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DOE OSTI2021

Tuning spin excitations in magnetic films by confinement

Spin excitations of magnetic thin films are the founding element for novel transport concepts in spintronics, magnonics, and magnetic devices in general. While spin dynamics have been extensively studied in bulk materials, their behaviour in mesoscopic films is less known due to experimental limitations. Here, we employ Resonant Inelastic X-Ray Scattering to investigate the spin excitation spectrum in mesoscopic Fe films, from bulk-like down to 3 unit cells thick. In bulk-like samples, we find isotropic, dispersive ferromagnons consistent with the dispersion observed by neutron scattering in bulk single crystals. As the thickness is reduced, these ferromagnons survive and evolve anisotropically: renormalising to lower energies along the out-of-plane direction while retaining their dispersion in the in-plane direction. This thickness dependence is captured by simple Heisenberg model calculations accounting for the confinement in the out-of-plane direction through the loss of Fe bonds. Overall, our findings highlight the effects of mesoscopic scaling on spin dynamics and identify thickness as a knob for fine-tuning and controlling magnetic properties in films.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Core performance predictions in projected SPARC first-campaign plasmas with nonlinear CGYRO

This work characterizes the core transport physics of SPARC early-campaign plasmas using the PORTALS-CGYRO framework. Empirical modeling of SPARC plasmas with L-mode confinement indicates an ample window of breakeven (Q > 1) without the need of H-mode operation. Extensive modeling of multi-channel (electron energy, ion energy, and electron particle) flux-matched conditions with the nonlinear CGYRO code for turbulent transport coupled to the macroscopic plasma evolution using PORTALS reveals that the maximum fusion performance to be attained will be highly dependent on the near-edge pressure. Stiff core transport conditions are found, particularly when fusion gain approaches unity, and predicted density peaking is found to be in line with empirical databases of particle source-free H-modes. Impurity optimization is identified as a potential avenue to increase fusion performance while enabling core-edge integration. Extensive validation of the quasilinear TGLF model builds confidence in reduced-model predictions. The implications of projecting L-mode performance to high-performance and burning-plasma devices is discussed, together with the importance of predicting edge conditions.

Rodriguez-Fernandez, P. (ORCID:0000000273611131)↗

DOE OSTI2019

Colloquium: Ice rule and emergent frustration in particle ice and beyond

Geometric frustration and the ice rule are two concepts that are intimately connected and widespread across condensed matter. The first refers to the inability of a system to satisfy competing interactions in the presence of spatial constraints. The second, in its more general sense, represents a prescription for the minimization of the topological charges in a constrained system. Both can lead to manifolds of high susceptibility and nontrivial, constrained disorder where exotic behaviors can appear and even be designed deliberately. This Colloquium describes the emergence of geometric frustration and the ice rule in soft condensed matter. It excludes the extensive developments of mathematical physics within the field of geometric frustration, but rather focuses on systems of confined microscopic or mesoscopic particles that emerge as a novel paradigm exhibiting spin degrees of freedom. In such systems, geometric frustration can be engineered artificially by controlling the spatial topology and geometry of the lattice, the position of the individual particle units, or their relative filling fraction. These capabilities enable the creation of novel and exotic phases of matter and also potentially lead toward technological applications related to memory and logic devices that are based on the motion of topological defects. The rapid progress in theory and experiments is reviewed and the intimate physical connections with other frustrated systems at different length scales are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1988

An Empirical Model of the Effects of Curvature and Convergence on Dilution Jet Mixing

An existing empirical model of the temperature field downstream of single and multiple rows of jets injected into a confined crossflow has been extended to model the effects of curvature and convergence on the mixing. This extension is based on the results of a numerical study of these effects using a 3-D turbulent flow computer code. Temperature distributions calculated with the empirical model are presented to show the effects of flow area convergence, radius of curvature, and inner and outer wall injection for single and opposed rows of jets.

