Computational Methods for Debonding in Composites

1 Computational Methods for Debonding in Composites 23
P [N]
3
2.5
2
1.5
1
0.5
Perfect bond
Debonding (Gc=0.8)
0
0 1 2 3 4 5
u [mm]
6
Fig. 1.24 Load-displacement curve and deformations of shell model after buckling and delamination
growth (true scale) [17]
the activation of these additional sets of degrees of freedom for a given (static)
delamination surface in the model. Both the geometrical and the internal nodes
are enhanced when the corresponding element is crossed by the discontinuity.
This implies that each geometrical node now contains three additional degrees-offreedom
next to the three regular ones, giving six degrees-of-freedom in total. Each
internal node has one extra degree-of-freedom added to the single regular degreeof-freedom.
As in the continuum elements, the discontinuity is assumed to always
stretch through an entire element. This avoids the need for complicated algorithms
to describe the stress state in the vicinity of a delamination front within an element.
As a consequence, the discontinuity ‘touches’ the boundary of an element. The geometrical
and internal nodes that support this boundary are not enhanced in order
to assure a zero crack tip condition. The elaboration of the strains, the equilibrium
equations and the linearisation follow standard lines [17].
The example of Fig. 1.20 has been reanalysed with a mesh composed of eight
node enhanced solid-like shell elements [17]. Again, only one element in thickness
direction has been used. In order to capture delamination growth correctly, the mesh
has been refined locally. Figure 1.24 shows the lateral displacement u of the beam as
a function of the external force P. The load-displacement response for a specimen
with a perfect bond (no delamination growth) is given as a reference. The numerically
calculated buckling load is in agreement with the analytical solution. Steady
delamination growth starts around a lateral displacement u ≈ 4mm,whichisin
agreement with the previous simulations, e.g. [2].
1.7 Concluding Remarks
Numerical models with separate finite elements for interfaces and plies are a powerful
tool to analyse delaminations in composite structures, but have some restrictions.
Because the interface elements have to be inserted a priori, spurious elastic deformations
will occur prior to delamination onset. These undesired deformations can
be partially suppressed by assigning a high value to the normal stiffness modulus