Skip to main content
SpringerLink
Log in

Investigation of macrocrack-microcrack interaction problems in anisotropic elastic solids – Part I: General solution to the problem and application of the J-integral

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

Abstract

A general solution is derived for the plane problem of multiple microcracks near the tip in process zone of a semi-infinite macrocrack in an anisotropic elastic solid. The pseudo-traction method, addressed thoroughly in isotropic cases, is extended to anisotropic cases. A system of Fredholm integral equations, with difficulty in evaluation of the singular integrals, is solved by invoking the asymptotic behavior of the pseudo-tractions on the macrocrack faces. The interaction effect of the release of residual stresses due to near-tip microcracking is then evaluated. The J-integral analysis is also performed to give a consistency check of the solution and some useful conclusions.

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

  • Binienda, W., Wang, A.S.D. and Delale, F. (1991). Analysis of bent crack in unidirectional fiber reinforced composites. International Journal of Fracture 47, 1-24.

    Article  Google Scholar 

  • Chen, Y.H. (1996). On the contribution of discontinuities in a near-tip stress field to the J-integral. International Journal of Engineering Science 34, 819-829.

    Article  MATH  Google Scholar 

  • Chen, Y.H. and Hasebe, N. (1994). Interaction between a main-crack and a parallel micro-crack in an orthotropic plane elastic solid. International Journal of Solids Structures 31, 1877-1890.

    Article  MATH  Google Scholar 

  • Chen, Y.H. and Hasebe, N. (1995). Investigation of EEF properties for a crack in a plane orthotropic elastic solid with purely imaginary characteristic roots. Engineering Fracture Mechanics 50(2), 249-259.

    Article  Google Scholar 

  • Chen, Y.Z. (1984a). General case of multiple crack problems in an infinite plate. Engineering Fracture Mechanics 20, 591-597.

    Article  Google Scholar 

  • Chen, Y.Z. (1984b). Multiple crack problems of antiplane elasticity in an infinite body. Engineering Fracture Mechanics 20, 767-776.

    Article  Google Scholar 

  • Chudnovsky, A., Dolgoplosky, A. and Kachanov, M. (1987). Elastic interaction of a crack with a micro-crack array - Parti I and II. International Journal of Solids Structures 23, 1-21.

    Article  MATH  Google Scholar 

  • Chudnovsky, A. and Kachanov, M. (1983). Interaction of a crack with a field of microcracks. Applied Engineering of Science 21, 1009-1018.

    MATH  Google Scholar 

  • Chudnovsky, A. and Wu, S. (1991). Elastic interaction of a crack with a random array of micro-cracks. International Journal of Fracture 49, 123-140.

    Google Scholar 

  • Fleck, N.A., Hutchinson, J.W. and Suo, Z. (1991). Crack path selection in a brittle adhesive layer. International Journal of Solids Structures 27, 1683-1703.

    Article  Google Scholar 

  • Gong, S.X. and Horii, H. (1989). General solution of the problem of micro-cracks neat the tip of a main-crack. Journal of Mechanical Physics of Solids 37, 27-46.

    Article  MATH  ADS  Google Scholar 

  • Gong, S.X. and Meguid, S.A. (1991). On the effect of the release of residual stresses due to near-tip microcracking. International Journal of Fracture 52, 257-274.

    Google Scholar 

  • Gross, D. (1982). Spanungintensitatsfaktoren von ribsystemen (stress intensity factor of systems of cracks). Ingineering Archives 51, 301-310.

    Article  MATH  Google Scholar 

  • Herrmann, A.G. and Herrmann, G. (1981). On energy-release retes for a plane crack. ASME Journal of Applied Mechanics 48, 525-528.

    Article  MATH  Google Scholar 

  • Horii, H. and Nemat-Nasser, S. (1985). Elastic fields of interacting in homogeneities. International Journal of Solids Structures 21, 731-745.

    Article  MATH  Google Scholar 

  • Horii, H. and Nemat-Nasser, S. (1987). Interacting micro-cracks near the tip in the process zone of a macro-crack. Journal of the Mechanical Physics of Solids 35, 601-629.

    Article  MATH  ADS  Google Scholar 

  • Hutchinson, J.W. (1987). Crack tip shielding by microcracking in brittle solids. Acta Metallurgica 35, 1605-1619.

    Article  Google Scholar 

  • Kachanov, M. (1993). Elastic solids with many cracks and related problems. Advances in Mechanics 30, 259-428.

    Article  Google Scholar 

  • Kachanov, M. and Montagut, E. (1986). Interaction of a crack with certain microcrack array. Engineering Fracture Mechanics 25, 625-636.

    Article  Google Scholar 

  • Lekhnitskii, S.G. (1963). Theory of Elasticity of an Anisotropic Body. Holden-Day, San Francisco.

    MATH  Google Scholar 

  • Mauge, C. and Kachanov, M. (1994). Anisotropic material with interacting arbitrarily oriented cracks. Stress intensity factors and crack-microcrack interactions. International Journal of Fracture 65, 115-139.

    Google Scholar 

  • Obada, M., Nemat-Nasser, S. and Goto, Y. (1989). Branched cracks in anisotropic elastic solids, ASME Journal of Applied Mechanics 65, 858-864.

    Article  Google Scholar 

  • Ortiz, M. (1987). A continuum theory of crack shielding in ceramics. ASME Applied Mechanics 54, 54-58.

    Article  MATH  Google Scholar 

  • Rice, J.R. (1968). Mathematical analysis in the mechanics of fracture. In: Fracture (Edited by H. Liebowitz), vol. 2, 191-311, Academic Press, New York.

    Google Scholar 

  • Rubenstein, A.A. (1985). Macrocrack interaction with semi-infinite microcrack array. International Journal of Fracture 27, 113-119.

    Google Scholar 

  • Rubenstein, A.A. (1986). Macrocrack-microdefect interaction. ASME Journal of Applied Mechanics 53, 505-510.

    Article  Google Scholar 

  • Rubenstein, A.A. and Choi, H.C. (1988). Macrocrack interaction with transverse array of microcracks. International Journal of Fracture 36, 15-26.

    Google Scholar 

  • Sih, G.C. and Chen, E.P. (1981). Cracks in composite materials. Mechanical Fracture 6, 1-99.

    MathSciNet  Google Scholar 

  • Ukadgaonker, V.G. and Naik, A.F. (1991a). Interaction effect of two arbitrarily oriented cracks - Part I. International Journal of Fracture 51, 219-230.

    Article  Google Scholar 

  • Ukadgaonker, V.G. and Naik, A.F. (1991b). Effect of interaction of two arbitrarily cracks - Applications Part II. International Journal of Fracture 51, 285-304.

    Article  Google Scholar 

  • Zhao, L.G. and Chen, Y.H. (1997). On the contribution of subinterface microcracks near the tip of an interface macrocrack to the J-integral in bimaterial solids. International Journal of Engineering Science 35, 387-407.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Civil Engineering and Mechanics, Xi'an Jiao Tong University, 710049, P.R. China

    Yi-Heng Chen & Hong Zuo

Authors
  1. Yi-Heng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Zuo
    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

Chen, YH., Zuo, H. Investigation of macrocrack-microcrack interaction problems in anisotropic elastic solids – Part I: General solution to the problem and application of the J-integral. International Journal of Fracture 91, 61–82 (1998). https://doi.org/10.1023/A:1007470512788

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007470512788

Search

Navigation