A method for predicting a fatigue crack initiation position based on probability statistics

Abstract

The present application relates to the field of fatigue crack initiation mode prediction, and particularly relates to a fatigue crack initiation position prediction method based on probability statistics, comprising: preparing a metallographic sample of a metal material, and using a microscope to shoot a microstructure picture of the metallographic sample; determining a defect type of the metal material, processing the microstructure picture, and counting defect sizes and quantities of the defect type; performing logarithmic normal distribution curve fitting on multiple defect sizes and corresponding defect quantities to obtain a probability density function of defect size distribution; obtaining a metal material fatigue crack initiation position prediction model based on a maximum defect size and the probability density function of defect size distribution; inputting a minimum defect size of a metal material to be detected into the metal material fatigue crack initiation position prediction model to obtain an initiation position probability prediction value; and the present application can improve the accuracy of fatigue performance analysis.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of fatigue crack initiation mode prediction, and in particular to a probability statistics-based fatigue crack initiation position prediction method. BACKGROUND

[0002] Advanced aero-engine needs to have high thrust-to-weight ratio and high boost ratio performance, wherein the compressor blade needs to bear a large amplitude of cyclic load at high temperature in actual service. High-temperature titanium alloy is widely used in the blade field of aero-engine due to its low density, good structural strength and high-temperature resistance.

[0003] Since the engine blade needs to reciprocate at a high speed and under a load, fatigue fracture is the most common failure mode of titanium alloy, and the initiation and early propagation of fatigue cracks are the key to the fatigue failure of metal materials. Within a certain range, the fatigue crack initiation position of titanium alloy includes the surface and the interior, but the S-N curve thereof presents a discontinuous double-line type distribution, that is, there is neither a continuous descending step arrangement nor a horizontal section between the two curves, and the low-life section of the curve is surface initiation and the high-life section is internal initiation.

[0004] This phenomenon is usually related to the special microstructure defects of titanium alloy. Taking Ti60 titanium alloy as an example, within a certain experimental stress range, the fatigue cracks of Ti60 titanium alloy are initiated in alpha phase grains larger than the critical size. When the grains only exist in the interior of the sample, the fatigue cracks will be initiated in the interior; if the grains appear on the surface of the sample, the fatigue cracks will be initiated on the surface, and since the environment of the sample surface region is much worse than that of the interior, the fatigue life of the surface initiation sample is also generally lower than that of the internal initiation sample.

[0005] Overall, titanium alloy fatigue cracks can be initiated from both the surface and the interior of the sample, and the probabilities of the two initiation modes are different and difficult to predict, which causes difficulty in the accuracy of titanium alloy fatigue performance analysis. Therefore, it is very meaningful to construct a model capable of predicting the probability of titanium alloy fatigue crack initiation position. SUMMARY

[0006] In view of the above problems, the present application provides a probability statistics-based fatigue crack initiation position prediction method, which solves the technical problem of how to accurately predict whether the fatigue crack initiation of a metal material is in the interior or on the surface.

[0007] The present application provides a probability statistics-based fatigue crack initiation position prediction method, which comprises the following steps:

[0008] Step S1, preparing a metallographic sample of a metal material, and taking a microstructure picture of the metallographic sample by using a microscope;

[0009] Step S2, determining a defect type of the metal material, processing the microstructure picture, counting defect sizes and quantities of the defect type, and obtaining a plurality of defect sizes and corresponding defect quantities;

[0010] Step S3, performing logarithmic normal distribution curve fitting on the plurality of defect sizes and corresponding defect quantities, and obtaining a probability density function of defect size distribution;

[0011] Step S4, obtaining a maximum defect size in the plurality of defect sizes, and obtaining a metal material fatigue crack initiation position prediction model based on the maximum defect size and the probability density function of defect size distribution;

[0012] Step S5, inputting a minimum defect size of a metal material to be detected into the metal material fatigue crack initiation position prediction model, and obtaining occurrence probability prediction values of a surface initiation mode and a non-surface initiation mode.

[0013] Preferably, the step S1 specifically comprises:

[0014] cutting a part of the sample from the metal material, forming a flat surface on the sample, and then embedding, polishing, polishing and etching the sample to obtain the metallographic sample after preparation;

[0015] observing and photographing the microstructure morphology of a unit area of the metallographic sample by using a microscope, and forming the microstructure picture.

