In ASME VIII-2 Code 2004 and previous versions, evaluation procedures for thermal stress ratcheting were provided, which is substantially based on Bree’s diagram. According to VIII-2-2004, the application scope of this method is limited to “in shell” and “general membrane stress due to pressure”. In ASME VIII-2 Code 2007 and later versions, the limitation of “in shell” has been removed and “general membrane stress” was extended to “general or local primary membrane equivalent stress”. However, these methods have their own limitations, and consequently can’t apply to the engineering project widely and rapidly. Rapid thermal stress ratcheting assessment calculations for pressured components with arbitrary geometries and discontinuity effects based on the Linear Matching Method (LMM) were available. Several cases are provided to show how to establish shakedown and ratchet boundaries quickly and easily for components subjected to arbitrary combinations of thermal-mechanical loads. The Bree-like ratchet boundaries for several typical components are obtained, which is useful and valuable for engineering design in Design-by-Analysis (DBA) for pressured components.

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