Stochastic approach to pitting-corrosion-extreme modelling in low-carbon steel

A stochastic model previously developed by the authors using Markov chains has been improved in the light of new experimental evidence. The new model has been successfully applied to reproduce the time evolution of extreme pitting corrosion depths in low-carbon steel. The model is shown to provide a better physical understanding of the pitting process.     

New insight into the pit-to-crack transition from finite element analysis of the stress and strain distribution around a corrosion pit

A finite element (FE) analysis has been undertaken to evaluate the stress and strain distribution associated with a single corrosion pit in a cylindrical steel specimen stressed remotely in tension. A key observation was the localisation of plastic strain to the pit walls (just below the surface of the specimen). Simulation of a growing pit in a static stress field indicated corresponding plastic strain rates that were commensurate with values associated with stress corrosion cracking. This observation introduces a wholly new concept in understanding of the evolution of stress corrosion cracks from pits and correlates with recent X-ray tomography measurements.     

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.     

Stochastic modeling of pitting corrosion: A new model for initiation and growth of multiple corrosion pits

In this work, a new stochastic model capable of simulating pitting corrosion is developed and validated. Pitting corrosion is modeled as the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time for pit initiation is simulated as the realization of a Weibull process. In this way, the exponential and Weibull distributions can be considered as the possible distributions for pit initiation time. Pit growth is simulated using a nonhomogeneous Markov process. Extreme value statistics is used to find the distribution of maximum pit depths resulting from the combination of the initiation and growth processes for multiple pits. The proposed model is validated using several published experiments on pitting corrosion. It is capable of reproducing the experimental observations with higher quality than the stochastic models available in the literature for pitting corrosion.     

Throwing power of cathodic prevention applied by means of sacrificial anodes to partially submerged marine reinforced concrete piles: Results of numerical simulations

The paper deals with the determination of current and potential distribution in reinforced concrete elements partially submerged in seawater aimed at predicting the throwing power of cathodic prevention applied by means of sacrificial anodes. Experimental results from previous laboratory tests showed that the throwing power of cathodic prevention is higher compared to that of cathodic protection [1]. In order to extend the results obtained on small-scale specimens to elements of higher dimensions, FEM numerical simulations of potential distribution were carried out. Several cases were considered, representative of conditions differing in electrochemical behaviour of steel bars, geometry of the pile and of sacrificial anodes, concrete resistivity. The results allowed to discuss the role of different factors on the throwing power that can be reached by using sacrificial anodes immersed in the seawater to protect reinforcing steel bars in the emerged part of a pile.     

A generic statistical methodology to predict the maximum pit depth of a localized corrosion process

This paper outlines a new methodology to predict accurately the maximum pit depth related to a localized corrosion process. It combines two statistical methods: the Generalized Lambda Distribution (GLD), to determine a model of distribution fitting with the experimental frequency distribution of depths, and the Computer Based Bootstrap Method (CBBM), to generate simulated distributions equivalent to the experimental one. In comparison with conventionally established statistical methods that are restricted to the use of inferred distributions constrained by specific mathematical assumptions, the major advantage of the methodology presented in this paper is that both the GLD and the CBBM enable a statistical treatment of the experimental data without making any preconceived choice neither on the unknown theoretical parent underlying distribution of pit depth which characterizes the global corrosion phenomenon nor on the unknown associated theoretical extreme value distribution which characterizes the deepest pits.Considering an experimental distribution of depths of pits produced on an aluminium sample, estimations of maximum pit depth using a GLD model are compared to similar estimations based on usual Gumbel and Generalized Extreme Value (GEV) methods proposed in the corrosion engineering literature. The GLD approach is shown having smaller bias and dispersion in the estimation of the maximum pit depth than the Gumbel approach both for its realization and mean. This leads to comparing the GLD approach to the GEV one. The former is shown to be relevant and its advantages are discussed compared to previous methods.     

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.     

Numerical simulation of a single corrosion pit in CO2 and acetic acid environments

The present paper bears on a numerical model of steady-state behaviour of a single corrosion pit in CO₂-containing media in the presence of acetic acid. The kinetics of electrochemical reactions occurring on the electrode surface is described by Tafel equations fitted to experimental data obtained on API 5L X65 pipeline steel. Simulation results provide an interesting insight into both the chemistry and electrochemistry inside the active pit. Particular attention is paid to the effect of HAc on the coupling behaviour between the attack base and the outer surrounding surface and to the comparison with experimental data obtained in similar conditions.     

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.     

