A method, apparatus, equipment, and program product for determining overload fatigue crack propagation path and life based on extended finite element method.

Abstract

This application provides a method, apparatus, device, and program product for determining overload fatigue crack propagation path and life based on the extended finite element method, relating to the field of mechanical technology. Specifically, this application designs a crack surface update method based on the extended finite element method, realizing automatic simulation of crack propagation. Since this method does not rely on complex level set traversal algorithms, it has high computational efficiency and good robustness. Based on a period-by-period algorithm using piecewise interpolation, combined with a fatigue crack propagation rate model considering overload effects, the high-cycle fatigue crack propagation life of structures under cyclic overload load spectra can be accurately calculated.

Description

Technical Field

[0001] This application relates to the field of mechanical technology, and more specifically, to a method, apparatus, equipment, and program product for determining the overload fatigue crack propagation path and life based on the extended finite element method. Background Technology

[0002] Fatigue fracture is one of the most common failure modes in engineering structures, and studying fatigue fracture has become an important means of assessing the fatigue life of engineering structures. Currently, damage tolerance methods based on fracture mechanics have become an important method for assessing the fatigue life of engineering structures. This method pre-determines an initial crack in the engineering structure and studies crack propagation through fracture mechanics to evaluate the fatigue level and fatigue life of the engineering structure. With the development of computer technology, numerical simulation has gradually become a cost-effective method for studying fatigue crack propagation; for example, crack path simulation based on the extended finite element method (XFEM).

[0003] However, traditional methods for crack path simulation based on XFEM generally suffer from problems such as inaccurate calculation results, difficulty in convergence, and low computational efficiency, which are obvious drawbacks. Summary of the Invention

[0004] This application provides at least one method, apparatus, device, and program product for determining the overload fatigue crack propagation path and life based on extended finite element method, so as to improve the accuracy and efficiency of crack propagation simulation and avoid the problem of non-convergence of calculation.

[0005] In a first aspect, embodiments of this application provide a method for determining the overload fatigue crack propagation path and life based on the extended finite element method, including:

[0006] For the target engineering structure, a finite element model is constructed, including the crack surface to be expanded; the finite element model also includes multiple element nodes. Using the element decomposition method, the displacement field corresponding to the finite element model is determined based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded. Based on the displacement field, the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type is determined by the interaction integral method. Based on the target stress intensity factor, the crack deflection angle is determined, and based on the crack deflection angle and the preset crack propagation increment, the new crack tip coordinates and the new crack surface to be propagated are determined. Returning to the step of using the element decomposition method, determining the displacement field corresponding to the finite element model based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded, until the crack expansion number reaches the set number, and obtaining each crack surface to be expanded; Based on the crack tip coordinates of each crack surface to be expanded and the target stress intensity factor, a piecewise interpolation method is used to determine the crack propagation path under a preset cyclic load and the correlation between crack length and the number of load cycles; the preset cyclic load includes variable amplitude cyclic load.

[0007] Secondly, embodiments of this application also provide a device for determining the overload fatigue crack propagation path and life based on extended finite element method, comprising: A construction module is used to build a finite element model, including the crack surface to be expanded, for the target engineering structure; the finite element model also includes multiple element nodes. The first determining module is used to determine the displacement field corresponding to the finite element model by using the element decomposition method, based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded in the finite element model. The second determining module is used to determine the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type, respectively, based on the displacement field and using the interaction integral method. The third determining module is used to determine the crack deflection angle based on the target stress intensity factor, and to determine the new crack tip coordinates and the new crack surface to be expanded based on the crack deflection angle and the preset crack propagation increment. The loop module is used to return to the step of using the element decomposition method to determine the displacement field corresponding to the finite element model based on the first additional displacement degree of freedom of each first element node in the crack tip region corresponding to the crack tip coordinate of the crack surface to be expanded, until the crack expansion number reaches the set number, and each crack surface to be expanded is obtained. The fourth determining module is used to determine the crack propagation path and the relationship between crack length and load cycle number under a preset cyclic load by using a piecewise interpolation method based on the crack tip coordinates of each crack surface to be propagated and the target stress intensity factor; the preset cyclic load includes variable amplitude cyclic load.

[0008] Thirdly, an optional implementation of this application also provides a computer device, a processor, and a memory, wherein the memory stores machine-readable instructions executable by the processor, and the processor is used to execute the machine-readable instructions stored in the memory, wherein the machine-readable instructions, when executed by the processor, perform the steps in the first aspect described above.

[0009] Fourthly, an optional implementation of this application also provides a computer program product, including a computer program that, when run, implements the steps in the first aspect described above.

[0010] The method, apparatus, equipment, and program products for determining overload fatigue crack propagation path and life based on extended finite element method provided in this application, after obtaining the finite element model corresponding to the target engineering structure and the crack surface to be propagated, perform numerical calculations using the first additional displacement degrees of freedom of each first element node in the crack tip region of the crack surface to be propagated, and continuously update the crack surface propagation by combining a preset crack propagation increment. This not only fully considers the influence of each first element node in the crack tip region on crack surface propagation, avoiding the problem of non-convergence in calculation and improving the accuracy of calculation results, but also eliminates the need for complex level set progression algorithms for crack surface updates, thus improving computational efficiency. By employing a piecewise interpolation method, combining the crack tip coordinates of each crack surface to be propagated and the target stress intensity factor, the crack propagation path is simulated under a preset cyclic load, avoiding the need for complex numerical calculations for each crack propagation, thereby improving the efficiency of crack propagation path determination. By establishing the correlation between crack length and the number of load cycles, the fatigue life of the target engineering structure under cyclic load can be effectively predicted.

[0011] For a description of the effects of the aforementioned apparatus, computer equipment, and program products for determining the overload fatigue crack propagation path and life based on extended finite element method, please refer to the description of the aforementioned method for determining the overload fatigue crack propagation path and life based on extended finite element method, which will not be repeated here.

[0012] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly described below. These drawings are incorporated in and constitute a part of this specification. They illustrate embodiments conforming to this application and, together with the specification, serve to explain the technical solutions of this application. It should be understood that the following drawings only show some embodiments of this application and should not be considered as limiting the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0014] Figure 1 A flowchart is shown below illustrating a method for determining the overload fatigue crack propagation path and life based on extended finite element method, as provided in an embodiment of this application. Figure 2 A schematic diagram of the load spectrum of a preset cyclic load containing periodic overload provided in an embodiment of this application is shown; Figure 3 A schematic diagram of crack propagation provided in an embodiment of this application is shown; Figure 4 This illustration shows a schematic diagram of the crack length and interpolated stress intensity factor amplitude based on the piecewise interpolation method provided in an embodiment of this application. Figure 5 This illustration shows a schematic diagram of the crack tip plastic zone size, crack length, and remaining crack tip plastic zone size at an overload moment and the current moment, as provided in an embodiment of this application. Figure 6 A detailed flowchart of a method for determining the overload fatigue crack propagation path and lifetime based on extended finite element method provided in an embodiment of this application is shown. Figure 7 A schematic diagram of a double-cracked plate with a central circular hole provided in an embodiment of this application is shown; Figure 8 A schematic diagram comparing a numerical solution and an analytical solution provided in an embodiment of this application is shown; Figure 9a A schematic diagram of a modified three-point bending specimen of a non-porous type provided in an embodiment of this application is shown; Figure 9b A schematic diagram of a modified three-point bending specimen with a hole type provided in an embodiment of this application is shown; Figure 10a This illustration shows a comparison of simulated paths constructed for types I to III, provided in an embodiment of this application. Figure 10b This illustration shows a comparison of simulated paths constructed for types IV to VI, provided in an embodiment of this application. Figure 11 A schematic diagram of a centrally cracked plate specimen provided in an embodiment of this application is shown; Figure 12a The accompanying diagram shows a comparison of crack propagation simulations under different overload cycles provided in the embodiments of this application. Figure 12b The accompanying diagram shows a comparison of crack propagation simulations under single-cycle overload with different overload intervals, as provided in the embodiments of this application. Figure 12c The accompanying diagram shows a comparison of crack propagation simulations under single-cycle overload with different overload ratios, as provided in the embodiments of this application. Figure 13a A schematic diagram of an I-beam structure with a joint provided in an embodiment of this application is shown; Figure 13b A schematic diagram of a finite element model of an I-beam structure with joints constructed using the body-shell coupling technology provided in this application embodiment is shown. Figure 14a This paper presents a comparison chart showing the results of crack propagation simulation of an I-beam structure of type A, as provided in the embodiments of this application. Figure 14b This paper presents a comparison chart showing the results of crack propagation simulation of an I-beam structure of type B, as provided in the embodiments of this application. Figure 15a This paper presents a schematic diagram comparing the calculation results under constant amplitude cyclic loading provided in the embodiments of this application; Figure 15b This paper presents a comparison chart of fatigue life calculation results under different overload cycles provided in the embodiments of this application; Figure 15c This paper presents a comparison chart of fatigue life calculation results under single-cycle overload with different overload intervals, provided in an embodiment of this application. Figure 15d This paper presents a comparison chart of fatigue life calculation results under single-cycle overload with different overload ratios, provided in an embodiment of this application. Figure 16 This illustration shows a schematic diagram of a device for determining the overload fatigue crack propagation path and life based on extended finite element method according to an embodiment of this application. Figure 17 A schematic diagram of the structure of a computer device provided in an embodiment of this application is shown. Detailed Implementation

[0015] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown herein can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0016] Furthermore, the terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein.

[0017] In this article, "multiple or several" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. The character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0018] Research has shown that, compared to traditional finite element method-based numerical simulations, XFEM is more widely used in studying fatigue crack propagation in engineering structures because it does not require refining the crack tip mesh or re-meshing, and can achieve crack propagation along arbitrary paths. However, current common XFEM-based crack propagation simulation methods generally suffer from inaccurate simulations and difficulty in convergence, requiring urgent improvement.

[0019] Based on the above research, this application provides a method, apparatus, equipment, and program product for determining the overload fatigue crack propagation path and life based on extended finite element method. After obtaining the finite element model corresponding to the target engineering structure and the crack surface to be propagated, numerical calculations are performed using the first additional displacement degrees of freedom of each first element node in the crack tip region of the crack surface to be propagated. Combined with a preset crack propagation increment, the crack surface propagation is continuously updated. This not only fully considers the influence of each first element node in the crack tip region on crack surface propagation, avoiding the problem of non-convergence in calculations and improving the accuracy of the calculation results, but also eliminates the need for complex level set progression algorithms for crack surface updates, thus improving computational efficiency. Using a piecewise interpolation method, combined with the crack tip coordinates of each crack surface to be propagated and the target stress intensity factor, the crack propagation path is simulated under a preset cyclic load. This avoids the problem of needing complex numerical calculations for each crack propagation, thereby improving the efficiency of crack propagation path determination. By establishing the correlation between crack length and the number of load cycles, the fatigue life of the target engineering structure under cyclic loads can be effectively predicted.

