A method for calculating the fracture toughness of elastic-plastic crack growth of a metal structure

Abstract

The application provides a calculation method for metal structure elastic-plastic crack propagation fracture toughness, comprising: performing energy analysis on elastic-plastic materials to determine energy component expressions of crack propagation driving force and resistance; screening influencing factors of the crack propagation driving force of the elastic-plastic crack; performing dimension analysis on the fracture toughness influencing factors, and giving dimensionless group variables according to the dimension analysis; and selecting elastic-plastic materials of the metal structure and designing tests; performing elastic-plastic crack propagation numerical calculation based on an elastic-plastic crack structure finite element model, and extracting crack propagation resistance information; using a regression analysis method to determine a fracture toughness calculation model, and accurately predicting elastic-plastic crack propagation; and taking the fracture toughness as a crack propagation criterion to perform elastic-plastic crack propagation numerical calculation. The application adopts dimension analysis to design a fracture toughness expression, combines a regression analysis method, calibrates unknown parameters in the fracture toughness, obtains a fracture toughness calculation model, and accurately predicts elastic-plastic crack propagation.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of crack propagation prediction in fracture mechanics, and particularly relates to a method for calculating fracture toughness of elastic-plastic crack propagation of a metal structure. BACKGROUND

[0002] In fracture mechanics, energy release rate is essential for evaluating crack propagation of a material under stress, and linear elastic fracture mechanics based on linear elastic theory can quantitatively analyze brittle fracture. For materials that exhibit both elastic and plastic behaviors during fracture, the analysis of crack propagation and related energy release rate is more complex than that of purely elastic materials. For elastic-plastic materials, it is a common practice to modify the energy release rate theory by considering plastic dissipation as a part of fracture toughness to account for the plastic deformation behavior of the material. However, this plastic modification is actually a compromise because existing theoretical and experimental techniques are insufficient to directly measure or accurately calculate the true fracture toughness during crack propagation, and this plastic modification is only applicable to calculating fracture toughness under small-scale yielding conditions.

[0003] When the size of the plastic zone in the elastic-plastic material exceeds the length of the crack or structure, the fracture problem becomes more complex. The above-mentioned classical method is no longer applicable to elastic-plastic crack propagation. Currently, the study of elastic-plastic fracture generally relies on simplified models and approximate calculations, such as J integral, crack tip opening angle / displacement (CTOA / CTOD), cohesive zone model, etc. Among them, the most widely used is the J integral method. When using J integral, the elastic-plastic constitutive relationship of the elastic-plastic material needs to be described by the full theory, i.e., without considering plastic unloading during crack propagation, the elastic-plastic constitutive relationship is approximated as a nonlinear elastic constitutive relationship, and the plastic deformation in the crack tip region during loading is characterized by nonlinear elastic theory. However, when the crack further propagates in the elastic-plastic material, a plastic unloading region appears in the crack wake zone, and the J integral method is no longer applicable. Moreover, a large number of experiments have shown that, in addition to being related to material parameters, the J integral method also depends on the form of external load and the geometry of the test piece, such as the J IC value measured by a center crack specimen is much higher than the J IC value measured by a bending specimen.

[0004] In order to more deeply understand the complex physical phenomenon of elastic-plastic crack propagation and lay a foundation for the further development of elastic-plastic fracture mechanics, it is necessary to develop a method that can accurately characterize the fracture toughness of crack propagation, and this method can judge the influence of each mechanical parameter (such as elastic modulus, Poisson's ratio, yield strength, etc.) on the fracture toughness. SUMMARY

[0005] The present application aims to solve the problem of the prior art that the elastic-plastic crack extension does not meet the small yield range, and cannot accurately describe the elastic-plastic crack extension, and provides a method for calculating the elastic-plastic crack extension fracture toughness of a metal structure, which directly calculates the fracture toughness of the material through the material mechanical property parameters and the failure load, designs a crack extension driving force expression by dimension analysis, calibrates and determines unknown parameters in the fracture toughness calculation model by combining a regression analysis method, obtains a crack extension driving force calculation model, and when the crack actually extends, the crack extension driving force is equal to the fracture toughness, i.e. the fracture toughness calculation model is determined, and the elastic-plastic crack extension is accurately predicted.

[0006] To achieve the above-mentioned purpose, the technical solution provided by the present application is:

[0007] A method for calculating the elastic-plastic crack extension fracture toughness of a metal structure, comprising:

[0008] Step one, energy analysis is performed on the elastic-plastic material to determine the energy component expressions of the crack extension driving force and the crack extension resistance; and the influencing factors of the crack extension driving force of the elastic-plastic crack are screened;

[0009] Step two, dimension analysis is performed on the crack extension driving force influencing factors, and dimensionless group variables are given according to the dimension analysis; and the elastic-plastic material of the metal structure is selected and a test is designed;

[0010] Step three, numerical calculation of the elastic-plastic crack extension is carried out based on the finite element model of the elastic-plastic crack structure, and crack extension driving force information is extracted;

[0011] Step four, the regression analysis method is used to determine the crack extension driving force calculation model, when the crack actually extends, the crack extension driving force is equal to the fracture toughness, i.e. the fracture toughness calculation model is determined, and the elastic-plastic crack extension is accurately predicted;

[0012] Step five, the fracture toughness is used as the crack extension criterion to carry out numerical calculation of the elastic-plastic crack extension, when the crack extension driving force is less than the fracture toughness, it is the static crack stage of the proportional loading stage, and the load is continuously increased, when the crack extension driving force is equal to the fracture toughness, the crack extends, and enters the extended crack stage of the non-proportional loading.

