Analysis of Three Dimensional Cracks Subjected to the Mode I Loading by Using FEAM

유한요소 교호법을 이용한 모드 I 하중 하의 삼차원 균열의 해석

Kim, Tae-Sun;Park, Jae-Hak

  • Published : 2000.04.01


The finite element alternating method is extended further for general three dimensional cracks in an isotropic body subjected to the mode I loading. The required analytical solution for a dime dimensional crack in an infinite isotropic body is obtained by solving the integral equations. In order to remove the high singularity in integration, the technique suggested by Keat et al. was used. With the proposed method several example problems are solved in order to check the accuracy and efficiency of the method.


Stress Intensity Factor;Finite Element Alternating Method;Integral Equation;Displacement Discontinuity;Three Dimensional Crack;Surface Crack


  1. Murakami, Y., 1987, Stress Intensity Factors Handbook, Pergamon Press, pp. 863-867
  2. Raju I. S. and Nemann Jr. J. C., 1979, 'Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates,' Engng Frac. Mech., Vol. 11, pp. 817-829
  3. Isida M., Noguchi H. and T. Yoshida, 1984, 'Tension and bending of finite thickness plates with a semi-elliptical surface crack, Int. J. Fracture, Vol. 26, pp. 157-188
  4. Vijayakumar K. and Atluri S. N., 1981, 'An embedded elliptical flaw in an infinite solid, subject to arbitrary crack-face tractions,' J. Appl. Mech., Vol. 48, pp. 88-96
  5. Forth S. C. and Keat W. D., 1996, 'Three-dimensional nonplanar fracture model using the surface integral method,' Int. J. Fracture, Vol. 77, pp. 243-262
  6. Nishioka T. and Atluri S. N., 1983, 'Analytical solution for embedded elliptical cracks, and finite element alternating method for elliptical surface cracks, subject to arbitrary loading,' Engng Frac. Mech., Vol. 17, pp. 247-268
  7. Keat W. D, Erguven M. E. and Dwyer J. F., 1996, 'Modeling of 3-D Mixed mode fractures near planar bimaterial interfaces using surface integrals,' Int. J. for Num. Methods in Eng., Vol. 39, pp. 3679-3703<3679::AID-NME19>3.0.CO;2-2
  8. Murakami Y., 1985, 'Analysis of stress Intensity Factors of Mode I, II and III for inclined surface cracks of arbitrary shape,' Engng Frac. Mech., Vol. 22, pp. 101-114
  9. Keat W. D., Annigeri B. S. and Cleary M. P., 1988, 'Surface integral and finite element hybrid method for two- and three-dimensional fracture mechanics analysis,' Int. J. Fracture, Vol. 36, pp. 35-53
  10. Wiles T. D. and Curran J. H., 1982, 'A general 3-D displacement discontinuity method,' Proceedings of the 4th international conference on numerical methods in geomechanics, Vol. 1, ed. Balkema A. A., Rotterdam, The Netherlands, pp. 103-111
  11. Murakami Y. and Nemat-Nasser S., 1983, 'Growth and stability of interacting surface flaws of arbitrary shape,' Engng Fracture Mech., Vol. 17, pp. 193-210
  12. Atluri, S. N., 1997, Structural Integrity and Durability, Tech Science Press, Forsyth
  13. 박재학, 김만원, Atluri, S. N., 1998, '등방성 유한판 내에 존재하는 곡선균열의 유한요소 교호법을 이용한 해석, 대한기계학회논문집(A), 제22권, 제12호, pp. 2296-2304
  14. Atluri, S. N., 1986, Computational Methods in the Mechanics of Fracture, Amsterdam, North Holland