A crack tip automatic positioning method based on deformation field

Abstract

The application discloses a crack tip automatic positioning method based on a deformation field, belongs to the technical field of engineering materials, structural deformation and mechanical experiments, and comprises the following steps: S1, acquiring a displacement field and a strain field near a crack tip, processing the acquired data, determining the size and shape of a plastic zone, and selecting fitting data points; S2, constructing a target function according to a displacement field model; S3, positioning the crack tip by using an immune algorithm; and S4, calculating key fatigue fracture mechanics parameters. The application realizes the automation of the algorithm, improves the operation efficiency of the algorithm, improves the accuracy of the calculation results, has the operation feasibility in extreme environments such as high and low temperatures, and provides a new test method and technology for studying fatigue crack propagation in extreme environments.

Description

Technical Field

[0001] This invention belongs to the field of engineering materials, structural deformation and mechanical experimental technology, and specifically relates to an automatic crack tip positioning method based on deformation field. Background Technology

[0002] The location of the crack tip during fatigue crack propagation has a significant impact on the accurate calculation of relevant fracture mechanics parameters. Traditional fracture parameter calculations often rely on visual methods for manual location, resulting in substantial errors. Combining displacement field analysis with crack tip location offers a potential solution. On one hand, based on the discontinuous nature of the displacement field at the crack, a threshold can be set to search for the critical point of displacement abrupt change as the crack tip location. However, this method requires stringent accuracy in the displacement field, and inconsistent threshold definitions lead to significant location errors. On the other hand, the crack tip location can be calculated by fitting the displacement field and fracture mechanics model, using the difference between the fitted data and the DIC displacement field data as the objective function for optimization. Yoneyama et al. treated the crack tip location as an unknown parameter and used the Newton-Raphson algorithm for iterative solution. Zanganeh et al. pointed out that the initial iteration value greatly affects the convergence and computation speed of the calculation results; a large deviation between the initial value and the true value can lead to an ill-conditioned matrix. While all related methods can achieve crack tip location, the lack of effective determination of the initial iteration value results in poor location accuracy, slow computation speed, and limited direct application.

[0003] Furthermore, methods for locating crack tips in extreme environments such as high temperatures typically involve manual location using digital images acquired by high-resolution cameras, or measuring crack length using long-distance microscopes during fatigue. Therefore, facing the challenge of generating massive amounts of digital images during long-term fatigue processes in extreme environments, there is an urgent need for an efficient and rapid automated crack tip location method to achieve accurate and rapid characterization of material mechanical parameters. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide an automatic crack tip positioning method based on deformation field, which combines the deformation field obtained by methods such as digital image correlation (DIC) with the crack tip displacement field model, and uses intelligent optimization algorithm to solve the initial value of crack tip, thereby realizing automatic crack tip positioning and characterizing fatigue fracture mechanical parameters.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] An automatic crack tip positioning method based on deformation field includes the following steps:

[0007] S1: Obtain the displacement and strain fields near the crack tip, process the obtained data, determine the size and shape of the plastic zone, and select the fitting data points;

[0008] S2: Construct the objective function based on the displacement field model;

[0009] S3: Crack tip localization using an immune algorithm;

[0010] S4: Calculate key fatigue fracture mechanical parameters.

[0011] Furthermore, step S1 specifically includes the following steps:

[0012] S11: Obtain the displacement and strain fields near the crack tip;

[0013] S12: Calculate the stress field according to the generalized Huke's law, including the plane strain state and the plane stress state:

[0014] Plane strain state:

[0015]

[0016] Plane stress state:

[0017]

[0018] Where σ x σ y τ xy Let E be the stress in the x-direction, μ be the shear stress in the xy-direction, μ be the elastic modulus, and ε be the shear stress in the xy-direction. xx ε yy ε xy The strains are in the x, y, and xy directions, respectively.

