Structural-scaling Transitions Research Articles

Metastability, adiabatic shear bands initiation and plastic strain localization in the AMg6 alloy under dynamic loading

New conception of adiabatic shear bands (ASB) and adiabatic shear failure mechanisms are proposed as special type of critical phenomen, structural-scaling transition, in the ensembles of microshears, governed by the characteristic non-linearity (metastability) of stored (free) energy of solid with mesodefects. Corresponding free energy release kinetics provides experimentally observed ASB induced staging of plastic strain localization and transition to adiabatic shear failure. ASB staging follows to collective properties of microshears ensemble given by the self-similar solutions of evolution equation providing spatial-temporal microshears localization, momentum transfer and damage localization. The criticality of ASB induced plastic strain localization and failure allows us to avoid the discrepancy in the interpretation of ASB effects as thermo-plastic instability in the balance of the stored energy and structural DRX transformation. The microshear ensemble is considered as the second phase and initiation of collective modes provide different staging according to the metastability decomposition and ASB scaling properties following to the self-similar solutions. Self-similar nature of microshears collective modes providing the ASB dynamics is analyzed as the mechanism of steady plastic wave front unversality in shocked materials. The dynamic split Hopkinson pressure bar tests were conducted with AlMg6 alloy combined with “in-situ” imaging of temperature kinetics by CEDIP Silver 450M high-speed infrared camera with conclusion of the secondary role of thermoplastic instability at the ASB staging. The microstructural study performed by an electron microscopy revealed the correlated behavior of the ensemble of defects, which can be classified as a structural transition and precursor of ASB induced strain localization and failure. The modeling reflecting the links of self-similar solutions in microshear ensembles with relaxation properies and damage localization was applied for the comparative analysis of ASB staging and temperature dynamics given be the infrared imaging.

Damage-failure transition in titanium alloy Ti-6Al-4V under dwell fatigue loads

The role of structural mechanisms responsible for the consequent staging of damage-failure transition as the combination and continuity of ductile and creep kinetics of the structure evolution and the modeling in dwell fatigue regime. Damage-failure transition is considered as critical phenomena, the structural-scaling transition, when the damage develops as specific phase with characteristic stages: nucleation of new phase and the phase growth kinetics. In the case of dwell fatigue, the nucleation stage is associated with slip localization, faceting, voids and microcrack initiation; the phase growth kinetics has the relation to specific non-linearity of the free energy release responsible for the staging of damage-failure transition. Statistically based phenomenological model of damage-failure transition specified the links of macroscopic material parameters with structural parameters responsible for the influence of microstructure on the structure sensitive mechanical properties. The developed conception of modeling of Ti alloys based on the duality of damage kinetics in dwell fatigue loads allowed us to propose the strategy of structural study to provide in perspective the links of structural parameters of /phases with phenomenological parameters responsible for different mechanisms of damage accumulation at LCF and stress hold regimes.

Localized shear as a quasi-plastic mechanism of momentum transfer in liquids

Two types of dispersion relations (DRs) in condensed media and associated momentum transfer mechanisms are discussed: gapless DRs corresponding to acoustic modes and DRs with energy (or frequency) gap. Studying the viscoelastic effects in condensed media based on the generalization of the Maxwell-Frenkel approach, the emphasis was placed on the gap states in the momentum transfer mechanisms (GMS), when the k-gap was accompanied by qualitative changes in the DRs type. In this paper, the gap states in the mechanisms of momentum transfer in liquids are associated with the effects of shear elasticity and the formation of collective modes of quasi-plastic shears under conditions of the established type of critical phenomena in the ensembles of shear defects — structural-scaling transitions. It has been found that the formation of collective shear modes, having the character of self-similar solutions of the autosoliton type, accounts for the qualitative change in the dispersion properties corresponding to the quasi-plastic momentum transfer mechanisms operating in the characteristic range of loading times. The results of comparison with the data of original experiments confirm the initiation of quasi-plastic mechanisms of momentum transfer in liquids during the formation of collective shear modes and corresponding change in dissipative properties.

