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NASA NTRS1973

Prior to failure extension of flaws in a rate sensitive Tresca solid.

Theoretical analysis shows that the amount of slow growth occurring prior to fracture in a plane stress tension specimen subjected to a subcritical stress intensity level is affected by the ductility and rheological sensitivity of the material, the rate of loading, the initial crack size, and the geometrical configuration of the test. These parameters enter the governing nonlinear differential equation which describes the quasi-static crack extension in a rate-sensitive Tresca solid. Examples of numerical integration are given and employed to predict the maximum fracture toughness attained in a plane stress tension test.

Wnuk, M. P.↗

NASA NTRS1973

Magnetospheric electric field measurements during sudden commencements

Direction measurements of electric fields were made in the outer magnetosphere during two sudden commencements in 1972. These measurements were observed with the double floating probe experiment carried aboard the IMP 6 satellite. The initial variations of the measured electric field consisted of an increase from a background of about 1 mv/meter to some 10 mv/meter at about 7 rE (earth radi) and to some 4 mv/meter at 3 rE. These initial electric field disturbances were longitudinal, oriented counter clockwise about an axis pointed north. A solution of Maxwell's third equation is derived for these measurements using a quasi-static version of Mead's model of the magnetosphere B (t). This solution seems to describe well the magnitude and direction of the initial perturbation of the electric field vectors observed during these two sudden commencements. After the initial increase, the measured electric field rings several times with periods of the order of minutes. This observed oscillatory behavior correlates with magnetic observatory records taken near the foot of the magetic field line passing through the satellite.

Aggson, T. L.↗

NASA NTRS1974

User's guide for analysis of finite elastoplastic deformation: The FIPDEF and FIPAX programs for the CDC 6600

Computer programs are presented which provide incremental finite-element analysis capability for problems of quasi-static, finite, elastoplastic deformation in two spatial dimensions (plane strain, plane stress, axisymmetric). Monotonic or cyclic loading of isotropic hardening materials is considered. The only restriction on the form of the stress-strain curve is that the rate of work hardening exceed some small positive value. The user's guide assumes familiarity with both finite-element analysis and FORTRAN IV programming for the CDC 6600. Sufficient information is provided to support problem solving ultization of the programs.

Osias, J. R.↗

NASA NTRS1973

Lunar electromagnetic scattering. II - Magnetic fields and transfer functions for parallel propagation

Magnetic field and transfer function amplitudes, resulting from a transverse electromagnetic wave in the interplanetary medium scattering from the moon and its diamagnetic cavity, are presented. Calculations are made using an asymmetric scattering theory for a spherical two-layer model of the lunar electrical conductivity profile and a nonconducting cylindrical model of the downstream lunar plasma void. Both the field and transfer function magnitudes are calculated as functions of position on the surface of the moon for frequencies relevant to the observations of the lunar surface and orbiting magnetometers. The amplitudes of the magnetic field components on the cavity boundary are also computed as functions of frequency and distance downstream from the lunar limb. Comparisons of the results are made with those of (1) spherically symmetric descriptions of lunar electromagnetic scattering, (2) the quasi-static approximation to asymmetric scattering theory, and (3) observations of the scattering phenomenon by lunar surface and orbiting magnetometers.

Schubert, G.↗

NASA NTRS1975

Bubble-domain circuit wafer evaluation coil set

Coil structures have been designed to permit nondestructive testing of bubble wafers. Wafers can be electrically or optically inspected and operated from quasi-static frequency to maximum device operating frequency.

Chen, T. T.↗

NASA NTRS1973

Dynamic response and stability of a gas-lubricated Rayleigh-step pad

The quasi-static, pressure characteristics of a gas-lubricated thrust bearing with shrouded, Rayleigh-step pads are determined for a time-varying film thickness. The axial response of the thrust bearing to an axial forcing function or an axial rotor disturbance is investigated by treating the gas film as a spring having nonlinear restoring and damping forces. These forces are related to the film thickness by a power relation. The nonlinear equation of motion in the axial mode is solved by the Ritz-Galerkin method as well as the direct, numerical integration. Results of the nonlinear response by both methods are compared with the response based on the linearized equation. Further, the gas-film instability of an infinitely wide Rayleigh step thrust pad is determined by solving the transient Reynolds equation coupled with the equation of the motion of the pad. Results show that the Rayleigh-step geometry is very stable for bearing number A up to 50. The stability threshold is shown to exist only for ultrahigh values of Lambda equal to or greater than 100, where the stability can be achieved by making the mass heavier than the critical mass.

