Skip to main content
SpringerLink
Log in

The interaction of a curved crack with a circular elastic inclusion

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The solution to a curved matrix crack interacting with a circular elastic inclusion is presented. The problem is formulated using the Kolosov–Muskhelishvili complex stress potential technique where the crack is represented by an unknown distribution of dislocations. After an appropriate parameterization, the resulting singular integral equations are solved with the Lobatto-Chebyshev quadrature technique. The accuracy of the current solution is shown by comparing these results to previously published results. A preliminary investigation is conducted to study the effects of crack curvature and inclusion stiffness on the stress intensity factors and it is shown that in certain instances, the effect of the crack curvature and the inclusion stiffness are competing influences.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anlas, G. and Santare, M.H. (1993a). A model for matrix cracks in short fiber composites. International Journal of Solids and Structures 30, 1701–1713.

    Google Scholar 

  • Anlas, G. and Santare, M.H. (1993b). Arbitrarily oriented crack inside an elliptical inclusion. Transactions of the ASME Journal of Applied Mechanics 60, 589–594.

    Google Scholar 

  • Atkinson, C. (1972). The interaction between a crack and an inclusion. International Journal of Engineering Science 10, 127–136.

    Google Scholar 

  • Banichuk, R.V. (1970). Determination of the form of a curvilinear crack by small parameter technique. Izv. An SSSR 7, 130–137.

    Google Scholar 

  • Bettin, A. and Gross, D. (1989). Crack Propagation in Materials with Local Inhomogeneities Under Thermal Load. In: Thermal Effects in Fracture of Multiphase Materials, Proceedings of the Euromech Colloquium 255, October 31-November 2, 1989, Panderborn, FRG. (edited by Herrmann, K.P. and Olesiak, Z.S.), Springer-Verlag, Berlin, pp. 85–93.

    Google Scholar 

  • Bergkvist, H. and Guex, L. (1979). Curved crack propagation. International Journal of Fracture 15, 429–441.

    Google Scholar 

  • Chen, Y.Z. (1990a). New integral equation for curved crack problem in antiplane elasticity. International Journal of Fracture 45, R33.

    Google Scholar 

  • Chen, Y.Z. (1990b). New integral equation for curve crack problem in plane elasticity with arbitrary loading condition. International Journal of Fracture 46, R43.

    Google Scholar 

  • Chen. Y.Z. (1991a). New singular integral equation for curved crack problem in plane elasticity. International Journal of Fracture 49, R39.

    Google Scholar 

  • Chen. Y.Z. (1991b). Image method for curved crack problem in antiplane elasticity. International Journal of Fracture 48, R75.

    Google Scholar 

  • Chen, Y.Z. (1993). Numerical solution of a curved crack problem by using hypersingular integral equation approach. Engineering Fracture Mechanics 46, 275–283.

    Google Scholar 

  • Chen, Y.Z. and Cheung, Y.K. (1990). New integral equation approach for the crack problem in elastic half-plane. International Journal of Fracture 46, 57–69.

    Google Scholar 

  • Chen, Y.Z. and Chen, R.S. (1997). Interaction between curved crack and elastic inculsion in an infinite plane. Archive of Applied Mechanics 67, 566–575.

    Google Scholar 

  • Chen, Y.Z., Gross, D. and Huang, Y.J. (1991). Numerical solution of the curved crack problem by means of polynomial approximation of the dislocation distribution. Engineering Fracture Mechanics 39, 791–797.

    Google Scholar 

  • Chen, Y.Z. (1995). A survey of new integral equations in plane elasticity crack problem. Engineering Fracture Mechanics 51, 97–134.

    Google Scholar 

  • Cheung, Y.K. and Chen, Y.Z. (1987). New integral equation for plane elasticity crack problems. Theoretical and Applied Fracture Mechanics 7, 177–184.

    Google Scholar 

  • Chao, C.K. and Shen, M.H. (1995). Solutions of thermoelastic crack problems in bonded dissimilar media or half-plane medium. International Journal of Solids and Structures 32, 3537.

    Google Scholar 

  • Cotterell, B. and Rice, J.R. (1980). Slightly curved or kinked cracks. International Journal of Fracture 16, 155–169.

