As early as the 1950’s, practitioners observed progressive distortion in thin-walled pressure vessels subjected to a constant axial stress and a cyclic thermal stress. In the late 1960’s, Bree [1] developed a theory and corresponding diagram plotting the primary membrane stress versus the cyclic thermal stress which delineates the various zones of plastic behavior. The zones include elastic cycling, plastic cycling, elastic cycling after initial plasticity, and ratcheting leading to incremental growth. This paper revisits the original Bree problem and investigates many of the recent advancements made to alleviate several of the simplifying assumptions Bree made in developing the diagram, to bring it in line with more modern operating conditions. In particular, a novel modification to the Bree diagram to account for the ratio of the yield stress at the operating extremums is proposed. This paper also reviews some advancements made to incorporate creep into the problem and discusses the operating conditions wherein creep effects may be significant. The outcomes of this paper will help expand the applicability of the Bree diagram, broadening its scope to encompass operating conditions more representative of modern applications.

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