Page 194 - Mechanics Analysis Composite Materials

Chapter 4. Mechanics of n composite layer 179

To determine the ultimate pressure, we can use two possible strength conditions -
for axial fibers and for circumferential fibers. Condition o~.~(p)= 0;' yields
p = 20.9 MPa, while condition o12so(p)= 17;gives p = 20.4 MPa. Thus, the burst
pressure governed by the failure of the fibers of circumferential plies is
p = 20.4 MPa.
The strains can be calculated for all three stages of loading using the following
equations:
e forp<p*

c.JP) = 4:;(PI;

e for p* < p d p**
E.Y..l.(P> = c:.:; w1 + E::; (p -P*1;

e forp**<pbp
= E:!,!($) + E:2;,,* -p*)+ E.tl,!(p -p**) .

For the pressure vessel under study, dependencies of strains on pressure are shown
in Fig. 4.47 (solid lines). Circles correspond to the failure of the matrix and the
fibers.
For comparison, consider two limiting cases. First, assume that no cracks occur in
the matrix, and the material stiffness is specified by Eqs. (4.123).The corresponding
diagrams are shown in Fig. 4.47 with broken lines. Second, assume that the load is
taken by the fibers only, Le., use the monotropic model of a ply introduced in

P,MPa
25 r

15t /,
2o
'/
10 -
I'
5 /'
/'
0 E, ,%
0 0.5 1 1.5
Fig. 4.47. Dependence of the axial and the circumferential strains of the carbon-epoxy pressure vessel on
pressure: -model allowing for cracks in the matrix; ---- model ignoring cracks in the matrix;
---_model ignoring the matrix.