Читать книгу Properties for Design of Composite Structures - Neil McCartney - Страница 71

For loading conditions characterised by the shear stress τ applied to an infinite sample of matrix in the absence of fibre (filling the entire region of space), the solution is given by

(4.82)

(4.83)

A comparison of (4.72) and (4.82) with (4.77) and (4.83) indicates that the identification α=τ/2 can be made. It then follows from (4.81) that

(4.84)

Substitution into (4.72) leads to the following expression for the displacement component uz:

(4.85)

It should be noted that when fibre is introduced, the displacement components are perturbed as a second term appears in expression (4.85) for the matrix displacement that is inversely proportional to the radial distance r. This additional term will now be considered when applying Maxwell’s method of estimating the effective properties of a fibre-reinforced composite.