Search NASA⌕ Search

SEARCH · Search NASA

Results for “deformation function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,459 records · Page 81

Utilizing integrated neutron diffraction and elastoplastic self-consistent crystal plasticity model to quantitatively assess the strengthening mechanism in Al–12.5Ce and Al–12.5Ce–0.4Mg alloys

An integrated in-situ neutron diffraction and elastic plastic self-consistent crystal plasticity (EPSC-CP) modeling scheme is performed on a binary Al–12Ce alloy and a ternary Al–12Ce–0.4Mg alloys. Using this scheme, the constitutive parameters, i.e. elastic constants and slip system parameters of individual phases can be calibrated which can be used in microstructure-based CP models to predict materials performance. From this study, it is shown that the elastic constants of Al 11 Ce 3 intermetallics calculated from density function theory calculation in the literature are rather accurate. When applied to the EPSC-CP model, the lattice strains of both the binary and ternary alloys are correctly predicted as compared with experiments, and large lattice strain differences between Al (100) plane and Al 11 Ce 3 (010) plane are demonstrated. The slip system parameters calibrated by the scheme shows that the addition of 0.4 wt% Mg in the alloy has little influence on the critical resolved shear stress of initial dislocation glide in the Al matrix which caused plastic yield in the material. This can be explained by the very dilute Mg solute content in the Al solid solution, causing large spacing of Al–Mg lattice misfit sites and little impact on resistance of dislocation glide at initial yield. The 0.4 wt% Mg addition, on the other hand, has a large influence on the hardening term in the slip system parameters, indicating those Al–Mg misfit sites do help dislocation accumulation during the deformation. The impact of dilute Mg addition on the Al slip system parameters is also reflected in the flow behavior of the ternary alloy: little impact on the yield stress, but a large impact on working hardening and tensile strength of the materials which is consistent with the literature.

36 MATERIALS SCIENCE↗

Assessing the ASME Section III, Division 5, Class A Primary Load Design Rules Against Creep Notch Effects

This report assesses the ASME Section III, Division 5, Subsection HB, Subpart B rules covering the design and construction of high temperature Class A nuclear reactor components for their robustness against creep notch effects. The creep notch effect combines the effect of multiaxial stresses on material creep deformation and damage. This report considers both effects, including the potential for creep mechanism shifts affecting the extrapolation of design data from high stress, short-time experimental data to low stress, long time operating component conditions. The report summarizes the history of and literature on multiaxial creep and surveys the current ASME design rules dealing with multiaxial effects. The report then describes the results of two dedicated numerical studies, one assessing the robustness of the ASME rules against uncertainty in extrapolating from uniaxial creep test data to multiaxial component conditions and a second study examining the potential effects of a mechanism shift from high stress, dislocation-mediated creep to diffusion-dominated creep at lower stresses. The final conclusion of the report is that the ASME rules adequately guard against multiaxial creep failure, though there are several aspects of the Code that could be optimized to provide less over-conservative design predictions or to provide a more consistent design margin as a function of temperature and stress. In a few areas, particularly the potential for mechanism shifts outside the currently-available experimental data, the Code rules should be revaluated as additional experimental data and new modeling and simulation results become available

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Buckling and postbuckling behavior of square compression-loaded graphite-epoxy plates with circular cutouts

Results are presented for unidirectional (0, 10)(sub s) and (90,10)(sub s) plates, ((0/90)(sub 5)(sub s)) plates, and for aluminum plates. Results are also presented for ((+/- theta)(sub 6)(sub s)) angle-ply plates for values of theta = 30, 45, and 60 degrees. The results indicate that the change in axial stiffness of a plate at buckling is strongly dependent upon cutout size and plate orthotropy. The presence of a cutout gives rise to an internal load distribution that changes, sometimes dramatically, as a function of cutout size coupled with the plate orthotropy. In the buckled state, the role of orthotropy becomes more significant since bending in addition to membrane orthotropy is present. Most of the plates with cutouts exhibited less postbuckling stiffness than the corresponding plate without a cutout, and the postbuckling stiffness decreased with increasing cutout size. However, some of the highly orthotropic plates with cutouts exhibited more postbuckling stiffness than the corresponding plate without a cutout. These results suggest the possibility of tailoring the cutout size and the stacking sequence of a composite plate to optimize postbuckling stiffness. It was found that plates with large radius cutouts do exhibit some postbuckling strength. The results also indicate that a cutout can influence modal interaction in a plate. Specifically, results are presented that show a plate with a relatively small cutout buckling at a higher load than the corresponding plate without a cutout, due to modal interaction. Other results are presented that indicate the presence of nonlinear prebuckling deformations, due to material nonlinearity, in the angle-ply plates with theta = 45 and 60 degrees. The nonlinear prebuckling deformations are more pronounced in the plates with theta = 45 degrees and become even more pronounced as the cutout size increases. Results are also presented that show how load-path eccentricity due to improper machining of the test specimens affects the buckling behavior. Some of the plates with cutouts and eccentricity exhibited a snap-through type of buckling behavior.

