Stress Corrosion Cracking (SCC) process through which cracks occur in a variety of susceptible materials is a result of a combination of residual or applied stresses and corrosion. In oil and gas field, buried pipeline steels are made of low-alloy steels with a ferritic-pearlitic structure, such as X70. In dilute solutions, these materials are prone to SCC failure. The Near-neutral simulated soil solution (NS4) solution is established to imitate SCC conditions and subsequently became the industry requirement for crack growth experiments in the majority of laboratories. The strain-assisted active crack pathways are considered while modelling SCC growth as an oxide film rupture and anodic dissolution process. It’s been hypothesized that increasing the strain concentration can help with dissolution at the film-free crack tip. This research focuses on estimating the SCC crack growth rate under various environmental conditions in oil and gas pipelines using finite element modelling. The simulation is carried out using the J-integral theory in the COMSOL Multiphysics program. Simulations are performed to model the crack growth rate (CGR) using slip anodic dissolution (film rupture) mechanism. The plastic strain gradient is required to compute the SCC CGR (da/dt). Because the plastic strain located at crack tip increases proportionally to the crack length as it propagates, the CGR increases as the stress intensity factor (SIF) increases. The crack growth rates increase when constant loads are applied and as the temperature rises, and elevating the cathodic potential has a minimal influence on the propagation rate of cracks but raises the material yield strength and imparts brittle behavior to it.

In stress corrosion cracking, cracking occurs due to a combination of applied or residual stresses and corrosion in a variety of susceptible materials. SCC has the potential to cause catastrophic failure in a large variation of engineering components and applications, including petrochemical pipelines and mechanical components operating in submerged environments [

In EAC, the hydrogen-induced cracking (HIC) or slip-dissolution processes have often been deemed constructed based hypotheses [

The film rupture/anodic dissolution approach, sometimes described to as the slip-dissolution mechanism, grown from a number of theories that explored strain-assisted active crack patterns. The strain concentration has been proposed as a method of enhancing dissolving at the film-free fracture tip. Crack propagating arises because of oxide rupture at the crack tip due to increased strain in the surrounding matrix or as a result of the appearance of slip steps in the slip-dissolution model [

SCC growth, according to Ford [_{a} is the oxidation rate, _{0}: oxidation current density, t_{0}: time prior to the current decays, and

Due to the difficulty of determining the strain rate near the tip, the strain, _{0}, ahead of the crack tip [

When the tip is positioned at the characteristic length r_{0} at the vicinity of the crack tip, the change in tensile plastic strain along with crack propagation is represented by the expression

Elastic plastic finite element method (EPFEM) gives a practical method to determine

As shown in _{i} to a_{i + 1}, the plastic strains _{0} may be determined from finite element modeling, and therefore,

After substituting

Elastoplastic and elastic analyses can both benefit from the use of the J-integral technique. The value of the J-integral in the case of elasticity may be proven to be corresponding to the strain energy release rate (G) and associated to the stress intensity factor (K) [_{s} is the density of the strain energy, σ represents the stress tensor, and m indicates the external normal of the integration contour Γ. For the purposes of _{tot} = Γ U Γ_{face}, which might be any closed route around the crack tip (see

The stress intensity factor K_{I} Crack opening, or mode I may be calculated using the J-integral [_{eff} is an functional Young’s modulus that reflects the crack front’s stress condition, and β is the coefficient that accounts for the mode mixture.

During the corrosion process the electrons are liberated Because of metal dissolution on the anodic site. These electrons are sent to the cathode, which reduces oxygenized water to hydrogen ions. During metal corrosion, the following reactions take place [

The local surface concentrations of reactive species and the local electrode potential determine the kinetics of electrochemical reactions. Except at the tip, where the kinetics are contingent on the oxide film rupture frequency and the local electrode potential, it is assumed that a constant anodic passive current density, i_{p}, flows everywhere across the interface [

The API 5L X70 and X60 steel are employed in the oil and gas pipeline sector due to their high strength-to-weight ratio, high fracture toughness, and most importantly, their high yield strength. API X70 chemical composition are in

Mn | Cu | Cr | Ni | Si | Nb | Al | C | P | Ti | V | S | Fe |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1.48 | 0.29 | 0.27 | 0.16 | 0.13 | 0.10 | 0.033 | 0.031 | 0.012 | 0.012 | 0.004 | 0.002 | Balanced |

In all of the electrochemical studies, the corrosive environment was a virtual soil solution (named NS4) with a pH equals to three [

