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Dynamical fracture instabilities due to local hyperelasticity at crack tips

Nature volume 439, pages 307–310 (2006)Cite this article

Abstract

As the speed of a crack propagating through a brittle material increases, a dynamical instability leads to an increased roughening of the fracture surface. Cracks moving at low speeds create atomically flat mirror-like surfaces; at higher speeds, rougher, less reflective (‘mist’) and finally very rough, irregularly faceted (‘hackle’) surfaces1,2,3,4,5 are formed. The behaviour is observed in many different brittle materials, but the underlying physical principles, though extensively debated, remain unresolved1,2,3,4. Most existing theories of fracture6,7,8,9,10,11,12 assume a linear elastic stress–strain law. However, the relation between stress and strain in real solids is strongly nonlinear due to large deformations near a moving crack tip, a phenomenon referred to as hyperelasticity13,14,15,16,17. Here we use massively parallel large-scale atomistic simulations—employing a simple atomistic material model that allows a systematic transition from linear elastic to strongly nonlinear behaviour—to show that hyperelasticity plays a governing role in the onset of the instability. We report a generalized model that describes the onset of instability as a competition between different mechanisms controlled by the local stress field6,7,8 and local energy flow13,14 near the crack tip. Our results indicate that such instabilities are intrinsic to dynamical fracture and they help to explain a range of controversial experimental1,2,3,4,5,18 and computational19,20,21,22,23,24,25,26 results.

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Figure 1: Simulation geometry with crystal orientation and interatomic force-separation laws.
Figure 2: Crack instability dynamics in the case of harmonic, linear elastic materials behaviour.
Figure 3: The critical instability speed as a function of the parameter rbreak for different choices of the smoothing parameter Ξ. Ξ = 50, Ξ = 150 and Ξ = 300.
Figure 4: The modified instability model and stable intersonic crack propagation in stiffening materials.

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Acknowledgements

We acknowledge discussions with F. F. Abraham on atomistic modelling of dynamic fracture.

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Author notes

  1. Markus J. Buehler and Huajian Gao: *These authors contributed equally to this work

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 1-272, Massachusetts, 02139, Cambridge, USA

    Markus J. Buehler

  2. Max Planck Institute for Metals Research, Heisenbergstrasse 3, D-70569, Stuttgart, Germany

    Huajian Gao

Authors
  1. Markus J. Buehler
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  2. Huajian Gao
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Correspondence to Markus J. Buehler.

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Supplementary information

Supplementary Notes

This file contains background information on important questions in the field of dynamical fracture, introducing classical theories, major experimental results and a summary of the concept of hyperelasticity. (PDF 118 kb)

Supplementary Methods

This file contains an introduction into the molecular dynamics simulation procedure and details about the simulation geometry used for the studies reported in this Letter. (PDF 117 kb)

Supplementary Figure

The concept of dynamical crack tip instabilities and nonlinear elasticity. (PDF 326 kb)

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Buehler, M., Gao, H. Dynamical fracture instabilities due to local hyperelasticity at crack tips. Nature 439, 307–310 (2006). https://doi.org/10.1038/nature04408

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