Molecular dynamics and continuum
approach for modeling grain boundary accomodation
Grain boundary sliding and separation is a predominant deformation
mechanism for nanocrystals. Grain boundary effects occur over a
small domain where atomistic effects play a crucial role. We studied a
method for obtaining grain boundary properties using results from
molecular dynamics (MD) simulations of bicrystal separation and
sliding. In recent years, cohesive interface models have been widely
used to numerically simulate fracture initiation and growth by the
finite element method either as mixed boundary conditions or have been
embedded into cohesive finite elements.
Typically, a cohesive interface is introduced in a finite element
discretization of the problem by the use of special interface elements
which obey a non-linear interface traction-separation constitutive
relation describing the complex microscopic processes that lead to the
formation of new traction-free crack faces. At the nanoscale, such
constitutive relations are obtained using molecular dynamics
simulations.
We have carried out simulations on polycrystals using MD-derived
cohesive properties and found that stress concentrations at the tips of
the distributed grain-boundary cracks (as shown in the left figure),
and at grain-boundary triple junctions, cause plastic deformation in
the grain interiors. Grain-boundary deformation dominates the observed
stress-strain response as expected.
- V. Sundararaghavan and N. Zabaras, "Combined MD and continuum approaches towards modeling inter-granular failure using cohesive zone models", presented at the `Deformation and Fracture from Nano to Macro: A Symposium Honoring W.W. Gerberich's 70th Birthday' symposium in the 2006 TMS Annual Meeting & Exhibition (D. F. Bahr, J. Lucas and N. R. Moody, organizers), San Antonio, TX, March 12-16, 2006.[PPT]
- B. Ganapathysubramanian, V. Sundararaghavan and N. Zabaras, "Molecular dynamics approach for investigation of grain boundary response with applications to continuum simulation of failure in nano-crystalline materials", Proceedings of the 3nd M.I.T. Conference on Computational Fluid and Solid Mechanics, presented at the Symposium on `Molecular Methods in Mechanics' (N. G. Hadjiconstantinou, organizer), Massachusetts Institute of Technology, Cambridge, MA, June 14 - 17, 2005. [PPT]
Ab-initio alloy modelling
Advances in electronic structure theory (in particular, the density
functional theory) have enabled fast computation of chemical formation
energies for prediction of phase structures. Identification of stable
phase structures with extraordinary mechanical properties using
ab-initio calculations is a problem of great relevance in materials
design. We have developed a multibody energy expansion formalism for
describing the describing structural relaxations in alloys. N-body
potentials in the multibody expansion are computed from energies of
isolated clusters, which, in turn, are calculated from empirical
potentials or self-consistent quantum mechanical calculations.
Convergence characteristics of multibody expansions MBEs are improved
by weighting energies obtained from various truncations of many-body
expansions in a method called weighted MBE. We have shown that
multibody expansions of alloy clusters can be efficiently constructed
using interpolation of isolated cluster energies from databases.
Combination of multibody potentials with cluster expansion in the form
of a hybid expansion can form a powerful tool for alloy design.
V. Sundararaghavan and N. Zabaras, "Many-body expansions for computing stable structures of multi-atom systems", Physical Review B, Vol. 77 (6) pp. 064101-1--064101-10, 2008.[PDF][PPT]