Properties of hemp fibre polymer composites -An optimisation of ...

E
⎛ dσ
c ⎞
= ⎜ ⎟
⎝ dε
⎠
c Equation 7b
ε = 0−0.
1%
Pure epoxy sheets were tested to obtain a stress-strain curve for the matrix material,
which was fitted to a second order polynomial, giving Em=2.93 GPa and k=32.5 GPa
(Figure ):
( )
σ ε ε
2
m = Em× − k×ε
Equation 8
The fibre strength σfu was calculated with the rule of mixtures using the matrix stress σm
at the strain of composite failure εu and the fibre stiffness Ef was calculated using Em
(Hull & Clyne, 1996). With porosity in the composites, σcu and Ec are reduced to a larger
extent than caused by the reduction of Vf and Vm; this is due to the potential stress
concentrations originating at the porosities, and is taken into account by the term (1-Vp) n
(Toftegaard & Lilholt, 2002). Based on detailed investigation of the composites in this
study, it was chosen to use nσ=2.1 and nE=1 for correction for porosity (Thygesen, 2006).
The fibre strength σfu and the fibre stiffness Ef are thus calculated from Equation 9.
n
n σ cup −V
m × σ m ( ε u )
σ
σ
σ cu = ( V f × σ fu + Vm
× σ m ( ε u ) )( 1 −V
p ) = σ cup ( 1−
V p ) ⇔ σ fu =
Equation 9a
V f
E
c
nE
( V × E + V × E )( −V
) = E ( −V
)
f
f
m
−V
× E
nE
cp m m
m 1 p cp p ⇔ E f =
Equation 9b
V f
= 1
Figure 1. Stress versus strain for epoxy sheets and composites with 33% (v/v) P. radiata
defibrated hemp fibres, to show the fracture strain (εu) and stress (σ) of matrix (σm),
composite (σcu) and fibres (σfu).
Risø-PhD-11 127
E