On the Diffuse Interface Models for High Codimension Dispersed Inclusions

Diffuse interface models are widely used to describe the evolution of multi-phase systems of various natures. Dispersed inclusions described by these models are usually three-dimensional (3D) objects characterized by phase field distribution. When employed to describe elastic fracture evolution, the dispersed phase elements are effectively two-dimensional (2D) objects. An example of the model with effectively one-dimensional (1D) dispersed inclusions is a phase field model for electric breakdown in solids. Any diffuse interface field model is defined by an appropriate free energy functional, which depends on a phase field and its derivatives. In this work we show that codimension of the dispersed inclusions significantly restricts the functional dependency of the free energy on the derivatives of the problem state variables. It is shown that to describe codimension 2 diffuse objects, the free energy of the model necessarily depends on higher order derivatives of the phase field or needs an additional smoothness of the solution, i.e., its first derivatives should be integrable with a power greater than two. Numerical experiments are presented to support our theoretical discussion.

Modification of Type B Inclusions by Calcium Treatment in High-Carbon Hard-Wire Steel

To investigate the modification of type B inclusions in high-carbon hard-wire steel with Ca treatment, Si-Ca alloy was added to high-carbon hard-steel, and the composition, morphology, size, quantity, and distribution of inclusions were observed. The samples were investigated by scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS). The experimental thermal results showed that the modification effect of inclusion was better in high-carbon hard-wire steel with Al of 0.0053% and Ca of 0.0029% than that in steel with Al of 0.011% and Ca of 0.0052%, in which the inclusions were mainly spherical semi-liquid and liquid CA2, CA, and C12A7. The inclusion size decreased from 3.2 μm to 2.1 μm. The degree of inclusions segregation was reduced in high-carbon hard-wire steels after calcium treatment. The results indicate that the modification of inclusions is conducive to obtaining dispersed inclusions with fine size. The ratio of length to width decreased and tended to be 1 with the increase in CaO content in the inclusion. When the content of CaO was higher than 30%, the aspect ratio was in the range of 1 to 1.2. The relationship between the activity of aluminum and calcium and the inclusions type at equilibrium in high-carbon hard-wire steel was estimated using classical thermodynamics. The calculated results were consistent with the experimental results. The thermodynamic software Factsage was used to analyze the effect of aluminum and calcium additions on the type and quality of inclusions in high-carbon hard-wire steels. The modification law and mechanism of type B inclusions in high-carbon hard-wire steels are discussed.

Intensification of Open Gutters Operation

The intensification of the work of open gutter by applying textured shells to their bottom surface, forming an artificial roughness, is considered. It is shown that the presence of corrugated surfaces contributes to vortex formation during water flow and improves the separation and transportation of mineral impurities previously dropped into the bottom of the gutters. The implementation of operations to improve the structure of the gutters is possible during the repair and restoration works with the use of modern polymer materials. The design of a small-sized hydraulic stand, which makes it possible to study the transport capacity of flows containing solid inclusions, is presented. The method of research is hydraulic testing, accompanied by the use of chiaroscuro effect, as well as photo and film equipment. The optimal structure of the inner surface of the gutters and pipes providing vortex formation, which will improve the ability of the flow to carry out and transport foreign dispersed inclusions (sand) of different granulometric compositions, is determined.

Stress concentration in frictional polymeric composites reinforced by oriented fibers

Multicomponent frictional polymer composites based on an epoxyphenol binder reinforced with E-glass fibers and dispersed inclusions of rubber, alumina, graphite, and barite are considered. It is believed that glass fibers are oriented along the X and Y axes of a rectangular coordinate system and have the same volume contents in these directions, which corresponds to the reinforcement of the material with fabric. Numerical calculations of the values of the components of the stress concentration operator (a fourth-rank tensor connecting the local stress values at an arbitrary point in an inhomogeneous medium with external stresses applied to the composite) were carried out for the considered frictional polymer composites, taking into account changes in the volume contents of their fillers.

The Effect of Material and Geometrical Uncertainty on the Homogenized Properties of Graphene Sheet-Reinforced Composites

This paper focuses on the computational homogenization of graphene sheet-reinforced composites with randomly dispersed inclusions and uncertainty in the constituent materials. Material uncertainty of the matrix and of the graphene inclusions are considered separately and their relative effect on the homogenized properties is assessed. The uncertainty in the inclusion material is due to structural defects of the graphene lattice and is taken into account using random variables for each component of the elasticity matrix. Moreover, Monte Carlo simulation is used to extract the statistical characteristics of the homogenized properties of the composite material. The results lead to useful conclusions regarding the effect of material and geometrical uncertainty on the macroscopic properties of graphene sheet-reinforced composites.

On the Color and Genesis of Prase (Green Quartz) and Amethyst from the Island of Serifos, Cyclades, Greece

The color of quartz and other minerals can be either caused by defects in the crystal structure or by finely dispersed inclusions of other minerals within the crystals. In order to investigate the mineral chemistry and genesis of the famous prase (green quartz) and amethyst association from Serifos Island, Greece, we used electron microprobe analyses and oxygen isotope measurements of quartz. We show that the color of these green quartz crystals is caused by small and acicular amphibole inclusions. Our data also shows that there are two generations of amphibole inclusions within the green quartz crystals, which indicate that the fluid, from which both amphiboles and quartz have crystallized, must have had a change in its chemical composition during the crystallization process. The electron microprobe data also suggests that traces of iron may be responsible for the amethyst coloration. Both quartz varieties are characterized by isotopic compositions that suggest mixing of magmatic and meteoric/marine fluids. The contribution of meteoric fluid is more significant in the final stages and reflects amethyst precipitation under more oxidizing conditions.