CN114330053A - Method and device for simulating corrosion morphology evolution of metal surface hydrogenation point - Google Patents
Method and device for simulating corrosion morphology evolution of metal surface hydrogenation point Download PDFInfo
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Abstract
The invention discloses a method and a device for simulating the appearance evolution of hydrogenated point corrosion on a metal surface, wherein an anisotropic elastic constant is adopted to establish a hydrogenated point corrosion phase field model coupling anisotropic elastic energy, an interpolation function method is utilized to construct an equivalent elastic constant to represent the heterogeneity of a system, the method is suitable for anisotropic metal materials, the appearance difference of the metal materials caused by the elastic anisotropic growth can be simulated, and the growth appearance characteristics of hydrogenated point corrosion can be better shown; in the pitting corrosion phase field model, a finite element method is adopted to solve a mechanical equilibrium equation of the non-periodic boundary condition, so that the problem of non-periodic physical parameter periodicity caused by the periodic elastic field solved by Fourier transform can be avoided.
Description
Technical Field
The invention relates to the technical field of metal hydrogenation corrosion, in particular to a method and a device for simulating the corrosion morphology evolution of a metal surface hydrogenation point.
Background
Pitting of the hydride on the metal surface leads to material failure. Hydriding corrosion is a chemical corrosion that, once it occurs, produces a phase structure of different composition. Nucleation and precipitation of hydrides generally occurs near the passivation layer/metal interface, with hydrogenation of the metal M by M + xH]＝MHxIn which [ H ] is generated]X is the H/M ratio for hydrogen dissolved in the metal or passivation layer. The hydrogenation process is mainly divided into three stages, early: nucleation phase, the initial phase of hydride formation depends on adsorption, dissociation and migration of hydrogen; in the middle stage: in the growth period, the hydride rapidly grows up; and (3) later stage: the oxide layer on the surface is broken, so that corrosion defects such as pitting and the like appear on the surface of the material. When the concentration of hydrogen exceeds the solid solution limit of the nuclear material, nucleation and growth processes occur until the surface of the material is eventually breached.
The research of the hydrogenation point corrosion at the present stage is divided into two aspects of experiment and theoretical research:
(1) experimental study: at present, the hydrogen diffusion and hydride growth mechanisms are mainly analyzed through the appearance characterization of a corrosion area, and physical property analysis can be carried out on a hydride microstructure based on the hydrogen diffusion and hydride growth mechanisms, but the evolution kinetic mechanisms of the hydride microstructure cannot be clarified.
(2) Theoretical research: hydrogenation pitting corrosion is currently studied mainly from the micro-mesoscopic scale. And (2) microcosmic: physical properties of hydride structures on an atomic scale can be obtained by utilizing a first principle method. Mesoscopic observation: and (3) researching the hydrogenated point corrosion morphology and a corresponding dynamic evolution mechanism by using a phase field method.
The existing spot corrosion phase field model mainly comprises:
(1) the 304 stainless steel electrochemical pitting corrosion phase field model proposed by Qasim et al, the total free energy of such model includes chemical free energy, gradient energy and electric field energy, and the evolution equations include phase field equations, diffusion equations and electric field equations.
(2) The cerium surface hydrogenation point corrosion phase field model proposed by Yang et al has total free energy including chemical free energy, gradient energy and isotropic elastic energy, and evolution equation including phase field equation, diffusion equation and mechanical equilibrium equation.
The disadvantages of the existing spot corrosion phase field model are as follows:
the pitting phase field model under the mesoscopic scale mainly couples a hydrogen diffusion equation and a phase field equation to study the dynamic process of the hydrogenation corrosion, but does not consider the physical phenomena accompanied in the pitting corrosion process: current conduction, material deformation. The 304 stainless steel electrochemical pitting corrosion phase field model proposed by Qasim and the like considers the current conduction phenomenon accompanied in the 304 stainless steel electrochemical corrosion process by introducing electric field energy and an electric field equation, but neglects the important effect of elastic energy on the corrosion morphology, while Yang and the like solve the isotropic elastic energy based on periodic Fourier transform but are not suitable for anisotropic metal materials, can not well reflect the morphology difference of the metal materials caused by elastic anisotropic growth, and meanwhile, the periodic boundary can cause aperiodic physical parameter periodicization and is not in line with the actual simulation condition. Meanwhile, the periodic fourier transform solution is not suitable for metal materials in more complex working environments, for example, when the internal force of the material itself or the external stress at the boundary are considered, the arrangement of the solution inevitably causes some problems and even interferes with the correctness of the result. In addition, the Yang et al set isotropic elasticity of two different materials with the same young's modulus and poisson's ratio has a problem, and the isotropic elasticity is not consistent with the non-uniform elasticity corresponding to the non-homogeneous material in the actual situation.
