A multi-crack propagation life analysis method suitable for multi-axial load conditions

Abstract

The application discloses a multi-crack propagation life analysis method suitable for a multi-axial load condition, and belongs to the technical field of fracture mechanics and finite element analysis, and comprises the following steps: constructing a crack-containing finite element model of at least two initial cracks; calculating stress intensity factor amplitudes of crack tips of the two initial cracks to obtain crack fracture parameters and crack propagation amounts of the two cracks; updating the crack fracture parameters and the crack propagation amounts of the two cracks to the crack-containing finite element model to obtain an updated crack-containing finite element model; and iteratively calculating the crack fracture parameters and the crack propagation amounts of the two cracks and updating the crack fracture parameters and the crack propagation amounts to the crack-containing finite element model. The multi-crack propagation life analysis method suitable for the multi-axial load condition accurately simulates multi-crack propagation paths and life under complex loads through crack stress intensity factor calculation, propagation step control and a synchronous propagation algorithm, and realizes efficient and high-precision crack propagation simulation by combining a mesh updating mechanism to construct a crack evolution model.

Description

Technical Field

[0001] This invention belongs to the field of fracture mechanics and finite element analysis technology, specifically relating to a method for analyzing the multi-crack propagation life under multiaxial loading conditions. Background Technology

[0002] In engineering practice, most metal structures are subjected to multiaxial loads. Some progress has been made in the research on methods for predicting the fatigue life of multiaxial constant amplitude fatigue. However, there is relatively little research on the propagation of multiple cracks under multiaxial constant amplitude loads.

[0003] Existing research primarily focuses on crack propagation problems with simple geometries and single cracks, especially crack behavior analysis under conventional loads such as tension and bending. Research on multi-crack propagation remains concentrated on in-plane crack interactions and fusion, with most models assuming independent crack propagation or only considering simple coplanar crack propagation. Furthermore, multi-crack simulations typically require handling extremely complex numerical models and rely on high-performance computing resources to meet high-precision calculation requirements. Therefore, a new method for multi-crack propagation life analysis under multiaxial loading conditions is needed to address these existing problems. Summary of the Invention

[0004] The purpose of this invention is to provide a multicrack propagation life analysis method applicable to multiaxial loading conditions, so as to solve the problem of being unable to accurately simulate the multicrack propagation path and life under complex loads.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for analyzing the multi-crack propagation life under multiaxial loading conditions, comprising the following steps:

[0006] Step 1: Model the initial structure. Insert two elements of length a into the finite element model of the initial structure. 01 and a 02 The initial crack model;

[0007] Step 2: Calculate the fracture parameters and crack propagation for the finite element model containing the crack;

[0008] Step 21: Calculate the stress intensity factor amplitude at the crack tips of the two cracks, and classify the two cracks as primary cracks and secondary cracks according to the magnitude of the stress intensity factor of the two cracks.

[0009] Step 22: Calculate the crack propagation direction using the stress intensity factor amplitude of the main crack;

[0010] Step 23: Calculate the main crack propagation to 1.01a 01 1.02a 01 1.03a 01up to 1.1a 01 Stress intensity factor amplitude at time The number of cycles when the main crack extends to 1 / 10 of its initial length is determined by fitting the relationship between the stress intensity factor and the crack length.

[0011] Step 24: Calculate the distance the secondary crack propagates 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 direction and propagation distance of the two cracks obtained in Step 24 and reintroduce it 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 certain 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 model is meshed using the mesh module of ABAQUS software to obtain the finite element model of the initial model.

[0015] Using the part module in ABAQUS software, two shell models with initial cracks were created using finite element software.

[0016] The initial crack finite element model is obtained by meshing the model using the mesh module.

[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 propagation distance of the leading edge nodes of the two cracks is calculated using the Paris formula. The expression for the Paris formula is:

[0019]

[0020] In the formula, C and m are material constants determined experimentally.

[0021] Preferably, in step 2, the propagation direction of the leading edge nodes of the two cracks is calculated using the maximum circumferential tensile stress criterion. For a plane problem, the expression is:

[0022] K I sinθ+K II (3cosθ-1)=0

[0023] In the formula, K I and KII Here are the type I and type II stress intensity factors, and θ is the crack propagation angle.

[0024] After solving, the expression for the crack lead propagation angle θ can be obtained:

[0025]

[0026] Preferably, in step 2, it is assumed that the length of each propagation of the main crack is the initial crack length a. 01 1 / 10;

[0027] To calculate the main crack propagation to a length of 1.1a. 01 The required number of cycles is determined by establishing 10 loops with a length of 1.01a using the crack modeling method. 01 1.02a 01 1.03a 01 up to 1.1a 01 Ten crack finite element models were interpolated into the initial model to obtain ten crack-containing finite element models. The stress intensity factor amplitude of the main crack front in the ten crack-containing finite element models was calculated.

