Double-notch test piece capable of quantifying influence of stress gradient on service life

Abstract

The invention discloses a double-gap test piece capable of quantifying the influence of stress gradient on life, which comprises the following steps of: firstly, determining a stress concentration coefficient required by the test piece, and determining the geometric dimension of a gap according to a related manual; then, single-notch test pieces are machined respectively, fatigue tests are completed, and parameters of the life prediction model are fitted according to test results; further arranging the two notches on one test piece, calculating the stress distribution of the double-notch test piece by using a finite element program, finely adjusting the geometric dimensions of the notches to meet the requirement that the stress and strain of the roots of the two notches are the same, and calculating the stress gradient influence factors of the two notches at the same time; further completing a double-notch fatigue test, recording experimental data, and determining a minimum observation number by adopting a variable coefficient method until the number meets a confidence coefficient requirement; and finally detecting the prediction precision by using the service life prediction model. According to the method, data errors caused by machining and casting of the test piece are eliminated, the test precision is improved, and the influence of the stress gradient on the fatigue life can be visually and quantitatively detected.

Description

Technical Field

[0001] The present invention belongs to the technical field of fatigue test design. Two notches with different stress concentration coefficients are placed on a fatigue test piece. Through this test device, the influence of the stress gradient on the fatigue life can be quantified, and the existing life prediction models can be verified. Background Art

[0002] In actual engineering structures, due to functional design, there are often positions where the geometric dimensions of components change suddenly, such as the ventilation holes and tenon grooves of the disk in an aeroengine. The positions where the geometric dimensions change suddenly will form stress concentration areas under the action of external loads. There will be an obvious stress gradient near the point with the maximum stress, and the stress at the point with the maximum stress will be significantly higher than that in other areas. If the stress gradient is not considered and the stress at the point with the maximum stress is directly used for life analysis, overly conservative calculation results are usually obtained. Therefore, in order to more accurately predict the fatigue life of the structure, the influence of the stress gradient on the fatigue life must be considered. For a standardized notched fatigue test piece, its stress concentration coefficient can be calculated. For actual components, it is necessary to analyze the stress distribution in the area near the maximum stress point and give a suitable parameter representing the magnitude of the stress gradient and substitute it into the life prediction model.

[0003] The high stress concentration areas on the actual structure are usually listed as dangerous positions that need special attention, and the life here is often used as the life limit point of the structure. Usually, there are more than one dangerous position in the key components of the engine. While predicting the fatigue life of each dangerous position, it is also necessary to determine the failure position of the structure, that is, to determine the position with the shortest life. Therefore, the fatigue life of the area with a stress gradient needs to be carefully analyzed, and the quantification of the stress gradient in the fatigue life prediction should also be as accurate as possible. It is relatively difficult and costly to directly conduct fatigue tests on the actual structure, so standardized notched test pieces are often used to simulate the working state of the actual structure. Generally, the notched test piece is a single-notch test piece, and the life is mainly judged by obtaining the number of cycles. However, the errors and defects during the machining of the test piece cause the data to be scattered, and it is difficult to judge the order of failure of different notches. Summary of the Invention

[0004] Based on the above problems, a fatigue test piece containing two different notches is proposed, which can directly determine the magnitudes of the fatigue lives of different notches through the failure positions, thereby quantifying the influence of the stress gradient on the fatigue life.

[0005] The present invention is a double-notch test piece that can quantify the influence of the stress gradient on the life, which is obtained by machining two notches with the same maximum root stress and maximum strain but different stress concentration coefficients on the same test piece; the distances between the two notches and the center of the test piece are equal, and there should be enough axial distance between the two notches; its design method is as follows:

[0006] First, design two single notches on two bar-shaped test pieces with equal diameters, and control the stress concentration factors of the two notches to the set factors by changing the notch depth and local radius.

[0007] Subsequently, machine two single-notch test pieces and conduct fatigue tests under different loads and load ratios to determine the parameters of the life prediction model and select the appropriate load magnitude for the double-notch fatigue test piece.

[0008] Finally, arrange the two single notches designed above on the same test piece, control the distance between the two notches to ensure that the stress distributions between different notches do not interfere, and machine to obtain a double-notch test piece; further, obtain the stress gradient curves of the two notches, calculate the stress gradient influence factor, and correct the life prediction model.

