A. M. Krivtsov

Molecular Dynamics Simulation of Impact Fracture in Polycrystalline Materials

Technique for creation of polycrystalline computer materials is presented. The method considered allows for the obtaining of not only polycrystalline particle packings with various grains sizes but also the creating of materials with the preset value of porosity. Plate impact experiments were performed to compare strength properties of mono- and polycrystalline computer materials and also to investigate influence of the material porosity on the shock wave penetration and spallation processes. The experiments show significant differences in the impact fracture processes between mono- and polycrystalline materials. Smearing the shock waves due to heterogeneity of the granular structure of the polycrystals decreases localization effects, and the fracture occupies larger areas but with the smaller level of injury. Porosity adds significant resistance due to the strong plastic deformation during the pore collapsing. This effect can strongly decrease the penetration distance of the shock wave and even prevent the spallation.

On using many-particle interatomic potentials to compute elastic properties of graphene and diamond

The elastic properties of diatomic crystals are considered. An approach is proposed that permits calculating the elastic characteristics of crystals by using the interatomic interaction parameters specified as many-particle potentials, i.e., potentials that take into account the effect of the environment on the diatomic interaction. The many-particle interaction is given in the general form obtained in the framework of linear elastic deformation. It is shown that, by expanding in series in small deformation parameters, a group of nonlinear potentials frequently used to model covalent structures can be reduced to this general form. An example of graphene and diamond lattices is used to determine how adequately these potentials describe the elastic characteristics of crystals.

Derivation of equations of state for ideal crystals of simple structure

We consider an approach to the derivation of thermodynamic equations of state by averaging the dynamic equations of particles of the crystal lattice. Microscopic analogs of macroscopic variables such as pressure, volume, and thermal energy are introduced. An analysis of the introduced variables together with the equations of motion permits obtaining the equation of state. Earlier, this approach was used to obtain the equation of state in the Mie-Grüneisen form for a one-dimensional lattice. The aim of this paper is to develop and generalize this approach to the three-dimensional case. As a result, we obtain the dependence of the Grüneisen function on the volume, which is compared with the computations performed according to well-known models with experimental data taken into account. It is proved that the Grüneisen coefficient substantially depends on the form of the strain state. Moreover, we refine the equation of state; namely, we show that the Grüneisen coefficient depends on the thermal energy, but this dependence in the three-dimensional case is much weaker than in the one-dimensional case. A refined equation of state containing a nonlinear dependence on the thermal energy is obtained

Application of moment interaction to the construction of a stable model of graphite crystal lattice

The aim of the present paper is to construct and study a model of pair moment interaction between carbon atoms in the two-dimensional graphite lattice. The carbon atom is modeled by a structure consisting of three rigidly connected mass points located at the vertices of an equilateral triangle. The interaction between mass points is described by a pair force potential, but the total interatomic interaction contains moment components owing to the finite size of the structure modeling the atom. We compute rank 4 tensors characterizing the elastic properties of the graphite crystal lattice constructed on the basis of our model. We determine lattice stability criteria depending on the number of coordination spheres taken into account. We show that this model permits one to ensure stability of the graphite lattice but significantly underestimates the transverse-to-longitudinal interatomic coupling rigidity ratio. We construct a generalized moment potential that permits one to obtain a rigidity ratio consistent with experimental data.

Modeling of Elastic Properties of Crystals with Hexagonal Close-Packed Lattice

In the present paper, we consider mechanical properties of an ideal hexagonal close-packed (HCP) crystal lattice. We construct three models for describing the elastic characteristics of metals with HCP lattice. Using examples of nine metals with different degree of geometric imperfection (beryllium, hafnium, cadmium, cobalt, magnesium, rhenium, titanium, zinc, and zirconium), we show that including the moment interaction into the model leads to a more accurate description of the elastic properties than taking into account the geometric features of a specific lattice. We also show that, depending on the type of the electron shell, it is efficient to use different models; namely, for d-elements, it suffices to use the two-parameter force model, while for the s-elements, it is required to take the moment interaction into account.

Stability and Structural Transitions in Crystal Lattices

Theadvanceinnanotechnologyhasleadtonecessitytodeterminestrength properties of crystal structures. Stability of a structure under finite deformations is closely connected with its strength. In this work stability of plane triangular (single atomic layer of FCC and HCP) and FCC lattices under finite strain is investigated. Analysisandmodelingbasedondiscreteatomisticmethodsisproposed.Themedium is represented by a set of particles which interact by a pair force central potential, e.g. Lennard-Jones and Morse. Direct tensor calculus is used. Dynamic stability criterion is established: frequency of elastic waves is required to be real for any real wave vector. The considered approach allows to describe structural transitions in solids on the base of stability investigation of pre-strained crystal lattices. The results of direct MD simulation do not contradict the results of the calculations.

Comparison of micromodels describing the elastic properties of diamond

A mechanical model of diatomic crystal lattice with force interaction between atoms and angular interaction between bonds taken into account is proposed. Some relations between the macroscopic moduli of elasticity and the microparameters of the longitudinal rigidity of interatomic bonds and of the angular interaction rigidity are obtained for crystals with diamond lattice. Comparison with experimental data and with other theories describing similar lattices is conducted by using two constants at the microlevel.

Equivalent thermo-mechanical parameters for perfect crystals

Thermo-elastic behavior of perfect single crystal is considered. The crystal is represented as a set of interacting particles (atoms). The approach for determination of equivalent continuum values for the discrete system is proposed. Averaging of equations of particles’ motion and long wave approximation are used in order to make link between the discrete system and equivalent continuum. Basic balance equations for equivalent continuum are derived from microscopic equations. Macroscopic values such as Piola and Cauchy stress tensors and heat flux are represented via microscopic parameters. Connection between the heat flux and temperature is discussed. Equation of state in Mie-Gruneisen form connecting Cauchy stress tensor with deformation gradient and thermal energy is obtained from microscopic considerations.