Fatigue crack growth rate test method based on incremental polynomial supplementary calculation

Abstract

The present invention discloses a fatigue crack growth rate test method based on incremental polynomial supplementary calculation, which belongs to the technical field of fatigue crack growth rate testing. The method comprises the following steps: (1) obtaining an a-N curve through a fatigue crack growth rate test; (2) using an incremental polynomial method to calculate the da / dN values ​​and ΔK values ​​of other data points in the a-N curve except for the front n data points and the end n data points; (3) supplementing n virtual data points at the front or end of the a-N curve; (4) using an incremental polynomial method to calculate the da / dN values ​​and ΔK values ​​of the front n data points or the end of the a-N curve based on the supplemented n virtual data points; (5) using the da / dN values ​​and ΔK values ​​obtained in steps (2) and (4) to draw a da / dN-ΔK curve, thereby obtaining a fatigue crack growth rate curve. The method of the present invention can obtain effective da / dN and ΔK data to the maximum extent.

Description

Technical Field

[0001] The present invention relates to the technical field of fatigue crack growth rate detection of metal materials, and in particular to a fatigue crack growth rate test method based on incremental polynomial supplementary calculation. Background Art

[0002] Aluminum alloy, a lightweight, high-strength, and corrosion-resistant material, is widely used in aerospace, rail transit, shipbuilding, automotive, and other fields. Fatigue failure is the primary mode of failure in engineering structures. Statistics show that 50% to 90% of mechanical component failures are due to fatigue, and in some applications, up to 80% to 90% is the cause. Fatigue crack growth rate testing is commonly used to predict fatigue performance.

[0003] In fatigue crack growth rate testing, to obtain the material's da / dN value (i.e., fatigue crack growth rate), the crack length a and the number of cycles N required to reach this crack length must be measured during crack growth. This means first testing the material's aN curve. After obtaining the aN curve, the da / dN value of the material's crack growth is determined using either the secant method or the incremental polynomial method, as specified in the fatigue crack growth rate test standard. However, since the da / dN calculated by the secant method is only related to adjacent a and N values, the a value measurement often fluctuates significantly during the test. Consequently, the da / dN calculated by the secant method also fluctuates dramatically, resulting in a less-than-smooth da / dN-ΔK curve (i.e., fatigue crack growth rate-stress intensity factor range curve) obtained by this method. In contrast, the incremental polynomial method typically fits a and N data at seven points into a second-order polynomial, which is then derived. This is equivalent to locally smoothing the a and N data. Therefore, the da / dN-ΔK curve obtained by this method is smoother than the curve obtained by the secant method.

[0004] Currently, the incremental polynomial method is commonly used to calculate da / dN values. Generally, when the resulting da / dN-ΔK curve covers the target test value, this calculation method has little impact on the test results. However, when the resulting da / dN-ΔK curve does not, using the incremental polynomial method to calculate da / dN values ​​can seriously affect the test results. This is because the incremental polynomial method is typically fitted based on (2n+1) a and N data points, where n can be 2, 3, or 4, but is generally 3. Each fitted curve can only calculate the da / dN and ΔK values ​​corresponding to the number of cycles for the middle point of these (2n+1) data points. Therefore, the corresponding da / dN and ΔK values ​​cannot be calculated for the first n and last n data points in the aN curve. In particular, the last n data points correspond to the maximum da / dN and ΔK values, which are crucial for determining material performance. If these data points are discarded due to data processing, previously qualified materials may require resampling and testing because their corresponding da / dN and ΔK values ​​cannot be calculated. Summary of the Invention

[0005] In order to solve the above technical problems, the present invention provides a fatigue crack growth rate test method based on incremental polynomial supplementary calculation.