[0020] The shortcomings of the above solutions are the result of the inventor's practical experience and careful research. Therefore, the discovery process of the above problems and the solutions proposed in this application below should be considered as the inventor's contributions to this application.

[0021] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0022] It is understood that before using the technical solutions disclosed in the various embodiments of this application, users should be informed of the types, scope of use, and usage scenarios of the personal information involved in this application in an appropriate manner in accordance with relevant laws and regulations, and user authorization should be obtained.

[0023] To facilitate understanding of this embodiment, a detailed description of the method for determining the overload fatigue crack propagation path and life based on extended finite element method disclosed in this application embodiment will be provided first. The execution subject of the method for determining the overload fatigue crack propagation path and life based on extended finite element method provided in this application embodiment is generally a terminal device or other processing device with certain computing capabilities. The terminal device can be a user equipment (UE), mobile device, user terminal, terminal, personal digital assistant device (PDA), handheld device, computer device, etc. In some possible implementations, the method for determining the overload fatigue crack propagation path and life based on extended finite element method can be implemented by a processor calling computer-readable instructions stored in memory.

[0024] The following describes the method for determining the overload fatigue crack propagation path and life based on extended finite element method provided in this application, taking a computer device as the executing entity as an example.

[0025] like Figure 1 The flowchart shown is a method for determining the overload fatigue crack propagation path and life based on the extended finite element method according to an embodiment of this application, which may include the following steps: S101: For the target engineering structure, construct a finite element model including the crack surface to be expanded; the finite element model also includes multiple element nodes.

[0026] Here, the target engineering structure can be any three-dimensional structure in the actual engineering scenario, such as a three-dimensional plate structure, I-beam structure, frame structure, arch structure, etc.

[0027] The finite element model can be a structural model constructed using shell-body coupling technology for a target engineering structure. The finite element model can include predefined element nodes. Furthermore, to implement the crack propagation module, an initial crack surface can be constructed within the finite element model. This initial crack surface can be a penetrating crack surface in the target engineering structure, characterized by a straight crack front perpendicular to the thickness direction.

[0028] The initial crack surface carried in the finite element model serves as the initial crack surface to be expanded. The method for determining the overload fatigue crack propagation path and life based on extended finite element method provided in this application can be divided into two parts: the first part is automatic crack surface updating based on XFEM, and the second part is cycle-by-cycle calculation of overload fatigue life based on piecewise interpolation. The second part is responsible for automatically updating the crack surface with arbitrary paths and calculating the crack tip stress intensity factor; this module can be developed based on the static crack analysis function of XFEM. Specifically, using the first part, crack propagation can be simulated based on XFEM on the initial crack surface to be expanded, thereby automatically updating each subsequent crack surface to be expanded corresponding to the target engineering structure. The second part is responsible for obtaining the relationship between crack length and the number of load cycles under constant or variable amplitude cyclic load spectra. Based on the second part, the fatigue life of the target engineering structure under cyclic loading can be calculated. The specific content of the second part will be described in detail later.

[0029] Understandably, the functions of the first and second parts mentioned above can be obtained by developing corresponding pre- and post-processing programs using finite element software (ABAQUS) to create the corresponding functional modules (i.e., the crack propagation simulation module corresponding to the first part and the fatigue life calculation module corresponding to the second part). Furthermore, since the geometric topological relationships between the target engineering structure and the crack surface in XFEM are independent (i.e., the crack surface can be processed independently compared to the target engineering structure), this provides a basis for developing corresponding pre- and post-processing programs based on ABAQUS software to achieve automatic updating of the crack surface.

[0030] In practice, for any 3D engineering structure requiring crack propagation simulation, it can be used as the target structure, and the initial crack surface and initial crack length of the target structure can be determined. Then, using shell-body coupling technology, a finite element model containing the initial crack surface is constructed to match the target structure. The initial crack surface in this finite element model is used as the initial crack surface to be propagated, and the crack tip coordinates of this crack surface in a preset coordinate system can be determined. Understandably, the crack tip coordinates of the initial crack surface are related to the initial crack length.

[0031] Optionally, when constructing a finite element model, the crack propagation zone can use smaller-sized solid elements, while the non-crack propagation zone can use larger-mesh shell elements. This simplifies the modeling process and provides a foundation for improving computational efficiency in the future.

[0032] S102: Using the element decomposition method, the displacement field corresponding to the finite element model is determined based on the first additional displacement degree of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates on the crack surface to be expanded.

[0033] Here, the finite element model can include multiple element nodes, with different element nodes located at different positions within the finite element model. The crack tip region can be the area where the crack tip coordinates of the current crack surface to be expanded are located.

[0034] The first element node can be any node located within the crack tip region of the current crack surface to be expanded, among all the element nodes included in the finite element model. Therefore, the first element node can also be called the crack tip reinforcement node. As the crack surface to be expanded is continuously updated, the crack tip coordinates will be continuously updated, and the first element node will also be continuously updated. The first additional displacement degree of freedom is an extra displacement degree of freedom pre-set for the first element node, and this degree of freedom can include multiple degrees.

[0035] The displacement field is used to characterize the approximate element displacement of the finite element model under each existing crack surface to be expanded.

[0036] In practical implementation, for the current crack surface to be expanded, the first element nodes located in the crack tip region can be determined from the element nodes included in the finite element model using the unit decomposition method. Then, the crack tip enhancement function is used, combined with the first additional displacement degree of freedom, to determine the enhancement result of each first element node. Then, based on the enhancement result and the conventional displacement degree of freedom of each element node in the finite element model, the displacement field of the finite element model under each existing crack surface to be expanded is determined.

[0037] In one embodiment, S102 described above can be implemented according to the following steps: S102-1: Determine each first element node in the crack tip region corresponding to the crack tip coordinates on the crack surface to be expanded in the finite element model.

[0038] For example, for the current crack surface to be expanded, the first element nodes located in the crack tip region can be determined from the element nodes included in the finite element model based on the unit decomposition method.

[0039] S102-2: Determine the second element node in each determined crack surface to be expanded in the finite element model.

[0040] Here, the identified crack surface to be expanded can be the initial crack surface and each updated crack surface that matches the current expansion process. For example, during the first crack surface expansion, the identified crack surface to be expanded can be the initial crack surface. During the third crack surface expansion, the identified crack surface to be expanded can include the initial crack surface and two crack surfaces to be expanded obtained from the two expansions based on the initial crack surface.

[0041] In practice, when updating the current crack surface, we can first determine each of the previously determined crack surfaces to be expanded. Then, based on the unit decomposition method, we can determine the second element nodes located within each of the previously determined crack surfaces to be expanded from the element nodes included in the finite element model.

[0042] S102-3: Using the element decomposition method, the displacement field corresponding to the finite element model is determined based on the displacement degrees of freedom of each element node, the first additional displacement degrees of freedom of each first element node, and the second additional displacement degrees of freedom of each second element node.

[0043] Here, the displacement degree of freedom can be the conventional displacement degree preset for each element node. The second additional displacement degree of freedom is an extra displacement degree of freedom preset for the second element node.

[0044] In practical implementation, when using XFEM to simulate cracks, an enhancement term is usually introduced into the displacement mode of the traditional finite element method based on the unit decomposition method. This enhancement term reflects the discontinuities caused by the crack surface and characterizes the singularities at the crack tip. Therefore, the element displacement approximation mode of the finite element model under the crack surface to be expanded can be expressed by the following formula: (Formula 1) in, This represents the displacement field of the finite element model under XFEM. This represents the set of all element nodes in a finite element model. b express The first in b Each unit node. Indicates the first b The shape function of each unit node, x It represents the spatial coordinate vector of any calculation point in the target engineering structure in the preset coordinate system. It can characterize the first b Unit node pair x The displacement contribution. Indicates the first b The displacement degrees of freedom of each element node. This represents the set of crack surface reinforcement nodes composed of the nodes of each second element in the finite element model. This represents the Heaviside function. express The Middle b The second additional displacement degree of freedom of the crack-enhanced node (i.e., the second element node). This represents the set of crack tip reinforcement nodes composed of all the nodes of the first element in the finite element model. This represents the crack tip enhancement function. Indicates that for the first b The first crack tip reinforcement node (i.e., the first unit node) e The first additional displacement degree of freedom, e The value of includes 1 to 4. The Heaviside function can be used to enhance each second element node on both sides of the crack surface to be propagated, resulting in an enhancement term reflecting the discontinuity caused by the crack surface. The region on both sides of the crack surface to be propagated can be preset empirically; this embodiment does not impose a specific limitation. The crack tip enhancement function... Each first unit node is enhanced to obtain an enhancement term that reflects the singularity at the crack tip. This enhancement term can reflect the asymptotic singular field at the crack tip.

[0045] For example, for any crack propagation, the nodes of the first and second elements before the propagation can be determined. Then, the displacement field of the finite element model under the crack propagation can be determined by using the element decomposition method and the above formula 1.

[0046] S103: Based on the displacement field, the interactive integral method is used to determine the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type, respectively.

[0047] Here, since cracks in engineering structures are mostly of mixed mode (i.e., cracks include opening mode (Type I) and sliding mode (Type II)) in actual engineering applications, in order to improve the accuracy of crack propagation simulation, this application simulates crack propagation by determining the target stress intensity factor corresponding to the crack tip under Type I and Type II cracks.

[0048] The target stress intensity factor includes the stress intensity factor K corresponding to the crack tip coordinates under type I crack. I and the stress intensity factor K corresponding to type II crack. II .

[0049] In practice, the stress and strain fields can be determined based on the displacement field. Then, based on the stress and strain fields, the interaction integral method can be used to solve for the interaction integrals under the type I crack. Based on these integrals, the target stress intensity factor K of the crack tip coordinates under the type I crack can be determined. I Similarly, based on the stress field and strain field, the interaction integral method can be used to solve for the interaction integral under a type II crack, and the target stress intensity factor K of the crack tip coordinates under a type II crack can be determined based on this integral. II .

[0050] In one embodiment, the above-described S103 can be implemented according to the following steps: S103-1: Determine the stress field corresponding to the finite element model based on the displacement field.

[0051] In practice, the coordinates can be differentiated based on the determined displacement field to obtain the strain field corresponding to the finite element model. Then, using the constitutive equation and the strain field, the actual stress field corresponding to each determined crack surface to be expanded in the finite element model can be determined.

[0052] S103-2: Using the interactive integral method, based on the displacement field, stress field, auxiliary fields corresponding to the open crack type and the slip crack type respectively, and the crack length in the crack tip coordinate, the interactive integral corresponding to the crack tip coordinate in the open crack type and the slip crack type respectively is determined.

[0053] Here, the crack length can be the crack length corresponding to the crack tip coordinate of the current crack surface to be expanded during the current crack propagation. This length can be understood as the total crack length that has been simulated.

[0054] The auxiliary field can include pre-set auxiliary fields for Type I cracks and Type II cracks respectively. The auxiliary field corresponding to each type of crack can include three types: auxiliary stress field, auxiliary strain field and auxiliary displacement field.