[0019] S13: Calculate the principal stresses according to the formulas in mechanics of materials:

[0020]

[0021]

[0022] Determining the plastic zone data based on the Von-Mises yield strength criterion:

[0023]

[0024] Where σ1, σ2, and σ3 are the first, second, and third principal stresses, respectively, and σ3 = 0. s Yield strength is an inherent property of the material itself. By using the above formula to determine all data points in the analysis area that satisfy the yield criterion, the size and shape of the plastic zone can be obtained.

[0025] S14: Randomly select an appropriate amount of displacement field data in the non-plastic region as calculation data points;

[0026] Furthermore, step S2 specifically includes:

[0027] For a mixed type I and II crack in a plane problem, the displacement field around the crack tip is expressed as:

[0028]

[0029]

[0030] In the formula, u and v are displacements along the x and y directions, respectively; the subscript i represents a point in the displacement field (x, y). i ,y i The index of the data is i = 1, 2, ..., m, where m is the total number of displacement field data; r and θ are the polar coordinates of the collected data points relative to the crack tip, n is the number of parameters, and G is the shear modulus; for the plane stress condition κ = (3-ν) / (1+ν), for the plane strain condition κ = 3-4ν, where κ is Poisson's ratio;

[0031] During actual loading, considering the inevitable rigid body motion of the specimen, the equations are rewritten as follows:

[0032]

[0033]

[0034] Where T x and T y Let R represent the rigid body translation in the x and y directions; R represents the rigid body rotation; expanding the displacement expression for m data points in the displacement field yields the matrix expression:

[0035] U = F(x) c ,y c A

[0036] At the crack tip (x) c ,y c Given the given conditions, the matrix F can be easily obtained according to the Williams displacement field model. The above equation is a system of linear equations, and the coefficient matrix A can be obtained by solving it using the least squares method.

[0037] A = (F T F) -1 F T U

[0038] At the crack tip (x) c ,y c In the case of unknowns, the above equations form a nonlinear system of equations. Taking the difference between the fitted displacement field and the target displacement field as the objective function, the objective function is established as follows:

[0039]

[0040] Uexp To obtain the true displacement field during the experiment, the objective function is a nonlinear function when the crack tip coordinates are unknown. By presetting the crack tip position, the objective function G is solved, and the crack tip position and coefficient matrix A that minimize the accuracy requirement of the objective function G are obtained by iteratively solving using an intelligent optimization algorithm.

[0041] Furthermore, step S3 specifically includes the following steps:

[0042] S31: First, antigen recognition is performed, and the selected objective function is:

[0043]

[0044] S32: Secondly, the crack tip position is randomly preset to generate an initial antibody population, based on the displacement field data U and the crack tip coordinates (x... c ,y c Given the information, solve matrix A using the least squares method to make the objective function G a linear function;

[0045] S33: Substitute the antibodies in the population into the objective function to calculate the affinity of each antibody. The smaller the G value of the objective function, the higher the affinity of the antibody. Based on the affinity value of the individual, select the antibody with the highest affinity to the antigen and add it to the memory cell, replacing the existing antibody with the lowest affinity in the memory cell.

[0046] S34: Based on the principles of the immune algorithm, perform selection, cloning, mutation, and clonal suppression operations;

[0047] S35: Repeat steps S31 to S34 until the crack tip position that minimizes the objective function G value is found.

[0048] Furthermore, step S4 specifically includes the following steps:

[0049] S41: After the location of the crack tip is known, the coefficient matrix A is obtained by solving the least squares method;

[0050] S42: In the displacement field formula around the crack tip, the first term A I1 and A II1 The coefficient is related to the Type I and Type II stress intensity factors K by the following relationship. I and K II Related, defined as At the same time A I2 =-σ 0x / 4, parameter σ 0x T is the stress, used to characterize the stress field at the crack tip.

[0051] The beneficial effects of this invention are as follows:

[0052] (1) The immune algorithm can perform optimization iterations without the need for initial values ​​at the crack tip and can obtain the global minimum value, thus realizing the automated implementation of the algorithm.

[0053] (2) By exploring the influence of displacement field model order, plastic zone and number of calculation points on the calculation results, the optimal parameter combination was obtained, which improved the running efficiency of the algorithm.

