Disclination Quadrupole Research Articles

Discrete dislocation simulation of the ultrasonic relaxation of non-equilibrium grain boundaries in a deformed polycrystal

For the first time, the relaxation of disordered dislocation arrays in a model 3 × 3 columnar polycrystal under ultrasonic action is studied using the discrete dislocation approach. All grains contain three non-parallel slip systems located at an angle of 60° to each other. The non-equilibrium state of the grain boundaries is modeled using two finite edge dislocation walls with Burgers vector of opposite signs, which are equivalent to a wedge junction disclination quadrupole. It is shown that ultrasonic treatment causes a significant rearrangement of the lattice dislocations and their gliding towards the grain boundaries. It results in a decrease in the internal stress fields associated with the presence of non-equilibrium grain boundaries and relaxation of dislocation structure. The model predicts an existence of optimal amplitude, at which the maximum relaxing effect can be achieved. Dependence of the relaxation of dislocation structure on the grain size is also investigated.

Effect of twin thickness-length ratio on twin-induced dynamic recrystallization of coarse-grained Mg alloys

In the current study, based on the disclination quadrupole, the thermodynamic process of the necklace-like TDRX structures with smooth and straight boundaries is theoretically modeled. The influence of the applied shear stress and the twin thickness-length ratio on the misorientation angle between TDRX and matrix grain and the volume ratio of TDRX to parent twin band are numerically analyzed and experimentally validated by the electron back-scatter diffraction characterization. The results show that: (1) the misorientation angle increases with increasing applied shear stress; (2) The greater the thickness-length ratio is, the lower the volume ratio of TDRX to parent twin is; (3) The elevation of the applied shear stress can clearly escalate the volume ratio of TDRX to parent twin. Based on the above results, some strategies regulating TDRX are given based on the control of the applied shear stress and twin thickness-length ratio.

A theoretical analysis of dislocation emission from an elliptical blunt crack tip in nanocrystalline solid

A theoretical model describing edge dislocation emission from an elliptical blunt crack tip in nanocrystalline solid is established to consider the effect of the nanotwin and dislocation pileup at twin boundary. The nanotwin is represented by a wedge disclination quadrupole and some dislocations are deposited on one of twin boundaries. The complex variable function method is used to calculate the force acting on the first dislocation emitted from the tip of blunt crack, and expressions of critical stress intensity factors corresponding to dislocation emission are obtained. Then the influence of the dislocation emission angle, the position and orientation of the twin, the strength of nanotwin, the shape and the surface effects of the elliptical blunt crack on the critical stress intensity factor for dislocation emission is analyze in detail. The results shows that the effect of nanotwin on dislocations emitting from crack tip depends on its position and azimuth. There is an optimal position that dislocations are most easily emitted from the crack tip. The dislocation pileup at the twin boundary will increase the critical stress intensity factors for dislocation emission, making the dislocation emission from crack tip difficult, thus reducing the toughness of the material contributed by dislocation emission. In addition, the surface stress has a significant effect on the critical stress intensity factor.

Simulation of the Effect of Ultrasound on the Dislocation Structure of Deformed Polycrystals

Computer simulation was used to study the relaxation of disordered systems of dislocations in the stress field of nonequilibrium grain boundaries upon ultrasonic treatment (UST). The effect of ultrasound is simulated by an oscillatory shear stress applied to the crystal. Edge dislocations in a model grain with three nonparallel slip systems located at an angle of 60° to each other were examined. The nonequilibrium state of grain boundaries is simulated with the aid of a quadrupole of wedge disclinations located at its junctions. This study showed that the UST caused a rearrangement of the dislocation structure and led to a reduction of internal stresses. The amplitude of ultrasound and the degree of the nonequilibrium state of grain boundaries (strength of the disclination quadrupole) significantly affect the relaxation of the dislocation structure. There are optimum values of the UST amplitude, at which a maximum reduction of the internal stresses is achieved. This study also investigated the dependence of the degree of relaxation of internal stresses on the amount of dislocations in the grain.

