Method and system for analyzing surface layer cracking failure probability of thermal barrier coating

Abstract

The invention discloses a thermal barrier coating surface layer cracking failure probability analysis method and system, and relates to the technical field of data processing, the method comprises the following steps: establishing a three-dimensional finite element model of a thermal barrier coating, using an extended finite element method to simulate thermal stress and crack propagation behaviors under thermal cycle loading for the three-dimensional finite element model under thermal cycle loading conditions, and calculating the thermal barrier coating surface layer cracking failure probability. And obtaining a crack propagation path sequence set, carrying out state transition trend feature analysis, constructing a state transition trend feature set to carry out crack development prediction, and carrying out failure probability judgment through a crack tip critical J integral value to obtain a surface layer crack failure probability analysis result. According to the method, the technical problems that an existing method cannot accurately simulate the crack propagation process and the influence of the crack propagation process on coating failure, and the failure analysis precision is low are solved, and the technical effects that high-precision simulation and failure probability quantification of crack propagation behaviors are achieved through the propagation finite element method, complex working conditions are effectively coped with, and the failure analysis precision is improved are achieved.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, specifically to a method and system for analyzing the probability of cracking and failure of thermal barrier coating surfaces. Background Technology

[0002] Thermal barrier coatings (TBCs) are widely used in high-temperature components, such as aero-engine blades and gas turbine combustors, to protect the substrate material from high-temperature oxidation and thermal fatigue. However, TBCs are prone to surface cracking failure under thermal cycling conditions, severely affecting the service life and reliability of components. Existing methods for analyzing the probability of surface cracking failure of TBCs largely rely on experimental observation and empirical judgment, which have limitations such as high cost, lack of predictability, and difficulty in quantifying the dynamic process of crack propagation. In addition, traditional finite element methods require frequent mesh re-division when simulating crack propagation and cannot fully consider thermal stress, crack propagation, and the thermal mismatch effect between the coating and the substrate, resulting in inaccurate failure prediction results. Summary of the Invention

[0003] This application provides a method and system for analyzing the probability of cracking failure of thermal barrier coatings, which solves the technical problem that existing methods cannot accurately simulate the crack propagation process and its impact on coating failure, resulting in low accuracy in failure analysis.

[0004] The first aspect of this application provides a method for analyzing the probability of surface cracking failure of a thermal barrier coating. The method includes: establishing a three-dimensional finite element model of the thermal barrier coating, wherein the three-dimensional finite element model includes at least the thermophysical properties of the coating and the substrate, the coefficient of thermal expansion, the thermal conductivity, and thermal mismatch; setting thermal cycling loading conditions, wherein the thermal cycling loading conditions include at least a temperature range, a thermal gradient, and a cooling rate; using the extended finite element method under thermal cycling loading conditions, simulating the thermal stress and crack propagation behavior of the three-dimensional finite element model under thermal cycling load to obtain a set of crack propagation path sequences; traversing the set of crack propagation path sequences to perform state transition trend feature analysis, constructing a set of state transition trend features; predicting crack development based on the set of state transition trend features to obtain a set of crack development prediction results; obtaining the critical J-integral value at the crack tip, and judging the failure probability of the crack development prediction result set based on the critical J-integral value at the crack tip to obtain the surface cracking failure probability analysis result of the thermal barrier coating.

[0005] A second aspect of this application provides a system for analyzing the probability of cracking failure of a thermal barrier coating surface layer. The system includes: a finite element model building module for building a three-dimensional finite element model of the thermal barrier coating, wherein the three-dimensional finite element model includes at least the thermophysical properties of the coating and the substrate, the coefficient of thermal expansion, the thermal conductivity, and thermal mismatch; a thermal cycling loading condition setting module for setting thermal cycling loading conditions, wherein the thermal cycling loading conditions include at least a temperature range, a thermal gradient, and a cooling rate; and a crack propagation simulation module for simulating thermal cycling loads on the three-dimensional finite element model under thermal cycling loading conditions using the extended finite element method. The system employs a combination of methods: a thermal stress and crack propagation behavior analysis module to obtain a set of crack propagation path sequences; a state transition trend analysis module to traverse the set of crack propagation path sequences and perform state transition trend feature analysis to construct a set of state transition trend features; a crack propagation prediction module to predict crack propagation based on the set of state transition trend features and obtain a set of crack propagation prediction results; and a failure probability discrimination module to obtain the critical J-integral value at the crack tip and perform failure probability discrimination on the set of crack propagation prediction results based on the critical J-integral value at the crack tip, thereby obtaining the surface cracking failure probability analysis results of the thermal barrier coating.

[0006] One or more technical solutions provided in this application have at least the following technical effects or advantages:

[0007] This application provides a method and system for analyzing the probability of cracking failure of thermal barrier coatings, relating to the field of data processing technology. By combining the extended finite element method and state transition trend characteristic analysis, it accurately simulates the crack propagation process of thermal barrier coatings under thermal cycling loading, and determines the failure probability based on the critical J integral value at the crack tip, quantifying the impact of crack development on coating failure. This provides a more accurate analytical tool for the reliability assessment and life prediction of thermal barrier coatings, solving the technical problem that existing methods cannot accurately simulate the crack propagation process and its impact on coating failure, resulting in low failure analysis accuracy. It achieves high-precision simulation of crack propagation behavior and quantification of failure probability through the extended finite element method, effectively coping with complex working conditions and improving the accuracy of failure analysis. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 A schematic flowchart of a method for analyzing the probability of cracking failure of a thermal barrier coating surface layer is provided in an embodiment of this application.

[0010] Figure 2 This is a schematic diagram of a thermal barrier coating surface cracking failure probability analysis system provided in an embodiment of this application.

