Simplified methods for the solution of thermal ratchetting problems.

This thesis presents a simple and conservative method for the analysis of inelastic cyclic thermal stress problems. It is developed for the analysis of severe cyclic thermal shocks combined with mechanical loads in thin walled tubes. The methods are intended to predict both the onset of ratchetting and the strains accumulated by small excursions into the ratchetting regime. The text begins by summarising the development of the upper bound shakedown theory-the main tool in this approach. Previous methods for simplified analysis using the upper bound method are reviewed and some ideas adopted. Building on this previous work, a new method of predicting the shakedown bound is developed. This is based on the upper bound analysis of particular ratchet mechanisms, resulting in a limiting equation for each mechanism. These equations are used to produce ratchet bounds for several thermal stress examples. These results are compared with the bounds produced by design code rules currently used for cyclic thermal stress. One observation reached in the prediction of these bounds was the lack of supporting evidence available. Therefore, a set of experiments were performed to show the bounds corresponding to two of these mechanisms. These used a new resistance heating method for applying the thermal cycles. The results are conservatively predicted by upper bound analysis. However, in some regions the effects of cyclic hardening reduces the strain accumulated, making the predictions over conservative. To investigate this effect some simple hardening rules are applied to the shakedown bounds. These are developed to give a prediction of accumulated strains within the ratchet region. Comparison is made both with the experiments and a finite element computer model. Finally, these predictions of shakedown and cyclic hardening controlled strain are combined to give a complete picture of cyclically heated tubes below the creep range.