A cross-scale structure multi-axial fatigue life prediction method

Abstract

The present application relates to the research of structural fatigue life, in particular to a method for predicting the fatigue life of a complex structural part under multi-axial load; the present application firstly carries out tensile and fatigue experiments of the structural material to obtain its macroscopic material properties; then measures the polycrystalline indentation modulus of the structural material to obtain the indentation modulus of different grain orientations and the single-crystal elastic coefficient and other microscopic material properties; finally, a cross-scale finite element analysis model of the structural part is established to predict the multi-axial fatigue life of the structural part; the present application considers the actual structural characteristics of the bearing part, and the description of its fatigue behavior is more accurate; by simulating the actual loading mode of the structural part, the fatigue life of the structural part under complex load can be predicted, and the error caused by simplifying the load can be reduced; by using the submodel nesting method, the macrostructure and microstructure of the part to be predicted are comprehensively considered, which can greatly improve the prediction accuracy.

Description

Technical Field

[0001] This invention relates to the study of fatigue life of structural components, and more specifically to a method for predicting the fatigue life of complex structural components under multiaxial loads. Background Technology

[0002] Transmission components of large transportation equipment such as high-speed trains, airplanes, and ships are frequently subjected to various loads, including tension, torsion, and bending, during use, leading to multiaxial fatigue failure. Furthermore, due to the complex and varied structures and load patterns of these components, traditional life prediction methods applicable to standard fatigue parts are not highly accurate in predicting the fatigue life of structural components. Therefore, finding a more accurate and effective multiaxial fatigue life prediction method for structural components remains a major challenge in current engineering. Patent CN202111512293.8 discloses a multiaxial fatigue life prediction method that predicts the multiaxial fatigue life of materials by simulating and calculating the plastic strain energy during the fatigue process. Patent CN202210859161.0 discloses a fatigue life prediction method under multiaxial variable amplitude loading, which predicts the multiaxial fatigue life of samples by considering the additional strengthening effect of non-proportional load paths and utilizing linear damage theory. Patent CN202210120848.2 discloses a multiaxial fatigue life prediction method for metallic materials based on virtual strain energy, applicable to fatigue life analysis under low-cycle, high-cycle, and different load paths. However, these fatigue life prediction methods still have the following shortcomings: ① They do not consider the influence of the actual structure on its multiaxial fatigue life; ② They are difficult to predict the fatigue life of structural components under complex loads; ③ They only analyze the fatigue behavior of materials at the macroscopic or microscopic level, ignoring the fact that fatigue failure is a cross-scale problem, thus resulting in low prediction accuracy. These shortcomings cause inconvenience for multiaxial fatigue life prediction of cross-scale structures. Summary of the Invention

[0003] The technical problem to be solved by this invention is to propose a method for predicting the multiaxial fatigue life of complex structural components across scales. This method predicts the multiaxial fatigue life by establishing a macro-micro coupled model to simulate the micro-mechanical response of the critical section of the structural component.

[0004] To solve the above technical problems, the present invention adopts the following technical solution, and the present invention adopts the following steps:

[0005] ① Conduct tensile and fatigue tests on structural component materials to obtain their macroscopic material properties;

[0006] 101 Conduct tensile and fatigue tests on structural components to obtain material properties such as Young's modulus, Poisson's ratio and shear modulus, as well as their stress-strain curves;

[0007] 102. The nonlinear combined hardening law of nonlinear kinematic hardening and isotropic hardening is applied to the macroscopic model. The nonlinear kinematic hardening components are as follows:

[0008]

[0009] Where C is the yield surface translation ratio; γ rt σ is the relaxation rate of the yield surface translation during the accumulation of plastic deformation; ij and α ij These are the flow stress and back stress, respectively; σ f and The distribution is equivalent stress and equivalent plastic strain;

[0010] The isotropic hardening components are as follows:

[0011]

