Multi-crack propagation life analysis method suitable for multi-axial load condition
By calculating the stress intensity factor and controlling the number of crack propagation steps, combined with the Paris formula and the maximum circumferential tensile stress criterion, the crack propagation process is decomposed into multiple sub-steps, which solves the simulation problem of multiple crack propagation under multi-axial loads and achieves efficient and high-precision crack propagation simulation.
Patent Information
- Application Number
- CN202510710658.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-29
- Publication Date
- 2025-09-12
AI Technical Summary
Existing multi-axial constant amplitude fatigue life prediction methods mainly focus on crack propagation of simple geometric shapes and single cracks, and lack research on multiple crack propagation, especially the simulation of multiple crack interactions under complex loading conditions. Moreover, existing models rely on high-performance computing resources, making it difficult to simulate multiple crack propagation paths and life efficiently and accurately.
The stress intensity factor calculation and crack propagation step control methods were adopted. Finite element modeling was performed using ABAQUS and FRANC3D software. Combined with the Paris formula and the maximum circumferential tensile stress criterion, the crack propagation process was decomposed into multiple sub-steps. The crack model and mesh were gradually updated to achieve the synchronous propagation simulation of multiple cracks.
It accurately simulates the multi-crack propagation paths and lifespan under complex loads, improves simulation accuracy and efficiency, effectively solves the interaction between multiple cracks, reduces computing resource requirements, and achieves high-precision crack propagation simulation.
Smart Images
Figure CN120633296A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of fracture mechanics and finite element analysis, and particularly relates to a multi-crack extension life analysis method suitable for multi-axial load conditions. Background Art
[0002] Most metal structures in engineering practice are subjected to multiaxial loading. At present, some progress has been made in the research of methods for predicting multiaxial constant amplitude fatigue life. However, there are relatively few studies on multiple crack propagation under multiaxial constant amplitude loading.
[0003] Existing research has primarily focused on crack growth in simple geometries and single cracks, particularly the analysis of crack behavior under conventional loads such as tension and bending. Research on multi-crack growth still focuses on the interaction and fusion of cracks within a plane, and most models assume independent growth between cracks or only consider simple coplanar crack propagation. Furthermore, multi-crack simulations typically require processing extremely complex numerical models and rely on high-performance computing resources to meet the demands of high-precision calculations. Therefore, a new multi-crack growth life analysis method suitable for multi-axial loading conditions is needed to address existing issues. Summary of the Invention
[0004] The purpose of the present invention is to provide a multi-crack propagation life analysis method suitable for multi-axial loading conditions, so as to solve the problem that it is impossible to accurately simulate the multi-crack propagation path and life under complex loads.
[0005] To achieve the above object, the present invention provides the following technical solution: a method for analyzing the multi-crack growth life under multiaxial loading conditions, comprising the following steps:
[0006] Step 1: Model the initial structure and insert two finite element models of length a into the initial structure. 01 and a 02 Initial crack model;
[0007] Step 2: Calculate the fracture parameters and crack extension of the finite element model containing cracks;
[0008] Step 21: Calculate the stress intensity factor amplitudes of the crack tips of the two cracks, and classify the two cracks into a primary crack and a secondary crack according to the magnitudes of the stress intensity factors of the two cracks;
[0009] Step 22: Calculate the crack propagation direction based on the stress intensity factor amplitude of the main crack;
[0010] Step 23: Calculate the main crack growth to 1.01a 01 , 1.02a 01 , 1.03a 01to 1.1a 01 The stress intensity factor amplitude at The number of cycles required for the main crack to extend to 1 / 10 of its initial length was obtained by fitting the relationship between stress intensity factor and crack length.
[0011] Step 24: Calculate the distance that the secondary crack extends after the number of cycles in step 23 by fitting the relationship between the secondary crack and the crack length;
[0012] Step 3: Update the finite element model containing cracks. Update the crack model based on the propagation directions and propagation distances of the two cracks obtained in step 24 and reintroduce the crack model into the structure.
