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At least 1,153 records · Page 64

Characterizing the Effects of Thermal Profile and Gas Environment on the Heat Treatment of JSC-1A Lunar Simulant Using Combined Thermogravimetry and Mass Spectroscopy

As NASA strives towards a long duration presence on the Moon, it has become increasingly important to learn how to better utilize resources from the lunar surface for everything from habitats, vehicle infrastructure, and chemical extraction. To that end, a variety of lunar simulants have been sourced from terrestrially available volcanic minerals and glass as Apollo regolith is a finite resource unavailable for experimentation needing large masses. However, while mineralogy and chemical composition can approach that of lunar material in these simulants, there are still distinct non-lunar phases such as hydrates, carbonates, sulfates, and clays that can cause simulants to behave distinctly non-lunar in a variety of processing conditions that would ideally be applied to lunar material. Notably, severe glassy bubbling has been documented in a variety of vacuum sintering experiments on JSC-1A lunar Maria simulant heated via microwaves. The origins of this outgassing have not been well understood, but are normally attributed to the decomposition of non-lunar contaminates intrinsic to virtually all terrestrially sourced simulants. As such, a series of controlled environmental tests were performed to ascertain the origins of the high temperature outgassing and to develop heat treatments that can drive JSC-1A closer to lunar composition and behavior. It was found that in JSC-1A that distinct gas evolutions of water, carbon dioxide, and sulfur dioxide occur in both inert gas and vacuum. Additionally, the presence of hydrogen during heat treatments was shown to dramatically change gas evolutions, leading to distinctly more lunar-like composition and behavior from JSC-1A simulant.

sinter↗

Low-Loss Charge Transfer Plasmons in Graphene/α-RuCl 3 Heterostructures Below 40 K

Charge transfer at material interfaces governs a wide range of physical properties, from electronic band structures to emergent collective excitations. In two-dimensional (2D) material heterostructures, charge transfer phenomena play important roles in enabling novel quantum phases, proximity effects, and tunable plasmonic responses. One representative charge transfer interface is formed between α-RuCl 3 , a van der Waals material with high electron affinity, and graphene. Significant charge transfer across this interface induces the formation of charge-transfer plasmon polaritons (CPPs), hybrid excitations between light and charge oscillations. However, previous studies found that as the charge transfer process takes place, α-RuCl 3 becomes lossy, which limits the quality factor of CPPs. Here, we investigate CPPs down to 10 K using a home-built scattering-type scanning near-field optical microscope (s-SNOM) optimized for low-temperature measurements. Our study reveals a dramatic suppression of plasmon loss channels below 40 K, contributing to a significant enhancement in the plasmonic quality factor. This reduction in loss is likely attributed to the blue shift of the correlation-induced Mott gap in α-RuCl 3 with decreasing temperature, along with the reduction of phonon scattering at low temperature. In conclusion, our results highlight the potential of using s-SNOM and CPPs to study complex 2D interfaces and reveal correlated electron dynamics in the underlying material.

36 MATERIALS SCIENCE↗

Enhancing carbon dioxide gas-diffusion electrolysis by creating a hydrophobic catalyst microenvironment

Electroreduction of carbon dioxide (CO 2 ) over copper-based catalysts provides an attractive approach for sustainable fuel production. While efforts are focused on developing catalytic materials, it is also critical to understand and control the microenvironment around catalytic sites, which can mediate the transport of reaction species and influence reaction pathways. Here, we show that a hydrophobic microenvironment can significantly enhance CO 2 gas-diffusion electrolysis. For proof-of-concept, we use commercial copper nanoparticles and disperse hydrophobic polytetrafluoroethylene (PTFE) nanoparticles inside the catalyst layer. Consequently, the PTFE-added electrode achieves a greatly improved activity and Faradaic efficiency for CO 2 reduction, with a partial current density >250 mA cm -2 and a single-pass conversion of 14% at moderate potentials, which are around twice that of a regular electrode without added PTFE. The improvement is attributed to a balanced gas/liquid microenvironment that reduces the diffusion layer thickness, accelerates CO 2 mass transport, and increases CO 2 local concentration for the electrolysis.