[0055] In practical implementation, the stress intensity factor, as an important parameter in linear elastic fracture mechanics, is typically calculated using the interaction integral method for mixed-mode cracks. However, for numerical calculation purposes, it is often transformed into an equivalent region integral. Therefore, in practice, the following formula (Formula 2) can be used to determine the interaction integrals corresponding to Mode I and Mode II cracks respectively: (Formula 2) in, Let A represent the interactive integration region, which can be a preset range around the crack tip region. The actual stress field, auxiliary stress field, and auxiliary strain field can all be... i × j A matrix, for example, can be a 2×3 matrix. It can represent the real stress field in ij The true stress tensor at the location. It can represent the auxiliary strain field in ij The auxiliary strain tensor at the location. It can represent an auxiliary displacement field; It can represent the axis of crack propagation direction. It can represent the coordinates of the crack tip. It can represent the auxiliary stress field in ij The auxiliary stress tensor at the location; It can represent the real strain field. Q It can represent a preset weight function. dA This indicates that the integration is performed over region A.

[0056] In practice, the determined displacement field, stress field, and various auxiliary fields set for Type I cracks can be substituted into Formula 2 above to obtain the interaction integral corresponding to Type I cracks. Similarly, the determined displacement field, stress field, and various auxiliary fields set for Type II cracks can be substituted into Formula 2 above to obtain the interaction integral corresponding to Type II cracks.

[0057] S103-3: Based on the interactive integral and the maximum load under the preset cyclic load, determine the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type, respectively.

[0058] Here, the preset cyclic load is a pre-set load spectrum, which can be a constant amplitude load spectrum or a variable amplitude load spectrum containing periodic overloads. The maximum load can be the reference maximum load in the preset cyclic load. For example... Figure 2 The diagram shown is a load spectrum diagram of a preset cyclic load containing periodic overload provided in an embodiment of this application. Figure 2 In this diagram, a single waveform can represent a single load, with the horizontal axis representing time (T) and the vertical axis representing the load. F min Indicates minimum load. F max Indicates the maximum load on the reference. F OL This indicates an overload. Figure 2 In p The second cycle represents a continuous loop. p The second applied non-overload load Figure 2 In q The second cycle represents a continuous loop. q The overload applied in this second instance. p and q The value can be set based on experience, and this application does not impose specific limitations on the embodiments. For actual engineering structures, the cyclic loads they are subjected to are mostly variable, and the effect of overload is unavoidable. Therefore, by studying the cyclic load spectrum including overload loads, this application can improve the accuracy and authenticity of the determined structural fatigue life.

[0059] In practice, the target stress intensity factor K of the type I crack under maximum load can be determined based on the interactive integral and XFEM corresponding to the type I crack. ISimilarly, based on the interaction integral and XFEM corresponding to the type II crack, the target stress intensity factor K of the type II crack under maximum load can be determined using the interaction integral method. II .

[0060] S104: Determine the crack deflection angle based on the target stress intensity factor, and determine the new crack tip coordinates and the new crack surface to be expanded based on the crack deflection angle and the preset crack propagation increment.

[0061] Here, the crack deflection angle indicates the direction of crack propagation when the crack propagates from the crack tip coordinates of the current crack surface to be propagated. Preset crack propagation increment. Δa A pre-set crack growth range, such as 1mm, 2mm, etc.

[0062] The new crack surface to be expanded is the new crack surface obtained after simulating crack propagation from the crack tip coordinates of the current crack surface. The new crack coordinates are used to indicate the crack coordinates of the next crack surface to be expanded after simulating crack propagation from the crack tip coordinates of the current crack surface.

[0063] In practical implementation, the K coordinates at the crack tip of the current crack surface to be expanded are obtained. I and K II Then, the crack deflection angle can be determined according to the maximum circumferential tensile stress criterion. For example, the crack deflection angle can be determined according to the following formula three: (Formula 3) in, It can represent the first i The crack deflection angle during secondary crack propagation, where the first crack propagation originates from the initial crack surface carried by the finite element model. Taking the initial crack surface carried by the finite element model as crack surface 0 as an example, the crack deflection angle of the first crack propagation can be: The resulting new crack surface to be extended is crack surface 1. The second crack extension can begin at the crack tip coordinates of crack surface 1, and the crack deflection angle of the second crack extension can be... The new crack surface to be expanded is obtained as crack surface 2, and so on. K can be the crack deflection angle calculated when crack propagation begins at the crack tip coordinates at crack surface i. I and K II These are the target stress intensity factors determined at the crack tip coordinates of crack surface i. The value of "±" in Formula 3 is related to K. II The positive and negative correlation in K II A positive sign is indicated by a "+" sign, while a negative sign is indicated by a "-" sign.

[0064] Furthermore, after calculating the crack deflection angle, the crack propagation direction can be determined based on the crack tip coordinates and the crack deflection angle of the current crack surface to be propagated. Then, the crack propagation can begin from the crack tip coordinates of the current crack surface to be propagated, following the crack propagation direction. Δa The length of the crack tip is used to obtain new crack tip coordinates. Then, based on these new crack tip coordinates, a new crack surface with the same shape and size as the previous crack surface to be expanded can be obtained, and this crack surface can be used as the new crack surface to be expanded.

[0065] S105: Return to the steps of using the element decomposition method to determine the displacement field corresponding to the finite element model based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded, until the crack expansion number reaches the set number, and obtain each crack surface to be expanded.

[0066] Here, the number N is set to indicate the maximum number of crack propagation cycles. This number can be set empirically, and this embodiment does not impose a specific limitation. After performing a set number of crack propagation cycles (crack surface propagation) based on the initial crack surface carried in the finite element model, N+1 consecutive crack surfaces can be obtained.

[0067] In practice, for any given crack surface to be expanded, after crack propagation according to S102~S104 above to obtain a new crack surface to be expanded, it can be determined whether the current crack propagation count has reached the set number. If so, crack propagation can be stopped, and each crack surface to be expanded simulated in the finite element model can be obtained. If not, based on the new crack surface to be expanded, the process can return to S102~S104 above to perform the next crack propagation, until the crack propagation count reaches the set number, and each crack surface to be expanded simulated in the finite element model can be obtained.

[0068] like Figure 3 The above is a schematic diagram of crack surface propagation provided in an embodiment of this application, wherein... Figure 3 The default coordinate system has its y-axis pointing vertically upwards, and the planes containing the x-axis and z-axis are perpendicular to the y-axis, with the origin at point O. O . Figure 3 The initial crack in the model is the initial crack surface carried in the finite element model. By taking this crack surface as the final crack to be expanded, and following the automatic update process of crack surface based on XFEM provided in S102~S104 of this application, the simulated crack surfaces to be expanded can be obtained. Figure 3 In O 1 ( x 1, y 1) This refers to the coordinates of the crack tip on the initial crack surface, which can be obtained directly. Δa This indicates the preset crack propagation increment used each time the crack propagates.O 2 ( x 2, y 2) This refers to the coordinates of the crack tip on the second crack surface. O i ( x i , y i The coordinates of the crack tip on the i-th crack surface are given. O i+1 ( x i+1 , y i+1 (i) represents the coordinates of the crack tip of the (i+1)th crack surface. This represents the crack deflection angle determined during the first crack propagation based on the initial crack surface. Similarly, , ... That is, respectively representing the 2nd to the 3rd. i The crack deflection angle obtained during secondary crack propagation.

[0069] Thus, based on Figure 3 It can be seen that, for a penetrating crack surface with a straight crack front perpendicular to the thickness direction in a three-dimensional target engineering structure, the crack deflection angle at the i-th crack propagation time is calculated according to Formula 3, and an appropriate crack propagation increment is set. Δa It can be achieved through the new crack tip coordinates O i ( x i , y i The crack surface is automatically updated. The entire crack surface update process does not require modification of the finite element model of the target engineering structure, i.e., it does not require modification of information including loads and constraints. Therefore, the crack surface update method provided in this application embodiment can conveniently and efficiently realize the crack propagation process. This crack propagation process is achieved through crack propagation increments in pre- and post-processing. Δa The crack surface is updated, so there is no need to rely on a complex level set marching algorithm. At the same time, the numerical calculation including the crack surface does not simplify the crack tip enhancement term and crack surface enhancement term in the element displacement mode, so the calculation results are more accurate.

[0070] S106: Based on the crack tip coordinates and target stress intensity factor of each crack surface to be expanded, the crack propagation path and the correlation between crack length and load cycle number under the preset cyclic load are determined by piecewise interpolation; the preset cyclic load includes variable amplitude cyclic load.

[0071] Here, the preset cyclic load can be such as Figure 2The cyclic load shown is a variable amplitude cyclic load, etc. The crack propagation path indicates the change in crack location from the initial crack in the finite element model to the end of the crack propagation simulation. Crack length. a With load cycle number T The relationship between them (i.e.) a ~ T The correlation is used to indicate the relationship between crack length and the number of cyclic loads applied. Based on this correlation, the fatigue life of the target engineering structure can be predicted.

[0072] In practice, after simulating each crack surface to be expanded in the finite element model, the crack propagation path in each crack surface under a preset cyclic load can be determined using a period-by-cycle overload fatigue life calculation method based on piecewise interpolation, based on the crack tip coordinates and target stress intensity factor of each crack surface. Simultaneously, based on the crack length along each crack propagation path and the number of applied cyclic loads, a correlation between the crack length and the number of load cycles in the target engineering structure can be constructed, and the fatigue life of the target engineering structure can be predicted based on this correlation.

[0073] Optionally, after simulating all the crack surfaces to be expanded in the finite element model, a piecewise interpolation method for calculating overload fatigue life cycle by cycle can be used to calculate the crack propagation path within each pair of adjacent crack surfaces, and then all the obtained crack propagation paths can be integrated into the final propagation path corresponding to the target engineering structure. Alternatively, after simulating a new crack surface, a piecewise interpolation method for calculating overload fatigue life cycle by cycle can be used to calculate the crack propagation path within the new crack surface and the previous crack surface. Then, the next new crack surface is simulated, and the crack propagation path within the next new crack surface and the previous crack surface is calculated, and so on, until the crack propagation path within the last crack surface and the penultimate crack surface is obtained.

[0074] In one embodiment, step S106 above can be implemented using the overload fatigue life calculation based on piecewise interpolation provided in this application, where one cycle can be understood as applying one cyclic load. Specifically, step S106 above can be implemented according to the following steps: S106-1: For any two adjacent crack surfaces to be expanded, the interaction integral method is used to determine the equivalent stress intensity factor amplitude corresponding to the target crack length under the crack tip coordinates of the two crack surfaces to be expanded, based on the minimum load in the preset cyclic load and the target stress intensity factor corresponding to the two crack surfaces to be expanded.

[0075] Here, the target stress intensity factor can be obtained by applying the maximum load from a preset cyclic load at the crack coordinates of the crack surface to be expanded. The target crack length can be the total crack length from the crack initiation position to the crack tip coordinates. The equivalent stress intensity factor amplitude is used to indicate the equivalent amplitude of the Type I stress intensity factor amplitude and the Type II stress intensity factor amplitude at the target crack length. For each crack surface to be expanded, the crack surface can correspond to a crack tip coordinate and a crack length at that crack coordinate. The equivalent stress intensity factor amplitude at the crack tip coordinates can be determined using the interactive integral method, based on the target stress intensity factor of the crack surface at the crack tip coordinates and the target stress intensity factor obtained by applying the minimum load from the preset cyclic loads at the crack coordinates of the crack surface.

