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NASA NTRS1979

Gradient and curvature drifts in magnetic fields with arbitrary spatial variation

It is shown that, for a magnetic field of arbitrary spatial variation, a nearly isotropic distribution of charged particles drifts with a velocity given by the usual first-order orbit theory drifts averaged over pitch angle. It is assumed that the near-isotropy brought about by scattering, but conclusions concerning drift are insensitive to the details of the scattering process. It is found that this drift velocity is correct even for arbitrarily large ratios of particle gyroradius to magnetic spatial scale, although this velocity must, like all drift effects, be viewed on a scale larger than a gyroradius. Hence for many astrophysical applications, such as cosmic rays, where anisotropies are small, the usual drift velocities provide a valid approximation to convective motions even if the magnetic field scales are very small.

Isenberg, P. A.↗

DOE OSTI2025

Assessment and Simulation of Particulate Transport for Delivery of Solid Amendments into the Subsurface: FY25 Status Report

For particulate-based amendments to be viable for field-scale remediation at the Hanford Site (e.g., the 200 DV-1 Operable Unit), amendment particles need to be delivered a reasonable distance away from an injection well to provide cost effective in situ treatment. Field-scale particle transport models can estimate spatial deposition of amendment particles in the subsurface, which is critical for developing an overall remediation strategy. However, field-scale particle simulations are currently limited due to insufficient simulation capability and a lack of experimental data to validate and parameterize particle transport models. During this fiscal year, the following progress has been made toward a field-scale particle transport modeling evaluation: (1) in addition to the two particle transport models implemented last FY, four additional particle transport models have been implemented within PFLOTRAN; (2) a Python-based pre-screening tool was finalized, enabling users to quickly estimate the particle radius of influence (ROI) for any given particle-amendment system; and (3) an initial compatibility assessment was completed using both particle transport simulations deployed through the pre-screening tool, in conjunction with general guidelines to (a) identify the most suitable amendment particle sizes for various Hanford sediments and (b) evaluate amendment-delivery fluid compatibility. The preliminary compatibility assessment revealed that for amendment delivery success to the various Hanford target formations, amendment particle sizes will likely need to be smaller than the amendment sizes tested in the DV-1 treatability study. It is recommended that amendment particles be decreased in size, or alternative smaller size amendments be obtained from the manufacture, prior to any further experimental testing. Also, preliminary testing suggests that xanthan gum may be the most broadly compatible delivery fluid. Planned laboratory experiments will be instrumental in validating and refining the PFLOTRAN particulate transport model formulations, ultimately enabling predictive capabilities to facilitate the design of field-scale amendment delivery systems. This work consists of acquiring new theoretical or experimental knowledge. The information associated with this report should not be used as design input or operating parameters without additional qualification.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1992

Issues and approach to develop validated analysis tools for hypersonic flows: One perspective

Critical issues concerning the modeling of low-density hypervelocity flows where thermochemical nonequilibrium effects are pronounced are discussed. Emphasis is on the development of validated analysis tools. A description of the activity in the Ames Research Center's Aerothermodynamics Branch is also given. Inherent in the process is a strong synergism between ground test and real-gas computational fluid dynamics (CFD). Approaches to develop and/or enhance phenomenological models and incorporate them into computational flow-field simulation codes are discussed. These models have been partially validated with experimental data for flows where the gas temperature is raised (compressive flows). Expanding flows, where temperatures drop, however, exhibit somewhat different behavior. Experimental data for these expanding flow conditions are sparse; reliance must be made on intuition and guidance from computational chemistry to model transport processes under these conditions. Ground-based experimental studies used to provide necessary data for model development and validation are described. Included are the performance characteristics of high-enthalpy flow facilities, such as shock tubes and ballistic ranges.

