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NASA NTRS1980

A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity

A very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented. The analysis is formulated on the basis of conservation laws of anisotropic elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is reduced to a system of linear algebraic equations in mixed-mode stress intensity factors. One of the salient features of the present approach is that it can determine directly the mixed-mode stress intensity solutions from the conservation integrals evaluated along a path removed from the crack-tip region without the need of solving the corresponding complex near-field boundary value problem. Several examples with solutions available in the literature are solved to ensure the accuracy of the current analysis. This method is further demonstrated to be superior to other approaches in its numerical simplicity and computational efficiency. Solutions of more complicated and practical engineering problems dealing with the crack emanating from a circular hole in composites are presented also to illustrate the capacity of this method.

Wang, S. S.↗

NASA NTRS1982

Comparison of transport equations based on Maxwellian and bi-Maxwellian distributions for anisotropic plasmas

A wide variety of plasma flow conditions is found in aeronomy and space plasma physics. Transport equations based on an isotropic Maxwellian vilecity distribution function can be used to describe plasma flows which contain 'small' temperature anisotropies. However, for plasma flows characterized by large temperature anisotropies, transport equations based on an anisotropic bi-Maxwellian (or two-temperature) velocity distribution function are expected to provide a much better description of the plasma transport properties. The present investigation is concerned with the extent to which transport equations based on both Maxwellian and bi-Maxwellian series expansions can describe plasma flows characterized by non-Maxwellian velocity distributions, giving particular attention to a modelling of the anisotropic character of the distribution function. The obtained results should provide clues as to the extent to which a given series expansion can account for the anisotropic character of a plasma.

Barakat, A. R.↗

NASA NTRS1985

The effects of anisotropic free-stream turbulence on turbulent boundary layer behavior

The effects of near-isotropic and highly anisotropic free-stream turbulence on mean flow properties of the turbulence structure of turbulent boundary layers in a near zero pressure gradient flow has been experimentally evaluated. Turbulence levels vary from 0.5% to 8.0% and the momentum thickness Reynolds number varies from 800 to 1100. The results indicate that the effects of free-stream turbulence on the classical boundary layer properties for near-isotropic turbulence which have been published by other investigators are similar to the case of highly anisotropic turbulence fields, while the effects of free-stream turbulence on the properties of the turbulent structure within the boundary layer for the case of near-isotropic turbulence are quite different compared to the highly anisotropic case.

Liang-Wei, F.↗

NASA NTRS1985

Model-size reduction technique for the analysis of symmetric anisotropic structures

A two-step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic (anisotropic) parts; and (2) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero nonorthotropic matrix and its various-order derivatives with respect to an anisotropic tracing parameter (identifying the nonorthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed technique is demonstrated by means of numerical examples and its potential for solving other quasi-symmetric problems is discussed.

Noor, A. K.↗

NASA NTRS1987

Anisotropic transport in modulation doped quantum well structures

The degree of anisotropy in the anisotropic electron transport that has been observed in GaAs modulation-doped quantum wells grown by MBE on Al(0.3)Ga(0.7)As is related to the thickness and growth parameters of this substrate, which is grown just prior to the inverted interface. It is presently observed that the inverted interface has an anisotropic roughness which affects the 77 K low field electron transport parallel to the interface, and gives rise to anisotropic electron scattering in the GaAs modulation-doped quantum well.

Radulescu, D. C.↗

NASA NTRS1987

Infrared properties of an anisotropically stirred fluid

A renormalization group is developed for the Navier-Stokes equations driven by an anisotropically correlated random stirring force. The stirring force generates homogeneous turbulence with a preferred direction. The force correlation is the sum of a small anisotropic perturbation and an isotropic correlation chosen, so that the fixed point of renormalization group has a k exp -5/3 energy spectrum. Fixed points for the anisotropic correlation are found near this isotropic fixed point. Two types of anisotropy are analyzed. when the additional stirring is in the plane perpendicular to the preferred direction, the renormalized viscosity is increased. When it is aligned with the preferred direction, the viscosity is decreased. A possible connection with the inverse energy cascade of two-dimensional turbulence is discussed.

Rubinstein, Robert↗

NASA NTRS1988

A hybrid-stress finite element for linear anisotropic elasticity

Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.

Fly, Gerald W.↗

NASA NTRS1991

Anisotropic elliptic optical fibers

The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.

