ABSTRACT
Composite solids can be treated as isotropic materials so long as the filler particles are positioned randomly in the matrix. The isotropic materials are fully characterized by two independent elastic constants, namely, bulk modulus (K) and shear modulus (G). The Young’s modulus (E) and Poisson’s ratio (ν) are related to K and G as follows:
E
GK K G
=
+
9 3
(12.1)
ν =
−
+
3 2 6 2 K G K G
(12.2)
For isotropic composites consisting of spherical fillers embedded in a matrix, the bulk and shear moduli at low filler concentration are given as [1]
K K
K G K
K K K Gm
= + +
−
+
1 3 4
3 3 3 3 4
φ
(12.3)
G G
G G G Gm
= + − −
− + −
1
15 1 2 4 5 7 5
( )( ) ( ) ( )
ν
ν ν φ
(12.4)
where K and G are bulk and shear moduli of the composite, Km and Gm are bulk and shear moduli of matrix, Kd and Gd are bulk and shear moduli of the dispersed phase (filler particles), νm is the Poisson’s ratio of the matrix, and ϕ is the volume fraction of the dispersed phase.