[0054] (3) The calculation results are accurate. The position of the crack tip and the stress intensity factor value are verified by metallographic microscope and empirical formula. In the existing case verification, the maximum error of the crack tip is 3 pixels, the maximum error of the crack length is no more than 1%, and the maximum error of the stress intensity factor value is no more than 4%.

[0055] (4) It has the feasibility of operating in extreme environments such as high and low temperatures. By adding noise of different intensities, the stability of the algorithm under the influence of noise in different extreme environments is ensured, providing a new test method and technology for studying fatigue crack propagation in extreme environments.

[0056] Other advantages, objectives, and features of the invention will be set forth in the following description and will be apparent to those skilled in the art in some respects, or may be learned by practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0057] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0058] Figure 1 This is a flowchart of the automatic crack tip positioning method based on deformation field described in this invention.

[0059] Figure 2 This describes the changes in the objective function value during the iteration process of the algorithm described in this invention.

[0060] Figure 3 This is an example of optimizing the position of the crack tip in the crack tip deformation field during the algorithm iteration described in this invention;

[0061] Figure 4 To illustrate the accuracy of crack tip location verification using a metallographic microscope in this invention, (a) shows a metallographic microscope image of the crack, and (b) shows a schematic diagram of calculating the match between the crack tip and the crack path.

[0062] Figure 5 A comparison diagram of the calculated crack tip position and the actual crack tip position in an example of the present invention;

[0063] Figure 6This paper compares the calculated stress intensity factor, the theoretical value based on empirical formulas, and the simulation value based on finite element method in examples of this invention. Detailed Implementation

[0064] like Figures 1-3 As shown, the purpose of this invention is to combine the deformation field obtained by methods such as Digital Image Correlation (DIC) with the crack tip displacement field model, and to solve for the initial value of the crack tip using an intelligent optimization algorithm, thereby achieving automated crack tip localization and characterization of fatigue fracture mechanical parameters. Its main process is as follows: Figure 1 As shown.

[0065] 1. Data Processing

[0066] Taking the DIC method to obtain the deformation field at the crack tip as an example, after analyzing and obtaining the displacement field and strain field near the crack tip through Ncorr software, the stress field is first calculated according to the generalized Huke's law. The plane strain state and the plane stress state correspond to Equation (1) and Equation (2) respectively.

[0067] Plane strain state:

[0068]

[0069] Plane stress state:

[0070]

[0071] After obtaining the stress field at the crack tip, the principal stresses are calculated according to the formulas of mechanics of materials:

[0072]

[0073] According to the Von-Mises yield criterion:

[0074]

[0075] Where σ3=0, σ s Yield strength is an inherent property of the material itself. By determining all data points within the analysis area that satisfy the yield criterion using equation (4), the size and shape of the plastic zone can be obtained.

[0076] After determining the plastic region, it is necessary to select an appropriate number of calculation data points from the non-plastic region. The number of points selected can be determined according to the needs. In this embodiment, 200 displacement field data points from the non-plastic region are randomly selected as calculation data points.

[0077] 2. Construct the objective function based on the displacement field model.

[0078] Taking the most widely used Williams model as an example, for a mixed type I and II crack in a plane problem, the displacement field around the crack tip is expressed as:

[0079]

[0080]

[0081] In the formula, u and v are displacements along the x and y directions, respectively; the subscript i represents a point in the displacement field (x, y). i ,y i The index of the data point is i = 1, 2, ..., m, where m is the total number of displacement field data points; r and θ are the polar coordinates of the collected data points relative to the crack tip, such as... Figure 1 As shown, n is the number of parameters, and G is the shear modulus. For the plane stress condition κ=(3-ν) / (1+ν), for the plane strain condition κ=3-4ν, where κ is Poisson's ratio.

[0082] During actual loading, considering the inevitable rigid body motion of the specimen, the equation can be rewritten as:

[0083]

[0084]

[0085] Where T x and T y Let R represent the rigid body translation in the x and y directions; R represents the rigid body rotation. Expanding the displacement expression for m data points in the displacement field yields the matrix expression:

[0086] U = F(x) c ,y c A (7)

[0087] At the crack tip (x) c ,y c Given the given conditions, the matrix F can be easily obtained from the Williams displacement field model. Equation (7) is a system of linear equations, and the coefficient matrix A can be obtained by solving it using the least squares method.

