No 2 (2023)

The problems of defect mechanics in dislocation-free silicon single crystals are relevant and technically significant due to the intensive development of microelectronics, which imposes increasingly high demands on minimizing the level of micro- and nanodefects in silicon wafers used to manufacture microelectronic chips. The solution of these problems is associated with the study of the regularities of thermomechanical processes both at the stage of growing silicon single crystals and at subsequent thermal annealing of wafers cut from them. The article provides an overview of theoretical and experimental work aimed at developing ways to control these processes. This includes the development of physical concepts of defect formation in dislocation-free single-crystal silicon and the development of mathematical models corresponding to different temperature ranges, implemented both during the growth of a single crystal and during thermal annealing of wafers cut from it. Thus, near the crystallization temperature, the processes of fast recombination and diffusion transfer of intrinsic point defects (vacancies and interstitial silicon atoms) are simulated, while at lower temperatures, the processes of their agglomeration into microdefects (pores and clusters of interstitial silicon atoms) are simulated. The verification of such models is illustrated for two experimental processes of growing silicon single crystals with a diameter of 150 mm by the Czochralski method, as well as for the process of rapid high-temperature thermal annealing of silicon wafers cut on their basis.

The article considers some problems of mechanics about the rolling of a wheel with impacts and one-way constraints under dry friction. Such tasks are often encountered in practice when a vehicle wheel collides with or leaves an obstacle. The contact of the wheel with the road is assumed to be point, the dry friction model is the classical Euler-Coulomb model. A complete analysis of various cases of impact and post-impact movements of the wheel is given.

The problems of discrete contact between an elastic layer and a rigid punch with unknown areas of actual contact are considered. A variational formulation of the problems is obtained in the form of a boundary variational inequality using the Poincaré-Steklov operator, which maps normal stresses into normal displacements on a part of the elastic layer boundary. To approximate this operator, a two-dimensional discrete Fourier transform is used, for the numerical implementation of which algorithms of the fast Fourier transform are used. A minimization problem equivalent to the variational inequality is presented. As a result of its approximation, a quadratic programming problem with constraints in the form of equalities and inequalities is obtained. To numerically solve this problem, we used an algorithm based on the conjugate gradient method, which takes into account the specifics of the set of constraints. Two-parameter families of punches rectangular in plan with surface relief are constructed. As a result of computational experiments, the existence of a single envelope of contact pressure, a single envelope of normalized contact forces, and a single envelope of the relative values of the actual contact areas of microprotrusions has been established for each family of punches. The shape and position of these envelopes for a family of punches depend on the parameters of the external load and the ratio of the dimensions of the nominal contact area to the layer thickness.

The article considers the problem of the motion of a gyrostat under the action of potential and gyroscopic forces in the case of a variable gyrostatic moment. The conditions for the existence of semi-regular precessions characterized by the constancy of their own rotation rate are studied. A new solution of the equations of the Kirchhoff–Poisson class is constructed, based on a special type of three invariant relations with respect to the main variables of these equations.

The development of viscoplastic flow in the material of a cylindrical layer placed on a rigid cylindrical shaft and rotating with it around their common axis is calculated. Depending on the increasing speed of rotation up to the maximum, the place and time points of the beginning of the viscoplastic flow, the patterns of propagation of the flow area, the changing strains and stresses in the deformable material are determined. As a condition for viscoplastic flow, the corresponding generalization of the condition for maximum octahedral stresses is taken. For the purposes of testing the calculation programs, an exact solution of the problem of a steady viscoplastic flow of a material during rotation of a compound cylinder at a constant speed has been obtained.

 The paper is devoted to the study of the general relations of the theory of torsion of rods from an ideal rigid-plastic anisotropic material. In this case, it is assumed that the rod is under the action of an external pressure that varies linearly along its generatrix. The stress-strain state of an anisotropic rod is determined under an arbitrary condition of plasticity. Equations for the characteristics of general relations and the stress and strain components along these characteristics are found.

The properties of metal honeycomb metamaterials with different internal structures were experimentally studied when they were punched along the normal by a rigid spherical striker. Experiments with metal samples of metamaterials with a negative Poisson’s ratio (auxetics) showed a greater resistance to penetration by impactors than experiments with metal samples having a honeycomb structure with a positive Poisson’s ratio.