Dynamic Stress Intensity Factors for Three Parallel Cracks in an Infinite Plate Subject to Harmonic Stress Waves

Abstract Full-Text HTML Download Download as PDF (Size:275KB) PP. 485-495
DOI: 10.4236/eng.2010.27064    3,493 Downloads   6,567 Views   Citations
Author(s)    Leave a comment

ABSTRACT

Dynamic stresses around three parallel cracks in an infinite elastic plate that is subjected to incident time-harmonic stress waves normal to the cracks have been solved. Using the Fourier transform technique, the boundary conditions are reduced to six simultaneous integral equations. To solve these equations, the differences of displacements inside the cracks are expanded in a series. The unknown coefficients in those series are solved using the Schmidt method such that the conditions inside the cracks are satisfied. Numerical calculations are carried out for some crack configurations.

Cite this paper

S. Itou, "Dynamic Stress Intensity Factors for Three Parallel Cracks in an Infinite Plate Subject to Harmonic Stress Waves," Engineering, Vol. 2 No. 7, 2010, pp. 485-495. doi: 10.4236/eng.2010.27064.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] J. F. Loeber and G. C. Sih, “Diffraction of Antiplane Shear by a Finite Crack,” Journal of the Acoustical Society of America, Vol. 44, No. 1, 1968, pp. 90-98.
[2] G. C. Sih and J. F. Loeber, “Wave Propagation in an Elastic Solid with a Line of Discontinuity or Finite Crack,” Quarterly of Applied Mathematics, Vol. 27, No. 2, 1969, pp. 193-213.
[3] A. K. Mal, “Interaction of Elastic Waves with a Griffith Crack,” International Journal of Engineering Science, Vol. 8, No. 9, 1970, pp. 763-776.
[4] G. C. Sih and J. F. Loeber, “Torsional Vibration of an Elastic Solid Containing a Penny-Shaped Crack,” Journal of the Acoustical Society of America, Vol. 44, No. 5, 1968, pp. 1237-1245.
[5] G. C. Sih and J. F. Loeber, “Normal Compression and Radial Shear Waves Scattering at a Penny-Shaped Crack in an Elastic Solid,” Journal of the Acoustical Society of America, Vol. 46, No. 3B, 1969, pp. 711-721.
[6] A. K. Mal, “Interaction of Elastic Waves with a Penny- Shaped Crack,” International Journal of Engineering Science, Vol. 8, No. 5, 1970, pp. 381-388.
[7] S. Itou, “Dynamic Stress Concentration around Two Coplanar Griffith Cracks in an Infinite Elastic Medium,” ASME Journal of Applied Mechanics, Vol. 45, No. 12, 1978, pp. 803-806.
[8] S. Itou, “Diffraction of an Antiplane Shear Wave by Two Coplanar Griffith Cracks in an Infinite Elastic Medium,” International Journal of Solids and Structures, Vol. 16, No. 12, 1980, pp. 1147- 1153.
[9] S. Itou, “Dynamic Stresses around Two Cracks Placed Symmetrically to a Large Crack,” International Journal of Fracture, Vol. 75, No. 3, 1996, pp. 261-271.
[10] K. Takakuda, “Scattering of Plane Harmonic Waves by Cracks (in Japanese),” Transactions of Japan Society of Mechanical Engineeris, Series A, Vol. 48, No. 432, 1982, pp. 1014-1020.
[11] H. So and J. Y. Huang, “Determination of Dynamic Stress Intensity Factors of Two Finite Cracks at Arbitrary Positions by Dislocation Model,” International Journal of Engineering Science, Vol. 26, No. 2, 1988, pp. 111-119.
[12] S. A. Meguid and X. D. Wang, “On the Dynamic Interac-tion between a Microdefect and a Main Crack,” Pro-ceedings of the Royal Society of London, Series A, Vol. 448, No. 1934, 1995, pp. 449-464.
[13] M. Ayatollahi and S. J. Fariborz, “Elastodynamic Analysis of a Plane Weakened by Several Cracks,” International Journal of Solids and Structures, Vol. 46, No. 7-8, 2009, pp. 1743-1754.
[14] S. Itou and H. Haliding, “Dynamic Stress Intensity Factors around Three Cracks in an Infinite Elastic Plane Subjected to Time-Hharmonic Stress Waves,” International Journal of Fracture, Vol. 83, No. 4, 1997, pp. 379- 391.
[15] S. Itou and H. Haliding, “Dynamic Stress Intensity Factors around Two Parallel Cracks in an Infinite-Orth- otropic Plane Subjected to Incident Harmonic Stress Waves,” In-ternational Journal of Solids and Structures, Vol. 34, No. 9, 1997, pp. 1145-1165.
[16] P. M. Morse and H. Feshbach, “Methods of Theoretical Physics,” McGraw-Hill, New York, Vol. 1, 1958.
[17] S. Itou, “Axisymmetric Slipless Indentation of an Infinite Elastic Hollow Cylinder,” Bulletin of the Calcutta Ma-thematical Society, Vol. 68, No. 17, 1976, pp. 157-165.
[18] M. Ishida, “Elastic Analysis of Cracks and Stress Intensity Factors (in Japanese),” Fracture Mechanics and Strength of Materials, Baifuukan Press, Tokyo, Vol. 2, 1976.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.