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Research Papers

An Extended Finite Element Method Based Approach for Modeling Crevice and Pitting Corrosion

[+] Author and Article Information
Ravindra Duddu

Department of Civil and Environmental Engineering,
Vanderbilt University,
400 24th Avenue South,
Nashville, TN 37212
e-mails: ravindra.duddu@vanderbilt.edu;
rduddu@gmail.com

Nithyanand Kota

Samsung Data Systems,
2665 North First Street,
San Jose, CA 95134
e-mail: nithyanandkota@gmail.com

Siddiq M. Qidwai

Fellow ASME
Multifunctional Materials Branch,
Code 6350,
U.S. Naval Research Laboratory,
4555 Overlook Avenue Southwest,
Washington, DC 20375
e-mail: siddiq.qidwai@nrl.navy.mil

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received December 15, 2015; final manuscript received April 7, 2016; published online May 20, 2016. Assoc. Editor: Harold S. Park.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States government purposes.

J. Appl. Mech 83(8), 081003 (May 20, 2016) (10 pages) Paper No: JAM-15-1676; doi: 10.1115/1.4033379 History: Received December 15, 2015; Revised April 07, 2016

A sharp-interface numerical approach is developed for modeling the electrochemical environment in crevices and pits due to galvanic corrosion in aqueous media. The concentration of chemical species and the electrical potential in the crevice or pit solution environment is established using the steady state Nernst–Planck equations along with the assumption of local electroneutrality (LEN). The metal-electrolyte interface fluxes are defined in terms of the cathodic and anodic current densities using Butler–Volmer kinetics. The extended finite element method (XFEM) is employed to discretize the nondimensionalized governing equations of the model and a level set function is used to describe the interface morphology independent of the underlying finite element mesh. Benchmark numerical studies simulating intergranular crevice corrosion in idealized aluminum–magnesium (Al–Mg) alloy microstructures in two dimensions are presented. Simulation results indicate that corrosive dissolution of magnesium is accompanied by an increase in the pH and chloride concentration of the crevice solution environment, which is qualitatively consistent with experimental observations. Even for low current densities the model predicted pH is high enough to cause passivation, which may not be physically accurate; however, this model limitation could be overcome by including the hydrolysis reactions that potentially decrease the pH of the crevice solution environment. Finally, a mesh convergence study is performed to establish the accuracy of the XFEM and a sensitivity study examining the relationship between crevice geometry and species concentrations is presented to demonstrate the robustness of the XFEM formulation in handling complex corrosion interface morphologies.

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Figures

Grahic Jump Location
Fig. 1

Schematic diagram of the intergranular crevice corrosion problem in the idealized aluminum (light gray)–magnesium (dark gray) alloy system. The union of the cathodic (blue) and anodic (red) surfaces defines the sharp interface between the solid domain and the liquid (aqueous) domain. Far-field concentration and zero potential conditions are assumed at the external (green) boundary (see online figure for color).

Grahic Jump Location
Fig. 2

Finite element mesh containing 103 × 103 square bilinear elements is used for corrosion simulation at all times. The interface for crevice length L≈0 (red) and for L={0.0025,0.005,0.0075,0.01,0.0125,0.015} mm (black) are implicitly defined by the zero contour of the level set function ϕ(x); thus, the proposed formulation entirely eliminates the need for remeshing or mesh moving procedures.

Grahic Jump Location
Fig. 3

Model predicted concentration and electrical potential for crevice length L≈0 for an assumed exchange current density io=10−7 A/m2. These results were validated with those obtained from comsol Version 5.2. Note that we only plot the contours of the field variables inside the liquid domain in all the figures. (a) Concentration of Mg2+, (b) Concentration ofCl−, (c) pH =14+log10[OH−], and (d) Electrical potential φ.

Grahic Jump Location
Fig. 4

Model predicted concentration and electrical potential for crevice length L≈0 for an assumed exchange current density io=10−5 A/m2. These results were validated with those obtained from comsol Version 5.2. Notice that the maximum pH value predicted by the model is around 13, which is unrealistically high. This discrepancy arises because we did not include the reactions corresponding to magnesium hydrolysis and self-ionization of water. (a) Concentration of Mg2+, (b) Concentration ofCl−, (c) pH =14+log10[OH−], and (d) Electrical potential φ.

Grahic Jump Location
Fig. 5

Mesh convergence study for the predicted Mg2+ concentration field for crevice length L≈0 with assumed exchange current densities io=10−5 and io=10−7 A/m2. All the errors are calculated with respect to the field result obtained from comsol Version 5.2 using a 210 × 105 element mesh for the 0.042 mm ×0.021 mm rectangular domain. Similar trends in convergence were also observed for the other field variables (not provided in this paper).

Grahic Jump Location
Fig. 6

Model predicted concentration and electrical potential for crevice length L=0.01 mm for an assumed exchange current density io=10−7 A/m2. (a) Concentration of Mg2+, (b) Concentration ofCl−, (c) pH =14+log10[OH−], and (d) Electrical potential φ.

Grahic Jump Location
Fig. 7

Sensitivity study examining the relationship between crevice length L and the predicted maximum/minimum ion concentration and electrical potential measured at the tip of the crevice for an assumed exchange current density io=10−7 A/m2

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