Computational Methods for Debonding in Composites

120 X. Martínez et al.
6.1 Introduction
The use of new materials in structural applications implies dealing with new failure
processes, not existing in traditional materials. One of these is the delamination
phenomenon found in laminated composites. The lost of adherence between the
different layers of the composite leads to a reduction of the section strength and
stiffness that can finish in a structural failure.
The importance of this phenomenon is demonstrated by the amount of authors
that have developed theories and formulations to deal with it. All authors that have
studied the problem agree that the delamination process is characterized by two
main phenomenons, the crack initiation and its propagation along the composite.
Crack initiation can be obtained by comparing the strain–stress state of the material,
in the region where delamination takes place, with a critical one [1, 4, 6, 15] or in
terms of the traction versus relative displacement [2, 3, 12]. And the delamination
propagation is usually treated opening the mesh to simulate the crack effect where it
takes place. To open the mesh different procedures are proposed. One of them is the
virtual crack closure technique (VCCT) [8], based on the assumption that when a
crack is extended, the energy required to open the crack is the same required to close
it. Another procedure, each time more used, is the use of a cohesive zone model [4].
The cohesion elements are placed in the interface of the layers that can suffer delamination
and its propagation is obtained with damage or plastic formulations applied
to those elements.
Besides the differences in the existing formulations found in literature to simulate
the delamination phenomenon, all of them agree in dividing the mesh where the
crack is developed. This procedure is computationally very expensive, as it requires
contact formulations to avoid the interpenetration of one body into the other. And,
also, all of them require an special formulation where the delamination will occur,
with interface elements [1], cohesive zones [2] or with coincident nodes, not connected
to allow the mesh opening, as it is done with the VCCT [8]. In contrast to
the scope used by these authors to solve the delamination problem, this work uses
the continuum mechanics to simulate the delamination initiation and propagation,
without making any distinction of the elements in which delamination takes place.
In this work, the Serial/Parallel (S/P) mixing theory developed by Rastellini [13],
is used to obtain the composite performance and to simulate the delamination process.
This theory is based on the definition of some compatibility equations between
the strain–stress states of the composite constituent materials. In the case of a composite
made of fibre and matrix, what the Serial/Parallel mixing theory does is to
impose an iso–strain condition on the parallel direction, usually the fibre direction,
and a iso–stress condition on the serial direction, usually the remaining directions
of the stress and strain tensors. With this scope, if the matrix structural capacity is
lost, the S/P mixing theory will reduce the structural capacity of fibre material in
the serial directions due to the iso–stress condition. Thus, it will be impossible for
the composite layer to develop shear or transversal stresses, less to transmit them to
the surroundings elements. The structural performance of a material in which serial