Deiwert, George S.↗

NASA NTRS1981

Analytical description of charged particles transport along arbitrary guiding-field configurations

A new description of focused transport was developed which is valid for arbitrary spatial dependences of both the scattering mean free path and the focusing length. In particular, it describes the supercoherent transition from the coherent modes that occurs when focusing is strong compared to scattering to the diffusive mode that occurs when focusing is weak. Because it specifies the pitch angle distribution in terms of relatively simple functions, the new formulation facilitates not only the detailed interpretation of solar particle events, but also the qualitative understanding of focused transport. In the steady state, it predicts that the angular distribution consists of a highly collimated 'strahl' which is superimposed on an anisotropic 'halo'. This picture provides new insight into observed configurations of steady-state particle fluxes.

Earl, J. A.↗

NASA NTRS1984

Comparison of an analytical approximation for particle motion in a current sheet with precise numerical calculations

Approximate analytic solutions exist for particle motion in a one-dimensional current sheet with a constant normal magnetic field component. These solutions are tested against precise numerical calculations, and a range of validity of the analytic solutions is inferred. For example, in the geomagnetic tail neutral sheet, for a dawn-dusk electric field of 0.1-1 mV/m, lobe field of 10-40 nT, and sheet thickness of 1000 km, the analytic solutions serve as a good predictor of particle motion when the normal magnetic field component is less than 3 or 4 nT. By using the analytic solutions, initial distribution functions are mapped into final (accelerated) distributions, and the analytic mappings are compared with numerical mappings.

Speiser, T. W.↗

NASA NTRS1986

Comments on Lambeck and Coleman - 'The earth's shape and gravity field: A report of progress from 1958 to 1982'

The accuracy and validation of global gravity models based on satellite data are discussed, responding to the statistical analysis of Lambeck and Coleman (1983) (LC). Included are an evaluation of the LC error spectra, a summary of independent-observation calibrations of the error estimates of the Goddard Earth Models (GEM) 9 and L2 (Lerch et al., 1977, 1979, 1982, 1983, and 1985), a comparison of GEM-L2 with GRIM-3B (Reigber et al., 1983), a comparison of recent models with LAGEOS laser ranging, and a summary of resonant-orbit model tests. It is concluded that the accuracy of GEMs 9, 10, and L2 is much higher than claimed by LC, that the GEMs are in good agreement with independent observations and with GRIM-3B, and that the GEM calibrations were adequate. In a reply by LC, a number of specific questions regarding the error estimates are addressed, and it is pointed out that the intermodel discrepancies of the greatest geophysical interest are those in the higher-order coefficients, not discussed in the present comment. It is argued that the differences among the geoid heights of even the most recent models are large enough to call for considerable improvements.

Lerch, F. J.↗

NASA NTRS2012

Global Modeling, Field Campaigns, Upscaling and Ray Desjardins

In the early 1980's, it became apparent that land surface radiation and energy budgets were unrealistically represented in Global Circulation models (GCM's), Shortly thereafter, it became clear that the land carbon budget was also poorly represented in Earth System Models (ESM's), A number of scientific communities, including GCM/ESM modelers, micrometeorologists, satellite data specialists and plant physiologists, came together to design field experiments that could be used to develop and validate the contemporary prototype land surface models. These experiments were designed to measure land surface fluxes of radiation, heat, water vapor and CO2 using a network of flux towers and other plot-scale techniques, coincident with satellite measurements of related state variables, The interdisciplinary teams involved in these experiments quickly became aware of the scale gap between plot-scale measurements (approx 10 - 100m), satellite measurements (100m - 10 km), and GCM grid areas (l0 - 200km). At the time, there was no established flux measurement capability to bridge these scale gaps. Then, a Canadian science learn led by Ray Desjardins started to actively participate in the design and execution of the experiments, with airborne eddy correlation providing the radically innovative bridge across the scale gaps, In a succession of brilliantly executed field campaigns followed up by convincing scientific analyses, they demonstrated that airborne eddy correlation allied with satellite data was the most powerful upscaling tool available to the community, The rest is history: the realism and credibility of weather and climate models has been enormously improved enormously over the last 25 years with immense benefits to the public and policymakers.

