Intelligent optimization design method and system for shape of crack arrest hole under complex load condition

Abstract

The invention discloses a crack arrest hole shape intelligent optimization design method and system under a complex load condition, and the method comprises the steps: generating stress field data of different hole shapes and loads through high-throughput finite element calculation, extracting a hole shape image, calculating a maximum SWT damage parameter, and constructing a training sample library; and a depth condition convolutional neural network is adopted to fuse geometric features and load coding, and an SWT damage parameter prediction agent model is established. And by taking a hole shape control point as a variable and taking the prediction model as a genetic algorithm objective function, optimizing the shape of the crack arrest hole so as to maximize the crack initiation life. Fatigue test verification is carried out by preparing an optimized hole shape test piece, the result shows that the crack arrest effect of a traditional round hole is remarkably improved through the method, an optimized design system self-adaptive to different working conditions is formed, the fatigue life of a repair structure can be greatly prolonged, and the method has important engineering value.

Description

Technical Field

[0001] The present invention belongs to the technical field of fatigue damage repair and life extension of metal structures, and specifically relates to a method and system for intelligent optimization design of crack arrest hole shapes under complex load conditions. Background Art

[0002] In the actual use of metal components, fatigue crack propagation is the main cause of their failure. For some critical structures, such as ships, bridges, aerospace components, etc., since replacement of components usually faces high time and economic costs, it is particularly important to study how to effectively stop fatigue crack propagation. At present, a method widely used in engineering practice is the crack stop hole method. This method removes a circular material area at the crack tip, converting the stress field close to the singularity at the crack tip into a limited stress concentration, thereby improving the fatigue life of the component after punching. In order to further enhance the crack arrest effect of the crack stop hole, researchers have made many improvements to the crack stop hole, such as creating auxiliary circular holes around the crack stop hole and creating two circular holes at the same time to optimize the shape of the crack stop hole. Although the previous traditional improvement strategy has achieved certain results in practical applications, it also has obvious shortcomings, which are mainly manifested in the following three points: First, the traditional crack arrest hole optimization strategy has limited crack arrest effect and can only stop the expansion of fatigue cracks for a short time, failing to significantly extend the fatigue life of the component.

[0003] Second, the traditional crack arrest hole optimization strategy targets the stress state of tensile loading (type I loading) and cannot consider the more complex stress state of mixed tensile and shear loading (type I-II mixed loading) in actual situations.

[0004] Third, the traditional crack stop hole optimization strategy relies on a lot of practical design experience, lacks clear design criteria, and is difficult to apply systematically.

[0005] Given the limitations of traditional crack stop hole optimization strategies, it is currently difficult to fundamentally address these issues. Therefore, it is particularly necessary to develop new crack stop hole shape optimization methods that overcome the three aforementioned shortcomings and more effectively improve the fatigue life of components.

[0006] As an emerging technology, intelligent design methods that combine machine learning and optimization algorithms have three outstanding advantages over traditional design strategies: First, the intelligent design method that combines machine learning and optimization algorithms can more easily find a crack-arresting hole shape that is close to the global optimal solution, significantly improving the crack-arresting effect.

[0007] Second, the intelligent design method that combines machine learning with optimization algorithms can uniformly incorporate complex loading states into the optimization framework without the need to retrain the model, thereby achieving rapid design of the crack arrest hole shape under different loading conditions.

[0008] Third, the intelligent design method that combines machine learning with optimization algorithms can automatically generate optimized crack-stop hole shapes based on the optimization algorithms, avoiding dependence on rich design experience and mechanical knowledge, and greatly lowering the design threshold.

[0009] Therefore, how to apply the intelligent optimization method of crack arrest hole shape to the field of fatigue damage repair and life extension technology of metal structures, and thus improve the fatigue life of metal engineering components, has become a topic that urgently needs in-depth research. Summary of the Invention

[0010] The technical problem to be solved by the present invention is to address the deficiencies in the above-mentioned existing technologies and provide a method and system for intelligent optimization design of crack stop hole shapes under complex load conditions. The method integrates high-throughput finite element calculations, machine learning agent models, optimization algorithms and experimental verification to solve the technical problems of the limitations of existing crack stop hole design methods under complex load conditions, achieve global optimization of the geometric morphology of crack stop holes under complex working conditions, and significantly improve the crack propagation inhibition efficiency.

[0011] The present invention adopts the following technical solutions: A method for intelligent optimization design of crack arrest hole shape under complex load conditions includes the following steps: Perform high-throughput finite element calculations to generate stress fields for different arrest hole shapes and loading conditions, extract arrest hole shape images, calculate the maximum SWT damage parameter of the structure that characterizes fatigue performance, extract binary topological images reflecting the hole geometry characteristics, and establish a training sample database containing various hole shapes and loading conditions; A deep conditional convolutional neural network architecture is constructed to couple the geometric features of the crack arrest hole with the load condition encoding through a feature fusion mechanism to build a predictive proxy model for SWT damage parameters. The predictive proxy model is then trained using a training sample database. Taking the control points of the crack stop hole contour as the design variables and the trained prediction agent model as the objective function of the genetic algorithm, the crack stop hole shape is iteratively optimized to maximize the crack initiation life under complex fatigue loading conditions.

