Methods, apparatus, products, and electronic devices that describe yielding behavior

Abstract

The application provides a method, device, product and electronic equipment for describing yield behavior, relates to the technical field of metal material mechanical property characterization, and can construct an original isotropic yield criterion based on stress invariants, the isotropic yield criterion comprises a first parameter and a second parameter for adjusting the symmetry of a third invariant of a deviatoric stress tensor and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor, and then the corresponding relationship between the first parameter and the second parameter and the value range of the third parameter can be determined through a Hessian matrix and a yield surface curvature algorithm, the isotropic yield criterion after the parameters are determined is transformed into an anisotropic yield criterion, the strength difference effect and the anisotropic behavior can be predicted, and thus the yield behavior of the metal material under a complex stress state can be characterized with high precision when the metal material is applied to a multi-load working condition and a complex stress state.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of mechanical property characterization of metal materials, in particular to a method for describing yield behavior, an apparatus for describing yield behavior, a computer program product and an electronic device. BACKGROUND

[0002] Metal materials are widely used in aerospace, shipbuilding, automobile, construction and other fields due to their mechanical properties. Generally, metal materials can be classified according to crystal structure: face-centered cubic (FCC), body-centered cubic (BCC) and hexagonal close-packed (HCP).

[0003] The plastic properties of metal materials are usually affected by load conditions (such as loading direction, stress state, etc.), which leads to complex yield behavior of metal materials (such as SD effect, anisotropy, etc.)

[0004] In order to obtain accurate results, it is necessary to accurately describe the yield behavior of metal materials. In related technologies, the way to describe the yield behavior of metal materials is to use yield criteria (such as Von Mises, Tresca, etc.), which can be used to describe the isotropic behavior of metal materials, but cannot predict the strength difference effect and anisotropic behavior of metal materials.

[0005] Based on this, when metal materials are applied to processes with multiple load conditions and complex stress states (such as sheet metal forming process, typical joint service process of aircraft, etc.), related technologies cannot accurately characterize the yield behavior of metal materials under complex stress states. Therefore, how to accurately predict the strength difference effect and anisotropic behavior of metal materials has become a problem to be solved.

[0006] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present application, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0007] The purpose of the present application is to provide a method for describing yield behavior, a device for describing yield behavior, a computer readable storage medium and an electronic device, which can construct an original isotropic yield criterion based on stress invariants, the isotropic yield criterion including a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor, and then the isotropic yield criterion after determining the parameters can be transformed into an anisotropic yield criterion by rating the corresponding relationship between the first parameter and the second parameter and the value range of the third parameter through the Hessian matrix and the yield surface curvature algorithm, so as to predict the material strength difference effect and anisotropic behavior, which can high-precision characterize the yield behavior of the metal material under complex stress state when the metal material is applied to multiple load working conditions and complex stress states.

[0008] Other characteristics and advantages of the present application will become apparent from the following detailed description, or will be learned by practice of the present application.

[0009] According to an aspect of the present application, a method for describing yield behavior is provided, the method comprising:

[0010] constructing an isotropic yield criterion based on stress invariants; wherein the isotropic yield criterion includes a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor;

[0011] determining the corresponding relationship between the first parameter and the second parameter and the value range of the third parameter based on the Hessian matrix and the yield surface curvature algorithm, and applying the corresponding relationship and the value range to the isotropic yield criterion;

[0012] transforming the isotropic yield criterion into an anisotropic yield criterion based on the generalized stress invariants corresponding to the stress tensor;

[0013] predicting the material strength difference effect and anisotropic behavior based on the anisotropic yield criterion.

[0014] In an exemplary embodiment of the present application, it further comprises:

[0015] generating first yield point data of face-centered cubic, second yield point data of body-centered cubic and third yield point data of hexagonal close-packed based on the viscoplastic self-consistent polycrystal plasticity model;

[0016] generating first data curve of face-centered cubic, second data curve of body-centered cubic and third data curve of hexagonal close-packed based on the isotropic yield criterion;

[0017] Determine the accuracy of the isotropic yield criterion based on the coincidence degree of the first yield point data and the first data curve, the coincidence degree of the second yield point data and the second data curve, and the coincidence degree of the third yield point data and the third data curve.

[0018] In an exemplary embodiment of the present application, further comprising:

[0019] According to a numerical simulation model based on the theory of crystal plasticity, generate fourth yield point data of the zirconium bell rolling plate in-plane compression process under different pre-strains and fifth yield point data of the zirconium bell rolling plate thickness compression process under different pre-strains;

[0020] Generate fourth data curves of the zirconium bell rolling plate in-plane compression process under different pre-strains and fifth data curves of the zirconium bell rolling plate thickness compression process under different pre-strains based on the anisotropic yield criterion;

[0021] Determine the accuracy of the anisotropic yield criterion based on the coincidence degree of the fourth yield point data and the fourth data curve, and the coincidence degree of the fifth yield point data and the fifth data curve.

[0022] In an exemplary embodiment of the present application, further comprising:

[0023] Stress components representing the anisotropic yield criterion in uniaxial tensile test, uniaxial compression test, equal biaxial tensile test, and equal biaxial compression test;

[0024] A stress state yield stress model based on the anisotropic yield criterion and the stress components; wherein the uniaxial tensile yield stress model is used to represent the relationship between the anisotropic yield criterion and the sampling angle.

[0025] In an exemplary embodiment of the present application, further comprising:

[0026] Generate a plastic strain ratio coefficient of the anisotropic yield criterion;

[0027] Verify the accuracy of the anisotropic yield criterion based on the plastic strain ratio coefficient.

[0028] In an exemplary embodiment of the present application, further comprising:

[0029] Based on the plastic strain ratio coefficient and the anisotropic yield criterion, construct an error function of the prediction result and the test result;

[0030] Minimize the value of the error function based on the down simplex method to identify the anisotropic material constant in the anisotropic yield criterion.