[0013] As a further limitation of the present application, in step one, the energy analysis is performed on the elastic-plastic material to determine the elastic-plastic crack extension driving force, comprising:

[0014] The elastic-plastic crack of the elastic-plastic material is analyzed from the energy angle, and the energy equation of the elastic-plastic crack in the extension process is:

[0015] delta W = delta U e + delta Up + 2γ·t·da Formula (1)

[0016] In Formula (1), δ represents a variation symbol, W represents work done by a quasi-static external load, U e represents elastic strain energy, U p represents plastic dissipation, γ represents surface energy density, t represents crack plate thickness, and da represents crack propagation increment.

[0017] During the propagation process of the elastic-plastic crack, the separation surface energy and the plastic dissipation are determined, the surface energy is determined as an elastic-plastic crack propagation resistance G c , and the plastic dissipation is determined as an elastic-plastic crack propagation driving force G; wherein the expression of the elastic-plastic crack propagation driving force G is:

[0018]

[0019] In Formula (2), d represents a differential symbol.

[0020] The expression of the elastic-plastic crack propagation resistance G c is:

[0021] G c = 2γ Formula (3);

[0022] In the step one, judging whether the elastic-plastic crack is an expanding crack comprises:

[0023] In Formula (1), when γ = 0, Formula (1) degenerates into a static crack, and when U p = 0, Formula (1) degenerates into Griffith theory.

[0024] In Formula (2) and Formula (3), when G = G c , the elastic-plastic crack is an expanding crack; and when G < G c , the elastic-plastic crack is in a proportional loading static crack stage.

[0025] In the step one, screening influencing factors of the crack propagation driving force of the elastic-plastic material comprises:

[0026] During the propagation process of the elastic-plastic crack, the influencing factors of the crack propagation driving force of the elastic-plastic material are expressed as:

[0027] f(G, E, υ, σ s , n, a0, P) = 0 Formula (4)

[0028] In Formula (4), E represents an elastic modulus, υ represents a Poisson's ratio, σ s represents a yield strength, n represents a strain hardening index, a0 represents an initial crack length, and P represents a function of an external load.

[0029] As a further limitation of the present application, in the step two, the dimensional analysis is performed on the influencing factors of the crack propagation driving force, and given dimensionless group variables, including:

[0030] According to the dimensional analysis on each of the influencing factors of the crack propagation driving force, the expression is:

[0031]

[0032] In formula (5), G represents the elastic-plastic crack propagation driving force, M represents the mass dimension, T represents the time dimension, L represents the length dimension, E represents the elastic modulus, σ s represents the yield strength, a0 represents the initial crack length, and P represents the function of external load;

[0033] According to formula (5), the dimensional relationship matrix is obtained, and the expression is:

[0034]

[0035] In formula (6), A represents the dimensional relationship matrix; wherein, the rank of the dimensional relationship matrix is 2, and the number of solutions of the homogeneous linear equation group is 3, so that the basic solutions y1, y2 and y3 of the linear homogeneous equation group are obtained, and three independent dimensionless quantities are obtained by solving the three solutions, and the expression is:

[0036]

[0037] In formula (7), π1 represents the first dimensionless quantity, G represents the elastic-plastic crack propagation driving force, π2 represents the second dimensionless quantity, and π3 represents the third dimensionless quantity;

[0038] Finally, the crack propagation driving force in the elastic-plastic crack propagation process is obtained, and the expression is:

[0039]

[0040] In formula (8), f(*) represents the unknown function relationship between the crack propagation driving force and its influencing factors, F(*) represents the function relationship in dimensionless form, and ψ(*) represents the undetermined function relationship between the first dimensionless quantity and the remaining dimensionless quantities.

[0041] As a further limitation of the present application, in the step two, the elastic-plastic material of the metal structure is selected and the test is designed, including:

[0042] The parameter range of the elastic-plastic material of the metal structure is selected, and the test is designed; wherein, the dimensionless group variables of the elastic-plastic material of the metal structure include: the ratio of the crack propagation driving force to the elastic modulus and the initial crack length The ratio of yield strength to elastic modulus The ratio of external load to elastic modulus and initial crack length square Poisson's ratio υ, strain hardening index n;

[0043] Determine the number of levels of all variables and the variable values of each level.

