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NASA NTRS1984

On the need for spectroscopic data in ultraviolet stellar spectral synthesis calculations

A general discussion of the quality of spectroscopic data for ultraviolet (less than 3000 A) spectral synthesis calculations is presented. It is pointed out that progress in the generation of complete and accurate lists of atomic lines, and in the computation and measurement of accurate transition probabilities of the spectra of many elements is lagging behind current and near-term observational capabilities. Theoretical syntheses of the line profiles in the spectra of three middle-to-late B type stars (Pi Cet, 134 Tau, and vCap) are computed. The computations are found to be complicated and ambiguous due to the low accuracy of the oscillator strengths used in the analysis. Some characteristics of star-to-star variations in elemental abundances are discussed.

Adelman, S. J.↗

NASA NTRS1989

Experience with advanced instrumentation in a hot section cascade

The Lewis Research Center gas turbine Hot Section Test Facility was developed to provide a real engine environment with known boundary conditions for the aerothermal performance evaluation and verification of computer design codes. This verification process requires experimental measurements in a hostile environment. The research instruments used in this facility are presented, and their characteristics and how they perform in this environment are discussed. The research instrumentation consisted of conventional pressure and temperature sensors, as well as thin-film thermocouples and heat flux gages. The hot gas temperature was measured by an aspirated temperature probe and by a dual-element, fast-response temperature probe. The data acquisition mode was both steady state and time dependent. These experiments were conducted over a wide range of gas Reynolds numbers, exit gas Mach numbers, and heat flux levels. This facility was capable of testing at temperatures up to 1600 K, and at pressures up to 18 atm. These corresponded to an airfoil exit Reynolds number range of 0.5 x 10(6) to 2.5 x 10(6) based on the airfoil chord of 5.55 cm. The results characterize the performance capability and the durability of the instrumentation. The challenge of making measurements in hostile environments is also discussed. The instruments exhibited more than adequate durability to achieve the measurement profile. About 70 percent of the thin-film thermocouples and the dual-element temperature probe survived several hundred thermal cycles and more than 35 hr at gas temperatures up to 1600 K. Within the experimental uncertainty, the steady-state and transient heat flux measurements were comparable and consistent over the range of Reynolds numbers tested.

Yeh, Frederick C.↗

NASA NTRS2020

Beam Propagation Through Atmospheric Turbulence Using an Altitude-Dependent Structure Profile with Non-Uniformly Distributed Phase Screens

Modeling the effects of atmospheric turbulence on optical beam propagation is a key element in the design and analysis of free-space optical communication systems. Numerical wave optics simulations provide a particularly useful technique for understanding the degradation of the optical field in the receiver plane when the analytical theory is insufficient for characterizing the atmospheric channel. Motivated by such an application, we use a split-step method modeling the turbulence along the propagation path as a series of thin random phase screens with modified von Karman refractive index statistics using the Hufnagel-Valley turbulence profile to determine the effective structure constant for each screen. In this work, we employ a space-to-ground case study to examine the irradiance and phase statistics for both uniformly and non-uniformly spaced screens along the propagation path and compare to analytical results. We find that better agreement with the analytical theory is obtained using a non-uniform spacing with the effective structure constant for each screen chosen to minimize its contribution to the scintillation in the receiver plane. We evaluate this method as a flexible alternative to other standard layered models used in astronomical imaging applications.

Chahine, Yousef K.↗

NASA NTRSDate not supplied

MISR Level 1B1 Radiance Data (MI1B1_V1)