Metastable states, relaxation and failure mechanisms in condensed matter with defects

The article is concerned with experimental studies of anomalous momentum transfer mechanisms in condensed matter exhibiting multiple defect-induced gaped momentum states. The performed experiments revealed the relationship between the metastable states, the specific critical phenomena in condensed matter with defects, the structural-scaling transitions, and the mechanisms of structural relaxation disclosing viscosity anomalies in solids and liquids due to the strong interactions between the structure constituents. The possibility of these mechanisms under intensive loading including turbulence was substantiated in Naimark (1998), Naimark (1997), Naimark (2004). The established regularities of criticality in the behavior of condensed matter with mesoscopic defects made it possible to study the thermodynamics and kinetics of the nonlinear liquid and solid systems exhibiting the metastable states, and to provide an explanation of the anomalous mechanisms of momentum transfer in systems with "strong interaction." Anomalous momentum transfer mechanisms are associated with the subjection of the dynamics of condensed matter to the established types of collective modes in ensembles of defects (breathers, autosolitons, dissipative blow-up structures) manifesting the character of self-similar solutions. The subordination of dynamics to collective modes is accompanied by a sharp increase in the effective relaxation times and absorption anomalies. The theoretical results are confirmed by the experimental data on the formation of self-similar (quasi-plastic) fronts in liquids and the attainment of viscosity asymptotics due to initiation of fracture waves under shock-wave loading of fused quartz (Naimark (2003), Naimark (2010)).

Critical dynamics of damage-failure transition in wide range of load intensity

The self-similarity of characteristic stages of damage-failure transition has been studied both theoretically and experimentally, with the damage localization kinetics analyzed according to the nonlinearity of free energy release of solids with defects: Free energy in the generalized Ginzburg–Landau form reflecting the specific criticality of solids with defects, and the structural-scaling transition in the presence of two critical points separating qualitatively different material responses corresponds to the types of collective modes of defects. These collective modes have the nature of the self-similar solutions of the damage evolution equation. The final damage stage is associated with the singular self-similar blow-up solutions localized on a set of spatial scales. The presence of two singularities (the stress field at the crack tip and the blow-up damage modes) allows the interpretation of self-similarity of damage localization kinetics to be construed as a criticality sign of damage-failure transition and has been illustrated by the original experimental statements: transition from the steady state to branching crack dynamics, dynamic fragmentation statistics, resonance regimes of failure in shocked materials.

Defects Induced Criticality and Gapped Momentum States in Condensed Matter

There are two conventionally discussed dispersion relations (DR) in condensed matter: the gapless phonon-like DR and the DR with the energy or frequency gap. The third type of DR has been emerging in different areas of condensed matter physics: the gapped momentum states (GMS) when the DR with the gap in momentum, or k-space. Increasing interest for the gapped momentum states are related to important implications for dynamical and thermodynamic properties of the system (hydrodynamic turbulence, plasticity, failure). Traditionally GMS emerge in the Maxwell-Frenkel approach to liquid or solid viscoelasticity, relate the k-gap to dissipation and observe how the gaps in DR can continuously change from the energy to momentum space. Generalized hydrodynamics seeks to start with hydrodynamic equations for liquid properties and subsequently add non-hydrodynamic effects. GMS can also be obtained starting from solid-like elastic equations and generalizing them by adding hydrodynamic flow effects. Original interpretation of GMS and dispersion properties in condensed matter is developed considering the defects induced criticality (structural-scaling transition) in shocked liquid and solid. The nature of the viscosity limit is discussed analyzing the scenario of GMS in the presence of dynamics of collective modes of defects.

DNA Transformation, Cell Epigenetic Landscape and Open Complex Dynamics in Cancer Development

Statistical thermodynamics allowed the formulation of mesoscopic approach of DNA transformation in course of the excitation of collective distortion modes (denaturation bubbles) associated with hydrogen bond breaking between the base pairs. Intermediate (non-continual limit) of DNA modeling (the Peyrard-Bishop model) is combined with the field description (generalized Ginzburg-Landau approach) to analyze the dynamics of collective open complex modes associated with mesodefects in the DNA ensemble. Collective modes dynamics describes different scenario of gene expression according to statistically predicted form of out-of-equilibrium potential (epigenetic landscape) reflecting specific type criticality of “soft matter” with mesodefects (open complexes) – the structural-scaling transition. Principal difference of thermodynamics of non-continual and continual models is thermalization conditions related to thermal fluctuations responsible for the DNA breathing (localized excitation with breather dynamics) and structural-scaling parameter responsible for spinodal decomposition of out-of-equilibrium potential metastability due to generation of open complex collective modes. Open complex collective modes have the nature of self-similar solutions (breathers, auto-solitary and blow-up modes) of open complex evolution equation accounting qualitative different types of potential metastabilities. Sub-sets of collective modes represent the phase variables of attractors associated with different scenario of expression dynamics, which allows the interpretation of multistability of the epigenetic landscape and the Huang diagram of gene expression. It was shown different epigenetic pathway in attractors phase space corresponding to normal and cancer expression scenario. These scenarios were supported by laser interference microscopy of living normal and cancer cells illustrating multi- and monofractal dynamics.

