Kinetic modelling of the attenuation of carbon steel canister corrosion due to diffusive transport through corrosion product layers

This work models the attenuation of the corrosion of carbon steel canisters due to the influence of diffusive transport through the corrosion product - a growing film of magnetite. The model makes use of an algorithm based on the analytical solution of 1D diffusion equations for the movement of Fe²⁺, H₂, H₂O and OH⁻ through this magnetite film.     

Markov chain modelling of pitting corrosion in underground pipelines

A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov’s forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.     

Probability distribution of pitting corrosion depth and rate in underground pipelines: A Monte Carlo study

The probability distributions of external-corrosion pit depth and pit growth rate were investigated in underground pipelines using Monte Carlo simulations. The study combines a predictive pit growth model developed by the authors with the observed distributions of the model variables in a range of soils. Depending on the pipeline age, any of the three maximal extreme value distributions, i.e. Weibull, Fréchet or Gumbel, can arise as the best fit to the pitting depth and rate data. The Fréchet distribution best fits the corrosion data for long exposure periods. This can be explained by considering the long-term stabilization of the diffusion-controlled pit growth. The findings of the study provide reliability analysts with accurate information regarding the stochastic characteristics of the pitting damage in underground pipelines.     

Modeling the cracking of cover concrete due to non-uniform corrosion of reinforcement

In situations when external chloride penetration is the cause of depassivation, the corrosion process may start from the outer region of a rebar, which might expand non-uniformly. Therefore, the main objective of the present work is to explore the effect of non-uniform corrosion on cracking behavior of cover concrete. The influences of concrete heterogeneities and the porous layer generated at the rebar/concrete interface on the failure patterns and the corrosion level of cover concrete are considered. The random aggregate structures of concrete are built, and the concrete is regarded as a composite composed of three phases, i.e. the aggregate, mortar matrix, and the interfacial transition zones (ITZs). The plasticity damaged model is employed to describe the mechanical properties of the mortar matrix and the ITZs, and it is assumed that the aggregate is elastic. Non-uniform radial displacement with a half ellipse shape is adopted to describe the expansion distribution of the corrosion products. The failure pattern and the corrosion pressure of cover concrete, and the critical corrosion level when the cover concrete cracks due to non-uniform corrosion expansion are studied based on the meso-scale numerical method. The comparison of the simulation results with the available test results on the failure pattern of cover concrete shows fairly good agreement. Moreover, the influence of meso-structural heterogeneities is explored, and the cracking behavior obtained under non-uniform and uniform expansion conditions are compared. Finally, the influences of cover thickness, rebar diameter and the location of rebar (namely side-located rebar and corner-located rebar), on the failure pattern and the corrosion level are examined.     

On the penetration of corrosion products from reinforcing steel into concrete due to chloride-induced corrosion

Reinforced concretes were corroded to varying degrees by exposing to cyclic NaCl spray and 40 °C drying. The amount of corrosion products and induced damage were measured using image analysis. We found that corrosion products can accumulate at steel-concrete interface as well as penetrate cement paste and deposit within hydration products, relicts of reacted slag, and air voids. As corrosion increases, the products tend to accumulate at the steel-concrete interface, while the amount penetrating cement paste remains relatively constant. Only a small amount of corrosion is needed to induce visible cover cracking. Implications on modelling time to cover cracking are discussed.     

Long-term corrosion of rebars embedded in aerial and hydraulic binders - Parametric study and first step of modelling

The prediction of long-term behaviour of reinforced concrete structures involved in the nuclear industry requires a phenomenological modelling of the rebars corrosion processes. Previous analytical characterisation of archaeological artefacts allowed to identify a typical layout constituted of four layers (the metal, the dense product layer, the transformed medium and the binder). Additional experiments leaded to identify the long-term corrosion mechanisms. Following these results, this paper proposes an analytical model of long-term corrosion of rebars embedded in concrete. This modelling is considering the kinetic of oxygen diffusion through the system and its consumption at the metal/dense product layer interface as a function of concrete water saturation degree. Corrosion products thicknesses estimated with the model are then compared to corrosion product thicknesses measured on archaeological artefacts. A parametric study is performed and demonstrates that the oxygen diffusivity and the kinetic constant of the cathodic reaction affect in a wide range the model results.     

