Introduction
The
material utilized for this design project is carbon fibers in an epoxy
matrix. It will be implemented using
lamina sheets of the material. When
dealing with composites, the term “matrix” is used to describe the material
that surrounds and binds together clusters of the stronger material which, in
this case, is the epoxy. The carbon
fiber is known as the “reinforcement” material.
When examined separately, carbon fiber and epoxy are quite different
materials when their individual properties are viewed. The carbon fiber is made out of long, thin
sheets of carbon. It is a chemically
inert rigid material that is difficult to stretch and compress. On the other hand, epoxy is a thermosetting
plastic, or resin, that is liquid when prepared but hardens and becomes rigid
(i.e., it cures)
when is heated. The setting process is
irreversible, so that it does not become soft again under high
temperatures. Epoxy plastics are good at
resisting wear and are highly durable when exposed to extreme environments.
The combination of these two materials into a
composite has many advantages. Along
with holding the fibers together, the matrix is advantageous since it protects
the carbon fiber from damage by sharing any stress incurred in the
element. It also provides flexibility to
the otherwise rigid material which aides in shaping and molding. Composites are
more versatile than metals and can be tailored to meet performance needs and
complex designs. As a whole, the
composite has a very high specific strength, which means it has a very high
strength and low weight. In many cases,
the composite is lighter than traditional materials for certain applications
with comparable strength. The joining of
the materials provides excellent fatigue endurance concerning the number of
load cycles and residual fatigue strength that is many times higher than that
of metals. In addition, the composite
has good resistance against, chemicals, acids, water, and varying
elements. There is very little corrosion
which leads to low maintenance costs over long periods of time.
The downside of composites is
usually the cost. Although manufacturing processes are often more efficient
when composites are used, the raw materials are expensive. Also, epoxy resins
are more expensive than polyester resins and vinyl ester resins, but generally
produce stronger more temperature resistant composite parts. Another usage concern is regarding the
material’s life-cycle. Since carbon
fiber reinforced plastics have an almost infinite lifetime, companies need to
find means in which to recycle the material.
The high amount of (often
manual) work required to manufacture composites has limited their use in
applications where a high number of complicated parts is required. Composites will never totally replace
traditional materials like steel, but in many cases they are very useful.
Carbon-epoxy
materials are finding increased structural uses in areas such as aerospace,
structural engineering, automotive, and sporting goods applications. It excels at replacing conventional materials
in objects ranging from space shuttle components, bridge reinforcements, car
body parts, and basketball backboards just to name a few. Furthermore, as technology evolves, new uses
will be found.
The primary goal of this design
project is to use the knowledge gained about composites and their advantages to
create a carbon fiber / epoxy pressure vessel.
The materials utilized in this project will consist of carbon / graphite
fibers acting as reinforcement in an epoxy matrix formed in several layers or
lamina. These materials are usually flexible, and can be molded into almost any
desired shape; in this case they will be molded into a cylinder and then baked
in a kiln or high pressure oven until both materials mesh together and become a
single hard structure. In order to
complete this goal, a $400 budget will be used to acquire all the materials
needed for design.
Geometry and Design constraints
A
pressure vessel is a container designed to operate at pressures typically over
15 P.S.I.G. The design of a pressure
vessel is entirely reliant upon mechanics of materials. Prediction of the ultimate strength of a
designed vessel is done using various failure theories. When building a pressure vessel out of
composite materials, some the theories employed to optimize strength and
predict failure are the Tsia – Hill energy-based interaction theory, and
maximum stress and strain theory. The
forces at applied in the different directions of the pressure vessel are
directly related to the magnitude of the pressure and are given below.
When comparing
the stresses at each location, it is clear from the above equations that the
hoop stress is twice as much as the stress in the hemispherical ends and axial
direction. This is a big consideration
when constructing the design and geometry of pressure vessel.
The geometry of the pressure vessel is
also a very important parameter. For
practicality issues a conventional pressure vessel shape is ideal. A pressure vessel used for nitrous oxide is
shown in figure 1 below.