[0012] Preferably, the high-throughput finite element calculation is performed as follows: Compact tensile shear specimens containing cracks are used to simulate different crack loading states. A crack arrest hole shape consisting of random control points and cubic spline interpolation curves is created at the crack tip. Random loading angles and load magnitudes are also assigned to the specimens. Finite element software is used for automated batch modeling to achieve high-throughput finite element analysis and obtain damage parameters that characterize the fatigue performance of the structure. .

[0013] Preferably, a reference circle with a radius of 2 mm is established with the crack tip as the origin, and 5 radial control points with an initial interval of 72° are set. Each control point has a random perturbation space with a radius of [1 mm, 3 mm] and an angle of [-14.4°, 14.4°]. The control points are connected by a cubic spline interpolation curve to construct a continuous hole profile, and random loading conditions are applied simultaneously to cover type I, type II and composite load conditions.

[0014] Preferably, the random loading condition is , .

[0015] Preferably, the damage parameter for:

[0016] in, is the maximum cyclic stress, is the strain amplitude, is the elastic modulus, 、 are fatigue strength and ductility coefficient, respectively. 、 is the material property index, is the number of cycles to fatigue failure.

[0017] Preferably, the binarized topological image is input into the constructed deep conditional convolutional neural network architecture, the loading angle and the maximum loading size, and the maximum SWT damage parameter of the structure is output; The Adam optimizer is used for end-to-end training. The constructed training sample database is used to control the generalization performance of the model through the early stopping mechanism to obtain a prediction agent model.

[0018] Preferably, the deep conditional convolutional neural network structure includes a convolution layer, a decoding layer for processing loading conditions, and a fully connected layer for predicting the maximum SWT damage parameter of the structure; the convolution layer is used to extract the geometric features of the hole shape, the maximum load size and angle are processed through the fully connected layer, the geometric features and the load features are spliced ​​and integrated, and finally the regression prediction layer composed of the fully connected layer outputs the predicted value of the maximum SWT damage parameter.

[0019] Preferably, the crack stop hole contour control points are used as design variables, the trained prediction agent model is used as the objective function of the genetic algorithm, and the crack stop hole shape is iteratively optimized, specifically: Generate 20 random hole-shaped individuals that meet the geometric constraints as the initial population, and use the set of their coordinate values ​​as genes; The maximum SWT damage parameter of each hole type under the target load is predicted by cCNN as the fitness value; The individuals with the lowest maximum SWT damage parameters in the top 20% are selected and crossover and mutation operations are performed through gene recombination and the introduction of random perturbations of radius and angle to maintain the adaptability and diversity of the population; 100 generations of evolutionary cycles were executed to make the individuals in the population gradually converge to the global optimal hole shape, and the crack arrest hole shape with the minimum maximum SWT damage parameter was obtained.

[0020] Preferably, the design variables are the coordinates of the control points, and the individual genes are the coordinate sets corresponding to the five control points; the offspring individuals are obtained by randomly selecting the gene positions of the parent individuals and crossing them; the mutation operation is to randomly increase the radius and angle fluctuations of the coordinate points of the newly generated offspring individuals.

[0021] In a second aspect, an embodiment of the present invention provides a system for intelligent optimization design of crack stop hole shapes under complex load conditions, comprising: The parameter module performs high-throughput finite element calculations, generates stress fields for different arrest hole shapes and loading conditions, extracts arrest hole shape images, calculates the maximum SWT damage parameter of the structure that characterizes fatigue performance, extracts binary topological images reflecting the hole geometry characteristics, and establishes a training sample database containing various hole shapes and loading conditions; The network module builds a deep conditional convolutional neural network architecture, couples the geometric features of the crack arrest hole with the load condition encoding through a feature fusion mechanism, builds a prediction agent model for SWT damage parameters, and trains the prediction agent model using a training sample database; The output module uses the control points of the crack stop hole contour as the design variables and the trained prediction agent model as the objective function of the genetic algorithm to iteratively optimize the crack stop hole shape to maximize the crack initiation life under complex fatigue load conditions.

[0022] In the third aspect, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the intelligent optimization design method for the shape of crack-stop holes under complex load conditions are implemented.

[0023] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, comprising a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for intelligent optimization design of crack stop hole shapes under complex load conditions.

[0024] In the fifth aspect, a chip includes a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the steps of the intelligent optimization design method for the shape of crack stop holes under complex load conditions are implemented.

[0025] In a sixth aspect, an embodiment of the present invention provides an electronic device, comprising a computer program, which, when executed by the electronic device, implements the steps of the above-mentioned method for intelligent optimization design of crack stop hole shapes under complex load conditions.

