Filon's construct for dislocations and related topics

A unified account is presented of the relationships in plane homogeneous isotropic linear elasticity between dislocations, thermoelasticity, inclusions, and the variation of Poisson's ratio. While basic principles are emphasised, there is also indicated how solutions in one theory may be used to generate solutions in another. The connexion between dislocations and the variation of Poisson's ratio, and between dislocations and thermoelasticity are due respectively to Filon and Mushkelishvili.     

A treatise on the stress-fields produced by moving dislocations

The stresses produced by a continuous distribution of moving dislocations are discussed. It is assumed that the material is elastic, homogeneous and isotropic. In the first part, the basic equations governing the stress-functions and stresses are given. These equations take the same form as those given by Kröner for the stress-field produced by stationary dislocations, except that the d'Alembertian operator appears in place of the Laplacian. In the next part, the stress-functions are obtained from the special solution of the basic equation. The stresses due to uniformly moving dislocation-aggregates, as well as those to finite straight dislocations, are calculated as special cases.     

Evolution equation of moving defects: dislocations and inclusions

Evolution equations, or equations of motion, of moving defects are the balance of the “driving forces”, in the presence of external loading. The “driving forces” are defined as the configurational forces on the basis of Noether’s theorem, which governs the invariance of the variation of the Lagrangean of the mechanical system under infinitesimal transformations. For infinitesimal translations, the ensuing dynamic J integral equals the change in the Lagrangean if and only if the linear momentum is preserved. Dislocations and inclusions are “defects” that possess self-stresses, and the total driving force for these defects consists only of two terms, one expressing the “ self-force” due to the self-stresses, and the other the effect of the external loading on the change of configuration (Peach–Koehler force). For a spherically expanding (including inertia effects) Eshelby (constrained) inclusion with dilatational eigenstrain (or transformation strain) in general subsonic motion, the dynamic J integral, which equals the energy-release rate, was calculated. By a limiting process as the radius tends to infinity, the driving force (energy-release rate) of a moving half-space plane inclusion boundary was obtained which is the rate of the mechanical work required to create an incremental region of eigenstrain (or transformation strain) of a dynamic phase boundary. The total driving force (due to external loading and due to self-forces) must be equal to zero, in the absence of dissipation, and the evolution equation for a plane boundary with eigenstrain is presented. The equation applied to many strips of eigenstrain provides a system to solve for the position/ evolution of strips of eigenstrain.     

Fourier‐based numerical approximation of the Weertman equation for moving dislocations

This work addresses the numerical approximation of solutions to a dimensionless form of the Weertman equation, which models a steadily moving dislocation and is an important extension (with advection term) of the celebrated Peierls‐Nabarro equation for a static dislocation. It belongs to the class of nonlinear reaction‐advection‐diffusion integro‐differential equations with Cauchy‐type kernel, thus involving an integration over an unbounded domain. In the Weertman problem, the unknowns are the shape of the core of the dislocation and the dislocation velocity. The proposed numerical method rests on a time‐dependent formulation that admits the Weertman equation as its long‐time limit. Key features are (1) time iterations are conducted by means of a new, robust, and inexpensive Preconditioned Collocation Scheme in the Fourier domain, which allows for explicit time evolution but amounts to implicit time integration, thus allowing for large time steps; (2) as the integration over the unbounded domain induces a solution with slowly decaying tails of important influence on the overall dislocation shape, the action of the operators at play is evaluated with exact asymptotic estimates of the tails, combined with discrete Fourier transform operations on a finite computational box of size L; (3) a specific device is developed to compute the moving solution in a comoving frame, to minimize the effects of the finite‐box approximation. Applications illustrate the efficiency of the approach for different types of nonlinearities, with systematic assessment of numerical errors. Converged numerical results are found insensitive to the time step, and scaling laws for the combined dependence of the numerical error with respect to L and to the spatial step size are obtained. The method proves fast and accurate and could be applied to a wide variety of equations with moving fronts as solutions; notably, Weertman‐type equations with the Cauchy‐type kernel replaced by a fractional Laplacian.     

The mechanism of hydrogen embrittlement: the stress interaction between a crack, a hydrogen cluster, and moving dislocations

Mechanisms of dissolvent anodic chemical reaction and hydrogen embrittlement have been proposed as stress corrosion cracking (SCC) mechanisms. The former is feasible for the case of plastic deformation dominant metals (low-yield stress), and the latter is for high-strength metals such as high-strength steels. However, in spite of low-yield stress, a discontinuous cleavage-like fracture is sometimes observed during SCC for ductile fcc alloys, which concerns the interaction between dislocations and the hydrogen cluster. The problem of when these mechanisms will be dominant remains. In this paper, the stress corrosion cracking model on the basis of hydrogen diffusion and concentration toward the elastic-plastic stress field around a crack and the interaction of dislocations and hydrogen around a crack tip are proposed to clarify the mechanism of stress corrosion cracking for ductile and brittle materials. We conducted numerical analyses using these proposed models.     

