A method and system for characterizing stress constraints at a crack tip of a power-hardened material

Abstract

The application relates to a method and system for characterizing stress constraint at a crack tip of a power hardening material, the method comprising the following steps: establishing a boundary layer model for the crack tip; applying a displacement boundary condition on an outer circular boundary of the boundary layer model; performing an elastic-plastic analysis on the boundary layer model by using a finite element method to obtain a stress field at the crack tip under different T stresses; extracting normal stresses perpendicular to a crack line at each node on a ligament line under different T stresses; calculating a ratio of the normal stresses perpendicular to the crack line under a negative T stress to the normal stresses perpendicular to the crack line under a zero T stress to determine a minimum value of the ratio in a plastic zone min as a characterization parameter of the stress constraint at the crack tip; and characterizing the stress constraint at the crack tip of the power hardening material based on the characterization parameter.

Description

Technical Field

[0001] This invention relates to the field of characterization technology of near-crack tip stress field, and in particular to a method and system for characterizing crack tip stress constraint in power-hardening materials. Background Technology

[0002] Crack tip confinement has a significant impact on the fracture toughness, crack propagation resistance, and fatigue crack propagation of a structure, and its effect needs to be considered in relevant analyses. Crack tip confinement is usually described by T stress (or dimensionless T / σ0, where σ0 is the yield stress), Q, or A1. Positive T stress, Q, or A1 indicates high crack tip confinement, while negative T stress, Q, or A1 indicates low crack tip confinement and stress release. Kirk et al.'s research shows that when T>0, the normal stress σ perpendicular to the crack line... yy The stress T remains essentially constant as the stress increases; however, when T < 0, σ yy As the T-stress decreases, the stress release increases. Since linear elastic fracture mechanics theory cannot describe this phenomenon, the JT, JQ, and J-A1 theories were developed to describe the near-crack tip stress field. All three theories can characterize crack tip constraint and have been successfully applied in describing the influence of constraint on fracture toughness, crack propagation resistance, and calculating the crack tip constraint factor. However, each theory has its own limitations. T-stress can only be applied under small-scale yielding conditions and is not suitable for large-scale yielding. The magnitude of T-stress can only indirectly reflect the strength of crack tip constraint and cannot quantify it. Furthermore, a relationship between T-stress and the elastoplastic crack tip stress field has not yet been established, limiting the application of T-stress in elastoplastic crack problems. Q and A1 are essentially equal. Because they are derived from the stress field within the plastic region, they are applicable to both small-scale and large-scale yielding, and can quantitatively describe crack tip constraint, as well as describe the elastoplastic crack tip field to some extent. However, for materials with low hardening index, such as high-carbon steel, Q and A1 can only describe the crack tip constraint at each point 2 J / σ0 in front of the crack tip, and cannot reflect the crack tip constraint in a region near the crack tip. This may result in the crack tip constraint not being objectively and fully characterized, thus affecting the handling of problems involving crack tip constraint. Summary of the Invention

[0003] Based on the above analysis, the embodiments of the present invention aim to provide a method and system for characterizing crack tip stress constraint of power-hardening materials, in order to solve the problem that existing characterization parameters have a small application range and cannot objectively and fully characterize crack tip constraint.

[0004] On one hand, embodiments of the present invention provide a method for characterizing crack tip stress constraint in power-hardening materials, comprising the following steps:

[0005] Establish a boundary layer model for the crack tip; apply displacement boundary conditions to the outer circular boundary of the boundary layer model;

[0006] The boundary layer model was subjected to elastoplastic analysis using the finite element method to obtain the crack tip stress field under different T stresses;

[0007] Extract the normal stress perpendicular to the crack line at each node along the ligament line under different T-stresses; calculate the ratio η of the normal stress perpendicular to the crack line under negative T-stress to that under zero T-stress, and determine the minimum value η within the plastic zone. min The crack tip constraint is characterized as a parameter for crack tip restraint; the crack tip stress constraint of the power-hardening material is characterized based on the parameter.

[0008] Based on further improvements to the above technical solution, the establishment of the boundary layer model includes:

[0009] The dimensions of the crack tip plastic zone were calculated based on the Dugdale model.

[0010] The boundary layer model is a circular region surrounding the crack tip with a radius of N times the size of the plastic zone, centered on the crack tip; wherein the crack tip is approximated by a circular arc.