[0016] Preferably, the step S2 specifically comprises:

[0017] Step S2-1, determining an alpha grain as a defect type of the metal material;

[0018] Step S2-2, using image processing software to count the size and quantity of defects in the microstructure picture;

[0019] Step S2-3, after obtaining all defects and corresponding sizes, dividing and counting according to size-quantity to obtain a plurality of defect sizes and corresponding defect quantities.

[0020] Preferably, in the step S2-2, the counting process of the size of the defect comprises:

[0021] using image processing software to obtain the effective area, effective length, effective width and equivalent aspect ratio of each defect;

[0022] When the equivalent aspect ratio of the defect is less than 2, the defect is determined as an equiaxed defect, and the square root of the effective area of the defect is determined as the equivalent length of the defect;

[0023] When the equivalent aspect ratio of the defect is greater than or equal to 2, the defect is determined as an elongated defect, and the effective length of the defect is determined as the equivalent length of the defect;

[0024] When multiple defects are adjacent and the adjacent distance is less than the average of the sizes of the multiple defects, the multiple defects are regarded as a combined defect, and the effective length of the combined defect is determined as the equivalent length of the defect.

[0025] Preferably, the step S2-3 specifically comprises:

[0026] Step S2-3-1, forming a size interval with the minimum size and the maximum size in the statistically obtained defects, determining an interval interval, and equally dividing the size interval into multiple interval segments with the interval interval;

[0027] Step S2-3-2, counting the defects with a defect size greater than or equal to the left end point value of the interval segment and less than the left end point value of the next interval, and obtaining the number of defects in each interval.

[0028] Preferably, the step S3 specifically comprises:

[0029] The probability density function f(x) of the defect size distribution adopts a lognormal distribution function, and the expression is:

[0030]

[0031] Wherein, x is the defect size, μ is the log mean, and σ is the log standard deviation;

[0032] The defect size is taken as the x value, and the number of defects is taken as the f(x) value; the fitting parameters μ and σ are obtained by least square fitting; the determination coefficient R of the fitting curve is calculated 2 ; When R 2 ≥ 0.95, it is determined that the fitting result meets the requirements, and is taken as the optimal fitting parameter;

[0033] The probability density function of the defect size distribution is determined by the optimal fitting parameter.

[0034] Preferably, the step S4 specifically comprises:

[0035] Determining the maximum defect size D max as the upper limit of the defect size, and obtaining the expression of the probability of the metal material fatigue crack from the surface as:

[0036]

[0037] wherein D min represents the critical size that can lead to the fatigue crack initiation of the target sample under a certain stress level, P(D min ) represents the probability of the critical size D min corresponding to the surface initiation, D max represents the maximum defect size, A represents a normalization coefficient, x c represents the characteristic size.

[0038] Preferably, the step S5 specifically comprises:

[0039] substituting the minimum defect size of the metal material to be detected into the fatigue crack initiation position prediction model of the metal material, to obtain the critical size D min , the probability P(D min ) corresponding to the surface initiation, and the probability 1-P(D min ) of the surface initiation;

[0040] judging the fatigue crack initiation position according to the calculated probability value, including: when P(D min )≥P cr , it is predicted that the fatigue crack will mainly initiate in the surface initiation mode; when P(D min )<P cr , it is predicted that the fatigue crack will mainly initiate in the non-surface initiation mode; wherein P cr is a critical probability value.

[0041] Compared with the prior art, the present application has at least the following beneficial effects:

[0042] (1) The present application realizes the quantitative prediction of the fatigue crack initiation position by establishing the probability density function of the defect size distribution through the systematic statistics and analysis of the size and quantity of the defects in the metallographic sample. The distribution characteristics of various size defects in the material are fully considered, and the reliability and accuracy of the prediction result are improved.

[0043] (2) The present application uses the logarithmic normal distribution function to fit the defect size-quantity data, establishes the prediction model based on probability statistics, and can effectively reflect the overall distribution law of the internal defects of the material. By introducing the minimum defect size as the prediction parameter, combining the maximum defect size and the defect size distribution characteristics, the quantitative prediction of the fatigue crack initiation position is realized.

[0044] (3) The method of the present application is simple to operate, has strong practicability and universality, and can be widely applied to the fatigue performance evaluation of various metal materials. Through the method, the possible initiation position of the fatigue crack can be predicted, which provides help for the design optimization and use safety of the engineering structure, and has important engineering application value. BRIEF DESCRIPTION OF DRAWINGS

[0045] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0046] Figure 1 This is a flowchart of the fatigue crack initiation location prediction method based on probability statistics disclosed in this invention.