[0011] Figure labeling: 11 Finite element model establishment module, 12 Thermal cycling loading condition setting module, 13 Crack propagation simulation module, 14 State transition trend analysis module, 15 Crack propagation prediction module, 16 Failure probability discrimination module. Detailed Implementation

[0012] This application provides a method and system for analyzing the probability of cracking failure of thermal barrier coatings, which solves the technical problem that existing methods cannot accurately simulate the crack propagation process and its impact on coating failure, resulting in low accuracy in failure analysis.

[0013] 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 them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0014] It should be noted that the terms "first," "second," etc., in the specification 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 of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or server that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or modules not explicitly listed or inherent to such processes, methods, products, or devices.

[0015] Example 1, as Figure 1 As shown, this application provides a method for analyzing the probability of cracking failure of a thermal barrier coating surface layer, the method comprising:

[0016] P10: Establish a three-dimensional finite element model of the thermal barrier coating, wherein the three-dimensional finite element model includes at least the thermophysical properties of the coating and the substrate, the coefficient of thermal expansion, the thermal conductivity, and the thermal mismatch.

[0017] Furthermore, step P10 in this embodiment of the application also includes:

[0018] P11: Construct an initial three-dimensional geometric structure according to the preset substrate thickness, preset coating thickness, preset coating material type, and preset substrate material type; P12: Define the thermophysical properties, coefficient of thermal expansion, and thermal conductivity of the coating and substrate for the initial three-dimensional geometric structure to obtain the three-dimensional geometric structure; P13: Based on the thermal mismatch difference between the coating and the substrate, set the thermal boundary conditions and mechanical boundary conditions for the three-dimensional geometric structure, and perform finite element analysis to obtain the three-dimensional finite element model.

[0019] It should be understood that a detailed three-dimensional finite element model needs to be established first. This model aims to simulate the thermodynamic behavior and crack propagation of thermal barrier coatings (TBCS) under actual thermal cycling loads. To ensure the accuracy of the model, factors such as the thermophysical properties of the coating and substrate, coefficient of thermal expansion, thermal conductivity, and thermal mismatch need to be incorporated into the modeling process.

[0020] First, an initial three-dimensional geometry is constructed according to preset substrate thickness, coating thickness, coating material type, and substrate material type. This process is the starting point for establishing the finite element model, and its purpose is to determine the geometry and dimensions of the thermal barrier coating and the substrate based on actual engineering requirements and design parameters. For example, the coating thickness is usually determined based on its thermal insulation performance requirements and the actual application environment, while the substrate thickness depends on the structural strength and dimensional constraints of the protected component. The selection of coating material type and substrate material type is based on their thermophysical and mechanical properties, which directly affect the service life and reliability of the thermal barrier coating.

[0021] Next, the thermophysical properties, coefficients of thermal expansion, and thermal conductivity of the coating and substrate are defined for the initial three-dimensional geometry to obtain the three-dimensional geometry. Thermophysical properties refer to the physical properties exhibited by a material under thermal influence, including but not limited to specific heat capacity and thermal diffusivity. These properties determine the heat transfer and distribution of the material when the temperature changes. The coefficient of thermal expansion is a measure of the change in volume or length of a material when the temperature changes. For thermal barrier coatings, the difference in the coefficients of thermal expansion between the coating and the substrate is one of the main causes of thermal stress. Thermal conductivity reflects the material's ability to conduct heat, determining the rate and path of heat transfer between the coating and the substrate. By accurately defining these parameters, the finite element model can more realistically reflect the thermal behavior of the actual thermal barrier coating.

[0022] Finally, based on the thermal mismatch difference between the coating and the substrate, thermal and mechanical boundary conditions were set for the three-dimensional geometry, and finite element analysis was performed to obtain a three-dimensional finite element model. Thermal mismatch refers to the relative displacement and stress generated between the coating and the substrate due to their different coefficients of thermal expansion during temperature changes. This thermal mismatch is one of the important factors contributing to the failure of thermal barrier coatings. Thermal boundary conditions refer to the heat exchange between the model and the external environment; for example, the coating surface may be heated by high-temperature gases, while the substrate may be in contact with a cooling medium. Mechanical boundary conditions involve the mechanical constraints on the model, such as the substrate being fixed to a structure or the coating being subjected to external loads. By reasonably setting these boundary conditions and performing finite element analysis, the stress distribution, deformation, and crack initiation and propagation probability of the thermal barrier coating under thermal cycling loads can be calculated, thus providing detailed and accurate mechanical and thermal information for subsequent failure probability analysis.

[0023] P20: Set the thermal cycling loading conditions, which include at least the temperature range, thermal gradient, and cooling rate.

[0024] Specifically, setting thermal cycling loading conditions is one of the key steps in simulating actual working conditions using a three-dimensional finite element model. These conditions determine the temperature changes and thermal loads experienced by the thermal barrier coating in the actual working environment, directly affecting the thermal stress distribution between the coating and the substrate, crack propagation, and ultimately, the failure process. Therefore, setting these conditions requires comprehensive consideration of the coating's working environment and the thermal properties of the coating material.

[0025] First, the temperature range needs to be clearly defined. This range typically includes the minimum and maximum temperatures the coating may experience during thermal cycling. This temperature range should be set based on the actual operating environment, such as the temperature conditions of an aircraft engine or gas turbine. Coatings often need to withstand extreme high and low temperatures; temperature changes cause thermal expansion and contraction of the material, resulting in thermal stress. Setting an appropriate temperature range not only allows for accurate simulation of the thermal stress of the coating during actual operation but also helps researchers predict the aging and failure of the coating over long-term use.

