This paper addresses load order effects on elastic-plastic J estimation under combined mechanical and thermal loads for circumferentially cracked pipes. The load order effects, for various thermal gradient types and mechanical loading, are evaluated for a range of magnitudes of the loadings, crack sizes and material hardening. Variations of elastic-plastic J obtained by finite element analysis are compared with existing and proposed methods for use with the R6 defect assessment procedure. The load order effects are presented on the R6 failure assessment diagram (FAD) by calculating the two parameters Kr and Lr from the finite element results. It is shown that there are significant load order effects at large secondary stress cases but these are successfully treated by simplified methods proposed for use with R6.