Crack initiation and propagation in composite structures exists as a prominent knowledge gap in computational fracture mechanics. Prior to the development and implementation of fracture modules in FEM solvers, most studies were constrained to simple geometries and load cases. The set of parametric studies that constitute this thesis aims to partially fill this knowledge gap by studying the fracture behavior of air-plasma sprayed thermal barrier coatings (APS-TBCs) using cohesive zone modelling (CZM) in conjunction with FEM. Two-dimensional projections of the TBC microstructures were developed and subjected to a thermomechanical analysis involving thermal strains between the different components of the TBC system. The parametric study was split into three sections. The preliminary study, set O, was executed to discern the most appropriate set of boundary conditions that would produce realistic crack patterns in an expedient manner. Set A and Set B studied the fracture behaviour of conventional TBCs and the recently developed self-healing TBC composite, comprised of lamellae and pores and for Set B, self-healing particles. Qualitative observations reveal the influence of feature dimensions and relative placement to one another. The results appear to indicate that TBC top-coats that are comprised of finer lamellae exhibit higher fracture resistance on both conventional and self-healing systems, and that smaller particles in self-healing systems mitigate damage caused by pores less than larger particles.