Nemeth, Michael P.↗

Embossed Teflon AF Laminate Membrane Microfluidic Diaphragm Valves

A microfluidic system has been designed to survive spaceflight and to function autonomously on the Martian surface. It manipulates microscopic quantities of liquid water and performs chemical analyses on these samples to assay for the presence of molecules associated with past or present living processes. This technology lies at the core of the Urey Instrument, which is scheduled for inclusion on the Pasteur Payload of the ESA ExoMars rover mission in 2013. Fabrication processes have been developed to make the microfabricated Teflon-AF microfluidic diaphragm pumps capable of surviving extreme temperature excursions before and after exposure to liquid water. Two glass wafers are etched with features and a continuous Teflon membrane is sandwiched between them (see figure). Single valves are constructed using this geometry. The microfabricated devices are then post processed by heating the assembled device while applying pneumatic pressure to force the Teflon diaphragm against the valve seat while it is softened. After cooling the device, the embossed membrane retains this new shape. This solves previous problems with bubble introduction into the fluid flow where deformations of the membrane at the valve seat occurred during device bonding at elevated temperatures (100-150 C). The use of laminated membranes containing commercial Teflon AF 2400 sheet sandwiched between spun Teflon AF 1600 layers performed best, and were less gas permeable than Teflon AF 1600 membranes on their own. Spinning Teflon AF 1600 solution (6 percent in FLOURINERT(Registered TradeMark) FC40 solvent, 3M Company) at 500 rpm for 1.5 seconds, followed by 1,000 rpm for 3 seconds onto Borofloat glass wafers, results in a 10-micron-thick film of extremely smooth Teflon AF. This spinning process is repeated several times on flat, blank, glass wafers in order to gradually build a thick, smooth membrane. After running this process at least five times, the wafer and Teflon coating are heated under vacuum at 220 C for one hour in order to drive off any residual solvent present in the composite film. After this, a second blank, glass wafer is brought down from above and the stack is held under vacuum at 3 atm mechanical pressure for ten 10 hours.

Willis, Peter↗

A study of electroactive polyvinyl chloride (PVC) gel actuators through the use of the electric modulus formalism and cyclic linear voltage sweeps

The conductivity and dielectric properties are integral to the function of polyvinyl chloride (PVC) gel actuators. The frequency-dependent properties of PVC gel actuators are investigated here in terms of their impedance, permittivity, and for the first time, electric modulus. The data shows that PVC gels’ conductive properties are just as, if not more, important as their dielectric properties in electromechanical transduction applications. The electrode polarization (EP) and its impact on the impedance and dielectric spectra of PVC gels, as well as the developed asymmetric space charge at the anode, are discussed. The electric modulus and tan δ spectra are used for the fitting of Cole-Cole (CC) and Debye relaxation models for gels of varying plasticizer content. The electrostatic adhesive force for PVC gels of varying plasticizer is also measured, indicating large electrostatic adhesion (>2 N cm -2 ). A cyclic linear voltage sweep is used to clarify the dynamics of space charge within the gels. The peak current (associated with space charge development) is seen to be concurrent with the onset of mechanical deformation, showing the asymmetric charge as the origin of electromechanical transduction. Additionally, the maximum charge transferred (as measured by the integration of current over time) before space charge development is found to correlate with the electrostatic adhesive force measured for the gels, pointing to a new method of characterizing PVC gels for actuation.

