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Abstract: The thermal fracture of a bimaterial consisting of a homogeneous material and a functionally graded material (FGM) with a system of internal cracks and an interface crack is investigated. The bimaterial is subjected to a heat flux. The thermal properties of FGM are assumed to be continues functions of the thickness coordinate, while the elastic properties are constants. The method of the solution is based on the singular integral equations. For a special case where the interface crack is much larger than the internal cracks in the FGM the asymptotic analytical solution of the problem is obtained as series in a small parameter (the ratio between sizes of the internal and interface crack) and the thermal stress intensity factors (TSIFs) are derived as functions of geometry of the problem and material characteristics. A parametric analysis of the effects of the location and orientation of the cracks and of the inhomogeneity parameter of FGM’s thermal conductivity on the TSIFs is performed. The results are applicable to such kinds FGMs as ceramic/ceramic FGMs, e.g., TiC/SiC, MoSi2/Al2O3 and MoSi2/SiC, and also some ceramic/metal FGMs. [Copyright &y& Elsevier]

• Thermal fracture of functionally graded coatings (FGCs) on a homogeneous substrate is studied. • The effect of residual stresses caused by temperature changes on ΔT (cooling) is investigated. • The mathematical description of the model is based on singular integral equations. • The stress intensity factors and fracture angles were derived. • Combinations of PSZ and mullite as FGCs and Ni superalloy and steel as substrates are used. • Illustrative examples are presented to study the interaction of edge cracks with internal cracks at a weak zone. The problem of fracture of functionally graded coatings (FGCs) on a homogeneous substrate (a semi-infinite medium) is investigated under the influence of thermal and/or mechanical loads (e.g. a heat flux, residual thermal stresses caused by cooling-heating, tension). These loads reflect the most important cases, which arise during the exploitation of FGC structures. The FGC contains pre-existing systems of cracks, such as edge, internal and interface cracks. The mathematical description of the model is based on singular integral equations. The properties of the FGC are continuous functions of the thickness coordinate. Furthermore, the non-homogeneity of the functionally graded material is revealed in the form of corresponding inhomogeneous traction distributions on the surfaces of cracks. This method is approximate and used with the assumption, that the gradation of material properties of the FGC with the depth of the layer is not abrupt. The influence of residual stresses caused by temperature changes on ΔT (e.g. cooling from operating temperatures) is investigated in detail. Different crack patterns (which are reported in experiments and available in the literature) are studied by carrying out numerical experiments with respect to stress intensity factors and fracture angles (a deviation of cracks from the initial direction of propagation). The proposed model in combination with a detailed parametric analysis can help to optimize FGCs in order to improve the fracture resistance of FGC/homogeneous structures. [ABSTRACT FROM AUTHOR]

In rock-like materials, mode I and II fracture toughness are distinctive while the compressive strength is much greater than the tensile strength. Besides, mixed-mode fractures instead of pure mode I or II fractures occur under complicated load cases in those materials. Therefore, to capture the mixed-mode cracking process, we developed a mixed-mode phase-field cohesive zone model based on the unified phase-field theory proposed by Wu. The model was built based on a strain energy decomposition scheme and the softening behavior of each mode is controlled by an independent degradation function. Thus, independent values of strength and toughness can be given for different failure modes simultaneously. A simple mixture rule of fracture toughness was introduced to describe the transition between different failure modes. The model can keep variational consistency perfectly and governing equations for displacement- and phase-field, which was never reported in other works. Several numerical examples verified the effectiveness and flexibility of this work. The present work showed a simple but effective way to simulate mixed-mode fracture. • A modified phase-field cohesive zone model is developed for mixed-mode fracture. • A simple mixture rule is utilized to describe the transition between each fracture mode. • The present model can keep the variational consistency perfectly. • Several numerical cases verify the present model. [ABSTRACT FROM AUTHOR]

[Display omitted] • Interfacial debonding of a porous TBC system is studied via SEM image-based FE analysis. • Microstructural pores of SEM image of TBC sample are imported into FE software via CMM. • Pores of TC force the stress to be concentrated adjacent to rough TC/TGO interface and develop TC/TGO interface damage. • Porosity within the BC diminishes stress and damage values along the TGO/BC interface. • Creep leads to stress relaxation of TC up to 24.82 % and lowers the damage level of TGO/BC interface. Numerical analysis of interfacial delamination and the effect of microstructural pores and rough interfaces on the field variables in thermal barrier coatings (TBCs) based on a real scanning electron microscope (SEM) image is performed. The interfacial delamination is modelled by the utilization of cohesive zone method (CZM) in finite element (FE) analysis. The empirical TBC sample considered in this study is constructed via air plasma spray (APS) method and comprises ZrO 2 7 - 8 wt. % Y 2 O 3 ceramic top coat (TC), thermally grown oxide (TGO) made of Al 2 O 3 and NiCrAlY metallic bond coat (BC). A compatible geometry is provided by applying image processing technique to SEM image of the sample's cross-section. SEM image-based geometry imported into FE software to scrutinize the interplay effects of porosity and rough interfaces on temperature fields, thermal stresses and interfacial debonding of TC/TGO and TGO/BC interfaces of the TBC structure. FE analysis reveal that porosity distribution has a prominent role on the stress concentration zones at the sharp corners of pores especially adjacent to undulations of the TC/TGO interface, which is responsible for possible internal cracks and interfacial fracture, respectively. The main findings demonstrate that the porosity near the TC/TGO interface has detrimental effect as leads to aggravation in the TC/TGO interface damage, which causes an increment in TC/TGO interfacial crack length. While, the porosity within the BC has the ability to reduce the stress and damage level along the TGO/BC interface. In addition, considering creep for all layers leads to lower stress levels up to 24.82 % and consequently alleviates the TC/TGO interface damage. [ABSTRACT FROM AUTHOR]