A numerical study of damage caused by combined pitting corrosion and axial stress in steel pipes

Localized pipe wall damage accounts for many failures. Numerical modelling of pipes under increasing axial load and constant internal pressure when there is corrosion pits on the exterior surface of the pipe is reported herein. It is shown that for the assumed ideal elastic–plastic material the shape and volume of the plastic field depend on pit depth and its geometry. Pipe wall fracture around a pit can be associated with a critical plastic section. The results reported herein should be relevant for estimating of the risk of perforation and of loss of contents for steel pipes under different loading.     

Quantum chemical study of some cyclic nitrogen compounds as corrosion inhibitors of steel in NaCl media

Corrosion inhibition efficiencies of 3-amino-1,2,4-triazole (3-ATA), 2-amino-1,3,4-thiadiazole (2-ATDA), 5-(p-tolyl)-1,3,4-triazole (TTA), 3-amino-5-methylmercapto-1,2,4-triazole (3-AMTA) and 2-aminobenzimidazole (2-ABA) as corrosion inhibitors on steel in sodium chloride media were investigated by using semiempirical PM3 and density functional theory (DFT) methods. Quantum chemical parameters such as highest occupied molecular orbital energy (E_HOMO), lowest unoccupied molecular orbital energy (E_LUMO), energy gap (ΔE) and dipole moment (μ) have been calculated for these compounds by using semiempirical PM3 and 6-31G(d), 6-311G(d,p) DFT methods. It was found that theoretical data support the experimental results.     

Model of physico-chemical effect on flow accelerated corrosion in power plant

Flow accelerated corrosion (FAC) is caused by the accelerated dissolution of protective oxide film under the condition of high flow rate and has been one of the most important subjects in fossil and nuclear power plants. The dominant factors of FAC are water chemistry, material, and fluid dynamics. Understanding of the thinning mechanism is very important to estimate the quantitative effects of the dominant factors on FAC. In this study, a novel model of chemical effect on FAC under the steady-state condition was developed in consideration of the diffusion of soluble iron and chromium species, dissolved hydrogen, and dissolved oxygen. The formula to evaluate the critical concentration of dissolved oxygen for FAC suppression was derived. The present model reproduced qualitatively the effect of major environmental parameters on FAC rate. The model could explain the following facts. (1) The FAC rate shows a peak around 413 K. (2) The FAC rate decreases with an increase in Cr content. (3) The FAC rate decreases with an increase in pH. (4) The FAC rate decreases with an increase in dissolved oxygen concentration. (5) The maximum of critical dissolved oxygen concentration is observed around 353 K. (6) The critical dissolved oxygen concentration decreases with an increase in pH. We conclude that the diffusion of soluble species from the saturated layer under the steady-state condition well reproduces the unique FAC behavior with variation of water chemistry parameters.     

A model for an anodic dissolution cell in connection to its dimensions for stress corrosion cracking

The anodic dissolution is modelled for pure iron for conditions simulating those of low alloy steels in high temperature water undergoing stress corrosion cracking. The dissolution is assumed to be initiated by the rupture of the protective oxide film and arrested by the repassivation. The goal of the model is to identify the relevant parameters of the anodic dissolution by a parameter sensitivity study. The cell is three-dimensional for taking into account the cathode to anode area ratio, at the price of the assumption of homogeneity of the electrolyte, and is assumed to be electrically uncoupled from the rest of the crack. The model uses the Butler-Volmer, the Ohm law, the charge conservation, and takes into account the passive current. The main results include the limited extent of the cell along the crack, depending on the values of the parameters, and non-linear and coupled effects for the occurrence and amplitude of the dissolution with as critical parameters the composition of the electrolyte, the exchange current densities and the anode dimensions.     

