Notch structure fatigue life prediction method based on probability crystal plasticity

Abstract

The invention discloses a notched structure fatigue life prediction method based on probabilistic crystal plasticity, is applied to the field of reliability analysis, and provides a probabilistic crystal plasticity modeling framework for solving the problems of notched effect (local stress concentration) and material uncertainty generally existing in notched metal structural parts under the action of external loads. And the influence of material dispersibility (including material performance and microstructure) on the fatigue life of the notched part is considered. According to the method, a dual-scale modeling method is adopted, the mechanical response of a notched sample is simulated by adopting Chboche and crystal plastic constitutive simulation in a macro-micro mode, the randomness of the microstructure of the material and the dispersity of the mechanical property are considered by adopting a Voronoi algorithm and a Latin hypercube sampling method, and the fatigue life under different loads is predicted by adopting a fatigue indication factor; and finally describing the dispersibility of the fatigue life by using a probability model.

Description

Technical Field

[0001] The invention belongs to the field of reliability analysis, and particularly relates to a notch structure fatigue life prediction technology. Background Art

[0002] With the increasing demand for high performance of modern engineering equipment, especially under extreme conditions such as high speed, heavy load, and lightweight, the strength and safety redundancy of structures tend to decrease. This trend leads to an increased probability of component damage and frequent failure events, especially at geometric discontinuities of key components (such as grooves, holes, keyways, and fillets), which are often the points of fatigue failure. Therefore, the study of structural fatigue becomes particularly important.

[0003] In fatigue research, one of the key issues is the influence of the notch effect. Studies have shown that geometric notches significantly affect the fatigue resistance of materials, which in turn affects the reliability and safety of the overall structure. Whether under large loads or under periodic fatigue loads, these geometric discontinuities become the starting point for crack initiation and expansion, greatly reducing the fatigue life of structural parts. The microstructure of the material (such as grain size, phase composition, grain boundary characteristics, etc.) plays a vital role in the initiation and expansion of fatigue cracks. Especially in metal materials, fatigue cracks usually initiate from microscopic defects (such as grain boundaries and holes), and then gradually expand as the loading cycle increases. Therefore, understanding and simulating the mechanical behavior of materials at the microscale is crucial for the accurate prediction of fatigue properties. The crystal plasticity finite element method combines the constitutive relationship of crystal plasticity mechanics with finite element analysis, and can simulate the plastic deformation process of metal materials from a microscopic scale, thereby more accurately predicting the fatigue behavior of materials under complex loads.

[0004] The fatigue properties of materials are inherently dispersed. Even under the same material and the same external load conditions, different samples may show different fatigue lives. This dispersion comes from factors such as the material's microstructure, defects, and random changes in material properties. Existing fatigue analysis methods usually assume that the material's properties are uniform and ignore the randomness of the microstructure, resulting in certain deviations in the prediction of fatigue life. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a notch structure fatigue life prediction method based on probabilistic crystal plasticity, introduces random factors into fatigue analysis, considers the statistical characteristics of the material microstructure, and describes the uncertainty in the fatigue process through multi-scale modeling, probabilistic analysis and other methods.

[0006] The technical solution adopted by the present invention is: a method for predicting fatigue life of notched structures based on probabilistic crystal plasticity, comprising:

[0007] S1. Carry out material tensile and fatigue tests on smooth specimens of the same material as the notched specimen to be tested, and obtain the stress-strain curves of the smooth specimens under uniaxial tension and fatigue load, as well as the fatigue life of the notched specimens;

[0008] S2. fitting the macroscopic Chaboche nonlinear kinematic hardening model and the microscopic crystal plasticity model parameters according to the stress-strain curve obtained in step S1;

[0009] S3. Based on the macroscopic Chaboche nonlinear kinematic hardening model and the microscopic crystal plasticity model parameters obtained by fitting in step S2, a dual-scale crystal plasticity finite element model is established according to the notched specimen and the material microstructure;

[0010] S4. Considering the randomness of the material microstructure and the dispersion of the mechanical properties, the random material parameters are used as the input of the dual-scale finite element model in step S3, and the fatigue life is used as the output to establish a probabilistic crystal plastic life prediction framework;

[0011] S5. Use the probabilistic crystal plasticity framework in step S4 to predict the fatigue life of the notched structure and obtain a probabilistic stress-life (PSN) curve by fitting.