[0012] Where σ0 is the initial yield stress, Q max b and b are the maximum change in yield surface and the rate of change in yield surface, respectively; 103 The established macroscopic model is used to simulate tensile tests and fatigue tests to obtain its stress-strain curves and determine the macroscopic hardening parameters of the material;

[0013] ② Measure the polycrystalline indentation modulus of the structural component material to obtain its microscopic material properties such as indentation modulus and single crystal elastic coefficient under different grain orientations;

[0014] ③ Establish a multi-scale finite element analytical model for structural components to predict the multiaxial fatigue life of structural components;

[0015] 301. Using electron backscatter diffraction image data, a microscopic representative volume element model of the structural component material is established; the crystal plastic constitutive equation of the material is as follows:

[0016]

[0017]

[0018] in, It is the shear strain rate, τ α and τ c α These are the analytical shear stress and the critical analytical shear stress, respectively, where m is the rate sensitivity parameter and q is the analytical shear stress. sl δ represents the ratio of latent hardening to spontaneous hardening. αr Let h be the Kronecker function. r Let h0 be the potential hardening modulus of the material and h0 be the initial hardening modulus τ. s τ is the saturation stress, and τ0 is the initial critical shear stress;

[0019] 302. Embed the microscopic representative volume element into the macroscopic model in step ①, map the displacement of the macroscopic model onto the boundary of the microscopic representative volume element, obtain the stress-strain curve of the microscopic representative volume element, and determine the microcrystalline plasticity parameters of the material.

[0020] 303 Extract the actual dimensions and boundary conditions of the structural components, establish a macroscopic finite element model of the structural components, and determine the critical sections where cracks are prone to initiation; embed the microscopic representative volume elements into the critical sections of the macroscopic model of the structural components, and map the displacement of the macroscopic model to the boundary of the corresponding microscopic representative volume elements;

[0021] 304. The fatigue response of the structural component in the early stage of crack initiation was simulated using the established multi-scale crystal plastic finite element model, and its local fatigue indicator parameters were calculated according to equation (5):

[0022]

[0023] in, This refers to the range of cyclic plastic shear strain. For peak stress, σ y It is the cyclic yield strength, and k is a constant that controls the effect of stress;

[0024] Calculate its non-local fatigue indication parameters according to formula (6):

[0025]

[0026] Among them, V grain (x) represents all regions of the grain containing point x, FIP FS (x) Local fatigue indicator parameters at point x;

[0027] The maximum non-local fatigue indicator parameter for each cycle can be calculated using equation (7):

[0028]

[0029] Calculate the maximum non-local fatigue indicator parameter FIP in standard fatigue tests. * cyc FIP * cyc and its fatigue life N i Substituting into equation (8), we obtain FIP. crit and m p :

[0030]

[0031] The obtained FIP crit and m p The value, compared with the calculated maximum nonlocal fatigue indicator parameter FIP of the structural member. *cyc Substituting into equation (8), the multiaxial fatigue life N of the structural component under actual load can be predicted. f .

[0032] Step ② includes: 201 wire cutting a portion of the material on the surface of the structural component and polishing the sample; 202 performing a nanoindentation experiment on the sample and then scanning its electron backscatter diffraction image;

[0033] 203. Obtain the indentation modulus of the structural component material with different grain orientations and calculate its elastic coefficient. The calculation process is as follows:

[0034]

[0035]

[0036]

[0037]

[0038] Among them, M (100) and M (111) for <100> and <111> Orientation indentation modulus, a hkl c hkl A 0,hkl and B hkl Let A be a constant, and C be the anisotropy ratio. 11 C 12 and C 44 Let be the elastic coefficients to be determined, and K, E, G, and v be the bulk modulus, Young's modulus, and Poisson's ratio, respectively.

[0039] Compared with the prior art, the present invention has the following advantages: the present invention takes into account the actual structural characteristics of the load-bearing component, and its fatigue behavior is described more accurately; by simulating the actual loading mode of the structural component, the fatigue life of the structural component under complex loads can be predicted, reducing the error caused by the simplified load; by using the nested sub-model method, the macroscopic and microscopic structures of the component to be predicted are comprehensively considered, which can greatly improve the accuracy of the prediction. Attached Figure Description

[0040] Figure 1 For tensile tests and macroscopic model stress-strain curves;

[0041] Figure 2 For tensile and compressive fatigue experiments and stress-strain curves of macroscopic models;

[0042] Figure 3 The graph shows the polycrystalline indentation modulus results.