Effect of nanotwin and dislocation pileup at twin boundary on dislocation emission from a semi-elliptical blunt crack tip in nanocrystalline materials

The effects of the nanotwin and dislocation pileup at the twin boundary on lattice dislocation emission from a surface semi-elliptical blunt crack in deformed nanocrystalline materials (NCMs) are investigated. The nanotwin as a stress source can be described by a wedge disclination quadrupole. Using the complex variable method, complex analytic solution of stress field, the dislocation force and the critical stress intensity factors (SIFs) for the first edge dislocation emission were obtained. Then, through numerical calculation, the influence of twin size, twin orientation, twin position, twin strength and dislocation pileup, the curvature radius of blunt crack tip on the critical stress intensity factors were discussed in detail. The results show that the nanotwin and dislocation pileup has significant influence on the dislocation emission from the blunt crack tip. The presence of nanotwin and dislocation pileup will increase the most probable emission angle, and increase the critical SIFs for dislocation emission, making it harder for the dislocation to emit from the blunt crack tip and thus to decrease the toughness of materials produced by dislocation emission.

Evolution of Dirac Cone in Disclinated Graphene

Abstract Graphene crystals, containing arrays of disclination defects, are modeled and their energies are calculated using molecular dynamics (MD) simulation technique. Two cases are analyzed in details: (i) pseudo-graphenes, which contain the alternating sign disclination ensembles and (ii) graphene with periodic distribution of disclination quadrupoles. Electronic band structures of disclinated graphene crystals are calculated in the framework of density functional theory (DFT) approach. The evolution of the Dirac cone and magnitude of band gap in the band structure reveal a dependence on the density of disclination quadrupoles and alternating sign disclinations. The electronic properties of graphene with disclination ensembles are discussed.

Relaxation of dislocation structures under ultrasonic influence

Relaxation of disordered dislocation structures under ultrasonic influence in a two-dimensional square-shaped grain is investigated using the discrete-dislocation approach. The model grain contains three non-parallel glide systems inclined at an angle of 60° to each other. Non-equilibrium grain boundary state is modeled by means of a mesodefect located at the corners of the square-shaped grain. The stress fields of this mesodefect are described by those of a wedge junction disclination quadrupole. Oscillating stresses result in a rearrangement of lattice dislocations and their gliding towards the grain boundaries. This process is accompanied by a reduction of internal stress fields and cancellation of the wedge disclination quadrupole. The presence of non-parallel glide systems leads to a formation of Lomer–Cottrell locks, when two or more dislocations belonging to different systems meet at one point. Influence of the amplitude of ultrasonic treatment on the relaxation of dislocation structures is studied. Ultrasound of low amplitudes results in a formation of dislocation walls in the grain interior, while at higher amplitudes the dislocation substructure is destroyed and majority of the lattice dislocations are absorbed by the grain boundaries. The model predicts an existence of optimal values of the ultrasound amplitudes, at which the maximum reduction of internal stresses can be achieved. Dependence of the relaxation of disordered dislocation structures on the grain size is explored. The results obtained are consistent with those of previous theoretical and experimental studies.

Dislocation-based crystal plasticity FE analysis for kink band formation in Mg-based LPSO phase considering higher-order stress

An FE analysis has been performed for a single crystal of long-period stacking ordered phase on the basis of the dislocation-based crystal plasticity model considering higher-order stress. The mesh dependence on the kink band formation has been discussed from the viewpoint of the strain gradient and size effect. Then, it is shown that the mesh dependence of kink deformation in the FE analysis can be removed even when the scale ratio is relatively small. Moreover, it is indicated that the disclination quadrupole structure in the kink band can be expressed qualitatively by use of the incompatibility of crystal slip.

Ultrasonic influence on evolution of disordered dislocation structures

Evolution of disordered dislocation structures under ultrasonic influence is studied in a model two-dimensional grain within the discrete-dislocation approach. Non-equilibrium grain boundary state is mimicked by a mesodefect located at the corners of the grain, stress field of which is described by that of a wedge junction disclination quadrupole. Significant rearrangement related to gliding of lattice dislocations towards the grain boundaries is found, which results in a noticeable reduction of internal stress fields and cancel of disclination quadrupole. The process of dislocation structure evolution passes through two stages: rapid and slow. The main dislocation rearrangement occurs during the first stage. Reduction of internal stress fields is associated with the number of dislocations entered into the grain boundaries. The change of misorientation angle due to lattice dislocations absorbed by the grain boundaries is evaluated. Amplitude of ultrasonic treatment significantly influences the relaxation of dislocation structure. Preliminary elastic relaxation of dislocation structure does not affect substantially the results of the following ultrasonic treatment. Substantial grain size dependence of relaxation of disordered dislocation systems is found. Simulation results are consistent with experimental data.

