


Vol 22, No 3 (2019)
- Year: 2019
- Articles: 10
- URL: https://journal-vniispk.ru/1029-9599/issue/view/12094
Article
Dispersion and Self-Modulation of Waves Propagating in a Solid with Dislocations
Abstract
In the paper, the basic equations describing ultrasonic wave propagation in a medium with dislocations are derived. Dispersion relations are given under the assumption that dislocations oscillate without damping, i.e., the dislocation component of the general system is conservative. It is shown that ultrasonic wave propagation is characterized by two dispersion branches (acoustic and optical). As the wave number increases, the phase velocity of the wave belonging to the acoustic branch decreases asymptotically from a finite value to zero, while the velocity of the wave belonging to the optical branch decreases asymptotically from infinity to a finite value corresponding to the longitudinal wave velocity. The Nighthill criterion is applied to study modulation instability. The form of the wave packets into which a quasi-harmonic wave is divided due to modulation instability is determined. There can be both periodic stationary wave envelopes and a solitary stationary wave envelope. It is found how the height and width of the wave packet formed due to self-modulation of a quasi-harmonic wave correlate with the basic characteristics of the dislocation structure.



Developed Turbulence: New Methods for Turbulence Modeling
Abstract
This paper completes the construction of the model of developed hydrodynamic turbulence, which has been elaborated over the past few years. For the first time, developed turbulence as a nonintegrability phenomenon in the Pfaffian sense in continuum dynamics is defined in terms of mathematical postulates. The main novelty is the direct modeling of classes of turbulent vortex wake trajectories by integral Pfaff distribution curves. This provided a basis for geodesic and almost geodesic variants of modeling. The model is extended with a new version of the solution of the averaging problem for developed turbulent states of the medium.



Finite Element Simulation of Chessboard Strain Localization in View of Statistical Spreads in Polycrystal Grain Parameters
Abstract
The paper presents a finite element simulation for research in the so-called chessboard effect of plastic strain localization. In the simulation, we consider a polycrystal metal strip under uniform tension on the assumption of a normal yield stress distribution over its grains. Using the simplest isotropic model, it is taken that all grains have the same linear hardening coefficient. The simulation results demonstrate that whether the problem statement is two- or three-dimensional the material reveals plastic strain localization in the form of numerous intersecting bands arranged into a chessboard system on the initially flat specimen surface.



Numerical Study of the Kinetic Aspects of Fracture of Metal Nanocrystals
Abstract
This paper deals with the investigation of the temperature effect on the fracture of a metal nanostructure during constant-rate uniaxial deformation. The temperature varied within the range from 0 to 550 K, and the velocity of the movable grip varied from 50 to 500 m/s. It has been demonstrated that the temperature significantly affects both the macrocharacteristics of fracture (fracture site, the number of structural fragments, grip stresses) and the kinetic characteristics (time to maximum grip stresses, fracture time, mass transfer, and necking).



Critical Grain Size Estimation in the γ-α Martensitic Transformation with Athermal Macrokinetics by the Example of Fe-Ni-Cr System
Abstract
The existence of the critical grain size Dc for reconstructive martensitic transformations implies that at austenite grain diameters D smaller than Dc the transformation is suppressed during cooling down to absolute zero temperature. In the case of athermal macrokinetics, martensite crystals divide connected (free from boundaries) volumes of austenite, which allows the use of fractal type models for the processing of results. This study shows that the symmetric model of orthogonal coupling of martensite crystals, developed to estimate the amount of formed martensite in single-crystal samples, can also be applied for an initial polycrystalline sample with a known austenite grain size distribution. A step-by-step algorithm for the theoretical estimation of Dc is proposed under the assumption that the formation of each succeeding generation of martensite crystals begins in the largest continuous volumes of retained austenite. If the estimated cumulative fraction of martensite coincides with the observed resultant value, the count is stopped, and the size of the largest of untransformed continuous volumes of retained austenite is taken as Dc. A detailed analysis of results was carried out for a sample of the alloy Fe - 29.96%Ni - 1.83% Cr in which the volume fraction of the largest grains (with the size D = 310–315 µm) was approximately 58% and four autocatalytic bursts were detected during cooling; the bursts corresponded mainly to the generations of martensite crystals associated with the austenite regions related to the transformation of the initial coarse grains. The amount of martensite crystals was determined by the increase in magnetization and by X-ray diffraction. With the cumulative fraction of martensite ≈70%, Dc was estimated to be ≈ 25.44 µm.



Influence of Surface Stresses on the Nanoplate Stiffness and Stability in the Kirsch Problem
Abstract
A system of von Karman equations for a nanoplate has been generalized by introducing effective tangential and flexural stiffnesses and elastic moduli, with regard to surface elasticity and residual surface stresses on the outer surfaces. A modified Kirsch problem was solved for the case of an infinite nanoplate with a circular hole under plane stress in terms of effective elastic moduli. Two forms of local stability loss in this problem and the corresponding critical load for two different elastic characteristics of all plate surfaces were determined numerically and analytically. The dependence of the effective stiffnesses and elastic moduli on the plate thickness, and of the critical load on the hole radius (size effect) was discussed.



