Structural high-cycle fatigue increment analysis method based on internal force amplitude correction

Abstract

The application discloses a structure high-cycle fatigue increment analysis method based on internal force amplitude correction, and belongs to the technical field of metal structure fatigue analysis. First, key fatigue details of a metal structure are determined, and S-N curves are determined according to the closest fatigue detail classification in a hot spot stress method suggestion. Correction factors are determined according to actual nodes of the key fatigue details, and a corrected F-N curve is obtained, and a pre-damage index is calculated. A non-steady-state high-cycle fatigue pre-damage evolution criterion based on a time domain increment is used to filter a non-steady-state loading original curve, and an input non-steady-state fatigue loading system is obtained. Finally, a metal structure high-cycle fatigue increment analysis model is established, kinematics relationship and mechanical equilibrium relationship between a rod element and nodes at two ends of the rod element are constructed, an elastic stiffness matrix is established, a high-cycle fatigue loading test is simulated, a non-steady-state high-cycle fatigue pre-damage evolution process of the metal structure is predicted in real time, and the high-cycle fatigue life of the metal structure such as a large-span steel bridge can be more accurately predicted.

Description

Technical Field

[0001] This invention belongs to the field of fatigue analysis technology for metal structures, and relates to a high-cycle fatigue incremental analysis method for structures based on internal force amplitude correction. Background Technology

[0002] Common metal structures such as steel and aluminum structures have been widely used in infrastructure projects such as large-span buildings, bridges, and offshore platforms due to their high strength, light weight, and advantages such as resource reuse and environmental friendliness. In order to make full use of the service performance and recycling value of metal structures, it is necessary to accurately assess the remaining high-cycle fatigue performance of in-service metal structure projects, especially a number of industrial infrastructures with long service lives. Accurately assessing their remaining fatigue life is not only an economic and environmental requirement, but also a necessity to ensure the safety of life and property.

[0003] Although the application demand for metal structures is increasing, fatigue problems are easily overlooked. Both the Shenyang Institute of Metal Research, Chinese Academy of Sciences, and the American Society of Civil Engineers have stated that "nearly 90% of failures in metal structures are caused by fatigue damage," and fatigue damage often leads to brittle fracture, which is difficult to detect and poses a significant threat. Current technologies for accurately predicting the fatigue life of metal structures still need improvement in two aspects. First, the complex fatigue details inherent in metal structures cannot strictly correspond to the fatigue details of the resistance curves recommended in domestic and international standards, requiring correction of the benchmark curves. Second, the existing stress-life (SN) fatigue resistance curve system is suitable for smaller components such as materials or machinery, making it difficult to match the needs of fatigue performance assessment for large engineering structures. In engineering applications, a more intuitive representation using axial force or bending rectangles is preferred.

[0004] Currently, research on metal fatigue, both domestically and internationally, focuses on materials and mechanical structures. In civil engineering, particularly for metal structures such as long-span steel bridges or aluminum alloy space frames, there is a lack of widely applicable and convenient high-cycle fatigue life prediction models. This is partly because traditional finite element simulation methods, when used for fatigue analysis, cannot efficiently determine key fatigue details, and the high time cost of fine mesh element analysis prevents real-time updates of the high-cycle fatigue performance of steel structures under long-term service conditions. Furthermore, current conventional methods for predicting high-cycle fatigue performance still rely on baseline SN curves and rainflow counting methods. The former makes it difficult to accurately account for special structures with fatigue details, while the latter prevents real-time prediction of high-cycle fatigue performance under unsteady loading. Existing high-cycle fatigue assessment methods are only applicable to constant or variable amplitude loading and cannot calculate unsteady, pulsating wind effects or other random fatigue loading. Summary of the Invention

[0005] This invention aims to provide a structural high-cycle fatigue incremental analysis method based on internal force amplitude correction, which solves the problems of existing high-cycle fatigue analysis methods, such as the inability to locate the initial crack position, the inability to obtain the true fatigue amplitude of the structure, and the inability to calculate the unsteady-state wind-induced fatigue effect. By outputting various state variables in real time to characterize the high-cycle fatigue pre-damage process of key fatigue details of metal structures, it can more accurately predict the high-cycle fatigue life of engineering-scale metal structures.

[0006] This invention is achieved using the following technical solution: a structural high-cycle fatigue incremental analysis method based on internal force amplitude correction, implemented according to the following steps:

[0007] Step A: First, determine the key fatigue details of the metal structure and determine the benchmark SN curve based on the closest fatigue detail classification suggested by the hot spot stress method;

[0008] Step B: Determine the correction factor based on the actual construction of key fatigue details nodes and obtain the ΔF-N correction curve, then calculate the high-cycle fatigue pre-damage index.

[0009] The correction factors include three categories: stress concentration, thickness, and stress ratio. The following method is used to determine the ΔF-N correction curve:

[0010] 1) Under cyclic loading of axial force or bending moment, the fatigue load amplitude is corrected by considering the cross-sectional area A or section moment W of the member and the stress concentration correction factor ψ at the welded ends of the member. c Thickness correction factor ψ t and stress ratio correction factor ψ R ;

[0011] a. Establish a refined finite element model to analyze the actual stress distribution of fatigue details at the nodes, and compare it with the pre-experiment before node loading. Define the maximum stress S of the fatigue detail weld. max With tube stress S nom The ratio is the stress concentration correction factor:

[0012]

[0013] Among them, the tube stress S nom The maximum nominal stress along the outer edge of the pipe wall under external force is expressed as:

[0014]

[0015] b. Thickness correction factor ψ t The effect of thick steel plates on welding quality is represented as:

[0016] ψ t =1 / f(t) =1 / (25 / t) n ;

[0017] Where f(t) is the thickness fatigue coefficient recommended by the International Welding Institute, and n is related to the welding method of the joint and is determined according to the joint classification in the International Welding Institute standard;

[0018] c. Stress ratio correction factor ψ R The effect of the compressed portion of the cyclic load amplitude on delaying fatigue cracking when the stress ratio R is less than 0 is expressed as:

[0019]

[0020] Combining the baseline SN curve and the correction coefficient, the corrected internal force amplitude-life relationship expression is obtained as follows:

[0021]

[0022]

[0023] Where, σ cr It is the high-cycle fatigue stress constant. The constant C is determined by the reference SN curve of the node; ΔF is the nominal axial force amplitude of the node under fatigue load, ΔM is the nominal bending moment amplitude of the node under fatigue load, and N is the fatigue life of the node.

