Modeling Localized Corrosion Propagation of Metallic Materials by Peridynamics: Progresses and Challenges
XIA Dahai1,2(), DENG Chengman1,2, CHEN Ziguang3, LI Tianshu4, HU Wenbin1,2
1.Tianjin Key Laboratory of Composite and Functional Materials, Tianjin University, Tianjin 300350, China 2.School of Materials Science and Engineering, Tianjin University, Tianjin 300350, China 3.School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, China 4.Fontana Corrosion Center, The Ohio State University, Columbus, OH, 43210, USA
Cite this article:
XIA Dahai, DENG Chengman, CHEN Ziguang, LI Tianshu, HU Wenbin. Modeling Localized Corrosion Propagation of Metallic Materials by Peridynamics: Progresses and Challenges. Acta Metall Sin, 2022, 58(9): 1093-1107.
Localized corrosion degradation of metallic materials is a key factor that significantly impacts their lifetime and safety. Existing localized corrosion assessment methods for metallic materials are mainly based on corrosion simulation experiments in laboratory and corrosion exposure experiments in real environmental. However, these experiments are often complex, lengthy, and costly. Localized corrosion simulation can be achieved with the continuous improvement in the theory and measurement of localized corrosion, and the rapid development of numerical calculation, simulation software, and programing. Numerical models based on the classical continuum mechanics (CCM) apply a spatial differential equation to describe the interaction between material points, and singularity appears when solving discontinuous problems such as corrosion degradation. The peridynamics (PD) theory based on nonlocal applies time differential-spatial integration to describe the interaction between the material points and breaks through the bottleneck of the CCM theory on discontinuous problems. This paper reviews the state of the art of PD applied in localized corrosion modeling, including pitting corrosion, crevice corrosion, intergranular corrosion, galvanic corrosion, and stress corrosion cracking by combing with the relevant theories and numerical implementations of the localized corrosion degradation model based on the PD theory. Finally, the challenges and outlook of PD applied in corrosion modeling are discussed.
Fig.1 Classical continuum mechanics interactions (a)[62] and peridynamics (PD) interactions (b)[48] (B—local interaction body; δ—horizon size; Hx —horizon- x in peridynamics; x, x ?—material points; y, y ?—locations of x and x ? with deformed state, respectively; u, u ?—displacements of x and x ?, respectively; f —constitutive force function; x1, x2, x3—coordinations)
Fig.2 A 1D diffusion-based PD corrosion model[60] (D—position, C(x)—concentration, t—time, —derivative of concentration, J1—diffusion of metal ions in solution, J2—dissolution of metal atoms losing electrons)
Fig.3 Phase change and concentration-dependent damage model[60] (Ω—peridynamic body)
Fig.4 Uniform discretization of horizon (a)[48] and area correction (b)[77] in 2D ( k —center point, Δx—size of uniform grid, i—material point xi, j—material point xj. Red stars are those with cells inside the neighborhood of i, brown triangles are those located inside the neighborhood of i, but with a cell having only a partial overlapping with the neighborhood of i, magenta squares are those located outside the neighborhood of i, with a nonzero overlapping between their cells and the neighborhood of i, blue points are those with cells outside the neighborhood of i)
