Phase-field model of pitting corrosion kinetics in metallic materials

doi:10.1038/s41524-018-0089-4

Title: Phase-field model of pitting corrosion kinetics in metallic materials

Abstract

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 metal’s physical state at each point in the entire domain. The free energy of the metal-electrolyte system is defined in terms of its metal ion concentration and the order parameter. The mass transport in the electrolyte and the electrochemical reactions in the electrolyte/metal interface are taken into consideration in the model to simulate metal corrosion in a corrosive environment. The governing equations for mass transport and the order parameter are solved in such a manner that the system’s free energy is reduced as a result of diffusion and migration processes, and the distribution of electrostatic potential is governed by Poisson’s equation. A calibration study is performed to couple the kinetic interface parameter with the corrosion current density, which results in a direct relationship between overpotential and the kinetic interface parameter. A comparative study is performed to validate the phase field model against the experimental results. Several case studies are also examined to understand the corrosion behavior of closely located pits, stressed material, ceramic particles-reinforced steel, and crystallographic orientation dependence.

Authors:

Ansari, Talha Qasim ^[1]; Xiao, Zhihua ^[1];

^[2]; Li, Yulan ^[2]; Luo, Jing-Li ^[3]; Shi, San-Qiang ^[1]

Hong Kong Polytechnic Univ., Hung Hom, Kowloon (Hong Kong)
Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
Univ. of Alberta, Edmonton, AB (Canada)

Publication Date:: 2018-07-24

Research Org.:: Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1558620

Report Number(s):: PNNL-SA-130881
Journal ID: ISSN 2057-3960; TRN: US2000232

Grant/Contract Number:: AC05-76RL01830

Resource Type:: Accepted Manuscript

Journal Name:: npj Computational Materials

Additional Journal Information:: Journal Volume: 4; Journal Issue: 1; Journal ID: ISSN 2057-3960

Publisher:: Nature Publishing Group

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE; Pitting corrosion; stainless steel

Citation Formats


                    Ansari, Talha Qasim, Xiao, Zhihua, Hu, Shenyang, Li, Yulan, Luo, Jing-Li, and Shi, San-Qiang. Phase-field model of pitting corrosion kinetics in metallic materials.  United States: N. p., 2018. 
        Web.  doi:10.1038/s41524-018-0089-4.

Copy to clipboard


                    Ansari, Talha Qasim, Xiao, Zhihua, Hu, Shenyang, Li, Yulan, Luo, Jing-Li, & Shi, San-Qiang. Phase-field model of pitting corrosion kinetics in metallic materials.  United States.  doi:https://doi.org/10.1038/s41524-018-0089-4

Copy to clipboard


                    Ansari, Talha Qasim, Xiao, Zhihua, Hu, Shenyang, Li, Yulan, Luo, Jing-Li, and Shi, San-Qiang. Tue .  
        "Phase-field model of pitting corrosion kinetics in metallic materials".  United States.  doi:https://doi.org/10.1038/s41524-018-0089-4.  https://www.osti.gov/servlets/purl/1558620.

Copy to clipboard


                    
@article{osti_1558620,

  title        = {Phase-field model of pitting corrosion kinetics in metallic materials},

  author       = {Ansari, Talha Qasim and Xiao, Zhihua and Hu, Shenyang and Li, Yulan and Luo, Jing-Li and Shi, San-Qiang},

  abstractNote = {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 metal’s physical state at each point in the entire domain. The free energy of the metal-electrolyte system is defined in terms of its metal ion concentration and the order parameter. The mass transport in the electrolyte and the electrochemical reactions in the electrolyte/metal interface are taken into consideration in the model to simulate metal corrosion in a corrosive environment. The governing equations for mass transport and the order parameter are solved in such a manner that the system’s free energy is reduced as a result of diffusion and migration processes, and the distribution of electrostatic potential is governed by Poisson’s equation. A calibration study is performed to couple the kinetic interface parameter with the corrosion current density, which results in a direct relationship between overpotential and the kinetic interface parameter. A comparative study is performed to validate the phase field model against the experimental results. Several case studies are also examined to understand the corrosion behavior of closely located pits, stressed material, ceramic particles-reinforced steel, and crystallographic orientation dependence.},

  doi          = {10.1038/s41524-018-0089-4},

  journal      = {npj Computational Materials},

  number       = 1,

  volume       = 4,

  place        = {United States},

  year         = {2018},

  month        = {7}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

DOI: https://doi.org/10.1038/s41524-018-0089-4

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 8 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method
journal, April 2014

