A method for predicting the residual fatigue life of KT-type joints of angle steel welded trusses

Abstract

The present invention relates to a fatigue life prediction method for KT-type nodes of angle steel welded trusses, which belongs to the technical field of bridge engineering. The present invention predicts the remaining fatigue life of KT-type nodes of angle steel welded trusses through finite element modeling and crack propagation simulation analysis. The method mainly includes the following steps: establishing a finite element model of the KT-type nodes of angle steel welded trusses; inserting cracks based on the crack propagation model; determining node geometric parameters and crack geometric parameters; and fitting a composite stress intensity factor calculation formula through parameter data to predict the remaining fatigue life. The present invention adopts a fatigue life prediction method based on fracture mechanics. Compared with the traditional stress amplitude-cycle number (S-N) curve method, the fracture mechanics method can make up for the defect of the S-N curve method that cannot consider the initial crack in the design stage, and can more accurately obtain the remaining fatigue life of each fatigue crack propagation stage.

Description

Technical Field

[0001] The invention belongs to the field of bridge engineering, and in particular relates to a method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss. Background Art

[0002] In recent years, angle steel welded truss structures have attracted widespread attention due to their good mechanical properties, superior economy and convenient construction. Bridges whose main load-bearing structures use angle steel include truss bridges, arch bridges and continuous rigid frame bridges. However, in this structure, welding defects and welding residual stress often exist at the connection between the web and the chord, resulting in stress concentration at the weld toe. Fatigue cracks are prone to occur under the action of reciprocating loads such as vehicles. In addition, the long-term use of bridge structures and complex environmental conditions, as well as the uncertainty of load effects, may aggravate the development of fatigue cracks and even lead to fatigue failure of nodes, posing a serious threat to the safety of bridge structures.

[0003] Regular inspection and maintenance can improve the fatigue performance of structures to a certain extent, but if the remaining life of the structure under specific crack defects cannot be calculated, it becomes difficult to develop a safe and applicable dynamic health monitoring program. The SN curve method has been successfully applied in production practice and has accumulated a large amount of data, but it cannot directly consider the impact of initial defects or damage on components. It is mainly suitable for evaluating the fatigue life of components in the design stage, but cannot be used to evaluate the remaining fatigue life of components in the service stage. The fracture mechanics method compensates for this shortcoming of the SN curve method. It considers the mechanical properties of components when they are damaged. Therefore, it can be used for fatigue verification of components with initial defects in the design stage and repair and reinforcement of damaged components in the service stage. It can accurately predict the fatigue remaining life of structural nodes through crack propagation. However, the evaluation method based on fracture mechanics started relatively late, so there are still many gaps to be filled in terms of crack propagation models and fracture parameters corresponding to various steel types. Summary of the Invention

[0004] In order to solve the problem of inaccurate structural fatigue life prediction in the prior art, the present invention provides a method for predicting the remaining fatigue life of KT-type nodes of angle steel welded trusses, which achieves accurate prediction of the remaining fatigue life by accurately calculating the stress intensity factor.

[0005] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for predicting the residual fatigue life of KT-type nodes of angle steel welded trusses, comprising the following steps:

[0006] Step S1: establishing a finite element model of the node and determining the node geometric parameters, wherein the node geometric parameters include: the angle θ between the web and the chord, the ratio β between the web width b1 and the chord width b2, and the ratio τ between the web thickness t1 and the chord thickness t2;

[0007] Step S2: performing calculations based on the finite element model to determine the crack initiation location;

[0008] Step S3: Importing the finite element model of the node into the crack analysis module, inserting an initial crack at the crack initiation location through the crack analysis module, determining the crack geometric parameters, and calculating the composite stress intensity factor amplitude; the crack geometric parameters include the ratio of the half crack length c to the crack depth a, and the ratio of the crack depth a to the chord thickness t2;

[0009] Step S4: changing the node geometric parameters and the crack geometric parameters, repeatedly calculating the composite stress intensity factor amplitude, performing data fitting based on the composite stress intensity factor amplitude under different node geometric parameters and crack geometric parameters, and obtaining a composite stress intensity factor amplitude calculation formula;

[0010] Step S5: Determine the geometric parameters and crack parameters of the node, calculate the composite stress intensity factor amplitude by fitting the composite stress intensity factor amplitude calculation formula, perform crack growth simulation based on the calculation results, and then calculate the remaining fatigue life based on the crack growth mode results.

