On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

Constraint effects on multiple void interaction in pressure sensitive plastic solids

In this work, effects of pressure sensitive yielding and plastic dilatancy on void growth and void interaction mechanisms in fracture specimens displaying high and low constraint levels are investigated. To this end, large deformation finite element simulations are carried out with discrete voids ahead of the notch. It is observed that multiple void interaction mechanism which is favored by high initial porosity is further accelerated by pressure sensitive yielding, but is retarded by loss of constraint. The resistance curves predicted based on a simple void coalescence criterion show enhancement in fracture resistance when constraint level is low and when pressure sensitivity is suppressed.

Re-use of fluoride contaminated bone char sludge in concrete

Managing sludge generated by treating groundwater contaminated with geogenic contaminants (fluoride, arsenic, and iron) is a major issue in developing nations. Their re-use in civil engineering applications is a possible pathway for reducing the impact on the geo-environment. This paper examines the re-use of one such sludge material, namely, fluoride contaminated bone char sludge, as partial replacement for fine aggregate (river-sand) in the manufacture of dense concrete specimens. Bone char sludge is being produced by defluoridation of contaminated groundwater in Nalagonda District, Andhra Pradesh, India. The impact of admixing 1.5-9% sludge contents on the compression strength and fluoride leaching potential of the sludge admixed concrete (SAC) specimens are examined. The compression strengths of the SAC specimensa re examined with respect to strength criteria for manufacture of dense, load-bearing concrete blocks. The fluoride release potential of the SAC specimens is examined with respect to standards specific to disposal of treated leachate into inland surface water.

Texture strengthening in warm-rolled cadmium-1% silver alloy

The variation in the tensile properties at 77 K and 300 K in warm-rolled (300 K) Cd-1% Ag alloy with deformation has been studied in longitudinal as well as transverse specimens. The low-temperature yield strength increases with warm rolling without much loss in ductility. The strength at 300 K, however, decreases with heavy warm deformation. From microstructural studies and X-ray investigations, it was observed that changes in grain size and texture occur during warm rolling. Both these changes are found to be important in deciding the tensile properties. The longitudinal and transverse strengths at 77 K vary linearly with l-frac12, where l is the average grain diameter, and thus they obey the Hall-Petch relation. The Hall-Petch slope, k, is lower in specimens with favourable lcub1013rcub texture while the intercept σo is higher when the lcub0002rcub texture is less favourable.

Deformation processing of an aluminum alloy containing particles: Studies on AI-5 pct Si alloy 4043

Al-5 wt pct Si alloy is processed by upset forging in the temperature range 300 K to 800 K and in the strain rate range 0.02 to 200 s−1. The hardness and tensile properties of the product have been studied. A “safe” window in the strain rate-temperature field has been identified for processing of this alloy to obtain maximum tensile ductility in the product. For the above strain rate range, the temperature range of processing is 550 K to 700 K for obtaining high ductility in the product. On the basis of microstructure and the ductility of the product, the temperature-strain rate regimes of damage due to cavity formation at particles and wedge cracking have been isolated for this alloy. The tensile fracture features recorded on the product specimens are in conformity with the above damage mechanisms. A high temperature treatment above ≈600 K followed by fairly fast cooling gives solid solution strengthening in the alloy at room temperature.

On the wear of aluminium-corundum composites

The effect of corundum particle content on the wear of aluminium was studied. Composites of different corundum contents were tested for their wear characteristics. Hardness and density measurements were made on specimens before and after test. Specimens were examined by scanning electron microscopy in the as-compacted, sintered and worn states. The wear decreased as the oxide content increased, showing an optimum value at a composition range of 25 wt.%–35 wt.% of corundum. The mechanism of reinforcement and its effect on the operative wear mode are discussed.

Toughness of as-cast and partially crystallized composites of a bulk metallic glass

The deformation and fracture response of a bulk metallic glass (BMG) post-annealing above the glass transition temperature is examined. The toughness of the glass-matrix composite exhibits a sharp transition beyond a critical volume fraction of crystallization to values as low as that of brittle silicate glass. Instrumented indentation tests supplemented by impact tests were used to study this ductile to brittle transition exhibited by the partially crystallized samples. Indentation on the anneal-embrittled specimens shows lateral cracks in addition to cracks along the corners. The applicability of the Poisson's ratio-toughness correlation with respect to partially crystallized samples is also investigated.

Determination of mode 1 notch stress intensity factor by the photoelastic technique

The structural integrity of any member subjected to a load gets impaired due to the presence of cracks or crack-like defects. The notch severity is one of the several parameters that promotes the brittle fracture. The most severe one is an ideal crack with infinitesimal width and infinitesimal or zero root radius. Though analytical investigations can handle an ideal crack, experimental work, either to validate the analytical conclusions or to impose the bounds, needs to be carried out on models or specimens containing the cracks which are far from the ideal ones. Thus instead of an ideal crack with infinitesimal width the actual model will have a slot or a slit of finite width and instead of a crack ending in zero root radius, the model contains a slot having a finite root radius. Another factor of great significance at the root is the notch angle along which the transition from the slot to the root takes place. This paper is concerned with the photoelastic determination of the notch stress intensity factor in the case of a “crack” subjected to Mode 1 deformation.

