A phase field model for simulating the pitting corrosion

Mai, Weijie; Soghrati, Soheil; Buchheit, R. G.

doi:10.1016/j.corsci.2016.04.001

Cited by 170 publications

(150 citation statements)

References 47 publications

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“…The corrosion rate is controlled by the kinetic interface parameter L. The shift in the corrosion mode from activation-controlled to diffusion-controlled can be modeled by continuous variation of the kinetic interface parameter L. The relationship between the kinetic interface parameter L and the corrosion rate is linear in the activation-controlled mode. 33 From the Butler-Volmer equation, as expressed in (2), the kinetic interface parameter has an effect on overpotential similar to that of the current density, as expressed below in (36). A similar technique is also implemented in a peridynamic model, in which the interface diffusivity is directly related to the current density for Tafel relation.…”

Section: Overpotentialmentioning

confidence: 99%

“…where φ m is the potential in the metal phase also known as applied potential; φ m,se is the standard electrode potential in the metal; and φ c is the concentration overpotential expressed in (33).…”

Section: Overpotentialmentioning

confidence: 99%

“…The PF simulations are performed at a lower metal potential of −400 mV SHE because it is believed that the crystallographic orientation dependence is limited to lower overpotentials when the corrosion process is activation controlled. 33,58 A small opening of 6 μm is considered at the surface of the material. The initial values and boundary conditions are the same as described in Fig.…”

Section: D Pf Modelmentioning

confidence: 99%

“…A few recent attempts have been made to use the PF method to model pitting corrosion and stress corrosion cracking without the consideration of cathodic reactions, ionic transport and in particular the dependence of overpotential on metal ion concentration in the electrolyte. 33,34 In reality, the transport of ionic species in the electrolyte often plays a very important role in diffusion controlled corrosion processes, and the effects of these ionic species must be incorporated to model the process adequately. In this study, a PF method is used to model pitting corrosion by considering both anodic and cathodic reactions, transport of ionic species and the dependence of overpotential on metal ion concentration in the electrolyte.…”

Section: Introductionmentioning

confidence: 99%

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Phase-field model of pitting corrosion kinetics in metallic materials

Ansari

Xiao

et al. 2018

npj Comput Mater

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Pitting corrosion is one of the most destructive forms of corrosion that can lead to catastrophic failure of structures. This study presents a thermodynamically consistent phase field model for the quantitative prediction of the pitting corrosion kinetics in metallic materials. An order parameter is introduced to represent the local physical state of the metal within a metal-electrolyte system. The free energy of the system is described in terms of its metal ion concentration and the order parameter. Both the ion transport in the electrolyte and the electrochemical reactions at the electrolyte/metal interface are explicitly taken into consideration. The temporal evolution of ion concentration profile and the order parameter field is driven by the reduction in the total free energy of the system and is obtained by numerically solving the governing equations. A calibration study is performed to couple the kinetic interface parameter with the corrosion current density to obtain a direct relationship between overpotential and the kinetic interface parameter. The phase field model is validated against the experimental results, and several examples are presented for applications of the phase-field model to understand the corrosion behavior of closely located pits, stressed material, ceramic particles-reinforced steel, and their crystallographic orientation dependence. INTRODUCTIONCorrosion is the gradual destruction of materials (usually metallic materials) via chemical and/or electrochemical reaction with their environment. It costs about 3.1% of the gross domestic product (GDP) in the United States, which is much more than the cost of all natural disasters combined. Localized corrosion, such as pitting corrosion, is one of the most destructive forms of corrosion; it leads to the catastrophic failure of structures and raises both human safety and financial concerns. 1-3 Pitting corrosion of stainless steel usually occurs in two different stages: (1) pit initiation from passive film breakage 4-6 and (2) pit growth. 2,3,[7][8][9][10][11][12] In this study, we focused on the development of a phase-field modeling capability to study pit growth by considering both anodic and cathodic reactions.In the past few decades, great efforts have been made to develop numerical models for pitting corrosion. The moving interface and the electrical double layer at the metal/electrolyte interface are the two challenging problems faced by most of these numerical models. These numerical models can be divided according to the method in which a moving interface is incorporated in their models. Several steady state 9,10,13-18 and transient state 19-28 models have been developed over the years that did not allow for changes in the shape and dimensions of the pits/crevices as corrosion proceeds.Recent advances in numerical techniques, such as the finite element method, the finite volume method, the arbitrary Lagrangian-Eulerian method, the mesh-free method, and the level set method have encouraged researchers to model the evolving morphology...