Holdeman, James D.↗

NASA NTRS1988

An empirical model of the effects of curvature and convergence on dilution jet mixing

Holdeman, James D.↗

NASA NTRS1989

Mechanical properties of lunar regolith and lunar soil simulant

Through the Surveyor 3 and 7, and Apollo 11-17 missions a knowledge of the mechanical properties of Lunar regolith were gained. These properties, including material cohesion, friction, in-situ density, grain-size distribution and shape, and porosity, were determined by indirect means of trenching, penetration, and vane shear testing. Several of these properties were shown to be significantly different from those of terrestrial soils, such as an interlocking cohesion and tensile strength formed in the absence of moisture and particle cementation. To characterize the strength and deformation properties of Lunar regolith experiments have been conducted on a lunar soil simulant at various initial densities, fabric arrangements, and composition. These experiments included conventional triaxial compression and extension, direct tension, and combined tension-shear. Experiments have been conducted at low levels of effective confining stress. External conditions such as membrane induced confining stresses, end platten friction and material self weight have been shown to have a dramatic effect on the strength properties at low levels of confining stress. The solution has been to treat these external conditions and the specimen as a full-fledged boundary value problem rather than the idealized elemental cube of mechanics. Centrifuge modeling allows for the study of Lunar soil-structure interaction problems. In recent years centrifuge modeling has become an important tool for modeling processes that are dominated by gravity and for verifying analysis procedures and studying deformation and failure modes. Centrifuge modeling is well established for terrestrial enginering and applies equally as well to Lunar engineering. A brief review of the experiments is presented in graphic and outline form.

Steven W Perkins↗

NASA NTRS1994

The growth of zeolites A, X and mordenite in space

Zeolites are a class of crystalline aluminosilicate materials that form the backbone of the chemical process industry worldwide. They are used primarily as adsorbents and catalysts and support to a significant extent the positive balance of trade realized by the chemical industry in the United States (around $19 billion in 1991). The magnitude of their efforts can be appreciated when one realizes that since their introduction as 'cracking catalysts' in the early 1960's, they have saved the equivalent of 60 percent of the total oil production from Alaska's North Slope. Thus the performance of zeolite catalysts can have a profound effect on the U.S. economy. It is estimated that a 1 percent increase in yield of the gasoline fraction per barrel of oil would represent a savings of 22 million barrels of crude oil per year, representing a reduction of $400 million in the United States' balance of payments. Thus any activity that results in improvement in zeolite catalyst performance is of significant scientific and industrial interest. In addition, due to their 'stability,' uniformity, and, within limits, their 'engineerable' structures, zeolites are being tested as potential adsorbents to purify gases and liquids at the parts-per-billion levels needed in today's electronic, biomedical, and biotechnology industries and for the environment. Other exotic applications, such as host materials for quantum-confined semiconductor atomic arrays, are also being investigated. Because of the importance of this class of material, extensive efforts have been made to characterize their structures and to understand their nucleation and growth mechanisms, so as to be able to custom-make zeolites for a desired application. To date, both the nucleation mechanics and chemistry (such as what are the 'key' nutrients) are, as yet, still unknown for many, if not all, systems. The problem is compounded because there is usually a 'gel' phase present that is assumed to control the degree of supersaturation, and this gel undergoes a continuous 'polymerization' type reaction during nucleation and growth. Generally, for structure characterization and diffusion studies, which are useful in evaluating zeolites for improving yield in petroleum refining as well as for many of the proposed new applications (e.g., catalytic membranes, molecular electronics, chemical sensors) large zeolites (greater than 100 to 1000 times normal size) with minimum lattice defects are desired. Presently, the lack of understanding of zeolite nucleation and growth precludes the custom design of zeolites for these or other uses. It was hypothesized that the microgravity levels achieved in an orbiting spacecraft could help to isolate the possible effects of natural convection (which affects defect formation) and minimize sedimentation, which occurs since zeolites are twice as dense as the solution from which they are formed. This was expected to promote larger crystals by allowing growing crystals a longer residence time in a high-concentration nutrient field. Thus it was hypothesized that the microgravity environment of Earth orbit would allow the growth of large, more defect-free zeolite crystals in high yield.

