Page 96 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics of a unidirectional ply 81

Fig. 3.29. A unidirectional ply under in-plane loading.

(3.58)

1
Y12 = -212
GI2
The inverse form of these equations is

(3.59)

where

and the following symmetry condition is valid

ElV12 = E2V21 . (3.60)

Constitutive equations, Eqs. (3.58) and (3.59), include effective or apparent
longitudinal, El, transverse, E2, and shear, G12, moduli of a ply and Poisson’s
ratios vl2 and v21 only one of which is independent, while the second one can be
found from Eq. (3.60).
Elastic constants, El, E2, Gl2 and v12 or v21, are governed by fibers and matrix
properties and the ply microstructure, i.e., the shape and size of the fibers’ cross-
sections, fiber volume fraction, distribution of fibers in the ply, etc. The problem of
micromechanics is to derive the corresponding governing relationships, i.e., to
establish the relation between the properties of a unidirectional ply and those of its
constituents.
To do this, we should know first the mechanical characteristics of the fibers and
the matrix material of the ply. To determine the matrix modulus, E,, its Poisson’s