SEARCH · Engineering Papers

Results for “yield strength”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,693 records · Page 94

All sources NASA NTRS DOE OSTI

NASA NTRS2020

A Modified Algorithm and Open-Source Computational Package for the Determination of Infrared Optical Constants Relevant to Astrophysics

Infrared (IR) telescopes, such as Spitzer and SOFIA, have revealed a rich variety of chemical species trapped in interstellar ices. The most fundamental parameters to be derived from observed IR spectra are the identity and abundance of each component. Several compounds have been conclusively or tentatively identified, but the band strengths and optical constants needed to derive accurate abundances for many of these are poorly constrained. We have developed a modified approach to the extraction of the real and imaginary parts of the refractive index (optical constants) of a thin film from a single transmission spectrum measured in the IR spectral range. Our algorithm is similar to those implemented by previous authors, with some major changes that yield results for strong absorptions where previous approaches fail: (1) an adaptive k-correction step size, (2) the use of a root-finding algorithm to obtain a more accurate k-correction at each iteration, and (3) a k-correction step that prevents non-physical results such as negative n-values that prevent convergence in the calculation algorithm. The algorithm is presented and described, with examples to show agreement with some existing results and improvements upon others. New optical-constants calculations for CH3OH, CO2, N2O, and CH4 are presented, and potential implications for the modeling of interstellar and planetary ice data from space telescopes are discussed. With the objective of being open-source and transparent, the full source code in the free Python programming language is made available along with the compiled version and the laboratory data used to produce the results shown.

Perry A. Gerakines↗

NASA NTRSDate not supplied

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials (3MDCP)

Carbon and phenolic fibers are commonly used in ablative thermal protection materials, such as 3-dimensional Mid-Density Carbon Phenolic (3MDCP), a 3D-woven composite comprised of mixed-fiber yarn bundles. Predicting the micro-mechanical response and fracture of twisted yarns composed of brittle and ductile fibers requires a modeling approach that captures per-fiber yielding, fiber fracture, and inter-fiber friction and contact. This work presents an extended bonded particle model (BPM) for discrete element method (DEM) simulation of fiber and yarn mechanics, implemented in LAMMPS. The model builds on the incremental bond formulation of Guo et al. and introduces a piecewise elasto-plastic constitutive law for axial extension, enabling representation of fibers that yield before failure. 3MDCP yarns were constructed using measured fiber radius distributions and helical twist geometry. Tensile simulations of single-ply 3MDCP yarns show good agreement with vender stress–strain results. Fiber breakage models also show details on yarn breakage propagration, centered radially in the yarn. Yarn breakage of multi-ply 3MDCP also matched experimental observations in per-ply breakage; however, predicted yarn breakage strength were found higher than experimental observations.

Woven↗

NASA NTRSDate not supplied

Simulations of Yarn Micro-Mechanics of Woven Heat Shield Materials

Discrete Element Method↗

NASA NTRS2006

Chemical, Physical, and Mechanical Characterization of Isocyanate Cross-linked Amine-Modified Silica Aerogels

We describe a new mechanically strong lightweight porous composite material obtained by encapsulating the skeletal framework of amine-modified silica aerogels with polyurea. The conformal polymer coating preserves the mesoporous structure of the underlying silica framework and the thermal conductivity remains low at 0.041 plus or minus 0.001 W m(sup -1 K(sup -1). The potential of the new cross-linked silica aerogels for load-carrying applications was determined through characterization of their mechanical behavior under compression, three-point bending, and dynamic mechanical analysis (DMA). A primary glass transition temperature of 130 C was identified through DMA. At room temperature, results indicate a hyperfoam behavior where in compression cross-linked aerogels are linearly elastic under small strains (less than 4%) and then exhibit yield behavior (until 40% strain), followed by densification and inelastic hardening. At room temperature the compressive Young's modulus and the Poisson's ratio were determined to be 129 plus or minus 8 MPa and 0.18, respectively, while the strain at ultimate failure is 77% and the average specific compressive stress at ultimate failure is 3.89 x 10(exp 5) N m kg(sup -1). The specific flexural strength is 2.16 x 10(exp 4) N m kg(sup -1). Effects on the compressive behavior of strain rate and low temperature were also evaluated.

