Supersonic crack growth in a solid of upturn stress-strain relation under anti-plane shear

Gaofeng Guo, Wei Yang*, Y. Huang

*Corresponding author for this work

Research output: Contribution to journalConference article

12 Citations (Scopus)

Abstract

This paper examines, from the prospect of continuum analysis, the possibility for a supersonic crack growth in a solid with an upturn stress-strain relation. The stress has a linear-upturn power-law relation with the strain, resulting in an elastic modulus, and consequently a wave speed, that increase with the strain. Though appearing to be "supersonic", the local wave speed in the crack tip vicinity of the solid with a sufficient upturn stress-strain relation exceeds the crack extension speed. A pre-request for such a supersonic crack growth is the storage of sufficient deformation energy within the solid to nurse the energy flux drawn to the crack tip that extends at an "apparent supersonic" speed. The idea is demonstrated for the simplest case, the anti-plane shear. We examine the steady-state supersonic crack growth in a hyperelastic material. The governing equation is elliptical in the crack tip vicinity but hyperbolic elsewhere. The boundary between two regions is determined with a certain extent. An asymptotic solution is constructed within the super-hardening zone. The solution connects to the hyperbolic radiation strips by weak discontinuity boundaries and to the pre-stressed frontal field by a strong discontinuity boundary.

Original languageEnglish (US)
Pages (from-to)1971-1985
Number of pages15
JournalJournal of the Mechanics and Physics of Solids
Volume51
Issue number11-12
DOIs
StatePublished - Nov 1 2003
EventProceedings of a Symposium on Dynamic Failure and Thin Film - Pasadena, United States
Duration: Jan 16 2003Jan 16 2003

Fingerprint

Crack propagation
crack tips
cracks
Crack tips
shear
discontinuity
supersonic speed
hardening
Hardening
strip
modulus of elasticity
Elastic moduli
Fluxes
continuums
Cracks
Radiation
energy
radiation

Keywords

  • (Self-selected) supersonic crack growth
  • Asymptotic analysis
  • Dynamic fracture
  • Elastic material

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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title = "Supersonic crack growth in a solid of upturn stress-strain relation under anti-plane shear",
abstract = "This paper examines, from the prospect of continuum analysis, the possibility for a supersonic crack growth in a solid with an upturn stress-strain relation. The stress has a linear-upturn power-law relation with the strain, resulting in an elastic modulus, and consequently a wave speed, that increase with the strain. Though appearing to be {"}supersonic{"}, the local wave speed in the crack tip vicinity of the solid with a sufficient upturn stress-strain relation exceeds the crack extension speed. A pre-request for such a supersonic crack growth is the storage of sufficient deformation energy within the solid to nurse the energy flux drawn to the crack tip that extends at an {"}apparent supersonic{"} speed. The idea is demonstrated for the simplest case, the anti-plane shear. We examine the steady-state supersonic crack growth in a hyperelastic material. The governing equation is elliptical in the crack tip vicinity but hyperbolic elsewhere. The boundary between two regions is determined with a certain extent. An asymptotic solution is constructed within the super-hardening zone. The solution connects to the hyperbolic radiation strips by weak discontinuity boundaries and to the pre-stressed frontal field by a strong discontinuity boundary.",
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Supersonic crack growth in a solid of upturn stress-strain relation under anti-plane shear. / Guo, Gaofeng; Yang, Wei; Huang, Y.

In: Journal of the Mechanics and Physics of Solids, Vol. 51, No. 11-12, 01.11.2003, p. 1971-1985.

Research output: Contribution to journalConference article

TY - JOUR

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AU - Guo, Gaofeng

AU - Yang, Wei

AU - Huang, Y.

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N2 - This paper examines, from the prospect of continuum analysis, the possibility for a supersonic crack growth in a solid with an upturn stress-strain relation. The stress has a linear-upturn power-law relation with the strain, resulting in an elastic modulus, and consequently a wave speed, that increase with the strain. Though appearing to be "supersonic", the local wave speed in the crack tip vicinity of the solid with a sufficient upturn stress-strain relation exceeds the crack extension speed. A pre-request for such a supersonic crack growth is the storage of sufficient deformation energy within the solid to nurse the energy flux drawn to the crack tip that extends at an "apparent supersonic" speed. The idea is demonstrated for the simplest case, the anti-plane shear. We examine the steady-state supersonic crack growth in a hyperelastic material. The governing equation is elliptical in the crack tip vicinity but hyperbolic elsewhere. The boundary between two regions is determined with a certain extent. An asymptotic solution is constructed within the super-hardening zone. The solution connects to the hyperbolic radiation strips by weak discontinuity boundaries and to the pre-stressed frontal field by a strong discontinuity boundary.

AB - This paper examines, from the prospect of continuum analysis, the possibility for a supersonic crack growth in a solid with an upturn stress-strain relation. The stress has a linear-upturn power-law relation with the strain, resulting in an elastic modulus, and consequently a wave speed, that increase with the strain. Though appearing to be "supersonic", the local wave speed in the crack tip vicinity of the solid with a sufficient upturn stress-strain relation exceeds the crack extension speed. A pre-request for such a supersonic crack growth is the storage of sufficient deformation energy within the solid to nurse the energy flux drawn to the crack tip that extends at an "apparent supersonic" speed. The idea is demonstrated for the simplest case, the anti-plane shear. We examine the steady-state supersonic crack growth in a hyperelastic material. The governing equation is elliptical in the crack tip vicinity but hyperbolic elsewhere. The boundary between two regions is determined with a certain extent. An asymptotic solution is constructed within the super-hardening zone. The solution connects to the hyperbolic radiation strips by weak discontinuity boundaries and to the pre-stressed frontal field by a strong discontinuity boundary.

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