JEC COMPOSITES MAGAZINE - Issue #101 - November/December 2015 - 46

simulation

The test results for dry fabrics with clamps
Tab. 1: Elements and constitutive laws, discrete approaches
show that twice as much tensile force is
FE model
1D
required than for specimens that are fastened with pins (Figure 2d). It is assumed
Truss_Membrane_P2P
Truss_Membrane_P2P_PA6
that there is a movement of the fibre roving
Elastic,
Truss_Shell_P2P
relative to the pins when the shear forces
Isotropic
Beam_Shell_P2P
increase and there is enough space between
Beam_Shell_Chk
them. If the specimens are clamped, the roving cannot move in that direction. Another reason could be the
orientation of fibres according to Figure 2c. If the fibres are not
exactly parallel to the clamps, there could be tensile stresses in
the fibres that lead to higher forces.

PA6 (2D)

Hyperelastic,
Neo Hooke

Elasto-plastic
-

Due to these problems while performing picture-frame tests
for dry and especially for impregnated sheets at the forming
temperature, the bias-extension test will be analyzed in further
studies. The applicable size and geometry of test specimens
should be identified to test reinforced thermoplastics over their
melting temperature.
Figure 2e shows the experimental result curves that were
chosen for the validation of the FE models. Simulations will be
performed for one fabric layer but the results curves for glass/
PA6 sheets are more balanced for three-layer materials than for
those having just a single layer (see Figures 2a and 2b). Thus,
the third specimen in Figure 2a was divided by a factor of three.

FE modelling
In this work, several discrete approaches for the FE analysis of
dry and impregnated fabrics and the *Fabric material model of
Abaqus/Explicit are introduced and compared.
Discrete approaches
The tensile stiffness of fibres is much higher than the shear
stiffness of fabrics. Therefore, a unit cell (Figure 3) is used that
consists of different 1D (truss or beam) and 2D elements (shell
or membrane). 1D elements represent the fibres with high
stiffness values. 2D elements represent the shear behaviour of
the fabric. To consider the matrix component for impregnated
fabrics, a further shell element is modelled in parallel to the unit
cell of the fabric according to [7]. Table 1 shows the different FE
models with elements and constitutive laws.
In Figure 3, the truss and beam elements share the same nodes
around one 2D element. The blue elements show the fibres in

Fig. 3: Unit cell for dry and impregnated fabrics - discrete approaches (cf. [2])

Fig. 4: Checkerboard model [5]

the warp direction and the red elements in the weft direction.
This meshing technique, called Pin-to-Pin (P2P), may result in
an over-prediction of the fibre angles in areas of high deformation [5].
[5] introduces the checkerboard model (Figure 8). The fibres
in the warp and weft directions do not share the same nodes.
Therefore, inter-tow sliding can occur in addition to the fibre
angle change. Inter-tow sliding is another important mode of
deformation when draping fabric reinforcements. In this model,
a unit cell consists of four 2D elements, while there are elements without crossing yarns (Figure 4).
The *Fabric material model of Abaqus/Explicit
The *Fabric material model has the advantage that the shear
and tensile behaviour of the fabric sheet can be directly defined
by test data for the in-plane behaviour (tensile and shear).
Therefore, the shear behaviour of the matrix component can be
considered easily if corresponding material test data are available. Bending stiffness is neglected in this model that just runs
with membrane elements. The implementation of shear test results from a picture-frame test requires the calculation of shear
stress (Equation 1) vs. shear angle (Equation 2) curves that are
standardized by the side length of the test specimens and their
thickness (Figure 5).
Figure 6 shows the shear stress vs. shear angle curves of the
picture-frame tests described previously (Figure 2a). The test
data for glass/PA6 were multiplied by factors of 1.5x and 2x to
take into account the increasing shear forces due to the decreasing sheet temperatures and thus increasing viscosity of the
thermoplastic matrices.

46 jec composites magazine / No101 November - December 2015

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #101 - November/December 2015