A method and system for predicting the fatigue crack growth life of a mechanical structure

Abstract

The present invention provides a method and system for predicting the fatigue crack growth life of a mechanical structure, which relates to the technical field of structural fatigue reliability, and includes solving the stress intensity factor of a cracked structure; measuring the correlation data between the stress intensity factor amplitude ΔK and the crack growth rate da / dN under different stress ratios; solving the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field; calculating the effective driving force for crack growth under variable amplitude loading based on the strip yield model; updating the crack length and the number of cycles until the crack grows to the termination length a f ; calibrating the fatigue crack growth rate model parameters based on ΔK CPD ; superimposing the variable amplitude load spectrum and the equivalent crack surface traction distribution onto a two-dimensional surrogate cracked body, and generating a fatigue crack growth life curve of the mechanical structure by the strip yield model. The present invention realizes the quantitative prediction of the fatigue crack growth life of the mechanical structure, and has high solution accuracy and applicability.

Description

Technical Field

[0001] The present invention relates to the technical field of structural fatigue reliability, and in particular, to a method and system for predicting the fatigue crack growth life of a mechanical structure. Background Art

[0002] Mechanical structures such as ships and rail transit vehicles often bear the action of random vibration loads (variable amplitude loads) under service conditions. Affected by machining processes (such as welding defects) or potential internal defects of materials (such as inclusions, pores, etc.), these defective mechanical structures may have the risk of fatigue failure due to local stress concentration caused by defects under service conditions. Therefore, establishing a method for predicting the fatigue crack growth life of defective mechanical structures under variable amplitude loads can provide theoretical guidance for the damage tolerance design of mechanical structures and ensure the service safety of the structures.

[0003] Due to the existence of initial defects, most existing methods use linear elastic fracture mechanics methods to predict the fatigue crack growth life of mechanical structures. These methods often predict the fatigue crack growth life of structures under variable amplitude loads based on fatigue crack growth rate models such as the classical Paris formula or the NASGRO equation that can consider the stress ratio effect. However, a large number of studies have shown that the action sequence of each level of load in variable amplitude loads has a significant impact on the fatigue crack growth rate, that is, the load sequence effect. The existing methods for predicting the fatigue crack growth life of mechanical structures do not consider the influence of the load sequence effect on fatigue crack growth, and often can only obtain prediction results that are conservative in engineering. There are also some methods that use models such as the Wheeler model that consider the interaction of crack tip plastic zones to consider the load sequence effect during variable amplitude loading. However, the model parameters determined by such models are often only applicable to specific load conditions. When the load conditions change, the prediction accuracy cannot be guaranteed, and there is a disadvantage of poor model applicability. At present, there is still a lack of a quantitative prediction method suitable for the fatigue crack growth life of mechanical structures under variable amplitude loading.

[0004] From a macroscopic perspective, the physical mechanism of fatigue crack growth is the generation of cyclic plastic damage at the crack tip. Therefore, by examining the cyclic elastoplastic response at the crack tip during variable amplitude loading and establishing an effective driving force for crack growth that characterizes the cyclic plastic damage at the crack tip, it is expected to comprehensively consider the stress ratio and load sequence effects existing in crack growth and achieve quantitative prediction of the fatigue crack growth life under variable amplitude loads. However, for mechanical structures existing in the actual engineering field, due to the complexity of the crack body geometry, it is very difficult to solve the elastoplastic response at its crack tip. Although the elastoplastic finite element method provides a relatively general method for solving such problems, it is difficult to be applied to complex structures due to problems such as complex modeling and low computational efficiency. Summary of the Invention

[0005] The object of the present invention is to provide a method and system for predicting the fatigue crack growth life of a mechanical structure to improve the above problems. To achieve the above object, the technical solutions adopted by the present invention are as follows:

[0006] In the first aspect, the present application provides a method for predicting the fatigue crack growth life of a mechanical structure, including:

[0007] Set the geometric parameters and initiation positions of the initial fatigue cracks in the mechanical structure, carry out crack growth analysis using the linear elastic finite element method, and establish the relationship between crack length and stress intensity factor under the action of residual stress field a~K res , and the relationship between crack length and stress intensity factor under the action of unit external load a~K unit ;

[0008] Prepare standard fatigue crack growth specimens of the mechanical structure material, perform multi-stress ratio constant amplitude load tests, and measure the correlation data between stress intensity factor amplitude ΔK and crack growth rate da / dN under different stress ratios;

[0009] Select a two-dimensional through-crack body as a substitute model, combine the relationship between a~K res and a~K unit , and adopt the weight function method and multi-objective optimization algorithm to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field;

[0010] Based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, construct a strip yield model in the two-dimensional substitute crack body, discretize the crack surface and plastic zone into elastoplastic rod elements, calculate the size of the plastic zone at the crack tip under variable amplitude load based on the strip yield hypothesis, and calculate the rod element stress and effective driving force ΔK through the Gauss-Seidel iteration algorithm CPD ; Calculate the single-cycle crack growth increment Δa according to ΔK CPD , update the crack length and number of cycles until the crack extends to the termination length a f ;

[0011] Simulate the crack growth process under constant amplitude load through the strip yield model, establish the conversion relationship between ΔK and ΔK CPD , combine the data of multi-stress ratio constant amplitude load tests for stress intensity factor conversion and data fitting, and calibrate the fatigue crack growth rate model parameters based on ΔK CPD ;

[0012] Superimpose the variable amplitude load spectrum and the equivalent crack surface traction distribution, and apply it to the crack surface of the two-dimensional surrogate crack body. Input the parameters of the fatigue crack growth rate model, and iteratively calculate the evolution relationship between the crack length and the number of cycles to generate the fatigue crack growth life curve of the mechanical structure.

[0013] Preferably, the combination of a~K res and a~K unit Between the relationships, use the weight function method and the multi-objective optimization algorithm to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field, including:

[0014] Establish the equivalent relationship between the mechanical structure and the two-dimensional surrogate crack body in terms of the stress intensity factor K, where the equivalent condition is that at any crack length a, the mechanical structure subjected to the external load and the residual stress field and the two-dimensional surrogate crack body subjected to the equivalent crack surface traction have the same stress intensity factor K;

[0015] Based on the weight function method, the K-value equivalent conditions corresponding to the external load and the residual stress field can be respectively expressed as:

[0016] ∫0 a σ eq，unit (x)·m(a, x)dx = K unit (a)

[0017] ∫0 a σ cq，res (x)·m(a, x)dx = K res (a)

[0018] In the formula, dx is the integration element. a is the crack length, x is the coordinate along the crack line, m(a, x) is the weight function of the two-dimensional surrogate crack body, K unit (a) is the a-K relationship of the mechanical structure under the action of a unit external load, σ eq,unit (x) is the corresponding first equivalent crack surface traction distribution acting on the two-dimensional surrogate crack body, K res (a) is the a-K relationship of the mechanical structure under the action of the residual stress field, σ eq,res (x) is the corresponding second equivalent crack surface traction distribution acting on the two-dimensional surrogate crack body;

[0019] Approximate the equivalent crack surface traction distribution as a piecewise spline function. Among them, the i-th spline function representing the equivalent crack surface traction distribution can be expressed as:

[0020]

[0021] In the formula, α i , β i , γ i and δi represent the coefficients of the i-th piecewise spline function, s i-1 and s i are the two side nodes of the i-th piecewise spline function respectively, x is the coordinate along the crack line, is the i-th spline function representing the equivalent crack surface traction distribution.

[0022] Preferably, based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, a strip yield model is constructed in the two-dimensional alternative crack body, and the crack surface and the plastic zone are discretized into elastoplastic bar elements, including:

[0023] Based on the weight function method, a strip yield model of the alternative two-dimensional crack body subjected to the equivalent crack surface traction distribution is established. In this strip yield model, based on the strip yield hypothesis, the virtual crack length under the combined action of the maximum external load and the residual stress field under variable amplitude load is calculated;

[0024] Based on the determined virtual crack length d, the physical crack surface and the crack tip plastic zone are discretized into multiple elastoplastic bar elements, and the following formula is used to calculate the crack surface displacement under the combined action of the maximum external load and the residual stress field in the current cycle of the variable amplitude load.

[0025] Preferably, the crack propagation process under constant amplitude load is simulated through the strip yield model, and the equivalent relationship between ΔK and ΔK CPD is established, where the calculation formula of the equivalent relationship between ΔK and ΔK CPD is as follows:

[0026]

[0027] In the formula, ΔK CPD is the effective driving force for fatigue crack propagation, R is the stress ratio of the constant amplitude load, ΔK is the stress intensity factor amplitude, P max is the maximum value of the constant amplitude load, P CPD is the external load corresponding to the plastic deformation at the crack tip, which is used to characterize the cyclic plastic damage at the crack tip.

[0028] Preferably, the variable amplitude load spectrum is superimposed on the equivalent crack surface traction distribution in the two-dimensional alternative crack body, including:

[0029] Based on the principle of linear superposition, the variable amplitude load spectrum applied to the mechanical structure is equivalent to the crack surface traction distribution applied to the two-dimensional alternative crack body, and the calculation formula of the crack body traction distribution is as follows:

[0030] σ eq，app (x, N) = P(N)·σ eq，unit

[0031] where x is the coordinate along the crack line, P(N) represents the load level at the Nth cycle of the variable amplitude load spectrum applied to the mechanical structure, and σ eq,app is the variable amplitude load spectrum, N is the number of cycles, and σ eq,unit is the first equivalent crack surface traction distribution acting on the two-dimensional alternative crack body corresponding thereto.