[0006] The technical solution adopted in the present invention is:

[0007] A fatigue crack growth rate test method based on incremental polynomial supplementary calculation comprises the following steps:

[0008] (1) Prepare the fatigue crack growth rate test specimen according to the test requirements, apply cyclic load to conduct the test, obtain the crack length-cycle number curve of the test specimen, that is, the aN curve, and obtain m groups of a i 、N i Data point, i is the serial number of the data point;

[0009] (2) Use the incremental polynomial method to calculate any data point a on the aN curve in step (1). i 、N i And n data points before and after this point are fitted to obtain the second-order polynomial equation of the (2n+1) consecutive data points. The calculation cycle is N i The crack length fitting value at , and calculate the fatigue crack growth rate fitting value by derivation , that is, the da / dN value of the data point; then use the value corresponding to the cycle number N i The crack length fitting value Calculate the corresponding ΔK value to obtain the da / dN value and ΔK value of the other data points in the aN curve except the front n data points and the end n data points;

[0010] (3) The average value of the cycle times of at least three data points at the front or end of the aN curve , continue to add n virtual data points at the front end or end of the aN curve, and use the second-order polynomial equation of the front end or end (2n+1) continuous data points in step (2) to calculate the fitting crack length corresponding to the number of cycles of the added n virtual data points;

[0011] (4) Based on the n virtual data points at the front end or the end supplemented in step (3), the da / dN value and ΔK value of the n data points at the front end or the end of the aN curve are calculated using the method in step (2);

[0012] (5) Using the da / dN and ΔK values ​​obtained in steps (2) and (4), the da / dN-ΔK curve is plotted to obtain the fatigue crack growth rate curve.

[0013] Furthermore, in step (2), the value of n is 1, 2, 3 or 4.

[0014] Furthermore, in step (2), the value of n is 3.

[0015] Furthermore, the second-order polynomial equation fitted by (2n+1) consecutive data points in step (2) is:

[0016] ;

[0017] in:

[0018] ;

[0019] ;

[0020] ;

[0021] Where N i is the cycle number of the i-th data point, N i-n is the cycle number of the (in)th data point, N i+n is the cycle number of the (i+n)th data point, is the number of cycles N i The crack length fitting value at a, b0, b1, b2 are i-n ≤a≤a i+n The regression parameters are determined by the least squares method within the range. C1 and C2 are coefficients used to scale the input data to avoid numerical calculation difficulties when determining the regression parameters.

[0022] Furthermore, the fatigue crack growth rate fitting value in step (2) The calculation formula is:

[0023] .

[0024] Furthermore, the number of cycles of the n virtual data points added to the front end of the aN curve in step (3) is 、…、 .

[0025] Furthermore, the number of cycles of the n virtual data points added at the end of the aN curve in step (3) is 、…、 .

[0026] The beneficial effects of the present invention are:

[0027] The present invention provides a fatigue crack growth rate test method based on incremental polynomial supplementary calculation. A second-order polynomial equation fitted to (2n+1) consecutive data points at the front or end of an aN curve is used to supplement n virtual data points at the front or end of the curve. The aN curve supplemented with the n virtual data points is then processed again using the incremental polynomial method to calculate the da / dN and ΔK values ​​corresponding to all measured data points on the aN curve. The method of the present invention can maximize the acquisition of valid da / dN and ΔK data, especially the da / dN and ΔK values ​​of the terminal n data points on the aN curve, thereby avoiding the problem that the test data originally contains the da / dN value corresponding to the maximum ΔK, but due to problems in the data processing method, the da / dN values ​​corresponding to the three data points with the largest ΔK cannot be calculated, thereby resulting in data invalidation. In particular, the da / dN and ΔK values ​​of the terminal n data points on the aN curve are very important for judging material properties. If they are discarded due to data processing, the previously qualified material may need to be resampled and tested because the corresponding da / dN and ΔK values ​​cannot be calculated. The test method provided by the present invention can solve this problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0029] Figure 1 is a flow chart of the present invention;

[0030] Figure 2 This is the measured aN curve obtained in Example 1 of the present invention;

[0031] Figure 3 The fitted curve of the last 7 data points of the aN measured curve obtained in Example 1 of the present invention;

[0032] Figure 4 The aN curve of Example 1 of the present invention is supplemented with three virtual data points;

[0033] Figure 5 This is the fitting curve of the 7 data points at the end of the aN measured curve obtained in Example 2 of the present invention, and the aN curve after adding 3 virtual data points. DETAILED DESCRIPTION