Katti, Atul↗

DOE OSTI2024

Detailed report on the measurement of the positive muon anomalous magnetic moment to 0.20 ppm

We present details on a new measurement of the muon magnetic anomaly, a μ =(g μ −2)/2. The result is based on positive muon data taken at Fermilab’s Muon Campus during the 2019 and 2020 accelerator runs. The measurement uses 3.1 GeV/c polarized muons stored in a 7.1-m-radius storage ring with a 1.45 T uniform magnetic field. The value of a μ is determined from the measured difference between the muon spin precession frequency and its cyclotron frequency. This difference is normalized to the strength of the magnetic field, measured using nuclear magnetic resonance. The ratio is then corrected for small contributions from beam motion, beam dispersion, and transient magnetic fields. We measure a μ =116592057(25)×10 −11 (0.21 ppm). This is the world’s most precise measurement of this quantity and represents a factor of 2.2 improvement over our previous result based on the 2018 dataset. In combination, the two datasets yield a μ (FNAL)=116592055(24)×10 −11 (0.20 ppm). Combining this with the measurements from Brookhaven National Laboratory for both positive and negative muons, the new world average is a μ (exp)=116592059(22)×10 −11 (0.19 ppm).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Combinatorial library design for improving isobutanol production in Saccharomyces cerevisiae

Saccharomyces cerevisiae is the dominant fermentative producer of ethanol in industry and a preferred host for production of other biofuels. That said, rewiring the metabolism of S. cerevisiae to produce other fermentation products, such as isobutanol, remains an academic challenge. Many studies report aerobic production of isobutanol, but ethanol remains a substantial by-product under these conditions due to the Crabtree effect. These studies indicate that the native isobutanol pathway is incapable of carrying sufficient flux to displace ethanol. In this report, we screened a combinatorial library of pathway enzymes to identify an isobutanol pathway cassette capable of supporting the growth of a non-ethanol producing S. cerevisiae . We began by identifying a diverse set of isobutanol pathway enzyme homologs and combined each open reading frame with varied-strength promoters in a combinatorial, pooled fashion. We applied a growth-coupled screen where a functional isobutanol pathway restored NAD + regeneration during glucose catabolism that is otherwise repressed via the Crabtree effect. Using this screen, we isolated a cassette consisting of a mosaic of bacterial and cytosol-localized fungal enzymes that conferred under aerobic conditions the ability to produce 364 mg/L isobutanol (8.8% of the theoretical maximum yield). We next shifted the cofactor usage of the isolated ketol-acid reductoisomerase enzyme in the cassette from NADPH to NADH-preferring to improve redox balance. The approach used herein isolated isobutanol producing strains that approach the best in the literature without producing substantial ethanol titers. Still, the best isolated cassette was insufficient to support anaerobic growth in the absence of ethanol fermentation - indicating the presence of further fundamental gaps in our understanding of yeast fermentation.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1982

Imide modified epoxy matrix resins

Results of a program designed to develop tough imide modified epoxy (IME) resins cured by bisimide amine (BIA) hardeners are presented. State of the art epoxy resin, MY720, was used. Three aromatic bisimide amines and one aromatic aliphatic BIA were evaluated. BIA's derived from 6F anhydride (3,3 prime 4,4 prime-(hexafluoro isopropyl idene) bis (phthalic anhydride) and diamines, 3,3 prime-diam nodiphenyl sulfone (3,3 prime-DDS), 4,4 prime-diamino diphenyl sulfone (4,4 prime-DDS), 1.12-dodecane diamine (1,12-DDA) were used. BIA's were abbreviated 6F-3,3 prime-DDS, 6F-4,4 prime-DDS, 6F-3,3 prime-DDS-4,4 prime DDS, and 6F-3,3 prime-DDS-1,12-DDA corresponding to 6F anhydride and diamines mentioned. Epoxy resin and BIA's (MY720/6F-3,3 prime-DDS, MY720/6F-3,3 prime-DDS-4,4 prime-DDS, MY720/6F-3,3 prime-DDS-1,12-DDA and a 50:50 mixture of a BIA and parent diamine, MY720/6F-3,3 prime-DDS/3,3 prime-DDS, MY720/6F-3,3 prime-DDS-4,4 prime-DDS/3,3 prime-DDS, MY720/6F-3,3 prime-DDS-1,12-DDA/3,3 prime-DDS were studied to determine effect of structure and composition. Effect of the addition of two commercial epoxies, glyamine 200 and glyamine 100 on the properties of several formulations was evaluated. Bisimide amine cured epoxies were designated IME's (imide modified epoxy). Physical, thermal and mechanical properties of these resins were determined. Moisture absorption in boiling water exhibited by several of the IME's was considerably lower than the state of the art epoxies (from 3.2% for the control and state of the art to 2.0 wt% moisture absorption). Char yields are increased from 20% for control and state of the art epoxies to 40% for IME resins. Relative toughness characteristics of IME resins were measured by 10 deg off axis tensile tests of Celion 6000/IME composites. Results show that IME's containing 6F-3,3 prime-DDS or 6F-3,3 prime-DDS-1,12-DDA improved the "toughness" characteristics of composites by about 35% (tensile strength), about 35% (intralaminar shear strength), and about 78% (shear strain to failure) relative to the control composite.

