Discrete dislocation plasticity analysis of crack-tip fields in polycrystalline materials

Small scale yielding around a mode I crack is analysed using polycrystalline discrete dislocation plasticity. Plane strain analyses are carried out with the dislocations all of edge character and modelled as line singularities in a linear elastic material. The lattice resistance to dislocation motion, nucleation, interaction with obstacles and annihilation are incorporated through a set of constitutive rules. Grain boundaries are modelled as impenetrable to dislocations. The polycrystalline material is taken to consist of two types of square grains, one of which has a bcc-like orientation and the other an fcc-like orientation. For both orientations there are three active slip systems. Alternating rows, alternating columns and a checker-board-like arrangement of the grains is used to construct the polycrystalline materials. Consistent with the increasing yield strength of the polycrystalline material with decreasing grain size, the calculations predict a decrease in both the plastic zone size and the crack-tip opening displacement for a given applied mode I stress intensity factor. Furthermore, slip-band and kink-band formation is inhibited by all grain arrangements and, with decreasing grain size, the stress and strain distributions more closely resemble the HRR fields with the crack-tip opening approximately inversely proportional to the yield strength of the polycrystalline materials. The calculations predict a reduction in fracture toughness with decreasing grain size associated with the grain boundaries acting as effective barriers to dislocation motion.

Physiological modelling for improved reliability in silhouette-driven gradient-based hand tracking

We present a gradient-based motion capture system that robustly tracks a human hand, based on abstracted visual information - silhouettes. Despite the ambiguity in the visual data and despite the vulnerability of gradient-based methods in the face of such ambiguity, we minimise problems related to misfit by using a model of the hand's physiology, which is entirely non-visual, subject-invariant, and assumed to be known a priori. By modelling seven distinct aspects of the hand's physiology we derive prior densities which are incorporated into the tracking system within a Bayesian framework. We demonstrate how the posterior is formed, and how our formulation leads to the extraction of the maximum a posteriori estimate using a gradient-based search. Our results demonstrate an enormous improvement in tracking precision and reliability, while also achieving near real-time performance. © 2009 IEEE.

Tensile response of passivated films with climb-assisted dislocation glide

The tensile response of single crystal films passivated on two sides is analysed using climb enabled discrete dislocation plasticity. Plastic deformation is modelled through the motion of edge dislocations in an elastic solid with a lattice resistance to dislocation motion, dislocation nucleation, dislocation interaction with obstacles and dislocation annihilation incorporated through a set of constitutive rules. The dislocation motion in the films is by glide-only or by climb-assisted glide whereas in the surface passivation layers dislocation motion occurs by glide-only and penalized by a friction stress. For realistic values of the friction stress, the size dependence of the flow strength of the oxidised films was mainly a geometrical effect resulting from the fact that the ratio of the oxide layer thickness to film thickness increases with decreasing film thickness. However, if the passivation layer was modelled as impenetrable, i.e. an infinite friction stress, the plastic hardening rate of the films increases with decreasing film thickness even for geometrically self-similar specimens. This size dependence is an intrinsic material size effect that occurs because the dislocation pile-up lengths become on the order of the film thickness. Counter-intuitively, the films have a higher flow strength when dislocation motion is driven by climb-assisted glide compared to the case when dislocation motion is glide-only. This occurs because dislocation climb breaks up the dislocation pile-ups that aid dislocations to penetrate the passivation layers. The results also show that the Bauschinger effect in passivated thin films is stronger when dislocation motion is climb-assisted compared to films wherein dislocation motion is by glide-only. © 2012 Elsevier Ltd.

Modeling fatigue crack growth in crystalline solids with discrete dislocation plasticity

Analyses of crack growth under cyclic loading conditions are discussed where plastic flow arises from the motion of large numbers of discrete dislocations and the fracture properties are embedded in a cohesive surface constitutive relation. The formulation is the same as used to analyse crack growth under monotonic loading conditions, differing only in the remote loading being a cyclic function of time. Fatigue, i.e. crack growth in cyclic loading at a driving force for which the crack would have arrested under monotonic loading, emerges in the simulations as a consequence of the evolution of internal stresses associated with the irreversibility of the dislocation motion. A fatigue threshold, Paris law behaviour, striations, the accelerated growth of short cracks and the scaling with material properties are outcomes of the calculations. Results for single crystals and polycrystals will be discussed.

Growth behavior of epitaxial semiconductor axial nanowire heterostructures

In this paper, we demonstrate the key issues of axial nanowire heterostructures, such as, the fundamental criteria for formation and failure of axial nanowire heterostructures via vapor-liquid-solid mechanism and lateral misfit strain relaxation in these structures. We show the failure of axial nanowire heterostructures by growing InAs axially on GaAs nanowires, and the lateral misfit strain relaxation by axial growth of GaSb on GaAs nanowires. © 2008 IEEE.

