Metal material and structure failure numerical analysis method and system based on fracture phase field model

Abstract

The invention discloses a metal material and structure failure numerical analysis method and system based on a fracture phase field model. The method comprises the following steps: 1, giving mechanical parameters of an analysis object; 2, discretizing geometric and physical models of an analysis object; and 3, setting a numerical solution scheme and starting simulation analysis, including selection of a linear equation set solution algorithm, convergence conditions of linear solution and nonlinear solution and convergence conditions of phase field and displacement field decoupling solution, ending analysis and outputting a result when a working condition meets a given load condition. The phase field model can establish the relation between fracture mechanics and damage mechanics, and complete description of the failure process of the metal material from deformation, yield, damage evolution, crack initiation to macrocrack generation is achieved. The selected elastic-plastic constitutive and stress updating algorithm suitable for metal material deformation is a classical and universal J2 plasticity and radial return method. The adopted finite element numerical solution method and decoupling algorithm can ensure the accuracy, convergence and calculation efficiency of numerical simulation.

Description

Technical Field

[0001] The present invention belongs to the technical field of method inventions, and particularly relates to a numerical analysis method and system for the failure of metal materials and structures based on the fracture phase field model. Background Art

[0002] With the continuous development of mechanical theories, the analysis of metal structures has evolved from traditional strength and stability design to a quantitative research stage of structural integrity analysis. To meet the safety design and effective analysis of metal structures under complex stress states, it is necessary to break through the traditional strength design theory and adopt new mechanical theories to guide engineering practice.

[0003] In recent years, the fracture phase field model based on fracture variational theory has been widely studied and applied. It is believed that the fracture of materials or structures depends on the system free energy functional and is controlled by energy minimization. The phase field model regularizes the material state by introducing the phase field variable d, and the discrete crack is transformed into a smeared crack, thereby reducing the difficulty of the mathematical description of the crack interface. When the phase field variable d→0, the material remains in a complete state; when the phase field variable d→1, cracks appear in the material, and the potential energy in the crack region will be released. The width of the smeared crack is controlled by the length scale parameter l c and when l c →0, the smeared crack will revert to a discrete crack. Researchers described the relationship between the phase field model and the discrete crack model from the geometric topological characteristics of the crack and demonstrated it from the perspective of the second law of thermodynamics, thus accelerating the popularization and application of the fracture phase field model in the engineering field.

[0004] In the domestic and foreign research and application of the fracture phase field model, the analyzed objects mostly consider elastic media. For the wide application of metal materials and their structures in actual engineering, in order to combine the fracture phase field model to improve the reliability and integrity of strength analysis and provide reference for engineering design and optimization, it is very necessary to develop a numerical analysis method based on the fracture phase field model for the failure of metal structures. Summary of the Invention

[0005] To solve the above problems, the present invention provides a numerical analysis method and system for the failure of metal materials and structures based on the fracture phase field model. The present invention is applicable to the failure analysis of metal materials and their structures.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A numerical analysis method for the failure of metal materials and structures based on the fracture phase field model includes:

[0008] Step 1: Determine the mechanical parameters of the metal material corresponding to the current analysis object and specify the phase field regularization parameter;

[0009] Step 2: Determine the mesh generation scheme for the geometric model of the analysis object according to the phase-field regularization parameter in Step 1, and simultaneously complete the discretization of the physical model;

[0010] Step 3: Set the numerical solution scheme based on the discretization result of Step 2. When the working condition meets the given conditions, end the analysis and output the calculated physical field results.

[0011] A further improvement of the present invention lies in that in Step 1, determine the mechanical parameters of the metal material corresponding to the current analysis object, and specify the phase-field regularization parameter, including:

[0012] Obtain the mechanical parameters of the metal material through experiments: including Young's modulus E, Poisson's ratio v, initial yield stress σ0, and plastic modulus H';

[0013] Obtain the fracture toughness G of the metal material through experiments IC ;

[0014] Determine the phase-field regularization parameter l according to the experimental data and material mechanical parameters c ≤l0~ σ c is the ultimate tensile strength.

