Pressure Vessels Stress Concentrations
The normal equations for stresses in pressure vessels are based on the assumption that there is continuous elastic action throughout the member, and that the stress, for simple tension and compression, is uniformly distributed over the entire cross section.
Abrupt changes in section geometries, however, can invalidate these assumptions, leading to great irregularities in stress distribution, with large stresses developed in a small portion of the member. These are called peak stresses or stress concentrations. In pressure vessels they occur at transitions between thick and thin portions of the shell, and at openings, nozzles, or other attachments.
The importance of these stresses depends not only on their absolute value, but also on material properties, such as ductility, the relative proportion of the stressed to the unstressed part of the member, and on the type of loading on the member (static or cyclic).
For example, stress concentrations in a pressure vessel subjected to only a steady pressure are of little importance if the vessel is made of a ductile material such as a mild steel. A ductile material yields at these highly stressed locations, allowing the stress to be transferred from the overstressed fibers to adjacent understressed ones. If the load is repetitive (cyclic), however, the stresses can become significant.
Stress concentrations create peak stresses (Section 116), and they are used to determine the design fatigue life of the vessel. Besides keeping the primary membrane stresses within the limits set by allowable tensile stresses, it is equally important to keep stress concentrations within acceptable limits when fatigue is a factor.
A rigorous mathematical analysis of peak stresses is frequently impossible or impracticable, and therefore experimental methods of stress analysis are used. The ASME Code, Section VIII, Division 1, does not require a consideration of peak stresses, but Division 2 gives some design rules to permit considering stress intensity factors and stress concentration factors in determining peak stresses.
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