[0024] 2) Based on the above correction strategy, derive the formula for the internal force amplitude-life correction curve of the welded steel pipe-spherical shell joint:

[0025] First, determine the stress concentration distribution, thickness, and stress ratio correction coefficient of the welded steel pipe-spherical shell joint, based on the maximum true stress S at the weld under various crane load amplitude levels. max The stress S in the tube body was obtained. nom The ratio of these values ​​is the stress concentration correction factor:

[0026]

[0027]

[0028] Next, the corrected expression for the internal force amplitude-life ΔF-N curve of the most unfavorable fatigue detail of the welded steel pipe-spherical shell joint is derived as follows:

[0029]

[0030] Where, ΔF 管 A represents the nominal axial force amplitude for fatigue details at the weld toe of the welded steel pipe-spherical shell joint. 管 N represents the cross-sectional area of ​​the steel pipe in the welded steel pipe-spherical shell joint. 管 For the fatigue life of the welded steel pipe-spherical shell joint, ψ c管 ψ t管ψ R管 These represent the stress concentration, thickness, and stress ratio correction factor for the welded steel pipe-spherical shell joint.

[0031] Furthermore, based on the ΔF-N correction curve, a high-cycle fatigue pre-damage index is proposed to quantitatively characterize the high-cycle fatigue performance evolution process of the most unfavorable fatigue details. Specifically:

[0032] The formula for calculating the pre-damage index w is derived from the ΔF-N correction curve formula.

[0033]

[0034] Where N is the number of cycles of high-cycle fatigue loading that the structure is subjected to, and F cr M is the corrected axial force constant for high-cycle fatigue. cr The corrected bending moment constant for high-cycle fatigue, where ΔF is the axial force amplitude under the most unfavorable fatigue detail and ΔM is the bending moment amplitude under the most unfavorable fatigue detail, is expressed as:

[0035]

[0036]

[0037] The accuracy of the ΔF-N correction curve was verified by simulating high-cycle fatigue loading tests.

[0038] Step C: Establish an unsteady high-cycle fatigue pre-damage evolution criterion based on time-domain increment, filter the original unsteady loading curve, and obtain the input unsteady fatigue loading regime;

[0039] (1) For fatigue load amplitude that is constant or changes periodically, it is called steady-state high-cycle fatigue. The fatigue life of this type can be obtained directly through the ΔF-N correction curve or by combining the Miners cumulative damage criterion. Fatigue load amplitude that changes irregularly with time period is considered as unsteady-state high-cycle fatigue. The real-time continuous evolution analysis of structural pre-damage under unsteady-state fatigue is achieved by using the time-domain incremental method.

[0040] Based on the pre-damage index formula, the time-domain increment formula for the unsteady high-cycle fatigue pre-damage index is further derived, expressed as:

[0041]

[0042] Among them, w(t) n w(t) represents the structural fatigue pre-damage value at the nth increment step. n-1 F(t) represents the structural fatigue pre-damage value at the (n-1)th increment step. n F(t) represents the axial force of the structural member at the nth increment step. n-1M(t) represents the axial force of the structural members at the (n-1)th increment step. n M(t) represents the structural member end bending moment at the nth increment step. n-1 ) represents the structural member end moment at the (n-1)th increment step;

[0043] (2) Data filtering is performed on the original curves of unsteady loading to obtain the equivalent loading regime for unsteady high-cycle fatigue incremental analysis. The data filtering method is as follows:

[0044] The high-cycle fatigue increment depends on the maximum load amplitude in one cycle. The peaks and troughs of each cycle are extracted, the data points between the peaks and troughs are ignored, and the near endpoints with a time interval of less than 0.05s in the obtained peak and trough data are deleted to obtain the incremental analysis load time history of fatigue pre-damage equivalent.

[0045] Step D: Finally, establish an incremental analysis model for high-cycle fatigue of metal structures. By constructing the kinematic and mechanical equilibrium relationships between the rod element and its two end nodes, and establishing the elastic stiffness matrix, the model can predict the evolution process of unsteady high-cycle fatigue pre-damage of steel structures in real time.

[0046] An incremental analysis model for high-cycle fatigue of metal structures based on internal force amplitude correction is established; an initial state variable matrix is ​​defined: nodal displacement, element deformation, element internal force, pre-damage index, nodal external force and boundary conditions; preliminary positioning of each fatigue detail of the structure is achieved; and the evolution process of pre-damage of unsteady high-cycle fatigue of steel structure is analyzed and predicted by combining the internal force amplitude-life ΔF-N correction curve of each fatigue detail.

[0047] (1) Define the unit of the internal force amplitude-life ΔF-N correction curve, define the nodes of the target steel structure, and divide the calculation rod elements;

[0048] (2) Input the displacement and force boundary conditions of each node of the structure, and construct the global node displacement matrix {U(t)} and the global node external force matrix {P(t)}:

[0049] The global node displacement matrix {U(t)} is defined as follows:

[0050] {U(t)}=[x1(t)z1(t)r1(t),......,x k (t)z k (t)r k (t)]

[0051] Where x(t), z(t), and r(t) are the translational displacement time histories of the node along the X-axis and Z-axis of the global coordinate system, and the rotational displacement time histories about the Y-axis, respectively;

[0052] Axial forces F acting on each node along the three degrees of freedom xk Fzk and bending moment M k The global nodal external force matrix {P(t)} is described as follows:

[0053] {P(t)}=[F x1 (t) F z1 (t) M1(t),......,F xk (t) F zk (t) M k (t)]

[0054] (3) The deformation matrix {Φ(t)} of the structural calculation rod element b b Including the rotational deformation of the two end nodes i and j, as well as the axial deformation of the rod, the corresponding internal force matrix {m(t)} b This includes the bending moments at nodes i and j, as well as the axial forces in the rods;

[0055] (4) Construct the kinematic and mechanical equilibrium relationships between the rod element and its two end nodes, and establish the elastic stiffness matrix:

[0056] Based on the counterclockwise angle of the rod element about the x-axis in the global plane coordinate system and its actual length, the global coordination matrix is ​​determined, and then the kinematic relationship between nodal displacement and element deformation, and the mechanical equilibrium relationship between nodal external force and element internal force are constructed. At the same time, the elastic constitutive relationship between element deformation and element internal force is established.