Scola, D. A.↗

DOE OSTI2020

Status, Challenges, and Plans for Consistent Modeling and Evaluation of Fission Data: Nubar, PFNS, and FPY [Slides]

This presentation discusses the importance of consistent evaluations for fission observables. Currently, prompt fission quantities (e.g., neutron multiplicity, neutron energy spectrum, and fission product yields) are evaluated independently of one another, either with separate models or data-only/non-model evaluations (few – if any – shared model inputs) and inconsistencies can arise in evaluated data (e.g. NSE 190, 258 (2018)). They have found that consistent, model-based evaluations lead to more physical constraints on free parameters in the model, more robust predictions for other observables and other isotopes, that there are correlations between the uncertainties on different observables, and that uncertainties can be propagated to unmeasured quantities. They are working on developing models to the point where fission observables are calculated at the quality needed for an evaluation. They are striving to consistently calculate fission observables, such as $\bar{v}$, PFNS, and FPY, to a quality suitable for an evaluation. Current evaluations for fission observables use separate models for each observable (with minimal shared input) or are purely data driven. LANL models, such as the Monte Carlo CGMF and deterministic BeoH, have different strengths; the similar fission fragment initial conditions and decay models leads to consistency between the two codes (FPY can be connected to $\bar{v}$ and PFNS, even when calculated by different codes). Work is underway by Lovell to optimize the models and Neudecker is working to perform detailed uncertainty quantification. The PFNS, in particular, presents a significant challenge.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2023

Constraining the $\overline{K}$N coupled channel dynamics using femtoscopic correlations at the LHC

The interaction of K – with protons is characterised by the presence of several coupled channels, systems like $\overline{K}$ 0 n and πΣ with a similar mass and the same quantum numbers as the K – p state. The strengths of these couplings to the K – p system are of crucial importance for the understanding of the nature of the Λ(1405) resonance and of the attractive K – p strong interaction. In this article, we present measurements of the K – p correlation functions in relative momentum space obtained in pp collisions at $\sqrt{s}$=13 Te, in p–Pb collisions at $\sqrt{s_{NN}}$= 5.02 Te, and (semi)peripheral Pb–Pb collisions at $\sqrt{s_{NN}}$= 5.02 Te. The emitting source size, composed of a core radius anchored to the K + p correlation and of a resonance halo specific to each particle pair, varies between 1 and 2 fm in these collision systems. The strength and the effects of the $\overline{K}$ 0 n and πΣ inelastic channels on the measured K – p correlation function are investigated in the different colliding systems by comparing the data with state-of-the-art models of chiral potentials. A novel approach to determine the conversion weights ω, necessary to quantify the amount of produced inelastic channels in the correlation function, is presented. In this method, particle yields are estimated from thermal model predictions, and their kinematic distribution from blast-wave fits to measured data. The comparison of chiral potentials to the measured K – p interaction indicates that, while the πΣ –K – p dynamics is well reproduced by the model, the coupling to the $\overline{K}$ 0 n channel in the model is currently underestimated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Environmental controls on simulated deep moist convection initiation occurring during RELAMPAGO-CACTI

