A fatigue analysis method for notched structures with coupled stress gradient under size effect

Abstract

The present invention discloses a notch structure fatigue analysis method of coupling stress gradient under size effect, which is applied to the field of structural integrity and reliability assessment of special vehicles. In order to solve the problem of fatigue life prediction of complex engineering components with different notch sizes, the present invention introduces the relative stress gradient of the notch tip on the basis of the initial relationship between the critical distance and the fatigue life to explain the size effect of the notch component and corrects the initial relationship between the critical distance and the fatigue life, thereby obtaining a new critical distance model, and thus obtaining a fatigue life prediction model based on stress gradient correction under size effect.

Description

Technical Field

[0001] The invention belongs to the field of special vehicle structural integrity and reliability assessment, and particularly relates to a notch fatigue life prediction technology taking size effect into consideration. Background Art

[0002] With the rapid development and progress of modern aviation, aerospace, navigation and other industrial fields, titanium alloys are used in aircraft, submarines and other fields due to their corrosion resistance, high strength, high toughness and low density. They are also ideal armor materials, which can reduce the weight of special vehicles and improve the protection strength, but they have problems such as high price and difficult welding. They are used in core components such as engine components, and the loads they bear are becoming more and more complex, which puts higher requirements on structural integrity and reliability. Taking special vehicle engine components as an example, in their structural design, in order to meet the requirements of weight reduction and strength increase, the cross-section of the components in the newly proposed design scheme is more and more complex, and stress concentration is inevitable in certain positions under the action of external loads. Therefore, fatigue failure is one of the main fatigue failure modes of special vehicle structural components. In the research and analysis of fatigue, the fatigue failure of notched structures under the effect of size effect has always been a hot topic of research. The stress concentration of notched components and the support effect of notches are key issues in the design of structural mechanical integrity. At present, the research on the size effect caused by the notch support effect is not perfect enough and needs further in-depth discussion. Based on the urgent need for notch structural strength and fatigue analysis, in order to ensure the structural integrity of engine components, a notch fatigue life prediction model considering size effect needs to be urgently solved.

[0003] The key to the multi-axial fatigue life prediction problem of notched parts is to find a suitable method to describe and analyze the stress concentration phenomenon at the notch, calculate its fatigue cumulative damage, and then link the calculated damage parameters with the life equation. So far, there has been a deep accumulation of research on the notch effect, and a series of analysis models have been established. According to the different interpretation ideas of the fatigue notch effect and the corresponding description parameters, the fatigue life analysis methods of notched parts can be divided into three categories: local stress-strain method, stress gradient method and critical method. Among them, the critical distance theory, stress field intensity method and high stress volume method are more commonly used fatigue life analysis methods for notched parts; and the above three commonly used methods highlight a common point-considering the effect of the overall effective damage area on fatigue damage accumulation.

[0004] In order to characterize the effect of notch on notch fatigue strength, the critical distance theory based on the effective stress method was proposed and widely used. The critical distance method has achieved good prediction results in notch fatigue analysis and has the characteristics of simple calculation. With in-depth research, it was found that the notch fatigue analysis results based on the critical distance method under different notch sizes showed large errors. Therefore, notch fatigue analysis under size effect is of great significance to engineering applications. Summary of the invention

[0005] In order to solve the above technical problems, the present invention comprehensively considers the influence of notch fatigue and size effect, couples stress gradient distribution on the basis of critical distance method to characterize the influence of notch size effect, and proposes a notch fatigue life prediction method which is simple in calculation and takes size effect into consideration.

[0006] The technical solution adopted by the present invention is: a fatigue analysis method for notch structures with coupled stress gradients under size effect. Based on the initial formula for the relationship between critical distance and fatigue life, the relative stress gradient at the notch tip is introduced to correct the size effect of the notch component, and a new critical distance model is obtained, thereby obtaining a fatigue life prediction model based on stress gradient correction under size effect; the fatigue life prediction model is used to predict the fatigue life of the notch structure.

