A method for predicting low cycle fatigue life of a coated turbine blade based on equivalent stress

Abstract

This application discloses a method for predicting the low-cycle fatigue life of coated turbine blades based on equivalent stress. The method includes: introducing an equivalent stress model based on the stress-life relationship in the fatigue limit formula to obtain a fatigue life prediction model; and predicting the low-cycle fatigue life of the coated turbine blades based on this model. By innovatively attributing fatigue life degradation to the increase in equivalent stress caused by microstructural changes, and drawing on the stress-fatigue life relationship in the Basquin model, a fatigue life prediction model based on equivalent stress is finally established. This establishes a direct link between fatigue life and the morphological parameters of the interface microstructure and material properties, giving the model stronger physical meaning and universality, and achieving high-precision life prediction.

Description

Technical Field

[0001] This invention relates to the field of aero-engine technology, and in particular to a method for predicting the low-cycle fatigue life of coated turbine blades based on equivalent stress. Background Technology

[0002] As a core hot-end component, aero-engine turbine blades endure the combined effects of extreme high temperatures, complex mechanical loads, and oxidation corrosion over long periods. To improve engine thermal efficiency, modern aero-engines operate at temperatures approaching or even exceeding the temperature limits of the high-temperature alloy matrix. Simply introducing high proportions of refractory elements such as Re and Ru into single-crystal high-temperature alloys to enhance high-temperature mechanical properties is no longer sufficient to meet engineering requirements. To address this issue, a high-temperature protective coating is typically applied to the turbine blades to isolate them from the substrate, thereby achieving resistance to oxidation and corrosion.

[0003] Existing methods are mostly based on traditional Basquin (fatigue limit) models, which incorporate the effects of temperature and time by fitting fatigue strength parameters. While these models can establish a statistical relationship between macroscopic service conditions and lifespan, they fail to reflect the dominant role of microstructural evolution in fatigue performance degradation. Some studies have attempted to use machine learning methods such as neural networks for lifespan prediction, which have shown some fitting ability in limited samples, but they are essentially "black box" models, lacking clear physical mechanism support.

[0004] Some existing low-cycle fatigue life prediction methods mainly target bare alloys or composite materials, failing to fully consider the significant impact of coatings on the microstructure and fracture behavior of the matrix. However, during turbine blade service, the presence of coatings can induce elemental interdiffusion and the precipitation of brittle phases such as the TCP phase at the interface, thereby altering the crack initiation and propagation mechanisms. Therefore, such methods are not suitable for the life assessment of actual coated turbine blades.

[0005] The TCP particles grow and coarsen as the thermal oxidation temperature and time increase, and the stress concentration caused by them leads to an increase in local stress. Therefore, linking the degradation of fatigue life with the change in equivalent stress caused by the morphological changes during the growth process of the particles is the direction considered in this application.

[0006] To address the aforementioned challenges, providing a method for predicting the low-cycle fatigue life of coated turbine blades based on equivalent stress is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] To address the aforementioned technical problems, the purpose of this application is to provide a method for predicting low-cycle fatigue life based on equivalent stress. By innovatively attributing the degradation of fatigue life to the increase in equivalent stress caused by microstructural changes, and based on the stress-life relationship of the Basquin formula, an equivalent stress model is introduced to finally obtain a fatigue life prediction model, ultimately obtaining life predictions for different conditions.

[0008] To achieve the above objectives, this application provides a method for predicting low-cycle fatigue life based on equivalent stress.

[0009] The above-mentioned objective of this application is achieved through the following technical solution:

[0010] A method for predicting low-cycle fatigue life based on equivalent stress, comprising:

[0011] Based on Hooke's law and Eshelby's equivalent inclusion theory, the local stress equation is obtained;

[0012] Define the stress amplification factor based on the stress amplification term in the local stress equation;

[0013] An equivalent stress model is established based on the stress amplification factor and the local stress equation.

[0014] Based on the Morita-Fujinaka theory of surface tension and non-diluted soft composite solids, the ratio of the equivalent modulus to the matrix elastic modulus is obtained and defined as the modulus ratio.

[0015] Based on the influence of hard inclusions on the matrix, the modulus increment formula is obtained through the modulus ratio;

[0016] The modulus increment formula is normalized to obtain the stress amplification factor;

[0017] The amplification function is established based on the amplification factor to obtain the stress amplification factor, and finally substituted into the equivalent stress model to obtain the equivalent stress.

