Deformation in spinel

Stoichiometric MgAl₂O₄ spinel was deformed in compression at temperatures from 1790 to 1895 C and the dislocation structures analysed by transmission electron microscopy. {1 1 1}1 1 0 slip was observed on both the primary and cross-slip systems, and there was much secondary slip as well; all six 1 1 0 Burgers vectors were present in electron micrographs. This secondary slip leads to very high work-hardening rates, approximately/70 at 1790 C, where is the shear modulus. Since it is known that deformation in nonstoichiometric (alumina-rich) spinel crystals occurs by {1 1 0}1 1 0 slip, the electrostatic and geometric aspects of 1/4 110 dislocations moving on {1 1 1} and {1 1 0} planes are considered in some detail. It is porposed that the octahedral cation vacancies present in non-stoichiometric spinel diffuse to dislocations during deformation and thus favour {1 1 0} slip.     

Flow visualization glass-ceramic: Preliminary experimental and modelling results

A glass-ceramic material was developed to act as a flow visualization material. Preliminary experiments indicate that aperiodic, thermally induced, convective flows can be sustained at normal processing conditions. These flows and the stress and temperature gradients induced are most likely responsible for the anomalous behaviour seen in these materials and the difficulties encountered in their development and in their production on industrial and experimental scales. A simple model describing the dynamics of variable-viscosity fluids was developed and was shown to be in qualitative agreement with more sophisticated models as well as with experimental results. The model was shown to simulate the dependence of the critical Rayleigh number for the onset of convection on the viscous properties of the fluid at low T, and also to simulate quenching behaviour when the temperature differences were high.Nomenclature C _p Heat capacity - D, E, F Expansion coefficients - H Height of the roll cell - Pr Prandtl number - R _a Rayleigh number - R _c Critical Rayleigh number for the onset of convection in a constant-viscosity fluid - S Dimensionless stream function - T Temperature - T _m Mean temperature - T ₀ Bottom surface temperature - T _r Reference temperature - a Aspect ratio of cell - g Acceleration due to gravity - k Thermal conductivity - k ₁ Function related to ²v/T ² - k ₂ Function related to ⁴v/T ⁴ - r Rayleigh number ratioR _a/R _c - t Time - w Dimensionless vertical coordinate - w _m Mean cell height - x Horizontal coordinate - y Dimensionless horizontal coordinate - z Vertical coordinate - , Constants - _t Thermal expansion coefficient - Constant in viscosity function - T Temperature difference between top and bottom surfaces - _i Viscosity coefficients - Kinematic viscosity - _m Mean kinematic viscosity - Dimensionless kinematic viscosity - Thermal diffusivity - Non-linear temperature function - Dimensionless non-linear temperature function - _o - Stream function - Dimensionless time - Eigenvalues     

The influence of brittle boundary layers on the strength of fibrous metallic composites

The brittle boundary layers often caused during the production of composites or by their treatment at higher temperatures, may change the mechanical properties. On the steel wire/aluminium system the growth of the intermetallic boundary phase and its influence on the strength of the composite were investigated. Hence followed a maximum strength at small layer thicknesses. By means of fracture investigations new models were developed which allow the calculation of the dependence of strength behaviour on layer thickness.List of symbols E _f Young's modulus of fibre - E _b Young's modulus of boundary layer - _c external load - _f tensile stress in the fibre - _m tensile stress in the matrix - _b tensile stress in the boundary layer - _uc,f,b ultimate strength of the composite, the fibre or the boundary layer, respectively - averaged stress in the fibre - _bf shear stress in the boundary layer-fibre interface - ₀ shear strength of the boundary layer-fibre-interface - _uf ultimate strain of the fibre - fraction of the layer which has grown into the matrix - Weibull parameter - ^–1 characteristic length of stress transfer between fibre and boundary layer - d diameter of the boundary layer - 2l length of the boundary layer segments - r _f fibre radius - u(x) displacement field - v _{f, b,m} volume fraction of fibres, boundary layer or matrix respectively.     

A mixed finite element formulation for shells through a reduced Reissner's principle in elastodynamics

Summary The use of Mixed models based in Reissner's principle in statics has been found to lead to some desirable simplifications in Finite Element formulations, in particular in plates and shells. Reduced formulations of Reissner's principle such as the one used by Prato have proved to be even more successful. In this paper, a reduction similar to that of Prato is attempted on a mixed elastodynamic variational principle by Karnopp.

