Image Contrast of Dislocation Loops Near a Free Surface

1977 ◽  
Vol 35 ◽  
pp. 52-53
Author(s):  
S. M. Ohr
Keyword(s):  
Free Surface ◽  
Dislocation Loop ◽  
Image Contrast ◽  
Stress System ◽  
Shear Stresses ◽  
Dislocation Loops ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Analytical Expressions

The image contrast of dislocation loops computed in the past has made use of the displacement fields which do not take into account the presence of stress- free foil surfaces. The free surface modifies the elastic fields around a dislocation loop and hence can influence the image contrast observed in the electron microscope. The effect can be significant particularly when the loops lie close to one of the foil surfaces. In general, the elasticity problem of dislocation loops that takes the free surface into account is difficult to handle mathematically. In the present paper, the method of Bastecka1 was extended to obtain explicitly the analytical expressions for the displacement fields around a pure edge circular dislocation loop lying parallel to the foil surface. In this method, the stress fields of an image dislocation loop and another axially symmetric stress system were added in order to eliminate the normal as well as shear stresses at the surface.

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.

Abnormality of the longitudinal Pochhammer–Chree waves in the vicinity of C2 phase speed

2018 ◽  
Vol 24 (23) ◽  
pp. 5642-5649 ◽  
Author(s):  
Sergey V Kuznetsov
Keyword(s):  
Spectral Analysis ◽  
Phase Speed ◽  
Harmonic Waves ◽  
Wave Polarization ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
The Matrix ◽  
Circular Frequency ◽  
Shear Speed ◽  
Analytical Expressions

The exact solutions of the linear Pochhammer–Chree equation for propagating harmonic waves in a cylindrical rod are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed and analytical expressions for displacement fields are obtained. The variation of wave polarization on the free surface due to the variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear speed all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer–Chree waves can propagate at this phase speed.

Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling

2002 ◽  
Vol 124 (3) ◽  
pp. 342-351 ◽  
Author(s):  
Tariq A. Khraishi ◽  
Hussein M. Zbib
Keyword(s):  
Free Surface ◽  
Stress Component ◽  
Dislocation Dynamics ◽  
Dislocation Segment ◽  
Shear Stresses ◽  
Dislocation Loops ◽  
Dislocation Interaction ◽  
Collocation Points ◽  
Image Segment ◽  
Selection Of

Recent advances in 3-D dislocation dynamics include the proper treatment of free surfaces in the simulations. Dislocation interaction and slip is treated as a boundary-value problem for which a zero-traction condition is enforced at the external surfaces of the simulation box. Here, a new rigorous method is presented to handle such a treatment. The method is semi-analytical/numerical in nature in which we enforce a zero traction condition at select collocation points on a surface. The accuracy can be improved by increasing the number of collocation points. In this method, the image stress-field of a subsurface dislocation segment near a free surface is obtained by an image segment and by a distribution of prismatic rectangular dislocation loops padding the surface. The loop centers are chosen to be the collocation points of the problem. The image segment, with proper selection of its Burgers vector components, annuls the undesired shear stresses on the surface. The distributed loops annul the undesired normal stress component at the collocation points, and in the process create no undesirable shear stresses. The method derives from crack theory and falls under “generalized image stress analysis” whereby a distribution of dislocation geometries or entities (in this case closed rectangular loops), and not just simple mirror images, are used to satisfy the problem’s boundary conditions (BCs). Such BCs can, in a very general treatment, concern either stress traction or displacements.