This design is
effective for conserving space and is moderately strong. Unlike the pressure vessels in figure 1, the
designed vessel will not have any sharp geometry. If strength is the sole concern, the ideal
geometry would be a sphere. This would
virtually eliminate stress being concentrated in one area, such as what occurs
with sharp geometry. In order to
compromise between strength and size practicality, the designed pressure vessel
employs a cylindrical body with curved end caps. The curved end caps provide a smooth
transition minimizing stress concentrations.
Due
to the potential health hazard involved with high pressure vessels, safety is a
very important design consideration. If
cracking occurs while the pressure vessel is in service blasting effects can
occur due to the sudden effects of the expanding gas. There can also be fragmentation damage and
injury if the vessel completely ruptures.
If leakage occurs the results can also be severe. Depending on what is contained in the
pressure vessel poisoning or suffocation can occur. In order to reduce chances of these hazards a
safety factor of at least two is typically employed. Industrial pressure vessels are used in the United States
are usually built to one of two pressure vessel design codes. The first being the ASME (American Society of
Mechanical Engineers), the second is the API Standard 620, or the American
Petroleum Institute code. This provides
guidelines for lower pressure vessels that are not covered by the ASME
code.
Pressure
vessels used in industry are typically constructed of metals due to their high
strength and ease of machining. Metals
can be formed into virtually any shape, making it possible to construct the
most effective geometries.
Composite Material Design
On normal
isotropic materials, it is sufficient to describe their mechanical properties
using just two engineering constants. Usually the Young’s Modulus and the
Poisson’s ratio. However, on anisotropic materials, much more is required to
fully describe the material’s behavior. An anisotropic material is a material
that its properties at a specified point vary with direction or depend on the
orientation of reference axes. For example the material’s Young’s Modulus in
the x-direction might not be the same than in the y-direction. For this reason
the engineering mechanics of composite materials are a lot more complex to
study than isotropic materials and most of the isotropic equations do not apply
to composite materials and must be modified to study such behavior.
In
order to fully describe anisotropic materials, more engineering constants are
required. In the case of thin lamina where it is assumed to be under a state of
2-dimensional plane stress, the engineering constants E1, E2,
G12 and ν12 are necessary to describe the composite
material’s properties. E1 and E2 represent the Young’s
Modulus in the 1-direction and 2-direction respectively, G12
represents the shear modulus in the 1-2 plane and ν12 represents the
Poisson’s ratio from 1-2. A
unidirectional lamina representation is shown in the following figure. All of the properties described above hold
true in their respective direction, for example, E1 is only
applicable in the 1-direction or along the direction of the fibers. Some
numerical manipulation must be performed in order to relate the properties to
the corresponding x or y axis.
Following
there are the basic equations that are used in the design of process of
composite materials.
If we define a matrix T as :
Then the following equations can be used to relate
the mechanical properties and the stress and strain relations with their
respective axis:
With
these equations it is now possible to study the mechanics of composite
materials using traditional, isotropic material equations. In pressure vessel
design, it is important to find the optimal angle of fiber orientation that
will reduce the stress along the principal axes (1, 2). This can be achieved
with some manipulation of the equations above.
The maximum stress must never
become equal or greater than the failure stress of the material in its
respective axis. In order to ensure safety so that we are able to test the
pressure vessel, three different strength theories were employed in this design
to make certain that this condition does not occur. After relating the pressure
inside the vessel with the stress and strain acting on the lamina, the value
for the stress is compared to the maximum stress allowable before the material
fails. This stress is denoted the Ultimate stress or the Failure stress.
The first strength theory used
in the design was the Maximum Stress theory. This theory basically ensures that
the stress in either the 1 or 2 direction will never exceed the Failure Stress
in its respective direction. This theory is expressed in the simple following
equation:
The design will fail if:
This equation is very useful and simple to employ in the design. The
next equation used ensures that the maximum strain will not be reach the
ultimate strain. This theory is called the Maximum Strain Theory is expressed
in the following equations.