[0031] In an exemplary embodiment of the present application, the isotropic yield criterion is represented as:

[0032]

[0033] wherein, I1 is the first invariant of stress tensor, J2 is the second invariant of deviatoric stress tensor, J3 is the third invariant of deviatoric stress tensor, σ1, σ2, σ3 represent three principal stresses respectively, S1, S2, S3 represent three principal deviatoric stresses respectively; σ Y is the yield stress obtained by uniaxial tension, a and n are the first and second parameters for adjusting the symmetry of J3, b is the third parameter for adjusting the asymmetry of J3, μ is a parameter for adjusting the sensitivity of hydrostatic pressure, k is derived based on the uniaxial condition, and the uniaxial condition is represented as:

[0034] According to an aspect of the present application, an apparatus for describing yield behavior is provided, comprising:

[0035] The isotropic yield criterion construction unit is configured to construct an isotropic yield criterion based on stress invariants; wherein the isotropic yield criterion comprises a first parameter and a second parameter for adjusting the symmetry of the third invariant of deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of deviatoric stress tensor;

[0036] The parameter determination unit is configured to determine a corresponding relationship between the first parameter and the second parameter and a value range of the third parameter based on a Hessian matrix and a yield surface curvature algorithm, and apply the corresponding relationship and the value range to the isotropic yield criterion;

[0037] The anisotropic yield criterion determination unit is configured to transform the isotropic yield criterion into an anisotropic yield criterion based on generalized stress invariants corresponding to the stress tensor;

[0038] The prediction unit is configured to predict material strength difference effects and anisotropic behavior based on the anisotropic yield criterion.

[0039] In an exemplary embodiment of the present application, further comprising:

[0040] The yield point data determination unit is configured to generate first yield point data of face-centered cubic, second yield point data of body-centered cubic, and third yield point data of hexagonal close-packed according to a viscoplastic self-consistent polycrystal plasticity model;

[0041] The data curve determination unit is configured to generate a first data curve of face-centered cubic, a second data curve of body-centered cubic, and a third data curve of hexagonal close-packed based on the isotropic yield criterion;

[0042] The precision determination unit is configured to determine the precision of the isotropic yield criterion based on the coincidence degree of the first yield point data and the first data curve, the coincidence degree of the second yield point data and the second data curve, and the coincidence degree of the third yield point data and the third data curve.

[0043] In an example embodiment of the present application, wherein:

[0044] The yield point data determination unit is further configured to generate, according to a numerical simulation model based on a crystal plasticity theory, fourth yield point data of the zirconium clock rolling plate in-plane compression process under different pre-strains and fifth yield point data of the zirconium clock rolling plate thickness compression process under different pre-strains.

[0045] The data curve determination unit is further configured to generate, based on the anisotropic yield criterion, fourth data curves of the zirconium clock rolling plate in-plane compression process under different pre-strains and fifth data curves of the zirconium clock rolling plate thickness compression process under different pre-strains.

[0046] The precision determination unit is further configured to determine the precision of the anisotropic yield criterion based on the coincidence degree of the fourth yield point data and the fourth data curves and the coincidence degree of the fifth yield point data and the fifth data curves.

[0047] In an example embodiment of the present application, further comprising:

[0048] The stress component determination unit is configured to represent stress components of the anisotropic yield criterion in the uniaxial tensile test, the uniaxial compression test, the equal biaxial tensile test, and the equal biaxial compression test.

[0049] The uniaxial tensile yield stress model determination unit is configured to determine, based on the anisotropic yield criterion and the stress components, a yield stress model of each stress state; wherein the uniaxial tensile yield stress model is used to represent the relationship between the anisotropic yield criterion and the sampling angle.

[0050] In an example embodiment of the present application, further comprising:

[0051] The plastic strain ratio coefficient generation unit is configured to generate a plastic strain ratio coefficient of the anisotropic yield criterion.

[0052] The accuracy verification unit is configured to verify the accuracy of the anisotropic yield criterion based on the plastic strain ratio coefficient.

[0053] In an example embodiment of the present application, further comprising:

[0054] The error function determination unit is configured to construct, based on the plastic strain ratio coefficient and the anisotropic yield criterion, an error function of the prediction result and the test result.

[0055] The constant identification unit is configured to minimize the value of the error function based on a down simplex method to identify anisotropic material constants in the anisotropic yield criterion.

[0056] In an example embodiment of the present application, the isotropic yield criterion is represented as:

[0057]

[0058] wherein I1 is the first invariant of stress tensor, J2 is the second invariant of deviatoric stress tensor, J3 is the third invariant of deviatoric stress tensor, σ1, σ2, σ3 represent three principal stresses respectively, S1, S2, S3 represent three principal deviatoric stresses respectively; σ Y is the yield stress obtained by uniaxial tension, a and n are the first and second parameters for adjusting the symmetry of J3, b is the third parameter for adjusting the asymmetry of J3, μ is a parameter for adjusting the sensitivity of hydrostatic pressure, k is derived based on the uniaxial condition, and the uniaxial condition is represented as:

[0059] According to an aspect of the present application, a computer program product is provided, comprising a computer program, the computer program being executed by a processor to implement the method of any one of the above.

[0060] According to an aspect of the present application, an electronic device is provided, comprising: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to execute the method of any one of the above via execution of the executable instructions.

[0061] The exemplary embodiments of the present application can have the following partial or all beneficial effects:

[0062] In the method for describing yield behavior provided in an example embodiment of the present application, an original isotropic yield criterion can be constructed based on stress invariants, the isotropic yield criterion comprising a first parameter and a second parameter for adjusting the symmetry of the third invariant of deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of deviatoric stress tensor, and then the isotropic yield criterion after determining the parameters can be transformed into an anisotropic yield criterion by rating the corresponding relationship between the first parameter and the second parameter and the value range of the third parameter through a Hessian matrix and a yield surface curvature algorithm, so as to predict the material strength difference effect and anisotropic behavior, which can characterize the yield behavior of the metal material under complex stress state with high precision when the metal material is applied to a multi-load working condition and a complex stress state.