KCI | NaHCO_{3} |
MgSO_{4}.7H_{2}O |
CaCl_{2}. 2H_{2}O |
---|---|---|---|

0.122 | 0.483 | 0.131 | 0.181 |

The Elastic Properties of the API X70 steel under soil Solution (NS4) are indicated in

Material name | Modulus of elasticity (GPa) | Poisson’s ratio | Yield stress (MPa) | Density (kg/m^{3}) |
---|---|---|---|---|

X70 Steel | 205 | 0.28 | 600 | 7850 |

To determine the mechanical characteristics of the X70 steel in a soil environment (NS4), Slow strain rate test (SSRT) was done on smooth cylindrical tensile specimens in air and a synthetic soil solution at an applied strain rate equals to 10^{−6} 1/s (NS4 solution) using a Mobile Constant Extension Rate Tests (MCERT) machine. Cathodic potential may have an effect on the mechanism of SCC cracking and on the susceptibility of steels to SCC, as it alters the concentration of hydrogen in the solution. According to Galván-martínez SCC tests with SSRT were conducted at corrosion potential equals to −0.650 V

The Ramberg–Osgood relationship can be used to express the real stress-strain curve of API X70 steel. The Ramberg-Osgood model describes the nonlinear behavior of a steel pipeline.
_{0} indicates the material’s yield strength, ε_{0} represents the material’s yield strain, respectively, α is the material’s yield offset coefficient, and the material’s exponent of the strain hardening is represented as n [

The simulation was done using COMSOL Multiphysics® (solid mechanics model) software [

The crack is defined in COMSOL as 3 j-integral contours. The first few contours may be erroneous if the first contour integral is generated by defining the nodes at the crack tip. Additional contours are sought to evaluate the accuracy of these contours and estimate the value of the contour integral, which tends to be relatively constant from one contour to the next. So, the j-integral values after the third contour remain the same, and their size are depending on the crack size as shown in

To define the change in temperature a multiphysics analysis of the solid mechanics and heat transfer analysis is assumed to define the thermal properties and thermal boundary conditions, the values of the temperature are, 25^{o}C, 50^{o}C, 90^{o}C. A stationary solver with parametric sweep analysis was done for different crack lengths from 10 to 15 mm, and a 0.1 mm difference at each run, this technique assumes the crack is propagating from 10--15 mm.

To obtain the SCC crack propagation rate (da/dt), the plastic strain gradient is required according to ^{o}C. The normal plastic strain increases from 6e-04 to 2e-03 with the crack length, so it is raising while the crack is propagating.

Parameters | Values |
---|---|

Atomic mass, M (g/mole) | 55.6 |

Faraday’s constant | 96500 |

Oxide film rupture strain, |
0.0025 |

Number of oxidation charge change, Z | 2.67 |

Exchange current density of oxidation, i0(A/mm^{2}) |
0.00015 |

The exponential of current decay, m | 0.4 |

The temperature in UAE is varying within the year, so it is important to consider the temperature as a factor that is affecting the SCC crack growth rate. The temperatures 25^{o}C, 60^{o}C, and 100^{o}C are applied on the crack boundaries. ^{o}C, 60^{o}C, 100^{o}C. It’s obvious from ^{o}C, and for 100^{o}C the crack growth rate increase from 2.8E-09 to 5.0E-09. The crack growth rate was same initially for both temperatures 25^{o}C and 60^{o}C, but the difference has increase with the crack length increases.

The corrosion potential values are taken from an experiment done by [

While the current study examines only SCC crack growth under static loading, future work under dynamic loading, such as in slow strain rate testing SSRT, may be beneficial. Another possibility is to combine two distinct types of loading, such as static and fatigue, which will be the focus of future work.

This article proposes a new technique for modeling the crack growth rate and examining the various factors that affect it using COMSOL Multiphysics finite elements. The plastic strain gradient is required to calculate the rate of SCC crack growth da/dt. The normal plastic strain increases proportionally to the length of the crack; thus, as the crack propagates, it increases in length. The J-integral rises exponentially with the crack length. This J-integral result explains why the normal plastic strain increases in proportion to the length of the crack. The CGR increases as the SIF value increases. As a result, the growing rate of the crack increases as it propagates, as does the stress intensity factor. As constant loads are applied and the temperature rises, the crack growth rates accelerate. Raising the cathodic potential has a minimal influence on the rate of crack propagation, but it increases the yield strength and causes the material brittle. Both applied load and temperature have an approximately equal effect on the crack growth rate, with applied load having the greatest effect at lower values and temperature having the greatest effect at higher values.