Fig.5 Flow chart of PA-HHB algorithm used for areas correction (||ξij ||—distance between material point xi and xj, factor—correction factors of areas in 2D, ΔVij —partial volume of uniformly discretized grid cells)
Fig.6 Initial and boundary conditions of 2D in PD of pitting corrosion (a)[60], crevice corrosion (b)[70], intergranular corrosion (c)[72], galvanic corrosion (d)[73], and stress corrosion cracking (e)[74] (X, Y—coordinates; C( x, 0)—concentration of material point x at t = 0; Csolid—concentration of solid node; and —derivative of concentration; C( x, 0) = Csolid, C( x, t) = 0, , and = 0—there is no flux around the boundary of the metal, except over the solid/liquid interface. δ0—subscripts are the values for the polar angle θ of the crevice; C(t ≥ 0) = 0—boundary concentration to the bulk dilute electrolyte; C(t = 0) = 0—concentration of electrolyte; C(t = 0) = Csolid—concentration of metal; C(t = 0) = 0.99Csat—concentration of the end of crevice. —derivative of concentration; C0 = Csolid—concentration of intact metal; C( x, t)—concentration of material point x. ϕ—second derivative of potential; ϕ = ϕ·n —potential gradient, n is normal vector; ic—cathode current density; ia—anodic current densities. u—displacement with tensile stress, σ—tensile stress, L—length of the domain, E—elastic modulus)
Fig.7 Comparison of polarization of PD model and experimental (a), and horizon factor (m)-convergence (b-d)[60] (h1—damage depth of subsurface layer, h2—pitting depth, DAM—corrosion damage index)
Fig.8 Illustrations of two cases of two-phase heterogeneous materials used to study pitting corrosion (a), damage profiles after 20 s corrosion for case A (b) and case B (c)[60]
Fig.9 Schematic of the 3D simulation domain with the initial and boundary conditions (a)[71], experimental (b, d) [84] and PD simulation (c, e) results for pit grown in 304 stainless steel and its lacy cover after 83 s of corrosion in 0.1 mol/L NaCl solution, at 600 mV (vs Ag/AgCl reference electrode) (f)[71] (Csat—the saturation value of metal ion concentration in the solution, CON—concentration)
Fig.10 Formation of the effect of the salt layer (a), time-evolution of corrosion damage (see legend) with the earlier PD model (left side of the figure) and the newly proposed PD model (right side of the figure) (b)[86] (Red bonds in Fig.10a are temporarily paused as a result of saturation at nodes in the nearby solution, Ccrit—critical concentration of metal cations corresponding to metal repassivation, C—concentration of solid node)
Fig.11 Self-accelerating anodic dissolution mechanism of crevice corrosion model in PD[70] ([M+z ]—concentration of positively charged metal ions, [Cl-]—the concentration of Cl-, i—current density, i(pH)—pH-dependent current density, i(C)—concentration-dependent current density)
Fig.12 Corrosion depth vs time for PD simulation of intergranular corrosion (IGC) of 2024-T3 aluminum alloy immersed to NaCl solution and comparison with data from experiments[72] (L—longitudinal, LT—long-transverse, ST—short-transverse)
Fig.13 Initial current density along the electrode surface of AE44 magnesium alloy/mild steel couple (a) and quantitative comparison of corrosion depth of AE44 magnesium alloy/6063 aluminum alloy galvanic couple (b)[73]
Fig.14 Snapshots of crack propagation for corrosion pits at 1500 time steps under compressive stress (a) and bending stress (b)[91] (DMG—damage index)
1
Xia D H, Deng C M, MacDonald D, et al. Electrochemical measurements used for assessment of corrosion and protection of metallic materials in the field: A critical review [J]. J. Mater. Sci. Technol., 2022, 112: 151
