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At least 199 records · Page 11

Machine learning accelerated turbulence modeling of transient flashing jets

We report modeling the sudden depressurization of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including ligaments and droplets, due to both mechanical and thermodynamic effects. As the simulation comprises increasingly numerous phenomena, the computational cost begins to increase. One way to moderate the additional cost is to use machine learning surrogacy for specific elements of the calculation. This study presents a machine learning-assisted computational fluid dynamics approach for simulating the atomization of flashing liquids accounting for distinct stages, from primary atomization to secondary breakup to small droplets using the Σ - Y model coupled with the homogeneous relaxation model. Notably, the models for thermodynamic non-equilibrium (HRM) and Σ - Y are coupled, for the first time, with a deep neural network that simulates the turbulence quantities, which are then used in the prediction of superheated liquid jet atomization. The data-driven component of this method is used for turbulence modeling, avoiding the solution of the two-equation turbulence model typically used for Reynolds-averaged Navier-Stokes simulations for these problems. Both the accuracy and speed of the hybrid approach are evaluated, demonstrating adequate accuracy and at least 25% faster computational fluid dynamics simulations than the traditional approach. This acceleration suggests that perhaps additional components of the calculation could be replaced for even further benefit. Published under an exclusive license by AIP Publishing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Secondary electron emission of reticulated foam materials

Complex material surfaces can reduce secondary electron emission (SEE) and sputtering via geometric trapping. In this work, the SEE yields for a range of open-cell reticulated carbon foam geometries are characterized using scanning electron microscopy. The total reduction in the SEE yield from carbon foams with a 3% volume fill density and 10–100 pores per inch (PPI) is shown to be between 23.5% and 35.0%. Contributions of a foam backplate are assessed by experimentally and analytically defining the critical parameter, transparency. The transparency of a foam is quantified and is shown to affect the primary electron angular dependence on the SEE yield. For the same thickness of 6 mm, it is found that higher PPI decreases foam transparency from 32% to 0% and reduces the SEE yield. The SEE yield from carbon foams is also shown to have weaker dependence on the morphology of the surface compared with fuzzes and velvets and less variation across individual sample surfaces due to the rigidity of their ligament structures and isotropic geometries.

Physics↗

Analysis of laser-induced modification of collagen structure using nonlinear optical microscopy

Nonlinear optical microscopy is used to monitor changes in the collagen structure of patellar ligament after IR laser heating up to a temperature of 60 °C. Pre-denaturation modification of the tissue matrix exhibits specific properties and consists in splitting of initially parallel fibre bundles into array of divergent fibres. Image processing employing Fast Fourier transform analysis is used for characterising images of the fibre structure and determining the collagen orientation index. An increase in manifestation of laser-induced disordering with an increase in IR laser radiation power from 0.3 to 2 W is accompanied by a decrease in the collagen orientation index. The specific disorganisation of the collagen tissue structure during laser heating is supposed to be due to fast speed and local action of the laser heating, which leads to mechanical distortions of the structural elements of tissue matrix. (paper)

36 MATERIALS SCIENCE↗

Development of Stochastic Voronoi Lattice Structures via Two-Photon Polymerization

Low-density polymer foams of varying sizes, shapes, and densities are of specific interest to the inertial confinement fusion (ICF) program and related high-energy density plasma physics research. Historically, these foams are comprised of polystyrene or other low atomic number materials and have densities in the 30 to 300 mg/cm 3 range. However, at the lower end of this density range, these traditional polymer foams become fragile and difficult to cast and machine into the geometries needed. Recently, the need by experimentalists for materials with densities below 30 mg/cm 3 has increased. To address these needs, we are developing three-dimensional (3-D) printing techniques to create high-precision, low-density, and repeatable complex lattice structures. Using two-photon polymerization 3-D printing, we recently developed the first 5 mg/cm3 low-density lattice structure having an annular hemispherical shape. These microscale to mesoscale structures were modeled and designed using the nTopology software, specifically utilizing the "Voronoi volume lattice" and "random points in body" option blocks. All printing operations were performed using the Nanoscribe Photonic Professional GT instrument. Characterization of these 3-D structures was conducted using various microscopic and X-ray tomographic imaging techniques. Furthermore, overall printed part sizes ranged from 1 to 5 mm in diameter and were composed of lattice ligaments having thicknesses in the 3- to 5-µm range. These structures have been incorporated into ICF targets recently shot on both the University of Rochester’s Laboratory of Laser Energetics Omega laser and the National Ignition Facility.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Additive manufacturing of multiscale NiFeMn multi-principal element alloys with tailored composition

