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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Thermal Protection Systems Technology Transfer from Apollo and Space Shuttle to the Orion Program

This paper describes how the Orion program is utilizing the Thermal Protection System (TPS) experience from the Apollo and Space Shuttle programs to reduce program risk and improve affordability to meet NASA's future manned exploration missions. The Orion program successfully completed the Exploration Flight Test (EFT-1) mission in 2014 and is currently assembling, integrating, and testing the next spacecraft for the Exploration Mission (EM-1) to meet the flight test objectives of an unmanned orbital mission to the moon and return to earth in 2019. The Orion spacecraft production operations are located in the Neil Armstrong Operations and Checkout (O&C) facility at the Kennedy Space Center (KSC) providing an affordable and seamless delivery approach of vehicles directly to the launch site eliminating spacecraft transportation and additional checkout testing. Innovative vehicle design, manufacturing and test operations approaches are maturing and evolving with each Orion vehicle build to support the challenging NASA exploration mission requirements beyond Low Earth Orbit (LEO) while reducing program cost and schedule impacts. An example of Orion's evolution is the incorporation of an improved heat shield design, assembly and testing approach to meet the higher re-entry velocities for a lunar return for the EM-1 mission. The EFT- 1 heat shield was based on the Apollo heat shield manufacturing processes and was assembled at a supplier location and then transported to KSC for final integration. The EM-1 heat shield is now manufactured, assembled, tested, and installed into the spacecraft at the O&C facility reducing program cost and production schedules. The transition of the Space Shuttle TPS capabilities has enabled Orion to provide a human rated capsule design using proven materials and processes established over years of orbiter re-entry missions. The Orion Crew Module (CM) TPS configuration is derived from the Apollo CM approach utilizing improved materials and processes developed from the Space Shuttle program. The Orion EFT-1 heat shield utilized the Avcoat ablative material from Apollo which was injected into a honeycomb substrate and has been updated for EM-1 incorporating a block configuration bonded to a composite shell structure. This approach utilizes the proven Avcoat material for the heat shield ablator and is utilizing derived bonding and inspection methods and techniques from the Space Shuttle tile experience. The Orion back shell TPS configuration is based on Space Shuttle tile designs using proven tile materials and coatings. The Orion forward bay cover utilizes the high temperature tiles similar to the back shell tiles and low temperature blankets derived from the Space Shuttle program reducing weight impacts. Space Shuttle Multi-Layer Insulation (MLI) is installed in the Orion capsule to control the interior temperature environment providing a light weight design. These TPS design approaches have performed successfully on the Orion first flight test on EFT-1 and are incorporated in the configuration for the next flight test for EM-1. Completion of these two flight tests will certify the TPS for the Orion program for human rated exploration missions and has reduced the development cost to the Orion program. In addition to transitioning the Space Shuttle TPS design configurations to Orion, the supporting manufacturing infrastructure, manufacturing processes, and inspection methods are also incorporated into the Orion assembly operations at KSC. This has avoided significant startup schedule and costs impacts of new capabilities and development of support operations necessary to fabricate, install, inspect, and validate the TPS installations for the Orion spacecraft. The Thermal Protection System Facility (TPSF) which supported the Space Shuttle program provides the heat shield Avcoat blocks and the back shell AETB-8 tiles for Orion program. Extending the existing Space Shuttle TPS operations at KSC provides onsite support to the Orion spacecraft assembly operations. A significant benefit to the Orion program is the transition of the Space Shuttle technician work force at KSC. This highly skilled workforce was able to transition to the Orion program and immediately support the TPS installation operations. They brought with them the human rated manufacturing and assembly operations culture that was critical to the Space Shuttle success avoiding the retraining cost and schedule impacts of a new workforce to Orion. The technician skills certification program from the Space Shuttle was found to be compatible with the Lockheed Martin technician certification programs enabling a seamless training process utilizing process similarity avoiding the cost of retraining the work force to Orion standards. The existing workforce is certificated for multiple processes enabling reassignment of technicians to other tasks in the Orion AI&P operations reducing the overall touch labor manpower requirements. Additional benefits of using the Space Shuttle workforce is the incorporation of the lessons learned from Space Shuttle processes to improve the Orion TPS processes. This has resulted in a continuous evolution of TPS processes to improve the producibility and reduce the program cost for the TPS for the Orion program. Transitioning the Apollo and Space Shuttle TPS designs, processes, and technician workforce has been instrumental in enabling Orion to successfully meet the program challenges for NASA's exploration missions of the future.

