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NASA NTRS1994

Narrowband Angular Reflectance Properties of the Alkali Flats at White Sands, New Mexico

Results from helicopter measurements of the angular properties of surface reflectance for the alkali flats regions of the White Sands Missile Range are presented for the wavelength interval of 0.4 to 0.85 microns. This work was performed to allow accurate radiative transfer calculations over the region. Detailed tables and interpolation equations are given that permit other investigators to perform satellite calibrations over the alkali flats site. The effects of wavelength and soil moisture on narrowband angular reflectance are also investigated. Although there is a spectral variation in surface albedo, there is little spectral effect in Anisotropic Factor except in the forward scattering peak at solar zenith angles greater than 60 deg. The magnitude of the forward-scattering peak is also sensitive to soil moisture, with wet conditions causing a larger peak. The significance of this result is that angular reflectance properties at the center of the alkali flats usually will be different than those at the flats edge because moisture differences typically exist.

Whitlock, Charles H.↗

NASA NTRS2012

Development and Calibration of a System-Integrated Rotorcraft Finite Element Model for Impact Scenarios

Two full-scale crash tests of an MD-500 helicopter were conducted in 2009 and 2010 at NASA Langley's Landing and Impact Research Facility in support of NASA s Subsonic Rotary Wing Crashworthiness Project. The first crash test was conducted to evaluate the performance of an externally mounted composite deployable energy absorber (DEA) under combined impact conditions. In the second crash test, the energy absorber was removed to establish baseline loads that are regarded as severe but survivable. The presence of this energy absorbing device reduced the peak impact acceleration levels by a factor of three. Accelerations and kinematic data collected from the crash tests were compared to a system-integrated finite element model of the test article developed in parallel with the test program. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests were conducted to evaluate the impact performances of various components and subsystems, including new crush tubes and the DEA blocks. Parameters defined for the system-integrated finite element model were determined from these tests. Results from 19 accelerometers placed throughout the airframe were compared to finite element model responses. The model developed for the purposes of predicting acceleration responses from the first crash test was inadequate when evaluating more severe conditions seen in the second crash test. A newly developed model calibration approach that includes uncertainty estimation, parameter sensitivity, impact shape orthogonality, and numerical optimization was used to calibrate model results for the full-scale crash test without the DEA. This combination of heuristic and quantitative methods identified modeling deficiencies, evaluated parameter importance, and proposed required model changes. The multidimensional calibration techniques presented here are particularly effective in identifying model adequacy. Acceleration results for the calibrated model were compared to test results and the original model results. There was a noticeable improvement in the pilot and copilot region, a slight improvement in the occupant model response, and an over-stiffening effect in the passenger region. One lesson learned was that this approach should be adopted early on, in combination with the building-block approaches that are customarily used, for model development and pretest predictions. Complete crash simulations with validated finite element models can be used to satisfy crash certification requirements, potentially reducing overall development costs.

Annett, Martin S.↗

NASA NTRS2011

Heterogeneity in Short Gamma-Ray Bursts

We analyze the Swift/BAT sample of short gamma-ray bursts, using an objective Bayesian Block procedure to extract temporal descriptors of the bursts' initial pulse complexes (IPCs). The sample comprises 12 and 41 bursts with and without extended emission (EE) components, respectively. IPCs of non-EE bursts are dominated by single pulse structures, while EE bursts tend to have two or more pulse structures. The medians of characteristic timescales - durations, pulse structure widths, and peak intervals - for EE bursts are factors of approx 2-3 longer than for non-EE bursts. A trend previously reported by Hakkila and colleagues unifying long and short bursts - the anti-correlation of pulse intensity and width - continues in the two short burst groups, with non-EE bursts extending to more intense, narrower pulses. In addition we find that preceding and succeeding pulse intensities are anti-correlated with pulse interval. We also examine the short burst X-ray afterglows as observed by the Swift/XRT. The median flux of the initial XRT detections for EE bursts (approx 6 X 10(exp -10) erg / sq cm/ s) is approx > 20 x brighter than for non-EE bursts, and the median X-ray afterglow duration for EE bursts (approx 60,000 s) is approx 30 x longer than for non-EE bursts. The tendency for EE bursts toward longer prompt-emission timescales and higher initial X-ray afterglow fluxes implies larger energy injections powering the afterglows. The longer-lasting X-ray afterglows of EE bursts may suggest that a significant fraction explode into more dense environments than non-EE bursts, or that the sometimes-dominant EE component efficiently p()wers the afterglow. Combined, these results favor different progenitors for EE and non-EE short bursts.

