The shakedown behavior of a thin cylinder subject to constant pressure and cyclic thermal loading is described by the well known Bree diagram. In this paper, the shakedown and ratchetting behavior of a thin cylinder, a thick cylinder, and a thick cylinder with a radial crosshole is investigated by inelastic finite element analysis. Load interaction diagrams identifying regions of elastic shakedown, plastic shakedown, and ratchetting are presented. The interaction diagrams for the plain cylinders are shown to be similar to the Bree diagram. Incorporating a radial crossbore, $Rc∕Ri=0.1$ or less, in the thick cylinder significantly reduces the plastic shakedown boundary on the interaction diagram but does not significantly affect the ratchet boundary. The radial crosshole, for the geometry considered in this study, can be regarded as a local structural discontinuity and neglected when determining the maximum shakedown or (primary plus secondary stress) load in design by analysis. This may not be apparent to the design engineer, and no obvious guidance, for determining whether a crosshole is a local or global discontinuity, is given in the codes.

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