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

Gaofeng Guo; Wei Yang; Y. Huang

doi:10.1016/j.jmps.2003.09.028

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

Civil and Environmental Engineering

Research output: Contribution to journal › Conference article › peer-review

17 Scopus citations

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 language	English (US)
Pages (from-to)	1971-1985
Number of pages	15
Journal	Journal of the Mechanics and Physics of Solids
Volume	51
Issue number	11-12
DOIs	https://doi.org/10.1016/j.jmps.2003.09.028
State	Published - Nov 2003
Event	Proceedings of a Symposium on Dynamic Failure and Thin Film - Pasadena, United States Duration: Jan 16 2003 → Jan 16 2003

Funding

W.Y. and Y.H. acknowledge the support from NSFC for the joint research collaboration grant between them on intersonic fracture investigation. G.F.G. and W.Y. appreciate the support from NSFC for grant “Multi-scale simulation for ultra-high speed impact”. Y.H. acknowledges the support from ONR (#N00014-01-1-0205, under program monitor Dr. Y.D.S. Rajapakse), and from ASCI Center for Simulation of Advanced Rockets at the University of Illinois supported by the U.S. Department of Energy through the University of California under subcontract B523819. Stimulating discussions with Prof. Huajian Gao of Max-Planck Instititue for Metal Research are beneficial in formulating our ideas.

Keywords

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

ASJC Scopus subject areas

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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10.1016/j.jmps.2003.09.028

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.",

keywords = "(Self-selected) supersonic crack growth, Asymptotic analysis, Dynamic fracture, Elastic material",

author = "Gaofeng Guo and Wei Yang and Y. Huang",

note = "Funding Information: W.Y. and Y.H. acknowledge the support from NSFC for the joint research collaboration grant between them on intersonic fracture investigation. G.F.G. and W.Y. appreciate the support from NSFC for grant “Multi-scale simulation for ultra-high speed impact”. Y.H. acknowledges the support from ONR (#N00014-01-1-0205, under program monitor Dr. Y.D.S. Rajapakse), and from ASCI Center for Simulation of Advanced Rockets at the University of Illinois supported by the U.S. Department of Energy through the University of California under subcontract B523819. Stimulating discussions with Prof. Huajian Gao of Max-Planck Instititue for Metal Research are beneficial in formulating our ideas.; Proceedings of a Symposium on Dynamic Failure and Thin Film ; Conference date: 16-01-2003 Through 16-01-2003",

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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.

KW - (Self-selected) supersonic crack growth

KW - Asymptotic analysis

KW - Dynamic fracture

KW - Elastic material

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JO - Journal of the Mechanics and Physics of Solids

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Y2 - 16 January 2003 through 16 January 2003

ER -

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

Abstract

Funding

Keywords

ASJC Scopus subject areas

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