CN111044443A - Transient dual-phase stainless steel micro galvanic corrosion process simulation method based on phase field method - Google Patents
Transient dual-phase stainless steel micro galvanic corrosion process simulation method based on phase field method Download PDFInfo
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Abstract
The invention relates to a transient dual-phase stainless steel galvanic corrosion process simulation method based on a phase field method, which comprises the following steps: establishing a duplex stainless steel galvanic corrosion simplified model based on the actual experimental situation; establishing a leading equation for simplifying potential distribution and phase field variable distribution of the model and a relation equation for combining the potential distribution and the phase field variable distribution; and acquiring initial conditions and boundary conditions of the simplified model, and realizing the simulation of the duplex stainless steel galvanic corrosion process based on the relation equation. Compared with the prior art, the invention has the advantages of avoiding interface tracking, being simple and convenient, being suitable for duplex stainless steel materials and the like.
Description
Technical Field
The invention relates to the technical field of double-phase stainless steel galvanic couple performance research, in particular to a transient double-phase stainless steel galvanic couple corrosion process simulation method based on a phase field method.
Background
Duplex stainless steel refers to stainless steel with about 50% ferrite and austenite, respectively, wherein the content of the minor phases also needs to reach 30% at minimum. The duplex stainless steel has strong corrosion resistance, and the corrosion resistance is not only related to the factors such as the property of a corrosion medium, the grain size, the roughness and the like, but also related to the micro-region galvanic corrosion formed by adjacent austenite phase and ferrite phase in the duplex stainless steel. The galvanic corrosion in the duplex stainless steel is a complicated and important field, the depletion or enrichment areas of composition phases, compounds, component elements, oxidation films and the like which present different electrode potentials in the stainless steel are possible to generate the galvanic corrosion, and meanwhile, the galvanic corrosion is also influenced by various factors such as temperature, pH value of corrosive liquid, area ratio of a cathode and an anode and the like.
The traditional research is mostly established on the basis of test data and experience, the research process is long in time and huge in capital cost, and quantitative research cannot be carried out due to the fact that austenite phase and ferrite phase in the duplex stainless steel are small in size and uneven in distribution, and the requirements for continuously improved process precision and accuracy are difficult to meet. With the development of computer technology and the continuous improvement of the theory of galvanic corrosion, it has become possible to research the internal micro-galvanic corrosion process of the duplex stainless steel by adopting numerical simulation. The numerical simulation technology is utilized to research the process of the internal micro-couple corrosion of the duplex stainless steel, the change of the anode surface appearance along with time and the current and potential distribution in the corrosion process in the micro-couple corrosion can be quantitatively simulated and predicted, and a new idea is provided for the numerical simulation of the micro-couple corrosion in the duplex stainless steel.
However, at present, numerical simulation related to galvanic corrosion is mostly based on a finite element method, the evolution of a two-phase interface needs to be tracked, and the calculation process is complicated.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a simple and reliable transient duplex stainless steel galvanic corrosion process simulation method based on a phase field method.
The purpose of the invention can be realized by the following technical scheme:
a transient dual-phase stainless steel galvanic corrosion process simulation method based on a phase field method comprises the following steps:
establishing a duplex stainless steel galvanic corrosion simplified model based on the actual experimental situation;
establishing a leading equation for simplifying potential distribution and phase field variable distribution of the model and a relation equation for combining the potential distribution and the phase field variable distribution;
and acquiring initial conditions and boundary conditions of the simplified model, and realizing the simulation of the duplex stainless steel galvanic corrosion process based on the relation equation.
Further, the initial state of the simplified model is a two-dimensional plane shape with the X-axis as the symmetry axis, the upper side of the symmetry axis represents the electrolyte, the lower side of the symmetry axis represents the cathode and anode composed of ferrite and austenite, the left side is the cathode composed of austenite phase, the right side is the anode composed of ferrite phase, and the cathode and the anode are uniformly immersed in the electrolyte.
Further, the cathode composed of austenite phase and the anode composed of ferrite phase are in close contact.
Further, the initial conditions are specifically:
c (x,0) in the electrolyte region is 0, phi (x,0) is 0, c (x,0) in the anode region is 1, phi (x,0) is 1, c is the molar concentration in the simulation region, phi is the phase field variable, and x represents the coordinates in the simulation region.
Further, the leading equation of the potential distribution is obtained based on the theory of galvanic corrosion, and is as follows:
in the formula (I), the compound is shown in the specification,
for local potentials, ▽ is the hamiltonian.