[0088] A = (F T F) -1 F T U (8)

[0089] At the crack tip (x) c ,y c In the case of unknowns, equation (7) is a nonlinear system of equations. The objective function is established as follows, using the difference between the fitted displacement field and the target displacement field as the objective function.

[0090]

[0091] U expTo obtain the true displacement field using DIC technology during the experiment, the objective function is a nonlinear function when the crack tip coordinates are unknown. By pre-setting the crack tip position, the objective function G is solved, and an intelligent optimization algorithm is used to iteratively solve for the crack tip position and coefficient matrix A that minimizes the accuracy requirements of the objective function G.

[0092] 3. Crack tip localization using an immune algorithm

[0093] In the immune algorithm, the antigen corresponds to the objective function, and the antibody corresponds to the feasible solution. In this problem, the feasible solution is the crack tip position. The specific operation process is as follows:

[0094] First, antigen recognition is performed, and the selected objective function is Equation (9);

[0095] Secondly, the crack tip position is randomly preset to generate an initial antibody population. This population is then compared with the displacement field data U and the crack tip coordinates (x...). c ,y c Given the information, matrix A can be solved using the least squares method to make the objective function G a linear function. Substituting the antibodies in the population into the objective function, the affinity of each antibody is calculated. In this problem, the smaller the value of the objective function G, the higher the affinity. Based on the individual's affinity value, the antibody with the highest affinity to the antigen is selected and added to the memory cell, replacing the existing antibody with the lowest affinity in the memory cell.

[0096] To iteratively obtain the optimal solution, based on the principle of the immune algorithm, selection, cloning, mutation, and clonal suppression operations are performed to avoid the optimal solution being a local optimum. These operations are repeated until the crack tip position that minimizes the objective function G is found. The optimization process for the objective function G and the crack tip position is as follows: Figure 2 , Figure 3 As shown.

[0097] 4. Calculation of key fatigue fracture mechanical parameters

[0098] Once the location of the crack tip is known, the coefficient matrix A can be obtained by solving the least squares method of equation (8).

[0099] In equation (5), the first term A I1 and A II1 The coefficient is related to the so-called Type I and Type II stress intensity factors K through the following relationship. I and K II Related, defined as At the same time A I2 =-σ 0x / 4, parameter σ 0x It is T-stress, which can also be used to characterize the stress field at the crack tip.

[0100] 5. Result Verification

[0101] To quantitatively verify the accuracy of the algorithm in locating crack tips, the algorithm's calculation results were compared with the actual crack tip positions under a metallographic microscope. After a certain number of fatigue tests, the specimen was removed and placed under a metallographic microscope to obtain the actual crack tip positions at that test cycle. The algorithm-derived crack tip positions were then compared with these actual positions. Figure 4 , Figure 5 As shown, the calculation results of the two methods show very good consistency, the crack tip location results can also match the crack path well, the error of the crack tip location results does not exceed 3 pixels, and the maximum error of the crack length does not exceed 1%.

[0102] To verify the accuracy of the calculated stress intensity factor, the theoretical value obtained by empirical formula and the value obtained by ABAQUS finite element simulation were compared. The empirical formula uses the standard elastic compliance function of the CT sample provided by ASTM, as shown in the formula:

[0103]

[0104] Where P is the applied load, t and W are the thickness and width of the specimen, respectively, and a is the crack length.

[0105] The comparison results of stress intensity factor values ​​are as follows Figure 6 As shown, the maximum error is 1.65%, which enables accurate characterization of key fracture mechanics parameters of materials.

[0106] This example combines the crack tip deformation field obtained by methods such as DIC full-field measurement with the crack tip displacement field model, and uses an immune algorithm to solve for the crack tip location, thereby realizing automated crack tip positioning and fatigue fracture mechanical parameter characterization.

