TY - JOUR
T1 - Unexpected strain-stiffening in crystalline solids
AU - Jiang, Chao
AU - Srinivasan, Srivilliputhur G.
N1 - Funding Information:
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.
PY - 2013/4/18
Y1 - 2013/4/18
N2 - 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 integrity. 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 (Fe 3 C) and aluminium borocarbide (Al 3 BC 3) 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 Fe 3 C and Al 3 BC 3, 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 Fe 3 C arises from the strain-induced reversible 'cross-linking' between weakly coupled edge- and corner-sharing Fe 6 C slabs. This new bond formation creates a strong, three-dimensional covalent bond network that resists large shear deformation. Unlike Fe 3 C, no new bond forms in Al 3 BC 3 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 materials, and provide new lessons for materials selection and design.
AB - 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 integrity. 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 (Fe 3 C) and aluminium borocarbide (Al 3 BC 3) 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 Fe 3 C and Al 3 BC 3, 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 Fe 3 C arises from the strain-induced reversible 'cross-linking' between weakly coupled edge- and corner-sharing Fe 6 C slabs. This new bond formation creates a strong, three-dimensional covalent bond network that resists large shear deformation. Unlike Fe 3 C, no new bond forms in Al 3 BC 3 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 materials, and provide new lessons for materials selection and design.
UR - https://www.scopus.com/pages/publications/84876285079
U2 - 10.1038/nature12008
DO - 10.1038/nature12008
M3 - Article
C2 - 23575634
AN - SCOPUS:84876285079
SN - 0028-0836
VL - 496
SP - 339
EP - 342
JO - Nature
JF - Nature
IS - 7445
ER -