Vladimir Hilarov

The optimization of the process of polymer film orientational drawing using the local heater was investigated. One of the problems with this technology is that the strength of the resulting fibers differs significantly from the theoretical estimates. It is assumed that one of the reasons is related to the peculiarity of this technology, when at the point of drawing the film is heated only on one side, which creates a temperature difference between the sides of the film in contact with the heater and the non-contact sides of the film in the air. Estimates show that even a small temperature difference of just 1 °C between these surfaces leads to a significant difference in the rate of plastic deformation of the corresponding near-surface layers. As a consequence, during hardening, in the stretching region, tensile stress is concentrated on the “cold” side of the film, and this effect can presumably lead to the generation of more defects overthere. It has been suggested that defects arising during first stage of hardening, namely, neck formation, can serve as a trigger for the formation of defects such as kink bands on the “cold” side with further orientational strengthening due to plastic deformation of the resulting fibrillar structure, at the boundaries of which microcracks are formed, leading to rupture of the oriented sample. The numerical calculation of heat propagation due to heat conduction in the film from the local surface of the heater is carried out and the temperature distribution along the thickness and width of the film during drawing is found. The temperature difference in the heated layer of the film between the contact and non-contact sides with the heater was calculated depending on the thickness of the film and the speed of its movement along the heater. It was found that the most homogeneous temperature distribution over the film thickness, which is required, by default, for the synchronous transformation of the unoriented initial folded lamellar structure into a fibrillar structure, is observed only for films with a thickness of less than 50 μm. The calculation allows us to scientifically justify the choice of orientation drawing speed and optimal thickness of the oriented polymer film, which is extremely important, for example, for obtaining super-strong and high-modulus UHMWPE filaments used in products for various purposes: from body armor to sports equipment and bioimplants,

—A computer model of fracture in heterogeneous materials (including rocks) is proposed to study evolution of the defect structure (cracks) during deformation process. The model is based on the Discrete Element Method (DEM), which, in contrast to the methods relying on continuum mechanics, naturally simulates the formation and evolution of cracks. We used the bonded particle model (BPM), which is widely used in various modifications to study the fracture process. The material is modeled by a set of spherical particles (simulating polycrystalline grains), connected by bonds placed at particle contact points, which simulate grain boundaries. In the BPM model, crack initiation is determined by the breakage of bonds, and its propagation is provided by the coalescence of a numerous set of broken bonds. Computer experiments were performed with different material parameters (different mechanical properties of grains and grain boundaries, different grain sizes) to determine their effect on the local stress patterns, defect formation, and fracture source nucleation and development. The calculations were performed in the open-source DEM simulation software MUSEN. Samples were modeled by cylinders filled with spherical particles of the same or different radii packed up to reaching the void ratio 0.35–0.37. The materials simulating grains and bonds (grain boundaries) were specified with mechanical parameters corresponding to granite, quartz, orthoclase, oligoclase, and glass. The sample was placed in a virtual press in which a bottom plate was fixed and a top plate was moved towards the lower plate at a constant rate until the sample failed. The maximum local stress calculations have shown that homogeneous materials yield more heterogeneous spatial distributions of local stresses and vice versa—material heterogeneity leads to more uniform stress distributions. Comparison with the results of laboratory rock deformation experiments has shown that the proposed model of polycrystalline materials realistically describes some features of fracture in these materials when the main processes occur along the grain boundaries. These features include the brittle type of fracture in homogeneous materials and the presence of nonlinear elasticity (plasticity) revealed for more heterogeneous materials based on the stress-strain diagrams, as well as the time behavior of “acoustic emission rate” (or acoustic activity)—the number of bonds broken per unit time. For heterogeneous materials, the model shows a two-stage pattern of the fracture process with uniform defect accumulation throughout the sample at the first stage and the formation and growth of fracture nucleation sites at the second stage.

