A fatigue crack growth life extension finite element analysis method

Abstract

The present application relates to a kind of fatigue crack propagation life extension finite element analysis method, comprising the following steps: establishing three-dimensional solid model, simplifying three-dimensional solid model, obtaining fatigue crack tip stress distribution, obtaining fatigue crack propagation life.The process of obtaining fatigue crack propagation life includes measuring the length of metal structure fatigue crack, calculating the critical equivalent strain energy release rate of metal structure fatigue crack tip, calculating fatigue crack propagation life.The method of the present application applies virtual crack closure technique to the extended finite element method, achieves the purpose of simulating crack propagation without pre-specifying crack propagation path, thereby generating fine mesh at crack tip, saving the time required for modeling, reducing workload, and improving the accuracy of crack propagation life calculation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of aircraft structure design and analysis, and particularly relates to a fatigue crack propagation life extension finite element analysis method for a metal structural part. BACKGROUND

[0002] Traditional fatigue analysis is a statistical analysis, and the S-N curve or E-N curve of the material is obtained through experiments, and then the stress fatigue analysis or strain fatigue analysis is used to predict the fatigue life of the structure. However, the test piece used in the experiment is usually a small test piece, and the obtained curve is not necessarily applicable to the fatigue life prediction of the whole and complex structure. The finite element method can calculate and analyze the whole structure, and the fatigue life obtained has high accuracy.

[0003] However, the conventional finite element method (CFEM) in China needs to use a continuous function as a shape (interpolation) function. The shape function and material performance inside the element must be continuous. When analyzing a structure with discontinuous surfaces such as cracks or cavities inside, the discontinuous surface needs to coincide with the grid boundary, and the grid node needs to coincide with the tip of the discontinuous surface. High-density grid division is required near the crack tip, so that the stress field near the crack tip can be accurately reflected. Moreover, when simulating crack propagation, the grid needs to be re-divided synchronously with the crack propagation, which is low in efficiency, large in workload, time-consuming, and cannot solve the problem of multiple cracks. The huge amount of data generated during solving often causes computer errors and crashes, and real-time grid division is extremely difficult, which often makes people lose patience.

[0004] In 1999, Professor Belytcshko's research group at Northwestern University in the United States proposed the extended finite element method. This method focuses on solving the discontinuity problem and provides a nearly perfect solution to the difficulties encountered by the conventional finite element method in solving crack problems. However, in 2019, the article "Extended Finite Element Method for Simulating Three-Dimensional Crack Problems" pointed out that the extended finite element method is the most effective numerical method for solving discontinuous mechanics problems so far. However, when simulating crack propagation, the extended finite element method does not need to divide the grid on the crack surface. The grid division does not need to coincide with the crack surface inside the structure. Only ordinary grid division of the structure is needed. The calculation of the stress field at the crack tip is independent of the calculation of the crack surface expansion, thereby avoiding the difficulty of high-density grid division at the crack tip. However, the problem is that the calculation result at the crack tip is not reliable. SUMMARY

[0005] In order to overcome the technical difficulty of the finite element analysis method and the problem of being unable to accurately calculate the fatigue crack propagation life, the present application provides a fatigue crack propagation life extension finite element analysis method.

[0006] The technical scheme adopted by the present application to solve its technical problems is:

[0007] A fatigue crack propagation life extension finite element analysis method, comprising the following steps:

[0008] Step 1, establishing a three-dimensional solid model

[0009] A three-dimensional modeling software CATIA is used to establish a three-dimensional structural model according to the actual size of the metal structural part, and a three-dimensional solid model of the metal structural part is obtained.

[0010] Step 2, simplifying the three-dimensional solid model

[0011] When the established three-dimensional solid model of the metal structural part has large stress concentration parts such as fillets, chamfers and small holes, the three-dimensional solid model is simplified, and the fillets, chamfers and small holes in the three-dimensional solid model are deleted to obtain a simplified three-dimensional solid model.

[0012] When the established three-dimensional solid model of the metal structural part does not have large stress concentration parts such as fillets, chamfers and small holes, the three-dimensional solid model of the metal structural part is the simplified three-dimensional solid model.