[0011] The specific steps of step S2 are:

[0012] The maximum stress concentration position of the KT joint is determined, and the crack initiation position is determined by finite element calculation results assuming that the initial crack is perpendicular to the web.

[0013] In the step S1, a node finite element model is established by using ABAQUS; in the step S3, a crack analysis module adopts FRANC3D software.

[0014] In step S3, the calculation formula of the composite stress intensity factor amplitude is:

[0015]

[0016] Among them, K eff Indicates the combined stress intensity factor amplitude, K I , K Ⅱ and K Ⅲ are the stress intensity factors of type I, type II and type III respectively; ν is the Poisson's ratio of steel.

[0017] In step S4, the calculation formula for the composite stress intensity factor amplitude obtained by fitting is:

[0018]

[0019] Among them, K eff Indicates the composite stress intensity factor amplitude, Y j and Y cThey represent the node geometry parameter correction coefficient and the crack geometry parameter correction coefficient respectively; σ n represents the nominal stress, and a represents the crack depth.

[0020] In step S4, the fitting results of the node geometric parameter correction coefficient and the crack geometric parameter correction coefficient are:

[0021] Y j =θ 0.214 (2.09β+0.251)(1.126τ+0.001);

[0022]

[0023] In step S5, the specific method of performing crack propagation simulation according to the calculation results is:

[0024] Determine whether the calculation result meets the expansion condition, the expansion condition is:

[0025]

[0026] Where ΔK th Represents the material fatigue crack growth threshold, a i and c i denote the crack depth and length of the i-th expansion step, respectively, a f and c f They represent the crack depth limit and crack length limit respectively.

[0027] In step S5, the calculation formula for the remaining fatigue life is:

[0028] N=N0+∑ΔN i ;

[0029]

[0030] Where N represents the remaining fatigue life, N0 represents the initial fatigue life of the steel tube node, ΔN i represents the fatigue life increment of each expansion step cycle, C and m represent fatigue crack growth parameters, a i-1 and a i denote the crack lengths obtained in the i-1th and i-th expansion step cycles, respectively.

[0031] In step S5, the crack extension step length of each step is determined in a stepwise decreasing manner.

[0032] In step S5, when performing crack propagation simulation, the crack propagation step length is:

[0033] Δa i =0.1Δa i-1 ;

[0034] Where Δa i represents the expansion step length in the i-th expansion step cycle, Δa i-1 Represents the expansion step length in the i-1th expansion step cycle.

[0035] Compared with the prior art, the present invention has the following beneficial effects:

[0036] The present invention proposes a method for predicting the residual fatigue life of KT-type nodes of angle steel welded trusses. This method compensates for the shortcomings of the SN curve method through the use of fracture mechanics. It takes into account the mechanical properties of components when they are damaged. Therefore, it can be used for fatigue verification of components with initial defects in the design stage and for repair and reinforcement of damaged components in the service stage. It can accurately predict the fatigue residual life of structural nodes through crack propagation. In addition, the present invention uses a crack analysis module based on FRANC3D software to realize the fitting calculation of the composite stress intensity factor amplitude, which can avoid the unidirectional deviation calculated by FRANC3D software and increase the accuracy of life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A flow chart of a method for remaining fatigue life of a KT-type angle steel welded truss node provided in an embodiment of the present invention;

[0038] Figure 2 This is a flow chart of fatigue fracture problem analysis based on FRANC3D software in an embodiment of the present invention;

[0039] Figure 3 This is a principle flow chart of the method for predicting the residual fatigue life of crack propagation in KT-type angle steel welded truss nodes based on the fracture mechanics method;

[0040] Figure 4 This is a schematic diagram of the KT type node structure;

[0041] Figure 5 Schematic diagram of the initial crack position of the sub-model;

[0042] Figure 6 Crack mesh division;

