PSI - Issue 80

Yohei Sonobe et al. / Procedia Structural Integrity 80 (2026) 368–377 Y. Sonobe et al. / Structural Integrity Procedia 00 (2023) 000–000

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10

0 . 06

0 . 20

n =0 n =2 n =4

n =1 n =3 n =5

0 . 05

0 . 15

0 . 04

z max o /a

z max o /a

0 . 10

0 . 03

0 . 05

0 . 02

0 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

0 . 0

0 . 1

0 . 2

0 . 3

0 . 4

0 . 5

ν

ν

(a) Even-order pressure

(b) Odd-order pressure

Fig. 6. Influence of Poisson’s ratio ν on the normalized depth, z max o / a , where the maximum normalized mode I SIF, F max I ( n ) occurs. (a) Results for even-order pressure distributions ( n = 0 , 2 , 4 ). (b) Results for odd-order pressure distributions ( n = 1 , 3 , 5 ).

The maximum 3D SIF for practical problems can be easily estimated by scaling the corresponding 2D plane strain SIF, K ∞ I ( n ) , with the maximum normalized SIF, F max I ( n ) , determined in this work, particularly for finite-thickness components where the crack face length is small relative to the thickness. Acknowledgements This work was supported by JSPS KAKENHI Grant Number 25K17513 and the Young Researcher Support Grant from the Kyushu Branch of Society of Materials Science, Japan. Bažant, Z.P., Estenssoro, L.F., 1979. Surface singularity and crack propagation. Int. J. Solids Struct. 15, 405–426. Benthem, J.P., 1977. State of stress at the vertex of a quarter-infinite crack in a half-space. Int. J. Solids Struct. 13, 479–492. Benthem, J.P., 1980. The quarter-infinite crack in a half space; alternative and additional solutions. Int. J. Solids Struct. 16, 119–130. England, A.H., 2012. Complex variable methods in elasticity. Dover Publications, Mineola, NY. He, Z., Kotousov, A., Berto, F., 2015. Effect of vertex singularities on stress intensities near plate free surfaces. Fatigue Fract. Eng. Mater. Struct. 38, 860–869. Irwin, G.R., 1957. Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24, 361–364. Kwon, S.W., Sun, C.T., 2000. Characteristics of three-dimensional stress fields in plates with a through-the-thickness crack. Int. J. Fract. 104, 289–314. Mindlin, R.D., 1936. Force at a point in the interior of a Semi‐Infinite solid. Physics 7, 195–202. Murakami, Y., 2001. Stress Intensity Factors Handbook. Elsevier. Nisitani, H., 1968. The two-dimensional stress problem solved using an electric digital computer. Bulletin of JSME 11, 14–23. Noda, N.A., Oda, K., 1992. Numerical solutions of the singular integral equations in the crack analysis using the body force method. Int. J. Fract. 58, 285–304. Noguchi, H., Smith, R.A., 1995. An analysis of a semi-infinite solid with three-dimensional cracks. Eng. Fract. Mech. 52, 1–14. Rice, J.R., 1972. Some remarks on elastic crack-tip stress fields. Int. J. Solids Struct. 8, 751–758. Shivakumar, K.N., Raju, I.S., 1990. Treatment of singularities in cracked bodies. Int. J. Fract. 45, 159–178. Tada, H., Paris, P.C., Irwin, G.R., 2000. The Stress Analysis of Cracks Handbook, Third Edition. References