Pressure and displacement fields inside an absorbing fluid sphere ensonified by a point acoustic source: comparison of analytic and numerical solutions.

2009 ◽  
Vol 126 (4) ◽  
pp. 2244
Author(s):  
Kenneth G. Foote ◽  
David T. I. Francis ◽  
Mario Zampolli
Keyword(s):  
Numerical Solutions ◽  
Fluid Sphere ◽  
Acoustic Source ◽  
Displacement Fields

scholarly journals A novel numerical approach for fracture analysis in orthotropic media

2017 ◽  
Vol 20 (K2) ◽  
pp. 5-13
Author(s):  
Minh Ngoc Nguyen ◽  
Nha Thanh Nguyen ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Numerical Approach ◽  
Fracture Analysis ◽  
Orthotropic Materials ◽  
Displacement Fields ◽  
Novel Approach ◽  
Interpolation Procedure ◽  
Orthotropic Media ◽  
Standard Finite Element Method

This paper presents a novel approach for fracture analysis in two-dimensional orthotropic domain. The proposed method is based on consecutive-interpolation procedure (CIP) and enrichment functions. The CIP were recently introduced as an improvement for standard Finite Element method, such that higher-accurate and higher-continuous solution can be obtained without smoothing operation and without increasing the number of degrees of freedom. To avoid re-meshing, the enrichment functions are employed to mathematically describe the jump in displacement fields and the singularity of stress near crack tip. The accuracy of the method for analysis of cracked body made of orthotropic materials is studied. For that purpose, various examples with different geometries and boundary conditions are considered. The results of stress intensity factors, a key quantity in fracture analysis, are validated by comparing with analytical solutions and numerical solutions available in literatures.

Electron microscope image contrast of small dislocation loops and stacking-fault tetrahedra

1979 ◽  
Vol 292 (1397) ◽  
pp. 523-537 ◽  
Keyword(s):  
Electron Microscope ◽  
Numerical Solutions ◽  
Preceding Paper ◽  
Stacking Fault ◽  
Image Contrast ◽  
Dislocation Loops ◽  
Displacement Fields ◽  
Microscope Image ◽  
Stacking Fault Tetrahedra ◽  
Electron Microscope Image

With the use of the method described in the preceding paper (to be referred to subsequently as I) for constructing the displacement fields, the electron microscope image contrast of small dislocation loops and of stacking-fault tetrahedra has been computed from numerical solutions of the Howie-Whelan (1961) equations. The computer-simulated images, displayed in the form of half-tone pictures, have been used to identify the nature and geometry of such defects in ion-irradiated foils. A systematic study of the contrast of small Frank loops in Cu + ion irradiated copper under a wide variety of diffraction conditions is reported. In particular the variations of the contrast of loops edge-on and inclined to the electron beam with the operating Bragg reflexion, the thickness and inclination of the foil, depth of the defect in the foil and deviation from the Bragg-reflecting condition have been studied. Methods of obtaining useful information, such as the diameters of the loops, are suggested. The contrast of stacking-fault tetrahedra, and of non-edge perfect dislocation loops in ion-irradiated molybdenum is also investigated.

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

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