The design will fail if:
These equations are very simple and in most cases work very well;
however, they does not take into account the interaction between these stresses
and the strains acting together in the design. For that reason, the Energy
Based Interaction Theory (Tsai-Hill) is used.
The design will fail if:
It is then with the application of these
three different strength theories that we are able to ensure that the design
being developed is safe and should provide us with the confidence that it will
perform as required.
Design Options
The
preliminary designs for the pressure vessel to be constructed from the carbon
fiber epoxy material were narrowed down to the five that showed the most
potential.
One of the first proposed designs
was to construct the pressure vessel in one piece with no end caps. The benefit of this design would be higher
strength due to its single piece construction.
However, the manufacturing process of this design has practicality
issues. In order to get the correct
shape a mould would have to be constructed.
The lamina sheets would then be wrapped around the mold and baked. Therefore, the problem with this design is
removing the mold from the finished product.
The
final design a previous group used consisted of a cylindrical tube for the
vessel body and plastic end caps. Due to
the end caps being made out of plastic they were much weaker then the carbon
fiber epoxy body. The result of using
the plastic end caps is that when pressure is sufficiently high they crack.
Also, since these end caps are glued on, failure occurs since the strength is
weaker at these points. The final design
chosen by this group is therefore to construct a cylindrical body, as well as
end caps out of the carbon fiber epoxy material. The difficulty results in designing the end
caps. The strongest design is a circular
one, which is difficult when working with lamina sheets. The lamina sheets resemble a stiff fabric,
and forming them into a curved surface would be difficult. The final design for these end caps is
therefore to use thin strips of the material overlapping each other and angled
offset from each other. The result is
expected to resemble the figure below.
Once there end
caps are made, they are then attached to the main cylindrical body. The
cylindrical body is the easiest to produce during the manufacturing process,
since the thin composite sheets, being the shape of paper, are easy to mold
into a cylinder. In this project, and final design, we will be using 6 layers
of the composites. This will come into play when finding the correct fiber
orientation between lamina, since when transforming the stresses in the x and y
axes to the 1 and 2 axes like in the above figures, must be done for each
layer.
Unidirectional Carbon Fiber Cloth
Unidirectional Carbon
fiber cloth will be purchased from Jamestown Distributors in Rhode Island . It is sold by the yard and the majority to be
purchased will have a width of 12.5’’. One yard of 50 inch width cloth will also be
purchased to allow 0o – 90o orientation of layers at the
end caps. It is estimated that to
construct one vessel with the planned dimensions six yards of cloth will be
necessary. Two vessels will be
constructed and in order to ensure ample supply of carbon cloth 14 yards of the
12.5 inch width cloth will be purchased.
Valve Connection
In order to make the connection between the
valve and the pressure vessel, a valve connector will be machined out of carbon
steel. The carbon fiber cloth will be
wrapped around this part during the construction procedure. The valve connector is shown in figure
1.
Figure
1. Valve Connector
The
valve connector will have a large radius of .5’’, a small radius of .25’’, an
inner diameter of .312’’, and a length of 2.5’’. This part will be machined from 1018 carbon
steel starting from rods with a 2’’ diameter and 3’’ length. It will be
purchased from McMaster.
VALVE
The valve will
also be purchased from McMaster. The one
selected is a high pressure needle valve with a .5'' pipe, 2.75’’ length and
orifice diameter of .312’’. The selected
valve is rated for pressures of up to 10000 Psi. A picture of the valve is shown in figure
2.
Figure
2. High Pressure Needle Valve.
EPOXY
As
is shown later in the construction procedure of this report, the first layer of
carbon fiber cloth will be cured with epoxy.
This will create an impermeable layer which will allow testing with
water if necessary. One quart of West
System 105 epoxy resin will be used as well as .44 pints of 206 West System
hardener. The hardener will allow curing
at room temperature. To ensure the
correct mixing ratios are used a mini pump set made to dispense the correct
ratios of hardener and epoxy will also be purchased.
