The ASME B&PV Code provides design by analysis rules that address failure mechanisms under cyclic loading. One of these potential failure mechanisms is incremental plastic collapse, or ratcheting. Miller presented the technical basis for the present Code requirements in a technical paper in 1959. Miller’s equations for the ratchet boundary address a beam under a cyclic through-thickness thermal gradient acting together with a steady axial mechanical load. This ratchet boundary applies approximately to a pressurized cylinder with through-thickness thermal bending stress. Conditions arise sometimes in practice where cooling or heating is applied simultaneously to the inner and outer surface of pressure boundary. The extreme case of such a scenario arises when both surfaces experience the same thermal condition such that there is a cyclic thermal stress but both zero membrane thermal stress and zero thermal bending stress The question is, could ratcheting occur in this case?
This paper derives the ratchet boundary for cases when the maximum temperature occurs mid-way through the thickness. The linearized stress due to thermal loading is zero. The solution is obtained using FE analysis and the Non-Cyclic Method (NCM) that has been proposed previously by the authors. The NCM is a generalization of the static shakedown theorem and allows the ratchet boundary to be calculated for both elastic and elastic-plastic cyclic stress states.