Steady plastic wave fronts and scale universality of strain localization in metals and ceramics

Mechanisms of structural relaxation are linked with the metastability of nonequilibrium potential of solid with defects and the generation of collective modes of defects responsible for the plastic strain and damage localization. It is shown that spatial-temporal dynamics of collective modes (auto-solitary and blow-up dissipative structures) provide the anomalous relaxation ability of nonlinear system “solid with defects” in the conditions of the specific type of criticality – structural-scaling transition. These modes have the nature of self-similar solutions of evolution equations for damage parameter (defect-induced strain) and represent the “universality class” providing the four power law for a steady plastic front, splitting of an elastoplastic shock wave front, and elastic precursor decay kinetics. Wide-range constitutive equations reflecting the linkage between defect-induced mechanisms and structural relaxation are used in the numerical simulation for shock wave loading of metals and ceramics in the comparison with experiments.

Energy release rate and criticality of multiscale defects kinetics

Configuration mechanics of solid with defects (microcracks, microshears) was used for statistical description of multiscale defect interaction, presentation of out-of-equilibrium free energy release rate and defects kinetics, which reveals specific type of criticality—structural-scaling transition. According to this transition defects kinetics occurs as generation of collective modes of defects that have the nature of self-similar solutions for defects kinetic equations. It is showm using original “in-situ” experiments that spatial-temporal scenario of collective modes leads to specific fractographic pattern on fracture surface and self-similar material responses in wide range of load intensity.

Some regularities of scaling in plasticity, fracture, and turbulence

The paper considers scaling regularities in the deformation and failure of condensed matter (solids and liquids) as effects of a special type of critical phenomena—structural scaling transitions in mesodefect ensembles— and associated structural relaxation mechanisms. The scaling regularities in nonequilibrium processes of plasticity, failure, and turbulence are analyzed with the use of self-similar intermediate asymptotic solutions describing the collective behavior of mesodefects. The predicted role of defect modes in the self-similar response of condensed media is confirmed by original experiments on dynamic, fatigue, and shock loading over a wide range of load intensities.

More singular? Self-similar dynamics of damage localization and instability in dynamic fracture

Dynamic fracture instability is studied for three characteristic statements: dynamic crack propagation, dynamic fragmentation and failure wave initiation to combine theoretical interpretation and “in-situ” high resolution experimental data for dynamically loaded quasi-brittle materials (PMMA, glasses, ceramics and fused quartz). Specific type of criticality (the structural-scaling transitions) was established in solid with defects in terms of two structural variables: defect density tensor (defect induced strain) and structural scaling parameter. Two critical values for structural scaling parameter were found that separate characteristic nonlinearity of free energy release in damage kinetic equation that allowed one to establish specific self-similar solution (blow-up dissipative structures) responsible for final stage of damage localization and crack initiation. The set of spatial scales of damage localization (that has the image of mirror zones) and corresponding “incubation” time follow from the self-similar solution as the “eigen-values” of non-linear problem. Different scenario of instability of dynamic fracture in mentioned experiments were analyzed as nonlinear dynamic problem in the presence of two self-similar solutions (two attractors): intermediate asymptotical solution for stress field in crack process zone (as the basement for stress intensity factor) and the set of blow-up self-similar solutions for damage localization kinetics playing the role of collective modes of damage localization. Theoretically predicted flicker noise temporal-spatial statistics was found in dynamic experiments for fused quartz and ceramic rod fragmentation combined with fracto-luminescence recording and analysis of fragment statistics. Resonance excitation of blow-up modes allowed explanation of self-similar pattern of multiple spall kinetics (“dynamic branch” under spall) due to “resonance” excitation of blow-up damage localization kinetics.

<i>In Situ</i> Dynamic Experiments and Modeling in Multiscale Kinetics of Damage-Failure Transition

Scaling regularities that reveal the power law statistics of fragmentation and self-similarity of damage-failure transitions are linked to specific type of critical phenomena in ensembles of typical mesoscopic defects – structural-scaling transition. Taking into account nonlinearity of damage-failure transition the scaling effects were explained as the consequence of subjection of damage kinetics to the intermediate asymptotical (self-similar) solution. This solution has the nature of multiscale blow-up dissipative structures, represents the set of collective modes of defects responsible for the damage localization stage. Original in-situ experiments supported the assumption concerning the role of multiscale blow-up collective modes of defects in qualitative different scenario of dynamic crack propagation, failure of shocked materials, fragmentation statistics.

