Calculation method for elastic-plastic crack propagation fracture toughness of metal structure

Abstract

The invention provides a calculation method for elastic-plastic crack propagation fracture toughness of a metal structure, which comprises the following steps: performing energy analysis on an elastic-plastic material, and determining an energy component expression of crack propagation driving force and resistance; screening influence factors of the crack propagation driving force of the elastic-plastic crack; performing dimensional analysis on the fracture toughness influence factors, and giving dimensionless group variables according to the dimensional analysis; selecting an elastoplastic material of a metal structure and designing a test; carrying out elastic-plastic crack propagation numerical calculation based on the elastic-plastic crack structure finite element model, and extracting crack propagation resistance information; a fracture toughness calculation model is determined by using a regression analysis method, and elastic-plastic crack propagation is accurately predicted; and carrying out elastic-plastic crack propagation numerical calculation by taking the fracture toughness as a crack propagation criterion. According to the method, a fracture toughness expression is designed through dimensional analysis, unknown parameters in fracture toughness are calibrated in combination with a regression analysis method, a fracture toughness calculation model is obtained, and elastic-plastic crack propagation is accurately predicted.

Description

Technical Field

[0001] The invention belongs to the field of fracture mechanics crack propagation prediction, and in particular relates to a calculation method for the fracture toughness of elastic-plastic crack propagation in metal structures. Background Art

[0002] In fracture mechanics, the energy release rate is essential for evaluating the crack propagation of materials under stress. Linear elastic fracture mechanics based on linear elastic theory can quantitatively analyze brittle fracture. For materials that exhibit both elastic and plastic behavior during the fracture process, the analysis of crack propagation and related energy release rates is more complicated than that of purely elastic materials. For elastoplastic materials, the usual practice is to modify the energy release rate theory and consider the plastic deformation behavior of the material by taking plastic dissipation as part of fracture toughness. However, this plastic correction approach is actually a compromise, because the existing theoretical and experimental techniques are not sufficient to directly measure or accurately calculate the true fracture toughness during crack propagation, and this plastic correction is only applicable to the calculation of fracture toughness under a small range of yield conditions.

[0003] When the size of the plastic zone in an elastoplastic material exceeds the length of the crack or structure, the fracture problem becomes more complicated. The above classical methods are no longer applicable to elastoplastic crack propagation. At present, the study of elastoplastic fracture usually 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 the J-integral, the full quantity theory is needed to describe the elastoplastic constitutive relationship of the elastoplastic material, that is, the plastic unloading during the crack propagation process is not considered, and the elastoplastic constitutive relationship is approximated as a nonlinear elastic constitutive relationship. The nonlinear elastic theory is used to characterize the plastic deformation of the crack tip area during loading. However, when the crack further extends in the elastoplastic material and a plastic unloading area appears in the crack wake area, the J-integral method is no longer applicable. And a large number of experiments have shown that in addition to being related to material parameters, the J-integral method also depends on the external load form and the geometry of the specimen, such as the J measured on the center crack specimen. IC Much higher than the J measured on the bending specimen IC .

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

[0005] The purpose of the present invention is to solve the shortcomings of the prior art that when the elastic-plastic expansion crack does not meet the small-range yield, the elastic-plastic crack expansion cannot be accurately described, and a calculation method for the fracture toughness of the elastic-plastic crack expansion of metal structures is provided. The fracture toughness of the material is directly calculated through the mechanical property parameters of the material and its destructive load, and the crack expansion driving force expression is designed by dimensional analysis. Combined with the regression analysis method, the unknown parameters in the fracture toughness calculation model are calibrated, that is, the calculation model of the crack expansion driving force is obtained. When the crack actually expands, the crack expansion driving force is equal to the fracture toughness, that is, the fracture toughness calculation model is determined, and the elastic-plastic crack expansion is accurately predicted.