Micromechanics of plastic deformation through grain-boundary migration in metal–graphene nanocomposites

A theoretical description of the plastic deformation of metal–graphene nanocomposites through stress-induced migration of grain boundaries is proposed. Within the micromechanical approach developed, the plastic deformation induced by this migration leads to the formation of disclination quadrupoles (intense elastic stress sources). The energy characteristics and critical stress are calculated for the plastic deformation mode under consideration. The influence of graphene nanoinclusions is shown to cause significant hardening of metal–graphene nanocomposites. This conclusion is consistent with the corresponding experimental data.

Effect of special rotational deformation on the dislocation emission from a branched crack tip in deformed nanocrystalline materials

The problem of the special rotational deformation interacting with an internal crack is studied by developing a theoretical model of deformed nanocrystalline materials. Using the complex variable method of Muskhelishvili and the conformal mapping technique, the expressions of complex potentials and stress fields are obtained analytically. The stress intensity factors (SIFs) near the crack tips and the critical SIFs for the first lattice dislocation emission from the branched crack tip are calculated. The effects of important parameters such as grain size, the length of internal crack, and the angle between the main crack and its branched crack on the critical SIFs for dislocation emission are evaluated in detail. As a result, the special rotational deformation has great influence on the growth of internal crack and the emission of lattice dislocations from the branched crack tip. The disclination quadrupole produced by the special rotational deformation will shield the branched crack tip under a certain condition. Moreover, when the main crack approaches its branched crack, it will stop the emission of lattice dislocations from the branched crack tip.

Toughening effect of the nanoscale twinning induced by particle/matrix interfacial fracture on fine-grained Mg alloys

This study theoretically analyzes the toughening effect of the nanoscale twinning induced by the high stress concentration at the particle/matrix interfacial crack tip on fine-grained magnesium (Mg) alloys. The nanoscale twinning within the interfacial crack-tip plastic zone is modeled by a wedge disclination quadrupole. The closed form expressions of the stress intensity factors (SIFs) and the energy release rate (ERR) for the arc-shaped interfacial crack are achieved applying the complex potential method for plane elasticity and conformal mapping. The impacts of twin dimensions, the shear modulus ratio of the particle to Mg matrix, the particle radius and spacing, twinning orientations, as well as the relative orientation between the twin and the crack on the toughening effect are discussed and presented as follows: (1) the nanoscale twin lath with a larger thickness-length ratio is an energetic energy dissipating mechanism for ductile fracture in fine-grained Mg alloys, which favors the fracture toughness enhancement; (2) the interface can be gradually weakened with increasing shear modulus of the particle; (3) under the toughening effect of nanoscale twinning, the interfacial fracture toughness is strongly dictated by the particle size and spacing. Specifically, the optimum particle radius and spacing that can strengthen the interface exist; and (4) the toughening effect is also dependent on the relative orientation and the twinning orientation. Based on the interaction among microstructures, this study essentially and quantitatively mends the classical fracture toughness models for particle reinforced metal matrix materials.

Effect of special rotational deformation on dislocation emission from interface collinear crack tip in nanocrystalline bi-materials

The work is devoted to investigate the interaction between the special rotational deformation and interface collinear cracks in nanocrystalline bi-materials. As an illustrative example, the effect of the disclination quadrupole produced by the special rotational deformation on the emission of lattice dislocation from a finite interfacial crack tip in nanocrystalline bi-material is explored theoretically using the complex variable method. The complex form expression of dislocation force and the critical stress intensity factors for the first edge dislocation emission under remote mode I loadings and mode II loadings are deduced. And the influences of material properties, grain size, disclination strength, disclination location and orientation, special rotational deformation orientations, and crack length on the critical stress intensity factors are discussed in detail. The results show that the special rotational deformation and the relative shear modulus of the upper the lower half plane have great effect on the lattice dislocation emission from the interface collinear crack tip.

