Advertisement

Dynamic Perturbation of A Propagating Crack: Implications for Crack Stability

  • John R. Willis
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)

Abstract

A general perturbation solution for the stress-intensity factors at the edge of a propagating crack whose surface is slightly undulating and whose edge is not quite straight is briefly reviewed, in the case that the medium through which the crack propagates is viscoelastic. This solution (which was generated in collaboration with A B Movchan) has already been exploited to demonstrate the persistence of “crack front waves” in the high-frequency limit, as well as to find the lowest-order corrections (which induce dispersion and attenuation) when the frequency is large but not infinite. So far, crack front waves have been studied, allowing only in-plane perturbation of the crack edge. Here, the corresponding formulae are summarised for a general three-dimensional perturbation, together with the forms to which they reduce in the high-frequency limit. Such formulae are expected to form the basis for an explanation of “Wallner lines”. At finite frequency, they provide a base for conducting a general study of the linear stability of a rectilinear propagating crack. Such a study has been completed in the special case of two-dimensional perturbation (plane strain), reported by O Obrezanova in these Proceedings.

Keywords

Crack propagation viscoelastic medium crack front waves crack stability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Morrissey, J W and Rice, J R (1998) Crack front waves, J. Mech. Phys. Solids 46, 467–487.CrossRefMathSciNetGoogle Scholar
  2. [2]
    Ramanathan, S and Fisher, D S (1997) Dynamics and instabilities of planar tensile cracks in heterogeneous media, Phy. Rev. Lett. 79, 877–880.CrossRefGoogle Scholar
  3. [3]
    Willis, J R and Movchan, A B (1995) Dynamic weight functions for a moving crack. I. Mode I loading, J. Mech. Phys. Solids 43, 319–341.CrossRefMathSciNetGoogle Scholar
  4. [4]
    Willis, J R and Movchan, A B (2002) Theory of crack front waves, Diffraction and Scattering in Fluid Mechanics and Elasticity, edited by I. D. Abrahams, P. A. Martin and M. J. Simons, pp. 235–250. Kluwer, Dordrecht.Google Scholar
  5. [5]
    Sharon, E and Cohen, G and Fineberg, J (2002) Propagating solitary waves along a rapidly moving crack front, Nature 410, 68–71.CrossRefGoogle Scholar
  6. [6]
    Obrezanova, O and Movchan, A B and Willis, J R (2002) Dynamic stability of a propagating crack, J. Mech. Phys. Solids, 50, 2637–2668.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Obrezanova, O and Movchan, A B and Willis, J R (2003) Dynamic crack stability, Asymptotics, Singularities and Homogenization in Problems of Mechanics, edited by A. B. Movchan, Kluwer, Dordrecht, 211–220.Google Scholar
  8. [8]
    Movchan, A B and Willis, J R (1995) Dynamic weight functions for a moving crack. II. Shear loading, J. Mech. Phys. Solids 43, 1369–1383.CrossRefMathSciNetGoogle Scholar
  9. [9]
    Woolfries, S and Movchan, A B and Willis, J R (2002) Perturbation of a dynamic planar crack moving in a model viscoelastic solid, Int. J. Solids Struct., accepted for publication.Google Scholar
  10. [10]
    Bueckner, H F (1987) Weight functions and fundamental solutions for the penny shaped and half-plane crack in three space, Int. J. Solids Struct. 23, 57–93.CrossRefzbMATHGoogle Scholar
  11. [11]
    Willis, J R and Movchan, A B (1997) Three-dimensional dynamic perturbation of a propagating crack, J. Mech. Phys. Solids 45, 591–610.CrossRefMathSciNetGoogle Scholar
  12. [12]
    Willis, J R (1999) Asymptotic analysis in fracture: An update, Int. J. Fract. 100, 85–103.CrossRefGoogle Scholar
  13. [13]
    Freund, L B (1990) Dynamic Fracture Mechanics. Cambridge: Cambridge University Press.Google Scholar
  14. [14]
    Oleaga, G (2003) On the dynamics of cracks in three dimensions, J. Mech. Phys. Solids, accepted for publication.Google Scholar
  15. [15]
    Bouchaud, E and Bouchaud, J P and Fisher, D S and Ramanathan, S and Rice, J R (2002) Can crack front waves explain the roughness of cracks? J. Mech. Phys. Solids 50, 1703–1725.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • John R. Willis
    • 1
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeUK

Personalised recommendations