[0034] The present invention provides a fatigue crack growth rate test method based on incremental polynomial supplementary calculation. To make the objectives, technical solutions, and effects of the present invention more clear and explicit, the present invention is further described below. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0035] Reference Figure 1 The present invention provides a fatigue crack growth rate test method based on incremental polynomial supplementary calculation, comprising the steps of:

[0036] (1) Prepare the fatigue crack growth rate test specimen according to the test requirements, apply cyclic load to conduct the test, obtain the crack length-cycle number curve of the test specimen, that is, the aN curve, and obtain m groups of a i 、N i Data point, i is the serial number of the data point;

[0037] (2) Use the incremental polynomial method to calculate any data point a on the aN curve in step (1). i 、N i And n data points before and after this point are fitted to obtain the second-order polynomial equation of the (2n+1) consecutive data points. The calculation cycle is N i The crack length fitting value at , and calculate the fatigue crack growth rate fitting value by derivation , that is, the da / dN value of the data point; then use the value corresponding to the cycle number N i The crack length fitting value Calculate the corresponding ΔK value to obtain the da / dN value and ΔK value of the other data points in the aN curve except the front n data points and the end n data points;

[0038] The second-order polynomial equation fitted by (2n+1) consecutive data points in this step is:

[0039] (1);

[0040] in:

[0041] (2);

[0042] (3);

[0043] (4);

[0044] The fatigue crack growth rate fitting value is obtained by derivation of the above formula (1): The calculation formula is:

[0045] (5);

[0046] Where N i is the cycle number of the i-th data point, N i-n is the cycle number of the (in)th data point, N i+n is the cycle number of the (i+n)th data point, is the number of cycles N i The crack length fitting value at a, b0, b1, b2 are i-n ≤a≤a i+n The regression parameters are determined by the least square method (i.e., minimizing the sum of squares of the deviations between the observed and fitted crack sizes) within the range. C1 and C2 are coefficients used to scale the input data to avoid numerical calculation difficulties when determining the regression parameters.

[0047] (3) The average value of the cycle times of at least three data points at the front or end of the aN curve , the number of cycles of adding n virtual data points at the front end or end of the aN curve, where the number of cycles of n virtual data points added at the front end of the aN curve is 、…、 The number of cycles of the n virtual data points added at the end are 、…、 , then use the second-order polynomial equation of the front or end (2n+1) consecutive data points in step (2) to calculate the fitting crack length corresponding to the number of cycles of the supplemented n virtual data points;

[0048] (4) Based on the n virtual data points at the front end or the end supplemented in step (3), the da / dN value and ΔK value of the n data points at the front end or the end of the aN curve are calculated using the method in step (2);

[0049] (5) Using the da / dN and ΔK values ​​obtained in steps (2) and (4), the da / dN-ΔK curve is plotted to obtain the fatigue crack growth rate curve.

[0050] The aN curves obtained in Examples 1 and 2 were processed using the above method.

[0051] Example 1

[0052] In this embodiment, fatigue crack growth rate test was conducted on 7050-T7451 aluminum alloy plate. According to the test requirements and GB / T6398-2017 standard, M (T) specimens were processed. The specimen thickness B = 6.45 mm, width W = 100.09 mm, the yield strength of the material was 463.2 MPa, and the maximum loading load was P. max =38889N, stress ratio R=0.1, initial crack length is 20.23mm, and loading frequency is 10Hz.

[0053] In this embodiment, fatigue crack growth rate test was carried out according to GB / T6398-2017 standard, and the following results were obtained: Figure 2 The aN curve shown in the figure has a total of 262 data points. The aN curve data obtained from the experiment are processed by the incremental polynomial method. A 7-point fitting is used in the data processing process. The da / dN values ​​and ΔK values ​​of the data points other than the first 3 data points and the last 3 data points can be calculated. For the first 3 data points and the last 3 data points, especially for the 260th, 261st, and 262nd data points at the end of the aN curve, the method of supplementing virtual data points is used for calculation, specifically:

[0054] The incremental polynomial method is used to fit the last 7 data points from 256 to 262, and the following is obtained: Figure 3 The parabola shown is fitted to the following second-order polynomial equation:

[0055] ;

[0056] According to the average of the cycle intervals of the last five data points at the end of the aN curve, three virtual data points are added. 258 =48801、N 259 =48819、N 260 =48846、N 261 =48863、N 262 =48880, the average value of the cycle interval is 20 times, and the number of cycles to add 3 virtual data points is N 263 =48900、N 264 =48920、N 265 =48940, and substitute them into the second-order polynomial equation fitted with the last 7 data points from 256 to 262 to obtain the corresponding crack length a 263 =40.15mm, a 264=40.28mm, a 265 =40.42mm, add these three virtual data points to the original aN curve, such as Figure 4 As shown, the total number of data points becomes 265 at this time;

[0057] Using the three supplemented virtual data points, the incremental polynomial method is used to calculate the da / dN values ​​and ΔK values ​​of the three data points 260, 261, and 262 at the end of the aN curve, as shown in Table 1 below.

[0058] Table 1 aN curve and calculation results of supplementary virtual data points in Example 1

[0059]

[0060] After adding three virtual data points to the end of the original aN curve, this embodiment can solve the da / dN and ΔK values ​​corresponding to the three measured data points at the end of the original aN curve. That is, this embodiment calculates the da / dN and ΔK values ​​corresponding to the 4th to 262nd data points, thereby maximizing the acquisition of valid da / dN and ΔK data. The da / dN-ΔK curve is then plotted based on the calculated da / dN and ΔK values ​​to obtain the fatigue crack growth rate curve.

[0061] Example 2

[0062] In this embodiment, fatigue crack growth rate test was conducted on 7050-T7451 aluminum alloy plate. According to the test requirements and GB / T6398-2017 standard, M (T) specimens were processed. The specimen thickness B = 6.45 mm, width W = 135.04 mm, yield strength of the material was 463.2 MPa, and the maximum loading load was P. max =43000N, stress ratio R=0.1, initial crack length is 26.9mm, and loading frequency is 10Hz.

[0063] In this embodiment, fatigue crack growth rate test was carried out according to GB / T6398-2017 standard, and the following results were obtained: Figure 5 The aN curve shown in the figure has 76 data points in total. The aN curve data obtained from the experiment are processed by the incremental polynomial method. The 7-point fitting is used in the data processing process. The da / dN values ​​and ΔK values ​​of the data points other than the first 3 data points and the last 3 data points can be calculated. For the first 3 data points and the last 3 data points, especially for the 74th, 75th, and 76th data points at the end of the aN curve, the method of supplementing virtual data points is used for calculation, specifically:

[0064] The incremental polynomial method is used to fit the last 7 data points from 70 to 76. The second-order polynomial equation obtained by fitting is as follows:

[0065] ;

[0066] According to the average of the cycle intervals of the last four data points at the end of the aN curve, three virtual data points are added. 73 =88813、N 74 =88981、N 75 =89128、N 76 =89254, the average value of the cycle interval is 147 times, and the number of cycles to add 3 virtual data points is N 77 =89401、N 78 =89548、N 79 =89695, and substitute them into the second-order polynomial equation fitted with the last 7 data points from 70 to 76 to obtain the corresponding crack length a 77 =53.55mm, a 78 =54.23mm, a 79 =54.94mm, add these three virtual data points to the original aN curve, such as Figure 5 As shown, the total number of data points becomes 79 at this time;

[0067] Using the three supplemented virtual data points, the incremental polynomial method is used to calculate the da / dN values ​​and ΔK values ​​of the three data points at the end of the aN curve, namely, the 74th, 75th, and 76th data points, as shown in Table 2 below.

[0068] Table 2 aN curve and calculation results of supplementary virtual data points in Example 2

[0069]

[0070] After adding three virtual data points to the end of the original aN curve, this embodiment can solve for the da / dN and ΔK values ​​corresponding to the three measured data points at the end of the original aN curve. That is, this embodiment calculates the da / dN and ΔK values ​​corresponding to the 4th to 76th data points, thereby maximizing the acquisition of valid da / dN and ΔK data. Based on the calculated da / dN and ΔK values, a da / dN-ΔK curve is plotted to obtain a fatigue crack growth rate curve. Of course, this embodiment can also use the same method to add three virtual data points to the front of the original aN curve to solve for the da / dN and ΔK values ​​corresponding to the three measured data points at the front of the original aN curve.

