Page 392 - Mechanics Analysis Composite Materials

Chapter 8. Optimal composite structures 377

Introducing average stresses a, = N,/h, 0,.= N,/h, and T.~.~.= N,,/h and solving
these equations for strains we have

I
E.: = -(O.r - VSV), (8.36)
E
whcrc

(8.37)

Changing strains for stresses in Eqs. (8.35) we can write the expression for the
optimal orientation angle as

(8.38)

As follows from Eqs. (8.36), the laminate consisting of two layers reinforced along
the directions of principal stresses behaves like an isotropic layer, and Eqs. (8.37)
specify elastic constants of the corresponding isotropic material. For typical
advanced composites, these constants are listed in Table 8.3 (the properties of
unidirectional plies are taken from Table 3.5). Comparing elastic moduli of the
optimal laminates with those for quasi-isotropic materials (see Table 5.1) we can see
that for polymeric composites the characteristics of the first group of materials are
about 40% higher than those for the second group. However, it should be
emphasized that while the properties of quasi-isotropic laminates are the universal

Table 8.3
Effective elastic constants of an optimal laminate.
Property Glass Carbon- Aramid- Boron- Boron- Carbon- A1203-
epoxy epoxy epoxy epoxy AI carbon AI

Elastic modulus, E (GPa) 36.9 75.9 50.3 114.8 201.1 95.2 205.4
Poisson’s ratio, Y 0.053 0.039 0.035 0.035 0.21 0.06 0.I76