Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Stress intensity factors for periodic edge cracks in a semi-infinite medium with distributed eigenstrain

  • Afsar, A.M. (Mechanical Engineering Department, Bangladesh University of Engineering and Technology) ;
  • Ahmed, S.R. (Mechanical Engineering Department, Bangladesh University of Engineering and Technology)
  • Received : 2004.11.10
  • Accepted : 2005.06.08
  • Published : 2005.09.10
⟨ Previous Next ⟩

Abstract

This study analyzes stress intensity factors for a number of periodic edge cracks in a semiinfinite medium subjected to a far field uniform applied load along with a distribution of eigenstrain. The eigenstrain is considered to be distributed arbitrarily over a region of finite depth extending from the free surface. The cracks are represented by a continuous distribution of edge dislocations. Using the complex potential functions of the edge dislocations, a simple as well as effective method is developed to calculate the stress intensity factor for the edge cracks. The method is employed to obtain the numerical results of the stress intensity factor for different distributions of eigenstrain. Moreover, the effect of crack spacing and the intensity of the normalized eigenstress on the stress intensity factor are investigated in details. The results of the present study reveal that the stress intensity factor of the periodic edge cracks is significantly influenced by the magnitude as well as distribution of the eigenstrain within the finite depth. The eigenstrains that induce compressive stresses at and near the free surface of the semi-infinite medium reduce the stress intensity factor that, in turn, contributes to the toughening of the material.

Keywords

References

  1. Afsar, A.M. (1997), 'Analysis of edge cracks in semi-infinite functionally gradient materials with distributed eigenstrains', M.Sc. Dissertation, Tohoku University, Japan
  2. Afsar, A.M. and Sekine, H. (2001), 'Optimum material distributions for prescribed apparent fracture toughness in thick-walled FGM circular pipes', Int. J. Pres. Vessels and Piping, 78, 471-484 https://doi.org/10.1016/S0308-0161(01)00061-8
  3. Afsar, A.M. and Sekine, H. (2002), 'Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around a circular hole in infinite elastic media', Compos. Sci. Tech., 62, 1063-1077 https://doi.org/10.1016/S0266-3538(02)00049-0
  4. Benthem, J.B. and Koiter, W.T. (1973), 'Asymptotic approximations to the crack problems', Mechanics of Fracture-I, Methods of Analysis and Solutions of Crack Problems, Edited by G.C. Sih, Noordhoff International Publishing, Leyden
  5. Bowie, O.L. (1973), 'Solutions of plane crack problems by mapping techniques', Mechanics of Fracture-1, Methods of Analysis and Solutions of Crack Problems, Edited by ac. Sih, Noordhoff International Publishing, Leyden
  6. Erdogan, F., Gupta, G.D. and Cook, T.S. (1973), 'Numerical solution of singular integral equations', Methods of Analysis and Solutions of Crack Problems (G.C. Sih Ed.), Noordhoff International Publishing, Leyden 1
  7. Hartranft, R.J. and Sih, G.C. (1973), 'Alternating method applied to edge and surface crack problems', Methods of Analysis and Solutions of Crack Problems 1 (G.C. Sih Ed.), Noordhoff International Publishing, Leyden
  8. Hills, D.A., Kelly, P.A., Dai, D.N. and Korsunsky, A.M. (1996), 'Distributed dislocation fundamentals', Solution of Crack Problems-The Distributed Dislocation Technique (Gladwell G.M.L. Ed.), Kluwer Academic Punlishers
  9. Krenk, S. (1975), 'On the use of the interpolation polynomial for solution of singular integral equation', Quart. Appl. Math., 32, 479-484 https://doi.org/10.1090/qam/474919
  10. Mura, T. (1987), Micromechanics of Defects in Solids: Mechanics of Elastic and Inelastic Solids 3, Kluwer Academic Publishers
  11. Muskhelishvili, N.I (1975), Some Basic Problems of The Mathematical Theory of Elasticity (Translated from the Russian by J.R.M Radok), Noordhoff International Publishers, The Netherlands
  12. Sekine, H. and Afsar, A.M. (1999), 'Composition profile for improving the brittle fracture characteristics in semi-infinite functionally graded materials', JSME Int. J., Ser. A, 42(4), 592-600 https://doi.org/10.1299/jsmea.42.592
  13. Sneddon, I.N. (1946), 'The distribution of stress in the neighborhood of a crack in an elastic solid', Proc. of The Royal Society of London, 187A, 229-260
  14. Sneddon, I.N. and Das, S.C. (1971), 'The stress intensity factor at the tip of an edge crack in an elastic half-plane', Int. J. Eng. Sci., 9, 25-36 https://doi.org/10.1016/0020-7225(71)90010-3
  15. Stallybrass, M.P. (1970), 'A crack perpendicular to an elastic half-plane', Int. J. Eng. Sci., 8, 351-362 https://doi.org/10.1016/0020-7225(70)90073-X

Cited by

  1. Variations of the stress intensity factors for a planar crack parallel to a bimaterial interface vol.30, pp.3, 2008, https://doi.org/10.12989/sem.2008.30.3.317