A method for constructing a high-temperature contact-corrosion coupling model

Abstract

The embodiment of the application provides a kind of high temperature contact-corrosion coupling model construction method, determine the type of high temperature contact corrosion and corrosion internal mechanism;Build force-chemical coupling theory model;Solve the force-chemical coupling theory model using finite element algorithm;Based on the result obtained by solving, build high temperature contact-corrosion coupling finite element model.The scheme, based on irreversible thermodynamics, establishes a force-chemical full-coupling high-temperature oxidation corrosion theory model considering the interaction of contact pressure, reactant (gaseous) diffusion and chemical reaction;The high-temperature corrosion model is realized by finite element using the pre-set UEL module, which can accurately simulate the corrosion evolution law, corrosion morphology characteristics, chemical reaction dynamic process in the contact area during high-temperature contact corrosion process, and the change of contact pressure with reaction process.Meanwhile, it can also accurately present the distribution of stress, strain, contact pressure, reactant and product concentration and other physical fields.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of model construction, in particular to a method for constructing a high-temperature contact-corrosion coupling model. BACKGROUND

[0002] The corrosion problem of metal contact components, especially the mechanism of oxidation, pitting and stress corrosion of metal components in high-temperature, acidic and alkaline environments, has been a widely concerned problem 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 of the existing researches mainly focus on the coupling of corrosion and a single field (such as heat or stress), ignoring the complex physicochemical processes at the material contact interface. For the corrosion problem under contact conditions, the coupling effects involving contact pressure, diffusion and chemical reactions are still lack of systematic theoretical research and numerical simulation methods, which makes the prediction of high-temperature contact corrosion have certain errors, and it is difficult to develop targeted corrosion resistance strategies based on the high-temperature contact-corrosion coupling mechanism, so as to take effective methods to improve the reliability of the contact components. SUMMARY

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

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

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

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

[0008] solving the force-chemistry coupling theoretical model by using a finite element algorithm;

[0009] based on the results obtained by solving, constructing a high-temperature contact-corrosion coupling finite element model.

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

[0011] determining the internal mechanism of corrosion includes:

[0012] determining the chemical reaction kinetics and thermodynamic equilibrium conditions of the reactants, and marking the phase state of the reactants and products; wherein the phase state includes solid, gaseous and liquid states;

[0013] Determine the effect of contact on the distribution of reactants, the effect of contact on the distribution of products, the correspondence between the concentration of reactants and products and the reaction rate, and the effect of reactant diffusion and material growth on internal stress.

[0014] Optionally, the force-chemistry coupled theoretical model comprises: mechanical equilibrium equation and mass conservation equation.

[0015] The mechanical equilibrium equation and the mass conservation equation comprise:

[0016] σ ij,j +b i =0, (i,j=1,2) (18)

[0017]

[0018] Wherein, σ represents stress, b represents body force, c α And j α represent the concentration and diffusion flux of the αth substance per unit volume, v αr represents the stoichiometric coefficient of the αth substance in the rth reaction, represents the chemical reaction rate of the rth reaction.

[0019] Optionally, the force-chemistry coupled theoretical model further comprises:

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

[0021] The energy conservation equation comprises:

[0022]

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

[0024] The entropy equation comprises:

[0025]

[0026] The Helmholtz free energy density function comprises:

[0027]

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

[0029] Optionally, the force-chemistry coupling theory model further comprises a constitutive relation between the force-diffusion-chemical reaction under the thermodynamic constraint:

[0030] The constitutive relation comprises:

[0031]

[0032] ε = ε e + ε c + ε g (24)

[0033]

[0034] wherein 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 the 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 reactants are in a gaseous state, the force-chemistry coupling theory model further comprises:

[0036]

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

[0038] Optionally, the force-chemistry coupling theory model further comprises:

[0039]

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

[0041] Optionally, the force-chemistry coupling theory model is solved by using a finite element algorithm, comprising:

[0042] discretizing the force-chemistry coupling theory model by using a standard Galerkin method;

[0043] inputting the discretized model, the constitutive relation, the residual and the stiffness matrix into a preset Abaqus UEL subroutine, and iteratively solving by using a Newton-Raphson method;

[0044] The discretizing the force-chemistry coupling theory model, comprising:

[0045]

[0046] The stiffness matrix and the residual include:

[0047]

[0048] Where N u is the shape function of displacement, is the transpose of the shape function of displacement, u e is the node displacement, N c is the shape function of concentration, is the transpose of the shape function of concentration, is the node 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 is the residual of displacement and concentration, K uu , and is the tangent stiffness.

