Surface internal stress driven fatigue crack area expansion rate model, construction method and application

Abstract

The invention relates to an in-plane internal stress driven fatigue crack area expansion rate model, the specific model is a formula (1), the in-plane internal stress driven fatigue crack expansion rate can be determined by using the model, and the crack expansion area and form are obtained; the model construction method comprises the following steps: establishing a global digital twinning model, introducing an initial crack and a welding residual stress field at typical details, loading by utilizing a fatigue load model, simulating fatigue crack propagation by adopting a digital twinning method, and constructing the model. Counting fatigue crack area increments corresponding to different loading times in the crack propagation process and I-type fatigue crack strain energy release rates, obtaining an in-plane internal stress driven fatigue crack area propagation rate / -delta GI curve by using a difference algorithm, and establishing an in-plane internal stress driven fatigue crack area propagation rate model by using a least square method in a fitting manner; the model can represent the surface internal stress driven crack three-dimensional expansion behavior, and can provide a basis for detail surface internal stress driven fatigue mechanism research and damage evaluation.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically relating to an in-plane stress-driven fatigue crack area propagation rate model, its construction method, and its application. Background Technology

[0002] Steel bridges are widely used in modern highway, railway, and urban road bridge construction due to their advantages such as light weight, strong span capacity, and short construction period. However, steel bridges have complex structures, numerous connecting welds, and are directly subjected to repeated wheel loads, making fatigue problems prominent. Under large in-plane stresses, fatigue cracking is prone to occur, posing a serious threat to the operational safety of steel bridges.

[0003] In recent years, digital twin simulations based on extended finite element method (XFEM) and numerical fracture mechanics have provided important tools for fatigue-resistant design and remaining life assessment of key structural details of steel bridges. However, existing studies, when quantifying crack propagation behavior, mostly still use one-dimensional evaluation indicators based on crack length propagation rate (da / dN) from traditional physical experiments. Although these methods characterize crack propagation features to some extent, they neglect factors such as crack propagation along the plate thickness direction, making the assessment results unsafe. Furthermore, they fail to fully describe the propagation behavior of fatigue cracks in three-dimensional space and cannot comprehensively reflect the morphology of fatigue crack propagation.

[0004] Therefore, to address the limitations of traditional fatigue crack propagation rate models that use surface crack length as an evaluation index, it is necessary to construct a fatigue crack propagation area rate model to achieve a realistic and accurate description of the propagation behavior and morphology of in-plane stress-driven Type I (opening) fatigue cracks in three-dimensional space. This will provide a more scientific and comprehensive evaluation index for assessing the detailed fatigue resistance and remaining life of steel bridge decks driven by in-plane stress, and has significant theoretical value and engineering application prospects. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a fatigue crack area propagation rate model driven by in-plane stress and a method for constructing the model.

[0006] Another technical problem to be solved by this invention is to obtain the in-plane stress-driven fatigue crack propagation area and the in-plane stress-driven fatigue crack morphology using this model.

[0007] The technical solution adopted to solve the above technical problems is: an in-plane stress-driven fatigue crack area propagation rate model, which is expressed by the following equation:

[0008] (1)

[0009] In equation (1), ΔG represents the fatigue crack area propagation rate; c1 and c2 are the fatigue crack propagation parameters of the steel; ΔG Ⅰ The value represents the strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 G Ⅰmax This represents the maximum strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 G Ⅰmin This represents the minimum strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 ;ΔG th This is the threshold value for strain energy release rate, in mJ / mm. 2 R is the stress ratio.

[0010] The value range of c1 in this invention is [1.60 × 10]. -6 1.10×10 -5 c2 takes values ​​in the range [1.1, 1.6], ΔG th The value range is [12.1, 39.3], and the unit is mJ / mm. 2 The value of R is in the range of (-1, 1).

[0011] In this invention, c1 is 1.65 × 10 -6 c2 is 1.5, ΔG th Take 20.5 mJ / mm 2 R is set to 0.

[0012] The application of the in-plane stress-driven fatigue crack area propagation rate model of the present invention in determining the in-plane stress-driven fatigue crack propagation area, which is determined by the following formula:

[0013] (2)

[0014] In equation (2), i represents the number of loading operations, which is a natural number, and A i Let A0 be the fatigue crack area after the i-th loading, where A0 is the initial fatigue crack area when i=0; n is the number of times the load is applied again after the i-th loading, taking the form of a finite positive integer. i+n Let be the fatigue crack area after the (i+n)th loading.