Numerical simulation of multiscale damage-failure transition and shock wave propagation in metals and ceramics

Statistical theory of evolution of typical mesoscopic defects revealed specific type of criticality - structural-scaling transitions and allowed the development of phenomenology of damage and plastic flow in materials under intensive loading, which established characteristic multiscale collective modes of defects responsible for formation of plastic waves and damage-failure transition. Original approach based on wide range constitutive equations was developed for simulation of multiscale damage-failure transition mechanisms and shock wave propagation in metals and ceramics in range of strain rate 103 − 108 s−1. It was shown that mechanisms of a plastic relaxation and damage-failure transitions are linked to multiscale kinetics of mesodefects collective modes with the nature of solitary waves and blow-up dissipative structures consequently. Numerical simulation of original plate impact tests showed that the model describes shock wave loading for metals and ceramics, and allowed us to explain the effect of power law phenomena of plastic wave fronts formation, its self-similar features under reloading and unloading. Analysis of shock wave profiles in ceramics for different thicknesses of specimens in terms of self-similar variables supports the universality of shock wave fronts.

Structural-scale transitions in solids with defects and symmetry aspects of field theory

Relaxation and failure mechanisms in solids with mesoscopic defects are considered in the context of a specific class of critical phenomena—structural-scaling transitions. The association of collective modes in mesodefect ensembles with gauge invariance in string theory is discussed. Statistical and thermodynamic properties of deformed solids are studied in relation to dynamics of collective modes of defects.

Structural-scaling transitions and thermodynamic and kinetic effects in submicro-(nano-)crystalline bulk materials

The size effects involved in the transition to a nanostructural bulk state is considered as a complex of phenomena associated with a change in material properties in response to a change in particle size and its attendant growth of grain-boundary defects in importance. Attention is focused on two fundamental problems: transition to submicro-(nano-)crystalline bulk states under severe plastic deformation and description of properties of nanocrystalline bulk materials. The key question to be resolved is whether a sharp distinction exists between the state of ordinary polycrystalline bulk materials and the state of nanostructured bulk materials. In qualitative terms, the transition to a nanostructural bulk state is related to new critical phenomena, namely structural-scaling transitions, occurring in systems with mesodefects. These transitions allow determination of the types of collective modes in defect ensembles for the characteristic solid states: quasibrittle, ductile and nanocrystalline.

Structural-scaling transitions and universality of fluctuation statistics under plastic deformation of metals

Structural-scaling transitions and universality of fluctuation statistics under plastic deformation of metals

Structural-scaling transitions and self-similar features of earthquake development

Self-similar features of seismic events are analyzed within the conception of structural-scaling transitions in mesodefect ensembles. Original investigations of crack dynamics are used to interpret model experiments on shear crack propagation along frictional interfaces for the simulation of wave dynamics of failure along the existing faults in the Earth's crust.

Energy accumulation and dissipation in metals as a result of structural-scaling transitions in a mesodefect ensemble

The localization of plastic deformation and its wave-like propagation are well-known and experimentally studied phenomena. Modern experiments carried out with highly sensitive infrared cameras have allowed us to investigate in detail energy accumulation and dissipation in the material which accompany the above process. It is found that plastic deformation occurs together with great energy accumulation in the material. The energy accumulation rate peaks on the initial stage of plastic deformation and vanishes at developed plastic flow. At the moment of elastic-plastic transition dissipative waves induced by plastic deformation localization can be generated and propagate in some metals. The given paper puts forward a theoretical model of energy accumulation and dissipation in metals under plastic deformation. The model is based on a statistical description of evolution of an ensemble of typical mesodefects (microshears). The derived constitutive equations adequately describe certain experimentally observed peculiarities of energy dissipation in metals.

Structural-scaling transitions and localized distortion modes in the DNA double helix

The paper reviews structural dynamic models of DNA and the role of nonlinear localized instabilities in the double helix denaturation. A statistical theory is developed to describe the evolution of localized distortion modes. Possible relations of structural-scaling transitions in ensembles of localized distortion modes with the replication and transcription phenomena are discussed.

Structural-scaling transitions in mesodefect ensembles as mechanisms of relaxation and failure in shocked and dynamically loaded materials (experimental and theoretical study)

Nonlinear aspects of relaxation and are related to new type of critical phenomena in ensembles of mesoscopic defects - structural-scaling transitions, generation of specific collective modes of mesodefects, which subject the relaxation and kinetics of damage-failure transition. Theoretical results were supported by original experiments and allowed us to propose the explanation: the transition from the steady-state to the branching and stochastic regimes of crack dynamics, fragmentation scenario, the steady-state structure and the four power law universality of the plastic front, the failure wave phenomenon as delayed effect related to the excitation and propagation of mesodefects collective mode with blow-up damage localization kinetics.