Angle steel welding trussed beam KT type node residual fatigue life prediction method

Abstract

The invention relates to a method for predicting the fatigue life of a KT type node of an angle steel welded truss girder, and belongs to the technical field of bridge engineering, the residual fatigue life of the KT type node of the angle steel welded truss girder is predicted through finite element modeling and crack propagation simulation analysis, and the method mainly comprises the following steps: establishing a finite element model of the KT type node of the angle steel welded truss girder; inserting cracks based on the crack propagation model; node geometric parameters and crack geometric parameters are determined; and fitting a composite stress intensity factor calculation formula through parameter data so as to predict the residual fatigue life. Compared with a traditional stress amplitude-cycle index (S-N) curve method, the fracture mechanics method has the advantages that the defect that initial cracks cannot be considered in the design stage of the S-N curve method can be overcome, and the residual fatigue life of each fatigue crack growth stage can be more accurately obtained.

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 with angle steel as the main load-bearing structure 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 action, 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 the structure to a certain extent, but if the remaining life of the structure under a specific crack defect 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 applicable to the evaluation of the fatigue life of components in the design stage, but cannot be used to evaluate the remaining fatigue life of components in the use stage. The fracture mechanics method makes up for this deficiency 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 use stage. It can accurately predict the fatigue remaining life of structural nodes by crack extension. However, the evaluation method based on fracture mechanics started late, so there are still many gaps to be filled in the crack extension model and the 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 residual fatigue life of a KT-type node of an angle steel welded truss, which achieves accurate prediction of the residual 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 a KT-type node of an angle steel welded truss, 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: an angle θ between the web member and the chord member, a ratio β between the web member width b1 and the chord member width b2, and a ratio τ between the web member thickness t1 and the chord member thickness t2;

[0007] Step S2: Calculate according to the finite element model to determine the crack initiation position;

[0008] Step S3: importing the finite element model of the node into the crack analysis module, inserting the initial crack at the crack initiation position 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 according to 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 propagation simulation according to the calculation results, and then calculate the remaining fatigue life according to the crack propagation mode results.

[0011] The specific steps of step S2 are:

[0012] The maximum stress concentration position of the KT-type node 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 uses FRANC3D software.

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

[0015]

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

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

[0018]

[0019] Among them, K eff represents the combined stress intensity factor amplitude, Y j and Y cThey represent the node geometry parameter correction coefficient and 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] Among them, ΔK th Represents the material fatigue crack extension threshold, a i and c i denote the crack depth and length of the i-th extension step, respectively, and a f and c f They represent the crack depth limit and crack length limit respectively.

[0027] In step S5, the remaining fatigue life is calculated as follows:

[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 the fatigue crack growth parameters, a i-1 and a i represent the crack lengths obtained in the i-1th and i-th extension step cycles, respectively.

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

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

[0033] Δa i =0.1Δa i-1 ;

[0034] Among them, 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 a KT-type node of an angle steel welded truss, which makes up for the deficiency of the SN curve method by using a fracture mechanics method. It takes into account the mechanical properties of a component when it is damaged, and can therefore be used for fatigue verification of components with initial defects in the design phase and for repair and reinforcement of damaged components in the use phase. It can accurately predict the fatigue residual life of a structural node by means of crack propagation. In addition, the present invention utilizes a crack analysis module based on FRANC3D software to realize fitting calculation of the composite stress intensity factor amplitude, which can avoid the unidirectional deviation calculated by the FRANC3D software and increase the accuracy of life prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 A flow chart of a method for residual 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 It is a schematic diagram of KT type node construction;

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

[0042] Figure 6 Mesh the cracks;

[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, rather than 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 construction 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: Calculate according to the finite element model to determine the crack initiation position.

[0049] Specifically, in this embodiment, it is assumed that the initial crack is perpendicular to the web, the possible position of the maximum stress concentration of the KT-type node is determined, and then the finite element model is used for calculation to determine the maximum stress position 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 position 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 composite, so the composite stress intensity factor amplitude is used for description. Figure 4 As shown, in this embodiment, the composite stress intensity factor amplitude can be expressed as: 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] In the formula, K eff is the equivalent stress intensity factor value; K I , K Ⅱ and K Ⅲ are type I, type II and type III stress intensity factors 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 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: changing the node geometric parameters and the crack geometric parameters, repeatedly calculating the composite stress intensity factor amplitude, performing data fitting according to 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. Specifically, in this embodiment, the composite stress intensity factor amplitude mainly considers the value in the crack depth direction.

[0056] Specifically, in this embodiment, when fitting, the fitting parameters are respectively fitted with two influencing factors, namely, 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 nodes and cracks, respectively. They 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] Among them, θ represents the angle between the web and the chord, expressed in radians, β represents the ratio of the web width b1 to the chord width b2, and τ represents 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 crack depth a to chord thickness t2.