[0043] Figure 7 Schematic diagram of the crack surface and crack tip mesh. DETAILED DESCRIPTION

[0044] In order to make the purpose, 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. Obviously, the described embodiments are part of the embodiments of the present invention, not all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0045] like Figures 1 to 3 As shown, an embodiment of the present invention provides a method for predicting the remaining fatigue life of a KT-type node of an angle steel welded truss, comprising the following steps:

[0046] Step S1: Establish the finite element model of the node and determine the node geometric parameters. The node structure diagram is as follows: Figure 4 As shown, the node geometric parameters include: the angle θ between the web and the chord, the ratio β between the web width b1 and the chord width b2, and the ratio τ between the web thickness t1 and the chord thickness t2.

[0047] Specifically, in step S1, a node finite element model is established through ABAQUS.

[0048] Step S2: performing calculations based on the finite element model to determine the crack initiation location.

[0049] Specifically, in this embodiment, it is assumed that the initial crack is perpendicular to the web, and the possible position of maximum stress concentration of the KT-type node is determined. Then, calculation is performed using a finite element model to determine the position of maximum stress as the crack initiation position.

[0050] Step S3: Import the finite element model of the node into the crack analysis module, insert the initial crack at the crack initiation location through the crack analysis module, determine the crack geometric parameters, and calculate the composite stress intensity factor amplitude; the crack geometric parameters include the ratio of half crack length c to crack depth a c / a, and the ratio of crack depth a to chord thickness t2 a / t2. The initial crack position of the submodel is shown in Figure 5 , the initial crack meshing and the crack surface and crack tip meshing are as follows Figure 6 and Figure 7 shown.

[0051] In this embodiment, due to the complex stress on the KT node, the cracks in the KT node are often complex, so the composite stress intensity factor amplitude is used for description. Figure 4 As shown in FIG. 1 , in this embodiment, the composite stress intensity factor amplitude can be expressed as follows: the fatigue crack at the weld toe is a composite crack under the combination of three basic cracking modes: opening type (type I), sliding type (type II), and tearing type (type III), that is:

[0052]

[0053] Where K eff is the equivalent stress intensity factor value; K I , K Ⅱ and K Ⅲ are the stress intensity factors of type I, type II and type III respectively; ν is the Poisson's ratio of steel, which is taken as 0.3.

[0054] Specifically, in this embodiment, the crack analysis module can use FRANC3D software, which can directly output the type I, type II and type III stress intensity factors K I , K Ⅱ and K Ⅲ , combined with formula (1), the composite stress intensity factor amplitude of the node can be calculated.

[0055] Step S4: Repeat the calculation of the composite stress intensity factor amplitude by varying the node and crack geometric parameters. Data fitting is performed based on the composite stress intensity factor amplitudes under different node and crack geometric parameters to obtain a composite stress intensity factor amplitude calculation formula. Specifically, in this embodiment, the composite stress intensity factor amplitude primarily considers the value in the crack depth direction.

[0056] Specifically, in this embodiment, when fitting, the fitting parameters are respectively fitted with the two influencing factors of the node geometry parameters and the crack geometry parameters, and the fitting formula is:

[0057]

[0058] Among them, Y j and Y c are the geometric correction coefficients considering the geometric dimensions of the node and crack, respectively. Both are dimensionless coefficients, and θ is expressed in radians. n represents the nominal stress, and a represents the crack depth.

[0059] Specifically, in this embodiment, multiple nonlinear regression analysis is performed on the finite element model calculation results to obtain Y j and Y c , correlation coefficient R 2 is 0.981, and the fitted Y j and Y c The calculation expression is:

[0060] Y j =θ 0.214 (2.09β+0.251)(1.126τ+0.001); (3)

[0061]

[0062] Where θ is the angle between the web and the chord, expressed in radians, β is the ratio of the web width b1 to the chord width b2, and τ is the ratio of the web thickness t1 to the chord thickness t2. It represents the ratio of half crack length c to crack depth a, It represents the ratio of the crack depth a to the chord thickness t2.

