PSI - Issue 60

D. Sen et al. / Procedia Structural Integrity 60 (2024) 44–59 Deeprodyuti Sen/ Structural Integrity Procedia 00 (2024) 000 – 000

58

15

1/2

R

a   





3 I D K a c p  ( , )

1

F

i

p          w Q

r

1 1.464          a c wR 2

Q

1/2 a c          

  

1.13 0.07  

F



o

p

2 R R 

2

(

)

o  Thus, using above equations, the stress concentration factor for the DFF was evaluated. i

A compar ison of numerical values of ‘ k t ’ for a DFF and a BPFF is provided in Fig.13 a. For a fixed value of axial flaw length, the variation of ‘ k t ’ with flaw root radius is analyzed. It is observed that the stress concentration factor for a DFF is significantly higher than that of a BPFF. This essentially means that for the same design loads, the permissible flaw size would be smaller for DFF as compared to a BPFF. A similar comparison depicting the variation of ‘ k t ’ with flaw length, for a fixed value of flaw tip root radius, is shown in Fig. 13 b. A saturation in stress concentration factor beyond a certain flaw length is observed. The closed- form equation for ‘ k t ’ for a DFF, provided in CSA Standard (2016), also exhibits a similar behavior.

a

b

Figure 13: Comparison of numerical values of Stress Concentration Factor for a Round Bottom BPFF and a DFF. The radial flaw depth (a) ‘ a ’is taken as 0.65 mm. ( b) ‘ a ’ is taken as 0.775 mm. References Bilby, B.A., Cottrell, A.H. and Swinden, K.H., 1963. The spread of plastic yield from a notch. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 272 (1350), pp.304-314. Bhachawat D., 2011. Operating experience with fuel channels in India (NPCIL) . IAEA workshop on prediction of axial and radial creep in HWR Pressure Tube. CSA Group, 2016 .N285.8-15, Technical requirements for in-service evaluation of zirconium alloy pressure tubes in CANDU reactors. Canadian Standards Association, Ontario . Dugdale, D.S., 1960. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids, 8 (2), pp.100-104. EACL, A., 1996. Technical Basis for the Fitness for Service Guidelines for Zirconium Alloy Pressure Tubes in Operating CANDU Reactor. COG-96-651 , Rev. 0. Eshelby, J.D., 1957. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the royal society of London. Series A. Mathematical and physical sciences, 241 (1226), pp.376-396. Glinka, G. and Newport, A., 1987. Universal features of elastic notch-tip stress fields. International Journal of Fatigue, 9 (3), pp.143-150. Metzger, D.R. and Sauvé, R.G., 1996. A self-induced stress model for simulating hydride formation at flaws No. CONF-960706-. American Society of Mechanical Engineers, New York, NY (United States). Northwood, D.O. and Kosasih, U., 1983. Hydrides and delayed hydrogen cracking in zirconium and its alloys . International metals reviews, 28 (1), pp.92-121. Pilkey, W.D., Pilkey, D.F. and Bi, Z., 2020. Peterson's stress concentration factors . John Wiley & Sons.