[0044] As a further limitation of the present application, in step three, based on the elastic-plastic crack structure finite element model, the numerical calculation of the elastic-plastic crack propagation is carried out, which includes:

[0045] (31) Based on the elastic-plastic crack structure finite element model, the node release technique is used to carry out the numerical calculation of the elastic-plastic crack propagation of the elastic-plastic crack structure finite element model;

[0046] (32) Based on the elastic-plastic crack structure finite element model, the loading analysis step and the release analysis step are established, and the difference between the loading analysis step and the release analysis step is the crack length;

[0047] (33) The elastic-plastic crack propagation is realized by modifying the boundary conditions along the crack propagation path, and the loading analysis step is loaded based on the elastic-plastic crack structure finite element model;

[0048] (34) After completing the loading, based on the elastic-plastic crack structure finite element model, the release analysis step is activated, while maintaining the same load, a node is released along the crack propagation path, realizing a complete elastic-plastic crack propagation analysis; wherein, in the release analysis step, a release force is applied to the initial crack tip node, so that the release force gradually decreases to zero to avoid convergence difficulty; when the release force is zero, the initial crack tip node is completely released, allowing the elastic-plastic crack to expand;

[0049] (35) After the analysis is completed, the maximum value of the crack propagation driving force is extracted;

[0050] In step three, the crack propagation driving force information is extracted, which includes:

[0051] In the process of crack propagation of elastic-plastic material, the maximum crack propagation driving force at the crack initiation time is extracted.

[0052] As a further limitation of the present application, in step four, the regression analysis method includes:

[0053] According to the influencing factors of the crack propagation driving force of step one, a functional relationship between the independent variable and the dependent variable is established; wherein, the independent variable includes υ, n; the dependent variable includes The function relationship of the crack propagation driving force expression is obtained by using multiple regression analysis method, and the expression is:

[0054]

[0055] In formula (9), Y represents an observed response, G represents an elastic-plastic crack propagation driving force, E represents an elastic modulus, a0 represents an initial crack length, X1 represents a first predictor, σ s represents a yield strength, X2 represents a second predictor, P represents a function of an external load, X3 represents a third predictor, υ represents a Poisson's ratio, X4 represents a fourth predictor, and n represents a strain hardening exponent.

[0056] In step four, a crack propagation driving force calculation model is provided, and the expression is as follows:

[0057]

[0058] In formula (10), β0 represents an intercept, β k represents a regression coefficient, X k represents a kth predictor, and ξ represents a regression error. represents a predicted response, represents an estimated intercept, represents an estimated coefficient.

[0059] In step four, accurately predicting the elastic-plastic crack propagation comprises the following steps.

[0060] In the regression analysis method, the fitting quality of the multiple regression is measured by a multiple determination coefficient, the multiple determination coefficient is used to explain the change proportion in the response by the crack propagation driving force calculation model, and the size of the multiple determination coefficient is between 0 and 1; when the multiple determination coefficient is 1, it indicates complete fitting, and when the multiple determination coefficient is 0, it indicates no prediction ability.

[0061] As a further limitation of the present application, in step five, the elastic-plastic crack propagation numerical calculation comprises the following steps.

[0062] (51) Based on the elastic-plastic crack structure finite element model, a node release technique is used to perform elastic-plastic crack propagation numerical calculation on the elastic-plastic crack structure finite element model;

[0063] (52) Based on the elastic-plastic crack structure finite element model, a loading analysis step and a release analysis step are established, and the difference between the loading analysis step and the release analysis step is the crack length.

[0064] (53) By modifying the boundary conditions along the crack propagation path, the elastic-plastic crack propagation is realized, and based on the elastic-plastic crack structure finite element model, a load is applied to the loading analysis step;

[0065] (54) after the load is completed, the release analysis step is activated based on the elastic-plastic crack structure finite element model, a node on the crack propagation path is released while maintaining the same load, and a complete elastic-plastic crack propagation analysis is realized; wherein, in the release analysis step, a release force is applied to the initial crack tip node, and the release force is gradually reduced to zero to avoid convergence difficulties; when the release force is zero, the initial crack tip node is completely released, and the elastic-plastic crack propagation is allowed;

[0066] (55) The fracture toughness obtained by the elastic-plastic crack propagation fracture toughness calculation method is used as a criterion to calculate the crack propagation driving force; when the crack propagation driving force is less than the fracture toughness, the load is increased; when the crack propagation driving force is equal to the fracture toughness, the crack propagates; repeat (53)-(55) until the elastic-plastic crack propagation is stable.

[0067] The advantages of the present application are:

[0068] 1、The present application directly calculates the fracture toughness of the material by the material mechanical property parameters and its failure load, designs the crack propagation driving force expression by dimension analysis, calibrates the unknown parameters in the crack propagation driving force by regression analysis method, obtains the crack propagation driving force calculation model, when the crack really expands, the crack propagation driving force is equal to the fracture toughness, i.e. the fracture toughness calculation model is obtained, and the elastic-plastic crack propagation is accurately predicted.

[0069] 2、Compared with the existing fracture criterion, the present application excludes the influence of plastic dissipation on the fracture toughness, proposes that the fracture toughness is the inherent property of the elastic-plastic material, and is irrelevant to external load, test piece geometry and other factors, and the present application can clearly show the contribution of mechanical property parameters to the fracture toughness.