The results of two types of processing are included in this product. First, the Radiance Scaling operation converts the camera's digital number output to a measure of energy incident on the front optical surface. The measurement is expressed in units called radiance (energy per unit area, wavelength, and solid angle) as defined by the International Standard (SI). Second, Radiance Conditioning modifies the radiances to remove instrument-dependent effects. Specifically, image sharpening is applied, and focal-plane scattering is removed. Additionally, all radiances are adjusted to remove slight spectral sensitivity differences among the 1504 detector elements of each spectral band and each camera. The Radiometric Product contains spectral radiances for all MISR channels (four spectral bands and nine cameras). Each radiance value represents the incident radiance averaged over the sensor's total band response. Processing includes both radiance scaling and conditioning steps. Radiance scaling converts the Level 1A data from digital counts to radiances using coefficients derived in combination with the On-Board Calibrator (OBC) and vicarious calibrations. The OBC contains Spectralon calibration panels which are deployed monthly and reflect sunlight into the cameras. The OBC detector standards then measure this reflected light to provide the calibration. Vicarious field campaigns are conducted less frequently but provide an independent methodology useful for reducing systematic errors. Radiance conditioning removes undesirable instrument effects. Image enhancement is provided by deconvolving the scene with the sensor's point-spread-function. Additionally, in-band scaling adjusts the reported radiances to correspond to a nominal band response profile. This frees the Level 2 software from the need to correct for detector element non-uniformities. No out-of-band correction is done for this product, nor are the data geometrically corrected or resampled at this point. In summary, the Level 1B1 Product contains the Data Numbers (DNs) radiometrically-scaled to radiances with no geometric resampling. [Location=GLOBAL] [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=275 m for red band only; Longitude_Resolution=275 m for red band only; Horizontal_Resolution_Range=250 meters - < 500 meters; Temporal_Resolution=about 15 orbits/day; Temporal_Resolution_Range=Daily - < Weekly, about 15 orbits/day, Daily - < Weekly].

EOSDIS↗

NASA NTRSDate not supplied

MISR Level 1B1 Radiance Data (MI1B1_V2)

The results of two types of processing are included in this product. First, the Radiance Scaling operation converts the camera's digital number output to a measure of energy incident on the front optical surface. The measurement is expressed in units called radiance (energy per unit area, wavelength, and solid angle) as defined by the International Standard (SI). Second, Radiance Conditioning modifies the radiances to remove instrument-dependent effects. Specifically, image sharpening is applied, and focal-plane scattering is removed. Additionally, all radiances are adjusted to remove slight spectral sensitivity differences among the 1504 detector elements of each spectral band and each camera. The Radiometric Product contains spectral radiances for all MISR channels (four spectral bands and nine cameras). Each radiance value represents the incident radiance averaged over the sensor's total band response. Processing includes both radiance scaling and conditioning steps. Radiance scaling converts the Level 1A data from digital counts to radiances using coefficients derived in combination with the On-Board Calibrator (OBC) and vicarious calibrations. The OBC contains Spectralon calibration panels which are deployed monthly and reflect sunlight into the cameras. The OBC detector standards then measure this reflected light to provide the calibration. Vicarious field campaigns are conducted less frequently but provide an independent methodology useful for reducing systematic errors. Radiance conditioning removes undesirable instrument effects. Image enhancement is provided by deconvolving the scene with the sensor's point-spread-function. Additionally, in-band scaling adjusts the reported radiances to correspond to a nominal band response profile. This frees the Level 2 software from the need to correct for detector element non-uniformities. No out-of-band correction is done for this product, nor are the data geometrically corrected or resampled at this point. In summary, the Level 1B1 Product contains the Data Numbers (DNs) radiometrically-scaled to radiances with no geometric resampling. [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=1.1 km; Longitude_Resolution=1.1 km; Temporal_Resolution=about 15 orbits/day; Temporal_Resolution_Range=about 15 orbits/day].

AM-1↗

NASA NTRS1974

Parachute dynamics and stability analysis

The nonlinear differential equations of motion for a general parachute-riser-payload system are developed. The resulting math model is then applied for analyzing the descent dynamics and stability characteristics of both the drogue stabilization phase and the main descent phase of the space shuttle solid rocket booster (SRB) recovery system. The formulation of the problem is characterized by a minimum number of simplifying assumptions and full application of state-of-the-art parachute technology. The parachute suspension lines and the parachute risers can be modeled as elastic elements, and the whole system may be subjected to specified wind and gust profiles in order to assess their effects on the stability of the recovery system.