Understanding the kink formation in GaAs/InAs heterostructural nanowires

The kinks formation in heterostructural nanowires was observed to be dominant when InAs nanowires were grown on GaAs nanowires. Nanowires were grown through vapor-liquid-solid (VLS) mechanism in an MOCVD (metalorganic chemical vapor deposition) reactor. GaAs nanowires were grown in [1 1 1 ]B direction on a GaAs (1 1 1 )B substrate. When InAs nanowires grown on the GaAs nanowires, most of the InAs nanowires changed their growth directions from [1 1 1 ]B to other 〈111〉B directions. The kinks formation is ascribed to the large compressive misfit strain at the GaAs/InAs interface (7.2% lattice mismatch between GaAs and InAs) and the high mobility of indium species during MOCVD growth. The in-depth analysis of the kinks formation was done by growing InAs for short times on the GaAs nanowires and characterizing the samples. The hindrance to compressively strain InAs to form coherent layers with GaAs pushed the InAs/Au interfaces to the sides of the GaAs nanowires growth ends. New InAs/Au interfaces have generated at the sides of GaAs nanowires, due to lateral growth of InAs on GaAs nanowires. These new interfaces led the InAs nanowires growth in other 〈111〉B directions. The morphological and structural features of these heterostructural kinked nanowires were characterized using scanning electron microscopy (SEM) and transmission electron microscopy (TEM) techniques. © 2006 IEEE.

Climb-enabled discrete dislocation plasticity

A small strain two-dimensional discrete dislocation plasticity framework coupled to vacancy diffusion is developed wherein the motion of edge dislocations is by a combination of glide and climb. The dislocations are modelled as line defects in a linear elastic medium and the mechanical boundary value problem is solved by the superposition of the infinite medium elastic fields of the dislocations and a complimentary non-singular solution that enforces the boundary conditions. Similarly, the climbing dislocations are modelled as line sources/sinks of vacancies and the vacancy diffusion boundary value problem is also solved by a superposition of the fields of the line sources/sinks in an infinite medium and a complementary non-singular solution that enforces the boundary conditions. The vacancy concentration field along with the stress field provides the climb rate of the dislocations. Other short-range interactions of the dislocations are incorporated via a set of constitutive rules. We first employ this formulation to investigate the climb of a single edge dislocation in an infinite medium and illustrate the existence of diffusion-limited and sink-limited climb regimes. Next, results are presented for the pure bending and uniaxial tension of single crystals oriented for single slip. These calculations show that plasticity size effects are reduced when dislocation climb is permitted. Finally, we contrast predictions of this coupled framework with an ad hoc model in which dislocation climb is modelled by a drag-type relation based on a quasi steady-state solution. © 2013 Elsevier Ltd. All rights reserved.

Grain boundary interface mechanics in strain gradient crystal plasticity

Interactions between dislocations and grain boundaries play an important role in the plastic deformation of polycrystalline metals. Capturing accurately the behaviour of these internal interfaces is particularly important for applications where the relative grain boundary fraction is significant, such as ultra fine-grained metals, thin films and microdevices. Incorporating these micro-scale interactions (which are sensitive to a number of dislocation, interface and crystallographic parameters) within a macro-scale crystal plasticity model poses a challenge. The innovative features in the present paper include (i) the formulation of a thermodynamically consistent grain boundary interface model within a microstructurally motivated strain gradient crystal plasticity framework, (ii) the presence of intra-grain slip system coupling through a microstructurally derived internal stress, (iii) the incorporation of inter-grain slip system coupling via an interface energy accounting for both the magnitude and direction of contributions to the residual defect from all slip systems in the two neighbouring grains, and (iv) the numerical implementation of the grain boundary model to directly investigate the influence of the interface constitutive parameters on plastic deformation. The model problem of a bicrystal deforming in plane strain is analysed. The influence of dissipative and energetic interface hardening, grain misorientation, asymmetry in the grain orientations and the grain size are systematically investigated. In each case, the crystal response is compared with reference calculations with grain boundaries that are either 'microhard' (impenetrable to dislocations) or 'microfree' (an infinite dislocation sink). © 2013 Elsevier Ltd. All rights reserved.

A fracture criterion for the notch strength of high strength steels in the presence of hydrogen

High strength steels can suffer from a loss of ductility when exposed to hydrogen, and this may lead to sudden failure. The hydrogen is either accommodated in the lattice or is trapped at defects, such as dislocations, grain boundaries and carbides. The challenge is to identify the effect of hydrogen located at different sites upon the drop in tensile strength of a high strength steel. For this purpose, literature data on the failure stress of notched and un-notched steel bars are re-analysed; the bars were tested over a wide range of strain rates and hydrogen concentrations. The local stress state at failure has been determined by the finite element (FE) method, and the concentration of both lattice and trapped hydrogen is predicted using Oriani's theory along with the stress-driven diffusion equation. The experimental data are rationalised in terms of a postulated failure locus of peak maximum principal stress versus lattice hydrogen concentration. This failure locus is treated as a unique material property for the given steel and heat treatment condition. We conclude that the presence of lattice hydrogen increases the susceptibility to hydrogen embrittlement whereas trapped hydrogen has only a negligible effect. It is also found that the observed failure strength of hydrogen charged un-notched bars is less than the peak local stress within the notched geometries. Weakest link statistics are used to account for this stressed volume effect. © 2013 Elsevier Ltd.