36 MATERIALS SCIENCE↗

Unraveling the intrinsic atomic physics behind x-ray absorption line shifts in warm dense silicon plasmas

Here, we present a novel free-energy density functional theory (DFT)-based methodology for optical property calculations of warm dense matter to cover a wide range of thermodynamic conditions and photon energies including the entire x-ray range. It uses Mermin–Kohn–Sham density functional theory with exchange-correlation (XC) thermal effects taken into account via a fully temperature dependent generalized gradient approximation XC functional. The methodology incorporates a combination of the ab initio molecular dynamics (AIMD) snapshotted Kubo–Greenwood optic data with a single-atom in simulation cell calculations to close the photon energy gap between the L and K edges and extend the K-edge tail toward many-keV photon energies. This gap arises in the standard scheme due to a prohibitively large number of bands required for the Kubo–Greenwood calculations with AIMD snapshots. Kubo–Greenwood data on snapshots provide an accurate description of optic properties at low photon frequencies slightly beyond the L-edge and x-ray absorption near edges structure (XANES) spectra, while data from periodic calculations with single atoms cover the tail regions beyond the edges. To demonstrate its applicability to mid-Z materials where the standard DFT-based approach is not computationally feasible, we have applied it to opacity calculations of warm dense silicon plasmas. These first-principles calculations revealed a very interesting phenomon of red-to-blue shift in K–L (1s → 2p) and K-edge absorptions along both isotherm and isochore, which are absent in most continuum-lowering models of traditional plasma physics. This new physics phenomenon can be attributed to the underlying competition between the screening of deeply bound core electrons and the screening of outer-shell electrons caused by warm-dense-plasma conditions. We further demonstrate that the ratio of 1s → 2p to the K-edge x-ray absorptions can be used to characterize warm-dense-plasma conditions. Eventually, based on our absorption calculations, we have established a first-principles opacity table (FPOT) for silicon in a wide range of material densities and temperatures.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Anomalous thermal transport under high pressure in boron arsenide

High pressure represents extreme environments and provides opportunities for materials discovery. Thermal transport under high hydrostatic pressure has been investigated for more than 100 years and all measurements of crystals so far have indicated a monotonically increasing lattice thermal conductivity. Here we report in situ thermal transport measurements in the newly discovered semiconductor crystal boron arsenide, and observe an anomalous pressure dependence of the thermal conductivity. We use ultrafast optics, Raman spectroscopy and inelastic X-ray scattering measurements to examine the phonon bandstructure evolution of the optical and acoustic branches, as well as thermal conductivity under varied temperatures and pressures up to 32 gigapascals. Using atomistic theory, we attribute the anomalous high-pressure behaviour to competitive heat conduction channels from interactive high-order anharmonicity physics inherent to the unique phonon bandstructure. Our study verifies ab initio theory calculations and we show that the phonon dynamics—resulting from competing three-phonon and four-phonon scattering processes—are beyond those expected from classical models and seen in common materials. In conclusion, this work uses high-pressure spectroscopy combined with atomistic theory as a powerful approach to probe complex phonon physics and provide fundamental insights for understanding microscopic energy transport in materials of extreme properties.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Evidence of non-isentropic release from high residual temperatures in shocked metals measured with ultrafast x-ray diffraction

Shock experiments are widely used to understand the mechanical and electronic properties of matter under extreme conditions. However, after shock loading to a Hugoniot state, a clear description of the post-shock thermal state and its impacts on materials is still lacking. We used diffraction patterns from 100-fs x-ray pulses to investigate the temperature evolution of laser-shocked Al–Zr metal film composites at time delays ranging from 5 to 75 ns driven by a 120-ps short-pulse laser. We found significant heating of both Al and Zr after shock release, which can be attributed to heat generated by inelastic deformation. A conventional hydrodynamic model that employs (i) typical descriptions of Al and Zr mechanical strength and (ii) elevated strength responses (which might be attributed to an unknown strain rate dependence) did not fully account for the measured temperature increase, which suggests that other strength-related mechanisms (such as fine-scale void growth) could play an important role in thermal responses under shock wave loading/unloading cycles. Our results suggest that a significant portion of the total shock energy delivered by lasers becomes heat due to defect-facilitated plastic work, leaving less converted to kinetic energy. This heating effect may be common in laser-shocked experiments but has not been well acknowledged. High post-shock temperatures may induce phase transformation of materials during shock release. Another implication for the study is the preservability of magnetic records from planetary surfaces that have a shock history from frequent impact events.

