Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-14T17:36:27.938Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamical Fracture Instabilities Due to Local Hyperelasticity at Crack Tips

Published online by Cambridge University Press:  01 February 2011

Markus J. Buehler  and
Huajian Gao
Markus J. Buehler
Affiliation:
mbuehler@MIT.EDU, Massachusetts Institute of Technology, Civil and Environmental Engrg., 77 Mass. Ave Room 1-272, Cambridge, MA, 02139, United States, 617 452 2750
Huajian Gao
Affiliation:
huajian_gao@brown.edu, Brown University, Division of Engineering, Rhode Island, 02912, United States
Get access

Abstract

When materials break and cracks propagate, bonds between atoms are broken generating two new material surfaces. Most existing theories of fracture assume a linear elastic stress-strain law. However, the relation between stress and strain in real solids is strongly nonlinear due to large deformation near a moving crack tip, a phenomenon referred to as hyperelasticity or nonlinear elasticity. Cracks moving at low speeds create atomically flat mirror-like surfaces, whereas cracks at higher speeds leave misty and hackly fracture surfaces. This change in fracture surface morphology is a universal phenomenon found in a wide range of different brittle materials, but the underlying physical reason has been debated over an extensive period. Using massively parallel large-scale atomistic simulations employing a new, simple atomistic material model allowing a systematic transition from linear elastic to strongly nonlinear material behaviors, we show that hyperelasticity can play a governing role in dynamical crack tip instabilities in fracture of brittle materials. We report a generalized model that treats the instability problem as a competition between different mechanisms controlled by local stress field and local energy flow near the crack tip. Our results indicate that the fracture instabilities do not only appear in defected materials, but instead are an intrinsic phenomenon of dynamical fracture. Our findings help to explain controversial experimental and computational results, including experimental observation of crack propagation at speeds beyond the shear wave speed in rubber-like materials.

Keywords

fracturedefectsbonding
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 929: Symposium II – Materials in Extreme Environments , 2006 , 0929-II01-02
Copyright
Copyright © Materials Research Society 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Freund, LB: Dynamic Fracture Mechanics. Cambridge University Press, ISBN 0-521-30330-3; 1990.Google Scholar
2. Yoffe, EH: The moving Griffith crack. Phil Mag 1951, 42:739–750.Google Scholar
3. Gao, H: Surface roughening and branching instabilities in dynamic fracture. J Mech Phys Solids 1993, 41:457–486.Google Scholar
4. Fineberg, J, Gross, SP, Marder, M, Swinney, HL: Instability and dynamic fracture. Phys Rev Lett 1991, 67:457–460.Google Scholar
5. Marder, M, Gross, S: Origin of crack tip instabilities. J Mech Phys Solids 1995, 43:1–48.Google Scholar
6. Abraham, FF, Brodbeck, D, Rafey, RA, Rudge, WE: Instability dynamics of fracture: A computer simulation investigation. Phys Rev Lett 1994, 73:272–275.Google Scholar
7. Abraham, FF: Unstable crack motion is predictable. Advances in Physics 2005, 53:1071–1078.Google Scholar
8. Heizler, SI, Kessler, DA, Levine, H: Mode I fracture in a nonlinear lattice with viscoelastic forces. Phys Rev E 2002, 6:016126.Google Scholar
9. Slepyan, LI: Models and Phenomena in Fracture Mechanics. Springer, Berlin; 2002.Google Scholar
10. Gao, H: A theory of local limiting speed in dynamic fracture. J Mech Phys Solids 1996, 44:1453–1474.Google Scholar
11. Gao, H: Elastic waves in a hyperelastic solid near its plane-strain equibiaxial cohesive limit. Philosphical Magazine Letters 1997, 76:307–314.Google Scholar
12. Cramer, T, Wanner, A, Gumbsch, P: Energy dissipation and path instabilities in dynamic fracture of silicon single crystals. Phys Rev Lett 2000, 85:788–791.Google Scholar
13. Fineberg, J, Gross, SP, Marder, M, Swinney, HL: Instability in the propagation of fast cracks. Phys Rev B 1992, 45:5146–5154.Google Scholar
14. Buehler, MJ, Gao, H: Dynamical fracture instabilities due to local hyperelasticity at crack tips. Nature 2006, 439:307–310.Google Scholar
15. Buehler, MJ, Abraham, FF, Gao, H: Hyperelasticity governs dynamic fracture at a critical length scale. Nature 2003, 426:141–146.Google Scholar
16. Abraham, FF, Brodbeck, D, Rudge, WE, Xu, X: A Molecular Dynamics Investigation of Rapid Fracture Mechanics. J Mech Phys Solids 1997, 45:1595–1619.Google Scholar