Constitutive relation of an orthorhombic polycrystal with the shape coefficients

An orthorhombic polycrystal is an orthorhombic aggregate of tiny crystallites. In this paper, we study the effect of the crystalline mean shape on the constitutive relation of the orthorhombic polycrystal. The crystalline mean shape and the crystalline orientation arrangement are described by the crystalline shape function （CSF） and the orientation distribution function （ODF）, respectively. The CSF and the ODF are expanded as an infinite series in terms of the Wigner D-functions. The expanded coefficients of the CSF and the ODF are called the shape coefficients s^lm0 and the texture coefficients c^lmn respectively. Assuming that Ceff in the constitutive relation depends on the shape coefficients s^lm0 and the texture coefficients c^lmn by the principle of material frame-indifference we derive an analytical expression for C^eff up to terms linear in s^lmo and c^lmn and the expression would be applicable to the polycrystal whose texture is weak and whose crystalline mean shape has weak anisotropy. C^cff contains six unspecified material constants （λ, μ, c, s1, s2, s3）, five shape coefficients （s^2 00, s^2 20, s^4 00, s^4 20, s^4 40）, and three texture coefficients （c^4 99,c^4 20, c^4 40）, The results based on the perturbation approach are used to determine the five material constants approximately. We also find that the shape coefficients 2 and a s^2mo and s^4m0 are all zero if the crystalline mean shape is a cuboid. Some examples are given to compare our computational results.

Modeling of the Shape Forming of Composite Roll

A shape modeling of spray formed composite roll, which is utilized to predict the shape and dimension of roll during spray forming process, is developed in this paper. The influences of the principal spray forming parameters, such as the spatial distribution of melt mass flux, spray distance, rotating and translating speeds of substrate bar etc. , on the geometry and dimension of spray formed product were investigated.

Description of the Shape Coexistence in 98Mo with IBM2

We investigate the properties of the low-lying states and the relevant shape dynamics of ^98 Mo within the frame- work of the proton-neutron interacting boson model （IBM2）. By considering the relative energy of the d proton boson to be different from that of the neutron bosons, the low-lying levels and the key observable B（E2） transition branching ratios are calculated. The characteristic feature of the energy spectrum and the most crucial available structure indicator indicate that the substantial mixing between the spherical-vibrational and γ-unstable shapes in 9SMo. The calculation results of the overall deformation in ^98Mo are almost the same for both the ground and the first excited 02^＋ states, showing a weak deformation. While the triaxiality parameter indicates that the mostly triaxial shape with some oblate for the ground state, and the triaxial shape with some prolate for the excited 02^＋ state, being equilibrium shapes of spherical-vibrational and γ-unstable in ^98 Mo.

Comparison between the Requirements of Flowability and Moldability and the Shape Retention of PIM Compacts during Debinding Process

To successfully employ powder injection molding (PIM) as a manufacturing technique, the function of the component, design of the part, material and process should be optimized for overall processing ability of the PIM process. A comparison between the requirements of flowability and moldability and the compacts shape retention has been made in this work. There is often a contradiction between the requirements of flowability and the compacts shape retention. Many works have been done to attain good molding conditions. However, they fail to take into account the effect of some factors that satisfies good molding conditions on the compacts shape retention during debinding. This paper studies the effect of the powder-binder mixture characteristics and the molding conditions on the flowability and moldability and the shape retention of PIM compacts during debinding process so as to attain the benefits of each.

The shape of incident shock wave in steady axisymmetric conical Mach reflection

For internal flow with supersonic inflow boundary conditions,a complicated oblique shock reflection may occur.Different from the planar shock reflection problem,where the shape of the incident shock can be a straight line,the shape of the incident shock wave in the inward-facing axisymmetric shock reflection in steady flow is an unknown curve.In this paper,a simple theoretical approach is proposed to determine the shape of this incident shock wave.The present theory is based on the steady Euler equations.When the assumption that the streamlines are straight lines at locations just behind the incident shock is adopted,an ordinary differential equation can be derived,and the shape of the incident shock wave is given by the solution of this ordinary differential equation.The predicted curves of the incident shock wave at several inlet conditions agree very well with the results of the numerical simulations.

Shielding Effectiveness of Superconductor in the Shape of Spherical Shell

The Shielding coefficient of superconductor in the shape of the spherical shell is derived on the basis of Maxwell's equations and London's two-liquid model. Some cases of superconductor shielding have also been discussed in this paper.

The Asymptotics of the Two-Dimensional Wave Equation for a General Multi-Connected Vibrating Membrane with Piecewise Smooth Robin Boundary Conditions

The asymptotic expansion for small |t| of the trace of the wave kernel , where and are the eigenvalues of the negative Laplacian in the (x 2,x 2)-plane, is studied for a multi-connected vibrating membrane ? in R 2 surrounded by simply connected bounded domains ? j with smooth boundaries ?? j (j = 1, ..., n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Γ i (i = 1+k j?1, ..., k j ) of the boundaries ?? j are considered, such that and k 0 = 0. The basic problem is to extract information on the geometry of ? using the wave equation approach. Some geometric quantities of ? (e. g. the area of ?, the total lengths of its boundary, the curvature of its boundary, the number of the holes of ?, etc.) are determined from the asymptotic expansion of the trace of the wave kernel for small |t|.

BOUNDARY LAYER ESTIMATION OF A SINGULAR PROBLEM WITH LIMIT EQUATION OF ORDER 2

In this paper, we gave boundary layer estimation of a singular equation of order 4 with limit equation of order 2. The results show that the thickness of boundary layer is intrinsically relative to the reciprocal of the order of equation of and independent of the order of equation of u.