[0015] A further improvement of the present invention lies in that in Step 2, determine the mesh generation scheme for the geometric model of the analysis object according to the phase-field regularization parameter in Step 1, and simultaneously complete the discretization of the physical model, including:

[0016] First, determine the mesh generation scheme for the analysis object: locally refine the mesh for the area where cracks may occur, and the maximum mesh size h in this area max is less than half of the phase-field regularization parameter l in Step 1 above c ;

[0017] Subsequently, discretize the physical model: determine the displacement field variable, phase-field variable, and intermediate variables related to the crack driving force according to the fracture phase-field model, and set the relevant initial and boundary conditions; the mathematical equation of the fracture phase-field model is as follows: When a metal material undergoes ductile fracture failure, there are two energy dissipation terms, namely plastic deformation and crack propagation. The corresponding fracture phase-field model is summarized under a unified thermodynamics and variational framework, and its system energy functional is shown in Equation (1); it includes the elastic strain energy density and plastic work density that drive crack propagation, the dissipated energy during the crack evolution process, and the work done by external forces;

[0018]

[0019] In the formula:

[0020] g(d)——elastic energy degradation function;

[0021] h(d)——Plastic work degradation function;

[0022] ——Tensile and compressive elastic strain energy density / J·m -3 ;

[0023] ψ p ——Plastic work / J·m -3 ;

[0024] G IC ——Fracture toughness / J·m -2 ;

[0025] l c ——Phase field regularization parameter / m;

[0026] d——Phase field variable;

[0027] α(d)——Crack surface geometry function;

[0028]

[0029] By additionally considering the driving effect of plastic work density on the phase field evolution and the influence of the phase field evolution on the yield condition, the coupling of plastic deformation and crack evolution is preliminarily achieved; the weak forms of the mechanical equilibrium equation and the phase field control equation and the yield condition are shown in Equations (2), (3), and (4) respectively; among them, in order to quantitatively describe the damage initiation point, a softening energy threshold w0 is additionally introduced in Equation (3) and h(d) = g(d) is assumed; the elastic strain energy density adopts the spherical - deviatoric decomposition method, corresponding to the tensile - compressive decomposition of the stress tensor, and the phase field variable only acts on the tensile stress part; at the same time, in order to avoid crack healing, that is, to satisfy the irreversible constraint condition of the phase field variable, due to the irreversibility of plastic deformation, the historical maximum value of the elastic strain energy density

[0030]

[0031] In the formula:

[0032] ——Effective stress tensor;

[0033] ——Equivalent plastic strain;

[0034] ——Equivalent stress / Pa;

[0035] ε——Strain tensor;

[0036] H(q)——Hardening function;

[0037] The discrete scheme corresponding to the elastoplastic constitutive model is shown in Eqs. (5)-(12), and the fully implicit backward Euler difference scheme is adopted; the discrete scheme of the KKT conditions corresponding to the loading / unloading case is shown in Eq. (12).

[0038] ε n+1 = ε n + dε (5)

[0039]

[0040] dλ = λ n+1 dt (8)

[0041]

[0042]

[0043] After obtaining the strain increment by the Newton iteration method, it is first assumed that the entire strain increment is elastic deformation, and then the trial stress tensor is calculated. Since the yield condition is a convex function, the loading / unloading condition is judged according to the equivalent trial stress, as shown in Eqs. (13)-(18).

[0044]

[0045] When in the plastic loading condition, the radial return algorithm is used to update the stress state and ensure that the KKT constraint conditions are satisfied; the radial return algorithm is shown in Eqs. (19)-(25), where the plastic deformation of the metal material remains incompressible; to obtain the value of the consistency parameter dλ, the Newton method is used for inner iteration of Eq. (22), as shown in Eqs. (23)-(25).

[0046]

[0047]

[0048] After obtaining the value of the consistency parameter dλ, the stress state is updated; at the same time, since the system Jacobian matrix is constructed in the finite element solution process, the consistent tangent modulus used to relate the change in the stress tensor and the change in the strain tensor is also required, as shown in Eqs. (26)-(29).

[0049] σ n+1 = K(tr[ε n+1 )I + 2μ(dev[ε n+1 - dλn n+1 ) (26)

[0050] dσ n+1 = C:dε n+1 - 2μ(d(dλ)n n+1 + dλd(nn+1 )) (27)

[0051]

[0052] Based on the weak form of the governing equations and boundary conditions of the above fracture phase field model, as well as the stress update algorithm of the elastoplastic constitutive relation, the finite element method is used for discrete solution.

[0053] A further improvement of the present invention lies in using the radial return algorithm to update the stress state, including the stress tensor, elastic strain tensor, and plastic strain tensor.

