Page 257 - Mechanics Analysis Composite Materials

242 Mechanics and analysis of composite materials
equal to zero for the homogeneous model and are specified by Eqs. (5.49) for the
laminated one. Because p6 = h/2, we can write these coefficients in the form

showing that C,, 4 0 for 6 + 0.

5.4.3. Laminate composed of angle-ply layers

Consider a laminate with the structure [+$/-+Ip, wherep is the number of layers
each consisting of +4 and -4 unidirectional plies. Constitutive equations (5.5) for
this laminate are

(5.50)

where

where, h is the laminate thickness, 6 the ply thickness, and A,, are material stiffness
coefficients specified by Eqs. (4.72). As can be seen, the laminate is anisotropic
because +4 and -4 plies are located in different planes. Homogeneous model of the
laminate ignores this fact and yields c14 = c24 = 0. Calculations show that these
coefficients, not being actually equal to zero, practically do not influence the
laminate behavior for h/6 220.
Laminates in which any ply or layer with orientation angle +#Jis accompanied
by the same ply or layer but with angle -4 are referred to as balanced laminates.
Being composed of only angle-ply layers these laminates have no shear-extension
coupling (B14 = B24 = 0), bending-stretching and shear-twisting coupling (CIl=
C12 = C22 = CU = 0). As follows from Eqs. (5.50), only stretching-twisting and
bending-shear coupling can exist in balanced laminates. These laminates can
include also 0" and 90" layers, but membrane-bending coupling can appear in such
laminates.