Crack growth model for pipelines exposed to concentrated carbonate–bicarbonate solution with high pH

doi:10.1016/j.corsci.2010.08.023

Corrosion Science

Volume 52, Issue 12, December 2010, Pages 4064-4072

https://doi.org/10.1016/j.corsci.2010.08.023 Get rights and content

Abstract

The crack tip strain rate (CTSR) and the dissolution/repassivation kinetics are the parameters controlling high pH SCC of pipeline steels because the repeated film rupture is the dominative mechanism. The CTSR is mainly produced by the crack tip advance and cyclic load. Theoretical expressions of the CTSR are given to account on these factors. After the anodic current density determined from a polarization curve measured with a potential scanning velocity 1 V/min and the repassivation kinetic exponent obtained by the strained electrode method are utilized, the crack growth model proposed gives a reasonably good prediction to the crack velocity experimentally observed. A numeric simulation in a 0.5 M carbonate + 0.5 M bicarbonate solution indicates that the effect of mass transfer within crack on the crack growth is negligible when the crack velocity is below 10⁻⁹ m/s. Various factors affecting the SCC are discussed.

Research highlights

► Corrected the mistake in applying Shoji’s equation in crack tip strain rate estimation and proposed a new one to estimate the crack tip strain rate produced by crack tip advance. ► Proposed the equation for estimation of crack tip strain rate produced by the cyclic loads due to the internal pipe pressure fluctuations. ► Built a physical model for crack growth of pipeline steel in concentrated carbonate–bicarbonate solution with high pH in accordance with the crack tip strain rate equation, anodic dissolution/repassivation kinetic parameters determined by experiments. The comparison with the existing experimental data indicated that the new model can provide a reasonably good prediction on the various factors on the high pH SCC of pipelines.

Section snippets

SCC mechanism of pipeline steel in concentrated carbonate–bicarbonate solution

The intergranular stress corrosion cracking (SCC) occurs on the external pipe surface exposed to concentrated carbonate–bicarbonate solutions with high pH. It is widely accepted that the crack growth is dominated by the repeated rupture of passive film at crack tip [1], [2]. The film rupture or slip-dissolution model has been proposed more than half century [2], [3], [4], [5], [6]. Theoretically, the average crack velocity produced by the film rupture mechanism can be formulated by Faraday’s

Local strain rate at crack tip

In the present study, pipelines are assumed to be under small scale yield condition, i.e., the local stress/strain is K-dominated. When tensile load is applied, a plastic zone will form at crack tip. If the time-dependent plastic strain is not considered, the local strain within the plastic zone is given by $ε_{ct} = ε_{ct} (r, K)$ where r is the distance from the crack tip. The local strain rate at the crack tip will be [10] ${\dot{ε}}_{ct} = (\frac{\partial ε_{ct}}{\partial K}) \dot{K} + (\frac{\partial ε_{ct}}{\partial r}) \dot{r} = (\frac{\partial ε_{ct}}{\partial K}) \dot{K} - (\frac{\partial ε_{ct}}{\partial r}) \dot{a} = {\dot{ε}}_{\dot{K}} + {\dot{ε}}_{\dot{a}}$ $\dot{r} \equiv - \dot{a}$ by definition and $\dot{a}$ is the

Crack growth model

Inserting Eq. (21) into Eq. (3), we have, $\dot{a} \approx A {\dot{ε}}_{ct}^{n} = A \{\frac{\dot{a}}{r_{0}} \frac{2 N}{N - 1} \frac{β σ_{y}}{E} {[In (\frac{K_{\max}^{2} - K_{ISCC}^{2}}{3 π r_{0} σ_{y}^{2}})]}^{\frac{N + 1}{N - 1}} + f ε_{0} (1 - R_{σ})^{2} (K_{\max}^{2} - K_{ISCC}^{2})\}$ Eq. (22) is expression of crack velocity dominated by the film rupture mechanism. To check the applicability of Eq. (22), the numeric simulation program originally developed by Song [7] was employed. In the present simulation, the following modifications were made.

(1)
The surface except at the crack tip was assumed to be under the passive condition and the passive current density was

Various factors affecting on SCC

In light of the mathematic model of SCC described in the previous section, three groups of parameters are involved in the crack velocity prediction:

(1)
the mechanical properties and microstructural characteristics of steels that affect the CTSR, including Young’s modulus E, the yield strength σ_y, the strain-hardening exponent N (or N∗), the specific length r₀ and the coefficient β and ε₀;
(2)
the parameters to characterize the external loads, such as the maximum stress σ_max, the stress intensity factor K

Summary

A predictive model is proposed for the crack growth of pipelines exposed to the concentrated carbonate–bicarbonate solution based on the following assumptions.

(1)
The crack growth is dominated by the repeated film rupture at the crack tip.
(2)
The crack tip strain rate due to crack advance can be estimated by Eq. (15), (16).
(3)
The crack tip strain rate induced by the cyclic load is dominated by the alternative crack tip opening displacement.
(4)
The anodic dissolution rate over the bare metal surface produced

Acknowledgements

The project was conducted under DOT Contract DTPH 56-08-T-000001. James Merritt of PHMSA/DOT provided management oversight for the project. This work is co-sponsored by CANMET Materials Laboratory of the Natural Resources of Canada (Winston Revie), Williams Pipeline Company (Sergio Limon), and TransCanada Pipeline Company (Richard Kania and Robert Worthingham) for their support. The project also benefited from the input of Dr. Raymond R. Fessler of BIZTEK Consulting Inc. earlier in this program.

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Crack growth model for pipelines exposed to concentrated carbonate–bicarbonate solution with high pH

Abstract

Research highlights

Section snippets

SCC mechanism of pipeline steel in concentrated carbonate–bicarbonate solution

Local strain rate at crack tip

Crack growth model

Various factors affecting on SCC

Summary

Acknowledgements

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J. Mech. Phys. Solids

J. Mech. Phys. Solids

J. Mech. Phys. Solids

Corros. Sci.

Corros. Sci.

Corros. Sci.

Eng. Fract. Mech.

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J. Electrochem. Soc.

Prediction and experimental verification of the slip-dissolution model for stress corrosion cracking of low strength alloys

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