Coupling quantum and continuum scales to predict crack tip dislocation nucleation

A quantum-continuum multiscale coupling of Kohn-Sham density functional theory to continuum material is presented that can handle mechanics problems in metals when long-range stress fields are present, such as occurs for dislocations and cracks. The method has quantifiable and controllable coupling errors that can be minimized at computationally tractable system sizes. Using both generalized gradient and local density approximation exchange correlation functionals, the nucleation of a dislocation from a crack tip in aluminum is then predicted. Both functionals yield similar results, and predictions using Rice's continuum Peierls model are within 20% of the quantum values. This multiscale method is easily extendable to crack-tip problems involving alloys and chemical embrittlements. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

[1]  G. Beltz,et al.  The effect of crack blunting on the competition between dislocation nucleation and cleavage , 2001 .

[2]  C. S. Hartley,et al.  Characterization and visualization of the lattice misfit associated with dislocation cores , 2005 .

[3]  P. Gumbsch,et al.  Low-speed fracture instabilities in a brittle crystal , 2008, Nature.

[4]  James B. Adams,et al.  Interatomic Potentials from First-Principles Calculations: The Force-Matching Method , 1993, cond-mat/9306054.

[5]  J. Q. Broughton,et al.  Concurrent coupling of length scales: Methodology and application , 1999 .

[6]  L E Shilkrot,et al.  Coupled atomistic and discrete dislocation plasticity. , 2002, Physical review letters.

[7]  M. Ortiz,et al.  An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method , 1997, cond-mat/9710027.

[8]  G. Schoeck.  The emission of dislocations from crack tips: A critical assessment , 2003 .

[9]  C. Woodward,et al.  Flexible Ab initio boundary conditions: simulating isolated dislocations in bcc Mo and Ta. , 2002, Physical review letters.

[10]  Rajiv K. Kalia,et al.  Environmental effects of H2O on fracture initiation in silicon: A hybrid electronic-density-functional/molecular-dynamics study , 2004 .

[11]  James R. Rice,et al.  Dislocation Nucleation from a Crack Tip" an Analysis Based on the Peierls Concept , 1991 .

[12]  Efthimios Kaxiras,et al.  From Electrons to Finite Elements: A Concurrent Multiscale Approach for Metals , 2005, cond-mat/0506006.

[13]  H. V. Swygenhoven,et al.  General-stacking-fault energies in highly strained metallic environments: Ab initio calculations , 2007 .

[14]  Fujio Izumi,et al.  VESTA: a three-dimensional visualization system for electronic and structural analysis , 2008 .

[15]  Noam Bernstein,et al.  Hybrid atomistic simulation methods for materials systems , 2009 .

[16]  Hafner,et al.  Ab initio molecular dynamics for open-shell transition metals. , 1993, Physical review. B, Condensed matter.

[17]  Michael J. Mehl,et al.  Interatomic potentials for monoatomic metals from experimental data and ab initio calculations , 1999 .