[0063] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present application. BRIEF DESCRIPTION OF DRAWINGS

[0064] The accompanying drawings, which are incorporated into and form part of the specification, illustrate an embodiment consistent with the present application and, together with the specification, serve to explain the principles of the application. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0065] Figure 1 A flowchart of a method of describing yield behavior is schematically illustrated according to an embodiment of the present application;

[0066] Figure 2 A correspondence between a first parameter and a second parameter is schematically illustrated according to an embodiment of the present application;

[0067] Figure 3 A relationship between a parameter μ and a yield criterion shape is schematically illustrated according to an embodiment of the present application;

[0068] Figure 4 A relationship between a third parameter b and a yield criterion shape is schematically illustrated according to an embodiment of the present application;

[0069] Figure 5 A relationship between a first parameter a and a yield criterion shape is schematically illustrated according to an embodiment of the present application;

[0070] Figure 6 A predicted result based on a viscoplastic self-consistent polycrystal plasticity model and an isotropic yield criterion is schematically illustrated according to an embodiment of the present application;

[0071] Figure 7 A fourth yield point data of a zirconium clock rolling plate under in-plane compression at different pre-strains is schematically illustrated according to an embodiment of the present application;

[0072] Figure 8 A fifth yield point data of a zirconium clock rolling plate thickness under compression at different pre-strains is schematically illustrated according to an embodiment of the present application;

[0073] Figure 9 A predicted result of an anisotropic yield criterion for different direction angle tensile yield stresses of AA2008-T4 aluminum alloy is schematically illustrated according to an embodiment of the present application;

[0074] Figure 10 A predicted result of an anisotropic yield criterion for different direction angle compressive yield stresses of AA2008-T4 aluminum alloy is schematically illustrated according to an embodiment of the present application;

[0075] Figure 11 A predicted result of an anisotropic yield criterion for different direction angle Lankford coefficients of AA2008-T4 aluminum alloy is schematically illustrated according to an embodiment of the present application;

[0076] Figure 12A diagram schematically illustrates a prediction of a yield surface of AA2008-T4 aluminum alloy by an anisotropic yield criterion according to an embodiment of the present application;

[0077] Figure 13 A block diagram schematically illustrates a structure of an apparatus for describing a yield behavior according to an embodiment of the present application;

[0078] Figure 14 A block diagram schematically illustrates a structure of a computer system of an electronic device suitable for implementing an embodiment of the present application. DETAILED DESCRIPTION

[0079] Example implementations will now be described more fully with reference to the accompanying drawings. Example implementations can be implemented in any

[0080] In addition, the drawings are merely schematic and are not drawn to scale. Like reference numerals are used to denote like parts throughout the drawings. Aspects and implementations can be modified, but need not be modified, in ways known to those skilled in the art. Accordingly, the drawings are intended to be illustrative, but not restrictive. Unless otherwise specified, like reference numerals denote like parts throughout the specification and figures.

[0081] Reference will now be made to the drawings, wherein: Figure 1 , Figure 1 A flowchart schematically illustrates a method for describing a yield behavior according to an embodiment of the present application. As shown in Figure 1 the method for describing a yield behavior can include steps S110-S140.

[0082] Step S110: constructing an isotropic yield criterion based on stress invariants; wherein the isotropic yield criterion includes a first parameter and a second parameter for adjusting symmetry of a third invariant of a deviatoric stress tensor, and a third parameter for adjusting asymmetry of the third invariant of the deviatoric stress tensor.

[0083] Step S120: determining the correspondence between the first parameter and the second parameter and the value range of the third parameter based on the Hessian matrix and the yield surface curvature algorithm, and applying the correspondence and the value range to the isotropic yield criterion.

[0084] Step S130: transforming the isotropic yield criterion into an anisotropic yield criterion based on the generalized stress invariants on the stress tensor.

[0085] Step S140: predicting the material strength difference effect and anisotropic behavior based on the anisotropic yield criterion.

[0086] Implementation Figure 1 The method shown can construct an original isotropic yield criterion based on stress invariants, the isotropic yield criterion including a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor, and then the correspondence between the first parameter and the second parameter and the value range of the third parameter can be determined by the Hessian matrix and the yield surface curvature algorithm, and the isotropic yield criterion after determining the parameters can be transformed into an anisotropic yield criterion to predict the material strength difference effect and anisotropic behavior, so that the yield behavior of the metal material under complex stress state can be characterized with high precision when the metal material is applied to multiple load conditions and complex stress states.

[0087] Next, the above steps of the present example embodiment are described in more detail.

[0088] In step S110, an isotropic yield criterion is constructed based on stress invariants; wherein the isotropic yield criterion includes a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor.

[0089] Wherein, the yield criterion refers to that under certain deformation conditions (such as deformation temperature, deformation speed, etc.), only when a certain relationship between stress components is met, the particle begins to enter the plastic state, and this relationship is the yield criterion. The yield criterion is usually expressed as a yield surface or a yield position, which is a hypothesis about the elastic limit under any stress combination.

[0090] The isotropy refers to the characteristic that physical, chemical and other properties of an object do not change with different directions, that is, the performance values measured in different directions of a certain object are completely the same, also known as homogeneity. The physical property does not change with the direction of measurement. That is, the performance measured in different directions of the object shows the same numerical value. The isotropic yield criterion can be applied to the isotropic scene. However, when the metal is subjected to large plastic deformation, the grain size and orientation change in the deformation direction. Thus, the plastic yield behavior of the material shows direction dependence. In this case, the anisotropic yield criterion is suitable.

[0091] The stress invariant can be expressed as I1-J2-J3, and specifically, the yield criterion can be established based on the I1-J2-J3 stress invariant architecture:

[0092] I1 is the first invariant of the stress tensor, J2 is the second invariant of the deviatoric stress tensor, and J3 is the third invariant of the deviatoric stress tensor; I1 = σ1 + σ2 + σ3, J3 = S1S2S3; where σ1, σ2, σ3 represent three principal stresses, and S1, S2, S3 represent three principal deviatoric stresses.

[0093] where σ Y is the yield stress obtained by uniaxial tension, a and n are parameters for adjusting the symmetry of J3, b is a parameter for adjusting the asymmetry of J3, and μ is a parameter for adjusting the sensitivity of hydrostatic pressure. In addition, k is derived based on the uniaxial condition, which is expressed as: It can be seen that the isotropic form of the yield criterion proposed in the present application considers the hydrostatic pressure sensitivity and introduces the asymmetry of the third invariant of the deviatoric stress tensor to simulate the strength differential (SD) effect of pressure-insensitive materials

[0094] In step S120, the correspondence between the first parameter and the second parameter and the value range of the third parameter are determined based on the Hessian matrix and the yield surface curvature algorithm, and the correspondence and the value range are applied to the isotropic yield criterion.