This study synthesizes the results of 13 high-resolution simulations of deep convective updrafts forming over idealized terrain using environments observed during the RELAMPAGO and CACTI field projects. Using composite soundings from multiple observed cases, and variations upon them, we explore the sensitivity of updraft properties (e.g., size, buoyancy, and vertical pressure gradient forces) to influences of environmental relative humidity, wind shear, and mesoscale orographic forcing that support or suppress deep convection initiation (CI). Emphasis is placed on differentiating physical processes affecting the development of updrafts (e.g., entrainment-driven dilution of updrafts) in environments typifying observed successful and null (i.e., no CI despite affirmative operational forecasts) CI events. Thermally-induced mesoscale orographic lift favors the production of deep updrafts originating from ~1–2-km-wide boundary layer thermals. Simulations without terrain forcing required much larger ( ~5-km-wide) thermals to yield precipitating convection. CI outcome was quite sensitive to environmental relative humidity; updrafts with increased buoyancy, depth, and intensity thrived in otherwise inhospitable environments by simply increasing the free tropospheric relative humidity. This implicates the entrainment of free-tropospheric air into updrafts as a prominent governor of CI, consistent with previous studies. Sensitivity of CI to the environmental wind is manifested by: 1) low-level flow affecting the strength and depth of mesoscale convergence along the terrain, and 2) clouds encountering updraft-suppressing pressure gradient forces while interacting with vertical wind shear in the free-troposphere. Among the ensemble of thermals occurring in each simulation, the widest deep updrafts in each simulation were the most sensitive to environmental influences.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1992

Regenerative Life Support Systems Test Bed performance - Lettuce crop characterization

Two crops of lettuce (Lactuca sativa cv. Waldmann's Green) were grown in the Regenerative Life Support Systems (RLSS) Test Bed at NASA's Johnson Space Center. The RLSS Test Bed is an atmospherically closed, controlled environment facility for the evaluation of regenerative life support systems using higher plants. The chamber encloses 10.6 m 2 of growth area under cool-white fluorescent lamps. Lettuce was double seeded in 480 pots, each containing about 250 cm 3 of calcined-clay substrate. Each pot was irrigated with half-strength Hoagland's nutrient solution at an average total applied amount of 2.5 and 1.8 liters pot -1 , respectively, over each of the two 30-day crop tests. Average environmental and cultural conditions during both tests were 23°C air temperature, 72% relative humidity, 1000 ppm carbon dioxide (CO 2 ), 16h light/8h dark photoperiod, and 356 μmol m -2 s -1 photosynthetic photon flux. After 30 days from seeding, average yield (g pot -1 ) for the first and second crop tests were 72 and 49 edible (shoot) fresh mass, 3.65 and 2.56 edible dry mass, and 0.44 and 0.45 inedible (root) dry mass, respectively. Averaging over both crop tests, the test bed met the requirements of 2.1 person-days of oxygen production, 2.4 person days of CO 2 removal and 129 person days of potential potable water production. The satisfactory growth of both crops demonstrates the potential of lettuce for air revitalization and water production in a controlled ecological life support system. Differences in crop performance resulting from engineering system effects provides evidence of the resilience of biological systems.

Life support systems↗

NASA NTRS1996

Comparison of aerobically-treated and untreated crop residue as a source of recycled nutrients in a recirculating hydroponic system

This study compared the growth of potato plants on nutrients recycled from inedible potato biomass. Plants were grown for 105 days in recirculating, thin-film hydroponic systems containing four separate nutrient solution treatments: (1) modified half-strength Hoagland's (control), 2) liquid effluent from a bioreactor containing inedible potato biomass, 3) filtered (0.2 micrometer) effluent, and 4) the water soluble fraction of inedible potato biomass (leachate). Approximately 50% of the total nutrient requirement in treatments 2-4 were provided (recycled) from the potato biomass. Leachate had an inhibitory effect on leaf conductance, photosynthetic rate, and growth (50% reduction in plant height and 60% reduction in tuber yield). Plants grown on bioreactor effluent (filtered or unfiltered) were similar to the control plants. These results indicated that rapidly degraded, water soluble organic material contained in the inedible biomass, i.e., material in leachate, brought about phytotoxicity in the hydroponic culture of potato. Recalcitrant, water soluble organic material accumulated in all nutrient recycling treatments (650% increase after 105 days), but no increase in rhizosphere microbial numbers was observed.

