Journal of Applied Mechanics and Technical Physics最新文献

This paper presents an overdeterministic algorithm for constructing the asymptotics of the stress field near the tip of a nanocrack in an anisotropic linear elastic body with cubic symmetry. A molecular dynamics solution of the problem of mixed loading (mode I fracture and transverse shear) of single-crystal copper and aluminum nanoplates with a central cut is described. Based on this solution, an asymptotic representation for the stress tensor components was derived. The atomistic stresses in the vicinity of the crack tip were calculated, and the coefficients of the series representing the stress field were determined using the values of the atomistic stress tensor components. The molecular dynamics calculations were performed for a temperature of 10 K to exclude the occurrence of nonlinear elastic deformation near the crack tip. The stress fields in the atomistic and analytical solutions were compared. The stresses at different distances from the nanocrack tip are in good agreement with the solutions of problems of classical macroscopic theory of anisotropic elasticity and can be described using a series that extends the Williams series to anisotropic media. In the series extended to anisotropic materials, the regular (nonsingular) terms are taken into account and the series coefficients of these terms are determined. It is shown that the developed algorithm can be used to effectively determine the coefficients of the higher-order terms of the series.

Erosion of electrodes in a three-electrode pulsed X-ray tube with a rechargeable insulated electrode operating in the explosive emission mode at a voltage of 600 kV and pulsed current up to 1000 A was investigated. Erosion was produced by the action of high pulsed electric fields and pulsed flows of electrons and plasma during vacuum breakdown in X-ray tubes. X-ray fluorescence microanalysis using a scanning microscope revealed the presence of numerous metal balls of size 10–40 (mu )m formed from both the tungsten anode material and the material of the third insulated Kovar electrode. Several stages of detachment of the balls by the electric field were detected on the insulated electrode. The critical values of the Coulomb forces at which droplets arise in accordance with a dynamic model (taking into account the kinetic energy accumulated by the mass during the time of exposure to the electric field and surface energy) and the electric field pressures during the operation of the tube were estimated, allowing an explanation of the observed phenomena.

In this paper, we have approximated the solutions of the Cahn–Hilliard equation (CH) with the logarithmic potential function which arises in the modeling of phase separation of binary alloys. The CH equation is a high-order nonlinear equation, consequently, utilizing a common difference scheme on the CH equation causes long stencil schemes. To resolve the faults of long stencil schemes, we split the CH equation to second-order system under the Neumann boundary condition and we applied second-order scheme based on the 2D Crank–Nicolson method to discrete it. The uniqueness and error estimation of the approximated solution is proved. Also, preserving the conservation of mass and decreasing the total energy are investigated. Finally, to confirm the theoretical results, three examples with various initial conditions are presented.

The behavior of calcite at pressures up to 1000 GPa is simulated taking into account the high-pressure phase transition. The shock loading of calcite was calculated using a thermodynamically equilibrium model. A few-parameter Mie–Grüneisen type equation of state is used to describe the behavior of condensed phases. In the phase-transition region, the components of the sample under study are considered as a mixture of low- and high-pressure phases. The single and double shock Hugoniots are constructed in the pressure range from 1 to 1000 GPa, and calculations were made to determined the heat capacity along the normal isobar, entropy as a function of temperature, and the thermodynamic potential along the shock Hugoniot. The simulation results were verified against experimental data and available calculation results.

Functionally graded B₄C–CrB₂ material with a CrB₂ concentration gradient along the thickness equal to 5, 15, and 25% was produced by reactive hot pressing of a mixture of boron carbide, chromium oxide, and a carbon material with high specific surface area. A general view of the microstructure and the size distribution of chromium diboride particles in each layer are presented. The change in mechanical properties with increasing CrB₂ concentration is shown to be nonmonotonic due to the features of the boron carbide reduction reaction.

A disturbance propagation in a supersonic boundary layer on a straight parabolic wing is numerically simulated. Near the leading edge, a mass flow rate disturbance is introduced into the boundary layer, resulting in the formation of a first-mode wave packet, and the first-mode amplitude increases downstream. It is shown that, upon reaching a critical amplitude, the disturbance begins evolving nonlinearly and longitudinal structures appear. The nonlinear interaction of the boundary layer modes leads to the formation of a turbulent spot. The characteristics of the resulting spot with known data for gradient-free flows are compared.

An unsteady heat conduction problem for a rod is considered. A classical heat conduction equation is obtained on the basis of the assumption of temperature differentiability with respect to time and coordinate. A solution is constructed for a model problem with boundary conditions of the second kind, which determines temperature distribution in a heat-insulated rod along its length and time. It is revealed that, for the classical formulation of the problem, the temperature variation rate at the initial moment is singular and the condition of temperature differentiability with respect to time is not satisfied. A modified heat conduction equation, which is based on a nonlocal definition of temperature as a time-dependent function, is proposed. Unlike the traditional definition of temperature, this function is not the temperature value at a fixed moment, but rather is an average value over a finite time interval, known as a nonlocal temperature. With the application of this approach, the heat conduction equation retains the classical form, but contains the nonlocal temperature rather than the traditionally used. As a rule, temperature is determined by solving the Helmholtz equation, which includes an unknown time interval over which the temperature is averaged and which is determined experimentally. The classical and the nonlocal solution are compared to experimental data. This paper also touches upon the Maxwell–Cattaneo nonclassical law of heat conduction, which assumes a finite temperature propagation velocity over time.

A two-dimensional problem of stationary nonlinear waves on the surface of a layer of finite-thickness ideal fluid is considered. The solution to the problem using the proposed technique includes the following steps. Firstly, the stream function trace is used to change the kinematic condition on the free surface. Secondly, the Bernoulli–Cauchy integral is applied to present the dynamic condition in a new form. Thirdly, an integral operator of the convolution type is introduced, which allows one to simplify the nonlinear boundary-value problem of determining four functions of one variable, the main ones of which are a wave profile shape and a stream function trace at the surface level. This technique allows reducing the two-dimensional problem to a one-dimensional one. Two forms of the nonlinear dispersion relation are obtained: the dependence of the wave velocity on the amplitude of the fundamental harmonic of the wave and the dependence of the wave velocity on the wave amplitude. The cases of short and long waves are considered.

A number of new formulas are obtained for the vector field characteristics used in vector field geometry, vector analysis, and differential geometry: curvature vector, associated vector field, degree of nonholonomy, and Laplacian. Nonclassical characteristics such as the vector potential of the curvature vector field of a vector field and the sum of three curvature vectors of vector lines of the Frenet unit vector fields of a family of curves are also studied. It is shown that all the listed quantities are related to Aminov’s divergent representations for the Gaussian curvature or for the total curvature of the second kind. The obtained formulas can be considered as properties of the family of curves. Some formulas have divergence form, which makes it possible to derive differential conservation laws for the family of curves as well as for the eikonal equation and the Euler equations of hydrodynamics.

The assessment of material toughness is governed by codes based largely on rigorous experimental results. However, the problem of transferability from the laboratory specimen to field-scale structures limits the extent to which these results can be used. The present work is a developmental contribution to a new approach for assessing the toughness of pipeline steels. The procedure concerns the interaction between material fracture curve based on the three-parameter fracture criterion ((K- T- {{A}_{3}})) and the surface longitudinal notch driving force of a pipe under internal pressure. This could be applied as an important engineering parameter for assessing the structural integrity of pipelines during long-term operation.