Application of a new iterative method for elastic-plastic stress analysis

A new iterative method for elastic-plastic stress analysis based on a new approximation of the constitutive equations is proposed and compared with standard methods on the accuracy and the computational time in a test problem. The proposed method appears to be better than the conventional methods on the accuracy and comparable with others on the computational time. Also the present method is applied to a crack problem and the results are compared with experimental ones. The agreement of both results are satisfactory.List of symbols u = (u ₁, u ₂) displacements u ^(H) = u ⁽ⁿ⁺¹⁾ - u ⁽ⁿ⁾ u _k ⁽ⁿ⁾ = u _(k ^{(n + 1)} - u ⁽ⁿ⁾ (n, k = 0, 1, 2, ...) - = ₁₁, ₂₂, ₁₂) stresses - = (₁₁, ₂₂, ₁₂) strains - = (₁₁, ₂₂, ₁₂) center of yield surface - D elastic coeffficient matrix, C = D ^–1 - von Mises yield function. The initial yielding is given by f() = _Y - f {f/} - ^* transposed f - H hardening parameter (assumed to be a positive constant for kinematic hardening problems) - time derivative of - [K] total elastic stiffness matrix - T traction vector - = [B] relation between nodal displacements and strains     

The athermal α → ω transformation in Zr-2 at% Nb alloy

The athermal transformation in Zr-2 at.% Nb alloy has been investigated by transmission electron microscopy. Analysis of the selected-area diffraction pattern has shown that the orientation relationships between the omega and the parent-phase in quenched Zr-2 at.% Nb alloy are the same as have been previously observed for the reaction in pure zirconium. Thus it was deduced that the direct transition has taken place in the alloy during cooling. The-originated -particles were visualized using the dark-field technique. The formation of the athermal omega in the-region of-stabilized Zr-Nb alloy is discussed in terms of the relative positions of the free energy equilibrium curvesT ₀ ,T ₀ ,T ₀ and the correspondingM _s ,M _s andT _s start curves. It is concluded that the omega phase can occur over a much wider range of alloy compositions than is usually recognized on the basis of transformation data.     

Does Vortex Lattice of YBa2Cu3O6.94 in H⊥c Melt Below Intrinsic-Pinning Irreversibility Line?

Vortex lattice melting in the Hc configuration of an YBa ₂ Cu ₃ O _6.94 single crystal has been investigated by means of the ac susceptibility – i and the magnetic torque . The melting transition of vortex lattice occurs in Hc, too. Since the torque curve shows a sharp peak in the irreversible torque at _c 90° due to intrinsic pinning at lower temperatures, we can determine the irreversibility line for the intrinsic pinning. The melting transition in the Hc configuration appears at temperatures where the intrinsic-pinning peak is absent. We consider that the intrinsic pinning does not affect the nature of the vortex melting transition in the Hc configuration.     

AC electrical conductivity of electron beam evaporated Cu-GeO2 thin cermet films

AC electrical properties of 410 nm think 30 at.wt% Cu-70 at.wt% GeO₂ thin films are reported for the frequency range 10⁴ to 10⁶ Hz and temperature range 150 to 425 K. The loss tangent (tan ) and the dielectric loss (/₀) are found to show striking minima around a cut-off frequency 10⁵ Hz. In the lower frequency range (10⁵ Hz), ₁() ^s T ⁿ is obeyed with s (0 to 0.51) increasing as a function of temperature and n (0.10 to 0.14) showing a very weak temperature dependence. In the higher frequency region (10⁵ Hz), ₁() and /₀ increase sharply leading to the quadratic behavior of ₁() with s equal to 2. These processes are discussed by analyzing an equivalent circuit which shows that at lower frequencies, the effects of series resistance in leads and contacts can be neglected, while at higher frequencies such effect give rise to spurious ² dependance for the conductance. A weakly activated AC conductivity and a frequency exponent s that increases with increasing temperature suggest that the low frequency behavior originates from carrier migration by tunneling process.     