doi: 10.1016/j.jmst.2021.11.004
2
Hou B R, Li X G, Ma X M, et al. The cost of corrosion in China [J]. npj Mater. Degrad., 2017, 4: 1
doi: 10.1038/s41529-019-0105-2
3
Xia D H, Mao Y C, Zhu Y, et al. A novel approach used to study the corrosion susceptibility of metallic materials at a dynamic seawater/air interface [J]. Corros. Commun., 2022, 6: 62
doi: 10.1016/j.corcom.2022.03.001
4
Xia D H, Qin Z B, Song S Z, et al. Combating marine corrosion on engineered oxide surface by repelling, blocking and capturing Cl-: A mini review [J]. Corros. Commun., 2021, 2: 1
doi: 10.1016/j.corcom.2021.09.001
5
Alkire R. Editors' choice-perspective-mathematical modeling of electrochemical systems at multiple scales [J]. J. Electrochem. Soc., 2020, 167: 013517
6
Ji Y Y, Xu Y Z, Zhang B B, et al. Review of micro-scale and atomic-scale corrosion mechanisms of second phases in aluminum alloys [J]. Trans. Nonferrous Met. Soc. China, 2021, 31: 3205
doi: 10.1016/S1003-6326(21)65727-8
7
Weidner J W, Balbuena P B, Weber A Z, et al. Mathematical modeling of electrochemical systems at multiple scales in honor of Professor John Newman [J]. J. Electrochem. Soc., 2017, 164: Y13
doi: 10.1149/2.0731711jes
8
Li T S, Wu J, Frankel G S. Localized corrosion: Passive film breakdown vs. pit growth stability, Part VI: Pit dissolution kinetics of different alloys and a model for pitting and repassivation potentials [J]. Corros. Sci., 2021, 182: 109277
doi: 10.1016/j.corsci.2021.109277
9
Li T S, Frankel G S. Repassivation underneath salt film on stainless steel pits [J]. Corros. Sci., 2022, 203: 110353
doi: 10.1016/j.corsci.2022.110353
10
Frankel G S, Li T S, Scully J R. Perspective-localized corrosion: Passive film breakdown vs pit growth stability [J]. J. Electrochem. Soc., 2017, 164: C180
doi: 10.1149/2.1381704jes
11
Li T S, Scully J R, Frankel G S. Localized corrosion: Passive film breakdown vs pit growth stability: Part II. A model for critical pitting temperature [J]. J. Electrochem. Soc., 2018, 165: C484
doi: 10.1149/2.0591809jes
12
Li T S, Scully J R, Frankel G S. Localized corrosion: Passive film breakdown vs. pit growth stability: Part III. A unifying set of principal parameters and criteria for pit stabilization and salt film formation [J]. J. Electrochem. Soc., 2018, 165: C762
doi: 10.1149/2.0251811jes
13
Li T S, Scully J R, Frankel G S. Localized corrosion: passive film breakdown vs pit growth stability: Part V. Validation of a new framework for pit growth stability using one-dimensional artificial pit electrodes [J]. J. Electrochem. Soc., 2019, 166: C3341
doi: 10.1149/2.0431911jes
14
Li T S, Scully J R, Frankel G S. Localized corrosion: Passive film breakdown vs. pit growth stability: Part IV. The role of salt film in pit growth: A mathematical framework [J]. J. Electrochem. Soc., 2019, 166: C115
doi: 10.1149/2.0211906jes
15
Li T S, Perea D E, Schreiber D K, et al. Cryo-based structural characterization and growth model of salt film on metal [J]. Corros. Sci., 2020, 174: 108812
doi: 10.1016/j.corsci.2020.108812
16
Wang Y C, Song S Z, Wang J Q, et al. Correlation between passivity breakdown and composition of passive film formed on alloy 690 studied by sputtering XPS and FIB-HRTEM [J]. J. Electrochem. Soc., 2019, 166: C332
doi: 10.1149/2.1291912jes
17
Turnbull A, Wright L, Crocker L. New insight into the pit-to-crack transition from finite element analysis of the stress and strain distribution around a corrosion pit [J]. Corros. Sci., 2010, 52: 1492
doi: 10.1016/j.corsci.2009.12.004
18
