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NASA NTRS1994

Processing and Mechanical Properties of NiAl-Based In-Situ Composites

In-situ composites based on the NiAl-Cr eutectic system were successfully produced by containerless processing and evaluated. The NiAl-Cr alloys had a fibrous microstructure while the NiAl-(Cr,Mo) alloys containing 1 at. percent or more molybdenum exhibited a lamellar structure. The NiAl-28Cr-6Mo eutectic displays promising high temperature strength while still maintaining a reasonable room temperature fracture toughness when compared to other NiAl-based materials. The Laves phase NiAlTa was used to strengthen NiAl and very promising creep strengths were found for the directionally solidified NiAl-NiAlTa eutectic. The eutectic composition was found to be near NiAl-15.5Ta (at. percent) and well aligned microstructures were produced at this composition. An off-eutectic composition of NiAl-14.5Ta was also processed, consisting of NiAl dendrites surrounded by aligned eutectic regions. The room temperature toughness of these two phase alloys was similar to that of polycrystalline NiAl even with the presence of the brittle Laves phase NiAlTa. Polyphase in-situ composites were generated by directional solidification of ternary eutectics. The systems investigated were the Ni-Al-Ta-X (X=Cr, Mo, or V) alloys. Ternary eutectics were found in each of these systems and both the eutectic composition and temperature were determined. Of these ternary eutectics, the one in the NiAl-Ta-Cr system was found to be the most promising. The fracture toughness of the NiAl-(Cr,Al)NiTa-Cr eutectic was intermediate between those of the NiAl-NiAlTa eutectic and the NiAl-Cr eutectic. The creep strength of this ternary eutectic was similar to or greater than that of the NiAl-Cr eutectic.

Johnson, David Ray↗

NASA NTRS2013

Design Issues for Using Magnetic Materials in Radiation Environments at Elevated Temperature

One of the challenges of designing motors and alternators for use in nuclear powered space missions is accounting for the effects of radiation. Terrestrial reactor power plants use distance and shielding to minimize radiation damage but space missions must economize volume and mass. Past studies have shown that sufficiently high radiation levels can affect the magnetic response of hard and soft magnetic materials. Theoretical models explaining the radiation-induced degradation have been proposed but not verified. This paper reviews the literature and explains the cumulative effects of temperature, magnetic-load, and radiation-level on the magnetic properties of component materials. Magnetic property degradation is very specific to alloy choice and processing history, since magnetic properties are very much entwined with specific chemistry and microstructural features. However, there is basic theoretical as well as supportive experimental evidence that the negative impact to magnetic properties will be minimal if the bulk temperature of the material is less than fifty percent of the Curie temperature, the radiation flux is low, and the demagnetization field is small. Keywords: Magnets, Permanent Magnets, Power Converters, Nuclear Electric Power Generation, Radiation Tolerance.

Bowman, Cheryl L.↗

NASA NTRS2000

Utilizing Controlled Vibrations in a Microgravity Environment to Understand and Promote Microstructural Homogeneity During Float-Zone Crystal Growth

Our previous experiments with NaNO3 float-zones revealed that steady thermocapillary flow can be balanced/offset by the controlled surface streaming flow induced by end-wall vibration. In the current experiments we are examining the effects of streaming flow on steadying/stabilizing nonsteady thermocapillary flow in such zones. To this effect we have set up a controlled NaNO3 half-zone experiment, where the processing parameters, like zone dimensions and temperature gradients, can be easily varied to generate nonsteady thermocapillary flows. In the present paper we present preliminary results of our investigations into stabilizing such flows by employing end-wall vibration.

Anilkumar, A. V.↗

NASA NTRS2001

Utilizing Controlled Vibrations in a Microgravity Environment to Understand and Promote Microstructural Homogeneity During Floating-Zone Crystal Growth