3-D tomography by automated in situ block face ultramicrotome imaging using an FEG-SEM to study complex corrosion protective paint coatings

Aircraft coatings are generally multi-layered with both barrier properties and are corrosion inhibitor filled to prevent corrosion. A new technique, automated in situ block face ultramicrotome imaging using an FEG-SEM has been employed for high resolution 3-D imaging of such aircraft coatings. A pristine and a cracked aged coating were visualised by this method clearly showing the coatings microstructure and subsequent crack growth properties. Filler particles were segmented and labelled allowing the coating to be more clearly visualised and enabling statistical particle analysis and meshing. Finally the method was used to investigate the inhibitor leaching properties of four aircraft primers.     

The effect of temperature on the corrosion of steel in concrete. Part 2: Model verification and parametric study

A comprehensive model for predicting the corrosion rate of steel in concrete has been developed using the concept of simulated polarization resistance experiments. This model is developed by carrying out a nonlinear regression analysis on data obtained from numerical experiments that are based on the solution of Laplace’s equation in a domain determined by the polarized length of the rebar. This part of the paper provides a comprehensive verification of the developed model and illustrates the application of the model to investigate the coupled effects of parameters affecting corrosion of steel in concrete. The results of the verification study show that the model predictions are in good agreement with the experimental data.     

Determination of corrosion rate of reinforcement with a modulated guard ring electrode; analysis of errors due to lateral current distribution

The main source of errors in measuring the corrosion rate of rebars on site is a non-uniform current distribution between the small counter electrode (CE) on the concrete surface and the large rebar network. Guard ring electrodes (GEs) are used in an attempt to confine the excitation current within a defined area. In order to better understand the functioning of modulated guard ring electrode and to assess its effectiveness in eliminating errors due to lateral spread of current signal from the small CE, measurements of the polarisation resistance performed on a concrete beam have been numerically simulated. Effect of parameters such as rebar corrosion activity, concrete resistivity, concrete cover depth and size of the corroding area on errors in the estimation of polarisation resistance of a single rebar has been examined. The results indicate that modulated GE arrangement fails to confine the lateral spread of the CE current within a constant area. Using the constant diameter of confinement for the calculation of corrosion rate may lead to serious errors when test conditions change. When high corrosion activity of rebar and/or local corrosion occur, the use of the modulated GE confinement may lead to significant underestimation of the corrosion rate.     

Vacancy mechanism of oxygen diffusivity in bcc Fe: A first-principles study

Diffusivity of interstitial oxygen (O) in bcc iron (Fe) with and without the effect of vacancy has been investigated in terms of first-principles calculations within the framework of transition state theory. Examination of migration pathway and phonon results indicates that O in octahedral interstice is always energetically favorable (minimum energy) with and without vacancy. It is found that vacancy possesses an extremely high affinity for O in bcc Fe, increasing dramatically the energy barrier (∼80%) for O migration, and in turn, making the predicted diffusion coefficient of O in bcc Fe in favorable accord with experiments.     

Early stages of oxidation observed by in situ thermogravimetry in low pressure atmospheres

A highly sensitive set-up for in situ mass-gain measurements during high temperature reaction is presented. By removing the inert gas components of a corrosive atmosphere and keeping the flows and partial pressures of the reactive species constant, the experiment is preformed in a low-pressure environment. A better signal-to-noise ratio which increases sensitivity down to 10 μg/cm² is achieved. The random behaviour of the mass-gain signal, caused by turbulences in the gas stream, could be reduced by a factor of 10.Compared to theoretical simulations, the mass-change during oxidation in binary iron-based model alloys is slower than expected from pure bulk diffusion behaviour.     

A first-principles study of the diffusion of atomic oxygen in nickel

In this study, the coefficients of diffusion of oxygen in nickel-based alloys are determined by atomistically modeling the oxygen diffusion process using a vacancy-mediated diffusion model. Density functional theory is used to calculate the energy of the system. The activation barrier energy for the diffusion of atomic oxygen in nickel is quantified by determining the most favorable path, i.e., the minimum-energy path, for diffusion. Phonon analysis is performed using the direct force-constant method. The calculated pre-exponential factor for the lattice diffusion of oxygen in nickel is 5.45 × 10⁻⁷ m²/s and the activation energy is 158.65 kJ/mol.