Further, the leading equation of the phase field variable distribution is obtained based on the jintsburgh-lanchoe theory, and is as follows:
where φ is the phase field variable, M is the diffusion coefficient, f is the system free energy density function, c' is the standard molal ion concentration, β1The coefficient is the energy gradient coefficient, L is the interface dynamics parameter, ▽ is the Hamiltonian, x represents the coordinate in the simulation region, t is the simulation time, and ζ is the system free energy.
Further, the relation equation is:
wherein L is an interface kinetic parameter, n is the average number of electrons lost by the anodic reaction in the process of the duplex stainless steel galvanic corrosion, F is a Faraday constant, v is the movement rate of the galvanic corrosion interface, i is a current density, csolid＝csIs the molar concentration of metal ions in the solid phase.
Further, the boundary conditions include cathode and anode boundary conditions based on the barrett-volmer equation.
Further, the simulation of the duplex stainless steel galvanic corrosion process was performed with the following additional conditions:
in formula (II), c'SAnd c'LStandardized concentrations of the solid and liquid phases respectively,
is local potential, f (c'S) And f (c'L) Respectively, solid-phase free energy density and liquid-phase free energy density, sigma is interfacial energy, and r is double potential well function
L is the diffusion interface layer thickness, α*Is constant, β1Is the energy gradient coefficient.
Compared with the prior art, the invention has the following beneficial effects:
1. the method is realized based on a phase field method, avoids interface tracking, and is suitable for solving the problem that the evolution of a solid-liquid interface is very complex.
2. According to the invention, through a guiding equation for simulating potential distribution and a guiding equation for simulating phase field variable change in the model, the distribution of phase field variables (c' and phi) at different moments in a calculation region can be conveniently simulated, and the purpose of simulating galvanic corrosion by using a phase field method is finally achieved.
3. The invention sets additional conditions in the simulation process, improves the reliability of the simulation and enables the simulation to be smoothly carried out.
4. The invention can quantitatively research the appearance and the corrosion rate of the corrosion surface.
Drawings
FIG. 1 is a schematic representation of a simplified model of the present invention;
FIG. 2 is a schematic diagram of the initial conditions and boundary conditions of the model of the present invention;
FIG. 3 is a graph of the results of the model calculation at 50000 seconds;
FIG. 4 is a flow chart of simulation steps of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
As shown in fig. 4, the present embodiment provides a method for simulating a transient duplex stainless steel galvanic corrosion process based on a phase field method, where the method uses the phase field method to simulate an established simplified model of duplex stainless steel galvanic corrosion, and includes the following steps:
firstly, simplifying conditions and initializing a model, and constructing the model according to the actual condition of the duplex stainless steel galvanic corrosion;
establishing a guide equation capable of simulating potential distribution at different moments in the region based on a galvanic corrosion theory;
establishing a guidance equation capable of simulating phase field variable changes at different moments in a model area based on the Kinzburg-Landau theory;
establishing a relation equation combining the guidance equation in the step two and the guidance equation in the step three;
and fifthly, applying boundary conditions and initial conditions to the model according to polarization curve data measured by experiments, and further calculating the phase field model.
In step one, as shown in fig. 1, the simplified model established in this embodiment has the following assumptions, which can facilitate computer calculation and make the simulation result easier to converge:
the initial state of the model is a two-dimensional plane form taking an X axis as a symmetry axis, the upper side of the symmetry axis represents electrolyte, the lower side of the symmetry axis represents a cathode and an anode which are composed of ferrite and austenite, the left side of the symmetry axis is a cathode which is composed of an austenite phase, the right side of the symmetry axis is an anode which is composed of a ferrite phase, and the cathode and the anode are uniformly immersed in the electrolyte; the cathode composed of austenite phase and the anode composed of ferrite phase are closely contacted; the cathode polarization is large and its potential is much smaller than the self-corrosion potential (-0.237V), which means that the anodic reaction at the cathode boundary is negligible; the cathode, the anode and the electrolyte have uniform components, and the inside of each part has no difference.
In this embodiment, the electrolyte is sodium chloride electrolyte.
Under initial conditions, c (x,0) in the electrolyte region is 0, phi (x,0) is 0, c (x,0) in the anode region is 1, phi (x,0) is 1, c is the molarity in the simulation region, phi is the phase field variable, and x represents the coordinates in the simulation region.
In the second step, the leading equation of the potential distribution is obtained based on the theory of galvanic corrosion and is a laplace equation.
The following relationship exists between the current density i on the metal surface and the electric field:
wherein k is the conductivity of the electrolyte,
is a local potential.
