New `ηplʹ and `γʹ functions to evaluate J–R curve from cracked pipes and elbows. Part I: theoretical derivation

Experimental evaluation of J–R curve in a crack growth situation requires `ηplʹ and `γʹ functions that are specific to a cracked geometry and loading condition. All derivations of existing `ηplʹ and `γʹ functions are for specific cracked geometry and loading. In this paper, direct limit load based general equations of `ηplʹ and `γʹ functions have been derived. Subsequently, new `ηplʹ and `γʹ functions, which are not available in the literature, for pipe and elbow geometry with various crack configurations under different loading conditions have been derived. The derivations of `ηplʹ and `γʹ functions for throughwall circumferentially cracked elbow under in-plane bending moment uses the very recently proposed new limit load formulas.