[0013] Step 4: Repeat the calculation until the crack propagation termination condition is reached. Repeat the above steps, and continuously update the stress intensity factor amplitude and crack front by gradually calculating and adjusting the crack propagation length until the stress intensity factor amplitude at a crack tip reaches the critical fracture toughness value of the material or the crack propagates to the engineering allowable crack size.
[0014] Preferably, in step 1, an initial three-dimensional model without cracks is established, and the mesh module of ABAQUS software is used to mesh the model to obtain a finite element model of the initial model;
[0015] Using the part module in ABAQUS software, a shell model with two initial cracks was established using finite element software;
[0016] The mesh module is used to mesh the model to obtain the finite element model of the initial crack;
[0017] The initial crack was inserted into the initial finite element model using FRANC3D software, and the mesh near the crack was refined.
[0018] Preferably, in step 2, the Paris formula is used to calculate the extension distance of the leading edge nodes of the two cracks. The expression of the Paris formula is:
[0019]
[0020] Where C and m are material constants determined by experiments.
[0021] Preferably, in step 2, the maximum circumferential tensile stress criterion is used to calculate the extension direction of the leading edge nodes of the two cracks. For a plane problem, the expression is:
[0022] K I sinθ+K II (3cosθ-1)=0
[0023] Where K I and KII are the stress intensity factors of mode I and mode II, and θ is the crack extension angle
[0024] After solving, the expression of the crack front extension angle θ can be obtained:
[0025]
[0026] Preferably, in step 2, it is assumed that the length of each main crack extension is the initial crack length a 01 1 / 10 of
[0027] In order to calculate the main crack growth to a length of 1.1a 01 The required number of cycles is established by the crack modeling method with 10 cracks of length 1.01a 01 , 1.02a 01 , 1.03a 01 to 1.1a 01 The crack finite element model of the initial model is inserted into the finite element model of the initial model to obtain 10 cracked finite element models. The stress intensity factor amplitude of the main crack front in the 10 cracked finite element models is calculated.
[0028] Establish the relationship between the amplitude of 10 stress intensity factors and their crack extension length, and fit the amplitude of 10 stress intensity factors by exponential function. The relationship between the crack length a;
[0029] Preferably, in step 2, the amplitude of the stress intensity factor of the secondary crack is fitted and crack extension length a 02 Using this relationship, reversely apply the Paris formula, and under the condition of knowing the initial crack length and the number of crack growth cycles, calculate the secondary crack after the main crack grows 0.1a. 01 The crack length and direction in the case of .
[0030] Preferably, in step 3, the position coordinates of each node of the crack front calculated in the previous crack extension step are read, and a B-spline curve is used for fitting and connection, thereby constructing the crack front of the next extension step;
[0031] Read the position coordinates of all nodes of all crack fronts starting from the first step, connect them with B-spline curves, and thus establish the crack fronts of all crack propagation steps starting from the first step;
[0032] Connect all the current crack front curves according to the node numbers to establish the crack model of the i-th crack extension step.
[0033] Preferably, in step 4, the number of cycles obtained by accumulating the life of each iteration is the final life of crack growth.
[0034] The technical effects and advantages of the present invention are as follows: the multi-crack propagation life analysis method applicable to multi-axial load conditions accurately simulates the multi-crack propagation path and life under complex loads through crack stress intensity factor calculation, expansion step control and synchronous expansion algorithm, and constructs a crack evolution model in combination with a grid update mechanism to achieve efficient and high-precision crack propagation simulation; the crack propagation process is divided into multiple sub-steps for solution, and the crack propagation is controlled by the relationship between the stress intensity factor and the crack length; it can not only solve the interaction between multiple cracks, but also effectively simulate the crack propagation process in complex structures on the basis of reducing simulation resources; step-by-step crack propagation and synchronous calculation, by decomposing the crack propagation process into Multiple sub-expansion steps can accurately simulate the gradual changes in crack propagation; based on the division and update of stress intensity factors: by calculating the stress intensity factor of each expansion step and dividing the cracks into primary cracks and secondary cracks according to the amplitude of the stress intensity factor, the crack propagation direction and rate can be accurately determined at each step, avoiding unreasonable predictions of crack propagation; reverse application of the Paris formula: by reversely calculating the propagation distance of the secondary crack with the known number of propagation cycles of the primary crack, the consistency and accuracy of the crack propagation model are guaranteed, ensuring the synchronous propagation of the two cracks; it can resolve the interaction between multiple cracks and effectively simulate the crack propagation process in complex structures while reducing simulation resources. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 Schematic diagram of the method flow in an embodiment of the present invention;
[0036] Figure 2 A flow chart for modeling a finite element model containing cracks according to the present invention;
[0037] Figure 3 This is a schematic diagram of the relationship between stress intensity factor and crack length according to the present invention;
[0038] Figure 4 Update the flow chart for the crack model of the present invention. DETAILED DESCRIPTION
[0039] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.