According to the charge neutrality principle, the current density will follow the following charge conservation formula:
▽·i＝0 (2)
and (2) combining the vertical type (1) and the vertical type (2), namely obtaining a guide equation for solving the potential distribution in the electrolyte:
in step three, the leading equation of the phase field variable distribution is obtained based on the Kinzburg-Landau theory, and is an Allen-Cahn and Cahn-Hilliard equation:
wherein M is the diffusion coefficient, f is the system free energy density function, c' is the standard molal ion concentration, β1And (3) representing an energy gradient coefficient, L representing an interface kinetic parameter, t representing simulation time, and zeta representing system free energy. Phase field variable phi is used to track the evolution of pitting interfacesAnd the phase field variable phi continuously changes in the diffusion interface on the assumption that phi in the liquid phase, i.e. the corrosive liquid, is 0, and phi in the solid phase, i.e. the metal material, is 1.
To simplify the calculation, the molar ion concentrations were normalized, i.e.:
wherein c issIs the molar concentration of metal ions in the solid phase, and c is the molar concentration in the calculated region (both solid and liquid phases included).
The system free energy density function f is represented by:
wherein the content of the first and second substances,
as an interpolation function, it is related to a double potential well function
Limiting the thickness of the diffusion interface, r is a double potential well function
Height of (d), f (c'S) And f (c'L) The solid-phase free energy density and the liquid-phase free energy density, respectively, can also be written as:
f(c'S)＝Z(c'S-c'S0)2(6)
f(c'L)＝Z(c'L-c'L0)2(7)
wherein Z is the curvature of a free energy density function, c'SAnd c'LNormalized concentrations for the solid and liquid phases, respectively, and the initial values are expressed as:
wherein, csatIs the saturation concentration within the diffusion interface.
Combining the formulas (4), (5), (6), (7), (8) and (9) to obtain:
wherein D is a system diffusion coefficient, and in order to enable the simulation to be smoothly carried out, the simulation system further comprises a plurality of additional conditions which can assist the simulation and enable the simulation to be smoothly carried out:
wherein l is the diffusion interface layer thickness, σ is the interface energy (solid-liquid interface), α*Is constant (see table 1).
The specific implementation process of the step four is as follows:
according to Faraday's law, the relationship between the current density i in the system and the migration rate of the corrosion interface of the micro-couple is as follows:
i＝nFcsolidv
wherein n is the average number of electrons lost by anodic reaction in the process of duplex stainless steel galvanic corrosion, F is the Faraday constant, v is the interface moving speed of galvanic corrosion, csolid＝cs。
In this phase field model, the erosion interface movement rate is linear with the interface dynamics parameters:
v＝ξ·L
wherein ξ is a constant, and the two equations are combined to obtain:
the above formula can combine the current density distribution of galvanic corrosion in the second step with the interface dynamic parameters of the phase field method in the third step, thereby achieving the purpose of simulating the duplex stainless steel galvanic corrosion by the phase field method.
In step five, the initial conditions and the boundary conditions are applied to the model by using the experimental data, and as shown in fig. 2, the model is simulated by using the COMSOL 5.3a software, so that the simulation result of the model is derived. The parameters required for the simulation are shown in table 1.
TABLE 1
In general, the non-linear form of the experimentally measured polarization curve can be expressed by the Butler-Wallem (B-V) equation:
wherein E iscorrTo corrosion potential, icorrFor corrosion current density, α, β are the tafel slopes of the polarization curves measured at room temperature, which equation is used to represent the boundary conditions in the galvanic phase field model, E, i correspond to the abscissa (potential) and ordinate (current density) of the butler-volmer (B-V) curve, respectively.
Substituting specific values, the barrett-volmer forms of the polarization curves of the anode (austenite) and cathode (ferrite) of this example are:
i＝1.64*10-2(e14.59(E+0.273)-e-7.79(E+0.273))
i＝0.31*10-2(e1.44(E+0.237)-e-23.39(E+0.237))
the simulation result of the model obtained in this example at 50000 seconds is shown in fig. 3.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions that can be obtained by a person skilled in the art through logic analysis, reasoning or limited experiments based on the prior art according to the concept of the present invention should be within the protection scope determined by the present invention.
Claims (9)
1. A transient dual-phase stainless steel galvanic corrosion process simulation method based on a phase field method is characterized by comprising the following steps:
establishing a duplex stainless steel galvanic corrosion simplified model based on the actual experimental situation;
establishing a leading equation for simplifying potential distribution and phase field variable distribution of the model and a relation equation for combining the potential distribution and the phase field variable distribution;
and acquiring initial conditions and boundary conditions of the simplified model, and realizing the simulation of the duplex stainless steel galvanic corrosion process based on the relation equation.