Kang, Soon Ahm↗

NASA NTRS1992

Mechanics of anisotropic plates and shells - A new look at an old subject

A number of aspects of the mechanics of anisotropic plates and shells are discussed. The topics covered include computational models of anisotropic plates and shells, consequences of anisotropy on deformation couplings, symmetry types, stress concentrations and edge effects, and importance of transverse shear deformation; recent applications and recent advances in the modeling and analysis of anisotropic plates and shells; and new research directions.

Noor, A. K.↗

NASA NTRS1992

Polarimetric emission from anisotropic media for passive remote sensing of sea ice

The polarimetric emission from an anisotropic medium with applications to the passive microwave remote sensing of sea ice is investigated. Based on the fluctuation-dissipation theory, the Stokes vector is obtained for the thermally exicted electromagnetic radiation from an anisotropic object. By modeling sea ice as a layered anisotropic medium, the Stokes vector representing the polarimetric emission is illustrated for various geophysical conditions. It is found that the difference in the brightness temperatures measured at two surface temperatures is correlated with the thickness of the sea ice. For cases where the c-axis of sea ice is aligned or not random in the horizontal plane, the calculated brightness temperatures show a periodic variation when plotted as a function of the azimuthal angle of the observation direction, indicating that the polarimetric Stokes parameters can be used to detect the direction of c-axes in sea ice.

Yueh, S. H.↗

NASA NTRS1994

Method of determining load in anisotropic non-crystalline materials using energy flux deviation

An ultrasonic wave is applied to an anisotropic sample material in an initial direction and the intensity of the ultrasonic wave is measured on an opposite surface of the sample material by two adjacent receiving points located in an array of receiving points. A ratio is determined between the measured intensities of two adjacent receiving points, the ratio being indicative of an angle of flux deviation from the initial direction caused by an unknown applied load. This determined ratio is then compared to a plurality of ratios of a similarly tested, similar anisotropic reference material under a plurality of respective, known load conditions, whereby the load applied to the particular anisotropic sample material is determined. A related method is disclosed for determining the fiber orientation from known loads and a determined flux shift.

Prosser, William H.↗

NASA NTRS1995

Emission line signatures of anisotropic turbulence in accretion disks

We investigate observable effects of anisotropic turbulence on the velocity profiles and eclipse behavior of emission lines from accretion disks. Turbulence expands the local line broadening profile, enhancing the surface brightness of saturated emission lines. Anisotropic turbulence produces anisotropic emission in such lines. The effects become observable when the turbulence exceeds the thermal velocity. Each term in the velocity-velocity correlation matrix produces a distinctive azimuthal pattern of enhanced emission-line surface brightness on the face of the accretion disk. These patterns express themselves as changes in the observable shapes of the disk's emission lines. The best place to look for turbulence effects is in saturated emission lines of heavy elements such as Ca, Mg, and Fe, which have a smaller thermal velocity at a given sound speed and at moderate inclination (60-70 degrees), since the Keplerian shear broadening dominates at higher inclinations.

Horne, Keith↗

NASA NTRS1994

Extension of the quasistatic far-wing line shape theory to multicomponent anisotropic potentials

The formalism developed previously for the calculation of the far-wing line shape function and the corresponding absorption coefficient using a single-component anisotropic interaction term and the binary collision and quasistatic approximations is generalized to multicomponent anisotropic potential functions. Explicit expressions are presented for several common cases, including the long-range dipole-dipole plus dipole-quadrupole interaction and a linear molecule interacting with a perturber atom. After determining the multicomponent functional representation for the interaction between the CO2 and Ar from previously published data, we calculate the theoretical line shape function and the corresponding absorption due to the nu(sub 3) band of CO2 in the frequency range 2400-2580 cm(exp -1) and compare our results with previous calculations carried out using a single-component anisotropic interaction, and with the results obtained assuming Lorentzian line shapes. The principal uncertainties in the present results, possible refinements of the theoretical formalism, and the applicability to other systems are discussed briefly.

