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NASA NTRS1994

A spectral formalism for computing three-dimensional deformations due to surface loads. 1: Theory

We outline a complete spectral formalism for computing high spatial resolution three-dimensional deformations arising from the surface mass loading of a spherically symmetric planet. The main advantages of the formalism are that all surface mass loads are always described using a consistent mathematical representation and that calculations of deformation fields for various spatial resolutions can be performed by simpley altering the spherical harmonic degree truncation level of the procedure. The latter may be important when incorporating improved observational constraints on a particular surface mass load, when considering potential errors in the computed field associated with mass loading having a spatial scale unresolved by the observational constraints, or when treating a number of global surface mass loads constrained with different spatial resolutions. The advantages do not extend to traditional 'Green's function' approaches which involve surface element discretizations of the global mass loads. Another advantage of the spectral formalism, over the Green's function approach, is that a posteriori analyses of the computed deformation fields are easily performed. In developing the spectral formalism, we consider specific cases where the Earth's mantle is assumed to respond as an elastic, slightly anelastic, or linear viscoelastic medium. In the case of an elastic or slightly anelastic mantle rheology the spectral response equations incorporate frequency dependent Love numbers. The formalism can therefore be used, for example, to compute the potentially resonant deformational response associated with the free core nutation and Chandler wobble eigenfunctions. For completeness, the spectral response equations include both body forces, as arise from the gravitational attraction of the Sun and the Moon, and surface mass loads. In either case, and for both elastic and anelastic mantle rheologies, we outline a pseudo-spectral technique for computing the ocean adjustment associated with the total gravitational perturbation induced by the external forcing. Three-dimensional deformations computed using the usual Love number approach are generally referenced to an origin at the center of mass of the undeformed planet. We derive a spectral technique for transforming the results to an origin located at the center of mass of the deformed planet.

Mitrovica, J. X.↗
NASA NTRS1994

A spectral formalism for computing three-dimensional deformations due to surface loads. 2: Present-day glacial isostatic adjustment

Using a spherically symmetric, self-gravitating, linear viscoelastic Earth model, we predict present-day three-dimensional surface deformation rates and baseline evolutions arising as a consequence of the late Pleistocene glacial cycles. In general, we use realistic models for the space-time geometry of the final late Pleistocene deglaciation event and incorporate a gravitationally self-consistent ocean meltwater redistribution. The predictions of horizontal velocity presented differ significantly, in both their amplitude and their spatial variation, from those presented in earlier analysis of others which adopted simplified models of both the late Pleistocene ice history and the Earth rheology. An important characteristic of our predicted velocity fields is that the melting of the Laurentide ice sheet over Canada is capable of contributing appreciably to the adjustment in Europe. The sensitivity of the predictions to variations in mantle rheology is investigated by considering a number of different Earth models, and by computing appropriate Frechet kernels. These calculations suggest that the sensitivity of the deformations to the Earth's rheology is significant and strongly dependent on the location of the site relative to the ancient ice sheet. The effects on the predictions of three-dimensional deformation rates of altering the ice history or adopting approximate models for the ocean meltwater redistribution have also been considered and found to be important (the former especially so). Finally, for a suite of Earth models we provide predictions of the velocity of a number of baselines in North America and Europe. We find that, in general, both radial and tangential motions contribute significantly to baseline length changes, and that these contributions are a strong function of the Earth model. We have, furthermore, found a set of Earth models which, together with the ICE-3G deglaciation chronology, produce predictions of baseline length changes that are consistent with very long baseline interferometry measurements of baselines within Europe.

Mitrovica, J. X.↗
NASA NTRS1994

A singularity free approach to post glacial rebound calculations

Calculating the post glacial response of a viscoelastic Earth model using the exponential decay normal mode technique leads to intrinsic singularities if viscosity varies continuously as a function of radius. We develop a numerical implementation of the Complex Real Fourier transform (CRFT) method as an accurate and stable procedure to avoid these singularities. Using CRFT, we investigate the response of a set of Maxwell Earth models to surface loading. We find that the effect of expanding a layered viscosity structure into a continuously varying structure is to destroy the modes associated with the boundary between layers. Horizontal motion is more sensitive than vertical motion to the viscosity structure just below the lithosphere. Horizontal motion is less sensitive to the viscosity of the lower mantle than the vertical motion is. When the viscosity increases at 670 km depth by a factor of about 60, the response of the lower mantle is close to its elastic limit. Any further increase of the viscosity contrast at 670 km depth or further increase of viscosity as a continuous function of depth starting from 670 km depth is unlikely to be resolved.