[0009] Conduct fatigue tests on the double-notch test piece with the load magnitude of the double-notch fatigue test piece obtained above, record and organize the test data; and use the notch where failure actually occurs observed in the fatigue test as a true experiment verification, compare it with the result obtained through the life prediction model, judge the consistency, and perform life prediction with the gradient life model with consistent results.

[0010] The advantages of the present invention are as follows:

[0011] 1. The present invention is a double-notch fatigue test piece that simultaneously contains notches with different stress concentration factors. By conducting fatigue tests on different notches simultaneously, it can quickly and intuitively determine which notch has a lower life. By corresponding the notch to the actual structure, it can be used to judge the failure position of the actual structure;

[0012] 2. For the double-notch test piece designed in the present invention, the stress and strain at the root of different notches are the same under tensile load, only the stress gradient is different. Therefore, the stress gradient can be used as the only factor affecting fatigue life, and the result of the fatigue test can quantitatively reflect the influence of the stress gradient on fatigue life;

[0013] 3. For the double-notch test piece designed in the present invention, since different notches are arranged in one test piece, the data dispersion caused by defects generated during machining and casting is excluded, greatly improving the reliability of the result. Description of the Drawings

[0014] Figure 1 It is the design and test flow chart of the double-notch test piece of the present invention that can quantitatively reflect the influence of stress gradient on life;

[0015] Figure 2 It is the relationship diagram between the stress concentration factor and the notch size of the single-notch test piece.

[0016] Figure 3 (a) is the design dimension diagram of the single-notch test piece with K t = 2.

[0017] Figure 3 (b) is the design dimension diagram of the single-notch test piece with K t = 3.

[0018] Figure 4 is the design dimension diagram of the double-notch test piece.

[0019] Figure 5 (a) is the stress distribution at the root of the notch with K t = 2 obtained by finite element calculation.

[0020] Figure 5 (b) is the stress distribution at the root of the notch with K t = 3 obtained by finite element calculation.

[0021] Figure 6 Normalized stress gradient curves for different notches.

[0022] Figure 7 is the schematic diagram of the double-notch fatigue test. Specific implementation manner

[0023] The present invention will be further described in detail below with reference to the accompanying drawings.

[0024] The present invention relates to a double-notch test piece capable of quantifying the influence of stress gradient on life, which is obtained by machining two notches with the same maximum stress and maximum strain at the root but different stress concentration coefficients on the same round bar or flat plate test piece. Here, the two notches are designed as simple-shaped notches (U-shaped or V-shaped notches) with the same or different structures, and it is necessary to ensure that the distances between the two notches and the center of the test piece are equal, and there should be enough axial distance between the two notches to ensure that the stress distributions between different notches do not interfere with each other.

[0025] As Figure 1 shown, the specific design method of the double-notch test piece with the above structure is as follows:

[0026] Step 1: Determine the stress concentration coefficients and notch sizes of the two notches.

[0027] Design two single-notch round bar test pieces to ensure that the diameters of the two single-notch test pieces remain unchanged. The stress concentration coefficients of the two notches should correspond to the engineering structure on the one hand and also consider stress gradient analysis on the other hand. For a simple-shaped notch test piece with a regular geometric shape, its stress concentration coefficient K t can be expressed as:

[0028]

[0029] where σmax represents the maximum stress at the notch root, σ net represents the average stress on the notch cross-section.

[0030] In engineering structures, excessive stress concentration will not occur. Generally, notches with Kt = 2 or 3 can be used; if the same stress concentration factor is used for two notches, in order to control the same stress at the roots of the two notches, the net cross-sectional area of one of the notches will be too small, which is likely to cause the test piece to become unstable during the test. Therefore, in the present invention, considering the stress gradient analysis, the stress concentration factors of the notches of the two single-notch test pieces are 2 and 3 respectively. As Figure 2 shown, according to the relationship between the stress concentration factor of the notched round bar and the notch size in the "Stress Concentration Factor Handbook", when designing the two single-notch test pieces, on the premise that the maximum diameters of the two single-notch test pieces are the same, by changing the notch depth and local radius, the stress concentration factors of the two single-notch test pieces are controlled to reach 2 and 3, and finally the curve of the relationship between the stress concentration factor and the geometric dimensions of the two single-notch test pieces is obtained. According to this curve, the two single-notch test pieces are designed and processed, as Figure 3 (a) and 3(b) shown.