[0018] Based on the relationship between stress and life in the fatigue limit formula, the equivalent stress model is introduced to obtain the fatigue life prediction model. Based on the fatigue life prediction model, the low-cycle fatigue life of the coated turbine blade is predicted.

[0019] Specifically, the fatigue life prediction model is as follows:

[0020] ;

[0021] Equivalent stress;

[0022] This is the fatigue strength coefficient;

[0023] This is the fatigue strength index.

[0024] Preferably, an equivalent stress model is established based on the stress amplification factor and the local stress equation, specifically as follows:

[0025] ;

[0026] in, This refers to the stress amplitude.

[0027] R is the aspect ratio of the TCP particle;

[0028] This represents the area fraction of TCP particles;

[0029] Equivalent modulus;

[0030] F is the stress amplification factor;

[0031] This represents the elastic modulus of the matrix.

[0032] Preferably, based on the Morita-Fujinaka theory of surface tension and undiluted soft composite solids, the ratio of the equivalent modulus to the matrix elastic modulus is obtained, specifically as follows:

[0033] ;

[0034] Where v is Poisson's ratio;

[0035] , , , This is the shape correction factor.

[0036] Preferably, the modulus increment formula is obtained through the modulus ratio, specifically as follows:

[0037] .

[0038] Preferably, the stress amplification factor is obtained by normalizing the modulus increment, specifically as follows:

[0039] ;

[0040] in, This is the stiffening scale factor;

[0041] Shape sensitivity index;

[0042] This is the volume fraction suppression coefficient;

[0043] It is a nonlinear coupling index;

[0044] This is the stiffened response index.

[0045] Preferably, the stress amplification factor is obtained by establishing an amplification function based on the amplification factor, specifically as follows:

[0046] ;

[0047] Wherein, η is used to control the nonlinear mapping relationship between the amplification factor and the equivalent stress.

[0048] Preferably, the specific formula for calculating the shape correction coefficient is as follows:

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] Where v is Poisson's ratio;

[0054] This represents the area fraction of the TCP particles.

[0055] This application introduces a stress amplification factor and draws on formulas from existing research on composite materials containing inclusions to establish an equivalent stress model that considers the material's elastic modulus, applied stress amplitude, TCP particle aspect ratio, and area fraction. Based on the stress-fatigue life relationship in the traditional Basquin model, a fatigue life prediction model is finally established that attributes fatigue life degradation to the increase in equivalent stress caused by microstructural changes under thermo-mechanical coupling. Through this fatigue life prediction model, the fatigue life of the component can be predicted. The fatigue life prediction model established by introducing equivalent stress establishes a direct relationship between fatigue life and interface microstructure morphological parameters and material properties, giving the model stronger physical meaning and universality, and achieving high-precision life prediction. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0057] Figure 1 This is a flowchart of a method for predicting the low-cycle fatigue life of a coated turbine blade based on equivalent stress, as described in an embodiment of this application.

[0058] Figure 2 This is a scatter plot of results from the conventional Basquin formula lifetime prediction method in the embodiments of this application;

[0059] Figure 3 This is a scattering diagram of the results from the low-cycle fatigue life prediction method for coated turbine blades in the embodiments of this application. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] Furthermore, the technical features in the various embodiments or individual embodiments provided in this application can be arbitrarily combined with each other to form a feasible technical solution. Such combination is not constrained by the order of steps and / or the structural composition mode, but must be based on the ability of a person skilled in the art to implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed in this application.

[0062] In the embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. The system embodiments described below are merely illustrative. For example, the division of units and modules is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or modules can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling communication connection between the various components shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, and can be electrical, mechanical or other forms.

[0063] In addition, each functional unit in the various embodiments of this application can be integrated into a single processor, or each unit can be a separate device, or two or more units can be integrated into a single device; each functional unit in the various embodiments of this application can be implemented in hardware or in the form of hardware plus software functional units.

[0064] Those skilled in the art will understand that all or part of the steps of the following method embodiments can be implemented by program instructions and related hardware. The aforementioned program instructions can be stored in a computer-readable storage medium. When the program instructions are executed, they perform the steps of the following method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), magnetic disks, or optical disks.

[0065] It should be understood that the use of terms such as "system," "device," "unit," and / or "module" in this application is merely one method of distinguishing different components, elements, parts, sections, or assemblies at different levels. However, if other terms can achieve the same purpose, they may be replaced by other expressions.

