Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks

Three-dimensional interactions of a crack front with arrays of penny-shaped microcracks are considered. The work extends the earlier analysis of 2-D crack-microcrack interactions to the 3-D configurations.After analysing simple elementary interaction events (involving only one microcrack) we solve the interaction problem for a number of sample arrays (containing up to 50 microcracks)-realizations of certain microcrack statistics.Statistical aspects of the problem are examined. The interaction effects are found to fluctuate, even qualitatively (from shielding to amplification) along the crack front: the intervals of reduced stress intensity factors (SIFs) alternate with local peaks of SIFs that enhance local front advances. Thus, no statistically stable effect of stress shielding is found (at least, for the microcrack statistics considered): the toughening by microcracking, if it exists, may be due to a statistics of the microcrack centers which is biased towards shielding configurations or to expenditure of energy on nucleation of new microcracks, rather than elastic interactions with them. Similarly to the 2-D case, stochastic asymmetries in the microcrack field produce noticeable secondary modes on the main crack (i.e., modes II and III under mode I loading); this may be partially responsible for crack kinking and an irregular crack path.The short range interactions (several microcracks closest to the main crack tip) play a dominant role. Their impact on the main crack is quite sensitive to the individual microcrack locations and cannot be adequately reproduced by modelling the short range microcracking zone by an effective elastic material of reduced stiffness.The interaction effects in 3-D are found to be weaker than in 2-D.     

Microstructure and crystallographic texture of rolled polycrystalline Fe3Al

An imperfectly B₂ ordered Fe₃Al aggregate was cast, thermomechanically hot rolled and finally annealed at 870 K. Subsequently, the specimen was rolled at 800–830 K to a strain of 80%. The microstructure and the crystallographic texture of the rolled polycrystalline sample was investigated within the range =20–80%. The microstructure consisted of flat, elongated grains. In numerous grains straight slip lines were detected. Even after =80% recrystallization was not observed. The rolling texture of Fe₃Al considerably deviates from that of non-ordered body centered cubic (b.c.c.) alloys and pure b.c.c. metals. The {111}uvw texture fibre (7-fibre) was very pronounced, while the {hkl}110 fibre (-fibre) was very weak. The {112}110 orientation which represents the strongest texture component in non-ordered b.c.c. alloys did not occur at all. The textures are discussed in terms of the {110}111, {112}111, {112}111 and {123}111 slip systems. The contribution of crystallographic slip of the various types of potential slip systems was simulated by means of the Taylor theory.     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

A novel X-ray technique for inspection of steel pipes

The corrosion-induced material loss in crude oil carrying steel pipelines was originally studied by making use of the backscatter X-ray technique. The steel thickness can be determined by studying the density profile of the backscatter intensity vs. the depth location of a voxel. There are, however, some practical limitations to the above method, and a new method for evaluating steel thickness, namely, the transcatter technique is described. This technique uses the intensity of the beam which is transmitted by the pipe wall and subsequently scattered by the hydrocarbon inside the pipeline. The thickness is evaluated using three techniques, namely, the sequential technique, the dual angle technique, and the reference technique. Of the three techniques, the sequential technique has been studied in detail. The mathematical equations and experimental results related to the transcatter technique show that the thickness can be measured with an accuracy of better than 10% for a nominal steel thickness of 8 mm with a measurement time of several minutes.     

Experimental status of the ac Josephson effect in liquid helium

The presence of an ac sound field causes several distinct effects in a system of two baths of superfluid liquid helium which are coupled by a small orifice. The primary effects of the sound field can be classified as a Z-T structure, steps, and anomalies. Each of these three effects has been subjected to various criteria which are necessary for an interpretation in terms of the ac Josephson effect. These three effects failed the criteria which were applied, and therefore they are not due to the Josephson effect. However, it is shown that the properties of these three effects correlate quite well with the expected properties of first-sound resonances within one of the two liquid baths.Financial support was provided in part by the National Science Foundation.     