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

[0007] A calculation method for elastic-plastic crack growth fracture toughness of metal structures, comprising:

[0008] Step 1: Perform energy analysis on the elastic-plastic material to determine the energy component expressions of the crack propagation driving force and the crack propagation resistance; and screen the influencing factors of the crack propagation driving force of the elastic-plastic crack;

[0009] Step 2: dimensional analysis is performed on the factors affecting the crack propagation driving force, and dimensionless group variables are given according to the dimensional analysis; and elastic-plastic materials of the metal structure are selected and experiments are designed;

[0010] Step 3: Based on the finite element model of elastic-plastic crack structure, numerical calculation of elastic-plastic crack propagation is carried out to extract the driving force information of crack propagation;

[0011] Step 4: Use regression analysis 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, that is, the fracture toughness calculation model is determined to accurately predict the elastic-plastic crack extension.

[0012] Step 5. Use fracture toughness as the crack extension criterion to carry out numerical calculation of 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. Continue to increase the load. When the crack extension driving force is equal to the fracture toughness, the crack extends and enters the non-proportional loading extension crack stage.

[0013] As a further limitation of the present invention, in step 1, performing energy analysis on the elastic-plastic material to determine the driving force for elastic-plastic crack propagation includes:

[0014] Analyzing the elastic-plastic crack of the elastic-plastic material from the energy perspective, the energy equation of the elastic-plastic crack during the expansion process is:

[0015] δW=δU e +δUp +2γ·t·da formula (1)

[0016] In formula (1), δ represents the variation sign, W represents the work done by the quasi-static external load, and U e represents the elastic strain energy, U p represents plastic dissipation, γ represents surface energy density, t represents crack plate thickness, and da represents crack extension increment;

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

[0018]

[0019] In formula (2), d represents the differential symbol;

[0020] The elastic-plastic crack growth resistance G c The expression is:

[0021] G c =2γ formula (3);

[0022] In the step 1, judging whether the elastic-plastic crack is an extended crack includes:

[0023] In formula (1), when γ = 0, formula (1) degenerates into a static crack. p When =0, formula (1) degenerates into Griffith theory;

[0024] In formula (2) and formula (3), when G = G c When G<G c When , the elastic-plastic crack is in the static crack stage of proportional loading;

[0025] In the step 1, the factors affecting the crack propagation driving force of the elastic-plastic material are screened, including:

[0026] During the expansion of elastic-plastic cracks, the factors affecting the driving force of crack expansion of elastic-plastic materials are expressed as follows:

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

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

[0029] As a further limitation of the present invention, in the step 2, the influencing factors of the crack extension driving force are subjected to dimensional analysis, and dimensionless group variables are given, including:

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

[0031]

[0032] In formula (5), G represents the driving force of elastic-plastic crack growth, M represents the mass dimension, T represents the time dimension, L represents the length dimension, E represents the elastic modulus, and σ s represents the yield strength, a0 represents the initial crack length, and P represents the function of the 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; the rank of the dimensional relationship matrix is ​​2, and the number of solutions to the homogeneous linear equation system is 3, thereby obtaining the basic solutions y1, y2, and y3 of the linear homogeneous equation system. The three solutions obtain three independent dimensionless quantities, and the expression is:

[0036]

[0037] In formula (7), π1 represents the first dimensionless quantity, G represents the driving force of elastic-plastic crack growth, 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 functional relationship between the crack propagation driving force and its influencing factors, F(*) represents the dimensionless functional relationship, and ψ(*) represents the unknown functional relationship between the first dimensionless quantity and the remaining dimensionless quantities.