Duddu, Ravindra
Computational Mechanics, Vol. 54, Issue 3
DOI: 10.1007/s00466-014-1010-8

Numerical modelling of the electrochemical behaviour of 316L stainless steel based upon static and dynamic experimental microcapillary-based techniques
journal, June 2008

Krawiec, H.; Vignal, V.; Akid, R.
Electrochimica Acta, Vol. 53, Issue 16
DOI: 10.1016/j.electacta.2008.02.063

Pit Initiation at Single Sulfide Inclusions in Stainless Steel
journal, January 2002

Webb, Eric G.; Alkire, Richard C.
Journal of The Electrochemical Society, Vol. 149, Issue 6
DOI: 10.1149/1.1474432

Thermodynamic description and growth kinetics of stoichiometric precipitates in the phase-field approach
journal, June 2007

Hu, S. Y.; Murray, J.; Weiland, H.
Calphad, Vol. 31, Issue 2
DOI: 10.1016/j.calphad.2006.08.005

Detection of Interactions among Localized Pitting Sites on Stainless Steel Using Spatial Statistics
journal, January 2005

Budiansky, N. D.; Organ, L.; Hudson, J. L.
Journal of The Electrochemical Society, Vol. 152, Issue 4
DOI: 10.1149/1.1869192

Pit growth studies in stainless steel foils. I. Introduction and pit growth kinetics
journal, May 2002

Ernst, P.; Newman, R. C.
Corrosion Science, Vol. 44, Issue 5
DOI: 10.1016/S0010-938X(01)00133-0

Phase-Field Models for Microstructure Evolution
journal, August 2002

Chen, Long-Qing
Annual Review of Materials Research, Vol. 32, Issue 1
DOI: 10.1146/annurev.matsci.32.112001.132041

Impact of the laminar flow on the electrical double layer development
journal, August 2017

Leblanc, P.; Cabaleiro, J. M.; Paillat, T.
Journal of Electrostatics, Vol. 88
DOI: 10.1016/j.elstat.2016.11.006

Ceramic reinforced high modulus steel composites: processing, microstructure and properties
journal, March 2014

Akhtar, F.
Canadian Metallurgical Quarterly, Vol. 53, Issue 3
DOI: 10.1179/1879139514Y.0000000135

Phase field modeling of electrochemistry. II. Kinetics
journal, February 2004

Guyer, J. E.; Boettinger, W. J.; Warren, J. A.
Physical Review E, Vol. 69, Issue 2
DOI: 10.1103/PhysRevE.69.021604

Corrosion under a porous layer: A porous electrode model and its implications for self-repair
journal, October 2011

Venkatraman, Murali Sankar; Cole, Ivan S.; Emmanuel, Bosco
Electrochimica Acta, Vol. 56, Issue 24
DOI: 10.1016/j.electacta.2011.06.020

Peridynamic modeling of pitting corrosion damage
journal, May 2015

Chen, Ziguang; Bobaru, Florin
Journal of the Mechanics and Physics of Solids, Vol. 78
DOI: 10.1016/j.jmps.2015.02.015

A mathematical model of the initiation of crevice corrosion in metals
journal, February 1992

Sharland, S. M.
Corrosion Science, Vol. 33, Issue 2
DOI: 10.1016/0010-938X(92)90144-R

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions
journal, July 1992

Friedly, John C.; Rubin, Jacob
Water Resources Research, Vol. 28, Issue 7
DOI: 10.1029/92WR00699

Transport Processes and the Mechanism of Pitting of Metals
journal, January 1976

Galvele, Jose R.
Journal of The Electrochemical Society, Vol. 123, Issue 4
DOI: 10.1149/1.2132857

Predictive modeling of localized corrosion: An application to aluminum alloys
journal, June 2011

Xiao, J.; Chaudhuri, S.
Electrochimica Acta, Vol. 56, Issue 16
DOI: 10.1016/j.electacta.2011.04.019

Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary
journal, February 2007

Scheiner, S.; Hellmich, C.
Corrosion Science, Vol. 49, Issue 2
DOI: 10.1016/j.corsci.2006.03.019