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

[0050] A static contact model including the indenter and the substrate is determined;

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

[0052] In another aspect of the embodiments of the present application, the embodiments of the present application provide an electronic device, including a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete the communication among each other through the communication bus;

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

[0054] The processor is used to execute the program stored on the memory, and realize the construction method of the high-temperature contact-corrosion coupling model.

[0055] The embodiments of the present application have the following beneficial effects:

[0056] The embodiment of the application provides a kind of high temperature contact-corrosion coupling model construction method, the type of high temperature contact corrosion and corrosion internal mechanism are determined;Force-chemical coupling theory model is constructed;The force-chemical coupling theory model is solved using finite element algorithm;Based on the result obtained by solving, high temperature contact-corrosion coupling finite element model is constructed.The scheme, based on irreversible thermodynamics, establishes the force-chemical full coupling high temperature oxidation corrosion theory model considering the interaction of contact pressure, reactant (gaseous) diffusion and chemical reaction;The high temperature corrosion model is realized by finite element using the preset UEL module, which can accurately simulate the corrosion evolution law, corrosion morphology characteristics, chemical reaction dynamic process of contact area in high temperature contact corrosion process, and the change of contact pressure with reaction process.At the same time, the distribution of stress, strain, contact pressure, reactant and product concentration and other physical fields can also be accurately presented.The scheme is suitable for aerospace, ship engineering, integrated circuit, energy chemical industry and other fields, and can be used for contact corrosion performance evaluation and failure prediction of key contact components (such as connectors, transmission systems, heat dissipation structure micro contacts, heat exchangers, etc.) of major equipment, to provide scientific basis and decision support for engineering design, material selection and equipment maintenance in related fields. BRIEF DESCRIPTION OF DRAWINGS

[0057] In order to more clearly illustrate the technical solutions of the embodiments of the application or the prior art, the drawings needed to be used in the embodiment or prior art description will be briefly introduced as follows.

[0058] Figure 1 The flow chart of the high temperature contact-corrosion coupling model construction method of the embodiment of the application.

[0059] Figure 2 The two-dimensional high temperature contact oxidation corrosion model of the application;

[0060] Figure 3 The contact pressure result verification in the Hertz theory and finite element simulation of the application;

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

[0062] Figure 5 The comparison verification of analytical solution and finite element solution of reaction equilibrium state under stress-free state of the application;

[0063] Figure 6 The influence of contact pressure on contact interface in high temperature corrosion process of the application;

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

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

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

[0067] Figure 10 is the gradient distribution of oxygen in the copper when the normal force of the application is 200kN. DETAILED DESCRIPTION

[0068] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of the present application.

[0069] In order to solve the problems in the prior art, the present application provides a construction method of a high-temperature contact-corrosion coupling model, which applies a force-chemistry coupling model to a static contact model base to simulate a corrosion process, a pressure head on the base applies a normal force, realizes a contact behavior, and completes construction of a high-temperature contact-corrosion coupling finite element model, which can accurately simulate the corrosion evolution law, corrosion topographic features, chemical reaction dynamic process of the contact area in the high-temperature contact corrosion process, and the change of contact pressure with the reaction process.

[0070] It should be noted that the construction method of a high-temperature contact-corrosion coupling model provided by the embodiments of the present application can be applied to electronic devices, and in actual application, the electronic devices can be: smart phones, tablet computers, notebook computers and other devices, which are all reasonable.

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

[0072] As shown in Figure 1 The construction method of a high-temperature contact-corrosion coupling model provided by the embodiments of the present application can include the following steps:

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

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

[0075] The type of contact can include static contact, and the high-temperature corrosion type can include oxidation corrosion, chemical corrosion, salt spray corrosion, and the like in a high-temperature environment. After determining the high-temperature contact corrosion type, the chemical reaction kinetics and thermodynamic equilibrium conditions can be determined based on the high-temperature corrosion reaction (such as a metal oxidation reaction M(s)+B(g)→MB(s), s represents a solid state, and g represents a gaseous state), and the phase state of the reactants and products is marked. The phase state can include a solid state, a gaseous state, and a liquid state.