[0054] A further improvement of the present invention lies in that in step 3, based on the discretization result of step 2, a numerical solution scheme is set, and when the working condition meets the given conditions, the analysis ends and the calculated physical field results are output, including:

[0055] Select the solution algorithm for the linear equations: After the discretization by the finite element method in step 2, nonlinear equations about the displacement field variables and phase field variables will be obtained respectively, and usually the Newton method is used for iterative solution; After the discretization by the finite element method and the linearization by the Newton method, solving the fracture phase field model will be transformed into solving a large sparse linear equation system; GMRES is used as the iterative algorithm for solving the linear equation system, and LU decomposition is used as the preprocessing algorithm to improve the condition number of the coefficient matrix;

[0056] Set the convergence conditions for linear and nonlinear solutions; Set the convergence conditions for decoupled solution of the phase field and displacement field; The alternating algorithm is used to achieve the decoupled solution of the displacement field and the phase field; The field variables to be solved include displacement field variables and phase field variables, and the intermediate variables are the crack driving force composed of elastic strain energy density and plastic deformation; In the current time step or load step, the phase field variables are fixed to solve the mechanical equilibrium equation to update the crack driving force, and the updated crack driving force is used to solve the phase field control equation to update the phase field variables; The mechanical equilibrium equation and the phase field control equation are continuously solved alternately until the solutions or residuals of the displacement field and the phase field meet the convergence conditions; The relative tolerance and absolute tolerance of the Picard iteration related to the displacement field-phase field decoupled solution strategy are 1×10 -7 and 8×10 -8 ;

[0057] When the working condition meets the given load conditions, the analysis ends and the results are output: After the numerical solution is completed, a result file will be generated.

[0058] A further improvement of the present invention lies in that the result file contains the distribution and evolution of the basic field variables, namely the displacement field and phase field variables, and also includes the variables that are set to be additionally concerned, namely the distribution of stress and strain.

[0059] A numerical analysis system for the failure of metal materials and structures based on the fracture phase field model, comprising:

[0060] A parameter determination module that determines the mechanical parameters of the metal material corresponding to the current analysis object and gives the phase field regularization parameter;

[0061] A mesh generation and model discretization module that determines the mesh generation scheme for the geometric model of the analysis object according to the determined phase field regularization parameter and synchronously completes the discretization of the physical model;

[0062] A calculation module that sets a numerical solution scheme based on the discretization results of the mesh generation and model discretization module, ends the analysis when the working condition meets the given conditions, and outputs the calculated physical field results.

[0063] A further improvement of the present invention lies in that the parameter determination module determines the mechanical parameters of the metal material corresponding to the current analysis object and gives the phase field regularization parameter, including:

[0064] Obtain the mechanical parameters of the metal material through experiments: including Young's modulus E, Poisson's ratio v, initial yield stress σ0, and plastic modulus H';

[0065] Obtain the fracture toughness G of the metal material through experiments IC ;

[0066] Determine the phase field regularization parameter according to the experimental data and material mechanical parameters σ c is the ultimate tensile strength.

[0067] An electronic device, comprising: a processor and a memory coupled to the processor, the memory storing a computer program, and when the computer program is executed by the processor, the steps of the numerical analysis method for the failure of metal materials and structures based on the fracture phase field model according to any one of claims 1-6 are implemented.

[0068] A computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the numerical analysis method for the failure of metal materials and structures based on the fracture phase field model according to any one of claims 1-6 are implemented.

[0069] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0070] 1. The present invention can consider the real mechanical parameters and deformation behaviors of metal materials, so it can ensure the rationality of the analysis results when guiding the design and optimization of engineering structures.

[0071] 2. The fracture phase field model adopted in the present invention takes into account the elastic deformation and plastic deformation of the research object, conforms to the deformation behavior of metal materials widely existing in engineering practice, and has a wide range of applicability.

[0072] 3. In the numerical solution process of the present invention, the finite element method and the Newton method are respectively used for the discretization and linearization processing of the physical field, the radial return method is applied to update the stress state, and the displacement field and the phase field are decoupled. The adopted numerical solution scheme ensures the reliability and stability of the analysis process. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for use in the description of the specific embodiments or the prior art. Obviously, the following drawings are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0074] Figure 1 is a flowchart of the numerical analysis method for the failure of metal materials and structures based on the fracture phase field model.

[0075] Figure 2 is a schematic diagram of an asymmetric circular hole metal plate, where Figure 2 (a) is the geometric model, Figure 2 (b) is the mesh division.