[0026] Secondly, a thermal gradient is established to simulate the temperature distribution changes between the coating and the substrate. A thermal gradient typically refers to the temperature difference between the coating surface and the substrate. Due to differences in the thermophysical properties (such as thermal conductivity and coefficient of thermal expansion) between the coating and the substrate, temperature changes lead to inconsistent thermal expansion between them, thereby generating thermal stress within the coating. The magnitude and distribution of the thermal gradient have a significant impact on crack formation and propagation, especially under rapid changes between high and low temperatures. The difference in thermal expansion between the coating and the substrate can lead to stress concentration and may cause the coating to crack or peel off.

[0027] Furthermore, the setting of the cooling rate is equally crucial for the reliability assessment of thermal barrier coatings. During thermal cycling, the cooling rate describes how quickly the coating cools from a high temperature to a low temperature. Different cooling rates affect the stress distribution of the coating and the process of thermal stress accumulation. Rapid cooling usually leads to a larger thermal stress gradient because the difference in thermal expansion is more pronounced, which may promote crack initiation. Conversely, a slower cooling rate may help reduce thermal stress, but it is still necessary to comprehensively consider the possible changes in thermal stress during the cooling process and the fatigue behavior of the material.

[0028] Therefore, when setting thermal cycling loading conditions, it is necessary to consider the actual application temperature conditions, thermal stress distribution, and thermal properties of the coating material. By comprehensively considering these factors, the behavior of the coating under real-world conditions can be accurately simulated, providing an important basis for subsequent finite element analysis and failure probability assessment.

[0029] P30: Using the extended finite element method under thermal cyclic loading conditions, the thermal stress and crack propagation behavior of a three-dimensional finite element model are simulated to obtain a set of crack propagation path sequences.

[0030] Furthermore, step P30 in this embodiment of the application also includes:

[0031] P31: Obtain the initial crack location set of the three-dimensional finite element model under thermal cycling loading conditions; P32: Use the extended finite element method to introduce crack functions and crack propagation criteria, perform crack propagation on the initial crack location set according to the cycle period in the thermal cycling loading conditions, and record the crack propagation path to obtain the crack propagation path sequence set.

[0032] Optionally, the three-dimensional finite element model can be simulated under thermal cycling loading conditions using the extended finite element method (XFEM) to study the thermal stress and crack propagation behavior under thermal cycling loading and obtain a set of crack propagation path sequences.

[0033] First, the set of initial crack locations is obtained from the three-dimensional finite element model under thermal cycling conditions. Determining the initial crack locations is fundamental to crack propagation simulation. These locations are typically defined based on the coating's structural characteristics, material properties, and stress concentration areas in the actual operating conditions. For example, in thermal barrier coatings, cracks may initiate at the coating-substrate interface, in stress concentration areas within the coating, or at weak points caused by material defects. By analyzing the coating's geometry and material properties, combined with the stress distribution results obtained from finite element analysis, the initial crack locations can be reasonably determined. This set of initial crack locations will serve as the starting point for subsequent crack propagation simulations.

[0034] Next, the extended finite element method (EBM) is used to introduce crack functions and crack propagation criteria. The EBM is an effective tool for handling crack and irregular crack propagation, capable of tracking crack propagation without re-meshing. Crack functions describe the presence and propagation path of cracks, while crack propagation criteria determine under what conditions cracks will continue to propagate. Common crack propagation criteria include stress intensity factor criteria and J-integral criteria, which determine the critical conditions for crack propagation based on the fracture mechanics properties of the material. In this application, a suitable crack propagation criterion can be selected based on the material properties of the thermal barrier coating and the actual operating conditions, and then applied to the initial set of crack locations.

[0035] Subsequently, crack propagation simulations were performed on the initial set of crack locations according to the cycle periods specified in the thermal cycling loading conditions. In each thermal cycle, the thermal stress distribution was calculated based on the set temperature range, thermal gradient, and cooling rate, and the crack propagation behavior under thermal stress was simulated using crack propagation criteria. During the simulation, the crack propagation path was recorded, including crack length, direction, and propagation velocity. Through multiple cycles of simulation, a series of crack propagation paths were obtained, forming a set of crack propagation path sequences. These sequences reflect the crack development under different thermal cycle numbers, providing detailed data support for subsequent failure probability analysis.

[0036] P40: Traverse the set of crack propagation path sequences to perform state transition trend feature analysis and construct a set of state transition trend features.

[0037] Furthermore, step P40 in this embodiment of the application also includes:

[0038] P41: Extract the first crack propagation path sequence from the crack propagation path sequence set; P42: Traverse and extract the crack propagation step size and propagation direction in the first crack propagation path sequence to perform crack propagation trend feature analysis and determine the first propagation trend sub-feature; P43: Traverse and extract the crack morphology in the first crack propagation path sequence to perform crack morphology propagation trend feature analysis and determine the first crack morphology propagation trend sub-feature; P44: Combine the first propagation trend sub-feature and the first crack morphology propagation trend sub-feature to obtain the first state transition trend feature; P45: Traverse the crack propagation path sequence set to perform state transition trend feature analysis from crack propagation and crack morphology propagation to obtain the state transition trend feature set.

[0039] It should be understood that by performing detailed analysis on each sequence in the crack propagation path sequence set, characteristic information of crack propagation can be extracted, thereby providing data support for subsequent crack development prediction and failure probability analysis.

[0040] First, the first crack propagation path sequence is extracted from the crack propagation path sequence set. This set contains crack propagation path information under different thermal cycles, with each sequence recording the gradual propagation of the crack from its initial position. Extracting the first crack propagation path sequence is for detailed analysis of the crack propagation characteristics within this sequence. This path represents the entire process of crack propagation from its initial position under specific conditions, including each step and state of crack propagation.

