Electrothermal crack analysis in a finite conductive layer with temperature-dependent material properties

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Abstract

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

Original languageEnglish
Pages (from-to)2468-2475
Number of pages8
JournalJournal of Physics D: Applied Physics
Volume38
Issue number14
DOIs
Publication statusPublished - 2005 Jul 21

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Acoustics and Ultrasonics
  • Surfaces, Coatings and Films

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