Wenman M R, Trethewey K R, Jarman S E, et al. A finite-element computational model of chloride-induced transgranular stress-corrosion cracking of austenitic stainless steel [J]. Acta. Mater., 2008, 56: 4125
doi: 10.1016/j.actamat.2008.04.068
19
Vankeerberghen M. Will finite-element analysis find its way to the design against stress corrosion cracking? [J]. Environ.-Induced Crack. Mater., 2008, 1: 115
20
Paraskevoulakos C, Tanner D W J, Scott T B. Finite element modelling approach to investigate the degradation of intermediate level waste drums induced from interior metallic corrosion [J]. Eng. Struct., 2017, 147: 385
doi: 10.1016/j.engstruct.2017.06.012
21
Fallahnezhad K, Oskouei R H, Taylor M. Development of a fretting corrosion model for metallic interfaces using adaptive finite element analysis [J]. Finite. Elem. Anal. Des., 2018, 148: 38
doi: 10.1016/j.finel.2018.05.004
22
Qin G J, Cheng Y F, Zhang P. Finite element modeling of corrosion defect growth and failure pressure prediction of pipelines [J]. Int. J. Press. Vessels Pip., 2021, 194: 104509
doi: 10.1016/j.ijpvp.2021.104509
23
Fatoba O O, Leiva-Garcia R, Lishchuk S V, et al. Simulation of stress-assisted localised corrosion using a cellular automaton finite element approach [J]. Corros. Sci., 2018, 137: 83
doi: 10.1016/j.corsci.2018.03.029
24
Roy K, Lau H H, Fang Z Y, et al. Effects of corrosion on the strength of self-drilling screw connections in cold-formed steel structures-experiments and finite element modeling [J]. Structures, 2022, 36: 1080
doi: 10.1016/j.istruc.2021.12.052
25
Bailly-Salins L, Borrel L, Jiang W, et al. Modeling of high-temperature corrosion of zirconium alloys using the eXtended finite element method (X-FEM) [J]. Corros. Sci., 2021, 189: 109603
doi: 10.1016/j.corsci.2021.109603
26
Jasra Y, Singhal S, Upman R, et al. Finite element simulation of stress corrosion cracking in austenitic stainless steel using modified Lemaitre damage model [J]. Mater. Today: Proc., 2020, 26: 2314
27
Onishi Y, Takiyasu J, Amaya K, et al. Numerical method for time-dependent localized corrosion analysis with moving boundaries by combining the finite volume method and voxel method [J]. Corros. Sci., 2012, 63: 210
doi: 10.1016/j.corsci.2012.06.001
28
Sun W, Liu G C, Wang L D, et al. An arbitrary Lagrangian-Eulerian model for studying the influences of corrosion product deposition on bimetallic corrosion [J]. J. Solid State Electrochem., 2013, 17: 829
doi: 10.1007/s10008-012-1935-9
29
Sun W, Wang L D, Wu T T, et al. An arbitrary Lagrangian-Eulerian model for modelling the time-dependent evolution of crevice corrosion [J]. Corros. Sci., 2014, 78: 233
doi: 10.1016/j.corsci.2013.10.003
30
Duddu R. Numerical modeling of corrosion pit propagation using the combined extended finite element and level set method [J]. Comput. Mech., 2014, 54: 613
doi: 10.1007/s00466-014-1010-8
31
Duddu R, Kota N, Qidwai S M. An extended finite element method based approach for modeling crevice and pitting corrosion [J]. J. Appl. Mech., 2016, 83: 081003
32
Ansari T Q, Xiao Z H, Hu S Y, et al. Phase-field model of pitting corrosion kinetics in metallic materials [J]. npj Comput. Mater., 2018, 4: 38
doi: 10.1038/s41524-018-0089-4
33
Ansari T Q, Huang H T, Shi S Q. Phase field modeling for the morphological and microstructural evolution of metallic materials under environmental attack [J]. npj Comput. Mater., 2021, 7: 143
doi: 10.1038/s41524-021-00612-7
34
Lin C, Ruan H H, Shi S Q. Phase field study of mechanico-electrochemical corrosion [J]. Electrochim. Acta, 2019, 310: 240
doi: 10.1016/j.electacta.2019.04.076