[0015] The application of the in-plane stress-driven fatigue crack area propagation rate model of the present invention in the in-plane stress-driven fatigue crack morphology, wherein the in-plane stress-driven fatigue crack morphology includes: fatigue crack depth coordinates after the (i+n)th loading. The length of one side of the fatigue crack after the (i+n)th loading. The length of the fatigue crack on the symmetrical side after the (i+n)th loading. Coordinates of fatigue crack depth after the (i+n)th loading. The length of one side of the fatigue crack after the (i+n)th loading. The length of the fatigue crack on the symmetrical side after the (i+n)th loading. Determined by the following formula:

[0016] (3)

[0017] In equation (3), Let y0 be the coordinate of the fatigue crack depth after the i-th loading; when i=0, y0 is the initial fatigue crack depth. The length of one side of the fatigue crack after the i-th loading; x is the length of the symmetrical side of the fatigue crack after the i-th loading; when i=0, x 1,0 x is the length of one side of the initial fatigue crack. 2,0 It is the length of the side symmetrical to the initial fatigue crack.

[0018] The method for constructing the in-plane stress-driven fatigue crack area propagation rate model of the present invention comprises the following steps:

[0019] Step 1: Construct a global digital twin model for typical fatigue details of bridges. Solid elements are used to construct simple and small specimens, while hierarchical refined modeling is used for complex models.

[0020] Step 2: Construct a welding model, use the welding heat source model to simulate the welding residual stress field, and use a three-dimensional linear interpolation method to map the welding residual stress field into the global digital twin model;

[0021] Step 3: Insert initial cracks at detailed locations, apply fatigue loads according to actual loading rules, apply fatigue loads according to the cyclic loads set in the test for fatigue tests, and use linear elastic fracture mechanics and extended finite element method to complete the digital twin simulation of fatigue cracks driven by in-plane stress.

[0022] Step 4: Statistically analyze the fatigue crack area increment and strain energy release rate of Type I fatigue crack corresponding to different loading cycles during crack propagation, and use a differential algorithm to obtain the in-plane stress-driven fatigue crack area propagation rate. / -ΔG Ⅰ The curve was fitted using the least squares method to establish a fatigue crack area propagation rate model driven by in-plane stress.

[0023] The beneficial effects of this invention are as follows:

[0024] This invention proposes an in-plane stress-driven fatigue crack area propagation rate defined by spatial area, and a method for constructing the in-plane stress-driven crack area propagation rate based on digital twin simulation. This model characterizes the fatigue crack propagation rate using crack area and strain energy release rate; it overcomes the limitation of traditional fatigue life assessments, which are confined to a single crack length direction and struggle to characterize the spatial propagation behavior of fatigue cracks, thus improving the accuracy and precision of in-plane stress-driven fatigue crack assessment in a three-dimensional spatial scale. Attached Figure Description

[0025] Figure 1 A schematic diagram of fatigue crack propagation driven by in-plane stress.

[0026] Figure 2 The stress-driven fatigue crack area propagation rate at the butt weld of the U-rib in a long-span cable-stayed bridge / -ΔG Ⅰ curve.

[0027] Figure 3 This is a three-dimensional structural diagram of the U-rib butt weld of a long-span cable-stayed bridge.

[0028] Figure 4 The results of digital fatigue tests on the butt welds of the U-ribs of a long-span cable-stayed bridge.

[0029] Figure 5 This is a flowchart of the model construction process for the present invention.

[0030] Figure 6 The fatigue crack area propagation rate driven by in-plane stress in the suspending cable wire / -ΔG Ⅰ curve.

[0031] Figure 7 This is a model of a suspension cable steel wire.

[0032] Figure 8 The results are from the fatigue test of the suspension cable steel wire.

[0033] Figure 9 The in-face stress of the riveted joint drives the fatigue crack area propagation rate. curve.

[0034] Figure 10 This is a digital fatigue test model for riveted joints.

[0035] Figure 11 The results are from the fatigue test of the riveted joint. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to these embodiments.

[0037] The Type I crack described in this invention is an open crack.

[0038] Example 1

[0039] The present invention relates to an in-plane stress-driven fatigue crack area propagation rate model, which is the following equation (1):

[0040] (1)

[0041] In equation (1), ΔG represents the fatigue crack area propagation rate; c1 and c2 are the fatigue crack propagation parameters of the steel; ΔG Ⅰ The value represents the strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 G Ⅰmax This represents the maximum strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 G Ⅰmin This represents the minimum strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 ;ΔG th This is the threshold value for strain energy release rate, in mJ / mm. 2 R is the stress ratio.

[0042] In this embodiment (1), taking the U-rib butt weld detail of a long-span cable-stayed bridge as an example, this detail is a typical fatigue detail driven by in-plane stress. The schematic diagram of fatigue crack propagation driven by in-plane stress is shown below. Figure 1 As shown, construct as follows Figure 2 The in-plane stress-driven fatigue crack area propagation rate shown / -ΔG Ⅰ The curve, the digital twin model, is like Figure 3 As shown. c1 is 1.65 × 10. -6 c2 is 1.5, ΔG th Take 20.5 mJ / mm 2 When R is 0, ΔG Ⅰmin The value is 0. Using formula (1), the amplitude ΔG of the sum of the strain energy release rates of type I cracks corresponding to different crack areas at typical detail locations can be obtained. Ⅰ and crack area propagation rate The specific results are shown in Table 1. The detailed fatigue crack propagation results are as follows: Figure 4 As shown.