Stewart, Michael↗
NASA NTRS2010

Orbital Debris Detection and Tracking Strategies for the NASA/AFRL Meter Class Autonomous Telescope (MCAT)

MCAT (Meter-Class Autonomous Telescope) is a 1.3m f/4 Ritchey-Chr tien on a double horseshoe equatorial mount that will be deployed in early 2011 to the western pacific island of Legan in the Kwajalein Atoll to perform orbital debris observations. MCAT will be capable of tracking earth orbital objects at all inclinations and at altitudes from 200 km to geosynchronous. MCAT s primary objective is the detection of new orbital debris in both low-inclination low-earth orbits (LEO) and at geosynchronous earth orbit (GEO). MCAT was thus designed with a fast focal ratio and a large unvignetted image circle able to accommodate a detector sized to yield a large field of view. The selected primary detector is a close-cycle cooled 4Kx4K 15um pixel CCD camera that yields a 0.9 degree diagonal field. For orbital debris detection in widely spaced angular rate regimes, the camera must offer low read-noise performance over a wide range of framing rates. MCAT s 4-port camera operates from 100 kHz to 1.5 MHz per port at 2 e- and 10 e- read noise respectively. This enables low-noise multi-second exposures for GEO observations as well as rapid (several frames per second) exposures for LEO. GEO observations will be performed using a counter-sidereal time delay integration (TDI) technique which NASA has used successfully in the past. For MCAT the GEO survey, detection, and follow-up prediction algorithms will be automated. These algorithms will be detailed herein. For LEO observations two methods will be employed. The first, Orbit Survey Mode (OSM), will scan specific orbital inclination and altitude regimes, detect new orbital debris objects against trailed background stars, and adjust the telescope track to follow the detected object. The second, Stare and Chase Mode (SCM), will perform a stare, then detect and track objects that enter the field of view which satisfy specific rate and brightness criteria. As with GEO, the LEO operational modes will be fully automated and will be described herein. The automation of photometric and astrometric processing (thus streamlining data collection for environmental modeling) will also be discussed.

Mulrooney, M.↗
DOE OSTI2018

Photoluminescent and Thermoluminescent Studies of Dy{sup 3+} and Eu{sup 3+} Doped Y{sub 2}O{sub 3} Phosphors

Eu{sup 3+} doped and Dy{sup 3+} codoped yttrium oxide (Y{sub 2}O{sub 3}) phosphors have been prepared using solid-state reaction technique (SSR). The prepared phosphors were characterized by X-ray diffractometer (XRD), energy dispersive X-ray (EDX) spectroscopy, scanning electron microscopy (SEM) and Fourier transforms infrared spectroscopy (FTIR) techniques. Photoluminescence (PL) and Thermoluminescence (TL) properties were studied in detail. PL emission spectra were recorded for prepared phosphors under excitation wavelength 254 nm, which show a high intense peak at 613 nm for Y{sub 2}O{sub 3}:Dy{sup 3+}, Eu{sup 3+} (1:1.5 mol %) phosphor. The correlated color temperature (CCT) and CIE analysis have been performed for the synthesized phosphors. TL glow curves were recorded for Eu{sup 3+}doped and Dy{sup 3+}codoped phosphors to study the heating rate effect and dose response. The kinetic parameters were calculated using peak shape method for UV and γ exposures through computerized glow curve deconvolution (CGCD) technique. The phosphors show second order kinetics and activation energies varying from 5.823 × 10{sup − 1} to 18.608 × 10{sup − 1} eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Image processing tools for petabyte-scale light sheet microscopy data

