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Unexpected strain-stiffening in crystalline solids

Abstract

Strain-stiffening—an increase in material stiffness at large strains—is a vital mechanism by which many soft biological materials thwart excessive deformation to protect tissue integrity1,2,3. Understanding the fundamental science of strain-stiffening and incorporating this concept into the design of metals and ceramics for advanced applications is an attractive prospect. Using cementite (Fe3C) and aluminium borocarbide (Al3BC3) as prototypes, here we show via quantum-mechanical calculations that strain-stiffening also occurs, surprisingly, in simple inorganic crystalline solids and confers exceptionally high strengths to these two solids, which have anomalously low resistance to deformation near equilibrium. For Fe3C and Al3BC3, their ideal shear strength to shear modulus ratios attain remarkably high values of 1.14 and 1.34 along the (010)[001] and slip systems, respectively. These values are more than seven times larger than the original Frenkel value of 1/2π (refs 4, 5) and are the highest yet reported for crystalline solids. The extraordinary stiffening of Fe3C arises from the strain-induced reversible ‘cross-linking’ between weakly coupled edge- and corner-sharing Fe6C slabs. This new bond formation creates a strong, three-dimensional covalent bond network that resists large shear deformation. Unlike Fe3C, no new bond forms in Al3BC3 but stiffening still occurs because strong repulsion between Al and B in a compressed Al–B bond unsettles the existing covalent bond network. These discoveries challenge the conventional wisdom that large shear modulus is a reliable predictor of hardness and strength of materials4,5,6,7, and provide new lessons for materials selection and design.

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Figure 1: Crystal structure of cementite.
Figure 2: Fe3C under tensile and shear deformations.
Figure 3: Valence charge density in cementite.
Figure 4: Shear deformation of Al3BC3 along two different slip systems.

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Acknowledgements

C.J. acknowledges the support of a Director’s Fellowship at Los Alamos National Laboratory (LANL), where a systematic study of cementite was conceived and initiated. S.G.S. acknowledges support from the National Science Foundation (grant number 0846444). We also thank J. Wills, M. I. Baskes, A. Caro, A. Misra, S. Maloy, A. Srivastava, V. Vitek and S. Ranganathan for their discussions.

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C.J. and S.G.S. contributed equally to this work.

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Correspondence to Chao Jiang or Srivilliputhur G. Srinivasan.

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The authors declare no competing financial interests.

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This file contains Supplementary Methods, a Supplementary Discussion, Supplementary References and Supplementary Figures 1-3. (PDF 1554 kb)

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Jiang, C., Srinivasan, S. Unexpected strain-stiffening in crystalline solids. Nature 496, 339–342 (2013). https://doi.org/10.1038/nature12008

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