[0041] As a further limitation of the present invention, in step 2, selecting an elastic-plastic material of the metal structure and designing an experiment include:

[0042] Select the parameter range of metal structural elastoplastic materials and design the experiment; the dimensionless group variables of metal structural elastoplastic materials include: the ratio of crack extension driving force to elastic modulus and initial crack length Ratio of yield strength to elastic modulus The ratio of the external load to the elastic modulus and the square of the initial crack length Poisson's ratio υ, strain hardening exponent n;

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

[0044] As a further limitation of the present invention, in the step 3, the numerical calculation of elastic-plastic crack extension is carried out based on the finite element model of the elastic-plastic crack structure, including:

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

[0046] (32) establishing a loading analysis step and a release analysis step based on the elastic-plastic crack structure finite element model, wherein the loading analysis step and the release analysis step differ in terms of crack length;

[0047] (33) realizing elastic-plastic crack propagation by modifying boundary conditions along the crack propagation path, and applying a load to the loading analysis step based on the elastic-plastic crack structure finite element model;

[0048] (34) After the load is applied, the release analysis step is activated based on the elastic-plastic crack structure finite element model, and while maintaining the same load, a node is released on the crack propagation path to achieve a complete elastic-plastic crack propagation analysis; 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, allowing the elastic-plastic crack to propagate;

[0049] (35) After the analysis is completed, the maximum driving force for crack growth is extracted;

[0050] In the step 3, extracting crack extension driving force information includes:

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

[0052] As a further limitation of the present invention, in step 4, the regression analysis method comprises:

[0053] According to the influencing factors of the crack extension driving force in step 1, a functional relationship between independent variables and dependent variables is established; wherein the independent variables include υ, n; dependent variables include The functional relationship of the crack extension driving force expression is obtained using the multivariate regression analysis method, and the expression is:

[0054]

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

[0056] In step 4, the crack extension driving force calculation model is expressed as:

[0057]

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

[0059] In the step 4, accurately predicting elastic-plastic crack growth includes:

[0060] The fitting quality of multiple regression in the regression analysis method is measured by the multiple determination coefficient. The multiple determination coefficient uses the crack extension driving force calculation model to explain the change proportion in the response. The size of the multiple determination coefficient is between 0 and 1; when the multiple determination coefficient is 1, it indicates a perfect fit, and when the multiple determination coefficient is 0, it indicates no predictive ability.

[0061] As a further limitation of the present invention, in step 5, the elastic-plastic crack extension numerical calculation is carried out, including:

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

[0063] (52) establishing a loading analysis step and a release analysis step based on the elastic-plastic crack structure finite element model, wherein the loading analysis step and the release analysis step differ in terms of crack length;

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

[0065] (54) After the load is applied, the release analysis step is activated based on the elastic-plastic crack structure finite element model, and while maintaining the same load, a node is released on the crack propagation path to achieve a complete elastic-plastic crack propagation analysis; 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, allowing the elastic-plastic crack to propagate;

[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; (53)-(55) are repeated until the elastic-plastic crack propagation stable stage is reached.

[0067] The advantages of the present invention are:

[0068] 1. The present invention directly calculates the fracture toughness of the material through the mechanical property parameters of the material and its failure load, adopts dimensional analysis to design the expression of crack extension driving force, combines with regression analysis method to calibrate the unknown parameters in the crack extension driving force, and obtains the crack extension driving force calculation model. When the crack actually extends, the crack extension driving force is equal to the fracture toughness, that is, the fracture toughness calculation model is obtained, which accurately predicts the elastic-plastic crack extension.

[0069] 2. Compared with the existing fracture criteria, the present invention eliminates the influence of plastic dissipation on fracture toughness, and proposes that fracture toughness is an inherent property of elastic-plastic materials and is independent of factors such as external loads and test piece geometry. The present invention can clarify the contribution of mechanical performance parameters to fracture toughness.