Ibrahim, S. K.↗

NASA NTRS2001

Development of a Mars Airplane Entry, Descent, and Flight Trajectory

An entry, descent, and flight (EDF) trajectory profile for a Mars airplane mission is defined as consisting of the following elements: ballistic entry of an aeroshell; supersonic deployment of a decelerator parachute; subsonic release of a heat shield; release, unfolding, and orientation of an airplane to flight attitude; and execution of a pull up maneuver to achieve trimmed, horizontal flight. Using the Program to Optimize Simulated Trajectories (POST) a trajectory optimization problem was formulated. Model data representative of a specific Mars airplane configuration, current models of the Mars surface topography and atmosphere, and current estimates of the interplanetary trajectory, were incorporated into the analysis. The goal is to develop an EDF trajectory to maximize the surface-relative altitude of the airplane at the end of a pull up maneuver, while subject to the mission design constraints. The trajectory performance was evaluated for three potential mission sites and was found to be site-sensitive. The trajectory performance, examined for sensitivity to a number of design and constraint variables, was found to be most sensitive to airplane mass, aerodynamic performance characteristics, and the pull up Mach constraint. Based on the results of this sensitivity study, an airplane-drag optimized trajectory was developed that showed a significant performance improvement.

Murray, James E.↗

NASA NTRS2008

Annular and Total Solar Eclipses of 2010

While most NASA eclipse bulletins cover a single eclipse, this publication presents predictions for two solar eclipses during 2010. This has required a different organization of the material into the following sections. Section 1 -- Eclipse Predictions: The section consists of a general discussion about the eclipse path maps, Besselian elements, shadow contacts, eclipse path tables, local circumstances tables, and the lunar limb profile. Section 2 -- Annular Solar Eclipse of 2010 Ja n 15: The section covers predictions and weather prospects for the annular eclipse. Section 3 -- Total Solar Eclipse of 2010 Jul 11: The se ction covers predictions and weather prospects for the total eclipse. Section 4 -- Observing Eclipses: The section provides information on eye safety, solar filters, eclipse photography, and making contact timings from the path limits. Section 5 -- Eclipse Resources: The final section contains a number of resources including information on the IAU Working Group on Eclipses, the Solar Eclipse Mailing List, the NASA eclipse bulletins on the Internet, Web sites for the two 2010 eclipses, and a summary identifying the algorithms, ephemerides, and paramete rs used in the eclipse predictions.

Espenak, Fred↗

NASA NTRS2015

Detached Eddy Simulation for the F-16XL Aircraft Configuration

Numerical simulations for the flow around the F-16XL configuration as a contribution to the Cranked Arrow Wing Aerodynamic Project International 2 (CAWAPI-2) have been performed. The NASA Langley Tetrahedral Unstructured Software System (TetrUSS) with its USM3D solver was used to perform the unsteady flow field simulations for the subsonic high angle-of-attack case corresponding to flight condition (FC) 25. Two approaches were utilized to capture the unsteady vortex flow over the wing of the F-16XL. The first approach was to use Unsteady Reynolds-Averaged Navier-Stokes (URANS) coupled with standard turbulence closure models. The second approach was to use Detached Eddy Simulation (DES), which creates a hybrid model that attempts to combine the most favorable elements of URANS models and Large Eddy Simulation (LES). Computed surface static pressure profiles are presented and compared with flight data. Time-averaged and instantaneous results obtained on coarse, medium and fine grids are compared with the flight data. The intent of this study is to demonstrate that the DES module within the USM3D solver can be used to provide valuable data in predicting vortex-flow physics on a complex configuration.

Elmiligui, Alaa↗

NASA NTRS2017

Heating and Thermal Control of Brazing Technique to Break Contamination Path for Potential Mars Sample Return

The potential return of Mars sample material is of great interest to the planetary science community, as it would enable extensive analysis of samples with highly sensitive laboratory instruments. It is important to make sure such a mission concept would not bring any living microbes, which may possibly exist on Mars, back to Earth’s environment. In order to ensure the isolation of Mars microbes from Earth’s Atmosphere, a brazing sealing and sterilizing technique was proposed to break the Mars-to-Earth contamination path. Effectively, heating the brazing zone in high vacuum space and controlling the sample temperature for integrity are key challenges to the implementation of this technique. The break-the-chain procedures for container configurations, which are being considered, were simulated by multi-physics finite element models. Different heating methods including induction and resistive/radiation were evaluated. The temperature profiles of Martian samples in a proposed container structure were predicted. The results show that the sealing and sterilizing process can be controlled such that the samples temperature is maintained below the level that may cause damage, and that the brazing technique is a feasible approach to breaking the contamination path.