A phase field model for simulating the stress corrosion cracking initiated from pits
journal, August 2017

Mai, Weijie; Soghrati, Soheil
Corrosion Science, Vol. 125
DOI: 10.1016/j.corsci.2017.06.006

An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part I: Smooth specimen
journal, August 2008

Guo, X. H.; Shi, S. Q.; Zhang, Q. M.
Journal of Nuclear Materials, Vol. 378, Issue 1
DOI: 10.1016/j.jnucmat.2008.05.008

Unification of the deterministic and statistical approaches for predicting localized corrosion damage. I. Theoretical foundation
journal, November 2004

Engelhardt, George; Macdonald, Digby D.
Corrosion Science, Vol. 46, Issue 11
DOI: 10.1016/j.corsci.2004.03.014

A mathematical model of crevice and pitting corrosion—II. The mathematical solution
journal, January 1988

Sharland, S. M.
Corrosion Science, Vol. 28, Issue 6
DOI: 10.1016/0010-938X(88)90028-5

An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part II: Specimen with flaws
journal, August 2008

Guo, X. H.; Shi, S. Q.; Zhang, Q. M.
Journal of Nuclear Materials, Vol. 378, Issue 1
DOI: 10.1016/j.jnucmat.2008.05.006

Pitting Corrosion of Metals
journal, January 1998

Frankel, G. S.
Journal of The Electrochemical Society, Vol. 145, Issue 6
DOI: 10.1149/1.1838615

Phase-Field Modeling of Transport-Limited Electrolysis in Solid and Liquid States
journal, January 2007

Pongsaksawad, Wanida; Powell, Adam C.; Dussault, David
Journal of The Electrochemical Society, Vol. 154, Issue 6
DOI: 10.1149/1.2721763

Numerical simulation of crevice corrosion: The effect of the crevice gap profile
journal, January 1991

Watson, M. K.; Postlethwaite, J.
Corrosion Science, Vol. 32, Issue 11
DOI: 10.1016/0010-938X(91)90136-D

Finite Volume model for diffusion- and activation-controlled pitting corrosion of stainless steel
journal, August 2009

Scheiner, Stefan; Hellmich, Christian
Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 37-40
DOI: 10.1016/j.cma.2009.04.012

In situ AFM detection of pit onset location on a 304L stainless steel
journal, January 2008

Martin, F. A.; Bataillon, C.; Cousty, J.
Corrosion Science, Vol. 50, Issue 1
DOI: 10.1016/j.corsci.2007.06.023

Effect of texture on corrosion behavior of AISI 304L stainless steel
journal, February 2005

Ravi Kumar, B.; Singh, Raghuvir; Mahato, Bhupeshwar
Materials Characterization, Vol. 54, Issue 2
DOI: 10.1016/j.matchar.2004.11.004

A numerical framework for the modeling of corrosive dissolution
journal, December 2012

Sarkar, Swarnavo; Warner, James E.; Aquino, Wilkins
Corrosion Science, Vol. 65
DOI: 10.1016/j.corsci.2012.08.059

Phase-field model for isothermal phase transitions in binary alloys
journal, May 1992

Wheeler, A. A.; Boettinger, W. J.; McFadden, G. B.
Physical Review A, Vol. 45, Issue 10
DOI: 10.1103/PhysRevA.45.7424

Free Energy of a Nonuniform System. I. Interfacial Free Energy
journal, February 1958

Cahn, John W.; Hilliard, John E.
The Journal of Chemical Physics, Vol. 28, Issue 2
DOI: 10.1063/1.1744102

Studies of the initiation of pitting corrosion on stainless steels
journal, December 1984

Williams, D. E.; Westcott, C.; Fleischmann, M.
Journal of Electroanalytical Chemistry and Interfacial Electrochemistry, Vol. 180, Issue 1-2
DOI: 10.1016/0368-1874(84)83606-0

On the theory of superconductivity
journal, December 1955

Ginzburg, V. L.
Il Nuovo Cimento, Vol. 2, Issue 6
DOI: 10.1007/BF02731579

Crevice Corrosion of Stainless Steels: I. A Mathematical Model
journal, January 1978

Oldfield, J. W.; Sutton, W. H.
British Corrosion Journal, Vol. 13, Issue 1
DOI: 10.1179/000705978798358671

