Pressurized piping systems are often subjected to cyclic loads resulting from flow transients caused by valve sequencing, seismic encounters, and thermal gradients. The current ASME Boiler and Pressure Vessel Code treats the combination of static and dynamic loads in the same manner as static loads alone. Experiments have shown that cyclically loaded piping fails in a manner different than a statically loaded pipe. On the other hand, cyclically loaded pipe often fails resulting from fatigue or fatigue ratcheting. Ratcheting is defined as the incremental plastic strain growth of a component subjected to cyclic loading.
The objective of this paper is to investigate the relationship between a elbows' bend radius and the degree of ratcheting encountered through the use of finite element code (ABAQUS), closed form solutions by Dodge and Moore, and Edmunds and Beer.
To validate the finite element model used in the analysis a linear stress analysis was made by modeling a 1" standard weight butt weld elbow and then comparing the results to solutions developed by Dodge and Moore. To study ratcheting effect, non-linear finite element analysis was performed by adding 6" straight pipe tangents to each end of the pipe elbow, pressurizing the pipe system to 750 psi, applying restraints to one end so that all rotations and translations are fixed and then applying a cyclic 4000 in-lb moment in-plane to the other end for 13 cycles. The model utilized kinematic strain hardening and ratcheting is observed at the pipe/elbow junction where the highest degree of ratcheting should occur due to ovalization effects.
In addition, non-linear finite element analysis will be performed for a 3" and 6" bend radii. From the results, the general relationship between the elbows' bend radius and ratcheting effect can be studied.

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