Bao, Xiaoqi↗

NASA NTRS2022

Cross-Cutting Flight Infrastructure Improvements on M2020

Mars2020 (M2020) was formulated as a mission that leveraged as much Mars Science Laboratory (MSL) heritage as possible, while focusing major new development efforts on the original and unique elements needed to accomplish the different mission objectives. Well publicized examples of high profile new developments include precision landing, the sampling and caching system, the specific instrument suite, improved mobility via Autonomous Navigation, and later the addition of the Ingenuity helicopter. Less well known are the refinements to the core flight infrastructure, primarily in the cross-cutting functions of Telecom, Avionics, Data Management, Communications Behaviors, and Parameter Management. These enhancements are introduced predominately via flight software, and represent increases in capability that justified their inclusion in an otherwise heritage-focused project environment.Perseverance’s cross-cutting flight infrastructure improvements fall into and across the following five categories. First is a trimming of the software footprint of infrastructure modules, in order to make room for memory demands elsewhere in the system. Second is the minimization of data volume to be downlinked, through various methods such as the incorporation of new compression options. Third is the maximization of the available downlink bandwidth for data, by curtailing content-less data (fill) and introducing an improved UHF proximity link protocol. Fourth is a reduction in vulnerabilities, through increased file system redundancy, robustness, and software process monitoring. Fifth is an increase in operations efficiency by lowering file system mount times, improving parallelism between simultaneous events, minimizing the time to recover from file system errors, streamlining the purging of obsolete data, and reducing the number of commands to service parameters by a factor of 100.Individually, none of the cross-cutting infrastructure improvements are likely to garner headlines, but collectively they appreciably improve the safety and operability of Perseverance over its predecessor. This paper will describe the improvements, their promise, and where applicable, their actual impact in operations.

Bohannon, Emily↗

NASA NTRSDate not supplied

MISR Level 1B1 Local Mode Radiance Data (MIB1LM_V1)

The results of two types of processing are included in this product. First, the Radiance Scaling operation converts the camera's digital number output to a measure of energy incident on the front optical surface. The measurement is expressed in units called radiance (energy per unit area, wavelength, and solid angle) as defined by the International Standard (SI). Second, Radiance Conditioning modifies the radiances to remove instrument-dependent effects. Specifically, image sharpening is applied, and focal-plane scattering is removed. Additionally, all radiances are adjusted to remove slight spectral sensitivity differences among the 1504 detector elements of each spectral band and each camera. In addition to the Level 1B1 radiometric product for MISR's Global Mode imagery, there is a separate Level 1B1 product for each high-resolution Local Mode scene. The Radiometric Product contains spectral radiances for all MISR channels (four spectral bands and nine cameras). Each radiance value represents the incident radiance averaged over the sensor's total band response. Processing includes both radiance scaling and conditioning steps. Radiance scaling converts the Level 1A data from digital counts to radiances using coefficients derived in combination with the On-Board Calibrator (OBC) and vicarious calibrations. The OBC contains Spectralon calibration panels which are deployed monthly and reflect sunlight into the cameras. The OBC detector standards then measure this reflected light to provide the calibration. Vicarious field campaigns are conducted less frequently but provide an independent methodology useful for reducing systematic errors. Radiance conditioning removes undesirable instrument effects. Image enhancement is provided by deconvolving the scene with the sensor's point-spread-function. Additionally, in-band scaling adjusts the reported radiances to correspond to a nominal band response profile. This frees the Level 2 software from the need to correct for detector element non-uniformities. No out-of-band correction is done for this product, nor are the data geometrically corrected or resampled at this point. In summary, the Level 1B1 Product contains the Data Numbers (DNs) radiometrically-scaled to radiances with no geometric resampling. [Location=GLOBAL] [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=275 m for red band only; Longitude_Resolution=275 m for red band only; Horizontal_Resolution_Range=250 km - < 500 km or approximately 2.5 degrees - < 5.0 degrees; Temporal_Resolution=about 15 orbits/day].