Nanostructured multi-principal element alloys (MPEAs) have been explored as next-generation engineering materials due to unique mechanical and functional properties which have significant advantages over traditional dilute alloys. However, the practical applications of nanostructured MPEAs are still limited due to the lack of scalable processing approaches to prepare a large quantity of nanostructured MPEAs, as well as lack of an efficient pathway for high-throughput discovery of better functional nanostructured MPEAs within their vast compositional space. Here we tackle these challenges by presenting an integrated approach by combining direct-ink-writing-based additive manufacturing, solid-state sintering, and chemical dealloying to manufacture hierarchically porous MPEAs. The hierarchical structure is comprised of macro- and micro-scale pores introduced via extrusion printing and polymer decomposition during sintering, as well as nanoscale pores formed via chemical dealloying. The macro- and micro-scale pores allow efficient dealloying of a large mass of material as the diffusion length that the corroding medium must penetrate remains at the scale of the ligaments formed after sintering (∼10 μm), despite the large volume of the 3D-printed samples. In addition, this integrated approach enables versatile control of the alloy composition via precisely tuning the ratio of elemental powders in the starting ink, thus offering a pathway for high-throughput discovery of novel functional MPEAs. As a case study, multiscale macro/micro/nanoporous NiFeMn MPEAs with three different compositions were investigated as catalysts to reduce the overpotential of oxygen evolution reaction (OER), where NiFeMn-based electrocatalysts display composition-dependent performance such that the overpotential measured at a current of 0.5 A g −1 for OER increases in the order of Ni 58 Fe 29 Mn 13 ⩽ Ni 64 Fe 26 Mn 10 < Ni 76 Fe 18 Mn 6 . This introduced manufacturing process offers new opportunities for scalable fabrication and rapid screening of nanostructured multi-component complex alloys.

36 MATERIALS SCIENCE↗

Nanoporous gold: a hierarchical and multiscale 3D test pattern for characterizing X-ray nano-tomography systems

Full-field transmission X-ray microscopy (TXM) is a well established technique, available at various synchrotron beamlines around the world as well as by laboratory benchtop devices. One of the major TXM challenges, due to its nanometre-scale resolution, is the overall instrument stability during the acquisition of the series of tomographic projections. The ability to correct for vertical and horizontal distortions of each projection image during acquisition is necessary in order to achieve the effective 3D spatial resolution. The effectiveness of such an image alignment is also heavily influenced by the absorption properties and strong contrast of specific features in the scanned sample. Here it is shown that nanoporous gold (NPG) can be used as an ideal 3D test pattern for evaluating and optimizing the performance of a TXM instrument for hard X-rays at a synchrotron beamline. Unique features of NPG, such as hierarchical structures at multiple length scales and high absorbing capabilities, makes it an ideal choice for characterization, which involves a combination of a rapid-alignment algorithm applied on the acquired projections followed by the extraction of a set of both 2D- and 3D-descriptive image parameters. This protocol can be used for comparing the efficiency of TXM instruments at different synchrotron beamlines in the world or benchtop devices, based on a reference library of scanned NPG samples, containing information about the estimated horizontal and vertical alignment values, 2D qualitative parameters and quantitative 3D parameters. The possibility to tailor the ligament sizes of NPG to match the achievable resolution in combination with the high electron density of gold makes NPG an ideal 3D test pattern for evaluating the status and performance of a given synchrotron-based or benchtop-based TXM setup.

36 MATERIALS SCIENCE↗

Early Unloading After ACL Rupture and Prior to Surgical Restabilization in Mice Slows Post-Traumatic Osteoarthritis Progression

