S. G. Psakhie

Movable cellular automata method for simulating materials with mesostructure

Mathematical formalism and applications of the movable cellular automata (MCA) method are presented for solving problems of physical mesomechanics. Since the MCA is a discrete approach, it has advantages over that of the finite element method (FEM). Simulation results agree closely with the experimental data. The MCA approach cab solves mechanical engineering problems ranging from those in material science to those in structures and constructions. Computer simulation using MCA can also provide useful information in situations where direct measurements are not possible.

METHOD OF MOVABLE CELLULAR AUTOMATA AS A TOOL FOR SIMULATION WITHIN THE FRAMEWORK OF MESOMECHANICS

ConclusionThe proposed MCA method is based on mesomechanics of heterogeneous media [4, 5, 9]. It is connected first with the ability to describe the material as a set of structural elements of deformation [9]. The role of the structural unit in the MCA method is played by the element (movable cellular automaton). The expressions of interparticle interactions used, as well as the rules of changing the state of the elements, allow us to simulate a wide range of phenomena including melting, chemical reactions, and phase transformations. The characteristic size of the element and its properties are defined based on the features of the model constructed in the framework of mesomechanics as described in [9]. Therefore the MCA method as a computational technique allows us to realize the principles of mesomechanics when simulating material response to external loading of different types. This method is highly recommended in computer-aided design of new materials.

Dynamic vortex defects in deformed material

The paper studies the generation and evolution of dynamic vortex structures in a material on different structural scales. It is shown that the generation of dynamic vortex structures can be the main accommodation mechanism in a material under external mechanical loading. On the microscale, these structures can provide inter-granular sliding and grain boundary migration with anomalously high rates. On higher structural scales, their evolution can be the main process responsible for nucleation and propagation of cracks, fragmentation of material, formation of a “quasiliquid” layer in friction pairs, etc. The data and conclusions derived from the study are confirmed by numerical calculations for different types of materials in the framework of molecular dynamics and movable cellular automaton methods.

MD simulation of plastic deformation nucleation in stressed crystallites under irradiation

The investigation of plastic deformation nucleation in metals and alloys under irradiation and mechanical loading is one of the topical issues of materials science. Specific features of nucleation and evolution of the defect system in stressed and irradiated iron, vanadium, and copper crystallites were studied by molecular dynamics simulation. Mechanical loading was performed in such a way that the modeled crystallite volume remained unchanged. The energy of the primary knock-on atom initiating a cascade of atomic displacements in a stressed crystallite was varied from 0.05 to 50 keV. It was found that atomic displacement cascades might cause global structural transformations in a region far larger than the radiation-damaged area. These changes are similar to the ones occurring in the process of mechanical loading of samples. They are implemented by twinning (in iron and vanadium) or through the formation of partial dislocation loops (in copper).

Modeling the behavior of complex media by jointly using discrete and continuum approaches

We propose a new approach to modeling the behavior of heterogeneous media, according to which such objects are represented as composed of regions of two types, one being described within the framework of a discrete, and the other, a continuum approach. This joint approach is promising for the numerical modeling of complex media with strongly different properties of components. Possibilities of the proposed method were verified by studying the propagation of elastic waves in a two-component medium with a discrete component, modeled by the method of movable cellular automata, and a continuum component described by a system of equations of motion of continuum solved by the finite difference method. The results of calculations show that this approach provides adequate description of the propagation of elastic waves in complex media and does not introduce nonphysical distortions at the boundaries where the two models are matched.

Local structural transformations in copper crystallites under nanoindentation

A molecular-dynamic simulation of the response of a copper crystallite at the atomic level at local contact interaction has been performed. The calculation results have shown that plastic deformation is nucleated and developed according to the mechanism of generation of local structural transformations, which, in turn, give rise to higher level defects (dislocations, stacking faults, interfaces, etc.). During loading, the formed structural defects pass from the contact region into the crystallite bulk and, when emerging on the free surface, change its shape.

Evolution of atomic collision cascades in vanadium crystal with internal structure

The formation of radiation-damage regions (radiation-damage cascades) in vanadium crystallites with internal structures (intergrain boundary) has been simulated by the molecular-dynamic method. The interatomic interaction is described within the embedded-atom method. A relatively small number of clusters of intrinsic point defects (vacancies and self-interstitial atoms) are formed both in ideal vanadium crystallites and in crystallites with boundaries after the relaxation of atomic-displacement cascades. The evolutionary character of atomic-displacement cascades is determined in many respects by the presence of extended boundaries in materials. The intergrain boundaries hinder the propagation of atomic-displacement cascades and store many radiation-induced defects.

Development of a formalism of movable cellular automaton method for numerical modeling of fracture of heterogeneous elastic-plastic materials

A general approach to realization of models of elasticity, plasticity and fracture of heterogeneous materials within the framework of particle-based numerical methods is proposed in the paper. It is based on building many-body forces of particle interaction, which provide response of particle ensemble correctly conforming to the response (including elastic-plastic behavior and fracture) of simulated solids. Implementation of proposed approach within particle-based methods is demonstrated by the example of the movable cellular automaton (MCA) method, which integrates the possibilities of particle-based discrete element method (DEM) and cellular automaton methods. Emergent advantages of the developed approach to formulation of manybody interaction are discussed. Main of them are its applicability to various realizations of the concept of discrete elements and a possibility to realize various rheological models (including elastic-plastic or visco-elasticplastic) and models of fracture to study deformation and fracture of solid-phase materials and media. Capabilities of particle-based modeling of heterogeneous solids are demonstrated by the problem of simulation of deformation and fracture of particle-reinforced metal-ceramic composites.

Effect of dynamic stress state perturbation on irreversible strain accumulation at interfaces in block-structured media

The paper studies how the stress state of the interface between structural elements in a block-structured medium affects its deformation response to dynamic loading. It is shown that the normalized shear stress and mean stress are the major factors that determine the deformation response of the interface. We propose to describe the dependence of the value of induced irreversible displacement at the interface on the normalized shear stress using a logistic function. The central point of this function is the point of transition from the quasi-elastic to quasi-plastic stage of the interface shear deformation. The obtained empirical dependences are important for understanding the mechanism of irreversible strain accumulation in fault zone fragments and, particularly, for the development of an earlier proposed approach to estimate the characteristic level of active shear stresses in separate tectonic fault regions.

Tribological aspects in nanostructuring burnishing of structural steels

The paper studies tribological aspects of nanostructuring burnishing of steels. The efficiency of the process in improving the tribological properties of steels is assessed as regards the choice of an indenter material and lubricant-coolant reasoning from the friction coefficient at the “indenter-treated part” contact and from the absence of adhesive bond and fatigue microcracks. It is shown that synthetic diamond and dense boron nitride are promising indenter materials for nanostructuring burnishing of corrosion-resistant 20X13 steel and cement 20X steel. It is demonstrated that nanostructuring burnishing increases the wear resistance of structural steels under abrasive action and sliding friction in different media (lubricant, water, air, and argon) due to suppressed processes of microcutting, plastic edging, fatigue and oxidation wear, and adhesive bonding.