Effect of inclusions on heterogeneous crack nucleation in nanocomposites

A two-dimensional theoretical model is proposed for the heterogeneous nucleation of a grain-boundary nanocrack in a nanocomposite consisting of a nanocrystalline matrix and nanoinclusions whose elastic moduli are identical to those of the matrix. The inclusions have the form of rods with a rectangular cross section and undergo dilatation eigenstrain induced by the differences in the lattice parameters and thermal expansion coefficients of the matrix and inclusions. In terms of the model, a mode-I–II nanocrack nucleates at the negative disclination of a biaxial dipole consisting of wedge grain-boundary (or junction) disclinations; then, the nanocrack opens along a grain boundary and reaches an inclusion boundary. Depending on the relative positions and orientations of the initial segment of the nanocrack and the inclusion, the nanocrack can either penetrate into the inclusion or bypass it along the matrix-inclusion interface. The nanocrack nucleation probability increases near an inclusion with negative (compressive) dilatation eigenstrain. A decrease in the inclusion size decreases (increases) the probability of a crack opening along the interface if the dilatation eigenstrain is negative (positive).     

Yield stress of nanocrystalline materials: role of grain-boundary dislocations,triple junctions and Coble creep

A theoretical model is suggested which describes the strengthening of nanocrystalline materials due to the effects of triple junctions of grain boundaries as obstacles for grain-boundary sliding. In the framework of the model, a dependence of the yield stress characterizing grain-boundary sliding on grain size and triple-junction angles is revealed. With this dependence we have found that, in as-fabricated nanocrystalline materials, the yield stress depends upon a competition between conventional dislocation slip and grain-boundary sliding. On the other hand, yield stress dependence on grain size in heat-treated nanocrystalline materials is described as that caused by a competition between conventional dislocation slip and Coble creep. Grain-size and triple-junction angle distributions are incorporated into the consideration to account for distributions of grain size and triple-junction angles, occurring in real specimens. The results of the model are compared with experimental data from as-fabricated and heat-treated nanocrystalline materials and shown to be in good agreement.     

Effect of cooperative nanograin boundary sliding and migration on dislocation emission from a blunt nanocrack tip in nanocrystalline materials

Theoretical model is suggested that describes the effects of the cooperative nanograin boundary sliding and stress-driven nanograin boundary migration (CNGBSM) process on the lattice dislocation emission from an elliptically blunt nanocrack tip in deformed nanocrystalline materials. Within the model, CNGBSM deformation near the tip of growing nanocrack carries plastic flow, produces two dipoles of disclination defects and creates high local stresses in nanocrystalline materials. By using the complex variable method, the complex form expression of dislocation force is derived, and critical stress intensity factors for the first lattice dislocation emission are obtained under mode I and mode II loading conditions, respectively. The combined effects of the geometric features and strengths of CNGBSM deformation, nanocrack blunting and length on critical SIFs for dislocation emission depend upon nanograin size and material parameters in a typical situation where nanocrack blunting and growth processes are controlled by dislocation emission from nanocrack tips. It is theoretically shown that the cooperative CNGBSM deformation and nanocrack blunting have great influence on dislocation emission from blunt nanocrack tip.     

Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

Micromechanics of the transition from intergrain to intragrain deformation in nanomaterials

A micromechanism of the transition from intergrain sliding to intragrain glide by nucleation and emission of lattice partial dislocations at grain-boundary dislocations is proposed and described theoretically. The energy characteristics of this process are calculated. It is shown that the nucleation of lattice partial dislocations is energetically efficient and can occur athermally (without the energy barrier) under conditions of the action of ultrahigh mechanical stresses. The critical stresses required for the athermal nucleation and emission of dislocations are calculated.     

Molecular-Dynamics Simulation of Grain-Boundary Diffusion Creep

Molecular-dynamics (MD) simulations are used, for the first time, to study grain-boundary diffusion creep of a model polycrystalline silicon microstructure. Our fully dense model microstructures, with a grain size of up to 7.5 nm, were grown by MD simulations of a melt into which small, randomly oriented crystalline seeds were inserted. In order to prevent grain growth and thus to enable steady-state diffusion creep to be observed on a time scale accessible to MD simulations (of typically 10^-9s), our input microstructures were tailored to (i) have a uniform grain shape and a uniform grain size of nm dimensions and (ii) contain only high-energy grain boundaries which are known to exhibit rather fast, liquid-like self-diffusion. Our simulations reveal that under relatively high tensile stresses these microstructures, indeed, exhibit steady-state diffusion creep that is homogenous (i.e., involving no grain sliding), with a strain rate that agrees quantitatively with that given by the Coble-creep formula.     