Microstructure of laser melted/rapidly solidified γ/Cr3Si metal silicide “in situ” composites

In order to improve the ductility of Cr₃Si metal silicide alloys, rapidly solidified /Cr₃Si metal silicide in situ composites were fabricated by laser melting/rapid solidification technology using Cr-Si-Ni alloy powders. Microstructure of the /Cr₃Si in situ composites was characterized by OM, SEM, XRD and EDS. The effect of Ni content in the alloy powder on microstructure and hardness of the /Cr₃Si composites was investigated. The /Cr₃Si metal silicide in situ composites have high hardness and rapidly solidified fine microstructure consisting of primary Cr₃Si dendrites and the interdendritic /Cr₃Si eutectics. The volume fraction of the Cr₃Si primary dendrites in the laser melted/rapidly solidified /Cr₃Si metal silicide in situ composites decreases with the increasing nickel content. Because of the presence of the ductile nickel-base solid solution and the rapidly solidified fine microstructure, the /Cr₃Si metal silicide in situ composites are expected to have adequate combination of strength and toughness. The results demonstrate that laser melting/rapid solidification for /Cr₃Si metal silicide in situ composites is a promising toughening method for improving the ductility of Cr₃Si metal silicide alloys.     

Finite state approximation algorithms for average cost denumerable state Markov decision processes

Summary In this paper we study three finite state, value and policy iteration algorithms for denumerable space Markov decision processes with respect to the average cost criterion. The convergence of these algorithms is guaranteed under a scrambling-type recurrency condition and various tail conditions on the transition probabilities. With the value iteration schemes we construct nearly optimal policies by concentrating on a finite set of important states and controlling them as well as we can. The policy space algorithm consists of a value determination scheme associated with a policy and a policy improvement step where a better policy is determined. Thus a sequence of improved policies is constructed which is shown to converge to the optimal average cost policy.

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Zusammenfassung Für Markovsche Entscheidungsprozesse mit abzählbarem Zustandsraum untersuchen wir für den Fall des Durchschnittskostenkriteriums drei endliche Wertiterations- und Politikiterations-Algorithmen. Die Konvergenz der Algorithmen wird durch scramblingtype Rekurrenzbedingungen und verschiene tail Bedingungen an die Übergangswahrscheinlichkeiten gesichert. Mit den Wertiterationsverfahren konstruieren wir fast optimale Politiken, indem wir uns auf eine endliche Menge von wichtigen Zuständen konzentrieren und diese bestmöglich kontrollieren. Der Politikiterations-Algorithmus besteht aus einem Schritt zur Wertbestimmung für eine Politik und einem Schritt zur Verbesserung der Politik. Auf diese Weise wird eine Folge verbesserter Politiken konstruiert, die Konvergenz zur optimalen Politik wird gezeigt.

     

Critical Behavior and Scaling of Confined 3He-4He Mixtures

When helium is confined to a uniform small dimension L, its behavior is modified due to the limitation of the growth of the correlation length. This has been explored for planar confinement over a wide range of L. Less is known about confined mixtures, especially in the case of the specific heat. Here two principal effects come into play: the magnitude of the correlation length increases, and the measured heat capacity C_px must be converted to C_p, where = ₃ – ₄ , before finite-size scaling predictions can be verified. The increase in makes a given confinement L look smaller as the concentration x is increased. This, as well as changes of L itself, can be used to test predictions of correlation-length scaling. We report measurements of the specific heat of confined mixtures and compare with the well established scaling for the pure system.     

Shadow prices and sensitivity analysis in linear programming under degeneracy

Summary In linear programming applications the economic meaning of shadow prices is important. In the case primal degeneracy occurs in the optimal solution, the values of the dual real variables are not, in general, identical with the corresponding shadow prices, or, in other words, these values have not the usual meaning in comparison with LP optimal solutions without primal degeneracy. Several proposals on how to interpret such values or how to find the true shadow prices have been made and terms like many-sided- or two-sided-shadowprices have been coined. Also, when performing sensitivity analysis in the case primal degeneracy occurs, the so called critical ranges of the right hand side or of the objective function coefficients cannot be determined in the usual way. In this paper, a state-of-the-art-survey on these questions is given.