[0032] Second, the present application also provides a fatigue crack growth life prediction system for a mechanical structure, including:

[0033] Analysis and establishment module: Set the geometric parameters and initiation positions of the initial fatigue cracks in the mechanical structure, use the linear elastic finite element method to carry out crack propagation analysis, and establish the relationship between the crack length and the stress intensity factor under the action of the residual stress field a~K res , and the relationship between the crack length and the stress intensity factor under the action of the unit external load a~K unit ;

[0034] Measurement module: Used to prepare standard fatigue crack growth specimens of the mechanical structure material, perform multi-stress ratio constant amplitude load tests, and measure the correlation data between the stress intensity factor amplitude ΔK and the crack growth rate da / dN under different stress ratios;

[0035] Solution module: Used to select a two-dimensional through crack body as an alternative model, combine a~K res and a~K unit relationship, adopt the weight function method and the multi-objective optimization algorithm to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field;

[0036] Calculation module: Used to construct a strip yield model in the two-dimensional alternative crack body based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, discretize the crack surface and the plastic zone into elastoplastic rod elements, calculate the size of the plastic zone at the crack tip under variable amplitude loads based on the strip yield hypothesis, and calculate the rod element stress and the effective driving force ΔK through the Gauss-Seidel iteration algorithm CPD ; Calculate the single-cycle crack propagation increment Δa according to ΔK CPD , update the crack length and the number of cycles until the crack propagates to the termination length a f ;

[0037] Fitting and calibration module: Used to simulate the crack propagation process under constant amplitude loads through the strip yield model, establish the conversion relationship between ΔK and ΔK CPD , combine the data of the multi-stress ratio constant amplitude load test for stress intensity factor conversion and data fitting, and calibrate the fatigue crack growth rate model parameters based on ΔK CPD ;

[0038] Prediction generation module: used to superimpose the variable amplitude load spectrum and the equivalent crack surface traction distribution, load it onto the crack surface of the two-dimensional alternative crack body, input the parameters of the fatigue crack growth rate model, iteratively calculate the evolution relationship between the crack length and the number of cycles, and generate the fatigue crack growth life curve of the mechanical structure.

[0039] In a third aspect, the present application also provides a fatigue crack growth life prediction device for a mechanical structure, including:

[0040] A memory for storing a computer program;

[0041] A processor for implementing the steps of the fatigue crack growth life prediction method for the mechanical structure when executing the computer program.

[0042] In a fourth aspect, the present application also provides a readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the above-mentioned fatigue crack growth life prediction method based on a mechanical structure.

[0043] The beneficial effects of the present invention are as follows:

[0044] The present invention proposes a method for predicting the fatigue crack growth life of a mechanical structure subjected to variable amplitude loading. By establishing an equivalent relationship between the mechanical structure and the two-dimensional alternative crack body in terms of the crack tip elastoplastic response, and based on the strip yield model of the two-dimensional alternative crack body, an approximate solution of the crack tip elastoplastic response of the mechanical structure under variable amplitude loading is realized. At the same time, on this basis, by solving the effective driving force for crack growth of the mechanical structure, a quantitative prediction of the fatigue crack growth life of the mechanical structure under variable amplitude loading is achieved.

[0045] The present invention establishes an equivalent relationship between the mechanical structure and the two-dimensional alternative crack body in terms of the crack tip elastoplastic response, and uses the strip yield model of the two-dimensional alternative crack body to realize an approximate solution of the crack tip elastoplastic response of the mechanical structure under variable amplitude loading. On this basis, the method of the present invention realizes a quantitative prediction of the fatigue crack growth life of the mechanical structure by establishing an effective driving force for crack growth that characterizes the cyclic plastic damage at the crack tip. When applied to the field of structural fatigue reliability, compared with the traditional fatigue crack growth life prediction methods, the advantages of the present invention are mainly reflected in: (1) using the cyclic plastic damage at the crack tip rather than the stress intensity factor amplitude corresponding to the complete opening of the crack as the driving force for fatigue crack growth. Compared with the stress intensity factor amplitude ΔK or the effective stress intensity factor amplitude ΔK based on crack closure effAs a traditional life prediction method for the driving force of fatigue crack growth, it can more accurately consider the stress ratio effect and load order effect of variable amplitude loading; (2) Based on the weight function theory of two-dimensional crack body, the strip yield model is used to establish the solution method of the effective driving force of fatigue crack growth in the two-dimensional alternative crack body when residual stress and cyclic external load act together, which represents the cyclic plastic damage of crack tip, and realizes the solution of the effective driving force of fatigue crack growth under variable amplitude loading. Since the strip yield model is established by the weight function method of two-dimensional crack body, once the weight function of the two-dimensional crack body is determined, the established strip yield model can be very conveniently extended to any two-dimensional crack body; (3) The equivalent relationship between the mechanical structure and the two-dimensional alternative crack body in the crack tip elastic-plastic response is established based on the K value equivalence principle, and the strip yield model of the two-dimensional alternative crack body subjected to the traction of the equivalent crack surface is proposed to predict the fatigue crack growth life of the mechanical structure, which solves the problem that the traditional life prediction method is difficult to accurately solve the effective driving force and fatigue crack growth life of complex three-dimensional structures under variable amplitude loading. Therefore, this method has high solution accuracy and applicability when solving the fatigue crack growth life of mechanical structures under arbitrary variable amplitude load conditions.

[0046] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or be understood by implementing the embodiments of the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description, claims, and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0048] Figure 1 It is a schematic flow chart of a method for predicting fatigue crack growth life of a mechanical structure according to an embodiment of the present invention;

[0049] Figure 2 It is a schematic diagram of the structure of the fatigue crack growth life prediction system of the mechanical structure described in the embodiment of the present invention;

[0050] Figure 3 It is a schematic diagram of the structure of a fatigue crack growth life prediction device for a mechanical structure according to an embodiment of the present invention;

[0051] Figure 4 Schematic diagram of the stress intensity factor K value equivalence principle described in an embodiment of the present invention;

[0052] Figure 5 Schematic diagram of the strip yield model of a two-dimensional alternative crack body that bears external loads and residual stresses jointly based on the principle of elastic superposition in the embodiments of the present invention;

[0053] Figure 6 Arrangement strategy of rod elements in the strip yield model of the two-dimensional alternative crack body in the embodiments of the present invention;

[0054] Figure 7 Schematic diagram of the finite element model of fatigue crack propagation of the welded frame as a calculation example in the embodiments of the present invention: (a) overall finite element model of the welded frame; (b) local mesh details of the crack initiation site of the welded frame; (c) fatigue crack mesh details of the welded frame;

[0055] Figure 8 Variation law of stress intensity factor of the welded frame with surface cracks in the embodiments of the present invention: (a) variation law of stress intensity factor at the surface point with the semi-length of the surface crack; (b) variation law of stress intensity factor at the deepest point with the depth of the surface crack;

[0056] Figure 9 Fatigue crack propagation rate curve of the material of the welded frame in the embodiments of the present invention, that is, the relationship between the stress intensity factor amplitude ΔK and the fatigue crack propagation rate da / dN under the action of constant amplitude loads with different stress ratios R (R~ΔK~da / dN data);

[0057] Figure 10 Equivalent crack surface traction distribution σ eq,unit (x) of the two-dimensional alternative crack body when a unit external load (P = 1 kN) acts on the welded frame and its reproduction effect on the a-K relationship of the welded frame;

[0058] Figure 11 Equivalent crack surface traction distribution σ eq,res (x) of the two-dimensional alternative crack body when welding residual stress acts on the welded frame and its reproduction effect on the a-K relationship of the welded frame;

[0059] Figure 12 Fatigue crack propagation rate curve of the material of the welded frame based on the effective driving force of fatigue crack propagation in the embodiments of the present invention, that is, the relationship between the effective driving force of fatigue crack propagation ΔK CPD and the fatigue crack propagation rate da / dN;

[0060] Figure 13 State of rod elements and stress changes when predicting the fatigue crack propagation life of the welded frame using the strip yield model in the embodiments of the present invention (the 2000th extended analysis step);

[0061] Figure 14 For the external load and load P when the welding rack described in the embodiment of the present invention as a calculation example is subjected to a variable amplitude load CPD The variation law with the number of cycles;

[0062] Figure 15 For the fatigue crack growth life curve of the welding rack described in the embodiment of the present invention as a calculation example under variable amplitude loading.

[0063] In the figure: 701, analysis and establishment module; 702, measurement module; 703, solution module; 704, calculation module; 705, fitting and calibration module; 706, prediction and generation module; 800, fatigue crack growth life prediction device for mechanical structures; 801, processor; 802, memory; 803, multimedia component; 804, I / O interface; 805, communication component. Specific implementation manners

[0064] To make the objectives, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and illustrated herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0065] It should be noted that: similar reference numerals and letters denote similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0066] Embodiment 1:

[0067] This embodiment provides a method for predicting the fatigue crack growth life of a mechanical structure.

[0068] See Figure 1 , which shows that this method includes steps S100, S200, S300, S400, S500 and S600, including:

[0069] S100. Set the geometric parameters and initiation positions of the initial fatigue cracks in the mechanical structure, conduct crack propagation analysis using the linear elastic finite element method, and establish the relationship between the crack length and the stress intensity factor under the action of the residual stress field a~K res , as well as the relationship between the crack length and the stress intensity factor under the action of the unit external load a~K unit .

[0070] It can be understood that in this step, the initial fatigue crack length, shape, and fatigue crack initiation position of the mechanical structure are set. Based on the linear elastic finite element method, fatigue crack propagation analysis is carried out to obtain the variation relationship between the stress intensity factor K at the crack tip and the crack length a under the action of the residual stress field and the unit external load, and they are respectively denoted as a~K res relationship and a~K unit relationship. For the opening mode fatigue crack, the stress intensity factor K is taken as the type I stress intensity factor K I during calculation; for the mixed mode fatigue crack, the stress intensity factor K is taken as the equivalent stress intensity factor K eq during calculation, and the calculation formula is as follows:

[0071]

[0072] In the formula, K I , K II and K III are the type I, type II, and type III stress intensity factors at the tip of the mixed mode crack. K eq is the equivalent stress intensity factor, and ν is the Poisson's ratio of the mechanical structure material.