Norris, Jay P.↗

NASA NTRS2017

Derivation of Aerosol Profiles for MC3E Convection Studies and Use in Simulations of the 20 May Squall Line Case

Advancing understanding of deep convection microphysics via mesoscale modeling studies of well-observed case studies requires observation-based aerosol inputs. Here, we derive hygroscopic aerosol size distribution input profiles from ground-based and airborne measurements for six convection case studies observed during the Midlatitude Continental Convective Cloud Experiment (MC3E) over Oklahoma. We demonstrate use of an input profile in simulations of the only well-observed case study that produced extensive stratiform outflow on 20 May 2011. At well-sampled elevations between -11 and -23 degree C over widespread stratiform rain, ice crystal number concentrations are consistently dominated by a single mode near 400 micrometer in randomly oriented maximum dimension (D[superscript max] ). The ice mass at -23 degree C is primarily in a closely collocated mode, whereas a mass mode near D[superscript max] -1000 micrometer becomes dominant with decreasing elevation to the -11 degree C level, consistent with possible aggregation during sedimentation. However, simulations with and without observation-based aerosol inputs systematically overpredict mass peak D[superscript max] by a factor of 3-5 and underpredict ice number concentration by a factor of 4-10. Previously reported simulations with both two-moment and size-resolved microphysics have shown biases of a similar nature. The observed ice properties are notably similar to those reported from recent tropical measurements. Based on several lines of evidence, we speculate that updraft microphysical pathways determining outflow properties in the 20 May case are similar to a tropical regime, likely associated with warm-temperature ice multiplication that is not well understood or well represented in models.

Fridlind, Ann M.↗

NASA NTRS2017

Shed Vortex Structure and Phase-Averaged Velocity Statistics in Symmetric/Asymmetric Turbulent Flat Plate Wakes

The near wake of a flat plate is investigated via direct numerical simulations (DNS). Many earlier experimental investigations have used thin plates with sharp trailing edges and turbulent boundary layers to create the wake. This results in large theta divided by D (sub TE) values (theta is the boundary layer momentum thickness towards the end of the plate and D (sub TE) is the trailing edge thickness). In the present study the emphasis is on relatively thick plates with circular trailing edges (CTE) resulting in theta divided by D values less than one (D is the plate thickness and the diameter of the CTE), and vigorous vortex shedding. The Reynolds numbers based on the plate length and D are 1.255 x 10 (sup 6) and 10,000, respectively. Two cases are computed; one with turbulent boundary layers on both the upper and lower surfaces of the plate (statistically the same, symmetric wake, Case TT) and, a second with turbulent and laminar boundary layers on the upper and lower surfaces, respectively (asymmetric case, Case TL). The data and understanding obtained is of considerable engineering interest, particularly in turbomachinery where the pressure side of an airfoil can remain laminar or transitional because of a favorable pressure gradient and the suction side is turbulent. Shed-vortex structure and phase-averaged velocity statistics obtained in the two cases are compared here. The upper negative shed vortices in Case TL (turbulent separating boundary layer) are weaker than the lower positive ones (laminar separating boundary layer) at inception (a factor 1.27 weaker in terms of peak phase-averaged spanwise vorticity at first appearance of a peak). The upper vortices weaken rapidly as they travel downstream. A second feature of interest in Case TL is a considerable increase in the peak phase-averaged, streamwise normal intensity (random component) with increasing streamwise distance (x divided by D) that occurs nears the positive vortex cores. This behavior is observed for a few diameters in the near wake. This is counter to Case TT where the peak value essentially decreases with increasing x divided by D. Both these effects are examined in detail and the important contributors are identified.

