Completion of continuity spaces with uniformly vanishing asymmetry

The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in question. For qausi-metric spaces and quasi-uniform spaces various non-equivalent completions exist, often defined on a certain subcategory of spaces that satisfy a key property required for the particular completion to exist. The classical filter completion of a uniform space can be adapted to yield a filter completion of a metric space. We show that this completion by filters generalizes to continuity spaces that satisfy a form of symmetry which we call uniformly vanishing asymmetry

An ordered framework for partial multivalued functors

The category Rel of sets and relations intimately ties the notions of function, partial multivalued function, and direct image under a function through the description of Rel as the Kleisli category of the covariant power set functor on Set. We present a suitable framework to obtain a similar relationship between the concepts of functor, partial multivalued functor, and the direct image under a functor.Comment: Accepted for presentation at the Asia-Pacific World Congress on Computer Science and Engineering 2015, Fij

Fracture behavior and self-sharpening mechanisms of polycrystalline cubic boron nitride in grinding based on cohesive element method

Unlike monocrystalline cubic boron nitride (CBN), polycrystalline CBN (PCBN) shows not only higher fracture resistance induced by tool-workpiece interaction but also better self-sharpening capability; therefore, efforts have been devoted to the study of PCBN applications in manufacturing engineering. Most of the studies, however, remain qualitative due to difficulties in experimental observations and theoretical modeling and provide limited in-depth understanding of the self-sharpening behavior/mechanism. To fill this research gap, the present study investigates the self-sharpening process of PCBN abrasives in grinding and analyzes the macro-scale fracture behavior and highly localized micro-scale crack propagation in detail. The widely employed finite element (FE) method, together with the classic Voronoi diagram and cohesive element technique, is used considering the pronounced success of FE applications in polycrystalline material modeling. Grinding trials with careful observation of the PCBN abrasive morphologies are performed to validate the proposed method. The self-sharpening details, including fracture morphology, grinding force, strain energy, and damage dissipation energy, are studied. The effects of maximum grain cut depths (MGCDs) and grinding speeds on the PCBN fracture behavior are discussed, and their optimum ranges for preferable PCBN self-sharpening performance are suggested

Completion of continuity spaces with uniformly vanishing asymmetry

The classical Cauchy completion of a metric space (by means of Cauchy sequences) as well as the completion of a uniform space (by means of Cauchy filters) are well-known to rely on the symmetry of the metric space or uniform space in question. For qausi-metric spaces and quasi-uniform spaces various non-equivalent completions exist, often defined on a certain subcategory of spaces that satisfy a key property required for the particular completion to exist. The classical filter completion of a uniform space can be adapted to yield a filter completion of a metric space. We show that this completion by filters generalizes to continuity spaces that satisfy a form of symmetry which we call uniformly vanishing asymmetry

Micromechanical Modelling of Advanced Ceramics with Statistically Representative Synthetic Microstructures

Advanced ceramics are a class of material used in extreme conditions, such as high speed turning of aerospace alloys and rock drilling. Their high hardness makes them suitable for these uses, however their lower toughness means that failure due to fracture and chipping is a problem. They are composed of micron-sized particles of a primary hard phase together with either a ceramic or metallic matrix material. A combined experimental-numerical method was used to investigate the role of microstructure on the fracture of advanced ceramics. Two dimensional, statistically representative microstructures of the advanced ceramics are created using Voronoi tessellation. The synthetic microstructures are compared to real microstructures in terms of particle size distribution and particle aspect ratio. Simulation results indicate that the computed elastic parameters are within the Hashin-Shtrikman bounds and agree closely with analytical predictions made with the Eshelby-Mori-Tanaka method. It is found that the local sts and strain distribution within the model is significantly affected by the underlying microstructure, which in turn affects fracture properties. Hence, tailoring the microstructure can optimise the bulk strength parameters of the material.Deposited by bulk impor

Micromechanical modelling of ceramic based composites with statistically representative synthetic microstructures

A combined experimental–numerical method was used to investigate the role of microstructure on the fracture of advanced ceramics. In particular, the effect of grain size and matrix content were examined. Two dimensional representative finite volume (FV) microstructures were created using Voronoi tessellation to synthetically represent the microstructure of a two phase ceramic composite. It is shown, by comparing with real micrographs, that the method captures the features of real microstructures in terms of grain size distribution, grain aspect ratio and the distribution of second phase agglomerations. Simulation results indicate the computed elastic parameters are within the Hashin–Shtrikman bounds and also agree well with the Eshelby–Mori–Tanaka method. It is found that the underlying microstructure significantly affects the local stress and strain distributions in these advanced ceramics.Deposited by bulk impor

The Role of Microstructure on the Fracture Behaviour and Statistics of Advanced Ceramics

Strength data of three advanced ceramics were fitted to the Weibull, normal and lognormal distributions. The three ceramics had similar grain size and varied in binder content. The role of microstructure in the failure mechanism of such ceramics was analysed in terms of the chosen strength distributions. The best-fit distributions were determined using the maximum log-likelihood criteria and a comparison between the best and worst fit was conducted using the Akaike Information Criteria (AIC). Both large and small samples were tested to investigate possible scaling effects for these ceramics. It was found that for two of the three ceramics tested that a lognormal distribution rather then the conventionally used Weibull distribution was preferable in characterising the strength data. A small drop in strength was noticed between large and small samples but this trend was not thought to be a result of scaling rather due to the decrease in binder content.Deposited by bulk impor

The influence of microstructure on the fracture statistics of polycrystalline diamond and polycrystalline cubic boron nitride

Flexural strength data of a number of grades of polycrystalline diamond (PCD), and polycrystalline cubic boron nitride (PCBN) were analyzed using Weibull, normal and lognormal distributions. The role of microstructure in the failure mechanism of such materials was analyzed in terms of the chosen strength distributions. The best-fit distributions were determined using the maximum log-likelihood criteria and a comparison between the best and worst fit was conducted using the Akaike Information Criteria (AIC). Both large and small specimens were tested to investigate possible volume scaling effects for these materials. The different microstructures between the two materials was shown to have an effect on the statistical strength distributions. It was found that for PCD, in general, a lognormal distribution provided a better fit than the other distributions and no specimen size effect was observed. For PCBN a significant specimen size effect was observed and this also corresponded to the data fitting to a Weibulldistribution.Deposited by bulk impor