423Accesses
57Citations
3Altmetric
Abstract
The problem of two elastic half-planes joined along the common part of their boundary by a cracked weak interface is considered. The central part of the joint is detached, while in the remaining part there is a continuous distribution of springs which assures continuity of stress which is proportional to the displacement gap. The adherents are homogeneous and isotropic, while the interface is allowed to be orthotropic with principal directions normal and tangential to the interface, respectively. The body is subjected to constant normal and tangential loads applied at infinity and at the crack faces. Using classical solutions for elastic half-planes as Green functions, the integral equation governing the problem is obtained and solved numerically. Attention is paid to the analysis of the solution around the crack tip, and an asymptotic estimate showing that the derivative of the solution is logarithmically unbounded is obtained analytically. Accordingly, it is shown that there may exist, at most, logarithmic stress singularities. It is further shown how, contrary to the case of perfect bonding, stress singularities are not related to the normal propagation of the crack, but possibly to the crack deviation. The crack propagation is analyzed by the energy Griffith criterion, and it is shown that some drawbacks of linear elastic fracture mechanics disappear in the case of weak interface.
This is a preview of subscription content,log in via an institution to check access.
Access this article
Subscribe and save
- Get 10 units per month
- Download Article/Chapter or eBook
- 1 Unit = 1 Article or 1 Chapter
- Cancel anytime
Buy Now
Price includes VAT (Japan)
Instant access to the full article PDF.
Similar content being viewed by others
Explore related subjects
Discover the latest articles and news from researchers in related subjects, suggested using machine learning.References
Achenbach, J.D. and Zhu, H. (1989). Effect of interfacial zone on mechanical behavior and failure of fiberreinforced composites.Journal of Mechanics and Physics of Solids37, 381-393.
Achenbach, J.D. and Zhu, H. (1990). Effect of interphases on micro and macromechanical behavior of hexagonalarray fiber composites.ASME Journal of Applied Mechanics,57, 956-963.
Antipov, Y.A., Avila-Pozos, O., Kolaczkowski, S.T. and Movchan, A.B. (2000). Mathematical model of delamination cracks on imperfect interfaces.Preprint, Department of Mathematical Science, University of Bath (U.K.).
Baremblatt, G.I. (1962). Mathematical theory of equilibrium cracks in brittle fracture.Advances in Applied Mechanics7, Academic Press, New York.
Bigoni, D., Ortiz, M. and Needleman, A. (1997). Effect of interfacial compliance on bifurcation of a layer bonded toa substrate.International Journal of Solids and Structures34, 4305-4326.
Bigoni, D., Serkov, S.K., Valentini, M., and Movchan, A.B. (1998). Asymptotic models of diluite composites with imperfectly bonded inclusions.International Journal of Solids and Structures35, 3239-3258.
Broek, D. (1974).Elementary Engineering Fracture Mechanics, Noordhoff International Publishing, Delft.
Clements, D.L. (1971). A crack between dissimilar anisotropic media.International Journal of Engineering Science9, 257-265.
Comninou, M. (1977). The interface crack.ASME Journal of Applied Mechanics44, 631-636.
Delves, L.M. and Walsh, J. (1974).Numerical Solutions of Integral Equations, Claredon Press, Oxford.
Dugdale, D.S. (1960). Yielding of steel sheets containing slits.Journal of Mechanics and Physics of Solids8, 100-104.
England, A.H. (1965). A Crack Between Dissimilar Media.ASME Journal of Applied Mechanics32, 400-402.
Ganghoffer, J.F., Brillard, A., and Schultz, J. (1997). Modelling of the mechanical behavior of joints bonded by a nonlinear incompressible elastic adhesive.European Journal of Mechanics A/Solids16, 255-276.
Gao, Z. (1995). A circular inclusion with imperfect interface: Eshelby's tensor and related problems.ASME Journal of Applied Mechanics62, 860-866.
Geymonat, G., Krasucki, F. and Lenci, s. (1999). Mathematical analysis of a bonded joint with soft thin adhesive.Mathematics and Mechanics of Solids4, 201-225.
Gilibert, Y. and Rigolot, A. (1979). Analyse asymptotique des assemblage collés à double recouvrement sollicités au cisaillement en traction.Journal de Mecanique Appliquée3, 341-372.
Goland, M. and Reissner, E. (1944). The Stresses in cemented joints.ASME Journal of Applied Mechanics11, A17-A27.
Gotoh, M. (1967). Some problems of bonded anisotropic plates with cracks along the bond.International Journal of Fracture Mechanics3, 253-260.
Griffith, A.A. (1921). The phenomena of rupture and flow in solids.Philosophical Transaction of the Royal Society LondonA-221, 163-198.
Griffith, A.A. (1924). The theory of rupture.Proceedings of the First International Congress on Applied Mechanics, Delft, pp. 55-63.
Hashin, Z. (1990). Thermoelastic properties of fiber composites with imperfect interface.Mechanics of Materials8, 333-348.
Hashin, Z. (1992). Extremum-principles for elastic heterogeneous media with imperfect interfaces and their application to bounding of effective moduli.Journal of Mechanics and Physics of Solids40, 767-781.
He, M.Y. and Hutchinson, J.W. (1989). Kinking of a crack out of an interface.ASME Journal of AppliedMechanics56, 270-278.
