PSI - Issue 2_B

F. Minami et al. / Procedia Structural Integrity 2 (2016) 1561–1568 Minami, F., et al./ Structural Integrity Procedia 00 (2016) 000–000

1566

6

tip. In order to correct the CTOD toughness for constraint loss, an equivalent CTOD concept was proposed by Minami et al. (1999) on the basis of the Beremin model (1983). The equivalent CTOD ratio, β , is defined as struc /     (10) where δ and δ struc are CTODs of the standard fracture toughness specimen and the structural component, respectively, at the same level of the Weibull stress (Fig. 6). The structural component at a CTOD level of δ struc and the fracture toughness specimen at the CTOD level of β • δ struc are equivalent in terms of the Weibull stress. When the CTOD fracture toughness, δ cr , of the material is given, the constraint-corrected toughness for the component is assigned as δ cr, struc = δ cr / β . Note that β is in the range, 0 < β < 1. Minami et al (2006) has standardized β in ISO 27306 for CSCP (center surface crack panel), CTCP (center surface crack panel), ESCP (edge surface crack panel) and ETCP (edge through-thickness crack panel) subjected to tension. The equivalent CTOD ratio, β , depends on the yield-to-tensile ratio R Y = σ Y / σ T ( σ Y : yield strength, σ T : tensile strength) and the Weibull shape parameter m of the material; decreasing with increasing R Y and m . WES 2808 specifies β with R Y = 0.6 and m = 20 for steel components under seismic conditions. The low R Y -value is selected in consideration of the Baushinger effect during cyclic loading at the earthquake. The m = 20 is a lower-bound m -value for structural steels with a moderate CTOD toughness of δ cr > 0.05 mm. The use of a low R Y -value along with a low m -value leads to a conservative fracture assessment of the structural component. It is shown by Ohata et al. (2016) that the beam-to-column component develops almost the same Weibull stress as the tension wide plate. Thereby WES 2808 employs the equivalent CTOD ratios, β , for CSCP, ESCP and ETCP with R Y = 0.6 and m = 20, which are formulated by Eq. (11), Eq. (12) and Eq. (13), respectively.

0.393



0.11 25 / (2 / 40) 0.15 25 / (2 / 40) 0.20 25 / (2 / 40)    t c t c t c

for / for / for /

0.04 0.12 0.24

a t a t a t

  



0.393

(11)





  

CSCP(2 , ) c t

0.393

0.44



0.44 0.077 25 / (2 / 30) for / 0.11 25 / (2 / 30) for / 0.18 25 / (2 / 30) for /    t c a t t c a t t c a t 0.44

0.04 0.12 0.24

  



(12)





  

ESCP(2 , ) c t

0.745

(13)

0.2 (2 / 11)

  a a



ETCP(2 )

Note that Eq. (11) and Eq. (12) hold under a given crack depth ratio, a / t , where t is the plate thickness. Eq. (12) and Eq. (13) give β for double-edge surface crack of length 2 × c and double-edge surface crack of depth 2 × a . In cases of single-edge surface crack (crack length c ) and single-edge through-thickness crack (crack depth a ), the equivalent CTOD ratios are given in the form:

0.44

(14) (15)

(1 / 2)

0.737

 











ESCP( , ) c t

ESCP(2 , ) c t

ESCP(2 , ) c t

ETCP(2 ) / 2 a

  a

ETCP( )

Eq. (14) and Eq. (15) are based on the volumetric effect in the Weibull stress. Fig. 7 shows the crack size dependence of β for CSCP, ESCP and ETCP provided by Eq. (11) to Eq. (13) with the plate thickness of t = 25 mm. The β -value increases with the crack size, which is more significant for ETCP. Minami et al. (2013) indicate that the β -solutions are applicable to components with a crack in welds. The strength mismatch in welds may exert an influence on β . But the numerical results show that the strength mismatch effect on β is marginal in the range, 0.9 < S r = σ T W / σ T B < 1.5, where σ T W and σ T Β are the tensile strengths of the weld metal and base metal .