[0040] The present invention provides Figure 1 A multi-crack growth life analysis method suitable for multi-axial loading conditions is shown in , which specifically includes the following steps:
[0041] Step 1: Modeling the finite element model with cracks, including initial model modeling and crack modeling;
[0042] Establish an initial three-dimensional model where cracks need to be inserted, and use the mesh module of ABAQUS software to pre-process the model to obtain a finite element model of the initial model;
[0043] Two two-dimensional shell models were established using the part module in ABAQUS software, and the mesh module was used to pre-process the models to obtain the finite element model of the initial crack.
[0044] The initial crack is inserted into the initial finite element model by FRANC3D software, and the mesh near the crack is refined. The process is as follows: Figure 2 As shown;
[0045] Step 2: Calculation of multiple crack fracture parameters and crack extension of the finite element model containing cracks;
[0046] The stress intensity factor amplitudes at the crack tips of the two cracks were calculated using the M-integral in FRANC3D software;
[0047] The M-integral is used to analyze the stress intensity factor amplitude at the crack front, where the M-integral can be expressed as:
[0048]
[0049] Where, σ ij is the stress tensor component, u is the displacement vector, W is the interaction strain energy density, δ 1j is the Kronecker delta symbol, is the gradient of the weight function, ds is the arc length element;
[0050] According to the calculated stress intensity factor amplitudes of the two cracks, the one with the larger stress intensity factor amplitude is considered as the main crack, and the one with the smaller stress intensity factor amplitude is considered as the secondary crack for subsequent analysis;
[0051] The amplitude of the stress intensity factor of the main crack is calculated by calculating the crack propagation direction;
[0052] The maximum circumferential tensile stress criterion is used to analyze the propagation direction of the nodes at the crack front. For plane problems, the maximum circumferential tensile stress criterion can be expressed as:
[0053] K I sinθ+K II(3cosθ-1)=0
[0054] Where K I and K II are the stress intensity factors of mode I and mode II, and θ is the crack extension angle;
[0055] After solving, the expression of the crack front extension angle θ can be obtained:
[0056]
[0057] Fitting the relationship between stress intensity factor and crack extension length;
[0058] Assume that the structure contains two 01 and a 02 The initial crack will be a by default. 01 The main crack is a 02 It is a minor crack.
[0059] By using the crack modeling method, 10 cracks with a length of 1.01a were established. 01 , 1.02a 01 , 1.03a 01 to 1.1a 01 The crack finite element model of the initial model is inserted into the finite element model of the initial model to obtain 10 cracked finite element models. The stress intensity factor amplitude of the main crack front in the 10 cracked finite element models is calculated.
[0060] Establish the relationship between the amplitude of 10 stress intensity factors and their crack extension length, and fit the amplitude of 10 stress intensity factors by exponential function. The relationship between the crack length a is as follows: Figure 3 shown; by with a 01 Substituting the relationship into the crack growth life model, we can find the main crack from a 01 Extension to 1.1a 01 The number of cycles experienced.
[0061] Use the Paris formula to analyze crack growth life;
[0062] The Paris formula is used to analyze the crack growth life. The expression of the Paris formula is:
[0063]
[0064] Where C and m are material constants determined by experiments.
