Computational Methods for Debonding in Composites

184 N. Zobeiry et al.
In compression, on the other hand, this softening occurs due to matrix cracking
or yielding and fibre instability. In addition, the instability and rotation of the
fibres combined with fibre breakage and splitting contribute to the overall softening
behaviour under compression. In fact, in compression, matrix cracking leads to
the instability of fibres which is not the case in tension.
The overall reduction in the laminate tangential stiffness, which leads to the softening
behaviour, has been modeled using fuses and springs. Fuses fail sequentially
upon application of a remote displacement to the laminate sub-model. This results
in the overall stiffness reduction of the laminate sub-model and an ensuing softening
behaviour similar to the composite response under tension.
The rubble sub-model represents the behaviour of the damaged material in compression.
Upon reaching the damage initiation strain under compressive loads, the
matrix starts to crack or yield resulting in the formation of multiple cracked surfaces
or rubble. With further damage growth under compression, the friction between the
newly cracked surfaces results in an increase in the load carrying capacity of the
material. This damaged material can continue to carry compressive loads.
The behaviour of the rubble sub-model can be represented with an analogue
model consisting of gap and spring elements to model the compressive load carrying
response with an increasing stiffness. The gap element is inactive (open)
before damage initiation. After damage initiates, new surfaces form resulting in an
increased stiffness of the damaged material. This is modeled by sequential closure
of the varying sized gaps in compression. By virtue of the gaps remaining open, the
rubble sub-model cannot carry any load in tension.
The slider simulates the damage band (kink band) propagation. The yield strain
is assumed to coincide with the saturation strain of the rubble sub-model. At the
instant of final gap closure, the slider activates, indicating progressive specimen end
shortening (damage zone broadening) under a constant applied load. This results
in the damage propagation into the undamaged interior material and an increasing
damage height for compressive failure.
Together, the Laminate and Rubble sub-models represent the overall response of
the composite in the force-displacement space during progressive damage growth
in tension or compression. Figure 9.3 shows a schematic example of the response
of a RVE under controlled displacement loading based on the analogue model. First
displacement is applied in the tensile mode until fibre and matrix damage occurs
in the RVE. Subsequently the RVE is unloaded and then reloaded in the compressive
regime. In this case, the initial reduced modulus (dashed line) compared
to the undamaged modulus (solid curve) is due to the previous damage incurred
in tension. After reaching a saturation state of matrix damage in the RVE, upon
further application of displacement, the damage broadens into the undamaged material
resulting in the band broadening phenomena and the corresponding plateau
stress. The band broadening then continues up to the point of complete failure (fibre
damage saturation).
The analogue model described above has been used to extend the compression
modeling capabilities of a continuum damage mechanics model (CODAM) previously
developed by Williams et al. [31] for gross damage development in polymeric