Issue 49

A.V. Vakhrushev et alii, Frattura ed Integrità Strutturale, 49 (2019) 370-382; DOI: 10.3221/IGF-ESIS.49.37 371 The introduction of nanocomposites requires their detailed study at various scale levels. Mathematical modeling is, in this case, a promising method for studying the fundamental laws of their formation, deformation and failure. The theoretical approach reduces the cost of conducting expensive natural experiments. Mathematical modeling also allows us to discover and predict the potentially new and promising properties of these materials [4-7]. Many physical characteristics of nanoobjects, such as thermal conductivity coefficient [8, 9], diffusion coefficient [10, 11] and electrical conductivity [12, 13], belong to macroparameters. Strain and stress tensors occupy a special place, since these values determine the deformation and failure of nanomaterials [14-16]. When calculating these values, the problem of consistency of scale levels arises when, due to the physical meaning of the parameters under consideration, or for other reasons, there is no uniquely defined methodology for determining them. In connection with the current situation, the question of describing macrocharacteristics at the nanoscale level, including their mechanical features, remains relevant. The operation of cryogenic mechanical system for the study of nano- and microscale behavior of materials at low temperatures is designed and investigated in the publication [17]. The experiments were carried out under the supervision of a scanning electron microscope, which was equipped with a module with simultaneous cooling of the sample subjected to uniaxial compression. Samples with diameters from 400 to 1300 nm made on the basis of Nb and W metals showed higher values of yield strength and greater deformations at lower temperatures. Comparison of characteristics was carried out with similar values obtained at temperatures close to normal. The authors explain these differences by nanoscale plasticity and internal resistance of the atomic crystal lattice of the sample material. The results obtained can be used in such materials as topological insulators [18]. A review of theoretical models of plastic deformation processes in crystalline nanomaterials is given in [19]. Two-phase nanocomposites with internal boundaries and grain boundaries along component phases are considered as target materials. Special attention is paid to the behavior of various mechanisms of plastic deformation depending on transitions between materials and on the grain size. Physical mechanisms in nanocomposites, such as sliding along the grain boundaries of a material, movement of crystal lattice dislocations, and processes of diffusion plasticity, are illustrated. The topical are the studies of nanomaterials based on supercarbon nanotubes. The authors of [20] analyzed the radial- deformation capabilities of super-carbon nanotubes under uniaxial tension using the method of molecular-dynamic modeling. The results obtained in this work demonstrate good reversible and adjustable parameters of the radial shrinkage of nanotubes, which may be due to their hierarchical structure. Depending on the topology in the areas of the nanotube junction, the levels of reversible deformation reached 50%. By the method of mathematical modeling, it is shown that the Poisson's ratio of super carbon nanotubes depends on the deformation processes occurring in them. Possessing a channel structure at the nanoscale, supercarbon nanotubes have a wide potential for use as nanotubes and nanomaterials. Models of the mechanical behavior of nanoparticles, nanostructures, and composite objects of them are considered in [21]. We used methods for modeling solid mechanics for the study of nanocomposites and experimental approaches. The processes of formation of defects and nanomaterials reinforced by particles and nanoinclusions are given. The analysis of the possibility of calculating and estimating the effective deformation parameters of nanostructures and nanocomposites has been carried out. In this paper, nanofilms, nanotubes, thin-layer nanocoatings are considered as nanomaterials. The processes of deformation, fracture and formation of cracks are discussed taking into account the influence of the internal structure, the appearance and modification of defects, the size factor and the dislocation mechanisms of plastic deformation with respect to nanostructured materials. The purpose of this work is to describe the theoretical foundations and mechanisms for modeling the deformation and fracture of nanocomposites. The work is a development and generalization of the earlier publications of the authors [22- 24], where the main attention is paid to the generalized macro characteristics of nanoparticles and nanocomposites based on them as a whole. T HEORETICAL BASES OF THE MOLECULAR DYNAMICS METHOD he study of the behavior and properties of nanosystems and nanoobjects was carried out by the method of molecular dynamics. Molecular dynamics can accurately reproduce the basic properties and parameters of nanomaterials, but the results will strongly depend on the choice of the power potential responsible for the interaction of atoms in the system. In the work, the many-particle potential of MEAM (modified embedded atom method) was used for the problems to be solved. The mathematical model of molecular dynamics and MEAM potential is described in more detail in previously published papers [25-27]. The total potential energy of the nanosystem in MEAM is represented by the sum of the energies of individual atoms T