卷 20, 编号 4 (2017)

Widespread approaches to generalizing geometrically linear constitutive relations to the case of large displacement gradients have been considered. These approaches are based on the replacement of the material derivatives of stress and strain tensors by frame-indifferent corotational or convective derivatives. The correctness of choosing the indifferent derivatives is analyzed from a more general viewpoint of motion decomposition into rigid and strain-induced motion. It is shown that the use of the Zaremba-Jaumann derivative in constitutive relations corresponds to motion decomposition by the Cauchy-Helmholtz theorem according to which instantaneous rigid rotation of a material particle with small neighborhood is described by the vorticity tensor. The relations derived with the use of the so-called "logarithmic spin" are analyzed. It is noted that the spin tensors entering into these relations are not associated with the material fibers (in particular with the symmetry axes of anisotropic materials) during the entire studied process of deformation. Hence these spins do not describe the rotation of the reference frame (crystallographic one for metals) in which the material property tensor is defined. A new method of motion decomposition is proposed on the basis of a two-level (macro and meso) approach for single and polycrystalline metals. The mesoscopic spin is determined by the rotation rate of the corotational coordinate system associated with the crystallographic direction and crystallographic plane. Mesoscopic constitutive relations are formulated using the proposed spin. The spin of a representative macrovolume is determined by averaging the spins of the crystallites contained in this volume. This spin is used to formulate rate-type elastic constitutive equations. Examples are given to illustrate the stress state determination for loading along closed strain paths and two-segment paths for isotropic and anisotropic (with cubic symmetry, hcp) elastic materials, and an elastoviscoplastic fcc crystallite. The determination is carried out by using the corotational derivatives in the constitutive relations which are obtained by different motion decomposition methods.

The identification algorithm developed here for scale parameters of gradient elasticity combines solutions for a deformed heterogeneous composite fragment in a continuous one-dimensional model and for a diatomic chain in a discrete atomistic model. For the identification, the models are taken equivalent and the effective stiffnesses of equivalent composite fragments are compared. In the discrete model, only the nearest neighbor atoms interact and the interaction between dissimilar atoms are determined by a modified Lorentz-Berthelot rule. As a result, the effective stiffness of the discrete composite represented as a nonuniform atomic chain is found. The continuous model is a gradient one and takes into account nonlocal effects in the volume and adhesive properties of phase boundaries. The problem of determining the effective stiffness of a composite fragment is solved analytically in the one-dimensional approximation. The study is aimed to develop a procedure of identifying the scale parameters of gradient theories such that the parameters would be independent of the choice of potentials used in discrete modeling. On the example of modeling using the Morse and Lennard-Jones potentials, we propose an identification methodology invariant with respect to the choice of potentials. It is shown that the invariance is provided if the potentials in discrete modeling are coincided in the vicinity of equilibrium points. It is demonstrated that for unambiguous determination of the scale parameters of gradient elasticity, it suffices to use the simplest two-parameter potentials approximating any other potentials subject to equal equilibrium bond distances and equal second derivatives at the equilibrium point (i.e., force constants). An example of identifying the gradient elasticity parameters is presented for a two-phase W-Si composite.

In this paper, we propose a numerical method to obtain an effective electrical resistivity of heterogeneous media under the influence of a direct current. The heterogeneous multiscale finite element method is used to solve the direct problem of simulation of an electrostatic field. The computational experiments using the developed software complex showed that even the small inclusion concentrations define the effective resistivity of the media. In addition, the change in the localization, orientation, and geometrical shape of inclusions also leads to a significant change of the effective properties of the media.

A discrete model of a linear chain of atoms has been developed with regard to the noncentral and rotational (moment) interactions between atoms. The transition from a discrete to continuous model is performed. It is shown that the obtained continuous model of a chain of atoms coincides with the model of the applied micropolar beam model. Lagrangians for the discrete and continuous models of linear chains of atoms are constructed.

The paper considers a new 3D nanostructuring technology of next-genergtion ceramic composites based on a ceramic matrix reinforced with titanium nitride (TiN) gnd silicon carbide (diC). Research data are reported on the formation of TiN and diC nanostructures on the surface of disperse alumina during successive gas chemisorption of organic Ti(N(CH₃)₂)₄ (tetrakis-dimethylamino-titanium, TDMAT) and ammonia NH₃ in the first case and Cl₂Si(CH₃)₂ and methane CH₄ in the second. Such chemisorption increases the number of surface-attached Ti-N groups crystallized on annealing at 1100°C with the formation of a TiN or a SiC nanoparticle layer. According to X-ray diffraction and electron microscopy, TiN nanoparticles with an average size of about 40 nm are formed on the surface of alumina particles after TDMAT and NH₃ treatment for 2 h and subsequent annealing at 1100°C. The mechanical properties of compacted α-A1₂O₃-based ceramics reinforced with TiN and SiC nanoparticles excel the properties of the best ceramic materials provided by different manufacturers.

The fracture of V-notches with end holes made of tungsten-copper functionally graded material under mode I has been studied in this paper. The averaged strain energy density over a well-defined control volume was employed to predict the fracture loads. A numerical approach was used to determine the outer boundary of the control volume. Mechanical properties such as elasticity modulus, Poisson’s ratio, fracture toughness K_Ic, and ultimate tensile stress have been considered to obey the power law function through the specimen width.

Scanning electron microscopy and atomic force microscopy have been applied to study the fracture of SiAlN coatings on Cu substrates under uniaxial tension. It is shown that coating spalling occurs in the zones of local curvature of the SiAlN-Cu interface which form due to dislocation glide in the substrate. Preliminary ion bombardment of the substrate suppresses dislocation-induced kinking at the coating-substrate interface and increases the adhesive strength of the coatings, thus preventing their edge delamination. At the same time, the wavy coatingsubstrate interface resulting from ion bombardment gives rise to normal stresses that lead to the buckling and spalling of the coatings in the zones of positive local curvature of the interface.

The Editor-in-Chief is retracting this article [1] because it contains a significant amount of overlap with [2].