[0041] Next, the crack propagation step size and direction are extracted from the first crack propagation path sequence to perform crack propagation trend feature analysis and determine the first propagation trend sub-features. The crack propagation step size refers to the distance the crack propagates in each thermal cycle, while the propagation direction reflects the crack's propagation path in three-dimensional space. During crack propagation, the crack typically propagates along a specific direction with a certain step size, and this propagation process is influenced by various factors (such as thermal stress and material properties). By analyzing the crack propagation step size and direction, the crack propagation trend can be identified, and the dynamic characteristics of crack propagation can be determined. These characteristics typically manifest as the crack propagation speed and the stability of the propagation direction. For example, a crack may propagate rapidly in some regions while remaining relatively stable in others; this trend can be used to predict the future development of the crack.

[0042] Then, the crack morphologies in the first crack propagation path sequence are extracted and analyzed to determine the sub-features of the first crack morphology propagation trend. Crack morphology includes the crack shape, branching, and stress concentration at the crack tip. Changes in crack morphology affect its propagation behavior; for example, crack branching may lead to multiple propagation paths, while the degree of stress concentration at the crack tip determines the driving force for crack propagation. By analyzing the propagation trend of crack morphology, the changing patterns of crack morphological characteristics at different stages can be obtained.

[0043] Next, the first propagation trend sub-feature and the first crack morphology propagation trend sub-feature are integrated to obtain the first state transition trend feature. The first state transition trend feature represents a comprehensive characteristic of the crack propagation process, taking into account multiple factors such as crack propagation step size, propagation direction, and morphological changes. This feature can comprehensively reflect the crack development trend under thermal cycling conditions and is a very important basis for crack failure prediction.

[0044] Finally, the set of crack propagation path sequences is traversed, and state transition trend characteristics are analyzed from two aspects: crack propagation and crack morphology propagation, to obtain a set of state transition trend characteristics. This process repeats the above analysis for all crack propagation path sequences, ultimately constructing a set of state transition trend characteristics that includes all crack propagation path sequences. This feature set can comprehensively and systematically reflect the various propagation modes and morphological changes that cracks may undergo under thermal cycling conditions, providing detailed data support for subsequent crack development prediction, failure probability assessment, and coating life prediction.

[0045] Furthermore, step P42 in this embodiment of the application also includes:

[0046] P42-1: Retrieve the spatiotemporal interactive crack propagation identification branch set, and perform crack propagation trend feature analysis on the crack propagation step size and propagation direction in the first crack propagation path sequence to obtain the first temporal propagation trend sub-feature and the first spatial propagation trend sub-feature; P42-2: Perform feature cross-fusion on the first temporal propagation trend sub-feature and the first spatial propagation trend sub-feature to obtain the first propagation trend sub-feature.

[0047] Optionally, the analysis process for the crack propagation trend characteristics in the first crack propagation path sequence can be further refined. By considering both the temporal and spatial dimensions of crack propagation, higher accuracy can be provided for predicting the crack propagation trend characteristics.

[0048] First, the spatiotemporal interactive crack propagation identification branch set is retrieved. This set contains crack propagation feature information in both time and space dimensions, used to identify key feature points and branch paths during crack propagation. Using this set, the crack propagation step size and propagation direction in the first crack propagation path sequence are analyzed. Crack propagation step size analysis focuses on the distance the crack propagates in each thermal cycle to obtain information on the crack propagation rate at different thermal cycle stages. This information reflects the crack propagation trend in the time dimension, including the crack propagation speed, periodicity, and dynamic characteristics of its changes; this is called the first temporal propagation trend sub-feature. Simultaneously, crack propagation direction analysis focuses on the path changes of the crack in three-dimensional space to obtain information on the crack propagation path at different spatial locations. This information reflects the crack propagation trend in the spatial dimension, including changes in crack morphology and whether the crack propagates along the coating surface or interface, etc.; this is called the first spatial propagation trend sub-feature.

[0049] Subsequently, the first temporal and first spatial crack propagation trend sub-features are cross-fused. This process aims to comprehensively analyze crack propagation features across time and space dimensions to obtain a more complete set of crack propagation trend features. Using mathematical models or algorithms, such as weighted average, principal component analysis, or other machine learning algorithms, the two sub-features are merged into a single comprehensive propagation trend sub-feature, thereby better reflecting the dynamic behavior of cracks during thermal cycling and fully considering the spatiotemporal interaction characteristics of crack propagation.

[0050] Ultimately, the comprehensive feature obtained through feature cross-fusion is called the first propagation trend sub-feature. It not only includes information on the crack propagation speed in the time dimension but also information on the crack path change in the spatial dimension. This process enhances the spatiotemporal analysis of crack propagation trends, enabling crack prediction to move beyond a single dimension and comprehensively consider crack propagation patterns from multiple perspectives. This provides a more detailed and reliable foundation for subsequent crack development prediction, failure probability analysis, and coating life prediction.

[0051] Furthermore, step P42-2 in the embodiments of this application also includes:

[0052] P42-21: Calculate the feature approximation coefficients of the first time-extended trend sub-feature and the first spatial-extended trend sub-feature to obtain a set of feature approximation coefficients; P42-22: Determine the time-guided matrix based on the set of feature approximation coefficients; P42-23: Use the time-guided matrix to perform feature cross-fusion on the first spatial-extended trend sub-feature to obtain the first extended trend sub-feature.