Anilkumar, A. V.↗

NASA NTRS2003

Gravitational Effects on Distortion in Sintering

During sintering a powder compact gains strength through low-temperature interparticle bonding, usually induced by solid-state surface diffusion, followed by further strength contributions from high-temperature densification. In cases where a liquid phase forms, sintering densification is accelerated and shape retention is sustained while open pores remain and contribute capillary forces. Unfortunately, sintering densification requires the compact become thermally softened to a point where creep strain rates reach levels near 10(exp -2)/s when the liquid forms. On the other hand, thermal softening of the powder compact substantially reduces the strength at high temperatures. Therefore, the in situ strength evolution during sintering is a primary focus to separate compact densification (as required for high performance) with minimized distortion (as required for net-shaping). With respect to gravitation effects on distortion during sintering there are two points of substantial weakness - prior to significant interparticle bonding and during final pore closure. This research is focused on understanding the competition among interparticle neck growth, densification, thermal softening, grain boundary wetting, capillary effects associated with liquid wetting and residual porosity, and gravity. Most surprising is the apparent role of gravity, where the deviatoric stress acting on the powder structure induces skeletal formation that reduces distortion. In contrast with theory, microgravity samples exhibit more distortion yet fail to fully densify. Results are presented on the experimental concepts supporting an emerging model of sintering strength evolution that enables understanding of both distortion and densification. The experiments have relied on tungsten heavy alloys, various combinations of dihedral angle, pore size, initial porosity, liquid:solid ratio, and heating rates. On Earth, the dominant factor with respect to distortion is the starting body heterogeneity. Current modeling efforts are seeking some means to uniformly predict the distortion based on a starting pore structure heterogeneity parameter. Densification is largely unaffected by the initial pore structure, but distortion is highly variable, suggesting that nonuniform pore closure might be a significant parameter during sintering. With respect to flight experiments, plans include removal of the solid body forces acting on the solid grains, allowing stabilization of the pore structure and examination of the buoyancy effects with regard to distortion. In microgravity there is the surprising result that compacts do not densify, yet distort a factor that is contrary to all current sintering models. Densification without distortion during liquid phase sintering was achieved by manipulating microstructure and its evolution during sintering. Microstructure parameters such as the solid volume fraction, dihedral angle, initial porosity, and pore size were varied to measure densification and distortion behavior during LPS using W-Ni-Cu alloys. Green compacts were formed using ethylene-bis-stearamide as a pore-forming agent with the amount of polymer controlling the initial porosity. Different initial pore sizes were generated by varying the polymer particle size. Dihedral angle was varied by changing the Ni:Cu ratio in the alloys. Finally, the solid volume fraction was adjusted via the tungsten content. Distortion was quantified using profiles determined with a coordinate measuring machine to calculate a distortion parameter. Sintering results showed that solid volume fraction and dihedral angle are the dominant factors on densification and distortion during liquid phase sintering. Distortion decreases with increasing solid volume fraction and dihedral angle, while initial porosity and pore size have no observable effect on distortion at nearly full densification. Various strategies emerge to improve distortion control in liquid phase sintering.

German, Randall M.↗

NASA NTRS1988

Distribution and diagenesis of microfossils from the lower Proterozoic Duck Creek Dolomite, Western Australia

Two distinct generations of microfossils occur in silicified carbonates from a previously undescribed locality of the Lower Proterozoic Duck Creek Dolomite, Western Australia. The earlier generation occurs in discrete organic-rich clasts and clots characterized by microquartz anhedra; it contains a variety of filamentous and coccoidal fossils in varying states of preservation. Second generation microfossils consist almost exclusively of well-preserved Gunflintia minuta filaments that drape clasts or appear to float in clear chalcedony. These filaments appear to represent an ecologically distinct assemblage that colonized a substrate containing the partially degraded remains of the first generation community. The two assemblages differ significantly in taxonomic frequency distribution from previously described Duck Creek florules. Taken together, Duck Creek microfossils exhibit a range of assemblage variability comparable to that found in other Lower Proterozoic iron formations and ferruginous carbonates. With increasing severity of post-mortem alteration, Duck Creek microfossils appear to converge morphologically on assemblages of simple microstructures described from early Archean cherts. Two new species are described: Oscillatoriopsis majuscula and O. cuboides; the former is among the largest septate filamentous fossils described from any Proterozoic formation.