NEAR IR IMAGERY↗

NASA NTRSDate not supplied

MISR Level 1B1 Local Mode Radiance Data (MIB1LM_V2)

The results of two types of processing are included in this product. First, the Radiance Scaling operation converts the camera's digital number output to a measure of energy incident on the front optical surface. The measurement is expressed in units called radiance (energy per unit area, wavelength, and solid angle) as defined by the International Standard (SI). Second, Radiance Conditioning modifies the radiances to remove instrument-dependent effects. Specifically, image sharpening is applied, and focal-plane scattering is removed. Additionally, all radiances are adjusted to remove slight spectral sensitivity differences among the 1504 detector elements of each spectral band and each camera. In addition to the Level 1B1 radiometric product for MISR's Global Mode imagery, there is a separate Level 1B1 product for each high-resolution Local Mode scene. The Radiometric Product contains spectral radiances for all MISR channels (four spectral bands and nine cameras). Each radiance value represents the incident radiance averaged over the sensor's total band response. Processing includes both radiance scaling and conditioning steps. Radiance scaling converts the Level 1A data from digital counts to radiances using coefficients derived in combination with the On-Board Calibrator (OBC) and vicarious calibrations. The OBC contains Spectralon calibration panels which are deployed monthly and reflect sunlight into the cameras. The OBC detector standards then measure this reflected light to provide the calibration. Vicarious field campaigns are conducted less frequently but provide an independent methodology useful for reducing systematic errors. Radiance conditioning removes undesirable instrument effects. Image enhancement is provided by deconvolving the scene with the sensor's point-spread-function. Additionally, in-band scaling adjusts the reported radiances to correspond to a nominal band response profile. This frees the Level 2 software from the need to correct for detector element non-uniformities. No out-of-band correction is done for this product, nor are the data geometrically corrected or resampled at this point. In summary, the Level 1B1 Product contains the Data Numbers (DNs) radiometrically-scaled to radiances with no geometric resampling. [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=275 m for red band only; Longitude_Resolution=275 m for red band only; Temporal_Resolution=about 15 orbits/day].

AM-1↗

NASA NTRS1980

Finite element stress analysis of a notched coupon specimen for in-plane shear behaviour of composites

The results of a linear elastic, plane stress finite element investigation of the stress distribution in a double V-notched coupon specimen are presented for an isotropic material (steel) and five graphite/polyimide laminates: (0), (90), (0/90)s, (plus or minus 45)s and (0/90/plus or minus 45)s. Stress contours, stress profiles, and stress concentration factors are presented for specimens loaded through rigid fixtures. It is shown that the finite element analysis predicts a region of essentially uniform pure shear in the central portion of the specimen for all laminates considered. Stress concentrations vary considerably with laminate configuration. The influences of elastic fixtures and thermal stresses on the stress distribution in (0) laminates are also investigated. The (0) laminate is predicted to exhibit maximum pure shear in the center of the test section for both rigid and elastic fixtures. It is concluded that the specimen is a practicable candidate for use as a composite shear specimen.

Herakovich, C. T.↗

NASA NTRS1996

Measurement of proton production cross sections of (sup 10)Be and (sup 26)Al from elements found in lunar rocks

Cosmic rays penetrate the lunar surface and interact with the lunar rocks to produce both radionuclides and stable nuclides. Production depth profiles for long-lived radionuclides produce in lunar rocks are measured using Accelerator Mass Spectrometry (AMS). For a particular radionuclide these production depth profiles can be interpreted to give an estimate for the solar proton flux over a time period characterized by the half life of the radionuclide under study. This analysis is possible if and only if all the cross sections for the interactions of all cosmic ray particles with all elements found in lunar rocks are well known. In practice, the most important cross sections needed are the proton production cross sections, because 98% of solar cosmic rays and (similar to)87% of galactic cosmic rays are protons. The cross sections for the production of long-lived radionuclides were very difficult to measure before the development of AMS and only in recent years has significant progress been made in determining these essential cross sections. Oxygen and silicon are major constituents of lunar rocks. We have reported already C-14 production cross sections from O and Si for proton energies 25-500 MeV, and O(p,x)(sup 10)Be from 58 160 MeV[6]. Here we present new measurements for the cross sections O(p,x)Be-10,O(p,x)Be-7, Si(p,x)Be-7,Si(p,x)Al-26, and Si(p,x)Na-22 from approximately 30 - 500 MeV.