[0028] Establish a graph showing the relationship between the amplitudes of 10 stress intensity factors and their crack propagation length, and fit the amplitudes of the 10 stress intensity factors using an exponential function. The relationship between the crack length a and the crack length α;

[0029] Preferably, in step 2, the amplitude of the secondary crack stress intensity factor is fitted. With crack propagation length a 02 Using the relationship between the two, and applying the Paris formula in reverse, given the initial crack length and the number of crack propagation cycles, we can calculate the extent to which the secondary crack extends after the primary crack has propagated by 0.1a. 01 The length and direction of the crack under the given conditions.

[0030] Preferably, in step 3, the position coordinates of each node of the crack front calculated in the previous crack propagation step are read and fitted and connected using B-spline curves to construct the crack front of the next propagation step.

[0031] Read the position coordinates of all nodes of all crack fronts starting from the first step, and connect them using B-spline curves to 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 for the i-th crack propagation step.

[0033] Preferably, in step 4, the number of cycles obtained by accumulating the lifetimes of each iteration is the final lifetime of crack propagation.

[0034] The technical effects and advantages of this invention are as follows: This multi-crack propagation life analysis method applicable to multiaxial loading conditions accurately simulates the multi-crack propagation path and life under complex loads through crack stress intensity factor calculation, propagation step control, and synchronous propagation algorithm. It also constructs a crack evolution model using a mesh update mechanism, achieving efficient and high-precision crack propagation simulation. By dividing the crack propagation process into multiple sub-steps for solution and controlling crack propagation through the relationship between stress intensity factor and crack length, it not only solves the interaction between multiple cracks but also effectively simulates the crack propagation process in complex structures while reducing simulation resources. The method involves step-by-step crack propagation and synchronous calculation, decomposing the crack propagation process into... Multiple sub-proliferation steps enable precise simulation of the gradual changes in crack propagation; based on the division and updating of stress intensity factors: by calculating the stress intensity factor of each propagation step and classifying the crack into primary and secondary cracks according to the magnitude of the stress intensity factor, the direction and rate of crack propagation can be accurately determined at each step, avoiding unreasonable predictions of crack propagation; reverse application of the Paris formula: by knowing the propagation cycle number of the primary crack, the propagation distance of the secondary crack is calculated in reverse, thus ensuring the consistency and accuracy of the crack propagation model and ensuring the synchronous propagation of two cracks; it can solve the interaction between multiple cracks, effectively simulating the crack propagation process in complex structures while reducing simulation resources. Attached Figure Description

[0035] Figure 1 This is a schematic diagram of the method flow in an embodiment of the present invention;

[0036] Figure 2 The flowchart for modeling the finite element model containing cracks in this invention is shown below;

[0037] Figure 3 This is a schematic diagram of the fitting of the relationship between stress intensity factor and crack length in this invention;

[0038] Figure 4 This is a flowchart of the crack model update process of the present invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] This invention provides, for example Figure 1 The multicrack propagation life analysis method shown herein, applicable to multiaxial loading conditions, specifically includes the following steps:

[0041] Step 1: Modeling the finite element model containing cracks, including initial model modeling and crack modeling;

[0042] An initial three-dimensional model for which cracks need to be inserted is established. The model is then preprocessed using the mesh module of ABAQUS software to obtain the finite element model of the initial model.

[0043] Using the part module in ABAQUS software, two two-dimensional shell models were built, and the mesh module was used to preprocess the models to obtain the finite element model of the initial crack.

[0044] The initial crack was inserted into the initial finite element model using FRANC3D software, and the mesh near the crack was refined. The process is as follows: Figure 2 As shown;

[0045] Step 2: Calculation of multi-crack fracture parameters and crack propagation in a finite element model containing cracks;

[0046] The stress intensity factor amplitude at the crack tip of the two cracks was calculated using the M-integral function in FRANC3D software.

[0047] The M-integral is used to analyze the stress intensity factor amplitude at the crack tip, where the M-integral can be expressed as:

[0048]

[0049] In the formula, σ ij Let u be the stress tensor component, W be the displacement vector, and δ be the interaction strain energy density. 1j For Kronecker delta notation, Let ds be the gradient of the weighting function, and ds be the arc length infinitesimal element.