42 ENGINEERING↗

Characterization of mechanical properties and deformation behavior of highly irradiated 316L stainless steel from target modules at the Spallation Neutron Source using digital image correlation analysis

Tensile specimens with irradiation doses ranging from approximately 0.7 to 7.6 displacements per atom (dpa) were fabricated from 316L samples removed from Spallation Neutron Source (SNS) target vessels after service. Tensile tests were performed in conjunction with digital image correlation (DIC) characterization, which permitted detailed analysis of the strain distribution and deformation behavior of the specimen gauge sections during testing. The results show, while considerable hardening (500–700 MPa increase in yield strength) occurred in the 316L SNS target material with increasing dose, appreciable ductility (19–23% total elongation) remained in the material after irradiation to 7.6 dpa in the mixed neutron/proton environment of the SNS target region. The DIC data showed the strain distribution and deformation behavior of all irradiated specimens were nonuniform during testing. Strain localization in the form of deformation bands or “hotspots” was observed during testing, and in some specimens, the bands propagated as deformation waves along the gauge section. The “traveling wave” deformation behavior affected the amount of elongation each specimen achieved, and the scatter in the elongation data was attributed to the large variation in deformation behavior observed among different specimens. Bands of localized strain, or deformation bands, oriented at specific angles were observed in two-dimensional plots of the strain distribution in the gauge sections of some specimens. Overall, this paper describes the experimental procedures, results, and deformation behavior of tensile specimens from SNS targets after service and illustrates the value of DIC characterization during tensile testing of irradiated materials.

36 MATERIALS SCIENCE↗

Nitrile/Buna N Material Failure Assessment for an O-Ring used on the Gaseous Hydrogen Flow Control Valve (FCV) of the Space Shuttle Main Engine

After the rollout of Space Shuttle Discovery in April 2005 in preparation for return-to-flight, there was a failure of the Orbiter (OV-103) helium signature leak test in the gaseous hydrogen (GH2) system. Leakage was attributed to the Flow Control Valve (FCV) in Main Engine 3. The FCV determined to be the source of the leak for OV-103 is designated as LV-58. The nitrile/Buna N rubber O-ring seal was removed from LV-58, and failure analysis indicated radial cracks providing leak paths in one quadrant. Cracks were eventually found in 6 of 9 FCV O-rings among the three Shuttle Orbiters, though none were as severe as those for LV-58, OV-103. Testing by EM10 at MSFC on all 9 FCV O- rings included: laser dimensional, Shore A hardness and properties from a dynamic mechanical analyzer (DMA) and an Instron tensile machine. The following test data was obtained on the cracked quadrant of the LV-58, OV-103 O-ring: (1) the estimated compression set was only 9.5%, compared to none for the rest of the O-ring; (2) Shore A hardness for the O.D. was higher by almost 4 durometer points than for the rest of the O-ring; and (3) DMA data showed that the storage/elastic modulus E was almost 25% lower than for the rest of the O-ring. Of the 8 FCV O-rings tested on an Instron, 4 yielded tensile strengths that were below the MIL spec requirement of 1350 psi-a likely influence of rubber cracking. Comparisons were made between values of modulus determined by DNA (elastic) and Instron (Young s). Each nitrile/Buna N O-ring used in the FCV conforms to the MIL-P-25732C specification. A number of such O-rings taken from shelf storage at MSFC and Kennedy Space Center (KSC) were used to generate a reference curve of DMA glass transition temperature (Tg) vs. shelf storage time ranging from 8 to 26 years. A similar reference curve of TGA onset temperature (of rubber weight loss) vs. shelf storage time was also generated. The DMA and TGA data for the used FCV O-rings were compared to the reference curves. Correlations were also made between the DMA modulus (at 22 C) and Shore A hardness for all 9 of the FCV O-rings used among the three Shuttle Orbiters. The radial cracking in the FCV O-rings was determined to be due to ozone attack, as nitrile/Buna N rubber is susceptible to such attack. Nitrile/Buna N material under MIL-P25732C should be used in a hydraulic fluid environment to help protect it from cracking. However, the FCV O-rings were used in an air only environment. The FCV design has as much as a 9-mil gap that allows the O.D. of the O-ring to be directly exposed to ozone, pressurized air and some elevated temperatures, accelerating the weathering process that leads to O-ring cracking. Space Shuttle flights will likely not continue past 2010. Therefore, Shuttle management decided to continue using the nitrile/Buna N material for the FCVs, but have each O-ring replaced after 3 years to minimize any chances for crack initiation.