Interaction between a dislocation and an impurity in KCl: Mg2+ single crystals

The interaction between a dislocation and the impurity in KCl: Mg²⁺ (0.035 mol% in the melt) was investigated at 77–178 K with respect to the two models: one is the Fleischer's model and the other the Fleischer's model taking account of the Friedel relation. The latter is termed the F-F. The dependence of strain-rate sensitivity due to the impurities on temperature for the specimen was appropriate to the Fleischer's model than the F-F. Furthermore, the activation enthalpy, H, for the Fleischer's model appeared to be nearly proportional to the temperature in comparison with the F-F. The Friedel relation between effective stress and average length of the dislocation segments is exact for most weak obstacles to dislocation motion. However, above-mentioned results mean that the Friedel relation is not suitable for the interaction between a dislocation and the impurity in the specimen. Then, the value of H(T _c) at the Fleischer's model was found to be 0.61 eV. H(T _c) corresponds to the activation enthalpy for overcoming of the strain field around the impurity by a dislocation at 0 K. In addition, the Gibbs free energy, G ₀, concerning the dislocation motion was determined to be between 0.42 and 0.48 eV on the basis of the following equation ln / = G ₀/(kT_p0)1 – (T/T _c)^{1/2 –1}(T/T _c)^1/2 + ln ₀/where k is the Boltzmann's constant, T the temperature, T _c the critical temperature at which the effective stress due to the impurities is zero, _p0 the effective shear stress without thermal activation, and ₀ the frequency factor.     

Shear viscosity measurements of liquid 3He-4He mixtures above 0.5 K

Simultaneous measurements of () and of the molar volume are reported for liquid mixtures of ³He in ⁴He over the temperature range between 0.5 and 2.5 K. Here is the shear viscosity and is the mass density. In the superfluid phase, the product of the normal components, _n and _n , is measured. The mixtures with ³He molefractions 0.30 < X < 0.80 are studied with emphasis on the region near the superfluid transition T and near the phase-separation curve. Along the latter, they are compared with data by Lai and Kitchens. For X > 0.5, the viscosity singularity near T becomes a faint peak, which however fades into the temperature-dependent background viscosity as X tends to the tricritical concentration X _t. Likewise, no singularity in is apparent when T _t is approached along the phase separation branches _– and ₊. Furthermore, viscosity data are reported for ³He and compared with previous work. Finally, for dilute mixtures with 0.01 X 0.05, the results for are compared with previous data and with predictions.     

The variation of the index of refraction in a vortex tube

Three models of a vortex tube (isentropic, isothermal, and isochoric) are considered as optical inhomogeneities. Expressions relating the index of refraction to the coordinate are obtained. The possibility of obtaining Schlieren pictures of such flows is discussed.Notation a speed of sound - n index of refraction - p pressure - r radius - T absolute temperature - v linear velocity - angular deflection of the beam - x adiabatic exponent - density - angular velocity - ¯v, ¯p etc. dimensionless parameters - v₀, ₀ values at the core bounboundary - p, etc. stagnation values - n_c index of refraction at center of vortex     

Thermophysical properties data on molten semiconductors

Thermophysical properties of molten semiconductors are reviewed. Published data for viscosity, thermal conductivity, surface tension, and other properties are presented. Several measurement methods often used for molten semiconductors are described. Recommended values of thermophysical properties are tabulated for Si, Ge, GaAs, InP, InSb, GaSb, and other compounds. This review shows that further measurements of thermophysical properties of GaAs and InP in the molten state are required. It is also indicated that a very limited amount of data on emissivity is available. Space experiments relating to thermophysical property measurements are described briefly.Nomenclature Density - C _p Specific heat - Kinematic viscosity - Dynamic viscosity= - Thermal diffusivity - Thermal conductivity=C_p - Volumetric thermal expansion coefficient - Surface tension - d/dT Temperature coefficient of surface tension - g Gravitational acceleration - T Temperature - T Temperature difference - L Characteristic dimension     

