编号 3 (2024)

Some effects of the stress-strain state, such as vibrocreep, creep acceleration and ratcheting, observed and studied in experimental mechanics of a deformable solid, are proposed to be modeled on the basis of constitutive relations implemented in tensor nonlinear viscoelastic Maxwell-type models. The apparatus of isotropic tensor functions depending on two symmetric tensor arguments is involved. Examples of a complex stress state in a tubular specimen are given, when there is a significant disproportionate increase in time of the axial component of strain under the combined action of constant axial and vibrational shear loads compared with the case of the action of only axial load. The concepts of generalized and combined ratcheting are introduced in conditions of a complex stress state.

The paper presents an analytical solution to the problem of a circular pipe turned inside out in a rigid gasket. Formulas were obtained for the magnitude of the radial stress, which is responsible for the adhesion between the pipe and the gasket. The solution is obtained for an arbitrary incompressible hyperelastic material with a hyperelastic potential that depends only on the first invariant of the left Cauchy – Green deformation tensor (various generalizations of the neo-Hookean solid) or on the second invariant of the logarithmic Hencky strain tensor (various generalizations of the incompressible Hencky material). The solution takes into account the occurrence of plastic flow in areas adjacent to the lateral surfaces of the pipe. Both ideally plastic and isotropically hardening materials of a general type are considered. For the latter, a solution scheme is given; in the particular case of a linearly hardening material, a closed-form solution is obtained. For the perfect plasticity model, a closed-form solution was obtained for the neo-Hookean solid, for an incompressible Hencky material, and for the Gent material.

The problem of natural vibrations of a flat strip of anisotropic two-dimensional Cosserat medium under the assumption of small deformations and in the absence of external forces and moments is investigated. It is shown that two natural frequencies correspond to each wave number. The natural forms of oscillations and the relationship between them are found. It is concluded that at oscillations with the lower of the two frequencies the inclusion rotations accompany the longitudinal displacement of the strip, and at oscillations with a higher frequency they prevent it. The obtained results are illustrated on the example of a medium model with specific parameter values. The plots show the dependences of natural frequencies, phase and group velocities on the wave number, and their asymptotic behavior is studied.

On the basis of experimental data on the fracture of an adhesive layer mating two plates along a given section and the known analytical solution corresponding to the calculation scheme, variants of the fracture criterion that take into account hydrostatic pressure and invariant components of elastic energy are considered. One- and two-parameter criteria are investigated, in which the products of volume and shape deformation energy per layer thickness form the critical flow of elastic energy density. It is shown that the loosening of a thin adhesive layer under a two-parameter criterion quasilinear with respect to the volume strain energy most accurately describes the critical state.

The problem of translational-rotational motion of a variable body is considered under the assumption that the inertial properties of the body, as well as the external forces acting on it and the moments of forces clearly depend on time. The conditions under which the equations of motion are reduced to classical equations describing the motion of a solid body in a force field independent of time are indicated. There are cases when the equations of motion are reduced to completely integrable ones. The elements of the discussion of the 1920-1930 on the description of the motion of a material point of variable mass in a time-dependent field of attraction are reproduced.

Problem of sliding of a periodic system of asperities along the boundary of a viscoelastic half-space with a coating is under consideration. The coating is modeled by a layer with flexural rigidity. The solution is based on reducing the problem to the contact of a limited system of asperities with the action of others being replaced by distributed pressure; the accuracy of such approach is evaluated. The numerical-analytical solution is based on double integral Fourier transforms, the boundary element method and the iterative procedure. The influence of the shape of asperities, sliding velocity, and coating thickness on the deformation component of the friction force and on the effect of mutual influence of asperities was analyzed. To identify the effect of mutual influence, a comparison was made of the results (distribution of contact pressure and friction force) obtained for multiple contacts and for the isolated asperity. For comparison, the results of solving a similar problem for viscoelastic half-space without a coating were obtained and analyzed.

The negative creep of single crystals of nickel-based superalloys SR99 and CMSX-4 has been investigated. This phenomenon was observed for both superalloys at temperatures of 980–1000 °C and low or zero loading stresses. It is assumed that the main reason for the negative creep is the formation of a short-range order of atoms in a strongly alloyed crystal lattice of the g-matrix. Additional factors affecting the magnitude and anisotropy of the negative creep strain may be the relaxation of residual stresses: at the microscopic level, misfit stresses between the g-matrix and strengthening g′-precipitates, and at the mesoscopic level, dendritic stresses between the dendrite axes and interdendritic regions.