[0012] Beneficial effects of the present invention: The method of the present invention is based on a dual-scale crystal plasticity modeling method, adopts a Voronoi algorithm and a Latin hypercube sampling method to consider the randomness of the material microstructure and the dispersion of mechanical properties, establishes a probabilistic crystal plasticity life prediction framework, and performs probabilistic fatigue life prediction of a notched structure based on the probabilistic crystal plasticity life prediction framework; it has the following advantages:

[0013] (1) A dual-scale modeling framework was established to analyze the impact of notch effect on fatigue life from a macro-micro scale;

[0014] (2) A fatigue indicator parameter corrected by mean stress is proposed, which can well predict fatigue life under different mean stresses;

[0015] (3) Combining dual-scale modeling and probabilistic methods, a probabilistic crystal plastic life prediction framework is proposed by quantifying the microstructure and crystal plasticity constitutive parameters. The influence of material microstructure and mechanical properties on the fatigue life dispersion is considered, and the dispersion of notched specimen fatigue life test data is effectively described. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is the fitting result of the crystal plasticity model and the stress-strain curve of the tensile test and fatigue test.

[0017] Figure 2 The GH4169 nickel-based high-temperature alloy fatigue test specimen size and dual-scale modeling method provided in an embodiment of the present invention;

[0018] Figure 3 It is the fatigue life prediction result obtained by the present invention based on the fatigue indication parameter corrected by the proposed mean stress;

[0019] Figure 4 It is a probabilistic crystal plastic life prediction framework provided by the implementation of the present invention;

[0020] Figure 5 It is a flowchart of the specific implementation of the probabilistic life prediction framework;

[0021] Figure 6 It is the PSN curve obtained by the present invention based on the proposed probabilistic crystal plastic life prediction framework. DETAILED DESCRIPTION

[0022] To facilitate those skilled in the art to understand the technical content of the present invention, the present invention is further explained below with reference to the accompanying drawings.

[0023] The present invention discloses a notch structure fatigue life prediction method based on probabilistic crystal plasticity. Based on a dual-scale crystal plasticity modeling method, a Voronoi algorithm and a Latin hypercube sampling method are used to consider the randomness of the material microstructure and the dispersion of mechanical properties, a probabilistic crystal plasticity life prediction framework is established, and probabilistic fatigue life prediction of the notch structure is performed based on the probabilistic crystal plasticity life prediction framework.

[0024] Taking the fatigue life prediction process of notched specimen as an example, a dual-scale finite element model is established to predict the fatigue life of the notched specimen using the fatigue indicator parameters corrected by the mean stress. Then, a probabilistic crystal plasticity framework is established to realize the probabilistic fatigue life prediction of the notched specimen. The specific steps include:

[0025] 1. Establish a dual-scale finite element model of the notched specimen

[0026] 11. Carry out material tensile and fatigue experiments to obtain the stress-strain curves of smooth specimens under uniaxial tension and fatigue load, as well as the fatigue life of notched specimens.

[0027] 12. Fit the parameters of the macroscopic Chaboche nonlinear kinematic hardening model and the microscopic crystal plasticity model.

[0028] 121. The macroscopic Chaboche nonlinear kinematic hardening model is used to simulate the macroscopic elastic-plastic behavior of materials:

[0029]

[0030] Among them, Δσ and Δε p denote the stress range and plastic strain range respectively, σ y is the yield strength, C i and γi is the Chaboche constitutive model parameter. Parameter C i and γ i The experimental stress-strain curve was fitted by the Ramberg-Osgood equation:

[0031]

[0032] where σ and ε are the stress and strain at a specific point; E is Young's modulus, K' is the cyclic strength coefficient, and n' is the cyclic strain hardening exponent.

[0033] The stress-strain curves of the smooth specimen under uniaxial tension and fatigue load in step 1 are used to fit the constitutive parameters of the macroscopic Chaboche nonlinear motion hardening model; specifically, the parameters of the macroscopic Chaboche nonlinear motion hardening model are obtained by comparing the stress-strain curves of the simulation and the experiment using the "trial and error method". The fitting results are shown in Table 1:

[0034] Table 1 Parameters of the macroscopic Chaboche nonlinear kinematic hardening model

[0035]

[0036] 122. Crystal plasticity constitutive model is used to explain the local crystallographic response between grains to simulate the micromechanical behavior of materials.

