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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.

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NASA NTRS1986

Accuracy of wind measurements using an airborne Doppler lidar

Simulated wind fields and lidar data are used to evaluate two sources of airborne wind measurement error. The system is sensitive to ground speed and track angle errors, with accuracy required of the angle to within 0.2 degrees and of the speed to within 1 knot, if the recovered wind field is to be within five percent of the correct direction and 10 percent of the correct speed. It is found that errors in recovered wind speed and direction are dependent on wind direction relative to the flight path. Recovery of accurate wind fields from nonsimultaneous sampling errors requires that the lidar data be displaced to account for advection so that the intersections are defined by air parcels rather than fixed points in space.

Carroll, J. J.↗
NASA NTRSDate not supplied

NASA’s Moon Trek Portal: New Capabilities Supporting Mission Planning and Engagement

Introduction: NASA’s Moon Trek (https://trek.nasa.gov/moon/) is one of a growing number of interactive, browser-based, online portals for planetary data visualization and analysis produced by NASA’s Solar System Treks Project (SSTP). Moon Trek continues to be enhanced with new data and new capabilities enabling it to facilitate the planning and conducting of upcoming lunar missions by NASA, its commercial partners, and its international partners, as well as advancing its role as a valuable outreach tool. A Comprehensive Online Web Portal: Developed at NASA’s Jet Propulsion Laboratory (JPL) and managed as a project of NASA’s Solar System Exploration Research Virtual Institute (SSERVI) at NASA Ames Research Center, Moon Trek is a browser-based web portal. The portal provides easy-to-use tools for browsing, data layering, data product blending, and feature search among thousands of data products covering topography, mineralogy, elemental abundance, geology, and much more. Visualizations are provided in var-ious map projections, interactive 3D viewing, and in virtual reality. Using an in-house stereo workflow, SSTP is able to produce new NAC-based high-resolution mosaics and DEMs. Diverse Applications for Lunar Exploration: Baseline analytic tools available to all users include dis-tance measurement, elevation profiling, sun angle calculation, and 3D print file generation. More advanced account-level tools allow users to perform more computationally intensive analyses. These include ray-traced lighting analysis for user-specified areas over user-specified time/date ranges and time intervals, electro-static surface potential analysis, subsetting of large data products, slope analysis, and Lunar Laser Ranging geometry calculation. Artificial intelligence (AI) and ma-chine learning (ML) based tools have been implemented for crater detection and hazard analysis, boulder detection and hazard analysis, and rockfall detection. New Tools Facilitating Exploration: Additional, new tools have recently been added and others are in development, offering even greater functionality in con-ducting analyses of potential landing sites and areas of surface operations. The new Line-of-Sight tool facilitates communications planning between locations on the lunar surface, between any given site on the lunar surface and a specified ground station on the Earth, and between a site on the lunar surface and a relay asset in lunar orbit, all taking into account local lunar topography. The new Data Plotter tool provides both tabular and graphical representations of pixel values along a user specified path for a growing number of data products. The new NAC Finder tool will identify and pro-vide access to NAC images that intersect a user-defined path or bounded area. The SSTP development team is looking to leverage the capabilities of its existing AI and ML crater, boulder, and rockfall detection and analysis tools, and extend that technology to a generalized feature detector that can be trained on instances of specific types of landforms and then search the lunar surface for more examples of such features. New traverse planning tools are being developed with use cases in generalized concept studies and specific mission planning in mind. These will facilitate finding optimal traverse paths based on constraints such as slope, lighting, hazard avoidance, and communications. These will be complemented by new traverse visualization capabilities. Users will be able to interactively ride along with a rover, examining 3D views of the terrain while adjusting camera height and viewing angle along with selecting different data layer overlays to drape across the terrain. Engaging the Public: The capabilities being developed for mission planning are being leveraged to further enhance Moon Trek’s proven utility as a valuable public outreach resource. This includes providing multiple lev-els of engagement with different points of entry. At its simplest level, promoting understanding through visualization, media and the public will be able to easily visualize and conduct their own exploration of lunar sites targeted by NASA and its partners. For a more in-depth experience, we are working with our stakeholders to promote understanding through interaction by extend-ing our current landing site and traverse analysis capabilities, making simplified access to these tools available to those who want to explore more deeply key factors in planning a mission through interactive and possibly even gamified experiences. The highest degree of public outreach, focusing on engagement through scientific participation, could be achieved through our work with missions and the NASA Office of the Chief Scientist on Moon Trek’s extension as a tool with specialized capabilities for facilitating citizen science. In such scenarios, participants become members of extended mis-sion science teams, using dedicated and integrated interfaces to analyze mission data to help answer questions key to lunar science and exploration. We are work-ing with NASA’s Office of Communications, museums, planetariums, and the media to help them easily integrate accurate, detailed visualizations of NASA’s lunar destinations and exploration into their content/productions and to engage diverse audiences in diverse venues.

