PSI - Issue 13

J Beswick et al. / Procedia Structural Integrity 13 (2018) 63–68 Beswick et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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Material stress-strain responses of AR and PS material were obtained with tensile specimens. These were machined from the broken halves of SENB specimens and tested at -140°C according to BS 10002 (1992). The results showed clear elastic behaviours up to proportionality stresses, with E =215.3 GPa,  0 =600 MPa for AR, and E =203.3 GPa,  0 =400 MPa for PS, followed by Lüders plateaus and strain-hardening regimes. The former were removed and the latter described by power-law curves for the purposes of FEA of cracked specimens. The data was firstly analysed using the J-Q approach, where Q is a parameter quantifying constraint by the difference in stress field between the small-scale yielding (SSY) scenario and that of the real geometry, see O’Dowd & Shih (1991) and Eq. (1). The Q parameter was calculated from FE analyses of 3D models of the test geometries and of boundary layer models (MBL), representing small-scale yielding conditions. The value of Q was taken as the normalised by  0 difference between the maximum principal stresses on the crack plane at a normalised distance from the crack tip r  0 / J =2, where r is the physical distance and the J -integral is determined from the analyses. ( 0 ⁄ , ) = ( 0 ⁄ , ) + 0 . (1) = [1 + (− ) ] . (2) The J-Q approach allows for defect assessment accounting for apparent toughness, J mat . Failure would occur when the J-Q loading curve from FE analysis of real geometry intersects the fracture toughness locus J c -Q c . Section III.9 of the UK nuclear industry assessment procedure R6 (2015) advises on the derivation of J mat through constraint-correction procedure given by Eq. (2) with parameters  and k , to be determined by look-up tables, e.g. Sherry et al. (2005), or testing to determine Q c =Q(J c ) in combination with FE analysis. The latter is used here. Second option for constraint correction is offered by local approaches (LA). Modified Beremin models are used here, where the probability of cleavage fracture is described by a Weibull distribution, Eq. (3), of an integral stress parameter,  w in Eq. (4), known as the Weibull stress. The function of plastic strains c (  p ) in Eq. (4) is intended to account for plasticity effects on the generation of micro-cracks eligible for propagation by the maximum principal stress,  1 . Different forms of this function have been recently reviewed by Ruggieri & Dodds (2018); the ones tested here are given by Eq. (5). The calibration of m ,  u,  , and  follows the work by Ruggieri et al. (2015). ( ) = 1 − exp [− ( ) ] . (3) = [ 1 0 ∫ ( ) 1 ] 1⁄ . (4) 1 ( ) = ; 2 ( ) = 1 − (− ) . (5) Finite strain FE analyses of models of tested specimens were performed in Abaqus (2015). Models with blunt crack tips (10  m crack tip radius) utilising the double symmetry of SENB specimens were used; example in Fig. 1. J integral s were evaluated by Abaqus’ domain integral method on layers through specimen thickness. The J values used in this work correspond to the mid-plane, while Q values are calculated by comparison with BLM analyses.

Fig. 1. Quarter-symmetric finite element model of the deeply-cracked SEN(B) specimen with detail of the crack tip mesh.