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A theory for flame spread above a solid fuel is presented. The special case is considered whereby the oxidation is an exothermic surface reaction. The spreading rate is predicted as a function of the thermochemical properties, fuel-bed thickness, and convective velocity. Also, the theory predicts temperature, mass fraction, and heat flux as a function of position.
Simulation of composites degradation due to aging are described. Laminate geometry, material properties, and matrix degradation states are specified as functions of position and time. Matrix shrinkage and property changes are modeled as functions of the degradation states. Aging effects at the laminate, ply, and micro levels are evaluated, to determine failure of any kind. The results obtained show substantial ply stress built up as a result of aging accompanied by comparable laminate strength degradation in matrix dominated composite strengths.
Sense lines are used in pressure measurements to passively transmit information from hostile environments to areas where transducers can be used. The transfer function of a sense line can be used to obtain information about the measured environment from the protected sensor. Several properties of this transfer function are examined, including frequency dependence, Helmholtz resonance, and time of flight delay.
The research results described in this paper presents a new understanding of the behavior of fatigue crack growth in the threshold region. It is believed by some crack growth experts that the ASTM load shedding test method does not produce true or valid threshold properties. The concern involves the observed fanning of threshold region da/dN data plots for some materials in which the low R-ratio data fans out or away from the high R-ratio data. This data fanning or elevation of threshold values is obviously caused by an increase in crack closure in the low R-ratio tested specimens. This increase in crack closure is assumed by some investigators to be caused by a plastic wake on the crack surfaces that was created during the load shedding test phase. This study shows that the increase in crack closure is the result of an extensive occurrence of crack bifurcation behavior in some materials, particularly in aluminum alloys, when the crack tip cyclic yield zone size becomes less than the grain size of the alloy. This behavior is related to the high stacking fault energy (SFE) property of aluminum alloys which results in easier slip characteristics. Therefore, the particular fanning behavior in aluminum alloys is a function of intrinsic dislocation property of the materials and that the fanned data represents valid material properties. However, for corrosion sensitive steel alloys used in this study the fanning was caused by a build-up of iron oxide at the crack tip from fretting corrosion.
This paper describes the results of a research program conducted to improve the understanding of fatigue crack growth rate behavior in the threshold growth rate region and to answer a question on the validity of threshold region test data. The validity question relates to the view held by some experimentalists that using the ASTM load shedding test method does not produce valid threshold test results and material properties. The question involves the fanning behavior observed in threshold region of da/dN plots for some materials in which the low R-ratio data fans out from the high R-ratio data. This fanning behavior or elevation of threshold values in the low R-ratio tests is generally assumed to be caused by an increase in crack closure in the low R-ratio tests. Also, the increase in crack closure is assumed by some experimentalists to result from using the ASTM load shedding test procedure. The belief is that this procedure induces load history effects which cause remote closure from plasticity and/or roughness changes in the surface morphology. However, experimental studies performed by the authors have shown that the increase in crack closure is a result of extensive crack tip bifurcations that can occur in some materials, particularly in aluminum alloys, when the crack tip cyclic yield zone size becomes less than the grain size of the alloy. This behavior is related to the high stacking fault energy (SFE) property of aluminum alloys which results in easier slip characteristics. Therefore, the fanning behavior which occurs in aluminum alloys is a function of intrinsic dislocation property of the alloy, and therefore, the fanned data does represent the true threshold properties of the material. However, for the corrosion sensitive steel alloys tested in laboratory air, the occurrence of fanning results from fretting corrosion at the crack tips, and these results should not be considered to be representative of valid threshold properties because the fanning is eliminated when testing is performed in dry air.
The fatigue lives of modem powder metallurgy disk alloys are influenced by variabilities in alloy microstructure and mechanical properties. These properties can vary as functions of variables the different steps of materials/component processing: powder atomization, consolidation, extrusion, forging, heat treating, and machining. It is important to understand the relationship between the statistical variations in life and these variables, as well as the change in life distribution due to changes in fatigue loading conditions. The objective of this study was to investigate these relationships in a nickel-base disk superalloy, U720, produced using powder metallurgy processing. Multiple strain-controlled fatigue tests were performed at 538 C (1000 F) at limited sets of test conditions. Analyses were performed to: (1) assess variations of microstructure, mechanical properties, and LCF failure initiation sites as functions of disk processing and loading conditions; and (2) compare mean and minimum fatigue life predictions using different approaches for modeling the data from assorted test conditions. Significant variations in life were observed as functions of the disk processing variables evaluated. However, the lives of all specimens could still be combined and modeled together. The failure initiation sites for tests performed at a strain ratio R(sub epsilon) = epsilon(sub min)/epsilon(sub max) of 0 were different from those in tests at a strain ratio of -1. An approach could still be applied to account for the differences in mean and maximum stresses and strains. This allowed the data in tests of various conditions to be combined for more robust statistical estimates of mean and minimum lives.
