Transmission conditions for thin curvilinear close to circular heat-resistant interphases in composite ceramics

Abstract

a b s t r a c tThis paper considers the problem of heat transfer in a composite ceramic material where the structural elements are bonded to the matrix via a thin heat resistant adhesive layer. The layer has the form of a circular ring or close to it. Using an asymptotic approach, the interphase is modelled by an infinitesimal imperfect interface, preserving the main features of the temperature fields around the interphase, and allowing a significant simplification where FEM analysis is concerned. The nonlinear transmission conditions that accompany such an imperfect interface are evaluated, and their accuracy is verified by means of dedicated analytical examples as well as carefully designed FEM simulations. The interphases of various geometries are analysed, with an emphasis on the influence of the curvature of their boundaries on the accuracy of the evaluated conditions. Numerical results demonstrate the benefits of the approach and its limitations.

Nonlinear transmission conditions for thin curvilinear low-conductive interphases

“…Real-life applications and use of composite materials, however, make it necessary to consider media with interphases of closed curvilinear rather than flat shape. For the first time, the transmission conditions for such a geometry were obtained and verified in [2], where the interphase was assumed to be a thin ring, or at least have a form close to circular, which significantly simplified the formulae. At the same time, the increase in curvature of the interphase led to an observable decrease in the reliability of the conditions.…”

“…At the same time, the increase in curvature of the interphase led to an observable decrease in the reliability of the conditions. The present paper achieves the necessary extension of [2] to a more general geometry concentrating on the case of thin interphases being represented as domains bounded by two smooth closed curves of small curvature. To be precise, we consider an interphase of curvilinear shape close to that of a four-ray star, as its geometry allows us to investigate an effect similar to the edge effects for planar domains, where singularities in the solution may occur due to the failure of initial assumptions or mismatch of the physical properties of the materials at the free edge [16,19,26].…”

“…To obtain the transmission conditions for the problem considered, the convenient method [2,18,20] is to rescale the thin interphase, as it is much thinner than the adherent media. This is done by rescaling the width of the interphase…”

“…while the second coordinate φ is unaltered (as in [2]). Taking into account the proportions between the physical parameters, the thermal conductivity of the interphase and the heat source are also rescaled…”

“…Following all these transformations (for details, see [2]), the heat equation and the transmission conditions take the form…”