GEOPOLYMER RESIN
Aside
from the first layer, all layers of carbon fiber cloth will be cured with
Geopolymer resin. Unlike the epoxy, Geopolymer
is an inorganic polymer matrix that is resistant to temperatures of up to 1000o
C. It consists of an Alumina
Silicate solution and can be cured at room temperature. Organic polymer resins such as the epoxy to
be used for the first layer soften and ignite at temperatures between 200oC
and 600oC. However, when
compared to the epoxy, the Geopolymer is water permeable and has poor strain
compensation. This is why the first
layer will be cured with epoxy.
Table 1. Materials and costs
PRESSURE VESSEL DIMENSIONS
The
pressure vessel will be constructed around a clay mold with the following
dimensions. It will have a cylindrical body which is six inches in diameter and
8 inches long. It will have spherical
end caps with three inch radii, which will make the entire mold 14 inches long. Carbon fiber cloth with a thickness of .027 and
.033 inches will be used, making the minimum thickness of the vessel .162
inches. Overlapping of the cloth at the
end caps will add an additional 1.44 inches to each end. This will make the total length of the vessel
16.88 inches. Figure 3 below shows the dimension of the mold which
the vessel will be constructed around.
Figure 3.
Mold dimensions
CONSTRUCTION PROCESS
The first step in the
construction process will be to construct a clay mold. A valve connector will then be placed on the
clay mold in the center of each spherical end cap. Once this is done the carbon
fiber cloth which will be used is sold with a width of 12.5 inches and 50
inches will be cut into strips that are 8 and 1.5 inches wide.
Figure 4. stage 1 of construction sequence .
The second layer
will consist of two stages, the first being to wrap an 8 inch width cloth
around only the cylindrical body.
Figure
3, stage 2 of construction sequence stage 2 (Geopolymer Resin).
`The second stage will be to wrap 1.5 inch
wide strips wetted with Geopolymer resin around the end caps and 2 inches of the
cylindrical body. The strips will extend
2 inches into the cylindrical body to strengthen the interface between the
cylindrical body and the end caps. This
is shown in figure 4 below.
Figure 4, stage 3 of construction
sequence.
Each time this
construction sequence is completed 2 layers of the carbon fiber are added to
the vessel. Although the construction
sequence shown above has a valve connector at only one end, one will built into
both ends. This will allow the
installation of 2 valves, giving better circulation when removing the clay. The
clay mold will also be constructed around a quarter inch diameter rod
protruding through each valve connector.
When the first layer, which will be water impermeable, is complete the
rod will be removed and water will be circulated through the vessel via the
valve connectors at each end. The water
will dissolve the clay and leave the first layer. The second and third stages of the
construction sequence will then be completed creating a total of 2 layers. The construction sequence will then be
repeated using only Geopolymer resin for the remaining 4 layers.
Design Changes
The
first design change was the construction of the mold. Instead of using clay as was proposed earlier
the mold was constructed using brown sugar.
The brown sugar was placed in a container with the desired shape and
allowed to harden. The design change was
made in order to ensure easy removal of the mold once the first layer of carbon
– fiber epoxy was completed. When
compared to clay the brown sugar dissolve much easier in water and was very
hard when dry, making it easy to wrap the carbon – fiber strips around.
The
second design change was the valve connector.
Instead of machining the whole component from one piece of carbon steel,
a tapered .5 inch diameter, 3 inch long plumbing nipple, (double threaded short
pipe), was used. A circular disk with a 1.4 inch diameter was
machined from the carbon steel, and threaded to fit the plumbing nipple. To ensure strength the disk was welded to the
nipple. Figure 5 shows the completed
valve connector.
Figure 5. Completed valve
connector.
The third design change was the
construction process. Instead of wetting
the first layer of carbon – fiber cloth with epoxy and the remaining 5 layers
with Geopolymer resin, all six layers were wetted with epoxy. The final layer
was wetted with epoxy only on the side in contact with the mold and then
painted with a Geopolymer – Glass/Carbon Fiber mixture. This change was made to
increase the strength of the vessel.