Instruments & Instrumentation↗

Preparation of silver nanoparticle functionalized polyamide fibers with antimicrobial activity and electrical conductivity

ABSTRACT In this work, silver nanoparticle functionalized polyamide 6 (PA6) fibers were prepared using the electroless plating method. The surface of PA6 fibers was modified by exploiting dopamine/CuSO 4 /H 2 O 2 system prior to electroless plating to enhance the bonding force between the fiber and the silver nanoparticles. It was found that both the formation rate and the chemical stability of polydopamine (PDA) coatings on the PA6 fiber surface were improved by the introduction of CuSO 4 /H 2 O 2 . The results confirmed the successful deposition of silver nanoparticles on PA6 fiber surface and the average particle diameter of 223 nm. Compared with uncoated fibers, the silver plated PA6 fibers exhibited excellent antimicrobial activity to both Escherichia coli and Staphylococcus aureus (with an antimicrobial efficiency of 99.9% and 100%, respectively). The electrical resistance of the silver coated PA6 fibers reached 0.98 Ω over a length of 1 cm, indicating a good electrical conductivity. In particular, coating durability of the formed silver layer was investigated by subjecting the fibers to various mechanical deformations, and the results showed that the formed silver layer was maintained well after 50 times of cyclic stretching at a constant displacement of 10 mm. © 2019 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136 , 47584.

Jiang, Liang↗

External-Field-Induced Phase Transformation and Associated Properties in a Ni 50 Mn 34 Fe 3 In 13 Metamagnetic Shape Memory Wire

Metamagnetic shape memory alloys exhibit a series of intriguing multifunctional properties and have great potential for applications in magnetic actuation, sensing and magnetic refrigeration. However, the poor mechanical properties of these alloys with hardly any tensile deformability seriously limit their practical application. In the present work, we developed a Ni-Fe-Mn-In microwire that exhibits both a giant, tensile superelasticity and a magnetic-field-induced first-order phase transformation. The recoverable strain of superelasticity is more than 20% in the temperature range of 233–283 K, which is the highest recoverable strain reported heretofore in Ni-Mn-based shape memory alloys (SMAs). Moreover, the present microwire exhibits a large shape memory effect with a recoverable strain of up to 13.9% under the constant tensile stress of 225 MPa. As a result of the magnetic-field-induced first-order phase transformation, a large reversible magnetocaloric effect with an isothermal entropy change ΔS m of 15.1 J kg –1 K –1 for a field change from 0.2 T to 5 T was achieved in this microwire. The realization of both magnetic-field and tensile-stress-induced transformations confers on this microwire great potential for application in miniature multi-functional devices and provides an opportunity for multi-functional property optimization under coupled multiple fields.

36 MATERIALS SCIENCE↗

An Improved Plastically Dilatant Unified Viscoplastic Constitutive Formulation for Multiscale Analysis of Polymer Matrix Composites Under High Strain Rate Loading

Polymer matrix composites are commonly used to fabricate energy-absorbing structures expected to experience impact loading. As such, a detailed understanding of the dynamic response of the constituent materials is necessary. Since the rate, temperature, and pressure dependence of carbon fiber reinforced polymer matrix composites are primarily manifestations of the rate, temperature, and pressure dependence of the polymer matrix, it is crucial that the constitutive behavior of the matrix be accurately characterized. In this work, an existing unified viscoplastic constitutive formulation is extended to ensure thermodynamic consistency and to more accurately account for the tension-compression asymmetry observed in the response of polymeric materials. A new plastic potential function is proposed, and elementary loading conditions are utilized to determine relations between model constants to ensure nonnegative plastic dissipation, a necessary thermodynamic requirement. Expressions for plastic Poisson’s ratios are derived and are bounded by enforcing nonnegative plastic dissipation. The model is calibrated against available experimental data from tests conducted over a range of strain rates, temperatures, and loading cases on a representative thermoset epoxy; good correlation between simulations and experimental data is obtained. Temperature rises due to the conversion of plastic work to heat are computed via the adiabatic heat energy equation. The viscoplastic polymer model is then used as a constitutive model in the generalized method of cells micromechanics theory to investigate the effects of matrix adiabatic heating on the high strain rate response of a unidirectional composite. The thermodynamic consistency of the model ensures plastic dissipation can only cause an increase in temperature. Simulation results indicate that significant thermal softening due to the conversion of plastic work to heat is observed in the composite for matrix dominated deformation modes.

Impact loading↗

A duality-based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement

High-rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement-based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality-based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf-sup-based skew-symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high-order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement-rotation-phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty-based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.

