Properties for Design of Composite Structures. Neil McCartney

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СКАЧАТЬ target="_blank" rel="nofollow" href="#fb3_img_img_b66d7340-b367-5f6c-ad6c-aa6d7abdb198.png" alt="upper V Subscript f Baseline equals StartFraction n a squared Over b squared EndFraction equals 1 minus upper V Subscript m Baseline comma"/>(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.

      4.5.1 Representation for Displacement Strain and Stress Distributions

      Consider the displacement field having the form

(4.93)

      where kT and μt are the transverse bulk and shear moduli, respectively.

      On using the strain–displacement relations (2.142), the corresponding strain field is given by

(4.94)

      When ΔT=0, the stress-strain relations (4.14)–(4.17) are written as

(4.95)

(4.96)

(4.97)

(4.98)

      where ET=2μt(1+νt). It follows directly from (4.94) and (4.98) that

(4.99)

      From (4.94) and (4.97) it is clear that

(4.100)

      and on summing (4.95) and (4.96)

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