Disclosure of Invention
In order to solve the problems, the invention provides a method for simulating the corrosion morphology evolution of a metal surface hydrogenation point, which comprises the following steps: acquiring initial physical parameters; the initial physical parameters comprise interfacial energy and kinetic coefficients; determining distribution parameters of the phase field and the concentration field under the corresponding time step; calculating the chemical energy driving force under the corresponding time step according to the distribution parameters; solving a mechanical equilibrium equation under the corresponding time step based on a finite element method to obtain elastic strain and stress components; the mechanical equilibrium equation comprises a preset elastic constant and a preset boundary condition, wherein the preset elastic constant comprises an anisotropic elastic constant, and the preset boundary condition comprises a non-periodic boundary condition; calculating elastic strain energy driving force under the corresponding time step according to the elastic strain and the stress component; calculating to obtain the total driving force under the corresponding time step according to the elastic strain energy driving force and the chemical energy driving force; inputting the total driving force under the corresponding time step into a phase field evolution and concentration diffusion equation to carry out evolution solution, and increasing the corresponding total time step; if the total time step length is judged to meet the output condition, outputting the evolution result under the corresponding time step; and if the total time step length is judged not to meet the output condition, taking the evolution result under the corresponding time step as the initial distribution parameters of a new phase field and a new concentration field to carry out a new round of evolution calculation until the output condition is met.
Optionally, the solving a mechanical equilibrium equation at the corresponding time step based on a finite element method to obtain elastic strain and stress components includes: initializing a global matrix, wherein the global matrix comprises a rigidity matrix and a force matrix; acquiring elastic constants of the metal matrix and the hydride, and calculating to obtain an equivalent elastic constant according to an interpolation function; the elastic constant is an isotropic elastic constant or an anisotropic elastic constant; converting the elastic constant and the equivalent elastic constant into a global stiffness matrix; applying an initially set intrinsic strain or stress matrix, applying a global load vector and applying preset boundary conditions; and solving the displacement field component, and calculating according to the displacement field component to obtain the elastic strain and stress component.
Optionally, the preset boundary condition further includes a period boundary condition; the non-periodic boundary conditions include fixed, load, free boundary conditions.
Optionally, the calculation formula of the equivalent elastic constant is as follows:
wherein, Cijkl(η) is the equivalent elastic constant, which is a function of the phase field variable η,
and
is the elastic constants of the metal substrate and the hydride, respectively, (η) is an interpolation function, Δ CijklIs that
And
the difference between them.
Optionally, calculating the physical effect of elastic strain energy in the corrosion morphology evolution of the metal surface hydrogenation point based on the micro-elasticity theory, as follows:
wherein, FelIs an elastic strain energy, felIs the mismatched elastic strain energy density,
and
respectively elastic strain and stress component, epsilonij(r) is the component u of the displacement field variable uiAnd ujThe total strain indicated is that of the strain,
and lattice intrinsic strain
Correlation, deltaijIs a kronecker sign, and h (η) is an interpolation function.
Optionally, the stress has the following relationship to the elastic strain component:
alternatively, the calculation formula of the total free energy F is as follows:
F＝Fbulk+Fint+Fel＝∫[fbulk(c，η)+fint]dV+Fel
wherein, FbulkIs a chemical free energy, FintIs the gradient energy of the interface, FelIs an elastic energy, fbulk(c,. eta.) is the bulk free energy density,. eta.is the phase field variable, c is the hydrogen concentration;
under the assumption of KKS phase field model
c＝(η)cβ+[1-(η)]cα
fbulk(c，η)＝(η)fβ(cβ)+[1-(η)]fα(cα)+wg(η)
Wherein, cαAnd cβRepresenting the mole fractions of hydrogen in the metal matrix and hydride, respectively; h (η) is a monotonically varying interpolation function, where (η) is 3 η2-2η3；fα(cα) And fβ(cβ) Is the free energy density of the metal substrate and the hydride, respectively, and w is the double potential well g (eta) ═ eta2(1-η)2The height of (d);
wherein f isintIs the gradient energy density, κ, associated with the diffusion interfaceηIs the gradient energy coefficient associated with the phase field variable η.