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

[0077] For example, the internal mechanism of the high-temperature contact-corrosion process can specifically include: (1) the dynamic evolution law of the contact on the concentration gradient of the reactants, the adsorption-diffusion behavior of the reactants (gaseous state) at the contact interface, and the local enrichment effect (equation 10); (2) the influence of the contact on the spatial distribution characteristics of the products, and the correlation between the formation of the products and the interfacial contact pressure (equations 9, 10, and 11); (3) the relationship between the reaction rate and the concentrations of the reactants and the products (equation 11); (4) the coupling effect of the transmission of the reactants (gaseous state) and the volume expansion of the products, the Fick behavior of the diffusion flux of the reactants (gaseous state) driven by the hydrostatic stress gradient (equation 8), and the influence mechanism of the growth stress of the products on the deformation of the substrate (equation 9), and the like.

[0078] S102, constructing a force-chemistry coupling theoretical model;

[0079] The force-chemistry coupling theoretical model can include a mechanical equilibrium equation and a mass conservation equation; wherein the mechanical equilibrium equation includes:

[0080] σ ij,j +b i = 0, (i,j=1,2) (35)

[0081] The mass conservation equation includes:

[0082]

[0083] wherein σ represents stress, b represents body force, c α and j α represent the concentration and diffusion flux per unit volume of the αth substance, v αr represents the stoichiometric coefficient of the αth substance in the rth reaction, represents the chemical reaction rate of the rth reaction.

[0084] For example, the force-chemistry coupling theoretical model further includes:

[0085] energy conservation equation, entropy production equation, and 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 a-th species, q, v, and T * is the heat flux, velocity, and stress vector, a T , a σ , a j are the boundary conditions for heat flux, stress, and chemical potential, respectively;

[0089] The entropy production 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] By way of example, the force-chemistry coupled theoretical model further includes a constitutive relation between the force, diffusion, and chemical reactions under the thermodynamic constraints:

[0095] The constitutive relation 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 composition strain (linearly related to the reactant (gas) concentration), ε g is the growth strain (proportional to the reaction rate, which can be neglected if the product is liquid), is the initial concentration of species a, η α is the composition expansion coefficient, L βis the chemical reaction rate constant. m is the molar volume of the material.

[0100] In addition, the diffusion of the reactants (gases) can be controlled by Fick's law and introduces a stress-dependent term.

[0101]

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

[0103] The chemical reaction rate is controlled by the activation energy of the chemical reaction, which is generally considered to be the sum of the chemical potentials of each substance and takes into account the influence of stress.

[0104]

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

[0106] S103, solving the force-chemical coupling theory model by using a finite element algorithm;

[0107] For example, in one implementation, solving the force-chemical coupling theory model by using a finite element algorithm can include:

[0108] Discretizing the force-chemical coupling theory model by using a standard Galerkin method;

[0109] Inputting the discretized model, the constitutive relation, the residual, and the stiffness matrix into a pre-set Abaqus UEL subroutine, and iteratively solving by using a Newton-Raphson method.

[0110] It can be understood that after the theoretical model is established, the coupling control equation of stress, diffusion, and chemical reaction can be discretized by using a standard Galerkin method, a weak form is derived, the constitutive relation, the residual, and the stiffness matrix are written into a pre-set UEL subroutine in Abaqus, and iteratively calculated and solved by using a Newton-Raphson method, so as to complete the finite element implementation of the force-chemical coupling theory model.

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

[0112]

[0113] The weak form is:

[0114]

[0115] ​The stiffness matrix and the residual are:

[0116]

[0117] where N u is the shape function of displacement, is the transpose of the shape function of displacement, u e is the node displacement, N c is the shape function of concentration, is the transpose of the shape function of concentration, is the node 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 stiffness.

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

[0119] S104, based on the results obtained by solving, a high-temperature contact-corrosion coupled finite element model is constructed.

[0120] In establishing the high-temperature contact-corrosion coupled 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 results obtained by solving, a high-temperature contact-corrosion coupled finite element model is constructed.

[0121] Exemplarily, the UEL module can be applied to the substrate subjected to high-temperature corrosion, wherein the material parameters used for high-temperature corrosion calculation inside the UEL module can include the elastic modulus, Poisson's ratio, substance concentration, bulk modulus of reactant product, the diffusion coefficient of reactant (gas), the diffusion expansion coefficient of reactant (gas), the chemical reaction proportionality coefficient for controlling growth strain, etc.