2. The phase-field-based transient duplex stainless steel galvanic corrosion process simulation method according to claim 1, wherein the initial state of the simplified model is a two-dimensional planar form with the X-axis as the symmetry axis, the upper side of the symmetry axis represents the electrolyte, the lower side of the symmetry axis represents the cathode and anode composed of ferrite and austenite, the left side is the cathode composed of austenite phase, the right side is the anode composed of ferrite phase, and the cathode and anode are uniformly immersed in the electrolyte.
3. The phase field method based transient duplex stainless steel galvanic corrosion process simulation method according to claim 2, wherein the cathode composed of austenite phase and the anode composed of ferrite phase are in close contact.
4. The phase-field-method-based transient duplex stainless steel galvanic corrosion process simulation method according to claim 2, wherein the initial conditions are specifically:
c (x,0) in the electrolyte region is 0, phi (x,0) is 0, c (x,0) in the anode region is 1, phi (x,0) is 1, c is the molar concentration in the simulation region, phi is the phase field variable, and x represents the coordinates in the simulation region.
5. The phase-field-method-based transient duplex stainless steel galvanic corrosion process simulation method according to claim 1, wherein the leading equation of the potential distribution is obtained based on a galvanic corrosion theory and is:
in the formula (I), the compound is shown in the specification,
in order to be a local electric potential,
is a hamiltonian.
6. The phase field method-based transient duplex stainless steel galvanic corrosion process simulation method according to claim 1, wherein the leading equation of the phase field variable distribution is obtained based on the Kiltzburg-Landau theory and is:
where φ is the phase field variable, M is the diffusion coefficient, f is the system free energy density function, c' is the standard molal ion concentration, β1Is the coefficient of energy gradient, L is the parameter of interface dynamics,
and the method is a Hamiltonian, x represents coordinates in a simulation area, t is simulation time, and zeta is system free energy.
7. The phase-field-method-based transient duplex stainless steel galvanic corrosion process simulation method according to claim 1, wherein the relation equation is as follows:
wherein L is an interface kinetic parameter, n is the average number of electrons lost by the anodic reaction in the process of the duplex stainless steel galvanic corrosion, F is a Faraday constant, v is the movement rate of the galvanic corrosion interface, i is a current density, csolid＝csIs the molar concentration of metal ions in the solid phase.
8. The phase field method based transient duplex stainless steel galvanic corrosion process simulation method of claim 1, wherein the boundary conditions comprise cathode and anode boundary conditions based on the barrett-volmer equation.
9. The phase field method-based transient dual-phase stainless steel galvanic corrosion process simulation method according to claim 1, wherein the dual-phase stainless steel galvanic corrosion process simulation is performed with the following additional conditions:
in formula (II), c'SAnd c'LStandardized concentrations of the solid and liquid phases respectively,
is local potential, f (c'S) And f (c'L) Respectively, solid-phase free energy density and liquid-phase free energy density, sigma is interfacial energy, and r is double potential well function
L is the diffusion interface layer thickness, α*Is constant, β1Is the energy gradient coefficient.
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Cited By (3)
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| CN111798930A (en) * | 2020-07-17 | 2020-10-20 | 西南石油大学 | CO considering influence of corrosion product film2Corrosion rate prediction method |
| CN111982799A (en) * | 2020-08-24 | 2020-11-24 | 中国人民解放军海军航空大学青岛校区 | Atmospheric corrosion prediction method for building block type airplane structural member |
| CN117219213A (en) * | 2023-11-07 | 2023-12-12 | 中北大学 | Method for quantitatively predicting precipitation rule of niobium-containing austenitic stainless steel niobate by phase field method |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111798930A (en) * | 2020-07-17 | 2020-10-20 | 西南石油大学 | CO considering influence of corrosion product film2Corrosion rate prediction method |
| CN111982799A (en) * | 2020-08-24 | 2020-11-24 | 中国人民解放军海军航空大学青岛校区 | Atmospheric corrosion prediction method for building block type airplane structural member |
| CN117219213A (en) * | 2023-11-07 | 2023-12-12 | 中北大学 | Method for quantitatively predicting precipitation rule of niobium-containing austenitic stainless steel niobate by phase field method |
| CN117219213B (en) * | 2023-11-07 | 2024-01-23 | 中北大学 | Method for quantitatively predicting precipitation rule of niobium-containing austenitic stainless steel niobate by phase field method |
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