The influence of the cohesive zone length on the crack driving force is quantified and analyzed in a representative system of particles dispersed in a matrix of a composite material. For heterogeneous material systems, e.g. particulate composites, it is known that as a crack approaches the particles, the crack driving force may increase (shielding) or decrease (anti-shielding) depending on the relative stiffness of the particles. These results have been established in numerous studies using the classical linear elastic fracture mechanics approach (LEFM). The cohesive zone method (CZM) introduces a length scale parameter, referred to as the cohesive zone (or fracture process zone) length scale, into the formulation of fracture mechanics. It is generally established that fracture mechanics predictions using the CZM are similar to those obtained using LEFM in the limit case where the process zone is very small relative to a suitable characteristic dimension of the problem. However, the influence of the length scale parameter has not been clearly demonstrated for crack propagation in a heterogeneous material system, especially when the cohesive zone length is not negligible. By considering a simple crack-particle-matrix system, it is shown that, in addition to the elastic properties, the process zone length scale parameter exhibits a critical influence on the crack driving force. For this study, the concept of configurational forces is utilized and the eXtended Finite Element Method (XFEM) is employed as a tool to simulate crack propagation. Through numerical simulations, it is shown that (i) the magnitude of the driving force vector directly depends on the length scale parameter and (ii) the direction of the driving force is largely influenced by the presence of a cohesive zone. This, in turn, alters the crack trajectory in the particulate system if the criterion for the direction of crack propagation depends on the orientation of the driving force vector. Towards this end, two different criteria for direction of crack propagation, namely maximum principal stress and maximum energy dissipation, are compared in the presence of a cohesive zone and the results are reported. The study reveals the crucial influence of the inherent length scale associated with the cohesive zone method when applied to crack propagation in particulate composite systems and elucidates important differences when comparing predictions from distinct theories of fracture mechanics.

The thermal cyclic behavior of self-healing thermal barrier coatings (SH-TBC) is analyzed numerically to develop a lifetime prediction model. Representative microstructures are studied adopting a unit cell based multiscale modeling approach along with a simplified evolution model for the thermally-grown oxide layer (TGO) to study the evolution of damage and healing in a self-healing TBC system. The fracture and healing process is modeled using the cohesive zone-based healing model along with a crack tracking algorithm. The microstructural model includes splat boundaries and a wavy interface between the Top Coat and the Bond Coat, typical of Air Plasma Sprayed TBCs. A particle-based self-healing mechanism is accounted for with a random distribution of healing particles subjected to a numerically accelerated thermal cyclic loading condition. Lifetime extension of the self healing TBCs is quantified by conducting thermal cyclic analyses on conventional TBCs (benchmark system without self-healing particles). Parametric analyses on healing parameters such as crack filling ratio and strength recovery of the healed crack are also conducted. The results are presented in terms of the evolution of the crack pattern and the number of cycles to failure. For self-healing TBCs with a suitable healing reaction (i.e., cracks being partially filled and a minimal local strength after healing), an improvement in TBC lifetime is observed. In contrast, if the healing mechanism is not activated, the presence of the healing particles is actually detrimental to the lifetime of the TBC. Correspondingly, in addition to superior crack filling ratio and healed strength, significant improvement in lifetime is achieved for self healing TBCs with a higher probability of crack-healing particle interaction. This highlights the importance of a robust activation mechanism and a set of key material requirements in order to achieve successful self-healing of the TBC system.

The effect of splat interfaces on the fracture behavior of air plasma-sprayed thermal barrier coatings (APS-TBC) is analyzed using finite element modeling involving cohesive elements. A multiscale approach is adopted in which the explicitly resolved top coat microstructural features are embedded in a larger domain. Within the computational cell, splat interfaces are modeled as being located on a sinusoidal interface in combination with a random distribution of pores. Parametric studies are conducted for different splat interface waviness, spacing, pore volume fraction and fracture properties of the splat interface. The results are quantified in terms of crack nucleation temperature and total microcrack length. It is found that the amount of cracking in TBCs actually decreases with increased porosity up to a critical volume fraction. In contrast, the presence of splats is always detrimental to the TBC performance. This detrimental effect is reduced for the splat interfaces with high waviness and spacing compared to those with low waviness and spacing. The crack initiation temperature was found to be linearly dependent on the normal fracture properties of the splat interface. Insights derived from the numerical results aid in engineering the microstructure of practical TBC systems for improved resistance against thermal fracture.

The influence of microstructural pore defects on fracture behaviour of Thermal Barrier Coatings (TBC) is analysed using finite element analysis involving cohesive elements. A concurrent multiscale approach is utilised whereby the microstructural features of the TBC are explicitly resolved within a unit cell embedded in a larger domain. Within the unit cell, a random distribution of pores is modelled along with three different layers in a TBC system, namely, the Top Coat (TC), the Bond Coat (BC) and the Thermally Grown Oxide (TGO). The TC/TGO and the TGO/BC interfaces are assumed to be sinusoidal of specified amplitude and frequency extracted from experimental observations reported in the literature. To simulate fracture in the TBC, cohesive elements are inserted throughout the inter-element boundaries in order to enable arbitrary crack initiation and propagation. A bilinear traction-separation relation with specified fracture properties for each layer is used to model the constitutive behaviour of the cohesive elements. Parametric studies are conducted for various pore geometrical features, porosity, fracture properties of Top Coat layer and Thermally Grown Oxide layer thicknesses. The results are quantified in terms of crack initiation and evolution. It is found that the presence of pores has a beneficial effect on the fracture behavior up to a certain value of porosity after which the pores become detrimental to the overall performance. Insights derived from the numerical results can help in understanding the failure behavior of practical TBC systems and further aid in engineering the TBC microstructure for a desired fracture behavior.