Construction method of high-temperature contact-corrosion coupling model

Abstract

The embodiment of the invention provides a construction method of a high-temperature contact-corrosion coupling model. The construction method comprises the following steps: determining a high-temperature contact corrosion type and a corrosion internal mechanism; constructing a force-chemical coupling theory model; solving the force-chemical coupling theoretical model by adopting a finite element algorithm; and constructing a high-temperature contact-corrosion coupling finite element model based on a result obtained by solving. According to the scheme, based on irreversible thermodynamics, a mechanical-chemical full-coupling high-temperature oxidation corrosion theoretical model considering interaction of contact pressure, reactant (gaseous) diffusion and chemical reaction is established; the preset UEL module is used for performing finite element implementation on the high-temperature corrosion model, and the corrosion evolution rule, the corrosion morphology characteristics and the chemical reaction dynamic process of the contact area in the high-temperature contact corrosion process and the change of the contact pressure along with the reaction process can be accurately simulated. Meanwhile, the distribution conditions of various physical fields such as stress, strain, contact pressure, reactant and product concentration and the like can be accurately presented.

Description

Technical Field

[0001] This application relates to the field of model construction, and particularly to a method for constructing a high-temperature contact-corrosion coupling model. Background Art

[0002] The corrosion problem of metal contact components, especially the mechanisms of oxidation, pitting corrosion, and stress corrosion of metal components in environments such as high temperature, acidic and alkaline media, has been a widely concerned issue in recent years. High-temperature contact interface corrosion is not only affected by surface reactions but also closely related to contact pressure, micro-deformation, and interface heat conduction.

[0003] However, most existing studies mainly focus on the coupling of corrosion with a single field (such as heat or stress), ignoring the complex physical and chemical processes at the material contact interface. For the corrosion problem under contact conditions, which involves the coupling effects of contact pressure, diffusion, and chemical reactions, there is currently a lack of systematic theoretical research and numerical simulation methods, resulting in certain errors in predicting high-temperature contact corrosion. It is difficult to formulate targeted anti-corrosion strategies based on the high-temperature contact-corrosion coupling mechanism, and thus it is impossible to adopt effective methods to improve the reliability of contact components. Summary of the Invention

[0004] The purpose of the embodiments of this application is to provide a method for constructing a high-temperature contact-corrosion coupling model, improve the simulation accuracy of the high-temperature contact corrosion process, and provide theoretical support for deeply understanding the corrosion behavior of the contact component interface. The specific technical solutions are as follows:

[0005] In a first aspect of the implementation of this application, a method for constructing a high-temperature contact-corrosion coupling model includes:

[0006] Determine the type of high-temperature contact corrosion and the internal corrosion mechanism;

[0007] Construct a force-chemistry coupling theoretical model;

[0008] Use the finite element algorithm to solve the force-chemistry coupling theoretical model;

[0009] Based on the obtained results, construct a high-temperature contact-corrosion coupling finite element model.

[0010] Optionally, the high-temperature corrosion types include at least one of oxidation corrosion, chemical corrosion, and salt spray corrosion in a high-temperature environment;

[0011] Determining the internal corrosion mechanism includes:

[0012] Determine the chemical reaction kinetic characteristics and thermodynamic equilibrium conditions of the reactants, and mark the phase states of the reactants and products; wherein, the phase states include solid, gaseous, and liquid;

[0013] Determine the influence of the contact pair on the reactant distribution, the influence of the contact pair on the product distribution, the corresponding relationship between the concentrations of reactants and products and the reaction rate, and the influence of reactant diffusion and material growth on the internal stress.

[0014] Optionally, the force-chemical coupling theoretical model includes: mechanical equilibrium equations and mass conservation equations;

[0015] The mechanical equilibrium equations and mass conservation equations include:

[0016] σ ij,j +b i =0,(i,j=1,2) (18)

[0017]

[0018] where σ represents stress, b represents body force, c α and j α represent the concentration and diffusion flux per unit volume of the α-th substance, v αr represents the stoichiometric coefficient of the r-th reaction of the α-th substance, represents the chemical reaction rate of the r-th reaction.

[0019] Optionally, the force-chemical coupling theoretical model further includes:

[0020] energy conservation equation, entropy increase equation, and Helmholtz free energy density function;

[0021] The energy conservation equation includes:

[0022]

[0023] where u is the energy density per unit volume, is the body heat source intensity, μ α is the chemical potential of the α-th substance, q, v, and T * are the heat flux, velocity, and tension force vector, a T ,a σ ,a j are the boundaries of the heat flux, stress, and chemical potential respectively;

[0024] The entropy increase equation includes:

[0025]

[0026] The Helmholtz free energy density function includes:

[0027]

[0028] where s is the entropy density per unit volume and T is the absolute temperature.

[0029] Optionally, the force-chemistry coupling theoretical model further includes a constitutive relationship between force-diffusion-chemical reaction under thermodynamic constraints:

[0030] The constitutive relationship includes:

[0031]

[0032] ε = ε e + ε c + ε g (24)

[0033]

[0034] where σ kk is the hydrostatic pressure, ε is the total strain, ε e is the elastic strain, ε c is the compositional strain, ε g is the growth strain, is the initial concentration of substance α, η α is the compositional expansion coefficient, L β is the chemical reaction proportionality coefficient, V m is the molar volume of the substance.