[0050] Based on the calculated stress intensity factor amplitudes of the two cracks, the crack with the larger stress intensity factor amplitude is considered the primary crack, and the crack with the smaller stress intensity factor amplitude is considered the secondary crack, for subsequent analysis.

[0051] The stress intensity factor amplitude of the main crack is obtained by calculation, and the crack propagation direction is determined by calculation.

[0052] The maximum circumferential tensile stress criterion is used to analyze the propagation direction of the crack front nodes. For plane problems, the maximum circumferential tensile stress criterion can be expressed as:

[0053] K I sinθ+K II(3cosθ-1)=0

[0054] In the formula, K I and K II θ represents the stress intensity factors for Type I and Type II, and θ is the crack propagation angle.

[0055] After solving, the expression for the crack lead propagation angle θ can be obtained:

[0056]

[0057] Fit the relationship between stress intensity factor and crack propagation length;

[0058] Assume the structure contains two elements of length a. 01 and a 02 The initial crack, and subsequent defaults will be a. 01 As the main crack, a 02 It is a minor crack.

[0059] Ten cracks with a length of 1.01a were established using crack modeling methods. 01 1.02a 01 1.03a 01 up to 1.1a 01 Ten crack finite element models were interpolated into the initial model to obtain ten crack-containing finite element models. The stress intensity factor amplitude of the main crack front in the ten crack-containing finite element models was calculated.

[0060] Establish a graph showing the relationship between the amplitudes of 10 stress intensity factors and their crack propagation length, and fit the amplitudes of the 10 stress intensity factors using an exponential function. The relationship between the crack length a and the crack length α is as follows: Figure 3 As shown; by With a 01 Substituting the relational expression into the crack propagation life model, we can calculate the path of the main crack from point a. 01 Extended to 1.1a 01 The number of cycles experienced.

[0061] Crack propagation life analysis using the Paris formula;

[0062] The Paris formula is used to analyze crack propagation life. The expression of the Paris formula is:

[0063]

[0064] In the formula, C and m are material constants determined experimentally.

[0065] The main crack propagation was determined to be 1.1a.01 After determining the number of iterations, the same method is used to fit the secondary crack stress intensity factor. The relationship between the secondary crack and the crack propagation distance *a* is determined by using a fitted formula and then applying the Paris formula in reverse. This means that, given the initial crack length and the number of crack propagation cycles, the secondary crack can be calculated when the primary crack has propagated to 1.1a. 01 The crack propagation distance after the number of cycles.

[0066] This allows us to obtain the propagation direction and distance of the primary and secondary cracks in a single propagation.

[0067] Step 3: Update the finite element model containing cracks. Update the crack model based on the propagation direction and distance of the two cracks obtained in the previous step, and re-insert it into the finite element model of the initial structure.

[0068] like Figure 4 As shown, for non-planar propagating cracks, establishing the crack model for the i-th crack propagation step and updating the crack propagation model requires the following: First, read the position coordinates of each node of the crack leading edge calculated in the previous crack propagation step, and use B-spline curves for fitting and connecting them to construct the crack leading edge for the next propagation step; then, read the position coordinates of all nodes of all crack leading edges starting from the first step, and also use B-spline curves for connecting them to establish the crack leading edges of all crack propagation steps starting from the first step; next, connect all the current crack leading edge curves according to the node numbers to establish the crack model for the i-th crack propagation step; finally, insert the crack model into the initial structural finite element model using the same method as in step 1 and re-mesh 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 certain 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 from each of the above steps, we can finally obtain the crack propagation path and crack propagation life of the structure containing multiple cracks under multiaxial loading conditions.

[0071] In summary, this 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 propagation rate model is established using the Paris formula, and the maximum tensile stress criterion is employed to determine the crack propagation direction, thereby achieving synchronous control of multiple crack propagation. The propagation model is iteratively updated using crack lead reconstruction and mesh re-division methods, ultimately achieving structural damage tolerance assessment and life prediction. This invention can effectively simulate the interaction of multiple cracks in complex structures, improving the accuracy and efficiency of crack propagation prediction, and has broad engineering application prospects.