Light sheet microscopy is a powerful technique for high-speed three-dimensional imaging of subcellular dynamics and large biological specimens. However, it often generates datasets ranging from hundreds of gigabytes to petabytes in size for a single experiment. Conventional computational tools process such images far slower than the time to acquire them and often fail outright due to memory limitations. To address these challenges, we present PetaKit5D, a scalable software solution for efficient petabyte-scale light sheet image processing. This software incorporates a suite of commonly used processing tools that are optimized for memory and performance. Notable advancements include rapid image readers and writers, fast and memory-efficient geometric transformations, high-performance Richardson–Lucy deconvolution and scalable Zarr-based stitching. These features outperform state-of-the-art methods by over one order of magnitude, enabling the processing of petabyte-scale image data at the full teravoxel rates of modern imaging cameras. The software opens new avenues for biological discoveries through large-scale imaging experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Experimental validation of wireless communication with chaos

The constraints of a wireless physical media, such as multi-path propagation and complex ambient noises, prevent information from being communicated at low bit error rate. Surprisingly, it has only recently been shown that, from a theoretical perspective, chaotic signals are optimal for communication. It maximises the receiver signal-to-noise performance, consequently minimizing the bit error rate. This work demonstrates numerically and experimentally that chaotic systems can in fact be used to create a reliable and efficient wireless communication system. Toward this goal, we propose an impulsive control method to generate chaotic wave signals that encode arbitrary binary information signals and an integration logic together with the match filter capable of decreasing the noise effect over a wireless channel. The experimental validation is conducted by inputting the signals generated by an electronic transmitting circuit to an electronic circuit that emulates a wireless channel, where the signals travel along three different paths. The output signal is decoded by an electronic receiver, after passing through a match filter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

High-performance strategies for the recent MRSF-TDDFT in GAMESS

Multiple ERI (Electron Repulsion Integral) tensor contractions (METC) with several matrices are ubiquitous in quantum chemistry. In response theories, the contraction operation, rather than ERI computations, can be the major bottleneck, as its computational demands are proportional to the multiplicatively combined contributions of the number of excited states and the kernel pre-factors. Here, this paper presents several high-performance strategies for METC. Optimal approaches involve either the data layout reformations of interim density and Fock matrices, the introduction of intermediate ERI quartet buffer, and loop-reordering optimization for a higher cache hit rate. The combined strategies remarkably improve the performance of the MRSF (mixed reference spin flip)-TDDFT (time-dependent density functional theory) by nearly 300%. The results of this study are not limited to the MRSF-TDDFT method and can be applied to other METC scenarios.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Worldwide Physics-Based Lifetime Prediction of c-Si Modules Due to Solder-Bond Failure

Lifetime prediction of the fielded c-Si solar modules due to location-specific weather conditions has been an important topic of photovoltaic research and the economic viability of solar energy. Data analytic techniques such as the performance ratio method, Statistical clear sky model, and Suns-Vmp methods quantify the degradation from measured data of a solar farm, however, the nonlinear time-dependence and correlated degradations make it difficult to use the empirical degradation rates for ultimate lifetime projection. In this article, we propose a complementary physics-based model to predict the solder bond failure caused by mechanical stress associated with the variations of the temperature. Integrating the worldwide weather information from NASA/NSRDB databases, the model predicts the location-specific output-power degradation and the lifetime of a module due to solder bond failure. The model parameters are calibrated against qualification tests involving thermal cycling of specific batches of modules from a specific technology/manufacturer. The results may be summarized as: 1) Modules installed at higher latitudes show a longer lifetime due to reduced damage accumulation. 2) The reduction of temperature fluctuation close to large bodies of water, such as seashores, increases solder bond lifetime significantly. 3) Relatively speaking, modules installed close to the Tropic of Cancer/Capricorn (23.5 degrees North/South) suffer from a higher solder bond damage and have a shorter lifetime, suggesting a conservative design. This model should serve as a building block of a comprehensive reliability framework that can predict the lifetime of a module that experiences simultaneous and correlated degradation mechanisms involving yellowing, corrosion, and potential-induced degradation.

