Elastic moduli of composites containing a low concentration of complex-shaped particles having a general property contrast with the matrix (original) (raw)
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The elastic constants of particulate composites are evaluated employing a theoretical cube-within-cube formation. Two new models of four and five components, respectively, formed by geometrical combination of three-component models existing in the literature, are used as Representative Volume Elements. Using the governing stress and strain equations of the proposed models, two new equations providing the static elastic and shear moduli of particulate composites are formulated. In order to obtain the dynamic elastic and shear moduli, the correspondence principle was applied successively to components connected in series and/or in parallel. The results estimated by the proposed models were compared with values evaluated from existing formulae in the literature, as well as with values obtained by tensile, dynamic, and ultrasonic experiments in epoxy/iron particulate composites. They were found to be close to values obtained by static and dynamic measurements and enough lower compared with values obtained from ultrasonic experiments. The latter is attributed to the high frequency of ultrasonics. Since measurements from ultrasonic's and from dynamic experiments depend on the frequency, the modulus of elasticity estimated by ultrasonic's is compared with that (storage modulus) estimated by dynamic experiments.
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We derive relations linking the conductivity a+ and elastic moduli of any two-dimensional, isotropic composite material. Specifically, upper and lower bounds are derived on the effective bulk modulus x+ in terms of a~and on the effective shear modulus p~in terms of a~. In some cases the bounds are attainable by certain microgeometries and thus optimal. Knowledge of the conductivity can yield sharp estimates of the elastic moduli (and vice versa) even for infinite phase contrast.
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Composites Part B: Engineering, 2016
The effects of an inhomogeneous interphase zone on the effective bulk modulus of particulate composites containing large concentrations of inclusions are analyzed. The composite is modeled as a suspension of elastic homogeneous hollow spherical particles in a continuous elastic matrix. An interphase zone surrounding inclusions where the matrix material has elastic moduli with radial variation that asymptotically assume a constant value far away from particles is then modeled. The related elastic problem of a single inclusion in a finite matrix subjected to a spherically symmetric load is considered and a closed-form solution in terms of hypergeometric functions is determined. This analytical solution is then employed to derive an explicit expression for the effective bulk modulus. A detailed parametric analysis is finally performed to investigate the influence of the geometric characteristics and elastic properties of the graded interphase zone for composites containing voids or solid/hollow inclusions.
Rigorous link between the conductivity and elastic moduli of fibre-reinforced composite materials
Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 1995
We derive rigorous cross-property relations linking the effective transverse electrical conductivity cr* and the effective transverse elastic moduli of any transversely isotropic, two-phase ‘fibre-reinforced’ composite whose phase boundaries are cylindrical surfaces with generators parallel to one axis. Specifically, upper and lower bounds are derived on the effective transverse bulk modulus k* in terms of cr* and on the effective transverse shear modulus //* in terms of cr*. These bounds enclose certain regions in the ct*-ac* and cr*-/r* planes, portions of which are attainable by certain microgeometries and thus optimal. Our bounds connecting the effective conductivity cr* to the effective bulk modulus ft* apply as well to anisotropic composites with square symmetry. The implications and utility of the bounds are explored for some general situations, as well as for specific microgeometries, including regular and random arrays of circular cylinders, hierarchical geometries correspo...