[0035] Optionally, when the reactant is gaseous, the force-chemistry coupling theoretical model further includes:

[0036]

[0037] where D α is the diffusion coefficient, and R is the gas constant.

[0038] Optionally, the force-chemistry coupling theoretical model further includes:

[0039]

[0040] where L is the chemical reaction rate constant.

[0041] Optionally, the finite element algorithm is used to solve the force-chemistry coupling theoretical model, including:

[0042] Discretizing the force-chemistry coupling theoretical model by using the standard Galerkin method;

[0043] Inputting the discretized model, the constitutive relationship, the residual, and the stiffness matrix into a preset Abaqus UEL subroutine, and performing iterative solution by using the Newton-Raphson method;

[0044] The discretization of the force-chemistry coupling theoretical model includes:

[0045]

[0046] The stiffness matrix and the residual include:

[0047]

[0048] Among them, N u is the shape function of displacement, is the transpose of the displacement shape function, u e is the nodal displacement, N c is the shape function of concentration, is the transpose of the concentration shape function, is the nodal concentration, B u is the displacement-strain matrix, is the transpose of the displacement-strain matrix, B c is the concentration gradient matrix, is the transpose of the concentration gradient matrix, is the boundary concentration flux, R u and are the residuals of displacement and concentration, K uu 、 and are the tangent stiffnesses.

[0049] Optionally, based on the obtained solution results, a high-temperature contact-corrosion coupling finite element model is constructed, including:

[0050] Determine a static contact model including an indenter and a substrate;

[0051] Based on the static contact model and the obtained solution results, construct a high-temperature contact-corrosion coupling finite element model.

[0052] In another aspect of the implementation of the present application, an electronic device is provided, including a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete communication with each other through the communication bus;

[0053] The memory is used to store a computer program;

[0054] The processor, when executing the program stored in the memory, implements a method for constructing a high-temperature contact-corrosion coupling model.

[0055] Advantages of the embodiments of the present application:

[0056] A method for constructing a high-temperature contact-corrosion coupling model provided by an embodiment of the present application determines the type of high-temperature contact corrosion and the internal corrosion mechanism; constructs a force-chemical coupling theoretical model; uses a finite element algorithm to solve the force-chemical coupling theoretical model; and constructs a high-temperature contact-corrosion coupling finite element model based on the obtained solution results. In this solution, based on irreversible thermodynamics, a force-chemical fully coupled high-temperature oxidation corrosion theoretical model considering the interaction of contact pressure, reactant (gaseous) diffusion, and chemical reaction is established; the finite element implementation of the high-temperature corrosion model is carried out using a preset UEL module, which can accurately simulate the corrosion evolution law, corrosion morphology characteristics, dynamic process of chemical reaction, and the change of contact pressure with the reaction process in the contact area during high-temperature contact corrosion. At the same time, the distribution of multiple physical fields such as stress, strain, contact pressure, and concentrations of reactants and products can also be accurately presented. This solution is applicable to multiple fields such as aerospace, ship engineering, integrated circuits, energy and chemical engineering, etc., and can be used to evaluate the contact corrosion performance and predict failures of key contact components (such as connectors, transmission systems, micro-contacts of heat dissipation structures, heat exchangers, etc.) of major equipment, providing a scientific basis and decision-making support for engineering design, material selection, and equipment maintenance in related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art.

[0058] Figure 1 It is a flowchart of a method for constructing a high-temperature contact-corrosion coupling model according to an embodiment of the present application.

[0059] Figure 2 It is a two-dimensional high-temperature contact oxidation corrosion model of the present application;

[0060] Figure 3 It is the verification of the contact pressure results in the Hertz theory and finite element simulation of the present application;

[0061] Figure 4 It is an isotropic plane model of the present application with stress-free equilibrium expansion and chemical reaction;

[0062] Figure 5 It is the comparative verification of the analytical solution and the finite element solution for obtaining the reaction equilibrium state under the stress-free state of the present application;

[0063] Figure 6 It is the influence on the contact pressure of the contact interface during the high-temperature corrosion process of the present application;

[0064] Figure 7 It is the influence of the normal force on the oxygen diffusion of the contact surface within 300 hours of the present application;

[0065] Figure 8 is the change of oxygen concentration at the contact center during the reaction equilibrium of the present application;

[0066] Figure 9 is the gradient distribution of oxygen inside copper when the normal force of the present application is 0 kN;

[0067] Figure 10 is the gradient distribution of oxygen inside copper when the normal force of the present application is 200 kN. Detailed implementation manners

[0068] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present application.

[0069] To solve the problems in the prior art, the present application provides a method for constructing a high-temperature contact-corrosion coupling model, which applies a force-chemical coupling model to the matrix of a static contact model to simulate the corrosion process. A normal force is applied to the indenter on the matrix to achieve the contact behavior, and the construction of a high-temperature contact-corrosion coupling finite element model is completed, which can accurately simulate the corrosion evolution law, corrosion morphology characteristics, dynamic process of chemical reactions, and the change of contact pressure with the reaction process in the high-temperature contact corrosion process.

