A direct method for the evaluation of lower and upper bound ratchet limits

The calculation of the ratchet limit is often vital for the assessment of the design and integrity of components which are subject to cyclic loading. This work describes the addition of a lower bound calculation to the existing Linear
Matching Method upper bound ratchet analysis method. This lower bound calculation is based on Melan's theorem, and makes use of the residual and elastic stress fields calculated by the upper bound technique to calculate the lower bound ratchet limit multiplier. By doing this, the method combines the stable convergence of the upper bound method but retains the conservatism offered by the lower bound. These advantages are complemented by the ability of the Linear Matching Method to consider real 3D geometries subject to complex load histories including the effect of temperature dependent yield stress.
The convergence properties of this lower bound ratchet limit are investigated through a benchmark problem of a plate with a central hole subject to cyclic thermal and mechanical loads. To demonstrate the effectiveness of the method,
the ratchet limit of a thick walled pipe intersection, also subject to cyclic thermal and mechanical loads, is considered. Validation of these results is provided by full elastic-plastic FEA in Abaqus.