[0076] Figure 3 is the example result obtained by setting based on the operation steps, where Figure 3 (a) is the distribution of the phase field variable, i.e., the crack, Figure 3 (b) is the displacement distribution in the z direction.

[0077] Figure 4 is the mechanical behavior under different softening thresholds w0, and the mechanical response obtained by applying the present method in a single mesh element, Figure 4 (a) is the mesh element, Figure 4 (b) is the stress-displacement curve.

[0078] Figure 5 is the structural block diagram of the numerical analysis system for the failure of metal materials and structures based on the fracture phase field model of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0079] In the following, only some exemplary embodiments are simply described. As those skilled in the art can recognize, the described embodiments can be modified in various different ways without departing from the spirit or scope of the present invention. Therefore, the drawings and the description are considered to be exemplary in nature rather than restrictive.

[0080] In the description of the present invention, it should be understood that when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their combinations.

[0081] It should also be understood that the terms used in the specification of the present invention are merely for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0082] It should be further understood that the term "and / or" used in the specification of the present invention and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes these combinations.

[0083] Schematic diagrams of various structures according to the disclosed embodiments of the present invention are shown in the drawings. These figures are not drawn to scale, where for the purpose of clear expression, some details are enlarged and some details may be omitted. The shapes of various regions and layers shown in the figures and their relative sizes and positional relationships are merely exemplary, and may actually deviate due to manufacturing tolerances or technical limitations. Those skilled in the art can additionally design regions / layers with different shapes, sizes and relative positions according to actual needs.

[0084] The embodiments of the present invention will be described in detail below with reference to the drawings.

[0085] Embodiment 1

[0086] The present invention provides a numerical analysis method for the failure of metal materials and structures based on the fracture phase field model. This method is applicable to the failure analysis related to common metal materials or structures. This analysis method can achieve a complete failure analysis of the research object from elastic deformation → plastic deformation → crack initiation → crack propagation under the given material mechanical parameters and boundary conditions of the current research object, and obtain the distributions of corresponding crack propagation behaviors, stress and strain and other field variables.

[0087] Step 1: Determine the mechanical parameters of the metal material corresponding to the current analysis object and specify the phase-field regularization parameter. Obtain the mechanical parameters of the metal material through experiments such as single-bar tension: including Young's modulus E, Poisson's ratio v, initial yield stress σ0, and plastic modulus H′. For example, for a certain aluminum alloy, Young's modulus E = 68.80 GPa, Poisson's ratio v = 0.30, initial yield stress σ0 = 113.00 MPa, and plastic modulus H′ = 100.00 MPa. Obtain the fracture toughness G of the metal material through experiments such as compact tension. IC For example, the fracture toughness G of a certain aluminum alloy IC = 5.00×10 3 J·m -2 . Determine the phase-field regularization parameter based on the experimental data and material mechanical parameters For example, set the phase-field regularization parameter l c = 4.00×10 -4 m for subsequent failure analysis.

[0088] Step 2: Discretize the geometric model and physical model of the analysis object. First, determine the mesh division scheme of the analysis object, and locally refine the mesh for the area where cracks may occur. The maximum mesh size h max in this area needs to be less than half of the phase-field regularization parameter l c in Step 1 above, as Figure 2 shown. Subsequently, discretize the physical model, determine the displacement field variable, phase-field variable, and intermediate variables related to the crack driving force according to the fracture phase-field model, and set the relevant initial and boundary conditions. The mathematical equation of the fracture phase-field model is as follows: When a metal material undergoes ductile fracture failure, there are two energy dissipation terms: plastic deformation and crack propagation. The corresponding fracture phase-field model can be summarized under a unified thermodynamics and variational framework, and its system energy functional is shown in Equation (1). It includes the elastic strain energy density and plastic work density that drive crack propagation, the dissipated energy during the crack evolution process, and the work done by external forces.

[0089]

[0090] In the formula:

[0091] g(d)——Elastic energy degradation function

[0092] h(d)——Plastic work degradation function

[0093] ——Tensile and compressive elastic strain energy density / J·m -3

[0094] ψ p ——Plastic work / J·m -3

[0095] G IC —— Fracture toughness / J·m -2

[0096] l c —— Phase field regularization parameter / md —— Phase field variable

[0097] α(d) —— Crack surface geometry function

[0098]

