Extended Finite Element Modelling of Progressive Cracking in Fibre Reinforced Composite Laminates

The modelling of damage in composites is critical for many applications. The main difficulty in the modelling is complex failure mechanisms intrinsic to composite materials, including their multi-scale nature and interaction of different damage modes. Fibre-reinforced plastics are the most promising of composites due to their low density combined with high mechanical performance. Predicting of crack patterns and their effect on the performance is of practical importance and has received a lot of attention from the research community.

The modelling of cracking in laminates is mainly done with Continuum Damage Mechanics. These methods are adequate in predicting the effect of damage on the composite effective properties but often predict not physical distributed damage zones instead of cracks as observed in experiments. In addition, numerical and analytical models of damage in laminates also exist but they are commonly developed for a simplified geometry, which is often assuming to be two-dimensional. Among relatively new methods is the eXtended Finite Element Method (XFEM). It allows three-dimensional modelling of the onset and propagation of multiple cracks without prior assumptions on their positions. With XFEM, interactions between different damage modes such as delaminations and intralaminar cracks can also be simulated. The XFEM approach to modelling of progressive cracking in laminated composites is investigated in the current work. The model is developed using commercially available ABAQUS tools. Four addressed problems are introduced in following paragraphs.

XFEM is examined for its capability to predict matrix cracking in three-dimensional cross-ply composite laminates under quasi-static tensile loading. The study focuses on the effect of numerical and physical parameters. The propagation of transverse cracks and delaminations is described by cohesive laws. The model requires multiple input parameters, such as the peak stress and critical energy release rate characteristics in the cohesive laws. These input parameters are difficult to determine experimentally, and their choice may be controversial. Hence, the influence of these parameters on the crack development history is studied, and issues are discussed.

The developed model is then extended to examine the influence of voids in laminates on the intralaminar crack density. The approach to simulate the influence of intra-laminar voids on cracking in cross-ply laminates is developed. It combines finite element models of two levels: the micro-level model representing the fibres and voids explicitly and the meso-level model based on XFEM predicting crack development in the laminates. The micro-level model provides input for the meso-level model. The analysis shows that the presence of voids leads to an earlier start of the cracking, depending on the void content, size and distribution. The developed approach proposes a way to extract input parameters from the micro-level models.

The model is validated and further extended to predict interactions of intra-ply cracks and delamination in the ply-by-ply unidirectional hybrid laminates. The latter exhibits different failure behaviour under tensile loading, which depends on the laminate design. The XFEM model is improved to predict ply fractures and delamination of the interface between plies. To validate the model and XFEM in particular, the model is applied to hybrid carbon/glass laminates. The latter contains a low-elongation ply of carbon/epoxy placed between two high-elongation plies of glass/epoxy. Four different configurations of thicknesses of the plies are considered. The results are found to be in good agreement with experimental observations and measurements, including predictions of the stress-strain curves and damage patterns.

Finally, the model is advanced to predict matrix cracks in laminates with angled lay-ups. To do that, a possible bridge to the next level of the hierarchy of the material structure is proposed. The idea is to obtain the macro damage model parameters by running meso-level simulations. Complex and laborious experiments have to be performed to obtain the input parameters for macro-level damage model. To replace this experimental work with simulations, the XFEM model is extended to laminates with lay-ups of angles other than 0 or 90 degrees. Trial problems have been created and calculated to examine the limitations of the model. Due to more complex geometry and load cases, and limitations of ABAQUS, there are many issues which should be addressed during the modelling. Possible ways to overcome these issues are proposed.

The four problems in this thesis are used to develop, to advance, and to validate the XFEM model for cracking in composite laminates. The developed model can successfully predict the number of cracks in the material in function of the applied load, and interactions between delaminations and intra-ply cracks.