Materials for engineering, 3rd Edition - (Malestrom)

Composite materials 203
fractures before the fibres and then all the load is transferred to the fibres: the
fibres are unable to support this load and they break, so
σc * = σ f ff + σ m * (1 – f f )
[6.5]
When f f is large, the matrix takes only a small proportion of the load, because
E f > E m , so that when the matrix fractures the fibres do not experience a
sufficient increase in load to cause them to fracture and the load on the
composite can be increased until the fracture stress of the fibres (σ * f ) is
reached, so
σc * = σ f * f f
[6.6]
The fracture strength of the composite varies with f f as illustrated in Fig.
6.12, and this analysis is applicable to glass fibre–polyester resin composites.
If the failure strain of the fibre is less than the failure strain of the matrix
(Fig. 6.13), at low values of f f , when fibre fracture occurs the extra load is
insufficient to fracture the matrix, so
σc * = σ m * ff + σ m * (1 – f f )
[6.7]
When f f is large, however, when fibre fracture occurs, the large extra load
cannot be carried by the matrix and so the matrix fractures (at σ m ) when the
fibres fail, giving:
σ = σ f + σ (1 – f )
[6.8]
c * f * f m f
σ f
*
σc * = σ * f f f
Stress
σc * = σf′ff+ σm * (1– ff)
σ m
*
0 f ’ f f f 1.0
6.12 Variation of fracture stress of composite with volume fraction of
fibres, when ε < ε .
m * f *