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At least 1,603 records · Page 89
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Effects of a CFD-improved dimple stepped-lip piston on thermal efficiency and emissions in a medium-duty diesel engine

Diesel piston-bowl shape is a key design parameter that affects spray-wall interactions and turbulent flow development, and in turn affects the engine’s thermal efficiency and emissions. It is hypothesized that thermal efficiency can be improved by enhancing squish-region vortices as they are hypothesized to promote fuel-air mixing, leading to faster heat-release rates. However, the strength and longevity of these vortices decrease with advanced injection timings for typical stepped-lip (SL) piston geometries. Dimple stepped-lip (DSL) pistons enhance vortex formation at early injection timings. Previous engine experiments with such a bowl show 1.4% thermal efficiency gains over an SL piston. However, soot was increased dramatically [SAE 2022-01-0400]. In a previous study, a new DSL bowl was designed using non-combusting computational fluid dynamic simulations. This improved DSL bowl is predicted to promote stronger, more rotationally energetic vortices than the baseline DSL piston: it employs shallower, narrower, and steeper-curved dimples that are placed further out into the squish region. In the current experimental study, this improved bowl is tested in a medium-duty diesel engine and compared against the SL piston over an injection timing sweep at low-load and part-load operating conditions. No substantial thermal efficiency gains are achieved at the early injection timing with the improved DSL design, but soot emissions are lowered by 45% relative to the production SL piston, likely due to improved air utilization and soot oxidation. However, these benefits are lost at late injection timings, where the DSL piston renders a lower thermal efficiency than that of the SL piston. Energy balance analyses show higher wall heat transfer with the DSL piston than with the SL piston despite a 1.3% reduction in the piston surface area. Vortex enhancement may not necessarily lead to improved efficiency as more energetic squish-region vortices can lead to higher convective heat transfer losses.

42 ENGINEERING↗
DOE OSTI2021

Model-based real-time surface heat flux and temperature estimation for the DIII-D tokamak

A control-oriented model for monitoring of wall power flux densities on the DIII-D tokamak has been successfully implemented and validated experimentally. Future reactors will have to withstand severe steady state high heat flux loads on plasma-facing components (PFCs). Due to the difficulty of directly-measuring local heat fluxes on these components, monitoring and protection of PFCs during the plasma discharge can benefit from simplified physics-based real-time (RT) functional models to estimate and guide heat load control. As a first step into the development, a control-oriented model for monitoring of wall power flux densities and temperatures on DIII-D tokamak has been successfully implemented. The paper discusses the experimental demonstration and comparison of the 2-D model-based wall heat flux algorithm on the DIII-Dinner wall limiter (IWL) against infra-red camera heat flux measurements for limited plasma configurations. The paper also reports on the benchmarking of the field line tracing environment, SMITER, developed at ITER organization on DIII-D tokamak against experimental IR diagnostic data and the derivation of the component shaping weighting factors for the 2-D model-based approach. Here, the extension of the model-based approach for surface temperature estimation on the DIII-D IWL is also presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1999

Disentangling the Hard X-ray Background ROSAT HRI

The goal of our investigation was to improve our understanding of the properties of the discrete X-ray sources that produce the X-ray background (XRB). Many surveys have shown that the XRB at energies of 0.5-3.0 keV is dominated by emission from extragalactic point sources and that a significant fraction of the XRB at higher energies also is produced by discrete sources. In spite of the fact that the bulk of the 0.5-10 keV XRB was demonstrated to arise from extragalactic point sources, the spectral shape of the background presented a difficulty, referred to as the "spectral paradox". Spectra for classes of individual sources generally have been found to be incompatible with the observed energy index, alpha = 0.4 of the XRB over the 2-10 keV energy range. For the 0.3-3.0 keV Einstein band, Macca'caro et al. (1988) derived a mean energy spectral index of a approx. 0.95 for 599 extragalactic sources and for a subset of X-ray selected AGN, found alpha = 1.03(sup +0-05, sub -0.06) . Wilkes and Elvis showed that radio "loudness" was strongly correlated with the source spectrum, such that radio-load quasars exhibited flatter spectra (alpha approx. 0.5), while radio-quiet quasars had steeper spectra (alpha approx. 1). Studies of moderately faint sources in the 0.1-2.0 keV ROSAT band also found rather steep spectra (alpha = 0.96 +/- 0.11 for sources with an average flux of 1.5 x 10(exp -14) ergs/sq cm sec). At higher energies and much higher fluxes, energy spectra of individual AGN suggested a "canonical" alpha = 0.7 energy spectrum. Thus, the best evidence suggested that known classes of AGN could not readily explain the observed X-ray background spectrum. In our ROSAT PSPC analysis, we studied not only the traditional log N - log S, but also the spectral properties of the sources. We computed hardness ratios for individual sources and performed spectral fits to the summed source spectra, averaged in flux bins from 10(exp -15) to 10(exp -12) ergs/sq cm sec. We found that the hardness ratios and source spectra consistently show a hardening in the source spectra as the source fluxes decrease, confirming the suggestion by Hasinger et al. (1993).