    Google Scholar 

  • Dundurs, J. and Mura, T. (1964). Interaction between an edge dislocation and a cirular inclusion. Journal of the Mechancis and Physics of Solids 12, 177–189.

    Google Scholar 

  • Erdogan, F. and Gupta, G.D. (1972). On the numerical solution of singular integral equations. Quarterly of Applied Mathematics 24, 525–534.

    Google Scholar 

  • Erdogan, F. and Gupta, G.D. (1975). The inclusion problem with a crack crossing the boudnary. International Journal of Fracture 11, 13–27.

    Google Scholar 

  • Erdogan, F., Gupta, G.D. and Ratwani, M. (1974). Interaction between a circular inclusion and an arbitrarily oriented crack. Transactions of the ASME Journal of Applied Mechanics 41, 1007–1013.

    Google Scholar 

  • Gerasoulis, A. (1982). The use of piecewise quadratic polynomials for the solution of singular integral equations of the Cauchy type. Computers and Mathematics with Applications 8, 15–22.

    Google Scholar 

  • Golberg, M.A. (1990). Introduction to the numerical solution of Cauchy singular integral equations. Numerical Solution of Integral Equations (edited by Golberg, M.A.), Plenum Press, New York.

    Google Scholar 

  • Goldstein, R.V. and Salganik, R.L. (1974). Brittle fracture of solids with arbitrary cracks. International Journal of Fracture 10, 507–523.

    Google Scholar 

  • Gross, D. and Heimer, S.T. (1993). Crack closure and crack path prediction for curved cracks under thermal load. Engineering Fracture Mechanics 46, 633–640.

    Google Scholar 

  • Herrmann, K.P. and Wang, R. (1995). Interaction of a crack with a circular inclusion in a thermally stressed material. ZAMM 75, 295–300.

    Google Scholar 

  • Hu, K.X., Chandra, A. and Huang Y. (1993a). Fundamental solutions for dilute distributions of inclusions embedded in microcracked solids. Mechanics of Materials 16, 281–294.

    Google Scholar 

  • Hu, K.X., Chandra, A. and Huang Y. (1993b). Multiple void-crack interaction. International Journal of Solids and Structures 30, 1473–1489.

    Google Scholar 

  • Hu K.X. and Kemeny, J. (1994). A fracture mechanics analysis of the effect of backfill on the stability of cut and fill mine workings. International Journal of Rock Mechancis, Mining Science and Geomechanical Abstracts 31, 231–241.

    Google Scholar 

  • Hwu, C., Liang Y.K. and Yen, W.J. (1995). Interactions between inclusions and various types of cracks. International Journal of Fracture 73, 301–323.

    Google Scholar 

  • Ioakimidis, N.I. and Theocaris, P.S. (1977). Array of periodic curvilinear cracks in an infinite isotropic medium. Acta Mechanica 28, 239–254.

    Google Scholar 

  • Ioakimidis, N.I. and Theocaris, P.S. (1979). A system of curvilinear cracks in an isotropic elastic half-plane. International Journal of Fracture 15, 299–309.

    Google Scholar 

  • Kemmer, G. (1995). Ñber die Anwendung Singularer Integralgleichungen zur Charakterisierung Gerkrummter Risse in der Ebenen Elastizitatstheorie. Studienarbeit, Universität Paderborn.

  • Kunin, I. and Gommerstadt, B. (1985). On the elastic crack-inclusion interaction. International Journal of Solids and Structures 21, 757–766.

    Google Scholar 

  • Lam, K.Y. and Wen, C. (1993). Enhancement/shielding effects of inclusion on arbitrarily oriented located cracks. Engineering Fracture Mechanics 46, 443–454.

    Google Scholar 

  • Lam, K.Y. and Zhang, J.M. (1992). A new integral equation formulation for the analysis of crack-inclusion interactions. Computational Mechanics 10, 217–229.

    Google Scholar 

  • Muller, W.H. and Schmauder, S. (1992). On the behavior of r-and θ-cracks in composite materials under thermal and mechanical loading. International Journal of Solids and Structures 29, 1907–1918.

