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.     

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.     

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.     

Modeling pitting corrosion by means of a 3D discrete stochastic model

Pitting corrosion is difficult to detect, predict and design against. Modeling and simulation can help to increase the knowledge on this phenomenon as well as to make predictions on the initiation and progression of it. A cellular automaton based model describing pitting corrosion is developed based on the main mechanisms behind this phenomenon. Further, a sensitivity analysis is performed in order to get a better insight in the model, after which the information gained from this analysis is employed to estimate the model parameters by means of experimental time series for a metal electrode in contact with different chloride concentrations.     

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.     

Probabilistic analysis of pipelines with corrosion defects by using FITNET FFS procedure

A probabilistic method based on the corrosion module of the FITNET FFS procedure is presented to perform the structural integrity analysis for pipelines. The comparison of the failure pressure determined by both deterministic and probabilistic methods shows that even for a high safety factor, the deterministic method may predict nonconservative results. FITNET FFS procedure predicts a similar probability to that given by the Shell-92 model. The sensitivity analysis of both the uncertainty of the variables and the underlying model shows that the corrosion depth has the most significant contribution to the pipeline failure at an inspection interval of 8 years.     

Use of a 3D optical measurement technique for stochastic corrosion pattern analysis of reinforcing bars subjected to accelerated corrosion

The 3D corrosion patterns of 23 reinforcing bars subjected to accelerated corrosion are characterised using an optical surface measurement technique. A stochastic signal processing methodology is employed for corrosion pattern analysis of the measured data. The statistical analysis of corrosion pattern data shows that a lognormal distribution model can represent the non-uniform distribution of pitted sections along the corroded bars. It was observed that the frequency of corrosion is independent from the mass loss ratio and the length of the bars. Finally, a set of probabilistic distribution models for the geometrical properties of corroded bars is developed.     

3D Numerical modelling of steel corrosion in concrete structures

The paper deals with a 3D numerical model for transient analysis of processes after depassivation of reinforcement in concrete, which are relevant for calculation of corrosion rate. The aim of the study is to investigate the influence of the concrete quality, cracking and water saturation in concrete on the current density. The results show that the corrosion rate is higher in poor quality concrete than in good quality concrete. The model predicts that cracks do not influence corrosion rate for the case where the only influence of the crack is on the rate at which oxygen can reach the steel.     

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.     

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.     

A model to predict the evolution of pitting corrosion and the pit-to-crack transition incorporating statistically distributed input parameters

A model based on deterministic equations with statistically distributed input parameters has been developed for simulating the evolution of the pit depth distribution at different exposure times and the percentage of pits that transform to stress corrosion cracks. The model has been applied to the specific case of steam turbine disc steel exposed to a range of environments under applied stress. With preliminary fitting at one exposure time, the simulation not only reflects the trends in the experimental measurement but also the model, uniquely, reproduces the statistical variability or “noise” associated with the measurements.     

Employing electrochemical frequency modulation for pitting corrosion

By using the electrochemical frequency modulation (EFM) technique, the non-linear behavior of a corroding system is measured. This non-linear behavior is likely to be different for a system undergoing uniform or pitting corrosion. The implementation of the EFM technique to detect pitting corrosion has been investigated by observing the fluctuations in the so-called causality factors. These causality factors, resulting from an EFM test and in the ideal case having values of 2 and 3, respectively, are normally used for quality and data validation purposes. While investigating pitting corrosion, they show different behavior leading to the CPT (critical pitting temperature) detection.     

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.     

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.     

Multifractal modelling of electrochemical noise in corrosion of carbon steel

Electrochemical noise analysis of corroding surfaces provides useful information regarding the temporal changes in material degradation, corrosion mechanisms and condition monitoring. In this study, we analyzed the electrochemical potential and current noise originating from the corrosion of carbon steel (ASTM A106) in distilled water using multifractal analysis. The empirical Legendre spectrum and large deviation singularity spectrum are determined for the electrochemical noise at different stages of corrosion. A wavelet-based multifractal model is introduced to describe the multiscaling behaviour.     

The initial stage of pitting corrosion on coated steels investigated by photon rupture in chloride containing solutions

A photon rupture method, film removal by a focused pulse of pulsed Nd-YAG laser beam irradiation, has been developed to enable oxide film stripping at extremely high rates without contamination from the film removal tools. In the present study, Zn-55mass%Al alloy and Al-9mass%Si alloy-coated steel specimens covered with protective nitrocellulose film were irradiated with a focused pulse of a pulsed Nd-YAG laser beam at a constant potential in 0.5 kmol m⁻³ H₃BO₃-0.05 kmol m⁻³ Na₂B₄O₇ (pH = 7.4) with 0.01 kmol m⁻³ of chloride ions to investigate the initial stage of localized corrosion. At low potentials, oxide films on both coated alloys were reformed after the nitrocellulose films were removed by this method. The oxide film formation kinetics follows an inverse logarithmic law, in agreement with Cabrera-Mott theory. However, at high potentials, localized corrosion producing corrosion products occurs at the area where nitrocellulose film was removed. Nevertheless, when the applied potential is less noble, the dissolution current of the Zn-55mass%Al-coated steel samples is higher than that of Al-9mass%Si-coated samples.     

Stable pitting corrosion of stainless steel as diffusion-controlled dissolution process with a sharp moving electrode boundary

This paper is devoted to explanation and prediction of pit propagation or stable pit growth, governed by ion transport properties in electrolytic solutions. Therefore, we vigorously derive the (3D) mass conservation law for a body hosting a sharp metal/solution interface separating the solid electrode from liquid electrolyte. The model for stable pitting corrosion is completed by Fick’s law of diffusion, governing the behavior of the dissolved metal ions. There are only three model input values, which are directly accessible from experiments, namely the ion concentration in the solid metal, as well as the diffusion coefficient and the saturation concentration of the dissolved metal ions in the electrolyte. The partial differential equations describing stable pitting corrosion as diffusion-controlled dissolution process are solved for boundary conditions related to 1D pencil electrode tests as well as to 2D foil electrode tests. The mathematical solution functions (model predictions) are related to pit growth in terms of depth and width, and to electric current evolution. Such model predictions reasonably agree with corresponding experiments, which shows the relevance of the proposed approach. In the case of pits with lacy covers, the boundary conditions for the ionic flux probably depend on complex depassivation-repassivation phenomena. However, once the extent of perforation of the lacy cover is known, the entire pit propagation characteristics, in particular the pit shape, can be predicted by the proposed model, relating to a classical Stefan problem.     

Effect of microcrystallization on pitting corrosion of pure aluminium

A microcrystalline aluminium film with grain size of about 400 nm was prepared by magnetron sputtering technique. Its corrosion behaviour was investigated in NaCl containing acidic solution by means of potentiodynamic polarization curves and electrochemical noise (EN). The polarization results indicated that the corrosion potential of the sample shifted towards more positive direction, while its corrosion current density decreased compared with that of pure coarse-grain Al. The EN analysis based on stochastic model demonstrated that there existed two kinds of effect of microcrystallization on the pitting behaviour of pure aluminium: (1) the rate of pit initiation is accelerated, (2) the pit growth process was impeded. This leads to the enhancement of pitting resistance for the microcrystallized aluminium.     

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.     

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.