Igor Sevostianov

Explicit cross-property correlations for anisotropic two-phase composite materials

Abstract Explicit correlations between two groups of anisotropic effective properties—conductivity and elasticity—are established for two-phase composite materials with anisotropic microstructures (non-randomly oriented inclusions of non-spherical shapes). The correlations are derived in the framework of the non-interaction approximation. The elasticity tensor is expressed in terms of the conductivity tensor in closed form. Applications to realistic microstructures, containing mixtures of diverse inclusion shapes are given. Compliance/stiffness contribution tensors of an inclusion, that characterize the inclusions contribution to the overall elastic response, are derived in the course of analysis; these results are of interest on their own.

Plasma-sprayed ceramic coatings: anisotropic elastic and conductive properties in relation to the microstructure; cross-property correlations

Effective anisotropic elastic stiffnesses and thermal conductivities of the plasma sprayed ceramic coating are calculated in terms of the relevant microstructural parameters. The dominant features of the porous space are identified as strongly oblate (crack-like) pores that tend to be either parallel or normal to the substrate. ‘Irregularities’ of the microstructure — the scatter in pore orientations — are shown to have a pronounced effect on the effective properties. The explicit elastic-conductive cross-property correlations are derived.

Connections between Elastic and Conductive Properties of Heterogeneous Materials

Abstract We discuss cross-property connections that interrelate effective linear elastic and conductive properties of heterogeneous materials. More precisely, they relate changes in the properties, as compared to the ones of the bulk material, caused by various inhomogeneities (cracks, pores, inclusions). They may also be developed for microstructures formed by multiple contacts, such as rough surfaces pressed against each other. Such connections are especially useful if one property (say, electrical conductivity) is easier to measure than the other (anisotropic elastic constants). For the properties governed by mathematically similar laws (for example, electrical and thermal conductivities), the connections are straightforward. However, for the elasticity–conductivity connections – the main focus of the present work – their very existence is nontrivial: not only the governing equations are different but even the ranks of tensors characterizing the properties are different (fourth-rank tensor of elastic constants versus second-rank conductivity tensor). We overview various approaches to the problem and then advance the approach rooted in similarity of the microstructural parameters that control the given pair of properties. This similarity leads to connections that, albeit approximate, have explicit closed form. They have been experimentally verified on several heterogeneous materials (metal foams, short fiber reinforced composites, metals with fatigue microcracks, sprayed coatings). Moreover, for properties controlled by entirely essentially different parameters (such as permeability or fracture of a microcracked material and its elasticity), the correlations may hold only qualitatively, at best.

Modeling of the anisotropic elastic properties of plasma-sprayed coatings in relation to their microstructure

Abstract The transversely isotropic elastic moduli of plasma-sprayed coatings are calculated in terms of microstructural parameters. The dominant features of the porous space are identified as strongly oblate pores, that tend to be either parallel or normal to the substrate. “Irregularities” in the porous space geometry—the scatter in pore orientations and the difference between pore aspect ratios of the two pore systems—are shown to have a pronounced effect on the effective moduli. They may be responsible for the “inverse” anisotropy (Young’s modulus in the direction normal to the substrate being higher than the one in the transverse direction) and for the relatively high values of Poisson’s ratio in the plane of isotropy. The analysis utilizes results of Kachanov et al . ( Appl. Mech. Rev. , 1994, 47 , 151) on materials with pores of diverse shapes and orientations.

Explicit cross-property correlations for porous materials with anisotropic microstructures

Abstract Explicit correlations between two groups of anisotropic effective properties—conductivity and elasticity—are established for porous materials with anisotropic microstructures (non-randomly oriented pores of non-spherical shapes). In the present work, the correlations are derived in the framework of the non-interaction approximation. The elasticity tensor is expressed in terms of the conductivity tensor in the closed form. These results are based on the possibility to represent, with good accuracy, the fourth rank tensor of elastic compliances in terms of a certain second rank symmetric tensor and a unit tensor. Applications to realistic microstructures, containing mixtures of diverse pore shapes are discussed.

On elastic compliances of irregularly shaped cracks

Several methods are suggested to estimate compliances of irregularly shaped cracks – quantities that determine the increase in the overall compliance of a solid due to introduction of such a crack. Besides, the compliance of an annular crack is given – a result that may be of interest on its own.

Point force and point electric charge in infinite and semi-infinite transversely isotropic piezoelectric solids

Abstract For an infinite three-dimensional transversely isotropic piezoelectric material, Greens functions (which give the fuli set of electromechanical fields due to a point electric charge and an arbitrarily oriented point force) are derived in elementary functions in a simple way, using methods of the potential theory. For a semi-infinite transversely isotropic piezoelectric material. Greens functions are also derived, but in a limited way: a point force and a point electric charge are assumed to be applied at the boundary of the half-space. The latter solutions constitute a generalization of Boussinesqs and Cerrutis problems of elasticity for piezoelectric materials. The strength of the piezoeffect (the difference from the purely elastic case) is estimated for the example of the piezoceramics PZT-6B.

Anisotropic thermal conductivities of plasma-sprayed thermal barrier coatings in relation to the microstructure

Anisotropic thermal conductivities of the plasma-sprayed ceramic coating are explicitly expressed in terms of the microstructural parameters. The dominant features of the porous space are identified as strongly oblate (cracklike) pores that tend to be either parallel or normal to the substrate. The scatter in pore orientations is shown to have a pronounced effect on the effective conductivities. The established quantitative microstructure-property relations, if combined with the knowledge of the processing parameters-resulting microstructure connections, can be utilized for controlling the conductivities in the desired way.

Rice’s Internal Variables Formalism and Its Implications for the Elastic and Conductive Properties of Cracked Materials, and for the Attempts to Relate Strength to Stiffness

Rice’s internal variables formalism [1975, “Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms,” in Constitutive Equations in Plasticity, edited by A. Argon, MIT Press, Cambridge, MA, pp. 23–75] is one of the basic tools in the micromechanics of materials. One of its implications is the possibility to relate the compliance/resistivity contributions of cracks—the key quantities in the problem of effective elastic/conductive properties—to the stress intensity factors (SIFs) and thus to utilize a large library of available solutions for SIFs. Examples include configurations that are common in materials science applications: branched and intersecting cracks, cracks with partial contact between crack faces, and cracks emanating from pores. The formalism also yields valuable physical insights of a qualitative character, such as the impossibility to correlate, in a quantitative way, the strength of microcracking materials and their stiffness reduction.

Non-interaction Approximation in the Problem of Effective Properties

We discuss modeling of the effective properties of microstructures that contain inhomogeneities of diverse and “irregular” shapes. We focus on the effects of shapes and their diversity, in the framework of the non-interaction approximation. We also clarify the difference between the non-interaction approximation and the “dilute limit” as well as the concept of “average shape” for a mixture of inhomogeneities of diverse shapes. Further, we give an overview of the approximate schemes that utilize the non-interaction approximation as the basic building block, and discuss the key role of this approximation in establishing explicit elasticity–conductivity connection.