[0026] Compared with the prior art, the present invention has at least the following beneficial effects: A method for intelligent optimization design of crack stop hole shapes under complex load conditions combines high-throughput finite element calculations, deep learning, and genetic algorithms to form a closed-loop optimization system. High-throughput finite element calculations solve the problem of insufficient samples in traditional methods by batch-generating stress field data for multiple hole shape-load combinations, providing a physically realistic training basis for proxy models. Deep conditional convolutional neural networks couple geometric and load features through a feature fusion mechanism, achieving high-precision prediction of SWT damage parameters and avoiding the simplified assumptions of traditional mechanical models for complex loads. The genetic algorithm uses the proxy model as the objective function and searches for the global optimal hole shape through iterative evolution, overcoming the local optimal limitations of empirical design. The method of the present invention achieves adaptive optimization of the shape of crack stop holes under complex loads through the collaboration of data-driven and physical models, significantly improving the prediction and design efficiency of crack initiation life.

[0027] Furthermore, the simulation of compact tensile shear specimens can cover mixed loads of type I-II, and the hole shape is constructed using random control points and spline curves to ensure that the database covers a diverse range of geometry and load combinations, enhancing the generalization ability of the proxy model.

[0028] Furthermore, the physical rationality of the reference circle and the perturbation space constraint control points, the cubic spline ensures the smoothness of the hole shape and avoids stress concentration. At the same time, the random load covers common engineering working conditions, improving the universality of the optimization results.

[0029] Furthermore, the load range (800-1800 N) and angle (0°-90°) are set based on typical engineering load spectra to ensure that the training data matches the actual working conditions and avoid over-design or under-design. Furthermore, the SWT damage parameter integrates the relationship between stress-strain amplitude and fatigue life to quantify the crack initiation resistance, which has a clear physical meaning and is suitable as the optimization target of the genetic algorithm.

[0030] Furthermore, the Adam optimizer and early stopping mechanism balance training efficiency and generalization, and the feature fusion architecture (convolutional layer + fully connected layer) effectively integrates multi-source information to improve prediction accuracy.

[0031] Furthermore, the adaptive crossover and mutation operations (e.g., radius / angle perturbations) of the genetic algorithm maintain population diversity, avoid premature convergence, and ensure the search for the global optimal solution.

[0032] It can be understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0033] In summary, the method of the present invention breaks through the empirical dependence and load limitations of traditional crack arrest hole design by combining data-driven modeling with intelligent optimization algorithms, realizes adaptive optimization of hole shape under complex working conditions, and significantly extends fatigue life; its systematic and automated features greatly reduce the design threshold and have important engineering value.

[0034] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0036] Figure 1 is a flow chart of the present invention; Figure 2 Schematic diagram of the compact tensile-shear specimen structure (left) and the actual loading and crack-stopping state (right) used in the present invention; Figure 3 Schematic diagram of the method for generating random crack stop holes and the collected binary images; Figure 4 This is a diagram of the deep conditional convolutional neural network model used in the present invention; Figure 5 This is a flow chart of the genetic algorithm used in the present invention.

[0037] Figure 6 A three-dimensional modeling diagram of the fixture used for the high cycle fatigue test verification of the present invention; Figure 7A schematic diagram of a computer device provided in accordance with an embodiment of the present invention; Figure 8 The present invention is a block diagram of an electronic device according to an embodiment of the present invention.

[0038] Among them, 60. Computer device; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / Utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. DETAILED DESCRIPTION

[0039] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0040] In the description of the present invention, it is to be understood that the terms “include” and “comprise” indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0041] It should also be understood that the terms used in the present specification are only for the purpose of describing particular embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, the singular forms "a", "an", and "the" are intended to include the plural forms unless the context clearly indicates otherwise.

[0042] It should be further understood that the term "and / or" as used in the present specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items. For example, A and / or B may represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0043] It should be understood that although the terms "first," "second," and "third" may be used to describe preset ranges in embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are merely used to distinguish one preset range from another. For example, without departing from the scope of embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0044] The word "if," as used herein, may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting," depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to the determination" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)," depending on the context.

[0045] The accompanying drawings illustrate various schematic diagrams of structures according to embodiments disclosed herein. These figures are not drawn to scale; for clarity, some details are exaggerated and some details may be omitted. The shapes of the various regions and layers shown in the figures, as well as their relative sizes and positional relationships, are merely exemplary and may deviate in practice due to manufacturing tolerances or technical limitations. Those skilled in the art may design regions / layers with different shapes, sizes, and relative positions as needed.