[0070] Additional aspects and advantages of the present application will be partially given in the following description, partially will become obvious from the following description, or will be understood by the practice of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0071] The above and / or additional aspects and advantages of the present application will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:

[0072] Figure 1 The present application provides a flow chart of a calculation method for elastic-plastic crack propagation fracture toughness of a metal structure;

[0073] Figure 2 The present application provides a flow chart of the implementation process of the calculation method;

[0074] Figure 3 The present application provides a schematic diagram of the boundary conditions on the crack propagation path;

[0075] Figure 4 : the response prediction and observation chart during the implementation of the calculation method provided by the present application;

[0076] Figure 5 : the crack propagation process chart during the implementation of the calculation method provided by the present application;

[0077] Figure 6 : the level of each prediction factor of the target metal structure and the corresponding dimensionless variable table selected by the present application;

[0078] Figure 7 : the orthogonal matrix table of the target metal structure designed by the Taguchi experimental design method selected by the present application;

[0079] Figure 8 : the regression result and the corresponding coefficient table provided by the present application;

[0080] Figure 9 : the data table of A-D in the mathematical relationship expression between the characteristic fracture energy and each parameter provided by the present application. DETAILED DESCRIPTION

[0081] The embodiments of the present application will be described in detail below, which are exemplary and intended to explain the present application, and cannot be understood as a limitation of the present application.

[0082] Please refer to Figure 1 and Figure 2 , the embodiments of the present application provide a calculation method for the elastic-plastic crack propagation fracture toughness of a metal structure, which comprises steps one to five:

[0083] Step one, energy analysis is performed on the elastic-plastic material to determine the energy component expression of the crack propagation driving force and the crack propagation resistance force; and the influencing factors of the crack propagation driving force of the elastic-plastic crack are screened. Specifically:

[0084] In the above step one of the embodiments of the present application, the energy analysis is performed on the elastic-plastic material to determine the elastic-plastic crack propagation driving force, which comprises:

[0085] From the energy analysis of the elastic-plastic crack of the elastic-plastic material, it is assumed that the fracture energy required for the formation of a new surface during the crack propagation process remains unchanged, and the energy equation of the elastic-plastic crack during the crack propagation process is:

[0086] δW = δU e + δU p + 2γ·t·da Formula (1)

[0087] In formula (1), δ represents the variation symbol, W represents the work done by the quasi-static external load, U e represents the elastic strain energy, and U prepresents plastic dissipation, γ represents surface energy density, t represents crack plate thickness, and da represents crack propagation increment.

[0088] Specifically, the judging whether the elastic-plastic crack is an expanding crack according to the above-mentioned embodiment of the present application comprises: when γ = 0 in formula (1), formula (1) degenerates into a static crack; when U p = 0, formula (1) degenerates into Griffith theory.

[0089] In the process of elastic-plastic crack propagation, the surface energy and plastic dissipation are separated, the surface energy is taken as the elastic-plastic crack propagation resistance G c , which is the inherent property of the material; the plastic dissipation is taken as the elastic-plastic crack propagation driving force G; and the expression of the elastic-plastic crack propagation driving force G is:

[0090]

[0091] In formula (2), d represents a differential symbol;

[0092] The expression of the elastic-plastic crack propagation resistance G c is:

[0093] G c = 2γ formula (3);

[0094] According to the above-mentioned formula (2) and formula (3) of the embodiment of the present application, when G = G c , the elastic-plastic crack is an expanding crack; and when G < G c , the elastic-plastic crack is in a static crack stage under proportional loading.

[0095] The embodiment of the present application screens the influencing factors of the crack propagation driving force of the elastic-plastic material, which comprises:

[0096] In the process of elastic-plastic crack propagation, the influencing factors of the crack propagation driving force of the elastic-plastic material in the non-proportional loading stage are expressed as:

[0097] f(G, E, υ, σ s , n, a0, P) = 0 formula (4)

[0098] In formula (4), E represents elastic modulus, υ represents Poisson's ratio, σ s represents yield strength, n represents strain hardening index, a0 represents initial crack length, and P represents a function of external load.

[0099] Step two, dimension analysis is performed on the influencing factors of the crack propagation driving force, non-dimensional group variables are given according to the dimension analysis; and an elastic-plastic material of a metal structure is selected and a test is designed. Specifically:

[0100] The step two in the embodiment of the present application is dimensionally analyzed to give dimensionless groups, including:

[0101] Each of the influencing factors of the crack propagation driving force is dimensionally analyzed, and the expression is:

[0102]

[0103] In formula (5), G represents the elastic-plastic crack propagation driving force, M represents the mass dimension, T represents the time dimension, L represents the length dimension, E represents the elastic modulus, σ s represents the yield strength, a0 represents the initial crack length, and P represents the function of the external load.

[0104] The dimension relationship matrix is obtained according to formula (5), and the expression is:

[0105]

[0106] In formula (6), A represents the dimension relationship matrix; the rank of the dimension relationship matrix is 2, and the number of solutions of the homogeneous linear equation group is 3. The linear equation group is written according to the matrix as:

[0107]

[0108] Suppose x1=k1; x3=k2; x5=k3; x6=k4, then the general solution is:

[0109]

[0110] Thus, the basic solutions y1, y2, y3 of the linear homogeneous equation group are obtained, and three independent dimensionless quantities are obtained by solving the three solutions, and the expression is:

[0111]

[0112] In formula (7), π1 represents the first dimensionless quantity, G represents the elastic-plastic crack propagation driving force, π2 represents the second dimensionless quantity, and π3 represents the third dimensionless quantity.

