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NASA NTRS1945

The Elastic Constants for Wrought Aluminum Alloys

There are several constants which have been devised as numerical representations of the behavior of metals under the action of loadings which stress the metal within the range of elastic action. Some of these constants, such as Young's modulus of elasticity in tension and compression, shearing modulus of elasticity, and Poisson's ratio, are regularly used in engineering calculations. Precise tests and experience indicate that these elastic constants are practically unaffected by many of the factors which influence the other mechanical properties of materials and that a few careful determinations under properly controlled conditions are more useful and reliable than many determinations made under less favorable conditions. It is the purpose of this paper to outline the methods employed by the Aluminum Research Laboratories for the determination of some of these elastic constants, to list the values that have been determined for some of the wrought aluminum alloys, and to indicate the variations in the values that may be expected for some of the commercial products of these alloys.

ALUMINUM ALLOYS, WROUGHT-ELASTICITY↗
NASA NTRS2006

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Helenbrook, B. T.↗
NASA NTRS2007

Managing Uncertainty Due to a Fundamental Error Source Arising from Scatterer Distribution Complexity in Radar Remote Sensing of Precipitation

The assumption that cloud and rain drops are spatially distributed according to a Poisson distribution within a scattering volume probed by a radar being used to estimate precipitation has represented bedrock theory in establishing 'rules of the game' for pulse averaging--the process needed to beat down noise to an acceptable level in the measurement of radar reflectivity factor. Based on relatively recent observations of 'realistic' spatial distributions of hydrometeor scatterers in a cloudy atmosphere motivates a renewed examination of the consequences of using a too simplified assumption underlying volume scattering--particularly in regards to the standard pulse averaging rule. Our investigation addresses two extremes, simple to complex, insofar as allowed for complexities in an underlying scatterer distribution. It is demonstrated that as the spatial distribution ranges from Poisson (a narrow distribution) to multi-fractal (much broader distribution), uncertainty in a measurement increases if the rule for pulse averaging goes unchanged from its Poisson distribution reference county. [A bounded cascade is used for the multi-fractal distribution, a regularly observed distribution vis-a-vis cloud liquid water content.] The resultant measurement uncertainty leads to a fundamental source of error in the estimation of rain rate from radar measurements, one that has been disregarded since the early 1950s when radar sets first began to be used for rainfall measuring. It is shown how this source of error can be 'managed'--under the assumption that number of data analysis experiments would be carried out, experiments involving pulse-by-pulse measurements obtained from a radar set modified to output individual pulses of reflectivity factor. For practical applications, a new parameter called normalized k-sample intensity invariance is developed to enable defining the required pulse average count according to a preferred degree of uncertainty.

Smith, Eric A.↗
NASA NTRSDate not supplied

Quantifying radiation quality for space relevant radiation types: Fitting excess risk models to outbred mice data

Accurately quantifying the differences in radiation quality between space and terrestrial environments is important for predicting health risks for astronauts.Recently, Edmundson et al. 2020[1] provided valuable new results from out-bred mice linking tumor induction and genetic background aer exposure to low and high-LET radiation. The goal of the current study is to more rigorously estimate a relative biological effectiveness (RBE) factor by leveraging the solid tumor data from Edmundson et al. 2020. Excess relative risk (ERR) models and excess absolute risk (EAR) models were fit using Poisson regression similar to the models that the Radiation Effects Research Foundation uses to fit atomic bomb survivor data. Linear ERR and EAR slopes were simulated usingBayesian analyses, and RBE values were calculated from the ratio of the heavy ion linear slope to the gamma linear slope using the full posterior distribution.

Lori J. Chappell↗
NASA NTRS2005

Characterization of Ice for Return-to-Flight of the Space Shuttle: Soft Ice - Part 2

In support of characterizing ice debris for return-to-flight (RTF) of NASA's space shuttle, we have determined the microstructure, density and compressive strength (at -10 C at approximately 0.3 per second) of porous or soft ice that was produced from both atmospheric water and consolidated snow. The study showed that the atmospheric material was generally composed of a mixture of very fine (0.1 to 0.3 millimeters) and coarser (5 to 10 millimeter) grains, plus air bubbles distributed preferentially within the more finely-grained part of the microstructure. The snow ice was composed of even finer grains (approximately 0.05 millimeters) and contained more pores. Correspondingly, the snow ice was of lower density than the atmospheric ice and both materials were significantly less dense than hard ice. The atmospheric ice was stronger (approximately 3.8 MPa) than the snow ice (approximately 1.9 MPa), but weaker by a factor of 2 to 5 than pore-free hard ice deformed under the same conditions. Zero Values are given for Young's modulus, compressive strength and Poisson's ratio that can be used for modeling soft ice from the external tank (ET).