First principles interatomic potential for tungsten based on Gaussian process regression

An accurate description of atomic interactions, such as that provided by first principles quantum mechanics, is fundamental to realistic prediction of the properties that govern plasticity, fracture or crack propagation in metals. However, the computational complexity associated with modern schemes explicitly based on quantum mechanics limits their applications to systems of a few hundreds of atoms at most. This thesis investigates the application of the Gaussian Approximation Potential (GAP) scheme to atomistic modelling of tungsten - a bcc transition metal which exhibits a brittle-to-ductile transition and whose plasticity behaviour is controlled by the properties of $\frac{1}{2} \langle 111 \rangle$ screw dislocations. We apply Gaussian process regression to interpolate the quantum-mechanical (QM) potential energy surface from a set of points in atomic configuration space. Our training data is based on QM information that is computed directly using density functional theory (DFT). To perform the fitting, we represent atomic environments using a set of rotationally, permutationally and reflection invariant parameters which act as the independent variables in our equations of non-parametric, non-linear regression. We develop a protocol for generating GAP models capable of describing lattice defects in metals by building a series of interatomic potentials for tungsten. We then demonstrate that a GAP potential based on a Smooth Overlap of Atomic Positions (SOAP) covariance function provides a description of the $\frac{1}{2} \langle 111 \rangle$ screw dislocation that is in agreement with the DFT model. We use this potential to simulate the mobility of $\frac{1}{2} \langle 111 \rangle$ screw dislocations by computing the Peierls barrier and model dislocation-vacancy interactions to QM accuracy in a system containing more than 100,000 atoms.

Structural and optical properties of Al1-xInxN epilayers on GaN template grown by metalorganic chemical vapor deposition

This paper reports that Al1-xInxN epilayers were grown on GaN template by metalorganic chemical vapor deposition with an In content of 7%-20%. X-ray diffraction results indicate that all these Al1-xInxN epilayers have a relatively low density of threading dislocations. Rutherford backscattering/channeling measurements provide the exact compositional information and show that a gradual variation in composition of the Al1-xInxN epilayer happens along the growth direction. The experimental results of optical reflection clearly show the bandgap energies of Al1-xInxN epilayers. A bowing parameter of 6.5 eV is obtained from the compositional dependence of the energy gap. The cathodoluminescence peak energy of the Al1-xInxN epilayer is much lower than its bandgap, indicating a relatively large Stokes shift in the Al1-xInxN sample.

Effects of AlGaN/AlN Stacked Interlayers on GaN Growth on Si (111)

We report the growth of high quality and crack-free GaN film on Si (111) substrate using Al0.2Ga0.8N/AlN stacked interlayers. Compared with the previously used single AlN interlayer, the AlGaN/AlN stacked interlayers can more effectively reduce the tensile stress inside the GaN layer. The cross-sectional TEM image reveals the bending and annihilation of threading dislocations (TDs) in the overgrown GaN film which leads to a decrease of TD density.

Effects of GaN Capping on the Structural and the Optical Properties of InN Nanostructures Grown by Using MOCVD

InN nanostructures with and without GaN capping layers were grown by using metal-organic chemical vapor deposition. Morphological, structural, and optical properties were systematically studied by using atomic force microscopy, X-ray diffraction (XRD) and temperature-dependent photoluminescence (PL). XRD results show that an InGaN structure is formed for the sample with a GaN capping layer, which will reduce the quality and the IR PL emission of the InN. The lower emission peak at similar to 0.7 eV was theoretically fitted and assigned as the band edge emission of InN. Temperature-dependent PL shows a good quantum efficiency for the sample without a GaN capping layers; this corresponds to a lower density of dislocations and a small activation energy.

High Al-content AlInGaN epilayers with different thicknesses grown on GaN/sapphire templates

We studied the structural and optical properties of high Al-content AlInGaN epilayers with different thicknesses grown on GaN/sapphire templates by metalorganic chemical vapor deposition (MOCVD). Direct evidences of the gradual evolution of the content of Al, Ga and In along the growth direction were obtained. When the film thickness was over a certain value, however, the AlInGaN epilayer with constant element contents began to form. These results were also supported by the blue shift and splitting of the photoluminescence (PL) peak. For the thinnest epilayer, the surface was featured with outcrops of threading dislocations (TDs) which suggested a spiral growth mode. With increase in thickness, step-flow growth mode and V-shaped pits were observed, and the steps terminated at the pits. (C) 2008 Elsevier B. V. All rights reserved.