35
Nguyen T T, Bolivar J, Réthoré J, et al. A phase field method for modeling stress corrosion crack propagation in a nickel base alloy [J]. Int. J. Solids Struct., 2017, 112: 65
doi: 10.1016/j.ijsolstr.2017.02.019
36
Ståhle P, Hansen E. Phase field modelling of stress corrosion [J]. Eng. Fail. Anal., 2015, 47: 241
doi: 10.1016/j.engfailanal.2014.07.025
37
Mai W J, Soghrati S, Buchheit R G. A phase field model for simulating the pitting corrosion [J]. Corros. Sci., 2016, 110: 157
doi: 10.1016/j.corsci.2016.04.001
38
Mai W J, Soghrati S. A phase field model for simulating the stress corrosion cracking initiated from pits [J]. Corros. Sci., 2017, 125: 87
doi: 10.1016/j.corsci.2017.06.006
39
Nguyen T T, Bolivar J, Shi Y, et al. A phase field method for modeling anodic dissolution induced stress corrosion crack propagation [J]. Corros. Sci., 2018, 132: 146
doi: 10.1016/j.corsci.2017.12.027
40
Xiao Z H, Hu S Y, Luo J L, et al. A quantitative phase-field model for crevice corrosion [J]. Comput. Mater. Sci., 2018, 149: 37
doi: 10.1016/j.commatsci.2018.03.011
41
Mai W J, Soghrati S. New phase field model for simulating galvanic and pitting corrosion processes [J]. Electrochim. Acta, 2018, 260: 290
doi: 10.1016/j.electacta.2017.12.086
42
Chadwick A F, Stewart J A, Enrique R A, et al. Numerical modeling of localized corrosion using phase-field and smoothed boundary methods [J]. J. Electrochem. Soc., 2018, 165: C633
doi: 10.1149/2.0701810jes
43
Tsuyuki C, Yamanaka A, Ogimoto Y. Phase-field modeling for pH-dependent general and pitting corrosion of iron [J]. Sci. Rep., 2018, 8: 12777
doi: 10.1038/s41598-018-31145-7
pmid: 30143681
44
Lishchuk S V, Akid R, Worden K, et al. A cellular automaton model for predicting intergranular corrosion [J]. Corros. Sci., 2011, 53: 2518
doi: 10.1016/j.corsci.2011.04.027
45
Di Caprio D, Vautrin-Ul C, Stafiej J, et al. Morphology of corroded surfaces: Contribution of cellular automaton modelling [J]. Corros. Sci., 2011, 53: 418
doi: 10.1016/j.corsci.2010.09.052
46
Córdoba-Torres P, Nogueira R P, De Miranda L, et al. Cellular automaton simulation of a simple corrosion mechanism: Mesoscopic heterogeneity versus macroscopic homogeneity [J]. Electrochim. Acta, 2001, 46: 2975
doi: 10.1016/S0013-4686(01)00524-2
47
Cui C J, Ma R J, Chen A R, et al. Experimental study and 3D cellular automata simulation of corrosion pits on Q345 steel surface under salt-spray environment [J]. Corros. Sci., 2019, 154: 80
doi: 10.1016/j.corsci.2019.03.011
48
Oterkus E, Oterkus S, Madenci E. Peridynamic Modeling, Numerical Techniques, and Applications [M]. Amsterdam: Elsevier, 2021: 186
49
Silling S A. Reformulation of elasticity theory for discontinuities and long-range forces [J]. J. Mech. Phys. Sol., 2000, 48: 175
doi: 10.1016/S0022-5096(99)00029-0
50
Rabczuk T, Ren H L. A peridynamics formulation for quasi-static fracture and contact in rock [J]. Eng. Geol., 2017, 225: 42
doi: 10.1016/j.enggeo.2017.05.001
51
Sanchez G, Aperador W, Cerón A. Corrosion grade classification: A machine learning approach [J]. Indian Chem. Eng., 2020, 62: 277
52
Hu W K, Ha Y D, Bobaru F. Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites [J]. Comput. Methods Appl. Mech. Eng., 2012, 217-220: 247
doi: 10.1016/j.cma.2012.01.016
53
Karpenko O, Oterkus S, Oterkus E. Peridynamic analysis to investigate the influence of microstructure and porosity on fatigue crack propagation in additively manufactured Ti6Al4V [J]. Eng. Fract. Mech., 2022, 261: 108212
doi: 10.1016/j.engfracmech.2021.108212
54