Fang, Ming↗
NASA NTRS1993

State of stress, faulting, and eruption characteristics of large volcanoes on Mars

The formation of a large volcano loads the underlying lithospheric plate and can lead to lithospheric flexure and faulting. In turn, lithospheric deformation affects the stress field beneath and within the volcanic edifice and can influence magma transport. Modeling the interaction of these processes is crucial to an understanding of the history of eruption characteristics and tectonic deformation of large volcanoes. We develop models of time-dependent stress and deformation for the Tharsis volcanoes on Mars. By means of a finite element code, we calculate stresses and displacements due to a volcano-shaped load emplaced on an elastic plate overlying a viscoelastic mantle. Models variously incorporate growth of the volcanic load with time and a detachment between volcano and lithosphere. The models illustrate the manner in which time-dependent stresses induced by lithospheric plate flexure beneath the volcanic load may affect eruption histories, and the derived stress fields can be related to tectonic features on and surrounding Martian volcanoes. As a result of flexure there are three regions where stresses become sufficiently large to cause failure by faulting, according to the Mohr-Coulomb criterion: at the surface of the plate just outward of the volcano, near the base of the elastic lithosphere beneath the center of the volcano, and on the upper flanks of the volcano early in its growth history.

Mcgovern, Patrick J.↗
NASA NTRS1995

Expendable launch vehicle studies

Analytical support studies of expendable launch vehicles concentrate on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed and linearized. The information from LeRC about the grids, masses, and modes is incorporated into the model. The eigenvalues of the plant are analyzed for several modeling factors: utilizing diagonal mass matrix, uniform beam assumption, inclusion of aerodynamics, and the interaction between the aerodynamics and the flexible bending motion. Preliminary PID, LQR, and LQG control designs with sensor and actuator dynamics for this system and simulations are also conducted. The initial analysis for comparison of PD (proportional-derivative) and full state feedback LQR Linear quadratic regulator) shows that the split weighted LQR controller has better performance than that of the PD. In order to meet both the performance and robustness requirements, the H(sub infinity) robust controller for the expendable launch vehicle is developed. The simulation indicates that both the performance and robustness of the H(sub infinity) controller are better than that for the PID and LQG controllers. The modelling and analysis support studies team has continued development of methodology, using eigensensitivity analysis, to solve three classes of discrete eigenvalue equations. In the first class, the matrix elements are non-linear functions of the eigenvector. All non-linear periodic motion can be cast in this form. Here the eigenvector is comprised of the coefficients of complete basis functions spanning the response space and the eigenvalue is the frequency. The second class of eigenvalue problems studied is the quadratic eigenvalue problem. Solutions for linear viscously damped structures or viscoelastic structures can be reduced to this form. Particular attention is paid to Maxwell and Kelvin models. The third class of problems consists of linear eigenvalue problems in which the elements of the mass and stiffness matrices are stochastic. dynamic structural response for which the parameters are given by probabilistic distribution functions, rather than deterministic values, can be cast in this form. Solutions for several problems in each class will be presented.

Bainum, Peter M.↗
NASA NTRS1995

Requirements for energy based constitutive modeling in tire mechanics

The history, requirements, and theoretical basis of a new energy based constitutive model for (rubber) material elasticity, hysteresis, and failure are presented. Energy based elasticity is handled by many constitutive models, both in one dimension and in three dimensions. Conversion of mechanical energy to heat can be modeled with viscoelasticity or as structural hysteresis. We are seeking unification of elasticity, hysteresis, and failure mechanisms such as fatigue and wear. An energy state characterization for failure criteria of (rubber) materials may provide this unification and also help explain the interaction of temperature effects with failure mechanisms which are described as creation of growth of internal crack surface. Improved structural modeling of tires with FEM should result from such a unified constitutive theory. The theory will also guide experimental work and should enable better interpretation of the results of computational stress analyses.

Luchini, John R.↗
NASA NTRS1995

Bend stress relaxation and tensile primary creep of a polycrystalline alpha-SiC fiber

Understanding the thermomechanical behavior (creep and stress relaxation) of ceramic fibers is of both practical and basic interest. On the practical level, ceramic fibers are the reinforcement for ceramic matrix composites which are being developed for use in high temperature applications. It is important to understand and model the total creep of fibers at low strain levels where creep is predominantly in the primary stage. In addition, there are many applications where the component will only be subjected to thermal strains. Therefore, the stress relaxation of composite consituents in such circumstances will be an important factor in composite design and performance. The objective of this paper is to compare and analyze bend stress relaxation and tensile creep data for alpha-SiC fibers produced by the Carborundum Co. (Niagara Falls, NY). This fiber is of current technical interest and is similar in composition to bulk alpha-SiC which has been studied under compressive creep conditions. The temperature, time, and stress dependences will be discussed for the stress relaxation and creep results. In addition, some creep and relaxation recovery experiments were performed in order to understand the complete viscoelastic behavior, i.e. both recoverable and nonrecoverable creep components of these materials. The data will be presented in order to model the deformation behavior and compare relaxation and/or creep behavior for relatively low deformation strain conditions of practical concern. Where applicable, the tensile creep results will be compared to bend stress relaxation data.