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Eine gemischte finite Elemente-Formulierung für Schalen durch ein reduziertes Reissnersches Prinzip der Elastodynamik

Zusammenfassung Die Verwendung von gemischten Modellen basiert auf Reissners Prinzip der Statik führt zu erwünschten Vereinfachungen bei der Formulierung von finiten Elementen im speziellen bei Untersuchungen von Platten und Schalen. Reduzierungen des Reissnerschen Prinzips, wie sie von Prato angewendet worden sind, haben sich sogar als noch erfolgreicher erwiesen. In dieser Untersuchung wird eine Reduktion, ähnlich der von Prato, für ein gemischtes elastodynamisches Variationsprinzip nach Karnopp, vorgenommen.

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Symbol Table A Domain of integration of the Functional. Also area of the triangle - b Second fundamental form of the shell middle surface - C ^ijkl Elastic Constants - E ₁,E ₁ ^* Strain Energy and Co-Energy density - e _ij Elastic strain tensor - f _i Body force density tensor - I _ks Karnopp's functional, specialized to shells - I _ksc Contracted Karnopp's functional, specialized to shells - i, j, k Index 1, 2, 3 - K ₁,K ₁ ^* Kinetic Energy and Co-Energy density - K ^* Kinetic co-energy density for shell - m Moment tensor defined at the mid-surface - n In-plane stress tensor defined at the middle surface - n Qualifier for the boundary normal - p ,p ³ Boundary forces - Prescribed boundary forces - p Shear force tensor defined at the mid-surface - R Position vector of a point in the volume of the shell - r Position vector of a point on the mid-surface - r _i Net impulse density tensor - S _u Portion of the boundary where displacements are preseribed - S Portion of the boundary where forces are prescribed - s Qualifier for the direction tangent to the boundary - t Time variable - t ^ij Stress tensor - u ,u ₃ Mid-surface displacements - Mid-surface velocities - V Volume - v _i Displacement tensor - , Indices. Range 1, 2 - Shear strain tensor for the middle surface - Variation operator - Mid-surface strain tensor - Mid-surface curvature strain tensor - Direction cosine tensor for boundary normal - Mid-surface rotation tensor - Mid-surface angular velocity tensor - _M Strain energy density - _M * Strain co-energy density - _B * Bending strain co-energy density - _TS ^* Transverse shear strain co-energy density - | Covariant differentiation with respect tox , etc - Partial differentiation with respect tox , etc - .(dot) Time differentiation - -(bar) Prescribed quantities     

Carbon fibre-reinforced cement

This review describes fabrication processes for aligned fibre and random fibre carbonreinforced cement and links important process parameters with composite theory. The way in which the material fits into the general framework of crack constraint and matrix cracking theories is discussed. A broad survey is made of the mechanical properties, durability and dimensional stability of a variety of carbon-reinforced cement composites, and economic constraints on potential applications are considered.List of symbols b breadth of three-point bend specimen - d depth of three-point bend specimen - E _c composite Young's modulus - E _f fibre Young's modulus - E _m matrix Young's modulus - l fibre length - l _c fibre critical transfer length - l _s specimen span in three-point bend test - m Weibull modulus - r fibre radius - P applied load - V _f fibre volume fraction - V _m matrix volume fraction - x length of fibre needed to transfer load _mu V _m - x _d crack spacing in a composite with short, aligned fibres - _fu fibre ultimate strain - _mu matrix ultimate strain - _fu fibre ultimate strength - _mu matrix ultimate strength - _cu composite ultimate strength - _MOR modulus of rupture - _T tensile strength - interlaminar shear strength - _i interfacial shear strength - _m matrix work of fracture - _F work of fracture     

Shear viscosity of liquid4He and3He-4He mixtures,especially near the superfluid transition

