A new method to analyse the Peierls-Nabarro model of an edge dislocation in a rectangular plate

A new method is presented here to analyse the Peierls-Nabarro model of an edge dislocation in a rectangular plate. The analysis is based on the superposition scheme and series expansions of complex potentials. The stress field and dislocation density field on the slip plane can be expressed as the first and the second Chebyshev polynomial series respectively. Two sets of governing equations are obtained on the slip plane and outer boundary of the rectangular plate respectively. Three numerical methods are used to solve the governing equations.

Refinement of edge-to-edge matching model and its application in the Mg17Al12/alpha-Mg and alpha-Y/alpha-Mg systems

A refined version of the edge-to-edge matching model is described here. In the original model, the matching directions were obtained from the planes with all the atomic centers that were exactly in the plane, or the distance from the atomic center to the plane which was less than the atomic radius. The direction-matching pairs were the match of straight rows-straight rows and zigzag rows-zigzag rows. In the refined model, the matching directions were obtained from the planes with all the atomic centers that were exactly in the plane.

Extended application of edge-to-edge matching model to HCP/HCP (alpha-Mg/MgZn2) system in magnesium alloys

In the present work, the edge-to-edge matching model has been introduced to predict the orientation relationships (OR) between the MgZn2 phase which has hexagonal close packed (HCP) structure and the HCP a-Mg matrix. Based on the crystal structures and lattice parameters only, the model has predicted the two most preferred ORs and they are: (1) [1 1 2 3](alpha-Mg) vertical bar vertical bar]1 1 2 3](alpha-Mg), (0 0 0 1)(alpha-Mg) 0.27 degrees from (0 0 0 1)(MgZn2), (1 0 1 1)(alpha-Mg) 26.18 degrees from (1 1 2 2)(MgZn2), (2) [1 0 1 0](alpha-Mg),vertical bar vertical bar[1 1 2 0](MgZn2), (0 0 0 1)(alpha-Mg) vertical bar vertical bar(0 0 0 1)(MgZn2), (1 0 1 1)(alpha-Mg) 3.28 degrees from ( 1 1 2 2)(MgZn2). Four experimental ORs have been reported in the alpha-Mg/MgZn2 system, and the most frequently reported one is ideally the OR (2). The other three experimental ORs are near versions of the OR (2). The habit plane of the OR (2) has been predicted and it agrees well with the experimental results.

General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.

Generalized Maugis-Dugdale Model of an Elastic Cylinder in Non-Slipping Adhesive Contact with a Stretched Substrate

We have recently developed a generalized JKR model for non-slipping adhesive contact between an elastic cylinder and a stretched substrate where both tangential and normal tractions are transmitted across the contact interface. Here we extend this model to a generalized Maugis-Dugdale model by adopting a Dugdale-type adhesive interaction law to eliminate the stress singularity near the edge of the contact zone. The non-slipping Maugis-Dugdale model is expected to have a broader range of validity in comparison with the non-slipping JKR model. The solution shares a number of common features with experimentally observed behaviors of cell reorientation on a cyclically stretched substrate.

Edge and Size Effects in Micro Composite Structure

Because of the load transfer effect of interface layer, the stress distribution inside the composite structure of film/substrate can be very different from the Timoshenko's model. In this paper, we give the derivation and analysis of such load transfer effect of shear-lag (S-L) model. The micro-structure size (boundary conditions) effect together with interface load transfer effect becomes more and more important as the microstructure size including the three dimensions of thickness, width and length shrinks. The microstructure size is also responsible for the so-called edge-induced stress. The edge effect and difference of S-L model and Timoshenko model are also demonstrated.

Anomalous scattering factor determined by semicircle fitting near the K-absorption edge of Ge

It is shown that the locus of the f' + if '' plot in the complex plane, f' being determined from measured f '' by using the dispersion relation, looks like a semicircle very near the absorption edge of Ge. The semicircular locus is derived from a quantum theory of X-ray resonant scattering when there is a sharp isolated peak in f '' just above the K-absorption edge. Using the semicircular behavior, an approach is proposed to determine the anomalous scattering factors in a crystal by fitting known calculated values based on an isolated-atom model to a semicircular focus. The determined anomalous scattering factors f' show excellent agreement with the measured values just below the absorption edge. In addition, the phase determination of a crystal structure factor has been considered by using the semicircular behavior.

Temperature dependence of absorption edge in MOCVD grown GaN

We have studied the temperature dependence of absorption edge of GaN thin films grown on sapphire substrate by metal-organic chemical vapor deposition using optical absorption spectroscopy. A shift in absorption edge of about 55 meV has been observed in temperature range 273-343 K. We have proposed a theoretical model to find the energy gap from absorption coefficient using alpha = alpha(max) + (alpha(min) - alpha(max))/[1 + exp 2(E - E-g + KT)/KT]. Temperature dependence of band gap has also been studied by finding an appropriate theoretical fit to our data using E-g(T) = E-g(273 K) - (8.8 x 10(-4)T(2))/(483 + T) + 0.088 (Varshni empirical formula) and E-g(T) = E-g(273 K)-0.231447/[exp(362/T)-1] + 0.082 relations. It has been found that data can be fitted accurately after adding a factor similar to 0.08 in above equations. Debye temperature (483 K) and Einstein temperature (362 K) in the respective equations are found mutually in good agreement.

A model of dislocations at the interface of the bonded wafers

Wafer bonding is regardless of lattice mismatch in the integration of dissimilar semiconductor materials. This technology differs from the heteroepitaxy mainly in the mechanism of generating dislocations at the interface. A model of dislocations at the bonded interface is proposed in this paper. Edge-like dislocations, which most efficiently relax the strain, are predominant at the bonded interface. But the thermal stress associated with large thermal expansion misfit may drive dislocations away from the bonded interface upon cooling.

Enhancements of the simulation method on the edge effect in resin transfer molding processes

In resin transfer molding processes, small clearances exist between the fiber preform and the mold edges, which result in a preferential resin flow in the edge channel and then disrupt the flow patterns during the mold filling stage. A mathematical model including the effect of cavity thickness on resin flow was developed for flow behavior involving the interface between an edge channel and a porous medium. According to the mathematical analysis of momentum equations in a fully developed rectangular duct and formulations of the equivalent edge permeability, comparing with three-dimensional Navier-Stokes equations, the governing equations were modified in the edge channel. The volume of fluid (VOF) method was applied to track the flow front. A simple case is numerically simulated using the modified governing equations. The effects of edge channel width and cavity thickness on flow front and inlet pressure are analyzed, and the evolution characteristics of simulated results are in agreement with the experimental results. (c) 2007 Elsevier B.V. All rights reserved

Reactive Mold Filling in Resin Transfer Molding Processes with Edge Effects

Reactive mold filling is one of the important stages in resin transfer molding processes, in which resin curing and edge effects are important characteristics. On the basis of previous work, volume-averaging momentum equations involving viscous and inertia terms were adopted to describe the resin flow in fiber preform, and modified governing equations derived from the Navier-Stokes equations are introduced to describe the resin flow in the edge channel. A dual-Arrhenius viscosity model is newly introduced to describe the chemorheological behavior of a modified bismaleimide resin. The influence of the curing reaction and processing parameters on the resin flow patterns was investigated.