A new stress gradient characterization and verification method

Abstract

The application discloses a new stress gradient characterization and verification method, belongs to the fatigue life prediction field of materials, and specifically comprises the following steps: firstly, a finite element model A of an actual mechanical structure is established, a dangerous point is selected, and an elastic stress gradient influence factor Y is calculated; then, notch finite element models with different stress concentration coefficients K t Values are established, and each dangerous point a' is arranged, stress gradient influence factors Y1, Y2,... Y n are calculated at the dangerous point a' in each model, compared with Y, and used for reflecting the stress gradient distribution at the dangerous point a; finally, Y is introduced into a life equation, fitting parameters are introduced simultaneously for correcting Y, a corrected life model is obtained, and the stress gradient at the dangerous point a is characterized; and a stretching test piece containing at least two notches is designed, different notch sizes are designed, and the stress gradient at the dangerous point a is verified; and the application improves the precision of predicting the fatigue life on the actual mechanical structure.

Description

Technical Field

[0001] This invention belongs to the field of fatigue life prediction of materials, specifically a new method for stress gradient characterization and verification. Background Technology

[0002] The fatigue life of materials has always been a key focus in engineering. Since the 19th century, researchers have proposed several mathematical models for predicting the fatigue life of materials, which can be divided into two categories according to the type of independent variable: strain life models and stress life models. Ultimately, both strain life models and stress life models need to be applied to actual structures.

[0003] Because of dimensional variations in actual structures, stress concentration points exist, and stress gradients also exist near these stress concentration points. The basic equations of the fatigue life equation are applicable to cases with uniform stress distribution. For actual structures with stress gradients, stress gradient correction terms need to be introduced into the equations.

[0004] How to comprehensively and accurately represent the influence of stress gradient has become an important issue. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a novel method for characterizing and verifying stress gradients. By analyzing the finite element model of a mechanical structure, points with high stress or strain are selected as critical points, and the stress gradient distribution near the critical points is obtained. After transformation, a stress gradient correction factor is obtained to represent the stress gradient distribution at the critical point location, and further verification is achieved through experiments.

[0006] The specific steps of the new stress gradient characterization and verification method are as follows:

[0007] Step 1: Establish a finite element model A of the actual mechanical structure, perform static analysis on the model under actual load, select the point with the largest stress or strain on model A as the critical point based on the analysis results, and calculate the elastic stress gradient influence factor Y at the critical point under actual load.

[0008] For the critical point a where the stress decreases the fastest, a corresponding stress decrease path is selected on the actual mechanical structure, and a normalized curve of stress versus distance is established along this path. The vertical axis of the curve is the ratio of the stress at each point on the path to the stress at the starting point of the path, and the horizontal axis is the ratio of the distance from each point on the path to the starting point of the path to the total length of the path.

[0009] Integrating the curve yields the area enclosed by the curve and the coordinate axes, denoted as S. The stress gradient influence factor at the critical point a is then Y = S.

[0010] Similarly, for the remaining critical points on the finite element model A of the actual mechanical structure, the stress gradient influence factor Y is calculated for each of them.

[0011] Step 2: Following the finite element model A, establish different stress concentration factors K. t The finite element model with gaps in the values ​​B1, B2, ... B n A critical point a' is set at a corresponding location on each model, and the stress gradient influence factors Y1, Y2, ... Y at the critical point a' under each model are calculated. n ;

[0012] Step 3: Calculate the stress gradient influence factors Y1, Y2, ... Y n By comparing the stress gradient influence factor Y at the critical point a, the stress gradient distribution at the critical point a is reflected, thereby obtaining the stress concentration factor of the actual mechanical structure and establishing a monotonic relationship between the stress gradient correction factor Y and the stress concentration factor.

[0013] Step 4: Introduce the stress gradient influence factor Y, which conforms to a monotonic relationship, into the life equation. At the same time, introduce fitting parameters to correct the stress gradient influence factor Y, and obtain the stress gradient corrected life model, which is used to characterize the stress gradient at the critical point a.

