A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underlying concepts, and allows new rates to be constructed. Mathematical and thermodynamic^ restrictions on these are shown. As a result, it can be demonstrated that the Eulerian strain rate is an objective rate of logarithmic strain, based on a spin easily derivable from the general form. Interrelations between other known spins and objective rates emerge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latter involving purely isotropic and purely kinematic hardening. The application of the resulting models to the simple shear deformation is shown.

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When the primary plus secondary stress range exceeds 3 Sm, the current ASME Code rules on simplified elastic-plastic analysis impose two separate requirements to evaluate the potential for ratcheting. The range of primary plus secondary stress excluding thermal bending must be less than 3 Sm, and the thermal stress must satisfy the Bree criterion for thermal stress ratchet. It has been shown previously that this method can be unconservative, i.e. predict shakedown when elastic-plastic analysis shows ratcheting. This paper clarifies the interaction between thermal membrane and bending stress in the presence of a primary membrane stress. An analytical model is used to derive the closed-form ratchet boundary for combined uniform loading of this type. The impact of having stress gradients along the wall that are typical for discontinuities is studied numerically. Simple modifications of the current Code methods are suggested that would achieve a clearer and better-justified set of rules.

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