Modeling Localized Corrosion Propagation of Metallic Materials by Peridynamics: Progresses and Challenges

doi:10.11900/0412.1961.2022.00249

Acta Metall Sin

2022, Vol. 58

Issue (9): 1093-1107 DOI: 10.11900/0412.1961.2022.00249

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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.

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Abstract

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.

Key words: metallic material localized corrosion numerical simulation peridynamics nonlocal theory

Received: 19 May 2022

ZTFLH:

TG172

Fund: National Natural Science Foundation of China(52171077);National Natural Science Foundation of China(52031007)

About author: XIA Dahai, associate professor, Tel: (022)27407338, E-mail: dahaixia@tju.edu.cn

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https://www.ams.org.cn/EN/10.11900/0412.1961.2022.00249 OR https://www.ams.org.cn/EN/Y2022/V58/I9/1093

Fig.1 Classical continuum mechanics interactions (a)^[62] and peridynamics (PD) interactions (b)^[48] (B—local interaction body; δ—horizon size; H_x —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, $∂ C x, t ∂ D$ —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 x_i, j—material point x_j. 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 (||ξ_ij ||—distance between material point x_i and x_j, factor—correction factors of areas in 2D, ΔV_ij —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; C_solid—concentration of solid node; $∂ C (x, t) ∂ x 2$ and $∂ C (x, t) ∂ x 1$ —derivative of concentration; C( x, 0) = C_solid, C( x, t) = 0, $∂ C (x, t) ∂ x 1 = 0$ , and $∂ C (x, t) ∂ x 2$ = 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)} = C_solid—concentration of metal; C₍_t_{= 0)} = 0.99C_sat—concentration of the end of crevice. $∂ C ∂ x$ —derivative of concentration; C₀ = C_solid—concentration of intact metal; C( x, t)—concentration of material point x. $? 2$ ϕ—second derivative of potential; $? n$ ϕ = $?$ ϕ·n —potential gradient, n is normal vector; i_c—cathode current density; i_a—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] (C_sat—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, C_crit—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)

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