Electrical behaviour of a single crack in a conductor and exponential laws for conductivity in micro cracked solids

Article type: Research Article

Authors: Giordano, Stefano^a

Affiliations: [a] Department of Physics, University of Cagliari, Cittadella Universitaria, I-09042 Monserrato (Ca), Italy. Sardinian Laboratory for Computational Material Science (SLACS, INFM-CNR). Tel.: +90 070 675 4839; Fax: +39 070 510 171; E-mail: stefano.giordano@dsf.unica.it; stefgiord14@libero.it

Abstract: In this paper we analyse the electrical effects of the presence of cracks in solid conductors. We have studied such problematic from different points of view. Firstly, we have analytically evaluated the behaviour of the electrical field near a crack in an isotropic solid where a uniform current density is flowing, drawing a comparison with the behaviour of the well known stress and strain tensor fields in the analogue elastic problem. This computation has been made with a slit-crack (two-dimensional field analysis) and with a circular crack (three-dimensional field analysis). So, in order to quantify the spatial fluctuations of the local electric field around the crack we have numerically found the density of states for the field showing that it exhibit sharp peaks and abrupt changes in the slope at certain critical points which are analogous to van Hove singularities in the density of states for phonons and electrons in solids. Finally, we have performed a theoretical analysis of the conductivity of a microcracked solid. The distribution of cracks in the solid follows a given orientational distribution, which modify the conduction properties of the overall material. In particular, we have shown that the conductivity depends exponentially on the cracks density and on the size of each crack embedded in the medium.

Keywords: Electric cracks, field intensity factors, density of states, order parameters

DOI: 10.3233/JAE-2007-815

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 26, no. 1-2, pp. 1-19, 2007