Schulson, Erland M.↗
NASA NTRS1998

Correlations Between the Cosmic X-Ray and Microwave Backgrounds: Constraints on a Cosmological Constant

In universes with significant curvature or cosmological constant, cosmic microwave background (CMB) anisotropies are created very recently via the Rees-Sciama or integrated Sachs-Wolfe effects. This causes the CMB anisotropies to become partially correlated with the local matter density (z less than 4). We examine the prospects of using the hard (2- 10 keV) X-ray background as a probe of the local density and the measured correlation between the HEAO1 A2 X-ray survey and the 4-year COBE-DMR map to obtain a constraint on the cosmological constant. The 95% confidence level upper limit on the cosmological constant is OMega(sub Lambda) less than or equal to 0.5, assuming that the observed fluctuations in the X-ray map result entirely from large scale structure. (This would also imply that the X-rays trace matter with a bias factor of b(sub x) approx. = 5.6 Omega(sub m, sup 0.53)). This bound is weakened considerably if a large portion of the X-ray fluctuations arise from Poisson noise from unresolved sources. For example, if one assumes that the X-ray bias is b(sub x) = 2, then the 95% confidence level upper limit is weaker, Omega(sub Lambda) less than or equal to 0.7. More stringent limits should be attainable with data from the next generation of CMB and X-ray background maps.

Boughn, S. P.↗
NASA NTRS1987

A numerical method for the solution of three dimensional, incompressible, viscous flows over slender bodies

A marching iterative method for the solution of the three dimensional, incompressibhle, steady and parabolized Navier-Stokes equations is described. The equations are written in primitive variables and discretized in general axisymmetric orthogonal coordinate systems. The coupled set of finite-difference equations are solved without any splitting or factorization errors. Moreover, the continuity equation and the two crossflow momentum equations are exactly satisfied at every step of the iterative process. The solution scheme is equivalent to the solution of one Poisson equation by the Successive Plane Over Relaxation method and has good convergence properties. Other existing solution methods resemble a Jacobi-type iterative scheme and therefore are less efficient. Numerical experiments include the laminar, incompressible flow over prolate spheroids at incidence.

Rosenfeld, Moshe↗
NASA NTRS1989

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two and three dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi↗
NASA NTRS1989

Operator induced multigrid algorithms using semirefinement

A variant of multigrid, based on zebra relaxation, and a new family of restriction/prolongation operators is described. Using zebra relaxation in combination with an operator-induced prolongation leads to fast convergence, since the coarse grid can correct all error components. The resulting algorithms are not only fast, but are also robust, in the sense that the convergence rate is insensitive to the mesh aspect ratio. This is true even though line relaxation is performed in only one direction. Multigrid becomes a direct method if an operator-induced prolongation is used, together with the induced coarse grid operators. Unfortunately, this approach leads to stencils which double in size on each coarser grid. The use of an implicit three point restriction can be used to factor these large stencils, in order to retain the usual five or nine point stencils, while still achieving fast convergence. This algorithm achieves a V-cycle convergence rate of 0.03 on Poisson's equation, using 1.5 zebra sweeps per level, while the convergence rate improves to 0.003 if optimal nine point stencils are used. Numerical results for two- and three-dimensional model problems are presented, together with a two level analysis explaining these results.

Decker, Naomi Henderson↗
NASA NTRSDate not supplied

Evaluating the Feasibility of Data Simulation for Radiation Research: Estimating RBE Values for HZE Radiation

