Modeling of a cracklike hollow filled with medium by an elongated ellipse
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MODELING OF A CRACKLIKE HOLLOW FILLED WITH MEDIUM BY AN ELONGATED ELLIPSE M. H. Stashchuk, V. H. Horopats’kyi, and O. M. Malyk
UDC 539.621
The influence of the stress field on the behavior of the electrode potential in a thin elongated elliptic hole made in an elastic metallic body and filled with media is studied analytically. The investigations are based on the solution of a system of Helmholtz equations used to describe the distributions of electric potentials in the metal, double electric layer, and media. We construct the plots of the electric potential in the elliptic hole filled with a medium and compute the values of shift of the electrode potential on the contact boundary of the medium with the metal under loading.
The investigation of the influence of mechanical loads on corrosion in the process of operation of structural elements requires the analysis of the action of electric fields induced by the corresponding stress–strain state near defects of different types [1, 2]. Statement of the Problem The problem of modeling cracklike hollows filled with medium by elongated ellipses is of primary importance. On the basis of the solution of this problem, it becomes possible to analyze the electrochemical situation at the tips of cracks filled with media in metallic bodies. In what follows, we consider the case of an elliptic cavity filled with a medium and its limiting case (elongated ellipse). It is necessary to establish the influence of the stress–strain state on the distributions of electric potentials in the metal and in the medium contained in the indicated defect and evaluate the corresponding electrode potential on the boundary of the medium with the deformed metal. To determine the distributions of electric potentials in the stressed and strained metal, in the double electric layer formed as a result of contact of the metal with the medium, and in the medium operating in contact with the metal, it is necessary to find the analytic solution of the system of equations [3, 4] ⎧ 1 2 βKε σ ( x, y) , ⎪ χ 2 ∇ ϕ m ( x, y ) − ϕ m ( x, y ) = 2 χ ε m m 0 ⎪ ⎪⎪ 1 2 ⎨ 2 ∇ ϕ mc ( x, y) − ϕ mc ( x, y) = 0, χ ⎪ mc ⎪ 1 ⎪ 2 ∇2ϕ c ( x, y) − ϕ c ( x, y) = 0, ⎪⎩ χ c
χ 2m = χ 2mc = χ c2 =
ρm Cm , ε0 2F2 I , εε 0 RT e2 kTεε 0
(1)
∑ zi2ni ,
Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, Lviv. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 42, No. 6, pp. 81–85, November–December, 2006. Original article submitted December 21, 2005. 808
1068–820X/06/4206–0808
© 2006
Springer Science+Business Media, Inc.
MODELING OF A CRACKLIKE HOLLOW FILLED
WITH
MEDIUM
BY AN
ELONGATED ELLIPSE
809
Fig. 1. Schematic diagram of a crack in the form of an elongated ellipse filled with a medium. where ∇ 2 is the Laplace operator, ϕ m (x, y ), ϕ mc( x, y ), ϕc ( x, y ) are the electric potentials in the metal, in the double electric layer, and in the medium, respectively, ρm and C m are, respectively, the density of the metal and its capacitance, ε0 is the electric constant, β is the electrostriction
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