[0076] That is, assuming the crack coordinates of the initial crack surface O 1 ( x 1, y The length of the crack at point 1) is a 1. The amplitude of the equivalent stress intensity factor is Crack coordinates of the second crack surface O 2 ( x 2, y The length of the crack at point 2) is a 2. The amplitude of the equivalent stress intensity factor is ..., the crack coordinates of the Nth crack surface O N ( x N , y N The length of the crack at point () is a N The equivalent stress intensity factor amplitude is Then a discrete interpolation reference table can be obtained ( a 1, (), a 2, ), ..., ( a N , ).

[0077] In practice, for any two adjacent crack surfaces to be extended after crack propagation (such as the first and second crack surfaces), the interaction integral method can be used to determine the Type I target stress intensity factor (defined as...) at the crack tip coordinates of the two crack surfaces under the minimum load, based on the minimum load in the preset cyclic load. ) and Type II target stress intensity factor (defined as ).

[0078] Then, for each of the two crack surfaces to be expanded, the type I target stress intensity factor (defined as...) at the crack tip coordinates of that crack surface under the maximum load can be used as a reference. ) and Type II target stress intensity factor (defined as ), and the Type I and Type II target stress intensity factors at the crack tip coordinates of the crack surface to be expanded under minimum load, to determine the amplitude of the Type I stress intensity factor at the crack tip coordinates of the crack surface to be expanded (defined as ), and the Type I target stress intensity factor at the crack tip coordinates of the crack surface to be expanded. ,in, = - ) and Type II stress intensity factor amplitude (defined as ,in, = - Then, the equivalent stress intensity factor amplitude corresponding to the target crack length in the crack tip coordinates of the crack surface to be expanded can be determined according to the following formula four. : (Formula 4) For example, for the first and second crack surfaces to be expanded, the target crack length corresponding to the crack tip coordinates of the first crack surface to be expanded is determined by using the interaction integral method and based on the minimum load in the preset cyclic loads. a 1 below and Then, the target crack length can be used. a 1 below and The target crack length of the first crack surface to be expanded is calculated according to Formula 4 above. a The equivalent stress intensity factor amplitude at level 1 is Similarly, this is analogous to determining the target crack length. a The equivalent stress intensity factor amplitude at level 1 is The process allows us to determine the target crack length for the second crack surface to be extended. a The amplitude of the equivalent stress intensity factor is 2. After that, it can be used and Follow the steps below to determine the crack propagation path between the first and second crack surfaces to be propagated.

[0079] S106-2: Based on the target crack length, the amplitude of the equivalent stress intensity factor, and the preset cyclic load, the piecewise interpolation method is used to determine the target crack propagation increment after each application of cyclic load in the two crack surfaces to be propagated, as well as the current crack length under the target crack propagation increment, until the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment, thus obtaining the crack propagation path in the two crack surfaces to be propagated.

[0080] Here, the target crack propagation increment indicates the crack length after one load in the preset cyclic loads is applied. The order of application of the cyclic loads is the load order in the load spectrum of the preset cyclic loads. Figure 2 For example, you can first apply p The second non-overload load, then p +1 times apply the first overload load, and then apply it continuously. q After one overload load, the next non-overload load can be applied.

[0081] In practical implementation, considering computational efficiency and cost, the cycle-by-cycle method is clearly not directly applicable to the numerical simulation of fatigue crack propagation for high-cycle fatigue problems. Therefore, this application, in order to calculate the high-cycle fatigue life of a structure using the cycle-by-cycle method, employs a suitable and fixed preset crack propagation increment, and uses the aforementioned XFEM-based method to calculate the target stress intensity factor at the crack tip of the crack surface to be propagated before and after each crack propagation. Simultaneously, a piecewise interpolation method is used to approximate the stress intensity factor at the crack tip position after each load cycle. Specifically, for any two adjacent crack surfaces to be propagated, after determining the target crack length and equivalent stress intensity factor amplitude under these two crack surfaces, the cycle-by-cycle method can be used to apply loads one after another according to the preset cyclic load. At each load application, interpolation is performed within the target crack length of these two adjacent crack surfaces to determine the target crack propagation increment after each load application. Furthermore, based on the target crack propagation increment and the crack length before the load application, the current crack length after the current load application can be determined. Then, it can be determined whether the sum of the target crack propagation increments determined under the two crack surfaces to be propagated after the load is applied is greater than or equal to the preset crack propagation increment. If not, the next load can be applied, and the crack length of the next load cycle can be approximately calculated using the piecewise interpolation method until the sum of the target crack propagation increments reaches the preset crack propagation increment. This indicates that the crack tip position after the next crack propagation will enter the next crack surface to be propagated. Therefore, it is necessary to use the target crack length and equivalent stress intensity factor amplitude of the next crack surface to be propagated for interpolation to end the crack propagation on the two adjacent crack surfaces to be propagated. At the same time, the crack propagation path in the two crack surfaces to be propagated can be obtained based on the target crack length of the two adjacent crack surfaces to be propagated and the crack length determined after each load application.

[0082] For example, using the target crack length and equivalent stress intensity factor amplitude corresponding to the first crack surface to be expanded ( a 1, ), and the target crack length and equivalent stress intensity factor amplitude corresponding to the second crack surface to be expanded ( a 2, Using piecewise interpolation, the target crack propagation increment after each cyclic load application on the two crack surfaces to be propagated, as well as the current crack length under the target crack propagation increment, can be determined. That is, the crack length from the point where the crack propagation increment is calculated can be determined. a 1. Starting from the beginning, the current crack length is obtained after each application of cyclic load. a cur Until the current crack length is determined. a cur achieve a2. This indicates that the crack tip after the next crack propagation will enter the third crack surface to be propagated, therefore ( ) can be used. a 2, ), and the target crack length and equivalent stress intensity factor amplitude corresponding to the third crack surface to be expanded, ( a 3, The piecewise interpolation method was used to calculate the value from... a Starting with 2, the current crack length is obtained after each application of cyclic load. a cur Until the current crack length is determined. a cur achieve a 3. Continue in this manner until the crack propagation path in each pair of adjacent crack surfaces to be propagated is determined.

[0083] Understandably, for any two adjacent crack surfaces to be expanded, the determined crack propagation path within these two adjacent crack surfaces is the crack formation path in the latter of the two adjacent crack surfaces to be expanded. For example, the crack propagation path within the first crack surface to be expanded is the crack growth path from the crack tip of the first crack surface to the crack tip of the second crack surface.

[0084] In one embodiment, S106-2 described above can be implemented according to the following steps: S106-2-1: Take the target crack length at the crack tip coordinate of the first crack surface to be expanded as the current crack length, and determine the new cyclic load based on the recorded number of cyclic loads and the preset cyclic load.

[0085] Here, when simulating the crack propagation path on two crack surfaces to be propagated, the crack tip coordinates of the first crack surface to be propagated can be used as the starting point of the simulation, and the crack tip coordinates of the second crack surface to be propagated can be used as the ending point, thus obtaining the complete path propagation within the second crack surface. The recorded number of cyclic loads is used to indicate the total number of loads applied from the crack tip position of the first crack surface to the current crack propagation simulation. The new cyclic load is the load to be applied next.

[0086] In practice, for any two adjacent crack surfaces to be expanded, the target crack length at the crack tip coordinates of the former crack surface to be expanded can be used as the current crack length. a cur Simultaneously, the recorded number of cyclic loads can be obtained, and based on this number, the load spectrum of the preset cyclic load can be determined. a curThe load that needs to be applied on the basis of the previous load is used as a new cyclic load, thereby from... a cur Initially, a cycle-by-cycle method was used to simulate the new crack length after each applied load.

[0087] S106-2-2: Using the piecewise interpolation method, the interpolated stress intensity factor amplitude corresponding to the current crack length is determined based on the current crack length, the two target crack lengths, and the amplitudes of the two equivalent stress intensity factors.

[0088] Here, the interpolated stress intensity factor amplitude is used to indicate the equivalent stress intensity factor amplitude interpolated for the current crack length using a piecewise interpolation method.

[0089] In practical implementation, the interpolated stress intensity factor amplitude under the current crack length can be determined according to the following formula five: (Formula 5) in, This represents the crack length at the interpolated stress intensity factor amplitude that needs to be interpolated. Mathematically, it can be any position, but in reality, it is the sum of the lengths that expand with each load cycle. The current crack length can be determined each time. a cur . It can be the target crack length before the i-th crack propagation, which is also the target crack length in the crack tip coordinates of the first crack surface to be propagated among the two crack surfaces to be propagated; It can be the target crack length after the i-th crack propagation, which is also the target crack length in the crack tip coordinates of the latter crack surface to be propagated among the two crack surfaces to be propagated; For targeting The equivalent stress intensity factor amplitude obtained by interpolation, It can be The magnitude of the equivalent stress intensity factor at the location; It can be The magnitude of the equivalent stress intensity factor at that location.

[0090] Optionally, in Formula 5 above and You can also substitute it first. and The target stress intensity factor under maximum load is calculated using Formula 5 above. The interpolated stress intensity factor under maximum load. Simultaneously, the stress intensity factor in formula five above... and Substitution and The target stress intensity factor under minimum load is calculated. The interpolated stress intensity factor under minimum load. Then, according to The difference between the interpolated stress intensity factors under maximum and minimum loads determines the The magnitude of the equivalent stress intensity factor at that location.

[0091] like Figure 4 The diagram shown is a schematic representation of the crack length and interpolated stress intensity factor amplitude obtained by piecewise interpolation according to an embodiment of this application. Figure 4 It can be in Figure 3 The results are obtained by piecewise interpolation based on the various crack surfaces to be expanded shown, with the horizontal axis being... , a The vertical axis represents the crack length, and the vertical axis represents the stress intensity factor. K . Indicates the first n -1 times the target crack length corresponding to the crack surface obtained after crack propagation. Indicates in The magnitude of the equivalent stress intensity factor at the location; Indicates the first n -1 Target crack length obtained before crack propagation Indicates in The magnitude of the equivalent stress intensity factor at that location.

[0092] S106-2-3: Based on the new cyclic load and the previous cyclic load, as well as the interpolated stress intensity factor amplitude, determine the target crack propagation increment under the new cyclic load, and determine the new current crack length based on the target crack propagation increment and the current crack length.

[0093] In practice, the crack propagation rate under the new cyclic load can be calculated based on the relationship between the new and previous cyclic loads, as well as the amplitude of the interpolated stress intensity factor. For example, if the preset cyclic load is a constant amplitude cyclic load, it can be determined that the new cyclic load is equal to the previous cyclic load. In this case, there is no delay effect caused by overload, so the crack propagation rate can be directly determined using the Paris formula. Then, the target crack propagation increment under the new cyclic load can be determined based on this rate. Finally, the sum of the target crack propagation increment and the current crack length is taken as the new current crack length.