Sellers, P. J.↗

NASA NTRS1997

Turbulence Modeling Validation, Testing, and Development

The primary objective of this work is to provide accurate numerical solutions for selected flow fields and to compare and evaluate the performance of selected turbulence models with experimental results. Four popular turbulence models have been tested and validated against experimental data often turbulent flows. The models are: (1) the two-equation k-epsilon model of Wilcox, (2) the two-equation k-epsilon model of Launder and Sharma, (3) the two-equation k-omega/k-epsilon SST model of Menter, and (4) the one-equation model of Spalart and Allmaras. The flows investigated are five free shear flows consisting of a mixing layer, a round jet, a plane jet, a plane wake, and a compressible mixing layer; and five boundary layer flows consisting of an incompressible flat plate, a Mach 5 adiabatic flat plate, a separated boundary layer, an axisymmetric shock-wave/boundary layer interaction, and an RAE 2822 transonic airfoil. The experimental data for these flows are well established and have been extensively used in model developments. The results are shown in the following four sections: Part A describes the equations of motion and boundary conditions; Part B describes the model equations, constants, parameters, boundary conditions, and numerical implementation; and Parts C and D describe the experimental data and the performance of the models in the free-shear flows and the boundary layer flows, respectively.

Bardina, J. E.↗

NASA NTRS2004

Current results from AlRS/AMSU/HSB

AIRS was launched on EOS Aqua on May 4,2002, together with AMSU A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU/HSB are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20%, in cases with up to 80% effective cloud cover. Pre-launch simulation studies indicated that these results should be achievable. Minor modifications have been made to the pre-launch retrieval algorithm as alluded to in this paper. Sample fields of parameters retrieved from AIRS/AMSU/HSB data are presented and temperature profiles are validated as a function of retrieved fractional cloud cover. As in simulation, the degradation of retrieval accuracy with increasing cloud cover is small. Select fields are also compared to those contained in the ECMWF analysis, done without the benefit of AIRS data, to demonstrate information that AIRS can add to that already contained in the ECMWF analysis. Assimilation of AIRS temperature soundings in up to 80% cloud cover for the month of January 2003 into the GSFC FVSSI data assimilation system resulted in improved 5 day forecasts globally, both with regard to anomaly correction coefficients and the prediction of location and intensity of cyclones.

Susskind, Joel↗

NASA NTRS1996

Helicopter Blade-Vortex Interaction Noise with Comparisons to CFD Calculations

A comparison of experimental acoustics data and computational predictions was performed for a helicopter rotor blade interacting with a parallel vortex. The experiment was designed to examine the aerodynamics and acoustics of parallel Blade-Vortex Interaction (BVI) and was performed in the Ames Research Center (ARC) 80- by 120-Foot Subsonic Wind Tunnel. An independently generated vortex interacted with a small-scale, nonlifting helicopter rotor at the 180 deg azimuth angle to create the interaction in a controlled environment. Computational Fluid Dynamics (CFD) was used to calculate near-field pressure time histories. The CFD code, called Transonic Unsteady Rotor Navier-Stokes (TURNS), was used to make comparisons with the acoustic pressure measurement at two microphone locations and several test conditions. The test conditions examined included hover tip Mach numbers of 0.6 and 0.7, advance ratio of 0.2, positive and negative vortex rotation, and the vortex passing above and below the rotor blade by 0.25 rotor chords. The results show that the CFD qualitatively predicts the acoustic characteristics very well, but quantitatively overpredicts the peak-to-peak sound pressure level by 15 percent in most cases. There also exists a discrepancy in the phasing (about 4 deg) of the BVI event in some cases. Additional calculations were performed to examine the effects of vortex strength, thickness, time accuracy, and directionality. This study validates the TURNS code for prediction of near-field acoustic pressures of controlled parallel BVI.