Wingard, Doug↗

NOMAD total scattering dataset for SMC data challenge

The data provided for this challenge was measured using the Nanoscale-Ordered Materials Diffractometer (NOMAD) at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. The data is stored in a hdf5 file following the NeXus standard and can be read with tools built for either. While the NeXus format is self-describing, there is benefit to explaining some details. The data is stored in 4 NXentries in the file. The NXentries that begin with 'amorphous_SiO2' are for the amorphous data, and the NXentries that begin with 'crystalbolite_SiO2' are for the crystalline material. Solutions that were produced by the scientist are in the entries that end with '_byhand'. Each of the NXdata groups are the plottable data with the 'signal', axes, and (in the case of by-hand components) 'auxiliary_signals' describing which fields should be used. The by-hand component ranges are listed in a 'component' attribute of the various signals. The filtered Sr data is the Fourier transform of the combined components. The data can be quickly viewed using tools such as Nexpy or HDFview. Most languages have libraries that can work with HDF5 (eg. H5py for python) a partial list is provided at https://manual.nexusformat.org/utilities.html The data can be quickly viewed using tools such as Nexpy or HDFview. https://neutrons.ornl.gov/nomad https://www.hdfgroup.org/solutions/hdf5 https://www.nexusformat.org/

36 MATERIALS SCIENCE↗

Single-Step Fabrication of Au-Fe-BaTiO3 Nanocomposite Thin Films Embedded with Non-Equilibrium Au-Fe Alloyed Nanostructures

Nanocomposite thin film materials present great opportunities in coupling materials and functionalities in unique nanostructures including nanoparticles-in-matrix, vertically aligned nanocomposites (VANs), and nanolayers. Interestingly the nanocomposites processed through a non-equilibrium processing method, e.g., pulsed laser deposition (PLD), often possess unique metastable phases and microstructures that could not achieve using equilibrium techniques, and thus lead to novel physical properties. In this work, a unique three-phase system composed of BaTiO3 (BTO), with two immiscible metals, Au and Fe, is demonstrated. By adjusting the deposition laser frequency from 2 Hz to 10 Hz, the phase and morphology of Au and Fe nanoparticles in BTO matrix vary from separated Au and Fe nanoparticles to well-mixed Au-Fe alloy pillars. This is attributed to the non-equilibrium process of PLD and the limited diffusion under high laser frequency (e.g., 10 Hz). The magnetic and optical properties are effectively tuned based on the morphology variation. This work demonstrates the stabilization of non-equilibrium alloy structures in the VAN form and allows for the exploration of new non-equilibrium materials systems and their properties that could not be easily achieved through traditional equilibrium methods.

36 MATERIALS SCIENCE↗

Pulsed laser synthesis of mesoporous metal chalcogenide thin films

Mesoporous films of the metal chalcogenide B-FeSe were grown on MgO substrates by KrF pulsed laser deposition (PLD) in an argon background. At 100 mTorr, gated intensified charge-coupled device imaging and ion probe measurements showed that the plasma plume responsible for crystal growth initially comprised three components, with distinct expansion velocities. Plume interactions with the substrate heater and ablation target gave rise to complex dynamics, including collisions between the charged leading edge—rebounding between the substrate and the target—and slower-moving species in the plume interior. Film growth was dominated by species with kinetic energies ≤0.5 eV/atom. X-ray reflectivity revealed that films grown in this environment—with a substrate temperature of 350 ° C, a laser fluence of 1.0 J cm −2 , and a 7.5 mm 2 spot area—formed a porous framework with 15% porosity. Atomic force microscopy showed surface features that suggest pore sizes below 100 nm. X-ray diffraction indicated that the porous films were epitaxial with respect to the substrate and likely grew by oriented-attachment of gas-phase molecular clusters or very small nanoparticles, in contrast to the conventional epitaxy of vacuum films from atomic constituents. The in-plane orientation of the mesoporous films was B-FeSe [100]||[110] MgO, attributed to the soft landing of pre-formed crystallites on the MgO substrates, where protruding Se rows of B-FeSe aligned with corrugations of the MgO surface. In conclusion, this work implies that growth of candidate electrocatalyst materials by PLD in inert gas background may allow mesoporous frameworks with a single crystallographic orientation that expose specific crystal facets for electrochemical reactions and active site engineering.

