Fatigue crack initiation position prediction method based on probability statistics

Abstract

The invention relates to the field of prediction of fatigue crack initiation modes, in particular to a fatigue crack initiation position prediction method based on probability statistics, which comprises the following steps: preparing a metallographic sample of a metal material, and shooting a microstructure picture of the metallographic sample by using a microscope; determining the defect type of the metal material, processing the microstructure picture, and counting the defect size and number of the defect type; performing logarithmic normal distribution curve fitting on the plurality of defect sizes and the corresponding defect numbers to obtain a probability density function of defect size distribution; 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; inputting the minimum defect size of the metal material to be detected into the metal material fatigue crack initiation position prediction model to obtain an initiation position probability prediction value; the accuracy of fatigue performance analysis can be improved.

Description

Technical Field

[0001] The invention relates to the field of prediction of fatigue crack initiation modes, and in particular to a method for predicting fatigue crack initiation positions based on probability statistics. Background Art

[0002] Advanced aircraft engines need to have high thrust-to-weight ratio and high compression ratio. The compressor blades need to withstand large cyclic loads at high temperatures during actual service. High-temperature titanium alloys have been widely used in the field of aircraft engine blades due to their low density, good structural strength and high temperature resistance.

[0003] Since engine blades need to perform reciprocating cyclic motion at high speeds and loads, fatigue fracture is the most common failure form of titanium alloys, among which the initiation and early expansion of fatigue cracks are the key to fatigue failure of metal materials. Within a certain range, the initiation locations of fatigue cracks in titanium alloys include the surface and the interior, but its SN curve presents a discontinuous bilinear distribution, that is, there is neither a continuously descending step-like arrangement nor a horizontal segment between the two curves, and the low-life segment of the curve is all surface initiation, and the high-life segment is all internal initiation.

[0004] This phenomenon is usually related to the special microstructural defects of titanium alloys. Taking Ti60 titanium alloy as an example, within a certain range of experimental stress, the fatigue crack of Ti60 titanium alloy initiates from α-phase grains larger than the critical size. When the grain only exists inside the sample, the fatigue crack will initiate inside; if the grain appears on the surface of the sample, the fatigue crack will initiate on the surface, and because the environment of the surface area of ​​the sample is much worse than that of the interior, the fatigue life of the surface initiated sample is generally lower than that of the internal initiated sample.

[0005] Overall, fatigue cracks in titanium alloys may initiate from the surface or from the inside of the specimen, and the probability of these two initiation modes is different and difficult to predict, which makes it difficult to accurately analyze the fatigue properties of titanium alloys. Therefore, it is very meaningful to construct a model that can predict the probability of the initiation location of fatigue cracks in titanium alloys. Summary of the invention

[0006] In view of the above problems, the present invention provides a method for predicting fatigue crack initiation positions based on probability statistics, which solves the technical problem in the prior art of how to accurately predict whether fatigue crack initiation of metal materials occurs inside or on the surface.

[0007] The present invention provides a method for predicting fatigue crack initiation positions based on probability statistics, comprising the following steps:

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

[0009] Step S2, determining the defect type of the metal material, processing the microstructure image, counting the defect size and quantity of the defect type, and obtaining multiple defect sizes and corresponding defect quantities;

[0010] Step S3, performing log-normal distribution curve fitting on the multiple defect sizes and the corresponding defect quantities to obtain a probability density function of the defect size distribution;

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

[0012] Step S5, inputting 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 occurrence probability prediction values ​​of the surface initiation mode and the non-surface initiation mode.

[0013] Preferably, the step S1 specifically includes:

[0014] Cutting a portion of the sample from the metal material to form a flat surface on the sample, then inlaying, grinding, polishing and corroding the sample to obtain a metallographic sample after the preparation is completed;

[0015] The microstructure morphology of a unit area of ​​the metallographic sample is observed and photographed using a microscope to preserve the microstructure morphology to form the microstructure picture.

[0016] Preferably, the step S2 specifically includes:

[0017] Step S2-1, determining α grains as the defect type of the metal material;

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

[0019] Step S2-3: After all defects and corresponding sizes are obtained, they are divided and counted according to size-quantity to obtain multiple defect sizes and corresponding defect quantities.

[0020] Preferably, in step S2-2, the process of calculating the size of the defects includes:

[0021] Use 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 equiaxial 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 length-to-width ratio of a defect is greater than or equal to 2, the defect is determined as a narrow and long 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 value of the multiple defect sizes, 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 includes:

[0026] Step S2-3-1, forming a size interval based on the minimum size and the maximum size of the defects obtained by statistics, determining the interval interval, and evenly dividing the size interval into a plurality of interval segments based on the interval interval;

[0027] Step S2-3-2: Defects whose defect size is greater than or equal to the left endpoint value of the interval segment and less than the left endpoint value of the next interval are classified into the interval and counted to obtain the number of defects in each interval.