Image contrast of dislocation in anisotropic cubic crystals

1978 ◽  
Vol 36 (1) ◽  
pp. 326-327
Author(s):  
S.M. Ohr
Keyword(s):  
Displacement Field ◽  
Finite Size ◽  
Anisotropic Elasticity ◽  
Dynamical Theory ◽  
Image Contrast ◽  
Dislocation Loops ◽  
Displacement Fields ◽  
Cubic Crystals ◽  
Circular Loop ◽  
The Fourier Transform

The calculations of the image contrast of dislocation loops reported in the past have made use of the displacement fields which are derived under the assumptions of elastic isotropy. The only exception is the work of Yoffe, but it is based on the asymptotic field of an infinitesimal loop applied to the first order analytical theory of image contrast. It is therefore desirable to calculate the image contrast by exact numerical integration of the equations of the dynamical theory of electron diffraction making use of the displacement field of a finite loop derived from the anisotropic elasticity theory. Recently, we have presented a scheme by which the displacement field of a circular loop of finite size can be calculated for anisotropic cubic crystals from the Fourier transform of the elastic Green's function. In the present study, this numerical scheme has been combined with the image simulation technique developed earlier to calculate the image contrast of dislocation loops in anisotropic cubic crystals.

Longitudinal Pochhammer — Chree Waves in Mild Auxetics and Non-Auxetics

2018 ◽  
Vol 35 (3) ◽  
pp. 327-334 ◽  
Author(s):  
A. V. Ilyashenko ◽  
S. V. Kuznetsov
Keyword(s):  
Poisson’S Ratio ◽  
Wave Speed ◽  
Poisson's Ratio ◽  
Abnormal Behavior ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Shear Wave Speed ◽  
The Matrix ◽  
The Waves ◽  
Analytical Expressions

ABSTRACTThe exact solutions of Pochhammer — Chree equation for propagating harmonic waves in isotropic elastic cylindrical rods, are analyzed. Spectral analysis of the matrix dispersion equation for the longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of the wave polarization due to variation of Poisson’s ratio for mild auxetics (Poisson’s ratio is greater than -0.5) is analyzed and compared with the non-auxetics. It is observed that polarization of the waves for both considered cases (auxetics and non-auxetics) exhibits abnormal behavior in the vicinity of the bulk shear wave speed.

Polarization of the Longitudinal Pochhammer–Chree Waves

2020 ◽  
Vol 22 (4) ◽  
pp. 1329-1336
Author(s):  
Alla V. Ilyashenko ◽  
Sergey V. Kuznetsov
Keyword(s):  
Wave Speed ◽  
Phase Speed ◽  
Harmonic Waves ◽  
Wave Polarization ◽  
Axially Symmetric ◽  
Displacement Fields ◽  
Shear Wave Speed ◽  
The Matrix ◽  
Circular Frequency ◽  
Analytical Expressions

AbstractThe exact solutions of the linear Pochhammer – Chree equation for propagating harmonic waves in a cylindrical rod, are analyzed. Spectral analysis of the matrix dispersion equation for longitudinal axially symmetric modes is performed. Analytical expressions for displacement fields are obtained. Variation of wave polarization on the free surface due to variation of Poisson’s ratio and circular frequency is analyzed. It is observed that at the phase speed coinciding with the bulk shear wave speed all the components of the displacement field vanish, meaning that no longitudinal axisymmetric Pochhammer – Chree wave can propagate at this phase speed.

scholarly journals GENERAL SCALARIZATION METHOD OF DYNAMIC ELASTIC FIELDS IN TRANSVERSALLY ISOTROPIC MEDIA AND ITS NEW APPLICATIONS

2018 ◽  
Vol 18 (3) ◽  
pp. 258-264
Author(s):  
I. P. Miroshnichenko ◽  
V. P. Sizov
Keyword(s):  
Symmetry Axis ◽  
Layered Structures ◽  
Mutual Arrangement ◽  
Material Symmetry ◽  
Displacement Fields ◽  
General Technique ◽  
Elastic Fields ◽  
Scalarization Method ◽  
Isotropic Media ◽  
Transversally Isotropic