Ma, Q.↗

NASA NTRS1995

Anisotropic microturbulence near the Sun

Interplanetary scintillation observations which sample the spatial spectrum of electron density at scales between 10 and 100 km show power-law spectra which are flatter than the Kolmogorov spectra observed at larger scales by spacecraft and also, indirectly, by phase scintillation of coherent radio signals. Furthermore, angular broadening observations of compact radio sources have shown that the microscale density fluctuations are field-aligned and become more anisotropic as R decreases inside 10 solar radius. We present angular broadening observations taken in October of 1992 which were recorded nearly simultaneously on the VLA and VLBA arrays. The VLA samples structure at scales between 3 and 30 km, whereas the VLBA samples scales between 200 and 4000 km. The small scale VLA measurements of the south polar source 1246-075 showed lower turbulence than those of the equatorial source 1256-057, consistent with previous work showing that the density delta N(exp 2)(sub e) is a factor of 10-15 lower in coronal holes. The VLA observations inside of 10 solar radius were anisotropic, as expected. We were not able to measure the equatorial source with the VLBA inside of 10 solar radius because the scattering was too strong, however we did observe the polar source just inside this distance with both the VLA and the VLBA. Significant anisotropy was seen on the smaller scales, but the larger scales were essentially isotropic. This suggests that the process responsible for the anisotropic microturbulence is distinct from the larger scale isotropic turbulence.

Coles, William A.↗

NASA NTRS1999

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.

So, R. M. C.↗

NASA NTRS2000

Anisotropic Nanomechanics of Boron Nitride Nanotubes: Nanostructured "Skin" Effect

The stiffness and plasticity of boron nitride nanotubes are investigated using generalized tight-binding molecular dynamics and ab-initio total energy methods. Due to boron-nitride BN bond buckling effects, compressed zigzag BN nanotubes are found to undergo novel anisotropic strain release followed by anisotropic plastic buckling. The strain is preferentially released towards N atoms in the rotated BN bonds. The tubes buckle anisotropically towards only one end when uniaxially compressed from both. A "skin-effect" model of smart nanocomposite materials is proposed which will localize the structural damage towards the 'skin' or surface side of the material.

Srivastava, Deepak↗

NASA NTRS2004

Subsurface Stress Fields in FCC Single Crystal Anisotropic Contacts

Single crystal superalloy turbine blades used in high pressure turbomachinery are subject to conditions of high temperature, triaxial steady and alternating stresses, fretting stresses in the blade attachment and damper contact locations, and exposure to high-pressure hydrogen. The blades are also subjected to extreme variations in temperature during start-up and shutdown transients. The most prevalent high cycle fatigue (HCF) failure modes observed in these blades during operation include crystallographic crack initiation/propagation on octahedral planes, and non-crystallographic initiation with crystallographic growth. Numerous cases of crack initiation and crack propagation at the blade leading edge tip, blade attachment regions, and damper contact locations have been documented. Understanding crack initiation/propagation under mixed-mode loading conditions is critical for establishing a systematic procedure for evaluating HCF life of single crystal turbine blades. This paper presents analytical and numerical techniques for evaluating two and three dimensional subsurface stress fields in anisotropic contacts. The subsurface stress results are required for evaluating contact fatigue life at damper contacts and dovetail attachment regions in single crystal nickel-base superalloy turbine blades. An analytical procedure is presented for evaluating the subsurface stresses in the elastic half-space, based on the adaptation of a stress function method outlined by Lekhnitskii. Numerical results are presented for cylindrical and spherical anisotropic contacts, using finite element analysis (FEA). Effects of crystal orientation on stress response and fatigue life are examined. Obtaining accurate subsurface stress results for anisotropic single crystal contact problems require extremely refined three-dimensional (3-D) finite element grids, especially in the edge of contact region. Obtaining resolved shear stresses (RSS) on the principal slip planes also involves considerable post-processing work. For these reasons it is very advantageous to develop analytical solution schemes for subsurface stresses, whenever possible.

Arakere, Nagaraj K.↗

NASA NTRS2005

The features of self-assembling organic bilayers important to the formation of anisotropic inorganic materials in microgravity conditions

Materials with directional properties are opening new horizons in a variety of applications including chemistry, electronics, and optics. Structural, optical, and electrical properties can be greatly augmented by the fabrication of composite materials with anisotropic microstructures or with anisotropic particles uniformly dispersed in an isotropic matrix. Examples include structural composites, magnetic and optical recording media, photographic film, certain metal and ceramic alloys, and display technologies including flat panel displays. The new applications and the need for model particles in scientific investigations are rapidly out-distancing the ability to synthesize anisotropic particles with specific chemistries and narrowly distributed physical characteristics (e.g. size distribution, shape, and aspect ratio).

Talham, Daniel R.↗