[0046] The present invention provides an intelligent optimization design method for the shape of crack stop holes under complex load conditions. First, high-throughput finite element calculations are performed to generate stress fields with different crack stop hole shapes and load conditions, and images of the crack stop hole shapes are extracted. The maximum Smith-Watson-Topper damage parameter (SWT) of the structure that characterizes fatigue performance is calculated, and a training sample database containing multiple hole shapes and load conditions is established. Secondly, a deep conditional convolutional neural network architecture is constructed, and the geometric features of the crack stop holes are coupled with the load condition encoding through a feature fusion mechanism to construct a prediction agent model for the SWT damage parameters, thereby achieving efficient and high-precision fatigue performance prediction. Then, the crack stop hole contour control points are used as design variables, and the trained SWT damage parameter prediction model is used as the objective function of the genetic algorithm. The crack stop hole shape is iteratively optimized to maximize the crack initiation life under complex fatigue load conditions. Finally, a compact tensile-shear specimen containing the optimized crack stop hole is prepared and a high-cycle fatigue test is carried out to verify the effectiveness of the design. The present invention integrates calculation and experimental methods to significantly improve the fatigue crack arrest effect of traditional circular crack arrest holes. It establishes a complete set of calculation and optimization method systems, adaptively provides the optimal crack arrest hole shape design scheme for different load conditions, and greatly extends the fatigue life of the repaired metal structure, which has important engineering application value.

[0047] Example 1 See also Figure 1 The present invention provides an intelligent optimization design method for the shape of a crack stop hole under complex load conditions, comprising the following steps: S1. Build high-throughput finite element calculations and datasets; Finite element software is used to automatically batch-build parametric models of compact tensile-shear specimens containing cracks, and random crack arrest holes are constructed at the crack tip based on the generation mechanism of the polar coordinate system: A reference circle with a radius of 2 mm was established with the crack tip as the origin, and five radial control points with an initial interval of 72° were set. Each control point had a random perturbation space with a radius of [1 mm, 3 mm] and an angle of [-14.4°, 14.4°] (positive for clockwise, negative for counterclockwise). The control points were connected using a cubic spline interpolation curve to construct a continuous hole profile.

[0048] The model is subjected to random loading conditions simultaneously ( , ) covers Type I, Type II and combined load conditions.

[0049] Finite element analysis is used to obtain key parameters that characterize the fatigue performance of the structure: Damage parameters based on the Smith-Watson-Topper criterion , whose expression is:

[0050] in, is the maximum cyclic stress, is the strain amplitude, is the elastic modulus, 、 are fatigue strength and ductility coefficient, respectively. 、 is the material property index, is the number of cycles to fatigue failure.

[0051] The maximum SWT damage parameter calculated at all material points of the structure is obtained through high-throughput finite element calculation results as a key parameter for evaluating the fatigue performance of the structure; a 1120×128 pixel binary image containing the hole geometry characteristics and the relative position of the crack is simultaneously generated and combined with the corresponding loading conditions to form a comprehensive training sample database.

[0052] S2. Construct a deep conditional convolutional neural network (cCNN) model, taking the image and loading conditions in step S1 as input and the corresponding maximum SWT damage parameter of the structure as output. After training, a fast calculation proxy model is obtained. A deep prediction model with a multimodal input structure is constructed, whose architecture includes an image processing branch, a load condition branch, a feature fusion module and a regression prediction layer.

[0053] The image processing branch uses a convolution module to extract the hole geometry features, and the load condition branch processes the maximum load size ( ) and angle ( ), and combined with the feature fusion module to splice and integrate the geometric features and load features, and finally the regression prediction layer composed of a fully connected network outputs the maximum SWT damage parameter prediction value.

[0054] The Adam optimizer is used for end-to-end training. The dataset constructed in step S1 is set to 80% training set and 20% validation set. The early stopping mechanism is used to control the generalization performance of the model, thereby obtaining a fast-calculating proxy model.

[0055] S3, genetic algorithm (GA) driven pass optimization; The surrogate model in step S2 is used as the objective function of the genetic algorithm, and the random coordinate points of the crack arrest hole are used as the design variables to optimize the hole shape that can minimize the maximum SWT damage parameter of the structure under different loading states. The evolutionary optimization framework with cCNN as the surrogate model is established as follows: S301, generating 20 random hole-shaped individuals that meet geometric constraints as the initial population, and using the set of their coordinate values ​​as genes; S302, using cCNN to quickly predict the maximum SWT damage parameter of each hole type under the target load as the fitness value; S303, select the individuals with the lowest maximum SWT damage parameters in the top 20% and perform crossover and mutation operations through gene recombination and introduction of random perturbations of radius and angle to maintain the adaptability and diversity of the population; S304, executing 100 generations of evolutionary cycles to make the individuals in the population gradually converge to the global optimal hole shape, and obtain the crack arrest hole shape with the minimum maximum SWT damage parameter.

[0056] S4. Compact tension-shear high-cycle fatigue tests are carried out on CTS samples with optimized hole profiles to verify the validity of the design results.

[0057] The crack arrest hole shapes optimized for different loading conditions were created at the crack tip of the compact tensile-shear specimen using the wire cutting method, and high-cycle fatigue tests were carried out under the corresponding loading conditions. The initial fatigue life of the experiment was compared with that of the compact tensile-shear specimen containing a single circular hole to verify the effectiveness of the optimization results.

[0058] Those skilled in the art will appreciate that various aspects of the present invention may be implemented as systems, methods, or program products. Accordingly, various aspects of the present invention may be implemented in the following forms: entirely in hardware, entirely in software (including firmware, microcode, etc.), or in a combination of hardware and software, collectively referred to herein as "circuits," "modules," or "platforms."

