Page 183 - Mechanics Analysis Composite Materials

168 Mechanics and analysis of composite materials

much higher stiffness and elongation fail because their ultimate elongation is
smaller. This failure is accompanied with a system of cracks parallel to fibers which
can be observed not only in cross-ply layers but in many other laminates that
include unidirectional plies experiencing transverse tension caused by interaction
with the adjacent plies (see Fig. 4.36).
Now assume that the acting stress 0 2 b, where 8 is specified by Eq. (4.109) and
corresponds to the load causing the first crack in the transverse ply as in Fig. 4.37.
To study the stress state in the vicinity of the crack, decompose the stresses in three
plies shown in Fig. 4.37 as

0
0x1 = 0x3 = 01 + 01, ax2 = 0; - 02 , (4.110)
and assume that the crack induces also transverse through-the-thickness shear and
normal stresses

zxz; = z;, azi = s;, i = 1, 2, 3 . (4.1 11)

Stresses 0: and 0; in Eqs. (4.1 10) are specified by Eqs. (4.108) with 0 = d
corresponding to the acting stress under which the first crack appears in the
transverse ply. Stresses 01 and 02 should be self-balanced, i.e.,

Fig. 4.36. Cracks in the circumferential layer of the failed pressure vessel induced by transverse (for the
vessel, axial) tension of the layer.

t'

Fig. 4.37. A cross-ply layer with a crack in the transverse ply.