[0095] Specifically, the Hessian matrix, also known as the Hessian matrix, the Hessian matrix, the Hessian matrix, etc., is a square matrix composed of second-order partial derivatives of a multivariate function, which describes the local curvature of the function, and is commonly used in Newton's method to solve optimization problems. The extreme value problem of a multivariate function can be determined using the Hessian matrix. In the optimization design of practical engineering problems, the objective function listed is often very complex. In order to simplify the problem, the objective function is often expanded into a Taylor polynomial in the neighborhood of a certain point to approximate the original function. At this time, the Hessian matrix will be involved in the matrix form of the Taylor expansion of the function at a certain point.

[0096] Specifically, convexity conditions of the isotropic yield criterion can be derived based on the Hessian matrix and the yield surface curvature algorithm, the convexity conditions include a corresponding relationship between the first parameter and the second parameter and a value range of the third parameter. When the isotropic yield surface satisfies the convexity conditions, the corresponding relationship between the first parameter and the second parameter can be expressed as Figure 2 , and Figure 2 In the formula, the second parameter n is expressed as an exponential factor n, and the value range can be expressed as:

[0097] In order to ensure the uniqueness of the solution in numerical simulation, the yield criterion should have convexity, and the process of deriving the convexity condition of the yield criterion is as follows:

[0098] In the formula, the parameter μ in the expression of the yield criterion disclosed in the application does not affect the convexity of the yield criterion, and the relationship between the parameter μ and the shape of the yield criterion can be referred to Figure 3 In addition, the relationship between the third parameter b and the shape of the yield criterion can be referred to Figure 4 , and the relationship between the first parameter a and the shape of the yield criterion can be referred to Figure 5 .

[0099] When b = 0, the isotropic yield function of the even function can be obtained: It can be seen that if the two-dimensional cross section is expressed as convex in the π plane, the three-dimensional yield surface satisfies convexity. The π plane can be expressed by the polar coordinate system, in which the effective stress is the radial coordinate, and the circumferential coordinate is the stress Lode angle (Lode angle) θ, which can be expressed as: In the formula, the stress Lode angle is a variable for expressing the deviatoric stress component in the π plane.

[0100] In addition, the curvature of the yield criterion is expressed as:

[0101] When is established, the convexity requirement of the yield criterion is satisfied.

[0102] Since the yield criterion is an even function, the yield conditions between uniaxial tension and uniaxial compression are the same. Therefore, when the π plane satisfies convexity in the stress state range , the yield criterion is convex.

[0103] When a = 0, the isotropic yield criterion containing the third invariant of the stress deviator tensor can be obtained: Further, the convexity condition can be calculated based on the Hessian matrix, and the Hessian matrix is expressed as In H, each In order to ensure the convexity of Lambda, the Hessian matrix H of Lambda is a semi-positive definite matrix.

[0104] The derivation process that the Hessian matrix is a semi-positive definite matrix lies in:

[0105]

[0106]

[0107] Wherein, O ij is the second-order partial derivative of B ij is the second-order partial derivative of J3 / J2.

[0108] Further, the limit of b can be determined by using the method of order principal minors.

[0109] Based on the foregoing formula, it can be expressed that:

[0110]

[0111] Wherein, for any i=1, 2, 3, when , Therefore, the determinant of the Hessian matrix is equal to 0.

[0112] The second-order principal minor of the Hessian matrix is:

[0113]

[0114] Based on this, if H 11 ≥0, then the Hessian matrix is semi-positive definite.

[0115] And since in is negative, it is only necessary to ensure that This expression satisfies g≥0 in a certain range. Further, g(ξ)≥0 can be allowed to calculate the specific range That is, the value range of b.

[0116] As an optional embodiment, it further includes:

[0117] According to the self-consistent polycrystalline plasticity model of viscoplasticity, first yield point data of face-centered cubic, second yield point data of body-centered cubic, and third yield point data of hexagonal close-packed are generated;

[0118] Based on the isotropic yield criterion, first data curves of face-centered cubic, second data curves of body-centered cubic, and third data curves of hexagonal close-packed are generated. ​

[0119] The accuracy of the isotropic yield criterion is determined based on the degree of overlap between the first yield point data and the first data curve, the degree of overlap between the second yield point data and the second data curve, and the degree of overlap between the third yield point data and the third data curve.

[0120] As can be seen, by implementing this optional embodiment, the accuracy of the isotropic yield criterion can be calculated to clarify the accuracy of the isotropic yield criterion.

[0121] For details, please refer to [link / reference]. Figure 6 Based on the viscoplastic self-consistent polycrystalline plasticity model (VPSC), the first yield point data for face-centered cubic (FCC) crystals were generated (in... Figure 6 The data is represented as VPSC data for BCC, and the second yield point data for body-centered cubic (BCC) is shown in [the original text]. Figure 6 The data is represented as VPSC data for FCC, and the third yield point data for hexagonal close-packed (HCP) is also shown. Figure 6 The data is represented as VPSC data for FCP; where there are multiple first yield point data, second yield point data, and third yield point data. Furthermore, based on the isotropic yield criterion, a first data curve for face-centered cubic (BCC), a second data curve for body-centered cubic (FCC), and a third data curve for hexagonal close-packed (FCP) can be generated. VPSC is a numerical simulation tool based on crystal plasticity theory, mainly used to predict and simulate the macroscopic plastic deformation behavior and microstructural evolution process of polycrystalline metallic materials under complex strain conditions.

[0122] Furthermore, the accuracy of the isotropic yield criterion can be determined based on the degree of overlap between the first yield point data and the first data curve, the degree of overlap between the second yield point data and the second data curve, and the degree of overlap between the third yield point data and the third data curve; the higher the degree of overlap, the higher the accuracy of the final calculation.

[0123] Furthermore, the parameters of the isotropic yield criterion can be adjusted based on its accuracy to improve the accuracy of the isotropic yield criterion.

[0124] In step S130, the isotropic yield criterion is transformed into an anisotropic yield criterion based on the stress tensor of the generalized stress invariant.

[0125] Specifically, the isotropic yield criterion can be transformed based on the stress tensor of the generalized stress invariant to obtain an orthogonal anisotropic yield criterion: Where, σ YJ'2 is a generalized expression of the second invariant of the deviatoric stress tensor, and J"3 is a generalized expression of the third invariant of the deviatoric stress tensor, is an anisotropic expression of the first invariant of the stress tensor.

[0126] wherein, Specifically, a i is an anisotropic parameter of the generalized second invariant of the deviatoric stress tensor, i = 1, 2, 3, 4, 5, 6.