[0053] In one possible embodiment of this application, the feature cross-fusion process can be further refined by introducing feature approximation coefficients and a time-guided matrix to more accurately fuse the first temporal extended trend sub-features and the first spatial extended trend sub-features.

[0054] First, the feature approximation coefficients for the first temporal propagation trend sub-feature and the first spatial propagation trend sub-feature are calculated. For example, these coefficients can be calculated based on correlation analysis, principal component analysis, or other statistical methods to ensure they accurately reflect the relationship between the two sub-features. This step transforms the temporal and spatial features into quantifiable approximation coefficients, which represent the degree of influence of these features during crack propagation. Calculating these coefficients generates a set of feature approximation coefficients.

[0055] Next, a temporal guiding matrix is ​​determined based on the set of feature approximation coefficients. The temporal guiding matrix is ​​a matrix used to adjust and guide the feature fusion process; it is constructed by normalizing the set of feature approximation coefficients. The purpose of normalization is to convert the feature approximation coefficients into relative weights, making them comparable during the fusion process. For example, each coefficient in the set of feature approximation coefficients is divided by their sum to obtain a normalized weight value. These normalized weight values ​​are then added to an initially empty matrix to form the temporal guiding matrix. The construction of the temporal guiding matrix ensures that features in both the temporal and spatial dimensions are combined in a reasonable manner during feature fusion.

[0056] Next, the temporal guiding matrix is ​​used to perform feature cross-fusion on the first spatial expansion trend sub-feature. This process can be achieved through graph convolution, a graph-based convolution operation that can effectively handle feature information in both spatial and temporal dimensions. Specifically, the temporal guiding matrix is ​​used as the weight matrix for the graph convolution operation to perform convolution on the first spatial expansion trend sub-feature, organically combining the feature information in the temporal dimension (i.e., the first temporal expansion trend sub-feature) with the feature information in the spatial dimension (i.e., the first spatial expansion trend sub-feature) to obtain a comprehensive first expansion trend sub-feature. This sub-feature can more comprehensively describe the crack propagation behavior during thermal cycling, providing more accurate data support for subsequent failure probability analysis.

[0057] Furthermore, step P43 in this embodiment of the application also includes:

[0058] P43-1: Extract trend features of crack morphology in the first crack propagation path sequence according to a preset sliding window to obtain the first initial crack morphology propagation trend sub-feature; P43-2: Perform coating substrate influence analysis based on crack morphology in the first crack propagation path sequence to determine the coating substrate influence factor; P43-3: Correct the first initial crack morphology propagation trend sub-feature according to the coating substrate influence factor to obtain the first crack morphology propagation trend sub-feature.

[0059] Specifically, the analysis process of crack morphology propagation trend characteristics in the first crack propagation path sequence can be further refined. By introducing sliding window technology, coating substrate influence analysis, and feature correction, a more accurate analysis of crack morphology propagation trends can be achieved.

[0060] First, trend features of the crack morphology in the first crack propagation path sequence are extracted according to a preset sliding window. A sliding window is a commonly used signal processing method; by sliding a fixed-size window across the sequence, local features can be extracted and their changing trends analyzed. In this application, the size of the preset sliding window can be adjusted according to the frequency of crack morphology changes and actual working conditions. By setting a sliding window in the crack propagation path, crack morphology features can be extracted step-by-step at different times and spatial locations, analyzing geometric changes such as crack width, depth, and shape, thereby obtaining the first initial crack morphology propagation trend sub-feature. This feature reflects the changing trend of the crack morphology within a local region, providing basic data for subsequent analysis.

[0061] Next, the interaction between the coating and the substrate is analyzed based on crack morphology to determine the coating-substrate influence factor. The coating-substrate influence factor quantifies the impact of the interaction between the coating and the substrate on crack morphology and propagation. For example, factors such as the difference in thermal expansion coefficients between the coating and the substrate, interfacial bonding strength, and coating thickness all affect the crack propagation path and morphology. By analyzing these factors, the coating-substrate influence factor can be determined, reflecting the comprehensive influence of the coating-substrate interaction. The calculation method for the coating-substrate influence factor can be based on experimental data, theoretical analysis, or numerical simulation results to ensure that it accurately reflects the interaction between the coating and the substrate.

[0062] Finally, the first initial crack morphology propagation trend sub-feature is modified based on the coating-substrate influence factor to obtain the first crack morphology propagation trend sub-feature. The modification process needs to consider the influence of the interaction between the coating and the substrate on crack morphology propagation, adjusting the initial crack morphology propagation trend sub-feature to better reflect actual working conditions. Modification methods can include weighted adjustment, correction coefficient multiplication, or other mathematical methods, depending on the nature of the coating-substrate influence factor and the characteristics of the crack morphology propagation trend sub-feature. The modified first crack morphology propagation trend sub-feature can more accurately reflect the actual crack morphology propagation trend during thermal cycling, providing more reliable data support for subsequent failure probability analysis.

[0063] This process not only considers the local changes in crack morphology, but also fully considers the interaction between the coating and the substrate, thus improving the accuracy and reliability of crack morphology propagation trend analysis.

[0064] P50: Based on the set of state transition trend features, crack development prediction is performed to obtain a set of crack development prediction results.

[0065] Furthermore, step P50 in this embodiment of the application also includes:

[0066] P51: Pre-construct a crack propagation predictor; P52: Analyze the state transition trend feature set using the crack propagation predictor to obtain the crack propagation prediction result set.

[0067] Optionally, crack propagation can be predicted based on the set of state transition trend characteristics. By predicting the development of cracks in future thermal cycles, an important basis can be provided for subsequent failure probability assessment.