[0014] The stress gradient influence factor Y is introduced into the life equation and expressed as:

[0015] N f =Y(N) f f(σ,ε)

[0016] N f Let σ represent fatigue life, ε represent stress-related terms, ε represent strain-related terms, and f represent the life equation function.

[0017] Introducing the fitting parameter p i The lifetime equation is modified as follows:

[0018] N f =Y(N) f ,p i f(σ,ε)

[0019] In the above modified equation, fatigue data N is obtained by conducting fatigue tests on the materials of actual mechanical structures. f Combining the stress gradient influence factor Y obtained from finite element calculations, the parameter system p is obtained by fitting using the multiple linear regression method. i Thus, the lifetime equation is determined.

[0020] Step 5: Design a tensile test specimen containing at least two notches, and verify the stress gradient at critical point a by designing different notch sizes;

[0021] In the tensile test specimen, the stress and strain at the root of each notch are the same under tension, thus eliminating the influence of stress and strain at the notch root on the notch life; however, the different notch shapes result in different stress gradients at the notch root, thus separately demonstrating the influence of different stress gradients on fatigue life.

[0022] Fatigue tests are performed using tensile test specimens, focusing on the fracture location. When the stress and strain at the notch root are the same, the notch with a smaller stress gradient has a lower fatigue life. The stress gradient distribution of the actual notch can be determined by the fatigue life of different notches. The stress gradient distribution at the danger point a calculated in step three is compared with the stress gradient distribution at the danger point a to achieve the verification purpose.

[0023] Meanwhile, the service life model predicts the fatigue life of the test specimens, and the fitting accuracy of the service life equation is verified by comparing it with the experimental results.

[0024] The advantages of this invention are:

[0025] 1. A novel stress gradient characterization and verification method that incorporates the influence of stress gradient into the prediction of fatigue life, thereby improving the accuracy of fatigue life prediction in actual mechanical structures.

[0026] 2. A novel method for characterizing and verifying stress gradients. The stress gradient correction factor Y obtained by this method can establish a monotonic relationship with the stress concentration factor, which can help in determining the notch strength factor and the notch fatigue limit.

[0027] 3. A new method for characterizing and verifying stress gradients, through verification, ensures the reliability of the calculation results through experiments. Attached Figure Description

[0028] Figure 1 This is a flowchart of a novel stress gradient characterization and verification method according to the present invention;

[0029] Figure 2 This is a schematic diagram of the smooth test specimen and the notched test specimen of the present invention.

[0030] Figure 3 This is a schematic diagram of the V-shaped notch of the present invention.

[0031] Figure 4 This is a schematic diagram of the stress gradient normalization curve of the present invention.

[0032] Figure 5 The present invention provides several stress concentration factors K. t A schematic diagram of the normalized curve of the notch stress.

[0033] Figure 6 This is a schematic diagram of the test piece containing two notches according to the present invention.

[0034] Figure 7 This is a graph showing the fatigue life test data of the present invention.

[0035] Figure 8 This is a schematic diagram of the notch finite element model of the present invention. Detailed Implementation

[0036] The present invention will now be described in further detail with reference to the accompanying drawings.

[0037] This invention discloses a novel method for characterizing and verifying stress gradients, and provides an experimental method to verify the influence of stress gradients. In the application example, this invention provides a demonstration case of a typical scenario, comparing the lifetime prediction results of the stress gradient correction method provided in this invention with those of a method without stress gradient correction, thus verifying the effectiveness of the correction method.

[0038] The novel stress gradient characterization and verification method obtains the stress gradient distribution near the critical point through finite element analysis of an actual mechanical structure. After transformation, a stress gradient correction factor is obtained, which can represent the stress gradient distribution at the critical point. At the same time, the present invention provides an experimental method to verify the conclusion.

[0039] like Figure 1 As shown, the specific steps are as follows:

[0040] Step 1: Establish a finite element model A of the actual mechanical structure, perform static analysis on the model under actual load, select the point with the largest stress or strain on model A as the critical point based on the analysis results, and calculate the elastic stress gradient influence factor Y at the critical point under actual load.

