Advanced Composites Final Paper

Aileen Vandenberg
December 10,2010
ECI 236
Memo: Pressure Vessel Project

To Ms. Composite Knowitall:

In the table below you will find the final design for the pressure vessel as well as the minimum mass
design and minimum cost design. I assumed a safety factor of 2.5 and used the Tsai-Wu failing criteria.

Laminate Material Cost (units) Mass (kg) Function
Code Value, F
Final Design [±45/±60/90]s Graphite/Epoxy 3180.86 6.36 2.418
Min Mass [±45/±60/90]s Graphite/Epoxy 3180.86 6.36 2.418
Min Cost [±60]8s Glass/Epoxy 2243.48 22.43 4.527

Here is a sketch of the pressure vessel.

The loads in the pressure vessel were calculated
by first calculating the hoop or circumferential
stress, σy, and the axial or longitudinal stress, σx,
as shown.

The hoop stress is defined as

σy = pr/t.

While the axial stress is

σx = pr/2t,

where p is the internal gauge pressure of
0.75MPa, r is the internal radius, and t is the
thickness.

The loads are then calculated as follows,

Nx = σxt = 93750 N/m Ny = σy t = 187500 N/m.

The volume of each lamina was found to be the same for both graphite/epoxy and glass/epoxy choices.
This is due to the fact that both had a ply thickness, tp, of 0.125mm. The volume for a very thin-walled
cylinder is

V = (surface area) x (ply thickness) = (лdL) x tp = (л x 0.5m x 2m) x (0.125e-3m) = 3.927 x 10-4 m3

The density of each lamina option was calculated by using the following equation,

ρ = ρfVf + ρmVm where,

the density of the fiber/matrix = (specific gravity of fiber/matrix) x (density of water).

ρgraphite = 1.8 x 1000 kg/m3` ρglass = 2.5 x 1000 kg/m3 ρepoxy = 1.2 x 1000 kg/m3
ρgraphite = 1800 kg/m3 ρglass = 2500 kg/m3` ρepoxy = 1200 kg/m3

Using these values and the volume fiber/matrix fraction values found in Table 2.1 of Kaw's text book,
the density of each lamina is

ρgraphite/epoxy = (1800 kg/m3)(0.70) + (1200 kg/m3)(0.30) = 1620 kg/m3`

ρglass/epoxy = (2500 kg/m3)(0.45) + (1200 kg/m3)(0.55) = 1785 kg/m3.

The mass of each lamina, calculated by the following formula M = ρ V, is then

Mgraphite/epoxy = (1620 kg/m3) x (3.927 x 10-4 m3) = 0.636 kg

Mglass/epoxy = (1785 kg/m3) x (3.927 x 10-4 m3) = 0.701 kg.

The cost per lamina, calculated by the formula C = M x c, where c = cost/unit mass, is

Cgraphite/epoxy = (0.636 kg) x (500 units/kg) = 318.09 units

Cglass/epoxy = (.701 kg) x (100 units/kg) = 70.10 units.

The lamina properties can be summarized in a table.

Density (kg/m3) Volume (m3) Mass (kg) Cost (units)
Graphite/Epoxy 1620 3.927 x 10-4 0.636 318.09
Glass/Epoxy 1785 3.927 x 10-4 0.701 70.1

After finding these properties, the next step was to choose an initial design. I started with minimum
mass design first. Since graphite/epoxy is lighter than glass/epoxy I looked only at this type of lamina
for minimum mass designs.

For my initial layout sequence I started with the cross-ply symmetric lamina sequence [0/90]s. This
was to insure that no coupling took place at all between forces and moments.

The minimum strength ratio for this sequence, using Tsai-Wu criteria and Promal, was 0.9196. Since
my safety factor was set to 2.5, I took this number and divided it by 0.9196, then multiplied by the
number of plies in the original layout sequence to get the total number of plies needed to satisfy this
condition.

2.5/0.9196 = 2.719 => 2.719 x 4 ≈ 12 plies needed.

Thus, the layout sequence that would satisfy this safety factor would be [0/90]3s. This results in a
minmum strength ratio of 2.759. This is greater than 2.5 and, therefore, is safe.

The cost and mass values were calculated by taking the number of plies and multiplying by the values
found in the previous table. For example, for a 12 ply laminate the total cost is

C = 12 x 318.09 = 3817.04 units

and the total mass is

M = 12 x .636 = 7.632 kg

Here are the summaries for minimum mass and minimum cost design trials. The highlighted rows
indicate the most minmum design found.

Minimum Mass Design
Lamina type # of Minimum Mass (kg) Cost (units) Function
Stacking Plies Strength Value, F
Sequence Ratio
[0/90]3s Graphite/Epoxy 12 2.612 7.632 3817.04 2.901
[±45/±602]s Graphite/Epoxy 12 3.181 7.632 3817.04 2.901
[±45/±60/90]s Graphite/Epoxy 10 2.588 6.360 3180.90 2.418
[0/90/90]s Graphite/Epoxy 10 2.566 6.360 3180.90 2.418
[0/904/0/904/0] Graphite/Epoxy 11 2.595 6.996 3498.99 2.660

Minimum Cost Design
Lamina type # of Minimum Mass (kg) Cost (units) Function
Stacking Plies Strength Value, F
Sequence Ratio
[0/902]6s Glass/Epoxy 36 2.506 25.236 2523.60 5.092
[±60]8s Glass/Epoxy 32 2.617 22.430 2243.48 4.527
[±45/±60/90]3s Glass/Epoxy 36 2.812 25.230 2523.60 5.092
[±45]10s Glass/Epoxy 40 2.737 28.04 2803.87 5.659
[45/60]29s Glass/Epoxy 87 2.548 60.987 6098.70 12.307

The function value, F, is computed by

F = A/B + C/D

where B = 6.36 kg and D = 2243.48 units.

For example for the initial design [0/90]3s the function is found as

F = 7.632/6.360 + 3817.04/2243.48 = 2.901

Here is the summary for minimum functional values, F.

Minimum Function Value Design
# of Minimum Strength Mass (kg) Cost (units) Function
Stacking Sequence Plies Ratio Value, F
GR GR GL 20 2.784 25.23 2523.48 5.092
[0 /90 /0GR/90 2]2s

[0GL/90GL/0GR/90GR2]2s 20 2.784 25.230 2523.48 4.527
[0GL/±60GR/90GL2]2S 20 2.784 25.230 2523.48 5.659

[0/90/90]s gr/ep 10 2.566 6.360 3180.90 2.418
[±45/±60/90]s gr/ep 10 2.588 6.360 3180.90 2.418

Thus, the final design is as indicated in the first table.

All the best,

Aileen Vandenberg

Advanced Composites Final Paper

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