[0065] When the main crack is extended to 1.1a01 After the number of cycles, the secondary crack stress intensity factor is fitted using the same method The relationship between the crack extension distance a and the initial crack length is calculated by using the fitting relationship and applying the Paris formula in reverse. That is, under the condition of knowing the initial crack length and the number of crack extension cycles, the secondary crack is calculated when the primary crack extends to 1.1a. 01 Crack extension distance after the number of cycles.
[0066] Thus, the expansion direction and expansion distance of the main crack and the secondary crack in a single expansion are obtained.
[0067] Step 3: Update the finite element model containing cracks. Update the crack model based on the propagation direction and propagation distance of the two cracks obtained in the previous step and reinsert it into the finite element model of the initial structure.
[0068] like Figure 4 As shown in the figure, for non-planar propagation cracks, establishing the crack model of the i-th crack propagation step and updating the crack propagation model require: first, reading the position coordinates of each node of the crack front calculated in the previous crack propagation step, and using B-spline curves to fit and connect them, so as to construct the crack front of the next propagation step; then, reading the position coordinates of all nodes of all crack fronts starting from the first step, and also using B-spline curves to connect them, thereby establishing the crack fronts of all crack propagation steps starting from the first step; then, connecting all the current crack front curves according to the node numbers, thereby establishing the crack model of the i-th crack propagation step; finally, using the same method as step 1 to insert the crack model into the initial structural finite element model and re-mesh it to obtain the final finite element model.
[0069] Step 4: Repeat the calculation until the crack propagation termination condition is reached. Repeat the above steps, and continuously update the stress intensity factor and crack front by gradually calculating and adjusting the crack propagation length until the stress intensity factor at a crack tip reaches the critical fracture toughness value of the material or the crack propagates to the engineering allowable crack size.
[0070] By accumulating the crack propagation distance, direction, and crack propagation life obtained in each of the above steps, we can finally obtain the crack propagation path and crack propagation life of the structure with multiple cracks under multi-axial loading conditions.
[0071] In summary, the present invention proposes a step-by-step calculation method. By constructing a three-dimensional structural model containing multiple cracks, the stress intensity factor at the crack tip is accurately calculated based on the M-integral method. A crack growth rate model is established in combination with the Paris formula. The maximum tensile stress criterion is used to determine the crack growth direction, thereby achieving synchronous growth control of multiple cracks. The crack front reconstruction and mesh re-division method is used to iteratively update the growth model, ultimately achieving structural damage tolerance assessment and life prediction. The present invention can effectively simulate the interaction of multiple cracks in complex structures, improve the accuracy and efficiency of crack growth prediction, and has broad engineering application prospects.
[0072] The crack propagation process is divided into multiple sub-steps for solution, and the crack propagation is controlled by the relationship between the stress intensity factor and the crack length. This method can not only solve the interaction between multiple cracks, but also effectively simulate the crack propagation process in complex structures on the basis of reducing simulation resources. Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.
Claims
1. A multi-crack growth life analysis method suitable for multi-axial loading conditions, characterized by: include: Constructing a cracked finite element model with at least two initial cracks; Calculate the stress intensity factor amplitudes at the crack tips of the two initial cracks to obtain the fracture parameters and crack extension of the two cracks; Updating the fracture parameters and crack extension of the two cracks into the finite element model of the crack to obtain an updated finite element model of the crack, and inserting the updated finite element model of the crack into the finite element model containing the crack; The fracture parameters and crack extension of the two cracks are iteratively calculated and updated to the finite element model containing the crack until the stress intensity factor amplitude at the crack tip meets the critical fracture toughness value or the crack extends to the allowable crack size.
2. The multi-crack growth life analysis method applicable to multiaxial loading conditions according to claim 1, characterized in that: The method of constructing a cracked finite element model having at least two initial cracks comprises: Establishing a three-dimensional model of the initial structure, and obtaining a finite element model of the initial model by meshing the three-dimensional model of the initial structure; Establishing two two-dimensional shell models, and obtaining a finite element model of the initial crack after meshing the two two-dimensional shell models; The finite element model of the initial crack is inserted into the finite element model of the initial model.