NASA Discipline Number 52-30↗

NASA NTRSDate not supplied

Next Generation Durability and Damage Tolerance to Support Certification of Flight Hardware

Durability and Damage Tolerance (D&DT), as currently applied to flight hardware throughout the Agency, is based on continuum and similitude assumptions and does not consider local material properties, environments and responses. These limitations impact our ability to support certification of new component designs, material systems and manufacturing approaches. The primary concern in this Engineering R&A plan is related to the imminent proliferation of parts produced by additive manufacturing (AM). These parts are being advocated by NASA’s suppliers for use on a myriad of flight hardware because of their design flexibility and cost advantages. AM provides opportunities to reduce part counts through complex geometry and reduce manufacturing costs of low volume parts. However, AM materials have some notable metallurgical and microstructural differences compared to traditionally fabricated materials. One of the challenges for the acceptance of AM is the greater tendency for a deleterious defect state, most commonly in the form of porosity, to exist in AM parts. Though this defect state is typically reduced through a hot isostatic pressing (HIP) processing step, the structural performance risks associated with the remaining defects and HIP-healed features is not known. Potential fracture control issues that must be resolved stem from the real possibility that an unhealed defect or a closed defect with less than pristine strength remains at a fracture critical location after HIP. As a result, NASA and the entire aerospace community have been confronted with the need to develop a robust and relevant certification methodology to enable safe implementation of these components. The present work is an important step toward positioning NASA to credibly respond to vendors’ push to implement this new AM materials technology by improving our understanding of AM processing and performance and transitioning that research-based understanding to next-generation engineering capabilities.

Edward H Glaessgen↗

NASA NTRS2002

Techniques Optimized for Reducing Instabilities in Advanced Nickel-Base Superalloys for Turbine Blades

The High-Speed Research (HSR) Airfoil Alloy program developed fourth-generation single-crystal superalloys with up to an 85 F increase in creep rupture capability over current production airfoil alloys. Recent results have been generated at the NASA Glenn Research Center on these fourth-generation alloys, but in coated form, for subsonic turbine blade applications under NASA's Ultra-Efficient Engine Technology (UEET) Program. One goal for UEET is to optimize the airfoil alloy/thermal barrier coating system for 3100 F turbine inlet temperatures. The state-of-the art turbine blade airfoil system consists of a superalloy single crystal that provides the basic mechanical performance of the airfoil. A thermal barrier coating is used to reduce the temperature of the base superalloy, and a bondcoat is deposited between the base material and the thermal barrier coating. The bondcoat improves the oxidation and corrosion resistance of the base superalloy and improves the spallation resistance of the thermal barrier coating. A commercial platinum aluminide bondcoat was applied to the HSR-developed alloys, and a diffusion zone developed as a result of interaction between the bondcoat and the superalloy. Optimized strength is obtained for superalloys when the refractory element content is high and the limits of microstructural stability are approached or exceeded slightly. For fourthgeneration alloys, instability leads to the formation of topologically close packed (TCP) phases, which form internally in the superalloy, and a secondary reaction zone (SRZ), which forms under the diffusion zone. There was a concern that excessive quantities of either TCP or SRZ might decrease the mechanical properties of the superalloy, with SRZ thought to be particularly detrimental and its formation unpredictable. Thus, an SRZreduction effort was initiated in the NASA UEET Program so that methods developed during the HSR project could be optimized further to reduce or eliminate the SRZ. An SRZ is a three-phase constituent composed of TCP and stringers of gamma phase in a matrix of gamma prime. An incoherent grain boundary separates the SRZ from the gammagamma prime microstructure of the superalloy. The SRZ is believed to form as a result of local chemistry changes in the superalloy due to the application of the diffusion aluminide bondcoat. Locally high surface stresses also appear to promote the formation of the SRZ. Thus, techniques that change the local alloy chemistry or reduce surface stresses have been examined for their effectiveness in reducing SRZ. These SRZ-reduction steps are performed on the test specimen or the turbine blade before the bondcoat is applied. Stressrelief heat treatments developed at NASA Glenn have been demonstrated to reduce significantly the amount of SRZ that develops during subsequent high-temperature exposures. Stress-relief heat treatments reduce surface stresses by recrystallizing a thin surface layer of the superalloy. However, in alloys with very high propensities to form SRZ, stress relief heat treatments alone do not eliminate SRZ entirely. Thus, techniques that modify the local chemistry under the bondcoat have been emphasized and optimized successfully at Glenn. One such technique is carburization, which changes the local chemistry by forming submicron carbides near the surface of the superalloy. Detailed characterizations have demonstrated that the depth and uniform distribution of these carbides are enhanced when a stress relief treatment and an appropriate surface preparation are employed in advance of the carburization treatment. Even in alloys that have the propensity to develop a continuous SRZ layer beneath the diffusion zone, the SRZ has been completely eliminated or reduced to low, manageable levels when this combination of techniques is utilized. Now that the techniques to mitigate SRZ have been established at Glenn, TCP phase formation is being emphasized in ongoing work under the UEET Program. The limitsf stability of the fourth-generation alloys with respect to TCP phase formation are currently being defined along with high-temperature creep rupture properties. In addition, a regression model is being developed at Glenn for the prediction of the presence of TCP phase in the microstructure and SRZ under the diffusion zone. The model is based on a design-of-experiments methodology with emphasis on the potential synergistic effects of alloying elements.

