68
3
shear are 3500 MPa, 70 GPa, 100 mm, 15 μm, and 24 MPa,
respectively. The composite has volume fractions of
reinforcement and a matrix at 0.5 each. Calculate the critical
aspect ratio of fibre in this composite.
v Answer
σ fu  = 3500 MPa
E f  = 70G Pa
l = 100 mm
d = 15 μm
τ y  = 24 MPa
v f  = 0.5
V m = 0 5
.
l
d
l d
l
c
f u
y
c
fu
y
c
mm
=
=
=
σ
τ
σ
τ
2
2
2 19
.
Energy
J
f ful
f
=
=
×
V
E
σ
2
3
6
145 8 10
.
Fiber pull out energy
J
f fu c
−
=
=
×
V
l
σ
12
319 38 10
2
.
3.1.4 Short Fibre Composites
In short fibre composites, the end effect of the fibres are not
neglected as is the case in long fibre composites. In short fibrereinforced composites, the ends of the fibres and region near the
ends bear the maximum stress. The maximum stress occurs at the
mid-fibre length. The load transfer length of the fibre for the applied
stress is a critical length for the fibre (l c ). The l c is calculated as
l
d
c
f u
y
=
σ
τ
2
(3.15)
where
5 l c  = Critical length for fibre
5 σ fu  = Ultimate tensile strength of fibre
5 d = Diameter of fibre
5 τ y  = Yield stress of matrix in shear
The yield stress of the matrix in shear (τ y ) is equal to interface shear
stress along the fibre length. It can be given as
σ
τ
fu
y
=
2 Z
r
(3.16)
Chapter 3 · Micromechanics and Macromechanics of Polymeric Composites