High-resolution measurements of are reported for liquid⁴He and³He-⁴He mixtures at saturated vapor pressures between 1.2 and 4.2 K with particular emphasis on the superfluid transition. Here is the mass density, the shear viscosity, and in the superfluid phase both and are the contributions from the normal component of the fluid ( _n and _n ). The experiments were performed with a torsional oscillator operating at 151 Hz. The mole fraction X of³He in the mixtures ranged from 0.03 to 0.65. New data for the total density and data for _n by various authors led to the calculation of . For⁴He, the results for are compared with published ones, both in the normal and superfluid phases, and also with predictions in the normal phase both over a broad range and close to T. The behavior of and of in mixtures if presented. The sloped/dT near T and its change at the superfluid transition are found to decrease with increasing³He concentration. Measurements at one temperature of versus pressure indicate a decreasing dependence of on molar volume asX(³He) increases. Comparison of at T, the minimum of _n in the superfluid phase and the temperature of this minimum is made with previous measurements. Thermal conductivity measurements in the mixtures, carried out simultaneously with those of , revealed no difference in the recorded superfluid transition, contrary to earlier work. In the appendices, we present data from new measurements of the total density for the same mixtures used in viscosity experiments. Furthermore, we discuss the data for _n determined for⁴He and for³He-⁴He mixtures, and which are used in the analysis of the data.     

Large deformation theory of coupled thermoplasticity including kinematic hardening

Summary Thermoplasticity is a topic central to important applications such as metalforming, ballistics and welding. The current investigation introduces a thermoplastic constitutive model accommodating the difficult issues of finite strain and kinematic hardening. Two potential functions are used. One is interpreted as the Helmholtz free energy. Its reversible portion describes elastic behavior, while its irreversible portion describes kinematic hardening. The second potential function describes dissipative effects and arises directly from the entropy production inequality. It is shown that the dissipation potential can be interpreted as a yield function. With two simplifying assumptions, the formulation leads to a simple energy equation, which is used to derive a rate variational principle. Together with the Principle of Virtual Work in rate form, finite element equations governing coupled thermal and mechanical effects are presented. Using a uniqueness argument, an inequality is derived which is interpreted as a finite strain thermoplastic counterpart to the classical inequality for stability in the small. A simple example is introduced using a von Mises yield function with linear kinematic hardening, linear isotropic hardening and linear thermal softening.Symbols D rate of deformation tensor - d VEC(D) - F deformation gradient tensor - h heat generation per unit mass - L velocity gradient tensor - q heat flux vector - workless internal variable - Lagrangian strain - e VEC() - E quasi-Eulerian strain - entropy - internal energy per unit mass - Helmholtz free energy - Cauchy stress tensor - Truesdell stress flux tensor - t VEC() - yield function - First Piola Kirchhoff stress - Second Piola Kirchhoff stress - s VEC() - s ^* backstress, center of the yield surface - Kronecker product symbol - VEC vectorization operator - tr(.) trace - DEV deviator of a tensor - TEN22 Kronecker tensor operator     

Determination of the local angular radiation coefficients in certain two-body systems

A method is shown and formulas are derived by which local angular radiation coefficients can be determined in certain two-body systems where the configuration is arbitrary but one of the bodies is either a cylinder or a rectangular plate.Notation _int radiation vector of body 1 - _E ^int intrinsic radiation intensity of body 1 - _x, _y, _z components of the geometrical radiation vector along rectangular coordinates - r₀=x²+z² shortest distance from point M(x, y, z) to linear radiator - ₀ , ₀ ^' angles subtending the two segments of the linear radiator from point M(x, y, z) on area element 2 of irradiated surface - l length of the cylinders - x, y, z space coordinates of point M Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1080–1088, June, 1972.     

Stress relaxation in hot-drawn low density polyethylene

The tensile stress relaxation behaviour of hot-drawn low density polyethylene, (LDPE), has been investigated at room temperature at various draw ratios. The drawing was performed at 85° C. The main result was an increase in relaxation rate in the draw direction, especially at low draw ratios when compared to the relaxation behaviour of the isotropic material. This is attributed to a lowering of the internal stress. The position of the relaxation curves along the log time axis was also changed as a result of the drawing, corresponding to a shift to shorter times. The activation volume, , varied with the initial effective stress ₀ ^* according to ₀ ^* 10kT, where ₀ ^* =₀ — _i, is the difference between the applied initial stress, ₀, and the internal stress _i. This result supports earlier findings relating to similarities in the stress relaxation behaviour of different solids.     