NASA Discipline Life Support Systems↗

DOE OSTI2021

CO 2 Hydrogenation on ZrO 2 /Cu(111) Surfaces: Production of Methane and Methanol

The conversion and utilization of carbon dioxide is a critical challenge for the control of greenhouse gas pollution and in the production of high value chemicals in C1 chemistry. ZrO 2 /Cu(111) is an inverse oxide/metal catalyst that displays high activity and stability for the hydrogenation of CO 2 into methanol at 500-600 K. At elevated temperatures, ZrO 2 grows on a CuO x /Cu(111) substrate forming islands of 10-12 nm in size and an average height of ~ 3 Å. Reaction with H 2 leads to the removal of the copper oxide producing ZrO 2 /Cu(111) surfaces which are very active for the binding and dissociation of CO 2 into CO and C. After exposing ZrO 2 /Cu(111) to moderate or elevated pressures of a CO 2 /H 2 mixture at 300 K, atomic C and minor amounts of CH x O and CO x are deposited on the catalyst surface. The adsorbed CH x O and CO x disappear upon heating above 400 K. The catalytic tests for CO 2 hydrogenation give CO as the main reaction product and CH 4 and CH 3 OH as secondary products. The relative yields of methane and methanol change with time and track the amount of atomic C deposited on the active ZrO 2 /Cu(111) surface. The formation of methane stops once the catalyst surface is saturated with C. Under steady-state conditions, ZrO 2 /Cu(111) is a much better catalyst for methanol synthesis than ZnO/Cu(111). This trend reflects variations in the size of the oxide islands and in the strength of oxide-metal interactions. The use of an inverse oxide/metal configuration is an important synthetic tool when preparing active, selective, and stable catalysts for CO 2 hydrogenation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Strong, thermo-reversible salogels with boronate ester bonds as thermal energy storage materials

Inorganic salt hydrates are promising phase change materials (PCMs) but suffer from low viscosity at temperatures above their melting point resulting in leakage problems during thermal storage applications. To achieve shape stabilization of one type of molten inorganic PCM – calcium nitrate tetrahydrate (CNH) – this work explored gelation of polyvinyl alcohol (PVA) in this solvent and the effect of dynamic boronate ester bonds on salogel strength. The occurrence of gelation of PVA in molten CNH but not in water is rationalized by the extremely high salt content and scarcity of hydration water in CNH, enabling intermolecular hydrogen bonding between PVA chains. While neat PVA salogels in CNH were weak, with a gel-to-sol transition temperature (T gel ) below room temperature, the addition of small amounts of borax (<~0.3 wt%) introduced dynamic covalent crosslinks and yielded salogels with T gel tunable over a wide temperature range from 7 to 70 °C. Here, the PVA/borax salogels were about one order of magnitude stronger than their well-known PVA/borax hydrogel counterparts, and, unlike PVA/borax hydrogels, were capable of retaining their shape and preventing leakage of molten CNH. Moreover, the salogels exhibited reversible and repeatable temperature-triggered gel-to-sol transitions and the ability to self-heal. The low polymer and crosslinker concentration also ensured that more than 95% of the heat of fusion of neat CNH was maintained in the salogels and was retained after twenty cycles of melting and crystallization, demonstrating the robust nature of these energy storage materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1986