[0011] Furthermore, the size of the crack tip plastic zone is calculated using the following formula based on the Dugdale model:

[0012] r p =π(K / σ0) 2 / twenty four

[0013] Where, r p σ represents the size of the plastic zone, K represents the stress intensity factor, and σ0 represents the yield strength of the material.

[0014] Furthermore, the following displacement boundary conditions are applied to the outer circular boundary of the boundary layer model:

[0015]

[0016]

[0017] Where u(r,θ) is the displacement in the x-direction, v(r,θ) is the displacement in the y-direction, r represents the distance from the outer boundary node to the crack tip, θ represents the angle between the line connecting the outer boundary node and the crack tip and the x-axis, υ represents Poisson's ratio, E represents the elastic modulus, K represents the stress intensity factor, and T represents the T stress.

[0018] Furthermore, the boundary layer model was subjected to elastoplastic analysis using the finite element method to obtain the crack tip stress field under different T stresses, including:

[0019] A finite element model of the boundary layer model is established, and an elastoplastic analysis is performed on the finite element model based on the material's elastoplastic constitutive relation to calculate the crack tip stress field under different T stresses.

[0020] Furthermore, the elastoplastic constitutive relation of the material is:

[0021]

[0022] Where ε0=σ0 / E, σ0 represents the yield strength, E represents the elastic modulus, α represents the dimensionless material constant, n represents the strain hardening exponent, σ represents the stress, and ε represents the strain.

[0023] Furthermore, the normal stress perpendicular to the crack line at each node along the ligament line under different T-stresses is extracted; the ratio η of the normal stress perpendicular to the crack line under negative T-stress to that under zero T-stress is calculated, and the minimum value η within the plastic zone is determined. min The characterization parameter is used as the crack tip constraint; based on the characterization parameter, the crack tip stress constraint of the power-hardening material is characterized, including:

[0024] Extract the normal stress perpendicular to the crack line at each node along the ligament line under different T stresses;

[0025] For each node, calculate the ratio η of the normal stress perpendicular to the crack line under negative T stress to the normal stress perpendicular to the crack line under zero T stress, and obtain... Dataset;

[0026] Based on the distance from the node to the crack tip, the minimum value of the ratio η is determined within the plastic region, and the minimum value of η is established. min and Relationship,

[0027] in, Let r be a dimensionless variable, where r represents the distance from the node to the crack tip. T represents the dimensionless stress.

[0028] Furthermore, Where J represents the J integral and σ0 represents the yield strength of the material.

[0029] Furthermore, establish η min The relationship with the stress value T includes:

[0030] use Establish the minimum value of η within the plastic region and The relationship, among which, T represents the dimensionless stress, and C0, C1, and b represent undetermined coefficients.

[0031] On the other hand, embodiments of the present invention provide a crack tip stress constraint characterization system for power-hardening materials, comprising the following modules:

[0032] The model building module is used to create a boundary layer model for the crack tip; and to apply displacement boundary conditions on the outer circular boundary of the boundary layer model.

[0033] The elastoplastic analysis module is used to perform elastoplastic analysis on the boundary layer model using the finite element method to obtain the crack tip stress field under different T stresses;

[0034] The constraint characterization module is used to extract the normal stress perpendicular to the crack line at each node along the ligament line under different T-stresses; calculate the ratio η of the normal stress perpendicular to the crack line under negative T-stress to that under zero T-stress, and determine the minimum value η within the plastic zone. min The crack tip constraint is characterized as a parameter for crack tip restraint; the crack tip stress constraint of the power-hardening material is characterized based on the parameter.

[0035] Compared with the prior art, the characterization parameter η proposed in this invention min This is based on the stress within the near-crack tip plastic zone. Therefore, regardless of whether the stress field in the near-crack tip plastic zone is dominated by J (corresponding to the large-scale yield condition) or by K and T (corresponding to the small-scale yield condition), η min Both can describe the crack tip constraint and can characterize the degree of crack tip constraint in a region near the crack tip, with a larger characterization range and more objective and accurate results.