[0013] Step 3, obtaining fatigue crack tip stress distribution

[0014] The simplified three-dimensional solid model obtained in step 2 is imported into ABAQUS finite element analysis software, and the actual fatigue load spectrum of the metal structural part is applied on the simplified three-dimensional solid model through the LOAD module of ABAQUS software, and the stress distribution of the fatigue crack tip is obtained through the ABAQUS finite element analysis software.

[0015] Step 4, obtaining fatigue crack propagation life

[0016] The fatigue crack tip stress distribution in step 3 is brought into the ABAQUS finite element software, and the fatigue crack propagation life is calculated based on the extended finite element method combined with the virtual crack closure technique, and the fatigue crack propagation life under different cycle conditions is obtained, that is, the fatigue crack propagation life.

[0017] The fatigue crack propagation life extension finite element analysis method described above, the step 4 of obtaining fatigue crack propagation life, further comprises:

[0018] The process of calculating the fatigue crack propagation life based on the extended finite element method of the virtual crack closure technique is:

[0019] First, measure the length of the fatigue crack of the metal structural part

[0020] The length of the fatigue crack is measured by using a crack detector, the crack detector is aligned with the tip of the fatigue crack, and the length of the fatigue crack is measured, that is, the length a of the fatigue crack of the metal structure.

[0021] In the second step, the critical equivalent strain energy release rate of the tip of the fatigue crack of the metal structure is calculated

[0022] According to the mechanical characteristics, cracks are divided into three types, namely Ι type, ΙΙ type and ΙΙΙ type, Ι type is opening type, ΙΙ type is sliding type and ΙΙΙ type is tearing type.

[0023] The crack propagation criterion is:

[0024] When the stress intensity factor K at the crack tip is greater than the critical stress intensity factor K c , the crack is unstable, that is, the crack propagates;

[0025] When the stress intensity factor K at the crack tip is less than or equal to the critical stress intensity factor K c , the crack does not propagate.

[0026] According to the principle of energy conservation of crack propagation process and closing process, the energy release rate G Ι of Ι type crack propagation is calculated as follows:

[0027]

[0028] In formula (1), K Ι is the Ι type stress intensity factor, and E is the elastic model of the material.

[0029] The value of the Ι type stress intensity factor K Ι is calculated by the following formula.

[0030]

[0031] In formula (2), α is the geometric shape factor of Ι type crack, σ is the normal stress, and a is the crack length.

[0032] According to the principle of energy conservation of crack propagation process and closing process, the energy release rate G II of ΙΙ type crack propagation is calculated as follows:

[0033]

[0034] In formula (3), K ΙΙ is the ΙΙ type stress intensity factor, and υ is the Poisson's ratio of the material.

[0035] The value of the ΙΙ type stress intensity factor K ΙΙ is calculated by the following formula.

[0036]

[0037] In formula (4), β is a geometry factor of mode II crack, and τ is an in-plane shear stress.

[0038] According to the principle of energy conservation of fatigue crack propagation process and closure process, the energy release rate G III of mode III crack propagation is calculated as follows:

[0039]

[0040] In formula (5), K ΙΙΙ is a mode III stress intensity factor.

[0041] The value of mode III stress intensity factor K ΙΙΙ is calculated as follows.

[0042]

[0043] In formula (6), γ is a geometry factor of mode III crack, and τ l is an out-of-plane shear stress.

[0044] Using Reeder criterion, the calculation formula of critical equivalent strain energy release rate G equiv of fatigue crack tip of metal structure is as follows:

[0045]

[0046] In formula (7), G Ι , G ΙΙ and G ΙΙΙ are strain energy release rates corresponding to mode I crack, mode II crack and mode III crack, respectively, G ΙC , G ΙΙC and G ΙΙΙC are critical strain energy release rates corresponding to mode I crack, mode II crack and mode III crack, respectively; η is a damage factor, η = 1.5.

[0047] The critical equivalent strain energy release rate G equiv of fatigue crack tip of metal structure is obtained.

[0048] Thirdly, the fatigue crack propagation life is calculated

[0049] The crack length a and the critical equivalent strain energy release rate G equiv of fatigue crack tip of metal structure are brought into ABAQUS finite element software, the fatigue crack propagation stress distribution of fatigue crack tip of metal structure obtained in step 3 is combined, ABAQUS finite element software is run, and the fatigue crack propagation life of metal structure is obtained, that is, the fatigue crack propagation life.