Cheng, C.↗

NASA NTRS1974

On the theory of thermal runaway in the hydrogen envelope of a white dwarf

An evolutionary sequence was calculated for a white dwarf on which a hydrogen rich envelope is assumed to increase with time. The stellar models were computed by integrating numerically the system of stellar structure equations by means of the Henyey method. The accretion of matter was assumed to be quasi-static. Near the point of the chemical discontinuity, a temperature maximum is shown to arise, and hydrogen ignites; a thin shell energy source is formed which is thermally unstable. The resulting thermal runaway was investigated numerically and by means of a simple approximation based on the energy balance in the hydrogen burning shell source.

Redkoborodyy, Y. N.↗

NASA NTRS1975

Electron precipitation in the post midnight sector of the auroral zones

Comprehensive measurements of the angular distributions and energy spectra of electron intensities with electrostatic analyzer arrays on board the low-altitude satellite Injun 5 are reported. These are for the post-midnight sector of the auroral zones during the high-intensity events accompanying magnetic substorms. Precipitation features on closed terrestrial field lines well equatorward of the trapping boundary for energetic electrons with E greater than 45 keV were examined. No evidences of maxima in the differential energy spectra or of strongly field-aligned currents which are indicative of quasi-static electric fields aligned parallel to the geomagnetic field were found. Precipitation of low-energy electron intensities fluctuated on time scales greater than 2 seconds as viewed at the satellite position. This precipitation was characterized by isotropy for all pitch angles outside the atmospheric backscatter cone.

Frank, L. A.↗

NASA NTRS1974

Calculations of the early evolution of Jupiter

The evolution of the protoplanet Jupiter is followed, using a hydrodynamic computer code with radiative energy transport. Jupiter is assumed to have formed as a subcondensation in the primitive solar nebula at a density just high enough for gravitational collapse to occur. The initial state has a density of 0.0015 nanograms per cu cm and a temperature of 43 K; the calculations are carried to an equilibrium state where the central density reaches 0.5 g per cu cm and the central temperature reaches 25,000 K. During the early part of the evolution the object contracts in quasi-hydrostatic equilibrium; later on hydrodynamic collapse occurs, induced by the dissociation of hydrogen molecules. After dissociation is complete, the planet regains hydrostatic equilibrium with a radius of a few times the present value. Further evolution beyond this point is not treated here; however the results are consistent with the existence of a high-luminosity phase shortly after the planet settles into its final quasi-static contraction.-

Bodenheimer, P.↗

NASA NTRS1975

Ionosphere-magnetosphere coupling. II - Electric fields

An attempt is made to fit individual observations and theories into the broader network of magnetosphere-ionosphere-atmosphere couplings as they affect the general behavior of quasi-static electric fields in the magnetosphere and ionosphere. Particular attention is given to high-latitude processes, however, mid-latitude penetration of electric fields of magnetospheric origin during disturbed periods is discussed.

Banks, P. M.↗

NASA NTRS1976

A technique using a nonlinear helicopter model for determining trims and derivatives

A technique is described for determining the trims and quasi-static derivatives of a flight vehicle for use in a linear perturbation model; both the coupled and uncoupled forms of the linear perturbation model are included. Since this technique requires a nonlinear vehicle model, detailed equations with constants and nonlinear functions for the CH-47B tandem rotor helicopter are presented. Tables of trims and derivatives are included for airspeeds between -40 and 160 knots and rates of descent between + or - 10.16 m/sec (+ or - 200 ft/min). As a verification, the calculated and referenced values of comparable trims, derivatives, and linear model poles are shown to have acceptable agreement.

