Summary
The dynamic response of a finite crack in an unbounded Functionally Graded Material (FGM) subjected to an antiplane shear loading is studied in this paper. The variation of the shear modulus of the functionally graded material is modeled by a quadratic increase along the direction perpendicular to the crack surface. The dynamic stress intensity factor is extracted from the asymptotic expansion of the stresses around the crack tip in the Laplace transform plane and obtained in the time domain by a numerical Laplace inversion technique. The influence of graded material property on the dynamic intensity factor is investigated. It is observed that the magnitude of dynamic stress intensity factor for a finite crack in such a functionally graded material is less than in the homogeneous material with a property identical to that of the FGM crack plane.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Erdogan, F.: Fracture mechanics of functionally graded materials. Comp. Engng.5, 753–770 (1995).
Nakagaki, M., Sasaki, H., Hagihara S.: A study of crack in functionally graded material under dynamic loading. Dynamic fracture failure and deformation. ASME PVP300, 1–6 (1995).
Parameswaran, V., Shukla, A.: Dynamic fracture of a functionally gradient material having discrete property variation. J. Mater. Sci.33, 3303–3311 (1998).
Babaei, R., Lukasiewicz, S. A.: Dynamic response of a crack in a functionally graded material between two dissimikar half planes under antiplane shear impact load. Engng. Fract. Mech.60, 479–487 (1998).
Wang, B. L., Han, J. C., Du, S. Y.: Dynamic fracture mechanics analysis for composite materials with material inhomogeneity in thickness direction. Acta Mech. Solida Sinica11, 84–93 (1998).
Li, C., Zou, Z.: Torsional impact response of a functionally graded material with a penny-shaped crack. J. Appl. Mech.66, 566–567 (1999).
Copson, E. T.: On certain dual integral equations. Proc. Glasgow Math. Asso.5, 19–24 (1961).
Sih, G. C., Chen, E. P.: Mechanics of fracture 6: Cracks in composite materials. The Hague: Martinus Nijhoff 1981.
Delale, F., Erdogan, F.: The crack problem for a nonhomogeneous plane. J. Appl. Mech.50, 609–614 (1983).
Konda, N., Erdogan, F.: The mixed mode crack problem in a nonhomogeneous elastic medium. Engng. Fract. Mech.47, 533–545 (1994).
Erdogan, F., Wu, B. H.: The surface crack problem for a plate with functionally graded properties. J. Appl. Mech.64, 449–456 (1997).
Noda, N., Jin, Z.-H.: Thermal stress intensity factors for a crack in a strip of a functionally gradient material. Int. J. Solids Struct.30, 1039–1056 (1993).
Jin, Z.-H., Noda, N.: Transient thermal stress intensity factors for a crack in a semi-infinte plate of a functionally gradient material. Int. J. Solids Struct.31, 203–218 (1994).
Gerasoulis, A., Srivastav, R. P.: A Griffith crack problem for a nonhomogeneous medium. Int. J. Engng Sci.18, 239–247 (1980).
Wang, X. Y., Zou, Z. Z., Wang, D.: On the Griffith crack in a nonhomogeneous interlayer of adjoining two different elastic materials. Int. J. Fract.79, R51-R56 (1996).
Miller, M. K., Guy, W. T.: Numerical inversion of the Laplace transform by use of Jacobi polynomials. SIAM J. Numer. Analysis3, 624–635 (1966).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Li, C., Weng, G.J., Duan, Z. et al. Dynamic stress intensity factor of a functionally graded material under antiplane shear loading. Acta Mechanica 149, 1–10 (2001). https://doi.org/10.1007/BF01261659
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01261659