Sacco, Albert, Jr.↗

NASA NTRS2015

Bone Loss During Spaceflight: Available Models and Counter-Measures

There is ongoing concern for human health during spaceflights. Of particular interest is the uncoupling of bone remodeling and its resultant effect on calcium metabolism and bone loss. The calculated average loss of bone mineral density (BMD) is approximately 1-1.5% per month of spaceflight. The effect of decreased BMD on associated fractures in astronauts is not known. Currently on the International Space Station (ISS), bone loss is managed through dietary supplements and modifications and resistance exercise regimen. As the duration of space flights increases, a review of the current methods available for the prevention of bone loss is warranted. The goal of this project is to review and summarize recent studies that have focused on maintaining BMD during exposure to microgravity. Interventions were divided into physical (Table 1), nutritional (Table 2), or pharmacologic (Table 3) categories. Physical modalities included resistance exercise, low level vibration, and low intensity pulsed ultrasound. Nutritional interventions included altering protein, salt, and fat intake; and vitamin D supplementation. Pharmacologic interventions included the use of bisphosphonates and beta blockers. Studies reported outcomes based on bone density determined by DXA bone scan, micro-architecture of histology and microCT, and serum and urine markers of bone turnover. The ground analog models utilized to approximate osseous physiology in microgravity included human patients previously paralyzed or subjects confined to bedrest. Ground analog animal models include paralysis, immobilization and ovariectomies. As a result of the extensive research performed there is a multi-modality approach available for the management of BMD during spaceflight that includes resistance training, nutrition and dietary supplements. However, there is a paucity of literature describing a formalized tiered protocol to guide investigators through the progression from animal models to human patient ground analogs to experiments on the ISS. With regards to testing, further evaluation to determine the association between non-invasive tests and fracture during and after spaceflight needs to be performed.

Morris, Jonathan↗

DOE OSTI2026

Geology of the One Earth Energy Site

The One Earth Energy site is one of two sites in the Illinois Storage Corridor (ISC) project. The objectives of the ISC project is to accelerate commercial deployment of carbon capture utilization and storage at two individual sites and receive approvals for Underground Injection Control (UIC) Class VI permits for construction at each site. At the One Earth Energy site, an extensive data collection program was undertaken, which included the drilling of a test well (One Earth Energy #1 [OEE #1]), four 2D seismic lines, and a small 3D seismic survey. The OEE #1 well was drilled in 2022 and acquired extensive core, log, and testing data to characterize the subsurface geology of the site. Coring was focused on the storage interval, the Mt. Simon Sandstone, and the confining interval, the Eau Claire Formation. The core and log data were used to evaluate the sedimentology and sequence stratigraphy, as well as to develop the conceptual geologic model. This report includes the geological summaries of the Mt. Simon Sandstone and the Eau Claire Formation. The extensive analysis of the log data is included in the petrophysical section, showing ranges of porosity, estimated pore size, and the mineral content of selected zones in the well. The separate petrographic technical report entitled “Petrographic and Advanced Geologic Characterization Report on One Earth Energy #1 (API# 1211325373)”, report number DOE-UIUC-0031892-04, details thin section point-counting analysis that includes mineralogical and pore space analysis, including grain size analysis, annotated thin section photomicrographs, scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS), and statistics of grain size analysis on Mt. Simon thin sections from OEE #1. The final OEE #1 well data to be included in this geology report is the routine core analysis of both whole core plugs and rotary sidewall core plugs. In addition to the OEE #1 well, four 2D seismic lines and a small 3D survey were acquired as part of the overall subsurface geological characterization. This geology report references the seismic interpretation report, entitled “One Earth Energy Site Seismic Interpretation Task 5.0”, report number DOE-UIUC-0031892-07. This report details the stratigraphic and structural interpretation of the 2D and 3D seismic data acquired at the One Earth Energy site. The 2D seismic data was acquired in 2019 and 2021, and the 3D survey was acquired in 2022. The objectives of the seismic programs were to contribute to the subsurface characterization of the Mt. Simon-Eau Claire Storage Complex by evaluating the continuity of potential storage reservoirs and containment intervals across the project area, and to determine if any geologic features are present that would increase containment risk to the proposed carbon storage project.