Correlation of burst pressure of GRP cylinders with the stress wave factor

Glass fibre-reinforced plastic (GRP) cylinders are increasingly used for highly stressed structural elements. The higher the demands on the materials, the higher are the fault detection requirements to be met by non-destructive materials testing methods. Acousto-ultrasonics is a valuable aid for the non-destructive evaluation of GRP composite materials, because it may be the answer to evaluating effects of subtle defects in composites. The aim of the research is to evaluate the burst pressure of GRP cylinders by acousto-ultrasonics techniques. The theoretical results have been found to be in good agreement with the experimental values. Hence the results strongly suggest that stress wave factor measurements can be exploited successfully to predict burst pressure of GRP cylinders.Nomenclature P Internal pressure, kgf cm^–2 - d Internal diameter, cm - t Thickness of cylinder, cm - (N ,N ,N ) Resultant forces, kgf - (M ,M ,M ) Moments, kg cm - [A] Extensional stiffness matrix - [B] Bending stretching coupling matrix - [D] Flexural stiffness matrix - ( ⁰ , ⁰ , ⁰ ) Midplane strains - (k ,k ,k ) Curvatures - n Number of laminae - Z Distance from midplane, cm - _u Ultimate tensile strength of GRP composite, kg cm^–2 - S _W Stress wave factor - m Material parameter - Filament winding angle     

Natural convection flow of a viscous fluid about a truncated cone with temperature dependent viscosity

Summary The two-dimensional natural convection flow of a viscous incompressible fluid with temperature dependent viscosity about a truncated cone is considered. The governing equations for the flow are obtained by using suitable transformations and solved by using an implicit finite difference method. Perturbation solutions are obtained near the leading edge and in the downstream regime, and the results are obtained in terms of the local skin friction coefficient and the local Nusselt number. Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement. The dimensionless velocity profiles and viscosity distribution are also presented graphically for various values of the viscosity variation parameter, , for small values of the Prandtl number appropriate for liquid metals.Nomenclature x Streamwise coordinate - x ^* Distance measured from the leading edge of the truncated cone - x ₀ Distance of the leading edge of the truncated cone measured from the origin - y Transverse coordinate - u Velocity component in thex-direction - v Velocity component in they-direction - f Dimensionless stream function - g Acceleration due to gravity - T Temperature of the fluid - T Temperature of the ambient fluid - T _w Surface temperature - Pr _x Prandtl number - Gr _x Local Grashof number - Stream function - Dimensionless temperature function - Dimensionless distance - Similarity variable - Nu _x Nusselt number - C _f Skin friction - Thermal conductivity - Fluid density - Kinematic viscosity - Viscosity variation parameter - Coefficient of thermal expansion - Viscosity of the fluid - Viscosity of the ambient fluid at infinity - Thermal diffusivity     

Coefficients of mass transfer between a fluidized bed and the surface of a capillary-porous body

Results are presented from a theoretical determination of coefficients of mass transfer between a fluidized bed of porous particles and a capillary-porous body.Notation a particle radius - F area of contact of particles with the surface of the body - f percentage of area of surface of product in contact with the bubble phase - g acceleration due to gravity - i flow of liquid mass from a unit area of the surface - N number of fluidizations - n number of particles coming into contact with a surface of unit area per unit of time - p_p, p_b capillary potentials of particles and product - R₂, R₁ radii of narrow and broad pores inside the product - r radius of capillaries in the particles - S area of the surface being treated - T temperature of the bed - t time of treatment - u percentage content of liquid in the specimen - V volume of the product being treated - v mean square component of the fluctuation velocity of the particles in the direction normal to the surface - , * standard and corrected mass-transfer coefficients determined from (5) and (9) - _b, _b, _p porosities of product determined for all and for only the small pores and the porosity of the material of the particles - _d, _m porosity of the dense phase and the porosity of the bed in the state of minimum fluidization - _b, _p angles of wetting of the materials of the product and particles, respectively, by the liquid binder - , viscosity and density of the liquid - ₀ density of the dry product - surface tension coefficient of the liquid - characteristic time of contact of particles with the surface - Re_m Reynolds number corresponding to particle radius and minimum-bed-fluidization velocity [6] Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 460–465, March, 1981.     

