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.     

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.     

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.     

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.     

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.     

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.     

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.     

In situ synchrotron X-ray micro-tomography study of pitting corrosion in stainless steel

Pitting corrosion of stainless steel has been investigated with high-resolution in situ X-ray microtomography. The growth of pits at the tip of stainless steel pins has been observed with 3D microtomography under different conditions of applied current and cell potential. The results demonstrate how pits evolve in stainless steel, forming a characteristic “lacy” cover of perforated metal. In addition, it is shown how the shape of pits becomes modified by MnS inclusions.     

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.     

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.     

Pit to crack transition in stress corrosion cracking of a steam turbine disc steel

Long term exposure tests have been carried out on a 3 NiCrMoV steam turbine disc steel in the form of cylindrical tensile test specimens self-loaded to 90% of σ_0.2 and exposed to three environmental conditions, viz. deaerated pure water, aerated pure water, and aerated water containing 1.5 ppm of chloride ion. Pitting occurred in all environments but the density and depth of pits in the chloride-containing medium was markedly greater. No cracking was observed in deaerated pure water but cracks initiated in aerated water between 13 and 19 months and in less than 7 months in aerated 1.5 ppm Cl⁻ solution. The probability of a crack initiating from a pit of specific depth in aerated solution could be described well by a Weibull function. Profiling of pits and cracks in the disc steel tested in aerated 1.5 ppm Cl⁻ solution showed that there while there were many cracks with a depth greater than that of the corresponding pit the depth of some cracks was smaller than that of the corresponding pit, suggesting that cracks do not necessarily initiate from the bottom of the pits. The growth rate of short cracks emerging from pits appeared greater than that of long cracks in fracture mechanics specimens.     

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.     

A theoretical study of some hydroxamic acids as corrosion inhibitors for carbon steel

The corrosion inhibition characteristics of two hydroxamic acids, i.e., oxalyl-dihydroxamic acid (C2) and pimeloyl-1,5-di-hydroxamic acid (C7), on carbon steel has been studied using density functional theory (DFT). Quantum chemical parameters such as highest occupied molecular orbital energy (E_HOMO), lowest unoccupied molecular orbital energy (E_LUMO), and energy gap (ΔE) have been calculated using B3LYP/6-31 + G∗∗ basis set. The relationship between the inhibition efficiency and quantum chemical parameters has been discussed in order to elucidate the inhibition mechanism of these compounds.     

Pitting corrosion in pipeline steel weld zones

Steel pipelines externally exposed to seawater pit more severely in heat-affected weld zones but longer-term quantitative data are scarce. Maximum pit depths and variability are reported for the longitudinal weld in API X56 Spec 5 L grade steel pipeline samples exposed continuously to natural Pacific Ocean seawater for 3.5 years. For the first year maximum pit depths and pit depth variability for the different weld zones were very similar. Both became much greater subsequently, with the greatest increases for the heat affected zone. This is compared with steel composition and grain size and potential reasons for the observations discussed.     

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.     

Electrochemical corrosion and impedance study of SAE1045 steel under gel-like environment

To present simulative study on corrosion of metal by sewage sludge, three kinds of gel-like systems based on SiO₂ gel and polyacrylamide gel are proposed. Comparative results of electrochemical polarization and impedance studies together with coupon test of SAE1045 steel under these gel-like surroundings and deionized water are investigated. Obvious pitting corrosion characteristic of the steel can be seen in gel-like systems with decreasing I_corr and more negative value of E_corr. It is considered to be caused by electric field concentration effect at defected sites in covering layer on the surface of the steel formed by gel particles.     

Microstructure and pitting corrosion resistance of annealed duplex stainless steel

The transition from metastable to stable pitting was studied in 0.5 M NaCl water solution for two cast duplex stainless steels under different microstructural conditions achieved by annealing in the range from 900 °C to 1200 °C. The ensuing microstructural changes in heat treated steels were defined and correlated with established pitting potentials (E_p) and sites of corrosion damage initiation. The variations in E_p have been discussed in terms of secondary phases precipitation. The critical condition for pit stability was quantified and used to select an appropriate microstructural state, resulting in the higher potential at which stable pit growth is first observed.