Phase field simulation method, device and equipment for simulating hydrogen-induced fatigue crack propagation of material and storage medium

Abstract

The invention relates to the technical field of computational material science, and discloses a phase field simulation method, device and equipment for simulating hydrogen-induced fatigue crack propagation of a material and a storage medium. The method comprises the following steps: acquiring hydrogen transmission parameters and mechanical property parameters of a target material, and establishing a material deformation equation, a hydrogen diffusion equation and a phase field evolution equation corresponding to the target material based on the hydrogen transmission parameters and the mechanical property parameters; constructing a three-field coupling relation by using a material deformation equation, a hydrogen diffusion equation and a phase field evolution equation to obtain a three-field coupling phase field simulation model; and building boundary conditions of a hydrogen diffusion equation based on a surface hydrogen absorption flux equation corresponding to the target material, and solving the three-field coupling phase field simulation model to obtain crack propagation parameters of the target material in the gaseous hydrogen environment. Therefore, through the constructed three-field coupling phase field simulation model, the dynamic crack propagation behavior of the material in the gaseous hydrogen environment is accurately described, and the prediction precision of the crack propagation process of the material in the complex environment is remarkably improved.

Description

Technical Field

[0001] The present application relates to the field of computational materials technology, and in particular to a phase field simulation method, device, equipment and storage medium for simulating hydrogen-induced fatigue crack propagation of materials. Background Art

[0002] In industrial applications, many key components (such as pressure vessels, pipelines, aerospace structures, etc.) often work in complex mechanical environments. These components not only bear cyclic loads, but may also face erosion from various environmental factors. The fatigue crack growth behavior of materials under cyclic loads has always been an important research topic in the field of materials science and engineering. However, the fatigue crack growth research in related technologies still has certain limitations, and a simulation method is needed that can target the crack growth behavior of materials in complex environments. Summary of the invention

[0003] The present application aims to solve at least one of the technical problems in the related art to a certain extent. To this end, the present application proposes a phase field simulation method, device, equipment and storage medium for simulating hydrogen-induced fatigue crack growth in materials. The main technical solutions adopted in the present application include: In a first aspect, an embodiment of the present application provides a phase field simulation method for simulating hydrogen-induced fatigue crack propagation of a material, the method comprising: obtaining hydrogen transport parameters and mechanical property parameters of a target material; establishing a material deformation equation, a hydrogen diffusion equation, and a phase field evolution equation corresponding to the target material based on the hydrogen transport parameters and the mechanical property parameters; wherein the material deformation equation is used to describe the deformation of the target material under elastic-plastic behavior, the hydrogen diffusion equation is used to reflect the diffusion of hydrogen in the target material under stress induction, and the phase field evolution equation is used to reflect the dynamic crack propagation of the target material under the combined action of hydrogen and fatigue loads; constructing a three-field coupling relationship using the material deformation equation, the hydrogen diffusion equation, and the phase field evolution equation to obtain a three-field coupled phase field simulation model; constructing the boundary conditions of the hydrogen diffusion equation based on the surface hydrogen absorption flux equation corresponding to the target material, solving the three-field coupled phase field simulation model based on the boundary conditions, and obtaining the crack propagation parameters of the target material in a gaseous hydrogen environment.

[0004] In the second aspect, an embodiment of the present application provides a phase field simulation device for simulating hydrogen-induced fatigue crack propagation of materials, the device comprising: a parameter acquisition module, used to acquire hydrogen transmission parameters and mechanical property parameters of the target material; an equation establishment module, used to establish a material deformation equation, a hydrogen diffusion equation, and a phase field evolution equation corresponding to the target material based on the hydrogen transmission parameters and the mechanical property parameters; wherein the material deformation equation is used to describe the deformation of the target material under elastic-plastic behavior, the hydrogen diffusion equation is used to reflect the diffusion of hydrogen in the target material under stress induction, and the phase field evolution equation is used to reflect the dynamic crack propagation of the target material under the combined action of hydrogen and fatigue loads; a simulation model establishment module, used to construct a three-field coupling relationship using the material deformation equation, the hydrogen diffusion equation, and the phase field evolution equation to obtain a three-field coupling phase field simulation model; a model solving module, used to construct the boundary conditions of the hydrogen diffusion equation based on the surface hydrogen absorption flux equation corresponding to the target material, solve the three-field coupling phase field simulation model based on the boundary conditions, and obtain the crack propagation parameters of the target material in a gaseous hydrogen environment.

[0005] In a third aspect, the present application further provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any of the above methods when executing the computer program.

[0006] In a fourth aspect, the present application further provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of any of the above methods when the computer program is executed by a processor.

[0007] In a fifth aspect, the present invention provides a computer program product, comprising a computer program, which implements the steps of any of the above methods when executed by a processor.

[0008] In the above embodiment, firstly, the hydrogen transmission parameters and mechanical property parameters of the target material are obtained, and based on these parameters, the material deformation equation, hydrogen diffusion equation and phase field evolution equation are established to accurately describe the deformation of the material under elastic-plastic behavior, the diffusion of hydrogen in the material and the dynamic crack expansion of the material under the combined action of hydrogen and fatigue load. Then, the three-field coupling relationship is constructed using the material deformation equation, hydrogen diffusion equation and phase field evolution equation to obtain a three-field coupling phase field simulation model. Further, boundary conditions are applied to comprehensively consider various influencing factors of the material under a complex environment. So far, the dynamic crack expansion behavior of the material under a hydrogen environment is accurately described by the constructed three-field coupling phase field simulation model, which can not only handle the situation where hydrogen atoms exist inside the material, but also is more suitable for the situation where the outside world is a gaseous hydrogen environment, which significantly improves the prediction accuracy and reliability of the crack expansion process of the material under a complex environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] In order to more clearly illustrate the specific implementation methods of the present application or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0010] Figure 1a A flow chart of a phase field simulation method for simulating hydrogen-induced fatigue crack growth of a material provided according to an embodiment of the present application; Figure 1b A comparison diagram of the da-N curve of the experimental results provided according to an embodiment of the present application; Figure 1c A comparison diagram of da / dN-ΔK curves of experimental results provided according to an embodiment of the present application; Figure 1d A schematic diagram of a finite element model provided according to an embodiment of the present application; Figure 1e A diagram showing an adaptive meshing result provided according to an embodiment of the present application; Figure 2 A flow chart of a method for determining a surface hydrogen absorption flux equation according to an embodiment of the present application; Figure 3 A flowchart of a method for constructing boundary conditions for a hydrogen diffusion equation according to an embodiment of the present application; Figure 4 A flowchart of a method for determining a phase field evolution equation according to an embodiment of the present application; Figure 5 It is a structural block diagram of a phase field simulation device for simulating hydrogen-induced fatigue crack growth of a material according to an embodiment of the present application; Figure 6 The figure is a diagram of the internal structure of a computer device according to one embodiment of the present application. DETAILED DESCRIPTION

[0011] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application.

[0012] In industrial applications, many key components (such as pressure vessels, pipelines, aerospace structures, etc.) often work in complex mechanical environments. These components not only bear cyclic loads, but may also face corrosion from various environmental factors. Taking the application scenario of hydrogen energy high-pressure storage and transportation equipment as an example, the hydrogen-related materials of hydrogen energy high-pressure storage and transportation equipment may produce high-pressure hydrogen embrittlement in a high-pressure hydrogen environment, which may cause the equipment to face the risk of fatigue failure. Therefore, in order to ensure the safe operation of hydrogen energy high-pressure storage and transportation equipment, it is very important to quantify the fatigue crack growth rate (FCGR) of materials in a high-pressure hydrogen environment. In this field, the FCGR of materials in a high-pressure hydrogen environment is mainly obtained through in-situ testing, but the test is difficult and costly. In addition, using numerical models to predict the accelerated growth of hydrogen-induced fatigue cracks is another feasible method. However, the research methods for material damage and fracture behavior in related technologies mainly include: cohesive force unit method, extended finite element method or gradient damage method. However, when the above methods are applied to the simulation of hydrogen-induced fatigue crack acceleration, they still face problems such as the difficulty in explicitly tracking the complex crack surface topology, the difficulty in establishing the coupling relationship between hydrogen diffusion and damage evolution, and the inability to accurately characterize the stress and strain field at the crack tip. In recent years, the phase field method has attracted people's attention. This method is based on the energy variation principle and can easily integrate multi-physical field factors into the phase field model. It has the potential to predict the accelerated propagation of hydrogen-induced fatigue cracks in hydrogen environments. However, the phase field model in the relevant technology ignores the surface hydrogen absorption process when describing the hydrogen transfer process in a high-pressure hydrogen environment, assuming that the hydrogen concentration boundary condition at the material-hydrogen environment interface is constant at the saturated hydrogen concentration value under the current environmental conditions. In fact, the surface hydrogen absorption process in a high-pressure hydrogen environment includes a series of complex dynamic processes such as physical adsorption, chemical adsorption, absorption, and dissolution of hydrogen on the material surface. The surface hydrogen absorption rate is affected by hydrogen pressure, stress, material properties, etc., resulting in the hydrogen concentration value at the material-hydrogen environment interface constantly changing. In addition, during the fatigue crack propagation process, hydrogen will be dynamically adsorbed on the crack tip surface along with the generation of a new crack surface. Especially in the high stress intensity factor range (ΔK), the surface dynamic hydrogen absorption behavior will have an important impact on the hydrogen distribution and FCGR at the crack tip. Therefore, the application of the constant hydrogen concentration boundary condition will lead to a large deviation between the calculated hydrogen concentration on the crack tip surface and the actual situation, which will eventually lead to inaccurate FCGR prediction results. In summary, the relevant technology has certain limitations in predicting the accelerated growth of hydrogen-induced fatigue cracks in high-pressure hydrogen environments. Therefore, it is necessary to propose a method that is suitable for high-pressure hydrogen environments and can accurately predict the accelerated growth of hydrogen-induced fatigue cracks in the full ΔK range.Based on this, according to the embodiments of the present application, embodiments of phase field simulation methods, devices, equipment and storage media for simulating hydrogen-induced fatigue crack propagation of materials are provided. It should be noted that the steps shown in the flowchart of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0013] In this embodiment, a phase field simulation method for simulating hydrogen-induced fatigue crack growth of a material is provided. Figure 1a is a flow chart of a phase field simulation method for simulating hydrogen-induced fatigue crack growth of a material according to an embodiment of the present application, such as Figure 1a As shown, the process includes the following steps: S110, obtaining hydrogen transport parameters and mechanical property parameters of the target material.