MacKay, Rebecca A.↗

NASA NTRS1984

Frictional and morphological properties of Au-MoS2 films sputtered from a compact target

AuMoS2 films 0.02 to 1.2 microns thick were sputtered from target compacted from 5 wt % Au + 95 wt % MoS2, to investigate the frictional and morphological film growth characteristics. The gold dispersion effects in MoS2 films are of interest to increase the densitification and strengthening of the film structure. Three microstructural growth stages were identified on the nano-micro-macrostructural level. During sliding both sputtered Au-MoS2 and MoS2 films have a tendency to break within the columner region. The remaining or effective film, about 0.2 microns thick, performs the lubrication. The Au-MoS2 films displayed a lower friction coefficient with a high degree of frictional stability and less wear debris generation as compared to pure MoS2 films. The more favorable frictional characteristics of the Au-MoS2 films are attributed to the effective film thickness and the high density packed columner zone which has a reduced effect on the fragmentation of the tapered crystallites during fracture.

Spalvins, T.↗

NASA NTRS1984

Frictional and morphological properties of Au-MoS2 films sputtered from a compact target

AuMoS2 films 0.02 to 1.2 microns thick were sputtered from target compacted from 5 wt percent Au + 95 wt percent MoS2, to investigate the frictional and morphological film growth characteristics. The gold dispersion effects in MoS2 films are of interest to increase the densification and strengthening of the film structure. Three microstructural growth stages were identified on the nano-micro-macrostructural level. During sliding both sputtered Au-MoS2 and MoS2 films have a tendency to break within the columner region. The remaining or effective film, about 0.2 microns thick, performs the lubrication. The Au-MoS2 films displayed a lower friction coefficient with a high degree of frictional stability and less wear debris generation as compared to pure MoS2 films. The more favorable frictional characteristics of the Au-MoS2 films are attributed to the effective film thickness and the high density packed columner zone which has a reduced effect on the fragmentation of the tapered crystallites during fracture.

Spalvins, T.↗

NASA NTRS1984

Frictional and morphological properties of Au-MoS2 films sputtered from a compact target

AuMoS2 films 0.02 to 1.2 microns thick were sputtered from target compacted from 5 wt pct. Au + 95 wt pct. MoS2, to investigate the frictional and morphological film growth characteristics. The gold dispersion effects in MoS2 films are of interest to increase the densitification and strengthening of the film structure. Three microstructural growth stages were identified on the nano-micro-macrostructural level. During sliding both sputtered Au-MoS2 and MoS2 films have a tendency to break within the columner region. The remaining or effective film, about 0.2 microns thick, performs the lubrication. The Au-MoS2 films displayed a lower friction coefficient with a high degree of frictional stability and less wear debris generation as compared to pure MoS2 films. The more favorable frictional characteristics of the Au-MoS2 films are attributed to the effective film thickness and the high density packed columner zone which has a reduced effect on the fragmentation of the tapered crystallites during fracture.

Spalvins, T.↗

NASA NTRS1986

Infrared observations of the Uranian system

Initial results are presented from analyses of IR interferometer spectrometer data collected by Voyager 2 during passes of Uranus and the moons Miranda and Ariel. The data covered reflected solar radiation in the visible and near-IR and thermal emissions between 25 and 50 microns. An equatorial atmospheric He mole fraction of 0.10-0.20 and a mass fraction of 0.16-0.34 was observed for Uranus. Para-hydrogen was also a significant fraction Uranus CH4 atmosphere. Average polar and equatorial spectra were employed to generate vertical temperature profiles between 60-900 mbar, with the finding that the temperatures at the equator and the poles are markedly similar between 400-900 mbar. The effective temperature of Uranus had a calculated upper limit of about 59.4 K, while the subsolar temperatures of Miranda and Arial were around 86 and 84 K, respectively. The albedos of the two satellites indicated surface microstructures composed of isotopically scattering grains.