Hee Man, Yun↗
NASA NTRS1996

Expendable Launch Vehicle Studies

Analytical support studies of expendable launch vehicles concentrates on the stability of the dynamics during launch especially during or near the region of maximum dynamic pressure. The in-plane linearized dynamic equations of a generic launch vehicle with multiple flexible bending and fuel sloshing modes are developed. The design of a robust LQR controller based on the reduced order system is accomplished using the parameter perturbation technique. The ELV modeling and analysis team has spent the past three years working on the theoretical development and application of sensitivity analysis to solve eigenvalue problems associated with structural dynamics. Specific application areas include stochastic vibrations, viscously damped vibrations and nonlinear dynamics. In stochastic linear vibrations, sensitivity analysis methods have been developed which determined the expectation and variance of the response for given probability density functions of various stochastic parameters. Examples worked include beam vibrations with up to six stochastic parameters; and the eigensensitivity results differ little from those obtained, with much effect, from Monte Carlo techniques. For viscously damped vibrations, eigensensitivity analysis has given excellent results for homogeneous beams, modeled by either quadratic or quartic eigenvalue equations. Specific applications include Kevin and Maxwell-type viscoelastic beams.

Bainum, P. M.↗
NASA NTRS1996

Analysis of Thick Sandwich Shells with Embedded Ceramic Tiles

The Composite Armored Vehicle (CAV) is an advanced technology demonstrator of an all-composite ground combat vehicle. The CAV upper hull is made of a tough light-weight S2-glass/epoxy laminate with embedded ceramic tiles that serve as armor. The tiles are bonded to a rubber mat with a carefully selected, highly viscoelastic adhesive. The integration of armor and structure offers an efficient combination of ballistic protection and structural performance. The analysis of this anisotropic construction, with its inherent discontinuous and periodic nature, however, poses several challenges. The present paper describes a shell-based 'element-layering' technique that properly accounts for these effects and for the concentrated transverse shear flexibility in the rubber mat. One of the most important advantages of the element-layering technique over advanced higher-order elements is that it is based on conventional elements. This advantage allows the models to be portable to other structural analysis codes, a prerequisite in a program that involves the computational facilities of several manufacturers and government laboratories. The element-layering technique was implemented into an auto-layering program that automatically transforms a conventional shell model into a multi-layered model. The effects of tile layer homogenization, tile placement patterns, and tile gap size on the analysis results are described.

Davila, Carlos G.↗
NASA NTRS1996

Magnetospheric Atmospheric X-ray Imaging Experiment (MAXIE)

This report summarizes the activities sponsored by the Office of Naval Research for the Magnetospheric Atmospheric X-ray Imaging Experiment (MAXIE). The MAXIE instrument was developed as a joint activity of Lockheed, The Aerospace Corporation, and the University of Bergen, Norway. Lockheed was responsible for the overall management of the program, interfacing with the appropriate government agencies, the overall electrical and mechanical design, flight software, environmental testing, spacecraft integration activities, on orbit checkout, and data processing activities. The Magnetospheric Atmospheric X-ray Imaging Experiment (MAXIE), the ONR 401 experiment, is the first in a new class of satellite-borne remote sensing instruments. The primary innovation is the ability to obtain rapid, sequential, images with high sensitivity of the earth's X ray aurora from a low altitude polar orbiting satellite. These images can be used to identify dynamic temporal variations in the three-dimensional (energy and position) distribution of electron precipitation into the atmosphere. MAXIE was launched on the TIROS NOAA-13 satellite on 9 August 1993. The experiment performed well during its turn-on sequence; however, the spacecraft bus failed on 21 August 1993. New spacebased technologies successfully used in MAXIE were mixed-mode ASIC microcircuits, a zero torque scanning system with associated viscoelastic damping, a paraffin stow release mechanism, a parallel integrating PHA processor, a low noise Si(Li) sensor telescope, and an advanced thermal cooling system. MAXIE's on orbit operation, control of penetrating particle backgrounds, and scientific data indicated good overall performance.