[0066] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "a plurality of" or "several" means two or more, unless otherwise explicitly specified.

[0067] It should be noted that the structures, proportions, sizes, etc., shown in the accompanying drawings of this specification are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which this application can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size should still fall within the scope of the technical content disclosed in this application, provided that they do not affect the effects and purposes that this application can produce.

[0068] If a flowchart is used in this application, it is used to illustrate the operations performed by the system according to embodiments of this application. It should be understood that the preceding or following operations are not necessarily performed in exact order. Instead, the steps can be processed in reverse order or simultaneously. Furthermore, other operations can be added to these processes, or one or more steps can be removed from them.

[0069] It should also be noted that, in this document, terms such as “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that an article or device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such an article or device. Without further limitation, an element defined by the phrase “comprising one…” does not exclude the presence of other identical elements in the article or device that includes the aforementioned element.

[0070] Equivalent stress is a physical quantity used to quantify the overall stress level of a material under complex stress conditions.

[0071] Hybrid composites refer to multiphase materials in which hard particles or short fibers are uniformly dispersed in a metal, ceramic, or polymer matrix, thereby forming a material with performance superior to that of a single component. Here, TCP particles are considered as hard inclusions in the matrix.

[0072] The implementation method of this application is written in a progressive manner.

[0073] A method for predicting the low-cycle fatigue life of coated turbine blades based on equivalent stress includes:

[0074] S1. Based on Hooke's law and Eshelby's equivalent inclusion theory, the local stress equation is obtained;

[0075] S2. Define the stress amplification factor based on the stress amplification term in the local stress equation;

[0076] S3. Establish an equivalent stress model based on the stress amplification factor and the local stress equation;

[0077] S4. Based on the Morita-Fujinaka theory of surface tension and non-diluted soft composite solids, the ratio of the equivalent modulus to the matrix elastic modulus is obtained and defined as the modulus ratio.

[0078] S5. Based on the influence of hard inclusions on the matrix, obtain the modulus increment formula through the modulus ratio;

[0079] S6. Normalize the modulus increment formula to obtain the stress amplification factor;

[0080] S7. Establish an amplification function based on the amplification factor to obtain the stress amplification factor, and finally substitute it into the equivalent stress model to obtain the equivalent stress.

[0081] S8. Based on the relationship between stress and life in the fatigue limit formula, an equivalent stress model is introduced to obtain a fatigue life prediction model. Based on the fatigue life prediction model, the low-cycle fatigue life of the coated turbine blade is predicted.

[0082] The fatigue life prediction model is as follows:

[0083] ;

[0084] Equivalent stress;

[0085] This is the fatigue strength coefficient;

[0086] This is the fatigue strength index.

[0087] Specifically, based on Te Wu T's 1966 paper, "The effect of inclusion shape on the elastic moduli of a two-phase material," and extending the Eshelby equivalent inclusion theory, the following exists: Therefore, we get: By relating the local strain concentration to the far-field strain of the matrix, and then applying Hooke's Law, which states that stress equals the elastic modulus multiplied by strain, we can obtain the following formula:

[0088] ;

[0089] in, Local stress;

[0090] It is the local elastic modulus;

[0091] For strain transformation tensor, this parameter depends on inclusion shape and volume fraction as well as elastic modulus;

[0092] For matrix strain;

[0093] formula lieutenant general It is considered as a stress amplification factor, which describes the degree to which local stress is amplified relative to the overall applied stress.

[0094] Therefore, this application also introduces a stress amplification factor to describe the amplification effect of material properties and TCP particle morphology parameters on the corresponding forces, thereby establishing an equivalent stress model.

[0095] Based on the article "Surface tension and the Mori-Tanaka theory of non-dilute soft composite solids" published by Mancarella F et al. in 2016, a formula for the modulus ratio of composite materials containing inclusions was obtained by drawing on this article.

[0096] Based on the relationship between the hardness of the composite material and the substrate material affected by hard inclusions (TCP particles), a modulus increment formula was obtained.

[0097] The formula means that when the substrate material does not contain TCP particles, the substrate material is the same as the composite material, and the calculation result is 0.

[0098] When the substrate material contains TCP particles, the substrate material is different from the composite material and the calculated result is positive.

[0099] Normalization limits the magnitude of the modulus increment to between 0 and 1, thus preventing the equivalent modulus from being too large when the hardness of TCP particles is very high, which would result in an infinitely large calculated modulus increment and affect the model fitting.