[0070] It should be noted that the method for constructing a high-temperature contact-corrosion coupling model provided in the embodiments of the present application can be applied to electronic devices. In practical applications, the electronic device can be: a smart phone, a tablet computer, a notebook computer, etc., which are all reasonable.

[0071] Next, a method for constructing a high-temperature contact-corrosion coupling model provided in the embodiments of the present application will be introduced first.

[0072] As Figure 1 shown, a method for constructing a high-temperature contact-corrosion coupling model provided in the embodiments of the present application may include the following steps:

[0073] S101, determine the type of high-temperature contact corrosion and the internal corrosion mechanism;

[0074] It can be understood that in order to construct a high-temperature contact-corrosion coupling model, it is necessary to first clarify the research objective, that is, it is necessary to determine the type of high-temperature contact corrosion, so as to establish a corresponding force-chemical coupling theoretical model according to the corrosion type, internal chemical reaction, internal mechanism and coupling form.

[0075] Among them, the types of contact can include static contact; the types of high-temperature corrosion can include oxidation corrosion, chemical corrosion, salt spray corrosion, etc. in a high-temperature environment. After determining the type of high-temperature contact corrosion, based on the high-temperature corrosion reaction (such as the metal oxidation reaction M(s)+B(g)→MB(s), where s represents solid state and g represents gaseous state), its chemical reaction kinetic characteristics and thermodynamic equilibrium conditions can be clarified, and the phase states of reactants and products can be marked. The phase states can include solid state, gaseous state, and liquid state.

[0076] In addition, determining the internal mechanism of the high-temperature contact-corrosion process can include determining the influence of contact on the distribution of reactants, the influence of contact on the distribution of products, the corresponding relationship between the concentrations of reactants and products and the reaction rate, and the influence of reactant diffusion and material growth on internal stress.

[0077] Exemplarily, the internal mechanism of the high-temperature contact-corrosion process can specifically include: (1) the dynamic evolution law of the concentration gradient of reactants by contact, the adsorption-diffusion behavior of reactants (gaseous) at the contact interface and its local enrichment effect (Equation 10); (2) the influence of contact on the spatial distribution characteristics of products, and analyzing the correlation between the formation of products and the interface contact pressure (Equations 9, 10, and 11); (3) the relationship between the reaction rate and the concentrations of reactants and products (Equation 11); (4) the coupling effect of reactant (gaseous) transport and product volume expansion, the Fick behavior of the diffusion flux of reactants (gaseous) driven by the hydrostatic stress gradient (Equation 8), and the influence mechanism of the growth stress of products on the deformation of the matrix (Equation 9), etc.

[0078] S102, construct a force-chemical coupling theoretical model;

[0079] The force-chemical coupling theoretical model can include: mechanical equilibrium equations and mass conservation equations; among them, the mechanical equilibrium equations include:

[0080] σ ij,j +b i =0, (i,j=1,2) (35)

[0081] The mass conservation equations include:

[0082]

[0083] Among them, σ represents stress, b represents body force, c α and j α represent the concentration and diffusion flux per unit volume of the α-th substance, v αr represents the stoichiometric coefficient of the r-th reaction of the α-th substance, represents the chemical reaction rate of the r-th reaction.

[0084] Exemplarily, the force-chemical coupling theoretical model further includes:

[0085] The energy conservation equation, the entropy increase equation, and the Helmholtz free energy density function;

[0086] The energy conservation equation includes:

[0087]

[0088] where u is the energy density per unit volume, is the body heat source intensity, μ α is the chemical potential of the α-th substance, q, v, and T * are the heat flux, velocity, and tension force vectors, a T , a σ , a j are the boundaries of the heat flux, stress, and chemical potential, respectively;

[0089] The entropy increase equation includes:

[0090]

[0091] The Helmholtz free energy density function includes:

[0092]

[0093] where s is the entropy density per unit volume and T is the absolute temperature.

[0094] Exemplarily, the force-chemistry coupling theory model further includes the constitutive relationship between force-diffusion-chemical reaction under thermodynamic constraints:

[0095] The constitutive relationship includes:

[0096]

[0097] ε = ε e + ε c + ε g (41)

[0098]

[0099] where σ kk is the hydrostatic pressure, ε is the total strain, ε e is the elastic strain, ε c is the compositional strain (linearly related to the concentration of the reactant (gas)), ε g is the growth strain (proportional to the reaction rate, negligible if the product is liquid), is the initial concentration of substance α, η α is the compositional expansion coefficient, L βis the reaction proportion coefficient of the chemical reaction. The compositional strain is driven by the change in the concentration of the reactant (gas state), and the growth strain results from the volume expansion caused by the chemical reaction. I2 is the unit second-order tensor, and V m is the molar volume of the substance.

[0100] In addition, the diffusion of the reactant (gas state) can be controlled by Fick's law, and a stress-related term is introduced.

[0101]

[0102] where D α is the diffusion coefficient, and R is the gas constant.

[0103] The chemical reaction rate is controlled by the activation energy of the chemical reaction, and its activation energy is generally considered as the sum of the chemical potentials of each substance, and the influence of stress is considered.

[0104]

[0105] where L is the chemical reaction rate constant.