[0063] Furthermore, in this embodiment, in order to ensure the safety of the structure in actual engineering, the fitted formula (2) can also be modified and multiplied by the corresponding safety factor to eliminate all samples with negative relative errors, thereby obtaining the calculation formula for the KT-type node stress intensity factor, namely:

[0064]

[0065] Among them, Y0 represents the safety factor, which is obtained by data fitting.

[0066] Step S5: Determine the geometric parameters and crack parameters of the node, calculate the composite stress intensity factor amplitude by fitting the composite stress intensity factor amplitude calculation formula, perform crack growth simulation based on the calculation results, and then calculate the remaining fatigue life based on the crack growth mode results.

[0067] Specifically, in this embodiment, the initial crack depth a0 and initial crack length c0 of the common elliptical or semi-elliptical cracks in the steel pipe node, as well as the crack depth limit a f and crack length limit c f Then, the equivalent stress intensity factor value is calculated using the fitted formula (3) or formula (5).

[0068] Then, the crack is judged whether it will continue to expand according to the judgment conditions. If the expansion conditions are met, the crack continues to expand and the next step is executed; if the expansion conditions are not met, the crack expansion is terminated and the remaining fatigue life N is output. f , end the calculation.

[0069] The judgment conditions for whether the crack continues to expand are:

[0070]

[0071] Where ΔK th Represents the material fatigue crack growth threshold, ΔK th The value is 63N·mm -3 / 2 ;a i and c i denote the crack depth and length of the i-th expansion step, respectively, a f and c f They represent the crack depth limit and crack length limit respectively.

[0072] Specifically, when performing crack propagation calculations, it is necessary to specify the propagation step length in the crack depth direction. Generally, the smaller the propagation step length, the higher the calculation accuracy, but the calculation time will also increase. In order to ensure the calculation accuracy, the crack propagation step length of each step can be determined in a step-by-step manner. Specifically, the crack propagation step length of step i can be taken as Δa i =0.1Δa i-1 Where, when i=1, Δa1=0.1Δa0. According to the Paris formula, the expansion step length Δc in the crack length direction is calculated. i for:

[0073]

[0074] Where Δc i represents the expansion step length in the crack length direction in the i-th crack growth cycle; ΔK c,eff The stress intensity factor amplitude at the tip of the crack in the length direction can also be calculated by fitting the method of steps S3 to S4 above, ΔK a,eff Indicates the amplitude of the stress intensity factor at the crack tip in the crack depth direction.

[0075] Therefore, the crack depth and the length after expansion in the longitudinal direction are determined to be a i =a0+∑Δa i and c i =c0+∑Δc i .

[0076] Specifically, in step S5, the calculation formula for the remaining fatigue life is:

[0077] N=N0+∑ΔN i ;(8)

[0078]

[0079] Where N represents the remaining fatigue life, N0 represents the initial fatigue life of the steel tube node, ΔN i represents the fatigue life increment of each expansion step cycle, C and m represent fatigue crack growth parameters, a i-1 and a i denote the crack lengths obtained in the i-1th and i-th expansion step cycles, respectively.

[0080] In this example, the model with β = 1 / 2, τ = 0.2, θ = 40°, c / a = 4, and a / t2 = 0.5 was selected from all parameter models and inserted as the FRANC3D submodel. The initial crack depth was 5 mm, and the crack was extended in four steps with a step length of 1 mm. A sinusoidal load with a stress ratio of 0.1 was applied. The crack extension parameter corresponding to the node steel was C = 8.02 × 10 -12, m = 2.92. The crack growth rate was calculated based on the Paris criterion using FRANC3D software to compare the remaining fatigue life with the method of the present invention. As the crack grows, the number of cycles increases. The cycle stops when the crack depth reaches 9 mm. At this time, if the crack continues to grow, it will penetrate the chord wall thickness. The corresponding number of cycles at this time is 1.4788×10 12 Second-rate.

[0081] Furthermore, based on the calculated cracking model, the stress intensity factor corresponding to each expansion step was obtained. The calculated values ​​using the fitted stress intensity factor calculation formula were compared with the values ​​simulated during the expansion process using FRANC3D software to assess the correctness of the crack expansion step simulation. The two showed the same trend and the difference in values ​​was within 7.2%. Furthermore, the values ​​calculated by the formula were slightly larger, indicating that the stress intensity factor calculation formula derived from multiple nonlinear regression analysis used in this invention yields a relatively safe result for evaluating the remaining fatigue life of K-type joints.

