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NASA NTRS1989

Mechanisms controlling fatigue damage development in continuous fiber reinforced metal matrix composites

Damage in continuous fiber reinforced metal matrix composite materials can be quite complex since there are a number of different constituents (fiber, matrix, and the fiber/matrix interface) that can fail. Multidirectional lay-ups have an even greater number of possible damage orientations and mechanisms. Based on the simplifying assumption of equivalent constituent strain states in the absence of damage, a strain based failure criteria may be applied to determine when and where initial damage will occur. Based on the relative strain to fatigue failure of the fiber and matrix, the possible damage mechanisms of an MMC can be grouped into three categories: (1) matrix dominated, (2) fiber dominated, and (3) self-similar damage growth. A fourth type of damage development, fiber/matrix interface failure, is dependent on the relative strength of the fiber/matrix interface and the matrix yield strength. These four types of damage are discussed and illustrated by examples.

Johnson, W. S.↗

NASA NTRS1991

Mode-II-Fracture Specimen And Holder

Test specimen and loading frame developed for fatigue and fracture testing of materials under mode-II (sliding-mode) loading. Assembly placed in compression-testing machine. Loads directed oppositely along centerline cause self-similar crack to propagate. Enables consistently accurate alignment of specimens before insertion of specimen/frame assemblies into compression-testing machine. Makes design attractive for testing in hostile environments in which access to machine or furnace limited. Additional feature, with little or no modification, placed horizontally into impact testing machine and subjected to loading at high speeds.

Buzzard, Robert J.↗

NASA NTRS1991

Predicting chaos for infinite dimensional dynamical systems: The Kuramoto-Sivashinsky equation, a case study

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Smyrlis, Yiorgos S.↗

NASA NTRS1991

Shock wave interaction with an abrupt area change

The wave patterns that occur when a shock wave interacts with an abrupt area changed are analyzed in terms of the incident shock wave Mach number and area-jump ratio. The solutions predicted by a semi-similar models are in good agreement with those obtained numerically from the quasi-one-dimensional time-dependent Euler equations. The entropy production for the wave system is defined and the principle of minimum entropy production is used to resolve a nonuniqueness problem of the self-similar model.

Salas, Manuel D.↗

NASA NTRS1990

Capture probabilities for secondary resonances

A perturbed pendulum model is used to analyze secondary resonances, and it is shown that a self-similarity between secondary and primary resonances exists. Henrard's (1982) theory is used to obtain formulas for the capture probability into secondary resonances. The tidal evolution of Miranda and Umbriel is considered as an example, and significant probabilities of capture into secondary resonances are found.

Malhotra, Renu↗

NASA NTRS1990

Fractal dimension of bioconvection patterns

Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2 x 10 to the 6th organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching, and a fractal dimension (d about 1.7). These agree well with the two-dimensional DLA.

Noever, David A.↗

NASA NTRS1989

A comparison of predicted and measured strengths of thick notched graphite/epoxy laminates

The effect of thickness on the notched strength of three graphite/epoxy laminates is studied. The strength of the laminates is shown to be a function of laminate thickness. The notched strength of (0/+ or - 45/90)ns and (0/90)ns laminates decreased toward asymptotic values with increasing laminate thickness, while that of the (0/+ or - 45)ns laminate increased toward an asymptotic value with increasing laminate thickness. For all three laminate types, the notched strength decreased with increasing notch size, regardless of thickness. The fracture of the thick laminates was essentially uniform and self-similar with the notch. The 'universal' value of the general toughness parameter developed by Poe (1981) successfully predicts the notched strength of the thick laminates.

Harris, C. E.↗

NASA NTRS1991

An examination of coherent structures in a lobed mixer using multifractal measures in conjunction with the proper orthogonal decomposition

A 'lobed mixer' device that enhances mixing through secondary flows and streamwise vorticity is presently studied within the framework of multifractal-measures theory, in order to deepen understanding of velocity time trace data gathered on its operation. Proper orthogonal decomposition-based knowledge of coherent structures has been applied to obtain the generalized fractal dimensions and multifractal spectrum of several proper eigenmodes for data samples of the velocity time traces; this constitutes a marked departure from previous multifractal theory applications to self-similar cascades. In certain cases, a single dimension may suffice to capture the entire spectrum of scaling exponents for the velocity time trace.

Ukeiley, L.↗

NASA NTRS1990

A robotic return to the moon

The autonomous lunar precursor mission presently proposed for low cost manned revisits to the lunar surface, designated 'Lunar Oasis by Automation and Robotics', employs two self-similar robotic vehicles, and three experimental 'biovolumes' which are directly derived from the lunar landers that are initially entrusted with fulfilling mission hardware-delivery requirements. The two vehicles would support the experimental biovolumes by returning resources for use in physicochemical or biological processing. Delivered resources would be combined with those in situ to furnish reconfigured biovolumes with the capabilities for autonomous biological growth and wastes-reprocessing demonstrations.

Luttges, Marvin W.↗

NASA NTRS1991

Modelling the spatial distribution of QSO absorption lines

A formalism has been developed for testing specific models for the three-dimensional spatial distributions of Ly-alpha clouds against the line-of-sight observations. The formalism can be used to compute the redshift density of lines and the distribution of line-interval sizes along a line-of-sight for comparison with the observations. A few simple models are considered: a Poisson distribution of Ly-alpha clouds, clouds arising from density fluctuations with a white-noise power spectrum, clouds distributed only on shells of constant comoving radii, clouds restricted to shells that are expanding in a self-similar fashion, and a Poisson distribution of clouds in the 'walls' between small-scale voids.