[0106] S103. Solve the force-chemistry coupling theoretical model by using the finite element algorithm;

[0107] Exemplarily, in one implementation manner, solving the force-chemistry coupling theoretical model by using the finite element algorithm may include:

[0108] Discretize the force-chemistry coupling theoretical model by using the standard Galerkin method;

[0109] Input the discretized model, the constitutive relation, the residual and the stiffness matrix into a preset Abaqus UEL subroutine, and use the Newton-Raphson method for iterative solution.

[0110] It can be understood that after establishing the theoretical model, the coupled control equations of stress, diffusion and chemical reaction can be discretized by the standard Galerkin method, the weak form can be deduced, the constitutive relation, the residual and the stiffness matrix are written into the UEL subroutine in the preset Abaqus, and the Newton-Raphson method is used for iterative calculation and solution to complete the finite element implementation of the force-chemistry coupling theoretical model.

[0111] Exemplarily, the displacement and concentration can be discretized as:

[0112]

[0113] The weak form is:

[0114]

[0115] The stiffness matrix and the residual are as follows:

[0116]

[0117] Among them, N u is the shape function of displacement, is the transpose of the displacement shape function, u e is the nodal displacement, N c is the shape function of concentration, is the transpose of the concentration shape function, is the nodal concentration, B u is the displacement-strain matrix, is the transpose of the displacement-strain matrix, B c is the concentration gradient matrix, is the transpose of the concentration gradient matrix, is the boundary concentration flux, R u and are the residuals of displacement and concentration, K uu 、 and are the tangent stiffnesses.

[0118] The concentration and displacement fields can be used as degrees of freedom, and the Newton-Raphson method can be used for iterative solution.

[0119] S104, based on the obtained results, construct a high-temperature contact-corrosion coupling finite element model.

[0120] When establishing the high-temperature contact-corrosion coupling finite element model, a static contact model including the indenter and the substrate can be established, and based on the static contact model and the obtained results, a high-temperature contact-corrosion coupling finite element model can be constructed.

[0121] Exemplarily, the UEL module can be applied to the substrate undergoing high-temperature corrosion. Among them, the material parameters for high-temperature corrosion calculation inside the UEL module can include the elastic modulus, Poisson's ratio, material concentration, bulk modulus of reactants and products, diffusion coefficient of reactants (gaseous), diffusion expansion coefficient of reactants (gaseous), chemical reaction proportionality coefficient for controlling growth strain, etc.

[0122] In addition, when constructing a high-temperature contact-corrosion coupled finite element model, the UEL calculation in Abaqus can be used. The calculation steps can include: (1) defining the element nodes and degrees of freedom, and allocating variables to describe the coupling behavior of chemical potential, concentration, temperature, and displacement fields; (2) implementing the calculation of the element stiffness matrix and residual vector in the UEL module to ensure its consistency with the results derived from the Galerkin method; (3) writing a numerical integration algorithm to efficiently evaluate the volume and surface integrals in the weak form; (4) calling the Abaqus solver for the overall analysis to verify the stability and accuracy of the model.

[0123] In addition, to verify the simulation accuracy of the high-temperature contact corrosion process, after the model is established, the accuracy of the model can be verified. For example, the UEL module of Abaqus can be used to simulate the corrosion process of the substrate, and at the same time, contact behavior can be introduced into the boundary conditions of the substrate to accurately characterize the multi-physics coupling effect; in the boundary conditions, the interaction between the substrate and external loads (such as pressure) can be simulated by defining the contact behavior, including the influence of contact pressure on oxygen diffusion (Diffusive oxygen) and chemical reactions. Input various parameters, calculate the high-temperature corrosion process, and apply contact behavior at the substrate boundary. By assuming stress-free equilibrium expansion of the isotropic plane of the substrate, simplifying the coupling equation and introducing the steady-state assumption, the Hertz solution is derived and compared with the numerical solution (FEM solution) of the finite element model to verify the accuracy of the model.

[0124] The accuracy of the model needs to be verified in two aspects: First, by defining that no chemical reaction occurs inside the custom element, a simple static contact model is established and compared with the Hertz solution of static contact for verification; Second, through the theoretical solution of the high-temperature corrosion model, the accuracy is verified by comparing the finite element solution of corrosion in the non-contact case.

[0125] In the embodiments of the present application, the type of high-temperature contact corrosion and the internal corrosion mechanism are determined; a force-chemical coupling theoretical model is constructed; a finite element algorithm is used to solve the force-chemical coupling theoretical model; based on the obtained results, a high-temperature contact-corrosion coupling finite element model is constructed. In this solution, based on irreversible thermodynamics, a force-chemical fully coupled oxidation corrosion theoretical model considering the interaction of contact pressure, reactant (gaseous) diffusion, and chemical reaction is established; the finite element implementation of the high-temperature corrosion model is carried out using a preset UEL module, which can accurately simulate the corrosion evolution law, corrosion morphology characteristics, dynamic process of chemical reaction, and the change of contact pressure with the reaction process in the contact area during high-temperature contact corrosion. At the same time, the distributions of multiple physical fields such as stress, strain, contact pressure, concentrations of reactants and products can also be accurately presented. This solution is applicable to multiple fields such as aerospace, ship engineering, integrated circuits, energy and chemical engineering, and can be used to evaluate the contact corrosion performance and predict failures of key contact components (such as connectors, transmission systems, micro-contacts of heat dissipation structures, heat exchangers, etc.) of major equipment, providing a scientific basis and decision-making support for engineering design, material selection, and equipment maintenance in related fields.

