We explore whether the continuum scaling behavior of the fracture energy of metals extends down to the atomistic level. We use an embedded atom method (EAM) model of Ni, thus bypassing the need to model strain-gradient plasticity at the continuum level. The calculations are performed with a number of different 3D periodic size cells using standard molecular dynamics (MD) techniques. A void nucleus of a single vacancy is placed in each cell and the cell is then expanded through repeated NVT MD increments. For each displacement, we then determine which cell size has the lowest energy. The optimal cell size and energy bear a power-law relation to the opening displacement that is consistent with continuum estimates based on strain-gradient plasticity (Fokoua et al., 2014, “Optimal Scaling in Solids Undergoing Ductile Fracture by Void Sheet Formation,” Arch. Ration. Mech. Anal. (in press); Fokoua et al., 2014, “Optimal Scaling Laws for Ductile Fracture Derived From Strain-Gradient Microplasticity,” J. Mech. Phys. Solids, 62, pp. 295–311). The persistence of power-law scaling of the fracture energy down to the atomistic level is remarkable.

General theory of semi-empirical potential methods including embedded-atom method and modified-embedded-atom method (MEAM) is reviewed. The procedures to construct these potentials are also reviewed. A multi-objective optimization (MOO) procedure has been developed to construct MEAM potentials with minimal manual fitting. This procedure has been applied successfully to develop a new MEAM potential for magnesium. The MOO procedure is designed to optimally reproduce multiple target values that consist of important material properties obtained from experiments and first-principle calculations based on density-functional theory. The optimized target quantities include elastic constants, cohesive energies, surface energies, vacancy-formation energies, and the forces on atoms in a variety of structures. The accuracy of the present potential is assessed by computing several material properties of Mg including their thermal properties. We found that the new MEAM potential shows a significant improvement over previously published potentials, especially for the atomic forces and melting temperature calculations.

For very shallow indentations in W, Al, Au, and Fe-3wt%Si single crystals, hardness decreased with increasing depth irrespective of increasing or decreasing strain gradients. As such, strain gradient theory appears insufficient to explain the indentation size effect (ISE) at depths less than several hundred nanometers. Present research links the ISE to a ratio between the energy of newly created surface and plastic strain energy dissipation. Also, the contact surface to plastic volume ratio was nearly constant for a range of shallow depths. Based on the above, an analytical model of hardness versus depth provides a satisfactory fit to the experimental data and correlates well with embedded atom simulations.

We analyze simple shear and torsion of single crystal copper by employing experiments, molecular dynamics simulations, and finite element simulations in order to focus on the kinematic responses and the apparent yield strengths at different length scales of the specimens. In order to compare torsion with simple shear, the specimens were designed to be of similar size. To accomplish this, the ratio of the cylinder circumference to the axial gage length in torsion equaled the ratio of the length to height of the simple shear specimens (0.43). With the [110] crystallographic direction parallel to the rotational axis of the specimen, we observed a deformation wave of material that oscillated around the specimen in torsion and through the length of the specimen in simple shear. In torsion, the ratio of the wave amplitude divided by cylinder circumference ranged from 0.02–0.07 for the three different methods of analysis: experiments, molecular dynamics simulations, and finite element simulations. In simple shear, the ratio of the deformation wave amplitude divided by the specimen length and the corresponding values predicted by the molecular dynamics and finite element simulations (simple shear experiments were not performed) ranged from 0.23–0.26. Although each different analysis method gave similar results for each type boundary condition, the simple shear case gave approximately five times more amplitude than torsion. We attributed this observation to the plastic spin behaving differently as the simple shear case constrained the dislocation activity to planar double slip, but the torsion specimen experienced quadruple slip. The finite element simulations showed a clear relation with the plastic spin and the oscillation of the material wave. As for the yield stress in simple shear, a size scale dependence was found regarding two different size atomistic simulations for copper (332 atoms and 23628 atoms). We extrapolated the atomistic yield stresses to the order of a centimeter, and these comparisons were close to experimental data in the literature and the present study.

In this study, atomistic finite deformation calculations employing the Embedded Atom Method show three items of interest related to continuum field theory. First, a spatial size scale effect on the yield stress is found. In these calculations, mechanical yield point occurred from dislocation initiation at the edge of the numerical specimens. The spatial size scale continued to affect the plastic response up to strains of 30 percent in simple shear for nickel oriented at 〈011〉. The second point is related to the continuum mechanics observation about oscillating global shear stress under simple shear conditions is shown to dampen as the spatial size scale increases. As the spatial length scale increases, the continuum rotational effect coupled with the increase in dislocation population reduces the oscillatory behavior. This confirms the notion proposed by Bammann and Aifantis (1987) in that when more dislocations are initiated with different orientations of the Burger’s vectors then the oscillations decrease. Finally, a length scale bridging idea is proposed by relating a continuum single degree of freedom loss coefficient, which relates the plastic energy to the total strain energy, to varying sizes of blocks of atoms. This study illustrates the usefulness of employing the Embedded Atom Method to study mechanisms related to continuum mechanics quantities.