[0037]

[0038] in, is the shear strain rate on the αth slip system, is the reference strain rate, k is the strain rate sensitive parameter, τ α and χ α are analytical shear stress and back stress respectively; q is the self-hardening h αα and latent hardening h αβ Modulus ratio, h 0 is the initial hardening modulus, τ c and τ s is the critical decomposed shear stress and its saturation value, γ α is the cumulative shear strain rate on the αth slip system; is the back stress evolution rate, sech represents the hyperbolic secant function, C and D represent the direct hardening modulus and dynamic recovery coefficient, respectively.

[0039] The parameters of the crystal plasticity constitutive model are fitted using representative volume elements with periodic boundary conditions. The fitting results are shown in Figure 1As shown. The present invention adopts the "trial and error method" to fit the crystal plastic constitutive parameters by comparing the simulated and experimental stress-strain curves. A total of 11 parameters need to be identified in the crystal plastic constitutive model. First, according to Young's modulus E and Poisson's ratio ν, the elastic constant C is calculated. 11 , C 12 and C 44 :

[0040]

[0041] parameter k=10,q=1,other parameters τ c , τ s ,h 0 , C, D adopt the "trial and error method" to fit the stress-strain curve by comparing the simulation and experiment. The fitting results of all parameters are shown in Table 2:

[0042] Table 2 Microscopic crystal plastic constitutive parameters

[0043]

[0044] 13. Use the sub-modeling method to establish a dual-scale crystal plasticity finite element model, such as Figure 2 As shown;

[0045] 131. The notched specimen is simplified into a two-dimensional rotationally symmetric model, and the Chaboche nonlinear kinematic hardening model is used for macroscopic elastic-plastic finite element analysis. Figure 2 The stress contour diagram is shown.

[0046] 132. According to the stress cloud map obtained by macroscopic finite element analysis, the high stress area is determined as the sub-model area. The Voronoi algorithm is used to divide the sub-model area into a crystal plasticity finite element model. The displacement field extracted from the macroscopic finite element model is used as the boundary condition of the sub-model to perform crystal plasticity finite element analysis.

[0047] 14. Use the fatigue indicator parameters corrected by mean stress to predict the fatigue life of notched specimens. The results are as follows: Figure 3 shown.

[0048] 141. Fatigue Indication Parameter FIP cyc Maximum accumulated plastic slip through a single stabilization cycle express:

[0049]

[0050] in, is the plastic slip rate, and n represents the number of cycles.

[0051] 142. Considering the mean stress effect, FIP cycCorrected to:

[0052]

[0053] Among them, S m is the mean nominal stress, S max is the maximum nominal stress, R σ is the stress ratio.

[0054] 143. Determine the parameter FIP by fitting the test data crit , specifically:

[0055] FIP obtained for different loads i and crystal plasticity models j cyc and experimental life N i Calculating FIP crit :

[0056]

[0057] Those skilled in the art will know that the more V-notch sub-models are used under different load conditions in actual applications, the more likely the analysis results FIP crit The more accurate, in this embodiment, three V-notch sub-models under different load conditions are used for finite element analysis, which can achieve better accuracy, eliminate the influence of load and model on the critical value, and obtain FIP crit =85.

[0058] 144. The obtained FIP crit With the calculated Used to predict fatigue life under actual load N f :

[0059]

[0060] Figure 3 The right side is a comparison chart of the fatigue life prediction value of GH4169 alloy under different loads and the fatigue life test value obtained in step 11. Almost all points fall within the ±2 times error band.