[0082] In this embodiment, a multivariate nonlinear regression analysis is performed on the numerical settlement results, and a calculation formula for the stress intensity factor of the KT-type node of the coal conveyor trestle is obtained by fitting. The calculation results of the formula are compared with the finite element calculation results. The ratio mean μ=1.0019, the mean square error σ=0.045, and the coefficient of variation σ / μ=0.045, indicating that the calculation formula for the stress intensity factor fitted by the present invention has high calculation accuracy.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the residual fatigue life of KT-type joints of angle steel welded trusses, characterized in that: The following steps are involved: Step S1: Establishing a finite element model of the node and determining the node geometric parameters, wherein the node geometric parameters include: the angle θ between the web and the chord, the ratio β between the web width b1 and the chord width b2, and the ratio τ between the web thickness t1 and the chord thickness t2. In step S1, the node finite element model is established using ABAQUS. Step S2: performing calculations based on the finite element model to determine the crack initiation location; The specific steps of step S2 are: Determine the maximum stress concentration position of the KT joint and, assuming that the initial crack is perpendicular to the web, determine the crack initiation position using finite element calculation results; Step S3: Importing the finite element model of the node into the crack analysis module, inserting an initial crack at the crack initiation location through the crack analysis module, determining the crack geometric parameters, and calculating the composite stress intensity factor amplitude; the crack geometric parameters include the ratio of the half crack length c to the crack depth a, and the ratio of the crack depth a to the chord thickness t2; In step S3, the crack analysis module uses FRANC3D software; In step S3, the calculation formula of the composite stress intensity factor amplitude is: in, represents the composite stress intensity factor amplitude, K I 、 K Ⅱ and K Ⅲ They are type I, type II and type III stress intensity factors respectively; ν is the Poisson's ratio of steel; Step S4: changing the node geometric parameters and the crack geometric parameters, repeatedly calculating the composite stress intensity factor amplitude, performing data fitting based on the composite stress intensity factor amplitude under different node geometric parameters and crack geometric parameters, and obtaining a composite stress intensity factor amplitude calculation formula; In step S4, the fitting results of the node geometric parameter correction coefficient and the crack geometric parameter correction coefficient are: ； ； The calculation formula of the composite stress intensity factor amplitude obtained by fitting is: ； in, represents the composite stress intensity factor amplitude, Y j and Y c They represent the node geometry parameter correction coefficient and the crack geometry parameter correction coefficient respectively; σ n represents the nominal stress, a represents the crack depth; Step S5: determining the geometric parameters and crack parameters of the node, calculating the composite stress intensity factor amplitude by using the composite stress intensity factor amplitude calculation formula obtained by fitting, performing crack growth simulation based on the calculation results, and then calculating the remaining fatigue life based on the crack growth mode results; In step S5, the specific method of performing crack propagation simulation based on the calculation results is: determining whether the calculation results meet the propagation conditions; if the propagation conditions are met, the crack continues to propagate; if the propagation conditions are not met, the crack propagation is terminated; the propagation conditions are: ； Among them, Δ K th Represents the fatigue crack growth threshold of the material, a i and c i Respectively represent i The crack depth and length of each expansion step, a f and c f Represent the crack depth limit and crack length limit respectively; The calculation formula for the remaining fatigue life is: ； ； Where N represents the remaining fatigue life, N 0 represents the initial fatigue life of the steel tube node, Δ N i represents the fatigue life increment per expansion step cycle, C and m represents the fatigue crack growth parameter, a i-1 and a i denote the crack lengths obtained in the i-1th and ith expansion step cycles, respectively, represents the amplitude of the stress intensity factor at the crack tip in the crack depth direction; In step S5, the crack extension step length of each step is determined in a gradually decreasing manner; when performing crack extension simulation, the crack extension step length is: ； Among them, Δ a i represents the expansion step length in the i-th expansion step cycle, Δ a i-1 Represents the expansion step length in the i-1th expansion step cycle.

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