Alternatively, the phase field control procedure is derived by minimizing the total free energy F by variational differentiation as follows:
wherein L is the kinetic coefficient of phase interface mobility, M is the diffusion mobility of hydrogen concentration, D is the diffusion coefficient, Δ GcAnd Δ GelRespectively, a chemical energy driving force and an elastic strain energy driving force.
The invention provides a device for simulating the corrosion morphology evolution of a metal surface hydrogenation point, which is characterized by comprising the following components: the initial physical parameter acquisition module is used for acquiring initial physical parameters; the initial physical parameters comprise interfacial energy and kinetic coefficients; the distribution parameter determining module is used for determining distribution parameters of the phase field and the concentration field under the corresponding time step; the chemical energy driving force calculation module is used for calculating the chemical energy driving force under the corresponding time step according to the distribution parameters; the mechanical balance equation solving module is used for solving the mechanical balance equation under the corresponding time step based on a finite element method to obtain elastic strain and stress components; the mechanical equilibrium equation comprises a preset elastic constant and a preset boundary condition, wherein the preset elastic constant comprises an anisotropic elastic constant, and the preset boundary condition comprises a non-periodic boundary condition; the elastic strain energy driving force calculation module is used for calculating the elastic strain energy driving force under the corresponding time step according to the elastic strain and the stress component; the total driving force calculation module is used for calculating the total driving force under the corresponding time step according to the elastic strain energy driving force and the chemical energy driving force; the phase field evolution solving module is used for inputting the total driving force under the corresponding time step into a phase field evolution and concentration diffusion equation to carry out evolution solving and increasing the corresponding total time step; the output module is used for outputting the evolution result under the corresponding time step if the total time step is judged to meet the output condition; and the circulation module is used for taking the evolution result under the corresponding time step as the initial distribution parameter of the new phase field and the new concentration field to carry out a new round of evolution calculation until the output condition is met if the total time step is judged not to meet the output condition.
Optionally, the mechanical balance equation solving module is specifically configured to: initializing a global matrix, wherein the global matrix comprises a rigidity matrix and a force matrix; acquiring elastic constants of the metal matrix and the hydride, and calculating to obtain an equivalent elastic constant according to an interpolation function; the elastic constant is an isotropic elastic constant or an anisotropic elastic constant; converting the elastic constant and the equivalent elastic constant into a global stiffness matrix; applying an initially set intrinsic strain or stress matrix, applying a global load vector and applying preset boundary conditions; and solving the displacement field component, and calculating according to the displacement field component to obtain the elastic strain and stress component.
The embodiment of the invention adopts the anisotropic elastic constant to establish a hydrogenated point corrosion phase field model coupling the anisotropic elastic performance, and utilizes the interpolation function method to construct the equivalent elastic constant to represent the heterogeneity of the system, so that the method is suitable for the anisotropic metal material, can simulate the morphological difference of the metal material caused by the elastic anisotropic growth, and better shows the growth morphological characteristics of the hydrogenated point corrosion; in the pitting corrosion phase field model, a finite element method is adopted to solve a mechanical equilibrium equation of the non-periodic boundary condition, so that the problem of non-periodic physical parameter periodicity caused by the periodic elastic field solved by Fourier transform can be avoided.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for simulating the corrosion morphology evolution of a metal surface hydrogenation point provided by an embodiment of the present invention;
FIG. 2 is a diagram illustrating boundary conditions set by the phase field model according to an embodiment of the present invention;
FIG. 3 is a simulation result diagram of the morphology evolution, hydrogen concentration and stress distribution of anisotropic hydrogenated point corrosion in the embodiment of the present invention;
fig. 4 is a schematic structural diagram of a device for simulating the corrosion morphology evolution of a metal surface hydrogenation spot provided by the embodiment of the invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
In order to overcome the defects of the existing phase field model, the embodiment of the invention innovatively adopts a finite element method to introduce various boundary conditions (periodic boundary conditions and non-periodic boundary conditions) and adopts an interpolation function and an elastic constant to introduce anisotropic elastic energy. Based on the above, the embodiment of the invention provides a method for simulating the evolution of the metal surface hydrogenated point corrosion morphology by using a coupled non-periodic anisotropic elastic energy surface hydrogenated point corrosion morphology evolution phase field model, wherein the phase field model can couple the non-periodic anisotropic elastic energy.