[0071] In the above-mentioned Examples 1 and 2, by using the method of the present invention, after adding three virtual data points at the end of the aN curve, the da / dN values ​​and ΔK values ​​of the three measured data points at the end of the aN curve can be calculated, and the valid da / dN and ΔK data can be obtained to the maximum extent, thereby avoiding the problem that the test data originally contains the da / dN value corresponding to the maximum ΔK, but due to problems in the data processing method, the da / dN values ​​corresponding to the three data points with the largest ΔK cannot be calculated, thereby causing data invalidation.

[0072] It should be noted that the parts not described in the present invention can be implemented by adopting or drawing on existing technologies.

[0073] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A fatigue crack growth rate test method based on incremental polynomial supplementary calculation, characterized in that: Including steps: (1) Prepare the fatigue crack growth rate test specimen according to the test requirements, apply cyclic load to conduct the test, obtain the crack length-cycle number curve of the test specimen, that is, the aN curve, and obtain m groups of a i 、N i Data point, i is the serial number of the data point; (2) Use the incremental polynomial method to calculate any data point a on the aN curve in step (1). i 、N i And n data points before and after this point are fitted to obtain the second-order polynomial equation of the (2n+1) consecutive data points. The calculation cycle is N i The crack length fitting value at , and calculate the fatigue crack growth rate fitting value by derivation , that is, the da / dN value of the data point; then use the value corresponding to the cycle number N i The crack length fitting value Calculate the corresponding ΔK value to obtain the da / dN value and ΔK value of the other data points in the aN curve except the front n data points and the end n data points; (3) The average value of the cycle times of at least three data points at the front or end of the aN curve , continue to add n virtual data points at the front end or end of the aN curve, and use the second-order polynomial equation of the front end or end (2n+1) continuous data points in step (2) to calculate the fitting crack length corresponding to the number of cycles of the added n virtual data points; (4) Based on the n virtual data points at the front end or the end supplemented in step (3), the da / dN value and ΔK value of the n data points at the front end or the end of the aN curve are calculated using the method in step (2); (5) Using the da / dN and ΔK values ​​obtained in steps (2) and (4), the da / dN-ΔK curve is plotted to obtain the fatigue crack growth rate curve.

2. A fatigue crack growth rate test method based on incremental polynomial supplementary calculation according to claim 1, characterized in that: In step (2), the value of n is 1, 2, 3 or 4.

3. A fatigue crack growth rate test method based on incremental polynomial supplementary calculation according to claim 2, characterized in that: In step (2), the value of n is 3.

4. A fatigue crack growth rate test method based on incremental polynomial supplementary calculation according to claim 1, characterized in that: The second-order polynomial equation fitted by (2n+1) consecutive data points in step (2) is: ； in: ； ； ； Where N i is the cycle number of the i-th data point, N i-n is the cycle number of the (in)th data point, N i+n is the cycle number of the (i+n)th data point, is the number of cycles N i The crack length fitting value at a, b0, b1, b2 are i-n ≤a≤a i+n The regression parameters are determined by the least squares method within the range. C1 and C2 are coefficients used to scale the input data to avoid numerical calculation difficulties when determining the regression parameters.

5. A fatigue crack growth rate test method based on incremental polynomial supplementary calculation according to claim 4, characterized in that: The fatigue crack growth rate fitting value in step (2) The calculation formula is: 。 6. A fatigue crack growth rate test method based on incremental polynomial supplementary calculation according to claim 1, characterized in that: The number of cycles of n virtual data points added to the front end of the aN curve in step (3) is 、…、 .

7. A fatigue crack growth rate test method based on incremental polynomial supplementary calculation according to claim 1, characterized in that: The number of cycles of n virtual data points added at the end of the aN curve in step (3) is 、…、 .

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