09 BIOMASS FUELS↗

NASA NTRS1987

Reactions of Atomic Oxygen (O(3P)) with Polybutadienes and Related Polymers

Thin films of the following polymers were exposed at ambient temperature to ground-state oxygen atoms (O(3P)), generated by a radio-frequency glow discharge in O2: cis- and trans-1,4-polybutadienes (CB and TB), amorphous 1,2-polybutadiene (VB), polybutadienes with different 1,4/1,2 contents, trans polypentenamer (TP), cis and trans polyoctenamers (CO and TO), and ethylene-propylene rubber (EPM). Transmission infrared spectra of CB and TB films revealed extensive surface recession, or etching, unaccompanied by any microstructural changes within the films, demonstrating that the reactions were confined to the surface layers. Contrary to the report by Rabek, Lucki, and Ranby (1979), there was no O(3P)-induced cis-trans isomerization in CB or TB. From weight-loss measurements, etch rates for polybutadienes were found to be markedly dependent on vinyl content, decreasing by two orders of magnitude from CB (2% 1,2) to structures with 30 to 40% 1,2 double bonds, thereafter increasing by half an order of magnitude to VB (97% 1,2). Relative etch rates for EMP and the polyalkenamers were in the order: EMP is greater than CO (or TO) is greater than TP is greater than CB. The sole non-elastomer examined, TB, had an etch rate about six times that of CB, ascribable to a morphology difference. Cis/trans content had a negligible effect on the etch rate of the polyalkenamers. Mechanisms involving crosslinking through units are proposed for the unexpected protection imparted to polybutadienes by the 1,2 double bonds.

Golub, Morton A.↗

DOE OSTI2023

Assessing the potential of composite confining systems for secure and long-term CO 2 retention in geosequestration

A potential geologic target for CO 2 storage should ensure secure containment of injected CO 2 . Traditionally, this objective has been achieved by targeting reservoirs with overlying seals-regionally extensive, low permeability units that have been proven capable of retaining buoyant fluid accumulations over geologic time. However, considering that the amount of CO 2 is limited by a decadal injection period, vertical migration of CO 2 can be effectively halted by a composite system of discontinuous shale/silt/mudstone barriers in bedded sedimentary rocks. Here, we studied the impact of depositional architectures in a composite confining system on CO 2 migration and confinement at reservoir scale. We stochastically generated lithologically heterogeneous reservoir models containing discontinuous barriers consistent with statistical distributions of net-sand-to-gross-shale ratio (NTG) and horizontal correlation lengths derived from well log data and observations of producing hydrocarbon fields in Southern Louisiana. We then performed an extensive suite of reservoir simulations of CO 2 injection and post-injection to evaluate the sensitivity of CO 2 plume migration and pressure response of the composite system to a series of geologic and fluid parameters including the lateral continuity of barriers, NTG, permeability anisotropy within the sand body, and capillary pressure contrast between the sand and shale facies. The results indicate that lateral continuity of barriers and NTG are the dominant controls on CO 2 plume geometry and pressure build-up in the reservoir, while the impact of NTG is particularly pronounced. The significance of intraformational barriers becomes apparent as they facilitate the local capillary trapping of CO 2 . Those barriers improve the pore space occupancy by promoting a more dispersed shape of the plume and ultimately retard the buoyancy-driven upward migration of the plume post injection.

58 GEOSCIENCES↗

DOE OSTI2022

Suppressing simulation bias in multi-modal data using transfer learning

Abstract Many problems in science and engineering require making predictions based on few observations. To build a robust predictive model, these sparse data may need to be augmented with simulated data, especially when the design space is multi-dimensional. Simulations, however, often suffer from an inherent bias. Estimation of this bias may be poorly constrained not only because of data sparsity, but also because traditional predictive models fit only one type of observed outputs, such as scalars or images, instead of all available output data modalities, which might have been acquired and simulated at great cost. To break this limitation and open up the path for multi-modal calibration, we propose to combine a novel, transfer learning technique for suppressing the bias with recent developments in deep learning, which allow building predictive models with multi-modal outputs. First, we train an initial neural network model on simulated data to learn important correlations between different output modalities and between simulation inputs and outputs. Then, the model is partially retrained, or transfer learned, to fit the experiments; a method that has never been implemented in this type of architecture. Using fewer than 10 inertial confinement fusion experiments for training, transfer learning systematically improves the simulation predictions while a simple output calibration, which we design as a baseline, makes the predictions worse. We also offer extensive cross-validation with real and carefully designed synthetic data. The method described in this paper can be applied to a wide range of problems that require transferring knowledge from simulations to the domain of experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Alfvén mode spectrum in the advanced steady-state tokamak scenario with negative triangularity