[0126] To further illustrate the solution of the present application, taking the high-temperature contact corrosion of copper as an example, the construction method of the high-temperature contact-corrosion coupling model of the present application is introduced below.

[0127] As Figures 2 - 10 shown, the type of high-temperature contact corrosion is determined to be high-temperature contact oxidation corrosion of copper, and the high-temperature contact corrosion process and internal mechanism are further clarified. Copper has two main products in a dry air environment, namely copper oxide and cuprous oxide. The fractions of the two oxides produced during the copper oxidation process vary within different temperature ranges. At 800 - 1000 °C, the fraction of copper oxide is extremely low and remains at a very low level between 600 °C and 800 °C; at 350 - 600 °C, the composition of copper oxide increases sharply. This embodiment mainly focuses on the high-temperature oxidation corrosion of copper at 800 °C. Therefore, the main product of copper oxidation is cuprous oxide, while the presence of copper oxide is ignored. The corrosion equation of copper is:

[0128] 2Cu + O → Cu2O (52)

[0129] In this embodiment, the oxidation corrosion of copper occurs under standard atmospheric pressure. In the early stage of oxidation, the initial growth of oxidation is achieved by forming cuprous oxide islands, which eventually aggregate to form an oxide layer. The thickness of the oxide layer gradually increases with time. Between 600 °C and 850 °C, the oxidation rate of copper is mainly controlled by grain boundary diffusion and lattice diffusion. Oxygen attaches to the copper surface to form oxygen ions, which react and gradually diffuse into the copper, while copper ions diffuse outward through grain boundaries and the lattice, generating cuprous oxide. During the oxidation process of copper, the presence of certain trace elements (such as arsenic and selenium) inhibits the diffusion of copper ions. Therefore, in this embodiment, the diffusion process of internal ions and the initial formation process of oxidation islands are ignored, and only the process of oxygen diffusing into copper to form cuprous oxide is concerned.

[0130] Furthermore, there is a mutual coupling relationship between contact and corrosion, and its internal mechanism is mainly that the presence of contact affects the diffusion of oxygen in copper and the formation of internal cuprous oxide. Gas diffusion determines the penetration rate of oxygen in the material and is a necessary condition for the oxidation reaction to proceed. Due to the presence of contact, corresponding stress changes occur inside the copper, affecting the distribution of oxygen in the copper. The reaction rate is affected by temperature, the chemical potentials of reactants and products, and the internal stress gradient generated by contact, and these factors determine the growth rate and thickness of the oxide layer.

[0131] Furthermore, a coupled force-chemistry theoretical model is established, and control equations for controlling gas diffusion, chemical reaction rate, stress, strain, and their interactions are established. Gas diffusion is affected by the stress gradient. Stress is related to the concentrations of reactants and products. The rate of a chemical reaction is controlled by chemical potential and hydrostatic pressure. During the initial oxidation process of copper, oxygen diffuses into the copper and reacts with it. According to Fick's law, the diffusion flux of oxygen can be given as:

[0132]

[0133] where μ O is the chemical potential of oxygen; c O is the concentration of oxygen; D O is the oxygen diffusion coefficient; R is the gas constant; T is the temperature; is the gradient operator.

[0134] Furthermore, the chemical potentials of the respective reactants are:

[0135]

[0136] where, μ Cu and are the chemical potentials of copper and cuprous oxide; and are the initial chemical potentials of copper, oxygen, and cuprous oxide; c Cu and The concentrations of copper and cuprous oxide; c Cu,max , c O,max , and is the maximum solubility of copper, oxygen, and cuprous oxide; V m The molar volume of the solid matrix; η O is the compositional expansion coefficient of oxygen.

[0137] Furthermore, the chemical reaction rate is as follows:

[0138]

[0139] where is the chemical reaction rate, L is the chemical reaction rate constant, L β is the chemical reaction proportionality coefficient. When the chemical reaction rate is greater than zero, the reaction begins.

[0140] Furthermore, during the oxidation reaction, in addition to the elastic strain, there should also be a compositional strain caused by oxygen diffusion and a growth strain caused by the formation of internal oxides in copper. Therefore, the total strain can be expressed as:

[0141] ε = ε e + ε c + ε g (58)

[0142] where ε e is the elastic strain, ε c is the compositional strain due to oxygen diffusion, ε g represents the growth strain of cuprous oxide.

[0143] Furthermore, the strain caused by oxygen diffusion is expressed as:

[0144]

[0145] where I2 is the unit second-order tensor.

[0146] Furthermore, the strain caused by the growth of cuprous oxide is:

[0147]

[0148] Furthermore, based on the small strain hypothesis and neglecting the action of body forces, the force balance equation can be expressed as:

[0149] σ ij,j = 0 (61)

[0150] Furthermore, the mass balance equations for the three reactants can be expressed as:

[0151]

[0152] Furthermore, the non-linear constitutive equation of the contact-corrosion coupling theoretical model is as follows:

[0153]

[0154] j O = Φ1 + Φ2 (66)

[0155]

[0156] where C is the material elastic matrix,

[0157] Furthermore, in the finite element implementation of the force-chemical coupling, based on the force balance equation and the mass conservation equation (see Eqs. (10)-(13)), the standard Galerkin method is adopted, weight functions (W1 and W2) are introduced, and using the boundary conditions, the weak forms of the force balance equation and the mass conservation equation are derived. The isoparametric element is used, and the displacement u is interpolated by the nodal displacement u e and the shape function N u The displacement c α is interpolated by the nodal displacement and the shape function N c as follows:

[0158]

[0159] where α represents the reactant or product.

