Calculation of KJ Under Secondary Loads in Isolation for R6

Abstract

A range of methods are currently available within R6 to calculate the inelastic secondary stress intensity factor under secondary loads in isolation, KJS. Each of these methods has different levels of associated conservatism depending on assumptions made, the complexity of the approach and the ability to account for different levels of elastic follow-up. Approaches that include an elastic follow-up factor, Z, for treating the interaction of combined primary and secondary stresses have recently been investigated by Ainsworth and James. However, the maturity of this recent work under combined primary and secondary loading means that one of the most significant aspect of the conservatisms in calculating the combined elastic-plastic stress intensity factor, KJ, is now in the calculation of KJS. This work considers existing approaches in R6 to calculate KJS and proposes a further approach allowing the value of Z to be altered. For comparison this work considers finite element analyses of a circumferentially cracked cylinder with four thermal distributions and two shallow cracks. These conditions were controlled to manipulate the level of Z. The magnitude of the temperature difference in these profiles has been increased over the analysis time to provide a relationship between the elastic and inelastic secondary stress intensity factors, KIS and KJS, with increasing secondary load to demonstrate any enhancement and subsequent redistribution of the secondary stress. These finite element estimates have been compared to existing methods in R6 to calculate KJS/KIS which reinforce the available advice in R6 for each case. The proposed approach also compares favourably with the finite element results through modification of Z. The proposed approach is also seen to be compatible with the other approaches within R6 as it has been shown to reproduce the Option 2 failure assessment curve for cases where the elastic follow-up is significant (i.e. Z ≫ 5) and conforms to the displacement controlled estimate of KJS in Section III.14.5 of R6.