Moon Trek↗
NASA NTRS1980

Incorporation of star measurements for the determination of orbit and attitude parameters of a geosynchronous satellite: An iterative application of linear regression

Currently on NOAA/NESS's VIRGS system at the World Weather Building star images are being ingested on a daily basis. The image coordinates of the star locations are measured and stored. Subsequently, the information is used to determine the attitude, the misalignment angles between the spin axis and the principal axis of the satellite, and the precession rate and direction. This is done for both the 'East' and 'West' operational geosynchronous satellites. This orientation information is then combined with image measurements of earth based landmarks to determine the orbit of each satellite. The method for determining the orbit is simple. For each landmark measurement one determines a nominal position vector for the satellite by extending a ray from the landmark's position towards the satellite and intersecting the ray with a sphere with center coinciding with the Earth's center and with radius equal to the nominal height for a geosynchronous satellite. The apparent motion of the satellite around the Earth's center is then approximated with a Keplerian model. In turn the variations of the satellite's height, as a function of time found by using this model, are used to redetermine the successive satellite positions by again using the Earth based landmark measurements and intersecting rays from these landmarks with the newly determined spheres. This process is performed iteratively until convergence is achieved. Only three iterations are required.

Phillips, D.↗
NASA NTRS2005

Face Gear Drive With Helical Involute Pinion: Geometry, Generation by a Shaper and a Worm, Avoidance of Singularities and Stress Analysis

A new type of face-gear drive with intersected axes of rotation formed by a helical involute pinion and conjugated face-gear has been investigated. Generation of face-gears by a shaper free of undercutting and pointing has been investigated. A new method of grinding or cutting of face-gears by a worm of special shape has been developed. A computerized design procedure has been developed to avoid undercutting and pointing by a shaper or by a generating worm. Also, a method to determine the limitations of the helix angle magnitude has been developed. The method provides a localization of the bearing contact to reduce the shift of bearing contact caused by misalignment. The analytical method provides a simulation of the meshing and contact of misaligned gear drives. An automatic mesh generation method has been developed and used to conduct a 3D contact stress analysis of several teeth. The theory developed is illustrated with several examples.

Litvin, Faydor L.↗
NASA NTRS1983

Factors controlling the location of the Venus bow shock

The location of the Venus bow shock determined from magnetic field measurements during the first and third years of Pioneer Venus orbiter operation is examined and compared with nearly simultaneously obtained interplanetary solar wind data to determine those factors that control the size of the Venus bow shock. The location of the intersection of the bow shock with the terminator that is best determined by the data does not vary significantly between years 1979 and 1981 and is only 16 percent more distant than the Venera 9 and 10 shock when account is taken of solar wind aberration. Alfvenic Mach number and magnetosonic Mach number affect the size of the bow shock significantly. Solar wind dynamic pressure has a lesser effect. No significant asymmetries in the shock shape were found either as a result of the orientation of the clock angle of the IMF in the terminator plane or the angle of the IMF relative to the shock normal.

Tatrallyay, M.↗
NASA NTRS1979

Definition of mutually optimum NDI and proof test criteria for 2219 aluminum pressure vessels. Volume 3: Applications to rail defect evaluation

The technique for inspection of railroad rails containing transverse fissure defects was discussed. Both pulse-echo and pitch-catch inspection techniques were used. The pulse-echo technique results suggest that a multiple-scan approach using varying angles of inclination, three-surface scanning, and dual-direction traversing may offer promise of characterization of transverse defects. Because each scan is likely to produce a reflection indicating only a portion of the defect, summing of the individual reflections must be used to obtain a reasonably complete characterization of the defect. The ability of the collimated pitch-catch technique to detect relatively small amounts of flaw growth was shown. The method has a problem in characterizing the portions of the defect near the top surface or web intersection. The work performed was a preliminary evaluation of the prospects for automated mapping of rail flaws.