[0099] By additionally considering the driving effect of plastic work density on phase field evolution and the influence of phase field evolution on the yield condition, the coupling of plastic deformation and crack evolution is preliminarily achieved. The weak forms of the mechanical equilibrium equation and the phase field control equation and the yield condition are shown in Eqs. (2), (3) and (4) respectively. Among them, in order to quantitatively describe the damage initiation point, a softening energy threshold w0 is additionally introduced in Eq. (3) and h(d) = g(d) is assumed. In particular, the equivalent stress based on the effective stress tensor and the degradation of the hardening function are considered in Eq. (4). The elastic strain energy density adopts the spherical-deviatoric decomposition method, corresponding to the tensile-compressive decomposition of the stress tensor, and the phase field variable only acts on the tensile stress part. At the same time, in order to avoid crack healing, that is, to satisfy the irreversible constraint condition of the phase field variable, due to the irreversibility of plastic deformation, the historical maximum value of the elastic strain energy density is set .

[0100]

[0101] In the formula:

[0102] —— Effective stress tensor

[0103] —— Equivalent plastic strain

[0104] —— Equivalent stress / Pa

[0105] ε —— Strain tensor

[0106] H(q) —— Hardening function

[0107] The discrete schemes corresponding to the elastoplastic constitutive are shown in Eqs. (5)-(12), and the fully implicit backward Euler difference scheme is adopted. The discrete scheme of the KKT conditions corresponding to the loading / unloading situation is shown in Eq. (12).

[0108] ε n+1 = ε n + dε (5)

[0109]

[0110] dλ = λ n+1 dt (8)

[0111]

[0112] After obtaining the strain increment by the Newton - Raphson method, it is first assumed that the entire strain increment is elastic deformation, and then the trial stress tensor is calculated. Since the yield condition is a convex function, the loading / unloading condition can be judged according to the equivalent trial stress, as shown in Eqs. (13) - (18).

[0113]

[0114]

[0115] When in the plastic loading condition, the radial return algorithm is needed to update the stress state, including the stress tensor, elastic strain tensor and plastic strain tensor, and ensure that the KKT constraint conditions are satisfied. The radial return algorithm is shown in Eqs. (19) - (25), where the plastic deformation of the metal material remains incompressible. To obtain the value of the consistency parameter dλ, the Newton method needs to be used for internal iteration of Eq. (22), as shown in Eqs. (23) - (25).

[0116]

[0117] After obtaining the numerical value of the consistency parameter dλ, the update of the stress state can be completed. At the same time, since the system Jacobian matrix needs to be constructed in the finite - element solution process, the consistent tangent modulus used to relate the change in the stress tensor and the change in the strain tensor is also needed, as shown in Eqs. (26) - (29).

[0118] σ n+1 = K(tr[ε n+1 )I + 2μ(dev[ε n+1 - dλn n+1 ) (26)

[0119] dσ n+1 = C:dε n+1 - 2μ(d(dλ)n n+1 + dλd(n n+1 )) (27)

[0120]

[0121] Based on the weak form of the control equation and boundary conditions of the above - mentioned fracture phase - field model, as well as the stress update algorithm of the elastoplastic constitutive relationship, the finite - element method can be used for discrete solution.

[0122] Step 3: Set the numerical solution scheme. When the working conditions meet the given conditions, end the analysis and output the calculated physical field results. First, select the linear equation system solving algorithm. After the discretization process of the finite element method in Step 2, nonlinear equation systems regarding the displacement field variables and the phase field variables will be obtained respectively. Usually, the Newton method is used for iterative solution. After the discretization process of the finite element method and the linearization process of the Newton method, solving the fracture phase field model will be transformed into solving a large-scale sparse linear equation system. Use GMRES as the iterative algorithm for solving the linear equation system, and use LU decomposition as the preprocessing algorithm to improve the condition number of the coefficient matrix.

[0123] Subsequently, set the convergence conditions for linear and nonlinear solutions. For example, the relative tolerance and absolute tolerance for the nonlinear solution of the mechanical equilibrium equation are 1×10 -7 and 1×10 -9 respectively, and the absolute tolerance for linear solution is 1×10 -10 ; the relative tolerance and absolute tolerance for the nonlinear solution of the phase field control equation are 1×10 -9 and 1×10 -12 respectively, and the absolute tolerance for linear solution is 1×10 -12 .