[0059] Example 2 The present invention provides an intelligent optimization design system for the shape of crack stop holes under complex load conditions. The system can be used to implement the above-mentioned intelligent optimization design method for the shape of crack stop holes under complex load conditions. Specifically, the intelligent optimization design system for the shape of crack stop holes under complex load conditions includes a parameter module, a network module and an output module.

[0060] Among them, the parameter module performs high-throughput finite element calculations, generates stress fields for different crack arrest hole shapes and loading conditions, extracts crack arrest hole shape images, calculates the maximum SWT damage parameter of the structure that characterizes fatigue performance, extracts binary topological images reflecting the geometric characteristics of the hole shape, and establishes a training sample database containing various hole shapes and loading conditions; The network module builds a deep conditional convolutional neural network architecture, couples the geometric features of the crack arrest hole with the load condition encoding through a feature fusion mechanism, builds a prediction agent model for SWT damage parameters, and trains the prediction agent model using a training sample database; The output module uses the control points of the crack stop hole contour as the design variables and the trained prediction agent model as the objective function of the genetic algorithm to iteratively optimize the crack stop hole shape to maximize the crack initiation life under complex fatigue load conditions.

[0061] Example 3 The present invention provides a terminal device, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, graphics processing units (GPU), tensor processing units (TPU), digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to implement corresponding method processes or corresponding functions; the processor described in the embodiment of the present invention can be used for the operation of the intelligent optimization design method of the crack stop hole shape under complex load conditions, including: High-throughput finite element calculations are performed to generate stress fields for different crack stop hole shapes and load conditions, extract crack stop hole shape images, calculate the maximum SWT damage parameter of the structure that characterizes fatigue performance, extract binary topological images reflecting the geometric characteristics of the hole shape, and establish a training sample database containing various hole shapes and load conditions; construct a deep conditional convolutional neural network architecture, couple the geometric characteristics of the crack stop hole with the load condition encoding through a feature fusion mechanism, construct a prediction agent model for the SWT damage parameters, and use the training sample database to train the prediction agent model; use the crack stop hole contour control points as design variables, and use the trained prediction agent model as the objective function of the genetic algorithm to iteratively optimize the crack stop hole shape to maximize the crack initiation life under complex fatigue load conditions.

[0062] See also Figure 7 The terminal device is a computer device. The computer device 60 of this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable by the processor 61. When executed by the processor 61, the computer program 63 implements the intelligent optimization design method for the shape of crack stop holes under complex load conditions in the embodiment. To avoid repetition, the details are not described here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the intelligent optimization design system for the shape of crack stop holes under complex load conditions in the embodiment. To avoid repetition, the details are not described here.

[0063] The computer device 60 may be a desktop computer, a notebook computer, a PDA, a cloud server, or other computing devices. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. It will be understood by those skilled in the art that Figure 7 This is merely an example of the computer device 60 and does not constitute a limitation of the computer device 60 . The computer device 60 may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0064] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, a graphics processing unit (GPU), a tensor processing unit (TPU), a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc.

[0065] The memory 62 may be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. equipped on the computer device 60.

[0066] Furthermore, the memory 62 may include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is about to be output.

[0067] See also Figure 8The terminal device is an electronic device 600, which is implemented as a general-purpose computing device. The components of the electronic device may include, but are not limited to, at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including the storage unit 620 and the processing unit 610), and a display unit 640.

[0068] The storage unit stores program codes, which can be executed by the processing unit 610, so that the processing unit 610 performs the steps according to various exemplary embodiments of the present invention described in the above method section of this specification. For example, the processing unit 610 can perform the following steps: Figure 1 Follow the steps shown in .

[0069] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 6201 and / or a cache memory unit 6202 , and may further include a read-only memory unit (ROM) 6203 .

[0070] The storage unit 620 may also include a program / utility 6204 having a set (at least one) of program modules 6205, such program modules 6205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0071] Bus 630 may represent one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0072] The electronic device 600 may also communicate with one or more external devices 700 (e.g., a keyboard, a pointing device, a Bluetooth device, etc.), one or more devices that enable a user to interact with the electronic device 600, and / or any device that enables the electronic device 600 to communicate with one or more other computing devices (e.g., a router, a modem). Such communication may occur via an input / output interface 650. Furthermore, the electronic device 600 may also communicate with one or more networks (e.g., a local area network, a wide area network, and / or a public network, such as the Internet) via a network adapter 660. The network adapter 660 may communicate with other modules of the electronic device 600 via a bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules may be used in conjunction with the electronic device 600, including but not limited to microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0073] Example 4 The present invention also provides a storage medium, specifically a computer-readable storage medium. The computer-readable storage medium is a memory device in a terminal device, used to store programs and data. It is understood that the computer-readable storage medium herein may include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. It may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for being loaded and executed by a processor. These instructions may be one or more computer programs (including program code). It should be noted that more specific examples of the computer-readable storage medium herein include: an electrical connection having one or more wires, a portable disk, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination thereof.

