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Hyperelastic effects in brittle materials failure

Published online by Cambridge University Press:  15 March 2011

Markus J. Buehler ,
Farid F. Abraham  and
Huajian Gao
Markus J. Buehler
Affiliation:
Max Planck Institute for Metals Research, 70569 Stuttgart, Germany
Farid F. Abraham
Affiliation:
IBM Almaden Research Center, San Jose, CA 95120-6099, USA
Huajian Gao
Affiliation:
Max Planck Institute for Metals Research, 70569 Stuttgart, Germany
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Abstract

A fact that has been neglected in most theories of brittle fracture is that the elasticity of a solid clearly depends on its state of deformation. Metals will weaken, or soften, and polymers stiffen as the strain approaches the state of materials failure. It is only for infinitesimal deformation that the elastic moduli can be considered constant and the elasticity of the solid linear. We show by large-scale atomistic simulations that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of fracture and that linear theory is incapable of capturing all phenomena. We introduce a new concept of a characteristic length scale ξ for the energy flux near the crack tip and demonstrate that the local hyperelastic wave speed governs the crack speed when the hyperelastic zone approaches this energy length scale. The new length scale ξ, heretofore missing in the existing theories of dynamic fracture, helps to form a comprehensive picture of crack dynamics, explaining super-Rayleigh and supersonic fracture. We further address the stability of cracks, and show agreement of the Yoffe criterion with the dynamics of cracks in harmonic systems. We find that softening hyperelastic effects lead to a decrease in critical instability speed, and stiffening hyperelastic effects leads to an increase in critical speed. The main conclusion is that hyperelasticity plays a critical role in forming a complete picture of dynamic fracture.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 821: Symposium P – Nanoscale Materials & Modeling-Relations Among Processing, Microstructure and Mechanical Properties , 2004 , P6.3
Copyright
Copyright © Materials Research Society 2004

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References

1. Freund, L.B. Dynamic Fracture Mechanics (Cambridge University Press, 1990).Google Scholar
2. Fineberg, J. Gross, S.P., Marder, M., and Swinney, H.L. Phys. Rev. Lett. 67, 141–144 (1991).Google Scholar
3. Ravi-Chandar, K. Int. J. of Fract. 90, 83–102 (1998).Google Scholar
4. Cramer, T., Wanner, A., Gumbsch, P., Phys. Rev. Lett. 85 (4): 788–791 (2000).Google Scholar
5. Abraham, F.F., Brodbeck, D., Rudge, W.E., Xu, X. Phys. Rev. Lett. 73, 272–275 (1994).Google Scholar
6. Falk, M.L., Needleman, A. and Rice, J.R. Journal de Phys. IV France 11, 5–43 (2001).Google Scholar
7. Gao, H. Mech. Phys. Solids 44, 1453–1474 (1996).Google Scholar
8. Abraham, F.F. et al. Proc. Nat. Acad. Sci. 99, 5777–5782 (2002).Google Scholar
9. Abraham, F.F., Gao, H., Phys. Rev. Lett. 84, 3113–3116 (2000).Google Scholar
10. Rountree, C.L. et al. Annu. Rev. Mater. Res. 32, 377–400 (2002).Google Scholar
11. Buehler, M.J. Abraham, F.F., Gao, H. Nature 49, 441–446 (2003)Google Scholar
12. Zimmermann, J. Continuum and atomistic modeling of dislocation nucleation at crystal surface ledges. PhD Thesis, Stanford University (1999).Google Scholar
13. Fratini, S., Pla, O., Gonzalez, P., Guinea, F., and Louis, E. Phys. Rev. B. 66, 104104 (2002).Google Scholar
14. Petersan, P.J., Deegan, R.D., Marder, M., Swinney, H.L., under submission, preprint available at: http://arxiv.org/abs/cond-mat/0311422.Google Scholar
15. Broberg, K.B. Int. J. Sol. Struct. 32 (6-7), 883–896 (1995).Google Scholar