Plastic distortion as a fundamental mechanism in nonlinear mesomechanics of plastic deformation and fracture

Any deformed solid represents two self-consistent functional subsystems: a 3D crystal subsystem and a 2D planar subsystem (surface layers and all internal interfaces). In the planar subsystem, which lacks thermodynamic equilibrium and translation invariance, a primary plastic flow develops as nonlinear waves of structural transformations. At the nanoscale, such planar nonlinear transformations create lattice curvature in the 3D subsystem, resulting in bifurcational interstitial states there. The bifurcational states give rise to a fundamentally new mechanism of plastic deformation and fracture—plastic distortion—which is allowed for neither in continuum mechanics nor in fracture mechanics. The paper substantiates that plastic distortion plays a leading role in dislocation generation and glide, plasticity and superplasticity, plastic strain localization and fracture.     

Scale invariance of plastic deformation of the planar and crystal subsystems of solids under superplastic conditions

The theory of structural transformations in the planar sybsystem (surface layers and internal interfaces) of solids under plastic deformation is developed. The theory is based on a consideration for local curvature of the crystal lattice, with new structural states arising in its interstices, responsible for plastic distortion. To satisfy the superplastic condition, such high-rate mechanisms should develop in both planar and 3D crystal subsystems. In a translation-invariant crystal, this condition is met by concentration fluctuations. The multiscale criterion of superplasticity is formulated based on the scale invariance of plastic deformation of the planar and crystal subsystems in a deformable solid. Beyond the criterion, superplasticity passes to the creep mode with restricted plasticity of the material.     

Fundamental role of crystal structure curvature in plasticity and strength of solids

In the paper, we use the nonlinear multiscale approach of physical mesomechanics to demonstrate that the scales of local crystal structure curvature in solids play a fundamental role in the generation of strain-induced defects and cracks. It is shown that strain-induced defects arise at the interfaces of 2D planar and 3D crystal subsystems by the mechanism of “laser pumping” and cracks nucleate as structural phase decay in the zones of crystal structure curvature where the nonequilibrium thermodynamic potential or so-called Gibbs energy is higher than zero. Nonlinear fracture mechanics eliminates the problem of singularity 1/r in equations of crack growth but requires accounting for local lattice curvature at the crack tip.     

Nonlinear wave processes in a deformable solid as a hierarchically organized system

Theoretical predictions and experiments demonstrate that solid state mechanics should consider, along with a structurally equilibrium 3D crystalline subsystem, a structurally nonequilibrium planar subsystem as a complex of all surface layers and internal interfaces with broken translation invariance. Primary plastic flow of a loaded solid develops in its structurally nonequilibrium planar subsystem as channeled nonlinear waves of local structural transformations that determine the self-organization law of multiscale plastic flow. These waves initiate mesoscale rotational deformation modes, giving rise to all types of microscale strain-induced defects in the planar subsystem. The strain-induced defects are emitted into the crystalline subsystem as an inhibitor of nonlinear waves of plastic flow in the planar subsystem. Plastic deformation of solids, whatever the loading type, evolves in the field of rotational couple forces. Loss of hierarchical self-consistency by rotational deformation modes culminates in fracture of material as an uncompensated rotational deformation mode on the macroscale.     

Scale invariance of structural transformations in plastically deformed nanostructured solids

The scale-invariant mechanical behavior of a nanostructured solid is associated with plastic distortion as a major mechanism of nano- and microscale structural transformations. Active grain boundary sliding in a deformed material (microscale) within its highly developed planar subsystem (nanograin boundaries) causes a progressive increase in lattice curvature and plastic distortion of atoms which produces nonequilibrium vacant sites in the nanostructure. The motion of nonequilibrium point defects in nanostructure curvature zones provides conditions for noncrystallographic plastic flow, dissolution or dispersion of initial phases, and formation of nonequilibrium phases in a deformed material. The possibility of reversible structural phase transformations in the presence of high lattice curvature opens the way to greatly increase the fatigue life of surface nanostructured polycrystalline materials.     