A computer model of fracture of the heterogeneous materials (including rocks) based on the Discrete Element Method (DEM) is proposed. We used the bonded particle model (BPM), various modifications of which are widely used in the study the fracture process. The material is modeled by a set of spherical particles (simulating polycrystalline grains) connected by bonds placed at the points of particle contacts (simulating grain boundaries). In BPM model, the initiation of cracks was determined by the bonds breakage, and their propagation is provided by the coalescence of many broken bonds. Computer experiments were carried out for the materials with different features (various grain mechanical properties and sizes, various mechanical properties of the grain boundaries), in order to find out the influence of these parameters on local stresses and the defect formation. Calculations were held in the MUSEN software. Cylindrical samples were filled with spherical particles of the same or different radii. The parameters of materials for grains and bonds (grain boundaries) were taken corresponding to granite, quartz, orthoclase, oligoclase, and glass. The sample was placed in a virtual press, in which the lower plate was stationary, and the upper plate moved towards the lower one at a constant velocity until the sample was destroyed. The calculation of the maximum local stresses showed that the homogeneity of material leads to greater space heterogeneity of local stresses and vice versa, heterogeneity contributes to their greater uniformity. Comparison with the results of laboratory experiments on rock deformation showed that the proposed model of polycrystalline materials realistically describes some features of their destruction when the main processes occur along the grain boundaries. These features include the brittle nature of homogeneous materials fracture and the presence of nonlinear elasticity (plasticity) for ones that were more heterogeneous. For heterogeneous materials, the model demonstrates a two-stage character of fracture process, when at the first stage the accumulation of defects occurs uniformly over the sample, and at the second stage – the formation and growth of the fracture site.

The NiTi metallic glass ribbon was subjected to 10-minute annealing at 400°C, 500°C and 600°C to detect changes in the surface relief and its statistical characteristics upon heating. Each annealing mode led to the ribbon crystallization with the formation of the Ni₅₀Ti₅₀ crystalline phases along with the transformation of the surface topography. Multifractal characteristics, such as the width of the singularity spectrum and fractal dimension, were calculated for the surface relief as a function of an annealing temperature. After the annealing at 500°C, along with the stepwise surface structure rearrangements, these parameters had extrema, including a local minimum of the width of the singularity spectrum, indicating a tendency towards monofractalization of the system. Abrupt changes in the parameters calculated by applying the multifractal formalism made it possible to detect the phase transition of the system in the form of its crystallization.

Time series of five financial indexes daily returns were analyzed by means of multifractal and recurrence quantification analysis (RQA) methods. It is shown that a financial crisis in 2008 year is accompanied with the increase in determinism and fractal self-organization. Such regularity is noted as analogous to other nonlinear systems behavior in catastrophic situations. At the same time, the global Hürst coefficient is minimal during the crises instead of maximum for physical systems.

The effect of uniaxial tensile stress on the atomic structure and relief of the subsurface layer of molybdenum ribbons has been studied. The destruction of the Mo (100) face with the formation of crystallites was revealed near the crack tip. At the same time, the block structures are found to rotate both in the lateral plane and in its perpendicular plane. The surface layer structure in the lateral plane of the ribbon is fragmented into sections, which is associated with the surface relief at different scales. With a help of the concept of multifractal formalism, the spectra of singularities of the initial, loaded and ruptured surface are calculated. It is found that the width of the singularity spectrum, can serve as an indication of the forthcoming rupture.. Keywords: molybdenum ribbon, mechanical load, annealing, destruction of material, block structures, surface, multifractal formalism.

The discrete element method (DEM) is used to reveal the main features of the fracture in materials with different degree of heterogeneity. It is shown that this method adequately describes the main properties of materials in the fracture process such as brittle and ductile behavior, two-staged nature of fracture in heterogeneous materials, heterogeneity of the spatial distribution of local internal stresses depending on the degree of heterogeneity. Keywords: discrete element method, fracture of heterogeneous materials, computer modelling.

Based on the analysis of the time intervals between acoustic emission signals obtained in the process of uniaxial compression of a cylindrical sample of a quartz single crystal, local stresses were estimated. It is shown that a decrease in the ability of a material to monotonic stress relaxation with time can serve as a signal for the imminent breakdown of the material. Keywords: acoustic emission, kinetic concept of strength, local mechanical stresses.

Local internal stresses in two natural inhomogeneous materials differing in the structure have been calculated using analysis of pauses between acoustic emission signals detected by a mechanical loading. It has been shown that the change in the accumulation type of these stresses can be considered as a prognostic criterion of forthcoming fracture.