Transport processes in passivity breakdown—II. Full hydrolysis of the metal ions
journal, January 1981

Galvele, JoséR.
Corrosion Science, Vol. 21, Issue 8
DOI: 10.1016/0010-938X(81)90009-3

A phase field model for simulating the pitting corrosion
journal, September 2016

Mai, Weijie; Soghrati, Soheil; Buchheit, Rudolph G.
Corrosion Science, Vol. 110
DOI: 10.1016/j.corsci.2016.04.001

Modeling localized aluminum alloy corrosion in chloride solutions under non-equilibrium conditions: Steps toward understanding pitting initiation
journal, February 2012

Abodi, L. C.; DeRose, J. A.; Van Damme, S.
Electrochimica Acta, Vol. 63
DOI: 10.1016/j.electacta.2011.12.074

Mathematical modelling of the electrochemistry in corrosion fatigue cracks in structural steel cathodically protected in sea water
journal, January 1986

Turnbull, A.; Ferriss, D. H.
Corrosion Science, Vol. 26, Issue 8
DOI: 10.1016/0010-938X(86)90027-2

Computer Simulation of Pitting Corrosion of Stainless Steels
journal, January 2014

Laycock, N. J.; Krouse, D. P.; Hendy, S. C.
Interface magazine, Vol. 23, Issue 4
DOI: 10.1149/2.F05144IF

Microstructure evolution and wear properties of in situ synthesized TiB2 and TiC reinforced steel matrix composites
journal, July 2008

Akhtar, Farid
Journal of Alloys and Compounds, Vol. 459, Issue 1-2
DOI: 10.1016/j.jallcom.2007.05.018

Numerical Simulation of Pitting Corrosion: Interactions Between Pits in Potentiostatic Conditions
conference, January 2006

Laycock, Nick; White, Stephen; Krouse, Donal
208th ECS Meeting, ECS Transactions
DOI: 10.1149/1.2214623

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials
journal, April 2017

Li, Yulan; Hu, Shenyang; Sun, Xin
npj Computational Materials, Vol. 3, Issue 1
DOI: 10.1038/s41524-017-0018-y

A Model of Crack Electrochemistry for Steels in the Active State Based on Mass Transport by Diffusion and Ion Migration
journal, January 1982

Turnbull, A.
Journal of The Electrochemical Society, Vol. 129, Issue 7
DOI: 10.1149/1.2124176

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method
journal, October 2012

Onishi, Yuki; Takiyasu, Jumpei; Amaya, Kenji
Corrosion Science, Vol. 63
DOI: 10.1016/j.corsci.2012.06.001

A review of the theoretical modelling of crevice and pitting corrosion
journal, January 1987

Sharland, S. M.
Corrosion Science, Vol. 27, Issue 3
DOI: 10.1016/0010-938X(87)90024-2

Processing and properties of particulate reinforced steel matrix composites
journal, May 1998

Pagounis, E.; Lindroos, V. K.
Materials Science and Engineering: A, Vol. 246, Issue 1-2
DOI: 10.1016/S0921-5093(97)00710-7

A mathematical model of crevice and pitting corrosion—I. The physical model
journal, January 1988

Sharland, S. M.; Tasker, P. W.
Corrosion Science, Vol. 28, Issue 6
DOI: 10.1016/0010-938X(88)90027-3

Mathematical modeling of mass transport and chemical reaction in crevice and pitting corrosion
journal, January 1990

Walton, John C.
Corrosion Science, Vol. 30, Issue 8-9
DOI: 10.1016/0010-938X(90)90013-U

Computer simulation of pitting potential measurements
journal, December 2005

Laycock, N. J.; Noh, J. S.; White, S. P.
Corrosion Science, Vol. 47, Issue 12
DOI: 10.1016/j.corsci.2005.07.003

Calculating chemical concentrations during the initiation of crevice corrosion
journal, April 2000

White, Stephen P.; Weir, Graham J.; Laycock, N. J.
Corrosion Science, Vol. 42, Issue 4
DOI: 10.1016/S0010-938X(99)00097-9

Dissolved Metal Species Mechanism for Initiation of Crevice Corrosion of Aluminum
journal, January 1983