Bobaru F, Duangpanya M. The peridynamic formulation for transient heat conduction [J]. Int. J. Heat Mass Transf., 2010, 53: 4047
doi: 10.1016/j.ijheatmasstransfer.2010.05.024
55
Bobaru F, Duangpanya M. A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities [J]. J. Comput. Phys., 2012, 231: 2764
doi: 10.1016/j.jcp.2011.12.017
56
Wang L J, Xu J F, Wang J X. A peridynamic framework and simulation of non-Fourier and nonlocal heat conduction [J]. Int. J. Heat Mass Transf., 2018, 118: 1284
doi: 10.1016/j.ijheatmasstransfer.2017.11.074
57
Nikolaev P, Sedighi M, Jivkov A P, et al. Analysis of heat transfer and water flow with phase change in saturated porous media by bond-based peridynamics [J]. Int. J. Heat Mass Transf., 2022, 185: 122327
doi: 10.1016/j.ijheatmasstransfer.2021.122327
58
Askari E, Bobaru F, LEhoucq R B, et al. Peridynamics for multiscale materials modeling [J]. J. Phys.: Conf. Ser., 2008, 125: 012078
59
Gerstle W, Silling S, Read D, et al. Peridynamic simulation of electromigration [J]. Comput. Mater. Contin., 2008, 8: 75
60
Chen Z G, Bobaru F. Peridynamic modeling of pitting corrosion damage [J]. J. Mech. Phys. Sol., 2015, 78: 352
doi: 10.1016/j.jmps.2015.02.015
61
Jafarzadeh S, Chen Z G, Bobaru F. Computational modeling of pitting corrosion [J]. Corros. Rev., 2019, 37: 419
doi: 10.1515/corrrev-2019-0049
62
Madenci E, Oterkus E. Peridynamic Theory and Its Applications [M]. New York: Springer, 2014: 19
63
Silling S A, Epton M, Weckner O, et al. Peridynamic states and constitutive modeling [J]. J. Elasticity, 2007, 88: 151
doi: 10.1007/s10659-007-9125-1
64
Macek R W, Silling S A. Peridynamics via finite element analysis [J]. Finite Elem. Anal. Des., 2007, 43: 1169
doi: 10.1016/j.finel.2007.08.012
65
Chen Z G. Advances in corrosion damage modeling [J]. Chin. J. Sol. Mech., 2019, 40: 99
陈子光. 腐蚀损伤模型研究进展 [J]. 固体力学学报, 2019, 40: 99
66
Cao C N. Principles of Electrochemistry of Corrosion [M]. 3rd Ed., Beijing: Chemical Industry Press, 2008: 60
曹楚南. 腐蚀电化学原理 [M]. 第 3版, 北京: 化学工业出版社, 2008: 60
67
Scheiner S, Hellmich C. Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary [J]. Corros. Sci., 2007, 49: 319
doi: 10.1016/j.corsci.2006.03.019
68
Oterkus S, Madenci E, Agwai A. Peridynamic thermal diffusion [J]. J. Comput. Phys., 2014, 265: 71
doi: 10.1016/j.jcp.2014.01.027
69
Chen Z G, Bobaru F. Selecting the kernel in a peridynamic formulation: A study for transient heat diffusion [J]. Comput. Phys. Commun., 2015, 197: 51
doi: 10.1016/j.cpc.2015.08.006
70
Jafarzadeh S, Zhao J M, Shakouri M, et al. A peridynamic model for crevice corrosion damage [J]. Electrochim. Acta, 2022, 401: 139512
doi: 10.1016/j.electacta.2021.139512
71
Jafarzadeh S, Chen Z G, Zhao J M, et al. Pitting, lacy covers, and pit merger in stainless steel: 3D peridynamic models [J]. Corros. Sci., 2019, 150: 17
doi: 10.1016/j.corsci.2019.01.006
72
Jafarzadeh S, Chen Z G, Bobaru F. Peridynamic modeling of intergranular corrosion damage [J]. J. Electrochem. Soc., 2018, 165: C362
doi: 10.1149/2.0821807jes
73
Zhao J M, Jafarzadeh S, Rahmani M, et al. A peridynamic model for galvanic corrosion and fracture [J]. Electrochim. Acta, 2021, 391: 138968
doi: 10.1016/j.electacta.2021.138968
74
Jafarzadeh S, Chen Z G, Li S M, et al. A peridynamic mechano-chemical damage model for stress-assisted corrosion [J]. Electrochim. Acta, 2019, 323: 134795
doi: 10.1016/j.electacta.2019.134795
75
Lehoucq R B, Silling S A, Seleson P, et al. Peridynamics with LAMMPS: A user guide [R]. Albuquerque: Sandia National Laboratories, 2011
76