[0160] Furthermore, through the discretized weak forms, the element-level residuals and the tangent matrices are calculated:

[0161]

[0162] where N u is the shape function of the displacement, is the transpose of the displacement shape function, u e is the nodal displacement, N c is the shape function of the concentration, is the transpose of the concentration shape function, is the nodal concentration, B u is the displacement-strain matrix, is the transpose of the displacement-strain matrix, B c is the concentration gradient matrix, is the transpose of the concentration gradient matrix, is the boundary concentration flux, R u and are the residuals of the displacement and the concentration, K uu 、 and are the tangent stiffnesses.

[0163] Furthermore, taking displacement and concentration as degrees of freedom, the constitutive relation in the force-chemistry coupling theory is written into the UEL module. The strain and concentration gradient are calculated through the shape function, and parameters such as stress, diffusion flux, and reaction rate are calculated according to the constitutive relation.

[0164] Furthermore, the mechanical field and chemical field residuals are calculated separately in the UEL module and assembled into the global vector according to the node degrees of freedom. According to the tangent matrix, the contributions of each coupling term are calculated. The calculation of the constitutive relation, residuals, and tangent matrix is embedded in the UEL module to achieve the displacement-concentration coupling finite element solution.

[0165] Furthermore, in establishing the high-temperature contact-corrosion coupling finite element model and verifying the model accuracy, the Abaqus finite element software is used to establish a two-dimensional contact oxidation corrosion model, as Figure 2 shown. The upper part is a circular indenter with a radius of 5 mm, and the lower part is a solid copper of 1.5 mm * 0.9 mm. The circular indenter is modeled as a discrete rigid body, and the solid copper is in a plane strain state. The bottom surface of the rigid body is set as the main surface, the top surface of the copper is set as the secondary surface, and the contact characteristics are set as frictionless and hard contact. The displacement of the circular indenter in the x direction is constrained, and a linearly increasing force (punch) is applied in the y direction over time. The displacements of the bottom of the solid copper in the x and y directions are constrained. The oxygen boundary is set as the lower boundary of the copper. The numerical calculation is completed at a constant temperature of 800 °C.

[0166] Furthermore, in establishing the high-temperature contact-corrosion coupling finite element model, the solid copper in the model uses a custom element, and its internal chemical reaction is realized in the finite element. The concentrations of reactants and products are defined as independent variables. The finite element formula is derived by the standard Galerkin method using the governing equations, initial conditions, and boundary conditions and is implemented in the UEL module. The solid copper uses UEL to simulate deformation and chemical reactions.

[0167] Furthermore, Table 1-3 lists the material parameters required in the model. Since the Young's modulus, Poisson's ratio, molar volume, and diffusion coefficient of oxygen in copper change during the chemical reaction, they can be expressed as:

[0168]

[0169] where E1, v1, V1, and D O1 are the Young's modulus, Poisson's ratio, molar volume, and diffusion coefficient of oxygen in copper, respectively, and E2, v2, V2, and D O2 are the Young's modulus, Poisson's ratio, molar volume, and diffusion coefficient of oxygen in cuprous oxide, respectively. And D O_1 and D O_2 are reference values, Q O_1 and Q O_2Activation energy of oxygen diffusion in copper and cuprous oxide.

[0170] Table 1 Copper-related material parameters

[0171]

[0172] Table 2 Cuprous oxide-related material parameters

[0173]

[0174] Table 3 Other parameters for simulation

[0175]

[0176]

[0177] Furthermore, for the verification of the accuracy of the finite element model, static contact simulation is carried out using the UEL module and compared with Hertz contact theory. Copper is modeled using UEL, and the chemical reaction rate constant (L), the component expansion coefficient (η O ) and the chemical reaction proportionality coefficient (L β ) are set to zero to ensure that no chemical reaction occurs inside the copper. The component strain caused by oxygen and the growth strain caused by the reaction are not included in this simulation. In the case of no reaction, the material parameters are set as E = 1.16×10 11 Pa, v = 0.348, and the load is F = 50 kN. Figure 3 Shows the contact pressure obtained from Hertz theory and finite element simulation. Good agreement is achieved between the theoretical results and the simulation results.