Hebert, Kurt
Journal of The Electrochemical Society, Vol. 130, Issue 5
DOI: 10.1149/1.2119874

Crystallographic effects in corrosion of austenitic stainless steel 316L: Crystallographic effects in corrosion
journal, November 2014

Lindell, D.; Pettersson, R.
Materials and Corrosion, Vol. 66, Issue 8
DOI: 10.1002/maco.201408002

Phase-field model for binary alloys
journal, December 1999

Kim, Seong Gyoon; Kim, Won Tae; Suzuki, Toshio
Physical Review E, Vol. 60, Issue 6
DOI: 10.1103/PhysRevE.60.7186

Elastoplastic phase field model for microstructure evolution
journal, November 2005

Guo, X. H.; Shi, San-Qiang; Ma, X. Q.
Applied Physics Letters, Vol. 87, Issue 22
DOI: 10.1063/1.2138358

The influence of crystallographic orientation distribution on 316LVM stainless steel pitting behavior
journal, March 2009

Shahryari, Arash; Szpunar, Jerzy A.; Omanovic, Sasha
Corrosion Science, Vol. 51, Issue 3
DOI: 10.1016/j.corsci.2008.12.019

Crevice Corrosion of Stainless Steels: II. Experimental studies
journal, January 1978

Oldfield, J. W.; Sutton, W. H.
British Corrosion Journal, Vol. 13, Issue 3
DOI: 10.1179/000705978798276258

An introduction to phase-field modeling of microstructure evolution
journal, June 2008

Moelans, Nele; Blanpain, Bart; Wollants, Patrick
Calphad, Vol. 32, Issue 2
DOI: 10.1016/j.calphad.2007.11.003

Finite element calculation of crack propagation in type 304 stainless steel in diluted sulphuric acid solutions
journal, March 2007

Gavrilov, S.; Vankeerberghen, M.; Nelissen, G.
Corrosion Science, Vol. 49, Issue 3
DOI: 10.1016/j.corsci.2006.06.025

Works referencing / citing this record:

Modeling the effect of insoluble corrosion products on pitting corrosion kinetics of metals
journal, July 2019

Ansari, Talha Qasim; Luo, Jing-Li; Shi, San-Qiang
npj Materials Degradation, Vol. 3, Issue 1
DOI: 10.1038/s41529-019-0090-5

Computational modeling of pitting corrosion
journal, September 2019

Jafarzadeh, Siavash; Chen, Ziguang; Bobaru, Florin
Corrosion Reviews, Vol. 37, Issue 5
DOI: 10.1515/corrrev-2019-0049

Pitting Corrosion of Natural Aged Al–Mg–Si Extrusion Profile
journal, April 2019

Guan, Quanmei; Sun, Jing; Wang, William
Materials, Vol. 12, Issue 7
DOI: 10.3390/ma12071081

Similar Records in DOE PAGES and OSTI.GOV collections:

Noninvasive surface measurement of corrosion impedance of reinforcing bar in concrete - part 1: experimental results

Journal Article Zhang, Jieying ; Monteiro, Paulo J.M. ; Morrison, H Frank - ACI Materials Journal

The corrosion state of a reinforcing steel bar in concrete can be characterized by the electrical impedance of the interface between the steel bar and the concrete. The experimental part of this study, has shown that changes in the interfacial impedance that are diagnostic of the rate and extent of the corrosion can be measured indirectly with an array of current and voltage electrodes on the concrete surface. The measured impedance, however depends on the electrical resistivity of the concrete, and the depth and diameter of the steel reinforcing bar as well as the interfacial properties. To relate the measuredmore »« less
Noninvasive surface measurement of corrosion impedance of reinforcing bar in concrete - part 2: forward modeling

Journal Article Zhang, Jieying ; Monteiro, Paulo J. M. ; Morrison, H Frank - ACI Materials Journal

The corrosion state of a reinforcing steel bar in concrete can be characterized by the electrical impedance of the interface between the steel bar and the concrete. The experimental part of this study, has shown that changes in the interfacial impedance that are diagnostic of the rate and extent of the corrosion can be measured indirectly with an array of current and voltage electrodes on the concrete surface. The measured impedance, however depends on the electrical resistivity of the concrete, and the depth and diameter of the steel reinforcing bar as well as the interfacial properties. To relate the measuredmore »« less
Prediction of Corrosion of Alloys in Mixed-Solvent Environments

Technical Report Anderko, Andrzej ; Wang, Peiming ; Young, Robert D. ; ...