[0122] In addition, when building a high-temperature contact-corrosion coupled finite element model, the UEL calculation in Abaqus can be used, which can include the following steps: (1) define the element nodes and degrees of freedom, and assign variables to describe the coupling behavior of chemical potential, concentration, temperature and displacement field; (2) implement the calculation of element stiffness matrix and residual vector in the UEL module, and ensure that it is consistent with the derivation result of Galerkin method; (3) write numerical integration algorithm to efficiently evaluate the volume and surface integrals in the weak form; (4) call Abaqus solver for overall analysis to verify the stability and accuracy of the model.

[0123] In addition, in order to verify the simulation accuracy of the high-temperature contact corrosion process, the model can be verified for accuracy after it is established. For example, the UEL module of Abaqus can be used to simulate the corrosion process of the substrate, while introducing contact behavior in the boundary conditions of the substrate to realize accurate characterization of the multi-physical field coupling effect; in the boundary conditions, the interaction between the substrate and the external load (such as pressure) is simulated by defining contact behavior, including the influence of contact pressure on diffusive oxygen and chemical reaction. Input parameters, calculate the high-temperature corrosion process, and apply contact behavior on the boundary of the substrate. By assuming isotropic plane stress-free equilibrium expansion of the substrate, simplifying the coupling equation and introducing steady-state assumption, Hertz solution is derived, which is 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 pure static contact model is established, and compared with the Hertz solution of static contact to verify; second, by comparing the finite element solution of corrosion in the non-contact case with the theoretical solution of the high-temperature corrosion model to verify the accuracy.

[0125] In the embodiments of the present application, the type and internal mechanism of high-temperature contact corrosion are determined; a force-chemistry coupling theoretical model is constructed; the force-chemistry coupling theoretical model is solved by using a finite element algorithm; and a high-temperature contact-corrosion coupling finite element model is constructed based on the results obtained by solving. Based on irreversible thermodynamics, the force-chemistry full coupling oxidation corrosion theoretical model considering the interaction of contact pressure, reactant (gaseous) diffusion and chemical reaction is established; the high-temperature corrosion model is implemented by using a preset UEL module, which can accurately simulate the corrosion evolution law, corrosion morphology characteristics, chemical reaction dynamic process of the contact area in the high-temperature contact corrosion process, and the change of the contact pressure with the reaction process. At the same time, the distribution of various physical fields such as stress, strain, contact pressure, reactant and product concentration can also be accurately presented. The present scheme is suitable for aerospace, ship engineering, integrated circuit, energy chemical industry and other fields, and can be used for contact corrosion performance evaluation and failure prediction of key contact components (such as connectors, transmission systems, heat dissipation structure micro contacts, heat exchangers, etc.) of major equipment, and can provide scientific basis and decision support for engineering design, material selection and equipment maintenance in related fields.

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

[0127] As shown in Figures 2-10 , it is determined that the type of high-temperature contact corrosion is high-temperature contact oxidation corrosion of copper (Copper), and the high-temperature contact corrosion process and internal mechanism are further determined. Copper has two main products in a dry air environment, namely copper oxide and cuprous oxide. The fractions of the two oxides produced during copper oxidation change in different temperature ranges. At 800-1000℃, the fraction of copper oxide is very low, and remains at a very low level between 600℃ and 800℃; at 350-600℃, the fraction of copper oxide increases sharply. The present embodiment mainly focuses on the high-temperature oxidation corrosion of copper at 800℃. Therefore, the main product of copper oxidation is cuprous oxide, and the existence of copper oxide is ignored. The corrosion equation of copper is:

[0128] 2Cu + O → Cu2O (52)

[0129] The oxidation of copper in this example occurs at standard atmospheric pressure. In the early stages of oxidation, the initial growth of the oxide is achieved by the formation of cuprous oxide islands, which eventually coalesce to form an oxide layer. The thickness of the oxide layer gradually increases with time. Between 600 °C and 850 °C, the rate of oxidation of copper is mainly controlled by grain boundary diffusion and lattice diffusion. Oxygen adheres to the copper surface to form oxygen ions, which react and gradually diffuse into the copper, while copper ions diffuse outward through the grain boundaries and lattice, resulting in cuprous oxide. During the oxidation of copper, the presence of certain trace elements, such as arsenic and selenium, inhibits the diffusion of copper ions. Therefore, this example ignores the internal ion diffusion process and the initial formation process of oxidation islands, and only focuses on the process of oxygen diffusion into copper to form cuprous oxide.