[0127] wherein,

[0128] Specifically, b i is an anisotropic parameter of the generalized third invariant of the deviatoric stress tensor, i = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.

[0129] wherein, Specifically, h x , h y , h z is an anisotropic parameter of the hydrostatic pressure.

[0130] As an optional embodiment, it further comprises:

[0131] According to a numerical simulation model based on the theory of crystal plasticity, fourth yield point data of the in-plane compression process of the zirconium bell rolling plate under different pre-strains (see FIG. 4 in which each closed curve represents a different pre-strain) and fifth yield point data of the thickness compression process of the zirconium bell rolling plate under different pre-strains (see FIG. 5 in which each closed curve represents a different pre-strain) are generated. Figure 7 , Figure 7 Figure 8 , Figure 8 According to the anisotropic yield criterion, fourth data curves of the in-plane compression process of the zirconium bell rolling plate under different pre-strains and fifth data curves of the thickness compression process of the zirconium bell rolling plate under different pre-strains are generated.

[0132] Based on the coincidence degree of the fourth yield point data and the fourth data curves and the coincidence degree of the fifth yield point data and the fifth data curves, the accuracy of the anisotropic yield criterion is determined.

[0133] Based on the coincidence degree of the fourth yield point data and the fourth data curves and the coincidence degree of the fifth yield point data and the fifth data curves, the accuracy of the anisotropic yield criterion is determined.

[0134] It can be seen that by implementing the optional embodiment, the accuracy of the anisotropic yield criterion can be calculated to determine the accuracy of the anisotropic yield criterion.

[0135] ​Specifically, the anisotropic yield criterion can be parameterized based on the accuracy of the anisotropic yield criterion to improve the accuracy of the anisotropic yield criterion. When the fourth yield point data completely hits the fourth data curve, and the fifth yield point data completely hits the fifth data curve, it can be determined that the anisotropic yield criterion has high accuracy and robustness.

[0136] As an optional embodiment, further comprising:

[0137] Stress components of the anisotropic yield criterion in uniaxial tension test, uniaxial compression test, equal biaxial tension test, and equal biaxial compression test;

[0138] A stress state yield stress model based on the anisotropic yield criterion and the stress components; wherein the uniaxial tension yield stress model is used to represent the relationship between the anisotropic yield criterion and the sampling angle.

[0139] It can be seen that by implementing the optional embodiment, the uniaxial tension yield stress model can be determined based on the anisotropic yield criterion and the stress components, so as to be applied to the uniaxial tension yield stress scenario.

[0140] Specifically, in the uniaxial tension test, the uniaxial compression test, the equal biaxial tension test, and the equal biaxial compression test, the stress components of the anisotropic yield criterion are represented as: σ xx = T θ (C θ )cos 2 θ, σ yy = T θ (C θ )sin 2 θ, σ xy = T θ (C θ )sinθcosθ, σ xx = σ yy = T b (C b ); wherein T θ and C θ represent the yield stress under uniaxial tension test and the yield stress under uniaxial compression test, respectively, T b and C b represent the yield stress under equal biaxial tension test and the yield stress under equal biaxial compression test, respectively.

[0141] Further, the stress components of the anisotropic yield criterion can be substituted into the expression of the anisotropic yield criterion to obtain the following expression:

[0142] Further, for the xy plane, taking the uniaxial tension test as an example, the stress components of the anisotropic yield criterion can be substituted into the expression of J'2, the expression of J"3, the expression of J'2, the expression of J"3,

[0143] Further, the above substitution result is substituted into the expression of T θ (T b ), and the final expression of the uniaxial tension yield stress can be obtained:

[0144]

[0145] As an optional embodiment, the method further comprises:

[0146] generating a plastic strain ratio coefficient of the anisotropic yield criterion;

[0147] verifying the accuracy of the anisotropic yield criterion based on the plastic strain ratio coefficient.

[0148] It can be seen that by implementing the optional embodiment, the plastic strain ratio coefficient can be accurately characterized, and the problem that the existing anisotropic yield criterion is difficult to accurately describe the anisotropic yield stress and the plastic strain ratio coefficient at the same time is solved.

[0149] Specifically, the way of calculating the plastic strain ratio (Lankford) coefficient of the anisotropic yield criterion is to first take the partial derivative of the anisotropic yield criterion, and the process of taking the partial derivative is as follows:

[0150]

[0151]

[0152] Further, based on the above partial derivative result and the Lankford coefficient calculation method of the anisotropic yield criterion the accuracy of the anisotropic yield criterion can be verified. Among them, and are the partial derivatives of the yield criterion with respect to the stress components.

[0153] As an optional embodiment, the method further comprises:

[0154] based on the plastic strain ratio coefficient and the anisotropic yield criterion, an error function of the prediction result and the test result is constructed;

[0155] based on the value of the error function minimized by the down simplex method, the anisotropic material constant in the anisotropic yield criterion is identified.

[0156] It can be seen that, by implementing the optional embodiment, the anisotropic material constant in the anisotropic yield criterion can be determined so as to be better applied in the prediction process for the anisotropic material.

[0157] Specifically, an error function of the prediction result and the test result is constructed according to the Lankford coefficient and the parameter involved in the plastic description of the yield criterion:

[0158]

[0159] Wherein, l, m, n represent the number of the test yield stress and the Lankford coefficient of different direction angles θ; are respectively the test obtained yield stress and the Lankford coefficient; are respectively the corresponding values predicted according to the proposed yield criterion; W Tθ , W Tb , W Cθ , W Cb , W rθ , W rb , are respectively the weight coefficients of the tensile yield stress, the compressive yield stress and the Lankford coefficient.

[0160] Further, the value of the error function can be minimized by the optimization algorithm of the down-hill simplex method to identify the anisotropic material constant in the proposed yield function.

[0161] Wherein, the basic idea of the simplex method is to construct a non-degenerate initial simplex in a multi-dimensional space, and to gradually move the simplex to the extreme point by a series of geometric operations such as reflection, expansion, contraction, etc.

[0162] In step S140, the material strength difference effect and the anisotropic behavior are predicted based on the anisotropic yield criterion.

[0163] Specifically, the anisotropic yield criterion constructed in the present application solves the problem that the conventional yield criterion such as Von Mises and Tresca can only describe the symmetric yield surface of the material, but cannot predict the strength difference effect of the hydrostatic pressure sensitive material and the hydrostatic pressure insensitive material, and realizes the simultaneous prediction of the material strength difference effect and the anisotropic behavior.