Schwartzberg, F. R.↗
NASA NTRS1990

Experimental investigation of a single flush-mounted hypermixing nozzle

The results of an experimental wind tunnel investigation of a circular supersonic jet (m sub j = 3.47) injected at a 10 degree angle into a supersonic freestream. The jet penetrates a boundary layer, which has a thickness approximately the same as the jet nozzle exit diameter. Measurements were made for nominal freestream Mach numbers of 1.6, 2.0, 2.5, and 3.0. Three jet total pressures were run at each freestream Mach number, resulting in twelve separate operating conditions. Mean data accumulated by means of static and total pressure probe instrumentation are presented at two axial stations: seven jet nozzle diameters upstream and 15 jet nozzle diameters downstream from where the centerline of the nozzle intersects the wind tunnel wall. For one condition at each freestream Mach number, the jet air was seeded with a hydrocarbon trace gas and the flow was sampled at the downstream measurement plane to quantify the mean mixing of the two streams. Surface oil flow visualization was also used to investigate the flow interaction. All results are for air-to-air mixing. The measurements indicate the presence of two pairs contra-rotating vortices. One pair follows the jet trajectory and tends to split the jet into two streams. A smaller pair, rotating in an opposite sense, develops in the near wall region. Reported results include Mach number and volume fraction distributions in the cross plane, as well as jet penetration and mixing efficiency.

Davis, David O.↗
NASA NTRS1984

Reflectance Modeling

The main thrust of the work conducted is in the modeling of spectral responses of discontinuous conifer forest canopies, considered as collections of conical forms that are illuminated at an angle and cast shadows on contracting background. The three first-year objectives are: (1) modification of the variance-driven model to incorporate overlapping of shadows and crowns; (2) collection and analysis of photographic data to calibrate tree-spacing functions; and (3) collection of field data to determine height, spacing, and shape of conifers in open and closed stands in the Goosenest (California) test area. Modification of the invertible model uses a linear approximation to correct for the reduction in shadow and canopy area that occurs when shadows fall on crowns or tree crowns intersect. Comparison of the results of the approximation with a series of Monte Carlo simulations shows that the mean area covered by crowns or shadows is approximated quite accurately, but the variance calculated departs significantly from simulated values. The analysis of tree spacing patterns using air photos showed that spacing tended to be somewhat regular at a scale approximately equal to the average distance between trees, but at larger distance scales counts of trees in cells could be approximated acceptably by a Poisson (random) function.

Strahler, A. H.↗
NASA NTRS1977

Scattering from a moving spherical particle by two crossed coherent plane waves

The Mie scattering properties of a homogeneous, isotropic spherical particle, moving at a constant velocity and illuminated by two intersecting coherent plane waves having the same polarization direction, have been analyzed based upon an exact solution to Maxwell's equations. The solutions are in a form suitable for the calculation of the time varying scattered signal integrated across a detector aperture of variable size that is centered on either the forward or backward scattering direction. This problem is of importance in defining the scattered signal in a cross beam laser Doppler velocimeter (LDV). Results obtained from calculating the integrated scattered signal indicate a strong dependence upon the following physical parameters: particle size, index of refraction, cross beam angle, and collection solid angle.

Chu, W. P.↗
NASA NTRS1987

Experimental Study of Shock Wave Interference Heating on a Cylindrical Leading Edge

An experimental study of shock wave interference heating on a cylindrical leading edge representative of the cowl of a rectangular hypersonic engine inlet at Mach numbers of 6.3, 6.5, and 8.0 is presented. Stream Reynolds numbers ranged from 0.5 x 106 to 4.9 x 106 per ft. and stream total temperature ranged from 2100 to 3400 R. The model consisted of a 3" dia. cylinder and a shock generation wedge articulated to angles of 10, 12.5, and 15 deg. A fundamental understanding was obtained of the fluid mechanics of shock wave interference induced flow impingement on a cylindrical leading edge and the attendant surface pressure and heat flux distributions. The first detailed heat transfer rate and pressure distributions for two dimensional shock wave interference on a cylinder was provided along with insight into the effects of specific heat variation with temperature on the phenomena. Results show that the flow around a body in hypersonic flow is altered significantly by the shock wave interference pattern that is created by an oblique shock wave from an external source intersecting the bow shock wave produced in front of the body.

