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

Appendix C: Porosity and mechanical properties
The fibre strength σfu was calculated using the matrix stress σm at the strain of composite
failure εu and the volume fractions of fibres and matrix as shown in Paper IV. The fibre
stiffness Ef was calculated using the matrix stiffness Em with “The rule of mixtures”
(Hull and Clyne, 1996).
f
( )
σ cu −Vmσmεu
σcu = Vfσ fu + Vmσm(
εu) ⇔ σ fu =
V
E −V
E
Ec = Vf Ef + VmEm ⇔ Ef
=
V
c m m
f
The equations above require that porosity does not affect σc and Ec to a larger extent than
the reduction of Vm and Vf caused by increased porosity content Vp. However, σc and Ec
depend on distribution, orientation and shape of the porosity voids since these can create
inhomogeneous stress concentrations in the material. The material will fracture at
locations with high stress concentration even though the average stress is low.
Investigation of whether consideration of porosity was necessary in this case was
performed by the term (1-Vp) n (Toftegaard and Lilholt, 2002). In which n=0 requires
homogeneous stress concentration, and n>0 is used when the stress-concentration pattern
decreases the composite strength σcu (Paper IV).
Calculation for fibre strength:
( V V ( ) )( 1 V ) ( 1 V )
nσnσ cu = f fu + m m u − p = cup − p
σ σ σ ε σ
c
−nσ
( ) σ cu ( 1−Vp)
−Vmσm(
εu)
σcup −Vmσm
σ fu =
V
εu
=
V
Calculation for fibre stiffness:
f f
( )( 1 ) ( 1 )
nEnE c = f f + m m − p = cp − p
E V E V E V E V
c
E
f
( 1 )
−nE
c − p − m m
Ecp −V
E V V E
mEm = =
V V
f f
76 Risø-PhD-11