Atomistic sliding mechanisms of the Σ=5 symmetric tilt grain boundary in bcc iron

Atomistic computer simulations were performed to investigate the mechanisms of grain-boundary sliding in bcc Fe using molecular statics and molecular dynamics with embedded-atom method interatomic potentials. For this study we have chosen the Σ?=?5, (310)[001] symmetrical tilt boundary with tilt angle θ?=?36.9°. Sliding was determined to be governed by grain-boundary dislocation activity with Burgers vectors belonging to the displacement shift complete lattice. The sliding process was found to occur through the nucleation and glide of partial grain-boundary dislocations, with a secondary grain-boundary structure playing an important role in the sliding process. Interstitial impurities and vacancies were introduced into the grain boundary to study their role as nucleation sites for the grain-boundary dislocations. While vacancies and H interstitials act as preferred nucleation sites, C interstitials to not.     

Constrained grain-boundary sliding and inelasticity of polycrystals

A model of inelastic behavior of polycrystals that is based on the idea of constrained grain-boundary sliding is developed. This model assumes that grain-boundary sliding is accommodated only through grain elastic deformation, which is valid under low stresses. By way of examples, the dynamic inelastic behavior and a decrease in the elastic moduli of polycrystals subjected to a small-amplitude ultrasonic field are investigated. It is shown that some of the available experimental data obtained on ultra-fine-grained materials can be explained in terms of the model. The theory predicts that the decrease in the elastic moduli is a size effect that is bound to be observed when the grain size is small. These predictions are supported experimentally.     

On the capacity of grain boundary dislocation pileups

It is demonstrated on model examples that inclusion of the interaction between pileups of grain boundary dislocations formed in the vicinity of triple grain-boundary junctions leads to a multifold increase in the capacity of these pileups.     

Structural mechanisms of fracture of nanocrystalline materials

Structural mechanisms and features of brittle and quasi-brittle fracture of nanocrystalline materials are theoretically analyzed. The role of size effects and internal stresses caused by a nonequilibrium structure during brittle trans-and intercrystallite fracture is studied. The dependence of the nanocrystalline material durability on the working stress and grain size is calculated. The conditions for certain mechanisms of plastic deformation to be operative in nanocrystalline materials are analyzed. The influence of the grain-boundary and dislocation mechanisms of plastic deformation on the conditions of nanocrack formation is studied. The dependence of the fracture toughness of nanomaterials on structure parameters is calculated.     

Features of migration of triple junctions of different configuration

The stationary motion of individual triple junctions of different crystal geometry has been experimentally investigated. It is shown that triple junctions are characterized by intrinsic finite mobilities and drag parameters. The difference in the temperature dependences of the drag parameters of triple junctions may lead to the formation of an inhomogeneous polycrystalline microstructure during isothermal annealings.     

Nucleation of deformation twins on gliding grain-boundary dislocations in nanomaterials

A new micromechanism of nucleating deformation twins in nanocrystalline and ultrafine-grained materials under action of severe mechanical stresses has been proposed and theoretically described. The mechanism is a subsequent splitting of grain-boundary dislocations into lattice partial and sessile grain-boundary dislocations. Ensembles of gliding partial dislocation forms deformation twins. The energy characteristics of this process are calculated. The nucleation of the twins is shown to be energetically profitable and can be athermic (without an energy barrier) under conditions of severe mechanical stress. The dependence of a critical stress at which the barrier-less nucleation of twins took place on the widths of these twins is calculated.     

Generation of disclination dipoles and nanoscopic cracks in deformed nanoceramic materials

The processes of generation of disclination dipoles and nanoscopic cracks (nanocracks) in deformed nanoceramic materials are investigated theoretically. It is demonstrated that disclination dipoles are formed at grain boundaries in the course of grain-boundary sliding. The geometric features of the generation of disclination dipoles are analyzed. The conditions under which the nucleation of nanocracks in the vicinity of the disclination dipoles is energetically favorable are calculated for the nanoceramic materials α-Al₂O₃ (corundum) and 3C-SiC (the cubic phase of silicon carbide). The equilibrium lengths of these nanocracks are also calculated. It is shown that the equilibrium lengths of nanocracks can be comparable to the grain size. As a consequence, these nanocracks can coalesce, thus eventually resulting in the brittle fracture of nanoceramic materials.     

Effect of triple junctions of nanotubes on strengthening and fracture toughness of ceramic nanocomposites

A theoretical model has been proposed for describing the influence of triple junctions of nanotubes on the strengthening of a nanocomposite. It has been assumed that the slip of nanotubes along the boundary with the matrix takes place via the nucleation and glide of prismatic dislocation loops enveloping the nanotubes. These loops are retarded by the triple junctions of nanotubes, which leads to a strengthening and increase in the fracture toughness (crack resistance) of the nanocomposite. It has been shown that, in order for the dislocation loop to overcome the triple junction, the shear stress acting on the loop should exceed a certain critical level. This critical stress increases as the radius and wall thickness of the nanotube decrease. The inference has been made that the triple junctions of thinnest nanotubes, such as single-walled carbon nanotubes, should lead to the greatest strengthening and to an increase in the crack resistance of these nanocomposites.     

