting Fatigue Parameter Calibration Determine the interfacial friction coefficient based on the material of the contact surface of the rolled concrete. =0.32, calibrating the fretting coupling correction coefficient based on downhole vibration load characteristics. α =1.8; The structural geometry correction factor is obtained by referring to a table based on the geometric form of the segment joint crack. Y =1.15; Fretting fatigue tests were conducted under two fracture modes, and the material constants according to the Paris formula were calibrated for two sets respectively: Mode I Surface open crack fatigue constant: C 1 =2.1×10 -11 , m 1 =3.2; Mode II subsurface shear crack fatigue constant: C 2 =8.6×10 -12 , m 2 =2.8.

[0065] Step S2: Calculate the contact stress field using the fundamental solution of surface modification. Take the horizontal coordinates of the joint center x =0, substitute into the fundamental solution of the plane normal concentrated force stress with surface elastic correction of this invention, and solve for the normal stress of the contact surface. ; Comparison with traditional Flamant planar concentrated force solutions: Traditional models at the load origin x → The stress at point 0 tends to infinity, exhibiting stress singularity; this invention introduces a modified characteristic length. βAfterwards, the stress in the near-surface region is a limited value, which truly restores the stress homogenization effect of the rolled modified layer, and the calculation results match the actual stress state of the component.

[0066] Step S3: Calculate the interfacial friction force, shear stress, and fretting slip amplitude. Formula for calculating interfacial friction: Substitute the normal stress of the contact surface, the coefficient of friction, and the contact area to solve for the interfacial friction force. Formula for calculating the average shear stress at the interface: The average shear stress at the interface is obtained by dividing the frictional force by the actual contact area. Formula for calculating the amplitude of interface micro-slip: The amplitude of the interfacial reciprocating slip is calculated by combining the matrix shear modulus and the contact characteristic length; the slip amplitude calculation results in this embodiment are as follows. d =1.2 μm Below the critical slip threshold for the initiation of fretting cracks in the same material d cr =1.2 μm This indicates that the surface modification layer of the rolling process can effectively constrain the reciprocating slippage of the interface and reduce the rate of fretting damage development from the source.

[0067] Step S4, Determining the micro-crack initiation mode This step retrieves the comprehensive modified surface enhancement feature length calculated by S1. β S1 Critical threshold determined by the test β cr By comparing the location of crack initiation and fracture mode in the numerical comparison zone, and matching the corresponding fatigue constant, the complete determination process is as follows: S41, Parameter Retrieval: Extracting the Length of Modified Characteristics β =0.092, critical threshold β cr =0.15; S42, Numerical comparison and determination: β≤β cr It meets the criteria for determining surface open-type cracks; Under this working condition, the effective influence range of the modified layer is limited. The local stress concentration caused by surface roughness cannot be completely offset by the residual compressive stress. The maximum shear stress at the interface is concentrated on the surface of the segment contact surface. Under alternating fretting, the crack opens and initiates along the normal direction of the contact surface, which belongs to Mode I surface-opening fretting crack. Parameter matching: Select Mode I specific fretting fatigue constant C 1 =2.1×10 -11 , m 1=3.2, and pass this set of constants to S5 to carry out the calculation of coupled mechanical parameters.

[0068] Steps S5-S7: Calculation of coupled mechanical parameters, crack propagation rate, and remaining fatigue life. S5, Calculate the mechanical parameters of the micro-motion coupling. The far-field alternating geostress amplitude Average interfacial shear stress Substituting into the coupling equivalent stress amplitude formula Solve for the equivalent stress amplitude of the fretting coupling; combine with the initial crack length. a 0. Geometric correction factor Y Substituting into the formula, we get Calculate the stress intensity factor amplitude at the crack tip. DK .

[0069] S6, Calculate the instantaneous propagation rate of the fretting crack. The fatigue constant of Mode I obtained by matching S4 C 1 , m 1 Stress intensity factor amplitude DK Substituting into the Paris fretting crack propagation formula This yields the instantaneous crack propagation rate corresponding to the current initial crack length.