Corrosion is much less predictable in organic or mixed-solvent environments than in aqueous process environments. As a result, US chemical companies face greater uncertainty when selecting process equipment materials to manufacture chemical products using organic or mixed solvents than when the process environments are only aqueous. Chemical companies handle this uncertainty by overdesigning the equipment (wasting money and energy), rather than by accepting increased risks of corrosion failure (personnel hazards and environmental releases). Therefore, it is important to develop simulation tools that would help the chemical process industries to understand and predict corrosion and to develop mitigation measures. To createmore »« less
DOI: https://doi.org/10.2172/811533

Full Text Available
A quantitative phase-field model for crevice corrosion

Journal Article Xiao, Z. H. ; Hu, S. Y. ; Luo, J. L. ; ... - Computational Materials Science

A quantitative phase-field model is developed for the investigation of crevice corrosion of iron in salt water. Six types of ionic species and some associated chemical reactions have been considered. In addition to the transient distributions of ion concentrations and electric potential in the electrolyte, some physical and chemical properties related to corrosion, such as overpotential, pH value and corrosion rate, under different metal potentials are studied. Benchmarking of the phase-field model against a sharp interface model is conducted. The corrosion rates predicted by the models are in the same order of magnitudes with experimental results.
DOI: https://doi.org/10.1016/j.commatsci.2018.03.011
Low Temperature Reduction of Alumina Using Fluorine Containing Ionic Liquids

Technical Report Reddy, R G

The major objective of the project is to establish the feasibility of using specific ionic liquids capable of sustaining aluminum electrolysis near room temperature at laboratory and batch recirculation scales. It will explore new technologies for aluminum and other valuable metal extraction and process methods. The new technology will overcome many of the limitations associated with high temperatures processes such as high energy consumption and corrosion attack. Furthermore, ionic liquids are non-toxic and could be recycled after purification, thus minimizing extraction reagent losses and environmental pollutant emissions. Ionic liquids are mixture of inorganic and organic salts which are liquid atmore »« less
DOI: https://doi.org/10.2172/926179

Full Text Available

Similar Records

Title: Phase-field model of pitting corrosion kinetics in metallic materials

Abstract

Citation Formats

Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method journal, April 2014

Numerical modelling of the electrochemical behaviour of 316L stainless steel based upon static and dynamic experimental microcapillary-based techniques journal, June 2008

Pit Initiation at Single Sulfide Inclusions in Stainless Steel journal, January 2002

Thermodynamic description and growth kinetics of stoichiometric precipitates in the phase-field approach journal, June 2007

Detection of Interactions among Localized Pitting Sites on Stainless Steel Using Spatial Statistics journal, January 2005

Pit growth studies in stainless steel foils. I. Introduction and pit growth kinetics journal, May 2002

Phase-Field Models for Microstructure Evolution journal, August 2002

Impact of the laminar flow on the electrical double layer development journal, August 2017

Ceramic reinforced high modulus steel composites: processing, microstructure and properties journal, March 2014

Phase field modeling of electrochemistry. II. Kinetics journal, February 2004

Corrosion under a porous layer: A porous electrode model and its implications for self-repair journal, October 2011

Peridynamic modeling of pitting corrosion damage journal, May 2015

A mathematical model of the initiation of crevice corrosion in metals journal, February 1992

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions journal, July 1992

Transport Processes and the Mechanism of Pitting of Metals journal, January 1976

Predictive modeling of localized corrosion: An application to aluminum alloys journal, June 2011

Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary journal, February 2007

A phase field model for simulating the stress corrosion cracking initiated from pits journal, August 2017

An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part I: Smooth specimen journal, August 2008

Unification of the deterministic and statistical approaches for predicting localized corrosion damage. I. Theoretical foundation journal, November 2004

A mathematical model of crevice and pitting corrosion—II. The mathematical solution journal, January 1988

An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part II: Specimen with flaws journal, August 2008

Pitting Corrosion of Metals journal, January 1998

Phase-Field Modeling of Transport-Limited Electrolysis in Solid and Liquid States journal, January 2007

Numerical simulation of crevice corrosion: The effect of the crevice gap profile journal, January 1991