[0028] Preferably, the step S3 specifically includes:

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

[0030]

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

[0032] The defect size is taken as the x value, and the corresponding defect number is taken as the f(x) value; fitting is performed by the least squares method to obtain fitting parameters μ and σ; and the determination coefficient R of the fitting curve is calculated. 2 ; When R 2 When ≥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 parameters.

[0034] Preferably, the step S4 specifically includes:

[0035] Determine the maximum defect size D among the multiple defect sizes max As the upper limit of the defect size, the expression for the probability of fatigue crack initiation from the surface of metal materials is obtained as follows:

[0036]

[0037] Among them, D min It indicates the critical size that can cause fatigue crack initiation in the target sample under a certain stress level, P(D min ) represents the critical size D min The corresponding probability of sprouting from the surface, D max represents the maximum defect size, A represents the normalization coefficient, x c Indicates feature size.

[0038] Preferably, the step S5 specifically includes:

[0039] Substitute the minimum defect size of the metal material to be tested into the fatigue crack initiation position prediction model of the metal material to obtain the critical size D min The corresponding probability of sprouting from the surface is P(D min ) and the probability of sprouting from the surface 1-P(D min );

[0040] The fatigue crack initiation position is determined based on the calculated probability value, including: when P(D min )≥P cr When P(D min ) <P cr When P cr is the critical probability value.

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

[0042] (1) The present invention systematically counts and analyzes the size and quantity of defects in metallographic samples, establishes a probability density function of defect size distribution, and realizes quantitative prediction of fatigue crack initiation location. The distribution characteristics of defects of various sizes in the material are fully considered, and the reliability and accuracy of the prediction results are improved.

[0043] (2) The present invention uses a log-normal distribution function to fit the defect size-quantity data and establishes a prediction model based on probability statistics, which can effectively reflect the overall distribution law of defects inside the material. By introducing the minimum defect size as a prediction parameter, combined with the maximum defect size and defect size distribution characteristics, the quantitative prediction of the fatigue crack initiation location is achieved.

[0044] (3) The method of the present invention is simple to operate, has strong practicality and universality, and can be widely used in fatigue performance evaluation of various metal materials. The method can predict the possible initiation location of fatigue cracks, provide assistance for the design optimization and use safety of engineering structures, and has important engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings are only for the purpose of illustrating particular embodiments and are not to be construed as limiting the invention.

[0046] Figure 1 The present invention is a flowchart of a method for predicting fatigue crack initiation locations based on probability statistics.

[0047] Figure 2 It is a schematic diagram of the distribution of the α-phase grain size of the original structure disclosed in the present invention.

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

[0049] Figure 4 It is a schematic diagram of the variation of the occurrence probability of fatigue crack initiation mode of titanium alloy disclosed in the present invention with the maximum defect size.

[0050] Figure 5 This is a schematic diagram of the proportion of surface initiation samples under different stress levels disclosed in the present invention. DETAILED DESCRIPTION

[0051] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In addition, the present invention can also be implemented in other ways different from those described herein, and therefore, the protection scope of the present invention is not limited by the specific embodiments disclosed below.

[0052] In order to illustrate the effectiveness of the method proposed by the present invention, the above technical solution of the present invention is described in detail below through a specific embodiment. Figure 1 As shown, a method for predicting the fatigue crack initiation position based on probability statistics is disclosed, and the specific implementation steps are as follows:

[0053] Step S1, preparing a metallographic sample of a metal material, and taking a microstructure picture of the metallographic sample using a microscope.

[0054] In an embodiment of the present invention, a Ti60 high-temperature titanium alloy blank sample that has undergone low-cycle pre-damage is used, and a small part of the sample is cut off by wire cutting to ensure that it has a relatively flat surface. The small part of the sample is then inlaid, ground, polished and corroded 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 preserve the microstructure morphology to form the microstructure picture.

[0056] Step S2: determine the defect type of the metal material, process the microstructure image, count the defect size and quantity of the defect type, and obtain multiple defect sizes and corresponding defect quantities.

[0057] In this step, it is first necessary to determine the microstructure types that may cause fatigue crack initiation, such as grains, pores, inclusions, etc., which vary with different materials and are collectively referred to as defects in the present invention. Within a certain stress range, fatigue cracks in titanium alloys usually initiate in α grains.

[0058] In some embodiments, the present invention determines α grains as the defect type of the metal material to be inspected.

