Читать книгу Properties for Design of Composite Structures - Neil McCartney - Страница 73

Consider a cluster of n cylindrical fibres of the same radius a embedded in an infinite matrix having different properties. The cluster is just enclosed by a cylinder of radius b and the fibre distribution is sufficiently homogeneous for it to lead to transverse isotropic properties for the composite formed by the cluster of fibres and the matrix lying within this cylinder. If the fibre volume fraction of the composite is denoted by V_f then

(4.92)

where V_m is the corresponding volume fraction of the matrix.

First, a single cylindrical fibre of radius a is placed in an infinite matrix and the origin of cylindrical polar coordinates (r, θ, z) is taken on the axis of the fibre. The system is then subject only to a transverse shear stress applied at infinity. The temperature change ΔT from the stress-free temperature, where the stresses and strains in fibre and matrix are everywhere zero, is also assumed to be everywhere zero.