[0094] In one embodiment, the preset cyclic load may include a variable amplitude cyclic load; for example, the preset cyclic load may be... Figure 2The diagram shows a cyclic load including overload. Since overload affects the fatigue crack propagation rate, its influence must be fully considered when determining the target crack propagation increment. Therefore, for S106-2-3 above, steps A1 to A5 can be followed: A1: When the new cyclic load is greater than the previous cyclic load, the new cyclic load is determined as an overload load, and the overload stress intensity factor under the overload load is determined according to the preset overload ratio of the cyclic load and the maximum load.

[0095] Here, the overload stress intensity factor is used to indicate the stress intensity factor at the current crack length when an overload is applied. Overload ratio ,in, This indicates an overload, which can be determined based on the load spectrum of a preset cyclic load. This represents the maximum load used as a reference, which can also be determined based on the load spectrum of a preset cyclic load.

[0096] In practice, it can be determined whether the new cyclic load is greater than the previous cyclic load. If so, the new cyclic load can be identified as an applied overload. Then, the overload stress intensity factor can be determined based on the product of the preset overload ratio and the maximum load of the reference under the preset cyclic load. .

[0097] A2: Based on the overload stress intensity factor, the equivalent overload stress amplitude under overload load is determined by the interaction integral method.

[0098] Here, the equivalent overload stress amplitude is used to indicate the equivalent stress factor amplitude under overload. The overload stress intensity factor may include Type I overload stress intensity factor and Type II overload stress intensity factor.

[0099] In practical implementation, the interaction integral method can be used. Based on the minimum load in the preset cyclic load, the Type I and Type II target stress intensity factors at the current crack length under the minimum load are determined. Then, based on the Type I and Type II overload stress intensity factors in the overload stress intensity factors, as well as the Type I and Type II target stress intensity factors under the minimum load, the amplitudes of the Type I and Type II stress intensity factors under the overload load are determined. Based on these two stress intensity factor amplitudes and the above formula (Formula 4), the equivalent overload stress amplitude under the overload load is determined. .

[0100] A3: Determine the size of the first crack tip plastic zone under the overload load based on the equivalent overload stress amplitude, and determine the size of the second crack tip plastic zone under the current crack length based on the interpolated stress intensity factor amplitude.

[0101] In practical implementation, according to the Wheeler model, overload causes the formation of a large plastic zone at the crack tip. When the load amplitude decreases, a smaller plastic zone at the crack tip is generated compared to the overload moment. At this time, the fatigue crack propagation rate decreases, resulting in a delay phenomenon. Therefore, the fatigue crack propagation rate is related to the size of the plastic zone at the crack tip. Thus, to fully consider the delay phenomenon caused by overload, it is necessary to determine the crack propagation rate by combining the plastic zones at the crack tip under both overload and non-overload conditions. Therefore, in the presence of an overload, the size of the first plastic zone at the crack tip can be determined using the following formula six: (Formula Six) in, This indicates the size of the first crack tip plastic zone under overload. This is a preset coefficient that takes into account the thickness constraint effect for three-dimensional target engineering structures. Indicates the yield strength of the target engineering structure; This is the equivalent overload stress amplitude.

[0102] At the same time, the size of the second crack tip plastic zone can be determined according to the following formula seven: (Formula 7) in, Indicates the current crack length a cur The size of the second crack tip plastic zone below; Indicates the current crack length a cur The interpolated stress intensity factor amplitude.

[0103] A4: Based on the size of the first crack tip plastic zone and the current crack length, determine the size of the remaining crack tip plastic zone under overload, and based on the size of the remaining crack tip plastic zone and the size of the second crack tip plastic zone, determine the crack propagation rate.

[0104] A5: Determine the target crack propagation increment under the new cyclic load based on the crack propagation rate.

[0105] In practical implementation, the size of the remaining crack tip plastic zone can be determined according to the following formula eight: (Formula 8) in, Indicates the size of the remaining crack tip plastic zone under overload; This indicates the current crack length. This indicates the crack length under overload conditions. When the currently applied load is an overload, This can be the current crack length. For ease of understanding, as shown below... Figure 5 The diagram shown is a schematic representation of the crack tip plastic zone size, crack length, and remaining crack tip plastic zone size at an overload moment and the current moment, as provided in an embodiment of this application.

[0106] After determining the size of the crack tip plastic zone, it can be determined whether the size of the second crack tip plastic zone is smaller than the size of the remaining crack tip plastic zone (i.e., whether...). < If not, then the correction factor for the overload effect can be determined. It is 1, and then according to the correction factor And the stress intensity factor amplitude, to determine the crack propagation rate. ;in, C and m The material coefficient is determined in advance through experiments. This represents the stress intensity factor amplitude, where, under the current overload condition, This can be the equivalent overload stress amplitude; when the current load is a non-overload load. The interpolation stress intensity factor amplitude can be used. .

[0107] Furthermore, according to Formula Nine below, based on the crack propagation rate... Determine the target crack propagation increment: (Formula Nine) in, a Indicates the crack length. da Indicates the increment of the target crack propagation. T This indicates the number of recorded cyclic loads, in this application. dT =ΔT=1.

[0108] Or, in < In this case, it can be based on and Determine the correction factor for the overload effect. for: ;in, This represents the preset material coefficient. Then, based on Formula Nine above and the overload condition... Determine the target crack propagation increment.

[0109] In another embodiment, when the new cyclic load is not greater than the previous cyclic load, S106-2-3 above can be implemented according to the following steps B1 to B4: B1: If the new cyclic load is not greater than the previous cyclic load, determine the size of the third crack tip plastic zone under the current crack length based on the interpolated stress intensity factor amplitude.

[0110] In practice, if the new cyclic load is not greater than the previous cyclic load, it can be determined based on the current crack length. a cur Interpolated stress intensity factor amplitude According to Formula 7 above, determine the size of the third crack tip plastic zone at the current crack length.

[0111] B2: Obtain the size of the remaining crack tip plastic zone under the overload condition when there is an overload before the new cyclic load.

[0112] In practice, to avoid the impact of the delayed effect of the overload applied before the new cyclic load on crack propagation, even if the new cyclic load is not greater than the previous cyclic load, it can be determined whether an overload has been applied before the new cyclic load; if not, it can be directly determined. If the value is 1, then the target crack propagation increment under the new cyclic load can be determined by referring to the content described in the above embodiments.

[0113] If so, then there is an overload that has already been applied, and the remaining crack tip plastic zone size determined under the most recently applied overload can be obtained.

[0114] B3: Determine the crack propagation rate based on the size of the plastic zone at the third crack tip and the size of the remaining plastic zone at the crack tip.

[0115] In practice, it can be determined whether the size of the third crack tip plastic zone is smaller than the size of the remaining crack tip plastic zone. If not, the correction factor for the overload effect can be determined. The coefficient is set to 1, and the crack propagation rate is determined based on this coefficient; if it is 1, then the crack propagation rate under the currently applied cyclic load can be determined. for: and based on this Determine the crack propagation rate.

[0116] B4: Determine the target crack propagation increment under the new cyclic load based on the crack propagation rate.

[0117] In practice, the interpolated stress intensity factor amplitude under the new cyclic load can be... And the determined crack propagation rate, substituted into Formula 9 above, yields the target crack propagation increment under the new cyclic load.

[0118] S106-2-4: Increment the number of cyclic loads and determine whether the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment.

[0119] For example, after obtaining the new current crack length, the sum of the determined target crack propagation increments in the two crack surfaces to be propagated can be determined, and it can be determined whether this sum is greater than or equal to the preset crack propagation increment. If so, it can be determined that the crack propagation path simulation in the two crack surfaces to be propagated has been completed, and the crack propagation path in the two crack surfaces to be propagated can be obtained. At the same time, the next set of two adjacent crack surfaces to be propagated can be determined, and the crack propagation path simulation between these two adjacent crack surfaces to be propagated can continue. That is, if so, the next set of two adjacent crack surfaces to be propagated can be determined, and then the step of "taking the target crack length under the crack tip coordinates of the previous crack surface to be propagated as the current crack length" can be returned, until the crack path simulation between each set of two adjacent crack surfaces to be propagated is completed, or until the current crack length determined at any time is greater than the target length.

[0120] If not, it means that the simulation of the crack propagation path in the two crack surfaces to be propagated has not yet been completed, and S106-2-5 can be executed as follows.

[0121] S106-2-5: If not, return to the step of determining a new cyclic load based on the recorded number of cyclic loads and the preset cyclic load, until the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment, and obtain the crack propagation path in the two crack surfaces to be propagated.

[0122] In practice, if the sum of the target crack propagation increments in the two crack surfaces to be propagated is less than the preset crack propagation increment, the process can return to the step "determine the new cyclic load based on the recorded number of cyclic loads and the preset cyclic load" in S106-2-1 above. This determines the new load to be applied next, and the current crack length is determined based on the new load using a piecewise interpolation method. This process continues until the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment. This yields the crack propagation path in the two crack surfaces, allowing the simulation of the crack propagation path between the next set of two adjacent crack surfaces to be propagated.

[0123] S106-3: Determine the crack propagation path under a preset cyclic load based on the crack propagation paths in every two adjacent crack surfaces to be propagated, and determine the correlation between crack length and load cycle number based on the crack lengths determined in every two adjacent crack surfaces to be propagated and the number of load applications.

[0124] For example, after obtaining the crack propagation paths in every two adjacent crack surfaces to be propagated, these paths can be connected in the order of the crack surfaces to obtain the overall crack propagation path of the target engineering structure under a preset cyclic load. Simultaneously, a correlation between crack length and the number of load cycles can be constructed based on the determined crack lengths in every two adjacent crack surfaces and the total number of load applications.

[0125] Optionally, during the process of applying loads to any two adjacent crack surfaces to be expanded and determining the crack length after each load application, if the determined current crack length is found to be greater than the target length, then the application of loads and the updating of crack lengths after these two adjacent crack surfaces to be expanded, as well as the application of loads and the updating of crack lengths after subsequent adjacent crack surfaces to be expanded, can be stopped. The target length can be determined based on the initial crack length corresponding to the crack tip coordinates of the initial crack surface, and the product of a set number of times and a preset crack expansion increment. For example, the target length is the initial crack length plus the target product. The reason for stopping the application of loads when the current crack length is greater than the target length is that once the target length is exceeded, there are no crack surfaces to be expanded that meet the requirement of exceeding the target length, and therefore there is no corresponding target crack length and equivalent stress intensity factor amplitude to support interpolation calculations.