[0059] The size and number of defects in the microstructure image are counted using image processing software, wherein the process of calculating the size of the defects includes:

[0060] Use image processing software to obtain the effective area, effective length, effective width and equivalent aspect ratio of each defect;

[0061] When the equivalent aspect ratio of the defect is less than 2, the defect is determined as an equiaxial 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 length-to-width ratio of a defect is greater than or equal to 2, the defect is determined as a narrow and long 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 multiple defect sizes, 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 defects and their corresponding sizes, they are sorted according to size-quantity, including:

[0065] First, the defects are divided according to their sizes to obtain multiple defect sizes, specifically: the minimum size and the maximum size of the defects obtained by statistics are used to form a size interval, the interval interval is determined, and the size interval is evenly divided into multiple interval segments according to the interval interval;

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

[0067] The actual distribution of the primary α-phase grain size in the original structure of the Ti60 alloy used in the embodiment of the present invention is as follows: Figure 2As shown, the statistical results show that it satisfies the log-normal distribution, the peak size is 14 μm, and from the identifiable range, the grain size range is 5-70 μm.

[0068] Step S3: performing log-normal distribution curve fitting on the multiple defect sizes and the corresponding defect quantities to obtain a probability density function of the defect size distribution.

[0069] In this step, the present invention performs curve fitting on the multiple defect sizes and the corresponding defect quantities in the form of log-normal distribution.

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

[0071]

[0072] Where x is the defect size, μ is the logarithmic mean, and σ is the logarithmic 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 is fitted by the least squares method to obtain fitting parameters μ and σ; and the determination coefficient R of the fitting curve is calculated. 2 , used to evaluate the goodness of fit; when R 2 When ≥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 were obtained by iterative calculation, and the logarithmic mean μ = 2.90 and the logarithmic standard deviation σ = 0.52 were obtained. The probability density function of the defect size distribution was determined by the optimal fitting parameters, and the probability density function curve obtained by fitting was as follows: Figure 3 shown.

[0075] Step S4, obtaining a maximum defect size among the multiple defect sizes; and obtaining a fatigue crack initiation position prediction model for a metal material based on the maximum defect size and a probability density function of the defect size distribution.

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

[0077] (1) The distribution of defects inside the specimen is uniform, and the probability of defects of the same size appearing in different areas of the specimen is consistent

[0078] (2) When defects of the same size exist simultaneously in the internal area and the surface area of ​​the specimen, fatigue cracks initiate preferentially on the surface.

[0079] Based on these two assumptions, two inferences can be drawn:

[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, so the probability of large-size defects appearing in the surface area should be the same as the probability density function of the original defect size distribution.

[0081] (2) As long as a large-scale defect of sufficient size appears in the surface area, that is, exceeds the critical size, it can be considered that fatigue cracks will initiate on the surface of the specimen.

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

[0083]

[0084] Among them, D min It indicates the critical size that can cause fatigue crack initiation in the target sample under a certain stress level, P(D min ) represents the critical size D min The corresponding probability of sprouting from the surface, D max represents the maximum defect size, A represents the normalization coefficient, x c It represents the characteristic size, i.e. the logarithmic mean of the defect size.

[0085] Step S5, inputting 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 occurrence probability prediction values ​​of the surface initiation mode and the 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 position prediction model of the metal material to obtain the critical size D min The corresponding probability of sprouting from the surface is P(D min ) and the probability of sprouting from the surface 1-P(D min );

[0087] The present invention also determines the initiation position of fatigue cracks according to the calculated probability value, including:

[0088] When P(D min )≥P cr When , it is predicted that fatigue cracks will be mainly surface initiation mode;

[0089] When P(D min ) <P cr When , it is predicted that fatigue cracks will be mainly in the non-surface initiation mode;

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

[0091] In this embodiment, the maximum grain size D that can be observed in the original material is max The upper limit of the grain size is 70 μm. It can be concluded that the probability of occurrence of surface initiation mode and non-surface initiation mode increases with D min The function of change is Figure 4 As shown in Figure 2, the probability of the surface initiation mode occurring decreases with the increase of the primary α phase grain size.

[0092] Generally speaking, in this case, titanium alloy D min The size of the cracks is between 20μm and 25μm, and the corresponding probability is 42%-27%. After completing the titanium alloy fatigue test in this case, the distribution of fatigue crack initiation positions of titanium alloy samples under different stress conditions was statistically analyzed. The statistical results are as follows: Figure 5 After eliminating the invalid data with 100% surface initiation, it can be found that the probability distribution of the actual fatigue crack initiation mode of the sample is similar to Figure 4 The calculated predictions are consistent, indicating that the prediction results are good.