[0047] Figure 2 This is a schematic diagram showing the distribution of the α-phase grain size in the original state structure disclosed in this invention.

[0048] Figure 3 This is a schematic diagram of the probability density function of the α-phase grain size distribution in the original state structure disclosed in this invention.

[0049] Figure 4 This is a schematic diagram showing the change in the probability of fatigue crack initiation mode in titanium alloys as a function of the maximum defect size, as disclosed in this invention.

[0050] Figure 5 This is a schematic diagram showing the proportion of surface germination samples under different stress levels disclosed in this invention. Detailed Implementation

[0051] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0052] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment, such as... Figure 1 As shown, a method for predicting the location of fatigue crack initiation based on probability statistics is disclosed. The specific implementation steps are as follows:

[0053] Step S1: Prepare a metallographic sample of the metallic material and take microscopic images of the metallographic sample using a microscope.

[0054] In this embodiment of the invention, a small portion of a Ti60 high-temperature titanium alloy blank sample that has undergone low-cycle pre-damage is cut off by wire cutting to ensure that it has a relatively flat surface. Then, the small portion of the sample is inlaid, ground, polished and etched to obtain a metallographic sample after preparation.

[0055] The microstructure morphology of a unit area of ​​the metallographic sample is observed and photographed using a microscope to form the microstructure image.

[0056] Step S2, determining the defect type of the metal material, processing the microstructure picture, counting the defect size and quantity of the defect type, obtaining multiple defect sizes and corresponding defect quantities.

[0057] In this step, it is first necessary to determine the microstructure type that will cause the fatigue crack initiation, such as grain, pore, inclusion, etc., which will vary with the material, and the present application collectively refers to the defects. Within a certain stress range, the fatigue crack of titanium alloy is usually initiated in the alpha grain.

[0058] In some embodiments, the present application determines the alpha grain as the defect type of the metal material to be detected.

[0059] The size and quantity of the defects in the microstructure picture are counted by using image processing software, wherein the process of counting the size of the defects includes:

[0060] The effective area, effective length, effective width and equivalent aspect ratio of each defect are obtained by using image processing software;

[0061] When the equivalent aspect ratio of the defect is less than 2, the defect is determined as an equiaxed defect, and the square root of the effective area of the defect is determined as the equivalent length of the defect;

[0062] When the equivalent aspect ratio of the defect is greater than or equal to 2, the defect is determined as an elongated defect, and the effective length of the defect is determined as the equivalent length of the defect;

[0063] When multiple defects are adjacent and the adjacent distance is less than the average value of the sizes of the multiple defects, the multiple defects are regarded as a combined defect, and the effective length of the combined defect is determined as the equivalent length of the defect.

[0064] After obtaining all the defects and corresponding sizes, the defects are sorted according to the size-quantity division, specifically including:

[0065] Firstly, the defects are divided according to the size, and multiple defect sizes are obtained, specifically: the minimum size and the maximum size of the counted defects form a size interval, the interval interval is determined, and the size interval is evenly divided into multiple interval segments by using the interval interval;

[0066] Secondly, the defects in each interval segment are counted to obtain the corresponding defect quantity, including: the defects with a size greater than or equal to the left end point value of the interval segment and less than the left end point value of the next interval are classified into the interval, and the defect quantity in each interval is counted.

[0067] The actual distribution of the primary alpha phase grain size in the original state of the Ti60 alloy used in the embodiment of the present application is as follows: Figure 2As shown, the statistical results show that it meets the lognormal distribution, the peak size is 14 μm, and from the identifiable category, the grain size ranges from 5 to 70 μm.

[0068] Step S3, the plurality of defect sizes and the corresponding defect numbers are fitted with a lognormal distribution curve to obtain a probability density function of the defect size distribution.

[0069] In this step, the plurality of defect sizes and the corresponding defect numbers are fitted with a lognormal distribution curve.

[0070] The probability density function f(x) of the defect size distribution of the present application adopts a lognormal distribution function, and the expression is:

[0071]

[0072] Wherein, x is the defect size, μ is the log mean, and σ is the log standard deviation.

[0073] In some embodiments, the defect size is taken as the x value, and the corresponding defect number is taken as the f(x) value; the experimental data are fitted by the least square method to obtain the fitting parameters μ and σ; the determination coefficient R 2 of the fitting curve is calculated for evaluating the goodness of fit; when R 2 ≥ 0.95, it is determined that the fitting result meets the requirements and is taken as the optimal fitting parameter.