[0057] Establish the kinematic relationships, mechanical equilibrium relationships, and elastic constitutive relationships for the crack incubation period for the rod element and each node; wherein, the deformation matrix of the rod element b and the total displacement matrix of all nodes including the two end nodes i and j satisfy the kinematic equations:

[0058] {Φ(t)} b =[B b (U)]{U(t)}

[0059] Among them, [B] b [(U)] is the global coordination matrix;

[0060] The internal force matrix of all rod elements b and the total external force matrix of all nodes satisfy the mechanical equilibrium equations:

[0061]

[0062] The deformation matrix and internal force matrix of the rod element b satisfy the high-cycle fatigue elastic constitutive equation:

[0063] {m(t)} b =[E]·{Φ(t)} b

[0064] The stiffness matrix [E] remains unchanged during the high-cycle fatigue crack incubation period, and is described as follows:

[0065]

[0066] (5) The quantitative index for the high-cycle fatigue incremental analysis process of the structure is the pre-damage index matrix {w(t)} of the calculated bar element. b The crack eventually initiated at the nodes at both ends of the member, therefore:

[0067] {w(t)}b=[w i w j ] b

[0068] The pre-damage index matrix is ​​obtained by iteratively calculating the element internal forces obtained in each incremental step of the TDI-FEL model by substituting them into the time-domain incremental formula;

[0069] (6) Real-time prediction of the pre-damage evolution process of unsteady high-cycle fatigue in metal structures;

[0070] Based on the ΔF-N correction curve of fatigue details in metal structures, the time-domain incremental expression of the high-cycle fatigue pre-damage index is obtained. The TDI-FEL high-cycle fatigue incremental analysis model for metal structures is used to predict the evolution process of unsteady high-cycle fatigue pre-damage in steel structures.

[0071] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0072] This scheme considers the actual construction of welded joints at fatigue details in metal structures and proposes a ΔF-N correction curve between the modified internal force amplitude and the structural life. Based on the time-domain incremental method for predicting unsteady high-cycle fatigue performance, it uses the TDI-FEL model and pre-damage evolution criteria to achieve real-time updates of nominal internal force, modified internal force, and high-cycle fatigue performance. This enables accurate and efficient prediction of the fatigue life of metal structures and key nodes subjected to high-cycle fatigue loading, and real-time updates of the high-cycle pre-damage evolution process. It provides a basis for reliability assessment and maintenance decisions for metal structures such as steel trusses, steel frames, and aluminum trusses, and achieves risk prediction and control throughout the entire structural life cycle. Attached Figure Description

[0073] Figure 1 This is a flowchart of the high-cycle fatigue performance prediction method for welded metal structures according to the present invention;

[0074] Figure 2 This is a flowchart of the time-domain incremental method for the evolution of unsteady high-cycle fatigue according to the present invention.

[0075] Figure 3 The following is a detailed schematic diagram of the steel structure fatigue in the embodiment: (a) welded steel pipe-spherical shell joint; (b) steel pipe weld toe and spherical shell weld toe.

[0076] Figure 4 The diagram shows a comparison of the pre-experimental stress distribution results for the embodiments.

[0077] Figure 5 The figure shows a comparison of the ΔF-N correction curves from the high-cycle fatigue test in the example.

[0078] Figure 6 The image shows a comparison between the filtered data and the original data in an example, where (a) is the original data and (b) is the filtered data.

[0079] Figure 7 The figure shows the result of the pre-damage evolution curve of unsteady high-cycle fatigue in the example. Detailed Implementation

[0080] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0081] This embodiment proposes a structural high-cycle fatigue incremental analysis method based on internal force amplitude correction for key welded steel pipe-spherical shell nodes in large-span steel structures that are not included in the fatigue detail classification in current specifications. First, the corrected internal force amplitude-life relationship of the node and the corresponding high-cycle fatigue corrected axial force constant and bending moment constant are obtained to more accurately predict the high-cycle fatigue life of this type of node. Furthermore, the real-time evolution process of unsteady high-cycle fatigue pre-damage of the key node is analyzed by the time-domain incremental method. This solves the problems of existing prediction methods, such as the inability to locate the initial crack position, the inability to obtain the true fatigue amplitude of the structure, and the inability to calculate the unsteady wind-induced fatigue effect.

[0082] like Figure 1 As shown, a structural high-cycle fatigue incremental analysis method based on internal force amplitude correction includes the following steps:

[0083] Step A: First, determine the key fatigue details of the metal structure and determine the SN curve based on the closest fatigue detail classification suggested by the hot spot stress method;

[0084] Step A1: Identify key fatigue details of the welded metal structure;

[0085] Fatigue in metal structures is most likely to occur at locations of stress concentration and weld concentration, such as nodes where members intersect. According to the principles of macroscopic damage mechanics, damage to members under fatigue loading concentrates at hinge nodes. Due to stress concentration and the complexity of connections, fatigue cracks in steel space frame structures are more likely to initiate at welded steel pipe-spherical shell nodes where members intersect. Figure 3This is a type of welded steel pipe-spherical shell node commonly used in steel structures such as large-span spatial trusses and space frames. This embodiment takes this node as an example to introduce the correction strategy for the reference stress-life (SN) curve of the welded steel pipe-spherical shell node, which is a key fatigue detail in steel space frame structures.