[0036] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0037] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0038] Figure 1 This is a flowchart illustrating the crack tip stress constraint characterization method for power-hardening materials according to an embodiment of the present invention;

[0039] Figure 2 This is a schematic diagram of the crack mode;

[0040] Figure 3 This is a schematic diagram of the boundary layer model according to an embodiment of the present invention;

[0041] Figure 4This is a schematic diagram of the finite element model of an embodiment of the present invention;

[0042] Figure 5 σ is an embodiment of the present invention. yy Schematic diagram of / σ0 as a function of r;

[0043] Figure 6 For different T values ​​in the embodiments of the present invention Schematic diagram of the curve;

[0044] Figure 7 For different T values ​​in the embodiments of the present invention Schematic diagram of the curve;

[0045] Figure 8 This is an embodiment η of the present invention. min and A schematic diagram of the fitting relationship;

[0046] Figure 9 This is a block diagram of the crack tip stress constraint characterization system for power-hardening materials according to an embodiment of the present invention. Detailed Implementation

[0047] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0048] Cracks take many forms. For the same material under the same environmental conditions, the deformation of the crack will differ depending on the external stress (external load). Therefore, crack (or fracture) modes are classified into three categories: opening (Type I), slip (Type II), and tearing (Type III), as described below. Figure 2 As shown in (a), (b), and (c), actual crack propagation is not limited to these three forms; it is often a combination of them, such as the I-II, I-III, and II-III composite forms. Among these different crack propagation forms, type I crack propagation is the most dangerous and easily leads to brittle fracture. Therefore, this type of crack is always the main focus when studying the fracture problem of cracked bodies. The crack tip stress constraint characterization method of the power-hardening material of this invention is proposed for open-type (type I) cracks.

[0049] Example 1

[0050] A specific embodiment of the present invention discloses a method for characterizing crack tip stress constraint in power-hardening materials, such as... Figure 1 As shown, it includes the following steps:

[0051] S1. Establish a boundary layer model for the crack tip; apply displacement boundary conditions to the outer circular boundary of the boundary layer model;

[0052] S2. The boundary layer model is subjected to elastoplastic analysis using the finite element method to obtain the crack tip stress field under different T stresses;

[0053] S3. Extract the normal stress perpendicular to the crack line at each node along the ligament line under different T-stresses; calculate the ratio η of the normal stress perpendicular to the crack line under negative T-stress to the normal stress perpendicular to the crack line under zero T-stress, and determine the minimum value η within the plastic zone. min The crack tip constraint is characterized as a parameter for crack tip restraint; the crack tip stress constraint of the power-hardening material is characterized based on the parameter.

[0054] Under wide-range yield conditions, the linear elastic field dominated by stress intensity factor K and stress T disappears. Therefore, stress T is not suitable for characterizing crack tip confinement under wide-range yield conditions. The characterization parameter η proposed in this invention... min This is based on the stress within the near-crack tip plastic zone. Therefore, regardless of whether the stress field in the near-crack tip plastic zone is dominated by J (corresponding to the large-scale yield condition) or by K and T (corresponding to the small-scale yield condition), η min Both can describe the crack tip constraint and can characterize the degree of crack tip constraint in a region near the crack tip, with a larger characterization range and more objective and accurate results.

[0055] Specifically, step S1 uses a boundary layer model to model the crack tip field, including:

[0056] S11. Calculate the size of the crack tip plastic zone based on the Dugdale model;

[0057] Specifically, the dimensions of the crack tip plastic zone are calculated using the following formula:

[0058] r p =π(K / σ0) 2 / 24 (1)

[0059] Where, r p σ represents the size of the plastic zone, K represents the stress intensity factor, and σ0 represents the yield strength of the material.

[0060] S12. The boundary layer model is a circular region surrounding the crack tip with the crack tip as the center and a radius of N times the size of the plastic zone; wherein the crack tip is approximated by a circular arc.

[0061] Specifically, the boundary layer model is a circular region surrounding the crack tip.

[0062] The crack tip plastic zone size r was calculated based on the Dugdale model. p Subsequently, to ensure that the entire crack tip plastic zone lies within the model boundary, the radius of the boundary layer model is set to the plastic zone size r. p It is N times that of the given value. In practice, N can be 10.

[0063] In practice, when the crack tip field is symmetrical about the crack line, a semi-model can be established to analyze the crack tip field, such as... Figure 3 As shown in the established boundary layer model, the crack tip is approximated by a circular arc segment. To eliminate the influence of the crack tip radius on the crack tip stress field, the radius of the crack tip arc should be sufficiently small. In practice, the crack tip arc radius ρ can be taken as r. p / 1000.

[0064] In the established boundary layer model, a coordinate system is established with the center of the crack tip arc as the origin and the horizontal and vertical directions as the x and y axes, respectively.