direct numerical simulations↗

DOE OSTI2024

High Performance Computing Peak Shaving for Microreactor Operation

There are multiple nuclear microreactors currently under development that are designed to provide autonomous power for as many as ten or more years without refueling and are designed to power high performance computing (HPC) datacenters. But the load-follow speeds for a nuclear microreactor will be much slower than grid power and slower than the power variance typical of a HPC system. HPC datacenters experience peak power load variance driven by several factors ranging from the operation of cooling systems to remove heat from the servers to supporting a wide range of user application workflows and architectures each with different power signatures. One mechanism to support the limited load-follow of a microreactor is peak shaving where an energy storage mechanism is used to shed peak load and reduce significant power variance. This work explores peak electrical load shaving using uninterruptible power supply (UPS) systems designed for HPC support in the context of peak shaving when operating using a nuclear microreactor with a load-follow limited to 10% of load per minute. Using a self contained HPC datacenter complete with stand-alone cooling system and provisioned with an x86 cluster, an ARM cluster, and a graphics processing unit (GPU) cluster, peak shaving for microreactor operation using the UPS battery backup is explored while running two classes of typical HPC user applications. HPC architecture suitability for microreactor operation under this type of peak shaving is examined.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1996

Optimizing Process Parameters to Produce Single Phase YBa2Cu3O7 Powder

Process parameters such as temperature and time are varied to obtain single phase (pure) YBa2Cu307 powders. X-ray diffraction patterns of superconducting and nonsuperconducting powders are observed in situ in normal and elevated temperature environments to confirm known strong peaks that are unique to YBa2Cu307. Peaks vary in magnitude as a result of superconducting - nonsuperconducting phase transitions. Known strong peaks serve as our basis in monitoring transitional changes. Peak isotherms obtained experimentally are correlated with theoretical models to identify the weighting factor that characterizes the optimum isotherm. By isolating the parameters under which 100% peak growth occurs most rapidly, we obtain the optimum isotherm. The choices made for firing temperature and atmosphere were determined to be the primary factors necessary to ensure sample purity.

Hurley, J. S.↗

DOE OSTI2025

Bulk viscosity of nuclear matter with pions in the neutrino-trapped regime

Recent work has shown that a population of thermal pions could modify the equation of state and transport properties of hot and dense neutron-rich matter and introduce new reaction pathways to change the proton fraction. In this article we study their impact on the bulk viscosity of dense matter, focusing on the neutrino-trapped regime that would be realized in neutron star mergers and supernovae. We find that the presence of a thermal population of pions alters the bulk viscosity by modifying the EoS (via the susceptibilities) and by providing new reaction pathways to achieve beta equilibrium. In neutron star merger conditions, the bulk viscosity in neutrino-trapped npeμ matter (without pions) has its peak at temperatures of at most a couple MeV and is quite small at temperatures of tens of MeV. We find that thermal pions enhance the low-temperature peak of the bulk viscosity by a factor of a few and shift it to slightly lower temperatures. At higher temperatures, where the pion abundance is large but the bulk viscosity is traditionally small, pions can increase the bulk viscosity by an order of magnitude or more, although it is still orders of magnitude smaller than its peak value.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2021

GRB 191016A: A Long Gamma-Ray Burst Detected by TESS

The Transiting Exoplanet Survey Satellite (TESS) exoplanet-hunting mission detected the rising and decaying optical afterglow of GRB 191016A, a long gamma-ray burst (GRB) detected by Swift-BAT but without prompt XRT or UVOT follow-up due to proximity to the Moon. The afterglow has a late peak at least 1000 s after the BAT trigger, with a brightest-detected TESS data point at 2589.7 s post-trigger. The burst was not detected by Fermi-LAT, but was detected by Fermi-GBM without triggering, possibly due to the gradual nature of the rising light curve. Using ground-based photometry, we estimate a photometric redshift of z(sub phot) = 3.29 ± 0.40. Combined with the high-energy emission and optical peak time derived from TESS, estimates of the bulk Lorentz factor Γ(sub BL) range from 90 to 133. The burst is relatively bright, with a peak optical magnitude in ground-based follow-up of R = 15.1 mag. Using published distributions of GRB afterglows and considering the TESS sensitivity and sampling, we estimate that TESS is likely to detect ∼1 GRB afterglow per year above its magnitude limit.