[0074] The optimal fitting parameters are obtained by iterative calculation, the log mean μ = 2.90 and the log standard deviation σ = 0.52 are obtained. The probability density function of the defect size distribution is determined according to the optimal fitting parameters, and the probability density function curve fitted is as shown in Figure 3 .

[0075] Step S4, the maximum defect size in the plurality of defect sizes is obtained; based on the maximum defect size and the probability density function of the defect size distribution, a metal material fatigue crack initiation position prediction model is obtained.

[0076] In order to further calculate the occurrence probability of the two initiation modes of surface initiation and internal initiation, the following assumptions are needed:

[0077] (1) The distribution of defects in the sample is uniform, and the occurrence probability of defects of the same size in each region of the sample is consistent

[0078] (2) When defects of the same size exist in the internal region and the surface region of the sample at the same time, the fatigue crack preferentially initiates on the surface.

[0079] Based on the two assumptions, two inferences can be obtained:

[0080] (1) The probability of defects of various sizes appearing in any selected area inside the sample should be consistent with that of the original material. Therefore, the probability of large-sized defects appearing in the surface area should be the same as the probability density function of the defect size distribution in the original state.

[0081] (2) As long as a large defect of sufficient size appears in the surface area, that is, exceeding the critical size, fatigue cracks can be considered to have started on the surface of the specimen.

[0082] Based on the above inferences, the present invention determines the largest defect size D among the plurality of defect sizes. max As the upper limit of the defect size, the expression for the probability of fatigue crack initiation from the surface in metallic materials is obtained as follows:

[0083]

[0084] Among them, D min P(D) represents the critical size at which fatigue cracks can be initiated in a target sample under a certain stress level. min ) represents the critical dimension D min The corresponding probability of germination from the surface, D max Let x represent the maximum defect size, A represent the normalization coefficient, and x represent the maximum defect size. c This represents the characteristic dimension, which is the logarithmic mean of the defect dimensions.

[0085] Step S5: Input the minimum defect size of the metal material to be tested into the fatigue crack initiation location prediction model of the metal material to obtain the predicted probability values ​​of the occurrence of surface initiation mode and non-surface initiation mode.

[0086] In this step, the minimum defect size of the metal material to be tested is substituted into the fatigue crack initiation location prediction model of the metal material to obtain the critical size D. min The corresponding probability P(D) of germination from the surface min ) and the probability of germination from the surface 1-P(D min );

[0087] The present invention also determines the initiation location of fatigue cracks based on calculated probability values, including:

[0088] When P(D) min )≥P cr At that time, fatigue cracks are predicted to be mainly initiated on the surface.

[0089] When P(D) min ) <P cr At that time, fatigue cracks are predicted to be mainly in the non-surface initiation mode;

[0090] Where P cr This is the critical probability value.

[0091] In the present embodiment, the maximum grain size D max observed for the original material was 70 pm, which was taken as the upper limit for the grain size. It was found that the probability of surface nucleation mode and non-surface nucleation mode varied with D min Figure 4 as shown in the following table, the probability of surface nucleation mode decreased with the increase of the primary alpha phase grain size.

[0092] In general, the size of the titanium alloy D min in the present embodiment was between 20 pm and 25 pm, and the corresponding probability was between 42% and 27%. After the fatigue experiment of the titanium alloy in the present embodiment was completed, the distribution of the fatigue crack initiation position of the titanium alloy sample under different stress conditions was counted, and the counting results are shown in the following table. After the invalid data with surface nucleation ratio of 100% was removed, it was found that the probability distribution of the actual fatigue crack initiation mode of the sample was consistent with the prediction calculated, indicating that the prediction result was good. Figure 5 Figure 4

[0093] The specific embodiments of the present application, although depicted in a particular order of actions or steps, should be understood to require that the actions or steps be performed in the particular order shown or in sequential order, or that all illustrated actions or steps be performed to achieve the desired results. In certain circumstances, multitasking and parallel processing can be advantageous. Likewise, although specific implementation details are included in the above discussion, these should not be construed as limiting the scope of the disclosure. Certain features described in the context of separate embodiments can also be combined in a single implementation. Conversely, various features described in the context of a single implementation can also be separated and implemented in multiple implementations. The above description is merely the preferred specific embodiments of the present application, but the scope of protection of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed by the present application should be covered within the scope of protection of the present application.

