Phase decomposition in extruded Zn-Al based alloy

Ageing characteristics of an extruded eutectoid Zn-Al based alloy were investigated using X-ray diffraction and scanning electron microscopy techniques. The extruded alloy consisted of Al rich phase and Zn rich _E and phases. The original cast eutectoid Zn-Al alloy was extruded at 250 °C. Both supersaturated _s and _s phase decomposed during extrusion and appeared as fine and coarse lamellar structures. The _E and phases particles formed in the original interdendritic region. It was found that two Zn rich phases _E and decomposed sequentially during ageing at 170, 140 °C. The decomposition of the _E phase occurred as a discontinuous precipitation in the early stage of ageing and the decomposition of the phase took place in a four phase transformation: + T + in the prolonged ageing. Two typical morphologies of the decomposition of the Zn rich phases _E and were distinctive in back-scattered scanning electron microscopy.     

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.     

Fermi liquid behaviour of the viscosity of3He-4He mixtures

We have investigated³He-⁴He mixtures at³He-concentrations 0.98%x9.5% by the vibrating wire technique in the temperature range 1 mKT 100 mK and at pressures 0 bar p 20 bar. In the degenerate regime of the mixtures the Landau theory of Fermi liquids predicts a temperature dependence of the viscosity proportionalT ^–2. We report on the first observation of this behaviour at 3 mKT 10 mK for all investigated concentrations and pressures. At temperatures below about 20 mK slip corrections had to be taken into account due to the increase of the quasiparticle mean free path at very low temperatures. The low-temperature cut-off in T ² = constant indicates the transition into the ballistic regime of the mixtures, where the mean free path of the quasiparticles exceeds the radius of the vibrating wire. Our results for the pressure dependence of the viscosity as well as for its magnitude show substantial differences from predictions based on pseudopotential theory. However, a calculation of with the quasiparticle interaction potential of recent solubility measurements in mixtures agrees well with our experimental data, in particular the pressure independence of .     

The behavior of the4He viscosity near the superfluid transition

Measurements of the shear viscosity at saturated vapor pressure through the lambda transition indicate a singular behavior of the form |1 – (/)|=A ^x , (where =|1–(T/T )|, with equal values for the critical exponent on both sides of the transition.Work sponsored by Consiglio Nazionale delle Ricerche, Rome (Italy).     

Temperature-, concentration- and pressure-dependence of the viscosity of liquid3He-4He mixtures at low temperatures

We have investigated the viscosity of liquid³He-⁴He mixtures at various³He - concentrations (0.98%x9.5%) in the temperature range1 mK T 100 mK and at pressures 0 bar P 20 bar. At T10 mK the Fermi-liquid behaviour T² = const. as well as x^4/3 could be confirmed. However, there are significant deviations from theoretical predictions for the magnitude of the viscosity as well as for its pressure dependence.     

Shear viscosity measurements of liquid 4He and 3He-4He mixtures near the tricritical point

A torsional oscillator cell is described, by means of which simultaneous precision measurements of () and of the molar volume can be made in liquid ⁴He-⁴He mixtures over the temperature range between 0.5 and 3 K. Here is the mass density, the shear viscosity and in the superfluid phase they become the contributions _n and _n of the normal component. The results of for ⁴He near the superfluid transition are compared with the predictions by Schloms, Pankert and Dohm, and by Ferrell. Measurements of () are reported for mixtures with 0.64X0.74, where X is the ³He mole fraction. Those for X = 0.67 and 0.70 are compared with data by Lai and Kitchens. The viscosity experiments show no evidence of a weak singularity at the tricritical point.     

First viscosity of dilute3He-4He mixtures below 0.6 K

Starting with the Boltzmann transport equation, the first viscosity of dilute³He-⁴He mixtures for various³He concentrations x is evaluated up to around T 0.6 K by including the contribution from three-phonon processes (3PP) in the anomalous elementary excitation spectrum of liquid⁴He. Due to 3PP, the characteristic time for³He viscosity at high temperatures, i.e., T2T_F where T_F is the³He Fermi temperature, is evaluated as 5 × 10^–12/xT, which is smaller than the value estimated by Rosenbaum et al. This is interpolated with in the degenerate (quantum) region, TT_F. The obtained viscosities are in better agreement with experimental results than those of Baym and Saam, whose theory does not include 3PP. However, at very low concentrations there exists a discrepancy between the present theory and experiments, so that an alternate treatment should be considered.     