[0113] Finally, the crack propagation driving force in the elastic-plastic crack propagation process is obtained, and the expression is:

[0114]

[0115] In formula (8), f(*) represents the unknown function relationship between the crack propagation driving force and its influencing factors, F(*) represents the dimensionless function relationship, and ψ(*) represents the undetermined function relationship between the first dimensionless quantity and the remaining dimensionless quantities.

[0116] The step two in the embodiment of the application is selecting the elastic-plastic material of the metal structure and designing the test, including:

[0117] The parameter range of the elastic-plastic material of the metal structure is selected, and the test is designed, wherein the dimensionless group variables of the elastic-plastic material of the metal structure include: the ratio of the crack propagation driving force to the elastic modulus and the initial crack length The ratio of the yield strength to the elastic modulus The ratio of the external load to the elastic modulus and the square of the initial crack length The Poisson's ratio υ and the strain hardening index n; the number of levels of all variables and the variable values of each level are determined.

[0118] The number of levels of all variables and the variable values of each level are determined when the elastic-plastic material of the metal structure is selected and the test is designed. Specifically:

[0119] Figure 2 In the implementation process of the calculation method, the target metal structure is an aviation metal, the number of levels selected for each prediction factor is 9, and the level of each prediction factor and the corresponding dimensionless variable table are as shown in Figure 6 81 groups of orthogonal tests are designed by using the Taguchi test design method, and the orthogonal matrix table designed is as shown in Figure 7 Each row of the orthogonal matrix represents a calculation case, has a specific combination of materials, geometry and parameters, and the parameters are taken as the input of the finite element to obtain the observed response.

[0120] Step three, establishing an elastic-plastic crack structure finite element model, carrying out elastic-plastic crack propagation numerical calculation based on the elastic-plastic crack structure finite element model, and extracting crack propagation driving force information. Specifically:

[0121] In the crack propagation process of the elastic-plastic material, the maximum crack propagation driving force at the crack initiation time is extracted.

[0122] In the step three in the embodiment of the application, the elastic-plastic crack propagation numerical calculation is carried out based on the elastic-plastic crack structure finite element model, including:

[0123] (31) based on the elastic-plastic crack structure finite element model, the node release technology is used to carry out the numerical calculation of the elastic-plastic crack propagation of the elastic-plastic crack structure finite element model;(32) according to the elastic-plastic crack structure finite element model, the loading analysis step and the release analysis step are established, and the difference between the loading analysis step and the release analysis step is the crack length;(33) the elastic-plastic crack propagation is realized by modifying the boundary condition along the crack propagation path, and the loading analysis step is loaded based on the elastic-plastic crack structure finite element model;(34) after completing the loading, the release analysis step is activated based on the elastic-plastic crack structure finite element model, and under the condition of keeping the same load, a node is released on the crack propagation path, so as to realize a complete elastic-plastic crack propagation analysis;Wherein, in the release analysis step, a release force is applied to the initial crack tip node, so that the release force gradually decreases to zero, so as to avoid convergence difficulty;When the release force is zero, the initial crack tip node is completely released, and the elastic-plastic crack propagation is allowed, as shown in Figure 3 (b);(35) after the analysis is completed, the maximum crack propagation driving force is extracted. The boundary condition on the crack path is as shown in Figure 3 (a).

[0124] As a preferred embodiment, in the crack propagation process of the elastic-plastic material, the maximum crack propagation driving force at the crack initiation moment is extracted, and the crack propagation resistance information is obtained based on the maximum crack propagation driving force.

[0125] Step four, using regression analysis method to determine crack propagation driving force calculation model, when the crack really expands, the crack propagation driving force is equal to the fracture toughness, that is, the fracture toughness calculation model is determined, and the elastic-plastic crack propagation is accurately predicted. Specifically:

[0126] In the above step four of the embodiment of the application, the regression analysis method comprises:

[0127] According to the influencing factors of the crack propagation driving force in step one, the function relationship between the independent variable and the dependent variable is established;Wherein, the independent variable includes υ, n;The dependent variable includes The function relationship of the crack propagation driving force expression is obtained by using the multiple regression analysis method, and the multiple regression analysis method assumes that the logarithmic linear relationship is:

[0128]

[0129] Wherein, β0 represents the intercept, β k (k=1,2,3,4) represents the regression coefficient, ξ represents the regression error, Y represents the observed response, X k represents the kth predictor. The specific expression is:

[0130]

[0131] In formula (9), Y represents an observed response, G represents an elastic-plastic crack propagation driving force, E represents an elastic modulus, a0 represents an initial crack length, X1 represents a first predictor, σ s represents a yield strength, X2 represents a second predictor, P represents a function of an external load, X3 represents a third predictor, v represents a Poisson's ratio, X4 represents a fourth predictor, and n represents a strain hardening exponent.

