|MadSci Network: Engineering|
For your math project, you are designing a "pressure vessel". A pressure vessel is any leak proof container. Choice of material and design is determined by the internal pressures that must be withstood. Aerosol cans are pressure vessels. Pressure vessel design is serious business, because pressure vessel failure is generally spectacular. Building steam boilers that failed have destroyed the buildings they were in. From the nature of your question, I think you are planning a controlled leak, i.e. send the "tennis" ball sized object into the neighbor's yard. (I was a teenager, too.) The basic design equation you want to work with is for "transverse hoop stress". For a unit length section of a cylindrical vessel, the simplified form of the equation is: stress = pressure * radius / wall thickness. For your example, 1000psi, 1.5inch radius, and 0.25inch wall thickness, the hoop stress is 6000psi, or 6ksi. (For more details, see "Pressure Component Construction, John F. Harvey.) In choosing your material, the key factor to consider is the yield stress. This is the stress that will begin to stretch the material. Choose a material that has a yield stress MUCH less than the calculated hoop stress. MUCH less means a factor of 5 or 10 times less. You want to do this for the following reasons. 1) Published yield stress values represent "typical". Due to defects in the material any particlular sample could yield and break at stress levels much less than "typical". A defect in a tube could be in the weld seam if it is a rolled and welded product; it could be along the region where the metal has flowed around a die and joined together in an extruded product. 2) You must consider the "rate" at which the pressure is applied. The faster the force is applied, the lower the level of stress before failure. You may have experienced this phenomoenon when breaking a string: pull slowly and the string can support a lot of weight; give it a quick yank and it snaps. Now, on to material choice. There are many "kinds" of aluminum, called alloys. An alloy is a base metal with other metals added to give different properties, such as increased strength. Each alloy can have many "tempers" which is an indication of processing done to the alloy. If you take a paper clip and begin bending it, you'll notice it gets harder to bend, then eventually breaks. You have changed the "temper" of the paper clip in the area of the bend through "work hardening". The following is a list of alloys (the number) and temper (the letter/number) and "typical" yield stress. (All values are from the Aluminum Association handbook of Standards and Data.) Aluminum foil aluminum: 1100-0 -- 5ksi 1100-H12 -- 15ksi 1100-H18 -- 22ksi Conduit aluminum, beverage can aluminum: 3003-O -- 6ksi 3003-H12 -- 18ksi 3003-H18 -- 27ksi Bicycle frame aluminum: 6061-O -- 8ksi 6061-T6 -- 40ksi I hope this gives you an understanding of what you are trying to design. 6061-T6 would be a safe material to use, but make sure you do your research before you launch any tennis balls. Christopher M. Seaman Alcoa Technical Center
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