[0124] Set the convergence conditions for decoupled solution of the phase field and displacement field: The fully coupled solution method based on Newton iteration has poor stability in solving the phase field damage fracture model and loses the information helpful for iterative convergence at the early stage of crack evolution. Therefore, a more stable alternative algorithm needs to be adopted to achieve the decoupled solution of the displacement field and the phase field. The fields to be solved include displacement field variables and phase field variables, and the intermediate variables are the crack driving force composed of elastic strain energy density and plastic deformation. In the current time step or load step, fix the phase field variables to solve the mechanical equilibrium equation to update the crack driving force, and use the updated crack driving force to solve the phase field control equation to update the phase field variables. The mechanical equilibrium equation and the phase field control equation are continuously solved alternately until the solutions or residuals of the displacement field and the phase field meet the convergence conditions. The relative tolerance and absolute tolerance of Picard iteration related to the displacement field-phase field decoupled solution strategy are 1×10 -7 and 8×10 -8 respectively.

[0125] End the analysis and output the results when the working conditions meet the given load conditions: After the numerical solution is completed, result files will be generated. The result files contain the distribution and evolution of basic field variables, such as displacement field and phase field variables, as Figure 3 shown. Additional variables that can be set for concern, such as the distribution of stress and strain, can also be set.

[0126] Example 2

[0127] As Figure 5As shown, the numerical analysis system for metal material and structure failure based on the fracture phase field model provided by the present invention includes:

[0128] A parameter determination module that determines the mechanical parameters of the metal material corresponding to the current analysis object and gives the phase field regularization parameter;

[0129] A mesh generation and model discretization module that determines the mesh generation scheme for the geometric model of the analysis object according to the determined phase field regularization parameter and synchronously completes the discretization of the physical model;

[0130] A calculation module that sets a numerical solution scheme based on the discretization result of the mesh generation and model discretization module, ends the analysis when the working condition meets the given conditions, and outputs the calculated physical field results.

[0131] Example 3

[0132] An electronic device provided by the present invention includes: a processor and a memory coupled to the processor, the memory stores a computer program, and when the computer program is executed by the processor, it implements the steps of the numerical analysis method for metal material and structure failure based on the fracture phase field model according to any one of claims 1-6.

[0133] The electronic device may further include one or more of a multimedia component, an input / output (I / O) interface, and a communication component.

[0134] Among them, the processor is used to control the overall operation of the electronic device to complete all or part of the steps in the storage medium sharing method. The memory is used to store various types of data to support the operation of the electronic device. These data may include, for example, instructions for any application or method operating on the electronic device, as well as application-related data, such as contact data, sent and received messages, pictures, audio, video, and so on. The memory can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic memory, flash memory, a magnetic disk, or an optical disc. The multimedia component may include a screen and an audio component. The screen may be a touch screen, for example, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone, and the microphone is used to receive external audio signals. The received audio signal may be further stored in the memory or sent through the communication component. The audio component also includes at least one speaker for outputting audio signals. The I / O interface provides an interface between the processor and other interface modules, and the above other interface modules may be a keyboard, a mouse, buttons, etc. These buttons may be virtual buttons or physical buttons. The communication component is used for wired or wireless communication between the electronic device and other devices. Wireless communication, such as Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination of one or more of them. Accordingly, the communication component may include: a Wi-Fi module, a Bluetooth module, and an NFC module.

[0135] In an exemplary embodiment, the electronic device may be implemented by one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components for executing the storage medium sharing method.

[0136] Embodiment 4

[0137] A computer-readable storage medium provided by the present invention stores a computer program, and when the computer program is executed by a processor, it implements the steps of the numerical analysis method for metal material and structure failure based on the broken phase field model according to any one of claims 1-6.

[0138] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0139] The present application is described with reference to the flowcharts and / or block diagrams of methods, systems, and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as the combination of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing devices generate a system for implementing the specified functions in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0140] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to operate in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction means that implements the function specified in one or more of the processes and / or blocks Figure 1 one or more of the processes and / or blocks Figure 1 specified in the function.

[0141] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, such that a series of operational steps are performed on the computer or other programmable apparatus to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the function specified in one or more of the processes and / or blocks Figure 1 one or more of the processes and / or blocks Figure 1 specified in the function.

[0142] The foregoing has shown and described the basic principles, main features and advantages of the present invention. For a person skilled in the art, it is apparent that the present invention is not limited to the details of the above-described exemplary embodiments, and without departing from the spirit or essential characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, in any aspect, the embodiments should be considered exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes that fall within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claim concerned.

[0143] In addition, it should be understood that although this specification is described in terms of embodiments, not every embodiment contains only a single technical solution, and this narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the claims of the present invention.