[0068] First, a crack propagation predictor is pre-built. This predictor is a tool based on prior data analysis and model training. Its main function is to predict the possible propagation path and development trend of a crack during future thermal cycling, based on the input set of crack state transition trend features. To build this predictor, techniques such as machine learning, data fitting, and regression analysis can be used, combined with historical data and experimental results, to train a model capable of accurately predicting crack propagation behavior. This predictor should be able to handle multiple factors extracted from the state transition trend feature set, including spatiotemporal interaction features, crack propagation step size, and propagation direction, providing comprehensive predictive support for crack propagation.

[0069] Next, a pre-built crack propagation predictor is used to analyze the state transition trend feature set. This set contains the crack propagation trend characteristics at different thermal cycling stages, obtained through detailed analysis of the crack propagation path sequence in previous steps. Based on the data in the state transition trend feature set, the predictor analyzes the future crack propagation path, velocity, and morphological changes, and, considering time and space factors, provides possible crack propagation modes and the final result. The prediction results include information such as crack propagation path, propagation length, propagation direction, and changes in crack morphology, which are integrated into a crack propagation prediction result set. This set provides detailed and accurate data support for subsequent failure probability analysis, enabling analysts to better assess the failure risk of thermal barrier coatings under different thermal cycling cycles.

[0070] P60: Obtain the critical J integral value at the crack tip, and perform failure probability discrimination on the crack propagation prediction result set based on the critical J integral value at the crack tip to obtain the surface cracking failure probability analysis result of the thermal barrier coating.

[0071] It should be understood that by obtaining the critical J integral value at the crack tip, the failure probability of the crack propagation prediction result set is judged, thereby obtaining the surface cracking failure probability analysis result of the thermal barrier coating.

[0072] First, it is necessary to obtain the critical J-integral value at the crack tip. The J-integral is an important parameter describing the stress field at the crack tip and is commonly used to assess the critical conditions for crack propagation. When the stress field of the crack reaches a certain critical value, the crack begins to propagate, leading to material failure. In the analysis of thermal barrier coatings, the critical value of the J-integral is often used to determine whether the crack has reached the critical point of propagation. This value can be obtained through experimental determination or theoretical calculation and is usually related to the fracture toughness of the material. In this application, by analyzing the crack propagation paths and morphologies in the crack propagation prediction result set, the J-integral value of each crack tip is calculated and compared with the critical J-integral value.

[0073] Next, the failure probability is determined based on the critical J-integral value at the crack tip of the crack propagation prediction set. Specifically, for each crack propagation scenario in the crack propagation prediction set, the J-integral value at the crack tip is calculated. If the calculated J-integral value exceeds the critical J-integral value, the crack is considered to have a risk of propagation under the current thermal cycling conditions, which may lead to the failure of the thermal barrier coating. Similarly, by statistically analyzing the proportion of all crack propagation scenarios exceeding the critical J-integral value, the failure probability of the thermal barrier coating at a specific number of thermal cycles is obtained. This probability reflects the likelihood of surface cracking failure of the thermal barrier coating under actual operating conditions.

[0074] Finally, based on the critical J-integral value at the crack tip, the surface cracking failure probability analysis results of the thermal barrier coating are generated. This analysis provides designers with a failure risk assessment of the coating under different service conditions, helping to optimize coating design and process selection, and improve the service life and performance reliability of the thermal barrier coating.

[0075] In summary, the embodiments of this application have at least the following technical effects:

[0076] This application utilizes a three-dimensional model based on the extended finite element method to accurately simulate the crack propagation process of thermal barrier coatings under complex thermal cycling conditions, and accurately predict crack paths and propagation trends. By combining state transition trend characteristic analysis and the critical J-integral value at the crack tip, it achieves a quantitative assessment of coating failure, effectively evaluating the failure probability of surface cracking in the coating. The failure analysis method based on crack propagation prediction provides a reliable theoretical basis for the design, optimization, and use of thermal barrier coatings, improving the coating's service life and engineering reliability. By comprehensively considering various factors such as thermal stress, crack morphology changes, and thermal mismatch between the coating and the substrate, it achieves a more detailed and comprehensive failure analysis.

[0077] It achieves high-precision simulation of crack propagation behavior and quantification of failure probability through the extended finite element method, effectively addressing complex working conditions and improving the accuracy of failure analysis.

[0078] Example 2, based on the same inventive concept as the thermal barrier coating surface cracking failure probability analysis method in the foregoing examples, such as... Figure 2 As shown, this application provides a system for analyzing the probability of cracking failure of thermal barrier coating surfaces. The system and method embodiments in this application are based on the same inventive concept. The system includes:

[0079] Finite element model establishment module 11 is used to establish a three-dimensional finite element model of the thermal barrier coating, wherein the three-dimensional finite element model includes at least the thermophysical properties of the coating and the substrate, the coefficient of thermal expansion, the thermal conductivity, and the thermal mismatch.

[0080] The thermal cycling loading condition setting module 12 is used to set thermal cycling loading conditions, wherein the thermal cycling loading conditions include at least temperature range, thermal gradient and cooling rate.

[0081] The crack propagation simulation module 13 is used to simulate the thermal stress and crack propagation behavior under thermal cycling load on a three-dimensional finite element model using the extended finite element method, and to obtain a set of crack propagation path sequences.

[0082] The state transition trend analysis module 14 is used to traverse the crack propagation path sequence set to perform state transition trend feature analysis and construct a state transition trend feature set.

[0083] Crack development prediction module 15 is used to predict crack development based on the set of state transition trend features and obtain a set of crack development prediction results.

[0084] The failure probability discrimination module 16 is used to obtain the critical J integral value at the crack tip, and to perform failure probability discrimination on the crack propagation prediction result set based on the critical J integral value at the crack tip, so as to obtain the surface cracking failure probability analysis result of the thermal barrier coating.