Specifically, non-periodic boundary conditions such as fixed conditions, loads, free conditions and the like are introduced through a finite element method, and the condition that a periodic boundary condition elastic field is solved by adopting Fourier transform in a previous phase field model is changed; based on the anisotropic elastic constants of the metal matrix and the hydride, the anisotropic elastic energy and the equivalent elastic constant are successfully introduced through an interpolation function, and the non-uniform distribution of the anisotropic elastic energy between the metal matrix and the hydride interface can be set.
Fig. 1 shows a schematic flow chart of a method for simulating the corrosion morphology evolution of a metal surface hydrogenation spot, which is provided by the embodiment of the invention, and the method comprises the following steps:
s102, acquiring initial physical parameters. The initial physical parameters include interfacial energy and kinetic coefficient.
And S104, determining distribution parameters of the phase field and the concentration field at the corresponding time step.
And S106, calculating the chemical energy driving force under the corresponding time step according to the distribution parameters.
And S108, solving a mechanical balance equation under the corresponding time step based on a finite element method to obtain elastic strain and stress components.
The mechanical equilibrium equation comprises a preset elastic constant and a preset boundary condition, wherein the preset elastic constant comprises an anisotropic elastic constant, and the preset boundary condition comprises a non-periodic boundary condition and a periodic boundary condition; the non-periodic boundary conditions may be fixed, load, free boundary conditions, etc.
The existing phase field model adopts Fourier transform to solve the periodic boundary condition elastic field, however, the periodic boundary can cause the aperiodic physical parameter to be periodic, and the periodic boundary does not conform to the actual simulation condition. Based on this, in the embodiment, various boundary conditions are introduced by using a finite element method, the boundary conditions may be non-periodic boundary conditions or periodic boundary conditions, and the metal surface hydrogenated point corrosion phase field model established by using the finite element method is more in line with the actual complex boundary environment than that under fourier transform, which can only be set by using periodic boundary conditions. Multiple aperiodic boundary conditions may be added compared to a single periodic boundary.
The existing phase field model adopts periodic Fourier transform to solve isotropic elastic energy, but is not suitable for anisotropic metal materials, and cannot accurately reflect the morphology difference of the metal materials caused by elastic anisotropic growth. Based on this, in this embodiment, the metal matrix and the hydride may freely select an anisotropic elastic constant or an isotropic elastic constant, and an equivalent elastic constant and anisotropic elastic energy are introduced through an interpolation function, so that a non-uniform distribution environment of the anisotropic elastic energy between the metal matrix and the hydride interface may be simulated.
Optionally, the finite element method solution process is as follows:
1. a global matrix is initialized that includes a stiffness matrix, a force matrix, and the like.
2. And acquiring elastic constants of the metal matrix and the hydride, and calculating to obtain an equivalent elastic constant according to an interpolation function. The elastic constants of the metal matrix and the hydride can be freely selected from an isotropic elastic constant or an anisotropic elastic constant. Interpolation functions are used to construct equivalent elastic constants to characterize the non-uniformity of the system.
3. And converting the elastic constant and the equivalent elastic constant into a global rigidity matrix.
4. Applying an initially set intrinsic strain or stress matrix, applying a global load vector, and applying a preset boundary condition.
5. And solving the displacement field component, and calculating according to the displacement field component to obtain the elastic strain and stress component.
And S110, calculating the elastic strain energy driving force under the corresponding time step according to the elastic strain and the stress component.
And S112, calculating to obtain the total driving force under the corresponding time step according to the elastic strain energy driving force and the chemical energy driving force.
And S114, inputting the total driving force at the corresponding time step into a phase field evolution and concentration diffusion equation for evolution solution, and increasing the corresponding total time step.
And S116, judging whether the total time step size meets the output condition. If so, step S118 is performed, otherwise, step S120 is performed.
And S118, outputting the evolution result under the corresponding time step.
And S120, taking the evolution result under the corresponding time step as the initial distribution parameters of the new phase field and the new concentration field, returning to continue executing the step S106 to perform a new round of evolution calculation until the output condition is met.
According to the method for simulating the morphology evolution of the hydrogenated point corrosion on the metal surface, provided by the embodiment of the invention, the anisotropic elastic constant is adopted to establish a hydrogenated point corrosion phase field model coupling the anisotropic elastic performance, and the equivalent elastic constant is constructed by utilizing an interpolation function method to represent the heterogeneity of the system, so that the method is suitable for anisotropic metal materials, can simulate the morphology difference of the metal materials caused by the elastic anisotropic growth, and better shows the growth morphology characteristics of the hydrogenated point corrosion; in the pitting corrosion phase field model, a finite element method is adopted to solve a mechanical equilibrium equation of the aperiodic boundary condition, so that the problem of aperiodic physical parameter periodicity caused by solving a periodic elastic field through Fourier transform can be avoided, and the actual simulation condition is better met.