[0043] Figure 4 The microscopic representative volume element model;

[0044] Figure 5 It is a macro-micro coupling model;

[0045] Figure 6 Stress-strain curves for tensile tests and macroscopic models representing microscopic volume elements;

[0046] Figure 7 For tensile and compressive fatigue experiments and stress-strain curves of macroscopic models representing microscopic volume elements;

[0047] Figure 8 A macro-micro coupling model for structural components;

[0048] Figure 9 The results are the fatigue life prediction results for structural components;

[0049] Figure 10 This is a flowchart of a method for predicting fatigue in multi-scale structures. Detailed Implementation

[0050] The present invention will now be described in detail with reference to the accompanying drawings and specific examples. The main steps are as follows:

[0051] ① Conduct tensile and fatigue tests on structural component materials to obtain their macroscopic properties;

[0052] 101 Given that the material of the structural component whose fatigue life needs to be predicted is AISI 9310 steel that has been quenched and tempered, tensile and fatigue tests are carried out to obtain its material properties such as Young's modulus E = 197.2 GPa, Poisson's ratio v = 0.3032 and shear modulus G = 75.7 GPa, as well as its stress-strain curve.

[0053] Programming 102 applies the nonlinear combined hardening laws of nonlinear kinematic hardening and isotropic hardening to a macroscopic model. The nonlinear kinematic hardening components are as follows:

[0054]

[0055] Where C is the yield surface translation ratio; γ rt σ is the relaxation rate of the yield surface translation during the accumulation of plastic deformation; ij and α ij These are the flow stress and back stress, respectively; σ f and The distribution is equivalent stress and equivalent plastic strain.

[0056] Furthermore, the isotropic hardening components are as follows:

[0057]

[0058] Where σ0 is the initial yield stress, Q maxb and b represent the maximum change in yield surface and the rate of change in yield surface, respectively.

[0059] 103. Tensile and fatigue tests were simulated using the established macroscopic model to obtain stress-strain curves. By continuously adjusting the input parameters to fit the experimentally obtained curves, the macroscopic hardening parameters of the material were finally determined. The fitted stress-strain curves are shown below. Figure 1 and Figure 2 As shown in Table 1, the macroscopic hardening parameters of this material are as follows.

[0060] Table 1 Material parameters of the macroscopic model

[0061]

[0062] ② Measure the polycrystalline indentation modulus of the structural component material to obtain its microscopic material properties;

[0063] 201. A portion of the material was wire-cut on the surface of the structural component, and the sample was polished to meet the surface requirements for nanoindentation and electron backscatter diffraction (EBSD) image scanning.

[0064] Nanoindentation experiments were performed on the 202 samples, and then their EBSD images were scanned. The results are as follows: Figure 3 As shown in Table 2, the calculation results of the polycrystalline indentation modulus are as follows.

[0065] Table 2 Calculation results of polycrystalline indentation modulus

[0066]

[0067] 203. Based on the above experimental results, the indentation modulus of the structural component material with different grain orientations was obtained, and its elastic coefficient was calculated. The calculation results are shown in Table 3, and the calculation process is as follows:

[0068]

[0069]

[0070]

[0071]

[0072] Among them, M (100) and M (111) for <100> and <111> Orientation indentation modulus, a hkl c hkl A 0,hkl and B hkl Let A be a constant, and C be the anisotropy ratio. 11 C 12 and C 44Let be the elastic coefficients to be determined, and K, E, G, and v be the bulk modulus, Young's modulus, and Poisson's ratio, respectively.

[0073] Table 3 shows the single-crystal elastic constants of AISI 9310 calculated using indentation modulus.