The analysis of a passive heterodyne receiver with respect to its imaging performance (transfer function) and its heterodyne efficiency shows departures from the results which are obtained in strictly coherent or incoherent imaging systems. The cascading property of modulation transfer function analysis must be carefully applied, since the coherent transfer function of the optical receiver and that due to the local oscillator-detector combination are not separable but are related by the convolution of their products. Application of these results to a spacelab-type optical heterodyne receiver shows that resolutions of the order of 1.5 to 2.0 km are possible for worst-case type orbital scenarios. In addition to an analysis of the derogatory effects of sampling (aliasing) a comparison of obscured-type receivers (e.g., Cassegrains) with unobscured receivers shows that both resolution and efficiency are severly degraded in an obscured-type receiver and, consequently, should not be used for passive heterodyne detection schemes.
This report primarily identifies a collection of relevant and necessary evidence for assurance of machine learnt components (MLCs)—also known as learning-enabled components—integrated into aircraft systems, and gives preliminary suggestions on the elements of a certification process that invoke the identified evidence. The main focus is on feedforward neural networks that are static and trained offline through supervised learning. A brief background on the generic elements of the lifecycle of an MLC is given to contextualize the assurance considerations and, consequently, the evidence that is relevant and necessary to support certification. At the level of an MLC, those considerations relate to: (i) the consistency and correctness of MLC contributions to system functions in the context of a validated functional intent; and (ii) the absence of MLC contributions to aircraft-level failure conditions. At an ML model level, confidence in model and data properties contribute to assurance of the containing MLC, in particular: (a) generalizability and robustness of models, in the presence of inputs not previously seen during training, disturbances to inputs, and unexpected inputs; and (b) valid data, i.e., data that are at least representative, relevant, complete, and accurate. Evidence for the above span the elements of the ML lifecycle, and includes, at a minimum, lifecycle artifacts that pertain to: (1) properties of requirements capturing functional intent, safety constraints, and aspects of the intended use and operating environment; (2) model performance, model complexity and design, and algorithm choice; (3) achievement of required performance at the levels of a trained model during model development, a trained model after model development is complete, and a trained model that is transformed into an executable equivalent; (4) model implementation aspects necessary for transforming a trained model into the executable equivalent; (5) integration of the executable trained model into the containing MLC, and eventually the larger system; and, (6) lastly, the verification and validation (V&V) of each of the above. Such V&V lifecycle artifacts themselves include: aspects of coverage, e.g., of various levels of requirements by the input space of the model and the data; traceability (where applicable); application of formal methods for property specification, analysis, and checking. Examples of evidence generation methods and tools further ground the discussion on what constitutes evidence, and the contribution to assurance during certification. The identified assurance considerations and supporting evidence is not a comprehensive set. Additionally, neither what should be considered as sufficient evidence relative to the assigned criticality of an MLC, nor how criticality ought to be determined and adjusted, have been considered in this report. However, suggestions are made for potential activities of the ML lifecycle that are aimed at providing confidence that an MLC can be relied upon when integrated into its containing (aircraft) system. Those activities are proposed as candidate elements of a certification process for MLCs. The main purpose of this report to inform regulatory guidance and consensus standards that may be used to meet the safety intent of the applicable regulations.
A random process is formed by the product of a local Gaussian process and a random amplitude process, and the sum of that product with an independent mean value process. The mathematical properties of the resulting process are developed, including the first and second order properties and the characteristic function of general order. An approximate method for the analysis of the response of linear dynamic systems to the process is developed. The transition properties of the process are also examined.
The physical mechanisms of excess attenuation are analyzed on the basis of a one-dimensional time-independent model of propagation in a random medium. Attenuation is regarded as the rate of decrease in the mean intensity and the mean energy flux within a propagation range. A source function is assumed to be determinate, appropriate statistical properties are chosen for the sound speed, and specified statistical properties are found for the wave functions, i.e., the mean intensity and the mean energy flux. The medium is considered to be weakly homogeneous, and expansions are developed for the intensity and mean energy flux, along with an attenuation coefficient in two parts, the second of which defines the excess attenuation. The mean radiated power is defined, and backscattering by the random inhomogeneities in the medium is modeled as redistributing the mean intensity and energy flux, with a resultant decay which occurs more quickly than with randomness.