Effects of pressure sensitivity on the η factor and the J integral estimation for compact tension specimens

In this paper, the effects of pressure-sensitive yielding on the factor and the J integral estimation for compact tension specimens are investigated. The analytical expressions for and J for pressure-insensitive von Mises materials are generalized to pressure-sensitive Drucker-Prager materials using a lower bound approach. The factor as a function of the pressure sensitivity and the normalized crack depth for compact tension specimens is derived under plane stress and plane strain conditions. The numerical results indicate that the factor decreases as the pressure sensitivity increases. The effects are more pronounced under plane strain conditions than under plane stress conditions. However, the effects of the pressure sensitivity on are found to be mild in general. For rigid perfectly-plastic materials, the J estimation for pressure-sensitive materials is also reduced to a simple expression of the tensile yield stress times the crack tip opening displacement as for the von Mises materials.     

The viscosity and some related properties of liquid3He at the melting curve between 1 and 100 mK

The viscosity of liquid ³ He has been measured along the melting curve from 1 to 100 mK by means of a vibrating wire viscometer. In the normal Fermiliquid region we find 1/T² = 1.17–3.10T, where is in P and T in K. At the transition temperature T _A = 2.6 mK a rapid decrease occurs in _n , the viscosity of the normal component. Within 0.3 mK below T _A , _n decreases to about 25% of _A, but then becomes essentially constant. In the B phase _n first decreases to 20% of _A and then seems to increase below 1.4 mK. Data on _n , the density of the normal component, are also presented in the A and B phases. The results show that viscous flow is accompanied by a flow of zero dissipation, thus proving superfluidity in the A and B phases. The viscosity data at magnetic fields up to 0.9T have been related to theoretical calculations of the energy gap of superfluid ³ He near T _A . The splitting of the A transition and the suppression of the B phase in an external field were also measured.     

Coupling of order parameter collective modes to spin density in3He-B

We derive a general expression for the dynamic spin susceptibility of³He-B which is valid for all magnetic fields. The coupling of real and imaginary modes by particle-hole asymmetry is taken into account. Then we calculate the contribution of the mode at frequency =2 – 1/4 ( is the effective Larmor frequency) to the transverse susceptibility. The spectral weight of this mode in magnetic resonance absorption is proportional to (/)^1/2 (–)², where and are particle-hole asymmetry parameters. From the experimental coupling strength of the real squashing mode to sound we estimate (–)²10^–4. The dynamic susceptibility satisfies the sum rules of Leggett. Finally we point out the difficulties in calculating the transverse NMR frequency of³He-B. These difficulties arise from theS _z =0 Cooper pairs and from the coupling ofJ _z =±1 modes forJ=1 andJ=2.     

Ageing characteristics of cast Zn-Al based alloy (ZnAl7Cu3)

Microstructure and ageing characteristics of a cast Zn-Al based alloy (ZnAl7Cu3) were studied using X-ray diffraction, electron scanning microscopy and back-scattered diffraction techniques. Two stages of phase transformation, i.e., decomposition of zinc rich phase and four phase transformation, + T + , were detected during ageing at 150°C. Electron back-scattered diffraction technique was applied in distinguishing both zinc rich and phases.     

Universality and the scaling laws in the superfluid phase transition of3He-4He mixtures

From the second-sound velocityU ₂ near the superfluid transition point, the superfluid densities in³He-⁴He mixtures, _s (X) and _s (), were deduced along the paths of constant³He concentrationX and of constant chemical potential difference of³He and⁴He. The following critical exponents of _s are determined: (a) =XX for _s (X) in the(X, T) plane,(b) X for _s (X) in the(, T) plane, and(c) for _s () in the(, T) plane. It is found that and _X change by about 4–6% relative to with increasing³He concentration up toX=0.4 and by 8–10% up toX=0.53. It seems that, belowX=0.53, universality hold for . Values of have been found to be in good agreement with the critical exponent of _s in pure⁴He under constant pressure. The values of and _X forX0.53 are also found to be consistent with the scaling relations in the (,T) plane of³He-⁴He mixture.Work performed in part while at the Electrotechnical Laboratory.     