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Zusammenfassung Bei den Anwendungen der linearen Optimierung ist der ökonomische Inhalt der Schattenpreise von Bedeutung. Falls eine optimale Lösung primal entartet ist, sind die Werte der dualen Strukturvariablen im allgemeinen nicht identisch mit den entsprechenden Schattenpreisen, oder — anders ausgedrückt — diese Werte kann man nicht so interpretieren wie bei nichtentarteten optimalen Lösungen eines linearen Optimierungsproblems. Es gibt in der Literatur verschiedene Vorschläge, wie diese Werte interpretiert werden sollen oder wie der richtige Schattenpreis bestimmt werden soll. Dabei werden Bezeichnungen wie vielseitige bzw. zweiseitige Schattenpreise eingeführt. Auch bei der Durchführung einer Sensitivitätsanalyse können im Falle einer primalen Entartung die kritischen Bereiche für Parameter in der rechten Seite oder in den Zielkoeffizienten nicht auf die übliche Weise bestimmt werden. In diesem Artikel ist eine Übersicht des gegenwärtigen Standes zu den obigen Problemen gegeben.

     

Effect of Intensification of Selenium‐Protection Properties in Laboratory Animals Drinking “Flint” Water Due to the Increase in the Coefficient of Diffusion of Selenium in Organs and Tissues

The influence of flint water on the development of biochemical processes which cause the accumulation of selenium in the body of laboratory animals has been studied experimentally. A decrease in the bond energy of the molecule of flint water with the anion SeO₃ ^2– in relation to the bond energy of the molecule of ordinary water and an increase in the coefficient of diffusion of this anion in bone and muscular tissues in filtration of flint water have been substantiated.     

Electromagnetic radiation emitted during friction process

A series of studies of electromagnetic radiation (EMR) emitted during fracture of materials, enabled us to obtain a relationship between the width of a fracture and the wavelength of the emitted EMR. Applying this relation to friction we could check one of its suggested mechanisms, namely the Bowden-Tabor model, which states that during a friction process, asperities on the two contacting surfaces are welded together (at a microscopic level) and fractured. A uniaxial tension machine was used, whereby two half cylinders of chalk (CaCO3) bound together, were moved one against the other, generating friction. Calculations based on EMR observations showed that the average width of the fractured asperities was 26.3 m, while mechanical profilograph measurements of the average width of the total number of long asperilies before and after the experiment, yielded values of 15.6 and 18.4 m, respectively, implying that 25% of long asperities were fractured during a single friction process.     

The mechanical behaviour of cuprous oxide

The stress-strain behaviour under compresion at constant strain rate of single crystals (051 and 122) compression axis) and polycrystalline samples of cuprous oxide have been examined at room temperature and hydrostatic pressure up to 12 kb and at atmospheric pressure and high temperature up to 600° C. At high environmental pressure, plastic flow occurs at 6 kb. At high temperatures and one atmosphere, extensive plastic deformation was observed after 500° C. The resultant slip planes were of the {110} and {100} types. Transmission electron microscopy of thin foils prepared from deformed specimens shows that the Burgers' vectors of the glide dislocations are of the 111, 110 and 100 types.     

On radiative heat exchange in a randomly inhomogeneous scattering medium

An expression is obtained for the density distribution of the optical thickness in a randomly inhomogeneous medium such as a boiling layer. In the approximation of scattering forward and backward with respect to the direction of the ray but with allowance for the angular distribution of the radiation, the problem of the transmissivity and reflectivity is solved for the randomly inhomogeneous medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 5, pp. 842–846, November, 1973.     

Diaphyseal fractures treated by polylactide and hydroxyapatite pins. Experimental study in rat

Hydroxyapatite (HAp) coatings were deposited onto substrates of metal biomaterials (Ti, Ti6Al4V, and 316L stainless steel) by electrophoretic deposition (EPD). Only ultra-high surface area HAp powder, prepared by the metathesis method 10Ca(NO₃)₂ + 6(NH₄)₂HPO₄ + 8NH₄OH), could produce dense coatings when sintered at 875–1000°C. Single EPD coatings cracked during sintering owing to the 15–18% sintering shrinkage, but the HAp did not decompose. The use of dual coatings (coat, sinter, coat, sinter) resolved the cracking problem. Scanning electron microscopy/energy dispersive spectroscopy (SEM/EDS) inspection revealed that the second coating filled in the valleys in the cracks of the first coating. The interfacial shear strength of the dual coatings was found, by ASTM F1044-87, to be 12 MPa on a titanium substrate and 22 MPa on 316L stainless steel, comparing quite favorably with the 34 MPa benchmark (the shear strength of bovine cortical bone was found to be 34 MPa). Stainless steel gave the better result since -316L (20.5 m mK^-1) > -HAp (14 m mK^-1), resulting in residual compressive stresses in the coating, whereas -titanium (10.3 m mK^-1) < -HAp, resulting in residual tensile stresses in the coating. © 1999 Kluwer Academic Publishers     