14 SOLAR ENERGY↗
DOE OSTI2017

Interaction of TiS 2 and Sulfur in Li-S Battery System

With the ability to adsorb polysulfide, electronically conductive and electrochemically active TiS 2 is an effective multifunctional cathode additive to improve Li-S battery cycling performance. Furthermore, by using X-ray Photoelectron Spectroscopy (XPS), direct evidence is obtained to demonstrate the strong interaction between Li-polysulfide and TiS 2 . The observation of Li signature on Li 2 S 8 treated TiS 2 proves that the TiS 2 possesses the ability to adsorb Li-polysulfides species on its surface. An electron density transfer from Ti to Li and S is identified based on the positions of the peaks in the XPS spectrum before and after the interaction, which is consistent with the theoretically predicted polysulfide-TiS 2 interaction models in the literature. TiS 2 sample with 2.5x higher BET surface area is obtained by milling the raw TiS 2 particles and used as cathode additive in the sulfur electrode. Furthermore, in the presence of TiS 2 additive, long cycle life and improved sulfur utilization of Li-S cells under high rate discharge are demonstrated. In addition, we find that a uniform TiS 2 distribution in the sulfur-TiS 2 hybrid electrode is vital in determining its effectiveness in enhancing the performance of sulfur electrodes. Thus, by processing method and condition should be very important considerations in future development of sulfur electrodes with TiS 2 additive.

25 ENERGY STORAGE↗
DOE OSTI2019

Roll-to-Roll Advanced Materials Manufacturing DOE Laboratory Collaboration - FY2018 Final Report

High-value R2R processing is used to support a wide range of products in applications which span many industrial business sectors. The overall R2R process technology can be considered as “mature” as the process methodology and has been in use for decades. This continuous processing technique traditionally involves deposition of material(s) onto moving webs or carriers or other continuous R2R, belt-fed, or conveyor-based processes that enable successive steps to build a final version which serves to support the deposited materials. Current process technologies, which typify “roll to roll”, include tape casting, silk-screen printing, reel-to-reel vacuum deposition/coating and R2R lithography. Products supported by R2R manufacturing include micro-electronics, electro-chromic window films, PVs, fuel cells for energy conversion, battery electrodes for energy storage, and barrier materials. Due to innovation in materials and process equipment, high-quality yet very low-cost multi-layer technologies can be manufactured on a very cost-competitive basis. To move energy-related products from high-cost niche applications to the commercial sector, a means must be available to enable manufacture of these products in a cost-competitive manner that is affordable by the general consumer. Fortunately, products such as fuel cells, thin- and mid-film PVs, batteries, electrochromic and piezoelectric films, water separation membranes, and other energy saving technologies readily lend themselves to manufacture using R2R approaches.Within the DOE EERE AMO, it was recognized that establishment of a program supported at the DOE National Laboratories, along with their immense design of materials and equipment modelling capabilities enabled with use of high-performance computing, could take advantage of available R2R infrastructure to manufacture new technologies. In FY 2016, a R2R Consortium was established and provided with initial “seed” funding to take an approach that was envisioned to be supportable by advanced manufacturing R2R processes. This collaborative approach was designed to foster identification and development of materials and processes related to R2R for clean-energy product development. Using computational and experimental capabilities by acknowledged subject matter experts within the supported National Laboratory system, this collaborative project would leverage the capabilities and expertise at each of four laboratories to further the development of an enabling high-volume cost-competitive platform technology. The collaboration team that is comprised of ORNL, ANL, NREL and LBNL, coordinating with EPB and other selected industry partners, was formed in April 2016 to initially address enhancing battery electrode performance and R2R manufacturing challenges. The research efforts were to predict and measure changes and results in electrode morphology and performance based on process condition changes; to evaluate mixed, active, particle size deposition and drying for novel electrode materials; to model various process condition changes and the resulting morphology and electrode performance; and to develop and validate NDE techniques for in-line measurement of battery electrode material properties. These efforts carried through FY 2017 and completed at the end of FY 2018.The approach was to look at compositions of materials with different particle sizes to make electrode samples using a R2R manufacturing process. The shape, size, and morphology of the materials, the chemistry of the formulation, the nature of slurries, their coating rate, the rate of drying all play a role in determining the final coating architecture, quality, and performance. A commercial cathode material was selected to make a series of cathodes and anodes by single pass, dual pass and slot die methods. Analysis of all the compiled results for this battery electrode development were that the best performing cathodes included: dual-pass electrode with large particles near the foil, mixed small and large particles, and small particles only. Whereas, the best performing anodes were with a mix of small and large graphite particles. An additional core project was added in FY 2017 to conduct studies of fuel cell materials that can be produced using R2R processes. The goal of this project is to explore, understand and optimize material and process parameters to support increased throughput, increased quality, and reduced cost for high volume production of gas-diffusion electrodes (GDEs) for PEMFCs. Project work in FY 2018 were to use a R2R process to fabricate electrodes without ionomer overlayer that can produce the equivalent mass activity as spray-coated electrodes with an ionomer overlayer. Oxygen-limiting current measurements were utilized to optimize oxygen mass transport. Alcohol-rich solvents were investigated, and results were that the alcohol and water ratio can be tuned to control ionomer distribution. Water-rich solvents produce a more dispersed ink which results in better high-current density performance.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Modeling Metallic Fuel using Peridynamics