42 ENGINEERING↗

Theoretical Development of an Orthotropic Elasto-Plastic Generalized Composite Material Model

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within LS-DYNA (Registered), there are several features that have been identified that could improve the predictive capability of a composite model. To address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed and is being implemented into LS-DYNA as MAT_213. A key feature of the improved material model is the use of tabulated stress-strain data in a variety of coordinate directions to fully define the stress-strain response of the material. To date, the model development efforts have focused on creating the plasticity portion of the model. The Tsai-Wu composite failure model has been generalized and extended to a strain-hardening based orthotropic material model with a non-associative flow rule. The coefficients of the yield function, and the stresses to be used in both the yield function and the flow rule, are computed based on the input stress-strain curves using the effective plastic strain as the tracking variable. The coefficients in the flow rule are computed based on the obtained stress-strain data. The developed material model is suitable for implementation within LS-DYNA for use in analyzing the nonlinear response of polymer composites.

Plasticity↗

An Accelerated Creep Testing Program For Nickel Based Superalloys

In order to improve the energy production within the United States, new materials are developed with the goal of increased functionality. These materials are required to perform at extreme pressures and temperatures (up to and beyond 200MPa and 650â??) as well as be sustainable beyond 105 hours. Before developing these materials into components for power generation, mechanical testing is required to better understand the behavior of these materials at various loads and temperatures. The longest of these tests is the conventional creep test which is a real time test that can beyond 105 hours depending on service conditions. Hundreds of specimens must be tested before being approved for use in power generation, but it is extremely difficult to rapidly qualify when each material is required to exceed 105 hours making testing through conventional means unfeasible. While others have designed accelerated testing methods to help qualify materials, many of these experiments use an empirical approach that requires test data to fit already existing creep data. In this study, an accelerated creep test called the stepped isostress method (SSM) is then applied to wrought Inconel 718 (IN 718) specimens. A test matrix is designed using deformation mechanism maps, time-temperature-transformation diagrams, and time-temperature-precipitation diagrams, in order to ensure that microstructurally, the accelerated creep tests fail similarly to the conventional creep tests. The data from the stepped isostress method is then applied to the McVetty and Sin-hyperbolic (Sinh) constitutive models in order to generate a creep master curve. The results from the model fits are then compared to the conventional creep data done from experiments as well as from the NIMS database for Inconel 718. Optical microscopy and scanning electron microscopy are used to compare the evolution of the microstructure from the conventional creep and accelerated creep tests. It is found that using the Sinh model on the accelerated creep data provides reasonable creep rupture predictions when compared to the scatter band of creep tests. It was also observed that the microstructural evolution between the SSM experiments and creep tests were very similar in terms of the volume fraction of precipitates and phases.

Mach, Robert↗

Detection of atmospheric pressure loading using very long baseline interferometry measurements

Loading of the Earth by the temporal redistribution of global atmospheric mass is likely to displace the positions of geodetic monuments by tens of millimeters both vertically and horizontally. Estimates of these displacements are determined by convolving National Meteorological Center (NMC) global values of atmospheric surface pressure with Farrell's elastic Green's functions. An analysis of the distances between radio telescopes determined by very long baseline interferometry (VLBI) between 1984 and 1992 reveals that in many of the cases studied there is a significant contribution to baseline length change due to atmospheric pressure loading. Our analysis covers intersite distances of between 1000 and 10,000 km and is restricted to those baselines measured more than 100 times. Accounting for the load effects (after first removing a best fit slope) reduces the weighted root-mean-square (WRMS) scatter of the baseline length residuals on 11 of the 22 baselines investigated. The slight degradation observed in the WRMS scatter on the remaining baselines is largely consistent with the expected statistical fluctuations when a small correction is applied to a data set having a much larger random noise. The results from all baselines are consistent with approximately 60% of the computed pressure contribution being present in the VLBI length determinations. Site dependent coefficients determined by fitting local pressure to the theoretical radial displacement are found to reproduce the deformation caused by the regional pressure to within 25% for most inland sites. The coefficients are less reliable at near coastal and island stations.