[0086] Step A2: Determine the reference stress-life (SN) curve based on the fatigue detail classification closest to the hot spot stress method. Hot spot stress refers to the stress increase effect at the welded details of the structure, which is caused by the geometrical abrupt change and residual stress in the weld due to the intersection of multiple components.

[0087] Welded joints in metal structures are often fixed connections between components of different directions and sizes, resulting in significant stress concentration. Based on numerous fatigue experiments, the hot spot stress method summarizes the reference SN curves for common engineering metal structures. The standard grades for hot spot stress in steel structures are FAT90 and FAT100, while the standard grades for hot spot stress in aluminum structures are FAT36 and FAT40.

[0088] Based on the actual structure of the welded steel pipe-spherical shell joint, the closest SN curve from the relevant fatigue levels provided by the hot spot stress method is selected. The high-cycle fatigue coefficient C and high-cycle fatigue index γ are then derived from the SN relationship expression using two data points (N1, S1) and (N2, S2) on the curve.

[0089]

[0090] This type of node includes the end of the round tube and the spherical shell, as well as the weld connecting the two. Compared to common butt welds and fillet welds, FAT100, which is closer to the structure of a welded steel tube-spherical shell node, is selected from the FAT90 and FAT100 series recommended by the hot spot stress method. The high-cycle fatigue stress coefficient C = 1.622456 × 10⁻⁶ is derived by reverse derivation. 12 The sum of the exponent γ = -2.95;

[0091] Step B: Determine the correction factor and obtain the corrected FN curve based on the actual construction of the nodes of key fatigue details, and calculate the pre-damage index.

[0092] Step B1, the ΔF-N correction curve differs from the SN curve in that it considers not only the component's dimensional parameters, but also three types of correction factors: stress concentration, thickness, and stress ratio. This includes the following technical steps:

[0093] 1) Under cyclic loading of axial force or bending moment, the modified fatigue load amplitude takes into account the cross-sectional area A or section moment W of the member and the stress concentration factor ψ at the welded end of the member. c Thickness correction factor ψ t and stress ratio correction factor ψ RThe concentrated stress at the actual fatigue details was obtained by finite element analysis that has been verified by pre-tests. The thickness and stress ratio correction coefficients were used to characterize the influence of thick steel plates (>25mm) on welding quality and the effect of the compressed part of the cyclic load amplitude on delaying fatigue cracking, respectively.

[0094] a. The actual stress distribution of nodal fatigue details was analyzed by establishing a refined finite element model, and compared with the pre-experiment before nodal loading. The results are referenced. Figure 4 To verify the accuracy of the stress analysis model, the maximum stress S of the fatigue detail weld was defined. max (Concentrated stress) and tube stress (nominal stress) S nom The ratio is the stress concentration correction factor.

[0095]

[0096] Wherein, the tube body stress is the maximum nominal stress along the outer edge of the tube wall under external forces (including axial force F and bending moment M), calculated as follows:

[0097]

[0098] Where A and W are the area and section moment of the circular tube, respectively;

[0099] b. Thickness correction factor ψ t Used to characterize the impact of thick steel plates (>25mm) on welding quality.

[0100] ψ t =1 / f(t) =1 / (25 / t) n

[0101] Where f(t) is the thickness fatigue coefficient recommended by the International Welding Association, and n is related to the welding method of the joint, and is taken as 0.1 to 0.3;

[0102] c. Stress ratio correction factor ψ R The effect of the compressed portion of the cyclic load amplitude on delaying fatigue cracking when the stress ratio R is less than 0 is described as follows:

[0103]

[0104] Based on the baseline SN curve and various correction coefficients, the expression for the corrected internal force amplitude-life relationship is derived as follows.

[0105]

[0106]

[0107] Where, σ cr It is the high-cycle fatigue stress constant.

[0108]

[0109] 2) Derive the formula for the internal force amplitude-life correction curve of the welded steel pipe-spherical shell joint based on the above correction strategy:

[0110] First, determine the stress concentration distribution and other correction factors of the welded steel pipe-spherical shell joint.

[0111] Based on the maximum true stress Smax at the weld under various crane load amplitude levels, the ratio of this stress to the pipe body stress (nominal stress) Snom is obtained, which is the stress concentration correction factor.

[0112]

[0113]

[0114] Furthermore, the thickness of the steel plate used in conventional welded steel pipe-spherical shell joints is generally less than 25mm, so the thickness correction factor ψ t The stress ratio is 1.0; in this embodiment, the stress ratio of the crane load is 0.4, therefore the stress ratio correction factor ψ is 1.0. R The value is 1.0; next, the expression for the corrected internal force amplitude-life (ΔF-N) curve of the most unfavorable fatigue detail of the welded steel pipe-spherical shell joint is derived as follows:

[0115]

[0116] Where, ΔF 管 A represents the nominal axial force amplitude for fatigue details at the weld toe of the welded steel pipe-spherical shell joint. 管 N represents the cross-sectional area of ​​the steel pipe in the welded steel pipe-spherical shell joint. 管 For the fatigue life of the welded steel pipe-spherical shell joint, ψ c管 ψ t管 ψ R管 These represent the stress concentration, thickness, and stress ratio correction factor for the welded steel pipe-spherical shell joint.

[0117] Step B2: Based on the ΔF-N correction curve, a high-cycle fatigue pre-damage index is proposed to quantitatively characterize the high-cycle fatigue performance evolution process of the most unfavorable fatigue details.

[0118] Since the incubation period before fatigue crack initiation accounts for more than 90% of the structural life cycle, and the structural stiffness matrix will not degrade due to damage during the incubation period, the pre-damage index is used as a key indicator to measure the evolution of high-cycle fatigue performance. The calculation formula of the pre-damage index w is derived through the ΔF-N correction curve formula.

