Unit Vectors for Similar Oblate Spheroidal Coordinates and Vector Transformation

The unit vectors transformation between the Cartesian and the novel Similar Oblate Spheroidal coordinates, and vice versa, is derived. It can help to transform vector fields between these two types of orthogonal coordinates which can advantageously simplify solutions of problems exhibiting oblate spheroidal geometry. Several examples demonstrate the use of the derived relations. Generalized sine and cosine applicable in Similar Oblate Spheroidal coordinate system are introduced.Comment: 33 pages, 1 figur

Interior solution of azimuthally symmetric case of Laplace equation in orthogonal similar oblate spheroidal coordinates

Curvilinear coordinate systems distinct from the rectangular Cartesian coordinate system are particularly valuable in the field calculations as they facilitate the expression of boundary conditions of differential equations in a reasonably simple way when the coordinate surfaces fit the physical boundaries of the problem. The recently finalized orthogonal similar oblate spheroidal (SOS) coordinate system can be particularly useful for a physical processes description inside or in the vicinity of the bodies with the geometry of an oblate spheroid. Such shape is aproximating well objects investigated within astrophysics. The solution of the azimuthally symmetric case of the Laplace equation was found for the interior space in the orthogonal SOS coordinates. In the frame of the derivation of the harmonic functions, the Laplace equation was separated by a special separation procedure. A generalized Legendre equation was introduced as the equation for the angular part of the separated Laplace equation. The harmonic functions were determined as relations involving generalized Legendre functions of the first and of the second kind. Several lower-degree functions are reported. Recursion formula facilitating determination of the higher-degree harmonic functions was found. The general solution of the azimuthally symmetric Laplace equation for the interior space in the SOS coordinates is reported.Comment: 36 pages, 1 figur

Characterization of innovative rotary swaged Cu-Al clad composite wire conductors

Cu/Al composites are perspective for applications in a wide range of industrial and commercial branches, from transportation to elecatrotechnics. This study focuses on Cu/Al clad composite wires with 5 mm diameter featuring unique sequencing produced via the technology of rotary swaging at the processing temperatures of 20 degrees C and 250 degrees C. During the swaging process, we continuously acquired samples for investigations and used our own KOMAFU S600 system for dynamic detection of swaging forces. The composite wires subjected to electrical resistivity measurement were further analysed via electron microscopy, neutron diffraction, and mechanical testing. The results showed that both the total imposed strain (swaging degree) and swaging temperature influenced the investigated parameters non-negligibly. The samples subjected to high reduction ratios (swaging degree > 3) at the temperature of 250 degrees C exhibited formation of intermetallics at the interfaces, which deteriorated the electric conductivity. However, the conductivity was also affected by structural phenomena, such as work hardening, texture development, dislocations density, and recrystallization. All the final 5 mm samples exhibited sufficient bonding of both the components and recrystallized ultra-fine grained structures providing them with the ultimate tensile strength of >200 MPa.Web of Science16083582

Correlating microstrain and activated slip systems with mechanical properties within rotary swaged WNiCo pseudoalloy

Due to their superb mechanical properties and high specific mass, tungsten heavy alloys are used in demanding applications, such as kinetic penetrators, gyroscope rotors, or radiation shielding. However, their structure, consisting of hard tungsten particles embedded in a soft matrix, makes the deformation processing a challenging task. This study focused on the characterization of deformation behavior during thermomechanical processing of a WNiCo tungsten heavy alloy (THA) via the method of rotary swaging at various temperatures. Emphasis is given to microstrain development and determination of the activated slip systems and dislocation density via neutron diffraction. The analyses showed that the grains of the NiCo2W matrix refined significantly after the deformation treatments. The microstrain was higher in the cold swaged sample (44.2 x 10(-4)). Both the samples swaged at 20 degrees C and 900 degrees C exhibited the activation of edge dislocations with {110} or {111} slip systems, and/or screw dislocations with slip system in the NiCo2W matrix. Dislocation densities were determined and the results were correlated with the final mechanical properties of the swaged bars.Web of Science131art. no. 20

Microstructural stability of Co-Re-Cr-Ta-C alloy strengthened by TaC precipitates

It is becoming increasingly clear that new materials that can operate at substantially higher temperatures than Ni-base superalloys are needed for future gas turbines. High melting Co-Re-Cr based alloy strengthened by carbides, particularly the MC type carbide, shows promise [1]. A fine dispersion of globular TaC precipitate is exploited for this purpose. Additionally Cr, which is mainly added to improve oxidation resistance, also stabilizes lamellar M23C6 type Cr carbide. The microstructure of a Co-Re-Cr-Ta-C alloy with the two types of carbides is seen in Fig. 1. Please click Additional Files below to see the full abstract

Residual stress distribution in a copper-aluminum multifilament composite fabricated by rotary swaging

Rotary swaging is a promising technique for the fabrication of clad Cu/Al composites. Residual stresses appearing during the processing of a special arrangement of Al filaments within the Cu matrix and the influence of the bar reversal between the passes were studied by (i) neutron diffraction using a novel evaluation procedure for pseudo-strain correction and (ii) a finite element method simulation. The initial study of the stress differences in the Cu phase allowed us to infer that the stresses around the central Al filament are hydrostatic when the sample is reversed during the passes. This fact enabled the calculation of the stress-free reference and, consequently, the analysis of the hydrostatic and deviatoric components. Finally, the stresses with the von Mises relation were calculated. Hydrostatic stresses (far from the filaments) and axial deviatoric stresses are zero or compressive for both reversed and non-reversed samples. The reversal of the bar direction slightly changes the overall state within the region of high density of Al filaments, where hydrostatic stresses tend to be tensile, but it seems to be advantageous for avoiding plastification in the regions without Al wires. The finite element analysis revealed the presence of shear stresses; nevertheless, stresses calculated with the von Mises relation show similar trends in the simulation and in the neutron measurements. Microstresses are suggested as a possible reason for the large width of the neutron diffraction peak in the measurement of the radial direction.Web of Science165art. no. 210

Formation and Dissolution of γ’ Precipitates in IN792 Superalloy at Elevated Temperatures

Precipitation of γ’ phase in nickel-base superalloy IN792-5A was studied using in-situ Small Angle Neutron Scattering (SANS). It was found that additional precipitates are formed after reheating above 600 °C when the material is previously fast cooled (100 K/min) from 900 °C. The size distribution and volume fraction of the additional γ’ precipitates as well as of the already present medium-size precipitates in dependence on temperature were evaluated. The small precipitates can influence mechanical properties of the alloy, which exhibits an anomaly in the temperature dependence of the yield stress. Volume fraction of all precipitate populations above 900 °C was estimated as well