[0070] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0072] Figure 1 : A flow chart of a method for calculating elastic-plastic crack propagation fracture toughness of metal structures provided by the present invention;

[0073] Figure 2 : Flow chart of the implementation process of the calculation method provided by the present invention;

[0074] Figure 3 : Schematic diagram of boundary conditions on the crack propagation path provided by the present invention;

[0075] Figure 4 : Predicted response and observed response diagrams during implementation of the calculation method provided by the present invention;

[0076] Figure 5 : A diagram of the crack propagation process during the implementation of the calculation method provided by the present invention;

[0077] Figure 6 : The present invention selects the level of each prediction factor of the target metal structure and its corresponding dimensionless variable table;

[0078] Figure 7 : The present invention selects an orthogonal matrix table designed by Taguchi experimental design method for the target metal structure;

[0079] Figure 8 : The regression results and corresponding coefficient table provided by the present invention;

[0080] Fig. 9 : Data table of AD in the mathematical relationship expression between characteristic fracture energy and various parameters provided by the present invention. DETAILED DESCRIPTION

[0081] Embodiments of the present invention are described in detail below. The embodiments are exemplary and intended to be used to explain the present invention, but should not be construed as limiting the present invention.

[0082] See also Figure 1 and Figure 2 The embodiment of the present invention provides a method for calculating the elastic-plastic crack propagation fracture toughness of a metal structure, comprising steps 1 to 5:

[0083] Step 1: Perform energy analysis on elastic-plastic materials to determine the energy component expressions of crack propagation driving force and crack propagation resistance; screen the factors affecting the crack propagation driving force of elastic-plastic cracks. Specifically:

[0084] In the above step 1 of the embodiment of the present invention, energy analysis is performed on the elastic-plastic material to determine the driving force for elastic-plastic crack extension, including:

[0085] From the energy perspective, the elastic-plastic crack of elastic-plastic materials is analyzed. Assuming that the fracture energy required to form a new surface during crack propagation remains unchanged, the energy equation of the elastic-plastic crack during propagation is:

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

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

[0088] Specifically, the above-mentioned determination of whether the elastic-plastic crack is an extended crack in the embodiment of the present invention includes: In formula (1), when γ=0, formula (1) degenerates into a static crack, when U p When =0, formula (1) degenerates into Griffith theory.

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

[0090]

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

[0092] Elastic-plastic crack growth resistance G c The expression is:

[0093] G c =2γ formula (3);

[0094] In the above formula (2) and formula (3) of the embodiment of the present invention, when G=G c When G<G c When , the elastic-plastic crack is in the static crack stage of proportional loading.

[0095] The present invention screens factors influencing the crack propagation driving force of elastic-plastic materials, including:

[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 the elastic modulus, υ represents the Poisson's ratio, σ s represents the yield strength, n represents the strain hardening exponent, a0 represents the initial crack length, and P represents the function of the external load.

[0099] Step 2: Conduct dimensional analysis on the factors affecting the driving force of crack extension, and give dimensionless group variables according to the dimensional analysis; and select elastic-plastic materials of metal structures and design experiments. Specifically:

[0100] In the above step 2 of the embodiment of the present invention, a dimension analysis is performed on the factors affecting the crack propagation driving force, and a dimensionless group variable is given, including:

[0101] According to the dimensional analysis of each factor affecting the crack propagation driving force, the expression is:

[0102]

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

[0104] According to formula (5), the dimensional relationship matrix is ​​obtained, and the expression is:

[0105]

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

[0107]

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

[0109]

[0110] Thus, the basic solutions y1, y2, and y3 of the linear homogeneous equations are obtained. The three solutions give three independent dimensionless quantities, expressed as follows:

[0111]

[0112] In formula (7), π1 represents the first dimensionless quantity, G represents the driving force of elastic-plastic crack growth, 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 functional relationship between the crack propagation driving force and its influencing factors, F(*) represents the dimensionless functional relationship, and ψ(*) represents the unknown functional relationship between the first dimensionless quantity and the remaining dimensionless quantities.

[0116] In the above step 2 of the embodiment of the present invention, the elastic-plastic material of the metal structure is selected and the test is designed, including:

[0117] Select the parameter range of metal structural elastoplastic materials and design the experiment; the dimensionless group variables of metal structural elastoplastic materials include: the ratio of crack extension driving force to elastic modulus and initial crack length Ratio of yield strength to elastic modulus The ratio of the external load to the elastic modulus and the square of the initial crack length Poisson's ratio υ, strain hardening exponent n; determine the number of levels of all variables and the variable values ​​at each level.

