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Microstructure-Sensitive Phase-Field Model of Pitting and Stress Corrosion Cracking in Polycrystalline Materials


Core Concepts
The core message of this work is the development of an electro-chemo-mechanical phase-field formulation that can accurately simulate pitting and stress corrosion cracking in polycrystalline materials by incorporating the sensitivity of mechanical properties and corrosion potential to crystallographic orientation.
Abstract
The paper presents a phase-field model that can simulate pitting and stress corrosion cracking in polycrystalline materials. The key highlights and insights are: The model incorporates dependencies of mechanical properties and corrosion potential on crystallographic orientation, allowing it to capture the microstructural influence on corrosion behavior. A new general boundary condition for the solution potential is proposed to account for the formation and charging dynamics of an electric double layer at the metal-electrolyte interface. The model is calibrated and validated against experimental measurements on a thin stainless steel wire immersed in a corrosive environment, accurately predicting pit depth evolution and current density. Two case studies are presented to demonstrate the model's ability to capture pitting corrosion initiated after the local breakdown of a protective layer and stress-assisted corrosion in a polycrystalline material with an initial defect. The results show that incorporating the underlying microstructure yields more extensive defects, faster defect kinetics, and irregular pit and crack shapes compared to a microstructurally-insensitive homogeneous material scenario.
Stats
The model considers the following key metrics and figures: Equilibrium concentration of metal ions in the liquid phase: cl,eq 1 = 5.1 mol/L Equilibrium concentration of metal ions in the solid phase: cs,eq 1 = 144.3 mol/L Diffusion coefficients of ionic species in the liquid phase ranging from 0.719 × 10-9 m/s2 to 9.311 × 10-9 m/s2 Interfacial energy: Γ = 2.10 J/m2 Chemical free energy density curvature parameter: A = 1.02 × 108 J/m3 Equilibrium constants for primary hydrolysis and water dissociation: K1 = 3.1622 × 10-7 mol/m3, K2 = 10-8 mol2/m6 Macroscopic equilibrium corrosion potential: Eeq = -0.729 V (vs. SCE) Solid phase electrical conductivity: λs = 106 S/m
Quotes
"The results show that incorporating the underlying microstructure yields more extensive defects, faster defect kinetics, and irregular pit and crack shapes relative to a microstructurally-insensitive homogeneous material scenario." "The present model is the first to consider the transient effect of the electric double layer charging behavior in a corrosion damage-prediction model, suitable for both accelerated corrosion tests and stress corrosion cracking predictions over arbitrary time scales."

Deeper Inquiries

How would the corrosion behavior change if the grain boundaries were explicitly modeled with distinct properties compared to the grain interiors?

Incorporating distinct properties for grain boundaries compared to grain interiors in the phase-field model would provide a more realistic representation of the microstructure-sensitive corrosion behavior. Grain boundaries are known to act as preferential sites for corrosion initiation due to their higher energy and different chemical composition compared to the grain interiors. Explicitly modeling grain boundaries with distinct properties, such as higher diffusivity for ions, lower mechanical strength, and altered electrochemical reactivity, would lead to the following changes in corrosion behavior: Localized Corrosion Initiation: Grain boundaries are often sites of localized corrosion initiation due to their inherent vulnerability. Modeling grain boundaries with higher diffusivity for ions would lead to faster penetration of corrosive species, resulting in accelerated localized corrosion at these sites. Intergranular Corrosion: The explicit modeling of grain boundaries with altered electrochemical reactivity could lead to enhanced susceptibility to intergranular corrosion. This type of corrosion occurs along the grain boundaries and is influenced by the chemical composition and structure of these interfaces. Stress Corrosion Cracking: Grain boundaries play a significant role in stress corrosion cracking (SCC) due to their susceptibility to environmental degradation. Modeling grain boundaries with lower mechanical strength could increase the likelihood of SCC initiation at these sites under applied stress in a corrosive environment. Pit Growth and Propagation: The presence of distinct properties at grain boundaries could affect the shape, size, and growth kinetics of corrosion pits. Pits may preferentially nucleate and propagate along grain boundaries, leading to more complex pit morphologies and faster pit growth rates. Overall, explicitly modeling grain boundaries with distinct properties compared to grain interiors would provide a more comprehensive understanding of the role of microstructural features in corrosion behavior and enable more accurate predictions of localized corrosion phenomena.

What are the limitations of the current phase-field approach in capturing the complex interactions between corrosion, mechanical deformation, and microstructural evolution, and how could these be addressed in future work?

The current phase-field approach, while effective in capturing the evolution of corrosion damage in polycrystalline materials, has some limitations in capturing the complex interactions between corrosion, mechanical deformation, and microstructural evolution: Mechanical Effects: The current model does not fully account for the mechanical effects on corrosion behavior, such as stress-induced corrosion or corrosion-assisted cracking. Incorporating a more comprehensive mechanical model that considers the coupling between mechanical deformation and corrosion processes would enhance the predictive capabilities of the model. Grain Boundary Effects: While the model considers the influence of crystallographic orientation on corrosion behavior, it does not explicitly account for the role of grain boundaries in corrosion initiation and propagation. Future work could focus on developing a more detailed representation of grain boundaries and their impact on corrosion susceptibility. Electrochemical Complexity: The model simplifies the electrochemical processes at the metal-electrolyte interface. Future research could explore more sophisticated electrochemical models to capture the intricacies of the electric double layer formation, ion transport, and solution potential distribution more accurately. Microstructural Evolution: The current model does not address the evolution of microstructure during corrosion processes. Incorporating mechanisms for microstructural changes, such as grain growth, phase transformations, and dislocation interactions, would provide a more comprehensive understanding of material degradation under corrosive conditions. To address these limitations, future work could focus on developing a more integrated multi-physics model that combines corrosion, mechanical deformation, and microstructural evolution in a cohesive framework. This would involve refining the constitutive equations, incorporating more detailed material properties, and implementing advanced numerical techniques to capture the complex interactions between these phenomena.

What other applications beyond pitting and stress corrosion cracking could this electro-chemo-mechanical phase-field framework be extended to, such as corrosion-fatigue or corrosion-assisted creep?

The electro-chemo-mechanical phase-field framework has the potential to be extended to various other corrosion-related phenomena beyond pitting and stress corrosion cracking. Some potential applications include: Corrosion-Fatigue: The framework could be adapted to study the synergistic effects of corrosion and cyclic loading on material degradation. By incorporating fatigue damage mechanisms and corrosion processes, the model could predict the initiation and propagation of corrosion-fatigue cracks in engineering components. Corrosion-Assisted Creep: Understanding the interaction between corrosion and creep deformation is crucial for assessing the long-term integrity of materials in high-temperature environments. The phase-field framework could be extended to investigate how corrosion accelerates creep deformation and influences the time-dependent behavior of materials. Hydrogen Embrittlement: Hydrogen-induced cracking is a significant concern in various industries. By incorporating hydrogen transport and trapping mechanisms into the model, the framework could be used to study the effects of hydrogen embrittlement on material properties and failure modes. Localized Corrosion in Coatings: The framework could be applied to study the behavior of protective coatings under corrosive conditions. By simulating the evolution of corrosion damage in coated systems, the model could help optimize coating designs for enhanced durability and performance. Overall, the electro-chemo-mechanical phase-field framework has the versatility to be extended to a wide range of corrosion-related phenomena, providing valuable insights into the complex interactions between material degradation processes in different engineering applications.
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