This work has been primarily conducted at the University of Limerick, Ireland.

The standard Finite Element Method (FEM) has been successfully employed for many decades in modelling. However, the method can be found, in cases, to be insufficient for accurate, efficient modelling of discontinuities, such as those inherently present within the morphology of composite materials and those induced in the fracture of these materials.

This thesis develops state-of-the-art approaches to quantify meso-scale cracking within compos- ite laminae. Both experimental and numerical techniques are employed and the findings of this research will aid the development of more damage tolerant approaches when designing with com- posite materials. The eXtended Finite Element Method (X-FEM) is used to develop a numerical model, sufficient to simulate crack growth in a typical aerospace composite, at lamina level. The XFE model developed herein is extended to analyse the interactions of multiple cracks within a carbon fibre epoxy lamina, represented as an orthotropic material. It is initially confirmed that, similar to isotropic materials, collinear cracks amplify the mode I stress intensity factor (KI). In contrast, parallel cracks are found to shield, and hence, reduce the KI value upon approach. However, the fibre orientation plays a far more significant role when cracks are configured ‘offset’ to each other. It is found that crack tips sharing a fibre orientation will significantly amplify KI . This phenomenon is also evident in studies featuring arrays of cracks. The insight gained from this study should better guide design when known stress raisers are to be included in composite structures. Notwithstanding this, it was found, both numerically and experimentally, that cracks do not interact on propagation, the crack trajectory is at all times controlled by the fibre orientation. Numerically, orthotropic strips, assumed to be perfectly bonded, were studied. The configuration of the material orientations was also found to affect the stress intensity. The crack trajectory how- ever, remained controlled by the fibre orientation.

Two bespoke experimental test series have confirmed the XFE model predictions for both load- displacement and the crack propagation direction. The test series have also allowed, in conjunction with the XFE model, fracture toughness values (KIc) to be calculated. The variation in fracture toughness, with changing fibre orientation, has been fitted by a hyperbolic function. This allows prediction of fracture toughness values, for a range of material orientations, knowing only the fracture toughness for the 0◦ lamina. The effect of crack geometry and configuration on fracture toughness is also addressed in detail.

A complete methodology for calculation of fracture toughness values from images acquired during the experimental testing is finally presented. The method relies on using digital image correlation to extract the displacement field about the crack tip, hence requiring high quality image acquisition. The combined experimental-numerical approach makes use of an interaction integral with the experimental displacement field to obtain KIc values. The method provides a simple yet robust technique for extraction of fracture parameters from non-standard test specimens.


Sample Publications:

LMA Cahill, S Natarajan, SPA Bordas, RM O’Higgins, CT McCarthy. An experimental/numerical investigation into the main driving force for crack propagation in uni-directional fibre-reinforced composite laminae. Composite Structures 107, 119-130. DOI:10.1016/j.compstruct.2013.05.039 · 
Lisa Cahill, Sundararajan Natarajan, Conor McCarthy, Stéphane Bordas, Pierre Kerfriden. Enriched finite elements (XFEM) for multi-crack growth simulations in orthotropic materials. IV European Conference on Computational Mechanics (ECCM), Palais des Congrès, Paris, France, May 16-21 2010.
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