[0126] To facilitate understanding of the embodiments of this application, the following will describe the method for determining the overload fatigue crack propagation path and life based on extended finite element method provided by the embodiments of this application, in conjunction with the developed crack propagation simulation module and fatigue life calculation module. The crack propagation simulation module can automatically update the crack surface of arbitrary path and calculate the crack tip stress intensity factor. This module is developed from the static crack analysis function based on XFEM. First, a target engineering structure containing the initial crack surface is established and static numerical calculation is performed to obtain the displacement field and stress field of the finite element model under the current crack surface to be propagated. The target stress intensity factor is calculated using the interaction integral method, and the crack deflection angle is calculated according to the maximum circumferential tensile stress criterion. Then, according to the preset crack propagation increment, the new crack tip coordinates (i.e., crack tip coordinates) are calculated and the crack surface is updated. The above process is automatically repeated to realize the simulation of crack propagation. The finite element model of the target structure only needs to be provided initially, and only the crack surface needs to be updated during the subsequent crack propagation process. It is not necessary to modify the target structure model. Therefore, this crack propagation simulation method is simple and efficient. Compared to the built-in XFEM crack propagation module in existing ABAQUS, applying the XFEM static crack analysis function to crack propagation simulation not only effectively solves the problems of convergence difficulty and low efficiency, but also compensates for the deficiency of ignoring the crack tip enhancement function, resulting in more accurate calculation results. The fatigue life calculation module can obtain the relationship between crack length and the number of load cycles under constant or variable amplitude cyclic load spectra. Due to the use of a cycle-by-cycle method, overload effects can be considered. Based on the piecewise interpolation method and combined with the load spectrum, the size of the crack tip plastic zone and the interpolated stress intensity factor value under each load cycle can be calculated. By judging whether a delay phenomenon occurs, an appropriate fatigue crack propagation rate model is selected, and the crack propagation increment under each load cycle is calculated. The crack length and the number of load cycles are accumulated cycle by cycle. When the critical crack length (i.e., the target length) is reached, the fatigue life calculation ends.

[0127] like Figure 6 The diagram shown is a detailed flowchart of a method for determining the overload fatigue crack propagation path and life based on extended finite element method, provided in an embodiment of this application. Figure 6 In the simulation module, the execution flow is as follows: A target engineering structure containing an initial crack surface is established and static numerical calculations are performed, while parameters are initialized. The initialized parameters include: crack propagation number i=1, and a preset crack propagation increment. Δa Current crack length a cur = a 0 ( a 0 represents the initial crack length below the initial crack surface, and the number of load applications. k =1. Initial fatigue life value N f=0, the set number of crack propagation times N, and the cumulative deflection angle. =0, where the cumulative deflection angle is equal to the superimposed deflection angle under each crack propagation. Then, based on the numerical calculation results, the target stress intensity factor under the first crack propagation is determined. Crack deflection angle Cumulative deflection angle ( = Then, update the crack propagation count, i.e., i = i + 1. Check if i > N; if yes, then the crack propagation is considered complete. If not, calculate the new crack coordinates and update the crack surface to obtain the next crack surface to be propagated. Then, continue with numerical simulation calculations to determine the target stress intensity factor under the i-th crack propagation. Crack deflection angle Cumulative deflection angle ( = +……+ Then you can enter the fatigue life calculation module and initialize the cumulative crack propagation increment. =0. Simultaneously, the number of times the load is applied... k When =1, initialize the maximum load applied for the first time. = The purpose of setting the maximum load during initialization is to ensure that the first applied load is not an overload. Specifically, This is used to characterize the sum of the individual target crack propagation increments determined under the current two adjacent crack surfaces to be propagated. Then, it is determined whether... < Δa If not, the process can return to the step of updating the crack propagation count (i.e., i=i+1) and proceed to the next crack propagation; if yes, it can be determined whether to proceed based on the load spectrum of the preset cyclic load. > If the value is greater than the applied load, then the applied load can be determined to be an overload load, and the equivalent overload stress amplitude can then be calculated. , ,make = Determine the size of the remaining crack tip plastic zone under overload. and the size of the crack tip plastic zone at the current crack length. If the length is not greater than the specified value, then the current crack length is determined using piecewise interpolation. Interpolated stress intensity factor amplitude and at the current crack length a cur Dimensions of the plastic zone at the crack tip and the remaining crack tip plastic zone size under the most recently applied overload. Then determine if... < If so, then it can be made dT =ΔT=1, and according to the crack propagation rate formula under overload delay ( ), determine the first k Incremental target crack propagation under repeated cyclic loading ;in, This represents the correction factor based on the overload effect when the k-th applied cyclic load is an overload load. And the target crack propagation increment determined by Formula 9 above. If Not less than Then it can make dT =ΔT=1, and according to the crack propagation rate formula under non-overload delay ( ), determine the first k Incremental target crack propagation under repeated cyclic loading ;in, This represents the correction factor based on the overload effect at the k-th applied cyclic load. The target crack propagation increment is determined by Formula 9 above. Then the cumulative crack propagation increment can be updated. (Right now = + ), and update the crack length (i.e. Furthermore, it can be determined whether... < ;in, = a 0+N× Δa This represents the target length. If so, the next load application can proceed, updating the load application count (i.e., ...). k = k +1), return to the execution judgment "whether Less than Δa The steps of "". If Not less than Then the final crack length can be determined. a = Fatigue life N f = k End the process.

[0128] To further illustrate the effectiveness of the method for determining overload fatigue crack propagation path and life based on extended finite element method provided in this application, this application has also conducted verification in different dimensions. First, the accuracy of the stress intensity factor calculated in this application is verified, specifically for hybrid model cracks (i.e., cracks including Type I and Type II), in situations such as... Figure 7The stress intensity factor of the double oblique crack plate with a central circular hole shown is calculated. Figure 7 The dimensions of the plate with the double oblique crack in the circular hole (i.e., the red line segment in the figure) are: 2 s =80mm, 2 w =40mm B =1mm, diameter of the center hole d =10mm, initial crack length is 2a; initial crack deflection angle is... θ .in, s Indicates length, w Indicates width, B Indicates thickness, Figure 7 In this context, σ represents a fixed applied load. For the initial crack inclination angles, respectively... θ =30° and θ For the two cases with an angle of 45°, the stress intensity factor at different initial crack lengths was calculated using the numerical calculation method of this application. K I and K II (The numerical calculation method of this application) K I and K II (Defined as a numerical solution), and compared with the analytical solution obtained by manual calculation. As shown in Figure 8, this is a schematic diagram comparing a numerical solution and an analytical solution provided in an embodiment of this application. Figure 8 The horizontal axis represents the crack length. a With width w The ratio (i.e.) a / w The vertical axis represents the stress intensity factor. K The unit is megapascal meter (Mpa) mm 1 / 2 ).according to Figure 5 It can be seen that the numerical solution agrees well with the theoretical solution, and the maximum error does not exceed 5%. Therefore, the numerical calculation method proposed in this application can ensure the accuracy of the calculation of the crack tip stress intensity factor for mixed-mode cracks.

[0129] Secondly, to verify the accuracy of this application's prediction of mixed-mode crack propagation paths, tests were conducted at... Figure 9a Provided non-porous type modified three-point bending specimens and Figure 9b The crack propagation path was verified on a modified three-point bending specimen with a provided hole type. Figure 9a and Figure 9b middle, a 0 represents the initial crack length. d This represents the distance from the initial offset crack to the center of the specimen. w Indicates width,s Indicates length, P Indicates the applied external pressure. B Indicates thickness. Furthermore, Figure 9b The specimen contains three circular holes, with the distance between each pair of holes being 50.8 mm and 50.8 mm. The distance between the topmost hole and the top of the specimen is 31.75 mm. For ease of explanation, the modified three-point bending specimens with different configurations are numbered as shown in Table 1 below. d This represents the distance from the initial offset crack to the center of the specimen. a 0 represents the initial crack length.

[0130] (Table 1)

[0131] Based on Table 1, it can be seen that, for Figure 9a The non-porous specimens shown illustrate three types. d and a The possible combinations of values ​​for 0 are defined as types I through III; for Figure 9b The perforated specimens shown illustrate three types. d and a The possible combinations of values ​​for 0 are defined as types IV to VI. Using the method proposed in this application, crack propagation paths of specimens with various configurations are simulated; using the ABAQUS built-in method in the prior art, crack propagation paths of specimens with various configurations are simulated; and using artificial experiments, crack propagation paths of specimens with various configurations are simulated (i.e., experimental results). The three results are then compared. Figure 10a The diagram shows a comparison of the simulated paths constructed for types I to III. (Experimental Result, I) represents the crack propagation path obtained through artificial experimentation on the type I construction; (Results of this paper, I) represents the crack propagation path simulated on the type I construction using the method of this application; (ABAQUS Built-in Method, I) represents the crack propagation path simulated on the type I construction using the existing ABAQUS built-in method. The descriptions of other paths are similar to those for type I and will not be repeated here. Figure 10b The image shown is a schematic diagram comparing the simulation path construction results for types IV to VI. Figure 10b The paper also illustrates the use of the method of this application to achieve different crack propagation increments Δ. a (i.e. Δ) a =1mm, Δ a =4mm and Δ a Simulation results at 10mm. Based on Figure 10a and Figure 10bIt can be seen that the crack propagation path simulated using the method of this application agrees well with the experimental results, while the results obtained using the ABAQUS built-in method show a large deviation from the experimental results. Furthermore, in actual simulations, the ABAQUS built-in method often suffers from severe computational non-convergence problems, while the method of this application only requires fewer iterations to obtain the final solution.

[0132] Furthermore, using the same computer and the same mesh finite element model, the comparison of the simulation time and crack propagation length calculated by the method in this application and the built-in ABAQUS method is shown in Table 2 below: (Table 2)

[0133] As can be seen from Table 2, the time required by the method in this application is significantly less than that of the built-in ABAQUS method. Therefore, the method in this application has higher computational efficiency and better robustness and efficiency.

[0134] To calculate the fatigue crack propagation life considering overload effects, in the case of... Figure 11 Based on the centrally cracked plate specimen shown, crack propagation simulations were conducted using the methods of this application and experimental methods under different overload cycles, single-cycle overload simulations at different overload intervals, and simulations at different overload ratios. R OL The crack propagation was simulated and compared using a single-cycle overload, and the results were obtained. Figures 12a-12c The comparison chart shown. Figures 12a-12c In this paper, numerical results represent simulation results obtained using the method described in this application, and experimental results represent simulation results obtained using the experimental method. p Indicates the overload interval. q The vertical axis represents the number of overload cycles. a Indicates crack length, horizontal axis N Indicates the number of times the load was applied. According to Figures 12a-12c It can be seen that the numerical results of fatigue life calculated under different cyclic overload load spectra in this application are in good agreement with the experimental results, which shows the effectiveness and accuracy of the method in this application in fatigue life calculation considering overload effects.

[0135] To demonstrate the engineering applicability of the method described in this application, the following is presented: Figure 13a Taking the I-beam structure with joints as an example, crack propagation was simulated using body-shell coupling technology, and fatigue life under different cyclic overload load spectra was calculated. Figure 13a I-beam structures can be either Type A or Type B, the difference between the two types being the location of the cracks. a 0 represents the initial crack length, and ρ represents the radius of curvature.P Indicates the applied pressure. t w Indicates the thickness of the web. t f Indicates the flange thickness. For example... Figure 13b The figure shows a schematic diagram of a finite element model of an I-beam structure with joints constructed using a body-shell coupling technique. In this model, the crack propagation zone (i.e., the I-beam region) uses smaller-sized body elements, while the non-propagation zone uses larger-mesh shell elements. This not only simplifies modeling but also greatly improves computational efficiency.