[0130] Further, there is a mutual coupling relationship between contact and corrosion, and the internal mechanism is mainly that the existence of contact affects the diffusion of oxygen in the copper and the generation of internal cuprous oxide. Gas diffusion determines the penetration rate of oxygen in the material, which is a necessary condition for the oxidation reaction to proceed. Due to the existence of contact, it causes corresponding stress changes in the copper, affecting the distribution of oxygen in the copper. The reaction rate is affected by temperature, chemical potential of reactants and products, and internal stress gradient generated by contact, which determines the growth rate and thickness of the oxide layer.

[0131] Further, a force-chemical coupling theory model is established to establish control equations for gas diffusion, chemical reaction rate, stress, strain, and their interactions. Gas diffusion is affected by stress gradient. Stress is related to the concentration of reactants and products. The rate of chemical reaction is controlled by chemical potential and hydrostatic pressure. In the initial oxidation process of copper, oxygen diffuses into 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 diffusion coefficient of oxygen; R is the gas constant; T is the temperature; is the gradient operator.

[0134] Further, the chemical potential of each reactant is:

[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 Concentrations of copper and cuprous oxide; c Cu,max , c O,max , and Maximum solubility of copper, oxygen and cuprous oxide; V m Molar volume of solid matrix; η O is the composition expansion coefficient of oxygen.

[0137] Further, the chemical reaction rate is:

[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 starts.

[0140] Further, during the oxidation reaction, in addition to the elastic strain, there should also be a composition 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 composition strain due to oxygen diffusion, and ε g represents the growth strain of cuprous oxide.

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

[0144]

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

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

[0147]

[0148] Further, based on the small strain assumption, we ignore the effect of body force, and the force balance equation can be expressed as:

[0149] σ ij,j = 0 (61)

[0150] Further, the mass balance equations of the three reactants can be expressed as:

[0151]

[0152] Further, the nonlinear constitutive equation of the contact-corrosion coupled theory model is:

[0153]

[0154] j O = Φ1+ Φ2 (66)

[0155]

[0156] where C is the material elastic matrix,

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

[0158]

[0159] where α represents the reactant or product.

[0160] Further, by the discretized weak forms, the element level residuals and tangent matrices are calculated:

[0161]

[0162] where 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.

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

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

[0165] Further, in the establishment of the high-temperature contact-corrosion coupling finite element model and the verification of the accuracy of the model, a two-dimensional contact oxidation corrosion model is established using Abaqus finite element software, as shown in Figure 2 The upper part is a circular punch with a radius of 5 mm, and the lower part is a solid copper with a size of 1.5 mm*0.9 mm. The circular punch 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 primary surface, and the top surface of the copper is set as the secondary surface, and the contact properties are set as no friction and hard contact. The displacement of the circular punch in the x direction is constrained, and a linearly increasing force is applied in the y direction over time. The displacement of the solid copper bottom in the x and y directions is 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] Further, in the establishment of the high-temperature contact-corrosion coupling finite element model, the solid copper in the model uses a user-defined element, and the 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 using the standard Galerkin method, using the control equation, initial condition and boundary condition, and is realized in the UEL module. The solid copper uses UEL to simulate deformation and chemical reaction.

[0167] Further, the material parameters required in the model are listed in Tables 1-3. Since the Young's modulus, Poisson's ratio, molar volume and diffusion coefficient inside the copper will change during the chemical reaction process, 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, 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 the reference values, Q O_1 and Q O_2Activation energy for 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 used for simulation

[0175]

[0176]

[0177] Further, finite element model accuracy verification was performed using the UEL module for static contact simulation and compared with Hertz contact theory. The UEL was used to model copper with chemical reaction rate constant (L), composition expansion coefficient (η O ) and chemical reaction proportionality coefficient (L β ) set to zero to ensure that no chemical reaction occurs inside the copper. The composition strain due to oxygen and the growth strain due to reaction were not included in this simulation. Without any reaction, the material parameters were set to E = 1.16 x 10 11 Pa, v = 0.348, and the load was F = 50 kN. Figure 3 The contact pressure obtained from Hertz theory and finite element simulation is shown. Good agreement between the theoretical and simulated results was achieved.