[0073] In this embodiment, it is assumed that the initial defect of the welded frame as an example of the mechanical structure calculation is a welding defect formed due to the welding process, resulting in the initiation of fatigue cracks in the middle weld area with the most severe stress concentration. The welding defect is simplified to a semi-elliptical surface crack, and the semi-length and depth of the surface crack are taken as 0.5 mm. Then, a finite element model for fatigue crack propagation analysis of the welded frame containing initial fatigue cracks is established as Figure 7 shown. Figure 7 (a) is the overall finite element model of the welded frame, Figure 7 (b) is the local mesh details of the crack initiation part of the welded frame. Figure 7 (c) is the fatigue crack mesh details of the welded frame. Based on this finite element model, fatigue crack propagation analysis is carried out, and the variation laws of the stress intensity at the surface point with the crack semi-length and the stress intensity factor at the deepest point with the crack depth under the action of the unit external load (P = 1 kN) and the welding residual stress field are as Figure 8 (a) and (b) shown.

[0074] S200. Prepare standard fatigue crack growth specimens from the welded frame material, conduct a multi-stress ratio constant amplitude load test, and measure the correlation data between the stress intensity factor amplitude ΔK and the crack growth rate da / dN at different stress ratios.

[0075] It can be understood that in this step, standard fatigue crack growth specimens are prepared from the welded frame material, and a fatigue crack growth test under constant amplitude loads with multiple stress ratios is carried out to record the relationship between the stress intensity factor amplitude ΔK and the fatigue crack growth rate da / dN of the specimens at different stress ratios (R~ΔK~da / dN data).

[0076] In this embodiment, standard compact tension specimens are prepared from the welded frame material. The specimen has a characteristic width of 50 mm, a thickness of 10 mm, and an initial crack length of 11 mm. By conducting fatigue crack growth tests on the compact tension specimens under constant amplitude loads with stress ratios R of 0.1, 0.3, and 0.5 respectively, the relationship between the stress intensity factor amplitude ΔK and the fatigue crack growth rate da / dN of the welded frame material at different stress ratios (R~ΔK~da / dN data) is obtained as Figure 9 shown.

[0077] S300. Select a two-dimensional through-crack body as a substitute model, and combine the relationship between a~K res and a~K unit to use the weight function method and the multi-objective optimization algorithm to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field.

[0078] It can be understood that in this step, a two-dimensional through-crack body with similar geometric characteristics to the cracked welded frame structure is selected as the substitute crack body, and an equivalent relationship between the welded frame and the two-dimensional substitute crack body in terms of the stress intensity factor K is established. The equivalent condition is that at any crack length a, the welded frame under the action of the external load and the welding residual stress field and the two-dimensional substitute crack body under the action of the equivalent crack surface traction have the same stress intensity factor K.

[0079] It should be noted that based on the weight function method, the K-value equivalent conditions corresponding to the external load and the residual stress field can be expressed as:

[0080] ∫0 a σ eq，unit (x)·m(a, x)dx = K unit (a)

[0081] ∫0 a σ eq，res (x)·m(a, x)dx = K res (a)

[0082] where \(dx\) is the integration element. \(a\) is the crack length, \(x\) is the coordinate along the crack line. \(m(a, x)\) is the weight function of the two-dimensional substituted crack body, which can be obtained by querying the handbook or finite element calculation. \(K unit (a)\) is the \(a - K\) relationship of the welded frame under the action of unit external load, \(\sigma eq,unit (x)\) is the corresponding equivalent crack surface traction distribution acting on the two-dimensional substituted crack body. \(K res (a)\) is the \(a - K\) relationship of the welded frame under the action of the welding residual stress field, \(\sigma eq,res (x)\) is the corresponding equivalent crack surface traction distribution acting on the two-dimensional substituted crack body.

[0083] The equivalent crack surface traction distribution is approximately discretized into a piecewise spline function. Among them, the \(i\)-th spline function representing the equivalent crack surface traction distribution can be expressed as:

[0084]

[0085] where \(\alpha i \), \(\beta i \), \(\gamma i \) and \(\delta i \) respectively represent the coefficients of the \(i\)-th piecewise spline function, \(s i-1 \) and \(s i \) are the two side nodes of the \(i\)-th piecewise spline function respectively. \(x\) is the coordinate along the crack line, \) is the \(i\)-th spline function representing the equivalent crack surface traction distribution. Then, based on the \(a - K\) relationship determined in the above steps, the multi-objective optimization algorithm can be used to solve the inverse problem of fracture mechanics established by the \(K\)-value equivalent condition to determine the piecewise spline function coefficients of the equivalent crack surface traction distribution \(\sigma eq,unit (x)\) and \(\sigma eq,res (x)\).

[0086] In this embodiment, a center cracked plate with similar geometric characteristics to the welded frame containing fatigue cracks is selected as the two-dimensional substituted crack body. Based on Figure 8 (a)\) shown in the variation law of the surface point stress intensity factor of the welded frame with the crack half-length under the action of unit external load and welding residual stress field, the equivalent crack surface traction \(\sigma eq,unit (x)\) and \(\sigma eq,res (x)\) acting on the center cracked plate are solved. The equivalent crack surface traction is expressed as a piecewise spline function with four segments. The piecewise spline function coefficients representing the equivalent crack surface traction distribution calculated based on the weight function of the center cracked plate are shown in Table 1 and

[0087] Table 2. For the equivalent crack surface traction distribution \(\sigma eq,unit(x), the stress distribution and the stress intensity factor variation curve obtained by applying the traction distribution on the crack surface to the center cracked plate are shown in Figure 10 (a) and (b) respectively. For the equivalent crack surface traction distribution σ eq,res (x) corresponding to the welding residual stress field, the stress distribution and the stress intensity factor variation curve obtained by applying the traction distribution on the crack surface to the center cracked plate are shown in Figure 11 (a) and (b) respectively. It can be seen from the figure that the variation law of the stress intensity factor of the welded frame with fatigue cracks under the action of unit external load and welding residual stress field can be accurately reproduced by the center cracked plate subjected to the equivalent crack surface traction distributions σ eq,unit (x) and σ eq,res (x).

[0088] Table 1 represents the piecewise spline function coefficients of the equivalent crack surface traction distribution σ eq,unit (x) of the two-dimensional alternative crack body when the unit external load (P = 1 kN) acts on the welded frame

[0089] i <![CDATA[α i > <![CDATA[β i > <![CDATA[γ i > <![CDATA[δ i > <![CDATA[s i-1 > <![CDATA[s i > 1 -7.14240 18.44465 -16.96874 19.65802 0 0.84745 2 -0.01769 0.33119 -1.61855 15.32187 0.84745 4.72658 3 -0.00866 0.20315 -1.01333 14.36832 4.72658 9.03631 4 -0.00269 0.04141 0.44817 9.96614 9.03631 13.17290

[0090] Table 2 represents the piecewise spline function coefficients of the equivalent crack surface traction distribution σ eq,res (x) of the two-dimensional alternative crack body when the welding residual stress acts on the welded frame

[0091] i <![CDATA[α i > <![CDATA[β i > <![CDATA[γ i > <![CDATA[δ i > <![CDATA[s i-1 > <![CDATA[s i > 1 -6.16435 20.99216 -29.22332 43.64953 0 1.06864 2 -0.04998 1.38998 -8.27565 36.18770 1.06864 5.91644 3 -0.15181 3.19734 -18.96877 57.27609 5.91644 7.45394 4 -0.00129 -0.16848 6.119790 -5.06008 7.45394 13.17290

[0092] S400. Based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, a strip yield model is constructed in the two-dimensional alternative crack body. The crack surface and the plastic zone are discretized into elastoplastic bar elements, and the size of the plastic zone at the crack tip, the stress of the bar elements, and the effective driving force ΔK under variable amplitude loading are calculated by the Gauss-Seidel iterative algorithm CPD ; According to ΔK CPD , the single-cycle crack propagation increment Δa is calculated, and the crack length and the number of cycles are updated until the crack propagates to the termination length a f .

[0093] It can be understood that in this step, first, a strip yield model of the alternative two-dimensional crack body subjected to the equivalent crack surface traction distribution is established based on the weight function method to solve the variation law of the effective driving force of the fatigue crack propagation of the welded frame under variable amplitude loading with the crack length. The process of establishing its strip yield model by using the principle of elastic superposition is as shown in Figure 5 . In this strip yield model, based on the strip yield hypothesis, the following formula is used to calculate the virtual crack length when the maximum external load and the residual stress field act together under variable amplitude loading:

[0094] ∫0d P max ·σ eq，unit (x)m(d, x)dx + ∫0 d σ eq，res (x)m(d, x)dx - ∫ a d λσ0·m(d, x)dx = 0

[0095] In the formula, dx is the integration element. x is the coordinate along the crack line. m(d, x) is the weight function for substituting the two-dimensional cracked body. P max is the maximum external load corresponding to the current cycle in the variable amplitude load; d is the virtual crack length to be calculated, which is equal to the sum of the physical crack length a and the crack tip plastic zone size r p and can be solved by iterative dichotomy; λ is the plastic constraint factor characterizing the crack tip plastic constraint effect; σ0 is the flow stress of the cracked body material. σ eq,unit is the first equivalent crack surface traction distribution, and σ eq,res is the second equivalent crack surface traction distribution.