    Google Scholar 

  • Muller, W.H, and Schmauder, S. (1993). Stress-intensity factors or r-cracks in fiber reinforced composites under thermal and mechanical loading. International Journal of Fracture 59, 307–343.

    Google Scholar 

  • Muller, W.H. and Kemmer, G. (1995). On the mathematical description of curved cracks in composite materials. Deutscher Verband fur Materialforschung und-prufung e. V. DVM, Berlin.

    Google Scholar 

  • Muller, W.H., Gao, H. and Chiu, C.H. (1996). A semi-infinite crack in front of a circular, thermally mismatched heterogeneity. International Journal of Solids and Structures 33, 731–746.

    Google Scholar 

  • Muskhelishvili, N.I. (1953). Some Basic Problems in the Mathematical Theory of Elasticity. P. Noordhoff, Ltd. Groningen.

    Google Scholar 

  • Patton, E.M. and Santare, M.H. (1990). The effect of rigid elliptical inclusion on a straight crack. International Journal of Fracture 46, 71–79.

    Google Scholar 

  • Patton, E.M. and Santare, M.H. (1993). Crack path prediction near an ellipitical inclusion. Engineering Fracture Mechanics 44, 195–205.

    Google Scholar 

  • Santare, M.H., O'Toole, B.J. and Patton, E.M. (1991). Two-dimensional crack inclusion interaction effects: analysis and experiments. Transactions of the ASME Journal of Pressure Vessel Technology 113, 392–397.

    Google Scholar 

  • Savruk, M.P. (1981). Two-Dimensional Problems of Elasticity for Body with Cracks. Naukova Dumka. Kiev (in Russian).

    Google Scholar 

  • Schultz, R.A. (1988). Stress intensity factors for curved cracks obtained with the displacement discontinuity method. International Journal of Fracture 37, R31–34.

    Google Scholar 

  • Sih, G.C., Paris, P.C. and Erdogan, F. (1962). Crack-tip, stress-intensity factors for plane extension and plate bending problems. Transactions of the ASME Journal of Applied Mechanics 29, 306–312.

    Google Scholar 

  • Sih, G.C. (1965). Stress distribution near internal crack tips for longitudinal shear problems. Transactions of the ASME Journal of Applied Mechanics 32, 51–58.

    Google Scholar 

  • Sur, U. and Altiero, N.J. (1988). An alternative integral equation approach for curved and kinked cracks. International Journal of Fracture 38, 25–41.

    Google Scholar 

  • Steif, P.S. (1987). A semi-infinite crack partially penetrating a circular inclusion. Transactinos of the ASME Journal of Applied Mechanics 54, 87–92.

    Google Scholar 

  • Tamate, O. (1968). The effect of a circular inclusion on the stresses around a line crack in a sheet under tension. International Journal of Fracture Mechanics 4, 257–265.

    Google Scholar 

  • Theocaris, P.S. and Ioakimidis, N.I. (1977). Numerical integration methods for the solution of singular integral equations. Quarterly of Applied Mathematics 35, 173–183.

    Google Scholar 

  • Ukadgaonker, V.G., Hargapurkar, S.M. and Maiti, S.K. (1988). Stress analysis of cracks of arbitrary shape in finite plate subjected to uniform tension. International Journal of Fracture 37, R27–30.

    Google Scholar 

  • Wang, R. (1995). A new method for calculating the stress intensity factor of a crack with a circular inclusion. Acta Mechanica 108, 77–85.

    Google Scholar 

  • Wu, C.H. (1988). A semi-infinite crack penetrating an inclusion. Transactions of the ASME Journal of Applied Mechanics 55. 736–738.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The Department of Mechanical Engineering and the Center for Composite Materials, University of Delaware, Newark, DE, 19716, USA

    B.A. Cheeseman & M.H. Santare

Authors
  1. B.A. Cheeseman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M.H. Santare
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cheeseman, B., Santare, M. The interaction of a curved crack with a circular elastic inclusion. International Journal of Fracture 103, 259–277 (2000). https://doi.org/10.1023/A:1007663913279

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007663913279

Search

Navigation