[0072] By dividing the crack propagation process into multiple sub-steps for solution and controlling crack propagation through the relationship between stress intensity factor and crack length, this method can not only solve the interaction between multiple cracks but also effectively simulate the crack propagation process in complex structures while reducing simulation resources. Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for analyzing the multi-crack propagation life under multiaxial loading conditions, characterized in that: include: Construct a finite element model containing at least two initial cracks; Calculate the stress intensity factor amplitude at the crack tips of the two initial cracks to obtain the fracture parameters and crack propagation of the two cracks; The two crack fracture parameters and crack propagation amount are updated into the crack finite element model to obtain the updated crack finite element model, and the updated crack finite element model is inserted into the crack-containing finite element model. Iteratively calculate the fracture parameters and crack propagation of the two cracks and update them in the finite element model containing the cracks until the stress intensity factor amplitude at the crack tip meets the critical fracture toughness value or the crack propagates to the allowable crack size. The calculation of the stress intensity factor amplitude at the crack tips of the two initial cracks includes: Calculate the stress intensity factor at the tips of the two cracks and identify the primary and secondary cracks; Calculate the propagation directions of the primary and secondary cracks; Fit the relationship between the main crack stress intensity factor and crack length; The number of cycles required to calculate the initial length of the main crack propagation to 1 / 10; Fit the relationship between the stress intensity factor of the minor crack and the crack length; Calculate the extension distance required for a secondary crack to extend to 1 / 10 of its initial length using the number of cycles required. The calculation of the stress intensity factor at the tips of the two cracks and the determination of the primary and secondary cracks include: The stress intensity factor amplitude at the crack tip is analyzed using M-integral. Based on the magnitude of the stress intensity factor amplitude of the two cracks, the one with the larger stress intensity factor amplitude is identified as the primary crack, and the one with the smaller stress intensity factor amplitude is identified as the secondary crack. The fitted relationship between the main crack stress intensity factor and crack length includes: The length of each propagation of the main crack is set to the initial crack length a. 01 1 / 10; By establishing 10 arrays with a length of 1.01a 01 1.02a 01 1.03a 01 up to 1.1a 01 Ten crack finite element models were interpolated into the initial model to obtain ten crack-containing finite element models. The stress intensity factor amplitude of the main crack front in the ten crack-containing finite element models was calculated. Establish a graph showing the relationship between the amplitude of 10 stress intensity factors and their crack propagation length; The amplitudes of 10 stress intensity factors were fitted using an exponential function. The relationship between the crack length a and the crack length α; The propagation direction and propagation distance of the main extended crack are obtained.

2. The method for analyzing the multi-crack propagation life under multiaxial loading conditions according to claim 1, characterized in that: The construction of a crack-containing finite element model with at least two initial cracks includes: A three-dimensional model of the initial structure is established, and the finite element model of the initial structure is obtained by meshing the three-dimensional model of the initial structure. Two two-dimensional shell models are established, and the initial crack finite element model is obtained by meshing the two two-dimensional shell models. Insert the finite element model of the initial crack into the finite element model of the initial model.

3. The method for analyzing the multi-crack propagation life under multiaxial loading conditions according to claim 1, characterized in that: The calculation of the propagation direction of the primary and secondary cracks includes: using the maximum circumferential tensile stress criterion to analyze the propagation direction of the nodes at the crack front.

4. The method for analyzing the multi-crack propagation life under multiaxial loading conditions according to claim 1, characterized in that: The calculation of the initial length of the main crack propagation (1 / 10) requires a number of iterations, including: adjusting the stress intensity factor amplitude by 10. Substituting the relationship between crack length *a* and crack length *a* into the crack propagation life model, we obtain the main crack propagation path from *a*. 01 Extended to 1.1a 01 The number of cycles experienced.

5. The method for analyzing the multi-crack propagation life under multiaxial loading conditions according to claim 4, characterized in that: The relationship between the fitted secondary crack stress intensity factor and the crack length includes: fitted secondary crack stress intensity factor The relationship between the crack propagation distance 'a' and the crack extension distance 'a'.

6. The method for analyzing the multi-crack propagation life under multiaxial loading conditions according to claim 5, characterized in that: The calculation of the extension distance requiring 1 / 10 of the initial length of the secondary crack includes: using the secondary crack stress intensity factor. The relationship between the secondary crack and the crack propagation distance *a* is reversed by applying the Paris formula, yielding that the secondary crack extends to 1.1a when the primary crack reaches this distance. 01 The crack propagation distance after the number of cycles.

7. The method for analyzing the multi-crack propagation life under multiaxial loading conditions according to any one of claims 1-6, characterized in that: The step of inserting the updated finite element model of the crack into the finite element model containing the crack includes: To establish the crack finite element model for the i-th crack propagation step and update the crack propagation model, the following is required: Read the position coordinates of each node of the crack front calculated in the previous crack propagation step, use B-spline curves to fit and connect them, and construct the crack front of the next propagation 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 propagation 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 propagation step; The crack finite element model is inserted into the initial structural finite element model and the mesh is re-generated to obtain the final finite element model.

Images