[0031] Since when designing the single-notch test piece, the curve of the relationship between the stress concentration factor of the notch of the single-notch test piece and the geometric dimensions is obtained by theoretical calculation, there will be a certain error between the single-notch test piece designed by the above method and the actually processed single-notch test piece. Therefore, after the single-notch test piece is processed, first, a finite element model is established and simulated for the single-notch test piece, and a commercial finite element analysis software is used to model and analyze the double-notch fatigue test piece to calculate the elastic stress distribution near the notch under the axial tensile state. Subsequently, check whether the stress concentration factor of the notch is consistent with the stress concentration factor during the design of the corresponding single-notch test piece, and whether the stresses and strains at the roots of the two notches are consistent. After being tested by the finite element method, the local dimensions of the two notches are finely adjusted to ensure that under the condition of meeting the designed stress concentration factor, the stresses and strains at the roots are the same while the stress gradients are different; further, according to the fine-tuning results, the two single-notch test pieces are processed and corrected to obtain the single-notch test pieces that meet the requirements.

[0032] Step 2: Conduct fatigue tests on the two obtained single-notch test pieces under different loads and load ratios to determine the parameters of the life prediction model and select the appropriate load magnitude for the double-notch fatigue test piece.

[0033] When selecting the load, it should be ensured that the life is as evenly distributed as possible within the full fatigue stage and appropriately concentrated within the service life of the actual structure. According to the results of single-notch fatigue tests, the parameters of the life prediction model of the material are fitted. The life prediction model is mainly divided into two types. One is the strain-life prediction model with strain as the fatigue parameter, and the other is the stress-life prediction model with stress as the fatigue parameter. The strain-life prediction model can be written as:

[0034]

[0035] where E is the elastic modulus; Δε t is the total strain, R′ is the local stress ratio, N f is the fatigue life, σ f ′, ε f ′, b, c, γ are all fatigue parameters obtained by fitting.

[0036] The stress-life prediction model can be written as:

[0037]

[0038] where S max is the maximum stress, N f is the fatigue life, R is the stress ratio, σ bH is the ultimate strength, σ -1 is the fatigue limit, p, q, g are all fitting parameters.

[0039] Regardless of which equation is used, after fitting the equation parameters according to the test data, the fatigue life of the material can be predicted according to the model. In order to control the dispersion degree of the test results, the test life should not be too large. At the same time, in order to conform to the actual structure, the test life should not be too small. Ensure that the life is between 30,000 and 100,000. Determine the load according to the life prediction model as the test load for the subsequent double-notch fatigue test.

[0040] Step 3: Design the double-notch fatigue test piece, obtain the stress gradient curves of the two notches, and calculate the stress gradient influence factor.

[0041] And arrange the two single notches on the same test piece. There should be enough axial distance between the two notches to ensure that the stress distributions between different notches do not interfere with each other, as Figure 4 shown.

[0042] Since the curve of the notch stress concentration factor of the single-notch test piece versus geometric dimensions is obtained by theoretical calculation during the design of the single-notch test piece, there will be a certain error between the double-notch test piece designed by the above method and the double-notch test piece obtained by actual machining. Therefore, after the double-notch test piece is machined, first perform finite element modeling and simulation on the double-notch test piece. Use commercial finite element analysis software to model and analyze the double-notch fatigue test piece, and calculate the elastic stress distribution near the notch under axial tension. The calculation results are as shown in Figure 5 (a) and 5(b). Subsequently, check whether the stress concentration factors of the two notches are consistent with the stress concentration factors during the design of the corresponding single-notch test piece, and whether the stresses and strains at the roots of the two notches are consistent. After being verified by the finite element method, finely adjust the local dimensions of the two notches to ensure that under the condition of meeting the designed stress concentration factor, the stresses and strains at the roots are the same while the stress gradients are different; further process and correct the double-notch test piece according to the fine-tuning results to obtain a double-notch test piece that meets the requirements.