[0094] The above description is merely the preferred specific embodiments of the present application, but the scope of protection of the present application is not limited thereto, and any changes or replacements within the technical scope disclosed by the present application should be covered within the scope of protection of the present application.​​​

Claims

1. A method for predicting the location of fatigue crack initiation based on probability statistics, characterized in that, Includes the following steps: Step S1: Prepare a metallographic sample of the metallic material and take microscopic images of the metallographic sample using a microscope; Step S2: Determine the defect type of the metal material, process the microstructure image, and count the defect size and number of the defect types to obtain multiple defect sizes and corresponding defect numbers; Step S3: Fit a log-normal distribution curve to the multiple defect sizes and the corresponding number of defects to obtain the probability density function of the defect size distribution; Step S4: Obtain the largest defect size among the multiple defect sizes; based on the largest defect size and the probability density function of the defect size distribution, obtain a prediction model for the location of fatigue crack initiation in metallic materials; Specifically, it includes: Determine the largest defect size among the plurality of defect sizes. As an upper limit for the defect size, the expression for the probability of fatigue crack initiation from the surface in metallic materials is: in, It represents the critical size at which fatigue cracks can be initiated in a target sample under a certain stress level. Indicates critical size The probability of it originating from the surface. Indicates the maximum defect size. Represents the normalization coefficient. Indicates the feature size; Step S5: Input the critical size that can cause fatigue crack initiation in the target sample under a certain stress level into the fatigue crack initiation location prediction model of the metal material to obtain the predicted probability values ​​of the occurrence of the surface initiation mode and the predicted probability values ​​of the occurrence of the non-surface initiation mode. Specifically, it includes: Substituting the critical size that can cause fatigue crack initiation in the target sample under a certain stress level into the fatigue crack initiation location prediction model of the metallic material, the critical size is obtained. The corresponding probability of germination from the surface And the probability of it arising from within. ; When large defects exceeding the critical size appear in the surface region, fatigue cracks will initiate on the sample surface.

2. The method for predicting the location of fatigue crack initiation based on probability statistics according to claim 1, characterized in that, Step S1 specifically includes: A portion of the sample is cut from the metal material, and a flat surface is formed on the sample. The sample is then inlaid, ground, polished, and etched to obtain a metallographic sample after preparation. The microstructure morphology of a unit area of ​​the metallographic sample is observed and photographed using a microscope to form the microstructure image.

3. The method for predicting the location of fatigue crack initiation based on probability statistics according to claim 2, characterized in that, Step S2 specifically includes: Step S2-1: Determine the α grain as the defect type of the metallic material; Step S2-2: Use image processing software to count the size and number of defects in the microstructure images; Step S2-3: After obtaining all defects and their corresponding dimensions, divide and count them according to size-quantity to obtain multiple defect sizes and their corresponding defect quantities.

4. The method for predicting the location of fatigue crack initiation based on probability statistics according to claim 3, characterized in that, In step S2-2, the statistical process for determining the size of the defect includes: Image processing software was used to obtain the effective area, effective length, effective width, and equivalent aspect ratio of each defect; When the equivalent aspect ratio of the defect is less than 2, the defect is identified as an equiaxial defect, and the square root of the effective area of ​​the defect is determined as the equivalent length of the defect. When the equivalent aspect ratio of a defect is greater than or equal to 2, the defect is defined as a narrow and elongated defect, and the effective length of the defect is defined as the equivalent length of the defect. When multiple defects are adjacent and the distance between them is less than the average size of the multiple defects, the multiple defects are regarded as a combined defect, and the effective length of the combined defect is determined as the equivalent length of the defect.

5. The method for predicting the location of fatigue crack initiation based on probability statistics according to claim 4, characterized in that, Step S2-3 specifically includes: Step S2-3-1: Form a size range from the minimum and maximum dimensions of the defects obtained from statistics, determine the interval interval, and divide the size range into multiple segments on average using the interval interval; Step S2-3-2: Defects whose size is greater than or equal to the left endpoint of the interval segment and less than the left endpoint of the next interval are included in the interval and counted to obtain the number of defects in each interval.

6. The method for predicting the location of fatigue crack initiation based on probability statistics according to claim 5, characterized in that, Step S3 specifically includes: The probability density function of the defect size distribution Using the log-normal distribution function, the expression is: in, For defect size, The logarithmic mean is... The standard deviation is the logarithm. The defect size is taken as the x-value, and the corresponding number of defects is taken as... Values; fit parameters by least squares method. and Calculate the coefficient of determination of the fitted curve. ;when When the fitting result meets the requirements, it is used as the optimal fitting parameter; The probability density function of the defect size distribution is determined by the optimal fitting parameters.

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