[0070] S7, Integral calculation of the remaining fatigue life of the component With initial crack length a 0 = 0.8 mm is the lower limit of integration and the critical failure crack length. a c =12mm is the upper limit of integration. The total number of failure cycles is calculated by integrating the crack propagation rate formula. By combining the daily train vibration load cycle frequency underground, the remaining actual safe service life of the segment joint components was calculated. The calculation results show that the remaining service life of the rolled modified segment far exceeds the design service life of the mine support, and the structural safety reserve is sufficient.

[0071] S8, Tiered Early Warning, Result Judgment and Report Output A three-level early warning threshold is preset, and the operating status of the component is divided into safe zone, warning zone, and danger zone based on crack propagation rate and remaining fatigue life. In this embodiment, the component has sufficient remaining life and extremely low crack propagation rate, and is judged to be in the safe zone. The corresponding treatment plan is to maintain quarterly routine ultrasonic flaw detection monitoring, without the need for interface reinforcement, secondary rolling, crack repair, or other defect treatment. The system integrates all operating parameters, material modification parameters, stress field calculation results, slip amplitude, crack propagation rate, remaining life, and operation and maintenance recommendations to output a micro-motion damage health assessment report for underground components.

[0072] S9, Reverse optimization of surface modification process If engineering requirements increase the target remaining fatigue life of components (With a 50% increase in lifetime required), the S7 lifetime calculation model is solved iteratively in reverse to obtain the optimal surface modification feature length required to meet the target lifetime. β =0.21; In practice, a binary search method can be used for iteration. The specific steps are as follows: (a) Preset target remaining fatigue life Given the surface modification feature length β Search range[ β min , β max ],in, β min Take the feature length corresponding to the state with no surface modification or the weakest modification. β max Take the feature length corresponding to the strongest modified state achievable by the process; (b) Take the midpoint of the interval β mid = ( β min + β max ) / 2, will β mid Substitute the values ​​into the forward calculation process of S1 to S7 to calculate the corresponding remaining fatigue life. ; (c) Comparison With target value :like < This indicates that the current modification intensity is insufficient, and the search lower limit should be updated. β min = β mid ;like > This indicates that the modification intensity is excessive, and the search upper limit should be updated. β max = β mid ; (d) Repeat steps (b) to (c) until the convergence criterion is met. - | / <ε (ε is taken as 1% to 5%) (for the target value), at this time β mid That is, the optimal surface modification feature length that satisfies the target lifetime; (e) according to the optimalβ The process control range for the shear modulus Gs of the surface modification layer or the modification thickness is determined by reverse calculation.

[0073] By reverse-engineering the formula for calculating the modified characteristic length, the process control index is derived: the shear modulus of the modified layer needs to be increased. Gs Upgrade to 58GP, increase the residual compressive stress amplitude of the surface layer during the rolling process, and reduce the root mean square roughness of the contact surface. R q It outputs the control range of rolling strengthening process parameters, providing a quantitative optimization basis for the surface modification process of precast segments in the factory.

[0074] Traditional model comparison and verification: Two types of traditional methods were used to perform parallel calculations on the same segment, and the prediction errors were compared.

[0075] Comparative Example 1 Comparative Example 1 uses a traditional modified characteristic length model that only considers the shear modulus ratio, without residual stress and roughness correction, and is paired with a Flamant stress solution without surface elasticity. The relative error in predicting the crack propagation rate is 37.2%.

[0076] Comparative Example 2 Comparative Example 2 uses a traditional fretting fatigue prediction method that does not distinguish between crack initiation modes and employs a single fatigue constant. This means that regardless of whether the actual crack is surface-opening or subsurface-shearing, the crack initiation mode is not determined, and the same set of Paris formula material constants is used throughout the process. C , m The crack propagation rate is calculated and the lifetime is predicted by integration. Since the propagation mechanism and stress field distribution of the two crack modes are different, their fatigue constants should be different. This method covers all modes with a single constant, resulting in low prediction accuracy.