[0132] The present embodiment gives n kinds of different X k (k=1, 2, 3, 4) combinations, and the coefficient β k (k=1, 2, 3, 4) is estimated by a least square method as The "wave" symbol is used to distinguish the estimated coefficient and the unknown coefficient β k . Similarly, the "wave" symbol is used to distinguish the predicted response (by regression analysis) and the observed response Y (obtained from the finite element results).

[0133] The crack propagation driving force calculation model in the above-mentioned step four of the present embodiment has an expression as follows:

[0134]

[0135] In formula (10), β0 represents an intercept, β k represents a regression coefficient, X k represents a kth predictor, and ξ represents a regression error. represents a predicted response, represents an estimated intercept, and β represents an estimated coefficient.

[0136] The fitting quality of the multiple regression in the above-mentioned step four regression analysis method of the present embodiment is measured by a multiple determination coefficient, the multiple determination coefficient explains the proportion of the change in the response by the crack propagation driving force calculation model, and the size of the multiple determination coefficient is between 0 and 1. When the multiple determination coefficient is 1, it indicates a complete fitting, and when the multiple determination coefficient is 0, it indicates no prediction ability.

[0137] Step five, fracture toughness is taken as a crack propagation criterion to carry out an elastic-plastic crack propagation numerical calculation. When the crack propagation driving force is less than the fracture toughness, it is a static crack stage in the proportional loading stage, and the load is continuously increased. When the crack propagation driving force is equal to the fracture toughness, the crack propagates, and enters an expanding crack stage in the non-proportional loading. Specifically:

[0138] In step five of this embodiment of the invention, numerical calculation of elastoplastic crack propagation is carried out, including: (51) based on the finite element model of the elastoplastic crack structure, numerical calculation of elastoplastic crack propagation is carried out on the finite element model of the elastoplastic crack structure using the nodal release technique; (52) based on the finite element model of the elastoplastic crack structure, a loading analysis step and a release analysis step are established, the difference between the loading analysis step and the release analysis step being the crack length; (53) by modifying the boundary conditions along the crack propagation path to achieve elastoplastic crack propagation, a load is applied to the loading analysis step based on the finite element model of the elastoplastic crack structure; (54) after the load is applied, the release analysis step is activated based on the finite element model of the elastoplastic crack structure, and in While maintaining the same load, a node is released on the crack propagation path to achieve a complete elastoplastic crack propagation analysis; in the release analysis step, a release force is applied to the initial crack tip node, and the release force is gradually reduced to zero to avoid convergence difficulties; when the release force is zero, the initial crack tip node is completely released, allowing elastoplastic crack propagation; (55) the fracture toughness obtained by the elastoplastic crack propagation fracture toughness calculation method is used as the criterion to calculate the crack propagation driving force; when the crack propagation driving force is less than the fracture toughness, the load is increased; when the crack propagation driving force is equal to the fracture toughness, the crack propagates; repeat (53)-(55) until the elastoplastic crack propagation stable stage is reached.

[0139] This invention employs a stepwise regression method, iteratively testing the statistical significance of each independent variable, eliminating independent variables that do not play a significant role in the regression, and selecting independent variables that have a significant impact on the dependent variable. This invention uses a significance level (p-value) of 0.05 and 0.1 as the entry and exit criteria for the regression model in the regression analysis method. Specifically, an independent variable with a p-value less than 0.05 (p < 0.05) is included in the regression model, while an independent variable with a p-value greater than 0.1 (p > 0.1) is excluded. The p-value is a statistical measure used to estimate the probability of rejecting the null hypothesis when it is true. The null hypothesis in the regression model is that there is no statistical significance between the independent and dependent variables. A smaller p-value indicates stronger evidence to reject the null hypothesis and a stronger correlation between the independent and dependent variables.

[0140] like Figure 8 The regression results and corresponding coefficients shown are from... Figure 8 It can be observed that predictor X3 was not included in the regression model due to its statistical insignificance. Furthermore, the p-values ​​of the intercept β0, the first predictor X1, the second predictor X2, and the fourth predictor X4 are less than 0.01, indicating that they have a significant impact on the response. The regression model of this embodiment is expressed as follows:

[0141] If the determination coefficient R of the regression model in the embodiment of the present application is 0.992 2 , it indicates that the crack propagation driving force calculation model of the embodiment of the present application can explain 99.2% of the observed response value changes. In addition, the crack propagation driving force calculation model of the embodiment of the present application has good fitting ability, and its very low significance level p-value (p=0.000) also proves that the crack propagation driving force calculation model has good fitting ability. As shown in Figure 4 , the embodiment of the present application compares the predicted response with the observed response, and proves the accuracy of the crack propagation driving force calculation model. The mathematical relationship between the characteristic fracture energy obtained by the crack propagation driving force calculation model and each parameter is represented as:

[0142]

[0143] The calibration parameters in formula (11) are as shown in Figure 9 . When the crack actually expands, the crack propagation driving force is equal to the fracture toughness. The fracture toughness obtained by using the crack propagation driving force calculation model is used as the fracture criterion to perform the crack propagation finite element numerical calculation of the 316L stainless steel, and the result is as shown in Figure 5 .