On the Origin and Energy of Triple Junction Defects Due to the Finite Length of Grain Boundaries

King [1] established that due to the discrete nature of their dislocation structure, finite length grain boundaries (GBs) in polycrystalline materials possess discrete values of misorientation angle. For a GB with a length that is not a multiple of the GB period, this leads to the formation of specific disclinations at their junctions with neighboring GBs, which compensate the difference between the misorientations of finite and infinite boundaries. In the present paper the origin of these compensating disclinations within GB triple junctions is elucidated and their strength is calculated using the disclination-structural unit model. It is shown that for a GB with length of about 10 nm the junction disclinations can have a strength value not more than 1°, in contrast to King's calculations that indicate much larger values. Elastic energies of triple junctions due to compensating disclinations are calculated for both equilibrium and non-equilibrium structures of a finite length GB, which differ by the position of the grain boundary dislocation network with respect to the junctions. The calculations show that triple junction energies are comparable to dislocation energies, and that compensating disclinations can play a significant role in the properties of nanocrystalline metals with grain sizes less than about 10 nm.     

Measuring relative grain-boundary energies in block-copolymer microstructures

The (relative) energies of symmetric tilt grain boundaries in a strongly segregated lamellar block copolymer are determined by analysis of the dihedral angles at grain-boundary triple junctions. The analysis reveals two regimes: at low and intermediate misorientations (corresponding to a tilt-angle range 0≤θ≤85°) the grain-boundary energy is found to depend on the tilt angle as E(θ)～θ(x), with 2.5>x≥0. At large misorientations the grain-boundary energy is found to be independent (within the experimental uncertainty) of the angle of tilt. The transition between the two scaling regimes is accompanied by the transition of the grain-boundary structure from the chevron to the omega morphology. Grain-boundary energy and frequency are found to be inversely related, thus suggesting boundary energy to be an important parameter during grain coarsening in block-copolymer microstructures, as it is in inorganic polycrystalline microstructures.     

Anisotropic distributions of electrical currents in high-<Emphasis Type="Italic">T</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> grain-boundary junctions

We developed a self-consistent method for the calculation of spatial current distributions in high-T _c grain-boundary junctions. It is found that crystallographic anisotropy of high-T _c superconducting electrodes results in the effects, which previously were not taken into account for interpretations of experimental data. Among them is a significant redistribution of electrical currents in superconducting electrodes in the vicinity of a grain boundary. In particular in the case of [100]-tilt bicrystal junctions, this current redistribution results in a substantial focusing to the top or bottom part of a thickness of the grain boundary, depending on “roof”- or “valley”-type of the grain boundary. This redistribution is accompanied by generation of vortex currents around the grain boundary, which leads to self-biasing of grain-boundary junctions by magnetic field nucleated by these vortex currents. It is shown that twinning or variation of geometrical shape of the high-T _c electrode may also result in intensive redistribution of electrical currents and nucleation of local magnetic fields inside a high-T _c superconducting electrodes.     

Reactive Solid State Dewetting: Interfacial Cavitation in the System Ag-Ni-O

Micron thick silver films, vapour deposited onto high purity polycrystalline nickel substrates, dewet the substrate after high temperature annealing in oxygen rich atmospheres, while the films remain stable after annealing at the same temperature in a nitrogen atmosphere. Dewetting occurs when a nickel oxide layer is formed at the silver-nickel interface as a consequence of oxygen diffusion through the silver film.The sensitivity of the dewetting process on various parameters such as the annealing: temperature, time and oxygen partial pressure has been determined.Scanning Electron Microscopy (SEM) of cross-sections reveal that the main mechanism of dewetting at short annealing time is the nucleation of cavities at the Ag-NiO interface which grow towards the free surface of the Ag film. They are formed not only at Ag grain boundaries and triple junctions but also in the core of Ag grains. Such cavities do not occur when the Ag film is deposited onto a NiO single crystal. We propose a simple model for the cavitation: a vacancy supersaturation is sustained in Ag, at the Ag-NiO interface, as a result of oxygen consumption by the oxidation reaction. In regions of fast oxidation, the vacancy supersaturation is large enough to promote the nucleation and growth of interfacial cavities. The model qualitatively accounts for all the observed trends; quantitatively, on top of the vacancy supersaturation, extra-contributions to the driving force for cavitation must be invoked.     

Nanovoid generation due to intergrain sliding in nanocrystalline materials

A theoretical model is suggested which describes the generation of nanoscale voids (nanovoids) at grain boundaries (GBs) in deformed nanocrystalline and nanocomposite materials. In the framework of the model, nanovoids are generated in the stress fields of the dislocations characterized by large Burgers vectors and formed at GB steps and triple junctions due to intense intergrain sliding. The model accounts for experimental observations of nanovoids at GBs in deformed nanomaterials, reported in the literature.