Page 385 - Mechanics Analysis Composite Materials

370 Mechanics and analysis of composiie materials

A = 1/3. Because Nxu = 0, the structure of the laminate is symmetric with respect to
the cylinder meridian, and Eqs. (8.12)-(8.14) can be reduced to

h=-3PR (8.16)
2a, '

k
Chi(3cos24i- 1) = 0 . (8.17)
i= 1
Comparing Eq. (8.16) with the corresponding expression for the thickness of the
metal pressure vessel which is h, =pR/G we can see that the thickness of an optimal
composite vessel is 1.5 times higher than h,. Nevertheless, because of higher
strength and lower density, composite pressure vessels are significantly lighter than
metal ones. To show this, consider pressure vessels with radius R = 100 mm made of
different materials and designed for the burst pressure p = 20 MPa. The results are
listed in Table 8.1. As can be seen, the thickness of the glass-poxy vessel is the same
as that of the thickness of the steel vessel, because the factor 1.5 in Eq. (8.16) is
compensated by the composite strength which is 1.5 times higher than the strength
of steel. However, the density of a glass-epoxy composite is much lower than the
density of steel, and as a result, the mass of the unit surface area of the composite
vessel makes only 27% of the corresponding characteristic for a steel vessel. The
most promising for pressure vessels are aramid composites having the highest tensile
specific strength (see Table 8.1).
Consider Eq. (8.17) which shows that there can exist an infinite number of
optimal laminates with one and the same thickness specified by Eq. (8.16).
The simplest is the cross-ply laminate having k = 2, Q,l = 0", hl =ha, and
+2 = 90",h2 = h90. For this structure, Eq. (8.17) yields h90 = 2ho. This result seems
obvious because Ny/Nx = 2. For symmetric &+ angle-ply laminate, we should take
k = 2, hl = h2 = h4/2, 4, = +4, 42= -6. Then

cos Q, = 1 4 = 40 = 54"44' .
2
3'
Table 8.1
Parameters of metal and composite pressure vessels.
Parameter Material

Steel Aluminum Titanium Glass- Carbon- Aramid-
epoxy epoxy epoxy
Strength, Z,5, (MPa) 1200 500 900 1800 2000 2500
Density, p (g/cm3) 7.85 2.7 4.5 2.1 1.55 1.32
Thickness of the vessel, 1.67 4.0 2.22 1.67 1.5 1.2
h,, h (mm)
Mass of the unit surface 13.1 I 10.8 10.0 3.51 2.32 1.58
area, ph (kg/m2)