Читать книгу Properties for Design of Composite Structures - Neil McCartney - Страница 65

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.