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205 records · Page 12

Numerical Simulations of Single and Multiple Scattering by Fractal Ice Clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4<=R<=10 cm and fractal dimensions D(sub f) 2.5 and 3. We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D(sub f) 2.5, but the differences can increase somewhat for D(sub f)3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.

Dlugach, Janna M.↗

Bidirectional Reflectance of a Macroscopically Flat, High-Albedo Particulate Surface: An Efficient Radiative Transfer Solution and Applications to Regoliths

Many remote sensing applications rely on accurate knowledge of the bidirectional reflection function (BRF) of surfaces composed of discrete, randomly positioned scattering particles. Theoretical computations of BRFs for plane-parallel particulate layers are usually reduced to solving the radiative transfer equation (RTE) using one of existing exact or approximate techniques. Since semi-empirical approximate approaches are notorious for their low accuracy, violation of the energy conservation law, and ability to produce unphysical results, the use of numerically exact solutions of RTE has gained justified popularity. For example, the computation of BRFs for macroscopically flat particulate surfaces in many geophysical publications is based on the adding-doubling (AD) and discrete ordinate (DO) methods. A further saving of computer resources can be achieved by using a more efficient technique to solve the plane-parallel RTE than the AD and DO methods. Since many natural particulate surfaces can be well represented by the model of an optically semi-infinite, homogeneous scattering layer, one can find the BRF directly by solving the Ambartsumian's nonlinear integral equation using a simple iterative technique. In this way, the computation of the internal radiation field is avoided and the computer code becomes highly efficient and very accurate and compact. Furthermore, the BRF thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. In this paper, we discuss numerical aspects and the computer implementation of this technique, examine the applicability of the Henyey-Greenstein phase function and the sigma-Eddington approximation in BRF and flux calculations, and describe sample applications demonstrating the potential effect of particle shape on the bidirectional reflectance of flat regolith surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web, and can be applied to a wide range of remote sensing problems. BRF computations for undulated (macroscopically rough) surfaces are more complicated and often rely on time consuming Monte Carlo procedures. This approach is especially inefficient for optically thick, weakly absorbing media (e.g., snow and desert surfaces at visible wavelengths since a photon may undergo many internal scattering events before it exists the medium or is absorbed. However, undulated surfaces can often be represented as collections of locally flat tilted facets characterized by the BRF found from the traditional plane parallel RTE. In this way the MOnte Carlo procedure could be used only to evaluate the effects of surface shadowing and multiple surface reflections, thereby bypassing the time-consuming ray tracing inside the medium and providing a great savings of CPU time.

Mishchenko, Michael I.↗

Simulated impact damage in a thick graphite/epoxy laminate using spherical indenters

A study was made to determine the extent of fiber damage caused by low-velocity impact of spherical impactors to a very thick graphite/epoxy laminate. The laminate was cut from a filament wound case being developed for the Space Shuttle solid rocket motors. The case was wound using a wet process with AS4W graphite fiber and HBRF-55A epoxy. Impacts were simulated under quasi-static conditions by pressing hemispherically shaped indenters against the laminate at different locations. The contact force and indenter diameter were varied from location to location. The forces were chosen for each indenter diameter to produce contact pressures below and above that required to initiate damage. After the forces were applied, the laminate was cut into smaller pieces so that each piece contained a test site. The pieces were then deplied and the individual plies examined to determine the extent of fiber damage. Broken fibers were found in the outer layers directly beneath the contact site. The locus of broken fibers in each layer resembled a crack normal to the direction of the fibers. The maximum length and depth of the cracks increased with increasing contact pressure and indenter diameter. The internal stresses in the laminate were calculated using Hertz's law and Love's solution for pressure applied on part of the boundary of a semi-infinite body. The maximum length and depth of the cracks were predicted using a maximum shear stress criterion. Predictions and measurements were in good agreement.

Poe, C. C., Jr.↗

Retrievals of Profiles of Fine And Coarse Aerosols Using Lidar And Radiometric Space Measurements

