Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes

Shafiro, Boris; Kachanov, Mark

doi:10.1063/1.373579

Cited by 109 publications

(90 citation statements)

References 17 publications

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“…Of course, the pore architecture is in most cases more complex and convoluted than a set of isolated ellipsoids [43]. The original Eshelby method is based on a set of identical inclusions, but it is possible to create a variety of inclusions, provided they are at dilute concentrations [4,5]. Furthermore, explicit relationships have been suggested [44] between the conductivity of a porous material in vacuum and its elastic constants.…”

Section: Eshelby-based Analytical Model For Porous Mediamentioning

confidence: 99%

“…Such systems can be modelled as incorporating randomly-distributed pores [3][4][5][6], contact resistance [7][8][9] or periodic structures [10,11]. Randomly-distributed inclusions, at dilute concentrations, have been modelled, assuming them to be non-interacting [4,5], whereas, for higher porosity levels, self-consistent [12,13] and effective medium [3,14] models have been developed. The latter considers an isolated inclusion to be located within a material with an effective conductivity, which differs from that of the real matrix.…”

Section: Introductionmentioning

confidence: 99%

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Heat Transfer Through Plasma-Sprayed Thermal Barrier Coatings in Gas Turbines: A Review of Recent Work

2009

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A review is presented of how heat transfer takes place in plasma sprayed (zirconia-based) thermal barrier coatings (TBCs) during operation of gas turbines. These characteristics of TBCs are naturally of central importance to their function. Current state-of-the-art TBCs have relatively high levels of porosity (~15%) and the pore architecture (ie its morphology, connectivity and scale) has a strong influence on the heat flow. Contributions from convective, conductive and radiative heat transfer are considered, under a range of operating conditions, and the characteristics are illustrated with experimental data and modelling predictions. In fact, convective heat flow within TBCs usually makes a negligible contribution to the overall heat transfer through the coating, although what might be described as convection can be important if there are gross through-thickness defects such as segmentation cracks. Radiative heat transfer, on the other hand, can be significant within TBCs, depending on temperature and radiation scattering lengths, which in turn are sensitive to the grain structure and the pore architecture. Under most conditions of current interest, conductive heat transfer is largely predominant. However, it is not only conduction through solid ceramic that is important. Depending on the pore architecture, conduction through gas in the pores can play a significant role, particularly at the high gas pressures typically acting in gas turbines (although rarely applied in laboratory measurements of conductivity). The durability of the pore structure under service conditions is also of importance, and this review covers some recent work on how the pore architecture, and hence the conductivity, is affected by sintering phenomena. Some information is presented concerning the areas in which research and development work needs to be focussed if improvements in coating performance are to be achieved.

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Section: Eshelby-based Analytical Model For Porous Mediamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Heat Transfer Through Plasma-Sprayed Thermal Barrier Coatings in Gas Turbines: A Review of Recent Work

2009

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“…The effective permeability of materials with this kind of cracks has been studied by many numericalempirical approaches. A more rigorous approach based on the homogenization scheme has been given by Shafiro and Kachanov (2000), Dormieux and Kondo (2004) and Barthélémy (2009) in which the crack is assimilated to oblate ellipsoidal inclusions obeying to a Darcy's law. This powerful approach easily provides results for the effective permeability of 3D cracked materials, but it can not take into account crack intersections explicitly.…”

Section: Introductionmentioning

confidence: 99%

Numerical Modelling of Steady-State Flow in 2D Cracked Anisotropic Porous Media by Singular Integral Equations Method

Pouya¹,

Vu²

2012

Transp Porous Med

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The equations governing plane steady-state flow in heterogeneous porous media containing curved-line intersecting cracks (Pouya and Ghabezloo 2010) and the potential solution obtained for these equations are considered here. The theoretical results are first completed for the mass balance at crack intersections points. Then, a numerical procedure based on a singular integral equations method is described concretely to derive this solution for cracked materials. Closed-form expressions of elementary integrals for special choice of collocation points lead to a very quick and easy numerical method. It is shown that this method can be applied efficiently to the study of the steady state flow in cracked materials with anisotropic matrix permeability and a dense distribution of curved-line intersecting cracks. Some applications of this method to the permeability of cracked materials are given.

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“…(3.10)) for A 1 -5 can be expressed in terms of parameters q 1 -6 that are given in Appendix A (formulas (A1-4)) and reflect the pore shapes: Following [3] and [10], we consider the orientational distribution that is intermediate between the random and the parallel ones, i.e. a distribution that has an orientational preference but possesses a scatter:…”

Section: Spheroidal Pores That Tend To Be Parallel (To X 3 ) and Ha6ementioning

confidence: 99%

On the yield condition for anisotropic porous materials

Sevostianov

Kachanov

2001

Materials Science and Engineering: A

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Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes

Cited by 109 publications

References 17 publications

Heat Transfer Through Plasma-Sprayed Thermal Barrier Coatings in Gas Turbines: A Review of Recent Work

Heat Transfer Through Plasma-Sprayed Thermal Barrier Coatings in Gas Turbines: A Review of Recent Work

Numerical Modelling of Steady-State Flow in 2D Cracked Anisotropic Porous Media by Singular Integral Equations Method

On the yield condition for anisotropic porous materials

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