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

Appendix B: Modelling of porosity content
The porosity content in the composites was determined by assuming that a composite on
a macroscopic scale can be divided into fibres, matrix and porosity. The volume fraction
of porosity Vp can then be calculated as
V = 1 −V
−V
p
m
f
where the subscripts p, m and f denotes porosity, matrix and fibres, respectively.
Equations for calculation of volume fractions of porosity, matrix and fibres based on
experimentally obtained composite data are outlined in Paper IV. The porosity content in
the composites was modelled versus the fibre weight fraction based on techniques
developed by Madsen and Lilholt (2003, 2005), in which it is assumed that the volume
fraction of porosity is linear dependent on both volume fraction of fibres Vf and of matrix
Vm using the porosity constants αf and αm.
Wf
ρm
V f =
W f ρm
( 1+
α f ) + ( 1−
Wf
) ρ f ( 1+
αm
)
( 1−
W f ) ρ f
( 1−
Wf
) ρ f
Vm
= V f =
W f ρm
W f ρm
( 1+
α f ) + ( 1−
W f ) ρ f ( 1+
αm
)
V = α V + α V
p
f
f
m
m
This expression for the volumetric distribution between fibres, matrix and porosity is
valid when the fibre content is below the maximum attainable volume fraction Vf,max
found by Madsen and Lilholt (2002). Vf,max increases versus the compaction pressure
applied when the liquid matrix and fibres are compacted before curing. If the weight
fraction of fibres corresponds to a higher Vf than Vf,max, matrix will be partly replaced
with air in the composite so the porosity content will increase while the fibre content
remains constant at Vf,max. The porosity constants αf and αm can be determined by linear
regression of Vp versus Vf as shown in Figure 35 using the following formulas.
V
p
c
V
p
= α V
f
( 1+
α ) = ( α − α )
m
f
+ α V
m
f
m
= α V
c
α f − αm
αm
Vp
= V f +
1+
αm
1+
αm
Expression for the regression line:
= a ⋅V
+ b
Vp f
m
f
V
f
f
+ α
+ α
m
m
( 1−
V −V
)
f
74 Risø-PhD-11
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