Claims

1. A numerical analysis method for the failure of metallic materials and structures based on a fracture phase field model, characterized in that, Including: Step 1: Determine the mechanical parameters of the metal material corresponding to the current analysis object and specify the phase-field regularization parameter; Step 2: Determine the mesh division scheme of the geometric model of the analysis object according to the phase-field regularization parameter in Step 1, and simultaneously complete the discretization of the physical model; Step 3: Set the numerical solution scheme based on the discretization result in Step 2. When the working condition meets the given conditions, end the analysis and output the calculated physical field results.

2. The numerical analysis method for metal material and structure failure based on the fracture phase field model according to claim 1, wherein In the said Step 1, determining the mechanical parameters of the metal material corresponding to the current analysis object and specifying the phase-field regularization parameter includes: Obtain the mechanical parameters of the metal material through experiments: including Young's modulus E, Poisson's ratio v, initial yield stress σ0, and plastic modulus H'; Obtain the fracture toughness G of the metallic material through experiments IC ; Determine the phase-field regularization parameter according to the experimental data and material mechanics parameters σ c is the ultimate tensile strength.

3. The numerical analysis method for failure of metal materials and structures based on the fracture phase field model according to claim 1, characterized in that In the said Step 2, determining the mesh division scheme of the geometric model of the analysis object according to the phase-field regularization parameter in Step 1 and simultaneously completing the discretization of the physical model includes: First, determine the mesh division scheme for the analysis object: locally refine the mesh for the area where cracks may occur, and the maximum mesh size h in this area max is less than half of the phase field regularization parameter l in Step 1 above c ; Subsequently, discretize the physical model: Determine the displacement field variable, phase-field variable, and intermediate variables related to the crack driving force according to the fracture phase-field model, and set the relevant initial and boundary conditions; The mathematical equation of the fracture phase-field model is as follows: When the metal material undergoes ductile fracture failure, there are two energy dissipation terms of plastic deformation and crack propagation. The corresponding fracture phase-field model is summarized under a unified thermodynamics and variational framework, and its system energy functional is as shown in Equation (1); including the elastic strain energy density and plastic work density that drive crack propagation, the dissipated energy during the crack evolution process, and the work done by external forces; In the formula: g(d) - Elastic energy degradation function; h(d) - Plastic work degradation function; ——Tensile and compressive elastic strain energy density / J·m -3 ; ψ p —— Plastic work / J·m -3 ; G IC —— Fracture toughness / J·m -2 ; l c —— Phase field regularization parameter / m; d - Phase-field variable; α(d) - Crack surface geometry function; By additionally considering the driving effect of plastic work density on the phase-field evolution and the influence of the phase-field evolution on the yield condition, the coupling of plastic deformation and crack evolution was preliminarily achieved; the weak forms of the mechanical equilibrium equation and the phase-field control equation and the yield condition are shown in Eqs. (2), (3), and (4), respectively; among them, in order to quantitatively describe the damage initiation point, a softening energy threshold \(w_0\) was additionally introduced in Eq. (3) and it was assumed that \(h(d)=g(d)\); the elastic strain energy density adopted the spherical-deviatoric decomposition method, corresponding to the tensile-compressive decomposition of the stress tensor, and the phase-field variable only acts on the tensile stress part; at the same time, in order to avoid crack healing, that is, to satisfy the irreversible constraint condition of the phase-field variable, due to the irreversibility of plastic deformation, the historical maximum value of the elastic strain energy density was set In the formula: —— effective stress tensor; —— Equivalent plastic strain; ——Equivalent stress / Pa; ε - Strain tensor; H(q) - Hardening function; The discrete scheme corresponding to the elastoplastic constitutive relation is as shown in Equations (5)-(12), and the fully implicit backward Euler difference scheme is adopted; The discrete scheme of the KKT condition corresponding to the loading / unloading situation is as shown in Equation (12); ε n+1 = ε n + dε (5) dλ = λ n+1 dt (8) After obtaining the strain increment through the Newton iteration method, first assume that the strain increment is all elastic deformation, and thus calculate the trial stress tensor; Since the yield condition is a convex function, the loading / unloading situation is judged according to the equivalent trial stress, as shown in Equations (13)-(18); When in the plastic loading working condition, use the radial return algorithm to update the stress state and ensure that the KKT constraint conditions are met; The radial return algorithm is as shown in Equations (19)-(25), where the plastic deformation of the metal material remains incompressible; To obtain the value of the consistency parameter dλ, use the Newton method for internal iteration for Equation (22), as shown in Equations (23)-(25); After obtaining the numerical value of the consistency parameter dλ, complete the update of the stress state; At the same time, since the system Jacobian matrix is constructed during the finite element solution process, it is also necessary to obtain the consistent tangent modulus used to correlate the change in the stress tensor and the change in the strain tensor, as shown in Equations (26)-(29); σ n+1 = K(tr[ε n+1 )I + 2μ(dev[ε n+1 - dλn n+1 ) (26) dσ n+1 = C:dε n+1 - 2μ(d(dλ)n n+1 + dλd(n n+1 )) (27) Based on the weak form of the control equation and boundary conditions of the above fracture phase-field model, and the stress update algorithm of the elastoplastic constitutive relation, use the finite element method for discrete solution.