Corrosion rate prediction of 3C steel under different seawater environment by using support vector regression

The support vector regression (SVR) approach combined with particle swarm optimization (PSO) for its parameter optimization is proposed to establish a model for prediction of the corrosion rate of 3C steel under five different seawater environment factors, including temperature, dissolved oxygen, salinity, pH value and oxidation-reduction potential. The prediction results strongly support that the generalization ability of SVR model consistently surpasses that of back-propagation neural network (BPNN) by applying identical training and test samples. The absolute percentage error (APE) of 80.43% test samples out of 46 samples does not exceed 1% such that the best prediction result was provided by leave-one-out cross validation (LOOCV) test of SVR. These suggest that SVR may be a promising and practical methodology to conduct a real-time corrosion tracking of steel surrounded by complicated and changeable seawater.     

Pitting corrosion in low carbon steel influenced by remanent magnetization

A new type of experiment is performed using a closed magnetic circuit configuration in order to study the influence of the magnetic field on pitting corrosion in low carbon pipeline steel. The statistical assessment of the pitting corrosion data shows that the magnetic field in the material under test reduces the extreme pit depths and also the average depth of the pit population. It is proposed that reduction in pit depth under the influence of remanent magnetization can be explained based on the behavior of the paramagnetic corrosion products under the influence of the magnetic field gradient produced inside pits.     

Spatial statistics of pitting corrosion patterning: Quadrat counts and the non-homogeneous Poisson process

This paper presents a stochastic analysis of spatial point patterns as effect of localized pitting corrosion. The Quadrat Counts method is studied with two empirical pit patterns. The results are dependent on the quadrat size and bias is introduced when empty quadrats are accounted for the analysis. The spatially inhomogeneous Poisson process is used to improve the performance of the Quadrat Counts method. The latter combines Quadrat Counts with distance-based statistics in the analysis of pit patterns. The Inter-Event and the Nearest-Neighbour statistics are here implemented in order to compare their results. Further, the treatment of patterns in irregular domains is discussed.     

Modelling sea-salt transport and deposition in marine atmosphere zone - A tool for corrosion studies

Atmospheric corrosion of metals and corrosion of reinforcements in concrete structures are influenced by salt concentration of marine aerosol inland. This work presents a model that represents marine aerosol behaviour in marine atmosphere zone. The model has the distance from the sea and wind speed as the major variables and takes into account changes in marine aerosol due to settlement of salts when being transported inland. The proposed equations M=M₀e^{(vdep₀/αh)[e(-αx/v)-1]}, D=D₀e^{(vdep₀/αh)[e(-αx/v)-1]} show good consistency with literature data and well represent the results obtained. This model can be a useful tool to indicate the salinity level expected at different distances from sea in marine atmosphere zone.     

Chloride threshold level for corrosion of steel in concrete

The steel rebar inside reinforce concrete structures is susceptible to corrosion when permeation of chloride from deicing salts or seawater results in the chloride content at the surface of the steel exceeding a chloride threshold level (CTL). The CTL is an important influence on the service life of concrete structures exposed to chloride environments. The present study discusses the state of art on the CTL for steel corrosion in concrete, concerning its measurement, representation, influencing factors and methods to enhance the CTL. As the CTL values reported in the majority of previous studies were varied with experimental conditions, corrosion initiation assessment method, the way in which the CTL was represented, direct comparison between the results from different sets and evaluation was subjected to the difficulty. As a result, total chloride by weight of cement or the ratio of [Cl⁻]:[H⁺] is the best presentation of CTL in that these include the aggressiveness of chlorides (i.e. free and bound chlorides) and inhibitive nature of cement matrix. The key factor on CTL was found to be a physical condition of the steel-concrete interface, in terms of entrapped air void content, which is more dominant in CTL rather than chloride binding, buffering capacity of cement matrix or binders. The measures to raise the CTL values using corrosion inhibitor, coating of steel, and electrochemical treatment are also studied.     

Hydrogen evolution in aqueous solutions containing dissolved CO2: Quantitative contribution of the buffering effect

The hydrogen evolution reaction (HER) occurring on steel in an oxygen-free aqueous solution containing dissolved CO₂ was investigated. This reaction was modelled by taking into account the two dissociation reactions of dissolved CO₂. The mathematical problem was solved numerically using a finite element method (FEM). A fair agreement between the measurements performed on a steel rotating disc electrode and the theoretical calculations was obtained. Thus, the cathodic behaviour of steel in CO₂-containing solutions can be fully explained by the buffering effect induced by the presence of CO₂. Some interfacial pH measurements performed on a gold electrode also support this conclusion.