Babul, Arif↗

NASA NTRS1991

Solar wind control of the magnetopause shape, location, and motion

A data set of 1821 magnetopause crossings was assembled. Separate fits to subsets of this data set determine the magnetopause location as a function of solar wind dynamic pressure and interplanetary magnetic field orientation. Solar wind dynamic pressure variations produce self-similar magnetopause motion on time scales of one hour or longer. In this paper, the pressure balance relationship between the solar wind dynamic pressure and the location of the subsolar magnetopause are verified. The relationship between the IMF Bz, region 1 Birkeland current strength, the position of the subsolar magnetopause, and the shape of the dayside magnetosphere is quantified. Cross sections of the dayside magnetopause in planes perpendicular to the earth-sun line are oblate.

Sibeck, D. G.↗

NASA NTRS1991

Do clusters of galaxies affect the spectrum of the microwave background?

The distortion, averaged over the sky, due to the Compton scattering of background photons with electrons in the hot gas in clusters of galaxies is calculated. Using an existing sample of X-ray clusters, various values of the density parameter Omega, and plausible models for cluster evolution, Monte Carlo realizations of the microwave sky are generated. The spatial structure of these simulations shows a network of discrete sources whose properties can be a strong function of both evolution and Omega. The amount of spectral distortion in the models is greatest for models characterized by self-similar cluster evolution in an open universe and is within an order of magnitude of the current upper limits. Thus, improved observational sensitivity must inevitably detect some deviation from a blackbody spectrum.

Markevitch, M.↗

NASA NTRS1991

The study of PDF turbulence models in combustion

In combustion computations, it is known that the predictions of chemical reaction rates are poor if conventional turbulence models are used. The probability density function (pdf) method seems to be the only alternative that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus is the only viable approach for more accurate turbulent combustion calculations. The fact that the pdf equation has a very large dimensionality renders finite difference schemes extremely demanding on computer memories and thus impractical. A logical alternative is the Monte Carlo scheme. Since CFD has a certain maturity as well as acceptance, it seems that the use of a combined CFD and Monte Carlo scheme is more beneficial. Therefore, a scheme is chosen that uses a conventional CFD flow solver in calculating the flow field properties such as velocity, pressure, etc., while the chemical reaction part is solved using a Monte Carlo scheme. The discharge of a heated turbulent plane jet into quiescent air was studied. Experimental data for this problem shows that when the temperature difference between the jet and the surrounding air is small, buoyancy effect can be neglected and the temperature can be treated as a passive scalar. The fact that jet flows have a self-similar solution lends convenience in the modeling study. Futhermore, the existence of experimental data for turbulent shear stress and temperature variance make the case ideal for the testing of pdf models wherein these values can be directly evaluated.

Hsu, Andrew T.↗

NASA NTRS1991

Fractal dynamics of bioconvective patterns

Biologically generated cellular patterns, sometimes called bioconvective patterns, are found to cluster into aggregates which follow fractal growth dynamics akin to diffusion-limited aggregation (DLA) models. The pattern formed is self-similar with fractal dimension of 1.66 +/-0.038. Bioconvective DLA branching results from thermal roughening which shifts the balance between ordering viscous forces and disordering cell motility and random diffusion. The phase diagram for pattern morphology includes DLA, boundary spokes, random clusters, and reverse clusters.

Noever, David A.↗

NASA NTRS1992

Structure and evolution of time-dependent intermediate shocks

A quantitative description of time-dependent intermediate shocks is formulated using the Cohen-Kulsrud-Burgers equations. In noncoplanar Riemann problems, time-dependent two-three transition intermediate shocks evolve in time as a localized self-similar structure whose strength decreases as 1/the square root of t, and whose width expands as the square root of t. Time-dependent intermediate shocks offer a way of solving the noncoplanar MHD Riemann problem.

Wu, C. C.↗

NASA NTRS1992

The contribution of galaxy clusters to the soft X-ray background

The present paper examines models for the expected contribution to the X-ray background (XRB) from clusters of galaxies in a flat universe with a spectrum of fluctuations corresponding to the standard cold dark matter picture and for a power-law spectrum P(k) varies as k sup n with n = -2. A self-similar scaling model for clusters proposed by Kaiser (1986) is presented, along with several variants. Photon statistics from synthesized maps of deep Einstein fields show a granularity similar to that deduced by Hamilton and Helfand (1987) from the Einstein data but overproduces by a large factor the number of discrete sources observed as clusters, and the fluctuation limit derived from the recent correlation analyses of the background. Two alternative models are designed to be consistent with the local luminosity function data; for these, expected deep images for the Rosat satellite are generated. Clusters of galaxies should be a significant source of background at energies around 2 keV, and it is proposed that clusters of galaxies contribute up to 30 percent of the unresolved component.

Blanchard, A.↗

NASA NTRS1991

Wave interactions with continuous fractal layers

Many natural structures possess self-similar multiscales which can be characterized by power law spectra. Under appropriate conditions, knowledge of the strength of these scale sizes provides information on the physical processes which formed these objects. In this paper, we investigate wave interactions with continuous fractal layers which model geological and variegated structures. Since fractal characteristics of the layers are embedded in the scattered field, they can be retrieved under appropriate conditions. This inversion can be performed in either the frequency or the time domain as desired.

Kim, Y.↗

NASA NTRS1988

Fatigue damage criteria - Matrix, fibers and interfaces of continuous fiber reinforced metal matrix composites

Continuous fiber reinforced metal matrix composites (MMC) are projected for use in high temperature, stiffness critical parts that will be subjected to cyclic loadings. Depending on the relative fatigue behavior of the fiber and matrix, and the interface properties, the failure modes of MMC can be grouped into four catagories: (1) matrix dominated, (2) fiber dominated, (3) self-similar damage growth, and (4) fiber/matrix interfacial failures. These four types of damage are discussed and illustrated by examples. The emphasis is on the fatigue of unnotched laminates.

Johnson, W. S.↗