Hashin’s bounds for elastic properties of particle-reinforced composites with graded interphase

Roberta Sburlati, Roberto Cianci, Maria Kashtalyan

Research output: Contribution to journalArticle

3 Citations (Scopus)
6 Downloads (Pure)

Abstract

The paper is focused on analytical prediction of the effective bulk and shear modulus for particulate composites reinforced with solid spherical particles surrounded by graded interphase zone. A three-dimensional elasticity problem for a single inclusion embedded in a finite matrix is studied. The graded interphase zone around the inclusion is assumed to have power law variation of the shear modulus with radial co-ordinate, with Poisson’s ratio assumed to be constant and equal to that of the matrix. Following Hashin’s approach, two boundary value problems are considered and stress and displacement fields in the interphase zone are determined. They are then used to calculate the elastic energy for the single inclusion composite under spherically symmetric state and pure shear state and derive closed-form expressions for the bulk modulus and the upper and lower bounds for the shear modulus. Numerical results for hard and soft interphase zones are presented and discussed for a range of the interphase zone thickness ratios.
Original languageEnglish
Pages (from-to)224-235
Number of pages11
JournalInternational Journal of Solids and Structures
Volume138
Early online date11 Jan 2018
DOIs
Publication statusPublished - 1 May 2018

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Particle reinforced composites
Elastic Properties
elastic properties
Elastic moduli
Composite
shear
composite materials
inclusions
Modulus
bulk modulus
Inclusion
particulate reinforced composites
thickness ratio
Poisson ratio
matrices
Bulk Modulus
boundary value problems
Elasticity Problem
Poisson's Ratio
stress distribution

Keywords

  • particle reinforced composites
  • elastic moduli
  • spherical inclusions
  • interphase effects

Cite this

Hashin’s bounds for elastic properties of particle-reinforced composites with graded interphase. / Sburlati, Roberta; Cianci, Roberto; Kashtalyan, Maria.

In: International Journal of Solids and Structures, Vol. 138, 01.05.2018, p. 224-235.

Research output: Contribution to journalArticle

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abstract = "The paper is focused on analytical prediction of the effective bulk and shear modulus for particulate composites reinforced with solid spherical particles surrounded by graded interphase zone. A three-dimensional elasticity problem for a single inclusion embedded in a finite matrix is studied. The graded interphase zone around the inclusion is assumed to have power law variation of the shear modulus with radial co-ordinate, with Poisson’s ratio assumed to be constant and equal to that of the matrix. Following Hashin’s approach, two boundary value problems are considered and stress and displacement fields in the interphase zone are determined. They are then used to calculate the elastic energy for the single inclusion composite under spherically symmetric state and pure shear state and derive closed-form expressions for the bulk modulus and the upper and lower bounds for the shear modulus. Numerical results for hard and soft interphase zones are presented and discussed for a range of the interphase zone thickness ratios.",
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AB - The paper is focused on analytical prediction of the effective bulk and shear modulus for particulate composites reinforced with solid spherical particles surrounded by graded interphase zone. A three-dimensional elasticity problem for a single inclusion embedded in a finite matrix is studied. The graded interphase zone around the inclusion is assumed to have power law variation of the shear modulus with radial co-ordinate, with Poisson’s ratio assumed to be constant and equal to that of the matrix. Following Hashin’s approach, two boundary value problems are considered and stress and displacement fields in the interphase zone are determined. They are then used to calculate the elastic energy for the single inclusion composite under spherically symmetric state and pure shear state and derive closed-form expressions for the bulk modulus and the upper and lower bounds for the shear modulus. Numerical results for hard and soft interphase zones are presented and discussed for a range of the interphase zone thickness ratios.

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