[0096] Based on the determined virtual crack length d, the physical crack surface and the crack tip plastic zone are discretized into several ideal elastoplastic bar elements, and the layout strategy of the bar elements is as Figure 6 shown. In Figure 6 , n t represents the total number of bar elements, and n p represents the number of bar elements in the plastic wake zone. w i is the width of the i-th bar element, and L(x i ) is the length of the bar element. x i is the central coordinate of the i-th bar element, and b l,i and b u,i are the lower and upper boundary coordinates of the i-th bar element respectively. V(x i ) is the crack surface displacement at the center of the i-th bar element.

[0097] Then, based on the determined virtual crack length d, the physical crack surface and the crack tip plastic zone are discretized into several ideal elastoplastic bar elements, and the following formula is used to calculate the crack surface displacement when the maximum external load and the residual stress field in the current cycle of the variable amplitude load act together:

[0098]

[0099] In the formula, x j is the central coordinate of the j-th bar element. V max (x j ) is the crack surface displacement at the center of the j-th bar element when the maximum external load P max and the residual stress field act together; n t is the total number of bar elements. σmax (x i ) is the stress value of the ith bar element under the combined action of the maximum external load P max and the residual stress field. F(d, x j ), R(d, x j ), and G(d, x i , x j ) are the crack surface displacement influence functions. Among them, F(d, x j ) represents the crack surface displacement generated at the center of the jth bar element due to the action of a unit external load under the virtual crack length d; R(d, x j ) represents the crack surface displacement generated at the center of the jth bar element due to the action of the residual stress; G(d, x i , x j ) represents the crack surface displacement generated at the center of the jth bar element due to the action of a unit crack surface traction force at the ith bar element. Based on the coordinate information of the bar element, the influence function of the crack surface displacement can be determined by substituting the weight function of the two-dimensional cracked body and can be expressed as:

[0100]

[0101] In the formula, E' is the effective elastic modulus. In the plane stress state, E' = E; in the plane strain state, E' = E / (1 - ν 2 ). E and ν are the elastic modulus and Poisson's ratio of the mechanical structure material respectively. τ is a dummy index used for integral calculation, and both dx and dτ are integral microelements. x is the coordinate along the crack line, d is the virtual crack length, and x j is the center coordinate of the jth bar element. m(τ, x) is the weight function of the two-dimensional substituted cracked body. B1 and B2 are the lower and upper limits of the integral respectively and can be expressed as:

[0102] B1 = b l，i B2 = min{b u，i , d, τ} 0 ≤ x j <b l，i

[0103] B1 = x j B2 = min{b u，i , d, τ} b l，i ≤ x j ≤ b u，i

[0104] B1 = x j B2 = min{b u，i , d} b u，i <x j ≤ d

[0105] In the formula, x jis the central coordinate of the j-th bar element, b l,i and b u,i are the lower and upper boundary coordinates of the i-th bar element respectively, d is the virtual crack length, and τ is a dummy variable used for integral calculation.

[0106] Subsequently, based on the determined crack surface displacement, the bar element stress is determined using the following formula:

[0107]

[0108] In the formula, σ max (x j ) is the stress value of the j-th bar element under the combined action of the maximum external load and the residual stress field; n p is the number of bar elements in the physical crack surface region. λ is the plastic constraint factor, and σ0 is the flow stress of the mechanical structure material.

[0109] Based on the determined crack surface displacement, the bar element length is determined using the following formula:

[0110]

[0111] In the formula, L(x j ) is the length of the j-th bar element, E is the elastic modulus of the cracked body material. λ is the plastic constraint factor, σ0 is the flow stress of the mechanical structure material, V max (x j ) is the crack opening displacement of the j-th bar element under the combined action of the maximum external load P max and the residual stress field, and n t is the total number of bar elements.

[0112] When the load level of the current cycle in the variable amplitude load changes from the maximum load to the minimum load, the crack surface displacement, bar element stress, and length of the two-dimensional surrogate cracked body are updated. From the displacement compatibility deformation condition of the crack surface displacement and bar element length, we can obtain:

[0113]

[0114] In the formula, P min is the minimum load of the current cycle in the variable amplitude load, σ min (x j ) is the stress value of the j-th bar element under the action of the minimum load, E is the material elastic modulus, L(x j ) is the length of the j-th bar element, n t is the total number of bar elements, and x j represents the central coordinate of the j-th bar element. F(d,x j ), R(d,x j ), and G(d,x i ,x j) is the influence function of crack surface displacement, where F(d,x j ) represents the crack surface displacement generated at the center of the j-th bar element due to the action of a unit external load under the virtual crack length d; R(d,x j ) represents the crack surface displacement generated at the center of the j-th bar element due to the action of residual stress under the virtual crack length d; G(d,x i ,x j ) represents the crack surface displacement generated at the center of the j-th bar element due to the action of a unit crack surface traction at the i-th bar element under the virtual crack length d.

[0115] The Gauss-Seidel method with constraints as shown in the following formula is used to update the stress of the bar element when the minimum load and the residual stress field act together in the current cycle:

[0116]

[0117] In the formula, [σ min (x j )] t+1 represents the stress value of the j-th bar element when the minimum load P min and the residual stress field act together obtained in the (t + 1)-th iteration. During the iterative calculation, when the relative change of the bar element stress obtained in two consecutive iterations is less than 5%, the iteration terminates. L(x j ) is the length of the j-th bar element. n t is the total number of bar elements. E is the elastic modulus. F(d,x j )、R(d,x j ) and G(d,x i ,x j ) are the influence functions of crack surface displacement.

[0118] In addition, for the bar elements in the plastic wake region (1 ≤ j ≤ n p ), the following constraint conditions should be satisfied during the iteration process:

[0119]

[0120] In the formula, σ0 is the flow stress of the material, σ min (x j ) is the stress value of the j-th bar element when the minimum load P min and the residual stress field act together.

[0121] For the bar elements in the crack tip plastic region (n p < j ≤ n t ), the following constraint conditions should be satisfied during the iteration process:

[0122]

[0123] In the formula, σ0 is the flow stress of the material, λ is the plastic constraint factor of the cracked body, and n p is the number of rod elements in the plastic wake region, and σ min (x j ) is the stress value of the j-th rod element under the combined action of the minimum load P min and the residual stress field.

[0124] Based on the stress of the rod element obtained by iterative operation, the crack face opening displacement under the combined action of the minimum load and the residual stress field is calculated using the formula shown below:

[0125]

[0126] In the formula, V min (x j ) is the crack face displacement at the center of the j-th rod element under the combined action of the minimum load P min and the residual stress field. σ min (x j ) is the stress value of the j-th rod element under the combined action of the minimum load P min and the residual stress field. n t is the total number of rod elements. F(d, x j ), R(d, x j ), and G(d, x i , x j ) are crack face displacement influence functions.

[0127] At this time, for the rod element that undergoes compressive yield under the minimum load, its rod element length should be updated to:

[0128]

[0129] In the formula, V min (x j ) is the crack face displacement at the center of the j-th rod element under the combined action of the minimum load P min and the residual stress field, L(x j ) is the length of the j-th rod element, σ0 is the flow stress of the material, and E is the elastic modulus.

[0130] For the current cycle in the variable amplitude load, when the load level changes from the minimum load to the maximum load of the next load cycle again, this method uses the stress intensity factor amplitude corresponding to the stage of cyclic plastic damage at the crack tip at this time as the effective driving force for controlling fatigue crack growth. The effective crack growth force ΔK CPD can be expressed as:

[0131] ΔK CPD = K max，tot - KCPD，tot

[0132] In the formula, K max，tot represents the stress intensity factor when the maximum external load P max in the variable amplitude load and the residual stress field act together. K CPD,tot represents the stress intensity factor when tensile plastic deformation occurs at the crack tip under the current cyclic loading, and can be calculated using the formulas shown below respectively:

[0133] K max，tot = ∫0 a P max ·σ eq，unit (x)·m(a, x)dx + ∫0 a σ eq，res (x)·m(a, x)dx

[0134] K CPD，tot = ∫0 a P CPD ·σ eq，app (x)·m(a, x)dx + ∫0 a σ eq，res (x)·m(a, x)dx

[0135] In the formula, a represents the crack length, P max represents the maximum load, and m(a, x) represents the weight function for replacing the two-dimensional crack body. σ eq,unit is the first equivalent crack surface traction distribution, and σ eq,res is the second equivalent crack surface traction distribution. P CPD represents the external load corresponding to the tensile plastic deformation occurring at the crack tip under the current cyclic loading, and can be iteratively solved using the formula shown below based on the Gauss - Seidel method with constraint conditions:

[0136]

[0137] In the formula, [P CPD (j)] t+1 represents the iterative value of the external load P CPD obtained from the displacement compatibility deformation condition of the j-th bar element in the (t + 1)-th iteration. L(x j ) represents the length of the j-th bar element when the external load P CPD and the residual stress field act together. n t is the total number of bar elements, and n p is the number of bar elements located in the plastic wake region. λ is the plastic constraint factor, σ0 is the flow stress of the crack body material, and E is the elastic modulus. F(d, x j ), R(d, x j ), and G(d, x i, x j ) is the influence function of the crack surface displacement. [σ CPD (x i )] t represents the external load P obtained in the t-th iteration CPD and the stress value of the i-th bar element under the combined action of the residual stress field. The iterative solution can be carried out using the formula shown below:

[0138]

[0139] In the formula, P CPD represents the external load corresponding to the tensile plastic deformation generated at the crack tip under the current cyclic loading. λ is the plastic constraint factor, σ0 is the flow stress of the crack body material, and E is the elastic modulus. n t is the total number of bar elements, and n p is the number of bar elements located in the plastic wake region. L(x j ) is the external load P CPD and the length of the j-th bar element under the combined action of the residual stress field. [σ CPD (x i )] t represents the stress value of the i-th bar element under the combined action of the external load P CPD obtained in the t-th iteration and the residual stress field. F(d, x j ), R(d, x j ), and G(d, x i , x j ) are the influence functions of the crack surface displacement.

