Effective properties of heterogeneous materials: Proper application of the non-interaction and the “dilute limit” approximations

Sevostianov, Igor; Kachanov, Mark

doi:10.1016/j.ijengsci.2012.03.031

Cited by 37 publications

(12 citation statements)

References 22 publications

(22 reference statements)

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“…Also, the latter may be weak if interactions between defects have opposite signs, such as in the case of shielding (stacked cracks) or amplification (coplanar cracks); the two effects may cancel each other out if mutual positions of defects are more or less random (see computational simulations of multiple cracks of Grechka and Kachanov). The issue of two versions of the NIA was discussed in detail by Sevostianov and Kachanov …”

Section: Effective Properties Of Porous Microcracked Ceramicsmentioning

confidence: 99%

Microstructure–Property Connections for Porous Ceramics: The Possibilities Offered by Micromechanics

Bruno

Kachanov

2016

J. Am. Ceram. Soc.

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Microstructure of porous ceramics is highly “irregular”: it comprises pores and microcracks of diverse shapes and orientations. This makes their quantitative modeling challenging, and one often resorts to empirical relations containing fitting parameters and having somewhat uncertain range of applicability. We review the substantial progress made in modeling of “irregular” microstructures that does not seem to have been sufficiently utilized in the context of ceramics. We discuss the possibilities offered by micromechanics in developing microstructure–property relations for porous microcracked ceramics. After an overview of relevant micromechanics topics, we focus on several issues of specific interest for ceramics: nonlinear stress–strain behavior, effective elastic properties, and thermally induced microcracking. We discuss extraction of microscale parameters (such as strength of the intergranular cohesion, density of cracks and pores, etc.) from macroscopic data and identify the extent of uncertainty in this process. We also argue that there is no quantitative correlation between fracturing process and the loss of elastic stiffness.

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Section: Effective Properties Of Porous Microcracked Ceramicsmentioning

confidence: 99%

Microstructure–Property Connections for Porous Ceramics: The Possibilities Offered by Micromechanics

Bruno

Kachanov

2016

J. Am. Ceram. Soc.

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“…Sevostianov & Kachanov [25] stated that a common drawback of any differential scheme is that a dilute concentration of a newly added group of inclusions in the matrix is considered. The differential schemes therefore neglect the interaction between the individual inclusions within the same group.…”

Section: Introductionmentioning

confidence: 99%

Modelling of elastic properties of sintered porous materials

2013

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Models for prediction of the elastic characteristics of natural and synthetic porous materials are reexamined and new models are introduced. First, the Vavakin-Salganik (VS) model for materials with isolated spherical pores is extended in order to take into account various statistical distributions of pore sizes. It is shown that the predictions of the extended VS model are in good agreement with experimental data for porous materials with isolated pores such as foamed titanium, porous glass and sandstone. However, the model is in a considerable disagreement with the experimental data for materials sintered from metal powders. The disagreement is explained by the presence of merged and open pores whose shapes cannot be well approximated as spheres. Using the theory of geometrical probabilities, the amount of pores that are close enough to overlap is estimated, and a model is introduced where merging pores are modelled as corresponding ellipsoids. Another modification is proposed to take into account open pores. This modification is based on the classical Rabotnov-Kachanov approach to damage accumulation in the loaded material. Finally, predictions given by the above models, and their combination is compared with experiments. A good agreement is observed between the combined model and the available experimental data for a variety of sintered materials.

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“…For a thorough analysis of many of such methods, see Torquato (2001), Jikov, Kozlov, andOlenik (1994), Hashin (1983) and Nemat-Nasser and Hori (1999) for mechanics oriented treatments and (Ghosh, 2011a;Ghosh & Dimiduk, 2011b;Zohdi & Wriggers, 2008) for computational aspects. For a recent review of general effective viscosity models, see Abedian and Kachanov (2010) and Sevostianov and Kachanov (2012). We note that a wide range of additives are possible to modify lubricant properties; for example, see Wu, Tsui, and Liu (2007) for extensive experiments.…”

Section: Simple Fluid Profilesmentioning

confidence: 99%

On the reduction of heat generation in lubricants using microscale additives

Zohdi

2013

International Journal of Engineering Science

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Effective properties of heterogeneous materials: Proper application of the non-interaction and the “dilute limit” approximations

Cited by 37 publications

References 22 publications

Microstructure–Property Connections for Porous Ceramics: The Possibilities Offered by Micromechanics

Microstructure–Property Connections for Porous Ceramics: The Possibilities Offered by Micromechanics

Modelling of elastic properties of sintered porous materials

On the reduction of heat generation in lubricants using microscale additives

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