4. The numerical analysis method for metal material and structure failure based on the fracture phase field model according to claim 3, wherein Update the stress state using a radial return algorithm, including the stress tensor, elastic strain tensor, and plastic strain tensor.

5. The numerical analysis method for metal material and structure failure based on the fracture phase field model according to claim 1, characterized in that In step 3, based on the discretization results of step 2, set a numerical solution scheme. End the analysis when the working condition meets the given conditions, and output the calculated physical field results, including: Select the solution algorithm for the linear equation system: After the discretization process of the finite element method in step 2, nonlinear equation systems regarding the displacement field variables and phase field variables will be obtained respectively. Usually, the Newton method is used for iterative solution; after the discretization process of the finite element method and the linearization process of the Newton method, solving the fracture phase field model will be transformed into solving a large sparse linear equation system; GMRES is used as the iterative algorithm for solving the linear equation system, and LU decomposition is used as the preprocessing algorithm to improve the condition number of the coefficient matrix; Set the convergence conditions for linear and nonlinear solvers; set the convergence conditions for decoupled solution of phase field and displacement field; adopt an alternating algorithm to achieve decoupled solution of displacement field and phase field; the fields to be solved include displacement field variables and phase field variables, and the intermediate variables are the crack driving force composed of elastic strain energy density and plastic deformation; in the current time step or load step, fix the phase field variables to solve the mechanical equilibrium equation to update the crack driving force, and use the updated crack driving force to solve the phase field control equation to update the phase field variables; the mechanical equilibrium equation and the phase field control equation are continuously solved alternately until the solutions or residuals of the displacement field and the phase field satisfy the convergence conditions; the relative tolerance and absolute tolerance of Picard iteration related to the displacement field-phase field decoupled solution strategy are 1×10 -7 and 8×10 -8 ; End the analysis and output the results when the working condition meets the given load conditions: After the numerical solution is completed, a result file will be generated.

6. The numerical analysis method for metal material and structure failure based on the fracture phase field model according to claim 5, characterized in that The result file contains the distribution and evolution of the basic field variables, namely the displacement field and phase field variables, and also includes the variables that are set to be additionally concerned, namely the distribution of stress and strain.

7. A numerical analysis system for the failure of metallic materials and structures based on the fracture phase field model, characterized in that, Including: A parameter determination module that determines the mechanical parameters of the metal material corresponding to the current analysis object and gives the phase field regularization parameter; A mesh generation and model discretization module that determines the mesh generation scheme for the geometric model of the analysis object according to the determined phase field regularization parameter and synchronously completes the discretization of the physical model; A calculation module that sets a numerical solution scheme based on the discretization results of the mesh generation and model discretization module, ends the analysis when the working condition meets the given conditions, and outputs the calculated physical field results.

8. The numerical analysis system for metal material and structure failure based on the fracture phase field model according to claim 7, characterized in that, The parameter determination module mentioned above determines the mechanical parameters of the metal material corresponding to the current analysis object and gives the phase field regularization parameter, including: Obtain the mechanical parameters of the metal material through experiments: including Young's modulus E, Poisson's ratio v, initial yield stress σ0, and plastic modulus H'; Obtain the fracture toughness G of the metallic material through experiments IC ; Determine the phase-field regularization parameter based on experimental data and material mechanics parameters σ c is the ultimate tensile strength.

9. An electronic device, characterized in that, Including: A processor and a memory coupled to the processor. The memory stores a computer program. When the computer program is executed by the processor, it implements the steps of the numerical analysis method for metal material and structure failure based on the fracture phase field model described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program. When the computer program is executed by the processor, it implements the steps of the numerical analysis method for metal material and structure failure based on the fracture phase field model described in any one of claims 1-6.

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