One of the common methods of construction of vessels for high to ultra-high pressure applications is the wrapping technique. In this method, relatively thin plates (normally in the range of 6 mm) are rolled to proper curvature, wrapped around the core or the preceding layers and then welded. In this fashion, a prestress is gradually built in the cylinder wall which would compensate and moderate the extreme stresses due to internal pressure. Relying on such prestress, however, should be done only with careful consideration of stress relaxation that will take place while the vessel is in service, especially in high temperature services. In this paper, the initial stresses due to wrapping are obtained. These stresses are due to shrinkage of the weld as well as the plate affected by the heat of welding. The power function stress-creep strain rate is employed to predict the relaxation of interface pressure between any two adjacent layers. The creep stress distribution based on relaxing interface pressures are given as a function of time. In such vessels, in order to maintain the same safety factor as existed when the vessel was constructed, the internal pressure must be decreased with time. A relationship between the internal pressure and time, based on a constant safety factor, is obtained. Alternately, for the case of internal pressure being kept at the same level, a relationship is obtained that would give the decreasing safety factor or the vessel as a function of time.

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