Imhof, W. L.↗
NASA NTRS1997

Analysis of Impact Induced Damage and its Effect on Structural Integrity of Space Flight Composite Overwrapped Pressure Vessels

The objective of this research work has been to provide analytical background and support to the ongoing experimental program at NASA, White Sands Test Facility, involving testing composite overwrapped pressure vessels (COPV) for impact damage and cyclic pressurization. Preliminary theoretical basis, including the governing equations for a shallow shell subjected to internal pressure, has been established. Effects of the Griffith type cracks on the structural integrity of the cylindrical vessel were evaluated by methods of Fracture Mechanics. The results indicate that the effective mass of the pressure vessel is an important factor influencing the response to impact events. We also have found that the material properties of the target, contained in the constitutive equations of the composite attached to the Aluminum liner, dominate the impact event in the low velocity range, the material properties become less important, while the target mass distribution and the impactor mass become more significant as the velocity of the impactor increases. Therefore, at high-velocity impact it is not only the kinetic energy of the impactor but also its mass which has a significant effect on the dynamics of the event, and consequently on the induced damage. This work also suggests a methodology for an assessment of the rate of loading effects on the degradation of the material toughness associated with a high-velocity impact where the rate effects become significant. To model the rate dependence of the material response a viscoelastic-plastic constitutive equations were assumed, and on this basis predictions are made regarding the rate dependent material resistance curve. Other dynamic phenomena associated with the impact event have been treated in the framework of the Computational Mechanics using the courtesy of Prof. P. Guebelle and his graduate student at University of Illinois at Urbana-Champaign who have an access to a super-fast computer located on their campus. Finally, the guidelines for a follow-up research program are provided in the body of this report. They address three major areas: theoretical research, numerical studies, and further experimental work.

Wnuk, Michael P.↗
NASA NTRS1997

A General Reversible Hereditary Constitutive Model: Application to a Titanium Alloy - Part 2

Given the mathematical framework and specific viscoelastic model in Part 1 our primary goal in this second part is focused on model characterization and assessment for the specific titanium alloy, TIMETAL 21S. The model is motivated by experimental evidence suggesting the presence of significant rate/time effects in the so-called quasilinear, reversible, material response range. An explanation of the various experiments performed and their corresponding results are also included. Finally, model correlations and predictions are presented for a wide temperature range.

Arnold, S. M.↗
NASA NTRS1998

Experimental Spin Testing of Integrally Damped Composite Plates

The experimental behavior of spinning laminated composite pretwisted plates (turbo-fan blade-like) with small (less than 10% by volume) integral viscoelastic damping patches was investigated at NASA-Lewis Research Center. Ten different plate sets were experimentally spin tested and the resulting data was analyzed. The first-four plate sets investigated tailoring patch locations and definitions to damp specific modes on spinning flat graphite/epoxy plates as a function of rotational speed. The remaining six plate sets investigated damping patch size and location on specific modes of pretwisted (30 degrees) graphite/epoxy plates. The results reveal that: (1) significant amount of damping can be added using a small amount of damping material, (2) the damped plates experienced no failures up to the tested 28,000 g's and 750,000 cycles, (3) centrifugal loads caused an increase in bending frequencies and corresponding reductions in bending damping levels that are proportional to the bending stiffness increase, and (4) the centrifugal loads caused a decrease in torsion natural frequency and increase in damping levels of pretwisted composite plates.

Kosmatka, John↗
NASA NTRS1997

A General Reversible Hereditary Constitutive Model: Theoretical Developments - Part 1

Using an internal-variable formalism as a starting point, we describe the viscoelastic extension of a previously-developed viscoplasticity formulation of the complete potential structure type. It is mainly motivated by experimental evidence for the presence of rate/time effects in the so-called quasilinear, reversible, material response range. Several possible generalizations are described, in the general format of hereditary-integral representations for non-equilibrium, stress-type, state variables, both for isotropic as well as anisotropic materials. In particular, thorough discussions are given on the important issues of thermodynamic admissibility requirements for such general descriptions, resulting in a set of explicit mathematical constraints on the associated kernel (relaxation and creep compliance) functions. In addition, a number of explicit, integrated forms are derived, under stress and strain control to facilitate the parametric and qualitative response characteristic studies reported here, as well as to help identify critical factors in the actual experimental characterizations from test data that will be reported in Part II.

