The Bree diagram shows, on a plot of primary stress and secondary stress range, the regions in which ratcheting, shakedown and cyclic plasticity occur. Although derived only for a very simple example problem, the Bree diagram is archetypal. We suppose the general case is similar. Not only are the regions of stress space corresponding to the qualitatively different types of behaviour determined, but the Bree analysis also provides expressions for the ratchet strain and the cyclic plastic strain range.
Unfortunately the original Bree paper is rather terse and short on detail. In the pdf linked below I have re-derived the diagram and the strain expressions in full detail.
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Read the detailed Derivation of the Bree Diagram
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