[0074] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, which carry readable program code. Such propagated data signals can take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than a readable storage medium, which can send, propagate, or transmit programs for use by or in conjunction with an instruction execution system, device, or device. The program code contained on the readable storage medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, radio frequency, etc., or any suitable combination of the above.

[0075] The program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, and the like, as well as conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a stand-alone software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device via any type of network, including a local area network or a wide area network, or may be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0076] The processor may load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the method for intelligent optimization design of crack stop hole shape under complex load conditions in the above embodiment; the processor may load and execute the following steps: High-throughput finite element calculations are performed to generate stress fields for different crack stop hole shapes and load conditions, extract crack stop hole shape images, calculate the maximum SWT damage parameter of the structure that characterizes fatigue performance, extract binary topological images reflecting the geometric characteristics of the hole shape, and establish a training sample database containing various hole shapes and load conditions; construct a deep conditional convolutional neural network architecture, couple the geometric characteristics of the crack stop hole with the load condition encoding through a feature fusion mechanism, construct a prediction agent model for the SWT damage parameters, and use the training sample database to train the prediction agent model; use the crack stop hole contour control points as design variables, and use the trained prediction agent model as the objective function of the genetic algorithm to iteratively optimize the crack stop hole shape to maximize the crack initiation life under complex fatigue load conditions.

[0077] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0078] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0079] Take aluminum alloy (7075-T651) as an example.

[0080] (1) The present invention uses compact tensile shear specimens to simulate actual complex loading conditions, with dimensions such as Figure 2 As shown in (left), the specimen thickness is 1 mm, and there is a through crack of 42.6 mm*0.2 mm in the middle of the specimen.

[0081] To control the variables of complex loading, random loading conditions are applied simultaneously ( , ) Covers type I, type II and composite load conditions, with constant amplitude loading and fixed load ratio ,Right now The generation method of crack stop hole is as follows: Figure 3 As shown, the present invention generates different crack stop hole shapes based on control points, and the control points are connected by cubic spline interpolation curves to generate random crack stop hole shapes.

[0082] Specifically, a hole generation mechanism based on a polar coordinate system was constructed at the crack tip. A reference circle with a radius of 2 mm was established with the crack tip as the origin. Five radial control points were set with an initial interval of 72°. Each control point had a random initial space with a radius of 1 to 3 mm and an angle of -14.4° to +14.4° (positive for counterclockwise, negative for clockwise). The number of control points can be greater than 4. In this example, the number is fixed to 5. The generated crack arrest hole penetrates the compact tensile shear specimen, as shown in the following figure. Figure 2 (right) As shown, it stops the growth of fatigue cracks. The finite element simulation uses a quadrilateral eight-node plane stress element.

[0083] By combining the commercial finite element software ABAQUS secondary development interface to write a Python language program, based on the crack stop hole generation mechanism, the finite element analysis of different crack stop holes can be automatically calculated in batches. At the same time, the Python program is used to post-process the finite element results to obtain the maximum SWT damage parameter of the structure and generate a binary image containing the crack and crack stop hole shape information, such as Figure 3 shown.

[0084] The collected pictures of different crack arrest holes, maximum SWT damage parameters and loading angles and maximum load size The conditions serve as the subsequent comprehensive training sample database.

[0085] (2) The cCNN model structure used in this invention can be found in Figure 4 The convolutional neural network part is used to extract multi-level features from image data, while the conditional input part processes additional conditional information and fuses it with the extracted features to finally perform regression prediction.

[0086] In this example, the network's convolutional layers include four. Each convolutional layer uses a 3x3 kernel with a stride of 1 and padding of 1 to maintain the image size. Each convolutional layer is followed by a ReLU activation function and a max pooling layer to gradually extract spatial features from the input image and reduce its size. Specifically, a 2x2 max pooling layer is used to halve the image size. cCNN differs from traditional convolutional neural networks in the introduction of conditional input.

[0087] In this example, the conditional input of the network consists of a 2D feature vector. This conditional information is mapped to a 16-dimensional feature space through a fully connected layer and then concatenated with the features extracted by the convolutional layer.

[0088] The concatenated features are further processed through three fully connected layers with a specific structure of <1024-512-64-1>, ultimately outputting a single prediction result: the maximum SWT damage parameter of the structure. During network training, the mean absolute error (MAE) loss function is used. The convolutional layers automatically adjust weights through backpropagation to minimize the loss function, thereby continuously optimizing feature extraction capabilities.

[0089] The conditional input, combined with convolutional features, enhances the network's adaptability to external conditions, enabling predictions for different loading states. The advantage of this network lies in its ability to simultaneously process image data and external condition information, enabling efficient and accurate regression predictions.

[0090] The Adam optimizer is used for end-to-end training. The dataset constructed in step (1) is set to 80% training set and 20% validation set. The generalization performance of the model is controlled by the early stopping mechanism, thereby obtaining a fast-calculating proxy model.