Saleeb, A. F.↗
NASA NTRS1998

Chemically Derived Dense Alumina-Zirconia Composites for Improved Mechanical and Wear Erosion Properties

As a result of this funded project high purity Zirconia-Toughened Alumina (ZTA) ceramic powders with and without yttria were produced using metal alkoxide precursors. ZTA ceramic powders with varying volume percents of zirconia were prepared (7, 15, and 22%). Aluminum tri-sec butoxide, zirconium propoxide, and yttrium isopropoxide were the reagents used. Synthesis conditions were varied to control the hydrolysis and the aging conditions for the sol to gel transition. FTIR analysis and rheological characterization were used to follow the structural evolution during the sol to gel transition. The greater extent of hydrolysis and the build-up of structure measured from viscoelastic properties were consistent. Heat treatment was conducted to produce submicron grain fully crystalline ZTA ceramic powders. This improved materials should have enhanced properties such strength, toughness, and wear resistance for advanced structural applications, for example engine components in high technology aerospace applications.

Source record↗
NASA NTRS1998

Global Failure Modes in High Temperature Composite Structures

Composite materials have been considered for many years as the major advance in the construction of energy efficient aerospace structures. Notable advances have been made in understanding the special design considerations that set composites apart from the usual "isotropic" engineering materials such as the metals. As a result, a number of significant engineering designs have been accomplished. However, one shortcoming of the currently favored composites is their relatively unforgiving behavior with respect to failure (brittleness) under seemingly mild impact conditions and large efforts are underway to rectify that situation, much along the lines of introducing thermoplastic matrix materials. Because of their relatively more pronounced (thermo) viscoelastic behavior these materials respond with "toughness" in fracture situations. From the point of view of applications requiring material strength, this property is highly desirable. This feature impacts several important and distinct engineering problems which have been' considered under this grant and cover the 1) effect of impact damage on structural (buckling) stability of composite panels, the 2) effect of time dependence on the progression of buckling instabilities, and the 3) evolution of damage and fracture at generic thickness discontinuities in structures. The latter topic has serious implications for structural stability problems (buckling failure in reinforced shell structures) as well as failure progression in stringer-reinforced shell structures. This grant has dealt with these issues. Polymer "toughness" is usually associated with uncrosslinked or thermo-plastic polymers. But, by comparison with their thermoset counterparts they tend to exhibit more pronounced time dependent material behavior; also, that time dependence can occur at lower temperatures which places restriction in the high temperature use of these "newer and tougher" materials that are not quite so serious with the thermoset matrix materials. From a structural point of view the implications of this material behavior are potentially severe in that structural failure characteristics are no longer readily observed in short term qualification tests so characteristic for aerospace structures built from typical engineering metals.

Knauss, W. G.↗
NASA NTRS1992

Buckling of Thermoviscoelastic Structures Under Temporal and Spatial Temperature Variations

The problem of lateral instability of a viscoelastic in-plane loaded structure is considered in terms of thermorheolgically simple materials. As an example of a generally in-plane loaded structure, we examine the simple column under axial load: Both cyclic loading is considered (with constant or in-phase variable temperature excursions) as well as the case of constant load in the presence of thermal gradients through the thickness of the structure. The latter case involves a continuous movement of the neutral axis from the center to the colder side and then back to the center. In both cases, temperature has a very strong effect on the instability evolution, and under in-phase thermal cycling the critical loads are reduced compared to those at constant temperatures. The primary effect of thermal gradients beyond that of thermally-induced rate accelerations is occasioned by the generation of an "initial imperfection" or "structural bowing." Because the coefficient of thermal expansion tends to be large for many polymeric materials, it it may be necessary to take special care in lay-up design of composite structures intended for use under compressive loads in high-temperature applications. Finally, the implications for the temperature sensitivities of composites to micro-instability (fiber crimping) are also apparent from the results delineated here.

Tsuyuki, Richard↗
NASA NTRS1998

High Strain Rate Deformation Modeling of a Polymer Matrix Composite: Matrix Constitutive Equations - Part 1

Recently applications have exposed polymer matrix composite materials to very high strain rate loading conditions, requiring an ability to understand and predict the material behavior under these extreme conditions. In this first paper of a two part report, background information is presented, along with the constitutive equations which will be used to model the rate dependent nonlinear deformation response of the polymer matrix. Strain rate dependent inelastic constitutive models which were originally developed to model the viscoplastic deformation of metals have been adapted to model the nonlinear viscoelastic deformation of polymers. The modified equations were correlated by analyzing the tensile/ compressive response of both 977-2 toughened epoxy matrix and PEEK thermoplastic matrix over a variety of strain rates. For the cases examined, the modified constitutive equations appear to do an adequate job of modeling the polymer deformation response. A second follow-up paper will describe the implementation of the polymer deformation model into a composite micromechanical model, to allow for the modeling of the nonlinear, rate dependent deformation response of polymer matrix composites.

Goldberg, Robert K.↗