Wieting, Allan R.↗
NASA NTRS1988

Precision in the perception of direction of a moving pattern

The precision of the model of pattern motion analysis put forth by Adelson and Movshon (1982) who proposed that humans determine the direction of a moving plaid (the sum of two sinusoidal gratings of different orientations) in two steps is qualitatively examined. The volocities of the grating components are first estimated, then combined using the intersection of constraints to determine the velocity of the plaid as a whole. Under the additional assumption that the noise sources for the component velocities are independent, an approximate expression can be derived for the precision in plaid direction as a function of the precision in the speed and direction of the components. Monte Carlo simulations verify that the expression is valid to within 5 percent over the natural range of the parameters. The expression is then used to predict human performance based on available estimates of human precision in the judgment of single component speed. Human performance is predicted to deteriorate by a factor of 3 as half the angle between the wavefronts (theta) decreases from 60 to 30 deg, but actual performance does not. The mean direction discrimination for three human observers was 4.3 plus or minus 0.9 deg (SD) for theta = 60 deg and 5.9 plus or minus 1.2 for theta = 30 deg. This discrepancy can be resolved in two ways. If the noises in the internal representations of the component speeds are smaller than the available estimates or if these noises are not independent, then the psychophysical results are consistent with the Adelson-Movshon hypothesis.

Stone, Leland S.↗
NASA NTRS1992

Imaging radar investigations of the Sudbury structure

This paper reports preliminary results of airborne imaging radar studies of the Sudbury structure carried out in preparation for a CCRS European Remote Sensing Satellite (ERS-1) investigation. The data used were synthetic aperture radar (SAR) C-band (5.66 cm) images acquired from about 6 km altitude in 1987. They cover the Sudbury area in both wide and narrow swath modes, with east-west flight paths and north-south illumination directions. Narrow swath resolution is 6 m in range and azimuth; wide swath resolution is 20 m in range and 10 m in azimuth. The STAR imagery has proven highly effective for field use, providing excellent rendition of topography and topographically expressed structure. Reasons for this include the illumination geometry, notably the look azimuth normal to the long axis of the Sudbury structure and Penokean fold axes, the good spatial resolution, and the short wavelength. Forested areas in the Sudbury area tend to be uniformly rough at C-band wavelength, with backscatter dominated by local incidence angle (i.e., topography). Field work using the SAR imagery has to date been concentrated in the North Range and Superior Province as far north as the Benny greenstone belt. This area was chosen for initial investigation of the original size and shape of the Sudbury structure because the effects of the Penokean Orogeny were minimal there. Field work using SAR indicates that there has been little postimpact deformation of the North Range or adjacent Superior Province rock. There appears to be no evidence for an outer ring concentric with the North Range as indicated by early Landsat imagery. The apparent ring shown by Landsat is visible on the SAR imagery as the intersection of two regional fracture patterns not related to the Sudbury structure. There is no outer ring visible southwest of the structure. This can reasonably be explained by Penokean deformation, but there is no outer ring to the northeast cutting the relatively undeformed Huronian sediments of the Cobalt Embayment.

Lowman, P. D.↗
NASA NTRS2010

Ballistics Model for Particles on a Horizontal Plane in a Vacuum Propelled by a Vertically Impinging Gas Jet