cluster epitaxy↗

Raman signatures from age-dating PuO 2 since last calcination

The self-irradiation of PuO 2 has been shown to affect the attributes of fifteen vibrational bands in the Raman spectrum. The vibrational bands correspond to the Raman allowed vibrational mode T 2g , overtones, defects, and bands from electronic origin. Defects in the crystal lattice from low-calcination temperature and alpha decay origins are responsible for the changes in the band attributes (band position, full-width half maximum (FWHM), intensity). Crystal lattice defects are also responsible for the growth of the defect bands. The temporal behavior of the vibrational bands can be used to estimate the age of the material since last calcination. Laser annealing was used to reset the material to full crystallinity prior to the aging study. 240 PuO 2 , with an alpha decay rate of 3.67 greater than the decay rate of 239 PuO 2 , was primarily used to assess the alpha decay-induced damage within 3 years. The aging study focused on the time-dependent properties of the T 2g band and the growth of defect bands. The FWHM of the T 2g band and the ratio of the areas of the defect bands/T 2g band were measured through a time period in excess of 3 years. The data from this study were found very close to the data describing the temporal evolution of the lattice constant measured with the X-ray diffraction (XRD) technique. The local physical properties of the material measured with Raman spectroscopy and the lattice parameter constant measured with XRD indicates a strong correlation between the two techniques. Although both techniques provide similar age-dating information, in contrast to the few milligram quantities required for XRD, Raman spectroscopy requires a 10 µm diameter PuO 2 particle to provide an estimate of the material age since last calcination.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Thermal conductivity measurement of U-Mo and U-Mo/Al interaction layers generated from in-pile irradiation using the suspended-bridge method

Here, this study presents the first measurement of the individual thermal conductivity of U-7wt.%Mo fuel particles and U-Mo/Al interaction layers (ILs) from in-pile irradiated dispersion fuel plates, using the suspended-bridge method. Nanorods of U-7wt.%Mo fuel and U-Mo/Al ILs were extracted by focused ion beam (FIB), and their microstructures were characterized with transmission electron microscopy (TEM). TEM revealed finely distributed nanobubbles in the U-7wt.%Mo matrix, along with an amorphous structure in the ILs. The thermal conductivity of in-pile irradiated U-7wt.%Mo was approximately 30% lower than that of the unirradiated material, ranging from 6.7 W/m·K at 300 K to 8.5 W/m·K at 380 K. The ILs exhibited even lower thermal conductivity, from 2.1 W/m·K at 300 K to 2.7 W/m·K at 380 K. These reductions, attributed to nanobubbles, fission products, and irradiation-induced point defects, were analyzed through a combination of microstructural characterization and literature-based transport models, which successfully reproduced the observed degradation trends.

42 - ENGINEERING↗

Probing Surface/Bulk Structural Chemistry of Key Components of Solid Oxide Electrochemical Cells with In Situ / Operando Raman Spectroscopy

The remarkable attributes of solid oxide electrochemical cell technology (e.g., energy efficiency, low cost, scalability, low emissions, and operational flexibility, etc.) drive the wider adoption of electrochemical conversion routes for sustainability. It is critical for the codevelopment of solid oxide cell materials and processes to establish the mechanistic understanding of the underlying chemical phenomena at the molecular level. Herein, we summarize the advancements in Raman spectroscopy that provide structural/molecular information on electrode/electrolyte materials typically used in solid oxide cells for energy conversion. In particular, we discuss the multifactorial environment induced chemical processes that govern the performance and longevity of solid oxide electrochemical devices. The in situ/operando Raman spectroscopic investigations on the electrode/electrolyte materials reported in the literature are summarized with the emphasis on identification of key material properties that control the functional aspects of the solid oxide cells. The molecular level understanding of the electrochemical processes will allow advancement of the rational design of electrochemical materials for process level deployment of solid oxide cell technology.

