Page 240 - Mechanics Analysis Composite Materials

Chapter 5

MECHANICS OF LAMINATES

A typical composite structure consists of a system of layers bonded together. The
layers can be made of different isotropic or anisotropic materials, and have different
structures (see Chapter 4), thicknesses, and mechanical properties. In contrast to
typical layers which are described in Chapter 4 and whose basic properties are
determined experimentally, the laminate characteristics are usually calculated using
the information concerning the number of layers, their stacking sequence, geometric
and mechanical properties which should be known. A finite number of layers can be
combined to form so many laminates that the idea to study them using
experimental methods does not look realistic. While the most complicated typical
layer is described with nine stiffness coefficients A,,,,, (mn= 11,22,12,14,24,44,55:
56,66), some of which can be calculated, the laminate is characterized with 21
coefficients and demonstrates coupling effects that can hardly be simulated in
experiments.
Thus, the topic of this chapter is to provide equations allowing us to predict the
behavior of a laminate as a system of layers with given properties. The only
restriction that is imposed on the laminate as an element of a composite structure
concerns its total thickness which is assumed to be much smaller than the other
dimensions of the structure.

5.1. Stiffness coefficients of a generalized anisotropic layer

For the sake of brevity, consider first a thin homogeneous layer, which is
anisotropic in the xy-plane and whose mechanical properties are some functions of
the normal coordinate z (see Fig. 5.1). Coordinate axes x and y belong to some
plane which is referred to as a reference plane such that z = 0 on this plane and
-e <z < s for the layer under study. There exist some special locations of the
reference plane discussed below, but in this section its coordinates e and s are not
specified. We introduce two assumptions both based on the fact that thickness
h = e +s is small.
First, it is assumed that the layer thickness, h, does not change under the action of
stresses shown in Fig. 5.1. Actually, the thickness does change, but because it is

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