[0100] The stress amplification factor was obtained based on the normalized modulus increment.

[0101] Finally, based on the established amplification function, the calculation method of the stress amplification factor is obtained, which is then substituted into the equivalent stress model to obtain the equivalent stress.

[0102] According to the traditional Basquin formula:

[0103] ;

[0104] By referencing the predictive relationship between stress and material life in the formula and substituting it into the equivalent stress model, a material fatigue life prediction model is obtained, and life prediction can be performed using this formula.

[0105] In some embodiments, an equivalent stress model is established based on the stress amplification factor F and the local stress equation, specifically as follows:

[0106] ;

[0107] in, This refers to the stress amplitude.

[0108] R is the aspect ratio of the TCP particle;

[0109] This represents the area fraction of TCP particles;

[0110] Equivalent modulus;

[0111] This represents the elastic modulus of the matrix.

[0112] The stress amplitude can be set according to your own predictions;

[0113] The area fraction of TCP particles can be obtained by scanning electron microscope (SEM) images of blade sample cross-sections under different thermal oxidation conditions. After image processing and cropping, the cropped area image is denoised and binarized into a black and white image (the white area is the TCP particle we want to extract) using the maximum threshold segmentation method of adaptive threshold segmentation through peak merging and dynamic valley detection. This distinguishes the target area from images of different gray levels. Finally, the area fraction of the white area in the binarized image is the area fraction of the TCP particle.

[0114] Watershed Algorithm: For clump-together TCP particles, they appear in an image like several connected mountains. The watershed algorithm accurately locates the "valley" lines between these "mountains" and constructs dams along these lowest points, effectively separating the clump-together particles. This is similar to the process of rainwater filling the terrain.

[0115] Skeleton extraction: Through a set of rules, edge pixels of an object are iteratively removed, while core pixels crucial for maintaining the object's basic shape and connectivity are preserved. Ultimately, regardless of the original object's thickness, it is simplified into thin lines that represent its topological structure. This effectively separates tightly coupled TCP (transformative data structures).

[0116] The watershed algorithm is used to initially segment the adhered TCP particles, and then the particles with a high degree of adhesion are further segmented by skeleton extraction. Based on the segmentation, a new binary image is generated. The TCP particles are regarded as ellipsoidal, and the major and minor axis parameters of each particle in the new image are determined by principal component analysis (PCA). (Specifically, a coordinate system is constructed for each particle, and after centering the coordinates, the major and minor axes of the particles in the binary image are determined by the covariance matrix, where the direction with the largest variance is the direction of the major axis.) The aspect ratio of the particles under different conditions is obtained.

[0117] In some embodiments, the ratio of the equivalent modulus to the matrix elastic modulus is obtained based on the Morita-Fujinaka theory of surface tension and undiluted soft composite solids, specifically:

[0118] ;

[0119] Where v is Poisson's ratio.

[0120] In other embodiments, the modulus increment formula is obtained through the modulus ratio, specifically as follows:

[0121] .

[0122] In other embodiments, the stress amplification factor is obtained by normalizing the modulus increment, specifically as follows:

[0123] ;

[0124] in, This is the stiffening scale factor;

[0125] Shape sensitivity index;

[0126] This is the volume fraction suppression coefficient;

[0127] It is a nonlinear coupling index;

[0128] This is the stiffened response index.

[0129] In other embodiments, the stress amplification factor is obtained by establishing an amplification function based on the amplification factor, specifically as follows:

[0130] ;

[0131] Wherein, η is used to control the nonlinear mapping relationship between the stress amplification factor F and the equivalent stress.

[0132] In other embodiments, the specific formula for calculating the shape correction factor is as follows:

[0133] ;

[0134] ;

[0135] ;

[0136] .

[0137] The lifetime prediction model of this application was validated using the following methods:

[0138] The second-generation nickel-based single-crystal superalloy was processed into a plate-shaped sample (32mm×8mm×1mm) with {001} orientation, and an MCrAlY coating with a thickness of about 70μm was prepared on it by physical vapor deposition.

[0139] To simulate the actual service environment of turbine blades, the coated samples were placed in a high-temperature creep testing machine and subjected to high-temperature oxidation experiments at different temperatures (850℃ / 1050℃ / 1100℃) and different durations (50 h / 100 h). Stress was applied to both ends of the samples during the oxidation process to realize the evolution of the interface microstructure under thermo-mechanical coupling conditions.

