Materials for engineering, 3rd Edition - (Malestrom)

204
Materials for engineering
σ f
*
Fibre
Stress
σ m
*
Resin
σ’ m
ε f
*
ε m
*
Strain
6.13 Stress–strain curves of fibre and matrix with failure strain of
matrix > that of fibre.
The variation of σ c
*
with f f is illustrated in Fig. 6.14, where f min defines
the volume fraction of fibres below which the fibre failure occurs below the
matrix ultimate strength, and f crit , above which the strengthening effect of
the fibres is felt. This analysis can be applied to carbon fibre–epoxy resin
composites.
The above approach has assumed that the fibre strength has a unique
value, whereas for brittle fibres like glass, boron and carbon this is not the
case and their strengths are statistically distributed. A more sophisticated
approach may be made to the problem, employing the Weibull statistics
described in Chapter 2.
Aligned, short fibre composites
If we assume the composite consists of an array of short fibres of uniform
length (l) and diameter (d = 2r), all aligned in the loading direction and
distributed uniformly throughout the material, then the matrix has the function
of transferring the applied load to the fibres. The situation is rather like that