[0041] For the critical point a where the stress decreases the fastest, a corresponding stress decrease path is selected on the actual mechanical structure, and a normalized curve of stress versus distance is established along this path. The vertical axis of the curve is the ratio of the stress at each point on the path to the stress at the starting point of the path, and the horizontal axis is the ratio of the distance from each point on the path to the starting point of the path to the total length of the path.

[0042] Integrating the curve yields the area enclosed by the curve and the coordinate axes, denoted as S. The stress gradient influence factor at the critical point a is then Y = S.

[0043] Similarly, for the remaining critical points on the finite element model A of the actual mechanical structure, the stress gradient influence factor Y is calculated for each of them.

[0044] Step 2: Following the finite element model A, establish different stress concentration factors K. t The finite element model with gaps in the values ​​B1, B2, ... B n A critical point a' is set at a corresponding location on each model, and the stress gradient influence factors Y1, Y2, ... Y at the critical point a' under each model are calculated.n ;

[0045] Step 3: Calculate the stress gradient influence factors Y1, Y2, ... Y n By comparing the stress gradient influence factor Y at the critical point a, the stress gradient distribution at the critical point a is reflected, thereby obtaining the stress concentration factor of the actual mechanical structure and establishing a monotonic relationship between the stress gradient correction factor Y and the stress concentration factor.

[0046] By comparing the relative magnitudes of the stress gradient influence factor Y, the stress gradient distribution at the actual mechanical structure's critical point a is determined.

[0047] In this embodiment, a stress concentration factor K is selected. t Finite element models with notches of 2, 3, and 4 were used. The stress gradient influence factor Y was repeatedly calculated for different notch models and compared with the Y obtained at the critical point a on the actual mechanical structure. The relative magnitude of these values ​​reflects the stress gradient distribution; a larger Y indicates a more drastic change in stress gradient at that point on the actual mechanical structure. Because the stress concentration factor on a mechanical structure is difficult to calculate in practice, while the stress gradient is readily calculable, the stress concentration factor of the actual structure can be approximated by calculating the stress gradient.

[0048] Step 4: Introduce the stress gradient influence factor Y, which conforms to a monotonic relationship, into the life equation. At the same time, introduce fitting parameters to correct the stress gradient influence factor Y, and obtain the stress gradient corrected life model, which is used to characterize the stress gradient at the critical point a.

[0049] The general lifetime equation is:

[0050] N f =f(σ,ε)

[0051] Where, N f Let σ represent fatigue life, ε represent stress-related terms, ε represent strain-related terms, and f represent the life equation function.

[0052] The stress gradient influence factor Y is introduced into the right-hand side of the lifetime equation and directly multiplied by the lifetime function f, expressed as:

[0053] N f =Y(N) f f(σ,ε)

[0054] Since the effect of stress gradient on fatigue life varies under different load magnitudes, it is necessary to consider the fatigue life N. f When incorporating this into the correction of Y, we also need to introduce fitting parameters; here, we use the fitting parameter p. i Correction:

[0055] Nf =Y(N) f ,p i f(σ,ε)

[0056] In the above modified equation, fatigue data N is obtained by conducting fatigue tests on the materials of actual mechanical structures. f Combining the stress gradient influence factor Y obtained from finite element calculations, the parameter system p is obtained by fitting using the multiple linear regression method. i Thus, the lifetime equation is determined.

[0057] Step 5: Design a tensile test specimen containing at least two notches, and verify the stress gradient at critical point a by designing different notch sizes;

[0058] In the tensile test specimen, the stress and strain at the root of each notch are the same under tension, thus eliminating the influence of stress and strain at the notch root on the notch life; however, the different notch shapes result in different stress gradients at the notch root, thus separately demonstrating the influence of different stress gradients on fatigue life.

[0059] Fatigue tests are performed using tensile test specimens, focusing on the fracture location. When the stress and strain at the notch root are the same, the notch with a smaller stress gradient has a lower fatigue life. The stress gradient distribution of the actual notch can be determined by the fatigue life of different notches. The stress gradient distribution at the danger point a calculated in step three is compared with the stress gradient distribution at the danger point a to achieve the verification purpose.