[0178] Furthermore, an isotropic plane with stress-free equilibrium expansion and chemical reaction is simulated to verify the accuracy of the oxidation corrosion model, as Figure 4 shown. Contact is not considered in this simulation. A constant c O = 200 mol / m 3 is set at the upper and right boundaries of the copper plane, while at the left and lower boundaries, the displacements in the x and y directions are constrained respectively. The initial concentrations of the reactants and products are considered to be and The initial value of copper is the molar concentration calculated according to the density of copper, while the initial values of oxygen and cuprous oxide are very small. When the gas diffuses into the copper, a reaction immediately occurs inside the metal until an equilibrium state is reached. The internal substances do not change with time, and the copper is in a stress-free state, i.e., σ 11 = σ 22 = 0 ε 11 = ε 22= ε0, where ε0 is a constant. The total strain is decomposed into elastic strain, compositional strain (caused by concentration changes), and growth strain (generated by chemical reactions). Combining Hooke's law, the expression for the stress σ3 in the vertical direction is derived. Further, based on the steady-state diffusion condition and chemical reaction equilibrium couple the diffusion flux, chemical potential, and stress to establish a nonlinear equation. By introducing the chemical potential expression and mass conservation relationship, a nonlinear equation regarding the product concentration is finally formed, and the Newton iteration method is used for numerical solution. Let the component expansion coefficient η O range from 0 to 0.05, and the chemical reaction proportionality coefficient L β range from 0 to 0.008. The analytical solution of the reaction equilibrium state can be obtained in the stress-free state, and the verification results are as Figure 5 shown

[0179] Furthermore, a certain numerical study on high-temperature contact corrosion is carried out Figure 6 showing the influence on the contact pressure of the contact interface during high-temperature corrosion and plotting the results without oxidation corrosion for comparison. It can be seen that there are significant differences between the contact pressures with and without oxidation corrosion, and the contact pressure gradually increases with the prolongation of the corrosion time. When the reaction reaches 500 hours, the reaction tends to equilibrium. The contact pressure under 500-hour oxidation corrosion is 757 MPa, which is significantly higher than the contact pressure of 647.8 MPa without oxidation corrosion. In addition, the contact area under corrosion decreases relatively. The reason for this phenomenon is that as the oxidation corrosion reaction proceeds, oxygen gradually diffuses into the interior of copper. The reaction diffuses from the lower boundary of the metal matrix to the upper boundary until the reaction reaches equilibrium, and the material composition within the metal matrix changes. Due to the reaction between copper and oxygen, copper is consumed and cuprous oxide increases. The Young's modulus of cuprous oxide is greater than that of copper. According to Equation (21), the Young's modulus inside copper gradually increases. As the reaction proceeds, this leads to an increase in the contact pressure and a slight decrease in the contact area. It can be seen that the main factor affecting the contact pressure in the oxidation corrosion reaction is the change in the internal material composition. As the oxidation reaction proceeds, the decrease in copper concentration and the increase in cuprous oxide concentration result in an increase in the Young's modulus inside copper. The change in the Young's modulus directly affects the increase in the contact pressure

[0180] Figure 7 and Figure 8 show the influence of different normal forces on oxygen diffusion. The results on the contact surface are as Figure 7 shown, with the contact center as the origin. The closer to the contact center area, the smaller the oxygen concentration. Obviously, the normal force has an inhibitory effect on the diffusion of oxygen on the contact surface Figure 8It shows the situation of the contact center during the reaction equilibrium. As time goes by, the inhibitory effect of the normal force on oxygen diffusion becomes more and more significant. It also has a significant impact on the final equilibrium concentration of oxygen.

[0181] Figure 9 It shows the gradient distribution of oxygen in copper when the normal force is 0 kN. Figure 10 It shows the distribution of oxygen inside copper when the normal force is 200 kN. Due to the influence of the compressive stress inside copper, the oxygen concentration shows a non-uniform distribution, even lower in the compressive stress area. The results show that the compressive stress caused by the normal force inside copper has an inhibitory effect on oxygen diffusion.

[0182] The embodiment of the present application also provides an electronic device, including a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete communication with each other through the communication bus.

[0183] The memory is used to store computer programs.

[0184] The processor is used to implement the construction method of the high-temperature contact-corrosion coupling model provided by the embodiment of the present application when executing the program stored on the memory.

[0185] The communication bus mentioned in the above terminal may be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into an address bus, a data bus, a control bus, etc. For the sake of representation, only a thick line is used in the figure, but it does not mean that there is only one bus or one type of bus.

[0186] The communication interface is used for communication between the above terminal and other devices.

[0187] The memory may include a Random Access Memory (RAM), or may also include a non-volatile memory, such as at least one disk memory. Optionally, the memory may also be at least one storage device located far from the aforementioned processor.

[0188] The above-mentioned processor may be a general-purpose processor, including a Central Processing Unit (CPU for short), a Network Processor (NP for short), etc.; it may also be a Digital Signal Processor (DSP for short), an Application Specific Integrated Circuit (ASIC for short), a Field-Programmable Gate Array (FPGA for short), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0189] In another embodiment provided by the present application, there is also provided a computer-readable storage medium, in which a computer program is stored, and when the computer program is executed by a processor, the method for constructing the high-temperature contact-corrosion coupling model described in any one of the above embodiments is realized.

[0190] In another embodiment provided by the present application, there is also provided a computer program product containing instructions, and when it runs on a computer, it causes the computer to execute the method for constructing the high-temperature contact-corrosion coupling model described in any one of the above embodiments.

[0191] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center in a wired manner (such as coaxial cable, optical fiber, Digital Subscriber Line (DSL)) or a wireless manner (such as infrared, wireless, microwave, etc.). The computer-readable storage medium may be any available medium that can be accessed by a computer, or a data storage device such as a server or a data center that includes one or more integrated available media. The available medium may be a magnetic medium (for example, a floppy disk, a hard disk, a magnetic tape), an optical medium (for example, a DVD), or a semiconductor medium (for example, a Solid State Disk (SSD)).

