Nanocrack nucleation in polycrystalline silicon during grain-boundary sliding

A theoretical model is proposed to describe nanocrack nucleation in polycrystalline silicon. In terms of this model, nanocrack nucleation is stimulated by grain-boundary sliding, which creates sources of local stresses in triple junctions of grain boundaries. The relaxation of these local stresses is the main driving force of nanocrack nucleation near triple junctions in polycrystalline silicon, in which grain-boundary sliding contributes substantially to plastic deformation under cyclic loading at room temperature. The model is used to calculate the critical external stress required for nanocrack nucleation in polycrystalline silicon.     

Effect of Thermoelastic Characteristics of Components,Shape of Non-Isometric Inclusions,and Their Orientation on Average Stresses in Matrix Structures

The paper presents model calculations on which to predict volume-average external stress under changes of local internal stress in matrix composites with non-isometric inclusions. It is assumed that the rise of local stress owes to different coefficients of linear thermal expansion of non-isometric inclusions and matrix. The inclusions are taken as ellipsoids of rotation (disks, short fibers) and their principal semiaxes as oriented either along three mutually perpendicular directions x, y, and z of a rectangular coordinate system, only along x and y, or only along x. The average stress in the heterogeneous material and its local stress within an individual inclusion are related through a stress concentration operator (fourth rank tensor) for which an explicit expression is derived in a generalized singular approximation of random field theory. The relations obtained for external stress take into account thermoelastic characteristics of the two components as well as inclusion concentrations and orientations in the matrix. The calculation is applied to estimate the average stress along three axes in a composite consisting of an ED-20 epoxy binder and non-isometric copper inclusions.     

Effective dynamic properties of 3D composite materials containing rigid penny-shaped inclusions

The propagation of time-harmonic plane elastic waves in infinite elastic composite materials consisting of linear elastic matrix and rigid penny-shaped inclusions is investigated in this paper. The inclusions are allowed to translate and rotate in the matrix. First, the three-dimensional (3D) wave scattering problem by a single inclusion is reduced to a system of boundary integral equations for the stress jumps across the inclusion surfaces. A boundary element method (BEM) is developed for solving the boundary integral equations numerically. Far-field scattering amplitudes and complex wavenumbers are computed by using the stress jumps. Then the solution of the single scattering problem is applied to estimate the effective dynamic parameters of the composite materials containing randomly distributed inclusions of dilute concentration. Numerical results for the attenuation coefficient and the effective velocity of longitudinal and transverse waves in infinite elastic composites containing parallel and randomly oriented rigid penny-shaped inclusions of equal size and equal mass are presented and discussed. The effects of the wave frequency, the inclusion mass, the inclusion density, and the inclusion orientation or the direction of the wave incidence on the attenuation coefficient and the effective wave velocities are analysed. The results presented in this paper are compared with the available analytical results in the low-frequency range.     

Stress analysis of multiple anisotropic elliptical inclusions in composites

A volume integral equation method is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple anisotropic elliptical inclusions subject to uniform remote tension or remote in-plane shear. This method is applied to two-dimensional problems involving long parallel elliptical cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central elliptical inclusion is carried out for square and hexagonal packing of anisotropic inclusions. The effects of the number of anisotropic inclusions and various inclusion volume fractions on the stress field at the interface between the isotropic matrix and the central elliptical cylindrical inclusion are investigated in detail. The stress field at the interface between the isotropic matrix and the central elliptical inclusion is also compared with that between the isotropic matrix and the central circular inclusion.     

Two-dimensional shear waves scattering by a large rigidity strip with interface crack

A two-dimensional problem of shear horizontal (SH) waves scattering by a finite width planar elastic (piezoelectric) inclusion partially debonded from its surrounding elastic matrix is investigated using the effective boundary conditions and singular integral equations technique. The case of large rigidity inclusions with blunted tips is considered, in which the upper face of the inclusion is perfectly bonded to the matrix. The debonding region is modeled as interface crack with non-contacting faces. Using the Green theorem the mixed boundary value problem is reduced to a system of the hypersingular integral equations. Numerical results of the scattering fields characteristics are presented. The effects of incidence direction, various material parameters of the strip on the scattering field are discussed and phenomenon of the non-specular reflection of SH waves is considered. The accuracy of the numerical results is confirmed by the use of analytical approximate problem solution of high-frequency SH waves scattering on a finite hard/soft inclusion.     

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.     

Brittle-ductile behavior of a nanocrack in nanocrystalline Ni: A quasicontinuum study

The effects of stacking fault energy, unstable stacking fault energy, and unstable twinning fault energy on the fracture behavior of nanocrystalline Ni are studied via quasicontinuum simulations. Two semi-empirical potentials for Ni are used to vary the values of these generalized planar fault energies. When the above three energies are reduced, a brittle-to-ductile transition of the fracture behavior is observed. In the model with higher generalized planar fault energies, a nanocrack proceeds along a grain boundary, while in the model with lower energies, the tip of the nanocrack becomes blunt. A greater twinning tendency is also observed in the more ductile model. These results indicate that the fracture toughness of nanocrystalline face-centered-cubic metals and alloys might be efficiently improved by controlling the generalized planar fault energies.     