Based on available modeling and simulation capabilities of peridynamics module in MOOSE framework for oxide fuel, the overall goal of this project is to further develop the peridynamics capabilities for modeling metallic fuel. It includes two major tasks: 1) develop validated scheme to handle the shape tensor singularity due to insufficient active neighbors of a material particle in the peridynamic correspondence model for fracture problems, and 2) develop failure modeling scheme including failure criterion for metallic fuels. Before the peridynamics can be applied to model metallic fuel, the formulation instability of the peridynamic correspondence model should be addressed. The PI first worked on developing new stabilization method to improve the performance of the peridynamic correspondence model and reduce the possibility of getting a singular shape tensor while applying the model for fracture problems. The new stabilization scheme uses bond-associated weight function rather than bond-associated horizon. Compared to bondassociated horizon stabilized method, this new stabilization scheme has better performance with improved prediction accuracy and reduced free surface effect. Using this newly developed stabilization, materials models from BISON can be directly used in peridynamics for metallic fuels, such as fission rate and burnup dependent creep and swell models. Publication of this work is under preparation.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Combustion of Butyl acetate as an alternative additive to petroleum fuels

Blending petroleum fuels with oxygenates is a common approach to stem the depletion of crude oil while also mitigating the impact of their combustion on the environment. It has recently been considered that butyl acetate (BA, C6H12O2 , boiling point of 399K) could be a viable oxygenate additive to diesel fuel. The platform used to study combustion of commercial and synthesized BA was an isolated droplet burning with spherical symmetry. The experiments were carried out in a drop tower to minimize buoyant convection. Restricting motion by supporting droplets on 14 micrometer fibers eliminated forced convection. Precise control of the initial diameter was achieved by first deploying large droplets and letting them evaporate to the size of interest, here being between 0.3 mm to 0.8 mm. The experimental results show that commercial and the newly synthesized BA burned almost identically for the evolution of droplet and flame diameters. Droplets burned slower as the initial diameter was increased and soot formation was noted for the larger sizes studied due to a residence size effect. Burning in a buoyant convective field showed higher burn rates due to the convective effect and that the asymmetric flames became nearly spherical as diameter decreased. The study illustrates the significant value that the microgravity environment brings to evaluating performance of oxygenated fuels synthesized by new production methods.

Wang, Yujie↗
DOE OSTI2017

Correcting Type Ia Supernova Distances for Selection Biases and Contamination in Photometrically Identified Samples

