Keywords: polysiloxane, plain weave textile, ceramic composite, electric conductivity, Mori-Tanaka, statistically equivalent periodic unit cell, homogenization.

Fibre-reinforced composites present a well-established and attractive material variant used in numerous branches of engineering design with applications ranging from rehabilitation and repair of concrete and masonry structures to the design of biocompatible medical implants. Nowadays, an increasing number of fibre reinforced composite components are being fabricated with load-carrying fibres, which are woven to form a fabric.

As a point of departure towards more advanced studies on elasticity the homogenization of the conduction problem is considerd in this paper. Attention is limited to the prediction of effective electric conductivities of polymer (polysiloxane) matrix based composites as initial precursors for ceramic composites derived through pyrolitic transformation at various temperatures to meet the desired properties required for particular applications. While the local properties are assumed to be known the final predictions should be corroborated by independent macroscopic laboratory measurements. These two irreplaceable steps in material modeling are investigated.

The proposed homogenization procedure combines two approaches employed independently at two separate scales. The Mori-Tanaka scheme, as a representative of various mean field theories, is used to predict the effective conductivities at a micro-scale (the level of yarns) which can be well approximated by a statistically isotropic distribution of aligned cylindrical fibers and cylindrical pores of a given volume fraction. Such homogenized properties are then used to represent a homogeneous yarn on the meso-scale. There, the deviations from an ideal yarn path caused by manufacturing are taken into account through the application of statistically equivalent periodic unit cell [1] as a representative volume element in the first-order finite element periodic homogenization.

The effective electric conductivities of polysiloxane matrix based textile composites were investigated both numerically and experimentally. At present, the experimental measurements were limited to transverse direction only. Comparative study of two classes of reinforcement clearly indicated that in this direction the charge flow is mainly driven by the properties of highly resistive polymer matrix. This was also confirmed numerically. A reasonable agreement between numerical and experimental results cannot, however, be overestimated as the resulting behaviour is highly anisotropic with inplane properties being highly dependent on the complex structure of the textile reinforcement. An extensive experimental program targeting the inplane properties is therefore required. This topic is currently under investigation.

1

J. Vorel, "Multi-scale Modeling of Composite Materials", PhD thesis, CTU in Prague, 2009.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £130 +P&P)