[0178] Further, an isotropic plane with stress-free equilibrium expansion and chemical reaction was simulated to verify the oxidation corrosion model accuracy, as shown in Figure 4 This simulation did not consider contact. A constant c O = 200 mol / m 3 was set at the upper and right boundaries of the copper plane, while the displacement in the x and y directions was constrained at the left and lower boundaries, respectively. The initial concentrations of the reactants and products were considered to be and The initial value of copper was the molar concentration calculated from the density of copper, while the initial values of oxygen and cuprous oxide were very small. When the gas diffuses into the copper, the reaction inside the metal will immediately occur until it reaches an equilibrium state. 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 ε0is a constant. The total strain is decomposed into elastic strain, compositional strain (caused by concentration change) and growth strain (caused by chemical reaction), and the expression of the vertical direction stress σ3is derived based on Hooke's law. Further based on the steady state diffusion condition and chemical reaction equilibrium The diffusion flux, chemical potential and stress are coupled to establish the nonlinear equation. By introducing the chemical potential expression and mass conservation relation, the nonlinear equation about the product concentration is finally formed, and the Newton iteration method is used for numerical solution. The component expansion coefficient η O is taken from 0 to 0.05, and the chemical reaction proportionality coefficient L β is taken from 0 to 0.008. The analytical solution of the reaction equilibrium state in the stress-free state is obtained, and the verification result is shown in Figure 5 .

[0179] Further, a certain high-temperature contact corrosion numerical study, Figure 6 shows the influence of contact pressure on the contact interface during high-temperature corrosion, and the results without oxidation corrosion are plotted for comparison. It can be seen that there is a significant difference between the contact pressure with and without oxidation corrosion, and the contact pressure gradually increases with the extension of the corrosion time. When the reaction reaches 500 hours, the reaction tends to be balanced. The contact pressure under oxidation corrosion for 500 hours 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 gradually spreads from the lower boundary of the metal matrix to the upper boundary until the reaction reaches equilibrium, and the material composition in 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 the copper gradually increases. As the reaction proceeds, this leads to an increase in contact pressure and a slight decrease in contact area. It can be seen that the main factor affecting the contact pressure due to 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 lead to an increase in the Young's modulus inside the copper. The change in the Young's modulus directly affects the increase in the contact pressure.

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

[0181] Figure 9 The gradient distribution of oxygen in copper when the normal force is 0 kN is shown, Figure 10 The distribution of oxygen inside copper when the normal force is 200 kN is shown. Due to the influence of compressive stress inside copper, the oxygen concentration shows an uneven 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 electronic device provided by the embodiment of the present application comprises a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete mutual communication through the communication bus,

[0183] The memory is used for storing a computer program.

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

[0185] The communication bus mentioned above can be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus, etc. The communication bus can be divided into an address bus, a data bus, a control bus, etc. For the convenience of representation, only one 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 terminal and other devices.

[0187] The memory can include a random access memory (RAM) and can also include a non-volatile memory, for example, at least one disk memory. Optionally, the memory can also be at least one storage device located away from the aforementioned processor.

[0188] The processor described above can be a general processor, including a central processing unit (CPU), a network processor (NP), etc.; or can be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, a discrete gate or transistor logic device, a discrete hardware component.

[0189] In another embodiment provided by the present application, a computer readable storage medium is provided, and the computer readable storage medium stores a computer program. The computer program is executed by a processor to implement the method for constructing the high-temperature contact-corrosion coupling model according to any one of the above embodiments.

[0190] In another embodiment provided by the present application, a computer program product is provided, and the computer program product includes instructions. When the computer program product is executed on a computer, the computer performs the method for constructing the high-temperature contact-corrosion coupling model according to any one of the above embodiments.

[0191] In the above embodiments, the method can be implemented by software, hardware, firmware or any combination thereof. When implemented by software, the method can be implemented in the form of a computer program product, entirely or partially. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the method described in the embodiments of the present application is entirely or partially generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network or other programmable device. The computer instructions can be stored in a computer readable storage medium or transferred from one computer readable storage medium to another computer readable storage medium, for example, the computer instructions can be transferred from one website, computer, server or data center to another website, computer, server or data center through wired (such as coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (such as infrared, wireless, microwave, etc.) mode. The computer readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid state disk (SSD)), etc.

[0192] It is to be noted that, in the present document, relational terms such as first and second and the like can be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the presence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0193] Each of the embodiments in the present specification is described in a related manner, and the same or similar parts between the embodiments can be mutually referred to. Each of the embodiments focuses on the difference from other embodiments. In particular, for the device embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the part of the description of the method embodiments.