Electrodes↗

Two-Dimensional Perovskite Single-Nanowire Photodetectors

High-performance microphotodetectors require materials that combine strong light–matter interaction, fast charge transport, and ambient stability. Here, we demonstrate single-nanowire devices based on the 2D perovskite (TPA3) 2 PbBr 4 , synthesized via a controlled slow-cooling self-assembly process that yields defect-minimized, anisotropic nanowires with smooth facets. These microphotodetectors exhibit ultralow dark currents (∼10 –15 A), high responsivity (up to 156 mA W –1 ), and exceptional specific detectivity (∼10 11 Jones) under near-UV (405 nm) illumination, with rise and fall times in the millisecond regime. The superior detectivity is primarily driven by the suppression of thermal noise through the material’s ultralow dark current, while the millisecond temporal response is governed by high-intensity trap-filling dynamics. The devices maintain stable operation over 4000 s of continuous on/off cycling and show remarkable ambient stability over weeks, attributed to dense crystal packing and robust organic cation layers. Furthermore, the influence of nanowire thickness on the charge collection efficiency is systematically elucidated through optical penetration depth analysis, highlighting design principles for optimizing low-dimensional perovskite photodetectors. This study introduces single 2D perovskite nanowires as a versatile platform for miniaturized, high-performance optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Statistically determined nickel cadmium performance relationships

A statistical analysis was performed on sealed nickel cadmium cell manufacturing data and cell matching data. The cells subjected to the analysis were 30 Ah sealed Ni/Cd cells, made by General Electric. A total of 213 data parameters was investigated, including such information as plate thickness, amount of electrolyte added, weight of active material, positive and negative capacity, and charge-discharge behavior. Statistical analyses were made to determine possible correlations between test events. The data show many departures from normal distribution. Product consistency from one lot to another is an important attribute for aerospace applications. It is clear from these examples that there are some significant differences between lots. Statistical analyses are seen to be an excellent way to spot those differences. Also, it is now proven beyond doubt that battery testing is one of the leading causes of statistics.

Gross, Sidney↗

Orbital transfer vehicle oxygen turbopump technology. Volume 2: Nitrogen and ambient oxygen testing

The testing of a rocket engine oxygen turbopump using high pressure ambient temperature nitrogen and oxygen as the turbine drive gas in separate test series is discussed. The pumped fluid was liquid nitrogen or liquid oxygen. The turbopump (TPA) is designed to operate with 400 F oxygen turbine drive gas which will be demonstrated in a subsequent test series. Following bearing tests, the TPA was finish machined (impeller blading and inlet/outlet ports). Testing started on 15 February 1989 and was successfully concluded on 21 March 1989. Testing started using nitrogen to reduce the ignition hazard during initial TPA checkout. The Hydrostatic Bearing System requires a Bearing Pressurization System. Initial testing used a separate bearing supply to prevent a rubbing start. Two test series were successfully completed with the bearing assist supplied only by the pump second stage output which entailed a rubbing start until pump pressure builds up. The final test series used ambient oxygen drive and no external bearing assist. Total operating time was 2268 seconds. There were 14 starts without bearing assist and operating speeds up to 80,000 rpm were logged. Teardown examination showed some smearing of silverplated bearing surfaces but no exposure of the underlying monel material. There was no evidence of melting or oxidation due to the oxygen exposure. The articulating, self-centering hydrostatic bearing exhibited no bearing load or stability problems. The only anomaly was higher than predicted flow losses which were attributed to a faulty ring seal. The TPA will be refurbished prior to the 400 F oxygen test series but its condition is acceptable, as is, for continued operating. This was a highly successful test program.

Brannam, R. J.↗

Estimation of crack closure stresses for in situ toughened silicon nitride with 8 wt pct scandia

An 8-wt pct-scandia silicon nitride with an elongated grain structure was fabricated. The material exhibited high fracture toughness and a rising R-curve as measured by the indentation strength technique. The 'toughening' exponent m was found to be m about 0.1. The high fracture toughness and R-curve behavior was attributed mainly to bridging of the crack faces by the elongated grains. The crack closure (bridging) stress distribution in the wake region of the crack tip was estimated as a function of crack size from the R-curve data, with an arbitrarily assumed distribution function.

Choi, Sung R.↗