McCluer, Megan S.↗

NASA NTRSDate not supplied

Comparing Low-Cost Sensors with Ground-Based and Airborne In-Situ and Column Observations of NO2 and HCHO during the FRAPPE Field Campaign in Colorado, USA

Even in the presence of more reliable air quality tools, low-cost sensors have the benefit of recording data on highly localized spatial and temporal scales, allowing for multiple measurements within a single satellite pixel and on pixel boundaries. However, they are less accurate than their regulatory-grade counterparts, requiring regular co-locations with accepted instruments to ensure their validity. Thus, the addition of low-cost sensors to a field campaign – where reference-grade air quality instruments are abundant – not only provides ample opportunities for low-cost sensor co-location and calibration, but also allows the low-cost instruments to be used for sub-pixel validation, covering more surface area than the regulatory instruments alone with a network of sensors. During the summer of 2014, our low-cost sensor network was deployed during the Front Range Air Pollution and Photochemistry Experiment (FRAPPÉ) campaign conducted to sample the composition of air at and above ground level in northeastern Colorado, USA. The low-cost sensor platform included a suite of gas-phase sensors, notably NO2 and two generalized volatile organic compound (VOC) sensors, which were leveraged together to quantify speciated hydrocarbons such as formaldehyde. These key pollutants were chosen for their impacts on human health and climate change, as well as their inclusion on the TEMPO satellite launching this year. Airborne campaign measurements included slant column optical observations of formaldehyde (HCHO), nitrogen dioxide (NO2), and ozone (O3). Myriad additional in-situ instruments described chemical composition up to approximately 5 km above surface level. Ground-based instrumentation included both stationary and mobile regulatory-grade instruments, which were used for sensor calibration. Machine learning techniques such as artificial neural networks (ANNs) were used to match the low-cost signals to that of the reference-grade instruments. Here, we compare calibrated low-cost sensor data collected at ground level in a variety of locations along Colorado’s Front Range to various data sources from the FRAPPÉ campaign to better understand how well airborne and regulatory ground-based measurements can be extrapolated to other locations. Further, as the slant column measurements act as satellite simulators, we explore how low-cost instruments can be used for satellite validation purposes. Comparisons among these different data types also have important implications in data fusion.

Kristen Okorn↗

NASA NTRS2001

PIV Measurements in Weakly Buoyant Gas Jet Flames

Despite numerous experimental investigations, the characterization of microgravity laminar jet diffusion flames remains incomplete. Measurements to date have included shapes, temperatures, soot properties, radiative emissions and compositions, but full-field quantitative measurements of velocity are lacking. Since the differences between normal-gravity and microgravity diffusion flames are fundamentally influenced by changes in velocities, it is imperative that the associated velocity fields be measured in microgravity flames. Velocity measurements in nonbuoyant flames will be helpful both in validating numerical models and in interpreting past microgravity combustion experiments. Pointwise velocity techniques are inadequate for full-field velocity measurements in microgravity facilities. In contrast, Particle Image Velocimetry (PIV) can capture the entire flow field in less than 1% of the time required with Laser Doppler Velocimetry (LDV). Although PIV is a mature diagnostic for normal-gravity flames , restrictions on size, power and data storage complicate these measurements in microgravity. Results from the application of PIV to gas jet flames in normal gravity are presented here. Ethane flames burning at 13, 25 and 50 kPa are considered. These results are presented in more detail in Wernet et al. (2000). The PIV system developed for these measurements recently has been adapted for on-rig use in the NASA Glenn 2.2-second drop tower.

