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;

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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Frankel, G. S. , and Sridhar, N. , 2008, “ Understanding Localized Corrosion,” Mater. Today, 11(10), pp. 38–44. [CrossRef]
Lee, D. , Huang, Y. , and Achenbach, J. D. , 2015, “ A Comprehensive Analysis of the Growth Rate of Stress Corrosion Cracks,” Proc. R. Soc. London, Ser. A, 471(2178), p. 20140703. [CrossRef]
Hoeppner, D. W. , and Taylor, A. M. H. , 2011, “ AVT-140 Corrosion Fatigue and Environmentally Assisted Cracking in Aging Military Vehicles,” Modeling Pitting Corrosion Fatigue: Pit Growth and Pit/Crack Transition Issues, NATO, RTO, France, Chap. 13.
Gurtin, M. E. , and Ian, M. A. , 1975, “ A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57(4), pp. 291–323. [CrossRef]
Gurtin, M. E. , and Voorhees, P. W. , 1993, “ The Continuum Mechanics of Coherent Two-Phase Elastic Solids With Mass Transport,” Proc. R. Soc. London, Ser. A, 440(1909), pp. 323–343. [CrossRef]
Scully, J. C. , 1990, The Fundamentals of Corrosion, 3rd ed., Pergamon Press, New York.
Sharland, S. M. , Jackson, C. P. , and Diver, A. J. , 1989, “ A Finite-Element Model of the Propagation of Corrosion Crevices and Pits,” Corros. Sci., 29(9), pp. 1149–1166. [CrossRef]
Song, G.-L. , 2014, “ The Grand Challenges in Electrochemical Corrosion Research,” Front. Mater., 1, p. 00002. [CrossRef]
Alkire, R. , and Siitari, D. , 1979, “ The Location of Cathodic Reaction During Localized Corrosion,” J. Electrochem. Soc., 126(1), pp. 15–22. [CrossRef]
Laycock, N. J. , White, S. P. , Noh, J. S. , Wilson, P. T. , and Newman, R. C. , 1998, “ Perforated Covers for Propagating Pits,” J. Electrochem. Soc., 145(4), pp. 1101–1108. [CrossRef]
Scheiner, S. , and Hellmich, C. , 2007, “ Stable Pitting Corrosion of Stainless Steel as Diffusion-Controlled Dissolution Process With a Sharp Moving Electrode Boundary,” Corros. Sci., 49(2), pp. 319–346. [CrossRef]
Scheiner, S. , and Hellmich, C. , 2009, “ Finite Volume Model for Diffusion and Activation-Controlled Pitting Corrosion of Stainless Steel,” Comput. Methods Appl. Mech. Eng., 198(37–40), pp. 2898–2910. [CrossRef]
Duddu, R. , 2014, “ Numerical Modeling of Corrosion Pit Propagation Using the Combined Extended Finite Element and Level Set Method,” Comput. Mech., 54(3), pp. 613–627. [CrossRef]
Sharland, S. M. , and Tasker, P. W. , 1988, “ A Mathematical Model of Crevice and Pitting Corrosion—I. The Physical Model,” Corros. Sci., 28(6), pp. 603–620. [CrossRef]
Sharland, S. M. , 1988, “ A Mathematical Model of Crevice and Pitting Corrosion—II. The Mathematical Solution,” Corros. Sci., 28(6), pp. 621–630. [CrossRef]
Walton, J. C. , 1990, “ Mathematical Modeling of Mass Transport and Chemical Reaction in Crevice and Pitting Corrosion,” Corros. Sci., 30(8/9), pp. 915–928. [CrossRef]
Malki, B. , Souier, T. , and Baroux, B. , 2008, “ Influence of the Alloying Elements on Pitting Corrosion of Stainless Steels: A Modeling Approach,” J. Electrochem. Soc., 155(12), pp. C583–C587. [CrossRef]
Oltra, R. , Malki, B. , and Rechou, F. , 2010, “ Influence of Aeration on the Localized Trenching on Aluminum Alloys,” Electrochim. Acta, 55(15), pp. 4536–4532. [CrossRef]
Xiao, J. , and Chaudhuri, S. , 2011, “ Predictive Modeling of Localized Corrosion: An Application to Aluminum Alloys,” Electrochim. Acta, 56(24), pp. 5630–5641. [CrossRef]
Sarkar, S. , and Aquino, W. , 2011, “ Electroneutrality and Ionic Interactions in the Modeling of Mass Transport in Dilute Electrochemical Systems,” Electrochim. Acta, 56(16), pp. 8969–8978. [CrossRef]
Sarkar, S. , Warner, J. E. , and Aquino, W. , 2012, “ A Numerical Framework for the Modeling of Corrosive Dissolution,” Corros. Sci., 65, pp. 502–511. [CrossRef]
Sarkar, S. , and Aquino, W. , 2013, “ Changes in Electrodic Reaction Rates Due to Elastic Stress and Stress-Induced Surface Patterns,” Electrochim. Acta, 11(16), pp. 814–822. [CrossRef]
Sarkar, S. , Warner, J. E. , Aquino, W. , and Grigoriu, M. D. , 2014, “ Stochastic Reduced Order Models for Uncertainty Quantification of Intergranular Corrosion Rates,” Corros. Sci., 80, pp. 257–268. [CrossRef]
Laycock, N. J. , and White, S. P. , 2001, “ Computer Simulation of Single Pit Propagation in Stainless Steel Under Potentiostatic Control,” J. Electrochim. Soc., 148(7), pp. B264–B275. [CrossRef]