Murray, Stephen S.↗
NASA NTRSDate not supplied

Structural Requirements and Scaling Analysis of a Fluidic Mirror Space Telescope Support Structure

The NASA FLUTE project proposes large-scale (50m) fluidic telescopes for astronomy applications. To continue to explore the universe, astronomers require larger and larger telescope apertures. The highest priority astrophysics targets such as exoplanets and early galaxies are extremely faint, motivating larger telescope apertures. However, mission costs depend on aperture diameter, and scaling apertures beyond 10-m apertures faces economic and technological viability challenges. An unsegmented primary mirror made in space via fluidic microgravity shaping would provide a scalable and cost-effective method to scale apertures to 50-m scale while achieving sub-nanometer (root mean square) surface quality. Such microgravity fluidic shaping has been demonstrated in laboratory neutral buoyance environments, parabolic microgravity experiments, as well aboard the International Space Station. One of the main components of a fluidic observatory is the mirror frame. The frame must provide a stable bounding circular ring which the edges of the fluid mirror surface can wet. The frame can optionally provide a ‘floor’ surface on the interior of the ring to provide additional fluid support and reduce required fluid volume. In this work, we evaluate several classes of structural frame architectures potentially suitable for a fluidic telescope support structure. We start by estimating stability requirements, orbital, station keeping, and slew loads based on a notional CONOPS. The scaling of overall fluid mass required for each architecture is evaluated. Preliminary results elucidate the importance of a support floor for overall mission viability above 10-m diameter. We then investigate the scaling of a tetrahedral truss frame support structure. We show that segmented solid shell support surfaces can provide sufficient stability at modest mass fractions. We estimate that the total fluid and frame mass for a 50-m telescope could be on the order of 15,000 kg. Finally, implementation considerations are discussed, including deployment/assembly methodologies. The results of this study establish feasibility of a large-scale fluidic telescope and will guide further architecture development and detailed structural design.

Christine Gregg↗
NASA NTRS1986

Aeorodynamic characteristics of an air-exchanger system for the 40- by 80-foot wind tunnel at Ames Research Center

A 1/50-scale model of the 40- by 80-Foot Wind Tunnel at Ames Research Center was used to study various air-exchange configurations. System components were tested throughout a range of parameters, and approximate analytical relationships were derived to explain the observed characteristics. It is found that the efficiency of the air exchanger could be increased (1) by adding a shaped wall to smoothly turn the incoming air downstream, (2) by changing to a contoured door at the inlet to control the flow rate, and (3) by increasing the size of the exhaust opening. The static pressures inside the circuit then remain within the design limits at the higher tunnel speeds if the air-exchange rate is about 5% or more. Since the model is much smaller than the full-scale facility, it is not possible to completely duplicate the tunnel, and it will be necessary to measure such characteristics as flow rate and tunnel pressures during implementation of the remodeled facility. The aerodynamic loads estimated for the inlet door and for nearby walls are also presented.