[0192] It should be noted that in this text, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising a..." does not exclude the presence of additional identical elements in the process, method, article or device comprising said element.

[0193] Each embodiment in this specification is described in a related manner. For the same or similar parts among the embodiments, reference can be made to each other. Each embodiment focuses on the differences from other embodiments. In particular, for the apparatus embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and for the related parts, reference can be made to the description of the method embodiments.

[0194] The above are only the preferred embodiments of the present application and are not intended to limit the protection scope of the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present application are all included in the protection scope of the present application.

Claims

1. A method for constructing a high-temperature contact-corrosion coupling model, characterized in that, Including: Determine the type of high-temperature contact corrosion and its internal corrosion mechanism; Construct a force-chemistry coupling theoretical model; Solve the force-chemistry coupling theoretical model using the finite element algorithm; Based on the obtained results, construct a high-temperature contact-corrosion coupling finite element model.

2. The method according to claim 1, wherein The high-temperature corrosion types include at least one of oxidation corrosion, chemical corrosion, and salt spray corrosion in a high-temperature environment; Determining the internal corrosion mechanism includes: Determine the chemical reaction kinetics characteristics and thermodynamic equilibrium conditions of the reactants, and mark the phase states of the reactants and products; wherein, the phase states include solid, gaseous, and liquid; Determine the influence of the contact on the distribution of reactants, the influence of the contact on the distribution of products, the corresponding relationship between the concentrations of reactants and products and the reaction rate, and the influence of reactant diffusion and material growth on internal stress.

3. The method according to claim 2, wherein The force-chemistry coupling theoretical model includes: mechanical equilibrium equations and mass conservation equations; The mechanical equilibrium equations and mass conservation equations include: σ ij,j +b i =0,(i,j=1,2) (1) Among them, σ represents stress, b represents body force, c α and j α represent the concentration and diffusion flux per unit volume of the α-th substance, v αr represents the stoichiometric coefficient of the r-th reaction of the α-th substance, represents the chemical reaction rate of the r-th reaction.

4. The method according to claim 3, characterized in that, The force-chemistry coupling theoretical model further includes: Energy conservation equation, entropy increase equation, and Helmholtz free energy density function; The energy conservation equation includes: where u is the energy density per unit volume, is the body heat source strength, μ α is the chemical potential of the α-th species, q, v, and T * are the heat flux, velocity, and tension force vectors, a T , a σ , a j are the boundaries of the heat flux, stress, and chemical potential, respectively; The entropy increase equation includes: The Helmholtz free energy density function includes: Where s is the entropy density per unit volume and T is the absolute temperature.

5. The method according to claim 4, wherein The force-chemistry coupling theoretical model further includes the constitutive relationship between force-diffusion-chemical reaction under thermodynamic constraints: The constitutive relationship includes: ε = ε e + ε c + ε g (7) where σ kk is the hydrostatic pressure, ε is the total strain, ε e is the elastic strain, ε c is the compositional strain, ε g is the growth strain, is the initial concentration of substance α, η α is the compositional expansion coefficient, L β is the chemical reaction proportionality coefficient, I2 is the unit second-order tensor, V m is the molar volume of the substance.

6. The method according to claim 5, wherein When the reactant is gaseous, the force-chemistry coupling theoretical model further includes: where D α is the diffusion coefficient and R is the gas constant.

7. The method according to any one of claims 5 or 6, characterized in that, The force-chemistry coupling theoretical model further includes: Where L is the chemical reaction rate constant.

8. The method according to claim 2, characterized in that, The step of solving the force-chemistry coupling theoretical model using the finite element algorithm includes: Discretize the force-chemistry coupling theoretical model using the standard Galerkin method; Input the discretized model, the constitutive relationship, the residual, and the stiffness matrix into the preset UEL subroutine of Abaqus, and use the Newton-Raphson method for iterative solution; The step of discretizing the force-chemistry coupling theoretical model includes: The stiffness matrix and the residual include: Among them, N u is the shape function of displacement, is the transpose of the displacement shape function, and u e is the nodal displacement. N c is the shape function of concentration, is the transpose of the concentration shape function, is the nodal concentration. B u is the displacement-strain matrix, is the transpose of the displacement-strain matrix. B c is the concentration gradient matrix, is the transpose of the concentration gradient matrix, and j α* is the boundary concentration flux. R u and are the residuals of displacement and concentration. K uu , and are the tangent stiffnesses.

9. The method according to any one of claims 2-6, characterized in that, The step of constructing a high-temperature contact-corrosion coupling finite element model based on the obtained results includes: Determine a static contact model including an indenter and a substrate; Based on the static contact model and the obtained results, construct a high-temperature contact-corrosion coupling finite element model.

10. An electronic device, characterized in that, Including a processor, a communication interface, a memory, and a communication bus. Among them, the processor, the communication interface, and the memory complete mutual communication through the communication bus; The memory is used to store computer programs; When the processor executes the programs stored on the memory, it realizes the method steps described in any one of claims 1-9.

Images