[0014] Among them, the target material refers to a specific material that needs to be analyzed and simulated in research or engineering applications. Exemplarily, the target material may refer to a material that withstands cyclic loads in a gaseous hydrogen environment, or it may refer to a high-strength steel or aluminum alloy material used in a high-pressure hydrogen storage container. Hydrogen transport parameters refer to physical quantities that describe the transport behavior of hydrogen in a material, and may include hydrogen diffusion coefficient, solubility, adsorption rate constant, and desorption rate constant. Specifically, the hydrogen transport parameters of the target material can be obtained by experimental measurement or literature search. Mechanical property parameters refer to physical quantities that describe the mechanical behavior of a material when subjected to force, and may include elastic modulus, tensile strength, Poisson's ratio, and hardening index. Specifically, the mechanical property parameters of the target material can also be obtained by experimental testing or literature search. Exemplarily, if 4130X alloy structural steel is used as the target material, the hydrogen transport parameters and mechanical property parameters of the target material may be shown in Table 1 below: Table 1 Hydrogen transport parameters and mechanical properties of 4130X material S120. Establishing a material deformation equation, a hydrogen diffusion equation, and a phase field evolution equation corresponding to the target material based on the hydrogen transport parameters and the mechanical property parameters.

[0015] Among them, the material deformation equation is used to describe the deformation of the target material under elastic-plastic behavior, the hydrogen diffusion equation is used to reflect the diffusion of hydrogen in the target material under stress induction, and the phase field evolution equation is used to reflect the dynamic crack expansion of the target material under the combined action of hydrogen and fatigue load. Specifically, the material deformation equation can adopt a constitutive model that takes into account the stress-strain relationship of the material in the elastic deformation and plastic deformation stages. Exemplarily, the classical J2 plasticity model with isotropic power-law hardening can be selected, and the material deformation equation can be obtained by combining the elastic-plastic constitutive equation describing the elastic-plastic behavior of the material. The hydrogen diffusion equation can be obtained by combining the stress-induced hydrogen diffusion theory and Oriani's equilibrium theory. To obtain the phase field evolution equation, first, the surface energy function related to crack formation can be established by defining the crack surface density function, combining the critical energy release rate of the material, and considering the fracture energy degradation function caused by hydrogen and fatigue loads respectively. Furthermore, the stiffness degradation function can be defined and based on the material deformation equation, the contribution ratio of elastic and plastic strain energy density to the fracture process can be determined to construct the total potential energy functional of the material, thereby deriving the phase field evolution equation.

[0016] S130. Constructing a three-field coupling relationship using a material deformation equation, a hydrogen diffusion equation, and a phase field evolution equation to obtain a three-field coupling phase field simulation model.

[0017] Wherein, phase field simulation model can refer to a numerical simulation method based on phase field theory, which can be used to describe the microstructure evolution and fracture behavior of materials. Specifically, the phase field model can describe the damage state of the material by introducing phase field variables, and the formation and expansion process of the material crack can be reflected by the change of phase field variables. Exemplarily, COMSOL finite element analysis software can be used to construct a three-field coupled finite element model of material deformation equation, hydrogen diffusion equation and phase field evolution equation, that is, a three-field coupled phase field simulation model. It is understandable that the phase field model can include a phase field evolution equation describing the change of phase field variables over time and space, and an energy functional describing the total energy of the system. Further, in the three physical processes of material deformation, hydrogen diffusion and phase field evolution, the interaction and influence between them are described by mathematical methods, and a comprehensive numerical model is finally derived, i.e., a three-field coupled phase field simulation model. In other words, the three-field coupling relationship can be constructed using the material deformation equation, hydrogen diffusion equation and phase field evolution equation, and the phase field variables can be linked to the material deformation and hydrogen diffusion. Finally, a three-field coupling phase field simulation model can be obtained that can simultaneously consider the material deformation, hydrogen diffusion and dynamic expansion of cracks.

[0018] S140. Construct boundary conditions of the hydrogen diffusion equation based on the surface hydrogen absorption flux equation corresponding to the target material, solve the three-field coupled phase field simulation model based on the boundary conditions, and obtain crack propagation parameters of the target material in a gaseous hydrogen environment.

[0019] Among them, the surface hydrogen absorption flux equation corresponding to the target material may refer to an equation that describes the adsorption and absorption behavior of hydrogen on the surface of the target material. The surface hydrogen absorption flux equation takes into account the physical adsorption and chemical adsorption processes of hydrogen on the surface of the material, as well as the diffusion process of hydrogen atoms from the surface into the interior of the material. The hydrogen diffusion equation may refer to an equation that describes the diffusion behavior of hydrogen in the target material. It should be noted that there is a surface hydrogen absorption process on any surface of the material, that is, the surface hydrogen absorption flux equation tends to be simple surface hydrogen absorption. The hydrogen diffusion equation can be understood as hydrogen transport, which focuses more on describing the diffusion behavior of hydrogen inside the material, including the concentration gradient of hydrogen in the material, the diffusion coefficient, and the hydrogen diffusion behavior under stress induction.

[0020] It is understandable that when using finite element analysis and numerical simulation, boundary conditions need to be applied. The boundary conditions refer to the conditions imposed on the boundaries of the model that can be used to simulate the constraints and external effects in actual physical problems. Specifically, the boundary conditions can include load boundary conditions (i.e. fatigue loads), surface hydrogen absorption flux boundary conditions, displacement boundary conditions, and initial internal hydrogen concentration boundary conditions.

[0021] Specifically, the load boundary condition can be implemented by applying a cyclically changing force in the model to simulate the fatigue load in the actual working condition. That is, a cyclic load can be defined so that the force changes from small to large and then from large to small within a certain range to form a cycle. This cyclic load can be expressed as a sine function or other periodic function to simulate the actual cyclic loading process. The displacement boundary condition can be implemented by applying displacement constraints to certain parts of the model to simulate the fixed or restricted conditions in the actual working condition. For example, displacement boundary conditions can be applied to certain nodes or regions of the model to limit its displacement in certain directions. The initial internal hydrogen concentration boundary condition can be implemented by setting the initial hydrogen concentration inside the model according to the initial hydrogen concentration of the material. If the target material is immersed in a hydrogen environment for a long time, its internal hydrogen concentration will be higher; if the target material has not been exposed to a hydrogen environment, its initial internal hydrogen concentration can be set lower. The surface hydrogen absorption flux boundary condition can realize the dynamic hydrogen absorption process by applying the surface hydrogen absorption flux equation to the dynamically expanding crack surface. First, mathematical tools can be used to track the crack surface, and then the surface hydrogen absorption flux is applied on it to simulate the adsorption and diffusion behavior of hydrogen on the crack surface, ultimately ensuring that the hydrogen diffusion equation can accurately reflect the dynamic adsorption process of hydrogen on the material surface.