[0091] (3) The crack stop hole optimization genetic algorithm process used in the present invention can be found in Figure 5 During the optimization process, each individual represents a crack arrest shape, and the fitness is calculated based on the corresponding binary image. The fitness is determined by the maximum SWT prediction of the structure obtained by the cCNN model. The smaller the maximum SWT value, the longer the fatigue life of the individual and the higher its fitness.

[0092] First, 20 random hole-shaped individuals that meet geometric constraints are generated as the initial population, and the set of their coordinate values ​​is used as the gene; Secondly, the maximum SWT damage parameter of each hole type under the target load is quickly predicted by cCNN as the fitness value; Subsequently, the top 20% individuals with the lowest maximum SWT damage parameters were selected and subjected to a crossover operation using two-point gene recombination.

[0093] For each coordinate value in the newly generated gene sequence, a mutation operation is performed with a probability of 0.2. This mutation will produce random perturbations of the coordinate point with a radius of [-2mm, 2mm] and an angle of [-14.4°, +14.4°] to help avoid local convergence. Constraints are imposed on the individual genome after crossover and mutation to ensure that the radius of each control point is within the random space of [1mm, 3mm] and the angle is within the initial angle range of [-14.4°, +14.4°] (positive is counterclockwise, negative is clockwise) generated equidistantly around the circumference of the circle. Any results exceeding this range are directly capped.

[0094] Finally, 100 generations of evolutionary iterations were performed to make the individuals in the population gradually converge to the global optimal hole shape, and the crack arrest hole shape with the minimum structural maximum SWT damage parameter was obtained.

[0095] This individual is the optimal crack arrest hole shape designed. Through this optimization method, the present invention can quickly and accurately design the optimal crack arrest hole shape under different loading conditions based on the consideration of the structural fatigue performance, thereby effectively improving the fatigue strength of the structure, extending the service life, and reducing the risk of crack propagation.

[0096] (4) For the fixtures used in the high cycle fatigue test verification of the present invention, please refer to Figure 6 Design of multi-hole seat and fork-type pull head related to compact tensile shear specimen, by changing the installation angle of the specimen and the load size to achieve and of adjustment.

[0097] Single circular holes and optimized hole profiles can be fabricated at the crack tip of compact tensile shear specimens using wire cutting. The fork-shaped puller can be connected to an external high-cycle fatigue testing instrument, such as the QBG-100 high-frequency testing machine (Changchun Qianbang Testing Equipment Co., Ltd.).

[0098] High-cycle fatigue experiments were conducted to compare the fatigue life of single circular holes and optimized holes at crack initiation under different loading states, ultimately verifying the effectiveness of the crack arrest effect of the optimized crack arrest hole.

[0099] In summary, the method and system for intelligent optimization design of crack stop hole shape under complex load conditions of the present invention have the following beneficial effects and advantages: 1. This paper proposes an intelligent optimization design method for crack-stop hole shapes under complex load conditions. Using existing data samples, a high-precision deep conditional convolutional neural network structure is trained. This method can quickly obtain the desired crack-stop hole shape, significantly improving crack-stop effectiveness and reducing design time. This paper provides an effective design method for crack-stop hole shapes that effectively prevent cracks under complex load conditions in actual engineering.

[0100] 2. High-throughput finite element calculation combining control points and spline curves to generate the shape of the crack arrest hole automatically acquires large amounts of data in batches, providing a complete training database for machine learning.

[0101] 3. A rapid design method for crack arrest holes under complex load conditions using machine learning saves time compared to traditional simulation.

[0102] 4. The conditional convolutional neural network structure can simultaneously consider different loading conditions under complex loading states without the need to repeatedly establish a neural network model.

[0103] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0104] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0105] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professionals and technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0106] In the embodiments provided by the present invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For example, the division of the modules or units is merely a logical functional division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed can be through some interface, indirect coupling or communication connection of devices or units, and can be electrical, mechanical, or other forms.

[0107] The units described as separate components may or may not be physically separate, and 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 these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0108] In addition, the functional units in the various embodiments of the present invention may be integrated into a single processing unit, each unit may exist physically separately, or two or more units may be integrated into a single unit. The aforementioned integrated units may be implemented in the form of hardware or software functional units.

[0109] If the integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the process in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, it can implement the steps of the above-mentioned various method embodiments. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electric carrier signals and telecommunication signals.

[0110] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices, and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0111] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0112] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0113] The above content is only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for intelligent optimization design of crack stop hole shape under complex load conditions, characterized in that: The following steps are involved: Perform high-throughput finite element calculations to generate stress fields for different arrest hole shapes and loading conditions, extract arrest hole shape images, calculate the maximum SWT damage parameter of the structure that characterizes fatigue performance, extract binary topological images reflecting the hole geometry characteristics, and establish a training sample database containing various hole shapes and loading conditions; A deep conditional convolutional neural network architecture is constructed to couple the geometric features of the crack arrest hole with the load condition encoding through a feature fusion mechanism to build a predictive proxy model for SWT damage parameters. The predictive proxy model is then trained using a training sample database. Taking the control points of the crack stop hole contour as the design variables and the trained prediction agent model as the objective function of the genetic algorithm, the crack stop hole shape is iteratively optimized to maximize the crack initiation life under complex fatigue loading conditions.