Purpose: People who sustain joint injuries such as anterior cruciate ligament (ACL) rupture often go on to develop post-traumatic osteoarthritis (PTOA). ACL injuries are often treated with ACL reconstruction, but there is typically a gap of several weeks between injury and surgery. However, it is unclear how loading or unloading of the injured joint during the early postinjury period affects the progression of PTOA. The goal of this study was to determine how unloading between noninvasive ACL injury and surgical restabilization of the injured joint affects PTOA progression in mice. Findings: Mice were subjected to noninvasive ACL injury or no injury followed by 1 week of hindlimb unloading (HLU) or normal cage activity. After 1 week of HLU or cage activity, mice underwent restabilization surgery or no surgery. ACL injury resulted in considerable epiphyseal trabecular bone loss regardless of HLU or cage activity. HLU groups exhibited significantly reduced chondrophyte/osteophyte formation, OA scoring, and synovitis at day 42. Single-cell RNA sequencing revealed that 1 week of HLU resulted in more neutrophils and less monocytes-macrophages in the injured joint. Conclusions: This study establishes that 1 week of HLU after ACL injury effectively slowed PTOA progression, suggesting that the early inflammatory response and joint instability play a key role in PTOA initiation and progression, and neutrophils and monocytes-macrophages play roles in the modulation. However, subsequent joint restabilization surgery caused greater inflammatory protease activity in the joint and exacerbated the loss of epiphyseal trabecular bone but did not significantly diminish OA score or synovitis.

ACL injury↗

CD206 + Trem2 + macrophage accumulation in the murine knee joint after injury is associated with protection against post-traumatic osteoarthritis in MRL/MpJ mice

Post-traumatic osteoarthritis (PTOA) is a painful joint disease characterized by the degradation of bone, cartilage, and other connective tissues in the joint. PTOA is initiated by trauma to joint-stabilizing tissues, such as the anterior cruciate ligament, medial meniscus, or by intra-articular fractures. In humans, ~50% of joint injuries progress to PTOA, while the rest spontaneously resolve. To better understand molecular programs contributing to PTOA development or resolution, we examined injury-induced fluctuations in immune cell populations and transcriptional shifts by single-cell RNA sequencing of synovial joints in PTOA-susceptible C57BL/6J (B6) and PTOA-resistant MRL/MpJ (MRL) mice. We identified significant differences in monocyte and macrophage subpopulations between MRL and B6 joints. A potent myeloid-driven anti-inflammatory response was observed in MRL injured joints that significantly contrasted the pro-inflammatory signaling seen in B6 joints. Multiple CD206 + macrophage populations classically described as M2 were found enriched in MRL injured joints. These CD206 + macrophages also robustly expressed Trem2 , a receptor involved in inflammation and myeloid cell activation. These data suggest that the PTOA resistant MRL mouse strain displays an enhanced capacity of clearing debris and apoptotic cells induced by inflammation after injury due to an increase in activated M2 macrophages within the synovial tissue and joint space.

60 APPLIED LIFE SCIENCES↗

Fluid Flow Observations of The Spray Near-Field Using High-Speed X-Ray Imaging

Sprays are important to may industrial processes, but the near-field region where spray formation takes place is difficult to visualize and characterize through visible light imaging because this region is typically optically dense. X-ray imaging is one technique that can penetrate this optically dense region and provide unique observations of the spray formation process. This study uses high-speed white beam X-ray imaging conducted at the Advanced Photon Source to capture spray formation dynamics from a canonical airblast atomizer. In this work, a range of momentum flux ratios are visualized by varying the gas flow rate while the liquid flow rate is held constant. The use of X-rays show overlapping flow structures including bags, ligaments, mushrooms, and webs. Air bubbles are captured within the liquid regions, and a very dynamic crown forms at the liquid needle exit at higher momentum flux ratios. Finally, at the highest momentum flux ratios, air bubbles and liquid droplets are observed migrating upstream in the center of the crown, and this motion is attributed to a toroidal recirculation cell at the nozzle exit.

47 OTHER INSTRUMENTATION↗

X-ray Diffraction and Neutron Scattering Analysis of Natural and Synthetic Spider Silk Fibers