[0060] Meanwhile, the service life model predicts the fatigue life of the test specimens, and the fitting accuracy of the service life equation is verified by comparing it with the experimental results.

[0061] like Figure 2 The diagram shows a comparison between a smooth test specimen and a notched test specimen. The cross-sectional area at the notch is the same as that of the smooth test specimen. When the notched test specimen is subjected to tensile forces at both ends, the stress distributed on the cross-section at the root of the notch is the same as that of the smooth test specimen. Stress concentration exists at the root of the notch; the stress at the root of the notch is greater than the average stress on the cross-section, while the stress at the inner side of the cross-section is less than the average stress. Although the average stress on both cross-sections is the same, the different stress distribution causes a difference in the fatigue life of the two test specimens under cyclic loading. The greater the stress gradient at the root of the notch, the greater the difference in stress between the inner and outer sides of the cross-section. By comparing the magnitude of the stress on the inner side of the cross-section with the magnitude of the stress on the outer side, a parameter measuring the stress gradient distribution can be obtained. This parameter reflects the stress gradient distribution at a certain point on the structure.

[0062] Based on the above ideas, this invention constructs a method for representing and verifying the influence of stress gradients, the establishment process of which is as follows:

[0063] Step 1: Calculate the stress gradient distribution at the check location;

[0064] (1) Construct a finite element model according to the actual structure's dimensions and materials.

[0065] (2) Apply boundary conditions to the model according to the actual working conditions, and reduce the load proportionally to ensure the elastic stress state.

[0066] (3) Starting from the critical location, proceed along the direction of the fastest stress decrease until the stress gradient is 0 or the part's symmetry plane is reached.

[0067] Obtain the stress values ​​along this path.

[0068] The finite element method is used to perform elastic stress analysis on an actual mechanical structure, requiring that no plastic strain occurs at the location of maximum stress. At the location of maximum stress, i.e., the critical point, the path of fastest stress reduction is determined, extending to where the stress gradient is zero or where the part stops at a plane of symmetry or an edge, and the stress value along this path is obtained.

[0069] Taking the V-shaped notch as an example, such as Figure 3 As shown, the actual mechanical structure has a V-shaped notch at its left end with a radius of curvature of r. x represents the depth direction of the notch, and the actual mechanical structure experiences stress σ in a direction perpendicular to the x-axis. The stress along the path is obtained along the direction of the fastest decrease in stress gradient (i.e., the x-direction of the notch bisector).

[0070] Step 2: Calculate the stress gradient influence factor from the stress gradient distribution;

[0071] Establish a normalized curve of stress versus path distance along the notch bisector. The vertical axis of the curve represents the ratio of stress at a point on the bisector to stress at the notch root, and the horizontal axis represents the ratio of the distance from a point on the bisector to the notch root to the total length of the bisector. Plot the curve as follows. Figure 4 As shown, the curve is integrated to obtain the area enclosed by the curve and the coordinate axes, denoted as S. The stress gradient influence factor is denoted as Y = S.

[0072] like Figure 5 As shown, several commonly used stress concentration factors K are given. t The normalized stress curve for the notch is plotted as follows: when there is no stress concentration in the structure, the normalized stress gradient curve is a horizontal straight line, and Y is 1, which has no effect on fatigue life. As stress concentration intensifies, the normalized stress gradient curve shifts downward as a whole, and Y decreases, indicating an increase in stress gradient. Y changes monotonically with the stress concentration factor. This method of calculating the stress gradient influence factor can effectively represent the stress concentration situation. By comparing the magnitudes of the stress gradient influence factor, it is possible to determine which structures have a larger stress gradient.

[0073] Step 3: Compare the magnitude of Y to determine the stress gradient distribution at the test location, and then incorporate Y into the life equation.

[0074] Step 4: Design fatigue test specimens with multiple notches;

[0075] (1) Determine the overall diameter of the test specimen;

[0076] (2) Based on the stress concentration factor of the actual model, the size of the first notch is given;

[0077] (3) Ensure that the stress at the root of the notch is the same. Given the size of the second notch, the stress concentration factor of the second notch can be a common value such as 2 or 3.

