Page 204 - Mechanics Analysis Composite Materials

Chapter 4. Mechanics of a composite layer I89

Functions 07 and WIZ include all the nonlinear terms. Inverse form of these
equations is

where

Repeating the derivation of Eqs. (4.127) but using this time Eqs. (4.133) as
constitutive equations for the ply we arrive at

where (s = sin 4, c = cos 4)

AI\ = (C??.? + C~~C')O?~C~~CSWI~, +
A?? = (C22c2+ CI~S~)W~~C~~CSWI,,
-
Al;k = (CQ - CZ2)CSW? + C44(C2- S2)WIZ .
These equations can be used in conjunction with the method of elastic solutions
described in Section 4.1.2.
As an example, consider the two-matrix glass-epoxy composite described in
Section 4.4.2 (see also Figs. 4.16, 4.30, and 4.31). Theoretical (solid lines) and
experimental (broken lines) stress-strain diagrams for f30", 2c45", and f75" angle-
ply layers under tension along the x-axis are shown in Fig. 4.59.
Angle-ply layers demonstrate a specific type of material nonlinearity - structural
nonlinearity that can occur in the layers composed of linear elastic plies due to the
change of the plies orientations caused by loading. Because this effect manifests
itself under high strains, consider a geometrically nonlinear problem of the ply
deformation. This deformation can be described with the longitudinal, EI, trans-
verse, E?, and shear, y12,strains that follow from Fig. 4.60 and can be expressed as

(4.134)

In addition to this, we introduce strain E:'- in the direction normal to the fibers

(4.135)