In couple of years we expect the launch of the CALIPSO lidar spaceborne mission designed to observe aerosols and clouds. CALIPSO will collect profiles of the lidar attenuated backscattering coefficients in two spectral wavelengths (0.53 and 1.06 microns). Observations are provided along the track of the satellite around the globe from pole to pole. The attenuated backscattering coefficients are sensitive to the vertical distribution of aerosol particles, their shape and size. However the information is insufficient to be mapped into unique aerosol physical properties and vertical distribution. Infinite number of physical solutions can reconstruct the same two wavelength backscattered profile measured from space. CALIPSO will fly in formation with the Aqua satellite and the MODIS spectro-radiometer on board. Spectral radiances measured by MODIS in six channels between 0.55 and 2.13 microns simultaneously with the CALIPSO observations can constrain the solutions and resolve this ambiguity, albeit under some assumptions. In this paper we describe the inversion method and apply it to aircraft lidar and MODIS data collected over a dust storm off the coast of West Africa during the SHADE experiment. It is shown that the product of the single scattering albedo, omega, and the phase function, P, for backscattering can be retrieved from the synergism between measurements avoiding a priori hypotheses required for inverting lidar measurements alone. The resultant value of (omega)P(180 deg.) = 0.016/sr are significantly different from what is expected using Mie theory, but are in good agreement with recent results obtained from lidar observations of dust episodes. The inversion is robust in the presence of noise of 10% and 20% in the lidar signal in the 0.53 and 1.06 pm channels respectively. Calibration errors of the lidar of 5 to 10% can cause an error in optical thickness of 20 to 40% respectively in the tested cases. The lidar calibration errors cause degradation in the ability to fit the MODIS data. Therefore the MODIS measurements can be used to identify the calibration problem and correct for it. The CALIPSO-MODIS measurements of the profiles of fine and coarse aerosols, together with CALIPSO measurements of clouds vertical distribution, is expected to be critically important in understanding aerosol transport across continents and political boundaries, and to study aerosol-cloud interaction and its effect on precipitation and global forcing of climate.

Kaufman, Yoram↗

Development of Additively Manufactured Complex Tools for Autoclave Cure Composites

IACMI Project 4.9, Tooling for Composites with Washout Features Produced by Additive Manufacturing, assembled a team including the industry lead, Ability Composites, NREL and Colorado State University (CSU). Ability Composites had originally expressed interest in alternate methods of producing tooling for composite parts. In follow-up discussions, it became clear that one of the bigger tooling challenges revolved around small production volume composite parts that were tooled on washout material due to the complex geometry. To build an understanding of the potential, both from a technology and a cost perspective, for replacing conventional washout tooling with 3D printed thermoplastic tooling, a number of commercially available dissolvable FDM printing materials were evaluated, leading to tooling representative of commercial articles of interest to Ability Composites. Ultimately, Ability Composites was able to directly compare autoclave processed prepreg composite parts produced on conventional washout tooling to composite parts molded on 3D printed dissolvable tooling produced at CSU. Small, laboratory test specimens were developed to investigate the structural performance of the candidate materials under autoclave processing conditions, which were nominally 121 °C (250 °F) and 345 kPa (50 psi). In addition, several internal structural configurations (infills) were evaluated under autoclave conditions using model materials. The results of these tests indicated that two materials, Stratasys ST 130 and Infinite Materials Solutions Aquasys 180 (AQ 180), were the best candidates, given the specified autoclave processing conditions. ST-130 was slightly more robust than AQ-180; however, the AQ-180 was carried forward as it was dissolvable in water, not requiring the basic solution needed to dissolve ST-130. Based on the preliminary material and 3D printed structures evaluations, larger tools with a truncated square pyramid geometry were created to produce prepreg composite test articles for 3D printed dissolvable tool evaluation under standard autoclave fabrication conditions. Two tools were manufactured using ST-130 and one tool using traditional ceramic washout tooling media. The tools were evaluated for geometric fidelity and surface roughness changes before and after carbon fiber/epoxy prepreg composites were manufactured on the tooling. The autoclave processing did not impact the geometry significantly and was completed at 121 °C and 345 kPa, indicating satisfactory tool performance. The results from surface roughness testing of both the resulting composite and the associated tooling indicated that an adequate surface resulted without the need for a surface sealing step, as was required for the conventional washout tooling. Based on results of the truncated pyramid tests as a basis, ST-130, AQ-120 and AQ-180 materials were carried forward to the tool geometry of interest to Ability Composites. These hollow rectangular bent ducts, which were complex in nature and not extractable after cure, were used to understand the impacts of tool material and thickness. One ST-130 tool was produced as a partially solid part, with an enclosed 40% dense infill region to reduce weight and material use. This was the same approach evaluated in the truncated pyramid portion of the study. This tool was to be envelope vacuum bagged and directly compared to a monolithic tool of conventional washout material. The traditional monolithic ceramic tool was manufactured by Ability composites using CNC-based subtractive methods. An additional five dissolvable polymer tools, manufactured from ST-130, AQ-120, and AQ-180, using a hollow design were 3D printed and used to produce carbon fiber/epoxy composite evaluation articles. These hollow dissolvable tools were expected to be less influenced by the autoclave conditions as the wall was solid and vacuum bagging was inside and outside the tool. This alternative geometry was also evaluated as an option in techno-economic modeling. Print times were reduced from in excess of 3 days to under 30 hours, while surface quality and and tool integrity were substantially improved in the transition from the partially solid tool to the hollow tooling concept. Ability Composites produced autoclave-cured prepreg ducts on each of these tools. The autoclave conditions utilized were more severe than those of the initial trials, reaching temperatures of 160 °C and a pressure of 414 kPa. Under these conditions, the partially solid 3D printed tool with skin and 40% dense infill crushed significantly; however, the thicker ST-130 hollow tool showed good promise, deforming only slightly. The thinner hollow tool walls were unsuccessful as were the other materials. Overall, the hollow tool manufacturing process saved significant amounts of time and material in manufacturing as compared to the solid ducts and produced composite surface quality improvements compared to the traditional washout tooling. The TEM was developed to allow direct comparisons between conventional washout tool manufacturing processes and those developed at CSU. It also allowed for two separate 3D printed tool geometries to be analyzed and compared. In this case, the square bent duct tool geometry was determined to be representative of common washout tools. This geometry was compared with a scaled-up version of it to assess differences in the two manufacturing processes based on tool size. The model was developed to make use of user input in the form of geometry details, process steps, manufacturing parameters, bulk material costs, capital equipment costs, and general costs to calculate overall labor, material, capital equipment, and energy costs per manufactured tool for the conventional and additive manufacturing processes for the two representative geometries. It was also able to estimate step-by-step process times for the manufacturing process and geometries. Based on significant input from Ability Composites and CSU from their knowledge gained from hands-on manufacturing of the 3D printed bent duct tool geometry, costs and process times were calculated for the two manufacturing processes. Results showed that the additive manufacturing techniques developed at CSU can substantially reduce the costs of tool manufacturing by reducing labor times and material usage. This is because additive manufacturing is a relatively hands-off process and allows for the tool design to be optimized to reduce material usage. The disadvantage, however, is that process times for additive manufacturing are significantly longer. The three-dimensional (3D) printing process is slow if tight tolerances are required, but the analysis did show that print times could be reduced with the hollow tool geometry. Also, further advances in additive manufacturing could expedite the process. Costs and process times for the tool washout process were calculated separately. They showed that costs are relatively insignificant when compared to the overall tool manufacturing processes, but with increases in tool size, costs for the conventional manufacturing approach are larger than for additive manufacturing. Again, the washout process for conventional tools is very hands-on, whereas for additively manufactured tools the print medium is dissolved in an automated detergent bath at the sacrifice of process time. The analysis showed that optimizing the additively manufactured tools may also reduce washout times. Overall, Project 4.9 demonstrated that commercially available dissolvable 3D printing materials exist that can be used to produce dissolvable tooling capable of surviving prepreg composites fabrication under autoclave conditions of 121 °C (250 °F) and 345 kPa (50 psi). An alternative hollow dissolvable tool design was developed which was structurally superior to the initial concept and was cost and time effective versus conventional washout tooling. The 3D printed sacrificial tool required no added surface sealing steps prior to composite part layup and cure, offering a significant advantage over the porous conventional washout tooling.