[0063] Furthermore, in this embodiment, in order to ensure the safety of the structure in the actual project, the fitted formula (2) can also be corrected by multiplying it by the corresponding safety factor to eliminate all samples with negative relative errors, thereby obtaining the calculation formula of 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 propagation simulation according to the calculation results, and then calculate the remaining fatigue life according to the crack propagation 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 will continue to expand according to the judgment conditions. If the expansion conditions are met, the crack will continue to expand and the next step will be executed; if the expansion conditions are not met, the crack expansion will stop and the remaining fatigue life N will be output. f , end the calculation.

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

[0070]

[0071] Among them, 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 extension step, respectively, and a f and c f They represent the crack depth limit and crack length limit respectively.

[0072] Specifically, when calculating crack extension, it is necessary to specify the extension step in the crack depth direction. Generally, the smaller the extension step, the higher the calculation accuracy, but the calculation time will also increase. In order to ensure the calculation accuracy, the crack extension step of each step can be determined in a step-by-step manner. Specifically, the crack extension step 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 extension step length in the crack length direction in the i-th crack extension 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 Represents 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 and 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 the fatigue crack growth parameters, a i-1 and a i represent the crack lengths obtained in the i-1th and i-th extension step cycles, respectively.

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

[0081] Furthermore, on the basis of calculating the cracking model, the stress intensity factor corresponding to each expansion step was obtained, and the calculated value of the fitted stress intensity factor calculation formula was compared with the simulated value of the expansion process of the FRANC3D software to judge the correctness of the simulation of the crack expansion step. It was found that the two trends were the same and the numerical difference was within 7.2%. In addition, the value calculated by the formula is too large, indicating that the stress intensity factor calculation formula obtained by the multiple nonlinear regression analysis in the present invention can obtain a relatively safe result for the residual fatigue life of the K-type node.

[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 handling trestle is fitted. 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 a very 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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 nodes 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: an angle θ between the web member and the chord member, a ratio β between the web member width b1 and the chord member width b2, and a ratio τ between the web member thickness t1 and the chord member thickness t2; Step S2: Calculate according to the finite element model to determine the crack initiation position; Step S3: importing the finite element model of the node into the crack analysis module, inserting the initial crack at the crack initiation position 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; Step S4: changing the node geometric parameters and the crack geometric parameters, repeatedly calculating the composite stress intensity factor amplitude, performing data fitting according to 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; 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 propagation simulation according to the calculation results, and then calculate the remaining fatigue life according to the crack propagation mode results.

2. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 1 is characterized in that: The specific steps of step S2 are: The maximum stress concentration position of the KT-type node is determined, and the crack initiation position is determined by finite element calculation results, assuming that the initial crack is perpendicular to the web.

3. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 1 is characterized in that: In the step S1, a node finite element model is established by using ABAQUS; in the step S3, a crack analysis module uses FRANC3D software.

4. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 1 is characterized in that: In step S3, the calculation formula of the composite stress intensity factor amplitude is: Among them, K eff Represents the combined stress intensity factor amplitude, K I , K Ⅱ and K Ⅲ are type I, type II and type III stress intensity factors respectively; ν is the Poisson's ratio of steel.

5. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 1 is characterized in that: In step S4, the calculation formula of the composite stress intensity factor amplitude obtained by fitting is: Among them, K eff represents the combined stress intensity factor amplitude, Y j and c They represent the node geometry parameter correction coefficient and crack geometry parameter correction coefficient respectively; σ n represents the nominal stress and a represents the crack depth.

6. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 5 is characterized in that: In step S4, the fitting results of the node geometric parameter correction coefficient and the crack geometric parameter correction coefficient are: Y j =θ 0.214 (2.09β+0.251)(1.126τ+0.001); 7. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 5 is characterized in that: In step S5, the specific method of performing crack propagation simulation according to the calculation results is: Determine whether the calculation result meets the expansion condition, the expansion condition is: Among them, ΔK th Represents the material fatigue crack extension threshold, a i and c i denote the crack depth and length of the i-th extension step, respectively, and a f and c f They represent the crack depth limit and crack length limit respectively.

8. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 1 is characterized in that: In step S5, the remaining fatigue life is calculated as follows: N=N0+∑ΔN i ; 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 the fatigue crack growth parameters, a i-1 and a i represent the crack lengths obtained in the i-1th and i-th extension step cycles, respectively.

9. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 1, characterized in that: In step S5, the crack extension step length of each step is determined in a step-by-step decreasing manner.

10. The method for predicting the residual fatigue life of a KT-type node of an angle steel welded truss according to claim 9, characterized in that: In step S5, when performing crack extension simulation, the crack extension step length is: Δa i =0.1Δa i-1 ; Among them, 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.

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