[0007] The process of obtaining the fatigue life prediction model based on stress gradient correction under size effect is as follows:

[0008] S1. Perform elastoplastic finite element analysis on the notched component to be analyzed, and determine the dangerous area near the notch tip where fatigue failure may occur based on the equivalent stress cloud diagram, wherein the dangerous area includes a number of units;

[0009] S2. Extract the maximum principal stress distribution of all elements near the notch tip within the stable cycle;

[0010] S3. Taking the maximum principal stress distribution of all units obtained in step S2 as input, combined with the SN curve of the smooth specimen, the critical distance value is determined according to the maximum principal stress distribution of all units in the direction of the fastest stress drop near the notch tip;

[0011] S4. Calculate the relative stress gradient at the notch tip according to the maximum principal stress distribution of all units in the direction of fastest stress drop near the notch tip obtained in S3;

[0012] S5. Combine the relative stress gradient with the critical distance and fatigue life to calculate the critical distance model based on the relative stress gradient correction;

[0013] S6. Substitute the critical distance value obtained in step S3 into the modified critical distance model to obtain the fatigue life prediction of the notched component.

[0014] The critical distance value of step S3 is obtained by integrating the maximum principal stress in the direction of the fastest stress drop near the notch tip from the notch tip to the position equal to the notch effective stress; the specific calculation formula is:

[0015]

[0016] Among them, σ effrepresents the effective stress, l0 is half of the critical distance value in the critical distance line method, σ1 is the maximum principal stress in the direction of the fastest stress drop near the notch tip, and θ is the angle between the maximum principal stress and the polar coordinate.

[0017] That is, according to the known effective stress, substituting it into the above formula, we can get l0, and then according to the relationship between l0 and the critical distance value, we can get the critical distance value.

[0018] Step S4: Relative stress gradient S at the notch tip σ The calculation formula is:

[0019]

[0020] Among them, σ max is the maximum principal stress at the notch tip, S σ is the normalized relative stress gradient at the notch tip.

[0021] The critical distance model for notch component correction described in step S5 is obtained based on finite element calculation of the notch component.

[0022] The critical distance model expression of the notch component correction is:

[0023] Where l is the critical distance of the notch, S σ is the relative stress gradient at the notch tip, N f is the fatigue life of the notched part, a m , a2, b2 are fitting parameters.

[0024] Beneficial effects of the invention: The method of the invention introduces the relative stress gradient at the notch tip to correct the size effect of the notched component based on the initial formula of the relationship between the critical distance and the fatigue life, and obtains a new critical distance model, thereby obtaining a fatigue life prediction model based on stress gradient correction under the size effect; it has the following advantages:

[0025] (1) The critical distance and fatigue life of notched components with different sizes are analyzed, reflecting the influence of size effect on notch fatigue analysis;

[0026] (2) A size effect correction factor based on stress gradient, namely relative stress gradient, is proposed. The extraction and normalization of relative stress gradient are simple and easy to operate. The critical distance model corrected by relative stress gradient has small dispersion in prediction results and high accuracy.

[0027] (3) By coupling the critical distance model and Weibull distribution, a notch fatigue failure probability assessment method considering the size effect is proposed, which effectively describes the dispersion of fatigue life test data of notched components. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is the size of the TC4 alloy fatigue test specimen provided in the embodiment of the present invention;

[0029] in Figure 1 (a) is the stress concentration factor K t =3 notched specimen size, Figure 1 (b) is the stress concentration factor K t =5 notched specimen size;

[0030] Figure 2 It is a flow chart of the scheme provided by the implementation of the present invention;

[0031] Figure 3 It is the critical distance data obtained by the present invention based on finite element simulation and experimental data;

[0032] Figure 4 is the critical distance prediction result obtained by the present invention according to the proposed critical distance model;

[0033] Figure 5 It is the notch fatigue predicted life obtained by the present invention according to the fatigue life prediction method proposed. DETAILED DESCRIPTION

[0034] 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.

[0035] Taking the fatigue life prediction process of notched components as an example, by establishing the relationship between effective stress and fatigue life, the effective stress of notched components is determined by using the critical distance to realize the fatigue life prediction of notched components, which specifically includes the following steps:

[0036] 1. Establish the relationship between effective stress and fatigue life

[0037] 1.1. The relationship between the effective stress and fatigue life of the notched part is established using the SN curve of the smooth specimen as follows:

[0038] σ eff =aN f b =σ0

[0039] Among them, σ eff is the effective stress of the notched specimen, σ0 is the fatigue strength of the smooth specimen, a and b are fitting parameters;

[0040] 1.2. Yes Figure 1 The notched specimens shown were subjected to fatigue life tests, wherein the test of the TC4 specimen was carried out at room temperature (20°C). Figure 1 In the figure, the notch radius of the TC4 specimen is r, the notch angle is θ, D is the diameter of the specimen clamping end, and d is the diameter of the specimen gauge section.