[0140] In a single iteration, the true iteration value of the external load P CPD can be calculated using the formula shown below based on the iteration values on each bar element:

[0141] [P CPD t+1 = max{[P CPD (1)] t+1 , … [P CPD (j)] t+1 , … [P CPD (n p )] t+1 , [P CPD (n p + 1)] t+1}

[0142] In the formula, [P CPD t+1 represents the true iteration value of the external load P CPD obtained in the (t + 1)-th iteration, and [P CPD (j)] t+1 ​​The external load P obtained from the displacement compatibility deformation condition of the j-th bar element in the (t + 1)-th iteration CPD Iterative value. n p is the number of bar elements located in the plastic wake region.

[0143] During the iteration process, the same constraint conditions as those in the state of the bar element for iteratively solving the minimum load still need to be satisfied. Also, when the relative change of the external load P CPD obtained in two consecutive iterations is less than 5%, the iteration process terminates.

[0144] Based on the effective driving force for crack growth ΔK CPD in the current cycle, the corresponding crack growth increment Δa is calculated using the formula shown below:

[0145] Δa = f(ΔK CPD )·ΔN

[0146] where ΔN represents the increment of the number of cycles. For random loads, ΔN = 1 can be taken to fully consider the load sequence effect. f(ΔK CPD ) represents the fatigue crack growth rate model based on the fatigue crack growth parameter ΔK CPD , which is used to describe the relationship between ΔK CPD and the fatigue crack growth rate da / dN, and needs to be determined based on the results of fatigue crack growth tests.

[0147] According to the calculated crack growth increment, the fatigue crack length and the corresponding number of cycles are updated using the formula shown below:

[0148] a k+1 = a k + Δa

[0149] N k+1 = N k + ΔN

[0150] where a k and N k represent the crack length and the number of cycles corresponding to the k-th crack growth step respectively. Δa represents the fatigue crack growth increment, and ΔN represents the increment of the number of cycles.

[0151] It should be noted that in this embodiment, after updating the crack length and the number of cycles, the rod elements within a range of Δa behind the current physical crack tip are broken, thereby realizing the physical process of fatigue crack growth in the strip yield model. Then, based on the new physical crack length and the size of the crack tip plastic zone, the rod elements are re-divided, and the state (length and stress value) of the rod elements before breaking is mapped to the new rod elements using the linear interpolation algorithm. Finally, based on the load level of the next cycle, the above steps are re-used to calculate the state of the rod elements under the maximum and minimum loads, as well as the fatigue crack growth process, which will be repeated until the fatigue crack length reaches the termination crack length a f 。

[0152] In this step, based on the weight function of the center cracked plate, a strip yield model of the center cracked plate subjected to an equivalent crack surface traction distribution is established to solve the variation law of the effective driving force for fatigue crack growth with the crack length under variable amplitude loading of the welded frame. Based on the material properties of the welded frame material, the elastic modulus E in the strip yield model is taken as 210 MPa, the Poisson's ratio ν is 0.3, and the flow stress σ0 is 472.5 MPa. The number of rod elements in both the plastic wake region and the crack tip plastic zone is 50

[0153] S500. Simulate the crack growth process under constant amplitude loading through the strip yield model, establish the conversion relationship between ΔK and ΔK CPD , and combine the data of the multi-stress ratio constant amplitude loading test for stress intensity factor conversion and data fitting to calibrate the fatigue crack growth rate model parameters based on ΔK CPD .

[0154] It can be understood that in this step, based on the strip yield model established in the above steps, the fatigue crack growth simulation under constant amplitude loading with different stress ratios is carried out using the load conditions obtained in the previous steps, and the stable value of the external load P CPD under constant amplitude loading and the ratio P max between the maximum value P CPD / P max 。

[0155] Based on this ratio, establish the relationship between the stress intensity factor amplitude ΔK and the effective driving force for fatigue crack growth ΔK CPD during the fatigue crack growth test:

[0156]

[0157] In the formula, R is the stress ratio of the constant amplitude load, and P max represents the maximum load in the constant amplitude load, and P CPDRepresents the load when tensile plastic deformation occurs at the crack tip during cyclic loading, used to characterize the cyclic plastic damage at the crack tip. When under constant amplitude loading, it takes the external load P CPD The stable value of the change curve.

[0158] Using the above relationship, convert the R~ΔK~da / dN data obtained from the fatigue crack growth test determined in the previous steps into R~ΔK CPD ~da / dN data. For the converted fatigue crack growth rate data, use an appropriate fatigue crack growth rate model to fit the data in a logarithmic coordinate system to obtain the fatigue crack growth rate model parameters based on the effective driving force ΔK CPD of the fatigue crack growth rate model.

[0159] S600. Superimpose the variable amplitude load spectrum and the equivalent crack surface traction distribution onto the two-dimensional alternative crack body, input the fatigue crack growth rate model parameters, and iteratively calculate the evolution relationship between the crack length and the number of cycles to generate the fatigue crack growth life curve of the welded frame.

[0160] It can be understood that in this step, based on the principle of linear superposition, the variable amplitude load spectrum applied to the welded frame is equivalent to the crack surface traction distribution applied to the two-dimensional alternative crack body. The crack body traction distribution can be calculated using the following formula:

[0161] σ eq，app (x, N) = P(N)·σ eq，unit

[0162] In the formula, P(N) represents the load level at the Nth cycle of the variable amplitude load spectrum applied to the welded frame. x represents the coordinate along the crack line, and σ eq,unit represents the first equivalent crack surface traction distribution.

[0163] Superimpose the equivalent variable amplitude load spectrum σ eq,app and the welding residual stress field σ eq,res into the strip yield model of the two-dimensional alternative crack body established in the previous step. Set the initial crack length a0 and the calculation termination crack length a f of the welded frame, and use the fatigue crack growth rate model parameters obtained previously to predict the fatigue crack growth life of the welded frame under variable amplitude loading and residual stress field, and output the relationship between the crack length a and the number of cycles N in the two-dimensional alternative crack body, which is the fatigue crack growth life curve of the welded frame under variable amplitude loading.

[0164] When simulating the fatigue crack growth of a compact tension specimen used for the fatigue crack growth test under the load conditions in the above steps, obtain the stable value of the external load P CPD under different stress ratios of the constant amplitude load and the maximum value P maxThe ratio P between CPD / P max Based on this ratio, the relationship between the stress intensity factor amplitude ΔK and the effective driving force for fatigue crack growth ΔK CPD is established. Using this relationship, the R~ΔK~da / dN data obtained from the fatigue crack growth test of the compact tension specimen is converted into R~ΔK CPD ~da / dN data, and the fatigue crack growth rate data of the welded frame material based on the effective driving force for fatigue crack growth ΔK CPD is as shown Figure 12 As shown in the figure, since there is a good logarithmic linear relationship between the effective driving force for fatigue crack growth ΔK CPD in the figure and the fatigue crack growth rate da / dN, linear fitting is performed on the ΔK CPD ~da / dN data under different stress ratios, and the fatigue crack growth rate model based on the effective driving force for fatigue crack growth ΔK CPD can be expressed as:

[0165]

[0166] where da / dN represents the fatigue crack growth rate.

[0167] Based on the principle of linear superposition, the variable amplitude load spectrum applied to the welded frame is equivalent to the crack surface traction distribution applied to the center cracked plate, and the equivalent crack surface traction distribution σ eq,app is obtained. In this calculation example, the ten-level variable amplitude load spectrum applied to the welded frame is shown in Table 3.

[0168] Table 3 Ten-level variable amplitude load spectrum applied to the welded frame

[0169] Serial number <![CDATA[Maximum load P max [kN]]]> <![CDATA[Minimum load P min [kN]]]> Number of cycles N [cycle] 1 8 2 <![CDATA[2.0×10 4 > 2 14 6 <![CDATA[1.0×10 4 > 3 5 1 <![CDATA[2.0×10 4 > 4 15 5 <![CDATA[0.5×10 4 > 5 9 7 <![CDATA[4.0×10 4 > 6 14 11 <![CDATA[2.5×10 4 > 7 9 2 <![CDATA[4.0×10 4 > 8 14 4 <![CDATA[3.0×10 4 > 9 12 2 <![CDATA[1.5×10 4 > 10 10 2 <![CDATA[1.5×10 4 >

[0170] The equivalent crack surface traction distribution σ eq,app representing the action of the variable amplitude load and the equivalent crack surface traction distribution σ eq,res (the second equivalent crack surface traction distribution) representing the action of the welding residual stress field are input into the strip yield model of the center cracked plate. Based on the half-length of the surface crack in the welded frame, the initial crack length a0 is taken as the half-length of the initial surface crack, with a value of 0.5 mm, and the termination crack length a f is the half-length of the surface crack corresponding to when the surface crack depth reaches 90% of the plate thickness, with a value of approximately 13 mm. Based on the parameters of the fatigue crack growth rate model obtained by fitting, the fatigue crack growth life of the welded frame under the combined action of the variable amplitude load and the welding residual stress field is predicted by the strip yield model of the center cracked plate. Figure 13Exemplarily, the state of the bar elements and the stress distribution of the bar elements in the strip yield model of the central cracked plate at the 2000th extended analysis step are given. Figure 13 (a), (c) and (c) respectively represent the maximum load P max , the minimum load P min and the external load P CPD The state of the bar elements under the action. It can be seen from the figure that under the maximum load, the crack is in a fully open state. Under the minimum load and the external load P CPD The plastic wake behind the crack tip is in a partially closed state under the action. This shows that the method described in the present invention can well describe the elastoplastic response of the crack tip of the welded frame with surface cracks under different load levels.