The theoretical process of the above surface hydrogenated pitting corrosion phase field model coupled with the non-periodic, anisotropic elastic energy is described below.
In the metal pitting system, the driving force for metal corrosion and microstructure evolution comes from the minimization of the total free energy F of the system, which in this embodiment includes a uniform chemical free energy FbulkInterfacial gradient energy FintAnd elastic energy Fel. The total free energy F is calculated as follows:
F＝Fbulk+Fint+Fel＝∫[fbulk(c,η)+fint]dV+Fel (1)
wherein f isbulk(c, η) is the chemical free energy density, η is the phase field variable, c is the hydrogen concentration; under the assumption of KKS phase field model
c＝(η)cβ+[1-(η)]cα (2)
fbulk(c,η)＝(η)fβ(cβ)+[1-(η)]fα(cα)+wg(η) (4)
Wherein, cαAnd cβRepresenting the mole fractions of hydrogen in the metal matrix and hydride, respectively; h (η) is a monotonically varying interpolation function, where (η) is 3 η2-2η3(ii) a F in equation (4)α(cα) And fβ(cβ) Is the free energy density of the metal substrate and the hydride, respectively, and w is the double potential well g (eta) ═ eta2(1-η)2Of (c) is measured.
fintIs the gradient energy density associated with the diffusion interface. FelTypically an elastic strain energy related to η. In the phase field framework, the gradient energy can generally be written as a function of the gradient of the phase field variable as follows:
wherein,κηis the gradient energy coefficient associated with the phase field variable η.
The phase field control equation is derived by minimizing the total free energy F by variational differentiation.
Wherein L is the kinetic coefficient of phase interface mobility; m is the diffusion mobility of the hydrogen concentration and can be expressed as
ΔGcAnd Δ GelRespectively, a chemical energy driving force and an elastic strain energy driving force. Equations (6) and (7) indicate that the evolution of the phase-field sequence parameter η and the hydrogen concentration c in time and space obeys the Allen-Cahn equation and the Cahn-Hilliard equation, respectively.
Where L is the kinetic coefficient of phase interface mobility and M is the diffusion mobility of hydrogen concentration, which can be expressed as
D is the diffusion coefficient, Δ GcAnd Δ GelRespectively, a chemical energy driving force and an elastic strain energy driving force. Equations (6) and (7) indicate that the evolution of the phase-field sequence parameter η and the hydrogen concentration c in time and space obeys the Allen-Cahn equation and the Cahn-Hilliard equation, respectively.
Regarding the physical effect of elastic strain energy in the model, the important role in the hydride nucleation and growth process can be revealed based on the theory of micro-elasticity, which is specifically as follows:
wherein, FelIs an elastic strain energy, felIs the mismatched elastic strain energy density,
and
respectively elastic strain and stress component, epsilonij(r) is the component u of the displacement field variable uiAnd ujThe total strain indicated is that of the strain,
and lattice intrinsic strain
Correlation, deltaijIs a kronecker sign, and h (η) is an interpolation function.
Elastic strain
Can be obtained by equation (9) where εij(r) is the component u of the displacement field variable u solved for by the mechanical equilibrium equation (12)iAnd ujThe total strain indicated.
The case of anisotropy or isotropy can be freely chosen on the basis of the elastic constants of the matrix and the hydride, while the inhomogeneous distribution of the elastic energy in the system is characterized by the introduction of an interpolation function (η). It is assumed that both the substrate and the hydride retain the theory of linear elasticity, and thus the stress and elastic strain have the following relationships
Wherein, Cijkl(η) is the equivalent elastic constant, which is a function of the phase field variable η,
and
is the elastic constants of the metal substrate and the hydride, respectively, (η) is an interpolation function, Δ CijklIs that
And
the difference between them.