Multiscaling of lattice curvature on friction surfaces of metallic materials as a basis of their wear mechanism

A comprehensive structural study has been performed to explore deformation and wear debris formation on friction surfaces of metallic materials. A hierarchy of structural scales of plastic deformation and failure during wear has been established. The nanoscale plays the major role in the hierarchical self-organization of multiscale debris formation processes. On this scale, bifurcational interstitial states arise in zones of local lattice curvature, with plastic distortion and motion of nonequilibrium point defects which determine the nonlinear dynamics of structure formation and wear of surface layers. Nonequilibrium vacancies on lattice sites form microporosity through the coalescence mechanism under plastic distortion. The microporosity is a precursor of meso- and macroscale plastic shearing that defines wear debris formation.     

Role of local curvature in grain boundary sliding in a deformed polycrystal

The paper considers experimental and theoretical principles of accounting for curvature in multiscale computer simulation of the behavior of interfaces as independent planar subsystems in a loaded polycrystal. Dynamics of matter and energy flows along grain boundaries is studied using a hybrid discrete-continuous method of excitable cellular automata, which combines synergetic principles of discrete switching and laws of continuum mechanics. It is shown that these flows have a rotational-wave nature and depend on the loading conditions of a grain boundary.     

Multiscale model of deformed polycrystals. Hall-Petch problem

The paper puts forward a multiscale model of deformed polycrystals according to which the basis for self-consistent deformation of grains is rotational wave flows of planar structural transformations at their boundaries. Computer-aided engineering of grain boundaries reveals two types of rotational wave flows defined by the misorientation angle of adjacent grains. Grain boundary flows of the first type develop at low-angle boundaries and feature low curvature. These flows generate dislocations in the grain bulk and the Hall-Petch equation for them has the form σ=σ₀+kd^?1/2. Grain boundary flows of the second type develop at high-angle boundaries and feature high curvature. These flows generate curvature bands in near-boundary zones and inject them into the grain bulk, resulting in fragmentation of grains and breakdown of translation invariance. For such self-consistency of grains in a polycrystal, the Hall-Petch equation has the form σ=σ₀+kd^?1. Experimental data in support of the proposed multiscale model are presented.     

On the nature of low-temperature brittleness of BCC steels

The study demonstrates the possibility to suppress the ductile-brittle transition in bcc-structured steels at low strain temperatures on the example of pipe steel subjected to severe plastic deformation. The suppression of the ductile-brittle transition in the material is associated with structural changes in its planar subsystem (surface layers and grain boundaries in polycrystals) and substructure formation in its 3D crystalline subsystem.     

Effects of plastic distortion in the lattice curvature zone of a crack tip

The paper proposes a discrete-continual method of excitable cellular automata for simulating the stress-strain state at crack tips and in notches with account of lattice curvature and plastic distortion through ion motion from lattice sites to interstices. The proposed nonlinear method allows one to determine the crack type and the character of fracture, to predict the possibility of dynamic rotations and structural turbulence, and to describe the processes of nonlinear wave structural transformations in strain localization bands involved in microporosity and tearing mode cracking.     

Viscous fingering as a first step toward understanding dendrites

The development of viscous fingering patterns has been observed for Hele-Shaw flows with both planar and circular initial interfaces. These flows have close formal connection with dendritic growth. Local curvature as a function of interfacial arclength has been extracted for all cases and modal analyses have been performed on these curvature functions. A crude measure of the content of the modal analyses comes from the behavior of the average wavenumber, , which at first increases during an initial ramifying flow period and then decreases with time as the pattern coarsens in the quiet regions behind the advancing fingers faster than it ramifies at the front.     

The role of curvature of the crystal structure in the formation of micropores and crack development under fatigue fracture of commercial titanium

The multiscale mechanism of fatigue fracture of titanium with the surface layer hydrogenated under alternating bending at room temperature is studied. It is shown that the generation of the fatigue fracture occurs in the surface layer subjected to plastic deformation in conjunction with an elastically loaded substrate. The latter causes the appearance of a strong curvature of the material and the appearance of micropores in these areas along with any fatigue cracks. The emergence of the local curvature of the crystal structure plays a central role in the origin and the development of the fatigue fracture as the structural phase decomposition of the material under cyclic loading.     