Sunderland, Peter B.↗

DOE OSTI2020

Simulations of Laser Experiments to Study the Origin of Cosmic Magnetic Fields

Magnetic fields are ubiquitous in the universe; however, their origin is not fully understood. Cosmologists and astrophysicists have proposed a variety of ways in which small seed magnetic fields could be created. It is widely thought that the much larger values of the cosmic magnetic fields that we observe are a result of the amplification of these seed fields by the nonlinear turbulent dynamo mechanism. Such a mechanism had not yet been demonstrated in a controlled laboratory environment. We conceived experiments designed to demonstrate and study the nonlinear turbulent dynamo mechanism in the laboratory. These experiments characterize the distribution of turbulent energy among the velocity, magnetic field, and density fluctuations, providing a comprehensive picture of the energy cascade in a magnetized, turbulent plasma. The experiments build on the pathfinder experiments we have conducted on the Vulcan laser at the Rutherford-Appleton Laboratory in the UK and the OMEGA laser at Laboratory for Laser Energetics at Rochester. They utilize the high-intensity lasers at the Omega Laser Facility, the National Ignition Facility (NIF) at LLNL and the Laser Megajoule (LMJ) Facility in France – the largest laser facilities in the world. The goal of this project was to design and model the highly demanding experiments through simulation campaigns using FLASH, a highly capable radiation-MHD code we have developed, and large-scale 3D simulations on the Mira supercomputer at ANL. The simulations were vital to ensuring the experiments achieve the strong turbulence and large magnetic Reynolds numbers required for the nonlinear turbulent dynamo mechanism to operate. The simulations were also critical to determining when to fire the diagnostics, since the experiments last tens of nanoseconds but the signals of the strongly amplified magnetic fields last only a few nanoseconds. Finally, high-fidelity, validated FLASH simulations were crucial to interpreting the results of the experiments. By combining theory, experiments, and simulations, we were able to succeed in demonstrating and characterizing the nonlinear turbulent dynamo mechanism. The effort leveraged (1) the emergence of the Flash Center for Computational Science as a leader in numerical modeling of academic High Energy Density Physics (HEDP) experiments; (2) the FLASH code, which has been developed by the Flash Center and is a leadership-class, multi- physics, publicly available community code that has been applied successfully in many laser-driven experiments; (3) the expertise acquired through pathfinder experiments we performed on the Vulcan laser at the Rutherford-Appleton Laboratory in the UK and on the Omega laser facility; (4) the experience we have gained in designing and interpreting these experiments using validated simulations done with FLASH; and (5) the close collaborations we have established with outstanding experimental groups in the US and abroad. The broader impacts of the project are two-fold: (1) the work furthered the transformation of the academic community’s ability to design and analyze HEDP experiments at large laser facilities that is happening through the availability of FLASH and its widespread adoption by the academic community – a community that previously had had limited access to open and validated hydro/MHD simulation tools for HEDP experiments; and (2) the work trained young scientists to design and interpret HEDP experiments using validated simulations – a critical national need.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2007

Solar Sources and Geospace Consequences of Interplanetary Magnetic Clouds Observed During Solar Cycle 23

We present results of a statistical investigation of 99 magnetic clouds (MCs) observed during 1995-2005. The MC-associated coronal mass ejections (CMEs) are faster and wider on the average and originate within +/-30deg from the solar disk center. The solar sources of MCs also followed the butterfly diagram. The correlation between the magnetic field strength and speed of MCs was found to be valid over a much wider range of speeds. The number of south-north (SN) MCs was dominant and decreased with solar cycle, while the number of north-south (NS) MCs increased confirming the odd-cycle behavior. Two-thirds of MCs were geoeffective; the Dst index was highly correlated with speed and magnetic field in MCs as well as their product. Many (55%) fully northward (FN) MCs were geoeffective solely due to their sheaths. The non-geoeffective MCs were slower (average speed approx. 382 km/s), had a weaker southward magnetic field (average approx. -5.2nT), and occurred mostly during the rise phase of the solar activity cycle.

Gopalswamy, N.↗

NASA NTRS2014

Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method

A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.