[0194] The preferred embodiments of the present application have been described above with the aid of drawing figures, and are not intended to limit the scope of the present application. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present application shall fall within the scope of the present application.

Claims

1. A method for constructing a high-temperature contact-corrosion coupling model, characterized in that: include: Determine the type of high temperature contact corrosion and the internal mechanism of corrosion; Construct a theoretical model of force-chemical coupling; The force-chemical coupling theoretical model is solved by using a finite element algorithm; Based on the results obtained, a high-temperature contact-corrosion coupled finite element model is constructed; The force-chemical coupling theoretical model includes: a mechanical equilibrium equation and a mass conservation equation; The mechanical equilibrium equation and mass conservation equation include: s ij,j +b i =0,(i,j=1,2) (1) Among them, σ represents stress, b represents body force, c α and j α represents the concentration and diffusion flux per unit volume of the αth substance, v αr represents the stoichiometric coefficient of the rth reaction of the αth substance, represents the chemical reaction rate of the rth reaction; The force-chemical coupling theoretical model also includes: Energy conservation equation, entropy increase equation, and Holmholtz free energy density function; The energy conservation equation includes: Where u is the energy density per unit volume, is the body heat source intensity, μ α is the chemical potential of the αth substance, q, v and T * is the heat flow, velocity and tension vector, a T , a σ , a j are the boundaries of heat flow, stress, and chemical potential, respectively, V is an isotropic elastic body, and n is the unit normal; The entropy increase equation includes: in, is the entropy increase per unit volume per unit time, and the Holmholtz free energy density function includes: Where s is the entropy density per unit volume, and T is the absolute temperature; The force-chemical coupling theoretical model also includes the constitutive relationship between force-diffusion-chemical reaction under thermodynamic constraints: The constitutive relations include: e=e e +e c +e g (7) Among them, σ kk is the hydrostatic pressure, ε is the total strain, ε e is the elastic strain, ε c is the component strain, ε g For growth strain, is the initial concentration of substance α, η α is the component expansion coefficient, L β is the chemical reaction proportional coefficient, I2 is the unit second-order tensor, V m is the molar volume of the substance; When the reactant is in a gaseous state, the mechanical-chemical coupling theoretical model further includes: Among them, D α is the diffusion coefficient, R is the gas constant, is the chemical potential gradient of the substance, is the substance concentration gradient, is the hydrostatic pressure gradient; The force-chemical coupling theoretical model also includes: Where L is the chemical reaction rate constant, v α is the stoichiometric coefficient of the substance, -v α u α It is the total chemical potential of the overall chemical reaction process of reactants and products.

2. The method according to claim 1, characterized in that The high temperature corrosion type includes at least one of oxidation corrosion, chemical corrosion, and salt spray corrosion in a high temperature environment; Determining the internal mechanism of corrosion includes: Determine the chemical reaction kinetics and thermodynamic equilibrium conditions of the reactants, and mark the physical phase states of the reactants and products; wherein the physical phase states include solid, gaseous, and liquid; Determine the effects of contact on reactant distribution, the effects of contact on product distribution, the correspondence between reactant and product concentrations and reaction rates, and the effects of reactant diffusion and material growth on internal stresses.

3. The method according to claim 2, characterized in that The method of solving the force-chemical coupling theoretical model using a finite element algorithm includes: The standard Galerkin method is used to discretize the mechanical-chemical coupling theoretical model; The discretized model, the constitutive relation, the residual and the stiffness matrix are input into the preset UEL subroutine of Abaqus, and the Newton-Raphson method is used for iterative solution; The discretizing of the force-chemical coupling theoretical model includes: in, is the change in material concentration per unit time, and the stiffness matrix and residual include: Among them, N u is the shape function of displacement, is the transpose of the displacement shape function, u e is the node displacement, N c is the shape function of concentration, is the transpose of the shape function of concentration, and is the node 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, j α* is the boundary concentration flux, R u and is the residual of displacement and concentration, K uu 、 and is the tangential stiffness.

4. The method according to claim 3, characterized in that Based on the results obtained from the solution, a high-temperature contact-corrosion coupled finite element model is constructed, including: Determine the static contact model including the indenter and substrate; Based on the static contact model and the results obtained by the solution, a high-temperature contact-corrosion coupling finite element model is constructed.

5. An electronic device, characterized in that: It includes a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus; Memory for storing computer programs; A processor, configured to implement the method steps described in any one of claims 1 to 4 when executing a program stored in a memory.

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