A scaled equation of state for real fluids in the critical region

A scaled equation of state is proposed for real fluids in the critical region which incorporates asymmetry with respect to the critical isochore. In the range of reduced densities 0.65(/ _c)1.4 and for reduced temperatures (T/T _c)1.2, the equation represents P-V-T data for steam within the experimental accuracy.     

An investigation of structural transformation during the solidification of copper-gallium alloys

Metallographic examination, X-ray diffraction, X-ray spectral microanalysis, and mlcrohardness measurements were used to study structural changes during the solidification of copper-gallium alloys. It was shown that the solidification of these alloys in the temperature interval 40–200°C takes place as a result of the formation of the -phase. Long-term holding at 200 and 300°C leads to the formation of ₃-, ₂-, ₁-, and-phases.     

The effective surface energy of brittle materials

The effective surface energy of four brittle materials, alumina, poly(methylmethacrylate), glass, and graphite, is calculated from load/deflection curves of notched bars deformed in three-point bending. Two of the methods, which are commonly used in fracture mechanics studies,viz the modified Griffith treatment and the compliance analysis method, are concerned with the effective surface energy at the initiation of fracture, _I . The third method, the work of fracture test, is concerned with the mean effective surface energy over the whole fracture process, _F . The two estimates of _I give consistent values, and there is no systematic variation of _I with notch depth. Values of _F decrease with increasing notch depth as the fracture process becomes more controlled. For alumina _{I F} . For PMMA and glass _I > _F because of a multiplicity of crack sources during fracture initiation. For graphite _I < _F because of subsidiary cracking as fracture proceeds.     

Thermodynamic properties of antiferromagnetic superconductors containing nonmagnetic,magnetic, and spin-orbit impurities

Effects of all types of impurities (nonmagnetic, magnetic, and spin-orbit) on an antiferromagnetic superconductor (AFSC) have been investigated by studying the transition temperatureT _c and the specific heat jump. We have assumed a one-dimensional electron band. The impurity scattering is treated within the self-consistent Born approximation. We find that: (a) the molecular fieldH _Q and the magnetic impurities depress superconductivity of AFSC and their pair-breaking effect is additive; (b) the effect of spin-orbit impurities is the same as that of nonmagnetic impurities—these enhance superconductivity by screening the molecular field; and (c) in the extreme dirty limit, the AFSC is described in terms of an effective pair-breaking parameter given by 1/_eff=1/₂+H _Q ² where 1/=1/₁+2/3_so(1/₁, 1/₂, and 1/_so, respectively, are the scattering rates from nonmagnetic, magnetic and spin-orbit impurities).     

Chemical Transformations of γ-Al(OH)3during Closed-System Heat Treatment

The chemical transformations of -Al(OH)₃during closed-system heat treatment in a self-generated gaseous atmosphere (water vapor) were studied. At t 200°C, -Al(OH)₃was found to convert into -AlOOH, which, in turn, converts into the equilibrium phase -Al₂O₃at t 400°C. The processes underlying the effect of water vapor on the kinetics and mechanisms of the chemical transformations of -Al(OH)₃and -AlOOH in a closed system are discussed.     

Viscous oscillating cascade aerodynamics and flutter by a locally analytical method

A mathematical model is developed to analyze the viscous aerodynamics of an harmonically oscillating flat plate airfoil cascade in an incompressible laminar flow. The steady flow field is described by the Navier-Stokes equations, with the unsteady viscous flow modeled as a small perturbation to this steady flow. Solutions for both the steady and the unsteady viscous flow fields are then obtained by developing locally analytical solutions. The significant effects of Reynolds number, elastic axis, interblade phase angle and incidence angle on the oscillating cascade unsteady aerodynamics and torsional flutter characteristics are then demonstrated.List of symbols C airfoil chord - C _M unsteady moment coefficient - k reduced frequency, U/U - Re Reynolds number, U C/v - S cascade spacing - U free-stream velocity magnitude - x _ea elastic axis location - x mean flow direction coordinate - y normal flow direction coordinate - y _m mean airfoil position - x x-direction step size - y y-direction step size - (x ₀, y ₀) center of grid element - ₀ mean flow incidence angle - amplitude of airfoil oscillation - interblade phase angle - nondimensional unsteady stream function - nondimensional steady stream function - nondimensional unsteady vorticity - nondimensional steady vorticity - cascade stagger angle     

