Department of Mechanical and Aerospace Engineering
Rutgers University
Piscataway, New Jersey 08854
PRESSURE VESSEL DESIGN USING COMPOSITE MATERIALS
GROUP 2
Graig Fergusson
David Pons
Ronnie Nomeir
Danielle Stephens
Russell Scola
Index
Index . . . . . . . . . 2
Introduction . . . . . . . . 3
Geometry and Design Constraints . . . . 6
Composite Material Design . . . . . 8
Preliminary Designs . . . . . . 13
Final Design . . . . . . . . 14
Materials . . . . . . . . . 15
Dimensions . . . . . . . . 18
Construction Procedure . . . . . . . 19
Design Changes . . . . . . . . 21
Testing . . . . . . . . . 24
Original Design Goal . . . . . . . 26
Future Plans . . . . . . . . 27
Introduction
Composite materials are widely used in industry and engineering processes today due to their many applications and advantages. A composite material is defined as a combination of two or more materials consisting of different properties. This union essentially creates a new material with properties that are unique from the beginning components. Although they are joined together, a visible separation between the individual materials is still present.
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.
The stress in the circumferential or hoop direction is given by equation 1.
[1. Hoop Stress]
The stress acting in the axial direction is given by equation 2.
[2. Axial Stress]
The stress acting on the hemispherical ends is given by equation 3.
[3. Hemispherical Ends]
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:
Where:
And
Also:
Where
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.