2. The intelligent optimization design method for crack stop hole shape under complex load conditions according to claim 1 is characterized in that: The high-throughput finite element calculation is specifically as follows: Compact tensile shear specimens containing cracks are used to simulate different crack loading states. A crack arrest hole shape consisting of random control points and cubic spline interpolation curves is created at the crack tip. Random loading angles and load magnitudes are also assigned to the specimens. Finite element software is used for automated batch modeling to achieve high-throughput finite element analysis and obtain damage parameters that characterize the fatigue performance of the structure. .

3. The intelligent optimization design method for crack stop hole shape under complex load conditions according to claim 2 is characterized in that: A reference circle with a radius of 2 mm was established with the crack tip as the origin, and five radial control points with an initial interval of 72° were set. Each control point had a random perturbation space with a radius of [1 mm, 3 mm] and an angle of [-14.4°, 14.4°]. The control points were connected by a cubic spline interpolation curve to construct a continuous hole profile. Random loading conditions were applied simultaneously to cover type I, type II and combined load conditions.

4. The intelligent optimization design method for crack arrest hole shape under complex load conditions according to claim 3 is characterized in that: The random loading condition is , .

5. The intelligent optimization design method for crack arrest hole shape under complex load conditions according to claim 2 is characterized in that: Damage parameters for: in, is the maximum cyclic stress, is the strain amplitude, is the elastic modulus, 、 are fatigue strength and ductility coefficient, respectively. 、 is the material property index, is the number of cycles to fatigue failure.

6. The intelligent optimization design method for crack arrest hole shape under complex load conditions according to claim 1 is characterized in that: The binary topological image is input into the constructed deep conditional convolutional neural network architecture, along with the loading angle and maximum loading size, and the maximum SWT damage parameter of the structure is output; The Adam optimizer is used for end-to-end training. The constructed training sample database is used to control the generalization performance of the model through the early stopping mechanism to obtain a prediction agent model.

7. The intelligent optimization design method for crack arrest hole shape under complex load conditions according to claim 6 is characterized in that: The deep conditional convolutional neural network structure includes a convolutional layer, a decoding layer for processing loading conditions, and a fully connected layer for predicting the maximum SWT damage parameter of the structure; the convolutional layer is used to extract the geometric features of the hole shape, the maximum load size and angle are processed through the fully connected layer, the geometric features are spliced ​​and integrated with the load features, and finally the regression prediction layer composed of the fully connected layers outputs the predicted value of the maximum SWT damage parameter.

8. The intelligent optimization design method for crack stop hole shape under complex load conditions according to claim 1 is characterized in that: The control points of the crack stop hole contour are used as design variables, and the trained prediction agent model is used as the objective function of the genetic algorithm to iteratively optimize the crack stop hole shape. Specifically, Generate 20 random hole-shaped individuals that meet the geometric constraints as the initial population, and use the set of their coordinate values ​​as genes; The maximum SWT damage parameter of each hole type under the target load is predicted by cCNN as the fitness value; The individuals with the lowest maximum SWT damage parameters in the top 20% are selected and crossover and mutation operations are performed through gene recombination and the introduction of random perturbations of radius and angle to maintain the adaptability and diversity of the population; 100 generations of evolutionary cycles were executed to make the individuals in the population gradually converge to the global optimal hole shape, and the crack arrest hole shape with the minimum maximum SWT damage parameter was obtained.

9. The intelligent optimization design method for crack arrest hole shape under complex load conditions according to claim 8 is characterized in that: The design variables are the coordinates of the control points, and the individual genes are the coordinate sets corresponding to the five control points. The offspring individuals are obtained by randomly selecting the gene positions of the parent individuals and crossing them. The mutation operation is to randomly increase the radius and angle fluctuations of the coordinate points of the newly generated offspring individuals.

10. An intelligent optimization design system for crack arrest hole shape under complex load conditions, characterized by: include: The parameter module performs high-throughput finite element calculations, generates stress fields for different arrest hole shapes and loading conditions, extracts arrest hole shape images, calculates the maximum SWT damage parameter of the structure that characterizes fatigue performance, extracts binary topological images reflecting the hole geometry characteristics, and establishes a training sample database containing various hole shapes and loading conditions; The network module builds a deep conditional convolutional neural network architecture, couples the geometric features of the crack arrest hole with the load condition encoding through a feature fusion mechanism, builds a prediction agent model for SWT damage parameters, and trains the prediction agent model using a training sample database; The output module uses the control points of the crack stop hole contour as the design variables and the trained prediction agent model as the objective function of the genetic algorithm to iteratively optimize the crack stop hole shape to maximize the crack initiation life under complex fatigue load conditions.

Images