Thermal membrane and bending stress fields exist where the thermal expansion of pressure vessel components is constrained. When such stress fields interact with pressure stresses in a shell, ratcheting can occur below the ratchet boundary indicated by the Bree diagram that is implemented in the design Codes. The interaction of primary and thermal membrane stress fields with arbitrary biaxiality is not implemented presently in the thermal stress ratchet rules of the ASME Code, and is examined in this paper.

An analytical solution for the ratchet boundary is derived based on a non-cyclic method that uses a generalized static shakedown theorem. The solutions for specific applications in pressure vessels are discussed, and a comparison with the interaction diagrams for specific cases that can be found in the literature is performed.

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