[0171] Among them, Figure 13 (d) gives the stress distribution of the bar elements under three load levels. It can be seen that under the external load P CPD The stress value at the crack tip just reaches the yield stress, while the plastic zone behind the crack tip has not yet entered the yield state. This shows that the effective driving force ΔK CPD corresponding to the load range from the external load P max to the maximum load P CPD can better characterize the cyclic plastic damage at the crack tip and realize the quantitative prediction of the fatigue crack growth life under variable amplitude loading. Figure 14 The variation law of the external load P CPD of the welded frame under variable amplitude loading is given, and the comparison of the maximum load and the minimum load of the variable amplitude load is also given in the figure.

[0172] It can be seen from the figure that since the external load P CPD reflects the evolution law of the cyclic plastic damage at the crack tip, it can well describe the load sequence effect existing in the variable amplitude load. The effective driving force ΔK CPD determined by the external load P CPD , combined with the crack growth rate model, the fatigue crack growth life curve of the welded frame under this variable amplitude load spectrum can be obtained as Figure 15 shown.

[0173] Therefore, the calculation results show that for this welded frame, the number of cycles corresponding to the fatigue crack propagating from a surface crack with a half-length of 0.5 mm to a crack approaching the thickness of the plate is about 860,000 cycles.

[0174] Example 2:

[0175] As Figure 2 shown, this embodiment provides a fatigue crack growth life prediction system for a mechanical structure. Refer to Figure 2 The system includes:

[0176] Analysis and Establishment Module 701: Set the geometric parameters and initiation positions of initial fatigue cracks in the mechanical structure, conduct crack propagation analysis using the linear elastic finite element method, and establish the relationship between crack length and stress intensity factor a~K under the action of the residual stress field res , as well as the relationship between crack length and stress intensity factor a~K under the action of unit external load unit ;

[0177] Measurement Module 702: Used to prepare standard fatigue crack propagation specimens of mechanical structure materials, perform multi-stress ratio constant amplitude load tests, and measure the correlation data between stress intensity factor amplitude ΔK and crack propagation rate da / dN under different stress ratios;

[0178] Solution Module 703: Used to select a two-dimensional through crack body as an alternative model, combine the relationship between a~K res and a~K unit , adopt the weight function method and multi-objective optimization algorithm to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field;

[0179] Calculation Module 704: Used to construct a strip yield model in the two-dimensional alternative crack body based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, discretize the crack surface and plastic zone into elastoplastic rod elements, calculate the size of the plastic zone at the crack tip under variable amplitude load based on the strip yield hypothesis, and calculate the rod element stress and effective driving force ΔK through the Gauss-Seidel iterative algorithm CPD ; Calculate the single-cycle crack propagation increment Δa according to ΔK CPD , update the crack length and number of cycles until the crack propagates to the termination length a f ;

[0180] Fitting and Calibration Module 705: Used to simulate the crack propagation process under constant amplitude load through the strip yield model, establish the conversion relationship between ΔK and ΔK CPD , combine the data of multi-stress ratio constant amplitude load tests for stress intensity factor conversion and data fitting, and calibrate the fatigue crack propagation rate model parameters based on ΔK CPD ;

[0181] Prediction and Generation Module 706: Used to superimpose the variable amplitude load spectrum and the equivalent crack surface traction distribution on the two-dimensional alternative crack body, input the fatigue crack propagation rate model parameters, iteratively calculate the evolution relationship between crack length and number of cycles, and generate the fatigue crack propagation life curve of the mechanical structure.

[0182] Specifically, the solution module 703 includes:

[0183] Establishment unit: used to establish the equivalent relationship between the mechanical structure and the two-dimensional alternative crack body in terms of the stress intensity factor K, where the equivalent condition is that for any crack length a, the mechanical structure under the action of external loads and residual stress fields and the two-dimensional alternative crack body under the action of equivalent crack surface traction forces have the same stress intensity factor K;

[0184] First calculation unit: used to, based on the weight function method, the K-value equivalent conditions corresponding to the external load and the residual stress field can be respectively expressed as:

[0185] ∫0 a σ eq，unit (x)·m(a, x)dx = K unit (a)

[0186] ∫0 a σ eq，res (x)·m(a, x)dx = K res (a)

[0187] In the formula, dx is the integration element. a represents the crack length, m(a, x) is the weight function of the two-dimensional alternative crack body, K unit (a) is the a-K relationship of the mechanical structure under the action of a unit external load, σ eq,unit (x) is the distribution of the first equivalent crack surface traction force acting on the two-dimensional alternative crack body, K res (a) is the a-K relationship of the mechanical structure under the action of the residual stress field, σ eq,res (x) is the distribution of the second equivalent crack surface traction force acting on the two-dimensional alternative crack body;

[0188] Discrete unit: used to approximately discretize the equivalent crack surface traction force distribution into a piecewise spline function, where the i-th spline function representing the equivalent crack surface traction force distribution can be expressed as:

[0189]

[0190] In the formula, α i , β i , γ i and δ i respectively represent the coefficients of the i-th piecewise spline function, s i-1 and s i are respectively the two side nodes of the i-th piecewise spline function, and x represents the coordinate along the crack line.

[0191] Specifically, the calculation module 704 includes:

[0192] The second calculation unit: It is used to establish a strip yield model of an alternative two-dimensional cracked body that bears the equivalent crack surface traction distribution based on the weight function method. In this strip yield model, based on the strip yield hypothesis, the virtual crack length under the combined action of the maximum external load and the residual stress field under variable amplitude loading is calculated, and its calculation formula is as follows:

[0193] ∫0 d P max ·σ eq，unit (x)m(d,x)dx + ∫0 d σ eq，res (x)m(d,x)dx - ∫ a d λσ0·m(d,x)dx = 0

[0194] In the formula, dx is the integration element. m(d,x) represents the weight function of the alternative two-dimensional cracked body. P max is the maximum external load corresponding to the current cycle in the variable amplitude load; d is the virtual crack length to be calculated, which is equal to the sum of the physical crack length a and the crack tip plastic zone size r p , λ is the plastic constraint factor characterizing the crack tip plastic constraint effect, and σ0 is the flow stress of the cracked body material. σ eq,unit represents the first equivalent crack surface traction distribution, and σ eq,res represents the second equivalent crack surface traction distribution.

[0195] The third calculation unit: It is used to discretize the physical crack surface and the crack tip plastic zone into multiple elastoplastic rod elements based on the determined virtual crack length d, and calculate the crack surface displacement under the combined action of the maximum external load and the residual stress field in the current cycle of the variable amplitude load using the following formula:

[0196]

[0197] In the formula, V max (x j ) is the crack surface displacement at the center of the j-th rod element under the combined action of the maximum external load P max and the residual stress field, and n t is the total number of rod elements. σ max (x i ) represents the stress value of the i-th rod element under the combined action of the external load P max and the residual stress field. F(d,x j ), R(d,x j ) and G(d,x i ,x j ) are crack surface displacement influence functions. Among them, F(d,x j ) represents the crack surface displacement generated at the center of the j-th rod element due to the action of a unit external load under the virtual crack length d, and R(d,xj ) represents the crack surface displacement generated at the center of the j-th bar element due to the action of residual stress, G(d,x i ,x j ) represents the crack surface displacement generated at the center of the j-th bar element when a unit crack surface traction acts at the i-th bar element.

[0198] Specifically, the fitting and calibration module includes:

[0199]

[0200] In the formula, ΔK CPD is the effective driving force for fatigue crack growth, R is the stress ratio of the constant amplitude load, ΔK is the amplitude of the stress intensity factor, P max is the maximum value of the constant amplitude load. P CPD represents the load when tensile plastic deformation occurs at the crack tip during cyclic loading, which is used to characterize the cyclic plastic damage at the crack tip. When under the action of a constant amplitude load, it takes the stable value of the external load P CPD variation curve.

[0201] Specifically, the prediction and generation module 706 includes:

[0202] The fourth calculation unit: For the purpose of equivalenting the variable amplitude load spectrum applied to the mechanical structure to the crack surface traction distribution applied to the two-dimensional alternative crack body based on the principle of linear superposition, the calculation formula for the crack body traction distribution is as follows:

[0203] σ eq，app (x, N) = P(N)·σ eq，unit

[0204] In the formula, P(N) represents the load level of the N-th cycle in the variable amplitude load spectrum applied to the mechanical structure, σ eq,app is the variable amplitude load spectrum, N is the number of cycles, and x represents the coordinate along the crack line. σ eq,unit is the corresponding first equivalent crack surface traction distribution acting on the two-dimensional alternative crack body.

[0205] It should be noted that regarding the system in the above embodiments, the specific manners in which each module performs operations have been described in detail in the embodiments related to the method, and will not be elaborated herein.

[0206] Embodiment 3:

[0207] Corresponding to the above method embodiment, in this embodiment, a device for predicting the fatigue crack growth life of a mechanical structure is also provided. A device for predicting the fatigue crack growth life of a mechanical structure described below can be mutually referred to with a method for predicting the fatigue crack growth life of a mechanical structure described above.