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.     

Dislocation mechanism of hollow fiber sliding during ceramic nanocomposite fracture

A dislocation model is proposed for describing the sliding of hollow fibers (and, in particular, carbon nanotubes) as a mechanism of elastic energy relaxation near cracks in ceramic nanocomposites. In this model, the sliding of a hollow cylindrical fiber occurs through the formation of a prismatic circular dislocation loop gliding along the boundary between the fiber and the matrix. The energy characteristics of this process are calculated, and the critical stress required for the barrierless nucleation and glide of such a loop is determined. It is shown that the critical stress increases with the ratio between the shear moduli of the matrix and the fiber and (over a wide range of changes in this ratio) with the fiber wall thickness.     

Analysis of stress field in a single anisotropic diamond/square shaped inclusion using the volume integral equation method and the numerical equivalent inclusion method

A volume integral equation method (VIEM) is used to study elastostatic problems in an unbounded elastic solid containing a single diamond/square shaped inclusion subject to uniform tensile stress at infinity. The inclusion is assumed to be a long parallel diamond/square cylinder composed of isotropic or anisotropic elastic materials and perfectly bonded to the isotropic matrix. The solid is assumed to be under plane strain on the plane normal to the cylinder. A detailed analysis of the stress field at the interface between the isotropic matrix and the single isotropic/orthotropic diamond/square shaped inclusion is carried out. The effects of a single isotropic/orthotropic diamond/square shaped inclusion on the stress field at the interface between the matrix and the inclusion are investigated in detail. The accuracy of the volume integral equation method for the interfacial stress field is validated and compared by the numerical equivalent inclusion method (NEIM) and the finite element method (FEM) using ADINA. Through detailed analysis of plane elastostatic problems using the parallel volume integral equation method (PVIEM) in an unbounded isotropic matrix with multiple isotropic diamond shaped inclusions under uniform remote tensile loading, it is demonstrated that the volume integral equation method can also be applied to solve general two- and three-dimensional elastostatic problems involving multiple isotropic/anisotropic inclusions whose shape and number are arbitrary.     

A new micromechanics-based scale transition model for the strain-rate sensitive behavior of nanocrystalline materials

An original two-step “three phase” elastic–viscoplastic scale transition model is developed based on the combined self-consistent and Mori–Tanaka schemes. A coated inclusion is embedded within a matrix, wherein the inclusion represents grain interiors and the coating of the inclusion mimics the effects of grain boundaries and triple junctions. The predominant behavior within the grain interiors is captured through dislocation glide, whereas grain boundary (GB) dislocation emission and absorption, as well as thermally assisted GB sliding, describe the deformation processes within the coating describing the GB affected zone. Furthermore, an imperfect interface is assumed between the inclusion and the coating to account for viscoplastic grain boundary sliding along a stick-slip mechanism. Results and discussion focus on the competitive roles of GB sliding, GB dislocation emission/absorption, dislocation sweep in grain cores and collective dislocation plasticity, and the origins of the pronounced strain rate sensitivity of fcc NC materials.     

Nucleation of dynamic recrystallization and variant selection in copper bicrystals

Orientation-controlled copper bicrystals containing [001] symmetrical tilt boundaries aligned parallel to the loading axis were deformed in tension at 923?K and a strain rate of 4.2?×?10^?4?s^?1. The nucleation of dynamic recrystallization (DRX) was investigated along the grain boundary. For this purpose, both optical and orientation imaging microscopy methods were used. After grain-boundary migration (GBM) and bulging, nuclei appeared behind the most deeply indented grain boundary regions. The critical strain for nucleation was about one-quarter to one-half of the peak strain and depended on the misorientation angle. All the nuclei were twin-related (Σ3) to the matrices. Furthermore, all the primary twin traces were parallel to those of the inactive slip planes of the parent single crystals. Crystallographic analysis revealed the important role of the direction of GBM on twinning-plane variant selection. The characteristics of grain boundary nucleation depended sensitively on grain boundary character and on grain boundary mobility. The observed DRX nucleation mechanism is discussed in relation to the occurrence of GBM and twinning.     

Statistical approach to bulk inclusion initialized damage in films

In experiments, we have found an abnormal relationship between probability of laser induced damage and number density of surface inclusion. From results of X-ray diffraction (XRD) and laser induced damage, we have drawn a conclusion that bulk inclusion plays a key role in damage process. Combining thermo-mechanical damage process and statistics of inclusion density distribution, we have deduced an equation which reflects the relationship between probability of laser induced damage, number density of inclusion, power density of laser pulse, and thickness of films. This model reveals that relationship between critical sizes of the dangerous inclusions (dangerous inclusions refer to the inclusions which can initialize film damage), embedded depth of inclusions, thermal diffusion length and tensile strength of films. This model develops the former work which is the statistics about surface inclusion.     