Nonlinear bending of unsymmetric angle-ply plates with edges elastically restrained against rotation

Summary Based on the von Kármán-type plate theory a solution is formulated for the large deflection of an unsymmetrically laminated angle-ply rectangular plate under transverse and inplane loads. Each pair of opposite edges is assumed to be elastically restrained against rotation to the same degree. The transverse deflection and force function in governing equations are expanded into generalize double Fourier series such that all required boundary conditions are exactly satisfied. Numerical results for maximum deflection, bending moment and inplane force in the plate are graphically presented for various aspect ratios, types of transverse load, high-modulus composite materials, numbers of layers, angles of orientation and boundary conditions. Present results for simple boundary conditions are in good agreement with previous data.Notations plate stiffnesses defined in [4], [9] - a, b, h length, width and thickness of plate - a _i ,b _i plate constants defined in [4] - E _L ,E _T ,G _LT ,v _itLT principal elastic constants of orthotropic material - F nondimensional force function defined in Eqs. (3) - F _mn ,Q _mn ,W _mn Fourier constants defined in Eqs. (9), (10) and (21) - H _i constant given by Eq. (19) - N ,M ,M nondimensional moments defined in Eqs. (6) - N ,N ,N nondimensional inplane forces defined in Eqs. (6) - nondimensional inplane load defined in Eqs. (8) - Q nondimensional transverse load defined in Eqs. (3) - q,q _o intensities of general and uniform transverse loads - R _m ,S _n ,X _m ,Y _n orthogonal functions of or defined by Eqs. (11) and (12) - r inplane load ratio defined in Eqs. (8) - x, y, z rectangular cartesian coordinates - W, w nondimensional deflection,w/h, and deflection - _m , _m , _m constant coefficients given by Eqs. (13)–(15) - , nondimensional coordinates defined in Eqs. (3) - aspect ratio (a/b) - ₁, ₂ rotational edge-restraint coefficients With 6 Figures     

A Viscosity Equation of State for R123 in the Form of a Multilayer Feedforward Neural Network

A multilayer feedforward neural network (MLFN) technique is adopted for developing a viscosity equation =(T, ) for R123. The results obtained are very promising, with an average absolute deviation (AAD) of 1.02% for the currently available 169 primary data points, and are a significant improvement over those of a corresponding conventional equation in the literature. The method requires a high-accuracy equation of state for the fluid to be known to convert the experimental P, T into the independent variables , T, but such equation may not be available for the target fluid. With a view to overcoming this difficulty, a viscosity implicit equation of state in the form of T=T(P, ), avoiding the density variable, is obtained using the MLFN technique, starting from the same data sets as before. The prediction accuracy achieved is comparable with that of the former equation, =(T, ).     

Effective Free Energy for Solidification of Superfluid 4He Under Pressure

Effective free energy for the solidification of the superfluid ⁴ He under pressure is presented. Since this free energy is a function of two parameters, the density change and the translational symmetry breaking parameter , it is expected to describe over both the superfluid phase and the solid phase.The experimentally established values below and equal to the melting pressure P_m are successfully reproducible by the free energy. For P>P_m, where the superfluid is metastable, the free energy predicts that the instability for should occur first and then accompanies. That is, -nucleation is essential for the solid nucleation in the superfluid ⁴ He.     

Rayleigh linewidth in4He near the gas-liquid critical point

Spectra of Rayleigh-scattered light in⁴He near the gas-liquid critical point have been measured, using a photon correlation method. Fitting the obtained relaxation times to Kawasaki's expression with background modification, we have obtained along the critical isochore the correlation length =(3.6±0.78)^{–0.534±0.046} Å and the high-frequency shear viscosity *=21.5±3.6 µP. * has been revealed to be in good agreement with the regular part of the viscosity _r=21±2µP. The singular part of the thermal diffusivity has been determined to beD _Ts =(4.9±2.7)×10^{–5–0.543±0.046} cm²/sec along the critical isochore.     

p-Version two-dimensional curved beam element using piecewise hierarchical approximation for laminated composites