Since the Geopolymer adds no tensile strength to the carbon fiber and is
very brittle cracking would occur. The
epoxy was used to ensure added tensile strength and better strain
capabilities.
Instead of using the needle valve
mentioned above, a ball valve was used.
The ball valve is rated for 500 psi as opposed to 10,000 when compared
to the needle valve. This change was
made because the needle valve was very difficult to work with.
COMPLETED VESSEL
Figures 6 and 7
show the completed pressure vessel before the Geopolymer was added to the last
layer. Figure 8 shows the pressure
vessel painted with the Geopolymer resin.
Figure 6
Figure 7
Figure 8
TESTING
The testing was
done to 100 psi with air using an air compressor. The pressure vessel was put under a wheel
barrow, which was weighed down with cinder blocks. The pressure vessel was tested at a distance
of 25 feet from the compressor. Figures
9 and 10 show the compressor and testing setup.
Figure 9
Figure 10
The pressure
vessel was examined for leaking at 20 psi.
Minor leaking did occur but it did not effect the performance at the
pressures tested. The pressure was then
increased to 70 psi, followed by 100 psi. The pressure was held and no failures
occurred aside from the slight leak somewhere on the cylindrical body. These results show that it is very difficult
to hand construct a cylindrical pressure vessel with spherical end caps using
carbon fiber cloth. Although all layers
overlapped there was still a leak possibly due to misalignment of strips or not
enough epoxy. The geo-polymer did not
stick well to the
Original Design Goal
Our original
design goal was to create a pressure vessel comprised of carbon fiber/ epoxy
matrix material. We were to use the fibers oriented at 0 and 90 degrees for a
total of six layers. Our end result was constructed completely of carbon fiber
epoxy. Our design was the first design to include carbon fiber epoxy end caps.
Previous groups used PVC piping end caps, attaching them with epoxy. These
groups found that failure always occurred where the caps were attached, forcing
us to find a better and stronger design. The design we used was to have
spherical end caps made from carbon fiber strips oriented offset from each
other. This after testing was found to be very strong, causing no failure at
the ends, solving the design failures of the other groups. However with this
problem solved, another one arose in our testing. While testing a leak occurred
somewhere along the cylindrical body, showing that our design may have been
good, however our construction may have had a flaw. Since this vessel was built
by hand, there is going to be some sort of human error associated, especially
this being our first manufacturing process. However, with this mind we still
completed our original design goal and improved on last years.
Future Plans
The
most important thing that would be solved in future work would be the
manufacturing process. Other procedures instead of manual construction could be
used, like filament finding, to create a more precise and overall better final
product. Also for future reference, it would be beneficial to create more than
one vessel so the manufacturing process would be smoother and each successive
vessel will be an improvement on the previous one. If more precise
manufacturing processes couldn’t be
employed, some improvements to the current manufacturing process could be
incorporated into the design to enhance the overall quality of the final
product. For Example, during the process, we learned that using different
techniques for the carbon fiber lay-up would have been more efficient. The
resin used had a relatively fast drying time so the team had a very short
amount of time to lay up a layer of carbon fiber. With practice, we learned
that it was better to work with small batches of Epoxy at a time and
consecutively make more as the lay-up process goes along. Also, all of the
layers should be laid up consecutively right after the other one, this ensures
that any irregularity on the surface could be covered up by the next layer and
thus resulting in a much smoother and uniform pressure vessel. Another thing
that could have been employed was the use of a Vacuum bag. This would have
ensured that the space between layers would have been drawn out, greatly
enhancing the strength, uniformity and quality of the pressure vessel. The last important point that the team learned
in the manufacturing process was that of Geopolymer resin is not suitable for
use in a pressure vessel. Since the resin does not have any strain capacity, it
cracks easily. Some component would have to be added to the Geopolymer resin to
increase its strain capacity in order to be considered suitable in pressure
vessels.
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