Gamma-ray bursts↗

DOE OSTI2021

Mechanical Loads on Spent Nuclear Fuel in the General 30 cm Package Drop Scenario

The U.S. Department of Energy Office of Nuclear Energy (DOE-NE) Spent Fuel and Waste Science & Technology (SFWST) research program is guided by the high-level goal of closing prioritized knowledge gaps related to spent nuclear fuel (SNF) storage and transportation, which are summarized by Saltzstein et al. (2020). One of the high-priority knowledge gaps is the identification and quantification of mechanical loads that are expected to affect SNF during normal conditions of transportation and storage to inform the range of physical SNF test programs. This report uses modeling and analysis methods to estimate the mechanical loads on spent nuclear fuel (SNF) in the general 30 cm package drop scenario. The drop scenario assumes impact limiters are in place in the transportation configuration and the impact surface is perfectly rigid. The goal of this analysis is to consider the universe of potential mechanical loading conditions that can happen to SNF and present the results in a manner that is useful for materials testing, decision making, and regulatory rule making purposes. This study uses validated finite element models and methods to perform a broad parametric study of key variables that can affect the mechanical loads on SNF during a hypothetical package free drop scenario. Physical drop test data from a cask and fuel assembly drop test campaign is the basis for model validation. Additionally, the results of the parametric study are used to inform a damage model, which uses multiple nonlinear regression to estimate the relationships between input variables and output response. The parametric finite element analyses consider thousands of input variable combinations, while the damage model estimates millions of combinations. The breadth of this study provides confidence that the potential range of mechanical loads that SNF might experience during the general 30 cm package drop scenario are characterized well enough to consider this knowledge gap closed. While this report documents the overall peak values calculated in this study, the 95 th percentile values, the histograms, and the observed trends are equally important. This study covered a large range of SNF temperatures, room temperature to 300°C, and burnups, 10 GWd/MTU to 62 GWd/MTU. Each temperature and burnup combination has a different cladding yield strain, so it is more meaningful to summarize the calculated cladding strain response as its factor of safety, which is defined relative to the yield strain. The factor of safety is calculated as the yield strain divided by the peak cladding strain. A factor of safety greater than unity indicates that the cladding remains below yield, whereas a value less than unity is indicative of plastic deformation. In all cases of this study a safety factor over 1.0 was calculated, although in the most limiting case at 300°C the safety factor was only 1.01, which suggests that yielding could occur when additional loads like rod internal pressure are included. When the temperature is restricted to 200°C the limiting safety factor increases to 1.28, which has significant margin to accommodate internal pressure and potential local cladding defects that could cause a local stress concentration. An important trend in the calculated fuel rod mechanical loads is that the 2 nd highest loaded fuel rod in an assembly tends to be significantly lower than the highest loaded rod. The implication is that even if one rod in an assembly experiences a failure the loads would have to be significantly higher to cause two or more rods to fail.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Quantitative Analysis and Prediction of Thermal Runaway Metrics of High-Nickel Oxide Cathodes by Machine Learning Models

The pursuit of higher energy density in lithium-ion batteries has made high-nickel (Ni) layered oxides leading cathode candidates for next-generation electric vehicles. However, their poor thermal stability, particularly at Ni contents ≥ 90%, increases the risk of cathode-initiated thermal runaway. Furthermore, we present a data-driven framework combining linear and nonlinear machine learning models to predict key thermal runaway descriptors from a high-throughput differential scanning calorimetry database. With cathode composition and state of charge (SOC) as input features, the ensemble model accurately predicts peak temperature, heat release, and peak heat flow. SHAP analysis identifies Ni content and SOC as the dominant factors controlling thermal runaway temperature, while SOC primarily governs heat release and peak heat flow. Al, Mg, and Mn improve thermal stability by strengthening metal–oxygen bonding and delaying structural transformation, whereas B mainly reduces heat release through surface passivation. Validation with a new cathode composition confirms accurate prediction of SOC-dependent thermal runaway behavior and critical SOC.