[0119]

[0120] Where N is the number of cycles of high-cycle fatigue loading that the structure is subjected to, and F cr M is the corrected axial force constant for high-cycle fatigue. cr The bending moment constant is corrected for high-cycle fatigue, where ΔF is the axial force amplitude under the most unfavorable fatigue detail, and ΔM is the bending moment amplitude under the most unfavorable fatigue detail, described as follows:

[0121]

[0122]

[0123] For the welded steel pipe-spherical shell joint in the embodiment, the crack initiation, i.e., the pre-damage evolution process under high-cycle fatigue, is controlled by the internal force amplitude. Furthermore, a calculation expression for the pre-damage index w, characterizing the high-cycle fatigue performance evolution process of the most unfavorable fatigue detail, is proposed as follows.

[0124]

[0125] Simulated high-cycle fatigue loading tests were conducted to verify the accuracy of the corrected FN curve;

[0126] The high-cycle fatigue test data of the welded steel pipe-spherical shell joint and the benchmark SN curve are plotted in the same coordinate system (refer to...). Figure 5 As can be seen, the formula for correcting the force amplitude-life of the most unfavorable fatigue detail in steel structures proposed in this invention matches the experimental data better.

[0127] Step C: Based on the time-domain increment nonsteady-state high-cycle fatigue pre-damage evolution criterion, filter the original nonsteady-state loading curve to obtain the input nonsteady-state fatigue loading regime;

[0128] This embodiment proposes a non-steady-state high-cycle fatigue pre-damage evolution criterion based on time-domain increments, and establishes a method for incremental analysis of structural pre-damage under high-cycle fatigue loading, especially under non-steady-state conditions.

[0129] Metal structures are subjected to high-cycle cyclic loads and wind loads during normal service. Among these, fatigue loads with constant or periodically varying amplitudes are considered steady-state high-cycle fatigue, such as the fatigue of steel beams and joints under crane loads in factory buildings. The fatigue life of this type can be directly obtained through the ΔF-N curve or by combining it with the Miners cumulative damage criterion. However, fatigue loads with irregularly varying amplitudes over time are considered unsteady-state high-cycle fatigue.

[0130] This invention replaces the traditional rainflow counting method with a time-domain increment method to achieve real-time continuous evolution analysis of structural pre-damage under unsteady-state fatigue. The time-domain increment formula for the pre-damage index is derived from the calculation formula for the pre-damage index of constant amplitude high-cycle fatigue, and is described as follows:

[0131]

[0132] Among them, w(t) n w(t) represents the structural fatigue pre-damage value at the nth increment step. n-1 F(t) represents the structural fatigue pre-damage value at the (n-1)th increment step. n F(t) represents the axial force of the structural member at the nth increment step. n-1 M(t) represents the axial force of the structural members at the (n-1)th increment step. n M(t) represents the structural member end bending moment at the nth increment step. n-1 ) represents the structural member end bending moment at the (n-1)th increment step.

[0133] During normal service, the welded steel pipe-spherical shell joint steel space frame structure is subjected to cyclic loads such as high-cycle crane loads and unsteady loads such as pulsating wind. Before the appearance of cracks can be detected, the crack incubation process caused by stress amplitude accumulation is characterized by pre-damage index. When the pre-damage w of the most unfavorable tension section reaches the critical value of 1.0, crack initiation occurs, indicating that the structure is not suitable for continued normal use. The evolution curve of the unsteady fatigue process is updated in real time based on the time-domain incremental method. Ultimately, high-cycle fatigue failure is controlled by the pre-damage index.

[0134] The incremental analysis method for high-cycle fatigue of structures includes a data filtering method for the original curves of unsteady loading to obtain an incremental analysis loading regime equivalent to the pre-damage result, specifically:

[0135] High-cycle fatigue depends on the maximum load amplitude in one cycle (period Tc). The peaks and troughs of each cycle of the curve are extracted, and the points between the peaks and troughs are ignored. In addition, there will be some adjacent peaks (troughs) with similar time histories (<0.05Tc) in the curve. At this time, the smaller one is ignored. Finally, the external load used to input the fatigue model is obtained.

[0136] Reference Figure 2 This invention proposes a time-domain incremental method to replace the traditional counting method, rainflow counting method. Like the latter, both are based on the linear elastic cumulative fatigue criterion and obtain consistent results. Unlike the latter, the new method can update the residual fatigue performance of steel structures under unsteady high-cycle fatigue loading by recording the evolution curve of pre-damage index in real time.

[0137] For the time-domain unsteady fatigue analysis of the welded steel pipe-spherical shell joint in this embodiment, the original unsteady fatigue loading curves first need to be filtered to accurately simplify the loading regime input into the model. The data filtering method is as follows:

[0138] like Figure 6 As shown, the original unsteady fatigue loading curve (2432 data points) was processed by data filtering to obtain the incremental analysis load time history (53 data points) equivalent to fatigue pre-damage.

[0139] Step D: Finally, establish an incremental analysis model for high-cycle fatigue of metal structures. By constructing the kinematic and mechanical equilibrium relationships between the rod element and its two end nodes, and establishing the elastic stiffness matrix, the model can predict the evolution process of unsteady high-cycle fatigue pre-damage of steel structures in real time.

[0140] Step D1: Establish the TDI-FEL incremental analysis model for high-cycle fatigue of metal structures based on internal force amplitude correction;

[0141] To perceive the changes in internal forces of each component at fatigue details in a metal structure during fatigue loading, to preliminarily locate the fatigue details of the structure, and to obtain the evolution of pre-damage values ​​for each unfavorable fatigue detail, a high-cycle fatigue incremental analysis model for metal structures, TDI-FEL (Time domain incremental-Fatigue Elements), based on internal force amplitude correction, is established.

[0142] The initial state variable matrix is ​​defined as follows: nodal displacements (rotation and translation), element deformations (bending and expansion), element internal forces (bending moment and axial force), pre-damage index, nodal external forces, and boundary conditions.

[0143] (1) Define the unit of the internal force amplitude-life (ΔF-N) correction curve as kN·m, define the nodes of the target steel structure, and divide it into calculation rod elements.