[0041] 1.3. Yes Figure 1 The notched specimen shown in the figure was modeled and subjected to elastic-plastic finite element modeling analysis to extract the maximum principal stress distribution of the unit near the notch tip within the stable cycle.

[0042] Finite element analysis including theoretical stress concentration factor K t =3, 5, and the material performance parameters are shown in Table 1.

[0043] Table 1 Static material parameters and fatigue parameters of TC4

[0044] alloy E(GPa) <![CDATA[v e ]]> <![CDATA[σ y (MPa)]]> K′(MPa) n′ TC4 109 0.34 834.1 1420 0.07

[0045] Combined with the maximum principal stress distribution data in the direction of the fastest stress drop near the notch obtained from the unit near the notch tip in a stable cycle, the effective stress and critical distance l under different notch sizes are calculated, and the relationship between the critical distance of the notched specimen and the fatigue life is constructed to prepare for the subsequent derivation of the fatigue life calculation formula.

[0046] 2. Construct a notch fatigue life prediction method considering size effect. The specific process is as follows: Figure 2 As shown:

[0047] 2.1. Elastic-plastic finite element analysis is performed on notched components, and the fatigue life prediction of notched components is determined through the SN curve of smooth components and the relationship between critical distance and fatigue life. It is worth noting that fatigue analysis of notched components based on the critical distance method reveals the influence of size effect on fatigue analysis results, that is, the relationship between critical distance and fatigue life will change due to the change of notch size. The relative stress gradient at the notch tip is introduced to explain the influence of size effect on critical distance and fatigue life.

[0048] 2.2. The relative stress gradient at the notch tip is calculated based on the maximum principal stress distribution in the direction of the fastest stress drop near the notch tip obtained by finite element simulation in step 2.1. The critical distance model considering the size effect is calculated based on the relative stress gradient, and then substituted into the notch fatigue life prediction iterative flow chart (such as Figure 2 The predicted life of the notched component is obtained by using the following method. The implementation process of step 2.2 is as follows:

[0049] A1. The initial formula based on the relationship between critical distance and fatigue life is:

[0050] l=AN f B

[0051] A2. Model the notched component and perform elastic-plastic finite element analysis to extract the maximum principal stress of the unit near the notch tip in the stable cycle. Generally, the unit within 2 mm near the notch tip can be extracted; obtain the maximum principal stress distribution in the direction of the fastest stress drop near the notch tip and the relative stress gradient at the notch tip:

[0052]

[0053] Among them, σ max is the maximum principal stress at the notch tip, S σ is the relative stress gradient at the notch tip, σ represents the maximum principal stress, and x represents the distance from the maximum principal stress in the direction of the fastest stress drop to the notch tip.

[0054] A3. According to the influence of the relative stress gradient at the notch tip on the critical distance and fatigue life in step A2, give physical meanings to parameters A and B:

[0055]

[0056] A4. The initial fatigue life prediction formula based on size effect proposed by the present invention is:

[0057]

[0058] Where l is the critical distance of the notch, S σ is the relative stress gradient at the notch tip, N f is the fatigue life of the notched part, a1, b1, a2, b2 are fitting constants;

[0059] A5. The intermediate formula for fatigue life prediction based on size effect is derived and simplified according to the mathematical model:

[0060]

[0061] Where l is the critical distance of the notch, S σ is the relative stress gradient at the notch tip, N f is the fatigue life of the notched part, a1, a2, b2, m are fitting constants;

[0062] A6. Based on the formula in step A1, combined with the relationship between the relative stress gradient and the size effect obtained in step A3 in step 2.2, the critical distance is corrected to obtain a new critical distance model expression:

[0063] Where l is the critical distance of the notch, S σ is the relative stress gradient at the notch tip, N f is the fatigue life of the notched part, a m, a2, b2 are fitting parameters.

[0064] In early studies, fatigue crack propagation and fatigue strength / life were proved to be functions of stress gradient. The present invention obtains relative stress gradient based on normalization of stress gradient at notch tip, and then uses relative stress gradient for size effect correction, which can expand the applicability of the model. The relative stress gradient at the tip of notch component is affected by specimen size and notch shape and size. Therefore, using relative stress gradient at notch tip to describe the influence of size effect on fatigue strength / life can improve the accuracy and reliability of the model.