Hanel, R.↗

NASA NTRS1987

Reactions of Atomic Oxygen (O(3P)) with Polybutadienes and Related Polymers

Thin films of the following polymers were exposed at ambient temperature to ground-state oxygen atoms (O(3P)), generated by a radio-frequency glow discharge in O2: cis- and trans-1,4-polybutadienes (CB and TB), amorphous 1,2-polybutadiene (VB), polybutadienes with different 1,4/1,2 contents, trans polypentenamer (TP), cis and trans polyoctenamers (CO and TO), and ethylene-propylene rubber (EPM). Transmission infrared spectra of CB and TB films revealed extensive surface recession, or etching, unaccompanied by any microstructural changes within the films, demonstrating that the reactions were confined to the surface layers. Contrary to the report by Rabek, Lucki, and Ranby (1979), there was no O(3P)-induced cis-trans isomerization in CB or TB. From weight-loss measurements, etch rates for polybutadienes were found to be markedly dependent on vinyl content, decreasing by two orders of magnitude from CB (2% 1,2) to structures with 30 to 40% 1,2 double bonds, thereafter increasing by half an order of magnitude to VB (97% 1,2). Relative etch rates for EMP and the polyalkenamers were in the order: EMP is greater than CO (or TO) is greater than TP is greater than CB. The sole non-elastomer examined, TB, had an etch rate about six times that of CB, ascribable to a morphology difference. Cis/trans content had a negligible effect on the etch rate of the polyalkenamers. Mechanisms involving crosslinking through units are proposed for the unexpected protection imparted to polybutadienes by the 1,2 double bonds.

Golub, Morton A.↗

NASA NTRS1999

Ultrasonic Nondestructive Characterization of Adhesive Bonds

Adhesives and adhesive joints are widely used in various industrial applications to reduce weight and costs, and to increase reliability. For example, advances in aerospace technology have been made possible, in part, through the use of lightweight materials and weight-saving structural designs. Joints, in particular, have been and continue to be areas in which weight can be trimmed from an airframe through the use of novel attachment techniques. In order to save weight over traditional riveted designs, to avoid the introduction of stress concentrations associated with rivet holes, and to take full advantage of advanced composite materials, engineers and designers have been specifying an ever-increasing number of adhesively bonded joints for use on airframes. Nondestructive characterization for quality control and remaining life prediction has been a key enabling technology for the effective use of adhesive joints. Conventional linear ultrasonic techniques generally can only detect flaws (delamination, cracks, voids, etc) in the joint assembly. However, more important to structural reliability is the bond strength. Although strength, in principle, cannot be measured nondestructively, a slight change in material nonlinearity may indicate the onset of failure. Furthermore, microstructural variations due to aging or under-curing may also cause changes in the third order elastic constants, which are related to the ultrasonic nonlinear parameter of the polymer adhesive. It is therefore reasonable to anticipate a correlation between changes in the ultrasonic nonlinear acoustic parameter and the remaining bond strength. It has been observed that higher harmonics of the fundamental frequency are generated when an ultrasonic wave passes through a nonlinear material. It seems that such nonlinearity can be effectively used to characterize bond strength. Several theories have been developed to model this nonlinear effect. Based on a microscopic description of the nonlinear interface binding force, a quantitative method was presented. Recently, a comparison between the experimental and simulated results based on a similar theoretical model was presented. A through-transmission setup for water immersion mode-converted shear waves was used to analyze the ultrasonic nonlinear parameter of an adhesive bond. In addition, ultrasonic guided waves have been used to analyze adhesive or diffusion bonded joints. In this paper, the ultrasonic nonlinear parameter is used to characterize the curing state of a polymer/aluminum adhesive joint. Ultrasonic through-transmission tests were conducted on samples cured under various conditions. The magnitude of the second order harmonic was measured and the corresponding ultrasonic nonlinear parameter was evaluated. A fairly good correlation between the curing condition and the nonlinear parameter is observed. The results show that the nonlinear parameter might be used as a good indicator of the cure state for adhesive joints.