Spider silks have the potential to provide new bio-inspired materials for numerous applications in bioenergetics and products ranging from protective clothing to artificial ligaments and tendons. A number of spider silk genes have been cloned and sequenced by the Lewis laboratory revealing the basis for understanding the key elements of spider silk proteins with respect to their materials performance. In particular, specific amino acid motifs have been identified which have been conserved for over 125 million years in all spiders that use their silk to physically trap prey. The key element in taking the next step toward generating bio-based materials from spider silks will be to move from the current descriptive data to predictive knowledge. Current efforts are focused on mimicking spider silk through synthetic proteins. In developing synthetic silk fibers, we first need to understand the complete secondary and tertiary structure of natural silk so that we can compare synthetic constructs to the natural material. Being able to compare the structure on a single fiber level is critical to the future of molecular directed mimic development because we can vary mechanical properties by different spinning methods. The new generation of synchrotron x-ray diffraction and neutron beamlines will allow, for the first time, determination of the molecular structure of silk fibers and synthetic mimics. We propose an exciting new collaborative research team working jointly between Argonne National Laboratory, Arizona State U. and the University of Wyoming to address the ?characterization of synthetic and natural spider silk fibers using x-ray and neutron diffraction.? Thus these new methodologies will provide understanding of current fibers and determine changes needed to produce fibers with specific properties. The following specific aims are proposed: ? Synthesize spider silk fibers with molecular structures mimicking that of natural silks. Test the mechanic properties of these materials and compare them to natural silk fibers. ? Develop x-ray and neutron diffraction techniques to better determine the structure in amorphous and semicrystalline biopolymers, such as spider silk fibers. ? Combine mechanical testing and structural x-ray and neutron diffraction data to develop a molecular understanding of the structure-function relationship in spider silk materials. ? Elucidate the role water plays in spider silk fiber formation and structure. Emphasis will be placed on combined neutron and NMR studies. ? Use solid-state Nuclear Magnetic Resonance (NMR) to characterize synthetic and natural spider silk materials that show potential as a biomimetic material or bio-inspired polymer architecture. ? Develop EPSCoR student and postdoctoral training and exposure to national laboratory facilities. ? Further develop scientific outreach and chemical education programs and research.

36 MATERIALS SCIENCE↗

Helium Bubble Growth and Retention Characteristics in Aging Palladium Tritide

The helium-related characteristics of aged palladium tritide, including tritium loss, the formation of He bubbles from tritium decay-induced He atoms, and He thermal desorption behavior are computed using a continuum model of bubble evolution that incorporates the log-normal bubble spacing distribution deduced from 3 He nuclear magnetic resonance (NMR) measurements. This spacing distribution produces significant differences between mean (expectation) values of the bubble size and pressure and the average (median) values of these aging characteristics obtained by a previous calculation. The new calculations find much of the He is retained in a large quantity of smaller bubbles with higher bubble pressures, improving the overall stability of the bubbles and extending the age of He retention. By contrast, the integrated tritide material characteristics of swelling and tritium pressure are found relatively insensitive to details of the bubble spacing distribution. Inter-bubble fracture is predicted to begin with small, closely-spaced bubbles and progress to include larger bubbles near the onset of rapid He release. The critical concentration for this onset increases almost linearly with material tensile strength and decreases with shear modulus. Release of He from the aging solid is modeled as a growing network of fractured inter-bubble ligaments. For small particle or small grain material, the physical size of the fracture cluster, relative to the material dimensions, becomes important. In contrast with normal aging, inter-bubble fracture occurring during thermal desorption appears to begin with large, widely-spaced bubbles, indicating elevated temperature techniques may be of limited use for evaluating development of the bubble fracture network.

74 ATOMIC AND MOLECULAR PHYSICS↗

Functional Photoresists for Energy Applications. Final Report

Monolithic ultralow-density porous bulk materials have recently attracted much interest due to many emerging applications in the areas of catalysis, energy storage and conversion, and thermal insulation. They are also important components of high energy density (HED) and inertial confinement fusion (ICF) targets. However, despite tremendous progress that has been made in the synthesis of porous materials, deterministic and independent control over microscopic architecture, density and composition remain key issues, and their integration in high precision devices requires cost and time-intensive mechanical machining that not only reduces reproducibility by generating debris but also limits the complexity of the 3D shapes that can be realized. In this project, we overcame these limitations by developing a universal templating capability that provides deterministic and independent control over density, composition, architecture, and macroscopic sample shape. This was achieved by developing the technology to 1) 3D print ultrahigh resolution, ultra-high precision polymeric micro-lattice templates, 2) coat these templates with the desired materials, and 3) removing the template (Fig. 1a). Atomic layer deposition (ALD) provides the atomic scale coating thickness accuracy required for precisely controlling density. While this templating approach had been demonstrated in prior work, limitations in suitable photoresists, 3D print technologies, print design, and template removal techniques did not allow the fabrication of millimeter-sized high-precision parts with sub-micron resolution. To enable this technology, we developed 1) two-photon polymerization (TPP) print designs that enable the fabrication of millimeter-sized, mechanically robust polymeric templates with sub-micron resolution and 2) a continuum level TPP printing simulation capability for additional print design guidance; 3) atomistic models to study photoresist polymerization kinetics and network topography, 4) refractive index matched polymeric and preceramic TPP photoresists, and 5) functional TPP photoresists including porous voxel structures and self-immolative polymer photoresist chemistries; and 6) damage free template removal techniques that enable the fabrication of defect-free high-precision low-density foam components. We also developed a templating approach for pure carbon microlattices with a unique tube-in-tube ligament morphology. As a test platform, we pursued the fabrication of foam liners that promise to further increase the neutron yield in indirect drive ICF experiments by improving implosion symmetry control and coupling between the laser and the deuterium-tritium fuel. This application requires fabrication and integration of a ultra-high precision, millimeter-sized, thin-walled (200-400 micrometer thick), low-density (10-30 mg/cc), high atomic number (high Z) cylindrical foam tube into the gold hohlraum of an indirect drive ICF target (Fig. 1b). While our hohlraum liner test case will mainly find application in HED and ICF experiments, the underlying science will also directly apply to previously developed nanoparticle and additive manufacturing technologies and will advance those techniques as well.