Science revolution and Ortega hypothesis in developing countries

The science revolution, the paradigm change and the Ortega hypothesis on the role of average scientists are discussed in the context of catchup of developing countries. The relative weight of scientific fields is compared between countries as revealing their values on science. Finding some significant difference between countries, the role of developing countries is discussed in view of a possible science revolution, the paradigm change and the Ortega hypothesis.Dedicated to the memory of Michael J. Moravcsik     

Effect of anharmonicity on Kapitza resistance

To understand the effect of anharmonicity on the Kapitza resistance, a one-dimensional model is used to simulate the system of heavy element-light element solids. The system is coupled to high- and low-temperature sources, respectively, at its end points. The Lennard-Jones potential is used as the interaction potential in the light solid. For various parameters in the potential, the Kapitza resistance is calculated. It is found that the stronger the anharmonicity in the light side, the smaller is the Kapitza resistance. Also, the cases that only one to four pairs of light atoms with anharmonic interaction across the boundary is considered. With the number of anharmonic pairs across the interface increasing, the Kapitza resistance is found to be decreasing.     

The effect of Si,Zr, Al and Mo on the structure and strength of Ti martensite

The structure and strength of martensite in near titanium alloys have been studied in the composition range (wt %) up to 10% Zr, 6%, Al, 1/2% Mo, 2.4% Si. [0001], 1/3 11¯20 dislocations, 1/3 10¯10 stacking faults and approximately {10¯11} twin related martensite plates are found to be common features of the martensite. Martensite midribs consist either of finely transformed material between martensite plates, or regions of low dislocation density within martensite plates.The martensite morphology is related to the alloy composition, changing from massive to plate-like with increasing solute content. The strength of the martensite is controlled largely by solid solution strengthening.     

Nonlinear behavior of some hydrostatically stressed isotropic elastomeric foams

Summary We calculate the stress-strain relation for elastomeric foam from anab initio theory, which shows that the plateau and densification regions should be described by a hyperbola. The theory seems to agree reasonably well with experiment.     

Multi-length scale modeling of CVD of diamond Part II A combined atomic-scale/grain-scale analysis

Chemical vapor deposition of polycrystalline diamond films is studied by combining an atomic-scale kinetic Monte Carlo model with two one three-dimensional and one two-dimensional grain-scale models. The atomic-scale model is used to determine the growth rates of 111- and 100-oriented surface facets, the surface morphology of the facets and the extent of incorporation of the crystal defects. Using the atomic-scale modeling predicted growth rates for the 111- and 100-oriented facets, grain-scale modelling is carried out to determine the evolution of grain structure, surface morphology and crystallographic texture in the polycrystalline diamond films. It is found that depending on the relative growth rates of the 111- and 100-oriented facets, which can be controlled by selecting the CVD processing conditions, one can obtain either 110-textured films with a relatively smooth faceted surface or 100-textured films with a highly pronounced deep facets. In both cases, however, the film surface is composed entirely of the 111 facets. This findings are found to be fully consistent with the available experimental results.     

Tilted and Crossing Vortex Chains in Layered Superconductors

No Heading In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [] and Josephson [_J] lengths, = /_J. The chain is composed of tilted vortices at large s (tilted chain) and at small s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate s and found two types of phase transitions. For 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a [2–3]_J. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and . The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]_J, and rather wide range of the ratio , 0.4 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a [20 – 30]_J, and only when exceeds a certain critical value 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.PACS numbers: 74.25.Qt, 74.25.Op, 74.20.De