Finite Volume model for diffusion- and activation-controlled pitting corrosion of stainless steel journal, August 2009

In situ AFM detection of pit onset location on a 304L stainless steel journal, January 2008

Effect of texture on corrosion behavior of AISI 304L stainless steel journal, February 2005

A numerical framework for the modeling of corrosive dissolution journal, December 2012

Phase-field model for isothermal phase transitions in binary alloys journal, May 1992

Free Energy of a Nonuniform System. I. Interfacial Free Energy journal, February 1958

Studies of the initiation of pitting corrosion on stainless steels journal, December 1984

On the theory of superconductivity journal, December 1955

Crevice Corrosion of Stainless Steels: I. A Mathematical Model journal, January 1978

Transport processes in passivity breakdown—II. Full hydrolysis of the metal ions journal, January 1981

A phase field model for simulating the pitting corrosion journal, September 2016

Modeling localized aluminum alloy corrosion in chloride solutions under non-equilibrium conditions: Steps toward understanding pitting initiation journal, February 2012

Mathematical modelling of the electrochemistry in corrosion fatigue cracks in structural steel cathodically protected in sea water journal, January 1986

Computer Simulation of Pitting Corrosion of Stainless Steels journal, January 2014

Microstructure evolution and wear properties of in situ synthesized TiB2 and TiC reinforced steel matrix composites journal, July 2008

Numerical Simulation of Pitting Corrosion: Interactions Between Pits in Potentiostatic Conditions conference, January 2006

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials journal, April 2017

A Model of Crack Electrochemistry for Steels in the Active State Based on Mass Transport by Diffusion and Ion Migration journal, January 1982

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method journal, October 2012

A review of the theoretical modelling of crevice and pitting corrosion journal, January 1987

Processing and properties of particulate reinforced steel matrix composites journal, May 1998

A mathematical model of crevice and pitting corrosion—I. The physical model journal, January 1988

Mathematical modeling of mass transport and chemical reaction in crevice and pitting corrosion journal, January 1990

Computer simulation of pitting potential measurements journal, December 2005

Calculating chemical concentrations during the initiation of crevice corrosion journal, April 2000

Dissolved Metal Species Mechanism for Initiation of Crevice Corrosion of Aluminum journal, January 1983

Crystallographic effects in corrosion of austenitic stainless steel 316L: Crystallographic effects in corrosion journal, November 2014

Phase-field model for binary alloys journal, December 1999

Elastoplastic phase field model for microstructure evolution journal, November 2005

The influence of crystallographic orientation distribution on 316LVM stainless steel pitting behavior journal, March 2009

Crevice Corrosion of Stainless Steels: II. Experimental studies journal, January 1978

An introduction to phase-field modeling of microstructure evolution journal, June 2008

Finite element calculation of crack propagation in type 304 stainless steel in diluted sulphuric acid solutions journal, March 2007

Modeling the effect of insoluble corrosion products on pitting corrosion kinetics of metals journal, July 2019

Computational modeling of pitting corrosion journal, September 2019

Pitting Corrosion of Natural Aged Al–Mg–Si Extrusion Profile journal, April 2019

Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method
journal, April 2014

Numerical modelling of the electrochemical behaviour of 316L stainless steel based upon static and dynamic experimental microcapillary-based techniques
journal, June 2008

Pit Initiation at Single Sulfide Inclusions in Stainless Steel
journal, January 2002

Thermodynamic description and growth kinetics of stoichiometric precipitates in the phase-field approach
journal, June 2007

Detection of Interactions among Localized Pitting Sites on Stainless Steel Using Spatial Statistics
journal, January 2005

Pit growth studies in stainless steel foils. I. Introduction and pit growth kinetics
journal, May 2002

Phase-Field Models for Microstructure Evolution
journal, August 2002

Impact of the laminar flow on the electrical double layer development
journal, August 2017

Ceramic reinforced high modulus steel composites: processing, microstructure and properties
journal, March 2014

Phase field modeling of electrochemistry. II. Kinetics
journal, February 2004

Corrosion under a porous layer: A porous electrode model and its implications for self-repair
journal, October 2011

Peridynamic modeling of pitting corrosion damage
journal, May 2015

A mathematical model of the initiation of crevice corrosion in metals
journal, February 1992