[0164] The application results of the anisotropic yield criterion can be referred to 9-11 Figure 12 , Figure 9 is the prediction result of the anisotropic yield criterion for the tensile yield stress of the AA20082008-T4 aluminum alloy at different direction angles, Figure 10are the predicted results of the anisotropic yield criterion for the yield stress of AA2008-T4 aluminum alloy at different direction angles, Figure 11 are the predicted results of the anisotropic yield criterion for the Lankford coefficient of AA2008-T4 aluminum alloy at different direction angles, Figure 12 is the predicted result of the anisotropic yield criterion for the yield surface of AA2008-T4 aluminum alloy.

[0165] Please refer to Figure 13 , Figure 13 Fig. 1 schematically shows a structural block diagram of an apparatus for describing yield behavior according to an embodiment of the present application. The apparatus 1300 for describing yield behavior corresponds to the method shown in Fig. 1, and as shown in Fig. 2, the apparatus 1300 for describing yield behavior comprises: Figure 1 Figure 13

[0166] The isotropic yield criterion construction unit 1301 is configured to construct an isotropic yield criterion based on stress invariants; wherein the isotropic yield criterion comprises a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor;

[0167] The parameter determination unit 1302 is configured to determine a corresponding relationship between the first parameter and the second parameter and a value range of the third parameter based on the Hessian matrix and the yield surface curvature algorithm, and apply the corresponding relationship and the value range to the isotropic yield criterion;

[0168] The anisotropic yield criterion determination unit 1303 is configured to transform the isotropic yield criterion into an anisotropic yield criterion based on the generalized stress invariants corresponding to the stress tensor;

[0169] The prediction unit 1304 is configured to predict the material strength difference effect and the anisotropic behavior based on the anisotropic yield criterion.

[0170] Wherein the isotropic yield criterion is expressed as:

[0171]

[0172] Wherein I1 is the first invariant of the stress tensor, J2 is the second invariant of the deviatoric stress tensor, J3 is the third invariant of the deviatoric stress tensor, σ1, σ2, σ3 represent three principal stresses respectively, S1, S2, S3 represent three principal deviatoric stresses respectively; σ Y is the yield stress obtained by uniaxial tension, a and n are the first parameter and the second parameter for adjusting the symmetry of J3, b is the third parameter for adjusting the asymmetry of J3, μ is a parameter for adjusting the sensitivity of hydrostatic pressure, k is derived based on the uniaxial condition, and the uniaxial condition is expressed as: ​​

[0173] It can be seen that, by implementing the device shown in the embodiment, an innovative isotropic yield criterion can be constructed based on stress invariants, the isotropic yield criterion including a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor, and then the isotropic yield criterion after determining the parameters can be transformed into an anisotropic yield criterion by eliminating the correspondence between the first parameter and the second parameter and the value range of the third parameter through the Hessian matrix and yield surface curvature algorithm, so as to predict the strength differential effect and anisotropic behavior, and thus high-precision characterization of the yield behavior of the metal material under complex stress states can be performed when the metal material is applied to a multi-load working condition and a complex stress state. Figure 13 In an example embodiment of the present application, the device further comprises:

[0174] The yield point data determination unit is configured to generate first yield point data of face-centered cubic, second yield point data of body-centered cubic, and third yield point data of hexagonal close-packed according to the self-consistent polycrystal plasticity model.

[0175] The data curve determination unit is configured to generate first data curves of face-centered cubic, second data curves of body-centered cubic, and third data curves of hexagonal close-packed based on the isotropic yield criterion.

[0176] The precision determination unit is configured to determine the precision of the isotropic yield criterion based on the coincidence degree of the first yield point data and the first data curves, the coincidence degree of the second yield point data and the second data curves, and the coincidence degree of the third yield point data and the third data curves.

[0177] It can be seen that, by implementing the optional embodiment, the precision of the isotropic yield criterion can be calculated to determine the accuracy of the isotropic yield criterion.

[0178] In an example embodiment of the present application, the device further comprises:

[0179] The yield point data determination unit is further configured to generate fourth yield point data of the in-plane compression process of the zirconium bell-shaped plate under different pre-strains and fifth yield point data of the thickness compression process of the zirconium bell-shaped plate under different pre-strains according to the numerical simulation model based on the theory of crystal plasticity.

[0180] The data curve determination unit is further configured to generate fourth data curves of the in-plane compression process of the zirconium bell-shaped plate under different pre-strains and fifth data curves of the thickness compression process of the zirconium bell-shaped plate under different pre-strains based on the anisotropic yield criterion.

[0181]

[0182] ​The precision determination unit is further configured to determine the precision of the anisotropic yield criterion based on coincidence degrees of the fourth yield point data and the fourth data curve and coincidence degrees of the fifth yield point data and the fifth data curve.

[0183] It can be seen that, by implementing the optional embodiment, the precision of the anisotropic yield criterion can be calculated to determine the accuracy of the anisotropic yield criterion.

[0184] In an example embodiment of the present application, the method further comprises:

[0185] The stress component determination unit is configured to determine stress components of the anisotropic yield criterion in uniaxial tension test, uniaxial compression test, equi-biaxial tension test and equi-biaxial compression test.

[0186] The uniaxial tension yield stress model determination unit is configured to determine a uniaxial tension yield stress model based on the anisotropic yield criterion and the stress components, wherein the uniaxial tension yield stress model is used to represent the relationship between the anisotropic yield criterion and the sampling angle.

[0187] It can be seen that, by implementing the optional embodiment, the uniaxial tension yield stress model can be determined based on the anisotropic yield criterion and the stress components, so as to be applied to the uniaxial tension yield stress scenario.

[0188] In an example embodiment of the present application, the method further comprises:

[0189] The plastic strain ratio coefficient generation unit is configured to generate a plastic strain ratio coefficient of the anisotropic yield criterion.

[0190] The accuracy verification unit is configured to verify the accuracy of the anisotropic yield criterion based on the plastic strain ratio coefficient.

[0191] It can be seen that, by implementing the optional embodiment, the plastic strain ratio coefficient can be accurately characterized, and the problem that the existing anisotropic yield criterion is difficult to accurately describe the anisotropic yield stress and the plastic strain ratio coefficient at the same time is solved.