In the earlier studies [Zheng et al. Fundam. Plasma Phys. 10, 100051 (2024)], the negative triangularity tokamak was shown to have a unique and outstanding feature for the steady-state confinement. In addition to relieving the divertor heat load concern, it can reach a much higher beta limit in the nearly steady-state confinement, about twice the Troyon limit in the positive triangularity case. In this work, we extend the investigation to the Alfvén spectrum and toroidal Alfvén eigenmodes (TAEs). This helps to evaluate the property of energetic particle confinement in this advanced scenario of a negative triangularity tokamak. We found that, because of the large safety factor and reversed magnetic shear in the core plasma region near the magnetic axis, the TAE gap tends to be closed or have only a short radial extension between the continua. in the on-axis core region and open primarily in the off-axis region, where TAEs are shown to be present. This indicates that energetic particle confinement in the core region near the magnetic axis, where nuclear fusion reactions prevail, is not seriously affected by the excitation of TAEs in this scenario. The configuration with off-axis TAEs helps the confinement of energetic particles as compared to the configuration with near-axis TAEs. The results show that the advanced steady-state tokamak scenario with negative triangularity, because of the rapid variation of the safety factor, also has a favorable feature for energetic particle confinement.

Fourier analysis↗

DOE OSTI2025

Facies Analysis and Depositional Environments of the Upper Cambrian Eau Claire Formation in Central and Northern Illinois

The Cambrian Eau Claire Formation is a confining unit for geologic carbon dioxide (CO2) storage, and potentially a confining unit for hydrogen storage, within the underlying Mount Simon Sandstone in the Central and Northern Illinois Basin. However, extensive regional studies on lateral continuity, environment of deposition, and depositional fabric of the Eau Claire Formation in the Illinois Basin are minimal compared to studies of the underlying Mount Simon Sandstone. This study presents an integrated facies analysis using sedimentological, stratigraphic, ichnological, and mineralogical data to interpret the depositional environments of the Eau Claire Formation, emphasizing the dynamic nature of sedimentary systems. By combining core analyses, thin-section analysis, facies interpretation from geophysical logs, and regional stratigraphic framework interpretation, this work provides insights into the integrated depositional framework across diverse depositional environments. These findings suggest that the Eau Claire Formation in the Central and Northern Illinois Basin was deposited in a shallow marine environment, ranging from tidal flats to offshore settings. Its mixed siliciclastic-carbonate succession was primarily controlled by relative sea-level change.

58 GEOSCIENCES↗

NASA NTRS1990

Synoptic conditions producing cirrus during the FIRE cirrus IFO

Although direct observations of cirrus clouds by the FIRE research aircraft were usually confined to the area of Intensive Field Observation (IFO) surface network, these cirrus were generally part of a more extensive zone of upper level cloudiness. It is these large scale patterns of cirriform cloud and their relationship to the corresponding synoptic environment which are the prime focus. Three conceptual models are presented and each of the individual cases are classified into one of these categories. Although the cases manifest significant differences in intensity and small scale structure, it is believed that they are best viewed in this unified context. The descriptions given are mostly qualitative, however, quantitative descriptions of the synoptic control and its relationship to cloud structure for all the IFO cases are summarized. The synoptic situations in which extensive cirriform clouds were observed are classified into three basic types: warm front cases, cold front cases, and closed low aloft cases. A simplified summary of each type of situation is presented.