3. The multi-crack growth life analysis method applicable to multi-axial loading conditions according to claim 1, characterized in that: The calculation of the stress intensity factor amplitudes at the crack tips of the two initial cracks includes: Calculate the stress intensity factors at the two crack tips and determine whether they are major cracks or minor cracks; Calculate the propagation direction of major and minor cracks; Fitting the relationship between the stress intensity factor of the main crack and the crack length; Calculate the number of cycles required for the main crack to grow to 1 / 10 of its initial length; Fitting the relationship between the stress intensity factor of the secondary crack and the crack length; Calculate the propagation distance of the secondary crack in the number of cycles required to grow to 1 / 10 of the initial length.
4. The method for analyzing multi-crack growth life under multiaxial loading conditions according to claim 3, characterized in that: The calculation of the stress intensity factors of the two crack tips and the determination of the major crack and the minor crack include: The M-integral is used to analyze the stress intensity factor amplitude of the crack front. According to the magnitude of the stress intensity factor amplitudes of the two cracks, the one with the larger stress intensity factor amplitude is determined as the primary crack, and the one with the smaller stress intensity factor amplitude is determined as the secondary crack.
5. The method for analyzing multi-crack growth life under multiaxial loading conditions according to claim 4, characterized in that: The calculation of the propagation directions of the main crack and the secondary crack includes: using a maximum circumferential tensile stress criterion to analyze the propagation direction of the node at the crack front.
6. The method for analyzing multi-crack growth life under multiaxial loading conditions according to claim 5, characterized in that: The relationship between the stress intensity factor of the main crack and the crack length is as follows: The length of each main crack extension is set as the initial crack length a 01 1 / 10 of By establishing 10 lengths of 1.01a 01 , 1.02a 01 , 1.03a 01 to 1.1a 01 The crack finite element model of the initial model is inserted into the finite element model of the initial model to obtain 10 cracked finite element models. The stress intensity factor amplitude of the main crack front in the 10 cracked finite element models is calculated. Establish the relationship between the amplitude of 10 stress intensity factors and their crack extension length; Fitting 10 stress intensity factor amplitudes by exponential function The relationship between the crack length a; The propagation direction and distance of the main propagation cracks are obtained.
7. The method for analyzing multi-crack growth life under multiaxial loading conditions according to claim 6, characterized in that: The calculation of the number of cycles required for the main crack to grow to 1 / 10 of the initial length includes: Substituting the relationship between the crack length a and the crack growth life model, we can get the main crack from a 01 Extension to 1.1a 01 The number of cycles experienced.
8. The method for analyzing multi-crack growth life under multiaxial loading conditions according to claim 7, characterized in that: The relationship between the stress intensity factor of the secondary crack and the crack length is as follows: Use the method in claim 6 to fit the stress intensity factor of the secondary crack The relationship between the crack extension distance a.
9. The method for analyzing multi-crack growth life under multiaxial loading conditions according to claim 8, characterized in that: The calculation of the extension distance of the number of cycles required for the secondary crack to extend 1 / 10 of the initial length includes: The relationship between the crack extension distance a and the distance of the crack is obtained by applying the Paris formula in reverse, and the secondary crack is obtained when the main crack extends to 1.1a 01 Crack extension distance after the number of cycles.
10. The multi-crack growth life analysis method applicable to multi-axial loading conditions according to any one of claims 1 to 9, characterized in that: Inserting the updated cracked finite element model into the cracked finite element model comprises: Establishing the crack finite element model of the i-th crack growth step and updating the crack growth model requires: Read the position coordinates of each node of the crack front calculated in the previous crack extension step, use B-spline curve fitting to connect them, and construct the crack front of the next extension step; Read the position coordinates of all nodes of all crack fronts starting from the first step, connect them using B-spline curves, and establish the crack fronts of all crack extension steps starting from the first step; Connect all the current crack front curves according to the node numbers to establish the crack finite element model of the i-th crack extension step; The crack finite element model is inserted into the initial structural finite element model and re-meshed to obtain the final finite element model.