The mechanism of hydrogen embrittlement: the stress interaction between a crack, a hydrogen cluster, and moving dislocations

Mechanisms of dissolvent anodic chemical reaction and hydrogen embrittlement have been proposed as stress corrosion cracking (SCC) mechanisms. The former is feasible for the case of plastic deformation dominant metals (low-yield stress), and the latter is for high-strength metals such as high-strength steels. However, in spite of low-yield stress, a discontinuous cleavage-like fracture is sometimes observed during SCC for ductile fcc alloys, which concerns the interaction between dislocations and the hydrogen cluster. The problem of when these mechanisms will be dominant remains. In this paper, the stress corrosion cracking model on the basis of hydrogen diffusion and concentration toward the elastic-plastic stress field around a crack and the interaction of dislocations and hydrogen around a crack tip are proposed to clarify the mechanism of stress corrosion cracking for ductile and brittle materials. We conducted numerical analyses using these proposed models.     

The behavior of misfit dislocations during interdiffusion

The behavior of misfit dislocations during interdiffusion was studied by means of a hot stage in an electron microscope. An analysis was made on the basis of previous theoretical calculations of forces on dislocations. Misfit dislocations were found to exist in an interwomen network such that each of the dislocations could not move independently of those in a perpendicular orientation. The analysis of the experimental results indicated that the motion of the misfit dislocations was controlled by the osmotic force arising from interdiffusion.     

On the assumptions of the generalized plane stress problem and the Filon average

In this article, we prove that the assumption of vanishing normal stress for the generalized plane stress problem can be further weakened, so that the normal stress is harmonic. The stress state under this harmonic assumption can also be decomposed into the plane stress state and the shear stress state. Finally, a necessary and sufficient condition is presented for the existence of the biharmonic Airy stress function for the Filon averaged in-plane stresses, which is shown to be weaker than the assumption of the harmonic normal stress.     

The cognitive construct of design conversation

The study provides an overview of architectural designers’ cognitive behaviour in a conceptual phase of design like studio tutorials. This involves formulating a Cognitive Interaction Matrix that preserves the dialectical and interactional characteristics of design conversation protocol being examined. The matrix facilitates the process of encoding, segmenting, tabulating and analysing design tutorial conversations based on a rich taxonomy of cognitive activities. Through the framework of aggregating ‘Formulate’, ‘Evaluate’ and ‘Move’ activities and relevant cognitive attributes across conversational protocols, the study found certain differences in the patterns, frequency and intensity of Cognitive Actions’ distribution recorded between tutors and students who had participated in the observed studio tutorials. Further examination of the ‘Formulate’, ‘Evaluate’ and ‘Move’ actions in terms of Cognitive Organisation and Transformational factors suggests the possibility of deriving and distinguishing the cognitive constructs between tutors and students’ design conversations.     

The structure and properties of dislocations in GaN

Transmission electron microscopy studies of the core structure and optoelectronic properties of dislocations in GaN films are described. It is shown that the core structure depends sensitively on the growth method and on the presence of dopants and impurities including Si, Mg and O, with edge, screw and mixed dislocations all becoming open core type under certain conditions. High-resolution electron energy-loss spectroscopy is used to confirm impurity segregation to dislocations. Electron holography and cathodoluminescence studies showing that dislocations possess band gap states and act as non-radiative recombination centres are reviewed, and correlated, tentatively, to impurity segregation.     

The relationship between cracks,holes and surface dislocations

International Journal of Fracture - It has been shown that surface cracks as well as holes can be represented in terms of surface dislocations. These surface dislocations exist in order to insure...     

The multidimensional driving style inventory--scale construct and validation

Two studies were conducted in order to develop a multidimensional instrument of driving style. In Study 1, we developed a self-report scale assessing four broad domains of driving style-the multidimensional driving style inventory (MDSI). A factor analysis revealed eight main factors, each one representing a specific driving style--dissociative, anxious, risky, angry, high-velocity, distress reduction, patient, and careful. In addition, significant associations were found between the eight factors, on the one hand, and gender, age, driving history, and personality measures of self-esteem, need for control, impulsive sensation seeking, and extraversion, on the other. In Study 2, further associations were found between the eight driving style factors and measures of trait anxiety and neuroticism. The discussion focused on the validity and utility of a multidimensional conceptualization of driving style.