[0078] (4) If multiple gaps need to be compared, repeat step (3).

[0079] (5) Given a load, the shortest lifespan of the notch is used as the standard, with a lifespan between 50,000 and 100,000 cycles.

[0080] Reference Manual 1 Regarding the data on stress concentration factors and notch sizes, taking a round bar specimen as an example: First, given the overall diameter of the specimen, the cross-sectional dimensions at the notch are calculated using the stress concentration factor of one notch as the standard. Then, based on the stress concentration factor of the other notch, the cross-sectional dimensions at the notch are calculated while ensuring that the stress at the roots of the two notches is equal.

[0081] Step 5: Complete the experiment and verify the calculation results;

[0082] (1) Use the test piece obtained in the previous step to complete the experiment.

[0083] (2) After multiple tests, compare the types of notches that cause damage, determine the magnitude of the stress gradient, and compare it with the settlement results.

[0084] After completing the experiment, focus on which notch the specimen failed from during fatigue failure. When the specimen is subjected to tensile force, the stress at the roots of the two notches is the same. At this point, the notch with the larger stress gradient has a longer fatigue life. Therefore, the notch with the smaller stress gradient fails first. Considering the randomness of fatigue failure, it is necessary to increase the number of tests and select a smaller load.

[0085] Example

[0086] There is a test piece with two notches, such as Figure 6As shown, the stress concentration factor of one notch is 2, and the stress concentration factor of the other notch is 3. The test piece is made of 45 steel, and the specific dimensions are shown in the drawing. Through dimensional design, when the test piece is subjected to tensile forces at both ends, the uniaxial stress and uniaxial strain generated at the roots of the two notches are equal. If the fatigue life is calculated using the fatigue life equation that does not consider stress gradient, it can be calculated that the fatigue life of the two notches is equal.

[0087] In previous experiments, fatigue parameters in the life equation were obtained using fatigue data; the experimental data can be found here. Figure 7 As shown.

[0088] For fatigue test specimens with two notches, loads with a load ratio of -1 and net section stresses of 160 MPa and 200 MPa were set at room temperature (in K). t The results of the experiment (based on 3 gaps) are shown in Table 1.

[0089] Experimental results show that although the strain amplitudes at the roots of the two notches are the same, most specimens fractured from the notch with a stress concentration factor of 2. After eliminating dispersion factors, it can be considered that K t =2 The lifetime of the notch is less than that of K t =3 gaps.

[0090] Table 1 Experimental data of notched test specimens

[0091]

[0092]

[0093] The stress gradient at the root of the notch is calculated using the method proposed in this invention.

[0094] (1) Finite element analysis. A two-dimensional finite element model of the notch is established as follows: Figure 8 As shown, boundary conditions and loads are applied. The elastic finite element calculation results are as follows: Figure 8 As shown, for both notches, the danger point is at the root of the notch. Therefore, the stress gradient curve should be taken from the root of the notch, along the direction of the fastest stress decrease, i.e., the notch bisector, and stop at the axis of symmetry.

[0095] (2) Calculate the stress gradient influence factor. Normalize the stress and distance; the normalized stress gradient curves for the two notches are shown below. Figure 4 As shown. Integrating the curve yields the area enclosed by the curve and the coordinate axes, thus obtaining the stress gradient influence factors for the two types of notches. For K... t =2 gap, Y = 0.52354; for K t =3 gap, Y = 0.3091.

[0096] (3) Calculate fatigue life. Substitute the fatigue parameters into the life equation, and combine the load conditions given in the experiment with the stress gradient influence factor obtained in (2) to calculate the fatigue life of each of the two notches under the two loads.

[0097] (4) The average fatigue test life values ​​in Table 1 are compared, and the results are shown in Table 2. The results show that the calculated life values ​​for the two notches are significantly different, K t =2 The lifetime of the notch is less than K t =3 gaps, which is consistent with the experimental results. Additionally, K t The calculated lifetimes of the two notches are close to the average of the experimental lifetimes, indicating that the stress gradient correction method used in this invention has good calculation accuracy.