[0043] According to the stress distribution at the roots of the two notches on the double-notch test piece, obtain the stress gradient curve, calculate the stress gradient influence factor, and correct the life prediction model. The specific method can refer to the following rules:

[0044] Starting from the point with the maximum stress at the roots of the two notches, construct a stress distribution curve along the stress decreasing direction (for the notch test piece, it is the notch bisector). It is stipulated that the curve terminates in the following 3 cases:

[0045] (1) The curve extends to the structural edge or the geometric symmetry line;

[0046] (2) The derivative of the stress with respect to the distance is 0:

[0047]

[0048] Among them, represents the gradient of the normal stress along the y direction; σ yy is the normal stress along the y direction, which is the normal stress perpendicular to the notch bisector direction for the notch test piece; x is the distance along the direction of the steepest stress decrease, which is the distance along the notch bisector direction for the notch test piece.

[0049] (3) The stress is equal to the fatigue limit of the material.

[0050] Normalize the stress on the curve with respect to the maximum stress, and normalize the distance of each point from the starting point with respect to the total length L of the curve to obtain the normalized stress gradient curve. The normalized stress gradient curves of different notches obtained according to the above steps are as shown in Figure 6 .

[0051] Integrate the part of the normalized stress gradient curve between 0 and 1, and define the result of the integration as the stress gradient influence factor Y at the point of maximum stress. Specifically, the calculation formula for Y is as follows:

[0052]

[0053] where the maximum stress at the root is the same as the maximum strain; is the normalized distance in the x direction.

[0054] The equations of the fatigue life prediction models shown in Equations (2) and (3) after being corrected by the stress gradient are as shown in Equations (6) and (7). Among them, Y is the stress gradient influence factor, and A, B, h, and f are all fitting parameters.

[0055]

[0056]

[0057] where

[0058] Carry out double-notch fatigue tests on the double-notch fatigue test specimens determined by the above method. As Figure 7 shown, apply axial tensile and compressive loads to the double-notch test specimens through a fatigue testing machine, and record the types of failed notches and the number of cycles. When organizing the test data, the fatigue data should be organized separately according to the types of failed notches. At the same time, the type of failed notch will be recorded as a separate test result; however, there is scatter in the fatigue test. Even if the fatigue life of one notch is lower than that of the other notch, there will inevitably be test specimens that fail from the notch with a higher life after repeating the test multiple times. In order to obtain convincing fatigue test results, a certain number of tests need to be completed. If the number of failures from a certain notch meets a certain proportion, it can be considered that the fatigue life at that notch is shorter. Therefore, in the present invention, the coefficient of variation of the data is calculated from the organized fatigue data, and the test is repeated enough times to ensure that the result meets the 95% confidence level. The specific process is as follows:

[0059] Assume that a total of N groups of double-notch fatigue tests are completed, and among them, m groups of tests fail from one type of notch. Calculate the average value of the fatigue life of the m groups of tests and the standard deviation s. Then the coefficient of variation of this group of data is:

[0060]

[0061] Then the following relationship exists for the minimum observed data of the test:

[0062]

[0063] where δmax is the error limit, generally taken as 5%; t γ is a parameter related to the confidence level (γ), generally taking the result at a 95% confidence level. According to Equation (9), the minimum value of the test quantity can be determined. Only when the inequality relationship in Equation (9) is satisfied can the test result be considered reliable. If the test quantity does not meet the confidence level requirement, the double-notch fatigue test needs to be repeated until the data and the test quantity meet the requirements of Equation (9).

[0064] For the double-notch test piece designed in the present invention, the stresses and strains of its two notches are the same, only the stress gradients are different. And since the fatigue parameters of the life prediction model mainly include strain, stress, and stress gradient, the stress gradient will have a dominant influence on the fatigue life of the double-notch test piece. The influence of the stress gradient on the fatigue life needs to be incorporated into the life prediction model, which can be characterized by the stress gradient influence factor.

[0065] During the fatigue test, since the two notches of the double-notch test piece are connected side by side, the termination of the test will occur when one notch is damaged, so it can be clearly observed which notch has a shorter life. Since the stress gradient influence factors obtained by different stress gradient analysis methods are generally different, the notch that actually fails (has a shorter life) observed in the fatigue test can be used as a true experiment verification. If the life prediction model corrected by the aforementioned gradient influence factor can consistently predict results that match the actual observation, it indicates that the results obtained by the life prediction model are accurate; otherwise, replace the method to calculate the gradient image factor and correct the life prediction model and return to the previous process.

[0066] The present invention predicts the life according to the life prediction model and the stress gradient correction method, in combination with the test load of the double-notch fatigue test and the finite element calculation results. The comparison of the life cycle number can provide a basis for verifying the stress gradient correction method, and at the same time, the type of the damaged notch can significantly distinguish which correction method is closer to the actual situation.

