Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Stress and Displacement Fields for a Propagating Crack in a Linear Functionally Gradient Material Along X Direction

X방향을 따라 선형적 함수구배인 재료에서 전파하는 균열의 응력장과 변위장

  • Published : 2002.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

Stress and displacement fields for a propagating crack in a functionally gradient material (FGM) which has shear modulus as $\mu$=$\mu$$\_$0/(1＋ζX) are derived. The equations of motion in FGM which is nonhomogeneous material are different from those of homogeneous material. The stress intensity factors in stress fields have influence on odd terms of γ$\^$n/2-1/(n=1,3,5,...,) but stress at crack tip only retains term of γ$\^$-1/2/, where the γ is a radius of cylindrical coordinates centered at crack tip. When the FGM constant ζ is zero or γ→0, the fields for FGM are almost same as the those for isotropic material.

Keywords

References

  1. Niino, M., Hirai, T. and Watanabe. R .. 1987. 'The Functionally gradient,' Journal of Japanese Society of Composite Materials, Vol. 13, No. 1, p. 257 https://doi.org/10.6089/jscm.13.257
  2. Butcher, R.J., Rousseau, C.E. and Tippu. H.V., 1999, 'A Functionally Graded Particulate Composite: Preparation, Measurements, Failure Analysis,' Acta Mater., Vol. 47, No. 1, pp. 259-268 https://doi.org/10.1016/S1359-6454(98)00305-X
  3. Jedamzik, R., Neubrand, A. and Rodel J., 2000, 'Production of Functionally Graded Materials from Electrochemically modified Carbon Preforms,' Journal of the American Ceramic Society, Vol. 83, No.4, pp. 983-985 https://doi.org/10.1111/j.1151-2916.2000.tb01312.x
  4. Zeng, Y.P., Jiang, D.L. and Watanabe T., 2000, 'Fabrication and Properties of Tape-Cast Laminated and Functionally Gradient Alumina-Titanium Carbide Materials,' Journal of the American Ceramic Society, Vol. 83. No. 12, pp. 2999-3003 https://doi.org/10.1111/j.1151-2916.2000.tb01673.x
  5. Parameswaran, V. and Shukla, A., 2000, 'Processing and Characterization of a Model Functionally Gradient Material,' Journal of Materials Science, Vol. 35, pp. 21-29 https://doi.org/10.1023/A:1004767910762
  6. Erdogan, F., 1995, 'Fracture Mechanics of Functionally Graded Materials,' Composite Engineering, Vol. 5, No.7, pp. 753-770 https://doi.org/10.1016/0961-9526(95)00029-M
  7. Gu, P. and Asaro, R.J., 1997, 'Cracks in Functionally Graded Materials,' Int. J. Solid Struct., Vol. 34, No. 1, pp. 1-17 https://doi.org/10.1016/0020-7683(95)00289-8
  8. Jin, Z.H. and Batra, R.C., 1996, 'Some Basic Fracture Mechanics Concept in Functionally Graded Materials,' J. Mech. Phys. Solids, Vol. 44, No. 8, pp. 1221- 1235 https://doi.org/10.1016/0022-5096(96)00041-5
  9. Parameswaran, V. and Shukla A., 1999, 'Crack-Tip Stress Fields for Dynamic Fracture in Functionally Gradient Materials,' Mechanics of Materials, Vol. 31, pp. 579-596 https://doi.org/10.1016/S0167-6636(99)00025-3
  10. Freund, L. B., 1990, 'Dynamic Fracture Mechanics,' Cambridge University Press, Cambridge
  11. Rosakis, A.J. and Ravi-Chandar, K., 1986, 'On Crack Tip Stress State : An Experimental Evaluation of Three-Dimension Effects,' Int. J. of Solid and Struct., Vol. 22, pp. 121-134 https://doi.org/10.1016/0020-7683(86)90002-8