25 ENERGY STORAGE↗

NASA NTRS2013

Empirical STORM-E Model

Auroral nighttime infrared emission observed by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument onboard the Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite is used to develop an empirical model of geomagnetic storm enhancements to E-region peak electron densities. The empirical model is called STORM-E and will be incorporated into the 2012 release of the International Reference Ionosphere (IRI). The proxy for characterizing the E-region response to geomagnetic forcing is NO+(v) volume emission rates (VER) derived from the TIMED/SABER 4.3 lm channel limb radiance measurements. The storm-time response of the NO+(v) 4.3 lm VER is sensitive to auroral particle precipitation. A statistical database of storm-time to climatological quiet-time ratios of SABER-observed NO+(v) 4.3 lm VER are fit to widely available geomagnetic indices using the theoretical framework of linear impulse-response theory. The STORM-E model provides a dynamic storm-time correction factor to adjust a known quiescent E-region electron density peak concentration for geomagnetic enhancements due to auroral particle precipitation. Part II of this series describes the explicit development of the empirical storm-time correction factor for E-region peak electron densities, and shows comparisons of E-region electron densities between STORM-E predictions and incoherent scatter radar measurements. In this paper, Part I of the series, the efficacy of using SABER-derived NO+(v) VER as a proxy for the E-region response to solar-geomagnetic disturbances is presented. Furthermore, a detailed description of the algorithms and methodologies used to derive NO+(v) VER from SABER 4.3 lm limb emission measurements is given. Finally, an assessment of key uncertainties in retrieving NO+(v) VER is presented

Mertens, Christopher J.↗

NASA NTRS1982

Reduction in peak oxygen uptake after prolonged bed rest

The hypothesis that the magnitude of the reduction in peak oxygen uptake (VO2) after bed rest is directly proportional to the level of pre-bed rest peak VO2 is tested. Complete pre and post-bed rest working capacity and body weight data were obtained from studies involving 24 men (19-24 years old) and 8 women (23-34 years old) who underwent bed rest for 14-20 days with no remedial treatments. Results of regression analyses of the present change in post-bed rest peak VO2 on pre-bed rest peak VO2 with 32 subjects show correlation coefficients of -0.03 (NS) for data expressed in 1/min and -0.17 for data expressed in ml/min-kg. In addition, significant correlations are found that support the hypothesis only when peak VO2 data are analyzed separately from studies that utilized the cycle ergometer, particularly with subjects in the supine position, as opposed to data obtained from treadmill peak VO2 tests. It is concluded that orthostatic factors, associated with the upright body position and relatively high levels of physical fitness from endurance training, appear to increase the variability of pre and particularly post-bed rest peak VO2 data, which would lead to rejection of the hypothesis.

Greenleaf, J. E.↗

NASA NTRS2001

Dependence of Aerosol Light Absorption and Single-Scattering Albedo On Ambient Relative Humidity for Sulfate Aerosols with Black Carbon Cores

Atmospheric aerosols frequently contain hygroscopic sulfate species and black carbon (soot) inclusions. In this paper we report results of a modeling study to determine the change in aerosol absorption due to increases in ambient relative humidity (RH), for three common sulfate species, assuming that the soot mass fraction is present as a single concentric core within each particle. Because of the lack of detailed knowledge about various input parameters to models describing internally mixed aerosol particle optics, we focus on results that were aimed at determining the maximum effect that particle humidification may have on aerosol light absorption. In the wavelength range from 450 to 750 nm, maximum absorption humidification factors (ratio of wet to 'dry=30% RH' absorption) for single aerosol particles are found to be as large as 1.75 when the RH changes from 30 to 99.5%. Upon lesser humidification from 30 to 80% RH, absorption humidification for single particles is only as much as 1.2, even for the most favorable combination of initial ('dry') soot mass fraction and particle size. Integrated over monomodal lognormal particle size distributions, maximum absorption humidification factors range between 1.07 and 1.15 for humidification from 30 to 80% and between 1.1 and 1.35 for humidification from 30 to 95% RH for all species considered. The largest humidification factors at a wavelength of 450 nm are obtained for 'dry' particle size distributions that peak at a radius of 0.05 microns, while the absorption humidification factors at 700 nm are largest for 'dry' size distributions that are dominated by particles in the radius range of 0.06 to 0.08 microns. Single-scattering albedo estimates at ambient conditions are often based on absorption measurements at low RH (approx. 30%) and the assumption that aerosol absorption does not change upon humidification (i.e., absorption humidification equal to unity). Our modeling study suggests that this assumption alone can introduce absolute errors in estimates of the midvisible single-scattering albedo of up to 0.05 for realistic dry particle size distributions. Our study also indicates that this error increases with increasing wavelength. The potential errors in aerosol single-scattering albedo derived here are comparable in magnitude and in addition to uncertainties in single-scattering albedo estimates that are based on measurements of aerosol light absorption and scattering.