Multiscale space-time dissipative structures in materials: Two-electron genesis of nonequilibrium electromechanical interfaces

The fundamental supra-atomic scale of nanometer attosecond processes in condensed matter creates a multiscale hierarchy of electromechanical interfaces through two-electron dissipation of energy of quantum nanoelectromechanical systems. The space-time scales of electromechanical interfaces are specified, beginning with the subatomic scale of electron Compton length λ_e, by a sequence of degrees n = 1, 2, 3,... of the fine structure constant α ^-n. The third scale, with n = 3, corresponds to quantum mesoelectromechanical 2D interfaces which form functional matrices of electromechanical energy stores and converters as active nucleation centers of fractal topological defects in adjacent crystal structure regions. The hierarchy of electromechanical interfaces creates a hierarchy of dissipative structures in mesomechanics of solids and biomimetics of soft materials.     

Lattice curvature evolution in metal materials on meso- and nanostructural scales of plastic deformation

The paper generalizes results of electron microscopy studies of structural states with high lattice curvature which arise in a wide class of materials under various conditions of severe plastic deformation: rolling, equal channel angular pressing, mechanical activation in planetary ball mills, and torsion in Bridgman anvils. The states are divided into two types: 1) a substructural state with elastoplastic lattice curvature of tens of degrees per micron due to high density of like-sign excess dislocations; and 2) a state with elastic lattice curvature up to several hundreds of degrees per micron in volumes of several nanometers. Analysis is performed to inquire into the formation of these states, peculiarities of their evolution, and their role in different mechanisms of plastic deformation and formation of nanocrystalline structures.     

Planar magnetic colloidal crystals

We report a novel form of planar magnetic colloidal crystals formed by coated magnetic microspheres floating on a liquid meniscus. Under an external magnetic field, the balance between the repulsive magnetic interaction and the "attractive" interaction, due to the weight of the particles projected along the surface tangent, yields not only the triangular lattice with a variable lattice constant, but also all the other planar crystal symmetries such as the oblique, centered-rectangular, rectangular, and square lattices. By using two different sized magnetic particles, local formations of 2D quasi-crystallites with fivefold symmetry are also observed.     

Dislocation-based plasticity model and micro-beam Laue diffraction analysis of polycrystalline Ni foil: A forward prediction

A physically-based, rate and length-scale dependent strain gradient crystal plasticity framework was employed to simulate the polycrystalline plastic deformation at the microscopic level in a large-grained, commercially pure Ni sample. The latter was characterised in terms of the grain morphology and orientation (in the bulk) by micro-beam Laue diffraction experiments carried out on beamline B16 at Diamond Light Source. The corresponding finite element model was developed using a grain-based mesh with the specific grain orientation assignment appropriate for the sample considered. Sample stretching to 2% plastic strain was simulated, and a post-processor was developed to extract the information about the local lattice misorientation (curvature), enabling forward-prediction of the Laue diffraction patterns. The ‘streaking’ phenomenon of the Laue spots (anisotropic broadening of two-dimensional (2D) diffraction peaks observed on the 2D detector) was correctly captured by the simulation, as constructed by direct superposition of reflections from different integration points within the diffraction gauge volume. Good agreement was found between the images collected from experiments and simulation patterns at various positions in the sample.     

Optical limitation in two-dimensional nonlinear photonic crystal with triangular lattice

Optical limitation in a 2D nonlinear photonic crystal (NPC) has been studied in this Letter. Since the optical limitation is due to Bragg scattering induced by the variation of nonlinear refractive index, it is sure that the optical limitation can be realized in nonlinear photonic crystal. The light propagation characteristics in a two-dimensional nonlinear photonic crystal with triangular lattice has been calculated by using the finite-difference time-domain algorithm, which is constructed by placing certain number of nonlinear dielectric rods in a linear photonic crystal. The optical limiting effects at 1.300 and 0.504 μm have been obviously obtained for TE polarization and TM polarization, respectively.     

瑞利-泰勒不稳定性的格子玻耳兹曼模拟

发展了一个不相混两相流体的格子玻耳兹曼模型，模拟瑞利-泰勒不稳定性．模型使用正方格阵并引入了一外力．数值模拟得到了界面扰动的线性和非线性发展图象，并与实验和其它方法的结果进行了比较 关键词：