[0022] Furthermore, after determining the boundary conditions, the three-field coupled phase-field simulation model can be solved using the COMSOL solver based on the boundary conditions, and finally the crack propagation parameters of the target material in a gaseous hydrogen environment can be obtained. The crack propagation parameters refer to parameters that describe the crack propagation behavior in the material, which may include the crack propagation rate, the crack propagation increment and the cycle number relationship curve (da-N curve) or the fatigue crack propagation rate and stress intensity factor range relationship curve (da / dN-ΔK curve), etc.

[0023] Optionally, after simulating the crack propagation parameters of the target material in a gaseous hydrogen environment, it can also be tested and verified. For example, a test material with the same parameters as the target material used in the simulation calculation can be used for the test, and the hydrogen transmission parameters and mechanical property parameters of the test material are kept the same as the hydrogen transmission parameters and mechanical property parameters of the target material. For example, 4130X alloy structural steel can also be used as a test material, and a fatigue crack growth rate (Fatigue Crack Growth Rate FCGR) test of a 4130X steel CT specimen can be carried out in a 100MPa high-pressure hydrogen environment. The chemical composition of 4130X is 0.322C-0.78Mn-0.216Si-0.997Cr-0.199Mo, and the yield strength is 663MPa. Before the test begins, the test chamber and the piping system are first evacuated, and then purged with hydrogen at a pressure between 0.2 and 3MPa for 3 times. After purging, hydrogen is filled into the test chamber. After the hydrogen pressure in the chamber reached the test pressure for 30 minutes, a 3 mm precrack was made with a decreasing force amplitude. The force amplitude at the end of the precrack was 15.3 kN. The FCGR test was performed with a constant force amplitude of 16.2 kN. For the precrack and FCGR tests, f was 1 Hz and R was 0.1. After the FCGR test, the da / dN-ΔK curve was extracted, as well as the da-N curve.

[0024] At the same time, in order to compare the parameters obtained by simulation, the traditional model with constant hydrogen concentration boundary conditions was also used for calculation under the condition that the conditions of hydrogen diffusion, material properties, force loading, etc. remain unchanged. For example, the point-by-point constraint method in COMSOL finite element analysis software can be used to calculate the The fracture zone specifies a constant hydrogen concentration , to obtain the model simulation results using the traditional constant hydrogen concentration boundary condition. Finally, please refer to Figure 1b and Figure 1c , Figure 1b and Figure 1cThe test material used is 4130X alloy structural steel. The hydrogen application conditions are a hydrogen pressure of 100 MPa, a loading frequency f of 1 Hz, and a stress ratio R of 0.1. Specifically, the stress ratio R = Kmin / Kmax, where Kmin and Kmax are the minimum and maximum stress intensity factors respectively. From Figure 1b and Figure 1c it can be seen that by constructing the three-field coupling relationship using the material deformation equation, hydrogen diffusion equation, and phase-field evolution equation, the obtained three-field coupled phase-field simulation model can more accurately predict the accelerated propagation of hydrogen-induced fatigue cracks in the entire ΔK range.

[0025] It should be understood that when solving and calculating the three-field coupled phase-field simulation model, a geometric model including a pin and a compact tension (CT) specimen can be first established in the COMSOL finite element analysis software. The pin is defined as a rigid body, and quadrilateral meshes are used on the crack propagation path to improve the calculation convergence. At the same time, adaptive refined meshes are set in the fracture region and the near-surface region with a higher hydrogen concentration to improve the calculation accuracy. Exemplarily, please refer to Figure 1d , to improve the calculation efficiency of the phase-field simulation model, in the finite element model, triangular meshes are used for the rest, and adaptive refined meshes are set in the fracture region and the near-surface region with a higher hydrogen concentration to determine the crack propagation path. Two error expressions are set in the error indicator to identify the regions that need to be refined: sqrt(comp1.p^2), comp1.c^2. The characteristic element length h after mesh refinement is 0.0156 mm, meeting the requirement of h < l0 / 5.4. The initial crack length is 3 mm, and the initial crack is defined by the method of defining a larger initial value of H, as shown in Figure 1e .

[0026] In the above embodiment, first, the hydrogen transport parameters and mechanical property parameters of the target material are obtained, and based on these parameters, the material deformation equation, hydrogen diffusion equation, and phase-field evolution equation are established to accurately describe the deformation of the material under elastoplastic behavior, the diffusion of hydrogen in the material, and the dynamic crack propagation of the material under the combined action of hydrogen and fatigue load. Then, the three-field coupling relationship is constructed using the material deformation equation, hydrogen diffusion equation, and phase-field evolution equation to obtain the three-field coupled phase-field simulation model. Further, boundary conditions are applied to comprehensively consider various influencing factors of the material in a complex environment. Thus, through the constructed three-field coupled phase-field simulation model, the dynamic crack propagation behavior of the material in a hydrogen environment is accurately described. It can not only handle the situation where hydrogen atoms exist inside the material, but is more applicable to the situation where the external environment is a gaseous hydrogen environment, significantly improving the prediction accuracy and reliability of the crack propagation process of the material in a complex environment.

[0027] In some embodiments, please refer to the appendix Figure 2, the surface hydrogen absorption flux equation corresponding to the target material is determined by the following method: S210, determining the physical adsorption process, chemical adsorption process, desorption process, absorption process and desorption process of hydrogen on the surface of the target material.

[0028] Among them, the physical adsorption process refers to the process in which hydrogen molecules interact with the material surface through van der Waals forces to form an adsorption layer. The process can be shown as follows: Right now Migrate to the outer surface of the metal and produce physical adsorption.

[0029] The chemical adsorption process refers to the process in which hydrogen molecules react chemically with the surface of the material to form chemical bonds. The process can be shown as follows: In the formula, It refers to hydrogen atoms adsorbed on the metal surface (adsorbed hydrogen). Decomposes into atomic hydrogen, producing chemical adsorption.

[0030] It can be understood that in the whole process of interaction between hydrogen and target material, physical adsorption process occurs first, then chemical adsorption process occurs, and the two together constitute the adsorption process, with an adsorption rate constant The desorption process refers to the process in which hydrogen molecules adsorbed on the surface of the material are released back into the gas phase. Specifically, the entire desorption process is the combination of two hydrogen atoms to form a hydrogen molecule, which can essentially be regarded as chemical desorption, with a desorption rate constant of The absorption process refers to the process in which hydrogen molecules enter the material from the surface, while the desorption process refers to the process in which hydrogen molecules escape from the material into the gas phase. These two processes can be expressed as follows: In the formula, Represents hydrogen atoms adsorbed on the metal surface (adsorbed hydrogen); H abs Indicates the hydrogen absorbed into the material. becomes H absorbed into the material abs In this process, the absorption process has an absorption rate constant , the desorption process has a desorption rate constant .

[0031] Specifically, the physical adsorption process, chemical adsorption process, desorption process, absorption process and desorption process of hydrogen on the surface of the target material can be determined by experimental measurement or literature search, so as to obtain the adsorption rate constant, desorption rate constant, absorption rate constant and desorption rate constant, etc., to describe the dynamic process of hydrogen molecules in the material.

[0032] S220. Determine a hydrogen adsorption flux equation based on the physical adsorption process, the chemical adsorption process, and the desorption process.

[0033] The hydrogen adsorption flux equation may refer to a mathematical model that describes the adsorption and desorption behavior of hydrogen molecules on the surface of a material. Specifically, based on the physical adsorption process, chemical adsorption process, and desorption process, and combined with the general formula of the adsorption isotherm, a hydrogen adsorption flux equation as shown below can be constructed: In the formula, represents the hydrogen adsorption flux; is the adsorption rate constant of hydrogen on the target crack surface; It represents the surface hydrogen coverage, which indicates the proportion of hydrogen atoms in the target crack surface; is the hydrogen fugacity, which indicates the pressure state of hydrogen on the target crack surface. , b is a constant , R is the gas constant; T is the absolute temperature; is the desorption rate constant of hydrogen on the target crack surface.

[0034] Specifically, the first part of the hydrogen adsorption flux equation is the adsorption term , which describes the process of hydrogen atoms adsorbing onto the surface of the target material. The second part of the formula is the desorption term , which describes the process of hydrogen atoms desorbing from the surface of a material. Through the hydrogen adsorption flux equation, the hydrogen adsorption behavior of materials under different hydrogen pressures and temperatures can be simulated and predicted, providing accurate theoretical support for the subsequent establishment of the surface hydrogen adsorption flux equation.

[0035] S230. Determine a hydrogen absorption flux equation based on the absorption process and the desorption process.

[0036] The hydrogen absorption flux equation may refer to a mathematical model that describes the rate at which hydrogen atoms enter the interior of a material from the surface of the material. Specifically, based on the absorption process and the desorption process, a hydrogen absorption flux equation as shown below may be constructed: In the formula, represents the hydrogen absorption flux; is the absorption rate constant of hydrogen on the target crack surface; is the partial molar volume of hydrogen; is the hydrostatic stress; is the surface hydrogen coverage, which indicates the proportion of hydrogen atoms on the target crack surface; is the desorption rate constant of hydrogen on the target crack surface; is the lattice hydrogen concentration near the inner surface of the target crack surface.