Catching the whispers from Uranus

Sophisticated telecommunications techniques are described that were used to acquire images of Uranus, its 14 moons and ten narrow rings darker than coal. The images, equal in quality to those transmitted from Saturn several years earlier despite the signal being weaker by 6 dB due to the increased distance, were received from Voyager 2 during its January 24, 1986 flyby of Uranus. Solutions to the problem of the weakening signal were found in modifications to Voyager's image processing system and NASA's ground tracking network. In April 1985, Voyager's prime flight data computer was reconfigured to accept only nonimaging science data, and its backup, only imaging data; the latter was reprogrammed to determine only arithmetic differences between adjacent pixel intensities rather than absolute intensities. By image compression, equivalent imaging information could be sent at lower bit rates. Instead of Golay coding, Reed-Solomon onboard encoding was used. These techniques gained the equivalent of 4-dB in imaging yield. Additional improvements were gained by using earth station antennas in pairs (the Parkes radio telescope and the Canberra ground station antenna). Moves under way to prepare for the Voyager encounter with Neptune in 1989 are described (using additional antennas and arrays, scaling up the Deep Space Network antennas from 64 m to 70 m, etc.) to assure almost Saturn-equivalent pictures despite a further 3.5-dB drop in signal strength.

Bartok, C. D.↗

DOE OSTI2021

New Fe 59 Stellar Decay Rate with Implications for the Fe 60 Radioactivity in Massive Stars

The discrepancy between observations from γ-ray astronomy of the 60 Fe/ 26 Al γ-ray flux ratio and recent calculations is an unresolved puzzle in nuclear astrophysics. The stellar β-decay rate of 59 Fe is one of the major nuclear uncertainties impeding us from a precise prediction. The important Gamow-Teller strengths from the low-lying states in 59 Fe to the 59 Co ground state are measured for the first time using the exclusive measurement of the 59 Co(t,3He+γ) 59 Fe charge-exchange reaction. The new stellar decay rate of 59 Fe is a factor of 3.5±1.1 larger than the currently adopted rate at T=1.2 GK. Stellar evolution calculations show that the 60 Fe production yield of an 18 solar mass star is decreased significantly by 40% when using the new rate. Our result eliminates one of the major nuclear uncertainties in the predicted yield of 60 Fe and alleviates the existing discrepancy of the 60 Fe/ 26 Al ratio.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

STFM: Accurate Spatio-Temporal Fusion Model for Weather Forecasting

Meteorological prediction is crucial for various sectors, including agriculture, navigation, daily life, disaster prevention, and scientific research. However, traditional numerical weather prediction (NWP) models are constrained by their high computational resource requirements, while the accuracy of deep learning models remains suboptimal. In response to these challenges, we propose a novel deep learning-based model, the Spatiotemporal Fusion Model (STFM), designed to enhance the accuracy of meteorological predictions. Our model leverages Fifth-Generation ECMWF Reanalysis (ERA5) data and introduces two key components: a spatiotemporal encoder module and a spatiotemporal fusion module. The spatiotemporal encoder integrates the strengths of convolutional neural networks (CNNs) and recurrent neural networks (RNNs), effectively capturing both spatial and temporal dependencies. Meanwhile, the spatiotemporal fusion module employs a dual attention mechanism, decomposing spatial attention into global static attention and channel dynamic attention. This approach ensures comprehensive extraction of spatial features from meteorological data. The combination of these modules significantly improves prediction performance. Experimental results demonstrate that STFM excels in extracting spatiotemporal features from reanalysis data, yielding predictions that closely align with observed values. In comparative studies, STFM outperformed other models, achieving a 7% improvement in ground and high-altitude temperature predictions, a 5% enhancement in the prediction of the u/v components of 10 m wind speed, and an increase in the accuracy of potential height and relative humidity predictions by 3% and 1%, respectively. This enhanced performance highlights STFM’s potential to advance the accuracy and reliability of meteorological forecasting.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1977

Flight inspection data and crack initiation times

Lockheed C-130 service-flight inspection data is reduced by means of fracture mechanics and statistical analysis into a form from which the probability of time to crack initiation and the distribution of initial flaw sizes for various locations on the aircraft can be determined. Crack sizes are normalized by extrapolating a growing crack backwards from its first recorded size to .03 inches (crack initiation size) yielding the time to crack initiation. In a similar fashion, the crack is grown backwards to a time equal to zero to yield an initial flaw size. In order to perform the discussed computations, crack growth constants were computed for each individual location and were analyzed statistically. Statistical distributions were fitted to times to crack initiation and to initial flaw sizes in order to describe their expected behavior. Weibull and Johnson distributions have been found to fit the data reasonably well but for a better fit convolution integrals of Poisson load distributions and Weibull strength distributions are needed.

Johnson, W. S.↗