[0140] Bare alloy specimens and oxide-coated specimens underwent stress-controlled low-cycle fatigue testing (thermal fatigue testing, test temperature 980℃) at different amplitudes (550 MPa / 600 MPa / 650 MPa), with a stress ratio of 0.1 and a load application rate of 400 MPa / s. Lifetime data were recorded (for some specimens, fatigue testing was not performed; instead, cross-sections were cut out, and the microstructure of the specimens under corresponding conditions was captured using a scanning electron microscope for image analysis).

[0141] The lifetimes of multiple samples tested were predicted using both the proposed model and a traditional lifetime prediction model. The results show that... Figure 2 As shown, the predicted dispersion band of the traditional model is ±16. Figure 3 As shown, the predicted dispersion band of this model is only ±2.5, and the prediction accuracy is significantly improved, which verifies the superiority and reliability of this model under thermo-mechanical coupling conditions.

[0142] Compared to prediction models established based on macroscopic parameters of thermal exposure conditions (such as temperature and time), this application's model can avoid prediction uncertainties caused by temperature fluctuations during service, achieving more stable predictions.

[0143] This application introduces a stress amplification factor and draws on formulas from existing research on composite materials containing inclusions to establish an equivalent stress model that considers the material's elastic modulus, applied stress amplitude, TCP particle aspect ratio, and area fraction. Based on the stress-fatigue life relationship in the traditional Basquin model, a fatigue life prediction model is finally established that attributes fatigue life degradation to the increase in equivalent stress caused by microstructural changes under thermo-mechanical coupling. Through this fatigue life prediction model, the fatigue life of the component can be predicted. The fatigue life prediction model established by introducing equivalent stress establishes a direct relationship between fatigue life and interface microstructure morphological parameters and material properties, giving the model stronger physical meaning and universality, and achieving high-precision life prediction.

[0144] The sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0145] In the above embodiments of this application, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0146] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the low-cycle fatigue life of coated turbine blades based on equivalent stress, characterized in that, include: Based on Hooke's law and Eshelby's equivalent inclusion theory, the local stress equation is obtained; Define the stress amplification factor based on the stress amplification term in the local stress equation; An equivalent stress model is established based on the stress amplification factor and the local stress equation. Based on the Morita-Fujinaka theory of surface tension and non-diluted soft composite solids, the ratio of equivalent stress to matrix elastic modulus is obtained and defined as the modulus ratio. Based on the influence of hard inclusions on the matrix, the modulus increment formula is obtained through the modulus ratio; The modulus increment formula is normalized to obtain the stress amplification factor; The amplification function is established based on the amplification factor to obtain the stress amplification factor, and finally substituted into the equivalent stress model to obtain the equivalent stress. Based on the relationship between stress and life in the fatigue limit formula, the equivalent stress model is introduced to obtain the fatigue life prediction model. Based on the fatigue life prediction model, the low-cycle fatigue life of the coated turbine blade is predicted. Specifically, the fatigue life prediction model is as follows: ； Equivalent stress; This is the fatigue strength coefficient; The fatigue strength index; An equivalent stress model is established based on the stress amplification factor and the local stress equation, specifically as follows: ； in, This refers to the stress amplitude. R is the aspect ratio of the TCP particle; This represents the area fraction of TCP particles; Equivalent modulus; F is the stress amplification factor; The elastic modulus of the matrix; The modulus increment formula is obtained through the modulus ratio, specifically as follows: ； The stress amplification factor is obtained by normalizing the modulus increment, specifically: ； in, This is the stiffening scale factor; Shape sensitivity index; This is the volume fraction suppression coefficient; It is a nonlinear coupling index; The stiffened response index; The stress amplification factor is obtained by establishing an amplification function based on the amplification factor, specifically as follows: ； Wherein, η is used to control the nonlinear mapping relationship between the stress amplification factor F and the equivalent stress.

2. The method for predicting the low-cycle fatigue life of coated turbine blades based on equivalent stress according to claim 1, characterized in that, Based on the Morita-Fujinaka theory of surface tension and undiluted soft composite solids, the ratio of equivalent stress to the matrix elastic modulus is obtained as follows: ； Where v is Poisson's ratio; , , , This is the shape correction factor.

3. The method for predicting the low-cycle fatigue life of coated turbine blades based on equivalent stress according to claim 2, characterized in that, The specific formula for calculating the shape correction coefficient is as follows: ； ； ； ； Where v is Poisson's ratio; This represents the area fraction of the TCP particles.

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