[0065] Specifically, in step S1, the following displacement boundary conditions are applied to the outer circular boundary of the boundary layer model:

[0066]

[0067]

[0068] Where u(r,θ) is the displacement in the x-direction, v(r,θ) is the displacement in the y-direction, r represents the distance from the outer boundary node to the crack tip, θ represents the angle between the line connecting the outer boundary node and the crack tip and the x-axis, υ represents Poisson's ratio, E represents the elastic modulus, K represents the stress intensity factor, and T represents the T stress.

[0069] Currently, displacement boundary conditions typically employ the following formula:

[0070]

[0071]

[0072] In the theory of linear elastic fracture mechanics, for a type I crack under plane strain conditions, when T = 0, In the formula, G is the shear modulus, G = E / 2(1+υ). Clearly, the above displacement expression is inconsistent with the theory of linear elastic fracture mechanics.

[0073] Therefore, in this embodiment of the invention, the following displacement boundary conditions are applied to the outer circular boundary of the boundary layer model:

[0074]

[0075]

[0076] In practice, for the established semi-model, symmetrical displacement boundary conditions are applied to the ligament line of the model. In fracture mechanics, if the crack length is *a* and the width of the crack-containing section of the specimen (i.e., the research object) is *W*, then the ligament length is *Wa*, which is the unbroken length. The ligament line is the unbroken portion along the crack propagation direction. For example, when the ligament line is perpendicular to the y-axis, the symmetrical displacement condition can be expressed as: y-displacement = 0, rotation angle = 0. The rotation angle is in the same direction as θ. Figure 3 The ligament line in the diagram is the positive x-axis line.

[0077] In practice, K in equations (2a) and (2b) takes a value greater than 0. To ensure convergence of the analysis at every T value, the value of K does not exceed [a certain value]. l = 1 mm. In practice, T is taken as 0, -0.2σ0, -0.4σ0, -0.6σ0, -0.8σ0 and -1σ0.

[0078] Specifically, in step S2, the finite element method is used to perform elastoplastic analysis on the boundary layer model to obtain the crack tip stress field under different T stresses, including:

[0079] A finite element model of the boundary layer model is established, and an elastoplastic analysis is performed on the finite element model based on the material's elastoplastic constitutive relation to calculate the crack tip stress field under different T stresses.

[0080] During implementation, a finite element model can be built in Abaqus to perform elastoplastic analysis of the crack tip field.

[0081] In practice, when performing elastoplastic analysis on the crack tip field, the Ramberg-Osgood equation can be used to describe the elastoplastic constitutive relationship of the material:

[0082]

[0083] In the formula: ε0=σ0 / E, σ0 represents the yield strength, E represents the elastic modulus, α represents the dimensionless material constant, and n represents the strain hardening exponent. σ represents stress, and ε represents strain.

[0084] During implementation,

[0085] The Abaqus analysis workflow is as follows:

[0086] (a) Abaqus calculation of load increment ΔP i Increment of the test stress field When i = 0, the load increment ΔP i The stiffness matrix is ​​specified by the user and is the stiffness matrix corresponding to the linear elastic constitutive relation of the isotropic material. When i > 0, the load increment is automatically determined by Abaqus, and the stiffness matrix is ​​the stiffness matrix calculated in the previous step.

[0087] (b) Calculation of test stress

[0088] (c) Calculate the yield function under the test stress state. In the formula I is the identity matrix, σ s (ε pe ) represents the material under equivalent plastic strain The yield stress below.

[0089] (d) Determine whether yielding has occurred; if f≤0, the material point has yielded; if f>0, the material point has not yielded.

[0090] (e) If yielding does not occur, re-stress. Turn (h); if yielding occurs, calculate the equivalent plastic strain increment Δε using Newton's iteration method. pe ;

[0091] (f) Calculate the stress increment Δσ and stiffness matrix

[0092] (g) Update stress and equivalent plastic strain: σ i+1 =σ i +Δσ,

[0093] (h) Repeat (a) through (g) until the sum of the load increments is reached. The external load value P is reached.

[0094] It should be noted that when the sum of the load increments is reached... The analysis ends when the external load value P is reached.