[0192] In an example embodiment of the present application, the method further comprises:

[0193] The error function determination unit is configured to construct an error function of the prediction result and the test result based on the plastic strain ratio coefficient and the anisotropic yield criterion.

[0194] The constant identification unit is configured to minimize the value of the error function based on the down simplex method, so as to identify anisotropic material constants in the anisotropic yield criterion.

[0195] It can be seen that, by implementing the optional embodiment, the anisotropic material constants in the anisotropic yield criterion can be determined, so as to be better applied to the prediction process for the anisotropic material.

[0196] It should be noted that although several modules or units of devices for action execution are mentioned in the foregoing detailed description, such division is not mandatory. Indeed, according to an embodiment of the application, the features and functionalities of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functionalities of one module or unit described above can be further divided into several modules or units embodied.

[0197] Since the various functional modules of the apparatus for yielding behavior of the example embodiments of the present application correspond to the steps of the example embodiments of the method for yielding behavior described above, for details not disclosed in the apparatus embodiments of the present application, please refer to the above-described embodiments of the method for yielding behavior of the present application.

[0198] Please refer to Figure 14 , Figure 14 A structural schematic diagram of a computer system of an electronic device suitable for implementing the embodiments of the present application is shown.

[0199] It should be noted that Figure 14 The computer system 1400 of the electronic device shown is only an example and should not impose any limitation on the functions and usage range of the embodiments of the present application.

[0200] As Figure 14 shown, the computer system 1400 includes a central processing unit (CPU) 1401, which can perform various appropriate actions and processes according to programs stored in a read-only memory (ROM) 1402 or loaded from a storage portion 1408 into a random access memory (RAM) 1403. Various programs and data required for system operation are also stored in the RAM 1403. The CPU 1401, the ROM 1402, and the RAM 1403 are connected to each other through a bus 1404. An input / output (I / O) interface 1405 is also connected to the bus 1404.

[0201] The following components are connected to the I / O interface 1405: an input portion 1406 including a keyboard, a mouse, and the like; an output portion 1407 including a cathode ray tube (CRT), a liquid crystal display (LCD), and the like, and a speaker, and the like; a storage portion 1408 including a hard disk, and the like; and a communication portion 1409 including a network interface card such as a LAN card, a modem, and the like. The communication portion 1409 performs communication processing via a network such as the Internet. A drive 1410 is also connected to the I / O interface 1405 as necessary. A removable recording medium 1411 such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, and the like is attached to the drive 1410 as necessary, so that a computer program read therefrom is installed into the storage portion 1408 as necessary.

[0202] In particular, according to embodiments of the present application, the processes described above with reference to the flowcharts can be implemented as a computer software program. For example, embodiments of the present application include a computer program product comprising a computer program carried on a computer readable medium, the computer program comprising program code for executing the methods illustrated by the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network by the communication section 1409, and / or installed from the detachable medium 1411. When the computer program is executed by the central processing unit (CPU) 1401, various functions defined in the methods and apparatuses of the present application are executed.

[0203] An exemplary embodiment of the present disclosure also provides a computer program product. The computer program product includes a computer program which, when executed by a processor, implements the method described above for yielding behavior.

[0204] In an embodiment, the computer program product can be a tangible product containing the computer program, such as a computer readable storage medium storing the computer program. The readable storage medium can be a storage medium based on electric, magnetic, optical, electromagnetic, infrared, and the like signals, including but not limited to random access memory (RAM), read only memory (ROM), magnetic tape, floppy disk, flash memory (Flash), mechanical hard disk (HDD), solid state disk (SSD), and the like. For example, the computer program product can be implemented as a non-volatile storage medium storing the computer program, such as read only memory, Nand flash, and the like.

[0205] In an embodiment, the computer program product can be an intangible product containing the computer program. For example, the computer program product can be implemented as a virtual digital product, such as an executable file, installation package, and the like digital file storing the computer program.

[0206] The code of the computer program can be written in one or more programming languages. Programming languages such as C, Java, C++, and the like. The program code can be executed entirely on the user computing device, or partially on the user computing device, or as a separate software package, or partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case involving a remote computing device, the remote computing device can be connected to the user computing device through any kind of network, such as a local area network (LAN), a wide area network (WAN), and the like, or can be connected to an external computing device (for example, through an Internet connection provided by an operator).

[0207] The computer program can be carried or transmitted by an electric, magnetic, optical, electromagnetic, infrared, or other signals. The electronic device can convert the signal carrying the computer program into a digital signal, and then run the computer program. When the computer program is run on the electronic device, its code is used to make the electronic device execute (more specifically, can make the processor of the electronic device execute) the method steps of various exemplary embodiments of the present disclosure, such as the method of describing the yield behavior described above, which includes the following steps: constructing an isotropic yield criterion based on stress invariants; wherein the isotropic yield criterion includes a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor; determining the correspondence between the first parameter and the second parameter and the value range of the third parameter based on the Hessian matrix and the yield surface curvature algorithm, and applying the correspondence and the value range to the isotropic yield criterion; transforming the isotropic yield criterion into an anisotropic yield criterion based on the generalized stress invariants of the stress tensor; and predicting the strength differential effect and anisotropic behavior of the material based on the anisotropic yield criterion.

[0208] By executing the above method steps through the computer program, an original isotropic yield criterion can be constructed based on stress invariants, which includes a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor, and then the correspondence between the first parameter and the second parameter and the value range of the third parameter can be determined through the Hessian matrix and the yield surface curvature algorithm, and the isotropic yield criterion after determining the parameters can be transformed into an anisotropic yield criterion to predict the strength differential effect and anisotropic behavior of the material, so that the yield behavior of the metal material under complex stress state can be characterized with high precision when the metal material is applied to multiple load conditions and complex stress states.

[0209] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectural, functional, and operational architectures of systems, methods, and computer program products according to various embodiments of the present application. In this regard, each block in the flowcharts or block diagrams can represent a module, a program segment, or a portion of code that contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions noted in the blocks can occur in different orders than that shown in the figures. For example, two blocks that are shown in succession can actually be executed substantially concurrently, or they can sometimes be executed in reverse order, depending on the functionality involved. It should also be noted that each block in the flowcharts or block diagrams, and combinations of blocks in the flowcharts or block diagrams, can be implemented by dedicated hardware-based systems that perform specified functions or operations, or can be implemented by a combination of dedicated hardware and computer instructions.