[0118] When designing the test for the selected metal structure elastoplastic material, determine the number of levels of all variables and the variable value of each level. Specifically:

[0119] Figure 2 In the implementation of the calculation method shown, the target metal structure is selected as aviation metal, and the number of levels selected for each prediction factor is 9. The level of each prediction factor and its corresponding dimensionless variable table are as follows: Figure 6 As shown. 81 groups of orthogonal experiments were designed using the Taguchi experimental design method. The designed orthogonal matrix is ​​shown in Figure 7 Each row of the orthogonal matrix represents a computational case with a specific combination of material, geometry, and parameters that were used as input to the finite element to obtain the observed response.

[0120] Step 3: Establish an elastic-plastic crack structure finite element model, carry out numerical calculation of elastic-plastic crack extension based on the elastic-plastic crack structure finite element model, and extract the crack extension driving force information. Specifically:

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

[0122] In the above step 3 of the embodiment of the present invention, the numerical calculation of elastic-plastic crack extension is carried out based on the finite element model of the elastic-plastic crack structure, 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 extension on the elastic-plastic crack structure finite element model; (32) According to 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 lies in the crack length; (33) The elastic-plastic crack extension is realized by modifying the boundary conditions along the crack extension path, and the load is applied to the loading analysis step based on the elastic-plastic crack structure finite element model; (34) After the load is applied, the release analysis step is activated based on the elastic-plastic crack structure finite element model, and while maintaining the same load, a node is released on the crack extension path to realize a complete elastic-plastic crack extension analysis; wherein, in the release analysis step, a release force is applied to the initial crack tip node, so that 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 elastic-plastic crack to extend, such as Figure 3 (b) As shown in (35), the maximum driving force for crack extension is extracted after the analysis is completed. The boundary conditions on the crack path are as follows: Figure 3 (a) shown.

[0124] As a preferred implementation, in the crack propagation process of the elastoplastic material, the embodiment of the present invention extracts the maximum crack propagation driving force at the crack initiation moment, and obtains the crack propagation resistance information based on the maximum crack propagation driving force.

[0125] Step 4: Use regression analysis 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, that is, the fracture toughness calculation model is determined to accurately predict the elastic-plastic crack extension. Specifically:

[0126] In the above step 4 of the embodiment of the present invention, the regression analysis method includes:

[0127] According to the factors affecting the crack propagation driving force in step 1, a functional relationship between independent variables and dependent variables is established; the independent variables include υ, n; dependent variables include The functional relationship of the crack growth driving force expression is obtained by using the multiple regression analysis method. Using the multiple regression analysis method, it is assumed that the logarithmic linear relationship is:

[0128]

[0129] Among them, 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 the observed response, G represents the driving force of elastic-plastic crack growth, E represents the elastic modulus, a0 represents the initial crack length, X1 represents the first prediction factor, and σ s represents yield strength, X2 represents the second predictor, P represents the function of external load, X3 represents the third predictor, υ represents Poisson’s ratio, X4 represents the fourth predictor, and n represents the strain hardening exponent.

[0132] In the embodiment of the present invention, n types of k For the combination (k=1,2,3,4), the coefficient β k (k=1,2,3,4) is estimated by the least squares method as The "wavy" symbol is used to distinguish the estimated coefficients and the unknown coefficient β k Again, the "wavy" symbol is used to distinguish the predicted responses (through regression analysis) and the observed response Y (obtained from the finite element results).

[0133] The crack extension driving force calculation model in the above step 4 of the embodiment of the present invention is expressed as:

[0134]

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

[0136] The fitting quality of the multivariate regression in the above-mentioned step 4 regression analysis method of the embodiment of the present invention is measured by the multivariate determination coefficient, which uses the crack extension driving force calculation model to explain the change ratio in the response, and the magnitude of the multivariate determination coefficient is between 0 and 1. When the multivariate determination coefficient is 1, it indicates a perfect fit, and when the multivariate determination coefficient is 0, it indicates no predictive ability.

