The objective of this report is to describe the development of analysis methods for estimating the decrease in crack initiation toughness, from a reference plane strain value, due to positive straining along the crack front of a circumferential flaw in a reactor pressure vessel. The analysis methods are based on two different approaches that are currently being developed to analyze and to explain the effects of transverse strain and stress states on fracture toughness. The first approach is a micro-mechanical approach that provides a relation between fracture toughness and more fundamental material properties that can be determined experimentally. The second approach focuses on the development of correlation parameters that relate fracture toughness with nominal stress and strain states. In the first phase of this work, the scope of the investigation is limited to crack front constraint conditions that can be described in terms of conventional one-parameter (K or J) in-plane near-tip fields and the transverse strain. Validation checks of the analysis methods against existing fracture data for conditions of contained crack tip yieldings are promising but incomplete. Recommendations for subsequent phases of the work considered necessary to provide more precise estimates on the effects of positive out-of-plane straining on themore » crack initiation toughness of circumferentially oriented flaws are included. 91 refs., 53 figs., 7 tabs.« less