Void growth in shear

1986 ◽  
Vol 407 (1833) ◽  
pp. 435-458 ◽  
Keyword(s):  
Growth Rate ◽  
Strain Rate ◽  
Void Growth ◽  
Three Dimensional ◽  
Shape Evolution ◽  
Two Dimensional ◽  
Simple Shearing ◽  
Hydrostatic Tension ◽  
Dilatation Rate ◽  
Approximate Formulas

The growth of an isolated void is analysed for a void contained in a block of material undergoing simple shearing combined with superimposed hydrostatic tension. The evolution of the size, shape and orientation of two- and three-dimensional voids in an incompressible, linearly viscous solid is first discussed. The main problem addressed is the behaviour of a two-dimensional cylindrical void in an incompressible, nonlinearly viscous solid for which the strain rate varies as the stress to a power. The growth rate of the void and its shape evolution are strong functions of the degree of material nonlinearity. Relatively simple approximate formulas are obtained for the dilatation rate of a circular void as well as for the void potential. The constitutive relation of a block of material containing a dilute distribution of circular cylindrical voids is obtained directly using the isolated void potential. The paper concludes with a summary of available results for the dilatation rates of voids and cracks under combinations of shear and hydrostatic tension.

A RHEED Study of MBE Growth of ZnSe on GaAs (111) A-(2 × 2)

2003 ◽  
Vol 10 (04) ◽  
pp. 669-675
Author(s):  
F. S. Gard ◽  
J. D. Riley ◽  
R. Leckey ◽  
B. F. Usher
Keyword(s):  
Growth Rate ◽  
Electron Diffraction ◽  
Substrate Temperature ◽  
Three Dimensional ◽  
High Energy ◽  
Growth Mode ◽  
Two Dimensional ◽  
High Energy Electron ◽  
Mbe Growth ◽  
Atomic Flux

ZnSe epilayers have been grown under various Se/Zn atomic flux ratios in the range of 0.22–2.45 at a substrate temperature of 350°C on Zn pre-exposed GaAs (111) A surfaces. Real time reflection high energy electron diffraction (RHEED) observations have shown a transition from a two-dimensional (2D) to a three-dimensional (3D) growth mode. The transition time depends directly upon the growth rate. A detailed discussion is presented to explore the cause of this change in the growth mode.

Density-driven instabilities of miscible fluids in a Hele-Shaw cell: linear stability analysis of the three-dimensional Stokes equations

2002 ◽  
Vol 451 ◽  
pp. 261-282 ◽  
Author(s):  
F. GRAF ◽  
E. MEIBURG ◽  
C. HÄRTEL
Keyword(s):  
Experimental Data ◽  
Growth Rate ◽  
Linear Stability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Interface Thickness ◽  
Gap Width ◽  
Stability Results ◽  
Hele Shaw Cell

We consider the situation of a heavier fluid placed above a lighter one in a vertically arranged Hele-Shaw cell. The two fluids are miscible in all proportions. For this configuration, experiments and nonlinear simulations recently reported by Fernandez et al. (2002) indicate the existence of a low-Rayleigh-number (Ra) ‘Hele-Shaw’ instability mode, along with a high-Ra ‘gap’ mode whose dominant wavelength is on the order of five times the gap width. These findings are in disagreement with linear stability results based on the gap-averaged Hele-Shaw approach, which predict much smaller wavelengths. Similar observations have been made for immiscible flows as well (Maxworthy 1989).In order to resolve the above discrepancy, we perform a linear stability analysis based on the full three-dimensional Stokes equations. A generalized eigenvalue problem is formulated, whose numerical solution yields both the growth rate and the two-dimensional eigenfunctions in the cross-gap plane as functions of the spanwise wavenumber, an ‘interface’ thickness parameter, and Ra. For large Ra, the dispersion relations confirm that the optimally amplified wavelength is about five times the gap width, with the exact value depending on the interface thickness. The corresponding growth rate is in very good agreement with the experimental data as well. The eigenfunctions indicate that the predominant fluid motion occurs within the plane of the Hele-Shaw cell. However, for large Ra purely two-dimensional modes are also amplified, for which there is no motion in the spanwise direction. Scaling laws are provided for the dependence of the maximum growth rate, the corresponding wavenumber, and the cutoff wavenumber on Ra and the interface thickness. Furthermore, the present results are compared both with experimental data, as well as with linear stability results obtained from the Hele-Shaw equations and a modified Brinkman equation.