[0061] 2. Construct a probabilistic fatigue life prediction method for notched structures based on a dual-scale modeling method. The specific process is as follows: Figure 5 As shown:

[0062] 21. Consider the dispersion of materials. Based on the statistical distribution of grain size and grain orientation of the material microstructure; use the Voronoi algorithm to generate random micromorphology, the grain size is randomly generated according to the statistical distribution of grain size obtained by measurement; the grain orientation is randomly generated according to the grain orientation distribution obtained by measurement, and the dual-scale crystal plasticity finite element model is given in the form of Euler angles;

[0063] 22. Through sensitivity analysis of crystal plasticity constitutive parameters, select parameters (E, h 0 ,τ c ) as random parameters, where E is the elastic modulus, h 0 is the material plastic hardening related parameter, τ c is a parameter related to the yield strength of the material. The constitutive parameters E and h are quantified using normal distribution. 0 ,τ c , to describe the uncertainty in the uniaxial tensile properties of the material.

[0064] 23. Use Latin hypercube sampling method to generate random constitutive parameters, then use the generated random constitutive parameters as material input in the dual-scale crystal plasticity finite element model, and use fatigue life as output to establish Figure 4 The probabilistic crystal plasticity lifetime prediction framework is shown.

[0065] 24. Perform crystal plasticity finite element analysis on the notched specimen to obtain the stress response of the notched specimen under fatigue load.

[0066] 25. Use the probabilistic crystal plastic life prediction framework to predict the fatigue life of notched specimens under the current stress level;

[0067] 26. Figure 6 As shown, repeat steps 21-25 to obtain the random fatigue life due to material dispersion at different stress levels, perform statistical analysis through normal distribution, and then use the least squares method to fit the formula:

[0068] S max =A(N f ) B

[0069] Among them, A and B are fitting parameters, S max is the maximum nominal stress. The fitting results are shown in Table 3:

[0070] Table 3 SN curve fitting results

[0071]

[0072] The predicted PSN curve is as follows Figure 6 As shown, the results can well describe the dispersion of experimental fatigue life, confirming the feasibility of the proposed probabilistic framework.

[0073] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A notch structure fatigue life prediction method based on probabilistic crystal plasticity, characterized in that: include: S1. Carry out material tensile and fatigue tests on smooth specimens of the same material as the notched specimen to be tested, and obtain stress-strain curves of the smooth specimens under uniaxial tension and fatigue loads; S2. fitting the macroscopic Chaboche nonlinear kinematic hardening model and the microscopic crystal plasticity model parameters according to the stress-strain curve obtained in step S1; S3. Based on the macroscopic Chaboche nonlinear kinematic hardening model and the microscopic crystal plasticity model parameters obtained by fitting in step S2, a dual-scale crystal plasticity finite element model is established according to the notched specimen and the material microstructure; S4. Considering the randomness of the material microstructure and the dispersion of the mechanical properties, the random material parameters are used as the input of the dual-scale finite element model in step S3, and the fatigue life is used as the output to establish a probabilistic crystal plastic life prediction framework; S5. Use the probabilistic crystal plasticity framework in step S4 to predict the fatigue life of the notched structure and obtain a probability-stress-life curve by fitting.

2. The notch structure fatigue life prediction method based on probabilistic crystal plasticity according to claim 1 is characterized in that: The stress-strain curve obtained in step S1 is fitted by the Ramberg-Osgood equation: where σ and ε are the stress and strain at a specific point; E is Young's modulus, K ′ is the cyclic strength coefficient, n ′ is the cyclic strain hardening exponent.

3. The notch structure fatigue life prediction method based on probabilistic crystal plasticity according to claim 2 is characterized in that: The process of fitting the parameters of the macroscopic Chaboche nonlinear kinematic hardening model in step S2 is: The macroscopic Chaboche nonlinear kinematic hardening model is used to simulate the macroscopic elastic-plastic behavior of materials. The macroscopic Chaboche nonlinear kinematic hardening model is expressed as: Among them, Δσ and Δε p denote the stress range and plastic strain range respectively, σ y is the yield strength, C i and γ i is the Chaboche nonlinear kinematic hardening model parameter; C i and γ i The "trial and error method" is used to obtain the stress-strain curves by comparing the simulation and the one obtained in step S1.