[0077] In Embodiment 1 of this invention, by coupling residual compressive stress strengthening and roughness weakening correction, surface elasticity is introduced to eliminate stress singularity, and differentiated fatigue constants are matched for Mode I / II cracks. The relative error between the predicted results and the measured values ​​of indoor fretting fatigue tests is only 6.8%. This verifies that the multiphysics coupling model provided by this invention can significantly improve the prediction accuracy of fretting crack propagation rate and remaining life in underground engineering.

[0078] Example 2 Embodiment 2 of the present invention provides a fretting crack propagation rate prediction system for underground engineering components considering surface modification, which is used in the above-mentioned method for predicting the fretting crack propagation rate of underground engineering components considering surface modification, including: The parameter acquisition and calibration module is used to acquire the geometric parameters, load parameters, material mechanical parameters, surface modification parameters, and fretting fatigue parameters of deep mine fretting-prone components that have undergone surface modification treatment, and to calculate the surface modification characteristic length and calibrate the critical surface modification characteristic length. The contact stress field solution module is used to calculate the normal stress and polar coordinate radial stress of the contact surface of the component based on the corrected fundamental solution of the surface modification concentrated force. The interface micro-motion parameter calculation module is used to calculate the interface friction force, the average interface shear stress, and the micro-motion slip amplitude based on the normal stress of the contact surface. The crack initiation mode determination module is used to compare the surface modification feature length with the critical surface modification feature length, determine the initiation location of fretting cracks, and select the corresponding fretting fatigue constant. The coupling calculation module is used to couple the far-field alternating ground stress with the micro-motion interface shear stress to obtain the comprehensive equivalent stress amplitude and calculate the stress intensity factor amplitude at the crack tip. The crack propagation and life calculation module is used to calculate the crack propagation rate based on the Paris formula and obtain the remaining fatigue life through integration. The graded early warning and output module is used to provide graded early warnings based on crack propagation rate and remaining fatigue life, and output an evaluation report. The process reverse optimization module is used to preset the target remaining fatigue life, reverse iteratively solve for the optimal value of the surface modification feature length required to meet the target life, and output the control range of the shear modulus or modification thickness of the surface modification layer.

[0079] In summary, this invention discloses a method for predicting the propagation rate of fretting cracks in deep mine components considering surface modification. Addressing the technical problem of low prediction accuracy caused by existing methods failing to consider the mechanical dispersion effect and stress singularity of the surface modification layer, this invention introduces the Gurtin-Murdoch surface elasticity model to construct a comprehensive surface modification characteristic length that includes a residual compressive stress strengthening factor and a roughness weakening factor. β By calibrating the critical characteristic length β cr ,in accordance with β and β cr The magnitude relationship automatically determines whether a fretting crack is surface-opening or subsurface-shearing, and adaptively switches fatigue crack propagation parameters. Combining the modified fundamental solution of contact stress with the equivalent stress amplitude of fretting coupling, the crack propagation rate and remaining life are calculated. This invention also uses inverse iteration based on the target life to solve for the optimal... βThe value is used to optimize the surface modification process parameters. This invention eliminates the singularity of traditional contact stress and enables accurate prediction of the fretting crack propagation rate, crack development trend, and remaining fatigue life of underground components with surface modification layers. It is applicable to the health monitoring and protection of key load-bearing components such as anchor bolts and segment bolts in deep mines, and can provide a theoretical basis for optimizing the surface modification process and preventing fretting damage.

[0080] It should be noted that the present invention is not limited to the above-described embodiments. The above embodiments are merely examples, and any embodiments that have the same structure and perform the same effects as the technical concept within the scope of the present invention are included within the scope of the present invention. Furthermore, various modifications that can be conceived by those skilled in the art to the embodiments, and other ways of constructing by combining some of the constituent elements of the embodiments, without departing from the spirit of the present invention, are also included within the scope of the present invention.