[0037] Specifically, the first part of the hydrogen absorption flux equation is the absorption term , which describes the process of hydrogen atoms entering the material from the surface. The second part of the formula is the desorption term , which describes the process of hydrogen molecules escaping from the inside of the material into the gas phase. Through the hydrogen absorption flux equation, the hydrogen absorption behavior of the material under different hydrogen pressure and temperature conditions can be simulated and predicted, providing accurate physical and mathematical support for the subsequent establishment of the surface hydrogen absorption flux equation.

[0038] S240, solving the hydrogen adsorption flux equation and the hydrogen absorption flux equation simultaneously to obtain the surface hydrogen absorption flux equation at any time.

[0039] Among them, the surface hydrogen absorption flux equation can be a mathematical model that comprehensively describes the adsorption and absorption behavior of hydrogen on the material surface. It is obtained by combining the hydrogen adsorption flux equation and the hydrogen absorption flux equation, and can comprehensively describe the dynamic process of hydrogen adsorption and absorption in the material at any time, thereby simulating and predicting the hydrogen absorption behavior of the material under different hydrogen pressure and temperature conditions.

[0040] Specifically, after combining the hydrogen adsorption flux equation and the hydrogen absorption flux equation, the surface hydrogen coverage at any time can be obtained: , as shown below: In the formula, is the desorption rate constant of hydrogen on the target crack surface; is the adsorption rate constant of hydrogen on the target crack surface; is the surface hydrogen coverage, which indicates the proportion of hydrogen atoms on the target crack surface; is the hydrogen fugacity, which indicates the pressure state of hydrogen on the target crack surface. , b is a constant , R is the gas constant; T is the absolute temperature; is the absorption rate constant of hydrogen on the target crack surface; is the partial molar volume of hydrogen; is the hydrostatic stress; is the desorption rate constant of hydrogen on the target crack surface; is the lattice hydrogen concentration near the inner surface of the target crack surface.

[0041] Furthermore, the obtained Substituting hydrogen into either the hydrogen adsorption flux equation or the hydrogen absorption flux equation, the surface hydrogen absorption flux equation at any time can be obtained. .

[0042] In the above-mentioned embodiment, by determining the physical adsorption, chemical adsorption, desorption, absorption and desorption processes of hydrogen on the surface of the target material and obtaining the corresponding rate constants, a hydrogen adsorption flux equation and a hydrogen absorption flux equation are constructed based on these processes. Finally, by jointly solving these two equations, a surface hydrogen absorption flux equation that can comprehensively describe the dynamic process of hydrogen adsorption and absorption on the material surface is obtained. This can accurately simulate and predict the hydrogen absorption behavior of the material under different hydrogen pressure and temperature conditions, and provide an important theoretical basis and precise quantitative analysis tool for studying the hydrogen embrittlement phenomenon and hydrogen storage performance of the material.

[0043] In some embodiments, please refer to the attached Figure 3 , based on the surface hydrogen absorption flux equation corresponding to the target material, the boundary conditions of the hydrogen diffusion equation are constructed, including: S310, selecting a target crack surface, and determining a Dirac function based on a phase field variable corresponding to the target crack surface.

[0044] The phase field variable is used to describe the failure state of the target material. It can be a scalar field used to describe the distribution of different phases in the material. For example, in the phase field method, the phase field variable needs to be defined first. The value of is between 0 and 1, then 0 can be used to indicate that the material is intact, and 1 can be used to indicate that the material is completely destroyed (crack area). The target crack surface can refer to the surface of a crack that has been formed or is about to be formed in the material. Specifically, the crack surface can be described by a phase field variable, that is, the phase field variable can be used to characterize the distribution of different phases inside the material, including the formation and expansion of cracks. Furthermore, the isosurface of a specific phase field variable can be selected as the target crack surface to construct the Dirac function of the crack surface. Exemplarily, the phase field variable can be selected The isosurface of is taken as the target crack surface, and the corresponding phase field variables are determined based on the crack surface, that is, , and then combine this phase field variable with the Dirac function to accurately represent the location of the crack surface.

[0045] S320. Based on the Dirac function and the surface hydrogen absorption flux equation, the boundary conditions of the hydrogen diffusion equation are constructed.

[0046] Specifically, by combining the Dirac function with the surface hydrogen absorption flux equation, a source term Q can be defined to specify the hydrogen flux on the moving crack surface. In other words, based on the surface hydrogen absorption flux equation, constraints are introduced into the hydrogen diffusion equation. The source term Q is actually the surface hydrogen absorption flux equation in flux form applied to the dynamically expanding crack surface, and then used as the boundary condition of the hydrogen diffusion equation. Exemplarily, the target crack surface can be tracked with the help of the mathematical tool Dirac function, and then the surface hydrogen absorption flux equation is multiplied by the Dirac function to obtain the source term Q. That is, the surface hydrogen absorption flux equation is applied to the target crack surface reflected by the Dirac function. The flux is used as the boundary condition for the hydrogen diffusion equation.

[0047] In the above implementation, by combining the Dirac function with the surface hydrogen absorption flux equation, the hydrogen flux can be accurately applied to the dynamically extending crack surface, thereby providing accurate boundary conditions for the hydrogen diffusion equation. Not only can the position and shape of the crack surface be accurately described, but also the adsorption and diffusion behavior of hydrogen on the crack surface can be accurately simulated, thereby improving the prediction accuracy of hydrogen-induced fatigue crack growth behavior.

[0048] In some embodiments, the boundary conditions are expressed as follows: In the formula, represents the source term in the target material; is the surface hydrogen absorption flux equation; is the Dirac function, which is used to describe the distribution of the source term; n is the normal vector, which indicates the normal direction of the target crack surface; I is the unit matrix.

[0049] Specifically, the above formula models the flow and distribution of hydrogen on the crack plane, especially when considering hydrogen embrittlement and hydrogen-induced crack growth. The surface hydrogen flux and the rate of change of the out-of-plane normal vector n of the target crack. It represents the direction of the target crack surface relative to the material coordinate system, and the Dirac function δ is used to smooth the crack tip in the numerical simulation, avoiding the singularity problem of the crack tip in traditional fracture mechanics.

[0050] The surface hydrogen uptake flux equation is expressed as follows: In the formula, is the desorption rate constant of hydrogen on the target crack surface; is the adsorption rate constant of hydrogen on the target crack surface; is the surface hydrogen coverage, which indicates the proportion of hydrogen atoms on the target crack surface; is the hydrogen fugacity, which indicates the pressure state of hydrogen on the target crack surface. , b is a constant , R is the gas constant; T is the absolute temperature; is the absorption rate constant of hydrogen on the target crack surface; is the partial molar volume of hydrogen; is the hydrostatic stress; is the desorption rate constant of hydrogen on the target crack surface; is the lattice hydrogen concentration near the inner surface of the target crack surface.

[0051] Specifically, after combining the hydrogen adsorption flux equation and the hydrogen absorption flux equation, as shown in the above formula, the surface hydrogen coverage at any time can be obtained: , further, the obtained Substituting hydrogen into either the hydrogen adsorption flux equation or the hydrogen absorption flux equation, the surface hydrogen absorption flux equation at any time can be obtained. .

[0052] where the Dirac function is approximated by: In the formula, the function It ensures that the Dirac function reaches its maximum value at the target crack surface, which is used to specify the position of the target crack surface; is the phase field variable; is the normalization coefficient, so that the function The integral on the interval [0,1] is 1, that is, , which satisfies the basic definition of the Dirac function.

[0053] Specifically, It is a reflection A measure of the rate of change in space. For example, if the phase field variable is chosen As the target crack surface, Can be used in The Dirac function is strengthened near the boundary to simulate the peak characteristics of the Dirac function.

[0054] In the above implementation, the flow and distribution of hydrogen on the crack surface are simulated by defining the source term in the target material and combining the surface hydrogen absorption flux equation and the Dirac function. Not only the effects of hydrogen embrittlement and hydrogen-induced crack growth are considered, but also the dynamic behavior of hydrogen on the crack surface is accurately described, achieving accurate prediction of the hydrogen-induced crack growth behavior of the material under complex stress state.

[0055] In some embodiments, see Figure 4 , the phase field evolution equation corresponding to the target material is determined by: S410, defining phase field variables, and establishing a crack surface density function corresponding to the target material.

[0056] The crack surface density function is used to describe the distribution and morphology of cracks in the target material. Specifically, the crack surface density function can be a function expressed as the gradient of the phase field variable or its higher-order derivative after the phase field variable is defined. For example, in numerical simulation, the crack surface density function can be defined by calculating the gradient of the phase field variable.