nickel alloys↗

DOE OSTI2024

Beam Dynamics of the Muon $g\textrm{-}2$ Experiment

The Muon $g\textrm{-}2$ Experiment (E989) at Fermilab aims to measure the muon anomalous magnetic moment $a_{\mu}$ with unprecedented precision, potentially uncovering physics beyond the Standard Model of particle physics. The result based on Runs 1-3, released in 2023, achieved a precision of 0.20 ppm. The experiment circulates muons in a storage ring, measuring $a_{\mu}$ from decay positron time and energy measurements collected with calorimeters. To achieve the required accuracy, it is crucial to measure and control the magnetic field in the ring with high precision. Beam dynamics corrections are necessary for muons not orbiting exactly in the midplane, for their oscillations, and for electric field effects. Highly accurate beam dynamics simulations are instrumental for quantifying and validating the beam dynamics corrections, ultimately improving the precision of the $a_{\mu}$ measurement and facilitating the achievement of the ambitious $70\:\mathrm{ppb}$ systematic uncertainty goal. The measured field data was incorporated into models for simulations using three codes: \texttt{gm2ringsim} (an internal Geant4-based code), \textit{COSY INFINITY}, and \textit{BMAD}. The advantages of \texttt{gm2ringsim} include using CAD-based geometry and modelling the detector effects. \textit{COSY INFINITY} is a highly accurate and efficient code that uses high-order differential-algebraic transfer maps, precise fringe field calculations, and advanced symplectification methods. Symplectification is important for maintaining the physical correctness of the muon beam behaviour with high precision over the storage time, ensuring conservation of phase space volume and preventing artificial damping or excitation of particle motion. The experiment completed its final Run 6 in July 2023, collecting 21 times more data than the previous BNL experiment. Analyses of data from Runs 4-6 are ongoing, with results planned for release in 2025, potentially resolving the current tension between experiment and theory.

43 PARTICLE ACCELERATORS↗

NASA NTRS2004

Atmospheric Soundings from AIRS/AMSU/HSB

AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU/HSB are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of lK, and 1 km tropospheric layer precipitable water with an rms error of 20%, in cases with up to 80% effective cloud cover. Pre-launch simulation studies indicated that these results should be achievable. Minor modifications have been made to the pre-launch retrieval algorithm as alluded to in this paper. Sample fields of parameters retrieved from AIRS/AMSU/HSB data are presented and temperature profiles are validated as a function of retrieved effective fractional cloud cover. As in simulation, the degradation of retrieval accuracy with increasing cloud cover is small. Select fields are also compared to those contained in the ECMWF analysis, done without the benefit of AIRS data, to demonstrate information that AIRS can add to that already contained in the ECMWF analysis. Assimilation of AIRS temperature soundings in up to 80% cloud cover for the month of January 2003 into the GSFC FVSSI data assimilation system resulted in improved 5 day forecasts globally, both with regard to anomaly correlation coefficients and the prediction of location and intensity of cyclones.

Susskind, Joel↗

NASA NTRS1999

Fracture Mechanics of Thin, Cracked Plates Under Tension, Bending and Out-of-Plane Shear Loading

Cracks in the skin of aircraft fuselages or other shell structures can be subjected to very complex stress states, resulting in mixed-mode fracture conditions. For example, a crack running along a stringer in a pressurized fuselage will be subject to the usual in-plane tension stresses (Mode-I) along with out-of-plane tearing stresses (Mode-III like). Crack growth and initiation in this case is correlated not only with the tensile or Mode-I stress intensity factor, K(sub I), but depends on a combination of parameters and on the history of crack growth. The stresses at the tip of a crack in a plate or shell are typically described in terms of either the small deflection Kirchhoff plate theory. However, real applications involve large deflections. We show, using the von-Karman theory, that the crack tip stress field derived on the basis of the small deflection theory is still valid for large deflections. We then give examples demonstrating the exact calculation of energy release rates and stress intensity factors for cracked plates loaded to large deflections. The crack tip fields calculated using the plate theories are an approximation to the actual three dimensional fields. Using three dimensional finite element analyses we have explored the relationship between the three dimensional elasticity theory and two dimensional plate theory results. The results show that for out-of-plane shear loading the three dimensional and Kirchhoff theory results coincide at distance greater than h/2 from the crack tip, where h/2 is the plate thickness. Inside this region, the distribution of stresses through the thickness can be very different from the plate theory predictions. We have also explored how the energy release rate varies as a function of crack length to plate thickness using the different theories. This is important in the implementation of fracture prediction methods using finite element analysis. Our experiments show that under certain conditions, during fatigue crack growth, the presence of out-of-plane shear loads induces a great deal of contact and friction on the crack surfaces, dramatically reducing crack growth rate. A series of experiments and a proposed computational approach for accounting for the friction is discussed.

Zehnder, Alan T.↗