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

Abstract Experimental evaluation of J–R curve in a crack growth situation requires `ηpl' and `γ' functions that are specific to a cracked geometry and loading condition. All derivations of existing `ηpl' and `γ' functions are for specific cracked geometry and loading. In this paper, direct limit load based general equations of `ηpl' and `γ' functions have been derived. Subsequently, new `ηpl' and `γ' 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 `ηpl' and `γ' functions for throughwall circumferentially cracked elbow under in-plane bending moment uses the very recently proposed new limit load formulas.

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