[0144] Therefore, compared with the existing fracture criterion, the embodiment of the present application excludes the influence of plastic dissipation on the fracture toughness, and proposes that the fracture toughness is an inherent property of the elastic-plastic material, and is irrelevant to factors such as external load and test piece geometry. It can be seen that the embodiment of the present application can clearly show the contribution of the mechanical property parameters to the fracture toughness.

[0145] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of various equivalent modifications or replacements within the technical range disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application.

Claims

1. A method for calculating the fracture toughness of elastoplastic crack propagation in metallic structures, characterized in that, include: Step 1: Perform energy analysis on the elastoplastic material to determine the energy component expressions for the crack propagation driving force and crack propagation resistance; Screening the factors influencing the crack propagation driving force of the elastoplastic crack; Step 2: Perform dimensional analysis on the factors influencing the crack propagation driving force, and provide dimensionless variables based on the dimensional analysis. And select elasto-plastic materials for metal structures and design experiments; Step 3: Perform numerical calculations of elastoplastic crack propagation based on the finite element model of the elastoplastic crack structure and extract the driving force information for crack propagation; Step 4: Use regression analysis to determine the calculation model of crack propagation driving force. When the crack actually propagates, the crack propagation driving force is equal to the fracture toughness, that is, determine the fracture toughness calculation model and accurately predict the propagation of elastic-plastic cracks. Step 5: Using fracture toughness as the crack propagation criterion, perform numerical calculations for elastoplastic crack propagation. When the crack propagation driving force is less than the fracture toughness, it is the static crack stage of the proportional loading stage. Continue to increase the load. When the crack propagation driving force equals the fracture toughness, the crack propagates and enters the non-proportional loading propagation crack stage.

2. The method for calculating the fracture toughness of elastoplastic crack propagation in metal structures according to claim 1, characterized in that, In step one, energy analysis is performed on the elastoplastic material to determine the driving force for elastoplastic crack propagation, including: From an energy perspective, the energy equation for the propagation of the elastoplastic crack in the elastoplastic material is: δW=δU e +δU p +2γ·t·da formula (1) In formula (1), δ represents the variational sign, W represents the work done by the quasi-static external load, and U e U represents elastic strain energy. p γ represents plastic dissipation, t represents the thickness of the cracked plate, and da represents the crack propagation increment. During the propagation of the elasto-plastic crack, surface energy and plastic dissipation are separated, and the surface energy is determined as the propagation resistance G of the elasto-plastic crack. c The plastic dissipation is defined as the driving force G for elastoplastic crack propagation; wherein the expression for the driving force G for elastoplastic crack propagation is: In formula (2), d represents the differential symbol; The elastic-plastic crack propagation resistance G c The expression is: G c =2γ formula (3); In step one, determining whether an elastic-plastic crack is a propagating crack includes: In formula (1), when γ = 0, formula (1) degenerates into a static crack; when U p When G = 0, formula (1) degenerates into Griffith theory; in formulas (2) and (3), when G = G c When G < G, the elastic-plastic crack is a propagating crack; when G < G c At that time, the elastoplastic crack is in the static crack stage of proportional loading; In step one, the factors influencing the crack propagation driving force of elastoplastic materials include: The influencing factors of the driving force for crack propagation in elastoplastic materials during crack propagation are expressed as follows: f(G, E, υ, σ s , n, a0, P) = 0 Equation (4) In formula (4): E represents the elastic modulus, υ represents Poisson's ratio, and σ s denoted by , where n represents the yield strength, a0 represents the strain hardening exponent, and P represents the initial crack length as a function of the external load.

3. The method for calculating the fracture toughness of elastoplastic crack propagation in metal structures according to claim 1, characterized in that, In step two, a dimensional analysis is performed on the influencing factors of the crack propagation driving force, providing a dimensionless set of variables, including: Based on the dimensional analysis of each influencing factor among the factors affecting crack propagation driving force, the expression is: In formula (5), G represents the driving force for elastoplastic crack propagation, M represents the mass dimension, T represents the time dimension, L represents the length dimension, E represents the elastic modulus, σ represents the yield strength, a0 represents the initial crack length, and P represents a function of the external load. The dimensional relation matrix is ​​obtained according to formula (5), and its expression is: In formula (6), A represents the dimensional relation matrix; where the rank of the dimensional relation matrix is ​​2, the number of solutions to the homogeneous linear equation system is 3, thus obtaining the basic solutions y1, y2, and y3 of the linear homogeneous equation system. The three solutions yield three independent dimensionless quantities, expressed as: In formula (7), π1 represents the first dimensionless quantity, G represents the driving force for elastoplastic crack propagation, π2 represents the second dimensionless quantity, and π3 represents the third dimensionless quantity. Finally, the driving force for crack propagation during the elastoplastic crack propagation process is obtained, and its expression is: In formula (8), f(*) represents the unknown functional relationship between the crack propagation driving force and its influencing factors, F(*) represents the dimensionless functional relationship, and ψ(*) represents the undetermined functional relationship between the first dimensionless quantity and the remaining dimensionless quantities.