36 MATERIALS SCIENCE↗

Application of Powder Diffraction Methods to the Analysis of the Atomic Structure of Nanocrystals: The Concept of the Apparent Lattice Parameter (ALP)

The applicability of standard methods of elaboration of powder diffraction data for determination of the structure of nano-size crystallites is analysed. Based on our theoretical calculations of powder diffraction data we show, that the assumption of the infinite crystal lattice for nanocrystals smaller than 20 nm in size is not justified. Application of conventional tools developed for elaboration of powder diffraction data, like the Rietveld method, may lead to erroneous interpretation of the experimental results. An alternate evaluation of diffraction data of nanoparticles, based on the so-called 'apparent lattice parameter' (alp) is introduced. We assume a model of nanocrystal having a grain core with well-defined crystal structure, surrounded by a surface shell with the atomic structure similar to that of the core but being under a strain (compressive or tensile). The two structural components, the core and the shell, form essentially a composite crystal with interfering, inseparable diffraction properties. Because the structure of such a nanocrystal is not uniform, it defies the basic definitions of an unambiguous crystallographic phase. Consequently, a set of lattice parameters used for characterization of simple crystal phases is insufficient for a proper description of the complex structure of nanocrystals. We developed a method of evaluation of powder diffraction data of nanocrystals, which refers to a core-shell model and is based on the 'apparent lattice parameter' methodology. For a given diffraction pattem, the alp values are calculated for every individual Bragg reflection. For nanocrystals the alp values depend on the diffraction vector Q. By modeling different a0tomic structures of nanocrystals and calculating theoretically corresponding diffraction patterns using the Debye functions we showed, that alp-Q plots show characteristic shapes which can be used for evaluation of the atomic structure of the core-shell system. We show, that using a simple model of a nanocrystal with spherical shape and centro-symmetric strain at the surface shell we obtain theoretical alp-Q values which match very well the alp-Q plots determined experimentally for Sic, GaN, and diamond nanopowders. The theoretical models are defined by the lattice parameter of the grain core, thickness of the surface shell, and the magnitude and distribution of the strain field in the surface shell. According to our calculations, the part of the diffraction pattern measured at relatively low diffraction vectors Q (below 10/angstrom) provides information on the surface strain, whle determination of the lattice parameters in the grain core requires measurements at large Q-values (above 15 - 20/angstrom).

Palosz, B.↗

Analysis and Design of Variable Stiffness Composite Cylinders

An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results lead to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that buckling behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response admirably. Thus, it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation.

Tatting, Brian F.↗