[0050] The beneficial effects of the present application are:

[0051] Although the Virtual Crack Closure Technique (VCCT) method is relatively simple and accurate, it needs to design defects and expansion path in advance when simulating crack expansion, and crack expansion simulation can only follow the known crack surface, and cannot simulate the initial crack without crack. A fatigue crack propagation life extension finite element analysis method applies VCCT to the Extended Finite Element Method (XFEM), thereby achieving the purpose of simulating crack propagation without pre-designing a specified crack propagation path, thereby generating a fine mesh at the crack tip, saving the time required for modeling, greatly reducing the workload, and improving the accuracy of crack propagation calculation.

[0052] A fatigue crack propagation life extension finite element analysis method has guiding significance in the design of machine wheels. Firstly, it can perform fatigue life analysis based on initial defect structure through finite element at the initial stage of product design, learn about the weak areas of the product structure, and improve the structure and take corresponding measures before testing, thereby improving the development cycle. Secondly, it can solve the fracture failure analysis and positioning caused by fatigue cracks in the field, and increase the reliability and safety of the product. Thirdly, it proposes the fatigue life analysis technology based on damage tolerance which is urgently needed in current structure design. BRIEF DESCRIPTION OF DRAWINGS

[0053] The present application will be further described below in conjunction with the drawings and examples.

[0054] Figure 1 is a schematic diagram of an I-type crack;

[0055] Figure 2 is a schematic diagram of an II-type crack;

[0056] Figure 3 is a schematic diagram of an III-type crack. DETAILED DESCRIPTION

[0057] Example 1

[0058] A fatigue crack propagation life extension finite element analysis method comprises the following steps:

[0059] Step 1, establishing a three-dimensional solid model

[0060] A three-dimensional modeling software CATIA is used to establish a three-dimensional structure model according to the physical size of the metal structural part, and a three-dimensional solid model of the metal structural part is obtained.

[0061] Step 2, simplifying the three-dimensional solid model

[0062] When the three-dimensional solid model of the established metal structure has large stress concentration parts such as fillets, chamfers, and small holes, the three-dimensional solid model is simplified. The specific simplification operation is: deleting the fillets, chamfers, and small holes in the three-dimensional solid model.

[0063] When the three-dimensional solid model is included in the simulation software calculation process, and there are large stress concentration parts such as fillets, chamfers, and small holes, it will result in large amount of calculation, and even cannot realize the extended finite element analysis calculation. Therefore, the three-dimensional solid model needs to be simplified to achieve the goal of reducing the amount of calculation while ensuring the accuracy of the calculation results.

[0064] When the three-dimensional solid model of the established metal structure does not have large stress concentration parts such as fillets, chamfers, and small holes, the three-dimensional solid model of the metal structure is the simplified three-dimensional solid model.

[0065] Step 3, calculating the fatigue crack tip stress distribution

[0066] The simplified three-dimensional solid model obtained in step 2 is imported into the ABAQUS finite element analysis software. According to the real fatigue load spectrum of the metal structure, the LOAD module of the ABAQUS software is used to apply the load on the simplified three-dimensional solid model. The stress distribution at the fatigue crack tip is obtained by using the ABAQUS finite element analysis software.

[0067] Step 4, calculating the fatigue crack propagation life

[0068] The results obtained in step 3 are imported into the ABAQUS finite element software. Based on the extended finite element method (XFEM) combined with the virtual crack closure technique (VCCT), the fatigue crack propagation life is calculated, and the fatigue crack propagation life under different cycle conditions is obtained.

[0069] The process of calculating the fatigue crack propagation life based on the extended finite element method of the virtual crack closure technique is as follows:

[0070] First step, measuring the length of the fatigue crack of the metal structure

[0071] The length of the fatigue crack is measured using a crack detector. The starting position of the crack detector is aligned with the fatigue crack tip, and the length of the fatigue crack a is measured.

[0072] The length a of the fatigue crack of the metal structure is obtained.

[0073] Second step, calculating the critical equivalent strain energy release rate at the fatigue crack tip of the metal structure

[0074] According to mechanical characteristics, cracks are divided into three types, namely, type I, type II and type III. Type I is opening type, type II is sliding type and type III is tearing type. The structures of the three types of cracks are shown in Figure 1 、 Figure 2 、 Figure 3 .