Rossow, V. J.↗
NASA NTRS1993

Issac, Jason Cherian ses in transonic flow

Flutter analysis of a two degree of freedom airfoil in compressible flow is performed using a state-space representation of the unsteady aerodynamic behavior. Indicial response functions are used to represent the normal force and moment response of the airfoil. The structural equations of motion of the airfoil with bending and torsional degrees of freedom are coupled to the unsteady air loads and the aeroelastic system so modelled is solved as an eigenvalue problem to determine the stability. The aeroelastic equations are also directly integrated with respect to time and the time-domain results compared with the results from the eigenanalysis. A good agreement is obtained. The derivatives of the flutter speed obtained from the eigenanalysis are calculated with respect to the mass and stiffness parameters by both analytical and finite-difference methods for various transonic Mach numbers. The experience gained from the two degree of freedom model is applied to study the sensitivity of the flutter response of a wing with respect to various shape parameters. The parameters being considered are as follows: (1) aspect ratio; (2) surface area of the wing; (3) taper ratio; and (4) sweep. The wing deflections are represented by Chebyshev polynomials. The compressible aerodynamic state-space model used for the airfoil section is extended to represent the unsteady aerodynamic forces on a generally laminated tapered skewed wing. The aeroelastic equations are solved as an eigenvalue problem to determine the flutter speed of the wing. The derivatives of the flutter speed with respect to the shape parameters are calculated by both analytical and finite difference methods.

Issac, Jason Cherion↗
NASA NTRS1995

Parallel volume ray-casting for unstructured-grid data on distributed-memory architectures

As computing technology continues to advance, computational modeling of scientific and engineering problems produces data of increasing complexity: large in size and unstructured in shape. Volume visualization of such data is a challenging problem. This paper proposes a distributed parallel solution that makes ray-casting volume rendering of unstructured-grid data practical. Both the data and the rendering process are distributed among processors. At each processor, ray-casting of local data is performed independent of the other processors. The global image composing processes, which require inter-processor communication, are overlapped with the local ray-casting processes to achieve maximum parallel efficiency. This algorithm differs from previous ones in four ways: it is completely distributed, less view-dependent, reasonably scalable, and flexible. Without using dynamic load balancing, test results on the Intel Paragon using from two to 128 processors show, on average, about 60% parallel efficiency.

Ma, Kwan-Liu↗
NASA NTRS2006

High-Strain-Rate Compression Testing of Ice

In the present study a modified split Hopkinson pressure bar (SHPB) was employed to study the effect of strain rate on the dynamic material response of ice. Disk-shaped ice specimens with flat, parallel end faces were either provided by Dartmouth College (Hanover, NH) or grown at Case Western Reserve University (Cleveland, OH). The SHPB was adapted to perform tests at high strain rates in the range 60 to 1400/s at test temperatures of -10 and -30 C. Experimental results showed that the strength of ice increases with increasing strain rates and this occurs over a change in strain rate of five orders of magnitude. Under these strain rate conditions the ice microstructure has a slight influence on the strength, but it is much less than the influence it has under quasi-static loading conditions. End constraint and frictional effects do not influence the compression tests like they do at slower strain rates, and therefore the diameter/thickness ratio of the samples is not as critical. The strength of ice at high strain rates was found to increase with decreasing test temperatures. Ice has been identified as a potential source of debris to impact the shuttle; data presented in this report can be used to validate and/or develop material models for ice impact analyses for shuttle Return to Flight efforts.

Shazly, Mostafa↗
NASA NTRS2015

Affordable Development and Demonstration of a Small NTR Engine and Stage: How Small is Big Enough?

The Nuclear Thermal Rocket (NTR) derives its energy from fission of uranium-235 atoms contained within fuel elements that comprise the engine's reactor core. It generates high thrust and has a specific impulse potential of approximately 900 seconds - a 100% increase over today's best chemical rockets. The Nuclear Thermal Propulsion (NTP) project, funded by NASA's AES program, includes five key task activities: (1) Recapture, demonstration, and validation of heritage graphite composite (GC) fuel (selected as the "Lead Fuel" option); (2) Engine Conceptual Design; (3) Operating Requirements Definition; (4) Identification of Affordable Options for Ground Testing; and (5) Formulation of an Affordable Development Strategy. During FY'14, a preliminary DDT&E plan and schedule for NTP development was outlined by GRC, DOE and industry that involved significant system-level demonstration projects that included GTD tests at the NNSS, followed by a FTD mission. To reduce cost for the GTD tests and FTD mission, small NTR engines, in either the 7.5 or 16.5 klbf thrust class, were considered. Both engine options used GC fuel and a "common" fuel element (FE) design. The small approximately 7.5 klbf "criticality-limited" engine produces approximately 157 megawatts of thermal power (MWt) and its core is configured with parallel rows of hexagonal-shaped FEs and tie tubes (TTs) with a FE to TT ratio of approximately 1:1. The larger approximately 16.5 klbf Small Nuclear Rocket Engine (SNRE), developed by LANL at the end of the Rover program, produces approximately 367 MWt and has a FE to TT ratio of approximately 2:1. Although both engines use a common 35 inch (approximately 89 cm) long FE, the SNRE's larger diameter core contains approximately 300 more FEs needed to produce an additional 210 MWt of power. To reduce the cost of the FTD mission, a simple "1-burn" lunar flyby mission was considered to reduce the LH2 propellant loading, the stage size and complexity. Use of existing and flight proven liquid rocket and stage hardware (e.g., from the RL10B-2 engine and Delta Cryogenic Second Stage) was also maximized to further aid affordability. This paper examines the pros and cons of using these two small engine options, including their potential to support future human exploration missions to the Moon, near Earth asteroids, and Mars, and recommends a preferred size. It also provides a preliminary assessment of the key activities, development options, and schedule required to affordably build, ground test and fly a small NTR engine and stage within a 10-year timeframe.