In the embodiment, a finite element method is used for establishing a surface hydrogenation point corrosion phase field model based on complex boundary conditions, and compared with the situation that only periodic boundary conditions can be adopted for setting under Fourier transform, the method is more practical. Fig. 2 is a schematic diagram of boundary conditions set by the phase field model in this embodiment, and exemplarily shows that both left and right sides of the zirconium α — Zr substrate are periodic boundaries (periodic boundaries), the lower side is a free boundary (free boundary), the upper side surface has a hydride bubble (hydride blower) and a passivation film (passive film), and a diffusion interface (diffusion interface) exists between the hydride bubble and the substrate. The upper surface is specifically set to u (x, t) ═ 0,
lower side watchThe noodle body is arranged as
Compared with a single periodic boundary, the phase field model can be additionally provided with various boundary conditions such as fixed freedom and the like, and the possibility is provided for establishing a more complex model in the future. For example, the work hardening phenomenon frequently existed in engineering can be simulated by setting external stress or fixing boundary conditions.
Aiming at the conditions of anisotropy and elastic non-uniform distribution of materials in actual hydrogenated point corrosion, isotropy or anisotropy is freely selected through an elastic constant, and an equivalent elastic constant is introduced by utilizing an interpolation function to solve the problem of elastic non-uniform distribution, so that the growth morphology characteristics of hydrogenated point corrosion can be displayed more accurately, and the influence of elastic energy anisotropy on the dynamic process of hydrogenated corrosion is further researched.
Fig. 3 is a simulation result diagram of the corrosion morphology evolution, hydrogen concentration and stress distribution of the anisotropic hydrogenated point in this embodiment, in which the substrate is zirconium (α -Zr) and the corrosion product is a hydride bubble. In fig. 3, each row corresponds to the evolution time t of 0s, 300s, and 600s, and each column represents the distribution of the elastic stress in the phase field η, the concentration field c, xx, and the yy direction in this order. The results of this example reveal the important effect of a non-uniform anisotropic elastic distribution on hydride bubble growth, in contrast to the prior art assumption of a continuous distribution of isotropic elastic constants or elastic energy in the matrix and the hydride.
Aiming at the common multipoint polycrystalline corrosion condition of actual pitting corrosion, the embodiment can also be used as a basis for researching different numbers of pitting corrosion and polycrystalline corrosion evolution conditions, and the distribution conditions of concentration fields, non-periodic elastic strain and stress and the interaction of adjacent sites under different evolution times are researched.
The method for simulating the corrosion morphology evolution of the metal surface hydrogenation point provided by the embodiment of the invention has the following advantages:
1. a pitting corrosion phase field model coupling the anisotropic elastic energy is established by utilizing the elastic constant, the equivalent elastic constant is constructed by adopting an interpolation function method to represent the heterogeneity of the system, and the growth morphology characteristics of the hydrogenated pitting corrosion are better shown.
2. In the spot corrosion phase field model, a finite element method is adopted to solve a mechanical equilibrium equation of a complex boundary condition, and the problem of aperiodic physical parameter periodicity caused by solving a periodic elastic field through Fourier transform is solved.
The embodiment of the present invention further provides a device for simulating the evolution of the hydrogenated point corrosion morphology of the metal surface, and fig. 4 is a schematic structural diagram of the device for simulating the evolution of the hydrogenated point corrosion morphology of the metal surface provided by the embodiment of the present invention, where the device includes:
an initial physical parameter obtaining module 401, configured to obtain an initial physical parameter; the initial physical parameters comprise interfacial energy and kinetic coefficients;
a distribution parameter determining module 402, configured to determine distribution parameters of the phase field and the concentration field at corresponding time steps;
a chemical energy driving force calculation module 403, configured to calculate a chemical energy driving force at the corresponding time step according to the distribution parameter;
a mechanical equilibrium equation solving module 404, configured to solve the mechanical equilibrium equation at the corresponding time step based on a finite element method to obtain elastic strain and stress component; the mechanical equilibrium equation comprises a preset elastic constant and a preset boundary condition, wherein the preset elastic constant comprises an anisotropic elastic constant, and the preset boundary condition comprises a non-periodic boundary condition;
an elastic strain energy driving force calculation module 405, configured to calculate an elastic strain energy driving force at the corresponding time step according to the elastic strain and the stress component;
a total driving force calculation module 406, configured to calculate, according to the elastic strain energy driving force and the chemical energy driving force, a total driving force at the corresponding time step;
a phase field evolution solving module 407, configured to input the total driving force at the corresponding time step into a phase field evolution and concentration diffusion equation to perform evolution solving, and increase a corresponding total time step;
an output module 408, configured to output the evolution result in the corresponding time step if it is determined that the total time step satisfies an output condition;
and a loop module 409, configured to, if it is determined that the total time step does not satisfy the output condition, use the evolution result at the corresponding time step as an initial distribution parameter of a new phase field and a new concentration field to perform a new round of evolution calculation until the output condition is satisfied.