[0144] (2) Input the displacement and force boundary conditions of each node of the structure, and construct the global node displacement matrix {U(t)} and the global node external force matrix {P(t)}.

[0145] The global node displacement matrix {U(t)} is defined as follows:

[0146] {U(t)}=[x1(t) z1(t) r1(t),......,x k (t) z k (t) r k (t)]

[0147] Where, x k (t), z k (t), r k (t) represents the time history of the translational displacement (m) of the node along the X and Z axes of the global coordinate system and the time history of the rotational displacement (rad) about the Y axis, respectively; further, the axial force F acting on each node along the three degrees of freedom directions. xk F zk and bending moment M k The global nodal external force matrix {P(t)} is described as follows:

[0148] {P(t)}=[F x1(t) F z1 (t) M1(t),......,F xk (t) F zk (t) M k (t)]

[0149] (3) The deformation matrix {Φ(t)} of the structural calculation rod element b b Including the rotational deformation of the two end nodes i and j, as well as the axial deformation of the rod, the corresponding internal force matrix {m(t)} b This includes the bending moments at nodes i and j, as well as the axial forces in the rods;

[0150] (4) Construct the kinematic and mechanical equilibrium relationships between the rod element and its two end nodes, and establish the elastic stiffness matrix.

[0151] Based on the counterclockwise angle of the rod element about the x-axis in the global plane coordinate system and its actual length, the global coordination matrix is ​​determined, and then the kinematic relationship between nodal displacement and element deformation, and the mechanical equilibrium relationship between nodal external force and element internal force are constructed. At the same time, the elastic constitutive relationship between element deformation and element internal force is established.

[0152] Establish the kinematic relationships, mechanical equilibrium relationships, and elastic constitutive relationships for the crack incubation period of the rod element and its nodes; wherein, the deformation matrix of the rod element b and the total displacement matrix of all nodes, including the two end nodes i and j, satisfy the kinematic equations:

[0153] {Φ(t)} b =[B b (U)]{U(t)}

[0154] Among them, [B] b [(U)] is the global coordination matrix.

[0155] Furthermore, the internal force matrix of all the rod elements b and the total external force matrix of all nodes satisfy the mechanical equilibrium equations:

[0156]

[0157] Since the incubation period before fatigue crack initiation accounts for more than 90% of the structure's lifespan, and the structural stiffness matrix during this incubation period does not exhibit degradation due to plastic accumulation or damage, the deformation matrix and internal force matrix of the aforementioned rod element b satisfy the high-cycle fatigue elastic constitutive equation.

[0158] {m(t)} b =[E]·{Φ(t)} b

[0159] The stiffness matrix [E] remains unchanged during the high-cycle fatigue crack incubation period, and is described as follows:

[0160]

[0161] (5) The quantitative index for the high-cycle fatigue incremental analysis process of the structure is the pre-damage index matrix {w(t)} of the calculated bar element. b The crack eventually initiated at the nodes at both ends of the member, therefore:

[0162] {W(t)}b=[w i w j ] b

[0163] The pre-damage index matrix can be obtained by substituting the element internal forces obtained in each incremental step of the TDI-FEL model proposed in step D2 into the time-domain incremental formula for iterative calculation.

[0164] Step D2: Real-time prediction of the pre-damage evolution process of unsteady high-cycle fatigue in metal structures; accurately analyze the initial crack location of the target steel structure using the TDI-FEL model, and obtain the true internal force amplitude of fatigue details by combining the ΔF-N correction curve, and calculate the pre-damage index of unsteady high-cycle fatigue.

[0165] Based on the ΔF-N correction curve of fatigue details in metal structures, the time-domain incremental expression of the high-cycle fatigue pre-damage index is obtained. The TDI-FEL high-cycle fatigue incremental analysis model for metal structures is used to predict the evolution process of unsteady high-cycle fatigue pre-damage in steel structures.

[0166] This embodiment uses a TDI-FEL model of a welded steel pipe-spherical shell joint to accurately locate the most unfavorable fatigue detail, i.e., the crack initiation site, of this type of steel structure. It also addresses the problem that traditional continuum finite element methods cannot obtain the pre-damage progress when analyzing fatigue problems, especially long-cycle fatigue assessment. Firstly, the initial input settings of the model mainly consist of three parts: boundary conditions, attribute constant parameters, and analysis steps. Boundary condition settings include displacement constraints and loading regimes for the nodes. Horizontal and vertical translational degrees of freedom are constrained for the support nodes. A 1-minute axial force time history under pulsating wind is applied to the loading nodes. The equivalent high-cycle fatigue incremental analysis loading cycle is 1, for a total of 53 cycles.

[0167] The incremental high-cycle fatigue analysis model of the welded steel pipe-spherical shell joint is a multi-bar physical system connected by potential damage nodes. In addition to the geometrically intersecting nodes of the bars, it also includes physically concentrated loading points. The length of the bar elements and the coordinates of each node are set in the fatigue analysis model. To overcome the scaling effect, the generalized internal force matrix and generalized deformation matrix of the bar elements are established. Furthermore, the kinematic equations, mechanical equilibrium equations and high-cycle fatigue elastic constitutive equations of the welded steel pipe-spherical shell joint model are constructed. The internal forces of each bar element of the structure at each incremental step are calculated, and the pre-damage index of each potential damage node at each time step is obtained to realize the high-cycle fatigue incremental analysis process of the structure under unsteady (pulsating wind) loading regime.

[0168] The evolution of the welded steel pipe-spherical shell joint during crack initiation determines the fatigue failure process. The joint is initially elastic, gradually accumulating internal force amplitude to form potential crack initiation sites, which in turn lead to crack initiation. To quantitatively characterize this process, the TDI-FEL model outputs the pre-damage index for each incremental step at the two most unfavorable fatigue details of the potential crack initiation sites, described as follows:

[0169] The pre-damage index at each moment reflects the high-cycle fatigue incremental analysis process of the steel structure. First, the weld toes of the two most unfavorable fatigue details at the welded steel pipe-spherical shell joint are corrected by ΔF-N to obtain the calculation formula for the pre-damage index:

[0170]

[0171]

[0172] Among them, w 管 w is the pre-damage index of the weld toe of the welded steel pipe-spherical shell joint. 球 The pre-damage index for the weld toe of the welded steel pipe-spherical shell joint is given.