[0136] like Figure 14a The image shown is a comparison of the results obtained from crack propagation simulation of the I-beam structure under type A. Figure 14a The diagram includes a comparison of numerical results obtained by simulating crack propagation of an I-beam structure of type A using the method of this application (i.e., the results in this paper), results obtained by experimental methods (i.e., the experimental results), and results from published literature in the prior art (i.e., the literature results (1996)). Figure 14a In this context, AI and A-II represent two thicknesses under type A. Regarding the front and back sides of the experimental results, since the I-beam is a three-dimensional structure with both front and back sides, the experimental results provide results for both sides. For example... Figure 14b The image shown is a comparison of the results obtained from crack propagation simulation of the I-beam structure under type B. Figure 14b The diagram includes a comparison of numerical results obtained by simulating crack propagation in an I-beam structure of type B using the method of this application (i.e., the results in this paper), results obtained by experimental methods (i.e., the experimental results), and results from published literature in the prior art (i.e., the literature results (1996)). Figure 14a and Figure 14b As can be seen, the numerical results obtained from the simulation in this application are basically consistent with the experimental results, and have higher accuracy than the results in existing literature. Therefore, crack propagation simulation based on the method of this application can effectively prevent cracks from damaging important components in the structure to a certain extent, while achieving accurate prediction of crack propagation paths, and has important guiding significance for the damage tolerance design of structures.

[0137] Finally, for the aforementioned I-beam structure, the fatigue life under different load spectra can also be calculated using the method of this application. For example... Figure 15a The diagram shown is a comparison of calculation results under constant amplitude cyclic loading. Figure 15aThe diagram includes a comparison of the fatigue life calculation results (i.e., the results AI, A-II, BI, B-II) obtained by using the method of this application to calculate the fatigue life of I-beam structures of types A and B at two thicknesses, and the results of published literature in the prior art for I-beam structures of types A and B at two thicknesses (i.e., the results of literature (1996) AI, A-II, BI, B-II). Figure 15a As can be seen, the calculation results of this application under constant amplitude cyclic loading agree well with the results in the literature, thus demonstrating the accuracy of the method in this application for predicting the fatigue life of complex practical engineering structures. Figure 15b The figure shown is a comparison of fatigue life calculation results under different overload cycles. q Indicates the number of overload cycles. Figure 15b This includes calculation results obtained by using the method of this application to calculate the fatigue life of I-beam structures under different overload cycles. Based on Figure 15b It is known that fewer overload cycles (e.g., 1, 5, 10, 20) can often delay crack propagation (the delay effect of 20 cycles is minimal), extending fatigue life; however, excessive overload cycles (e.g., 50 cycles) will reduce fatigue life. Figure 15c The figure shown is a comparison of fatigue life calculation results under single-cycle overload with different overload intervals. p Indicates the overload interval. Figure 15c This includes calculation results obtained by using the method of this application to calculate the fatigue life of I-beam structures under single-cycle overload with different overload intervals. Based on Figure 15c It is evident that both too few and too many overload intervals will weaken the hysteresis effect caused by overload. For example... Figure 15d The figure shown is a comparison of fatigue life calculation results under single-cycle overload with different overload ratios. R OL Indicates the overload ratio. Figure 15d This includes calculation results obtained by using the method of this application to calculate the fatigue life of I-beam structures under single-cycle overload with different overload ratios. Based on Figure 15d It is known that for single-cycle overload with different overload ratios, an overload ratio within a suitable range can significantly increase the fatigue life of the structure. Figures 15a-15d In the middle, vertical axis a Both represent crack length, and the horizontal axis represents the crack length. N Each indicates the number of times the load was applied.

[0138] In summary, this application proposes a numerical method based on XFEM capable of simulating hybrid-mode crack propagation paths and calculating fatigue life considering overload effects. The corresponding functions are implemented through secondary development based on ABAQUS, ensuring the accuracy of calculating the crack tip stress intensity factor, predicting crack propagation paths, and calculating overload fatigue life. Specifically, this application first designs a crack surface update method based on XFEM, realizing automatic simulation of crack propagation. Since this method does not rely on complex level set traversal algorithms, it has high computational efficiency and good robustness. Moreover, the method in this application does not suffer from computational non-convergence issues and does not require simplification of the displacement enhancement mode of XFEM. The crack tip stress intensity factor can be accurately calculated through interaction integrals, laying the foundation for accurately predicting the propagation path of hybrid-mode cracks. Furthermore, based on a period-by-period algorithm using piecewise interpolation, combined with a fatigue crack propagation rate model considering overload effects, the high-cycle fatigue crack propagation life of structures under cyclic overload load spectra can be accurately calculated. Finally, combined with body-shell coupling technology, it is applicable to the evaluation of fatigue crack propagation life of practical engineering structures under complex loads, showing promising engineering application prospects.

[0139] Those skilled in the art will understand that, in the above-described method of the specific implementation, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0140] Based on the same inventive concept, this application also provides an apparatus for determining the overload fatigue crack propagation path and life based on extended finite element method, which corresponds to the method for determining the overload fatigue crack propagation path and life based on extended finite element method. Since the principle of the apparatus in this application is similar to the method for determining the overload fatigue crack propagation path and life based on extended finite element method described above, the implementation of the apparatus can refer to the implementation of the method, and the repeated parts will not be described again.

[0141] like Figure 16 The diagram shown is a schematic of a device for determining the overload fatigue crack propagation path and life based on the extended finite element method, according to an embodiment of this application. The device includes: The construction module 1601 is used to construct a finite element model including the crack surface to be expanded for the target engineering structure; the finite element model also includes multiple element nodes. The first determining module 1602 is used to determine the displacement field corresponding to the finite element model by using the element decomposition method, based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded in the finite element model. The second determining module 1603 is used to determine the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type, respectively, based on the displacement field and using the interaction integral method. The third determining module 1604 is used to determine the crack deflection angle based on the target stress intensity factor, and to determine the new crack tip coordinates and the new crack surface to be expanded based on the crack deflection angle and the preset crack propagation increment. The loop module 1605 is used to return to the step of using the element decomposition method to determine the displacement field corresponding to the finite element model based on the first additional displacement degree of freedom of each first element node in the crack tip region corresponding to the crack tip coordinate of the crack surface to be expanded, until the crack expansion number reaches the set number, and each crack surface to be expanded is obtained. The fourth determining module 1606 is used to determine the crack propagation path and the relationship between crack length and load cycle number under a preset cyclic load by using a piecewise interpolation method based on the crack tip coordinates of each crack surface to be propagated and the target stress intensity factor; the preset cyclic load includes a variable amplitude cyclic load.

[0142] In one possible implementation, the first determining module 1602 is specifically used for: In the finite element model, each first element node is located within the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded; in the finite element model, each second element node is located within the determined crack surfaces to be expanded; using the element decomposition method, the displacement field corresponding to the finite element model is determined based on the displacement degrees of freedom of each element node, the first additional displacement degrees of freedom of each first element node, and the second additional displacement degrees of freedom of each second element node.

[0143] In one possible implementation, the second determining module 1603 is specifically used for: Based on the displacement field, the stress field corresponding to the finite element model is determined; using the interaction integration method, based on the displacement field, the stress field, and the auxiliary fields corresponding to the open crack type and the sliding crack type respectively, the interaction integrals corresponding to the crack tip coordinates under the open crack type and the sliding crack type are determined; based on the interaction integrals and the maximum load under the preset cyclic load, the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the sliding crack type is determined.

[0144] In one possible implementation, the fourth determining module 1606 is specifically used for: For any two adjacent crack surfaces to be expanded, the interaction integral method is used to determine the equivalent stress intensity factor amplitude corresponding to the target crack length in the crack tip coordinates of the two crack surfaces to be expanded, based on the minimum load in the preset cyclic load and the target stress intensity factor corresponding to the two crack surfaces to be expanded. Based on the target crack length, the equivalent stress intensity factor amplitude, and the preset cyclic load, the piecewise interpolation method is used to determine the target crack expansion increment after each cyclic load is applied in the two crack surfaces to be expanded and the current crack length under the target crack expansion increment, until the sum of the target crack expansion increments in the two crack surfaces to be expanded is greater than or equal to the preset crack expansion increment, thus obtaining the crack expansion path in the two crack surfaces to be expanded. Based on the crack expansion path in every two adjacent crack surfaces to be expanded, the crack expansion path under the preset cyclic load is determined, and based on the crack lengths determined in every two adjacent crack surfaces to be expanded and the number of load applications, the correlation between crack length and the number of load cycles is determined.

[0145] In one possible implementation, the fourth determining module 1606 is specifically used for: The target crack length at the crack tip coordinates of the first of the two crack surfaces to be expanded is taken as the current crack length. A new cyclic load is determined based on the recorded number of cyclic loads and the preset cyclic load. Using a piecewise interpolation method, the interpolated stress intensity factor amplitude corresponding to the current crack length is determined based on the current crack length, the two target crack lengths, and the amplitudes of the two equivalent stress intensity factors. The target crack length under the new cyclic load is determined based on the new cyclic load, the previous cyclic load, and the interpolated stress intensity factor amplitude. The target crack propagation increment is set, and a new current crack length is determined based on the target crack propagation increment and the current crack length. The number of cyclic loads is incremented by one, and it is determined whether the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment. If not, the process returns to the step of determining a new cyclic load based on the recorded number of cyclic loads and the preset cyclic load, until the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment, thus obtaining the crack propagation path in the two crack surfaces to be propagated.

[0146] In one possible implementation, the fourth determining module 1606 is specifically used for: When the new cyclic load is greater than the previous cyclic load, the new cyclic load is determined as an overload load. Based on the overload ratio of the preset cyclic load and the maximum load, the overload stress intensity factor under the overload load is determined. Based on the overload stress intensity factor, the equivalent overload stress amplitude under the overload load is determined using the interaction integral method. Based on the equivalent overload stress amplitude, the size of the first crack tip plastic zone under the overload load is determined, and based on the interpolated stress intensity factor amplitude, the size of the second crack tip plastic zone at the current crack length is determined. Based on the first crack tip plastic zone size and the current crack length, the remaining crack tip plastic zone size under the overload load is determined, and based on the remaining crack tip plastic zone size and the second crack tip plastic zone size, the crack propagation rate is determined. Based on the crack propagation rate, the target crack propagation increment under the new cyclic load is determined.

[0147] In one possible implementation, the fourth determining module 1606 is specifically used for: If the new cyclic load is not greater than the previous cyclic load, determine the size of the third crack tip plastic zone at the current crack length based on the interpolated stress intensity factor amplitude; if there is an overload before the new cyclic load, obtain the size of the remaining crack tip plastic zone under the overload; determine the crack propagation rate based on the size of the third crack tip plastic zone and the size of the remaining crack tip plastic zone; determine the target crack propagation increment under the new cyclic load based on the crack propagation rate.