Vandam, T. M.↗

Reflector Surface Error Compensation in Dual-Reflector Antennas

By probing the field on a small subreflector at a minimal number of points, the main reflector surface errors can be obtained and subsequently used to design a phase-correction subreflector that can compensate for main reflector errors. The compensating phase-error profile across the subreflector can be achieved either by a surface deformation or by the use of an array of elements such as patch antennas that can cause a phase shift between the incoming and outgoing fields. The second option is of primary interest here, but the methodology can be applied to either case. The patch array is most easily implemented on a planar surface. Therefore, the example of a flat subreflector and a parabolic main reflector (a Newtonian dual reflector system) is considered in this work. The subreflector is assumed to be a reflector array covered with patch elements. The phase variation on a subreflector can be detected by a small number of receiving patch elements (probes). By probing the phase change at these few selected positions on the subreflector, the phase error over the entire surface can be recovered and used to change the phase of all the patch elements covering the subreflector plane to compensate for main reflector errors. This is accomplished by using a version of sampling theorem on the circular aperture. The sampling is performed on the phase-error function on the circular aperture of the main reflector by a method developed using Zernike polynomials. This method is based upon and extended from a theory previously proposed and applied to reflector aperture integration. This sampling method provides for an exact retrieval of the coefficients of up to certain orders in the expansion of the phase function, from values on a specifically calculated set of points in radial and azimuthal directions in the polar coordinate system, on the circular reflector aperture. The corresponding points on the subreflector are then obtained and, by probing the fields at these points, a set of phase values is determined that is then transferred back to the main reflector aperture for recovering the phase function. Once this function is recovered, the corresponding phase function on the subreflector is calculated and used to compensate for main reflector surface errors. In going back and forth between sub and main reflectors, geometrical (ray) optics is employed, which even though it ignores edge diffraction and other effects, is shown to be accurate for phase recovery.

Jamnejad, Vahraz↗

The universal suppressor mutation restores membrane budding defects in the HSV-1 nuclear egress complex by stabilizing the oligomeric lattice

Nuclear egress is an essential process in herpesvirus replication whereby nascent capsids translocate from the nucleus to the cytoplasm. This initial step of nuclear egress–budding at the inner nuclear membrane–is coordinated by the nuclear egress complex (NEC). Composed of the viral proteins UL31 and UL34, NEC deforms the membrane around the capsid as the latter buds into the perinuclear space. NEC oligomerization into a hexagonal membrane-bound lattice is essential for budding because NEC mutants designed to perturb lattice interfaces reduce its budding ability. Previously, we identified an NEC suppressor mutation capable of restoring budding to a mutant with a weakened hexagonal lattice. Using an established in-vitro budding assay and HSV-1 infected cell experiments, we show that the suppressor mutation can restore budding to a broad range of budding-deficient NEC mutants thereby acting as a universal suppressor. Cryogenic electron tomography of the suppressor NEC mutant lattice revealed a hexagonal lattice reminiscent of wild-type NEC lattice instead of an alternative lattice. Further investigation using x-ray crystallography showed that the suppressor mutation promoted the formation of new contacts between the NEC hexamers that, ostensibly, stabilized the hexagonal lattice. This stabilization strategy is powerful enough to override the otherwise deleterious effects of mutations that destabilize the NEC lattice by different mechanisms, resulting in a functional NEC hexagonal lattice and restoration of membrane budding.

60 APPLIED LIFE SCIENCES↗

Functionality Improvements to Overaero

The functionality of the overset, static aeroelasticity, Navier-Stokes flow solver OVERAERO was increased by adding capability to the flow solver and enhancing code performance. Improvements were made to the fluids/structure interface, an MLP version of the parallel OVERAERO code was developed, and the OVERAERO-MPI code was ported to the Cray T3E. The OVERFLOW-MPI and OVERAERO-MPI codes were tested successfully on the IPG testbed and a means of reducing communication overhead within OVERFLOW-MPI was investigated. To solve an aeroelastic problem computationally, a structures grid surface definition and a fluids grid surface definition are required. Typically, the structures grid surface has a lower fidelity than the fluids grid surface. Thus, the methods developed to transfer data between the two grid systems are vital to the accuracy and efficiency of the aeroelasticity code. The fluids/structures interface developed for the OVERAERO code was improved to more accurately treat fluids surfaces that bridge between two different structural surfaces. For example, the method allowed the forward portion of a flap track fairing to deform with the wing and the aft end of the fairing to deform with the flap. A tightly-coupled version of the code based on OVERFLOW-MLP was developed to improve code performance on the SGI Origin 2000. This required a new parallelization strategy to couple the fluids and structures codes. The OVERAERO-MPI code was ported to the Cray T3E to extend the usability of the code. The port required extensive use of dynamic memory management techniques to fit large problems within the memory limitations of the T3E. The OVERFLOW-MPI and OVERAERO-MPI codes were tested on the IPG testbed being developed within NASA. For small problems with minimal data transfer between grids, there was little to no performance penalty spreading the computation across two machines. For very large problems, methods were developed to minimize intermachine communication via the grid partitioning scheme. By minimizing the intermachine communication requirements of the problem, it may still be beneficial to run a tightly-coupled flow solver across two machines within the IPG.