[0075] Fatigue crack is a typical crack.

[0076] Under the action of stress, fatigue crack is always in the stage of fatigue crack propagation before fracture.

[0077] Stress intensity factor is used to represent the stress field near the crack tip. Therefore, the criterion for unstable crack propagation, i.e. crack propagation criterion, can be established by the relationship between stress intensity factor and the critical stress intensity factor K c of the material.

[0078] The crack propagation criterion is as follows:

[0079] When the stress intensity factor K of the crack tip is greater than the critical stress intensity factor K c , the crack is unstable, i.e. the crack propagates.

[0080] When the stress intensity factor K of the crack tip is less than or equal to the critical stress intensity factor K c , the crack does not propagate.

[0081] According to the principle of energy conservation in the process of crack propagation and closure, the energy release rate G Ι of type I crack propagation is calculated as follows:

[0082]

[0083] In formula (1), K Ι is type I stress intensity factor and E is the elastic model of the material.

[0084] The value of type I stress intensity factor K Ι is calculated as follows.

[0085]

[0086] In formula (2), α is the geometric shape factor of type I crack, σ is normal stress and a is crack length.

[0087] According to the principle of energy conservation in the process of fatigue crack propagation and closure, the energy release rate G II of type II crack propagation is calculated as follows:

[0088]

[0089] In formula (3), KΙΙ K is the mode II stress intensity factor, and υ is the Poisson's ratio of the material.

[0090] K is the mode II stress intensity factor ΙΙ The value of K is calculated by the following equation.

[0091]

[0092] In equation (4), β is the geometry factor of mode II crack, and τ is the in-plane shear stress.

[0093] According to the principle of energy conservation of fatigue crack propagation process and closure process, the energy release rate G III of mode III crack propagation is calculated as follows:

[0094]

[0095] In equation (5), K ΙΙΙ is the mode III stress intensity factor.

[0096] The value of K ΙΙΙ is calculated by the following equation.

[0097]

[0098] In equation (6), γ is the geometry factor of mode III crack, and τ l is the out-of-plane shear stress.

[0099] Using Reeder criterion, the calculation formula of critical equivalent strain energy release rate G equiv of fatigue crack tip of metal structure is as follows:

[0100]

[0101] In equation (7), G Ι , G ΙΙ and G ΙΙΙ are the strain energy release rates corresponding to mode I crack, mode II crack and mode III crack, G ΙC , G ΙΙC and G ΙΙΙC are the critical strain energy release rates corresponding to mode I crack, mode II crack and mode III crack, and η is the damage factor, η = 1.5.

[0102] The critical equivalent strain energy release rate G equiv of fatigue crack tip of metal structure is obtained.

[0103] Thirdly, the fatigue crack propagation life is calculated

[0104] The crack length a of the fatigue crack tip of the metal structure and the critical equivalent strain energy release rate G equiv The fatigue crack propagation stress distribution of the fatigue crack tip of the metal structure obtained in step 3 is brought into the ABAQUS finite element software, the ABAQUS finite element software is run, and the fatigue crack propagation life of the metal structure, i.e., the fatigue crack propagation life, is obtained.

[0105] The fatigue crack propagation life test verification of the aviation metal structure is as follows:

[0106] Taking an aviation structure as an example, the fatigue crack propagation life test is carried out by using a fatigue test bench, the fatigue crack propagation situation is observed by using a high-power magnifying glass, and the fatigue crack propagation life is obtained. The fatigue crack propagation life of the aviation connecting structure is calculated by using the extension finite element method. The test result of the fatigue crack propagation life is compared with the calculation result of the extension finite element method, and the result shows that the error of the fatigue crack propagation life calculated by using the extension finite element method is 8.2%, and it is proved that the extension finite element calculation method is suitable for the aviation connecting structure and is accurate and reliable.