36 MATERIALS SCIENCE↗

Cyclic tensile strain enhances human mesenchymal stem cell Smad 2/3 activation and tenogenic differentiation in anisotropic collagen-glycosaminoglycan scaffolds

Orthopaedic injuries, particularly those involving ligaments and tendons, are some of the most commonly treated ailments in the United States and are associated with both high costs and poor outcomes. Regenerative medicine strategies for tendon injuries could be enhanced by three-dimensional biomaterials that can promote cell alignment and pro-tenogenic differentiation of patientderived MSCs. We have previously described a collagenglycosaminoglycan (CG) scaffold possessing aligned structural features able to promote bone marrow MSC differentiation towards a tenogenic lineage, in the absence of growth factor supplementation. We aimed to employ a bioreactor to enhance MSC tenogenic differentiation within the aligned CG scaffold via cyclic tensile strain (CTS), and further to evaluate the relative effects of strain cycle duration and extended application of repeated cycles of CTS on MSC response. Human MSCs were cultured in CG scaffolds for up to 6 d under static (unloaded) or cyclic tensile strain (1 Hz) for 10 min every 6 h. Time-dependent activation of ERK 1/2 and p38 mechanotransduction pathways was observed within each 6 h strain cycle. MSCs remained viable throughout the experiment and application of CTS robustly upregulated the expression of tendon-specific extracellular matrix proteins and phenotypic markers. Simultaneously, CTS promoted increased phosphorylation of Smad 2/3, suggesting a link between tensile stimulation and TGF-β family growth factor production. Together, we demonstrated the design, fabrication and validation of a high-throughput tensile stimulation bioreactor to increase MSC tenogenic differentiation in porous CG scaffolds.

59 BASIC BIOLOGICAL SCIENCES↗

Long-Term Creep Behavior of the Intervertebral Disk: Comparison between Bioreactor Data and Numerical Results

The loaded disk culture system is an intervertebral disk (IVD)-oriented bioreactor developed by the VU Medical Center (VUmc, Amsterdam, The Netherlands), which has the capacity of maintaining up to 12 IVDs in culture, for approximately 3 weeks after extraction. Using this system, eight goat IVDs were provided with the essential nutrients and submitted to compression tests without losing their biomechanical and physiological properties, for 22 days. Based on previous reports (Paul et al., 2012, 2013; Detiger et al., 2013), four of these IVDs were kept in physiological condition (control) and the other four were previously injected with chondroitinase ABC (CABC), in order to promote degenerative disk disease (DDD). The loading profile intercalated 16 h of activity loading with 8 h of loading recovery to express the standard circadian variations. The displacement behavior of these eight IVDs along the first 2 days of the experiment was numerically reproduced, using an IVD osmo-poro-hyper-viscoelastic and fiber-reinforced finite element (FE) model. The simulations were run on a custom FE solver (Castro et al., 2014). The analysis of the experimental results allowed concluding that the effect of the CABC injection was only significant in two of the four IVDs. The four control IVDs showed no signs of degeneration, as expected. In what concerns to the numerical simulations, the IVD FE model was able to reproduce the generic behavior of the two groups of goat IVDs (control and injected). However, some discrepancies were still noticed on the comparison between the injected IVDs and the numerical simulations, namely on the recovery periods. This may be justified by the complexity of the pathways for DDD, associated with the multiplicity of physiological responses to each direct or indirect stimulus. Nevertheless, one could conclude that ligaments, muscles, and IVD covering membranes could be added to the FE model, in order to improve its accuracy and properly describe the recovery periods.