We present a new technique to create a bin-averaged Hubble diagram (HD) from photometrically identified SN Ia data. The resulting HD is corrected for selection biases and contamination from core-collapse (CC) SNe, and can be used to infer cosmological parameters. This method, called “BEAMS with Bias Corrections” (BBC), includes two fitting stages. The first BBC fitting stage uses a posterior distribution that includes multiple SN likelihoods, a Monte Carlo simulation to bias-correct the fitted SALT-II parameters, and CC probabilities determined from a machine-learning technique. The BBC fit determines (1) a bin-averaged HD (average distance versus redshift), and (2) the nuisance parameters α and β, which multiply the stretch and color (respectively) to standardize the SN brightness. In the second stage, the bin-averaged HD is fit to a cosmological model where priors can be imposed. We perform high-precision tests of the BBC method by simulating large (150,000 event) data samples corresponding to the Dark Energy Survey Supernova Program. Our tests include three models of intrinsic scatter, each with two different CC rates. In the BBC fit, the SALT-II nuisance parameters α and β are recovered to within 1% of their true values. In the cosmology fit, we determine the dark energy equation of state parameter w using a fixed value of Ω{sub M} as a prior: averaging over all six tests based on 6 × 150,000 = 900,000 SNe, there is a small w-bias of 0.006±0.002. Finally, the BBC fitting code is publicly available in the SNANA package.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1971

Investigation of techniques for improving Saturn 5 RF tracking and ranging systems

Results of theoretical analyses of 12 problems are presented and comparisons of theoretical and experimental results are given. The investigations covered were: (1) techniques for improving the Saturn radar altimeter, (2) performance of the phase lock loop of the offset Doppler transponder, (3) signal processing equipment design for an orbital altitude radar return experiment, (4) spectral studies of signals present in the command and communication system (CCS) up-link transmitter, (5) intermodulation in the CCS down-link data demodulators, (6) error rate performance of the CCS transponder command demodulator, (7) flame attenuation effects on telemetry transmissions during Saturn launches, (8) design of a digital television system which converts a standard monochrome picture to a slow-scan picture, (9) methods of obtaining an additional CCS 72-kilobit/sec telemetry channel, (10) computation of the CCS S-band down-link spectra, (11) modeling of portions of the communications systems, and (12) modeling of a telemetry transmitter.

Walsh, J. R., Jr.↗
NASA NTRS1973

Long-term cryogenic space storage system

Discussion of the design, fabrication and testing of a 225-cu ft spherical cryogenic storage system for long-term subcritical applications under zero-g conditions in storing subcritical cryogens for space vehicle propulsion systems. The insulation system design, the analytical methods used, and the correlation between the performance test results and analytical predictions are described. The best available multilayer insulation materials and state-of-the-art thermal protection concepts were applied in the design, providing a boiloff rate of 0.152 lb/hr, or 0.032% per day, and an overall heat flux of 0.066 Btu/sq ft hr based on a 200 sq ft surface area. A six to eighteen month cryogenic storage is provided by this system for space applications.

Hopkins, R. A.↗
NASA NTRS1982

An evaluation of an ICCD imager of dynamic range expansion technique and application of insitu procedures for life-time extension

Research toward practical implementation of the Intensified Charge Coupled Device (ICCD) as a photon-counting array detector for astronomy is reported. The first area of concentration was to determine the rate and extent of the lifetime limiting damage to the CCD caused by the impact of high energy electrons, and to find whether various methods of annealing the damage were productive. The second effort was to determine the performance of the ICCD in a photon-counting mode to produce extended dynamic range measurements. There are two main effects that appear as the practical results of the electron damage to the CCD. One is an increase in the leakage current, i.e., the normal thermal generation of charge carriers in the silicon that provides a background dark signal that adds to the light produced image. In an undamaged CCD, the leakage current is usually fairly uniform across the photosensitive area of the silicon chip, with the exception of various bright pixels which have an anomalous leakage current well above the overall level.

Currie, D. G.↗
NASA NTRS1985

Texture classification by local rank correlation

A new approach to texture classification based on local rank correlation is proposed here. Its performance is compared with Laws' method which uses local convolution with feature masks. In the experiments, texture samples are classified based on their distribution of local statistics, either rank correlations or convolutions. The new method achieves generally optimal classification rates. It appears to be more robust because local order statistics are unaffected by local sample differences due to monotonic shifts of texture gray values and are less sensitive to noise.

Harwood, D.↗
NASA NTRS1993

Coupling finite and boundary element methods for 2-D elasticity problems

A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.

Krishnamurthy, T.↗