Spacecraft design↗
DOE OSTI2026

Investigation of nonlinear mechanical behavior of two superfine-grained graphites with DIC assisted disc splitting test

Using standardized uniaxial tensile test specimens is not practical due to the limited volumes in irradiation capsules, molten salt degradation facilities, or oxidation apparatus. The ASTM International Standard Test Method for Tensile Strength Estimate by Disc Compression of Manufactured Graphite (ASTM D8289) was developed to provide a convenient way for estimating tensile strength. Unlike the traditional uniaxial tensile test in ASTM C749 (International Standard Test Method for Tensile Stress–Strain of Carbon and Graphite), which uses dog-bone shaped specimens larger than 12.95 mm × 120.65 mm, the ASTM D8289 standard uses smaller discs with diameters of 6–12.7 mm. A digital image correlation (DIC) system, which uses a full-field noncontact surface displacement measurement technique, was applied along with the ASTM D8289 disc splitting test on IG-110 samples and compared with previous measurements from Mersen 2114 samples. Results confirmed that the DIC technique can measure the surface displacement/strain on these small (Ø6 mm × 3 mm) graphite specimens with good repeatability. However, Mersen 2114 and IG-110 samples exhibited strain discrepancies when DIC measurements were compared with analytical and finite element simulation values. The loading history and strain results also indicated different mechanical behaviors between Mersen 2114 and IG-110, particularly the nonlinear behavior of the IG-110 samples. Good agreement was observed by comparing the splitting tensile strengths of two superfine-grained grades with results from other work. The specimen size effect is discussed when comparing the splitting tensile strength with corresponding uniaxial tensile strength of these two graphite grades.

Lin, Lianshan [ORNL] (ORCID:0000000203399219)↗
NASA NTRS1994

Low NO.sub.x combustor

A combustor includes a dome assembly having radially outer and inner liners joined thereto and defining therebetween a combustion zone. The dome assembly includes at least one annular dome having a pair of axially extending first flanges between which are disposed a plurality of circumferentially spaced apart carburetors for discharging a fuel/air mixture into the combustion zone for generating combustion gases. An annular heat shield includes a pair of axially extending legs integrally joined to a radially extending face in a generally U-shaped configuration, with the face including a plurality of circumferentially spaced apart ports disposed concentrically with perspective ones of the carburetors for allowing the fuel/air mixture to be discharged therefrom through the heat shield. At least one of the heat shield legs includes a plurality of circumferentially spaced apart mounting holes disposed adjacent to a respective one of the dome flanges, and a plurality of mounting pins are fixedly joined to the dome flange and extend radially through respective ones of the mounting holes without interference therewith for allowing unrestrained thermal movement between the heat shield and the dome while supporting the heat shield against axial pressure loads thereon. In a preferred embodiment, the dome assembly includes three domes having respective ones of the heat shield, and respective baffles are spaced from the heat shields for providing impingement cooling thereof.