[0057] S420, determining a hydrogen damage degradation function caused by hydrogen and a fatigue damage degradation function caused by fatigue load, and constructing a critical energy release rate of the target material based on the hydrogen damage degradation function and the fatigue damage degradation function.

[0058] Among them, the hydrogen damage degradation function can be a function that describes the influence of hydrogen on material properties, which is used to quantify the degree of damage caused by hydrogen in the material. Specifically, the hydrogen damage degradation function can be established by measuring experimental data such as the diffusion behavior of hydrogen in the material and the influence of hydrogen on the mechanical properties of the material, combined with theoretical models. The fatigue damage degradation function can be a function that describes the damage accumulation of the material under cyclic loads, which is used to quantify the degree of damage of the material during the fatigue process. Specifically, the fatigue damage degradation function can be established by measuring experimental data such as the fatigue life and crack growth rate of the material under different load conditions, combined with theoretical models. Furthermore, based on the hydrogen damage degradation function and the fatigue damage degradation function, the critical energy release rate of the target material can be constructed. Similarly, the critical energy release rate can be a function that describes the critical value of energy released by the material during crack growth, taking into account the influence of factors such as the fracture toughness, crack length, and load of the material on crack growth, and can be used to determine whether the crack will spontaneously grow.

[0059] S430: Establishing a surface energy function related to crack formation based on the critical energy release rate and the crack surface density function.

[0060] The surface energy function can be an energy functional in an integrated form, which is used to evaluate the energy changes during crack formation and propagation. After determining the critical energy release rate and the crack surface density function, the two can be integrated at the volume level of the entire target material to construct a surface energy function related to crack formation.

[0061] S440. Determine a storage strain energy function based on the stiffness degradation function.

[0062] Among them, the stored strain energy function is used to evaluate the total strain energy stored in the target material during the stress process. The stiffness degradation function can be used to describe the gradual change in the stiffness (i.e., the ability to resist deformation) of a material after continuous loading or damage. It can indicate how the stiffness of a material decreases with the increase of phase field variables, thereby quantifying the change in stiffness of the material during the damage process, and ultimately reflecting how the mechanical properties of the material are affected.

[0063] It should be noted that before determining the storage strain energy function, it is also necessary to determine the strain energy density of the material in the undamaged state according to the mechanical parameters of the target material, that is, the undamaged isotropic storage strain energy density function. First, a symmetric small strain tensor can be defined, and the elastic strain and plastic strain can be considered simultaneously using standard partitioning to construct an undamaged isotropic storage strain energy density function. In the calculation process, based on the spherical / deviation splitting theory, the proportional relationship between the contribution of elastic strain energy density and plastic strain energy density to the fracture process can be defined as 1:1. Furthermore, based on the stiffness degradation function, the undamaged isotropic storage strain energy density function is combined to determine the storage strain energy function.

[0064] S450, constructing a phase field evolution equation corresponding to the target material based on the surface energy function and the storage strain energy function.

[0065] Specifically, the total potential energy functional of the material can be established based on the surface energy function and the storage strain energy function, and then the phase field evolution equation corresponding to the target material can be constructed using the product rule and Gaussian divergence theorem. A historical variable can also be added, and the historical variable term is defined as the maximum storage strain energy density reached at each time point to ensure the irreversible growth of the phase field variable.

[0066] In the above-mentioned implementation mode, by comprehensively considering the influence of multiple factors such as hydrogen damage, fatigue damage, and changes in material mechanical properties on the formation and expansion of material cracks, the crack evolution process of the target material under complex working conditions can be described more accurately and comprehensively, providing strong theoretical support and effective simulation means for the study of material fracture and damage, thereby optimizing material design and engineering application solutions, and even improving the reliability and service life of the material.

[0067] In some embodiments, the surface energy function is represented by: In the formula, represents the surface energy function, which can represent the crack surface energy within the entire material volume; represents the critical energy release rate; represents the crack surface density function.

[0068] Specifically, it can be seen from the above formula that by integrating the crack surface density over the entire material volume To calculate the total crack surface energy, in order to describe the energy changes during crack formation and propagation.

[0069] where the crack surface density function is expressed as follows: In the formula, represents the crack surface density function; is the length scale parameter; is the phase field variable. Specifically, It is a characteristic length that can be used to control the width of the diffuse crack area and affect the continuity and smoothness of crack propagation. It is a term proportional to the crack volume and can represent the surface energy inside the crack. The term is proportional to the width of the crack tip area and can represent the surface energy of the crack surface. The phase field variable is The gradient of , which represents the phase field variable Furthermore, by minimizing the crack surface density function, the optimal shape and propagation path of the crack can be obtained, thereby simulating the crack formation and propagation process.

[0070] where the critical energy release rate is expressed as follows: In the formula, represents the critical energy release rate; is the coverage of grain boundary trap hydrogen, which indicates the proportion of trap sites at the grain boundary occupied by hydrogen atoms. is the cumulative history variable of fatigue damage; is the initial critical energy release rate without degradation, which indicates the minimum energy release rate required for crack propagation when the target material is not affected by any damage or degradation; represents the hydrogen damage degradation function; represents the fatigue damage degradation function.

[0071] Specifically, the critical energy release rate It can be used to describe the ability of a material to absorb energy during crack propagation, that is, the ability of a material to resist crack propagation, and is defined as a function of hydrogen and fatigue load. It can be used to describe the effect of hydrogen on the critical energy release rate of materials. is the cumulative history variable of fatigue damage, which can be expressed as cumulative plastic strain or damage variable. It can refer to the critical energy release rate of the material in the reference state, that is, the critical energy release rate under standard conditions (such as a hydrogen-free environment and without plastic deformation).

[0072] Wherein, the hydrogen damage degradation function is expressed as follows: In the formula, represents the hydrogen damage degradation function, is the grain boundary trap hydrogen coverage; is the damage coefficient, which can be taken ; is the lattice hydrogen concentration; is the lattice site density; R is the gas constant; T is the absolute temperature; is the grain boundary trap binding energy, which can be taken as =30 kJ / mol.

[0073] That is to say, to determine the hydrogen damage degradation function caused by hydrogen, we can first determine the grain boundary trap hydrogen coverage based on the lattice hydrogen concentration, lattice site density and grain boundary trap binding energy, and then construct the hydrogen damage degradation function based on the grain boundary trap hydrogen coverage and damage coefficient. Specifically, The coverage of grain boundary trap hydrogen can be described by How does it affect the critical energy release rate of the material? is a dimensionless proportionality factor used to adjust the influence of hydrogen coverage on the critical energy release rate. It can be calculated based on the discrete Fourier transform (DFT) of surface energy degradation and can be taken as . Lattice hydrogen concentration It can represent the concentration of hydrogen atoms in the material lattice, expressed as atomic percentage (at.%), and the lattice site density It can represent the number of sites in the crystal lattice per unit volume and is used to calculate the distribution of hydrogen atoms in the crystal lattice. The grain boundary trap binding energy can represent the change in the Gibbs free energy for hydrogen atoms to escape from the grain boundary, while It describes the probability of hydrogen escaping from the grain boundary, thus affecting the calculation of the hydrogen coverage of the grain boundary trap. It is understandable that because the presence of hydrogen atoms will reduce the fracture toughness of the material, the hydrogen damage degradation function can be used. To accurately measure the impact of hydrogen atoms on material properties, the hydrogen damage degradation function , it is possible to predict how the fracture toughness of a material will change under different conditions of hydrogen concentration, temperature and material structure.

[0074] Wherein, the fatigue damage degradation function is expressed as follows: In the formula, represents the fatigue damage degradation function; is the cumulative history variable of fatigue damage; is the threshold parameter, indicating the point at which performance degradation begins to be observed; It is a material parameter used to adjust the degradation rate.

[0075] That is, the fatigue damage degradation function can be constructed based on the cumulative historical variables of fatigue damage, threshold parameters, and material parameters. The threshold parameter represents the point at which performance degradation begins to be observed, and the material parameter is used to adjust the degradation rate. Specifically, the threshold parameter That is, the fatigue threshold parameter, which can be assumed to be . Material parameters It is a material parameter that characterizes the slope of the logarithmic function. According to the material properties of low alloy steel, it can be taken as .

[0076] Furthermore, the fatigue damage degradation function It can be used to describe how the performance of a material changes with the accumulated historical variables after fatigue loading. From the above formula, it can be seen that when When , the function value is 1. This means that in the initial stage of fatigue damage, the performance of the material has not yet begun to degrade and still maintains its original state. When , within this range, as the accumulated historical variables As the temperature increases, the performance of the material begins to deteriorate. When , the function value is 0. This means that the performance of the material has been completely degraded and may have reached the end of fatigue life.