[0208] Figure 3 is a block diagram of a fatigue crack growth life prediction device 800 for a mechanical structure shown according to an exemplary embodiment. As Figure 3 shown, the fatigue crack growth life prediction device 800 for the mechanical structure includes: a processor 801 and a memory 802. The fatigue crack growth life prediction device 800 for the mechanical structure further includes one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0209] Among them, the processor 801 is used to control the overall operation of the fatigue crack growth life prediction device 800 of the mechanical structure to complete all or part of the steps in the above-mentioned fatigue crack growth life prediction method of the mechanical structure. The memory 802 is used to store various types of data to support the operation of the fatigue crack growth life prediction device 800 of the mechanical structure. These data may include, for example, instructions for any application or method operating on the fatigue crack growth life prediction device 800 of the mechanical structure, as well as application-related data, such as contact data, received and sent messages, pictures, audio, video, and so on. The memory 802 can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic memory, flash memory, a magnetic disk, or an optical disk. The multimedia component 803 may include a screen and an audio component. The screen can be, for example, a touch screen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone, and the microphone is used to receive external audio signals. The received audio signal can be further stored in the memory 802 or sent through the communication component 805. The audio component also includes at least one speaker for outputting audio signals. The I / O interface 804 provides an interface between the processor 801 and other interface modules, and the above-mentioned other interface modules can be a keyboard, a mouse, or buttons, etc. These buttons can be virtual buttons or physical buttons. The communication component 805 is used for wired or wireless communication between the fatigue crack growth life prediction device 800 of the mechanical structure and other devices. Wireless communication, such as Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination of one or more of them. Therefore, the corresponding communication component 805 may include: a Wi-Fi module, a Bluetooth module, or an NFC module.

[0210] In an exemplary embodiment, the fatigue crack growth life prediction device 800 of the mechanical structure can be implemented by one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors or other electronic components, and is used to execute the above-mentioned fatigue crack growth life prediction method of the mechanical structure.

[0211] In another exemplary embodiment, a computer-readable storage medium including program instructions is further provided. When the program instructions are executed by a processor, the steps of the above-mentioned fatigue crack growth life prediction method of the mechanical structure are implemented. For example, the computer-readable storage medium can be the above-mentioned memory 802 including program instructions, and the above-mentioned program instructions can be executed by the processor 801 of the fatigue crack growth life prediction device 800 of the mechanical structure to complete the above-mentioned fatigue crack growth life prediction method of the mechanical structure.

[0212] Embodiment 4:

[0213] Corresponding to the above method embodiment, a readable storage medium is further provided in this embodiment. A readable storage medium described below can be correspondingly referred to with a fatigue crack growth life prediction method of a mechanical structure described above.

[0214] A computer program is stored on the readable storage medium. When the computer program is executed by a processor, the steps of the fatigue crack growth life prediction method of the welding structure in the above method embodiment are implemented.

[0215] The readable storage medium can specifically be various readable storage media such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disc that can store program codes.

[0216] In summary, the present invention provides a method for predicting the fatigue crack growth life of a mechanical structure under variable amplitude loading. Different from other fatigue crack growth life prediction methods, it proposes to use the stress intensity factor amplitude that can characterize the cyclic plastic damage at the crack tip as the effective driving force for fatigue crack growth, overcoming the limitation of traditional life prediction methods that are difficult to consider the load sequence effect, and having higher calculation accuracy when predicting the fatigue crack growth life of a mechanical structure under variable amplitude loading. At the same time, by establishing the equivalent relationship between the mechanical structure and the two-dimensional alternative crack body in terms of the stress intensity factor, and using the strip yield model to solve the elastoplastic response at the crack tip of the complex mechanical structure, the problem of low calculation efficiency existing in the traditional finite element method is solved, and the high-efficiency solution of the effective driving force for fatigue crack growth of the mechanical structure under variable amplitude loading is realized. When applied to the field of fatigue strength and reliability of mechanical structures, it is expected to achieve high-precision prediction of the fatigue crack growth life of mechanical structures under variable amplitude loading.

[0217] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention can have various changes and modifications. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0218] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or replacements, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for predicting the fatigue crack growth life of a mechanical structure, characterized in that, Including: Set the geometric parameters and initiation positions of the initial fatigue cracks in the mechanical structure, conduct crack propagation analysis using the linear elastic finite element method, and establish the relationship between the crack length and the stress intensity factor under the action of the residual stress field a~K res , as well as the relationship between the crack length and the stress intensity factor under the action of the unit external load a~K unit ; Prepare standard fatigue crack growth specimens of mechanical structure materials, perform multi-stress ratio constant amplitude load tests, and measure the correlation data between the stress intensity factor amplitude ΔK and the crack growth rate da / dN under different stress ratios; Select a two-dimensional through-crack body as the alternative model, and combine the stress intensity factor relationships a~K res and the stress intensity factor relationships a~K unit Based on the relationship between them, use the weight function method and the multi-objective optimization algorithm to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field; Based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, a strip yield model is constructed in a two-dimensional surrogate crack body. The crack surface and the plastic zone are discretized into elastoplastic rod elements. Based on the strip yield hypothesis, the size of the plastic zone at the crack tip under variable amplitude loading is calculated, and the stress of the rod elements and the effective driving force ΔK for fatigue crack growth are calculated by the Gauss-Seidel iterative algorithm CPD ; According to ΔK CPD calculate the single-cycle crack growth increment Δa, update the crack length and the number of cycles until the crack propagates to the termination length a f ; Simulate the crack propagation process under constant amplitude loading through the strip yield model, and establish the conversion relationship between the amplitude of the stress intensity factor ΔK and the effective driving force for fatigue crack growth ΔK CPD . Combine the data of the multi-stress ratio constant amplitude loading test for stress intensity factor conversion and data fitting, and calibrate the fatigue crack growth rate model parameters based on the effective driving force for fatigue crack growth ΔK CPD . Superimpose the variable amplitude load spectrum with the equivalent crack surface traction distribution, apply it to the crack surface of the two-dimensional surrogate crack body, input the fatigue crack growth rate model parameters, and iteratively calculate the evolution relationship between the crack length and the number of cycles based on the strip yield model of the two-dimensional surrogate crack body to generate the fatigue crack growth life curve of the mechanical structure.

2. The fatigue crack growth life prediction method for the mechanical structure according to claim 1, characterized in that The combined stress intensity factor relationship a~K res and the stress intensity factor relationship a~K unit Between the relationships, the weight function method and the multi-objective optimization algorithm are used to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field, including: Establish the equivalent relationship between the mechanical structure and the two-dimensional surrogate crack body in terms of the stress intensity factor K, where the equivalent condition is that at any crack length a, the mechanical structure under the action of external loads and residual stress fields and the two-dimensional surrogate crack body under the action of equivalent crack surface traction have the same stress intensity factor K; Based on the weight function method, the K-value equivalent conditions corresponding to the external load and the residual stress field can be respectively expressed as: ∫0 a σ eq,unit (x)·m(a,x)dx = K unit (a) ∫0 a σ eq,res (x)·m(a,x)dx = K res (a) where \(dx\) is the integration element, \(a\) is the crack length, \(x\) is the coordinate along the crack line, \(m(a,x)\) is the weight function of the two-dimensional surrogate crack body, and \(K\) unit (a) is the \(a - K\) relationship of the mechanical structure under the action of a unit external load, and \(\sigma\) eq,unit (x) is the corresponding traction distribution on the first equivalent crack surface acting on the two-dimensional surrogate crack body, and \(K\) res (a) is the \(a - K\) relationship of the mechanical structure under the action of the residual stress field, and \(\sigma\) eq,res (x) is the corresponding traction distribution on the second equivalent crack surface acting on the two-dimensional surrogate crack body; Approximately discretize the equivalent crack surface traction distribution into a piecewise spline function, where the i-th spline function representing the equivalent crack surface traction distribution can be expressed as: where α i , β i , γ i and δ i represent the coefficients of the i-th piecewise spline function respectively, s i-1 and s i are the nodes on both sides of the i-th piecewise spline function respectively, x is the coordinate along the crack line, is the i-th spline function representing the equivalent crack surface traction distribution.

3. The fatigue crack growth life prediction method for the mechanical structure according to claim 1, characterized in that, Based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, construct a strip yield model in the two-dimensional surrogate crack body, and discretize the crack surface and the plastic zone into elastoplastic rod elements, including: Establish a strip yield model of the surrogate two-dimensional crack body under the action of the equivalent crack surface traction distribution based on the weight function method. In this strip yield model, based on the strip yield hypothesis, calculate the virtual crack length under the combined action of the maximum external load and the residual stress field under variable amplitude loads, and its calculation formula is as follows: where \(dx\) is the integration element, \(P\) max is the maximum external load corresponding to the current cycle in the variable amplitude load, \(d\) is the virtual crack length to be calculated, which is equal to the sum of the physical crack length \(a\) and the crack tip plastic zone size \(r\) p \(\lambda\) is the plastic constraint factor characterizing the crack tip plastic constraint effect, \(\sigma_0\) is the flow stress of the cracked body material, \(x\) is the coordinate along the crack line, \(m(d,x)\) is the weight function for replacing the two-dimensional cracked body, \(\sigma\) eq,unit (x) is the first equivalent crack surface traction distribution, \(\sigma\) eq,res (x) is the second equivalent crack surface traction distribution; Based on the determined virtual crack length d, discretize the physical crack surface and the crack tip plastic zone into multiple elastoplastic rod elements, and use the following formula to calculate the crack surface displacement under the combined action of the maximum external load and the residual stress field in the current cycle of the variable amplitude load: where x j is the central coordinate of the j-th bar element, V max (x j ) is the crack face displacement at the center of the j-th bar element under the combined action of the maximum external load P max and the residual stress field, n t is the total number of bar elements, x i is the central coordinate of the i-th bar element, F(d, x j ), R(d, x j ) and G(d, x i , x j ) are crack face displacement influence functions, where F(d, x j ) represents the crack face displacement generated at the center of the j-th bar element due to the action of a unit external load at the virtual crack length d, R(d, x j ) represents the crack face displacement generated at the center of the j-th bar element due to the action of the residual stress, G(d, x i , x j ) represents the crack face displacement generated at the center of the j-th bar element due to the action of a unit crack face traction at the i-th bar element, σ max (x i ) is the stress value of the i-th bar element under the combined action of the maximum external load P max and the residual stress field.

