Subscript m Baseline EndFraction EndEndFraction plus StartStartFraction upper V Subscript m Baseline nu Subscript m Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction comma"/>(4.67)
It should be noted that the quantity αT+νAαA is the transverse thermal expansion coefficient for plane strain conditions such that uz=0. On using (4.1), relation (4.66) may also be expressed as
On using (4.1) and (4.66), relations (4.67) and (4.68) may be written as
4.4 Axial Shear of Anisotropic Fibres
The following analysis applies to an isolated cylindrical fibre perfectly bonded to an infinite matrix, subject to a uniform temperature change ΔT and to a uniform axial shear stress. The fibre and matrix are regarded as transverse isotropic solids so that the stress-strain relations are given by (4.14)–(4.17).
4.4.1 Solution for an Isolated Fibre Perfectly Bonded to the Matrix
A solution is now sought of the following form
where A, α and β are constants to be determined. On differentiating the displacement field using the strain-displacement relations (2.139), it follows that