Introduction. An efficient technique of tensor field scalarization  is  successfully  used  while  investigating  tensor  elastic fields of displacements, stresses and deformations in the layered structures of different materials, including transversally isotropic composites. These fields can be expressed through the scalar potentials corresponding to the quasi-longitudinal, quasi-transverse, and transverse-only waves. Such scalarization is possible if the objects under consideration are tensors relating to  the subgroup  of general coordinate conversions, when the local affine basis has one invariant vector that coincides with the material symmetry axis of the material. At this, the known papers consider structures where this vector coincides with the normal to the boundary between layers. However, other cases of the mutual arrangement of the material symmetry axis of the  material  and  the boundaries between layers are of interest on the practical side.Materials and Methods. The work objective is further development of the scalarization method application in the boundary value problems of the dynamic  elasticity theory for the cases of an arbitrary arrangement of the material symmetry axis relative to the boundary between layers. The present research and methodological apparatus are developed through the general technique of scalarization of the dynamic elastic fields of displacements, stresses and strains in the transversally isotropic media.Research Results. New design ratios for the determination of the displacement fields, stresses and deformations in the transversally isotropic media are obtained for the cases of an arbitrary arrangement of the material symmetry axes of the layer materials with respect to the boundaries between layers. Discussion and Conclusions. The present research and methodological apparatus are successfully used in determining the stress-strain  state  in  the  layered  structures  of  transversally isotropic materials, and in analyzing the diagnosis results of the state of the plane-layered and layered cylindrical structures under operation.

Defects and Polytype Instabilities

2018 ◽  
Vol 924 ◽  
pp. 147-150
Author(s):  
Jörg Pezoldt ◽  
Andrei Alexandrovich Kalnin
Keyword(s):  
Long Range ◽  
Basal Plane ◽  
Partial Dislocation ◽  
Stacking Faults ◽  
Dislocation Loops ◽  
Elastic Fields ◽  
Basal Plane Dislocation ◽  
The Stability ◽  
Shockley Dislocation ◽  
Polytype Structure

A model based on the generation and recombination of defect was developed to describe the stability of stacking faults and basal plane dislocation loops in crystals with layered polytype structures. The stability of the defects configuration was analysed for stacking faults surrounded by Shockley and Frank partial dislocation as well as Shockley dislocation dipoles with long range elastic fields. This approach allows the qualitative prediction of defect subsystems in polytype structure in external fields.

Nonlinear Local Analysis of Steady Flow About a Ship

1991 ◽  
Vol 35 (04) ◽  
pp. 288-294
Author(s):  
F. Noblesse ◽  
D. M. Hendrix ◽  
L. Kahn
Keyword(s):  
Free Surface ◽  
Fluid Velocity ◽  
Wave Profile ◽  
Local Analysis ◽  
Experimental Measurements ◽  
Surface Boundary ◽  
Nonlinear Method ◽  
Rapid Variation ◽  
Wigley Hull ◽  
Analytical Expressions

A nonlinear local analysis of the steady potential flow at a ship bow and stern, and more generally at any point along a ship waterline, is presented. The hull boundary condition and the nonlinear kinematic and dynamic free-surface boundary conditions are satisfied exactly, at the actual position of the free surface, in this analysis. The bow-flow analysis shows that the free surface at a ship bow is tangent to the stem. This theoretical result appears to agree with existing experimental measurements of steady bow waves of the Wigley hull. Simple analytical expressions defining the fluid velocity at the bow and the stern, and more generally at any point along the wave profile, in terms of the elevation of the free surface at the corresponding point are also given. These analytical expressions and the available experimental measurements of wave profiles along the Wigley hull show that the velocity of the flow disturbance due to this hull is fairly small compared to the hull speed everywhere along the wave profile except in very small regions around the bow and the stern, where the total fluid velocity is nearly equal to the hull speed in magnitude but directed vertically. Nonlinearities therefore appear to be quite important, although only in very small regions surrounding a ship bow and stern. A genuine nonlinear method of calculation must then be able to represent the very rapid variation in the direction of the fluid velocity occurring within small regions around a ship bow and stern. In particular, a sufficiently fine discretization is required in these regions.

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