Sisterson, J. M.↗

NASA NTRS2002

Major Element Analysis of the Target Rocks at Meteor Crater, Arizona

We collected approximately 400 rock chips in continuous vertical profile at Meteor Crater, Arizona, representing, from bottom to top, the Coconino, Toroweap, Kaibab, and Moenkopi Formations to support ongoing compositional analyses of the impact melts and their stratigraphic source depth(s) and other studies at Meteor Crater that depend on the composition of the target rocks. These rock chips were subsequently pooled into 23 samples for compositional analysis by XRF (x ray fluorescence) methods, each sample reflecting a specific stratigraphic "subsection" approximately 5-10 in thick. We determined the modal abundance of quartz, dolomite, and calcite for the entire Kaibab Formation at vertical resolutions of 1-2 meters. The Coconino Formation composes the lower half of the crater cavity. It is an exceptionally pure sandstone. The Toroweap is only two inches thick and compositionally similar to Coconino, therefore, it is not a good compositional marker horizon. The Kaibab Formation is approximately 80 in thick. XRD (x ray diffraction) studies show that the Kaibab Formation is dominated by dolomite and quartz, albeit in highly variable proportions; calcite is a minor phase at best. The Kaibab at Meteor Crater is therefore a sandy dolomite rather than a limestone, consistent with pronounced facies changes in the Permian of SE Arizona over short vertical and horizontal distances. The Moenkopi forms the 12 in thick cap rock and has the highest Al2O3 and FeO concentrations of all target rocks. With several examples, we illustrate how this systematic compositional and modal characterization of the target ideologies may contribute to an understanding of Meteor Crater, such as the depth of its melt zone, and to impact cratering in general, such as the liberation of CO2 from shocked carbonates.

See, Thomas H.↗

NASA NTRS2012

Measuring Gap Fraction, Element Clumping Index and LAI in Sierra Forest Stands Using a Full-Waveform Ground-Based Lidar

The Echidna Validation Instrument (EVI), a ground-based, near-infrared (1064 nm) scanning lidar, provides gap fraction measurements, element clumping index measurements, effective leaf area index (LAIe) and leaf area index (LAI) measurements that are statistically similar to those from hemispherical photos. In this research, a new method integrating the range dimension is presented for retrieving element clumping index using a unique series of images of gap probability (Pgap) with range from EVI. From these images, we identified connected gap components and found the approximate physical, rather than angular, size of connected gap component. We conducted trials at 30 plots within six conifer stands of varying height and stocking densities in the Sierra National Forest, CA, in August 2008. The element clumping index measurements retrieved from EVI Pgap image series for the hinge angle region are highly consistent (R2=0.866) with those of hemispherical photos. Furthermore, the information contained in connected gap component size profiles does account for the difference between our method and gap-size distribution theory based method, suggesting a new perspective to measure element clumping index with EVI Pgap image series and also a potential advantage of three dimensional Lidar data for element clumping index retrieval. Therefore further exploration is required for better characterization of clumped condition from EVI Pgap image series.

Zhao, Feng↗

NASA NTRS1991

Modeling of crack bridging in a unidirectional metal matrix composite

The effective fatigue crack driving force and crack opening profiles were determined analytically for fatigue tested unidirectional composite specimens exhibiting fiber bridging. The crack closure pressure due to bridging was modeled using two approaches; the fiber pressure model and the shear lag model. For both closure models, the Bueckner weight function method and the finite element method were used to calculate crack opening displacements and the crack driving force. The predicted near crack tip opening profile agreed well with the experimentally measured profiles for single edge notch SCS-6/Ti-15-3 metal matrix composite specimens. The numerically determined effective crack driving force, Delta K(sup eff), was calculated using both models to correlate the measure crack growth rate in the composite. The calculated Delta K(sup eff) from both models accounted for the crack bridging by showing a good agreement between the measured fatigue crack growth rates of the bridged composite and that of unreinforced, unbridged titanium matrix alloy specimens.

Ghosn, Louis J.↗