[0137] Step 5: Use fracture toughness as the crack extension criterion to carry out numerical calculation of 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. Continue to increase the load. When the crack extension driving force is equal to the fracture toughness, the crack extends and enters the non-proportional loading extension crack stage. Specifically:

[0138] In step 5 of the embodiment of the present invention, numerical calculation of elastic-plastic crack extension is carried out, including: (51) based on the elastic-plastic crack structure finite element model, the node release technology is used to carry out numerical calculation of elastic-plastic crack extension on the elastic-plastic crack structure finite element model; (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 lies in the crack length; (53) elastic-plastic crack extension is realized by modifying the boundary conditions along the crack extension path, and load is applied to the loading analysis step based on the elastic-plastic crack structure finite element model; (54) after the load is applied, the release analysis step is activated based on the elastic-plastic crack structure finite element model, and in While maintaining the same load, a complete elastic-plastic crack propagation analysis is performed by releasing a node on the crack propagation path; 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, allowing the elastic-plastic crack to propagate; (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 stable stage is reached.

[0139] The embodiment of the present invention adopts the stepwise regression method, and through iterative testing of the statistical significance of each variable, eliminates the independent variables that do not play a significant role in the regression, and selects the independent variables that have a significant impact on the dependent variable; the embodiment of the present invention adopts the significance level (p-value) 0.05 and 0.1 as the entry standard and elimination standard of the regression model in the regression analysis method. Among them, the independent variable enters the regression model when the p-value is less than 0.05 (p<0.05), and is eliminated when the p-value of the independent variable is greater than 0.1 (p>0.1). The p-value is a statistical measure used to estimate the probability of rejecting the null hypothesis when the null hypothesis is true. The null hypothesis in the regression model is that there is no statistical significance between the independent variable and the dependent variable. A smaller p-value indicates that there is stronger evidence to reject the null hypothesis and indicates that there is a stronger correlation between the independent variable and the dependent variable.

[0140] like Figure 8 The regression results and corresponding coefficients shown are from Figure 8 It can be observed that the predictor X3 was not included in the regression model due to its statistical insignificance. In addition, 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 great impact on the response. The regression model of the embodiment of the present invention is expressed as:

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

[0142]

[0143] The calibration parameters in formula (11) are as follows: Fig. 9 As shown in Figure 2, when the crack actually expands, the crack expansion driving force is equal to the fracture toughness. The fracture toughness obtained by this crack expansion driving force calculation model is used as the fracture criterion to perform finite element numerical calculation of crack expansion of 316L stainless steel. The results are shown in Figure 2. Figure 5 shown.

[0144] Therefore, compared with the existing fracture criteria, the embodiments of the present invention exclude the influence of plastic dissipation on fracture toughness, and propose that fracture toughness is an inherent property of elastic-plastic materials and is independent of factors such as external loads and test piece geometry. It can be seen that the embodiments of the present invention can clarify the contribution of mechanical property parameters to fracture toughness.

[0145] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should be included in the protection scope of the present invention.

Claims

1. A method for calculating the elastic-plastic crack growth fracture toughness of metal structures, characterized in that: include: Step 1: Perform energy analysis on elastic-plastic materials to determine the energy component expressions of crack growth driving force and crack growth resistance; Screening the factors influencing the crack extension driving force of the elastic-plastic crack; Step 2: Performing dimensional analysis on the factors affecting the crack propagation driving force, and giving a dimensionless group variable according to the dimensional analysis; and selecting elastic-plastic materials for metal structures and designing experiments; Step 3: Based on the finite element model of elastic-plastic crack structure, numerical calculation of elastic-plastic crack propagation is carried out to extract the information of crack propagation driving force; Step 4: Use regression analysis 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, that is, the fracture toughness calculation model is determined to accurately predict the elastic-plastic crack extension. Step 5. Use fracture toughness as the crack extension criterion to carry out numerical calculation of 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. Continue to increase the load. When the crack extension driving force is equal to the fracture toughness, the crack extends and enters the non-proportional loading extension crack stage.