According to the device for simulating the morphology evolution of the hydrogenated point corrosion on the metal surface, provided by the embodiment of the invention, the anisotropic elastic constant is adopted to establish a hydrogenated point corrosion phase field model coupling the anisotropic elastic performance, and the equivalent elastic constant is constructed by using an interpolation function method to represent the heterogeneity of the system, so that the device is suitable for anisotropic metal materials, can simulate the morphology difference of the metal materials caused by the elastic anisotropic growth, and better shows the growth morphology characteristics of the hydrogenated point corrosion; in the pitting corrosion phase field model, a finite element method is adopted to solve a mechanical equilibrium equation of the non-periodic boundary condition, so that the problem of non-periodic physical parameter periodicity caused by the periodic elastic field solved by Fourier transform can be avoided.
Optionally, the mechanical balance equation solving module is specifically configured to: initializing a global matrix, wherein the global matrix comprises a rigidity matrix and a force matrix; acquiring elastic constants of the metal matrix and the hydride, and calculating to obtain an equivalent elastic constant according to an interpolation function; the elastic constant is an isotropic elastic constant or an anisotropic elastic constant; converting the elastic constant and the equivalent elastic constant into a global stiffness matrix; applying an initially set intrinsic strain or stress matrix, applying a global load vector and applying preset boundary conditions; and solving the displacement field component, and calculating according to the displacement field component to obtain the elastic strain and stress component.
Those skilled in the art will appreciate that all or part of the processes in the methods of the above embodiments may be implemented by instructing a control device to implement the methods, and the programs may be stored in a computer-readable storage medium, and when executed, the programs may include the processes of the above method embodiments, where the storage medium may be a memory, a magnetic disk, an optical disk, and the like.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
The above description of the present invention is intended to be illustrative. The present invention is not limited to the above-described embodiments, and various changes and modifications may be made without departing from the spirit and scope of the present invention, and these changes and modifications fall within the scope of the claimed invention. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (10)
1. A method for simulating the corrosion morphology evolution of a metal surface hydrogenation point is characterized by comprising the following steps:
acquiring initial physical parameters; the initial physical parameters comprise interfacial energy and kinetic coefficients;
determining distribution parameters of the phase field and the concentration field under the corresponding time step;
calculating the chemical energy driving force under the corresponding time step according to the distribution parameters;
solving a mechanical equilibrium equation under the corresponding time step based on a finite element method to obtain elastic strain and stress components; the mechanical equilibrium equation comprises a preset elastic constant and a preset boundary condition, wherein the preset elastic constant comprises an anisotropic elastic constant, and the preset boundary condition comprises a non-periodic boundary condition;
calculating elastic strain energy driving force under the corresponding time step according to the elastic strain and the stress component;
calculating to obtain the total driving force under the corresponding time step according to the elastic strain energy driving force and the chemical energy driving force;
inputting the total driving force under the corresponding time step into a phase field evolution and concentration diffusion equation to carry out evolution solution, and increasing the corresponding total time step;
if the total time step length is judged to meet the output condition, outputting the evolution result under the corresponding time step;
and if the total time step length is judged not to meet the output condition, taking the evolution result under the corresponding time step as the initial distribution parameters of a new phase field and a new concentration field to carry out a new round of evolution calculation until the output condition is met.
2. The method of claim 1, wherein solving the mechanical equilibrium equations at the corresponding time step based on the finite element method to obtain elastic strain and stress components comprises:
initializing a global matrix, wherein the global matrix comprises a rigidity matrix and a force matrix;
acquiring elastic constants of the metal matrix and the hydride, and calculating to obtain an equivalent elastic constant according to an interpolation function; the elastic constant is an isotropic elastic constant or an anisotropic elastic constant;
converting the elastic constant and the equivalent elastic constant into a global stiffness matrix;
applying an initially set intrinsic strain or stress matrix, applying a global load vector and applying preset boundary conditions;
and solving the displacement field component, and calculating according to the displacement field component to obtain the elastic strain and stress component.
3. The method of claim 2, wherein the preset boundary conditions further comprise periodic boundary conditions; the non-periodic boundary conditions include fixed, load, free boundary conditions.
4. The method according to claim 2, wherein the equivalent elastic constant is calculated as follows:
wherein, Cijkl(η) is the equivalent elastic constant, which is a function of the phase field variable η,
and
is the elastic constants of the metal substrate and the hydride, respectively, (η) is an interpolation function, Δ CijklIs that
And
the difference between them.