Tensile Fracture Loci for Brittle Materials Containing Spherical Voids

1986 ◽  
Vol 108 (3) ◽  
pp. 222-229 ◽  
Author(s):  
M. C. Shaw ◽  
J. P. Avery
Keyword(s):  
Three Dimensional ◽  
Brittle Materials ◽  
Dimensional Case ◽  
Tensile Fracture ◽  
Detailed Result ◽  
Three Dimension ◽  
Two Dimensional ◽  
Stress Criterion ◽  
Hydrostatic Tension ◽  
Spherical Voids

When very brittle materials are subjected to a complex state of stress they fail by maximum intensified tensile stress criterion first introduced by Griffith [1]. Nominal applied stresses are intensified by defects present in all real materials. It appears that defects controlling the strength of brittle materials are of two types—open ones characterized by circular voids found in sintered materials such as tungsten carbide and thin, essentially closed ones found in brittle polyphase rock such as granite. This paper is concerned with the extension of a very simple two dimensional theory for circular voids [3] to the three dimensional case involving spherical voids. While the fracture locus for the two dimensional case represents a conservative approximation sufficient for most engineering applications, the three dimension solution is necessary to give detailed result for cases involving near hydrostatic tension or compression.

Spall Study in Mild Steel

1997 ◽  
Vol 119 (4) ◽  
pp. 374-379
Author(s):  
Ze-Ping Wang
Keyword(s):  
Theoretical Model ◽  
Mild Steel ◽  
High Strain Rate ◽  
Strain Rate ◽  
Void Growth ◽  
High Strain ◽  
Two Dimensional ◽  
Ductile Materials ◽  
Major Factors ◽  
Viscoplastic Solid

The influence of inertial, thermal, and rate-sensitive effects on the void growth at high strain rate in a thermal-viscoplastic solid is investigated by means of a theoretical model proposed in the present paper. Numerical analysis of the model suggests that inertial, thermal, and rate-sensitive effects are three major factors which greatly influence the behavior of the void growth in porous ductile materials in high strain rate case. One and two-dimensional plate-impact tests of mild steel are performed. Microscopic observations of the softly recovered specimens reveal the mechanism of micro-damage. As an application of the theoretical model, the processes of one and two dimensional spallation in mild steel are successfully simulated by a finite-difference Lagrangian dynamic code in which the mathematical model presented in this paper is incorporated.

MAGNETIC COLLIMATION AND MAGNETOHYDRODYNAMIC KINK INSTABILITY DRIVEN BY DIFFERENTIAL ROTATION

2008 ◽  
Vol 17 (10) ◽  
pp. 1707-1713 ◽  
Author(s):  
C. S. CAREY ◽  
C. R. SOVINEC ◽  
S. HEINZ ◽  
J. E. EVERETT
Keyword(s):  
Growth Rate ◽  
Accretion Disk ◽  
Differential Rotation ◽  
Rotation Rate ◽  
Three Dimensional ◽  
Small Scale ◽  
Two Dimensional ◽  
Extragalactic Jets ◽  
Magnetohydrodynamic Simulations ◽  
Kink Instability

We investigate the launching and stability of extragalactic jets through magnetohydrodynamic simulations of jet evolution. In these simulations, a small scale equilibrium magnetic corona is twisted by a differentially rotating accretion disk. Two-dimensional calculations show the formation of a collimated outflow. This outflow is divided into two regions by the Alfvén surface: a magnetically dominated Poynting region, and a kinetically dominated region. Three-dimensional calculations show that the outflow is unstable to the m = 1 kink instability, and that the growth rate of the kink instability decreases as the rotation rate of the accretion disk increases.

scholarly journals Self-consistent mean-field magnetohydrodynamics

2009 ◽  
Vol 466 (2114) ◽  
pp. 583-601 ◽  
Author(s):  
A. Courvoisier ◽  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Growth Rate ◽  
Large Scale ◽  
Mean Field Theory ◽  
Mean Field ◽  
Three Dimensional ◽  
Nonlinear Regime ◽  
Two Dimensional ◽  
Link Type ◽  
Forcing Function ◽  
Basic States

We consider the linear stability of two-dimensional nonlinear magnetohydrodynamic basic states to long-wavelength three-dimensional perturbations. Following Hughes & Proctor (Hughes & Proctor 2009 Proc. R. Soc. A 465 , 1599–1616 ( doi:10.1098/rspa.2008.0493 )), the two-dimensional basic states are obtained from a specific forcing function in the presence of an initially uniform mean field of strength . By extending to the nonlinear regime the kinematic analysis of Roberts (Roberts 1970 Phil. Trans. R. Soc. Lond. A 266 , 535–558 ( doi:10.1098/rsta.1970.0011 )), we show that it is possible to predict the growth rate of these perturbations by applying mean-field theory to both the momentum and the induction equations. If , these equations decouple and large-scale magnetic and velocity perturbations may grow via the kinematic α -effect and the anisotropic kinetic alpha instability, respectively. However, if , the momentum and induction equations are coupled by the Lorentz force; in this case, we show that four transport tensors are now necessary to determine the growth rate of the perturbations. We illustrate these situations by numerical examples; in particular, we show that a mean-field description of the nonlinear regime based solely on a quenched α coefficient is incorrect.