Vagbharathi, A. S. , and Gopalakrishnan, S. , 2014, “ An Extended Finite Element Model Coupled With Level Set Method for Analysis of Growth of Corrosion in Pits in Metallic Structures,” Proc. R. Soc. London, Ser. A, 470(2168), p. 20140001. [CrossRef]
Lee, D. , Huang, Y. , and Achenbach, J. D. , 2015, “ Probabilistic Analysis of Stress Corrosion Crack Growth and Related Structural Reliability Considerations,” ASME J. Appl. Mech., 83(2), p. 021003. [CrossRef]
Chen, Z. , and Bobaru, F. , 2015, “ Peridynamic Modeling of Pitting Corrosion Damage,” J. Mech. Phys. Solids, 78, pp. 352–381. [CrossRef]
Chen, Z. , Zhang, G. , and Bobaru, F. , 2016, “ The Influence of Passive Film Damage on Pitting Corrosion,” J. Electrochem. Soc., 163(2), pp. C19–C24. [CrossRef]
Stahle, P. , and Hansen, E. , 2015, “ Phase Field Modeling of Stress Corrosion,” Eng. Fail. Anal., 47(B), pp. 241–251. [CrossRef]
Bard, A. J. , and Faulkner, L. R. , 2001, Electrochemical Methods: Fundamentals and Applications, 2nd ed., Wiley, Hoboken, NJ.
Zienkiewicz, O. C. , Taylor, R. L. , and Zhu, J. Z. , 2013, The Finite Element Method: Its Basis and Fundamentals, 7th ed., Butterworth-Heinemann, Oxford, UK.
Duddu, R. , Kota, N. , and Qidwai, S. , 2015, “ An Extended Finite Element Model of Crevice and Pitting Corrosion,” ASME Paper No. IMECE2015-50423.
Belytschko, T. , and Black, T. , 1999, “ Elastic Crack Growth in Finite Elements With Minimal Remeshing,” Int. J. Numer. Methods Eng., 45(5), pp. 601–620. [CrossRef]
Moës, N. , Dolbow, J. , and Belytschko, T. , 1999, “ A Finite Element Method for Crack Growth Without Remeshing,” Int. J. Numer. Methods Eng., 6(1), pp. 131–150. [CrossRef]
Duddu, R. , Bordas, S. , Chopp, D. L. , and Moran, B. , 2008, “ A Combined Extended Finite Element and Level Set Method for Biofilm Growth,” Int. J. Numer. Methods Eng., 74(5), pp. 848–870. [CrossRef]
Duddu, R. , Chopp, D. L. , and Moran, B. , 2009, “ A Two-Dimensional Continuum Model of Biofilm Growth Incorporating Fluid Flow and Shear Stress Based Detachment,” Biotechnol. Bioeng., 103(1), pp. 92–104. [CrossRef] [PubMed]
Duddu, R. , Chopp, D. L. , Voorhees, P. W. , and Moran, B. , 2009, “ Diffusional Evolution of Precipitates in Elastic Media Using the Extended Finite Element and the Level Set Methods,” J. Comput. Phys., 230(4), pp. 1249–1264. [CrossRef]
Zhao, X. , Duddu, R. , Bordas, S. P. A. , and Qu, J. , 2013, “ Effects of Elastic Strain Energy and Interfacial Stress on the Equilibrium Morphology of Misfit Particles in Heterogeneous Solids,” J. Mech. Phys. Solids, 61(6), pp. 1433–1445. [CrossRef]
Sethian, J. A. , 1999, Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science, Cambridge University Press, Cambridge, UK.
Chopp, D. L. , 2001, “ Some Improvements of the Fast Marching Method,” SIAM J. Sci. Comput., 23(1), pp. 230–244. [CrossRef]
Vaughan, B. L. , Smith, B. G. , and Chopp, D. L. , 2006, “ A Comparison of the Extended Finite Element Method With the Immersed Interface Method for Elliptic Equations With Discontinuous Coefficients and Singular Sources,” Commun. Appl. Math. Comput. Sci., 1(1), pp. 207–228. [CrossRef]
Li, Y.-H. , and Gregory, S. , 1974, “ Diffusion of Ions in Seawater and in Deep-Sea Sediments,” Geochim. Cosmochim. Acta, 38(5), pp. 703–714. [CrossRef]
Kus, S. , and Mansfeld, F. , 2006, “ An Evaluation of the Electrochemical Frequency Modulation (EFM) Technique,” Corros. Sci., 48(4), pp. 965–979. [CrossRef]
Pourbaix, M. J. N. , 1963, Atlas d'equilibres electrochimiques, Gauthier-Villars, Paris.
Pourbaix, M. J. N. , and Franklin, J. A. , 1966, Atlas of Electrochemical Equilibria in Aqueous Solutions, Pergamon Press, Oxford, UK.
Lichtner, P. C. , 1984, “ Continuum Model for Simultaneous Chemical Reactions and Mass Transport in Hydrothermal Systems,” Geochim. Cosmochim. Acta, 49(3), pp. 779–800. [CrossRef]
Song, G. L. , and Atrens, A. , 1999, “ Corrosion Mechanisms of Magnesium Alloys,” Adv. Eng. Mater., 1(1), pp. 11–33. [CrossRef]


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. 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

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. 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.



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