[0148] The processing flow of each module in the device and the interaction flow between each module can be referred to the relevant descriptions in the above method embodiments, and will not be detailed here.

[0149] Based on the same technical concept, embodiments of this application also provide a computer device. (Refer to...) Figure 17 The diagram shown is a structural schematic of a computer device provided in an embodiment of this application, comprising: The processor 1701, memory 1702, and bus 1703 are included. Memory 1702 stores machine-readable instructions that can be executed by the processor 1701. The processor 1701 executes the machine-readable instructions stored in memory 1702. When the machine-readable instructions are executed by the processor 1701, the processor 1701 performs the steps S101 to S106 described above.

[0150] The aforementioned memory 1702 includes a main memory 1721 and an external memory 1722. The main memory 1721, also known as internal memory, is used to temporarily store the computational data in the processor 1701, as well as the data exchanged with external memory such as a hard disk. The processor 1701 exchanges data with the external memory 1722 through the main memory 1721. When the computer device is running, the processor 1701 and the memory 1702 communicate through the bus 1703, so that the processor 1701 executes the execution instructions mentioned in the above method embodiments.

[0151] This application also provides a computer-readable storage medium storing a computer program. When a processor runs this computer program, it executes the steps of the method described in the above-described method embodiments for determining the overload fatigue crack propagation path and life based on extended finite element method. The storage medium can be a volatile or non-volatile computer-readable storage medium.

[0152] This application also provides a computer program product carrying program code. The program code includes instructions that can be used to execute the steps of the method for determining the overload fatigue crack propagation path and life based on extended finite element method described in the above method embodiments. For details, please refer to the above method embodiments, which will not be repeated here. This computer program product can be implemented specifically through hardware, software, or a combination thereof. In one optional embodiment, the computer program product is specifically embodied as a computer storage medium; in another optional embodiment, the computer program product is specifically embodied as a software product, such as a software development kit (SDK), etc.

[0153] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the several embodiments provided in this application, it should be understood that the disclosed device and method can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division; in actual implementation, there may be other division methods. Furthermore, multiple units or components may be combined, or some features may be ignored or not executed. Another point is that the displayed or discussed mutual coupling or direct coupling or communication connection may be through some communication interface; the indirect coupling or communication connection of devices or units may be electrical, mechanical, or other forms.

[0154] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0155] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0156] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a processor-executable, non-volatile, computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0157] Finally, it should be noted that the above-described embodiments are merely specific implementations of this application, used to illustrate the technical solutions of this application, and not to limit them. The scope of protection of this application is not limited thereto. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features, within the scope of the technology disclosed in this application. Such modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for determining the overload fatigue crack propagation path and life based on extended finite element method, characterized in that, include: For the target engineering structure, a finite element model is constructed, including the crack surface to be expanded; the finite element model also includes multiple element nodes. Using the element decomposition method, the displacement field corresponding to the finite element model is determined based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded. Based on the displacement field, the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type is determined by the interaction integral method. Based on the target stress intensity factor, the crack deflection angle is determined, and based on the crack deflection angle and the preset crack propagation increment, the new crack tip coordinates and the new crack surface to be propagated are determined. Returning to the step of using the element decomposition method, determining the displacement field corresponding to the finite element model based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded, until the crack expansion number reaches the set number, and obtaining each crack surface to be expanded; For any two adjacent crack surfaces to be expanded, the interaction integral method is used to determine the equivalent stress intensity factor amplitude corresponding to the target crack length under the crack tip coordinates of the two crack surfaces to be expanded, based on the minimum load in the preset cyclic load and the target stress intensity factor corresponding to the two crack surfaces to be expanded. The preset cyclic load includes a variable amplitude cyclic load; The target crack length at the crack tip coordinate of the first crack surface to be expanded is taken as the current crack length, and a new cyclic load is determined based on the recorded number of cyclic loads and the preset cyclic load. Using a piecewise interpolation method, the interpolated stress intensity factor amplitude corresponding to the current crack length is determined based on the current crack length, the two target crack lengths, and the amplitudes of the two equivalent stress intensity factors. If the new cyclic load is greater than the previous cyclic load, the new cyclic load is determined to be an overload load, and the overload stress intensity factor is determined based on the overload ratio of the preset cyclic load and the maximum load. Based on the overload stress intensity factor, the equivalent overload stress amplitude is determined using the interaction integral method. Based on the equivalent overload stress amplitude, determine the size of the first crack tip plastic zone under the overload load, and based on the interpolated stress intensity factor amplitude, determine the size of the second crack tip plastic zone under the current crack length; Based on the size of the first crack tip plastic zone and the current crack length, the size of the remaining crack tip plastic zone under the overload is determined, and the crack propagation rate is dynamically determined based on the relationship between the size of the remaining crack tip plastic zone and the size of the second crack tip plastic zone. Based on the crack propagation rate, determine the target crack propagation increment under the new cyclic load, and based on the target crack propagation increment and the current crack length, determine the new current crack length; Increment the number of cyclic loads by one, and determine whether the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment. If not, return to the step of determining a new cyclic load based on the recorded number of cyclic loads and the preset cyclic load, until the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment, and obtain the crack propagation path in the two crack surfaces to be propagated. Based on the crack propagation paths in every two adjacent crack surfaces to be propagated, the crack propagation path under the preset cyclic load is determined, and based on the individual crack lengths determined in every two adjacent crack surfaces to be propagated and the number of load applications, the correlation between crack length and the number of load cycles is determined.

2. The method according to claim 1, characterized in that, The element decomposition method is adopted to determine the displacement field corresponding to the finite element model based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded, including: In the finite element model, determine each first element node within the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded; In the finite element model, determine the second element node located in each of the determined crack surfaces to be expanded; The displacement field corresponding to the finite element model is determined by using the element decomposition method, based on the displacement degrees of freedom of each element node in the finite element model, the first additional displacement degrees of freedom of each first element node, and the second additional displacement degrees of freedom of each second element node.

3. The method according to claim 1, characterized in that, The step of determining the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type, respectively, based on the displacement field and using the interaction integration method, includes: Based on the displacement field, determine the stress field corresponding to the finite element model; The interactive integral method is adopted to determine the interactive integrals corresponding to the crack tip coordinates under the open crack type and the slip crack type, respectively, based on the displacement field, the stress field, the auxiliary fields corresponding to the open crack type and the slip crack type. Based on the interactive integral and the maximum load under the preset cyclic load, the target stress intensity factor corresponding to the crack tip coordinates under the opening crack type and the sliding crack type is determined respectively.

4. The method according to claim 1, characterized in that, The method further includes: If the new cyclic load is not greater than the previous cyclic load, the size of the third crack tip plastic zone at the current crack length is determined according to the amplitude of the interpolated stress intensity factor. In the case of an overload prior to the new cyclic load, the remaining crack tip plastic zone size under the overload load is obtained; The crack propagation rate is determined based on the size of the third crack tip plastic zone and the size of the remaining crack tip plastic zone; Based on the crack propagation rate, the target crack propagation increment under the new cyclic load is determined.

5. A device for determining the overload fatigue crack propagation path and life based on extended finite element method, characterized in that, include: A construction module is used to build a finite element model, including the crack surface to be expanded, for the target engineering structure; the finite element model also includes multiple element nodes. The first determining module is used to determine the displacement field corresponding to the finite element model by using the element decomposition method, based on the first additional displacement degrees of freedom of each first element node in the crack tip region corresponding to the crack tip coordinates of the crack surface to be expanded in the finite element model. The second determining module is used to determine the target stress intensity factor corresponding to the crack tip coordinates under the open crack type and the slip crack type, respectively, based on the displacement field and using the interaction integral method. The third determining module is used to determine the crack deflection angle based on the target stress intensity factor, and to determine the new crack tip coordinates and the new crack surface to be expanded based on the crack deflection angle and the preset crack propagation increment. The loop module is used to return to the step of using the element decomposition method to determine the displacement field corresponding to the finite element model based on the first additional displacement degree of freedom of each first element node in the crack tip region corresponding to the crack tip coordinate of the crack surface to be expanded, until the crack expansion number reaches the set number, and each crack surface to be expanded is obtained. The fourth determining module is used to determine the equivalent stress intensity factor amplitude corresponding to the target crack length under the crack tip coordinates of any two adjacent crack surfaces to be expanded by using the interaction integral method, based on the minimum load in the preset cyclic load and the target stress intensity factor corresponding to the two crack surfaces to be expanded. The preset cyclic load includes a variable amplitude cyclic load; The target crack length at the crack tip coordinate of the first crack surface to be expanded is taken as the current crack length, and a new cyclic load is determined based on the recorded number of cyclic loads and the preset cyclic load. Using a piecewise interpolation method, the interpolated stress intensity factor amplitude corresponding to the current crack length is determined based on the current crack length, the two target crack lengths, and the amplitudes of the two equivalent stress intensity factors. If the new cyclic load is greater than the previous cyclic load, the new cyclic load is determined to be an overload load, and the overload stress intensity factor is determined based on the overload ratio of the preset cyclic load and the maximum load. Based on the overload stress intensity factor, the equivalent overload stress amplitude is determined using the interaction integral method. Based on the equivalent overload stress amplitude, determine the size of the first crack tip plastic zone under the overload load, and based on the interpolated stress intensity factor amplitude, determine the size of the second crack tip plastic zone under the current crack length; Based on the size of the first crack tip plastic zone and the current crack length, the size of the remaining crack tip plastic zone under the overload is determined, and the crack propagation rate is dynamically determined based on the relationship between the size of the remaining crack tip plastic zone and the size of the second crack tip plastic zone. Based on the crack propagation rate, determine the target crack propagation increment under the new cyclic load, and based on the target crack propagation increment and the current crack length, determine the new current crack length; Increment the number of cyclic loads by one, and determine whether the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment. If not, return to the step of determining a new cyclic load based on the recorded number of cyclic loads and the preset cyclic load, until the sum of the target crack propagation increments in the two crack surfaces to be propagated is greater than or equal to the preset crack propagation increment, and obtain the crack propagation path in the two crack surfaces to be propagated. Based on the crack propagation paths in every two adjacent crack surfaces to be propagated, the crack propagation path under the preset cyclic load is determined, and based on the individual crack lengths determined in every two adjacent crack surfaces to be propagated and the number of load applications, the correlation between crack length and the number of load cycles is determined.

6. A computer device, characterized in that, include: The processor and the memory, wherein the memory stores machine-readable instructions executable by the processor, the processor is used to execute the machine-readable instructions stored in the memory, and when the machine-readable instructions are executed by the processor, the processor performs the steps of the method for determining the overload fatigue crack propagation path and life based on the extended finite element method as described in any one of claims 1 to 4.

7. A computer program product, comprising a computer program, characterized in that, When the computer program is run by the computer device, the computer device performs the steps of the method for determining the overload fatigue crack propagation path and life based on the extended finite element method as described in any one of claims 1 to 4.

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