[0074]

[0075] Furthermore, step ③ includes:

[0076] 301. Based on the previously obtained EBSD data, a microscopic representative volumetric element model of the structural component material is established, such as... Figure 4 As shown;

[0077] Furthermore, a crystal plasticity model for this material is established, and the crystal plasticity constitutive equation is shown below:

[0078]

[0079]

[0080] in, It is the shear strain rate, τ α and τ c α These are the analytical shear stress and the critical analytical shear stress, respectively, where m is the rate sensitivity parameter and q is the analytical shear stress. sl δ represents the ratio of latent hardening to spontaneous hardening. αr Let h be the Kronecker function. r Let h0 be the potential hardening modulus of the material and h0 be the initial hardening modulus τ. s τ is the saturation stress, and τ0 is the initial critical shear stress.

[0081] Furthermore, the microscopic representative volume element is embedded into the previously established macroscopic model, and the displacement of the macroscopic model is mapped onto the boundary of the microscopic representative volume element to determine its boundary conditions, specifically as follows: Figure 5 As shown; simulations of previous tensile and fatigue tests were performed to obtain stress-strain curves representing the microscopic volume elements; by continuously adjusting the input parameters to fit the experimentally obtained curves, the microcrystalline plasticity parameters of the material were finally determined, where the fitted curves representing the microscopic volume elements are shown in the figure. Figure 6 and Figure 7 As shown in Table 4, the microcrystalline plasticity parameters are as follows.

[0082] Table 4. Microcrystalline Plasticity Parameters of AISI 9310 Steel

[0083]

[0084] 302 Here, fatigue components subjected to 90° out-of-phase loading with different strain amplitudes and tensile-torsional multiaxial loads are selected as examples to predict fatigue life, extract their actual dimensions and boundary conditions, establish a macroscopic finite element model of the structural component, and perform simulation to find the dangerous section where cracks are prone to initiation.

[0085] Furthermore, the microscopic representative volume element is embedded into the critical section of the macroscopic model of the structural component, and the displacement of the macroscopic model is mapped to the boundary of the corresponding microscopic representative volume element, such as... Figure 8 As shown.

[0086] 303 The fatigue response of the structural component in the early stage of crack initiation was simulated using the established multi-scale crystal plastic finite element model, and its local fatigue indicator parameters were calculated according to Equation (5):

[0087]

[0088] in, This refers to the range of cyclic plastic shear strain. For peak stress, σ y It is the cyclic yield strength, and k is a constant that controls the effect of stress.

[0089] Furthermore, its non-local fatigue indication parameters are calculated according to equation (6):

[0090]

[0091] Among them, V grain (x) represents all regions of the grain containing point x, FIP FS (x) Local fatigue indicator parameters at point x.

[0092] Furthermore, the maximum nonlocal fatigue indicator parameter for each cycle can be calculated using equation (7):

[0093]

[0094] Furthermore, the maximum non-local fatigue indicator parameter FIP from the previously performed standard fatigue test was calculated. * cyc FIP * cyc and its fatigue life N i Substituting into equation (8), we obtain FIP. crit =3.722×10 -5 and m p =3.614:

[0095]

[0096] Furthermore, the obtained FIP crit and mp The value, compared with the calculated maximum nonlocal fatigue indicator parameter FIP of the structural member. * cyc Substituting into equation (8), the multiaxial fatigue life N of this structural component under actual load is calculated. f Predictions were made, and the results were as follows: Figure 9 As shown, the model's prediction accuracy is within the 50% error range. The entire process of the multi-scale structural fatigue prediction method is as follows: Figure 10 As shown.

[0097] The embodiments described above are merely preferred embodiments of the present invention, and not an exhaustive list of all possible implementations of the present invention. Any obvious modifications made by those skilled in the art without departing from the principles and spirit of the present invention should be considered to be included within the scope of protection of the claims of the present invention.

