Page 193 - Mechanics Analysis Composite Materials

178 Mechanics and analysis of composite materials

where p is measured in MPa. For axial plies, E.~= E~,O and E, = Q,O. The
corresponding stresses are

For circumferential plies, ex = 82.90, E, = El.90 and

As can be seen, 0;: > CT:'~,.This means that the cracks appear first in the axial plies
under the pressure p*that can be found from the equation c$;i(P*)= if;. The result
is p* = 5.53 MPa.
To study the second stage of loading for p >p*, we should put E2 = 0, and
v12 = 0 in Eqs. (4.121) for the axial plies. Then, stiffness coefficients and elastic
constants become

All = 54.06GPa, A12 = 2GPa, A22 = 93.4GPa,
E, = 54 GPa, E, = 93.3 GPa, v,, = 0.037, vp = 0.021 ,

Strains and stresses in the plies are

&L2)(p(p)= 0.59 x 10-~~,&;2)(p) = 0.7 10-3~,

a$2i(p)= 82.6p, c$i0(p) = 99.8p,
d$,(p) = 8.62~.

Total transverse stress in the circumferential plies can be calculated as

Using condition 62,90(P**) = a$ we find pressure p**= 5.95 MPa at which the
cracks appear in the matrix of the circumferential plies.
For p 2 p**,we should take E2 = 0 and v12 = 0 for all the plies. Then

Ai1 = 46.2GPa, A12 = 0, A22 = 93.4GPa,
(4.124)
E, =46.2 GPa, E, = 93.4 GPa, v.,, = v-~= 0
&i3)(p)= 0.72 x 10-~~, = 0.71 10-3~,
o[:i(p) = 100.8p, o\:J0(p) = 99.4~.

The total stresses acting along the fibers are