[0095] After the analysis, in step S3, the normal stress perpendicular to the crack line at each node on the ligament line under different T stresses is extracted; the ratio η of the normal stress perpendicular to the crack line under negative T stress to the normal stress perpendicular to the crack line under zero T stress is calculated, and the minimum value η in the plastic zone is determined. min The characterization parameter is used as the crack tip constraint; based on the characterization parameter, the crack tip stress constraint of the power-hardening material is characterized, including:

[0096] S31. Extract the normal stress perpendicular to the crack line at each node on the ligament line under different T stresses;

[0097] Specifically, the normal stress perpendicular to the crack line at each node along the ligament is extracted, and the normal stress perpendicular to the crack line at each node along the ligament is obtained, resulting in (r,σ) yyThe dataset contains the extracted normal stresses, which are the normal stresses at the end of the elastoplastic analysis.

[0098] Where r represents the distance from the node to the crack tip, σ yy This represents the normal stress perpendicular to the crack line.

[0099] The distance from the node to the crack tip is the distance from the node to the center of the arc at the crack tip.

[0100] Specifically, normal stress σ yy That is, the stress component perpendicular to the crack line direction. Because σ yy The crack tip constraint is closely related to physical parameters characterizing the stress field strength at the crack tip, such as K and J. yy The effect is significant, especially under weak constraints, σ yy A significant decrease will occur, therefore, based on σ yy Calculate the characterization parameters.

[0101] S32. For each node, calculate the ratio η of the normal stress perpendicular to the crack line under negative T stress to the normal stress perpendicular to the crack line under zero T stress, and obtain... Dataset;

[0102] Specifically, Where J represents the J-integral, Let r be a dimensionless value, where r represents the distance from the node to the crack tip, and σ0 represents the yield strength.

[0103] During implementation, under small-scale yielding conditions, J = K 2 / E', under plane stress, E'=E; under plane strain, E'=E / (1-υ 2 Under wide-range yielding conditions, J = K 2 / E'+λ p U p / BL, where λ p U represents a dimensionless function relating to the geometry of the cracked body. p The area under the plastic segment of the load-crack opening displacement (CMOD) curve is represented by B, the thickness of the crack body is represented by B, and the ligament length is represented by L.

[0104] Specifically, σ0 is used to make the stress T dimensionless, and... T represents the dimensionless stress.

[0105] Specifically, calculate the ratio of the normal stress perpendicular to the crack line under negative T stress to the normal stress perpendicular to the crack line under zero T stress. That is, for each node, calculate the ratio of the normal stress under negative T stress to the normal stress under zero T stress. For example, for a certain node, calculate the ratio of the normal stress at T = -0.2σ0 to the normal stress at T = 0.

[0106] S33. Based on the distance from the node to the crack tip, determine the minimum value of the ratio η within the plastic zone, and establish the minimum value η. min and Relationship;

[0107] During implementation, since the crack tip field of interest is located within the plastic region, the dimensionless size of the plastic region is r. p σ0 / J, while when At that time, σ yy It will be affected by crack tip blunting; therefore, the range of the plastic zone can be set to... For the stress results at each node within this range, determine the minimum value of η and establish η. min and The relationship between stress values. That is, for each stress T, in By determining the minimum value of η, we can obtain η corresponding to different stresses T. min .

[0108] Specifically, adopt Fitting Data, establishing the minimum value of η within the plastic region and The relationship, among which, T represents the dimensionless stress, and C0, C1, and b represent undetermined coefficients.

[0109] Thus, a calculation expression for crack tip constraint was established for a given material, namely a given power-hardening material.

[0110] Get η min After establishing the relationship with T, η can be used. min Characterizes the crack tip field under negative T stress.

[0111] Specifically, since when the stress T is 0, the distance from the crack tip is 0.2r p ~0.25r p The normal stress perpendicular to the crack line within the range can be described by the HRR formula, i.e. In the formula: ε0=σ0 / E, E is the elastic modulus; I n It is a function of the material hardening index, a dimensionless stress function. It is a function of the material hardening index and stress state. The minimum value σ is used. yy,min To approximate the σ within the dominant range of the HRR field yy σ within the HRR field dominance range yy It can be approximated by the following formula:

[0112]

[0113] Since the fracture toughness of a material is related to the degree of constraint at the crack tip, the lower the degree of constraint, the higher the fracture toughness test value. η min It can be used to unify the test results of fracture toughness under different constraints and establish the relationship between fracture toughness and crack tip constraint. c =f(η min ).