Claims

1. A method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification, characterized in that, Includes the following steps: S1. Parameter acquisition and calibration: On-site measurement of working parameters, correction and calibration of mechanical parameters of matrix and surface modified layer, and calibration of interface and fatigue parameters for underground engineering components prone to micro-motion after surface modification treatment. The surface modification characteristic length and critical surface modification characteristic length are calculated based on the mechanical parameters. S2. Solution of contact stress field: Based on the mechanical model of the surface modified layer, the fundamental solution of the plane surface modified concentrated force is used to calculate the normal stress and polar coordinate radial stress of the component contact surface, and obtain the true contact stress distribution under the action of the modified layer. S3. Calculation of interface micro-motion parameters: The interface friction force is calculated by combining the normal stress of the contact surface with the friction model, the average shear stress of the interface is solved, and the interface micro-motion slip amplitude is calculated according to the slip theory. S4. Determination of fretting crack initiation mode: Compare the surface modification characteristic length with the critical surface modification characteristic length to determine the initiation location and cracking mode of fretting cracks, and select the corresponding fretting fatigue constant; S5. Calculation of micro-motion coupled mechanical parameters: Couple the far-field alternating ground stress with the interface shear stress to obtain the comprehensive equivalent stress amplitude. Combine the geometric shape correction coefficient and the instantaneous crack length to solve the stress intensity factor amplitude at the crack tip. S6. Crack propagation rate calculation: Substitute the stress intensity factor amplitude and the fretting fatigue constant of the corresponding mode into the Paris formula adapted to the fretting condition to calculate the crack propagation rate under the current load cycle. S7. Calculation of remaining fatigue life: Using the initial crack length as the lower limit of integration and the critical failure crack length as the upper limit of integration, the crack propagation rate is integrated to obtain the remaining fatigue life of the component. S8. Graded Early Warning and Output: Based on the crack propagation rate and / or remaining fatigue life, graded early warning is issued, differentiated treatment plans are formulated, and an evaluation report is output.

2. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 1, characterized in that, In step S4, when the surface modification characteristic length is less than or equal to the critical surface modification characteristic length, the maximum shear stress is determined to be located on the surface of the component, and the crack initiates in a surface-opening mode. The first set of fretting fatigue parameters is selected. When the surface modification characteristic length is greater than or equal to the critical surface modification characteristic length, the maximum shear stress is determined to migrate to the subsurface of the component, and the crack initiates in a subsurface shearing mode. The second set of fretting fatigue parameters is selected.

3. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 2, characterized in that, The calculation process for the surface modification characteristic length is as follows: Based on the ratio of the matrix shear modulus to the shear modulus of the surface modification layer, the ideal surface modification characteristic length is determined; [The following is a separate, unrelated sentence:] Introducing... Strengthening correction of residual compressive stress in the surface layer yields the surface modification feature length after residual stress correction; weakening correction of surface roughness is introduced to obtain the final surface modification feature length. The calculation formula is as follows: ； in, β The characteristic length of surface modification. β 0 For the ideal surface modification feature length, σ res This represents residual compressive stress on the surface. R q The root mean square roughness of the surface. k 1 The residual stress fitting coefficients are... k 2 The surface roughness fitting coefficient is... σ s To provide force dimension parameters, l 0 This is a parameter with length dimensions.

4. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 2, characterized in that, The critical surface modification characteristic length is obtained by standard specimen fretting fatigue test. The calibration rules include: preparing multiple sets of standard specimens with only the surface modification intensity changed and the other parameters being the same; subjecting each set of specimens to fretting fatigue loading and observing the crack initiation position; fitting the surface modification characteristic length corresponding to the surface / subsurface transformation at the crack initiation position as the critical surface modification characteristic length.

5. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 1, characterized in that, Also includes: S9. Surface modification process reverse optimization: Preset the target remaining fatigue life of the component, reverse the calculation process of step S7, and solve the optimal value of the surface modification characteristic length required to meet the target life. Based on this, output the control range of the shear modulus or modification thickness of the surface modification layer as a quantitative basis for surface modification process optimization.

6. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 1, characterized in that, In step S1, the field working parameters include: the concentrated force of the contact surface normal of the component, the far-field alternating ground stress amplitude, the contact characteristic length, the actual contact area and the initial crack length, and the critical failure crack length is determined. Interface and fatigue parameters include: interface friction coefficient, fretting coupling correction coefficient, geometry correction coefficient, and fretting fatigue constant; The mechanical parameters of the matrix and the surface modified layer include: shear modulus of the component matrix, shear modulus of the surface modified layer, residual stress of the surface layer, root mean square roughness of the surface, residual stress influence coefficient and surface roughness influence coefficient.

7. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 1, characterized in that, In step S2, the mechanical model of the surface modification layer is the Gurtin–Murdoch surface elastic model, and the modified fundamental solution is the modified fundamental solution of the concentrated force on the surface of a planar semi-infinite body. In step S3, the friction model is the Coulomb friction model, and the slip theory is the elastic slip theory.

8. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 1, characterized in that, In step S5, the comprehensive equivalent stress amplitude is obtained by superimposing the far-field alternating geostress amplitude with the interface average shear stress corrected by the micro-motion coupling correction coefficient. The calculation formula is as follows: ； in, The comprehensive equivalent stress amplitude is given by α, which is the micro-motion coupling correction coefficient, Δσ, which is the far-field alternating geostress amplitude, and τ, which is the average shear stress at the interface.

9. The method for predicting the propagation rate of fretting cracks in underground engineering components considering surface modification according to claim 1, characterized in that, In step S8, the graded early warning includes: dividing the working state of the component into a safe zone, a warning zone, and a danger zone according to the crack propagation rate and / or remaining fatigue life; the differentiated treatment plan includes: maintaining routine monitoring in the safe zone, increasing the detection frequency and assessing the integrity of the surface modification layer in the warning zone, and immediately carrying out reinforcement, crack repair, or interface retreatment in the danger zone.

10. A system for predicting the propagation rate of microcracks in underground engineering components considering surface modification, characterized in that, The method for predicting the microcrack propagation rate of underground engineering components considering surface modification, as described in any one of claims 1 to 9, comprises: The parameter acquisition and calibration module is used to acquire the geometric parameters, load parameters, material mechanical parameters, surface modification parameters, and fretting fatigue parameters of deep mine fretting-prone components that have undergone surface modification treatment, and to calculate the surface modification characteristic length and calibrate the critical surface modification characteristic length. The contact stress field solution module is used to calculate the normal stress and polar coordinate radial stress of the contact surface of the component based on the corrected fundamental solution of the surface modification concentrated force. The interface micro-motion parameter calculation module is used to calculate the interface friction force, the average interface shear stress, and the micro-motion slip amplitude based on the normal stress of the contact surface. The crack initiation mode determination module is used to compare the surface modification feature length with the critical surface modification feature length, determine the initiation location of fretting cracks, and select the corresponding fretting fatigue constant. The coupling calculation module is used to couple the far-field alternating ground stress with the micro-motion interface shear stress to obtain the comprehensive equivalent stress amplitude and calculate the stress intensity factor amplitude at the crack tip. The crack propagation and life calculation module is used to calculate the crack propagation rate based on the Paris formula and obtain the remaining fatigue life through integration. The graded early warning and output module is used to provide graded early warnings based on crack propagation rate and remaining fatigue life, and output an evaluation report. The process reverse optimization module is used to preset the target remaining fatigue life, reverse iteratively solve for the optimal value of the surface modification feature length required to meet the target life, and output the control range of the shear modulus or modification thickness of the surface modification layer.

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