N-Bar Problems As Approximations to the Bree Problem

The Bree solution to the problem of a ratcheting cylinder under constant pressure and cyclic thermal load is a fundamental result in nuclear engineering and widely used as the technical basis for the ASME Boiler and Pressure Vessel Code and other design methods. However, because the loading conditions in the Bree problem are difficult to achieve experimentally there have been relatively few works experimentally examining the problem and extending it to other relevant design situations, for example cladded components. In contrast, 2-bar problems are widely studied experimentally and are relatively easy to setup. These 2-bar problems are thought to be representative of Bree-type geometries, but a formal connection has not been demonstrated. This work formally establishes the connection between the Bree cylinder and an n-bar problem — a coupled bar experiment with, in general, more than two bars linked in parallel. The connection suggests that n-bar experiments using a fairly limited number of bars might be an experimentally-accessible setup that better represents ratcheting phenomenon in actual nuclear pressurized components. Such experiments could test surrogate cladded or multi-material components by using bars of different materials. Finally, this work suggests control schemes that yield optimally efficient n-bar experiments — experiments that best replicates a Bree cylinder with a limited number of bars.