Halila, Ely E.↗
NASA NTRS2004

Space Shuttle Crawler Transporter Vibration Analysis in Support of Rollout Fatigue Load Spectra Verification Program

The Crawler Transporter (CT), designed and built for the Apollo Program in the 1960's and surpassing its initial operational life, has become an integral part of the Space Shuttle Program (SSP). The CT transports the Space Shuttle Vehicle (SSV) stack, atop the Mobile Launch Platform (MLP), from the Vehicle Assembly Building (VAB) to the launch pad. This support structure provides hydraulic jacking, leveling and load equalization for the 12 million pound stack on its 3.5-5.0 mile rollout to the launch pad. Major elements of the SSV, consisting of the orbiter, solid rocket boosters (SRB) and external tank (ET) have required fatigue analyses as part of the mission life certification. Compared to rollout vibration, the SSV sees relatively high vibration loads during launch, ascent, descent and landing phases of the mission. Although preliminary measured SRB vibration levels during rollout were of low amplitude and frequency, the duration of the rollout phase is typically high, from 5-6 hours. As part of an expanded mission life assessment, additional certification effort was initiated to define fatigue load spectra for rollout. This study addresses the CT vibration analyses in support of the rollout fatigue study. Structural models developed for modal and vibration analyses were used to identify unique CT, CT/MLP and CT/MLP/SRB vibration characteristics for comparison to instrumented rollout tests. Whereas the main structural and vibration characteristics of the SSV are well defined, minimum analytical and vibration test data on the Crawler Transporter were available. Unique vibration characteristics of the CT are attributable to the drive mechanism, hydraulic jacking system, structural framing and the CT-to-MLP support pad restraints. Initial tests performed on the CT/MLP/SRB configuration showed reasonable correlation with predicted mode shapes and frequencies.

Margasahayam, Ravi N.↗
NASA NTRS2014

Coupling Damage-Sensing Particles to the Digitial Twin Concept

The research presented herein is a first step toward integrating two emerging structural health management paradigms: digital twin and sensory materials. Digital twin is an emerging life management and certification paradigm whereby models and simulations consist of as-built vehicle state, as-experienced loads and environments, and other vehicle-specific history to enable high-fidelity modeling of individual aerospace vehicles throughout their service lives. The digital twin concept spans many disciplines, and an extensive study on the full domain is out of the scope of this study. Therefore, as it pertains to the digital twin, this research focused on one major concept: modeling specifically the as-manufactured geometry of a component and its microstructure (to the degree possible). The second aspect of this research was to develop the concept of sensory materials such that they can be employed within the digital twin framework. Sensory materials are shape-memory alloys that undergo an audible phase transformation while experiencing sufficient strain. Upon embedding sensory materials with a structural alloy, this audible transformation helps improve the reliability of crack detection especially at the early stages of crack growth. By combining these two early-stage technologies, an automated approach to evidence-based inspection and maintenance of aerospace vehicles is sought.

Hochhalter, Jacob↗
DOE OSTI2026

Advancing the quantification of aerosol-cloud interactions with the CALIPSO-CloudSat-Aqua/MODIS record

Aerosol-cloud-precipitation interactions are assessed over the non-polar ocean using more than 11 years of combined Aqua-MODIS, CALIPSO-CALIOP, and CloudSat products. The analysis first shows the benefit of incorporating vertically resolved aerosol extinction coefficient (σext) in aerosol-cloud interactions (ACI) assessments, demonstrating that: σext vertically collocated with the cloud layer () correlates best with cloud droplet number concentration (Nd), column-integrated aerosol optical depth (AOD) cannot explain the Nd variability in the extratropics, and the S-shape of the AOD-Nd relationship reported in previous studies is not replicated when using instead of AOD, with a Nd- linearity more consistent with in-situ studies over the ocean. ACI metric, estimated as the log-scale regression between CALIOP and MODIS Nd reveals that the eastern Pacific is the region with the strongest ACI, followed by the Southern Ocean. The susceptibility of clouds to changes in their liquid water path (LWP) and frequency of precipitation followed a 2-step calculation by combining the Nd- regression (ACI) with the regression between these macrophysical variables and Nd. LWP susceptibility is negative (LWP decreases with aerosol loading) and statistically significant over the eastern Pacific, eastern Atlantic, and extratropics. In contrast, vast areas of the tropical and subtropical ocean feature negligible changes in LWP with aerosol. Precipitation frequency susceptibility is negative, but the values are only significant over the coastal eastern Pacific and Atlantic. The findings suggest that previous modeling assessments relying on AOD may need to be revisited by taking advantage of the synergy between passive and active sensors.