[0043] Table 1 Crack area propagation rate at the butt weld of the U-rib in the top plate

[0044]

[0045] like Figure 5 As shown, the method for constructing the above-mentioned in-plane stress-driven fatigue crack area propagation rate model consists of the following steps:

[0046] Step 1: Construct a global digital twin model for typical fatigue details of bridges. For simple specimens, solid elements are used for construction, while for complex models, hierarchical refined modeling is adopted.

[0047] Step 2: Construct a welding model, use the welding heat source model to simulate the welding residual stress field, and use a three-dimensional linear interpolation method to map the welding residual stress field into the global digital twin model;

[0048] Step 3: Insert initial cracks at detailed locations, apply fatigue loads according to actual loading rules, apply fatigue loads according to the cyclic loads set in the test for fatigue tests, and use linear elastic fracture mechanics and extended finite element method to complete the digital twin simulation of fatigue cracks driven by in-plane stress.

[0049] Step 4: Statistically analyze the fatigue crack area increment and strain energy release rate of Type I (opening) fatigue cracks corresponding to different loading cycles during crack propagation. Use a differential algorithm to obtain the in-plane stress-driven fatigue crack area propagation rate. / -ΔG Ⅰ The curve was fitted using the least squares method to establish a fatigue crack area propagation rate model driven by in-plane stress.

[0050] Example 2

[0051] In the above embodiment 1, this embodiment takes the fatigue test of the suspension cable wire as an example to construct the corresponding in-plane stress-driven fatigue crack area propagation rate. / -ΔG Ⅰ Curves Figure 6 As shown, the three-dimensional structure is as follows Figure 7 As shown. c1 is 1.10 × 10 -5 c2 is 1.6, ΔG th Take 39.3 mJ / mm 2 R is taken as 0.8. Using formula (1), the amplitude ΔG of the sum of strain energy release rates of type I cracks corresponding to different crack areas at typical detail locations can be calculated. Ⅰ and crack area propagation rate As shown in Table 2, the crack propagation results are as follows: Figure 8 As shown.

[0052] Table 2 Crack area propagation rate of steel wire

[0053]

[0054] The method for constructing the in-plane stress-driven fatigue crack area propagation rate model in this embodiment is the same as that in Embodiment 1.

[0055] Example 3

[0056] In the above embodiment 1, this embodiment takes a typical detailed test of a riveted steel bridge as an example to construct the corresponding in-plane stress-driven fatigue crack area propagation rate. / -ΔG Ⅰ Curves Figure 9 As shown, the three-dimensional structure is as follows Figure 10 As shown. c1 is 1.60 × 10 -6 c2 is 1.1, ΔG th Take 12.1 mJ / mm 2 When R is 0, ΔG Ⅰmin The value is 0. Using formula (1), the amplitude ΔG of the sum of the strain energy release rates of the Type I cracks corresponding to different crack areas at typical detail locations can be calculated. Ⅰ and crack area propagation rate As shown in Table 3, the crack propagation results are as follows: Figure 11 As shown.

[0057] Table 3 Crack area propagation rate of riveted joints

[0058]

[0059] The method for constructing the in-plane stress-driven fatigue crack area propagation rate model in this embodiment is the same as that in Embodiment 1.

[0060] Example 4

[0061] The application of the in-plane stress-driven fatigue crack area propagation rate model constructed in Example 1 above in determining the in-plane stress-driven fatigue crack propagation area, which is determined by the following formula:

[0062] (2)

[0063] In equation (2), i represents the number of loading operations, which is a natural number, and A i Let A0 be the fatigue crack area after the i-th loading, where A0 is the initial fatigue crack area when i=0; n is the number of times the load is applied again after the i-th loading, taking the form of a finite positive integer. i+n Let be the fatigue crack area after the (i+n)th loading.

[0064] The initial crack area A0 is 161.6 mm. 2 ΔG Ⅰ 120.0 mJ / mm2 The crack area A after the 10000th loading. 10000 It is 183.6mm 2 .

