67
3
The energy required per unit area of composite for the fracture of
the fibres in tension mode is given as
Energy
f fu
f
=
V
l
E
σ
2
6
(3.12)
where
5 σ fu = Ultimate tensile strength of fibre
5 l = Fibre length
5 E f = Young’s modulus of fibre
The composite may fail due to either debonding of the fibre with the
matrix and/or by fibre pull-out. Fibre pull-out occurs in brittle or
short fibre polymeric composites, and the fibre pull-out energy per
unit area is given as
Fiber pull out energy
f fu c
−
=
V
l
σ
12
(3.13)
where
5 σ fu = Ultimate tensile strength of fibre
5 l c = Critical length
Similarly, the energy required for the fracture in the matrix per unit
area of composite is given as
Energy
f
m u
m
f
=
−
(
)
1
4
2
V
dU
V
σ
τ
(3.14)
where
5 σ mu = Ultimate tensile strength of the matrix
5 d = Fibre diameter
5 U m = Work done to deform the matrix to rupture per unit
volume (U m is negligible in brittle matrix composites and,
therefore, may be ignored.)
5 τ = Interfacial shear stress
The coefficient of thermal expansion of UD composites is lower in
the longitudinal direction than that of the transverse direction.
The coefficient of thermal expansion of fibres is less than that of
the matrix. Therefore, fibres in the longitudinal direction put the
restrain in the longitudinal coefficient of thermal expansion. The
transverse coefficient of expansion of UD composites is large at
low V f and can be larger than that of unreinforced matrix because
the matrix that is restrained to expand in longitudinal direction
due to fibres is forced to expand in transverse direction [5].
? Example 3.3 Find the energy required for fibre fracture and
pulling out the fibre for a glass fibre-reinforced composite.The
tensile strength of fibres, Young’s modulus of fibres, length of
fibre, diameter of glass fibre, and yield stress of the matrix in
3.1 · Micromechanics of Polymeric Composites
3
The energy required per unit area of composite for the fracture of
the fibres in tension mode is given as
Energy
f fu
f
=
V
l
E
σ
2
6
(3.12)
where
5 σ fu = Ultimate tensile strength of fibre
5 l = Fibre length
5 E f = Young’s modulus of fibre
The composite may fail due to either debonding of the fibre with the
matrix and/or by fibre pull-out. Fibre pull-out occurs in brittle or
short fibre polymeric composites, and the fibre pull-out energy per
unit area is given as
Fiber pull out energy
f fu c
−
=
V
l
σ
12
(3.13)
where
5 σ fu = Ultimate tensile strength of fibre
5 l c = Critical length
Similarly, the energy required for the fracture in the matrix per unit
area of composite is given as
Energy
f
m u
m
f
=
−
(
)
1
4
2
V
dU
V
σ
τ
(3.14)
where
5 σ mu = Ultimate tensile strength of the matrix
5 d = Fibre diameter
5 U m = Work done to deform the matrix to rupture per unit
volume (U m is negligible in brittle matrix composites and,
therefore, may be ignored.)
5 τ = Interfacial shear stress
The coefficient of thermal expansion of UD composites is lower in
the longitudinal direction than that of the transverse direction.
The coefficient of thermal expansion of fibres is less than that of
the matrix. Therefore, fibres in the longitudinal direction put the
restrain in the longitudinal coefficient of thermal expansion. The
transverse coefficient of expansion of UD composites is large at
low V f and can be larger than that of unreinforced matrix because
the matrix that is restrained to expand in longitudinal direction
due to fibres is forced to expand in transverse direction [5].
? Example 3.3 Find the energy required for fibre fracture and
pulling out the fibre for a glass fibre-reinforced composite.The
tensile strength of fibres, Young’s modulus of fibres, length of
fibre, diameter of glass fibre, and yield stress of the matrix in
3.1 · Micromechanics of Polymeric Composites