Claims

1. A method for predicting the multiaxial fatigue life of structures across scales, characterized in that... It includes the following steps: ① Conduct tensile and fatigue tests on structural component materials to obtain their macroscopic material properties; 101 Conduct tensile and fatigue tests on structural components to obtain Young's modulus, Poisson's ratio, shear modulus, and their stress-strain curves; 102. The nonlinear combined hardening law of nonlinear kinematic hardening and isotropic hardening is applied to the macroscopic model. The nonlinear kinematic hardening components are as follows: Where C is the yield surface translation ratio; γ rt The relaxation rate of the yield surface translation during the accumulation of plastic deformation; and These are flow stress and back stress, respectively; and These are equivalent stress and equivalent plastic strain, respectively; The isotropic hardening components are as follows: in, Q is the initial yield stress. max b and b represent the maximum change in yield surface and the rate of change in yield surface, respectively; 103. Using the established macroscopic model, tensile and fatigue tests were simulated to obtain stress-strain curves and determine the macroscopic hardening parameters of the material. ② Measure the polycrystalline indentation modulus of the structural component material to obtain the indentation modulus and single-crystal elastic coefficient for different grain orientations; ③ Establish a multi-scale finite element analytical model for structural components to predict their multiaxial fatigue life; 301. Using electron backscatter diffraction image data, a microscopic representative volume element model of the structural component material is established; the crystal plastic constitutive equation of the material is as follows: in, It is the shear strain rate. and These represent the analytical shear stress and the critical analytical shear stress, respectively, with m being the rate sensitivity parameter. The ratio of latent hardening to spontaneous hardening. Let h be the Kronecker function. r h0 is the potential hardening modulus of the material, and h0 is the initial hardening modulus. For saturation stress, The initial critical shear stress; 302. Embed the microscopic representative volume element into the macroscopic model in step ①, map the displacement of the macroscopic model onto the boundary of the microscopic representative volume element, obtain the stress-strain curve of the microscopic representative volume element, and determine the microcrystalline plasticity parameters of the material. 303 Extract the actual dimensions and boundary conditions of the structural components, establish a macroscopic finite element model of the structural components, and determine the critical sections where cracks are prone to initiation; embed the microscopic representative volume elements into the critical sections of the macroscopic model of the structural components, and map the displacement of the macroscopic model to the boundary of the corresponding microscopic representative volume elements; 304 The fatigue response of the structural component in the early stage of crack initiation was simulated using the established multi-scale crystal plastic finite element model, and the local fatigue indicator parameters were calculated according to equation (5): in, This refers to the range of cyclic plastic shear strain. Peak stress, It is the cyclic yield strength, and k is a constant that controls the effect of stress; Calculate the non-local fatigue indicator parameters according to formula (6): in, This represents the entire region containing the grain at point x. The local fatigue indicator parameter represents point x; The maximum non-local fatigue indicator parameter for each cycle is calculated by equation (7): Calculate the maximum non-local fatigue indicator parameter FIP in standard fatigue tests. * cyc FIP * cyc and its fatigue life N i Substituting into equation (8), we obtain FIP. crit and m p : The obtained FIP crit and m p The value, compared with the calculated maximum nonlocal fatigue indicator parameter FIP of the structural member. * cyc , scaling This allows for the prediction of the multiaxial fatigue life of the structural component under actual load. .

2. The method for predicting multiaxial fatigue life of a multi-scale structure according to claim 1, characterized in that... Step ② includes:

201. Cut a portion of the material on the surface of the structural component by wire cutting, and then polish the sample. 202 nanoindentation experiments were performed on the sample, and then electron backscatter diffraction images were obtained by scanning.

203. Obtain the indentation modulus of the structural component material with different grain orientations and calculate the elastic coefficient. The calculation process is as follows: Among them, M (100) and M (111) for <100> and <111> Orientation indentation modulus, a hdl c hdl A 0,hdl and B hdl Let A be a constant, and C be the anisotropy ratio. 11 C 12 and C 44 Let be the elastic modulus to be determined, and K, E, G, and v be the bulk modulus, Young's modulus, shear modulus, and Poisson's ratio, respectively.

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