[0173] Furthermore, based on the pre-damage index w(t) from the previous moment... n-1 ), calculate the pre-damage index w(t) at the current moment using the incremental analysis method. n This is used to update the high-cycle fatigue pre-damage index for the most unfavorable fatigue details in real time. The evolution formula of the pre-damage index, which characterizes the crack initiation process, with the total loading time is:

[0174]

[0175]

[0176] Among them, t n For the current increment step, t n-1 ΔF is the absolute value of the difference between the internal forces at the current time and the previous time step.

[0177] The pre-damage evolution curves of the weld toes at the two most unfavorable fatigue details of the welded steel pipe-spherical shell joint, obtained by the high-cycle fatigue incremental analysis method of this invention, are shown below. Figure 7 As shown, the curves describe the unsteady fatigue evolution process of the two weld toes in real time, reflecting the time-domain variation characteristics of the unsteady loading amplitude. Simultaneously, the comparison of the two curves also reveals that the pre-damage evolution processes of the two weld toes at the same steel pipe-shell node—the pipe weld toe and the shell weld toe—are significantly differentiated due to the influence of the correction factor. The final difference in crack initiation rate matches the difference in the actual stress at the two weld toes, indicating that at this shell node, the most unfavorable fatigue detail is located at the interface where the weld intersects with the circular pipe. This demonstrates that the numerical simulation method of this invention not only has high efficiency in long-period macroscopic analysis but also possesses the accuracy to accurately describe the pre-damage evolution of the most unfavorable fatigue detail.

[0178] By modifying the fatigue internal force amplitude-life relationship and defining the evolution method of high-cycle fatigue pre-damage index in this invention, the entire process from crack incubation period to fatigue cracking failure of stress concentration nodes is described. According to the time-domain incremental iteration process set by the loading regime, the fatigue internal force amplitude and pre-damage index of the most unfavorable fatigue details are simulated in real time, and the high-cycle fatigue life is finally calculated. The accuracy is comparable to that of the traditional rainflow counting method. However, the method of this invention realizes the real-time update of high-cycle fatigue performance controlled by modified internal force amplitude, which can be used for the high-cycle fatigue performance evolution analysis of metal structures such as long-span steel bridges.

[0179] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A structural high-cycle fatigue incremental analysis method based on internal force amplitude correction, characterized in that, Includes the following steps: Step A: First, determine the key fatigue details of the metal structure and determine the benchmark SN curve based on the closest fatigue detail classification suggested by the hot spot stress method; Step B: Determine the correction factor based on the actual construction of key fatigue details nodes and obtain the ΔF-N correction curve, then calculate the high-cycle fatigue pre-damage index. Step C: Establish an unsteady high-cycle fatigue pre-damage evolution criterion based on time-domain increment, filter the original unsteady loading curve, and obtain the input unsteady fatigue loading regime; Step D: Finally, establish an incremental analysis model for high-cycle fatigue of metal structures. By constructing the kinematic and mechanical equilibrium relationships between the rod element and its two end nodes, and establishing the elastic stiffness matrix, the model can predict the evolution process of unsteady high-cycle fatigue pre-damage of steel structures in real time. In step B, the correction factors include three categories: stress concentration, thickness, and stress ratio. The following method is used to determine the ΔF-N correction curve: 1) Under cyclic loading of axial force or bending moment, the fatigue load amplitude is corrected by considering the cross-sectional area A or section moment W of the member and the stress concentration correction factor at the welded ends of the member. Thickness correction factor and stress ratio correction factor ; a. Establish a refined finite element model to analyze the actual stress distribution of fatigue details at the nodes, and compare it with the pre-experiment before node loading. Define the maximum stress S of the weld in the fatigue detail. max With tube stress S nom The ratio is the stress concentration correction factor: ； Among them, the tube stress S nom The maximum nominal stress along the outer edge of the pipe wall under external force is expressed as: ； b. Thickness correction factor The effect of thick steel plates on welding quality is represented as: ； Where f(t) is the thickness fatigue coefficient recommended by the International Welding Institute, and n is related to the welding method of the joint and is determined according to the joint classification in the International Welding Institute standard; c. Stress ratio correction factor The effect of the compressed portion of the cyclic load amplitude on delaying fatigue cracking when the stress ratio R is less than 0 is expressed as: Combining the baseline SN curve and the correction coefficient, the corrected internal force amplitude-life relationship expression is obtained as follows: in, It is the high-cycle fatigue stress constant. The constant C is determined by the reference SN curve of the node; ΔF is the nominal axial force amplitude of the node under fatigue load, ΔM is the nominal bending moment amplitude of the node under fatigue load, and N is the fatigue life of the node. 2) Based on the above correction strategy, derive the formula for the internal force amplitude-life correction curve of the welded steel pipe-spherical shell joint: First, determine the stress concentration distribution, thickness, and stress ratio correction coefficient of the welded steel pipe-spherical shell joint, based on the maximum true stress S at the weld under various crane load amplitude levels. max The stress S in the tube body was obtained. nom The ratio of these values ​​is the stress concentration correction factor: Next, the corrected expression for the internal force amplitude-life ΔF-N curve of the most unfavorable fatigue detail of the welded steel pipe-spherical shell joint is derived as follows: ； Where, ΔF 管 A represents the nominal axial force amplitude for fatigue details at the weld toe of the welded steel pipe-spherical shell joint. 管 N represents the cross-sectional area of ​​the steel pipe in the welded steel pipe-spherical shell joint. 管 For the fatigue life of the welded steel pipe-spherical shell joint, , , These represent the stress concentration, thickness, and stress ratio correction factor for the welded steel pipe-spherical shell joint.