A three node two-dimensional laminated composite curved beam finite element formulation for linear static analysis is presented where the displacement approximation for the laminate is piecewise hierarchical and is derived based on p-version. The displacement approximation for the element is developed by establishing a hierarchical displacement approximation for each lamina of the laminate and then by imposing interlamina continuity conditions of displacement at the interfaces between the laminas. The approximation functions and the nodal variables for each lamina are derived directly from the Lagrange family of interpolation functions of order p and p . This is accomplished by first establishing one-dimensional hierarchical approximation functions and the corresponding nodal variable operators in the and directions for the three and one node equivalent configurations that correspond to p +1 and p +1 equally spaced nodes in the and directions and then taking their products. The nodal variables for the entire laminate are derived from the nodal variables of the laminas and the interlamina continuity conditions of displacements. The element formulation ensures C ⁰ continuity of displacement across the interelement as well as interlamina boundaries.The individual lamina stiffness matrices and the equivalent nodal force vectors are derived using principle of virtual work and the hierarchical displacement approximation for the laminas. Interlamina continuity conditions are used to construct the transformation matrices for the laminas. These matrices permit transformation of the lamina degrees of freedom to the laminate degrees of freedom. Using these transformation matrices, individual lamina stiffness matrices and the equivalent load vectors are transformed and then summed to obtain the laminate element stiffness matrix and equivalent load vectors. There is no restriction on the number of laminas and their lay up pattern. Each layer can be generally orthotropic. The material directions and the layer thickness may vary from point to point within each lamina. The geometry of the curved beam element is defined by the nodes located at the middle surface of the element and the lamina thicknesses.Numerical examples are presented to demonstrate the accuracy, efficiency, convergence characteristics and the advantages of the present formulation. The results obtained from the present formulation are compared with the analytical solution and with those reported in the literature.     

Transport properties of Fermi fluids at finite temperatures

A method based on Landau's Fermi-fluid theory is presented for calculating the temperature-dependent viscosity and thermal conductivity of a Fermi fluid. It is argued that both O(T) and O(T² ln T) terms appear in the temperature series expansions for T ² and T. Exact expressions for the zero-temperature limit of T ² and T are derived for the dilute hard-sphere Fermi gas (DHSFG). The leading finite-temperature corrections to these quantities due to the s dependence of the quasiparticle scattering amplitude are also derived for the DHFSG (s is a dimensionless ratio of energy transfer to momentum transfer). The results are compared with previous expressions of Emery and of Dy and Pethick; some discrepancies are noted and discussed.Based in part on a Ph.D. thesis by J.C.R. submitted to the University of Colorado.     

Viscoelastic and rheological behavior of concentrated colloidal suspensions

Molecular approaches are discussed to the density (), viscoeleastic (), and rheological () behavior of the viscosity(,,) of concentrated colloidal suspensions with 0.3 < < 0.6, where, is the volume fraction, the applied frequency, and ; the shear rate. These theories are based on the calculation of the pair distribution functionP ₂(r,,), wherer is the relative position of a pair of colloidal particles. The linear viscoelastic behavior(,,=0) follows from an equation forP ₂(r,,) derived from the Smoluchowski equation for small, generalized to large by introducing the spatial ordering and (cage) diffusion typical for concentrated suspensions. The rheological behavior(,,=0) follows from an equation forP ₂(r,) of a dense hard-sphere fluid derived from the Liouville equation. This leads to a hard-sphere viscosity^hs(,) which yields the colloidal one(,) by the scaling relation(,) ₀=^hs(,) _B, where ₀ is the solvent viscosity. _B is the dilute hard-sphere (Boltzmann ) viscosity and the's are appropriately scaled,(,) and(,) agree well with experiment. A unified theore for(,,) is clearly needed and pursued.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994. Boulder, Colorado, U.S.A.     

A finite volume technique to simulate the flow of a viscoelastic fluid

Hydrodynamically developing flow of Oldroyd B fluid in the planar die entrance region has been investigated numerically using SIMPLER algorithm in a non-uniform staggered grid system. It has been shown that for constant values of the Reynolds number, the entrance length increases as the Weissenberg number increases. For small Reynolds number flows the center line velocity distribution exhibit overshoot near the inlet, which seems to be related to the occurrence of numerical breakdown at small values of the limiting Weissenberg number than those for large Reynolds number flows. The distributions of the first normal stress difference display clearly the development of the flow characteristics from extensional flow to shear flow.List of symbols D rate of strain tensor - L slit halfheight - P pressure, indeterminate part of the Cauchy stress tensor - R the Reynolds number - t time - U average velocity in the slit - u velocity vector - u,v velocity components - W the Weissenberg number based on the difference between stress relaxation time and retardation time - W ₁ the Weissenberg number based on stress relaxation time - x,y rectangular Cartesian coordinates - ratio of retardation time to stress relaxation time - zero-shear-rate viscosity, ₁ + ₂ - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to - ₁ stress relaxation time - ₂ retardation time - density - (, , ) xx, yy and xy components of ₁, respectively - determinate part of the Cauchy stress tensor - ₁ non-Newtonian contribution to - ₂ Newtonian contribution to