Microstructure and mechanical properties of rapidly quenched L20 and L20+L12 alloys in Ni-Al-Fe and Ni-Al-Co systems

Ductile L2₀-type wires and+L1₂-type duplex wires with high strengths and large elongation in the Ni-Al-Fe and Ni-Al-Co ternary systems have been manufactured directly from the liquid state by an in-rotating-water spinning method. The wire diameter was in the range 80 to 180m and the average grain size was 2 to 4m for the wires and 0.2 to 1.0m for the+ wires. _y, _f and _p of the wires were found to be about 360 to 760 MPa, 560 to 960 MPa, and 0.2 to 5.5%, respectively, for the Ni-Al-Fe system, those of the+ wires were about 395 to 660 MPa, 670 to 1285 MPa, and 3.5 to 17%, respectively, for the Ni-Al-Fe system, and about 260 to 365 MPa, 600 to 870 MPa, and 4.0 to 7.0%, respectively, for the Ni-Al-Co system. Cold-drawing caused a significant increase in _y and _f and the values attained were about 1850 and 2500 MPa, respectively, for Ni-20Al-30Fe and Ni-25Al-30Co wires drawn to about 90% reduction in area. The high strengths, large elongation and good cold-workability of the melt-quenched and+ compound wires have been inferred to be due to the structural change into a low-degree ordered state containing a high density of phase boundaries, suppression of grain-boundary segregation and refinement of grain size.     

Determination of In-Plane Anisotropy from Magnetoresistivity Measurements on YBa2Cu3O7−δ

The magnetoresistance of six untwinned YBa ₂ Cu ₃ O _7– crystals has been measured above T _c for IBc. Fluctuation theories allowing for an in-plane coherence length anisotropy ( _{a b} ) were used in the analyses. The results suggest that the anisotropy, = _b / _a , is considerably lower than that expected from the resistivity ratio, i.e., . Some magnetoresistive measurements with the field in the ab-plane are also presented.     

A modified Weibull treatment for the analysis of strength-test data from non-identical brittle specimens

Powder compacts (e.g., pharmaceutical tablets) manufactured on commerically available machines are not strictly identical but show inevitable variability in their weights, thicknesses and compaction pressures. Consequently, the variability in fracture-stress data obtained from such brittle specimens is greater than that due to the inherent strength variability of the material itself. A modified Weibull analysis has been developed so that a more accurate estimate of the inherent variability of the mechanical strength of the material can be derived from test data obtained from commercially produced compacts; its application is illustrated.Nomenclature D diameter - f() relative frequency of occurrence of specimens with density and volume - F minimization function - i ascending rank number of a fracture stress - m Weibull modulus - N _tot number of specimens in a batch - N() number of specimens with densities in the range to + d and volumes in the range to + d - P _f failure probability - p _u upper punch compaction pressure - t thickness - volume - w weight - W _f fracture load - density - _f fracture stress - ¯ _f mean fracture stress of a batch - ¯ _f() mean fracture stress of specimens with density and volume - ₀ scale parameter or normalizing factor - _u location parameter or threshold stress     