Claims

1. A double-notch test piece capable of quantifying the influence of stress gradient on life, characterized in that: Obtained by machining two notches with the same maximum root stress and maximum strain but different stress concentration factors on the same test piece; the distances from the two notches to the center of the test piece are equal, and there should be sufficient axial distance between the two notches; its design method is as follows: First, design two single notches on two equal-diameter rod-shaped test pieces respectively, and control the stress concentration factors of the two notches to the set factors by changing the notch depth and local radius; Subsequently, machine the two single-notch test pieces, and conduct fatigue tests under different loads and load ratios to determine the parameters of the life prediction model and select the appropriate load magnitude for the double-notch fatigue test piece; Finally, arrange the two single notches designed above on the same test piece, control the distance between the two notches to ensure that the stress distributions between different notches do not interfere, and machine to obtain the double-notch test piece; further, obtain the stress gradient curves of the two notches and calculate the stress gradient influence factor; Carry out fatigue tests on the double-notch test piece with the load magnitude of the double-notch fatigue test piece obtained above, and record and organize the test data; And take the notch that actually fails observed in the fatigue test as the true experiment verification, compare it with the test, and judge whether the notch failure sequence is consistent. When it is consistent, correct the predicted life model with the gradient influence factor to predict the life.

2. The double-notch test piece capable of quantifying the influence of stress gradient on life according to claim 1, characterized in that: The two notches are simple-shaped notches with the same or different structures.

3. The double-notch test piece capable of quantifying the influence of stress gradient on life according to claim 1, wherein: The two notches adopt U-shaped and V-shaped notches, and the stress concentration factors are selected as 2 and 3 respectively.

4. The double-notch test piece capable of quantifying the influence of stress gradient on life according to claim 1, characterized in that: When selecting the fatigue test load of the single-notch test piece, it should be ensured that the life is as evenly distributed as possible within the full fatigue stage and appropriately concentrated within the service life range of the actual structure.

5. The double-notch test piece capable of quantifying the influence of stress gradient on life according to claim 1, wherein: Select the strain-life prediction model with strain as the fatigue parameter or the stress-life prediction model with stress as the fatigue parameter for the life prediction model. After fitting the equation parameters according to the test data, predict the fatigue life of the material according to the model, ensure that the life is between 30,000 and 100,000, and determine the load according to the life prediction model as the test load for the double-notch fatigue test.

6. The double-notch test piece capable of quantifying the influence of stress gradient on life according to claim 1, wherein: After machining the single-notch test piece and the double-notch test piece, correct the test piece. The method is as follows: First, conduct finite element modeling and simulation on the test piece, use commercial finite element analysis software to model and analyze the double-notch fatigue test piece, and calculate the elastic stress distribution near the notch under the axial tensile state; Subsequently, check whether the stress concentration factors of the two notches are consistent with the design factors, and whether the stresses and strains at the roots of the two notches are consistent; After being tested by the finite element method, slightly adjust the local dimensions of the two notches to ensure that under the condition of meeting the designed stress concentration factor, the stresses and strains at the roots are the same while the stress gradients are different; further, machine and correct the test piece according to the fine-tuning results to obtain the test piece that meets the requirements.

7. The double-notch test piece capable of quantifying the influence of stress gradient on life according to claim 1, characterized in that: When organizing the test data, the fatigue data should be organized separately according to the type of the failed notch; at the same time, the type of the failed notch will be recorded as a separate test result; and calculate the coefficient of variation of the data through the organized fatigue data, repeat the test enough times to ensure that the result meets the 95% confidence level. The specific process is as follows: Suppose a total of N sets of double-notch fatigue tests are completed, and among them, m sets of tests fail from one type of notch. Calculate the average value of the fatigue lives of the m sets of tests respectively. And the standard deviation is s. Then the coefficient of variation of this set of data is: Then the minimum observed data of the test has the following relationship: where δ max is the error limit, generally taken as 5%; t γ is a parameter related to the confidence level (γ), generally taken as the result at a 95% confidence level. The minimum value of the test quantity is determined according to the above formula, and the test result is considered reliable only when the inequality relationship of the above formula is satisfied; if the test quantity does not meet the confidence level requirement, the double-notch fatigue test needs to be repeated until the data and the test quantity meet the requirements of the above formula.

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