Atomic-Level and Effective Elastic Moduli at Grain Boundaries

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1992

The relation between atomic structure and elastic properties of grain boundaries is investigated theoretically from both atomistic and continuum points of view. A heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic level elastic moduli determined from the discrete model. The effective elastic moduli for sub-blocks from an infinite bicrystal are then calculated for a relatively small number of atom layers above and below the grain boundary. These effective moduli can be determined exactly for the discrete atomistic model, while estimates from upper and lower bounds are evaluated in the framework of the continuum model. The complete fourth-order elastic modulus tensor is calculated for both the local and the effective properties. Comparison between the discrete atomistic results and those for the continuum model establishes the validity of this model and leads to criteria to assess the stabilit...

2008

This research utilizes a method for calculating an atomic-scale deformation gradient within the framework of continuum mechanics using atomistic simulations to examine bicrystal grain boundaries subjected to shear loading. We calculate the deformation gradient, its rotation tensor from polar decomposition, and estimates of lattice curvature and vorticity for thin equilibrium bicrystal geometries deformed at low temperature. These simulations reveal pronounced deformation fields that exist in small regions surrounding the grain boundary, and demonstrate the influence of interfacial structure on mechanical behavior for the thin models investigated. Our results also show that more profound insight is gained concerning inelastic grain boundary phenomena by analyzing the deformed structures with regard to these continuum mechanical metrics.

International Journal of Plasticity, 2011

Grain boundary influence on material properties becomes increasingly significant as grain size is reduced to the nanoscale. Nanostructured materials produced by severe plastic deformation techniques often contain a higher percentage of high-angle grain boundaries in a non-equilibrium or energetically metastable state. Differences in the mechanical behavior and observed deformation mechanisms are common due to deviations in grain boundary structure. Fundamental interfacial attributes such as atomic mobility and energy are affected due to a higher non-equilibrium state, which in turn affects deformation response. In this research, atomistic simulations employing a biased Monte Carlo method are used to approximate representative non-equilibrium bicrystalline grain boundaries based on an embedded atom method potential, leveraging the concept of excess free volume. An advantage of this approach is that non-equilibrium boundaries can be instantiated without the need of simulating numerous defect/grain boundary interactions. Differences in grain boundary structure and deformation response are investigated as a function of non-equilibrium state using Molecular Dynamics. A detailed comparison between copper and aluminum bicrystals is provided with regard to boundary strength, observed deformation mechanisms, and stress-assisted free volume evolution during both tensile and shear simulations.

Materials Science and Engineering: A, 2000

The relation between two elastic continuum approaches to grain boundary structure, the dislocation and disclination models, is discussed. It is shown that the disclination model has two advantages: a well-behaved expression for the elastic energy of disclination dipole walls, which describes the elastic energy over a wide interval of misorientations, and a continuous misorientation angle dependence of the elastic energy of grain boundaries in an interval between two delimiting boundaries. The elastic energy of the most general, faceted disclination wall is calculated. For cases in which both the energies of delimiting boundaries and elastic constants are available from atomic simulations (001 and 111 tilt boundaries in copper and 001 and 011 tilt boundaries in diamond) quantitative agreement between the disclination model and simulation results is obtained.

Archives of Metallurgy and Materials, 2015

Different Au-Ag-Cu samples have been studied by mechanical spectroscopy. Both polycrystals and bi-crystals show a relaxation peak at 800 K, accompanied by an elastic modulus change. Since this peak is absent in single crystals it is related to the presence of grain boundaries. Molecular dynamics simulations reveal two microscopic mechanisms, when a shear stress is applied onto a Σ5 grain boundary: at 700 K, the boundary migrates perpendicularly to the boundary plane under an external stress. At 1000 K, only sliding at the boundary is observed. These two mechanisms acting in different temperature intervals are used to model the mechanic response of a polycrystal under an applied stress. The models yield expressions for the relaxation strength Δ and for the relaxation time τ as a function of the grain size. A comparison with the mechanical spectroscopy measurements of polycrystals and the bi-crystals show that the grain boundary sliding model reproduces correctly the characteristics o...

Continuum Mechanics and Thermodynamics, 2008

We propose a new method of constructing a series of nested quasicontinuum models, which describe linear elastic behavior of crystal lattices at successively smaller scales. The relevant scales are dictated by the interatomic interactions and are not arbitrary. The novelty of the model is in the use of a decomposition of the displacement field into the coarse part and the micro-level corrections. The coarse contribution is the conventional homogenized displacement field used in classical continuum elasticity. The micro-level corrections are sub-continuum fields representing the fine structure of the boundary layers exhibited by the discrete equilibrium configuration. The model is based on a multi-point Padé approximation in the Fourier space of the discrete Green's function. We systematically compare the new model with the conventional strain gradient model.

International Journal of Engineering Science, 2011

Motivated by a desire to incorporate micro-and nanoscale deformation mechanisms into continuum mechanical models of material behavior, we apply recently developed volumeaveraged metrics to the results of atomistic simulations to investigate deformation and microrotation in the vicinity of grain boundaries. Three-dimensional bicrystalline structures are employed to study the inelastic deformation behavior under uniaxial tension and simple shear at a temperature of 10 K. Each bicrystal is constructed by molecular statics followed by thermal equilibration under NPT using an embedded atom method potential for copper. Strain is imposed in each simulation cell at a constant 10 9 s À1 strain rate applied perpendicular and parallel to the grain boundary plane for tension and shear, respectively. A variety of grain boundary deformation mechanisms arise and the resulting deformation and microrotation fields are examined. We also include an analysis showing how microrotation varies as a function of distance from the grain boundary with increasing strain for different grain boundary deformation mechanisms. This work demonstrates that critical interface behavior can be extracted from atomistic simulations using volumeaveraged metrics, offering a potential avenue for translating fundamental information to continuum theories of grain boundary deformation in polycrystalline materials.

Physical Review B, 2014

Motivated by interest in the elastic properties of high strength amorphous metals, we examine the elastic properties of select crystalline phases. Using first principles methods, we calculate elastic moduli in various chemical systems containing transition metals, specifically early (Ta,W) and late (Co,Ni). Theoretically predicted alloy elastic properties are verified for Ni-Ta by comparison with experimental measurements using resonant ultrasound spectroscopy. Comparison of our computed elastic moduli with effective medium theories shows that alloying leads to enhancement of bulk moduli relative to averages of the pure elements, and considerable deviation of predicted and computed shear moduli. Specifically, we find an enhancement of bulk modulus relative to effective medium theory and propose a candidate system for high strength, ductile amorphous alloys. Trends in the elastic properties of chemical systems are analyzed using force constants, electronic densities of state and Crystal Overlap Hamilton Populations. We interpret our findings in terms of the electronic structure of the alloys.

Scripta Metallurgica, 1983

Chinese Science Bulletin, 2002

Many properties of nanocrystalline materials are associated with interface effects. Based on their microstructural features, the influence of interfaces on the effective elastic property of nanocrystalline materials is investigated. First, the Mori-Tanaka method is employed to determine the overall effective elastic moduli by considering a nanocrysta lline material as a binary composite solid consisting of a crystal or inclusion phase with regular lattice connected by an amorphous-like interface or matrix phase. The effects of strain gradients are then examined on the effective elastic property by using the strain gradient theory to analyze a representative unit cell. Two interface mechanisms are elucidated that influence the effective stiffness and other mechanical properties of materials. One is the softening effect due to the distorted atomic structures and the i ncreased atomic spacings in interface regions, and the other is the baffling effect due to the existence of boundary layers near interfaces.