2. A method for calculating the elastic-plastic crack propagation fracture toughness of metal structures according to claim 1, characterized in that: In the step 1, energy analysis is performed on the elastic-plastic material to determine the driving force for elastic-plastic crack propagation, including: Analyzing the elastic-plastic crack of the elastic-plastic material from the energy perspective, the energy equation of the elastic-plastic crack during the expansion process is: δW = δU e + δU p + 2γ·t·da Formula (1) In formula (1), δ represents the variation sign, W represents the work done by the quasi-static external load, and U e represents the elastic strain energy, U p represents plastic dissipation, γ represents surface energy density, t represents crack plate thickness, and da represents crack extension increment; During the expansion of the elastic-plastic crack, the surface energy and plastic dissipation are separated, and the surface energy is determined as the elastic-plastic crack expansion resistance G c , the plastic dissipation is determined as the elastic-plastic crack extension driving force G; wherein the expression of the elastic-plastic crack extension driving force G is: In formula (2), d represents the differential symbol; The elastic-plastic crack growth resistance G c The expression is: G c =2γ formula (3); In the step 1, judging whether the elastic-plastic crack is an extended crack includes: In formula (1), when γ = 0, formula (1) degenerates into a static crack. p When =0, formula (1) degenerates into Griffith theory; In formula (2) and formula (3), when G = G c When G<G c When , the elastic-plastic crack is in the static crack stage of proportional loading; In the step 1, the factors affecting the crack propagation driving force of the elastic-plastic material are screened, including: During the expansion of elastic-plastic cracks, the factors affecting the driving force of crack expansion of elastic-plastic materials 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 the Poisson's ratio, σ s represents the yield strength, n represents the strain hardening exponent, a0 represents the initial crack length, and P represents the function of the external load.

3. A method for calculating the elastic-plastic crack propagation fracture toughness of metal structures according to claim 1, characterized in that: In the step 2, a dimension analysis is performed on the factors affecting the crack extension driving force, and a dimensionless group variable is given, including: According to the dimensional analysis of each influencing factor of the crack propagation driving force, the expression is: In formula (5), G represents the driving force of elastic-plastic crack growth, M represents the mass dimension, T represents the time dimension, L represents the length dimension, E represents the elastic modulus, and σ s represents the yield strength, a0 represents the initial crack length, and P represents the function of the external load; According to formula (5), the dimensional relationship matrix is ​​obtained, and the expression is: In formula (6), A represents the dimensional relationship matrix; the rank of the dimensional relationship matrix is ​​2, and the number of solutions to the homogeneous linear equation system is 3, thereby obtaining the basic solutions y1, y2, and y3 of the linear homogeneous equation system. The three solutions obtain three independent dimensionless quantities, and the expression is: In formula (7), π1 represents the first dimensionless quantity, G represents the driving force of elastic-plastic crack growth, π2 represents the second dimensionless quantity, and π3 represents the third dimensionless quantity; Finally, the crack propagation driving force in the elastic-plastic crack propagation process is obtained, and the 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 unknown functional relationship between the first dimensionless quantity and the remaining dimensionless quantities.

4. A method for calculating the elastic-plastic crack propagation fracture toughness of metal structures according to claim 1 or 3, characterized in that: In the step 2, the elastic-plastic material of the metal structure is selected and the test is designed, including: Select the parameter range of metal structural elastoplastic materials and design the experiment; the dimensionless group variables of metal structural elastoplastic materials include: the ratio of crack extension driving force to elastic modulus and initial crack length Ratio of yield strength to elastic modulus The ratio of the external load to the elastic modulus and the square of the initial crack length Poisson's ratio υ, strain hardening exponent n; Determine the number of levels for all variables and the variable values ​​for each level.