Gee, Ken↗

Using Digital Image Correlation for Material Testing at Cryogenic Temperatures

Recent efforts were made to parametrize an aluminum alloy at cryogenic temperatures to calibrate finite element models simulating material deformation. Digital image correlation (DIC) was used to measure material properties using front/back strains of specimens during tensile tests. Data acquired from DIC was compared to physical extensometer measurements. Two camera pairs (front and back) were mounted via aluminum extrusion to the exterior of an environmental chamber of a hydraulic test stand. Images were taken through single-pane optical glass windows of the environment chamber. Positive pressure bags encased the cameras, attaching to the perimeter of the glass to keep out moisture and prevent windows from frosting. Figure 1 shows the environmental setup and the camera setup during cryogenic testing. Some of the challenges during testing at cryogenic temperatures include the gaseous flow of liquid nitrogen in the optical path of the mounted cameras, frost buildup on the windows as seen in Figure 1b, and frost on the test coupon. The temperature gradient present during the introduction of liquid nitrogen into the chamber can increase the projection error of images captured of the specimen. Figure 2 shows the estimated projection error from DIC as a function of temperature during the cool down process. This presentation addresses some of the concerns and observations when using DIC for testing at cryogenic temperatures using methods of isolated camera system and techniques for maintaining the glass panel clear from frost.

Joseph Cochran↗

Acceleration effects in solid propellant rocket motors

The performance variations due to acceleration loads imposed on spinning solid propellant rocket motors are investigated. The four potentially most significant modes of acceleration-induced phenomena are identified from a study of the literature and modeled. The four modes are a mechanical mode which deals with deformations of the propellant and case: a thermodynamic mode which covers acceleration-induced combustion phenomena; a stress mode which covers the stressed propellant's effect on burn rate; and a gas dynamic mode which deals with changes in gas flow in the chamber and through the nozzle. Simplified models of each mode are developed or taken from the literature and are added to an internal ballistics evaluation computer program. The resulting analysis is the first to include all of the modes. In order to do this an original analysis of the mechanical and stress modes was necessary. However, the analysis shows that the stress mode is not important for the circular perforated grains studied. The other effects are shown to have a significant influence on solid rocket motor performance. The magnitude of the different mode effects are such that one may not be ignored over the others as has been done in the past. The results of the analysis are compared to published rocket motor data. The comparisons indicate an erosive burning effect that is a function of spin rate. A qualitative explanation of the erosive effect is presented.

Langhenry, M. T.↗

Coronagraph Design Optimization for Segmented Aperture Telescopes

The goal of directly imaging Earth-like planets in the habitable zone of other stars has motivated the design of coronagraphs for use with large segmented aperture space telescopes. In order to achieve an optimal trade-o between planet light throughput and di racted starlight suppression, we consider coronagraphs comprised of a stage of phase control implemented with deformable mirrors (or other optical elements), pupil plane apodization masks (gray scale or complex valued), and focal plane masks (either amplitude only or complex-valued, including phase only such as the vector vortex coronagraph). The optimization of these optical elements, with the goal of achieving 10 or more orders of magnitude in the suppression of on-axis (starlight) di racted light, represents a challenging non-convex optimization problem with a nonlinear dependence on control degrees of freedom. We develop a new algorithmic approach to the design optimization problem, which we call the "Auxiliary Field Optimization" (AFO) algorithm. The central idea of the algorithm is to embed the original optimization problem, for either phase or amplitude (apodization) in various planes of the coronagraph, into a problem containing additional degrees of freedom, speci cally ctitious "auxiliary" electric elds which serve as targets to inform the variation of our phase or amplitude parameters leading to good feasible designs. We present the algorithm, discuss details of its numerical implementation, and prove convergence to local minima of the objective function (here taken to be the intensity of the on-axis source in a "dark hole" region in the science focal plane). Finally, we present results showing application of the algorithm to both unobscured o -axis and obscured on-axis segmented telescope aperture designs. The application of the AFO algorithm to the coronagraph design problem has produced solutions which are capable of directly imaging planets in the habitable zone, provided end-to-end telescope system stability requirements can be met. Ongoing work includes advances of the AFO algorithm reported here to design in additional robustness to a resolved star, and other phase or amplitude aberrations to be encountered in a real segmented aperture space telescope.

Redding, Dave↗