A simple trajectory model has been developed and is presented. The particle trajectory path is estimated by computing the vertical position as a function of the horizontal position using a constant horizontal velocity and a vertical acceleration approximated as a power law. The vertical particle position is then found by solving the differential equation of motion using a double integral of vertical acceleration divided by the square of the horizontal velocity, integrated over the horizontal position. The input parameters are: x(sub 0) and y(sub 0), the initial particle starting point; the derivative of the trajectory at x(sub 0) and y(sub 0), s(sub 0) = s(x(sub 0))= dx(y)/dy conditional expectation y = y((sub 0); and b where bx(sub 0)/y(sub 0) is the final trajectory angle before gravity pulls the particle down. The final parameter v(sub 0) is an approximation to a constant horizontal velocity. This model is time independent, providing vertical position x as a function of horizontal distance y: x(y) = (x(sub 0) + s(sub 0) (y-y(sub 0))) + bx(sub 0) -(s(sub 0)y(sub 0) ((y - y(sub 0)/y(sub 0) - ln((y/y(sub 0)))-((g(y-y(sub 0)(exp 2))/ 2((v(sub 0)(exp 2). The first term on the right in the above equation is due to simple ballistics and a spherically expanding gas so that the trajectory is a straight line intersecting (0,0), which is the point at the center of the gas impingement on the surface. The second term on the right is due to vertical acceleration, which may be positive or negative. The last term on the right is the gravity term, which for a particle with velocities less than escape velocity will eventually bring the particle back to the ground. The parameters b, s(sub 0), and in some cases v(sub 0), are taken from an interpolation of similar parameters determined from a CFD simulation matrix, coupled with complete particle trajectory simulations.

Lane, J. E.↗
NASA NTRS2001

Thermal Analysis for Orbiter and ISS Plume Impingement on International Space Station

The NASA Reaction Control System (RCS) Plume Model (RPM) is an exhaust plume flow field and impingement heating code that has been updated and applied to components of the International Space Station (ISS). The objective of this study was to use this code to determine if plume environments from either Orbiter PRCS jets or ISS reboost and Attitude Control System (ACS) jets cause thermal issues on ISS component surfaces. This impingement analysis becomes increasingly important as the ISS is being assembled with its first permanent crew scheduled to arrive by the end of fall 2000. By early summer 2001 , the ISS will have a number of major components installed such as the Unity (Node 1), Destiny (Lab Module), Zarya (Functional Cargo Block), and Zvezda (Service Module) along with the P6 solar arrays and radiators and the Z-1 truss. Plume heating to these components has been analyzed with the RPM code as well as additional components for missions beyond Flight 6A such as the Propulsion Module (PM), Mobile Servicing System, Space Station Remote Manipulator System, Node 2, and the Cupola. For the past several years NASA/JSC has been developing the methodology to predict plume heating on ISS components. The RPM code is a modified source flow code with capabilities for scarfed nozzles and intersecting plumes that was developed for the 44 Orbiter RCS jets. This code has been validated by comparison with Shuttle Plume Impingement Flight Experiment (SPIFEX) heat flux and pressure data and with CFD and Method of Characteristics solutions. Previous analyses of plume heating predictions to the ISS using RPM have been reported, but did not consider thermal analysis for the components nor jet-firing histories as the Orbiter approaches the ISS docking ports. The RPM code has since been modified to analyze surface temperatures with a lumped mass approach and also uses jet-firing histories to produce pulsed heating rates. In addition, RPM was modified to include plume heating from ISS jets to ISS components where the jet coordinates are specified, together with the engine cant angle. These latter studies have been focused on the PM with plumes from its reboost and ACS jets impinging on various ISS components and also focused on the Japanese H2 Transfer Vehicle (HTV) with the plumes from its reboost engines impinging on the Cupola window. This paper will present plume heating and surface temperature results on a number of ISS components with and without jet-firing histories, evaluate post-flight data, and describe any potential thermal issues