[0077] It is important to understand that cumulative historical variables The evolution process over time can be expressed as follows: In the formula, It represents the cumulative history variable function at time t, that is, it represents the accumulation of fatigue damage experienced by the target material from the beginning to time t. is the Heaviside function (unit step function), so that the accumulated historical variables Increases only when loaded, can be based on fatigue damage variables and its time derivative In the above formula, the damage experienced by the material during fatigue loading is accumulated by integration. For example, when the damage change rate When it is larger, it means that the damage to the material is increasing rapidly, which will be reflected in the integral as a larger damage accumulation.

[0078] Furthermore, according to the energy balance principle, the fatigue damage variable It can be defined as the process shown below: In the formula, It is a fatigue damage variable, which represents the accumulation of fatigue damage experienced by the material and can be used to evaluate the remaining life of the material and predict fatigue failure. The stiffness degradation function due to damage evolution can be used to adjust the dependence of damage accumulation on the crack state. is the elastic strain tensor, represents the elastic strain energy density, which describes the contribution of elastic strain to fatigue damage. is the plastic strain tensor, Represents the plastic strain energy density, which describes the contribution of plastic strain to fatigue damage.

[0079] In the above implementation, by defining the crack surface density function, the crack formation and expansion process is accurately described. At the same time, by defining the critical energy release rate, the effects of hydrogen and fatigue on material properties are described respectively, where the hydrogen damage degradation function takes into account factors such as grain boundary trap hydrogen coverage, damage coefficient, and lattice hydrogen concentration, while the fatigue damage degradation function describes the performance degradation of the material under fatigue loading through cumulative historical variables. Through precise modeling and quantitative analysis, the crack extension behavior of the material under complex stress states is comprehensively evaluated, significantly improving the prediction accuracy of the crack extension process of the material under complex environments.

[0080] In some embodiments, the stored strain energy function is expressed as follows: In the formula, represents the stored strain energy function, is the displacement vector, is the phase field variable; represents the undamaged isotropic stored strain energy density function, is a symmetric small strain tensor, which means that ; represents the stiffness degradation function.

[0081] That is to say, the storage strain energy function can be constructed based on the stiffness degradation function and the undamaged isotropic storage strain energy density function. Among them, the undamaged isotropic storage strain energy density function can be determined based on the elastic strain energy density and the plastic strain energy density; the elastic strain energy density can be determined based on the first Latin parameter, the second Latin parameter and the elastic strain tensor of the target material; the plastic strain energy density can be determined based on the elastic strain tensor, the undamaged Cauchy stress tensor and the plastic strain rate tensor; the undamaged Cauchy stress tensor can be used to represent the stress state of the target material when it is not damaged.

[0082] It should be noted that the symmetric small strain tensor It can be used to describe the degree of deformation inside the material due to external forces. In small deformation theory, the strain tensor is linear and corresponds to the linear part of the deformation gradient. It means that , which is used to describe small deformations of materials in continuum mechanics. is a displacement vector, which represents the displacement of a point in the material in all directions after being acted upon by an external force. It can be understood that in continuum mechanics, for a continuous material body, the displacement vector It can be expressed as u(x), where x is the position of a point in the material when it is not deformed. When the material is deformed by an external force, the new position of the point can be expressed as x + u(x). Displacement gradient describes the distribution of this displacement in space, and the small strain tensor This further describes the degree of deformation of the material. Optionally, the constitutive theory of the material also considers elastic strain and plastic strain , and use standard partitioning for it: .

[0083] where the undamaged isotropic stored strain energy density function is expressed as follows: In the formula, represents the undamaged isotropic stored strain energy density function; It represents the elastic strain energy density, which indicates the energy stored in the target material during the elastic deformation stage; It represents the plastic strain energy density, which indicates the energy stored in the target material during the plastic deformation stage; is the first Latin American parameter of the target material; is the second Latin American parameter of the target material; is the elastic strain tensor; is the deviatoric part of the elastic strain tensor, which is used to ignore the contribution of volume change to the strain energy; brackets for Macaulay; is the undamaged Cauchy stress tensor, which represents the stress state of the target material when no damage occurs; is the plastic strain tensor; is the plastic strain rate tensor.

[0084] It is important to understand that Represents the trace of the elastic strain tensor, that is, the sum of the diagonal elements of the elastic strain tensor. The above formula combines the elastic and plastic strain energy densities to provide a comprehensive energy description. Based on the spherical / deviation splitting theory, the proportional relationship between the contribution of the elastic strain energy density and the plastic strain energy density to the fracture process is defined as 1:1. Finally, combined with the stiffness degradation function, the storage strain energy function representing the total strain energy stored in the material during the stress process is obtained.

[0085] where the stiffness degradation function is expressed as follows: In the formula, represents the stiffness degradation function; is the phase field variable; k is the stability parameter, which can be .

[0086] Specifically, the stability parameter k can be a parameter used to maintain the good state of the equation system. Its value should be as small as possible to avoid affecting the calculation. . Furthermore, when the phase field variable When the phase field variable increases from 0 to 1, it means that the crack has grown from the beginning to the full extension. When it is close to 1, the stiffness degradation function is close to 0, indicating that the stiffness of the target material is significantly reduced. Function at the crack tip (phase field variable There is a smooth transition near 1), thus avoiding the singularity problem at the crack tip in traditional fracture mechanics.

[0087] In the above-mentioned embodiment, the energy state of the material is comprehensively described by combining the elastic strain energy density and the plastic strain energy density, and the stiffness degradation function is used to reflect the change in stiffness of the material during crack formation and expansion, thereby being able to more accurately, reasonably and effectively simulate and analyze the mechanical behavior of the material during the stress process as well as damage, fracture, etc.

[0088] In some embodiments, the phase field evolution equation is expressed as follows: In the formula, represents the critical energy release rate; is the coverage of grain boundary trap hydrogen, which indicates the proportion of trap sites at the grain boundary occupied by hydrogen atoms. is the cumulative history variable of fatigue damage; is the phase field variable; is the length scale parameter, which is used to control the width of the crack tip region in the target material; H represents the history variable, which is used to ensure the irreversible growth of the phase field variable.

[0089] Among them, historical variables are represented in the following way: In the formula, is the undamaged isotropic stored strain energy density, is a symmetric small strain tensor, which means that , is the displacement vector.

[0090] Specifically, It represents the resistance of crack surface energy to crack extension, that is, it is related to the crack surface energy and describes the influence of crack surface energy on crack evolution. It represents the evolution of crack shape and can reflect the influence of crack shape change on crack propagation. These two factors work together to simulate the dynamic propagation process of cracks in target materials.

[0091] It should be understood that before constructing the phase field evolution equation corresponding to the target material, it is also necessary to establish the total potential energy functional of the target material based on the surface energy function and the storage strain energy function, which can be shown as follows: In the formula, represents the total potential energy functional of the target material; represents the stored strain energy function, is the displacement vector, is the phase field variable; Represents the surface energy function. Specifically, the total potential energy functional can comprehensively describe the energy changes of the target material during the strain and internal crack formation and expansion process under the action of external forces. Furthermore, based on the total potential energy functional of the target material, the product rule and Gaussian divergence theorem are used to obtain the phase field evolution equation that ultimately reflects the dynamic crack expansion of the target material under the combined action of hydrogen and fatigue loads.

[0092] In the above implementation, the total potential energy functional established based on the surface energy function and the storage strain energy function uses the product rule and Gaussian divergence theorem to comprehensively consider the influence of hydrogen and fatigue load, and introduces historical variables to avoid problems such as reverse crack expansion that may occur during the simulation process. Ultimately, the dynamic crack expansion of the target material under the combined action of hydrogen and fatigue load can be accurately reflected.

[0093] In some embodiments, the material deformation equation corresponding to the target material is expressed as follows: In the formula, is the current yield stress; is the initial yield stress, which is the starting stress for the material to undergo plastic deformation; E is Young's modulus; n is the hardening index; is the equivalent plastic strain, which is expressed as , is the component of the plastic strain tensor, i can be any one of 1, 2, 3, and j can be any one of 1, 2, 3.

[0094] Specifically, the material deformation equation can be understood as a part of the classical J2 plasticity model with isotropic power-law hardening. In this model, the hardening behavior of the target material is assumed to be related to the power law of the plastic strain to predict the stress-strain behavior of the target material during the plastic deformation stage. is the current stress state of the target material, that is, the stress level of the target material under a given strain. It should be understood that the components of the plastic strain tensor are The i and j in can be understood as indices in the three-dimensional space. It is necessary to traverse all the index indices, indicating that all components in each direction in all spaces need to be considered. Further, The term describes the hardening behavior of the target material, that is, as the plastic strain increases, this term also increases, resulting in the current yield stress Also increased.