Enhancement of three-dimensional instability of free shear layers

1999 ◽  
Vol 379 ◽  
pp. 23-38 ◽  
Author(s):  
VIVEK SAXENA ◽  
SIDNEY LEIBOVICH ◽  
GAL BERKOOZ
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Maximum Growth ◽  
Shear Layers ◽  
Base Flow ◽  
Two Dimensional ◽  
Free Shear Layers ◽  
Dimensional Instability

Enhancement of the temporal growth rate of inviscid three-dimensional instability waves in free shear layers by deformation of the basic flow is studied. The deformation of a two-dimensional mixing layer is assumed to yield a base flow that remains unidirectional, but has a steady spanwise speed variation in addition to the two- dimensional shear. The computed growth rates for hyperbolic tangent base flow, perturbed this way, show enhanced instability in the sense that the neutral waves of the unperturbed flow exhibit positive growth rates. For each imposed spanwise periodicity, an oblique mode is selected that shows maximum growth rate. The results are consistent with related theoretical studies and with qualitative observations in experiments.

scholarly journals Late-time growth of the Richtmyer–Meshkov instability for different Atwood numbers and different dimensionalities

2003 ◽  
Vol 21 (3) ◽  
pp. 363-368 ◽  
Author(s):  
A. YOSEF-HAI ◽  
O. SADOT ◽  
D. KARTOON ◽  
D. ORON ◽  
L.A. LEVIN ◽  
...  
Keyword(s):  
Growth Rate ◽  
Theoretical Model ◽  
Numerical Simulations ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Single Mode ◽  
Late Time ◽  
Two Dimensional ◽  
Good Agreement

The late-time growth rate of the Richtmyer–Meshkov instability was experimentally studied at different Atwood numbers with two-dimensional (2D) and three-dimensional (3D) single-mode initial perturbations. The results of these experiments were found to be in good agreement with the results of the theoretical model and numerical simulations. In another set of experiments a bubble-competition phenomenon, which was observed in previous work for 2D initial perturbation (Sadotet al., 1998), was shown to exist also when the initial perturbation is of a 3D nature.

Linear Fluctuation Growth during Frontogenesis

2009 ◽  
Vol 39 (12) ◽  
pp. 3111-3129 ◽  
Author(s):  
James C. McWilliams ◽  
M. J. Molemaker ◽  
E. I. Olafsdottir
Keyword(s):  
Growth Rate ◽  
Kinetic Energy ◽  
Energy Conversion ◽  
Deformation Rate ◽  
Three Dimensional ◽  
Mesoscale Eddies ◽  
Two Dimensional ◽  
Near Surface ◽  
Secondary Circulations ◽  
Frontal Instability

Abstract Near-surface, two-dimensional (2D) baroclinic frontogenesis induced by a barotropic deformation flow enhances the growth of three-dimensional (3D) fluctuations that occur on an ever smaller scale as the front progressively sharpens. The 3D fluctuation growth rate further increases with a larger deformation rate. The fluctuations grow by a combination of baroclinic and barotropic energy conversions from the 2D frontal flow, with the former dominating for most of the situations examined, ranging from small to 𝒪(1) values of the Rossby and Froude numbers and nondimensional deformation rate. Averaged 3D fluctuation buoyancy fluxes resist the 2D frontogenesis by a frontolytic tendency. They also augment the buoyancy restratification and potential-to-kinetic energy conversion tendencies of the 2D frontogenesis itself, and the 2D frontogenetic and 3D eddy-induced secondary circulations are mostly reinforcing (unlike in turbulent baroclinic jets). This shows that frontal instability coexists with, and potentially may even overcome, active frontogenesis; this conclusion is contrary to some previous studies. Frontal instability thus can augment frontogenesis in accomplishing a forward cascade of energy from oceanic mesoscale eddies into the submesoscale regime en route to finescale dissipation.

High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

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