Vol 29, No 4 (2023)

The present study describes the influence of the mutual effect of damage accumulation on the stress fields at the central crack tip in the plate subjected to uniaxial tension. The objective of the study is to analyze the cracked plate experiencing uniaxial loading under creep conditions using the CAE software SIMULIA ABAQUS taking into account the damage accumulation processes near the crack tip. Computations were performed by means of the user procedure UMAT (User material), which is based on the Bailey-Norton creep power law and the Kachanov — Rabotnov damage evolution equation describing the power-law damage accumulation processes. The analysis of the obtained results showed that in the creep and elasticity zones, in computations without taking into account the damage effect, there are asymptotics of stress fields that correspond to well-known analytical solutions of fracture mechanics (Hutchinson — Rice — Rosengren asymptotics for the creep zone, the asymptotics of linear fracture mechanics corresponding to the stress dependence. inversely proportional to the square root of the distance from the tip of the crack – for the zone of elastic behavior of the material. The presence of damage in the cracked specimen affected the asymptotic behavior of the crack tip fields. It is felt that the proposed procedure could pave the way for the analytical solution of the boundary value problem and allow us to determine the structure of the asymptotic solution of the problem. The finite element analysis clearly shows that the process of damage accumulation affects the change in the asymptotic behavior of the stress field in the vicinity of the crack tip and leads to a new asymptotic distribution of the stress tensor components. The proposed procedure can pave the way to an analytical solution of the boundary value problem and allow us to determine the structure of the asymptotic solution of the problem.

The work develops differential-geometric methods for modeling finite incompatible deformations of hyperelastic solids with enhanced kinematics. The response of such bodies, along with the standard kinematic field represented by the deformation gradient, is characterized by additional tensor fields. As such, the paper considers: 1) the second deformation gradient and 2) the tensor field of the second rank, modeling the microstructure of the body. For each of these two cases, compatibility conditions are obtained and their geometric interpretation is proposed. Geometry is synthesized on the material manifold representing a body with enhanced kinematics. The corresponding affine connection has non-zero torsion and curvature, which can be useful for modeling a body with dislocations and disclinations.

In this work, a good coincidence of atomistic and continuum stress fields at the crack tip under mixed mode loading conditions in an anisotropic medium with cubic symmetry of elastic properties is revealed. The atomic stress distributions associated with the crack tip are obtained using the molecular dynamics method. Continuum distributions are obtained from the theoretical solution of the problem of determining the stress-strain state at the crack tip, based on the methods of the elasticity theory of anisotropic media and the subsequent decomposition of complex potentials by eigenfunctions. In the framework of a molecular dynamics computational experiment, a single-crystal face-centered copper at low temperature was considered in order to isolate the elastic mode of deformation of a single crystal, and the embedded atom potential was used. A distinctive feature of the conducted molecular dynamic modeling is the consideration of a crack that makes up various angles with planes of symmetry of the crystal. In the vicinity of the crack tip, points lying in annular regions at different distances from the crack tip and of different thickness were selected, and the dependences of the stress tensor components depending on the polar angle were plotted. A comparison of the angular dependencies obtained by atomistic calculation and using a theoretical solution showed their good consistency. It is found that the similarity of the angular dependences of the stress tensor components is observed for all the studied values of two angles: the angle between the axis of symmetry of the crystal lattice (in the plane of the plate) and the direction of the crack and the angle between the action of the tensile load and the crack line.

By virtue of this property of solutions, it can be concluded that solutions of continuous fracture mechanics can serve to describe stress fields at atomistic distances from the crack tip.

Within the framework of the general problem of calculating the kinematic characteristics of the mobile antenna of the spacecraft, the problem of the kinematics of the complex movement of the line of sight "Sc — IRP" ("spacecraft — information reception point") is considered. The solution of this problem is given, with the help of which the relationship of kinematic characteristics in the absolute and relative movements of the line of sight "Sc — IRP" is established in the form of theorems on the addition of its angular velocities and accelerations.

In this paper, the electrophysical properties and efficiency of energy converters — betavoltaic elements, which contain a GaN and GaP heterojunction on Si and 3C-SiC/Si substrates, are modeled. For conversion into electrical energy, external ⁶³Ni or internal ¹⁴C radioactive sources with a test specific activity of 100 mCi・cm^-2 are investigated in the simulation. The system of parameters and characteristics is optimized: diffusion lengths, short-circuit current, open circuit voltage, filling factor, reverse saturation current and efficiency. It was shown in simulation results, that in the device structure with junction depth of 0.1 microns, the good operation of a betavoltaic element is determined, the short-circuit current density is up to 200 nA・cm^-2, the open circuit voltage is up to 3.7 V, the power density is up to 700 nW・cm^-2, efficiency up to 25 %. The conversion efficiency reaches its maximum value when using a radioisotope source with an activity density from 25 to 100 mCi・cm^-2. The conversion efficiency with the location of the injector source inside is estimated to be about 30 times higher than with the external location.