Materials for engineering, 3rd Edition - (Malestrom)

210
Materials for engineering
But l c /r = σ f /τ y , so
W f f l c
= σ l 12
f c
[6.11]
l
For maximum work of fracture, therefore, l c should be maximized and
fibre length should be equal to l c . If the fibre length is less than l c , the work
of fracture is obtained by setting l c = l in the integral:
ff
W =
πr
2
∫
lc /2 2
0
(2 πrτx
) d x
l
= f f πτ l 2 /12r. [6.12]
Thus, for fibres of a given constant value of critical length, as the fibre
length in the composite is increased, the work of pullout initially increases
as l 2 (equation [6.12]). When the fibre length is greater than the critical
length, the work of pullout decreases as l –1 , (equation [6.11]), as more fibres
break rather than pull out. These relationships are illustrated in Fig. 6.20.
6.4.4 Fatigue behaviour of fibre composites
The introduction of short fibres into a polymer can enhance its resistance to
both the nucleation and the growth of fatigue cracks. Thus, Fig. 6.21 presents
a series of S–N curves for injection moulded PSF with increasing volume
I 2 1
Pull-out energy
l
I c
Fibre length (I)
6.20 Pull-out energy as a function of fibre length.