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of the form

(4.14)

(4.15)

(4.16)

(4.17)

(4.18)

      Superscript ‘f’ is used to denote anisotropic fibre properties and subscript ‘m’ is used to denote the properties Em, νm, μm and αm of an isotropic matrix such that Em=2μm(1+νm). If the fibres are also isotropic then

      (4.19)

      The equilibrium equations for the fibres and matrix in the absence of body forces are (see (2.125)–(2.127))

(4.20)

      (4.21)

(4.22)

      4.3.1 Properties Defined from Axisymmetric Distributions

      The following analysis applies to an isolated cylindrical fibre of radius a that is perfectly bonded to an infinite matrix, subject to a uniform temperature change ΔT, where the system is subject to a uniform axial strain ε and a uniform transverse stress σT. The equilibrium equations (4.20)–(4.22) for the fibre and matrix, assuming symmetry about the fibre axis so that stress components are independent of θ and the shear stresses σrθ and σθz are zero, then reduce to the form

      (4.23)

      (4.24)

      In regions away from the loading mechanism it is reasonable to assume that

(4.25)

      where ε is the axial strain applied to the composite. A solution is now sought of the following classical Lamé form

(4.26)

(4.27)

      where A_f, A_m and ϕ are constants to be determined.

      4.3.2 Solution for an Isolated Fibre Perfectly Bonded to the Matrix

      The boundary and interface conditions that must be satisfied are

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