[0065] Fitting parameters a1, b1, a2, b2, a m , k is determined as follows: firstly, fatigue tests are performed on at least two notched specimens of different sizes, and then finite element analysis is performed by applying the same load as in the fatigue test to the specimens of different sizes to obtain the stress distribution and critical distance near the notch tip under each loading, and the stress gradient at the notch tip is normalized to obtain the relative stress gradient of each notched specimen; according to the relationship among the critical distance, fatigue life and relative stress gradient and the model proposed in the present invention, the values ​​of the model parameters a1, b1, a2, b2 are determined by fitting with the mathematical analysis software Matlab by the least squares method, and then the model parameter a is calculated according to the parameters a1, b1, a2, b2. m , the value of k determines the final form of the model proposed in this invention.

[0066] like Figure 5 The figure shows the comparison between the predicted life and the tested life of the TC4 notched specimen at room temperature by the proposed method. From the comparison results, it can be seen that the method proposed in the present invention can effectively characterize the influence of the size effect on the notch fatigue analysis; in addition, the fatigue life prediction results of the notched specimens of different sizes for each material by the method proposed in the present invention are all within the 2-fold error band, with high accuracy. The fatigue test data of the TC4 specimen and the relative stress gradient at the notch tip are shown in Table 2.

[0067] Table 2 Fatigue test data of TC4 under symmetrical load

[0068]

[0069]

[0070] 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 analysis method with coupled stress gradient under size effect, characterized in that: Based on the initial relationship between critical distance and fatigue life, the relative stress gradient at the notch tip is introduced to explain the size effect of the notched component and correct the initial relationship between critical distance and fatigue life, thus obtaining a new critical distance model, thereby obtaining a fatigue life prediction model based on stress gradient correction under size effect; the fatigue life prediction model is used to predict the fatigue life of the notched structure; The process of using this fatigue life prediction model to predict the fatigue life of the notched structure is as follows: S1. Perform elastoplastic finite element analysis on the notched component to be analyzed, and determine the dangerous area near the notch tip where fatigue failure may occur based on the equivalent stress cloud diagram, wherein the dangerous area includes a number of units; S2. Extract the maximum principal stress distribution of all elements near the notch tip within the stable cycle; S3. Taking the maximum principal stress distribution obtained in step S2 as input, combined with the SN curve of the smooth specimen, the critical distance value is determined according to the maximum principal stress distribution of all units in the direction of the fastest stress drop near the notch tip; S4. Calculate the relative stress gradient at the notch tip according to the maximum principal stress distribution of all units in the direction of fastest stress drop near the notch tip obtained in S3; S5. Combining the relative stress gradient with the critical distance and fatigue life, a critical distance model based on relative stress gradient correction is calculated; the critical distance model expression of the notched component correction is: Where l is the critical distance of the notch, S σ is the relative stress gradient at the notch tip, N f is the fatigue life of the notched part, a m , a2, b2 are fitting parameters; S6. Substitute the critical distance value obtained in step S3 into the modified critical distance model to obtain the fatigue life prediction of the notched component.

2. The notch structure fatigue analysis method of coupled stress gradient under size effect according to claim 1 is characterized in that: The critical distance value of step S3 is calculated according to the following formula: Among them, σ eff represents the effective stress determined by the SN curve of the smooth specimen, l0 is half of the critical distance value in the critical distance line method, σ1 is the maximum principal stress in the direction of the fastest stress drop near the notch tip, x represents the distance from the maximum principal stress to the notch tip, and θ is the angle between the maximum principal stress and the polar coordinate.

3. The notch structure fatigue analysis method of coupled stress gradient under size effect according to claim 2 is characterized in that: Step S4: Relative stress gradient S at the notch tip σ The calculation formula is: Among them, σ max is the maximum principal stress at the notch tip, i.e., σ max =σ1(x=0),S σ is the normalized relative stress gradient at the notch tip.

4. The notch structure fatigue analysis method of coupled stress gradient under size effect according to claim 1 is characterized in that: The critical distance model for notch component correction described in step S5 is obtained based on finite element calculation of the notch component.

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