Nonlinear asymptotic theory of hypersonic flow past a circular cone

Summary The hypersonic small-disturbance theory is reexamined in this study. A systematic and rigorous approach is proposed to obtain the nonlinear asymptotic equation from the Taylor-Maccoll equation for hypersonic flow past a circular cone. Using this approach, consideration is made of a general asymptotic expansion of the unified supersonic-hypersonic similarity parameter together with the stretched coordinate. Moreover, the successive approximate solutions of the nonlinear hypersonic smalldisturbance equation are solved by iteration. Both of these approximations provide a closed-form solution, which is suitable for the analysis of various related flow problems. Besides the velocity components, the shock location and other thermodynamic properties are presented. Comparisons are also made of the zeroth-order with first-order approximations for shock location and pressure coefficient on the cone surface, respectively. The latter (including the nonlinear effects) demonstrates better correlation with exact solution than the zeroth-order approximation. This approach offers further insight into the fundamental features of hypersonic small-disturbance theory.Notation a speed of sound - H unified supersonic-hypersonic similarity parameter, - K hypersonic similarity parameter, M - M freestream Mach number - P pressure - T temperature - S entropy - u, v radial, polar velocities - V freestream velocity - shock angle - cone angle - density - density ratio, /() - ratio of specific heats - polar angle - stretched polar angle, / - (), (), () gage functions     

Knudsen molecular flow in a channel with a small temperature difference at its ends

The thermomolecular pressure difference (TPD) of helium, argon, and krypton is measured in a packet of glass capillaries for temperatures 273 and 293 K at their ends in a 10–100 range of Knudsen numbers.Notation exponent of the thermomolecular pressure difference effect - Kn Knudsen number - rarefaction parameter - Q_T reduced thermal creep flux - Q_P reduced Poiseuille flux - C(_t) Cercignani-Lampis scattering kernel - R specular scattering kernel - (1 – ) fraction of specular reflection - _t accommodation coefficient of the tangential momentum - P_c, P_h gas pressure in the cold and hot volumes, respectively - coefficient of dynamic viscosity - m mass of gas molecules - k Boltzmann constant - D, L the capillary diameter and length, respectively Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 719–724, May, 1988.     

Energy Scales in the High-Tc Superconductor YBa2Cu3O6+x

The optical conductivity sum rule is used to examine the evolution of the spectral weight N() in both the normal and superconducting states of optimally and underdoped YBa₂Cu₃O_6+x along the a axis. Differences in N() above and below T _c allow the strength of the superconducting condensate _s to be determined. In the optimally-doped material, _s is fully formed at energies comparable to the full superconducting gap maximum (0.1 eV), while in the underdoped material the energy scale for convergence is considerably higher (0.6 eV). This difference is discussed in terms of normal-state properties.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

TEM study of metastable β-phase decomposition in rapidly solidified Ti-6Al-4V alloy

A new rationale is presented for various decomposition products obtained from the metastable -phase found in Ti-6A1-4V alloy produced by hot isostatic pressing comminuted melt-spun fibres and cooled to room temperature by furnace cooling. This alloy has an -matrix with about 8 vol% retained -phase, which is supersaturated with -stabilizers to such an extent that the martensitic transformation has been suppressed. The metastable -phase decomposes by different modes during continuous cooling, depending on the actual composition of individual -grains. Less enrichment of vanadium and iron favours the direct formation of the equilibrium -phase from the -matrix, while greater enrichment of vanadium and iron leads to a spinodal decomposition of the metastable -phase, resulting in a + two-phase structure. During further continuous cooling, the -phase which is lean in -stabilizers will transform into isothermal -phase. In addition, an unknown phase has also been observed in the -phase, which is typified by the appearance of 1/2{112} reflections in the SAD patterns.     

Thermal Expansion and Isothermal Compressibility of TlIn1 – xNdxSe2 (0 ≤ x≤ 0.08) Crystals

The thermal expansion coefficient () and isothermal compressibility ( _T ) of TlIn_{1 – x} Nd _x Se₂(0 x 0.08) crystals were measured between 77 and 400 K. In the range 77–160 K, both and _T increase with temperature, the increase in being much steeper. At higher temperatures, and _T change very little. The observed composition dependences of and _T are interpreted in terms of energy-band structure.