[0114] In practice, the test material can be subjected to different η values ​​without crack tip restraint. min The fracture toughness at the value is obtained (J) c η min ) dataset, where J c This represents fracture toughness. By selecting an appropriate function to fit the dataset, the relationship between the material's fracture toughness and the crack tip constraint can be obtained. Based on this relationship, fracture toughness prediction can be performed under different crack tip constraint conditions.

[0115] Example 2

[0116] One embodiment of the present invention discloses a crack tip stress constraint characterization system for power-hardening materials, such as... Figure 9 As shown, it includes:

[0117] The model building module is used to create a boundary layer model for the crack tip; and to apply displacement boundary conditions on the outer circular boundary of the boundary layer model.

[0118] The elastoplastic analysis module is used to perform elastoplastic analysis on the boundary layer model using the finite element method to obtain the crack tip stress field under different T stresses;

[0119] The constraint characterization module is used to extract the normal stress perpendicular to the crack line at each node along the ligament line under different T-stresses; calculate the ratio η of the normal stress perpendicular to the crack line under negative T-stress to that under zero T-stress, and determine the minimum value η within the plastic zone. min The crack tip constraint is characterized as a parameter for crack tip restraint; the crack tip stress constraint of the power-hardening material is characterized based on the parameter.

[0120] The above-described method and system embodiments are based on the same principles, and their related aspects can be referenced from each other to achieve the same technical effects. For specific implementation processes, please refer to the foregoing embodiments, which will not be repeated here.

[0121] Example 3

[0122] Taking the following material parameters as an example, the implementation process and effect of the crack tip stress constraint characterization method of the power hardening material of the present invention are explained.

[0123] The parameters of the power-hardening material are: elastic modulus E = 206896 MPa, Poisson's ratio υ = 0.3, yield strength σ0 = 413.8 MPa, coefficient α = 3 / 7, hardening exponent n = 3, and K is taken as 0.3. Right now

[0124] T is taken as 0, -0.2σ0, -0.4σ0, -0.6σ0, -0.8σ0 and -σ0, which are 0, -82.76MPa, -165.52MPa, -248.28MPa, -331.04MPa and -413.8MPa respectively.

[0125] First, according to the formula r p =π(K / σ0) 2 / 24 Calculate the dimensions of the plastic zone. Take 10r. p The radius of the boundary layer model.

[0126] A finite element model of the corresponding boundary layer model is established in Abaqus. The deformationplasticity model in Abaqus corresponds to the Ramberg-Osgood equations; therefore, the deformationplasticity model is used to describe the material constitutive model. The mesh is generated using the quadratic plane strain element CPE8R. An example finite element model is shown below. Figure 4 As shown.

[0127] Displacement boundary conditions described by equations (2a) and (2b) are applied to the outer circular boundary, and symmetric displacement conditions are applied to the ligament line. Elastoplastic analysis is performed in Abaqus to calculate the crack field under six KT combinations. The normal stress σ perpendicular to the crack line is obtained. yy , use σ0 to represent σ yy Dimensionless, σ yy / σ0 as Figure 5 As shown.

[0128] Calculate the ratio η of the normal stress perpendicular to the crack line under negative T stress to the normal stress perpendicular to the crack line under zero T stress, and obtain... Dataset, will Data plotted Figure 6 .

[0129] In comparison, under the same material parameters Data plotted Figure 7 .contrast Figure 6 and Figure 7 It can be observed that: when When η changes by no more than 5% in the range [3.36, 60], η minIt can describe the constraint situation over a relatively large area at the crack tip. However, Q varies considerably over the same range, especially under high negative T stress. In this case, Q can only reflect the constraint situation at a single point and cannot reflect the constraint situation over a large area.

[0130] extract Minimum value of η within the range min ,get Dataset, using functional programming Fitting Figure 8 From the data, we obtain C0 = 1.357 and C1 = -0.356. Therefore, η min and The relationship can be used describe.

