JEC COMPOSITES MAGAZINE - Issue #82 - July 2013 - 58

3D fabrics
directions as well as the through-thickness permeability was
calculated based on Darcy’s law from the average pressure drop
and flow rate obtained from the CFD simulation.

Mechanical analysis
The composites are modelled with two constituents, the isotropic elastic matrix and the transversely isotropic fibre/resin
tow. The resin system used in the composites with the orthogonal weave as reinforcement was Gurit Prime 20LV epoxy. The
nominal properties of the cured resin are listed in Table 3. The
nominal carbon fibre properties are listed in the same table. The
transverse modulus of carbon fibre was assumed to be 15 GPa,
approximated from published experimental data [6]. These
were the input constants in a hexagonally-packed single fibre
unit cell model. The elastic constants for the tow were derived
from solving six load cases on the unit cell using Abaqus (Figure
4). The longitudinal strength of the tow was derived from the
stress at fibre fracture at a strain of 1.8 %. The transverse tensile
strength of the tow was assumed to be equal to the tensile
strength of cured resin, while the longitudinal shear strength
was assumed to be equal to the interlaminar shear strength
(Table 3). The effective tow properties are listed in Table 4.
A failure model introduced by Ruijter [7] was implemented to
reduce the stiffness gradually by defining the modulus (in any
direction) as:
(4)
where E0 is the initial value and P represents a penalty function.
In axial loading, yarn failure is dominated by the brittle properties of the fibres, such that:
(5)

(6)
In transverse or shear loading, the yarn stiffness is reduced
gradually due to matrix failure. The penalty function is modelled as:
(7)
where c1 = 8 and c2 = 13 are empirical constants. In shear,
damage is derived from the partial distortion energy:
(8)
while the maximum principal stress criterion:
(9)

58 jec composites magazine / No82 July 2013

Tab. 3: Nominal properties of resin matrix and fibres

E
(GPa)

Tensile
strength
(MPa)

Tensile
failure
strain (%)

Interlaminar
shear
strength (MPa)

Cured
resin

3.5

Fibre

230

3,450

1.5

Tab. 4: Tow properties derived from FE analysis, Vf = 66 %

E11
(GPa)

E22,
G12,
G23 ν12,
E33
G13
(GPa) ν13
(GPa) (GPa)

152.6 8.15

3.02

2.9

ν23

0.3 0.345

Longitudinal Transverse Longitudinal
tensile
tensile
shear
strength
strength
strength
(MPa)
(MPa)
(MPa)
2,289

Results and discussion

The damage parameter, D, is determined from the maximum
stress according to:

is applied for transverse loading.

Fig. 4: Screenshot of the six load cases of a single fibre unit cell model in
Abaqus for calculation of tow elastic properties

Permeability predictions
After assessing the sensitivity of permeability prediction on
the mesh density for flow simulation, the number of elements
was chosen as 50 × 50 × 50 (warp × weft × thickness) for the
unit cell mesh to obtain a reasonable balance between computation time and accuracy. To assess the sensitivity of permeability prediction on the level of detail in geometrical textile
modelling, incremental variations were implemented in the
geometrical models. A unit cell of the orthogonal weave was
defined with average dimensions based on μ-CT image analysis
(Table 2). The local refinement on binder cross-sections,
surface crimp and warp yarn cross-sections was made step by
step in successive unit cell models. The geometrical variations
addressed observations from the μ-CT images shown in Figure
5. The predictions from CFD simulations are plotted together
with the experimental data in Figure 6, which demonstrates a
clear benefit from local geometrical refinement for improving
permeability prediction.
The same principles were applied for modelling the reinforcement at a higher fibre volume fraction, Vf = 67 %, under

JEC COMPOSITES MAGAZINE - Issue #82 - July 2013

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