Effect of Heat Treatment on the Mechanical Behavior and Fracture of TiNi Alloy
Abstract
The mechanical properties and fracture of a TiNi alloy (Ti-55.8 wt % Ni) have been investigated under vacuum heat treatment at 700–1200°C. Three-point bending and low cycle fatigue tests were conducted on heat treated wire samples under extreme loading conditions (large strains and alternating bending loads) to determine the effect of the annealing temperature on the superelastic behavior of the alloy. It was found that an increase in the heat treatment temperature leads to grain coarsening in the alloy, but the coarsening effect on its superelastic behavior is insignificant at low bending strains (4.0–4.5%). With heat treatment temperature variation from 700 to 1200°C, the shape of the alloy stress-strain curves remains almost unchanged for all bended samples, but with increasing heat treatment temperature the martensitic shear stress and residual strain slightly increase. In low cycle bending tests, the alloy ductility reduces significantly after heat treatment above 1100°C. Fractographic analysis of the tested alloy samples revealed different fracture surface structures depending on the heat treatment conditions, but the same fracture mechanism. In all cases, fracture occurs by quasi-cleavage, and the microcrack nucleus is associated with Ti2Ni/Ti4Ni2O inclusion particles or surface defects. The general results indicate the possibility of diffusion welding of TiNi alloys at a temperature of 1000–1100°C, without pronounced changes in their mechanical properties and ductility.



Two-Level Elastoviscoplastic Model: An Application to the Analysis of Grain Structure Evolution under Static Recrystallization
Abstract
Multilevel modeling of structural evolution in polycrystals, which determines the macroscopic material properties, is currently one of the central research problems. The defect and grain/subgrain structure of polycrystalline materials changes greatly during thermomechanical processing. The grain structure is significantly affected by recrystallization, which leads to the formation of slightly defective recrystallization nuclei and their subsequent growth due to the absorption of more defective neighboring grains. This paper is aimed to develop a mathematical model for describing the behavior of polycrystalline materials during plastic deformation and subsequent heating to recrystallization temperatures. The main task is to describe grain structure evolution in polycrystals during this process. The considered recrystallization mechanism is based on the displacement of original grain boundary segments. As a result of preliminary cold plastic deformation, energy accumulates at defects (primarily dislocations) in neighboring grains. The energy difference between neighboring grains is the main driving force of grain boundary migration. When the recrystallized grain grows, the extent of the new high-angle boundary increases; the amount of energy expended for the boundary formation must be smaller than the decrease in the stored energy due to defect elimination. The subgrains adjacent to the grain boundary are the recrystallization nuclei in the considered deformation mechanism. They start to grow into the more defective grain when the Bailey-Hirsch criterion is satisfied. This study deals with polycrystalline materials with low stacking fault energy for which the effect of heating on the subgrain structure is insignificant. The energy stored in grains and subgrains is calculated using a two-level statistical model that considers individual grains and subgrains. Plastic deformation is assumed to occur through edge dislocation glide. A method is proposed for isolating flat boundary regions (facets) of new (recrystallized) grains, based on minimizing the grain boundary energy in the vicinity of the new boundary. This approach describes some experimentally observed recrystallization effects, such as the elongation of recrystallized grains in the initial recrystallization direction and the appearance of grain boundary facets that allow for boundary mobility.



The Laws of Rolling
Abstract
The man-made transport was born when the wheel was invented. Since then the study of rolling has started. In 1781 the problem of rolling was mathematically formulated by Ch. Coulomb who offered Coulomb’s law of rolling, but the science of rolling has been purely empirical still until recently. In this paper the exact laws of rolling are analytically derived in terms of elastic and geometric properties of rolling bodies and foundations. Using the mathematical theory of elasticity and the CH-rule, the rolling resistance coefficient is calculated in the cases of: (i) an elastic cylinder rolling over another elastic cylinder of another material, in particular, over an elastic half-space, and an elastic wheel rolling over the rail of another elastic material; (ii) an elastic ball rolling over another elastic ball of another material, particularly over an elastic half-space; (iii) an elastic torus rolling over an elastic half-space of another material, and (iv) a cylinder, or a ball, or a torus rolling over a tightly stretched membrane or over a thin elastic plate. Empirical results of the measurement of the rolling resistance coefficient gained earlier by the railroad and automobile engineers appeared to be in excellent agreement with the results of this analytical calculation based on the suggested rule of rolling. The effect of adhesion was also studied using the exemplary case of an elastic cylinder rolling over an elastic half-space.



Ductile Failure Prediction of U-Notched Bainitic Functionally Graded Steel Specimens Using the Equivalent Material Concept Combined with the Averaged Strain Energy Density Criterion
Abstract
In this paper, the ductile fracture of bainitic functionally graded steel has been studied. Fracture tests was performed on U-notched specimens made of bainitic functionally graded steel under mode I. The averaged strain energy density criterion combined with equivalent material concept was employed to predict the ductile fracture of bainitic functionally graded steel. For this purpose, first, based on equivalent material concept, the mechanical properties of virtual brittle functionally graded steel were obtained. Then the averaged value of strain energy density over a well-defined control volume was calculated by finite element analysis for U-notched virtual brittle functionally graded steel. After that, the fracture loads was obtained based on the averaged strain energy density criterion. The agreement between experimental fracture loads and theoretical predictions was good.