[0131] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0132] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for characterizing crack tip stress constraint in power-hardening materials, characterized in that, Includes the following steps: Establish a boundary layer model for the crack tip; apply displacement boundary conditions to the outer circular boundary of the boundary layer model; The finite element method was used to perform elastoplastic analysis on the boundary layer model, and different results were obtained. T Stress field at the crack tip under stress; Extract different T Normal stress perpendicular to the crack line at each node along the ligament line under stress; Calculate negative T Normal stress perpendicular to the crack line under stress and zero T The ratio of the normal stress perpendicular to the crack line under stress Determine the plastic region minimum value As a characterization parameter of crack tip constraint; The crack tip stress constraint of the power-hardening material is characterized based on the aforementioned characterization parameters, including: Extract different T Normal stress perpendicular to the crack line at each node along the ligament line under stress; For each node, calculate the negative T Normal stress perpendicular to the crack line under stress and zero T The ratio of the normal stress perpendicular to the crack line under stress ,get Dataset; The ratio is determined within the plastic zone based on the distance from the node to the crack tip. The minimum value, establish minimum value and Relationship, in, Represents dimensionless , This represents the distance from the node to the crack tip. Represents dimensionless T stress; Establish and T The relationship between stress values ​​includes: use Establishing the plastic zone The minimum value and The relationship, among which, Represents dimensionless T stress, , and This represents the coefficients to be determined.

2. The method for characterizing crack tip stress constraint in power-hardening materials according to claim 1, characterized in that, The establishment of the boundary layer model includes: The dimensions of the crack tip plastic zone were calculated based on the Dugdale model. The boundary layer model is a circular region surrounding the crack tip with a radius of N times the size of the plastic zone, centered on the crack tip; wherein the crack tip is approximated by a circular arc.

3. The method for characterizing crack tip stress constraint in power-hardening materials according to claim 2, characterized in that, The dimensions of the crack tip plastic zone are calculated using the following formula based on the Dugdale model: in, Indicates the size of the plastic zone. Indicates the stress intensity factor. This indicates the yield strength of the material.

4. The method for characterizing crack tip stress constraint in power-hardening materials according to claim 1, characterized in that, Apply the following displacement boundary conditions to the outer circular boundary of the boundary layer model: in, for x Displacement in direction, for y Displacement in direction, This represents the distance from the outer circle boundary node to the crack tip. The line connecting the outer circle boundary node and the crack tip is... x The included angle of the axis, Represents Poisson's ratio. Indicates the elastic modulus. Indicates the stress intensity factor. express T stress.

5. The method for characterizing crack tip stress constraint in power-hardening materials according to claim 1, characterized in that, The finite element method was used to perform elastoplastic analysis on the boundary layer model, and different results were obtained. T The stress field at the crack tip under stress includes: A finite element model of the boundary layer model is established, and an elastoplastic analysis is performed on the finite element model based on the material's elastoplastic constitutive relation to calculate different... T Stress field at the crack tip under stress.

6. The method for characterizing crack tip stress constraint in power-hardening materials according to claim 5, characterized in that, The elastic-plastic constitutive relation of the material is: in, , Indicates yield strength. Indicates the elastic modulus. α Represents a dimensionless material constant. n Indicates the strain hardening index. Indicates stress, Indicates strain.

7. The method for characterizing crack tip stress constraint in power-hardening materials according to claim 1, characterized in that, ,in, express J integral, This indicates the yield strength of the material.

8. A crack tip stress constraint characterization system for power-hardening materials, characterized in that, Includes the following modules: The model building module is used to create a boundary layer model for the crack tip; and to apply displacement boundary conditions on the outer circular boundary of the boundary layer model. The elastoplastic analysis module is used to perform elastoplastic analysis on the boundary layer model using the finite element method to obtain different... T Stress field at the crack tip under stress; The constraint representation module is used to extract different T Normal stress perpendicular to the crack line at each node along the ligament line under stress; Calculate negative T Normal stress perpendicular to the crack line under stress and zero T The ratio of the normal stress perpendicular to the crack line under stress Determine the plastic region minimum value As a characterization parameter of crack tip constraint; The crack tip stress constraint of the power-hardening material is characterized based on the aforementioned characterization parameters, including: Extract different T Normal stress perpendicular to the crack line at each node along the ligament line under stress; For each node, calculate the negative T Normal stress perpendicular to the crack line under stress and zero T The ratio of the normal stress perpendicular to the crack line under stress ,get Dataset; The ratio is determined within the plastic zone based on the distance from the node to the crack tip. The minimum value, establish minimum value and Relationship, in, Represents dimensionless , This represents the distance from the node to the crack tip. Represents dimensionless T stress; Establish and T The relationship between stress values ​​includes: use Establishing the plastic zone The minimum value and The relationship, among which, Represents dimensionless T stress, , and This represents the coefficients to be determined.

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