Qu, Jianmin↗

NASA NTRS2004

Implementation Challenges for Ceramic Matrix Composites in High Temperature Applications

Ceramic matrix composites are leading candidate materials for a number of applications in aeronautics, space, energy, electronics, nuclear, and transportation industries. In the aeronautics and space exploration systems, these materials are being considered for applications in hot sections of jet engines such as the combustor liner, nozzle components, nose cones, leading edges of reentry vehicles and space propulsion components. Applications in the energy and environmental industries include radiant heater tubes, heat exchangers, heat recuperators, gas and diesel particulate filters (DPFs), and components for land based turbines for power generation. These materials are also being considered for use in the first wall and blanket components of fusion reactors. There are a number of critical issues and challenges related to successful implementation of composite materials. Fabrication of net and complex shape components with high density and tailorable matrix properties is quite expensive, and even then various desirable properties are not achievable. In this presentation, microstructure and thermomechanical properties of composites fabricated by two techniques (chemical vapor infiltration and melt infiltration), will be presented. In addition, critical need for robust joining and assembly technologies in successful implementation of these systems will be discussed. Other implementation issues will be discussed along with advantages and benefits of using these materials for various components in high temperature applications.

Singh, Mrityunjay↗

NASA NTRS2017

Sintered Cathodes for All-Solid-State Structural Lithium-Ion Batteries

All-solid-state structural lithium ion batteries serve as both structural load-bearing components and as electrical energy storage devices to achieve system level weight savings in aerospace and other transportation applications. This multifunctional design goal is critical for the realization of next generation hybrid or all-electric propulsion systems. Additionally, transitioning to solid state technology improves upon battery safety from previous volatile architectures. This research established baseline solid state processing conditions and performance benchmarks for intercalation-type layered oxide materials for multifunctional application. Under consideration were lithium cobalt oxide and lithium nickel manganese cobalt oxide. Pertinent characteristics such as electrical conductivity, strength, chemical stability, and microstructure were characterized for future application in all-solid-state structural battery cathodes. The study includes characterization by XRD, ICP, SEM, ring-on-ring mechanical testing, and electrical impedance spectroscopy to elucidate optimal processing parameters, material characteristics, and multifunctional performance benchmarks. These findings provide initial conditions for implementing existing cathode materials in load bearing applications.

Ceramics↗

NASA NTRS2020

Efficient production of a high-performance dispersion strengthened, multi-principal element alloy

Additive manufacturing currently facilitates new avenues for materials discovery that have not been fully explored. In this study we reveal how additive manufacturing can be leveraged to produce dispersion strengthened (DS), multi-principal element alloys (MPEA) without the use of traditional mechanical alloying or chemical reactions. This new processing technique employed resonant acoustic mixing to coat an equiatomic NiCoCr powder with nano-scale yttrium oxides. Then, through laser powder bed fusion (L-PBF), the coated powder was successfully consolidated into 99.9% dense parts. Microstructural analysis confirmed the successful incorporation and dispersion of nano-scale oxides throughout the build volume. Furthermore, high temperature mechanical testing of the DS alloys showed significant improvements in strength and ductility over the baseline NiCoCr. As a result, this recently discovered processing route opens a new alloy design and production path that is synergistic between additive manufacturing and dispersion strengthening, possibly enabling a new generation of high-performance alloys.

T.M. Smith↗

NASA NTRS1997

Micromechanics Analysis Code (MAC) Developed

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers in performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions, it must be based on a micromechanics approach that uses physically based deformation and life constitutive models, and it must allow one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Only then can such a model be used by a material scientist to investigate the effect of different deformation mechanisms on the overall response of the composite and, thereby, identify the appropriate constituents for a given application. However, if a micromechanical model is to be used in a large-scale structural analysis it must be (1) computationally efficient, (2) able to generate accurate displacement and stress fields at both the macro and micro level, and (3) compatible with the finite element method. In addition, new advancements in processing and fabrication techniques now make it possible to engineer the architectures of these advanced composite systems. Full utilization of these emerging manufacturing capabilities require the development of a computationally efficient micromechanics analysis tool that can accurately predict the effect of microstructural details on the internal and macroscopic behavior of composites. Computational efficiency is required because (1) a large number of parameters must be varied in the course of engineering (or designing) composite materials and (2) the optimization of a material's microstructure requires that the micromechanics model be integrated with optimization algorithms. From this perspective, analytical approaches that produce closed-form expressions which describe the effect of a material's internal architecture on the overall material behavior are preferable to numerical methods such as the finite element or finite difference schemes.

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