[0095] In the above implementation, by establishing a material deformation equation and utilizing parameters such as current yield stress, initial yield stress, Young's modulus, hardening exponent and equivalent plastic strain, the stress-strain behavior of the target material in the plastic deformation stage is simulated, accurately reflecting the strengthening process of the target material under continuous plastic deformation.

[0096] In some embodiments, the hydrogen diffusion equation corresponding to the target material is expressed as follows: In the formula, is the lattice hydrogen diffusion coefficient, which describes the diffusion ability of hydrogen in the lattice; is the lattice hydrogen concentration; R is the gas constant; T is the absolute temperature; represents the effective hydrogen diffusion coefficient; t is the diffusion time; is the partial molar volume of hydrogen; is the hydrostatic stress.

[0097] It is important to understand that first the lattice hydrogen concentration needs to be defined and trapped hydrogen concentration If the trap types are defined to include dislocations, grain boundaries, carbides and other traps, then the lattice hydrogen concentration and the trapped hydrogen concentration of the ith trap The expressions are: In the formula, is the lattice site density; is the trap site density of the ith trap; is the trap site occupancy; is the trap site occupancy of the i-th trap. And the trap site occupancy and the trap site occupancy of the ith trap Satisfy Oriani's balance between: , where is the binding energy with the trap The equilibrium constant .

[0098] Furthermore, by combining the stress-induced hydrogen diffusion theory and the Oriani's equilibrium theory of trapped hydrogen and lattice hydrogen, the hydrogen diffusion equation corresponding to the target material can be established.

[0099] where the effective hydrogen diffusion coefficient is expressed as follows: In the formula, represents the effective hydrogen diffusion coefficient; is the lattice hydrogen diffusion coefficient; is the lattice hydrogen concentration; n is the total number of trap types; is the trapped hydrogen concentration; is the trap site occupancy; is the trapped hydrogen concentration of the ith trap; is the trap site occupancy of the ith trap.

[0100] Specifically, the effective hydrogen diffusion coefficient The calculation of takes into account the distribution balance between hydrogen atoms in the lattice and trap sites. When the trap sites are not fully occupied by hydrogen atoms (i.e. <1), they can capture more hydrogen atoms, thus affecting the diffusion of hydrogen in the material. In the formula, the denominator represents the total available hydrogen capacity in the material after considering the unoccupied part of the trap sites. This total capacity is related to the lattice hydrogen diffusion coefficient The ratio of gives the effective hydrogen diffusion coefficient under stress-induced , thus reflecting the actual situation of hydrogen diffusion in the material under actual conditions.

[0101] In the above implementation, by defining the lattice hydrogen concentration and the trapped hydrogen concentration, combined with the stress-induced hydrogen diffusion theory and the Oriani's equilibrium theory of trapped hydrogen and lattice hydrogen, a hydrogen diffusion equation corresponding to the target material is established. In addition, the calculation of the effective hydrogen diffusion coefficient fully considers the distribution balance of hydrogen atoms between the lattice and the trap sites, so that it can accurately reflect the actual situation of hydrogen diffusion of the material under actual stress conditions, and provides a reliable theoretical basis and quantitative description means for in-depth research on the hydrogen embrittlement behavior of the material.

[0102] It should be understood that, although the steps in the above flowchart are shown in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear description in this article, there is no strict order restriction on the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the above flowchart may include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, and the execution order of these steps or stages is not necessarily carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0103] The embodiment of this specification also provides a phase field simulation device 500 for simulating hydrogen-induced fatigue crack growth of a material. Figure 5 As shown, it includes: a parameter acquisition module 510, an equation establishment module 520, a simulation model establishment module 530 and a model solving module 540, wherein: The parameter acquisition module 510 is used to acquire the hydrogen transmission parameters and mechanical property parameters of the target material.

[0104] The equation establishment module 520 is used to establish the material deformation equation, hydrogen diffusion equation, and phase field evolution equation corresponding to the target material based on the hydrogen transmission parameters and the mechanical property parameters; wherein the material deformation equation is used to describe the deformation of the target material under elastic-plastic behavior, the hydrogen diffusion equation is used to reflect the diffusion of hydrogen in the target material under stress induction, and the phase field evolution equation is used to reflect the dynamic crack expansion of the target material under the combined action of hydrogen and fatigue load.

[0105] The simulation model building module 530 is used to construct a three-field coupling relationship using the material deformation equation, the hydrogen diffusion equation and the phase field evolution equation to obtain a three-field coupling phase field simulation model.

[0106] The model solving module 540 is used to construct the boundary conditions of the hydrogen diffusion equation based on the surface hydrogen absorption flux equation corresponding to the target material, solve the three-field coupled phase field simulation model based on the boundary conditions, and obtain the crack extension parameters of the target material in the gaseous hydrogen environment.

[0107] In some embodiments, the model solving module 540 is also used to determine the surface hydrogen absorption flux equation corresponding to the target material in the following manner: determine the physical adsorption process, chemical adsorption process, desorption process, absorption process and desorption process of hydrogen on the surface of the target material; determine the hydrogen adsorption flux equation based on the physical adsorption process, chemical adsorption process and desorption process; determine the hydrogen absorption flux equation based on the absorption process and desorption process; and solve the hydrogen adsorption flux equation and the hydrogen absorption flux equation simultaneously to obtain the surface hydrogen absorption flux equation at any time.

[0108] In some embodiments, the model solving module 540 is also used to construct the boundary conditions of the hydrogen diffusion equation based on the surface hydrogen absorption flux equation corresponding to the target material, including: selecting a target crack surface, and determining the Dirac function based on the phase field variables corresponding to the target crack surface; wherein the phase field variables are used to describe the destruction state of the target material; based on the Dirac function and the surface hydrogen absorption flux equation, to construct the boundary conditions of the hydrogen diffusion equation.

[0109] In some embodiments, the equation building module 520 is also used to determine the phase field evolution equation corresponding to the target material in the following manner: define phase field variables, and establish a crack surface density function corresponding to the target material; wherein the crack surface density function is used to describe the distribution and morphology of cracks in the target material; determine the hydrogen damage degradation function caused by hydrogen and the fatigue damage degradation function caused by fatigue load, and construct the critical energy release rate of the target material based on the hydrogen damage degradation function and the fatigue damage degradation function; establish a surface energy function related to crack formation based on the critical energy release rate and the crack surface density function; wherein the surface energy function is used to evaluate the energy change during crack formation and propagation; determine the storage strain energy function based on the stiffness degradation function; wherein the storage strain energy function is used to evaluate the total strain energy stored in the target material during the stress process; and construct the phase field evolution equation corresponding to the target material based on the surface energy function and the storage strain energy function.

[0110] In some embodiments, the equation building module 520 is also used to determine the hydrogen damage degradation function caused by hydrogen, including: determining the grain boundary trap hydrogen coverage based on the lattice hydrogen concentration, the lattice site density and the grain boundary trap binding energy; and constructing the hydrogen damage degradation function based on the grain boundary trap hydrogen coverage and the damage coefficient.

[0111] In some embodiments, the equation building module 520 is also used to determine the fatigue damage degradation function caused by fatigue load, including: constructing the fatigue damage degradation function based on the accumulated historical variables of fatigue damage, threshold parameters, and material parameters; wherein the threshold parameters represent the point at which performance degradation begins to be observed, and the material parameters are used to adjust the degradation rate.

[0112] In some embodiments, the equation building module 520 is also used to determine the storage strain energy function based on the stiffness degradation function, including: constructing a fatigue damage degradation function based on the accumulated historical variables of fatigue damage, threshold parameters, and material parameters; wherein the threshold parameters represent the point at which performance degradation begins to be observed, and the material parameters are used to adjust the degradation rate. Constructing a storage strain energy function based on the stiffness degradation function and the undamaged isotropic storage strain energy density function; wherein the undamaged isotropic storage strain energy density function is determined based on the elastic strain energy density and the plastic strain energy density, the elastic strain energy density is determined based on the first Latin parameter, the second Latin parameter, and the elastic strain tensor of the target material, and the plastic strain energy density is determined based on the elastic strain tensor, the undamaged Cauchy stress tensor, and the plastic strain rate tensor; the undamaged Cauchy stress tensor is used to represent the stress state of the target material when it is not damaged.

[0113] For the specific definition of a phase field simulation device for simulating hydrogen-induced fatigue crack extension of a material, please refer to the definition of a phase field simulation method for simulating hydrogen-induced fatigue crack extension of a material above, which will not be repeated here. Each module in the above-mentioned phase field simulation device for simulating hydrogen-induced fatigue crack extension of a material can be implemented in whole or in part by software, hardware and a combination thereof. The above-mentioned modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory in the computer device in the form of software, so that the processor can call and execute the operations corresponding to the above modules. In this embodiment, a phase field simulation device for simulating hydrogen-induced fatigue crack extension of a material is presented in the form of a functional unit, where the unit refers to an ASIC (Application Specific Integrated Circuit) circuit, a processor and memory that executes one or more software or fixed programs, and / or other devices that can provide the above-mentioned functions.

