• cohesive zone model
• delamination
• interlaminar fracture
• multi-directional laminates
• composite materials

The object of this study is the development and implementation of a Cohesive Zone Model (CZM) for interlaminar fracture toughness numerical tests for multidirectional laminated composite specimens. This work is correlated to the PhD thesis of Torquato Garulli in which a novel class of stacking sequences to test delamination interfaces between plies of any orientation was created. These specimens are called Fully-Uncoupled Multi-Directional, and they have a thermoelastic behavior similar to that of unidirectional ones.
Moreover, Garulli carried out an experimental campaign to test the mode I behavior of these new stacking sequences.
The focus is narrowed in the delamination as one of the most common failure modes in composite structures. In fact, it can be the result of several phenomena such as impact damage, manufacturing defects, out-of-plane loading and hygrothermal loads. The characterization of the delamination growth behavior is important to ensure safe design and numerical simulations are a vital part to this characterization to decrease the necessity of experimental tests, which are time-consuming and expensive.

In order to analyze the delamination growth in Multi-Directional interfaces (MD), a generalization of the interface damage model is presented. The generalization is presented with an energy-based theoretical model based on the work of Allix-Ladévèze \cite{allix}. The interface damage is described with three independent penalty components and three damage components. Due to difficulties in interpreting the behavior of the internal variables, a simplified version has been formulated with the description of the interface behavior with the bilinear and polynomial Allix-Ladévèze law. The simplified model is then implemented in a FORTRAN User-material subroutine that is used in Abaqus to perform Finite Element (FE) simulations.
First, the UMAT is validated for one-cohesive element in mode I, II and mixed-mode I/II. Afterward, 2D and 3D Double Cantilever Beam (DCB) specimens are built to test the interface damage model in only mode I. After the validation of the UMAT, DCB specimens with the same materials and dimensions as the experimental FUMD specimens, are built and simulated in mode I.

The results of the simulations are compared to the experimental ones in terms of force-displacement jump plot and shape of crack fronts to assess the capability of the numerical simulations with CZM to represent the correct mechanical behavior of mode I delamination.

For both aspects, the numerical specimens yield results similar to those obtained experimentally with some differences related to the numerical modeling. In fact, with respect to force-displacement jump plot, the numerical results yield to the same global behavior of the experimental specimens but with different values of maximum force reached. This difference could be related to the assigned numerical properties of the interface.
For the shape of the crack front, even if the global behavior is quite similar to the experimental one, the shape of the numerical crack fronts shows some differences with the experimental one.
Maintaining the focus on the crack fronts, a comparison starting from different initial delamination lengths is also carried out. The results of these analyses, performed for the benchmark and FUMD DCB specimens, show the dependence of the numerical crack front with the initial precrack length.

This work represents a preliminary study and further research is clearly required to complete the generalization of the CZM and the validation of the UMAT code in mode II and mixed-mode I/II for more complicated structures. Instead, the numerical FUMD simulations show a good representation of the real behavior of the experimental specimens and the analyses of the crack front exhibit an interesting potential in reducing the computational time of simulations.