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Section: Overpotentialmentioning

confidence: 99%

Section: Overpotentialmentioning

confidence: 99%

Section: D Pf Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase-field model of pitting corrosion kinetics in metallic materials

Ansari

Xiao

et al. 2018

npj Comput Mater

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“…For the dissolution of metal in a one dimensional (1D) pit electrode, the concentration of metal ion outside of the pit is commonly assumed to be zero, [1][2][3][4][5][6][7][8] so that C M+ is simply the concentration of metal ion at the pit bottom (C M+ ). It is also usually supposed that L is equal to the pit depth (δ), [9][10][11][12] although the diffusion of metal ions may extend out of pit, forming additional layer of hemispherical diffusion and causing L to be longer than δ.…”

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confidence: 99%

Further Modeling of Chloride Concentration and Temperature Effects on 1D Pit Growth

Jun

Frankel

Sridhar³

2016

J. Electrochem. Soc.

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The product of diffusion coefficient and saturation concentration of metal ions (D M+ · C tot ) is associated with steady state dissolution of metal in corrosion pits. In our previous paper, D M+ · C tot was modeled for one dimensional (1D) pit dissolution of super 13Cr stainless steel (S13Cr) by taking into account the common ion effect, as well as viscosity and temperature influences. However, the modeled values were only half of the experimentally-measured D M+ · C tot , implying that D M+ and/or C tot were underestimated. To improve the modeling of D M+ · C tot , the effects of complexation and electromigration were additionally considered, which led to the definition of effective diffusion coefficient (D eff ) applicable for the diffusion of metal ionic species under the combined effect of viscosity, temperature and electric field inside a growing 1D pit. The newly modeled D eff · C tot values were very close to the experimental values, validating the modeling approach described in this paper. Dissolution of metal under steady state diffusion can be described by the modified Fick's first law, which relates the limiting current density (i lim ) with the product of diffusion coefficient (D M+ ) and concentration difference ( C M+ ) of the metal ion through the diffusion length (L):where F is the Faraday constant, and n is the charge of the metal ion.For the dissolution of metal in a one dimensional (1D) pit electrode, the concentration of metal ion outside of the pit is commonly assumed to be zero, 1-8 so that C M+ is simply the concentration of metal ion at the pit bottom (C M+ ). It is also usually supposed that L is equal to the pit depth (δ), 9-12 although the diffusion of metal ions may extend out of pit, forming additional layer of hemispherical diffusion and causing L to be longer than δ.11 The effect of this additional diffusion layer on i lim was found to diminish if δ of 1D pit with 1 mm diameter was greater than 0.4 mm (aspect ratio of pit depth/mouth: 0.4) for SS 304 11 and super martensitic stainless steel. 10 More recent study on 1D pit growth of SS 316L, however, has suggested that the length of additional diffusion layer (L') is approximately 40% of pit diameter, and δ should be much larger than L' to apply the L ≈ δ condition for the calculation of i lim . 13In a previous paper, the authors suggested that i lim in 1D pit electrode of super 13Cr stainless steel (S13Cr) can be related to the sum of D M+ · C M+ from each metal component, if the transport of all metal ions is under diffusion control.14 In this case, i lim can be expressed as:Here each C M+ is replaced by the concentration of metal ions at the pit bottom (C Fe2+/pb , C Cr3+/pb and C Ni2+/pb ). The content of Mo in S13Cr is small (2 wt% or 1.16 at%), so it was omitted for the calculation of i lim . For Eq. 2, three conditions were postulated: 1) The diffusion coefficients of all metal ions are the same (, 2) Fe 2+ is the major dissolved species, and the precipitating metal salt at the pit bottom is considered to be FeCl 2 at which ...

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