Li, Zhujun↗
NASA NTRS1992

Pressure vessel flex joint

An airtight, flexible joint is disclosed for the interfacing of two pressure vessels such as between the Space Station docking tunnel and the Space Shuttle Orbiter bulkhead adapter. The joint provides for flexibility while still retaining a structural link between the two vessels required due to the loading created by the internal/external pressure differential. The joint design provides for limiting the axial load carried across the joint to a specific value, a function returned in the Orbiter/Station tunnel interface. The flex joint comprises a floating structural segment which is permanently attached to one of the pressure vessels through the use of an inflatable seal. The geometric configuration of the joint causes the tension between the vessels created by the internal gas pressure to compress the inflatable seal. The inflation pressure of the seal is kept at a value above the internal/external pressure differential of the vessels in order to maintain a controlled distance between the floating segment and pressure vessel. The inflatable seal consists of either a hollow torus-shaped flexible bladder or two rolling convoluted diaphragm seals which may be reinforced by a system of straps or fabric anchored to the hard structures. The joint acts as a flexible link to allow both angular motion and lateral displacement while it still contains the internal pressure and holds the axial tension between the vessels.

Kahn, Jon B.↗
NASA NTRS1992

Guidance and dispersion studies of National Launch System ascent trajectories

The National Launch System (NLS) is a joint concept, between DoD and NASA, for building a family of new launch vehicles. Two of the many choices to be made are the trajectory shaping methods and the onboard guidance scheme. This paper presents results from some ongoing studies to address these issues. First, potential gains from new guidance concepts are listed. Next the paper gives a list of possible discriminators between different guidance schemes, lists a number of potential guidance schemes, and explains two in some detail. A reference scheme is tested to determine its performance versus the discriminators. Finally, results from some special studies using the reference guidance scheme are given, including the effects of closed-loop guidance initiation time, time of enforcement of sideslip, vehicle roll for engine out, time and location of an engine out, use of load relief control, and use of day of launch wind biasing.

Hanson, John M.↗
DOE OSTI2022

Disruption prediction with artificial intelligence techniques in tokamak plasmas

In nuclear fusion reactors, plasmas are heated to very high temperatures of more than 100 million kelvin and, in so-called tokamaks, they are confined by magnetic fields in the shape of a torus. Light nuclei, such as deuterium and tritium, undergo a fusion reaction that releases energy, making fusion a promising option for a sustainable and clean energy source. Tokamak plasmas, however, are prone to disruptions as a result of a sudden collapse of the system terminating the fusion reactions. As disruptions lead to an abrupt loss of confinement, they can cause irreversible damage to present-day fusion devices and are expected to have a more devastating effect in future devices. Disruptions expected in the next-generation tokamak, ITER, for example, could cause electromagnetic forces larger than the weight of an Airbus A380. Furthermore, the thermal loads in such an event could exceed the melting threshold of the most resistant state-of-the-art materials by more than an order of magnitude. In this work, to prevent disruptions or at least mitigate their detrimental effects, empirical models obtained with artificial intelligence methods, of which an overview is given here, are commonly employed to predict their occurrence—and ideally give enough time to introduce counteracting measures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1988

A re-evaluation of finite-element models and stress-intensity factors for surface cracks emanating from stress concentrations

A re-evaluation of the 3-D finite-element models and methods used to analyze surface crack at stress concentrations is presented. Previous finite-element models used by Raju and Newman for surface and corner cracks at holes were shown to have ill-shaped elements at the intersection of the hole and crack boundaries. These ill-shaped elements tended to make the model too stiff and, hence, gave lower stress-intensity factors near the hole-crack intersection than models without these elements. Improved models, without these ill-shaped elements, were developed for a surface crack at a circular hole and at a semi-circular edge notch. Stress-intensity factors were calculated by both the nodal-force and virtual-crack-closure methods. Both methods and different models gave essentially the same results. Comparisons made between the previously developed stress-intensity factor equations and the results from the improved models agreed well except for configurations with large notch-radii-to-plate-thickness ratios. Stress-intensity factors for a semi-elliptical surface crack located at the center of a semi-circular edge notch in a plate subjected to remote tensile loadings were calculated using the improved models. The ratio of crack depth to crack length ranged form 0.4 to 2; the ratio of crack depth to plate thickness ranged from 0.2 to 0.8; and the ratio of notch radius to the plate thickness ranged from 1 to 3. The models had about 15,000 degrees-of-freedom. Stress-intensity factors were calculated by using the nodal-force method.

Tan, P. W.↗