Rochelle, William C.↗
NASA NTRS1994

Mode properties of low-frequency waves: Kinetic theory versus Hall-MHD

In fluid theory, the ordering of low-frequency modes in a homogeneous plasma is based on the phase velocity, since modes do not intersect each other in dispersion diagrams as a function of wavenumber or other parameters. In linear kinetic theory, modes cross each other. Thus a consistent and useful classification should be based on the physical properties of the modes instead. This paper attempts such a classification by documeting the dispersion and general mode properties of the low-frequency waves (omega much less than (OMEGA(sub ci) OMEGA(sub ce) (exp 1/2)), where OMEGA(sub ci), OMEGA(sub ce) are the cyclotron frequencies of the ions and electrons, respectively) in kinetic theory, and by comparing them to the results of two-fluid theory. Kinetic theory gives a seperate Alfven/ion-cyclotron (A/IC) wave with phase speed Omega/k approximately = v(sub A) cos theta for omega much less than OMEGA(sub ci), where v(sub A) is the Alfven velocity and theta the angle of propagation between wave vector k and background magnetic field B(sub o). For a given wavenumber, the magnetosonic mode is a double-valued solution with a singular point in theta, beta parameter space, where beta is the ratio of thermal pressure to magnetic pressure. It is shown that a branch cut starting at the singular point theta approximately 30 deg, beta approximately 3 and leading to larger beta gives a practical and consitent seperation of this double-valued magnetosonic solution. Selection of this branch cut results in a moderately damped fast/magnetos onic and a heavily damped slow/sound wave. A comprehensive review of the polarization, compressibility and other mode properties is given and shown to be consistent with the selected branch cut. At small wavenumbers, the kinetic mode properties typically start to deviate significantly from their fluid counterparts at beta approximately 0.5. At larger beta, there is no longer a consistent correspondence between the fluid and kinetic modes. Kinetic theory also dictates the use of different mode properties to distinguish between them in observational data. For example, the phase between the density and magnetic field perturbation may become useless at high beta, whereas the direction of the magnetic field perturbations with respect to k and B(sub o) remains a useful characteristic. Two quantities based on this characteristic are suggested and are shown to be useful also to distinguish between the mirror mode and A/IC waves in a plasma with temperature anisotropy.

Krauss-Varban, D.↗
NASA NTRS1993

Investigation of a strut/endwall interaction in supersonic annular flow

A combined experimental and numerical investigation of strut/endwall interactions within an annular duct having a supersonic core flow has been conducted. Four diamond-shaped struts with a 7 deg half angle were positioned circumferentially equidistant within an annular duct having a gap height of 0.7 strut chords, and an inner-to-outer wall radius ratio of 0.7. Turbulent boundary layers exist on both inner and outer walls of the duct, but have not merged. The core flow upstream of the struts is uniform at a nominal Mach number of 3.0 and a Reynolds number of 3 x 10 exp 5 based on the strut chord length. Experimental results, which include Pitot pressure distributions within the flow field, static pressure distributions on the inner and outer walls of the duct, and oil flow visualization on the centerbody and strut, are presented and compared with CFD predictions. Secondary flows associated with the interactions are examined including the trajectories of the horseshoe vortices formed at the leading and trailing edges of the strut and the trajectories of the vortices formed in the corner of the strut/endwall intersection.

Williams, K. E.↗
NASA NTRS1991

Analysis of matrix cracking and local delamination in (0/theta/-theta)sub s graphite epoxy laminates under tension load

Several 3D finite element analyses of (0/theta/-theta)sub s graphite epoxy laminates, where theta=15, 20, 25, 30, and 45 deg, subjected to axial tension load were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized mode I component near the free edge, within one ply distance from the matrix crack. In order to examine the stress state causing the matrix cracking the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increases through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface. Crack profiles on the laminate edge in the -theta ply were constructed from the principal stress directions. The cracks were found to be more curved for layups with smaller theta angles, which is consistent with experimental observations in the literature.

Salpekar, S. A.↗
NASA NTRS1991

Analysis of matrix cracking and local delamination in (O/theta/-theta)sub s graphite epoxy laminates under tension load

Several 3D finite element analyses of (O/theta/-theta)sub s graphite epoxy laminates, where theta = 15, 20, 25, 30, and 45 deg, subjected to axial tension load were performed. The interlaminar stresses in the theta/-theta interface were calculated with and without a matrix crack in the central -theta plies. The interlaminar normal stress changes from a small compressive stress when no matrix crack is present to a high tensile stress at the intersection of the matrix crack and free edge. The analysis of local delamination from the -theta matrix crack indicates a high strain energy release rate and a localized mode I component near the free edge, within one ply distance from the matrix crack. In order to examine the stress state causing the matrix cracking the maximum principal normal stress in a plane perpendicular to the fiber direction in the -theta ply was calculated in an uncracked laminate. The corresponding shear stress parallel to the fiber was also calculated. The principal normal stress at the laminate edge increases through the ply thickness and reached a very high tensile value at the theta/-theta interface indicating that the crack in the -theta ply may initiate at the theta/-theta interface. Crack profiles on the laminate edge in the -theta ply were constructed from the principal stress directions. The cracks were found to be more curved for layups with smaller theta angles, which is consistent with experimental observations in the literature.

Salpekar, S. A.↗