As the drive for deep space exploration intensifies, a comprehensive understanding of the health effects of radiation exposure becomes paramount to the future of human space flight. However, epidemiological data for radiation exposure, particularly to high-energy (HZE) ions, is limited, partially due to the financial and logistical costs of radiation studies. As an alternative, this study aims to assess the viability of data simulation strategies to accurately model potential study parameters prior to utilizing laboratory conditions. This study estimates a relative biological effectiveness (RBE) factor based on the solid tumor data for outbred mice provided by Edmundson et al. 2020. Excess relative risk (ERR) models for HZE-Fe ions and gamma radiation were estimated using Poisson regression with Weibull models to represent the background solid tumor hazard without radiation. RBE values were calculated from the ratio of the heavy ion linear slope to the gamma linear slope. The parameters from these models were then applied to simulate iterations of 300 datasets across HZE-Fe doses of 0.05, 0.2, 0.4, and 0.75 Gy; gamma radiation doses of 0.75, 2, and 3 Gy, as well as an unirradiated control group. Sample size per dose varied from 100-500 mice across simulations (800-4000 mice total per dataset). 1500 datasets were generated total (300 each for sample sizes 800, 1600, 3200, and 4000). For each dataset, ERR per radiation type and RBE for HZE-Fe were calculated. The RBE from the Edmondson data was calculated to be 5.55. The RBEs from the simulated data converged around this value across the increasing sample sizes. For n = 4000, the mean RBE across the 300 datasets was 5.71 (95% CI: 5.47-5.95). These results suggest that RBEs calculated from simulated data are credible. Based on this exploration, data simulation is a viable method of testing radiation studies. It provides a method of testing study assumptions and refining research questions prior to embarking on costly laboratory experiments.

Sneha Mehta↗
NASA NTRS1985

Quantitative analysis of hard X-ray 'footpoint' flares observed by the solar maximum mission

Amplifier gain and collimator hole size variations across the field of view, amplifier/filter efficiency, variations in effective collimator hole size and angular response with photon energy, dead-time, and hard X-ray plate transmission, are among the factors for which instrumental corrections have to be incorporated to effect reliable correction and deconvolution of images from the SMM satellite's Hard X-ray Imaging Spectrometer (HXIS). Attention is given to the substantial Poisson noise in these energy bands. The maximum entropy deconvolution/correction routine developed for establishing the spatial structure reliably inferrable from HXIS data is presented, together with the results of the application of this routine to the three impulsive flares reported by Duijemian et al. (1982) from April 10, May 21, and November 5, 1980.

Mackinnon, A. L.↗
NASA NTRS2006

Estimating Random Errors Due to Shot Noise in Backscatter Lidar Observations

In this paper, we discuss the estimation of random errors due to shot noise in backscatter lidar observations that use either photomultiplier tube (PMT) or avalanche photodiode (APD) detectors. The statistical characteristics of photodetection are reviewed, and photon count distributions of solar background signals and laser backscatter signals are examined using airborne lidar observations at 532 nm using a photon-counting mode APD. Both distributions appear to be Poisson, indicating that the arrival at the photodetector of photons for these signals is a Poisson stochastic process. For Poisson-distributed signals, a proportional, one-to-one relationship is known to exist between the mean of a distribution and its variance. Although the multiplied photocurrent no longer follows a strict Poisson distribution in analog-mode APD and PMT detectors, the proportionality still exists between the mean and the variance of the multiplied photocurrent. We make use of this relationship by introducing the noise scale factor (NSF), which quantifies the constant of proportionality that exists between the root-mean-square of the random noise in a measurement and the square root of the mean signal. Using the NSF to estimate random errors in lidar measurements due to shot noise provides a significant advantage over the conventional error estimation techniques, in that with the NSF uncertainties can be reliably calculated from/for a single data sample. Methods for evaluating the NSF are presented. Algorithms to compute the NSF are developed for the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) lidar and tested using data from the Lidar In-space Technology Experiment (LITE). OCIS Codes:

Liu, Zhaoyan↗
NASA NTRS1977

Transverse shear effects on the stress-intensity factor for a circumferentially cracked, specially orthotropic cylindrical shell

The problem of a cylindrical shell containing a circumferential through crack is considered by taking into account the effect of transverse shear deformations. The formulation is given for a specially orthotropic material within the confines of a linearized shallow shell theory. The particular theory used permits the consideration of all five boundary conditions regarding moment and stress resultants on the crack surface. Consequently, aside from multiplicative constants representing the stress intensity factors, the membrane and bending components of the asymptotic stress fields near the crack tip are found to be identical. The stress intensity factors are calculated separately for a cylinder under a uniform membrane load, and that under a uniform bending moment. Sample results showing the nature of the out-of-plane crack surface displacement and the effect of the Poisson's ratio are presented.