[0098] (5) Verify the influence of stress gradient. From the stress gradient influence factor obtained in (2), it can be seen that K... t =2 The stress gradient of the notch should be less than K t =3 gaps. Experiments show that K t =2 notches, fatigue life is less than K t =3 notches. The experimental results verified the calculation results, indicating that this method of representing the influence of stress gradient is consistent with reality.

[0099] Table 2 Comparison of calculated lifetime and experimental lifetime

[0100] Load / MPa <![CDATA[K t =2 notch calculation lifetime]]> <![CDATA[K t =3-notch calculation of lifetime]]> Average experimental lifespan 160 97969 130720 94345 200 25452 40379 28993

Claims

1. A novel method for characterizing and verifying stress gradients, characterized in that, The specific steps are as follows: Step 1: Establish a finite element model A of the actual mechanical structure, perform static analysis on the model under actual load, select the point with the largest stress or strain on model A as the critical point based on the analysis results, and calculate the elastic stress gradient influence factor Y at the critical point under actual load. The danger point is the point where the stress decreases the fastest. The corresponding stress decrease path is selected on the actual mechanical structure, and a normalized curve of stress versus distance is established along this path. The vertical axis of the curve is the ratio of the stress at each point on the path to the stress at the starting point of the path, and the horizontal axis is the ratio of the distance from each point on the path to the starting point of the path to the total length of the path. Integrating the curve, we obtain the area enclosed by the curve and the coordinate axes, denoted as S. Then, the stress gradient influence factor at the danger point a is Y = S. Similarly, for the remaining critical points on the finite element model A of the actual mechanical structure, the stress gradient influence factor Y is calculated for each of them. Step 2: Following the finite element model A, establish different stress concentration factors K. t The finite element model with gaps in the values ​​B1, B2, ... B n A critical point a' is set at a corresponding location on each model, and the stress gradient influence factors Y1, Y2, ... Y at the critical point a' under each model are calculated. n ; Step 3: Calculate the stress gradient influence factors Y1, Y2, ... Y n By comparing the stress gradient influence factor Y at the critical point a, the stress gradient distribution at the critical point a is reflected, thereby obtaining the stress concentration factor of the actual mechanical structure and establishing a monotonic relationship between the stress gradient correction factor Y and the stress concentration factor. Step 4: Introduce the stress gradient influence factor Y, which conforms to a monotonic relationship, into the life equation. At the same time, introduce fitting parameters to correct the stress gradient influence factor Y, and obtain the stress gradient corrected life model, which is used to characterize the stress gradient at the critical point a. The stress gradient influence factor Y is introduced into the life equation and expressed as: Indicates fatigue life. Indicates stress-related terms, Indicates strain-related terms, Represents the lifetime equation function; Introducing fitting parameters The lifetime equation is modified as follows: In the above modified equation, fatigue data is obtained by conducting fatigue tests on the materials of actual mechanical structures. Combining the stress gradient influence factor Y obtained from finite element calculations, the parameter system is fitted using a multiple linear regression method. Thus, the lifetime equation is determined; Step 5: Design a tensile test specimen that contains at least two notches. By designing different notch sizes, verify the stress gradient at critical point a.

2. The novel stress gradient characterization and verification method as described in claim 1, characterized in that, In step five, the stress and strain at the root of each notch in the tensile test specimen are the same under tension, thus eliminating the influence of stress and strain at the notch root on the notch life; while different notch shapes result in different stress gradients at the notch root, thus individually demonstrating the influence of different stress gradients on fatigue life. Fatigue tests were conducted using tensile test specimens, with attention paid to the fracture location. When the stress and strain at the root of the notch are the same, the notch with a smaller stress gradient has a lower fatigue life. The fatigue life of different notches can be used to determine the stress gradient distribution of the actual notch. The stress gradient distribution at the critical point a of the actual mechanical structure can be compared to achieve the verification purpose. Meanwhile, the service life model predicts the fatigue life of the test specimens, and the fitting accuracy of the service life equation is verified by comparing it with the experimental results.

Images