[0210] The units described in the embodiments of the present application can be implemented in the form of software, or can be implemented in the form of hardware, and the described units can also be arranged in a processor. In some cases, the names of these units do not constitute a limitation on the units themselves.

[0211] Other embodiments of the application will be apparent to those skilled in the art from consideration of the specification and practice of the application disclosed herein. It is intended that the specification and examples be considered as exemplary only, with the true scope and spirit of the application being indicated by the following claims.

Claims

1. A method of describing the yielding behavior, characterized by The method comprises the following steps: constructing an isotropic yield criterion based on stress invariants; wherein the isotropic yield criterion comprises a first parameter and a second parameter for adjusting the symmetry of the third invariant of the deviatoric stress tensor, and a third parameter for adjusting the asymmetry of the third invariant of the deviatoric stress tensor; determining the correspondence between the first parameter and the second parameter and the value range of the third parameter based on the Hessian matrix and the yield surface curvature algorithm, and applying the correspondence and the value range to the isotropic yield criterion; transforming the isotropic yield criterion into an anisotropic yield criterion based on the generalized stress invariants of the stress tensor; predicting the strength differential effect and anisotropic behavior of the material based on the anisotropic yield criterion; wherein the isotropic yield criterion is expressed as: where I1is the first invariant of the stress tensor, J2is the second invariant of the deviatoric stress tensor, and J3is the third invariant of the deviatoric stress tensor; σ Y the yield stress obtained for uniaxial tension, a and n are first and second parameters for adjusting the symmetry of J3, b is a third parameter for adjusting the asymmetry of J3, μ is a parameter for adjusting the hydrostatic pressure sensitivity, and k is derived based on the uniaxial condition, which is expressed as: wherein the anisotropic yield criterion is expressed as: wherein σ Y ' is the yield stress obtained by uniaxial tension in the rolling direction, J'2 is a generalized expression of the second invariant of the deviatoric stress tensor, J"3 is a generalized expression of the third invariant of the deviatoric stress tensor, is an anisotropic expression of the first invariant of the stress tensor.

2. The method of claim 1, wherein, The method further comprises the following steps: generating first yield point data of face-centered cubic, second yield point data of body-centered cubic, and third yield point data of hexagonal close-packed according to a viscoplastic self-consistent polycrystal plasticity model; generating first data curves of face-centered cubic, second data curves of body-centered cubic, and third data curves of hexagonal close-packed based on the isotropic yield criterion; determining the accuracy of the isotropic yield criterion based on the coincidence degree of the first yield point data and the first data curves, the coincidence degree of the second yield point data and the second data curves, and the coincidence degree of the third yield point data and the third data curves.

3. The method of claim 1, wherein, The method further comprises the following steps: generating fourth yield point data of in-plane compression process of zirconium bell rolling plate under different pre-strains and fifth yield point data of thickness compression process of zirconium bell rolling plate under different pre-strains according to a numerical simulation model based on the theory of crystal plasticity; generating fourth data curves of in-plane compression process of zirconium bell rolling plate under different pre-strains and fifth data curves of thickness compression process of zirconium bell rolling plate under different pre-strains based on the anisotropic yield criterion; determining the accuracy of the anisotropic yield criterion based on the coincidence degree of the fourth yield point data and the fourth data curves, and the coincidence degree of the fifth yield point data and the fifth data curves.

4. The method of claim 1, wherein, The method further comprises the following steps: expressing the stress components of the anisotropic yield criterion in uniaxial tension test, uniaxial compression test, equi-biaxial tension test, and equi-biaxial compression test; generating a yield stress model of each stress state based on the anisotropic yield criterion and each stress component; wherein the yield stress model is used to represent the relationship between the anisotropic yield criterion and the sampling angle.

5. The method of claim 1, wherein, The method further comprises the following steps: generating a plastic strain ratio coefficient of the anisotropic yield criterion; verifying the accuracy of the anisotropic yield criterion based on the plastic strain ratio coefficient.

6. The method of claim 1, wherein, The method further comprises the following steps: constructing an error function of the prediction result and the test result based on the plastic strain ratio coefficient and the anisotropic yield criterion; minimizing the value of the error function based on the downhill simplex method to identify the anisotropic material constant in the anisotropic yield criterion.

7. An apparatus for describing the behavior of yielding, characterized in that The method comprises the following steps: The isotropic yield criterion construction unit is configured to construct an isotropic yield criterion based on stress invariants, wherein the isotropic yield criterion comprises a first parameter and a second parameter for adjusting symmetry of a third invariant of a deviatoric stress tensor, and a third parameter for adjusting asymmetry of the third invariant of the deviatoric stress tensor; The parameter determination unit is configured to determine a corresponding relationship between the first parameter and the second parameter and a value range of the third parameter based on a Hessian matrix and a yield surface curvature algorithm, and apply the corresponding relationship and the value range to the isotropic yield criterion; The anisotropic yield criterion determination unit is configured to transform the isotropic yield criterion into an anisotropic yield criterion based on generalized stress invariants of a stress tensor; The prediction unit is configured to predict material strength difference effects and anisotropic behaviors based on the anisotropic yield criterion. The isotropic yield criterion is expressed as: where I1is the first invariant of the stress tensor, J2is the second invariant of the deviatoric stress tensor, and J3is the third invariant of the deviatoric stress tensor; σ Y the yield stress obtained for uniaxial tension, a and n are first and second parameters for adjusting the symmetry of J3, b is a third parameter for adjusting the asymmetry of J3, μ is a parameter for adjusting the hydrostatic pressure sensitivity, k is derived based on uniaxial conditions expressed as: wherein the anisotropic yield criterion is expressed as: wherein σ Y ' is the yield stress obtained by uniaxial tension in the rolling direction, J'2 is a generalized expression of the second invariant of the deviatoric stress tensor, J"3 is a generalized expression of the third invariant of the deviatoric stress tensor, is an anisotropic expression of the first invariant of the stress tensor.

8. A computer program product comprising a computer program, characterized in that, The computer program, when executed by a processor, implements the method of any one of claims 1-6.

9. An electronic device, comprising: Comprise: A processor; And A memory for storing executable instructions of the processor; Wherein the processor is configured to execute the method of any one of claims 1-6 by executing the executable instructions.

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