[0114] The embodiment of the present application also provides a computer device, which may be a terminal, and its internal structure diagram may be as follows: Figure 6As shown. The computer device includes a processor, a memory, a communication interface, a display screen and an input device connected via a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The communication interface of the computer device is used to communicate with an external terminal in a wired or wireless manner. When the computer program is executed by the processor, a phase field simulation method for simulating hydrogen-induced fatigue crack propagation of materials is implemented. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer device can be a touch layer covered on the display screen, etc.

[0115] Those skilled in the art will understand that Figure 6 The structure shown in the figure is only a block diagram of a part of the structure related to the scheme of the present application, and does not constitute a limitation on the computer device to which the scheme of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0116] The embodiments of the present application also provide a computer-readable storage medium, and the above-mentioned method according to the embodiments of the present application can be implemented in hardware, firmware, or implemented as a computer code that can be recorded in a storage medium, or is implemented as a computer code that is originally stored in a remote storage medium or a non-temporary machine-readable storage medium and will be stored in a local storage medium and downloaded through a network, so that the method described herein can be stored in such software processing on a storage medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware. Among them, the storage medium can be a magnetic disk, an optical disk, a read-only storage memory, a random access memory, a flash memory, a hard disk or a solid-state drive, etc.; further, the storage medium can also include a combination of the above-mentioned types of memory. When the software or computer code is accessed and executed by a computer, a processor or hardware, the method shown in the above embodiment is implemented.

[0117] The embodiment of the present application provides a computer program product, which includes computer instructions, which are stored in a computer-readable storage medium. The processor of the computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the method of any embodiment of the present application. The phase field simulation method, device and storage medium for simulating hydrogen-induced fatigue crack propagation of materials described in the above embodiments can be specifically implemented by a computer chip or entity. A typical implementation device is a computer. Specifically, the computer can be, for example, a personal computer, a laptop computer, a cellular phone, a smart phone, etc., or a combination of any of these devices.

[0118] For the convenience of description, the above device is described in various units according to their functions. Of course, when implementing the present application, the functions of each unit can be implemented in the same or multiple software and / or hardware. It should be understood by those skilled in the art that the present application can be implemented in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware.

[0119] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In addition, the terms "first" and "second" are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. In the description of the present application, the meaning of "multiple" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined. It should also be noted that the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion. In the absence of further restrictions, the elements defined by the statement "include one..." do not exclude the presence of other identical elements in the process, commodity or equipment including the elements.

[0120] Each embodiment in this specification is described in a progressive manner, and the same and similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. Since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The above is only an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present application should be included in the scope of the claims of the present application. Although the embodiments of the present application are described in conjunction with the drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present application, and such modifications and variations all fall within the scope defined by the attached claims.

Claims

1. A phase field simulation method for simulating hydrogen-induced fatigue crack growth of a material, characterized in that: The method comprises: Obtain hydrogen transport parameters and mechanical property parameters of target materials; A material deformation equation, a hydrogen diffusion equation, and a phase field evolution equation corresponding to the target material are established based on the hydrogen transport parameters and the mechanical property parameters; wherein the material deformation equation is used to describe the deformation of the target material under elastic-plastic behavior, the hydrogen diffusion equation is used to reflect the diffusion of hydrogen in the target material under stress induction, and the phase field evolution equation is used to reflect the dynamic crack expansion of the target material under the combined action of hydrogen and fatigue load; A three-field coupling relationship is constructed using the material deformation equation, the hydrogen diffusion equation and the phase field evolution equation to obtain a three-field coupling phase field simulation model; The boundary conditions of the hydrogen diffusion equation are constructed based on the surface hydrogen absorption flux equation corresponding to the target material, and the three-field coupled phase field simulation model is solved based on the boundary conditions to obtain the crack propagation parameters of the target material in a gaseous hydrogen environment.

2. The method according to claim 1, characterized in that The surface hydrogen absorption flux equation corresponding to the target material is determined by the following method: determining a physical adsorption process, a chemical adsorption process, a desorption process, an absorption process, and a desorption process of hydrogen on the surface of the target material; Determining a hydrogen adsorption flux equation based on the physical adsorption process, the chemical adsorption process, and the desorption process; determining a hydrogen absorption flux equation based on the absorption process and the desorption process; The hydrogen adsorption flux equation and the hydrogen absorption flux equation are solved simultaneously to obtain the surface hydrogen absorption flux equation at any time.

3. The method according to claim 1, characterized in that The boundary conditions of the hydrogen diffusion equation are constructed based on the surface hydrogen absorption flux equation corresponding to the target material, including: Selecting a target crack surface, and determining a Dirac function based on a phase field variable corresponding to the target crack surface; wherein the phase field variable is used to describe the failure state of the target material; Based on the Dirac function and the surface hydrogen absorption flux equation, the boundary conditions of the hydrogen diffusion equation are constructed.

4. The method according to claim 1, characterized in that: The phase field evolution equation corresponding to the target material is determined by: Defining phase field variables and establishing a crack surface density function corresponding to the target material; wherein the crack surface density function is used to describe the distribution and morphology of cracks in the target material; Determining a hydrogen damage degradation function caused by hydrogen and a fatigue damage degradation function caused by the fatigue load, and constructing a critical energy release rate of the target material based on the hydrogen damage degradation function and the fatigue damage degradation function; Establishing a surface energy function related to crack formation based on the critical energy release rate and the crack surface density function; wherein the surface energy function is used to evaluate energy changes during crack formation and expansion; Based on the stiffness degradation function, determining a stored strain energy function; wherein the stored strain energy function is used to evaluate the total strain energy stored in the target material during the stress process; A phase field evolution equation corresponding to the target material is constructed based on the surface energy function and the storage strain energy function.

5. The method according to claim 4, characterized in that Determining a hydrogen damage degradation function caused by the hydrogen, including: The grain boundary trap hydrogen coverage is determined based on the lattice hydrogen concentration, the lattice site density, and the grain boundary trap binding energy; The hydrogen damage degradation function is constructed based on the grain boundary trap hydrogen coverage and damage coefficient.

6. The method according to claim 4, characterized in that Determining a fatigue damage degradation function caused by the fatigue load, including: The fatigue damage degradation function is constructed based on the accumulated historical variables of fatigue damage, threshold parameters, and material parameters; wherein the threshold parameters represent the point at which performance degradation begins to be observed, and the material parameters are used to adjust the degradation rate.

7. The method according to claim 4, characterized in that The step of determining the stored strain energy function based on the stiffness degradation function comprises: The storage strain energy function is constructed based on the stiffness degradation function and the undamaged isotropic storage strain energy density function; wherein the undamaged isotropic storage strain energy density function is determined based on the elastic strain energy density and the plastic strain energy density, the elastic strain energy density is determined based on the first Latin parameter, the second Latin parameter and the elastic strain tensor of the target material, and the plastic strain energy density is determined based on the elastic strain tensor, the undamaged Cauchy stress tensor and the plastic strain rate tensor; the undamaged Cauchy stress tensor is used to represent the stress state of the target material when it is not damaged.

8. A phase field simulation device for simulating hydrogen-induced fatigue crack growth of materials, characterized in that: The device comprises: Parameter acquisition module, used to obtain hydrogen transport parameters and mechanical property parameters of target materials; An equation building module, used to build a material deformation equation, a hydrogen diffusion equation, and a phase field evolution equation corresponding to the target material based on the hydrogen transport parameters and the mechanical property parameters; wherein the material deformation equation is used to describe the deformation of the target material under elastic-plastic behavior, the hydrogen diffusion equation is used to reflect the diffusion of hydrogen in the target material under stress induction, and the phase field evolution equation is used to reflect the dynamic crack expansion of the target material under the combined action of hydrogen and fatigue load; A simulation model building module, used to construct a three-field coupling relationship using the material deformation equation, the hydrogen diffusion equation and the phase field evolution equation to obtain a three-field coupling phase field simulation model; A model solving module is used to construct the boundary conditions of the hydrogen diffusion equation based on the surface hydrogen absorption flux equation corresponding to the target material, solve the three-field coupled phase field simulation model based on the boundary conditions, and obtain the crack propagation parameters of the target material in a gaseous hydrogen environment.

9. A computer device, characterized in that: include: A memory and a processor, wherein the memory and the processor are communicatively connected to each other, the memory stores computer instructions, and the processor executes the method according to any one of claims 1 to 7 by executing the computer instructions.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a computer to execute the method according to any one of claims 1 to 7.

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