Abstract
In this paper, the scattering of harmonic antiplane shear waves by a finite crack is studied using the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual integral equations is solved using the Schmidt method instead of the first or the second integral equation method. Contrary to the classical elasticity solution, it is found that no stress singularity is presented at the crack tip. The non- local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length.
Similar content being viewed by others
References
Amemiya, A. and Taguchi, T. (1969). Numerical Analysis and Fortran. Maruzen, Tokyo.
Edelen, D.G.B. (1976). Non-local field theory. Continuum Physics. (Edited by A.C. Eringen) Vol. 4, Academic Press, New York, 75-204.
Erdelyi, A. (ed.) (1954). Tables of Integral Transforms, Vol. 1, McGraw-Hill, New York.
Eringen, A.C. (1972a). Linear theory of non-local elasticity and dispersion of plane waves. International Journal of Engineering Science 10, 425-435.
Eringen, A.C. (1972b). On non-local fluid mechanics. International Journal of Engineering Science 10, 561.
Eringen, A.C. (1973). On non-local microfluid mechanics. International Journal of Engineering Science 11, 291.
Eringen, A.C. (1976). Non-local polar field theory. Continuum Physics Vol. 4, Academic Press, New York, 205- 267.
Eringen, A.C. (1977a). State of stress in the neighborhood of a sharp crack tip. Transactions of the Twenty-Second Conference of Army Mathematicians, 1-18.
Eringen, A.C. (1977b). Continuum mechanics at the atomic scale. Crystal Lattice Defects 7, 109-130.
Eringen, A.C. (1978). Linear crack subject to shear. International Journal of Fracture 14, 367-379.
Eringen, A.C. (1979). Linear crack subject to antiplane shear. Engineering Fracture Mechanics 12, 211-219.
Eringen, A.C. (1981). On non-local plasticity. International Journal of Engineering Science 19, 1461.
Eringen, A.C. and Kim, B.S. (1974). Stress concentration at the tip of crack. Mechanics Research communications 1, 233.
Eringen, A.C., Speziale, C.G. and Kim, B.S. (1977). Crack tip problem in non-local elasticity. Journal of Mechanics and Physics of Solids 25, 339.
Gradshteyn, I.S. and Ryzhik, I.M. (1980). Table of Integral, Series and Products. Academic Press, New York.
Green, A.E. and Rivlin, R.S. (1965). Multipolar continuum mechanics: Functional theory I. Proceedings of the Royal Society, London, Series A 284, 303.
Itou, S. (1978). Three-dimensional waves propagation in a cracked elastic solid. ASME Journal of Applied Mechanics 45, 807-811.
Itou, S. (1979). Three-dimensional problem of a running crack. International Journal of Engineering Science 17, 59-71.
Kroener, A. (1966). Continuum mechanics and range of atomic cohesion forces. Proceedings, International Conference on Fracture, Vol. 1, Japanese Society for Fracture of Materials, Sendai.
Kunin, I.A. (1982, 1983). Elastic Media with Microstructure. Vols. 1 and 2, Springer, Berlin.
Morse, P.M. and Feshbach, H. (1958). Methods of Theoretical Physics, Vol. 1, McGraw-Hill, New York.
Nowinski, J.L. (1984a). On non-local aspects of the propagation of love waves. International Journal of Engineering Science 22, 383-392.
Nowinski, J.L. (1984b). On non-local theory of wave propagation in elastic plates. ASME Journal Applied Mechanics 51, 608-613.
Srivastava, K.N., Palaiya, R.M. and Karaulia, D.S. (1983). Interaction of shear waves with two coplanar Griffith cracks situated in an infinitely long elastic strip. International Journal of Fracture 23, 3-14.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhou, Z., Wang, B. & Du, S. Investigation of the scattering of harmonic elastic antiplane shear waves by a finite crack using the non-local theory. International Journal of Fracture 91, 13–22 (1998). https://doi.org/10.1023/A:1007489931327
Issue Date:
DOI: https://doi.org/10.1023/A:1007489931327