60 APPLIED LIFE SCIENCES↗

Single-cell RNA-Seq reveals changes in immune landscape in post-traumatic osteoarthritis

Osteoarthritis (OA) is the most common joint disease, affecting over 300 million people world-wide. Accumulating evidence attests to the important roles of the immune system in OA pathogenesis. Understanding the role of various immune cells in joint degeneration or joint repair after injury is vital for improving therapeutic strategies for treating OA. Post-traumatic osteoarthritis (PTOA) develops in ~50% of individuals who have experienced an articular trauma like an anterior cruciate ligament (ACL) rupture. Here, using the high resolution of single-cell RNA sequencing, we delineated the temporal dynamics of immune cell accumulation in the mouse knee joint after ACL rupture. Our study identified multiple immune cell types in the joint including neutrophils, monocytes, macrophages, B cells, T cells, NK cells and dendritic cells. Monocytes and macrophage populations showed the most dramatic changes after injury. Further characterization of monocytes and macrophages reveled 9 major subtypes with unique transcriptomics signatures, including a tissue resident Lyve1 hi Folr2 hi macrophage population and Trem2 hi Fcrls + recruited macrophages, both showing enrichment for phagocytic genes and growth factors such as Igf1 , Pdgfa and Pdgfc. We also identified several genes induced or repressed after ACL injury in a cell type-specific manner. This study provides new insight into PTOA-associated changes in the immune microenvironment and highlights macrophage subtypes that may play a role in joint repair after injury.

60 APPLIED LIFE SCIENCES↗

Comparative Transcriptomics Identifies Novel Genes and Pathways Involved in Post-Traumatic Osteoarthritis Development and Progression

Anterior cruciate ligament (ACL) injuries often result in post-traumatic osteoarthritis (PTOA). To better understand the molecular mechanisms behind PTOA development following ACL injury, we profiled ACL injury-induced transcriptional changes in knee joints of three mouse strains with varying susceptibility to OA: STR/ort (highly susceptible), C57BL/6J (moderately susceptible) and super-healer MRL/MpJ (not susceptible). Right knee joints of the mice were injured using a non-invasive tibial compression injury model and global gene expression was quantified before and at 1-day, 1-week, and 2-weeks post-injury using RNA-seq. Following injury, injured and uninjured joints of STR/ort and injured C57BL/6J joints displayed significant cartilage degeneration while MRL/MpJ had little cartilage damage. Gene expression analysis suggested that prolonged inflammation and elevated catabolic activity in STR/ort injured joints, compared to the other two strains may be responsible for the severe PTOA phenotype observed in this strain. MRL/MpJ had the lowest expression values for several inflammatory cytokines and catabolic enzymes activated in response to ACL injury. Furthermore, we identified several genes highly expressed in MRL/MpJ compared to the other two strains including B4galnt2 and Tpsab1 which may contribute to enhanced healing in the MRL/MpJ. Overall, this study has increased our knowledge of early molecular changes associated with PTOA development.

59 BASIC BIOLOGICAL SCIENCES↗

The line spring model for surface flaws.

A model is discussed for the analysis of long part-through surface cracks in the walls of plate or shell structures. Such problems are formulated within the context of two dimensional plate and shell theory with the part-cracked section represented as a line-spring in the middle surface. The spring allows relative separations and rotations of the middle surface, and constitutive laws relating these discontinuities to the prevailing force and moment per unit length at any point are taken from the plane strain solution for a strip in combined tension and bending, which contains an edge crack of a corresponding depth. Prior work is reviewed and further line spring constitutive laws are discussed as appropriate to elastic analysis with thermal or residual stresses and to elastic-plastic analysis, with yielding in the ligament between the crack front and far wall in the latter case.

Rice, J. R.↗

The problem of edge cracks in an infinite strip

The elastostatic plane problem of an infinite strip containing two symmetrically located internal cracks perpendicular to the boundary is formulated in terms of a singular integraL equation with the derivative of the crack surface displacement as the density function. The solution of the problem is obtained for various crack geometries and for uniaxial tension applied to the strip away from the crack region. The limiting case of the edge cracks is then considered in some detail. The fundamental function of the integral equation is obtained and a numerical technique for solving the singular integral equations with this particular type of fundamental function which is characteristic of the edge cracks is described. The stress intensity factor for the complete range of net ligament-to-width ratio is calculated. The results also include the solution of the edge crack problem in an elastic half plane.

Gupta, G. D.↗