The machinability of a cast aluminium alloy-graphite particle composite

The microstructure of a cast Al---Si alloy-graphite particle composite is examined using optical and analytical scanning electron microscopy. Specimens containing different percentages of graphite were machined by orthogonal planning with 25° and 45° rake angle tools at both 6.5 and 13.2 m min−1. The machining forces are reported and the chip-rake-face friction coefficients and shear flow stresses are calculated. It is shown that the reduction in machining forces with increasing graphite content is due mostly to a decrease in the shear flow stress rather than to lower chip-rake-face friction. Both the polished and the machined surfaces of the composite are rougher than those of the simple alloy, apparently owing to the greater porosity, the tearing out of graphite particles, or the opening of cracks at the graphite particles in the wake of the tool.

An Electron-Microscopic Investigation Of Oxides Related To Beta-Alumina

High resolution electron microscopic (HREM) investigation of potassiumbeta-alumina and the related gallate and ferrite has revealed that whereas the aluminate and gallate are highly disordered, consisting of random sequence ofbeta andbetaPrime units, the ferrite is more ordered. The aluminate and gallate are sensitive to electron beam irradiation exhibiting beam-induced damage similar to sodiumbetaPrime-alumina. Significantly, the ferrite is beamstable, the difference in behaviour amongst these related oxides arising from the different mechanisms by which alkali metal nonstoichiometry is accommodated. Barium hexaaluminate and hexaferrite are both highly ordered; specimens prepared by the barium borate flux method exhibit a new radic3a×radic3a superstructure of the hexagonal magnetoplumbite cell.

Photoelastic determination of mode i stress intensity factor in tensile strips—effect of crack length

This paper reports an experimental investigation carried out, using the photoelastic technique, to determine the Mode I stress intensity factor in case of cracks of varying a/w ratio in single edge-notch specimens. The photoelastic information was analysed using the several methods proposed by earlier workers. The experimental results are compared with the analytical expressions.

Texture dependent stress corrosion failure of commercial titanium sheets in bromine-methanol solution

The stress corrosion cracking (SCC) characteristics of agr-titanium sheets in a bromine-methanol solution have been studied in the annealed and cold-rolled conditions using longitudinal and transverse specimens. The times to failure for annealed longitudinal specimens were longer than those for similarly tested transverse specimens. The cold-rolled specimens developed resistance to SCC, but failed by cleavage when notched, unlike the intergranular separation in annealed titanium. The apparent activation energy was found to be texture dependent and was in the range 30 to 51 kJ mol–1 for annealed titanium, and 15kJ mol–1 for cold-rolled titanium. The dependence of SCC behaviour on the texture is related to the changes in the crack initiation times. These are caused by changes in the passivation and repassivation characteristics of the particular thickness plane. The thickness planes are identified with the help of X-ray pole figures obtained on annealed and cold-rolled material. On the basis of the activation energy and the electrochemical measurements, the mechanism of SCC in annealed titanium is identified to be the one involving stress-aided anodic dissolution. On the other hand, the results on the cold-rolled titanium are in support of the hydrogen embrittlement mechanism consisting of hydride precipitation. The cleavage planes identified from the texture data match with the reported habit planes for hydride formation.

Texture strengthening in warm-rolled cadmium-1% silver alloy

The variation in the tensile properties at 77 K and 300 K in warm-rolled (300 K) Cd-1% Ag alloy with deformation has been studied in longitudinal as well as transverse specimens. The low-temperature yield strength increases with warm rolling without much loss in ductility. The strength at 300 K, however, decreases with heavy warm deformation. From microstructural studies and X-ray investigations, it was observed that changes in grain size and texture occur during warm rolling. Both these changes are found to be important in deciding the tensile properties. The longitudinal and transverse strengths at 77 K vary linearly with l-frac12, where l is the average grain diameter, and thus they obey the Hall-Petch relation. The Hall-Petch slope, k, is lower in specimens with favourable lcub1013rcub texture while the intercept σo is higher when the lcub0002rcub texture is less favourable.

Kinetics of thermal decomposition of barium zirconyl oxalate

Kinetics of the thermal decomposition of anhydrous barium zirconyl oxalate and a carbonate intermediate have been studied. Decomposition of the anhydrous oxalate, though it could be explained based on a contracting-cube model, is quite complex. Kinetics of decomposition of the intermediate carbonate Ba2Zr2O5CO3 is greatly influenced by thermal effects during its formation. (agr-t) curves are sigmoidal and obey a power law equation followed by first order decay. Presence of carbon in the vacuum-prepared carbonate has a strong deactivating effect. Decomposition of the carbonate is accompanied by growth in particle size of the product barium zirconate.

Stress path effects on the strength behaviour of a layered soil

An experimental investigation dealing with the influence of stress path on the shear behaviour of a layered soil prepared in the laboratory is described. Specimens trimmed in vertical and horizontal directions have been sheared under three different stress paths in compression and extension tests. Either in compression or extension, the stress–strain behaviour of the specimens with both orientations was apparently the same, although the volume change behaviour was different. The effective stress parameters C′ and ′ were found to be unique and independent of the stress path and two principal orientations. However, the values of ′ in extension tests were 6–7° higher than those in compression tests.