[0065] Example 5

[0066] The application of the in-plane stress-driven fatigue crack area propagation rate model constructed in Example 1 above in the morphology of in-plane stress-driven fatigue cracks, which includes: the fatigue crack depth coordinates after the (i+n)th loading. The length of one side of the fatigue crack after the (i+n)th loading. The length of the fatigue crack on the symmetrical side after the (i+n)th loading. Coordinates of fatigue crack depth after the (i+n)th loading. The length of one side of the fatigue crack after the (i+n)th loading. The length of the fatigue crack on the symmetrical side after the (i+n)th loading. Determined by the following formula:

[0067] (3)

[0068] In equation (3), Let y0 be the coordinate of the fatigue crack depth after the i-th loading; when i=0, y0 is the initial fatigue crack depth. The length of one side of the fatigue crack after the i-th loading; x is the length of the symmetrical side of the fatigue crack after the i-th loading; when i=0, x 1,0 x is the length of one side of the initial fatigue crack. 2,0 It is the length of the side symmetrical to the initial fatigue crack.

[0069] The initial crack A0 is 161.6 mm. 2 ΔG Ⅰ 120.0 mJ / mm 2 y0 is 4.14mm, x 1,0 It is 12.42mm, x 2,0 The value is -12.42mm. After the 10,000th loading, y 10000 It is 4.41mm, x 1,10000 It is 13.24mm, x 2,10000 It is -13.24mm.

Claims

1. A model for the area propagation rate of fatigue cracks driven by in-plane stress, characterized in that, The model is as follows: （1） In equation (1), ΔG represents the fatigue crack area propagation rate; c1 and c2 are the fatigue crack propagation parameters of the steel; ΔG Ⅰ The value represents the strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 ; G Ⅰmax This represents the maximum strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 ; G Ⅰmin This represents the minimum strain energy release rate of a type I crack under a single fatigue loading event, expressed in mJ / mm. 2 ;ΔG th This is the threshold value for strain energy release rate, in mJ / mm. 2 R is the stress ratio.

2. The in-plane stress-driven fatigue crack area propagation rate model according to claim 1, characterized in that: The value range of c1 is [1.60 × 10]. -6 1.10×10 -5 c2 takes values ​​in the range [1.1, 1.6], ΔG th The value range is [12.1, 39.3], and the unit is mJ / mm. 2 The value of R is in the range of (-1, 1).

3. The in-plane stress-driven fatigue crack area propagation rate model according to claim 1, characterized in that: The value of c1 is 1.65 × 10. -6 c2 is 1.5, ΔG th Take 20.5 mJ / mm 2 R is set to 0.

4. The use of the in-plane stress-driven fatigue crack area propagation rate model of claim 1 in determining the in-plane stress-driven fatigue crack propagation area, which is determined by the following formula: (2) In equation (2), i represents the number of loading operations, which is a natural number, and A i Let A0 be the fatigue crack area after the i-th loading, where A0 is the initial fatigue crack area when i=0; n is the number of times the load is applied again after the i-th loading, taking the form of a finite positive integer. i+n Let be the fatigue crack area after the (i+n)th loading.

5. The application of the in-plane stress-driven fatigue crack area propagation rate model of claim 1 in the morphology of in-plane stress-driven fatigue cracks, wherein the in-plane stress-driven fatigue crack morphology includes: Coordinates of fatigue crack depth after the (i+n)th loading event The length of one side of the fatigue crack after the (i+n)th loading. The length of the fatigue crack on the symmetrical side after the (i+n)th loading. Coordinates of fatigue crack depth after the (i+n)th loading event The length of one side of the fatigue crack after the (i+n)th loading. The length of the fatigue crack on the symmetrical side after the (i+n)th loading. Determined by the following formula: (3） In equation (3), Let y0 be the coordinate of the fatigue crack depth after the i-th loading; when i=0, y0 is the initial fatigue crack depth. The length of one side of the fatigue crack after the i-th loading; The length of the symmetrical side of the fatigue crack after the i-th loading; when When i=0, x 1,0 x is the length of one side of the initial fatigue crack. 2,0 It is the length of the side symmetrical to the initial fatigue crack.

6. The method for constructing the in-plane stress-driven fatigue crack area propagation rate model of claim 1, characterized in that, It consists of the following steps: Step 1: Construct a global digital twin model for typical fatigue details of bridges. Solid elements are used to construct simple and small specimens, while hierarchical refined modeling is used for complex models. Step 2: Construct a welding model, use the welding heat source model to simulate the welding residual stress field, and use a three-dimensional linear interpolation method to map the welding residual stress field into the global digital twin model; Step 3: Insert initial cracks at detailed locations, apply fatigue loads according to actual loading rules, apply fatigue loads according to the cyclic loads set in the test for fatigue tests, and use linear elastic fracture mechanics and extended finite element method to complete the digital twin simulation of fatigue cracks driven by in-plane stress. Step 4: Statistically analyze the fatigue crack area increment and strain energy release rate of Type I fatigue crack corresponding to different loading cycles during crack propagation, and use a differential algorithm to obtain the in-plane stress-driven fatigue crack area propagation rate. / -ΔG Ⅰ The curve was fitted using the least squares method to establish a fatigue crack area propagation rate model driven by in-plane stress.

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