Claims

1. A fatigue crack growth life extension finite element analysis method, characterized by, It comprises the following steps: Step 1, establishing a three-dimensional entity model: A three-dimensional entity model of the metal structure is established by using CATIA three-dimensional modeling software according to the actual size of the metal structure, and the three-dimensional entity model of the metal structure is obtained. Step 2, simplifying the three-dimensional entity model: When the three-dimensional entity model of the metal structure established has large stress concentration parts such as fillets, chamfers and small holes, the three-dimensional entity model is simplified, and the fillets, chamfers and small holes in the three-dimensional entity model are deleted to obtain a simplified three-dimensional entity model. When the three-dimensional entity model of the metal structure established does not have large stress concentration parts such as fillets, chamfers and small holes, the three-dimensional entity model of the metal structure is the simplified three-dimensional entity model. Step 3, calculating the fatigue crack tip stress distribution: The simplified three-dimensional entity model obtained in step 2 is imported into ABAQUS finite element analysis software, and the actual fatigue load spectrum of the metal structure is applied on the simplified three-dimensional entity model by ABAQUS software LOAD module, and the stress distribution of the fatigue crack tip is obtained by ABAQUS finite element analysis software. Step 4, calculating the fatigue crack propagation life: The fatigue crack tip stress distribution in step 3 is brought into ABAQUS finite element software, and the fatigue crack propagation life is calculated based on the extended finite element method combined with virtual crack closure technique, and the fatigue crack propagation life under different cycle numbers is obtained, that is, the fatigue crack propagation life. The step 4 further comprises: The process of calculating the fatigue crack propagation life based on the extended finite element method combined with virtual crack closure technique is: First, measure the length of the fatigue crack of the metal structure: The length of the fatigue crack is measured by using a crack detector, the starting position of the crack detector is aligned with the fatigue crack tip, and the length of the fatigue crack is measured, that is, the length a of the fatigue crack of the metal structure. Second, calculate the critical equivalent strain energy release rate of the fatigue crack tip of the metal structure: According to the mechanical characteristics, cracks are divided into three types, namely type I, type II and type III, type I is opening type, type II is sliding type, and type III is tearing type. The crack propagation criterion is: When the stress intensity factor at the crack tip K is greater than the critical stress intensity factor Kc , the crack is unstable, i.e., the crack propagates; when the stress intensity factor at the crack tip K is less than or equal to the critical stress intensity factor Kc , the crack does not propagate; According to the principle of energy conservation of crack propagation process and closure process, the energy release rate of Ι type crack propagation is calculated as follows: G Ι The calculation is as follows: （1） In formula (1), K Ⅰ is the stress intensity factor of type I, E is the elastic model of the material; Mode I stress intensity factor K Ι The value of Kic is calculated from the following equation; （2） In formula (2), α is the geometric shape factor of type I crack, σ is the normal stress, and a is the crack length. According to the principle of energy conservation of fatigue crack propagation process and closure process, the energy release rate of type II crack propagation is calculated as follows: G Ⅱ The calculation is as follows: （3） In formula (3), K Ⅱ K is the stress intensity factor, and υ is the Poisson's ratio of the material. Mode ii stress intensity factor K Ⅱ The value of Kii is calculated from the following equation; （4） In formula (4), β is the geometric shape factor of type II crack, and τ is the in-plane shear stress. According to the principle of energy conservation of fatigue crack propagation process and closure process, the energy release rate of type Ⅲ crack propagation is calculated as follows: G Ⅲ The calculation is as follows: （5） In formula (5), K Ⅲ is the stress intensity factor of mode III. Mode Ⅲ stress intensity factor K Ⅲ The value of K is calculated from the following equation; （6） In formula (6), γ is a geometry factor of the type III crack, τ l is the out-of-plane shear stress; The critical equivalent strain energy release rate of the fatigue crack tip of the metal structure is calculated by using the Reeder criterion G equiv The calculation formula is as follows: （7） In formula (7), G Ⅰ , G Ⅱ and G Ⅲ are the strain energy release rates corresponding to mode I, mode II and mode III cracks, respectively, G ΙC , G ⅡC and G ⅢC are the critical strain energy release rates corresponding to mode I, mode II and mode III cracks, respectively; η is the damage factor, η = 1.5; Obtaining critical equivalent strain energy release rate at the tip of a fatigue crack in a metal structural component G equiv ; Third, calculate the fatigue crack propagation life: The crack length a of the fatigue crack tip of the metal structure and the critical equivalent strain energy release rate G equiv The fatigue crack propagation stress distribution of the fatigue crack tip of the metal structure obtained in step 3 is brought into the ABAQUS finite element software, the ABAQUS finite element software is run, and the fatigue crack propagation life of the metal structure is obtained, that is, the fatigue crack propagation life.

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