[0093] Although the specific embodiments of the present invention depict various actions or steps in a specific order, this should be understood as requiring such actions or steps to be performed in the specific order shown or in a sequential order, or requiring all illustrated actions or steps to be performed to obtain the desired results. Under certain circumstances, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be interpreted as limiting the scope of the present disclosure. Certain features described in the context of a separate embodiment can also be implemented in a single implementation in combination. On the contrary, the various features described in the context of a single implementation can also be implemented in multiple implementations individually or in any suitable sub-combination. The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

[0094] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for predicting fatigue crack initiation location based on probability statistics, characterized in that: The following steps are involved: Step S1, preparing a metallographic sample of a metal material, and taking a microstructure picture of the metallographic sample using a microscope; Step S2, determining the defect type of the metal material, processing the microstructure image, counting the defect size and quantity of the defect type, and obtaining multiple defect sizes and corresponding defect quantities; Step S3, performing log-normal distribution curve fitting on the multiple defect sizes and the corresponding defect quantities to obtain a probability density function of the defect size distribution; Step S4, obtaining a maximum defect size among the multiple defect sizes; and obtaining a fatigue crack initiation position prediction model for a metal material based on the maximum defect size and a probability density function of the defect size distribution; Step S5, inputting 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 occurrence probability prediction values ​​of the surface initiation mode and the non-surface initiation mode.

2. The method for predicting fatigue crack initiation position based on probability statistics according to claim 1, characterized in that: The step S1 specifically includes: Cutting a portion of the sample from the metal material to form a flat surface on the sample, then inlaying, grinding, polishing and corroding the sample to obtain a metallographic sample after the preparation is completed; The microstructure morphology of a unit area of ​​the metallographic sample is observed and photographed using a microscope to preserve the microstructure morphology to form the microstructure picture.

3. The method for predicting fatigue crack initiation position based on probability statistics according to claim 2, characterized in that: The step S2 specifically includes: Step S2-1, determining α grains as the defect type of the metal material; Step S2-2, using image processing software to count the size and number of defects in the microstructure image; Step S2-3: After all defects and corresponding sizes are obtained, they are divided and counted according to size-quantity to obtain multiple defect sizes and corresponding defect quantities.

4. The method for predicting fatigue crack initiation position based on probability statistics according to claim 3, characterized in that: In step S2-2, the process of calculating the size of the defects includes: Use image processing software 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 determined 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 length-to-width ratio of a defect is greater than or equal to 2, the defect is determined as a narrow and long defect, and the effective length of the defect is determined as the equivalent length of the defect; When multiple defects are adjacent and the adjacent distance is less than the average value of the multiple defect sizes, 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 fatigue crack initiation position based on probability statistics according to claim 4, characterized in that: The step S2-3 specifically includes: Step S2-3-1, forming a size interval based on the minimum size and the maximum size of the defects obtained by statistics, determining the interval interval, and evenly dividing the size interval into a plurality of interval segments based on the interval interval; Step S2-3-2: Defects whose defect size is greater than or equal to the left endpoint value of the interval segment and less than the left endpoint value of the next interval are classified into the interval and counted to obtain the number of defects in each interval.

6. The method for predicting fatigue crack initiation position based on probability statistics according to claim 5, characterized in that: The step S3 specifically includes: The probability density function f(x) of the defect size distribution adopts a log-normal distribution function, and the expression is: Where x is the defect size, μ is the logarithmic mean, and σ is the logarithmic standard deviation; The defect size is taken as the x value, and the corresponding defect number is taken as the f(x) value; fitting is performed by the least squares method to obtain fitting parameters μ and σ; and the determination coefficient R of the fitting curve is calculated. 2 ; When R 2 When ≥0.95, it is determined that the fitting result meets the requirements and is taken as the optimal fitting parameter; The probability density function of the defect size distribution is determined by the optimal fitting parameters.

7. The method for predicting fatigue crack initiation position based on probability statistics according to claim 6, characterized in that: The step S4 specifically includes: Determine the maximum defect size D among the multiple defect sizes max As the upper limit of the defect size, the expression for the probability of fatigue crack initiation from the surface of metal materials is obtained as follows: Among them, D min It indicates the critical size that can cause fatigue crack initiation in the target sample under a certain stress level, P(D min ) represents the critical size D min The corresponding probability of sprouting from the surface, D max represents the maximum defect size, A represents the normalization coefficient, x c Indicates feature size.

8. The method for predicting fatigue crack initiation position based on probability statistics according to claim 7, characterized in that: The step S5 specifically includes: Substitute the minimum defect size of the metal material to be tested into the fatigue crack initiation position prediction model of the metal material to obtain the critical size D min The corresponding probability of sprouting from the surface is P(D min ) and the probability of sprouting from the surface 1-P(D min ); The fatigue crack initiation position is determined based on the calculated probability value, including: when P(D min )≥P cr When P(D min ) <P cr When P cr is the critical probability value.

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