4. The notch structure fatigue life prediction method based on probabilistic crystal plasticity according to claim 3 is characterized in that: The process of fitting the microscopic crystal plasticity model parameters in step S2 is: The microscopic crystal plasticity model is used to explain the local crystallographic response between grains to simulate the microscopic mechanical behavior of the material. The microscopic crystal plasticity model is expressed as: in, is the shear strain rate on the αth slip system, is the reference strain rate, k is the strain rate sensitive parameter, τ α and χ α are analytical shear stress and back stress respectively; q is the self-hardening h αα and latent hardening h αβ modulus ratio, h0 is the initial hardening modulus, τ c and τ s is the critical decomposed shear stress and its saturation value, γ α is the cumulative shear strain rate on the αth slip system; is the back stress evolution rate, sech represents the hyperbolic secant function, C and D represent the direct hardening modulus and dynamic recovery coefficient, respectively; The parameters of the microscopic crystal plasticity model include the elastic constant C 11 , C 12 and C 44 , k, q, τ c , τ s ,h0,C,D; First, the elastic constant C is calculated based on Young's modulus E and Poisson's ratio ν 11 , C 12 and C 44 : parameter k=10, q=1; Parameter τ c , τ s , h0, C, D are fitted by the "trial and error method" by comparing the stress-strain curves obtained by simulation and step S1.

5. The notch structure fatigue life prediction method based on probabilistic crystal plasticity according to claim 4 is characterized in that: Step S3 is specifically as follows: S31. The notched specimen is simplified into a two-dimensional rotationally symmetric model, and the macroscopic Chaboche nonlinear kinematic hardening model is used for macroscopic elastic-plastic finite element analysis. S32. According to the results of macroscopic elastic-plastic finite element analysis, the high stress area is determined as the sub-model area, and the sub-model area is divided into a microscopic crystal plasticity model using the Voronoi algorithm. The displacement field extracted from the macroscopic elastic-plastic finite element model is used as the boundary condition of the sub-model to perform crystal plasticity finite element analysis.

6. A notch structure fatigue life prediction method based on probabilistic crystal plasticity according to claim 5, characterized in that: Step S4 specifically includes: S41, considering the material dispersion; based on the statistical distribution of grain size and grain orientation of the material microstructure; using the Voronoi algorithm to generate random micromorphology, the grain size is randomly generated in accordance with the statistical distribution of the measured grain size; the grain orientation is randomly generated in accordance with the measured grain orientation distribution, and the dual-scale crystal plasticity finite element model established in step S3 is assigned in the form of Euler angles; S42, through the sensitivity analysis of the microscopic crystal plasticity model parameters, select the parameters (E, h0, τ c ) as random parameters, where E is the elastic modulus, h0 is the material plastic hardening related parameter, τ c is the material yield strength related parameter; the constitutive parameters E, h0, τ are quantified using normal distribution c , to describe the uncertainty in the uniaxial tensile properties of the material; S43. Use the Latin hypercube sampling method to generate random constitutive parameters, and then use the generated random constitutive parameters as material input in the dual-scale crystal plasticity finite element model established in step S3, and use fatigue life as output, thereby establishing a probabilistic crystal plasticity life prediction framework.

7. A notch structure fatigue life prediction method based on probabilistic crystal plasticity according to claim 6, characterized in that: Step S5 is specifically as follows: S51, performing crystal plasticity finite element analysis on the notched specimen to obtain the stress response of the notched specimen under fatigue load; S52. Use the probabilistic crystal plasticity life prediction framework to predict the fatigue life of the notched specimen under the current stress level; S53, repeating steps S51-S52, obtaining the random fatigue life due to material dispersion under different stress levels, and performing statistical analysis through normal distribution, and then fitting the formula using the least squares method: S max =A(N f ) B 。 8. The notch structure fatigue life prediction method based on probabilistic crystal plasticity according to claim 7, characterized in that: Step S52 is specifically as follows: A1. Fatigue Indication Parameter FIP cyc Maximum accumulated plastic slip through a single stabilization cycle express: in, is the plastic slip rate, n represents the number of cycles; A2. Considering the mean stress effect, FIP cyc Corrected to: Among them, S m is the mean nominal stress, S max is the maximum nominal stress, R σ is the stress ratio; A3. Determine the parameter FIP by fitting the test data crit , specifically: FIP obtained for different loads i and microscopic crystal plasticity models j cyc and experimental life N i Calculating FIP crit : A4. The obtained FIP crit With the calculated Used to predict fatigue life under actual load N f :

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