4. The fatigue crack growth life prediction method for the mechanical structure according to claim 1, characterized in that, The process of crack propagation under constant amplitude load is simulated by the strip yield model, and the conversion relationship between the amplitude of the stress intensity factor ΔK and the effective driving force ΔK for fatigue crack propagation is established, where the conversion relationship between the amplitude of the stress intensity factor ΔK and the effective driving force ΔK for fatigue crack propagation is as follows: CPD The conversion relationship between the amplitude of the stress intensity factor ΔK and the effective driving force ΔK for fatigue crack propagation is as follows: CPD The calculation formula for the conversion relationship is as follows: where ΔK CPD is the effective driving force for fatigue crack growth, R is the stress ratio of the constant amplitude load, ΔK is the stress intensity factor amplitude, P max is the maximum value of the constant amplitude load, and P CPD is the external load corresponding to the plastic deformation at the crack tip.

5. The fatigue crack growth life prediction method for the mechanical structure according to claim 1, characterized in that, The superimposing the variable amplitude load spectrum with the equivalent crack surface traction distribution and applying it to the crack surface of the two-dimensional surrogate crack body includes: Based on the principle of linear superposition, equivalent the variable amplitude load spectrum applied to the mechanical structure to the crack surface traction distribution applied to the two-dimensional surrogate crack body, and its calculation formula for the crack body traction distribution is as follows: σ eq,app (x,N) = P(N)·σ eq,unit where P(N) represents the load level at the Nth cycle of the variable amplitude load spectrum applied to the welded structure, σ eq,app is the variable amplitude load spectrum, N is the number of cycles, and σ eq,unit is the corresponding traction distribution on the first equivalent crack surface acting on the two-dimensional surrogate crack body, and x is the coordinate along the crack line.

6. A fatigue crack growth life prediction system for a mechanical structure, based on the fatigue crack growth life prediction method for the mechanical structure according to claim 1, characterized in that, Including: Analysis and establishment module: used to set the geometric parameters and initiation positions of initial fatigue cracks in a mechanical structure, conduct crack propagation analysis of the mechanical structure under the action of residual stress and cyclic external loads by using the linear elastic finite element method, and establish the relationship between crack length and stress intensity factor under the action of residual stress field a~K res , and the relationship between crack length and stress intensity factor under the action of unit external load a~K unit ; Measurement module: used to prepare standard fatigue crack growth specimens of mechanical structure materials, perform multi-stress ratio constant amplitude load tests, and measure the correlation data between the stress intensity factor amplitude ΔK and the crack growth rate da / dN under different stress ratios; Solution module: used to select a two-dimensional through-crack body as a surrogate model, and combine the relationship between stress intensity factors a~K res and the relationship between stress intensity factors a~K unit Between them, the weight function method and the multi-objective optimization algorithm are used to solve the first equivalent crack surface traction distribution corresponding to the external load and the second equivalent crack surface traction distribution corresponding to the residual stress field; Calculation module: used to construct a strip yield model in a two-dimensional surrogate cracked body based on the first equivalent crack surface traction distribution and the second equivalent crack surface traction distribution, discretize the crack surface and the plastic zone into elastoplastic rod elements, calculate the size of the plastic zone at the crack tip under variable amplitude loads based on the strip yield hypothesis, and calculate the rod element stresses and the effective driving force for fatigue crack growth ΔK through the Gauss-Seidel iterative algorithm CPD ; Based on ΔK CPD calculate the single-cycle crack growth increment Δa, update the crack length and the number of cycles until the crack propagates to the termination length a f ; Fitting and calibration module: used to simulate the crack propagation process under constant amplitude load through the strip yield model, establish the conversion relationship between the stress intensity factor amplitude ΔK and the effective driving force for fatigue crack propagation ΔK CPD ; combine the data of multi-stress ratio constant amplitude load tests to perform stress intensity factor conversion and data fitting, and calibrate the fatigue crack propagation rate model parameters based on ΔK CPD ; Prediction generation module: used to superimpose the variable amplitude load spectrum with the equivalent crack surface traction distribution, apply it to the crack surface of the two-dimensional surrogate crack body, input the fatigue crack growth rate model parameters, iteratively calculate the evolution relationship between the crack length and the number of cycles, and generate the fatigue crack growth life curve of the mechanical structure.

7. The fatigue crack growth life prediction system of the mechanical structure according to claim 6, characterized in that, The solution module, including: Establishment unit: used to establish the equivalent relationship between the mechanical structure and the two-dimensional surrogate crack body in terms of the stress intensity factor K, where the equivalent condition is that at any crack length a, the mechanical structure under the action of external loads and residual stress fields and the two-dimensional surrogate crack body under the action of equivalent crack surface traction have the same stress intensity factor K; The first calculation unit: For the K - value equivalent conditions corresponding to the external load and the residual stress field based on the weight - function method, they can be respectively expressed as: ∫0 a σ eq,unit (x)·m(a,x)dx = K unit (a) ∫0 a σ eq,res (x)·m(a,x)dx = K re s(a) where \(dx\) is the integration element, \(a\) is the crack length, \(x\) is the coordinate along the crack line, \(m(a, x)\) is the weight function of the two-dimensional alternative crack body, \(K\) unit (a) is the \(a - K\) relationship of the mechanical structure under the action of a unit external load, \(\sigma\) eq,unit (x) is the corresponding traction distribution on the first equivalent crack surface acting on the two-dimensional alternative crack body, \(K\) res (a) is the \(a - K\) relationship of the mechanical structure under the action of the residual stress field, \(\sigma\) eq,res (x) is the corresponding traction distribution on the second equivalent crack surface acting on the two-dimensional alternative crack body; The discrete unit: For approximately discretizing the equivalent crack - face traction distribution into a piece - wise spline function. Among them, the i - th spline function representing the equivalent crack - face traction distribution can be expressed as: where α i , β i , γ i and δ i represent the coefficients of the i-th piecewise spline function respectively, s i-1 and s i are the two side nodes of the i-th piecewise spline function respectively, x is the coordinate along the crack line, is the i-th spline function representing the equivalent crack surface traction distribution.

8. The fatigue crack growth life prediction system for the mechanical structure according to claim 6, characterized in that The calculation module, which includes: The second calculation unit: For establishing a strip - yield model of an alternative two - dimensional cracked body subjected to the equivalent crack - face traction distribution based on the weight - function method. In this strip - yield model, based on the strip - yield hypothesis, calculate the virtual crack length under the combined action of the maximum external load and the residual stress field under variable - amplitude loading. Its calculation formula is as follows: where \(dx\) is the integration element, and \(P\) max is the maximum external load corresponding to the current cycle in the variable amplitude load; \(d\) is the virtual crack length to be calculated, which is equal to the sum of the physical crack length \(a\) and the crack tip plastic zone size \(r\) p , \(\lambda\) is the plastic constraint factor characterizing the crack tip plastic constraint effect, \(\sigma_0\) is the flow stress of the crack body material, \(x\) is the coordinate along the crack line, \(\sigma\) eq,unit is the first equivalent crack surface traction distribution, and \(\sigma\) eq,res is the second equivalent crack surface traction distribution; The third calculation unit: For discretizing the physical crack surface and the crack - tip plastic zone into multiple elastoplastic rod elements based on the determined virtual crack length d, and calculating the crack - face displacement under the combined action of the maximum external load and the residual stress field in the current cycle of the variable - amplitude loading by using the following formula: where x j is the central coordinate of the j-th bar element, V max (x j ) is the crack face displacement at the center of the j-th bar element under the combined action of the maximum external load P max and the residual stress field, n t is the total number of bar elements, F(d, x j ), R(d, x j ) and G(d, x i , x j ) are crack face displacement influence functions, where F(d, x j ) represents the crack face displacement generated at the center of the j-th bar element due to the action of a unit external load at the virtual crack length d, R(d, x j ) represents the crack face displacement generated at the center of the j-th bar element due to the action of the residual stress, G(d, x i , x j ) represents the crack face displacement generated at the center of the j-th bar element due to the action of a unit crack face traction force at the i-th bar element, σ max (x i ) is the stress value of the i-th bar element under the combined action of the maximum external load P max and the residual stress field.

9. The fatigue crack growth life prediction system of the mechanical structure according to claim 6, characterized in that, The fitting and calibration module, which includes: where ΔK CPD is the effective driving force for fatigue crack growth, R is the stress ratio of the constant amplitude load, ΔK is the stress intensity factor amplitude, P max is the maximum value of the constant amplitude load, and P CPD is the external load corresponding to the plastic deformation at the crack tip.

10. The fatigue crack growth life prediction system of the mechanical structure according to claim 6, characterized in that, The prediction and generation module, which includes: The fourth calculation unit: For equivalenting the variable - amplitude load spectrum applied to the mechanical structure to the crack - face traction distribution applied to the two - dimensional alternative cracked body based on the principle of linear superposition. The calculation formula of the crack - body traction distribution is as follows: σ eq，app (x,N) = P(N)·σ eq,unit where x represents the coordinate along the crack line, P(N) represents the load level at the Nth cycle of the variable amplitude load spectrum applied to the mechanical structure, σ eq,app is the variable amplitude load spectrum, N is the number of cycles, and σ eq,unit is the corresponding first equivalent crack surface traction distribution acting on the two-dimensional alternative crack body.

Images