Ostroff, A. J.↗

NASA NTRS1975

Unsteady flow in cavitating turbopumps

Unsteady flow in a cavitating axial inducer pump is analyzed with the help of a simple two-dimensional cascade model. This problem was motivated by a desire to study the effect of unsteady cavitation on the so-called POGO instability in the operation of liquid rocket engines. Here, an important feature is a closed loop coupling between several different modes of oscillation, one of which is due to the basic unsteady characteristics of the cavitation itself. The approaching and leaving flow velocities up- and downstream of the inducer oscillate, and the cavity-blade system participates dynamically with the basic pulsating flow. In the present work, attention is focused on finding a transfer matrix that relates the set of upstream variables to those downstream. This quantity, which is essentially equivalent to cavitation compliance in the quasi-static analyses, is found to be complex and frequency dependent.

Kim, J. H.↗

NASA NTRS1976

Radiation of whistlers by helical electron and proton beams

The feasibility of generating whistlers by means of an array of helical electron and proton beams is investigated. It is found that quasi-static beam-plasma instabilities will play a vital role in limiting the effective coherent length of the beam. The total radiated power for the whistlers is consequently decreased by 2 orders of magnitude below previously predicted levels (Dowden, 1973). A proton beam is shown to be somewhat less efficient than an electron beam for generating whistlers.

Kuo, Y.-Y.↗

NASA NTRS1976

Rock failure analysis by combined thermal weakening and water jet impact

The influence of preheating on the initiation of fracture in rocks subjected to the impingement of a continuous water jet is studied. Preheating the rock is assumed to degrade its mechanical properties and strength in accordance with existing experimental data. The water jet is assumed to place a quasi-static loading on the surface of the rock. The loading is approximated by elementary functions which permit analytic computation of the induced stresses in a rock half-space. The resulting stresses are subsequently coupled with the Griffith criteria for tensile failure to estimate the change, due to heating, in the critical stagnation pressure and velocity of the water jet required to cause failure in the rock.

Nayfeh, A. H.↗

NASA NTRS1976

Analytical comparison of effects of solid-friction and viscous structural damping on panel flutter

A Galerkin modal analysis is presented that accounts for the effects of both solid friction and viscous structural damping on panel flutter, based on unsteady aerodynamic forces from supersonic potential flow. The eigensolutions are made by complex eigenvalue computer routines. Markedly different effects on the flutter boundary of the two types of structural damping are obtained. This result establishes that there is not, in general, an "equivalent viscous" damping for solid-friction damping. For the limiting case of the static-aerodynamic approximation, a substantially different flutter dynamic pressure is obtained for solid friction identically zero compared with solid friction approaching zero as a limit. Use of the quasi-static aerodynamic approximation eliminates that difference.

Cunningham, H. J.↗

NASA NTRS1976

Miniature biaxial strain transducer

A reusable miniature strain transducer for use in the measurement of static or quasi-static, high level, biaxial strain on the surface of test specimens or structures was studied. Two cantilever arms, constructed by machining the material to appropriate flexibility, are self-aligning and constitute the transducing elements of the device. Used in conjunction with strain gages, the device enables testing beyond normal gage limits for high strains and number of load cycles. The device does not require conversion computations since the electrical output of the strain gages is directly proportional to the strain measured.

Hoffman, I. S.↗

NASA NTRS1976

Sensitivity of inelastic response to numerical integration of strain energy

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.

Kamat, M. P.↗

NASA NTRS1977

Crack propagation and arrest in pressurized containers

The problem of crack propagation and arrest in a finite volume cylindrical container filled with pressurized gas is considered. It is assumed that the cylinder contains a symmetrically located longitudinal part-through crack with a relatively small net ligament. The net ligament suddenly ruptures initiating the process of fracture propagation and depressurization in the cylinder. The problem is formulated by making two major assumptions, namely, that the shell problem is quasi-static and the gas dynamics problem is one-dimensional. The problem is reduced to a proper initial value problem by introducing a dynamic fracture criterion which relates the crack acceleration to the difference between a load factor and the corresponding strength parameter. The main results are demonstrated by considering two examples, an aluminum cylinder which may behave in a quasi-brittle manner, and a steel cylinder which undergoes ductile fracture. The results indicate that generally in gas-filled cylinders fracture arrest is not possible unless the material behaves in a ductile manner and the container is relatively long.

Erdogan, F.↗