Steady-state growth of an interfacial crack by corrosion

The Wiener–Hopf technique is used to obtain a 2D steady-state solution for the progressive conversion of a pristine interface into a corroded interface between two dissimilar solids. The interface is of infinite extent, and comprises a semi-infinite pristine portion and a semi-infinite corroded port...

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Bibliographic Details
Published in:Journal of the mechanics and physics of solids 2021-03, Vol.148, p.104268, Article 104268
Main Authors: Fleck, N.A., Willis, J.R.
Format: Article
Language:English
Subjects:
Asymptotic methods
Chemical reactions
Corrosion
Corrosion products
Crack propagation
Diffusion
Diffusion theory
Fourier transforms
Front velocity
Half spaces
Interfacial cracks
Interfacial fracture
Scaling laws
Steady state
Wiener–Hopf technique
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Summary:The Wiener–Hopf technique is used to obtain a 2D steady-state solution for the progressive conversion of a pristine interface into a corroded interface between two dissimilar solids. The interface is of infinite extent, and comprises a semi-infinite pristine portion and a semi-infinite corroded portion. Fickian diffusion of the active species (solute) occurs in the upper half-space, with no diffusion in the lower half-space. Corrosion occurs by chemical reaction between the solute and the top surface of the lower half-space, and the path of solute diffusion involves 3 stages. The solute (i) leaves a solute-rich zone of disbonded and previously corroded interface, (ii) enters into and diffuses through the upper half-space, and (iii) leaves the upper half-space and enters the upstream pristine interface where it reacts with the surface of the lower half-space to produce the corrosion product. A steady state is established: the corrosion front moves at a constant velocity V which is dictated by the critical value of accumulated solute on the interface that is needed to form corrosion product and disbond the interface. The reaction zone directly ahead of the corrosion front has a characteristic length that depends upon the diffusion parameters and front velocity V. An asymptotic solution by the Wiener–Hopf analysis is obtained for the diffusion problem at large V. Scaling laws emerge and support the predictions of a much simpler 1D physical model.
ISSN:0022-5096
1873-4782
DOI:10.1016/j.jmps.2020.104268