2. The structural high-cycle fatigue incremental analysis method based on internal force amplitude correction according to claim 1, characterized in that: In step B, a high-cycle fatigue pre-damage index is proposed based on the ΔF-N correction curve to quantitatively characterize the high-cycle fatigue performance evolution process of the most unfavorable fatigue details. Specifically: The formula for calculating the pre-damage index w is derived by using the ΔF-N correction curve formula. ； Where N is the number of high-cycle fatigue loading cycles the structure undergoes. To correct the axial force constant for high-cycle fatigue, Let ΔF be the nominal axial force amplitude of the node under fatigue load, and ΔM be the nominal bending moment amplitude of the node under fatigue load, expressed as: The accuracy of the ΔF-N correction curve was verified by simulating high-cycle fatigue loading tests.

3. The structural high-cycle fatigue incremental analysis method based on internal force amplitude correction according to claim 2, characterized in that: In step C, a nonsteady-state high-cycle fatigue pre-damage evolution criterion based on time-domain increment is proposed, and the input nonsteady-state fatigue loading regime is obtained by filtering the original data. (1) For fatigue load amplitude that is constant or changes periodically, it is steady-state high-cycle fatigue. The fatigue life of this type can be obtained directly through the ΔF-N correction curve or by combining the Miners cumulative damage criterion. For fatigue load amplitude that changes irregularly with time period, it is considered unsteady-state high-cycle fatigue. The real-time continuous evolution analysis of structural pre-damage under unsteady-state fatigue can be realized by the time-domain incremental method. Based on the pre-damage index formula, the time-domain increment formula for the unsteady high-cycle fatigue pre-damage index is further derived, expressed as: Among them, w(t) n w(t) represents the structural fatigue pre-damage value at the nth increment step. n-1 F(t) represents the structural fatigue pre-damage value at the (n-1)th increment step. n F(t) represents the axial force of the structural member at the nth increment step. n-1 M(t) represents the axial force of the structural members at the (n-1)th increment step. n M(t) represents the structural member end bending moment at the nth increment step. n-1 ) represents the structural member end moment at the (n-1)th increment step; (2) Data filtering is performed on the original curves of unsteady loading to obtain the equivalent loading regime for unsteady high-cycle fatigue incremental analysis. The data filtering method is as follows: The high-cycle fatigue increment depends on the maximum load amplitude in one cycle. The peaks and troughs of each cycle are extracted, the data points between the peaks and troughs are ignored, and the near endpoints with a time interval of less than 0.05s in the obtained peak and trough data are deleted to obtain the incremental analysis load time history of fatigue pre-damage equivalent.

4. The structural high-cycle fatigue incremental analysis method based on internal force amplitude correction according to claim 1, characterized in that: In step D, a high-cycle fatigue incremental analysis model TDI-FEL for metal structures based on internal force amplitude correction is established; the initial state variable matrix is ​​defined as: nodal displacement, element deformation, element internal force, pre-damage index, nodal external force and boundary conditions; To achieve the initial location of each fatigue detail in the structure, and to analyze and predict the pre-damage evolution process of the unsteady high-cycle fatigue of the steel structure by combining the internal force amplitude-life ΔF-N correction curve of each fatigue detail; (1) Define the unit of the internal force amplitude-life ΔF-N correction curve, define the nodes of the target steel structure, and divide the calculation rod elements; (2) Input the displacement and force boundary conditions of each node of the structure, and construct the global node displacement matrix {U(t)} and the global node external force matrix {P(t)}: The global node displacement matrix {U(t)} is defined as follows: Where, x k (t), z k (t), r k (t) represents the translational displacement time history of node k along the X-axis and Z-axis of the global coordinate system and the rotational displacement time history about the Y-axis, respectively; Axial force F at each node xk F zk and bending moment M k The global nodal external force matrix {P(t)} is described as follows: (3) Deformation matrix of structural calculation rod element b Including the rotational deformation of the two end nodes i and j, as well as the axial deformation of the rod, correspondingly, the internal force matrix This includes the bending moments at nodes i and j, as well as the axial forces in the rods; (4) Construct the kinematic and mechanical equilibrium relationships between the rod element and its two end nodes, and establish the elastic stiffness matrix: Based on the counterclockwise angle of the rod element about the x-axis in the global plane coordinate system and its actual length, the global coordination matrix is ​​determined, and then the kinematic relationship between nodal displacement and element deformation, and the mechanical equilibrium relationship between nodal external force and element internal force are constructed. At the same time, the elastic constitutive relationship between element deformation and element internal force is established. Establish the kinematic relationships, mechanical equilibrium relationships, and elastic constitutive relationships for the crack incubation period for the rod element and each node; wherein, the deformation matrix of the rod element b and the total displacement matrix of all nodes including the two end nodes i and j satisfy the kinematic equations: in, This is the global coordination matrix; The internal force matrix of all member element b and the total external force matrix of all nodes satisfy the mechanical equilibrium equations: The deformation matrix and internal force matrix of the rod element b satisfy the high-cycle fatigue elastic constitutive equation: The stiffness matrix [E] remains unchanged during the high-cycle fatigue crack incubation period, and is described as follows: (5) The quantitative index for the high-cycle fatigue incremental analysis process of the structure is the pre-damage index matrix {w(t)} of the calculated rod element. b The crack eventually initiated at the nodes at both ends of the member, therefore: {w(t)} b =[w i w j ] b The pre-damage index matrix is ​​obtained by iteratively calculating the element internal forces obtained in each incremental step of the TDI-FEL model by substituting them into the time-domain incremental formula; (6) Real-time prediction of the pre-damage evolution process of unsteady high-cycle fatigue in metal structures; Based on the ΔF-N correction curve of fatigue details in metal structures, the time-domain incremental expression of the high-cycle fatigue pre-damage index is obtained. The TDI-FEL high-cycle fatigue incremental analysis model for metal structures is used to predict the evolution process of unsteady high-cycle fatigue pre-damage in steel structures.

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