Silling S A, Askari E. A meshfree method based on the peridynamic model of solid mechanics [J]. Comput. Struct., 2005, 83: 1526
doi: 10.1016/j.compstruc.2004.11.026
77
Seleson P. Improved one-point quadrature algorithms for two-dimensional peridynamic models based on analytical calculations [J]. Comput. Methods Appl. Mech. Eng., 2014, 282: 184
doi: 10.1016/j.cma.2014.06.016
78
Liu J J, Lin Y Z, Li X Y. Numerical simulation for carbon steel flow-induced corrosion in high-velocity flow seawater [J]. Anti-Corros. Methods Mater., 2008, 55: 66
doi: 10.1108/00035590810859430
79
Bobaru F, Yang M J, Alves L F, et al. Convergence, adaptive refinement, and scaling in 1D peridynamics [J]. Int. J. Numer. Methods Eng., 2009, 77: 852
doi: 10.1002/nme.2439
80
Silling S A. Linearized theory of peridynamic states [J]. J. Elasticity, 2010, 99: 85
doi: 10.1007/s10659-009-9234-0
81
Bai X M, Tang J Q, Gong J M. Numerical modeling of 1D corrosion pit propagation under different overpotentials using peridynamic method [J]. J. Nanjing Tech Univ. (Nat. Sci. Ed.) 2017, 39(6): 91
Laycock N J, White S P, Noh J S, et al. Perforated covers for propagating pits [J]. J. Electrochem. Soc., 1998, 145: 1101
doi: 10.1149/1.1838423
83
Laycock N J, White S P. Computer simulation of single pit propagation in stainless steel under potentiostatic control [J]. J. Electrochem. Soc., 2001, 148: B264
doi: 10.1149/1.1376119
84
Almuaili F A. Characterisation off 3D pitting corrosion kinetics of stainless steel in chloride containing environments [D]. Manchester: University of Manchester, 2017
85
Gaudet G T, Mo W T, Hatton T A, et al. Mass transfer and electrochemical kinetic interactions in localized pitting corrosion [J]. AIChE J., 1986, 32: 949
doi: 10.1002/aic.690320605
86
Jafarzadeh S, Chen Z G, Bobaru F. Peridynamic modeling of repassivation in pitting corrosion of stainless steel [J]. Corrosion, 2018, 74: 393
doi: 10.5006/2615
87
Deshpande K B. Experimental investigation of galvanic corrosion: comparison between SVET and immersion techniques [J]. Corros. Sci., 2010, 52: 2819
doi: 10.1016/j.corsci.2010.04.023
88
De Meo D, Diyaroglu C, Zhu N, et al. Modelling of stress-corrosion cracking by using peridynamics [J]. Int. J. Hydrog. Energy, 2016, 41: 6593
doi: 10.1016/j.ijhydene.2016.02.154
89
De Meo D, Russo L, Oterkus E, et al. Peridynamics for predicting pit-to-crack transition [A]. 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference [C]. Grapevine: American Institute of Aeronautics and Astronautics, 2017: 0568
90
Li S M, Chen Z G, Wang F, et al. Analysis of corrosion-induced diffusion layer in ZK60A magnesium alloy [J]. J. Electrochem. Soc., 2016, 163: C784
doi: 10.1149/2.1001613jes
91
Shi C X, Gong Y, Yang Z G, et al. Peridynamic investigation of stress corrosion cracking in carbon steel pipes [J]. Eng. Fract. Mech., 2019, 219: 106604
doi: 10.1016/j.engfracmech.2019.106604
92
Chen Z G, Jafarzadeh S, Zhao J M, et al. A coupled mechano-chemical peridynamic model for pit-to-crack transition in stress-corrosion cracking [J]. J. Mech. Phys. Sol., 2021, 146: 104203
doi: 10.1016/j.jmps.2020.104203
93
Council N R. Research Opportunities in Corrosion Science and Engineering [M]. Washington: The National Academies Press, 2011: 120
94
Xia D H, Ji Y Y, Mao Y C, et al. Localized corrosion mechanism of 2024 aluminum alloy in a simulated dynamic seawater/air interface [J]. Acta Metall. Sin., 2022, DOI: 10.11900/0412.1961.2022.00196
Mao Y C, Zhu Y, Sun S K, et al. Localized corrosion of 5083 Al-alloy in simulated marine splash zone [J]. J. Chin. Soc. Corr. Prot., 2022, DOI: 10.11902/1005.4537.2022.162