Grain-boundary grooving and agglomeration of alloy thin films with a slow-diffusing species

We present a general phase-field model for grain-boundary grooving and agglomeration of polycrystalline alloy thin films. In particular, we study the effects of slow-diffusing species on the grooving rate. As the groove grows, the slow species becomes concentrated near the groove tip so that further grooving is limited by the rate at which it diffuses away from the tip. At early times the dominant diffusion path is along the boundary, while at late times it is parallel to the substrate. This change in path strongly affects the time dependence of grain-boundary grooving and increases the time to agglomeration. The present model provides a tool for agglomeration-resistant thin film alloy design.     

Grain-boundary faceting at a = 3, [110]/{112} grain boundary in a cubic zirconia bicrystal

The atomic structure of a = 3, [110]/{112} grain boundary in a yttria-stabilized cubic zirconia bicrystal has been investigated by high-resolution transmission electron microscopy (HRTEM). It was found that the grain boundary migrated to form periodic facets, although the bicrystal was initially joined so as to have the symmetric boundary plane of {112}. The faceted boundary planes were indexed as {111}/{115}. The structure of the {111}/{115} grain boundary was composed of an alternate array of two types of structure unit: {112}- and {111}-type structure units. HRTEM observations combined with lattice statics calculations verified that both crystals were relatively shifted by (α/4)[110] along the rotation axis to form a stable grain-boundary structure. A weak-beam dark-field image revealed that there was a periodic array of dislocations along the grain boundary. The grain-boundary dislocations were considered to be introduced by the slight misorientation from the perfect = 3 orientation. The fact that the periodicity of the facets corresponded to that of the grain-boundary dislocations must indicate that the introduction of the grain-boundary dislocations is closely related to the periodicity of the facets. An atomic flipping model has been proposed for the facet growth from the initial = 3, {112} grain boundary.     

Initiation of discontinuous precipitation at interphase boundaries in a two-phase Zn–6.3 at.% Ag alloy

Discontinuous precipitation (DP) was found to initiate at both η′–ε interphase and η′–η′ grain boundaries in a two-phase Zn–6.3?at.%?Ag alloy consisting of ε and supersaturated η′ phases. The η′–ε interphase boundaries at which DP has initiated illustrated a sinusoidal interface during ageing, which implies that the morphological instability is a prerequisite for the DP initiation at an η′–ε interphase boundary. The application of the morphological instability model for solid–solid interfaces has indicated that the interface protuberances grow into the supersaturated η′ and the interphase boundary becomes unstable since the observed wavelength of serrated η′–ε interphase boundaries was larger than the critical value predicted by the model. A solute-depleted region is therefore established in front of the η′–ε interphase boundary, which provides an appropriate site leading to a DP reaction. Based on this, a nucleation mechanism of DP at the interphase boundaries is proposed accordingly: the allotriomorphs of DP can be directly developed from ε protuberances of a serrated interphase boundary.     

Predicting performance of polymer-bonded Terfenol-D composites under different magnetic fields

Considering demagnetization effect, the model used to calculate the magnetostriction of the single particle under the applied field is first created. Based on Eshelby equivalent inclusion and Mori-Tanaka method, the approach to calculate the average magnetostriction of the composites under any applied field, as well as the saturation, is studied by treating the magnetostriction particulate as an eigenstrain. The results calculated by the approach indicate that saturation magnetostriction of magnetostrictive composites increases with an increase of particle aspect and particle volume fraction, and a decrease of Young's modulus of the matrix. The influence of an applied field on magnetostriction of the composites becomes more significant with larger particle volume fraction or particle aspect. Experiments were done to verify the effectiveness of the model, the results of which indicate that the model only can provide approximate results.     

Mechanism of deformation-twin formation in nanocrystalline metals

A theoretical model is proposed to describe the nucleation of deformation twins at grain boundaries in nanocrystalline materials under the action of an applied stress and the stress field of a dipole of junction or grain-boundary wedge disclinations. The model is used to consider pure nanocrystalline aluminum and copper with an average grain size of about 30 nm. The conditions of barrier-free twinning-dislocation nucleation are studied. These conditions are shown to be realistic for the metals under study. As the twin-plate thickness increases, one observes two stages of local hardening and an intermediate stage of local flow of a nanocrystalline metal on the scale of one nanograin. In all stages, the critical stress increases with decreasing disclination-dipole strength. The equilibrium thickness and shape of the twin plate are analyzed and found to agree well with the well-known results of experimental observations.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

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.