T-stress solutions for through-wall circumferential cracks in straight pipes under bending M. Gintalas a, * , R.A. Ainsworth b , F. Scenini c a The University of Cambridge, Department of Materials Science and Metallurgy, Maxwell Centre, JJ Thomson Ave, Cambridge, CB3 0HE, UK b The University of Manchester, School of Mechanical, Aerospace and Civil Engineering, Pariser Building, Sackville Street, Manchester M13 9PL, UK c The University of Manchester, School of Materials, Sackville Street, Manchester M13 9PL, UK article info Article history: Received 14 December 2016 Received in revised form 2 April 2017 Accepted 20 April 2017 Available online 22 April 2017 Keywords: T-stress Crack Pipe abstract This paper reports the results of an extensive series of finite element calculations to provide normalised T-stress solutions for through-wall cracked pipes under bending for a range of crack sizes and pipe radius to wall thickness ratios. Comparisons with the limited solutions in the literature are used to give con- fidence in the numerical solutions obtained, which are shown to be sensitive to mesh refinement. The results are provided in a form that is suitable for use in practical constraint based defect assessment approaches. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction The fracture toughness of a material generally depends on the structural thickness, nature of the loading, relative crack size and crack-tip constraint [1]. However, these dependencies are dis- regarded for many engineering purposes and the plane strain fracture toughness, measured using deeply cracked standard bend specimens, is often used as a material property because it leads to the most conservative fracture assessments. Where cracks are small, for instance in pipes in the oil and gas industry and in nuclear power plant, this approach can be overly conservative because the constraint levels at the crack-tip are lower than those in standard cracked bend specimens. While full-scale pipe tests could be used to avoid introduction of this conservatism, this would require custom testing facilities and high testing costs. A more attractive option is to find a small-scale cracked specimen geometry which has a crack-tip constraint level similar to that in a large-scale cracked pipe. For example, low constraint levels and correspond- ing higher toughness values can be obtained by testing Single Edge Notch Bend (SENB) specimens with shallow cracks [2]. New designs of fracture toughness test specimen, such as curved compact tension specimens and compact pipe tension specimens [3,4], which would ensure similar or even the same constraint level at the crack-tip as cracked pipes, have been investigated. This has led to the application of Single Edge Notch Tension (SENT) speci- mens in the offshore industry, as this type of specimen has been shown to adequately reproduce the stress and strain fields in a pipe for a range of loadings [2,5]. In particular, it was found that the crack-tip constraint of a SENT specimen is close to that of an axially cracked pipe [6,7]. Additionally, it has been found that the fracture toughness obtained from low constraint SENT and shallow-notched SENB specimens is appropriate for the assessment of circumfer- ential flaws in pipes [8]. Analysis based on SENT and SENB speci- mens showed that an approach based on quantifying constraint using the elastic T-stress could be used not only to estimate initi- ation fracture toughness but also to develop constraint-corrected resistance curves [8]. In fact, T-stress has been considered suc- cessfully for resistance curve modelling by Nyhus et al. [9]. It has been shown that the ductile crack resistance curves can be nor- malised not only by Q but also by the T stress. This finding implies that the T stress influences ductile fracture. To apply elastic constraint based failure assessment methods to cracked structural analysis, the stress intensity factor, K I , may be paired with the T-stress. Such two parameter approaches may be used to apply material fracture toughness from small-scale labo- ratory specimens to fracture in large-scale components [10].A constraint-based fracture mechanics methodology based on a two- parameter K I e T characterization of the crack-tip fields has been * Corresponding author. E-mail address: [email protected] (M. Gintalas). Contents lists available at ScienceDirect International Journal of Pressure Vessels and Piping journal homepage: www.elsevier.com/locate/ijpvp http://dx.doi.org/10.1016/j.ijpvp.2017.04.004 0308-0161/© 2017 Elsevier Ltd. All rights reserved. International Journal of Pressure Vessels and Piping 152 (2017) 27e37
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