5. The method according to any one of claims 2 to 4, wherein the physical effect of elastic strain energy in the evolution of the corrosion morphology of the hydrogenated spot on the metal surface is calculated based on the theory of micro-elasticity as follows:
wherein, FelIs an elastic strain energy, felIs the mismatched elastic strain energy density,
and
respectively elastic strain and stress component, epsilonij(r) is the component u of the displacement field variable uiAnd ujThe total strain indicated is that of the strain,
and lattice intrinsic strain
Correlation, deltaijIs a kronecker sign, and h (η) is an interpolation function.
6. The method of claim 5, wherein the stress is related to the elastic strain component by:
7. method according to any of claims 2-4, characterized in that the total free energy F is calculated as follows:
F＝Fbulk+Fint+Fel＝∫[fbulk(c,η)+Fint]dV+Fel
wherein, FbulkIs a chemical free energy, FintIs the gradient energy of the interface, FelIs an elastic energy, fbulk(c,. eta.) is the bulk free energy density,. eta.is the phase field variable, c is the hydrogen concentration;
under the assumption of KKS phase field model
fbulk(c,η)＝(η)fβ(cβ)+[1-(η)]fα(cα)+wg(η)
Wherein, cαAnd cβRepresenting the mole fractions of hydrogen in the metal matrix and hydride, respectively; h (η) is a monotonically varying interpolation function, where (η) is 3 η2-2η3；fα(cα) And fβ(cβ) Is the free energy density of the metal substrate and the hydride, respectively, and w is the double potential well g (eta) ═ eta2(1-η)2The height of (d);
wherein f isintIs the gradient energy density, κ, associated with the diffusion interfaceηIs the gradient energy coefficient associated with the phase field variable η.
8. The method of claim 7, wherein minimizing the total free energy F by variational differentiation derives the phase field control procedure as follows:
wherein L is the kinetic coefficient of phase interface mobility, M is the diffusion mobility of hydrogen concentration, D is the diffusion coefficient, Δ GcAnd Δ GelRespectively, a chemical energy driving force and an elastic strain energy driving force.
9. An apparatus for simulating the evolution of the corrosion morphology of a hydrogenated spot on a metal surface, comprising:
the initial physical parameter acquisition module is used for acquiring initial physical parameters; the initial physical parameters comprise interfacial energy and kinetic coefficients;
the distribution parameter determining module is used for determining distribution parameters of the phase field and the concentration field under the corresponding time step;
the chemical energy driving force calculation module is used for calculating the chemical energy driving force under the corresponding time step according to the distribution parameters;
the mechanical balance equation solving module is used for solving the mechanical balance equation under the corresponding time step based on a finite element method to obtain elastic strain and stress components; the mechanical equilibrium equation comprises a preset elastic constant and a preset boundary condition, wherein the preset elastic constant comprises an anisotropic elastic constant, and the preset boundary condition comprises a non-periodic boundary condition;
the elastic strain energy driving force calculation module is used for calculating the elastic strain energy driving force under the corresponding time step according to the elastic strain and the stress component;
the total driving force calculation module is used for calculating the total driving force under the corresponding time step according to the elastic strain energy driving force and the chemical energy driving force;
the phase field evolution solving module is used for inputting the total driving force under the corresponding time step into a phase field evolution and concentration diffusion equation to carry out evolution solving and increasing the corresponding total time step;
the output module is used for outputting the evolution result under the corresponding time step if the total time step is judged to meet the output condition;
and the circulation module is used for taking the evolution result under the corresponding time step as the initial distribution parameter of the new phase field and the new concentration field to carry out a new round of evolution calculation until the output condition is met if the total time step is judged not to meet the output condition.
10. The apparatus of claim 9, wherein the mechanical balance equation solving module is specifically configured to:
initializing a global matrix, wherein the global matrix comprises a rigidity matrix and a force matrix;
acquiring elastic constants of the metal matrix and the hydride, and calculating to obtain an equivalent elastic constant according to an interpolation function; the elastic constant is an isotropic elastic constant or an anisotropic elastic constant;
converting the elastic constant and the equivalent elastic constant into a global stiffness matrix;
applying an initially set intrinsic strain or stress matrix, applying a global load vector and applying preset boundary conditions;
and solving the displacement field component, and calculating according to the displacement field component to obtain the elastic strain and stress component.
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