4. A method for calculating the fracture toughness of elastoplastic crack propagation in metal structures according to claim 1 or 3, characterized in that, In step two, selecting an elastic-plastic material with a metallic structure and designing an experiment includes: Select the parameter range for the elastoplastic material of the metallic structure and design an experiment; the dimensionless variables of the elastoplastic material of the metallic structure include: the ratio of crack propagation driving force to elastic modulus and initial crack length. The ratio of yield strength to elastic modulus The ratio of external load to elastic modulus and the square of initial crack length Poisson's ratio v, strain hardening exponent n; Determine the number of levels for all variables and the variable values ​​for each level.

5. The method for calculating the fracture toughness of elastoplastic crack propagation in metal structures according to claim 1, characterized in that, In step three, numerical calculations of elastic-plastic crack propagation are performed based on the finite element model of the elastic-plastic crack structure, including: (31) Based on the finite element model of the elastic-plastic crack structure, the node release technique is used to carry out numerical calculation of elastic-plastic crack propagation in the finite element model of the elastic-plastic crack structure. (32) Based on the finite element model of the elastic-plastic crack structure, a loading analysis step and a release analysis step are established. The difference between the loading analysis step and the release analysis step is the crack length. (33) Elastic-plastic crack propagation is achieved by modifying the boundary conditions along the crack propagation path, and the load is applied to the loading analysis step based on the finite element model of the elastic-plastic crack structure. (34) After the load is applied, the release analysis step is activated based on the finite element model of the elastic-plastic crack structure. While maintaining the same load, a node is released on the crack propagation path to achieve a complete elastic-plastic crack propagation analysis. In the release analysis step, a release force is applied to the initial crack tip node, and the release force is gradually reduced to zero to avoid convergence difficulties; when the release force is zero, the initial crack tip node is completely released, allowing the elastoplastic crack to propagate. (35) After the analysis is completed, extract the maximum value of the crack propagation driving force; In step three, the crack propagation driving force information is extracted, including: In the crack propagation process of elastoplastic materials, the maximum crack propagation driving force at the moment of crack initiation is extracted.

6. The method for calculating the fracture toughness of elastoplastic crack propagation in metal structures according to claim 1, characterized in that, In step four, the regression analysis method includes: Based on the influencing factors of crack propagation driving force in step one, a functional relationship between independent and dependent variables is established; wherein, the independent variables include υ, n; dependent variables include The functional relationship of the crack propagation driving force expression was obtained using multiple regression analysis. The expression is as follows: In formula (9), Y represents the observed response, G represents the driving force for elastoplastic crack propagation, E represents the elastic modulus, a0 represents the initial crack length, X1 represents the first predictor, and σ s X1 represents the yield strength, X2 represents the second predictor, P represents the function of external load, X3 represents the third predictor, v represents Poisson's ratio, X4 represents the fourth predictor, and n represents the strain hardening exponent. In step four, the calculation model for the crack propagation driving force is expressed as follows: In formula (10), β0 represents the intercept, β k X represents the regression coefficient. k Let ξ represent the k-th predictor and ξ represent the regression error. Indicates the predicted response. Indicates the estimated intercept. Indicates the estimated coefficient; In step four, accurately predicting the propagation of elastoplastic cracks includes: In regression analysis, the quality of fit of multiple regression is measured by the multivariate coefficient of determination. The multivariate coefficient of determination is used to explain the proportion of change in the response by the crack propagation driving force calculation model. The value of the multivariate coefficient of determination is between 0 and 1. A multivariate coefficient of determination of 1 indicates a perfect fit, while a multivariate coefficient of determination of 0 indicates no predictive ability.

7. The method for calculating the fracture toughness of elastoplastic crack propagation in metal structures according to claim 1, characterized in that, Step five involves performing numerical calculations for elastic-plastic crack propagation, including: (51) Based on the finite element model of the elastic-plastic crack structure, the node release technique is used to carry out numerical calculation of elastic-plastic crack propagation on the finite element model of the elastic-plastic crack structure. (52) Based on the finite element model of the elastic-plastic crack structure, a loading analysis step and a release analysis step are established. The difference between the loading analysis step and the release analysis step is the crack length. (53) Elastic-plastic crack propagation is achieved by modifying the boundary conditions along the crack propagation path, and the load is applied to the loading analysis step based on the finite element model of the elastic-plastic crack structure. (54) After the load is applied, the release analysis step is activated based on the finite element model of the elastic-plastic crack structure. While maintaining the same load, a node is released on the crack propagation path to achieve a complete elastic-plastic crack propagation analysis. In the release analysis step, a release force is applied to the initial crack tip node, and the release force is gradually reduced to zero to avoid convergence difficulties; when the release force is zero, the initial crack tip node is completely released, allowing the elastoplastic crack to propagate. (55) The fracture toughness obtained by the elastic-plastic crack propagation fracture toughness calculation method is used as the criterion to calculate the crack propagation driving force; when the crack propagation driving force is less than the fracture toughness, the load is increased; when the crack propagation driving force is equal to the fracture toughness, the crack propagates. Repeat (53)-(55) until the elastoplastic crack propagation stabilization stage is reached.

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