[0085] Furthermore, the finite element model establishment module 11 is also used to perform the following steps:

[0086] An initial three-dimensional geometric structure is constructed according to the preset substrate thickness, preset coating thickness, preset coating material type, and preset substrate material type; the thermophysical properties, coefficient of thermal expansion, and thermal conductivity of the coating and substrate are defined for the initial three-dimensional geometric structure to obtain the three-dimensional geometric structure; based on the thermal mismatch difference between the coating and the substrate, thermal boundary conditions and mechanical boundary conditions are set for the three-dimensional geometric structure, and finite element analysis is performed to obtain the three-dimensional finite element model.

[0087] Furthermore, the crack propagation simulation module 13 is also used to perform the following steps:

[0088] Obtain the initial set of crack locations in the three-dimensional finite element model under thermal cycling loading conditions; introduce a crack function and crack propagation criterion using the extended finite element method, and propagate cracks in the initial set of crack locations according to the cycle period in the thermal cycling loading conditions, recording the crack propagation paths to obtain the set of crack propagation path sequences. The crack propagation path includes the crack propagation step size, propagation direction, and crack morphology.

[0089] Furthermore, the state transition trend analysis module 14 is also used to perform the following steps:

[0090] Extract a first crack propagation path sequence from the crack propagation path sequence set; traverse and extract the crack propagation step size and propagation direction in the first crack propagation path sequence to perform crack propagation trend feature analysis and determine a first propagation trend sub-feature; traverse and extract the crack morphology in the first crack propagation path sequence to perform crack morphology propagation trend feature analysis and determine a first crack morphology propagation trend sub-feature; fuse the first propagation trend sub-feature and the first crack morphology propagation trend sub-feature to obtain a first state transition trend feature; traverse the crack propagation path sequence set to perform state transition trend feature analysis from crack propagation and crack morphology propagation to obtain a set of state transition trend features.

[0091] Furthermore, the state transition trend analysis module 14 is also used to perform the following steps:

[0092] The spatiotemporal interactive crack propagation identification branch set is retrieved, and crack propagation trend feature analysis is performed on the crack propagation step size and propagation direction in the first crack propagation path sequence to obtain the first temporal propagation trend sub-feature and the first spatial propagation trend sub-feature; the first temporal propagation trend sub-feature and the first spatial propagation trend sub-feature are cross-fused to obtain the first propagation trend sub-feature.

[0093] Furthermore, the state transition trend analysis module 14 is also used to perform the following steps:

[0094] Calculate the feature approximation coefficients of the first temporal expansion trend sub-feature and the first spatial expansion trend sub-feature to obtain a feature approximation coefficient set; determine the temporal guidance matrix based on the feature approximation coefficient set; and use the temporal guidance matrix to perform feature cross-fusion on the first spatial expansion trend sub-feature to obtain the first expansion trend sub-feature.

[0095] Furthermore, the state transition trend analysis module 14 is also used to perform the following steps:

[0096] The trend features of crack morphology in the first crack propagation path sequence are extracted according to a preset sliding window to obtain the first initial crack morphology propagation trend sub-feature; the influence of the coating substrate on the crack morphology in the first crack propagation path sequence is analyzed to determine the coating substrate influence factor; the first initial crack morphology propagation trend sub-feature is corrected according to the coating substrate influence factor to obtain the first crack morphology propagation trend sub-feature.

[0097] Furthermore, the crack propagation prediction module 15 is also used to perform the following steps:

[0098] A crack propagation predictor is pre-constructed; the crack propagation predictor is used to analyze the set of state transition trend features to obtain the set of crack propagation prediction results.

[0099] It should be noted that the order of the embodiments described above is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. Furthermore, the above description focuses on specific embodiments of this specification. Additionally, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some implementations, multitasking and parallel processing are possible or may be advantageous.

[0100] The above description is only a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0101] This specification and accompanying drawings are merely illustrative examples of this application and are intended to cover any and all modifications, variations, combinations, or equivalents within the scope of this application. Clearly, those skilled in the art can make various alterations and modifications to this application without departing from its scope. Therefore, if such modifications and variations fall within the scope of this application and its equivalents, this application intends to include such modifications and variations.

Claims

1. A method of analyzing the probability of failure of a thermal barrier coating layer cracking, characterized in that, The method includes: A three-dimensional finite element model of the thermal barrier coating is established, wherein the three-dimensional finite element model includes at least the thermophysical properties of the coating and the substrate, the coefficient of thermal expansion, the thermal conductivity, and the thermal mismatch. Set the thermal cycling loading conditions, which include at least the temperature range, thermal gradient, and cooling rate; Using the extended finite element method, thermal stress and crack propagation behavior under thermal cycling loading conditions were simulated in a three-dimensional finite element model to obtain a set of crack propagation path sequences. The state transition trend feature set is constructed by traversing the set of crack propagation path sequences and performing state transition trend feature analysis. Crack propagation prediction is performed based on the set of state transition trend features to obtain a set of crack propagation prediction results. Obtain the critical J integral value at the crack tip, and perform failure probability discrimination on the crack propagation prediction result set based on the critical J integral value at the crack tip to obtain the surface cracking failure probability analysis result of the thermal barrier coating.