Inglish, C.E. (1913). Stresses in a plate due to the presence of cracks and sharp corners.Transactions of the Institute of Naval Architects60, 219-230.
Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate.ASME Journal of Applied Mechanics24, 361-364.
Jones, J.P. and Whittier, J.S. (1967). Waves at flexibly bonded interface.ASME Journal of Applied Mechanics34, 905-909.
Klarbring, A. (1991). Derivation of a model of adhesively bonded joints by the asymptotic expansion method.International Journal of Engineering Science29, 493-512.
Lipton, R. and Vernescu, B. (1995). Variational methods, size effects and extremal microstructures for elastic composites with imperfect interface.Mathematical Models and Methods in Applied Science5, 1139-1173.
Lene, F. and Leguillon, D. (1982). Homogeneized constitutive law for a partially cohesive composite material.International Journal of Solids and Structures18, 443-458.
Levy, A.J. (1991). The debonding of elastic inclusions and inhomogeneities.Journal of Mechanics and Physics of Solids39, 477-505.
Levy, A.J. (1996). The effective dilatational response of fiber-reinforced composites with nonlinear interface.ASME Journal of Applied Mechanics63, 357-364.
Love, A.E.H. (1944).A Treatise on the Mathematical Theory of Elasticity. Dover Publications, New York.
de Montleau, P. and Rigolot, A. (1997). Mécanique de la rupture fragile des couches fortement hétérogènes.Compte Rendus Academie Science Paris 324 série IIb, 83-89.
Movchan, N.V. and Willis, J.R. (1993). Asymptotic analysis of the reinforcement of a brittle crack by bridging fibres.Quarterly Journal of Mechanics and Applied Mathematics46, 331-350.
Movchan, N.V. and Willis, J.R. (1996). Critical load for a mode-1 crack reinforced by bridging fibres.Quarterly Journal of Mechanics and Applied Mathematics49, 545-564.
Mulville, D.R. and Mast, P.W. (1976). Strain energy release rate for interfacial cracks between dissimilar media.Engineering Fracture Mechanics8, 555-565.
Muskhelishvili, N.I. (1953).Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Leyden.
Neuber, H. (1985).Kerbspannungslehre. Springer-Verlag, New York, Berlin.
Needleman, A. (1990). An analysis of tensile decohesion along an interface.Journal of Mechanics and Physics of Solids38, 289-324.
Qu, J. and Bassani, J.L. (1993). Interfacial fracture mechanics for anisotropic bimaterials.ASME Journal of Applied Mechanics60, 422-431.
Rice, J.R. and Sih, G.C. (1965). Plane problems of cracks in dissimilarmedia.ASME Journal of AppliedMechanics32, 418-423.
Rice, J.R. (1988). Elastic fracture mechanics concepts for interfacial cracks.ASME Journal of Applied Mechanics55, 98-103.
Rice, J.R. and Wang, J.-S. (1989). Embrittlement of interfaces by solute segregation.Material Science and EngineeringA107, 23-40.
Rose, L.R.F. (1987). Crack reinforcement by distributed springs.Journal of Mechanics and Physics of Solids35, 383-405.
Sneddon, I.N. and Lowengrub, M. (1969).Crack Problems in the Classical Theory of Elasticity. John Wiley and Sons, New York.
Suo, Z., Ortiz, M. and Needleman, A. (1992). Stability of solids with interfaces.Journal of Mechanics and Physics of Solids40, 613-640.
Sun, C.T. and Jih, C.J. (1987). On strain energy release rates for interfacial cracks in bi-material media.Engineering Fracture Mechanics28, 13-20.
Volkersen, O. (1938). Die Nietkraftverteilung in zugbeansprutchen Nietverbindungen mit konstanten Laschenquerschnitten.Luftfahrtvorschung15, 41-47.
Walton, J.R. and Weitsman, Y. (1984). Deformations and stress intensities due to a craze in an extended elastic material.ASME Journal of Applied Mechanics51, 84-92.
Williams, M.L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in extension.ASME Journal of Applied Mechanics19, 526-528.
Williams, M.L. (1959). The stress around a fault or crack in dissimilar media.Bulletin of the Seismologic Society of America49, 199-204.
Willis, J.R. (1971). Fracture mechanics of interfacial cracks.Journal of Mechanics and Physics of Solids19, 353-368.
Zhong, Z. and Meguid, S.A. (1997). On the elastic field of a spherical inhomogeneity with an imperfectly bonded inteface.Journal of Elasticity46, 91-113.
Author information
Authors and Affiliations
Istituto di Scienza e Tecnica delle Costruzioni, Università di Ancona, via Brecce Bianche, Monte D'Ago
Stefano Lenci
60131, Ancona, Italy
Stefano Lenci
Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie, (Paris 6), Tour 66, Case 162, 4 place Jussieu, 75252, Paris Cedex 05, France
Stefano Lenci
- Stefano Lenci
You can also search for this author inPubMed Google Scholar
Rights and permissions
About this article
Cite this article
Lenci, S. Analysis of a crack at a weak interface.International Journal of Fracture108, 275–290 (2001). https://doi.org/10.1023/A:1011041409243
Issue Date:
Share this article
Anyone you share the following link with will be able to read this content:
Sorry, a shareable link is not currently available for this article.
Provided by the Springer Nature SharedIt content-sharing initiative