Sol-gel derived silica aerogels are attractive candidates for many unique thermal, optical, catalytic, and chemical applications because of their low density and high mesoporosity. However, their inherent fragility has restricted use of aerogel monoliths to applications where they are not subject to any load. We have previously reported cross-linking the mesoporous silica structure of aerogels with di-isocyanates, styrenes or epoxies reacting with amine decorated silica surfaces. These approaches have been shown to significantly increase the strength of aerogels with only a small effect on density or porosity. Though density is a prime predictor of properties such as strength and thermal conductivity for aerogels, it is becoming clear from previous studies that varying the silica backbone and size of the polymer cross-link independently can give rise to combinations of properties which cannot be predicted from density alone. Herein, we examine the effects of four processing parameters for producing this type of polymer cross-linked aerogel on properties of the resulting monoliths. We focus on the results of C-13 CP-MAS NMR which gives insight to the size and structure of polymer cross-link present in the monoliths, and relates the size of the cross-links to microstructure, mechanical properties and other characteristics of the materials obtained.
Sol-gel derived silica aerogels are attractive candidates for many unique thermal, optical, catalytic, and chemical applications because of their low density and high mesoporosity. However, their inherent fragility has restricted use of aerogel monoliths to applications where they are not subject to any load. We have previously reported cross-linking the mesoporous silica structure of aerogels with di-isocyanates, styrenes or epoxies reacting with amine decorated silica surfaces. These approaches have been shown to significantly increase the strength of aerogels with only a small effect on density or porosity. Though density is a prime predictor of properties such as strength and thermal conductivity for aerogels, it is becoming clear from previous studies that varying the silica backbone and size of the polymer cross-link independently can give rise to combinations of properties which cannot be predicted from density alone. Herein, we examine the effects of four processing parameters for producing this type of polymer cross-linked aerogel on properties of the resulting monoliths. We focus on the results of 13C CP-MAS NMR which gives insight to the size and structure of polymer cross-link present in the monoliths, and relates the size of the cross-links to microstructure, mechanical properties and other characteristics of the materials obtained.
The technical function of numerous engineering systems - such as vehicles, machines, and instruments - depends on the processes of motion and on the surface systems. Many processes in nature and technology depend on the motion and dynamic behavior of solids, liquids, and gases. Smart surface systems are essential because of the recent technological push toward higher speeds, loads, and operating temperatures; longer life; lighter weight and smaller size (including nanotechnology); and harsh environments in mechanical, mechatronic, and biomechanical systems. If proper attention is not given to surface systems, then vehicles, machines, instruments, and other technical systems could have short lives, consume excessive energy, experience breakdowns, result in liabilities, and fail to accomplish their missions. Surface systems strongly affect our national economy and our lifestyles. At the NASA Glenn Research Center, we believe that proper attention to surface systems, especially in education, research, and application, could lead to economic savings of between 1.3 and 1.6 percent of the gross domestic product. Wear coatings and surface systems continue to experience rapid growth as new coating and surface engineering technologies are discovered, more cost-effective coating and surface engineering solutions are developed, and marketers aggressively pursue, uncover, and exploit new applications for engineered surface systems in cutting tools and wear components. Wear coatings and smart surface systems have been used widely in industrial, consumer, automotive, aerospace, and biomedical applications. This presentation expresses the author's views of and insights into smart surface systems in wear coatings. A revolution is taking place in carbon science and technology. Diamond, an allotrope of carbon, joins graphite, fullerenes, and nanotubes as its major pure carbon structures. It has a unique combination of extreme properties: hardness and abrasion resistance; adhesion and friction; thermal conductivity; chemical and thermal inertness; corrosion and wear resistance; radiation resistance and biocompatibility; electronic, acoustic, and electrochemical characteristics; and environmental compatibility. These properties make diamond attractive for a wide range of diverse applications. In particular, chemical-vapor-deposited (CVD) diamond coatings offer a broad potential, since size and cost are not as limiting. The production of large, superhard diamond films or sheets at low cost make designer materials possible. This presentation is divided into two sections: properties and applications of hard coatings. The first section is concerned with the fundamental properties of the surfaces of CVD diamonds and related materials. The surface properties of hard coatings with favorable coefficients of friction (less than or equal to 0.1) and dimensional wear coefficients (less than or equal to 10(exp -6) cubic millimeters/N.m) in specific environments are discussed. The second section is devoted to applications. Examples of actual, successful applications and of potential challenging applications of the coatings.such as CVD diamond, diamondlike carbon, and cubic boron nitride-are described. Cutting tools coated with CVD diamond are of immediate commercial interest. Other applications, such as microelectromechanical systems (MEMS), valves, and bearings of CVD diamond, are being developed, but at a slow pace. There is a continually growing interest in commercializing diamondlike carbon for wear parts applications, such as biomedical parts and implants, forming dies, transport guides, magnetic tapes and disks, valves, and gears. Cubic boron nitride films are receiving attention because they can be used on tools to machine ferrous materials or on wear parts in sliding contact with ferrous materials.
