A cohesive zone-based constitutive model, originally developed to model fracture, is extended to include a healing variable to simulate crack healing processes and thus recovery of mechanical properties. The proposed cohesive relation is a composite-type material model that accounts for the properties of both the original and the healing material, which are typically different. The constitutive model is designed to capture multiple healing events, which is relevant for self-healing materials that are capable of generating repeated healing. The model can be implemented in a finite element framework through the use of cohesive elements or the extended finite element method (XFEM). The resulting numerical framework is capable of modeling both extrinsic and intrinsic self-healing materials. Salient features of the model are demonstrated through various homogeneous deformations and healing processes followed by applications of the model to a self-healing material system based on embedded healing particles under non-homogeneous deformations. It is shown that the model is suitable for analyzing and optimizing existing self-healing materials or for designing new self-healing materials with improved lifetime characteristics based on multiple healing events.@en

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.@en

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.@en

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.@en

A wedge loaded testing methodology to determine the fracture energy and strength of (semi-) brittle (metallo-)ceramics is presented. The methodology combines a tailored specimen geometry and a comprehensive finite element analysis based on cohesive zone modelling. The use of a simulation-based approach to extract both fracture strength and energy from experimental data avoids the inherent inaccuracies found in closed-form expressions that rely on a priori assumptions about the deformation field. Results from wedge splitting tests on Ti3SiC2 and Ti2AlC (MAX phase) materials are used to illustrate the procedure. The simulation-based approach is further validated by comparing the fracture strength and fracture energies predicted by the proposed method and those indicated by a conventional four-point bending fracture toughness test (ASTM standard). The new protocol offers the possibility to measure not only the fracture properties of brittle material in its pristine state but also in the healed state.@en

The performance of a self-healing Thermal Barrier Coating (TBC) containing dispersed healing particles depends crucially on the mismatch in thermomechanical properties between the healing particles and the TBC matrix. The present work systematically investigates this phenomenon based on numerical simulations using cohesive element-based finite element analysis. The effect of the mismatch in Coefficient of Thermal Expansion (CTE) and fracture strength between the healing particles and the matrix on the fracture characteristics is quantified in detail. Unit cell-based analyses are conducted on a representative self-healing TBC system under a thermal loading step typically experienced by TBC systems in jet turbines. Two different simulation setups are considered within the TBC unit cell namely (i) a single pair of healing particles and (ii) a randomly distributed array of healing particles. The results of the simulations are reported in terms of the fracture pattern, crack initiation temperature and crack length for various CTE mismatch ratios. Correlations are established between the results obtained from the two simulation setups essentially revealing the effect of spatial distribution and proximity of healing particles on the fracture pattern. The results obtained from the analyses can be utilised to achieve a robust design of a self-healing TBC system.@en

A computational fracture analysis is conducted on a self-healing particulate composite employing a finite element model of an actual microstructure. The key objective is to quantify the effects of the actual morphology and the fracture properties of the healing particles on the overall mechanical behaviour of the (MoSi2) particle-dispersed Yttria Stabilised Zirconia (YSZ) composite. To simulate fracture, a cohesive zone approach is utilised whereby cohesive elements are embedded throughout the finite element mesh allowing for arbitrary crack initiation and propagation in the microstructure. The fracture behaviour in terms of the composite strength and the percentage of fractured particles is reported as a function of the mismatch in fracture properties between the healing particles and the matrix as well as a function of particle/matrix interface strength and fracture energy. The study can be used as a guiding tool for designing an extrinsic self-healing material and understanding the effect of the healing particles on the overall mechanical properties of the material.@en

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.@en

Thermal Barrier Coating (TBC) systems are protective layers applied to critical structural components of gas turbines operating at high-temperature. A typical TBC system consists of three different layers, namely a ceramic Top Coat (TC), an active Thermally Grown Oxide (TGO) layer and a metallic Bond Coat (BC). The outer ceramic TC that protects the substrate from high temperature gases and an intermediate BC acts as a bonding layer and also provides oxidation resistance to the underlying components by acting as a sacrificial layer. As a result of the oxidation process, TGO layer is formed at the interface between the TC and BC layer. Lifetime of a typical system lies around several hundred cycles after which, a cost and time intensive maintenance operation is necessary to replace the coating in order to continue safe operation of the engine. Earlier research on TBC micromechanical studies have been focussed on evaluating the influence ofmicrostructure on thermomechanical properties or stress distribution in the TBC system. Numerical efforts on TBC failure such asmodelling the different coating composition, TGOgrowth process and interface irregularities have been made in the past to predict its influence on lifetime of the TBC system. In this research, microstructural features and a novel self healing TBCs are explored through numerical simulations to predict its lifetime enhancement. The overall objective of this research is to develop a modelling and analysis tool capable of simulating fracture and healing processes in the TBC system. The resulting numerical tool aids in setting up design guidelines for the successful development of the proposed self healing TBC system. @en