ScienceWeek

MATERIALS SCIENCE: ON CRACKS

The following points are made by M.J. Buehler et al (Nature 2003 426:141):

1) Why and how cracks spread in brittle materials is of essential interest to numerous scientific disciplines and technological applications, and a theoretical understanding is essential for many engineering applications. The authors demonstrate by large-scale atomistic simulation that hyperelasticity, the elasticity of large strains, can play a governing role in the dynamics of brittle fracture. This is in contrast to many existing theories of dynamic fracture where the linear elastic behavior of solids is assumed to be sufficient to predict materials failure(1-3). Real solids have elastic properties that are significantly different for small and for large deformations.

2) Many phenomena associated with rapidly propagating cracks are not thoroughly understood. Some experimental work(4,5) as well as many computer simulations have shown a significantly reduced crack propagation speed in comparison with the predictions by the theory. In contrast, other experiments indicated that over 90% of the Rayleigh wave speed can be achieved. Such discrepancies between theories, experiment, and simulations cannot always be attributed to the fact that real solids have all sorts of imperfections such as grain boundaries and micro-cracks (either pre-existing or created during the crack propagation), because similar discrepancies also appear in molecular-dynamics simulations of cracks travelling in perfect atomic lattices.

3) Several researchers have independently proposed that hyperelastic effects at the crack tip may play an important role in the dynamics of fracture, and their suggestions have been used to help interpret phenomena related to crack branching and dynamic crack tip instability, as well as explaining the significantly lower maximum crack propagation speed observed in some experiments and many computer simulations. However, it is not generally accepted that hyperelasticity should play a significant role in dynamic fracture. One reason for this belief stems from the fact that the zone of large deformation in a loaded body with a crack is highly confined to the crack tip, so that the region where linear elastic theory does not hold is extremely small compared to the extensions of the specimen(1,2).

4) In summary: The elasticity of a solid can vary depending on its state of deformation. For example, metals will soften and polymers may stiffen as they are deformed to levels approaching failure. It is only when the deformation is infinitesimally small that elastic moduli can be considered constant, and hence the elasticity linear. Nevertheless, many existing theories model fracture using linear elasticity, despite the fact that materials will experience extreme deformations at crack tips. The authors demonstrate by large-scale atomistic simulations that the elastic behavior observed at large strains -- hyperelasticity -- can play a governing role in the dynamics of fracture, and that linear theory is incapable of fully capturing all fracture phenomena. The authors introduce the concept of a characteristic length scale 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.

References (abridged):

1. Freund, L. B. Dynamic Fracture Mechanics 2nd edn (Cambridge Univ. Press, Cambridge, UK, 1998)

2. Broberg, B. Cracks and Fracture (Academic, San Diego, 1999)

3. Slepyan, L. I. Models and Phenomena in Fracture Mechanics (Springer, Berlin, 2002)

4. Fineberg, J., Gross, S. P., Marder, M. & Swinney, H. L. Instability in dynamic fracture. Phys. Rev. Lett. 67, 141-144 (1991)

5. Ravi-Chandar, K. Dynamic fracture of nominally brittle materials. Int. J. Fract. 90, 83-102 (1998)

Nature http://www.nature.com/nature

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ON PLASTIC DEFORMATION OF CRYSTALS

The following points are made by J. Li et al (Nature 2002 418:307):

1) Nanometer-scale contact experiments(1-5) and simulations demonstrate the potential to probe incipient plasticity -- the onset of permanent deformation -- in crystals. Such studies also point to the need for an understanding of the mechanisms governing defect nucleation in a broad range of fields and applications.

2) Characteristic discontinuities have been observed consistently in the measured load-penetration depth (P-h) response of single crystals indented to nanometer-scale depths(1-5). Before the first discontinuity, local shear stresses beneath the nominally sharp indenter approach the theoretical strength of the indented crystal, indicating that homogeneous defect nucleation is a logical starting event for subsequent incipient (that is, early-stage) plasticity. This hypothesis is supported by recent in situ experiments using the Bragg-Nye bubble raft analogue, showing that nanoindentation of a two-dimensional (2D) crystal indeed results in homogeneous dislocation nucleation. However, the present level of quantitative understanding of the mechanisms by which contact-induced plasticity initiates and evolves in three-dimensional (3D) crystals is still limited.

3) The authors present a fundamental framework for describing incipient plasticity that combines results of atomistic and finite-element modeling, theoretical concepts of structural stability at finite strain, and experimental analysis. The authors quantify two key features of the nucleation and subsequent evolution of defects. A position-sensitive criterion based on elastic stability determines the location and character of homogeneously nucleated defects. The authors validate this stability criterion at both the atomistic and the continuum levels. The authors then propose a detailed interpretation of the experimentally observed sequence of displacement bursts to elucidate the role of secondary defect sources operating locally at stress levels considerably smaller than the ideal strength required for homogeneous nucleation. The authors suggest these findings provide a self-consistent explanation of the discontinuous elastic-plastic response in nanoindentation measurements, and a guide to fundamental studies across many disciplines that seek to quantify and predict the initiation and early stages of plasticity.

References (abridged):

1. Gerberich, W. W., Venkataraman, S. K., Huang, H., Harvey, S. E. & Kohlstedt, D. L. The injection of plasticity by millinewton contacts. Acta Metal. Mater. 43, 1569-1576 (1995)

2. Suresh, S., Nieh, T.-G. & Choi, B. W. Nanoindentation of copper thin films on silicon substrates. Scripta Mater. 41, 951-957 (1999)

3. Kiely, J. D., Jarausch, K. F., Houston, J. E. & Russell, P. E. Initial stages of yield in nanoindentation. J. Mater. Res. 15, 4513-4519 (1999)

4. Gouldstone, A., Koh, H.-J., Zeng, K. Y., Giannakopoulos, A. E. & Suresh, S. Discrete and continuous deformation during nanoindentation of thin films. Acta Mater. 48, 2277-2295 (2000)

5. Kramer, D. E., Yoder, K. B. & Gerberich, W. W. Surface constrained plasticity: Oxide rupture and the yield point process. Phil. Mag. A 81, 2033-2058 (2001)

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