[0107] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made to it in form and detail without departing from the scope defined by the claims of the present invention.

Claims

1. A method for automatic crack tip positioning based on deformation field, characterized in that: Includes the following steps: S1: Obtain the displacement and strain fields near the crack tip, process the obtained data, determine the size and shape of the plastic zone, and select the fitting data points; S2: Construct the objective function based on the displacement field model; S3: Crack tip localization using an immune algorithm; S4: Calculate key fatigue fracture mechanical parameters; Step S1 specifically includes the following steps: S11: Obtain the displacement and strain fields near the crack tip; S12: Calculate the stress field according to the generalized Huke's law, including the plane strain state and the plane stress state: Plane strain state: Plane stress state: in , , These represent the stresses in the x and y directions, and the shear stress in the xy direction, respectively. For elastic modulus, Poisson's ratio, , , The strains are in the x-direction, y-direction, and xy-direction, respectively. S13: Calculate the principal stresses according to the formulas in mechanics of materials: Determining the plastic zone data based on the Von-Mises yield strength criterion: in , , These are the first, second, and third principal stresses, respectively. , The yield strength is an inherent property of the material itself. By using the above formula to determine all data points in the analysis area that satisfy the yield criterion, the size and shape of the plastic zone can be obtained. S14: Randomly select an appropriate amount of displacement field data in the non-plastic region as calculation data points; Step S2 specifically includes: For a mixed type I and II crack in a plane problem, the displacement field around the crack tip is expressed as: In the formula, and These represent displacements along the x and y directions, respectively; subscripts. A point in the displacement field index, , This represents the total number of displacement field data. and These are the polar coordinates of the collected data points relative to the crack tip. It refers to the number of parameters. It is the shear modulus; for plane stress conditions For plane strain conditions ,in Poisson's ratio; During actual loading, considering the inevitable rigid body motion of the specimen, the equations are rewritten as follows: in and For rigid body translations in the x and y directions; For rigid body rotation; for displacement field Expanding the displacement expression for each data point yields the matrix expression: At the crack tip Given the given information, the matrix can be easily obtained from the Williams displacement field model. The above equation is a system of linear equations, and the coefficient matrix is ​​obtained by solving it using the least squares method. : At the crack tip In the case of unknown conditions, the above equations form a nonlinear system of equations. Taking the difference between the fitted displacement field and the target displacement field as the objective function, the objective function is established as follows: in To obtain the actual displacement field during the experiment, the objective function is a nonlinear function when the coordinates of the crack tip are unknown. The objective function is solved by pre-setting the crack tip position. The value is obtained by iteratively solving the objective function using an intelligent optimization algorithm. The minimum crack tip location and coefficient matrix that meets accuracy requirements ; Step S3 specifically includes the following steps: S31: First, antigen recognition is performed, and the selected objective function is: S32: Secondly, randomly preset the crack tip position to generate an initial antibody population, in the displacement field data. Coordinates of the crack tip Given the given information, solve the matrix using the least squares method. , so that the objective function It is a linear function; S33: Substitute the antibodies in the population into the objective function to calculate the affinity of each antibody, wherein the antibody makes the objective function... The smaller the value, the higher the affinity; based on the individual's affinity value, the antibody with the highest affinity to the antigen is selected and added to the memory cell, replacing the existing antibody with the lowest affinity in the memory cell; S34: Based on the principles of the immune algorithm, perform selection, cloning, mutation, and clonal suppression operations; S35: Repeat steps S31 to S34 until the objective function is found. The value ends at the crack tip location where the value is smallest.

2. The automatic crack tip positioning method based on deformation field according to claim 1, characterized in that: Step S4 specifically includes the following steps: S41: After the location of the crack tip is known, the coefficient matrix is ​​obtained by solving the least squares method. ; S42: In the formula for the displacement field around the crack tip, the first term... and The coefficients are related to the Type I and Type II stress intensity factors through the following relationship. and Related, defined as , ;at the same time ,parameter T is the stress, used to characterize the stress field at the crack tip.

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