Abstract
Closed-form equations are derived for the asymptotic stresses in the neighborhood of a crack tip impinging on an interface between two isotropic materials. The symmetric problem is considered and follows from an exact elasticity solution formulated by Gupta [1]. The equations are valid for the planar problem, where the interface is straight and also for an axisymmetric problem in the presence of an annular or penny-shaped crack. The equations may serve to establish a tentative criterion that defines the subsequent direction of a crack impinging on a bimaterial interface. The ambiguity of the asymptotic stress state is highlighted and plausible application of the results is discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G.D. Gupta, International Journal of Solids and Structures 9 (1973) 1141–1154.
J.A. Cornie, A.S. Argon and V. Gupta, MRS Bulletin 16 (1991) 32–36.
V. Gupta, A.S. Argon and Z. Suo, ASME Journal of Applied Mechanics 59 (1992) 579–587.
T.S. Cook and F. Erdogan, International Journal of Engineering Science 10 (1972) 677–697.
M.E. Kipp and G.C. Sih, International Journal of Solids and Structures 11 (1975) 153–174.
J.M. Whitney and G.J. Nuismer, Journal of Composite Materials 8 (1974) 253–265.
E.S. Folias, Journal of Composite Materials 25 (1991) 869–886.
J. Ahmad, ASME Journal of Applied Mechanics 58 (1991) 964–972.
N.J. Pagano and H.W. BrownIII, Composites 24 (1993) 69–83.
M.Y. He and J.W. Hutchinson, International Journal of Solids and Structures 25 (1989) 1053–1067.
J. Dundurs, ASME Journal of Applied Mechanics 36 (1969) 650–652.
D. Martinez and V. Gupta, ‘Energy Criterion for Crack Deflection at an Interface Between Two Orthotropic Media II. Results and Experimental Verification’, under review.
J.G. Goree and W.A. Venezia, International Journal of Engineering Science 15 (1977) Part I, pp 1–17, Part II, pp 19–27.
T.J. Lardner, J.E. Ritter, M.L. Shiao and M.R. Lin, International Journal of Fracture 44 (1990) 133–143.
A.K. Kaw and N.J. Pagano, Journal of Composite Materials 27 (1993) 541–571.
N.J. Pagano and R.Y. Kim, Mechanics of Composite Materials and Structures 1 (1994) 3–29.
M.V. Barton, ASME Journal of Applied Mechanics 8 (1941) A-97-A-104.
A.R. Zak, Journal of Applied Mechanics 31 (1964) 150–152.
N.E. Ashbaugh, ASME Journal of Applied Mechanics 40 (1973) 533–540.
I.N. Sneddon and M. Lowengrub, Crack Problems in the Classical Theory of Elasticity, John Wiley (1969) 62–72.
F. Erdogan and G.D. Gupta, International Journal of Solids and Structures 7 (1971) 39.
P.D. Hilton and G.C. Sih, International Journal of Solids and Structures 7 (1971) 913–930.
MACSYMA Reference Manual, Version 11, Symbolics Inc., Boston (1985).
N.I. Muskhelishvili, Singular Integral Equations, P. Noordhoff, Groningen, The Netherlands (1953).
E. Reissner, Journal of Mathematics and Physics 23 (1944) 192–194.
J.M. Bowen and W.G Knauss, in Advances in Experimental Mechanics and Biomimetics, ASME AD-Vol 29/AMD-Vol 146 (1992) 41–49.
Author information
Authors and Affiliations
Additional information
The U.S. Government right to retain a non-exclusive, royalty-free licence in and to any copyright is acknowledged.
Rights and permissions
About this article
Cite this article
Pagano, N.J., Kaw, A.K. Asymptotic stresses around a crack tip at the interface between planar or cylindrical bodies. Int J Fract 71, 151–164 (1995). https://doi.org/10.1007/BF00033753
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00033753