Starr, David OC.↗

DOE OSTI2022

Development of a Direct Neutral Density Diagnostic for Fusion Edge Plasmas

As magnetically confined plasmas progress towards ignition and long pulse experiments, measurement and control of the neutral density in the plasma edge has become a critical issue for stability, formation of transport barriers, and fueling. Recent experiments by our research group have demonstrated that is possible to use two-photon absorption laser induced fluorescence (TA-LIF) to directly measure the density of neutral hydrogen in helicon sources and in the HIT-SI3 spheromak. While those experiments validated key elements of a diagnostic system that would enable similar measurements in tokamak plasmas, they did not fully address the issue of performance optimization in the presence of intense background light at the fluorescence wavelength and they also identified a number of other issues that must be resolved before successful TALIF neutral density measurements in a tokamak are likely to be achieved. Additional specific concerns raised during design reviews with the leadership of the DIII-D tokamak facility included: the minimum detection threshold for this TALIF diagnostic (currently ~ 5 x 10 15 m -3 ) and the rate at which neutral density measurements could be obtained. Improving the system performance to reduce the minimum detection threshold and demonstrating a faster rate of density determination are required to advance this diagnostic to the level where it could be considered for implementation on a major tokamak facility in the USA. The key issues that will be addressed through additional technological development are: validation of a new, chromatic aberration-free, xenon calibration scheme; increasing the output power of the laser; and suppression of background emission at the fluorescence wavelength through optimization of the collection optics and gating of the photomultiplier detector with a goal of obtaining a minimum detection threshold of 5 x 10 14 m -3 . Another key technological development, so far only tested in helicon source experiments, is the validation of Doppler-free TALIF as a means of obtaining higher speed, calibrated, neutral density measurements in tokamak-like conditions at the full cadence of the pulsed TALIF laser. In this work, we propose to complete these technological advancements through installation and testing of our prototype TALIF system on the proto-MPEX experiment at Oak Ridge National Laboratory (ORNL). The proto-MPEX facility will provide plasma conditions similar to the edge plasma of a major tokamak experiment but with pulse lengths and pulse repetition rates ideally suited for extensive development of a TALIF neutral density diagnostic. Measurement of the absolute neutral density in the edge of a magnetically confined plasma is necessary for plasma density control; calculation of charge-exchange power losses; control of plasma-wall interactions; determination of the braking of plasma flow; determination of the fuel mixture in deuterium-tritium plasma; and understanding the dynamics of the divertor region in the plasma edge. In terms of potential impact on the worldwide fusion program, we note that in burning plasma experiments, such as ITER, a 100 mJ/pulse Doppler-free TALIF diagnostic should be capable of directly measuring the deuterium/tritium (D/T) isotope ratio in the outer 0.5 to 1.0 m of the plasma radius. The D/T ratio is a critically important parameter for the control and optimization of burning plasmas. Therefore, development of the diagnostic system proposed here is also relevant to long-term US participation in diagnostic development for large tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2004

Aqueous Alteration of Carbonaceous Chondrites: New Insights from Comparative Studies of Two Unbrecciated CM2 Chondrites, Y 791198 and ALH 81002

Carbonaceous chondrites are an important resource for understanding the physical and chemical conditions in the early solar system. In particular, a long-standing question concerns the role of water in the cosmochemical evolution of carbonaceous chondrites. It is well established that extensive hydration of primary nebular phases occurred in the CM and CI chondrites, but the location where this alteration occurred remains controversial. In the CM2 chondrites, hydration formed secondary phases such as serpentine, tochilinite, pentlandite, carbonate and PCP. There are several textural observations which suggest that alteration occurred before the accretion of the final CM parent asteroid, i.e. preaccretionary alteration. Conversely, there is a significant body of evidence that supports parent-body alteration. In order to test these two competing hypotheses further, we studied two CM chondrites, Y-791198 and ALH81002, two meteorites that exhibit widely differing degrees of aqueous alteration. In addition, both meteorites have primary accretionary textures, i.e. experienced minimal asteroidal brecciation. Brecciation significantly complicates the task of unraveling alteration histories, mixing components that have been altered to different degrees from different locations on the same asteroidal parent body. Alteration in Y-791198 is mostly confined to chondrule mesostases, FeNi metal and fine-grained matrix and rims. In comparison, the primary chondrule silicates in ALH81002 have undergone extensive replacement by secondary hydrous phases. This study focuses on compositional and textural relationships between chondrule mesostasis and the associated rim materials. Our hypothesis is: both these components are highly susceptible to aqueous alteration and should be sensitive recorders of the alteration process. For parent body alteration, we expect systematic coupled mineralogical and compositional changes in rims and altered mesostasis, as elemental exchange between these components occurs. Conversely, for preaccretionary alteration, there should be no clear relationships between the rims and mesostases.

Chizmadia, L. J.↗

NASA NTRS1973

Slow growth of cracks in a rate sensitive Tresca solid.

Extension of the classical theory of fracture to viscoelastic and elastic-plastic materials in which the plasticity effects are confined to a narrow band encompassing the crack front. It is suggested that the Griffith-Irwin criterion of fracture, which requires that the energy release rate computed for a given boundary value problem equal the critical threshold, ought to be replaced by a differential equation governing the slow growth of a crack prior to the onset of rapid propagation. A new term which enters the equation of motion in the dissipative media is proportional to the energy lost within the end sections of the crack, and thus it reflects the extent of inelastic behavior of a solid. A concept of 'apparent' surface energy is introduced to account for the geometry-dependent and the rate-dependent phenomena which influence toughness of an inelastic solid. Three hypotheses regarding the condition for fracture in the subcritical range of load are compared.

Wnuk, M. P.↗