The master failure curve of pipe steels and crack paths in connection with hydrogen embrittlement A. Elazzizi a , M. Hadj Meliani b,c,* , A. Khelil b , G. Pluvinage c , Y.G. Matvienko d a Depart. of Mechanics, Faculty of Mechanics, USTO University, Algeria b LPTPM, FT, Hassiba BenBouali University of Chlef, 02000 Chlef, Algeria c LaBPS-ENIM, Paul Verlaine University of Metz, Ile de Saulcy 57045, France d Mechanical Engineering Research Institute of the Russian Academy of Sciences, 4 M. Kharitonievsky Per., 101990 Moscow, Russia article info Article history: Received 19 October 2013 Received in revised form 6 November 2014 Accepted 10 December 2014 Available online 7 January 2015 Keywords: Master failure curve Notch Hydrogen embrittlement abstract This paper provides some critical review of the history and state of two elastic fracture mechanics (K and T) and relationship to crack paths. A particular attention is given in the case of hydrogen embrittlement. A fracture toughness transferability curve (K rc eT ef ) has been established for the X52 pipe steels described by a linear relationship where T ef is the average value of T stress over the characteristic length of the fracture process. A mechanism involving influence of the T ef ;c -stress on void growth for ductile failure is proposed; the ef- fects of hydrogen on crack paths from the viewpoint of microstructural aspects are disputed. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. Introduction Fracture toughness is now considered as not intrinsic to ma- terial but depends on geometry, thickness, loading mode and more generally to constraint. Recent numerical and experi- mental studies have attempted to describe fracture in terms of two or three fracture parameters [1e3]. The elastic stress fields in a region surrounding the crack tip can be characterized by the following solution [1]: s ij ¼ K I ffiffiffiffiffiffiffiffi 2pr p f ij ðqÞþ Td xi d xj þ A 3 ffiffiffiffiffiffiffiffi 2pr p þ 0ðrÞ (1) where K I is the stress intensity factor, f ij (q) is the angular function, d ij is the symbol of Kronecker's determinant. A polar coordinate system (r,q) with origin at crack tip is used. Several methods have been proposed in literature to determine the T- stress for cracked specimen. The stress difference method has been proposed by Yang et al. [4]. It was noted [5e8] that T- stress, which is the non-singular linear elastic stress compo- nent parallel to the crack, characterizes the local crack tip stress field for elastic linear material, and the elastic plastic material with the restriction of small-scale yielding condi- tions. Various studies have shown that T-stress has signifi- cant influence on fracture toughness, crack growth direction, A 3 has some influence crack stability [9e15]. The KeT and KeA 3 approaches lead to a two-parameter fracture criterion. With K as the driving force and T or A 3 a constraint parameters, a master failure curve can be suc- cessfully used to take into account the constraints of stress * Corresponding author. LPTPM, FT, Hassiba BenBouali University of Chlef, 02000 Chlef, Algeria. E-mail address: hadjmeliani@yahoo.fr (M. Hadj Meliani). Available online at www.sciencedirect.com ScienceDirect journal homepage: www.elsevier.com/locate/he international journal of hydrogen energy 40 (2015) 2295 e2302 http://dx.doi.org/10.1016/j.ijhydene.2014.12.040 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.