Redemann, Jens↗

NASA NTRS1995

Constraints on the gamma-ray burst luminosity function from Pioneer Venus Orbiter and BATSE observations

We examine the width of the gamma ray burst luminosity function through the distribution of Gamma Ray Burst (GRB) peak fluxes as detected by the Pioneer Venus Orbiter (PVO) and the Burst and Transient Source Experiment (BATSE). The strength of the analysis is greatly enhanced by using a merged catalog of peak fluxes from both instruments with good cross-calibration of their sensitivities. The range of peak fluxes is increased by approximately a factor of 20 relative to the BATSE catalog. Thus, more sensitive investigations of the log N - log P distribution are possible. We place constraints on the width of the luminosity function of gamma-ray bursts brighter than the BATSE completeness limit by comparing the intensity distribution in the merged catalog with those produced by a variety of spatial density and luminosity functions. For the models examined, 90% of the detectable bursts have peak luminosities within a range of 10, indicating that the peak luminosities of gamma-ray bursts span a markedly less wide range of values than many other of their measurable properties. We also discuss for which slopes of a power-law luminosity function the observed width is at the upper end of the constrained range. This is essential in determining the power-law slopes for which luminosity-duration correlations could be important.

Ulmer, Andrew↗

NASA NTRS1980

Axisymmetric elastodynamic response from normal and radial impact of layered composites with embedded penny-shaped cracks

A method is developed for the dynamic stress analysis of a layered composite containing an embedded penny-shaped crack and subjected to normal and radial impact. Quantitatively, the time-dependent stresses near the crack border can be described by the dynamic stress intensity factors. Their magnitude depends on time, on the material properties of the composite and on the relative size of the crack compared to the composite local geometry. Results obtained show that, for the same material properties and geometry of the composite, the dynamic stress intensity factors for an embedded (penny-shaped) crack reach their peak values within a shorter period of time and with a lower magnitude than the corresponding dynamic stress factors for a through-crack.

Sih, G. C.↗

DOE OSTI2022

Modeling and Analysing the Impact of Heat Pump Water Heaters on Distribution Systems Using GridLAB-D

With the constant increase in energy demand, finding ways to reduce peak load and the energy-costs factors has become more imperative. Domestic water heating showcases a significant opportunity for such applications. Water heating is the second-highest energy consumer in the residential sector across the United States. Electric Water Heaters (EWHs), in particular, constitute nearly 43% of American household water heating energy consumption. Heat Pump Water Heater (HPWH), on the other hand, are an advanced water heating technology that has recently emerged in the United States residential market. The objectives of this work are to develop a HPWH model and build a case study that evaluates various penetration levels of HPWH in providing reduced peak load and cost-effective energy savings for both utilities and customers. The HPWH model was developed and integrated within the GridLAB-D simulation environment. The model behavior was then validated against a real HPWH unit at Portland State University (PSU). The case studies incorporated five HPWH penetration levels, ranging from 20% to 100%. In each case, EWHs were replaced with HPWHs. The results showed that a high penetration level of HPWHs can reduce the energy consumption on a distribution system to 38%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1979

Normal and radial impact of composites with embedded penny-shaped cracks

A method is developed for the dynamic stress analysis of a layered composite containing an embedded penny-shaped crack and subjected to normal and radial impact. The material properties of the layers are chosen such that the crack lies in a layer of matrix material while the surrounding material possesses the average elastic properties of a two-phase medium consisting of a large number of fibers embedded in the matrix. Quantitatively, the time-dependent stresses near the crack border can be described by the dynamic stress intensity factors. Their magnitude depends on time, on the material properties of the composite and on the relative size of the crack compared to the composite local geometry. Results obtained show that, for the same material properties and geometry of the composite, the dynamic stress intensity factors for an embedded (penny-shaped) crack reach their peak values within a shorter period of time and with a lower magnitude than the corresponding dynamic stress intensity factors for a through-crack.

Sih, G. C.↗