Density Response and Equilibration in a Pure Fluid Near the Liquid-Vapor Critical Point: 3He

We report measurements of the local density response inside a quasi 1-D horizontal ³ He fluid layer to a step-like change T of the boundary temperature, where |T| 80 K and much smaller than |T – T_c| where T_c is the critical temperature. These experiments used a new cell design, described in the text, and were carried out along the critical isochore both above and below T_c. The observed temporal and spatial density response (t, z) and its equilibration time are described adequately by the relations developed from the thermodynamic theory of Onuki and Ferrell. We verify that over the temperature range of low stratification, where computer simulations and closed-form calculations can be compared, they are in exact agreement. The systematic differences of experimental results from predictions can be accounted for by the departure of the cell from the ideal 1-D geometry. The much larger disagreement between the experimental and predicted equilibration time scale in earlier experiments is also explained. Finally, deviations from linearity observed in the density response for steps |T| larger than 90 K are reported and the implications of such nonlinearity for the (t, z) profile and especially the effective relaxation time _eff are analyzed. We also discuss the predicted onset of convection near T_c for the conditions in our experiment. In the Appendix, the likely sources for systematic deviations in the density response function for the experimental cell from calculations in the ideal 1-D geometry are presented and their effects calculated. The so-obtained response function Z_F(, z) is compared with previously published data.     

Die Herleitung von Schalengleichungen über ein erweitertes Variationsprinzip bei Berücksichtigung der Querschubverzerrungen

Ohne ZusammenfassungBezeichnungen L Bezugsgrößen für dimensionslose Koordinaten - L charakteristische Schalenabmessung - t Schalendicke - Schalenparameter - körperfeste, krummlinige, dimensionslose Koordinaten der Schalenmittelfläche - Dimensionslose Koordinate in Richtung der Schalennormalen - i, j,...=1,2,3 Indizierung des dreidimensionalen Euklidischen Raumes - ,,...=1,2 Indizierung des zweidimensionalen Riemannschen Raumes - (...), Partielle Differentiation nach der Koordinate - (...), Kovariante Differentiation für Tensorkomponenten des zweidimensionalen Raumes nach der Koordinate - (...)| Kovariante Differentiation für Tensorkomponenten des dreidimensionalen Raumes nach der Koordinate - Variationssymbol - a ,a ₃ Basisvektoren der Schalenmittelfläche - V Verschiebungsvektor - U ,U ₃ Verschiebungskomponenten des Schalenraumes - v ,w,w ,W Verschiebungskomponenten der Schalenmittelfläche - Verhältnis der Metriktensoren des Schalenraumes und der Schalenmittelfläche - _ik Verzerrungstensor des Raumes - _{(, )}, Symmetrische Verzerrungstensoren der Schalenmittelfläche - _{[, ]} Antimetrischer Term des Verzerrungsmaßes - ^, Spannungstensor - n ,m ,q Tensorkomponenten der Schnittgrößenvektoren - p ,p,c Tensorielle Lastkomponenten     

Heat capacity near the lambda point in 4He under pressure. Experimental test of scaling laws and universality

C _p along six isobars was determined near T from measurements of C _v and (P/T) _v along isochores. The critical exponent was independent of pressure, while was dependent on pressure, when the data are fitted to a single power law. The value of A/A was found to be 1.04 ± 0.05 over the entire pressure range by adding a higher order singularity. That is, the results obtained are the best fit using renormalization group theory, but are partly inconsistent with the heat capacity measurement by Ahlers.     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

Dependence of helium II viscosity properties on oscillation frequency

The causes of a discrepancy in the results of measurements of He II viscosity below T 1.6 k obtained with different measurement methods are investigated. It is shown that to obtain correct results in oscillation experiments, the condition _ph should obtain, where is the depth of viscous wave penetration and _ph is the phonon free path length. Results of viscosity measurements at different ratios /_ph (by a wire viscometer) are presented. It is shown that for the condition _ph, the results obtained are in good agreement with the results of Andronikashvili (in which /_ph > 100). If the mentioned relation is not satisfied, then, as the value of the ratio /_ph is decreased, the value measured for the viscosity is increasingly lower than the results of Andronikashvili.