Design of Thick-Walled Vessels

Much information is available on the deformation and fatigue behavior of simple thick-walled cylinders [10-17], but it must be remembered that most process reactors will not be a simple hollow cylinder. Components such as connectors, threads and sleeves, windows, and removable closures make a complete analytical solution for a high-pressure system design problem quite involved. Useful design criteria for thick-walled vessels can be derived, however, under the assumption that the material of which the vessel is made is isotropic and that the cylinder is long (more than five diameters) and initially free from stress. The radial and tangential stresses in the walls are then only functions of the radius coordinate (r) and the internal pressure. Given the outer-to-inner wall radius ratio as o/i = w, and the yield point (To) of the material, the yield pressure (py) is 

An alternative strengthening mechanism is prestressing, called autofrettage, which ensures a more uniform stress distribution under load [16-20]. This intentional over-pressurizing of the vessel leads to a plastic-elastic interface that moves outward as the pressure increases. When the pressure is released, the residual stresses left as a result of radial expansion allow the vessel to be used up to the pressure at which it was subjected to autofrettage, without exceeding the yield point of the material. 

Easier to achieve than the autofrettage in order to increase the yield pressure is the construction of a compound cylinder. Here a second cylinder (or jacket) 

Steel Composition (wt. %) Maximum yield strength (bar) Maximum tensile strength (bar) Elongation (%) Hardness (Rb) 

Both high and low temperatures have a tremendous effect on the physical properties of materials used to construct high pressure vessels. With regard to very low temperatures, the toughness and impact strength of most alloy steels decrease as the temperature is reduced and one has to choose the applied materials carefully to avoid embrittlement. At high temperatures, however, the 

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Voorhees, Sliepcevich, and Freeman (204) have presented a procedure for calculating the time of rupture from creep and stress-rupture data normally available to a designer. Prior to the work of Voorhees the design of thick-walled vessels at high pressures and elevated temperatures was usually based upon the maximum principal stress and an allowable stress determined from creep and stress-rupture test data. This is the current method recommended by the ASME code (11) for vessels operating at pressures up to 3000 psi. 

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