A disclination model for twinning and de-twinning of nanotwinned copper

The twinning and de-twinning processes within grains of nanotwinned copper (nt-Cu) are schematically demonstrated using the concept of wedge disclination quadrupoles. The stable twin nucleus size and the equilibrium equation of the applied shear stress and twin width during twin growth are obtained. The dependence of the critical resolved shear stress for twinning on the grain size, which conforms to the classic Hall–Petch relationship, is theoretically modelled. Additionally, the disclination quadrupole model for de-twinning is used to interpret the strength softening in nt-Cu. Relative to the classic kinetic and energetic models, this novel approach is more compatible with the experiments.

Disclination mediated dynamic recrystallization in metals at low temperature.

Recrystallization is one of the most important physical phenomena in condensed matter that has been utilized for materials processing for thousands of years in human history. It is generally believed that recrystallization is thermally activated and a minimum temperature must be achieved for the necessary atomic mechanisms to occur. Here, using atomistic simulations, we report a new mechanism of dynamic recrystallization that can operate at temperature as low as T = 10 K in metals during deformation. In contrast to previously proposed dislocation-based models, this mechanism relies on the generation of disclination quadrupoles, which are special defects that form during deformation when the grain boundary migration is restricted by structural defects such as triple junctions, cracks or obstacles. This mechanism offers an alternative explanation for the grain refinement in metals during severe plastic deformation at cryogenic temperature and may suggest a new method to tailor the microstructure in general crystalline materials.

Effect of special rotational deformation on dislocation emission from a semielliptical blunt crack tip in nanocrystalline solids

Abstract

Special rotational deformation effect on the emission of dislocations from a crack tip in deformed nanocrystalline solids

The interaction between the special rotational deformation and the crack in deformed nanocrystalline ceramics and metals is investigated by the complex variable method. We have theoretically described the effects of the disclination quadrupole produced by the special rotational deformation on the emission of lattice dislocations from the crack tip. The complex form expressions of the stress field and the force field are divided. The critical stress intensity factors for the first dislocation emission are calculated. The influence of the disclination strength, the grain size (the quadrupole arms), the location of the disclinations and the angle between the crack plane and one of the quadrupole arms, as well as the crack length on the critical stress intensity factors is discussed in detail. And the results show that, the special rotational deformation has great influence on the dislocation emission from the crack tip.

Nanoscale amorphization at disclination quadrupoles in deformed nanomaterials and polycrystals

Special micromechanism of nanoscale amorphization (crystal-to-glass transition in nanoscale regions) in deformed nano- and polycrystalline materials is suggested and theoretically described. The nanoscale amorphization occurs through transformation of disclination quadrupoles generated during plastic deformation. It is shown that the nanoscale amorphization at disclination quadrupoles is energetically favorable in nano- and polycrystalline Si and Si3N4 deformed at high applied stresses in certain ranges of their structural parameters.

Defect kinetics and dynamics of pattern coarsening in a two-dimensional smectic-A system

Two-dimensional simulations of the coarsening process of the isotropic/smectic-A phase transition are presented using a high-order Landau–de Gennes-type free energy model. Defect annihilation laws for smectic disclinations, elementary dislocations and total dislocation content are determined. The computed evolution of the orientational correlation length and disclination density is found to be in agreement with previous experimental observations showing that disclination interactions dominate the coarsening process. The mechanism of smectic disclination movement, limited by the absorption and emission of elementary dislocations, is found to be facilitated by curvature walls connecting interacting disclinations. At intermediate times in the coarsening process, split-core dislocation formation and interactions displaying an effective disclination quadrupole configuration are observed. This work provides the framework for further understanding of the formation and dynamics of the diverse set of curvature defects observed in smectic liquid crystals and other layered material systems.

Structural Evolution and Alignment of Cylinder-Forming PS-b-PEP Thin Films in Confinement Studied by Time-Lapse Atomic Force Microscopy

ABSTRACTWe have utilized time-resolved high-temperature atomic force microscopy (AFM) to investigate the mechanism by which topographic templates induce alignment of cylinder-forming diblock copolymer thin films. By tracking the same sample spot during thermal annealing, we observed that the structural evolution and alignment of thin films in confinement involve an intermediate state with disordered morphology and the evolution and annihilation of disclination quadrupoles guided by the channel edges, which ultimately lead to the essentially perfect alignment of cylindrical microdomains.