Properties for Design of Composite Structures. Neil McCartney
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where Af, Am 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
On differentiating the displacement field, it follows, on using (2.139) on setting uθ≡0, that.
It follows directly from (4.17), (4.30) and (4.32) that for fibre and matrix
On subtracting (4.14) and (4.15), it follows that for fibre and matrix
Relations (4.29) and (4.31) then assert that
On substituting (4.33) and (4.34) into the equilibrium equations (4.20)–(4.22) it follows that
On integrating (4.38)1 subject to the condition (4.28)1,
and from (4.36) it follows that