2. A method of TBCs layer cracking failure probability analysis according to claim 1, characterized in that, A three-dimensional finite element model of the thermal barrier coating is established, wherein the three-dimensional finite element model includes at least the thermophysical properties of the coating and the substrate, the coefficient of thermal expansion, the thermal conductivity, and the thermal mismatch, including: Construct the initial three-dimensional geometry according to the preset substrate thickness, preset coating thickness, preset coating material type, and preset substrate material type; The thermophysical properties, coefficient of thermal expansion, and thermal conductivity of the coating and substrate are defined for the initial three-dimensional geometric structure to obtain the three-dimensional geometric structure. Based on the thermal mismatch difference between the coating and the substrate, thermal and mechanical boundary conditions are set for the three-dimensional geometric structure, and finite element analysis is performed to obtain the three-dimensional finite element model.

3. A method of TBCs layer cracking failure probability analysis according to claim 1, characterized in that, Using the extended finite element method (EFM), thermal stress and crack propagation behavior under thermal cycling loading were simulated in a three-dimensional finite element model, yielding a set of crack propagation path sequences, including: Obtain the initial set of crack locations of the three-dimensional finite element model under thermal cycling loading conditions; Using the extended finite element method, a crack function and a crack propagation criterion are introduced. The initial set of crack locations is subjected to crack propagation according to the cycle period in the thermal cycling loading conditions, and the crack propagation path is recorded to obtain the set of crack propagation path sequences.

4. A method of TBCs layer cracking failure probability analysis according to claim 3, characterized in that, Crack propagation path includes crack propagation step size, propagation direction, and crack morphology.

5. The method for analyzing the probability of cracking failure of a thermal barrier coating surface layer as described in claim 1, characterized in that, The set of crack propagation path sequences is traversed to perform state transition trend feature analysis, and a set of state transition trend features is constructed, including: Extract the first crack propagation path sequence from the set of crack propagation path sequences; The crack propagation step size and propagation direction in the first crack propagation path sequence are extracted and the crack propagation trend feature is analyzed to determine the first propagation trend sub-feature. The crack morphology in the first crack propagation path sequence is extracted and crack morphology propagation trend feature analysis is performed to determine the first crack morphology propagation trend sub-feature. By integrating the first expansion trend sub-feature and the first crack morphology expansion trend sub-feature, a first state transition trend feature is obtained; By traversing the set of crack propagation path sequences, state transition trend characteristics are analyzed from crack propagation and crack morphology propagation to obtain a set of state transition trend characteristics.

6. The method for analyzing the probability of cracking failure of a thermal barrier coating surface layer as described in claim 5, characterized in that, The crack propagation step size and propagation direction are extracted from the first crack propagation path sequence to perform crack propagation trend feature analysis, and the first propagation trend sub-features are determined, including: Retrieve the spatiotemporal interactive crack propagation identification branch set, and perform crack propagation trend feature analysis on the crack propagation step size and propagation direction in the first crack propagation path sequence to obtain the first temporal propagation trend sub-feature and the first spatial propagation trend sub-feature; The first temporal extended trend sub-feature and the first spatial extended trend sub-feature are subjected to feature cross-fusion to obtain the first extended trend sub-feature.

7. The method for analyzing the probability of cracking failure of a thermal barrier coating surface layer as described in claim 6, characterized in that, include: Calculate the feature approximation coefficients of the first temporal expansion trend sub-feature and the first spatial expansion trend sub-feature to obtain a set of feature approximation coefficients; The time guidance matrix is ​​determined based on the set of characteristic approximation coefficients. The first spatial expansion trend sub-feature is obtained by using the time-guided matrix to perform feature cross-fusion on the first spatial expansion trend sub-feature.

8. The method for analyzing the probability of cracking failure of a thermal barrier coating surface layer as described in claim 5, characterized in that, The crack morphology in the first crack propagation path sequence is extracted and analyzed for crack morphology propagation trend characteristics to determine the first crack morphology propagation trend sub-features, including: According to the preset sliding window, the trend features of the crack morphology in the first crack propagation path sequence are extracted to obtain the first initial crack morphology propagation trend sub-feature; The influence of the coating substrate on the crack morphology in the first crack propagation path sequence is analyzed to determine the influence factor of the coating substrate. The first initial crack morphology propagation trend sub-feature is modified based on the coating substrate influence factor to obtain the first crack morphology propagation trend sub-feature.

9. The method for analyzing the probability of cracking failure of a thermal barrier coating surface layer as described in claim 1, characterized in that, Based on the aforementioned set of state transition trend features, crack propagation prediction is performed to obtain a set of crack propagation prediction results, including: Pre-built crack propagation predictor; The crack development predictor is used to analyze the set of state transition trend features to obtain the set of crack development prediction results.

10. A system for analyzing the probability of cracking failure of thermal barrier coating surfaces, characterized in that, The system includes: A finite element model building module is used to build a three-dimensional finite element model of the thermal barrier coating. The three-dimensional finite element model includes at least the thermophysical properties of the coating and the substrate, the coefficient of thermal expansion, the thermal conductivity, and the thermal mismatch. A thermal cycling loading condition setting module is used to set thermal cycling loading conditions, wherein the thermal cycling loading conditions include at least a temperature range, a thermal gradient, and a cooling rate. A crack propagation simulation module is used to simulate the thermal stress and crack propagation behavior under thermal cycling load on a three-dimensional finite element model using the extended finite element method, and to obtain a set of crack propagation path sequences. A state transition trend analysis module is used to traverse the crack propagation path sequence set to perform state transition trend feature analysis and construct a state transition trend feature set. A crack development prediction module is used to predict crack development based on the set of state transition trend features, and obtain a set of crack development prediction results. The failure probability discrimination module is used to obtain the critical J integral value at the crack tip, and to perform failure probability discrimination on the crack propagation prediction result set based on the critical J integral value at the crack tip, so as to obtain the surface cracking failure probability analysis result of the thermal barrier coating.

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