Delale, F.↗
NASA NTRS1989

Two-dimensional high temperature strain measurement system

Two-dimensional optical strain measurements on high temperature test specimens are presented. This two-dimensional capability is implemented through a rotatable sensitive strain axis. Three components of surface strain can be measured automatically, from which the first and second principal strains are calculated. One- and two-dimensional strain measurements at temperatures beyond 750 C with a resolution of 15 microstrain are demonstrated. The system is based on a one-dimensional speckle shift technique. The speckle shift technique makes use of the linear relationship between surface strain and the differential shift of laser speckle patterns in the diffraction plane. Laser speckle is a phase effect that occurs when spatially coherent light interacts with an optically rough surface. Since speckle is generated by any diffusely reflecting surface, no specimen preparation is needed to obtain a good signal. Testing was done at room temperature on a flat specimen of Inconel 600 mounted in a fatigue testing machine. A load cell measured the stress on the specimen before and after acquiring the speckle data. Strain components were measured at 0 C (parallel to the load axis) and at plus or minus 45 C, and plots indicate the calculated values of the first and second principal strains. The measured values of Young's modulus and Poisson's ratio are in good agreement with handbook values. Good linearity of the principal strain moduli at high temperatures indicate precision and stability of the system. However, a systematic error in the high-temperature test setup introduced a scale factor in the slopes of the two-dimensional stress-strain curves. No high temperature effects, however, have been observed to degrade speckle correlation.

Lant, Christian T.↗
NASA NTRS1973

On the effect of orthotropy in a cracked cylindrical shell

A pressurized cylindrical shell containing a longitudinal crack is considered. The shear modulus of the sheet may be evaluated from the measured Young's moduli and the Poisson's ratios rather than being an independent material constant. Two examples, one for a mildly orthotropic (titanium) and the other for a strongly orthotropic (graphite) material approximately satisfying the condition of special orthotropy are given. The results show that the stress intensity factors are rather strongly dependent on the degree of orthotropy.

Erdogan, F.↗
NASA NTRS1974

On the effect of orthotropy in a cracked cylindrical shell

A pressurized cylindrical shell containing a longitudinal crack is considered. It is assumed that the material has a special orthotropy - namely, that the shear modulus of the sheet may be evaluated from the measured Young's moduli and the Poisson's ratios and is not an independent material constant. Two examples, one for a mildly orthotropic (titanium) and the other for a strongly orthotropic (graphite) material approximately satisfying the condition of special orthotropy are given. The results show that the stress intensity factors are rather strongly dependent on the degree of orthotropy.

Erdogan, F.↗
NASA NTRSDate not supplied

Quantifying radiation quality for space relevant radiation types: Fitting excess risk models to three combined HZE-irradiated mouse datasets

Radiation health risks are predominantly derived from low linear energy transfer (LET) terrestrial exposures; however, space radiation includes exposure to high-LET and high-charge, high-energy (HZE) particles. Accurately quantifying the differences in radiation quality between the space and terrestrial radiation environments is important for assessing and predicting health risks for astronauts. Weil et al. 2009 and 2014 used two different inbred mouse strains to study differences in hepatocellular carcinoma (HCC) tumorigenesis after exposures to low- and high- LET radiation[1-2]. More recently, Edmondson et al. 2020 provided valuable new tumor data in outbred mice that were exposed to low- and high-LET radiation[3]. The present study aims to rigorously investigate a relative biological effectiveness (RBE) factor by leveraging the HCC tumor data from the three datasets[1-3]. The three experiments were similarly designed, allowing the raw data to be combined into a pooled dataset to estimate excess relative risk (ERR) and excess absolute risk (EAR) models using Bayesian Poisson regression.

Lori J. Chappell↗
NASA NTRS1976

Seismic investigation of the lunar interior

The velocity and attenuation structure of the moon below the crust is examined using surface events. The moon is divided into an upper mantle and a lower mantle, the division at a depth of about 500 km being marked by a reflector identified on polarization filtered record sections. The upper mantle has a P-wave velocity of about 8 km/sec, a Poisson's ratio of about 0.25 and a Q for P waves of about 5000. This region contains no partial melt and is depleted in volatiles, notably water. The lower mantle has a lower S-wave velocity and probably a lower P-wave velocity than the upper mantle, with a Poisson's ratio of about 0.34. The lower mantle has a Q for P waves of approximately 1500, substantially lower than the upper mantle but probably still high enough to preclude partial melting. The velocity structure and the current value of the moment of inertia factor indicate an increase of density below about 500 km, perhaps due to an increase in iron content. We do not have any information directly pertaining to seismic velocities below 1000 km depth.

Dainty, A. M.↗