Solute transport with multiple equilibrium-controlled or kinetically controlled chemical reactions
journal, July 1992

Transport Processes and the Mechanism of Pitting of Metals
journal, January 1976

Predictive modeling of localized corrosion: An application to aluminum alloys
journal, June 2011

Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary
journal, February 2007

A phase field model for simulating the stress corrosion cracking initiated from pits
journal, August 2017

An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part I: Smooth specimen
journal, August 2008

Unification of the deterministic and statistical approaches for predicting localized corrosion damage. I. Theoretical foundation
journal, November 2004

A mathematical model of crevice and pitting corrosion—II. The mathematical solution
journal, January 1988

An elastoplastic phase-field model for the evolution of hydride precipitation in zirconium. Part II: Specimen with flaws
journal, August 2008

Pitting Corrosion of Metals
journal, January 1998

Phase-Field Modeling of Transport-Limited Electrolysis in Solid and Liquid States
journal, January 2007

Numerical simulation of crevice corrosion: The effect of the crevice gap profile
journal, January 1991

Finite Volume model for diffusion- and activation-controlled pitting corrosion of stainless steel
journal, August 2009

In situ AFM detection of pit onset location on a 304L stainless steel
journal, January 2008

Effect of texture on corrosion behavior of AISI 304L stainless steel
journal, February 2005

A numerical framework for the modeling of corrosive dissolution
journal, December 2012

Phase-field model for isothermal phase transitions in binary alloys
journal, May 1992

Free Energy of a Nonuniform System. I. Interfacial Free Energy
journal, February 1958

Studies of the initiation of pitting corrosion on stainless steels
journal, December 1984

On the theory of superconductivity
journal, December 1955

Crevice Corrosion of Stainless Steels: I. A Mathematical Model
journal, January 1978

Transport processes in passivity breakdown—II. Full hydrolysis of the metal ions
journal, January 1981

A phase field model for simulating the pitting corrosion
journal, September 2016

Modeling localized aluminum alloy corrosion in chloride solutions under non-equilibrium conditions: Steps toward understanding pitting initiation
journal, February 2012

Mathematical modelling of the electrochemistry in corrosion fatigue cracks in structural steel cathodically protected in sea water
journal, January 1986

Computer Simulation of Pitting Corrosion of Stainless Steels
journal, January 2014

Microstructure evolution and wear properties of in situ synthesized TiB2 and TiC reinforced steel matrix composites
journal, July 2008

Numerical Simulation of Pitting Corrosion: Interactions Between Pits in Potentiostatic Conditions
conference, January 2006

A review: applications of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials
journal, April 2017

A Model of Crack Electrochemistry for Steels in the Active State Based on Mass Transport by Diffusion and Ion Migration
journal, January 1982

Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method
journal, October 2012

A review of the theoretical modelling of crevice and pitting corrosion
journal, January 1987

Processing and properties of particulate reinforced steel matrix composites
journal, May 1998

A mathematical model of crevice and pitting corrosion—I. The physical model
journal, January 1988

Mathematical modeling of mass transport and chemical reaction in crevice and pitting corrosion
journal, January 1990

Computer simulation of pitting potential measurements
journal, December 2005

Calculating chemical concentrations during the initiation of crevice corrosion
journal, April 2000

Dissolved Metal Species Mechanism for Initiation of Crevice Corrosion of Aluminum
journal, January 1983

Crystallographic effects in corrosion of austenitic stainless steel 316L: Crystallographic effects in corrosion
journal, November 2014

Phase-field model for binary alloys
journal, December 1999

Elastoplastic phase field model for microstructure evolution
journal, November 2005

The influence of crystallographic orientation distribution on 316LVM stainless steel pitting behavior
journal, March 2009

Crevice Corrosion of Stainless Steels: II. Experimental studies
journal, January 1978

An introduction to phase-field modeling of microstructure evolution
journal, June 2008

Finite element calculation of crack propagation in type 304 stainless steel in diluted sulphuric acid solutions
journal, March 2007

Modeling the effect of insoluble corrosion products on pitting corrosion kinetics of metals
journal, July 2019

Computational modeling of pitting corrosion
journal, September 2019

Pitting Corrosion of Natural Aged Al–Mg–Si Extrusion Profile
journal, April 2019