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This work is devoted to the problem of thermal fracture of a functionally graded coating on a homogeneous substrate (FGC/H) with an emphasis on the analysis of a special system of cracks that simulates a curved interface. The FGC/H structure contains the pre-existing crack system in the FGC, both edge cracks (which are often seen in FGC/H structures) and internal cracks. The stress intensity factors are calculated. (Generally, both Mode I and Mode II are nonzero.) Then, using the appropriate fracture criterion for mixed-mode fracture conditions, the crack propagation direction (so-called fracture angles) and critical loads, when this propagation is initiated, are determined. The application of fracture criteria requires knowledge of the fracture toughness near the crack tips. Thus, it is assumed that the fracture toughness of an FGC, as well as other material properties, continuously varies through the thickness of the coating. For multiple cracks, it is also important to know the weakest crack that starts to propagate first, and the initial direction of this growth. Therefore, the main attention is paid to the evaluation of the fracture angles for the cracks for different parameters of the FGC/H structure. Both cases of a homogeneous semi-infinite medium with a system of cracks imitating a curved interface and FGC/H structures with identical crack systems are studied. [ABSTRACT FROM AUTHOR]

In the presented model the microstructure of a functionally graded material (FGM) is accounted in two ways: via FGM properties and by distributed small cracks which could be on grain boundaries of the material. The contribution to the solution of material gradation of FGM and of material structure reflected via geometry of distributed cracks is investigated. Besides, some additional effects arising due to possible crack closure and contact of crack surfaces are taken into account in the model and its contribution is also assessed. The goal of this investigation is to show these affects and to estimate the contribution on the SIFs of each of these, if they are strong or can be neglected. [ABSTRACT FROM AUTHOR]

Fracture criteria for prediction of extension of the interface crack and of the crack growth direction in a bimaterial consisting of a homogeneous and a functionally graded material (FGM) with systems of internal defects are studied. The bimaterial is subjected to a heat flux and a tensile load applied at infinity. It is assumed that the thermal properties of the FGM have exponential form. The Young’s modulus and Poisson’s ratio are assumed to be constant. In the previous papers (Petrova and Schmauder, 2011a,b, 2012a,b) asymptotic analytical formulas for the stress intensity factors (SIFs) at the interface crack tips were obtained as a series of a small parameter (the ratio between sizes of the internal and interface cracks). These SIFs are used in fracture criteria to obtain the possible direction of crack propagation and critical loads. The maximum circumferential stress criterion is used and some results for the fracture angles is obtained by the minimum strain energy density in order to compare the predictions for the fracture angles by two fracture criteria. The influence of geometry of the problem (location and orientation of cracks) and the parameters of non-homogeneity of FGMs on the main fracture characteristics is investigated. [ABSTRACT FROM AUTHOR]

Abstract: The work is devoted to the investigation of fracture processes in the vicinity of an interface crack in functionally graded/homogeneous bimaterials with internal defects subjected to tensile loading and a heat flux. A previously obtained solution () for the case of thermal loading on the same geometry is used as a part of the present solution. The solution is based on the integral equation method and it is assumed that thermal properties of the functionally graded material (FGM) possess exponential form. An asymptotic analytical solution is derived for a special case where an interface crack is larger than internal cracks in the FGM. The stress intensity factors are presented as asymptotic analytical functions of geometry of the problem and material properties. Analyses of the effects of the location and orientation of the cracks and the material non-homogeneity parameters on the stress intensity factors in FGM/homogeneous bimaterials is performed in the presence of thermal and mechanical loading. Examples of some FGM/homogeneous bimaterial are discussed. [Copyright &y& Elsevier]

Abstract: The work is devoted to mathematical modeling of the fracture processes in the vicinity of an interface crack in functionally graded/homogeneous bimaterials with internal defects subjected to a thermal flux. A previously obtained solution (Petrova and Schmauder, 2009, 2011) is used and supplemented with the additional possibility to take into account the crack closure. The solution is based on the integral equation method and it is assumed that thermal properties of the functionally graded material (FGM) have exponential form. For a special case where an interface crack length is much larger than the internal cracks in the FGM an asymptotic analytical solution of the problem is obtained as series of a small parameter (the ratio between sizes of the internal and interface cracks). Analyses of the effects of the location and orientation of the cracks, the material non-homogeneity parameters and the crack closure effects on the thermal stress intensity factors of the interface crack in FGM/homogeneous bimaterials are performed. Examples of some FGM/homogeneous bimaterial combinations (i.e., metal/metal, ceramic/metal) are discussed. [Copyright &y& Elsevier]

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]

The present paper deals with a class of functionally graded materials (FGM), called active FGM that has electro-elastically graded material phases. An active FGM system leads to minimization of stress concentration that arises due to mismatch in the electrical and elastic properties of the constituent phases. This work focuses on the characterization of the through thickness stresses of an active FGM subjected to electrical excitation. The structure is comprised of a substrate, an electro-elastically graded layer and an active layer. A formulation for exact solutions of the system based on Euler–Bernoulli theory is presented. Power-law variation of the composition of the two phases in the graded layer is considered. Performance of linearly gradient FGM for a range of stiffness and electrical property ratios of the active and substrate materials have been studied. It is observed that the electrical strain component and the compositional gradation significantly influence the stress characteristics of the active FGM. [Copyright &y& Elsevier]