5. A method for calculating the elastic-plastic crack propagation fracture toughness of metal structures according to claim 1, characterized in that: In the step 3, the elastic-plastic crack extension numerical calculation is carried out based on the elastic-plastic crack structure finite element model, including: (31) Based on the elastic-plastic crack structure finite element model, a node release technology is used to perform a numerical calculation of elastic-plastic crack propagation on the elastic-plastic crack structure finite element model; (32) establishing a loading analysis step and a release analysis step based on the elastic-plastic crack structure finite element model, wherein the loading analysis step and the release analysis step differ in terms of crack length; (33) realizing elastic-plastic crack propagation by modifying boundary conditions along the crack propagation path, and applying a load to the loading analysis step based on the elastic-plastic crack structure finite element model; (34) After the load is applied, the release analysis step is activated based on the elastic-plastic crack structure finite element model, and while maintaining the same load, a node is released on the crack propagation path to achieve a complete elastic-plastic crack propagation analysis; 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, allowing the elastic-plastic crack to propagate; (35) After the analysis is completed, the maximum driving force for crack growth is extracted; In the step 3, extracting crack extension driving force information includes: During the crack propagation process of elastic-plastic materials, the maximum crack propagation driving force at the crack initiation moment is extracted.

6. A method for calculating the elastic-plastic crack propagation fracture toughness of metal structures according to claim 1, characterized in that: In step 4, the regression analysis method includes: According to the influencing factors of the crack extension driving force in step 1, a functional relationship between independent variables and dependent variables is established; wherein the independent variables include υ, n; dependent variables include The functional relationship of the crack extension driving force expression is obtained using the multivariate regression analysis method, and the expression is: In formula (9), Y represents the observed response, G represents the driving force of elastic-plastic crack growth, E represents the elastic modulus, a0 represents the initial crack length, X1 represents the first prediction factor, and σ s represents yield strength, X2 represents the second predictor, P represents the function of external load, X3 represents the third predictor, υ represents Poisson's ratio, X4 represents the fourth predictor, and n represents the strain hardening exponent; In step 4, the crack extension driving force calculation model is expressed as: In formula (10), β0 represents the intercept, β k represents the regression coefficient, X k represents the kth predictor, ξ represents the regression error, represents the predicted response, represents the estimated intercept, represents the estimated coefficient; In the step 4, accurately predicting elastic-plastic crack growth includes: The fitting quality of multiple regression in the regression analysis method is measured by the multiple determination coefficient. The multiple determination coefficient uses the crack extension driving force calculation model to explain the change proportion in the response. The size of the multiple determination coefficient is between 0 and 1; when the multiple determination coefficient is 1, it indicates a perfect fit, and when the multiple determination coefficient is 0, it indicates no predictive ability.

7. A method for calculating the elastic-plastic crack propagation fracture toughness of metal structures according to claim 1, characterized in that: In the step 5, the elastic-plastic crack extension numerical calculation is carried out, including: (51) Based on the elastic-plastic crack structure finite element model, a node release technology is used to perform a numerical calculation of elastic-plastic crack propagation on the elastic-plastic crack structure finite element model; (52) establishing a loading analysis step and a release analysis step based on the elastic-plastic crack structure finite element model, wherein the loading analysis step and the release analysis step differ in terms of crack length; (53) realizing elastic-plastic crack propagation by modifying boundary conditions along the crack propagation path, and applying a load to the loading analysis step based on the elastic-plastic crack structure finite element model; (54) After the load is applied, the release analysis step is activated based on the elastic-plastic crack structure finite element model, and while maintaining the same load, a node is released on the crack propagation path to achieve a complete elastic-plastic crack propagation analysis; 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, allowing the elastic-plastic crack to propagate; (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; (53)-(55) are repeated until the elastic-plastic crack propagation stable stage is reached.

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