Multiple scattering theory (MST) combined with density functional theory (DFT) allows to predict properties of chemically disordered materials from the first principles. However, such predictions often suffer from the systematic errors, which depend on crystal geometry. Each computed property of a particular crystal structure typically has a relatively small random error and a larger systematic error. Cancellation of systematic errors allows more accurate predictions. We propose a computational methodology based on the subtraction of the systematic errors in MST. To exemplify it, we apply it to the precipitated alloys. Considering precipitation strengthening in Ni superalloys, we compute the relative enthalpies of the competing Ni_3(Al_{1-x}Ti_x)_1 crystal structures with a chemical disorder on the Al+Ti sublattice. Such predicted composition-structure-property dependencies are useful for the guided design of the next-generation alloys with improved strength. Our predictions are validated by comparison with the results of other DFT methods (having a higher computational cost) and with experiment.
A simple power law model consisting of a single spectral index, sigma(sub 2), is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index sigma(sub 2) greater than sigma(sub 1) above E(sub k). The maximum likelihood (ML) procedure was developed for estimating the single parameter sigma(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (Pl) consistency (asymptotically unbiased), (P2) efficiency (asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only be ascertained by calculating the CRB for an assumed energy spectrum- detector response function combination, which can be quite formidable in practice. However, the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are stained in practice are investigated.
A simple power law model consisting of a single spectral index, a is believed to be an adequate description of the galactic cosmic-ray (GCR) proton flux at energies below 10(exp 13) eV, with a transition at the knee energy, E(sub k), to a steeper spectral index alpha(sub 2) greater than alpha(sub 1) above E(sub k). The Maximum likelihood (ML) procedure was developed for estimating the single parameter alpha(sub 1) of a simple power law energy spectrum and generalized to estimate the three spectral parameters of the broken power law energy spectrum from simulated detector responses and real cosmic-ray data. The statistical properties of the ML estimator were investigated and shown to have the three desirable properties: (P1) consistency (asymptotically unbiased). (P2) efficiency asymptotically attains the Cramer-Rao minimum variance bound), and (P3) asymptotically normally distributed, under a wide range of potential detector response functions. Attainment of these properties necessarily implies that the ML estimation procedure provides the best unbiased estimator possible. While simulation studies can easily determine if a given estimation procedure provides an unbiased estimate of the spectra information, and whether or not the estimator is approximately normally distributed, attainment of the Cramer-Rao bound (CRB) can only he ascertained by calculating the CRB for an assumed energy spectrum-detector response function combination, which can be quite formidable in practice. However. the effort in calculating the CRB is very worthwhile because it provides the necessary means to compare the efficiency of competing estimation techniques and, furthermore, provides a stopping rule in the search for the best unbiased estimator. Consequently, the CRB for both the simple and broken power law energy spectra are derived herein and the conditions under which they are attained in practice are investigated. The ML technique is then extended to estimate spectra information from an arbitrary number of astrophysics data sets produced by vastly different science instruments. This theory and its successful implementation will facilitate the interpretation of spectral information from multiple astrophysics missions and thereby permit the derivation of superior spectral parameter estimates based on the combination of data sets.
Stability theorem based on Liapunov function, and using invariance property of limit sets of solutions to differential equations
A class of nonideal solutions is defined by constructing a function to represent the composition dependence of thermodynamic properties for members of the class, and some properties of these solutions are studied. The constructed function has several useful features: (1) its parameters occur linearly; (2) it contains a logarithmic singularity in the dilute solution region and contains ideal solutions and regular solutions as special cases; and (3) it is applicable to N-ary systems and reduces to M-ary systems (M or = N) in a form-invariant manner.