Convective instability of a layer of a ferromagnetic fluid rotating about a vertical axis

Thermal instability in a layer of a ferromagnetic fluid rotating about a vertical axis and permeated by a vertical magnetic field is investigated within the framework of linear theory. Overstability cannot occur if the Prandtl number $\text{P > 1}$. For overstable oscillations, Rayleigh number is plotted as a function of wave number for several values of the magnetization parameter $\text{M}{}_3$. Critical Rayleigh number is found to decrease with increase in $\text{M}{}_3$.     

Magnetohydrodynamic stratified flow past a sphere

This paper considers the uniform, steady, horizontal flow of a vertically stratified, electrically conducting, non-diffusive fluid over a non-conducting sphere in the presence of a uniform magnetic field. The force exerted on the sphere is investigated on the basis of the method of matched asymptotic expansions, for small values of a stratification parameter α, $\text{R}{}_{\mathrm{e}}\text{? ¦α¦}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$, $\text{F}{}_{\mathrm{r}}{}^2\text{? ¦α¦}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ and for $\text{M}{}^2\text{= 0(α}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Up to the first order of calculations the drag is computed for a few typical values of magnetic interaction parameter when, (a) The applied magnetic field lies in the vertical plane and inclined with the ambient flow direction. (b) The applied magnetic field lies in the horizontal plane and perpendicular to the flow direction. Further it is shown that the sphere has no tendency to rotate nor it experiences a lift force upto the order of calculations which we have made. The drag experienced by the sphere is found to be increased due to the combined effects of stratification and magnetic field.     

Stiffness derivative finite element technique to determine nodal weight functions with singularity elements

The use of the stiffness derivative technique coupled with “quarter-point” singular crack-tip elements permits very efficient finite element determination of both stress intensity factors and nodal weight functions. Two-dimensional results are presented in this paper to demonstrate that accurate stress intensity factors and nodal weight functions can be obtained from relatively coarse mesh models by coupling the stiffness derivative technique with singular elements.The principle of linear superposition implies that the calculation of stress intensity factors and nodal weight functions with crack-face loading, σ($\text{r}{}_{\mathrm{s}}$), is equivalent to loading the cracked body with remote loads, which produces σ($\text{r}{}_{\mathrm{s}}$) on the prospective crack face in the absence of crack. The verification of this equivalency is made numerically, using the virtual crack extension technique. Load independent nodal weight functions for two-dimensional crack geometry is demonstrated on various remote and crack-face loading conditions. The efficienct calculation of stress intensity factors with the use of the “uncracked” stress field and the crack-face nodal weight functions is also illustrated.In order to facilitate the utilization of the discretized crack-face nodal weight functions, an approach was developed for two-dimensional crack problems. Approximations of the crack-face nodal weight functions as a function of distance, ($\text{r}{}_{\mathrm{s}}$), from crack-tip has been sucessfully demonstrated by the following equation: $\text{h(a, r}{}_{\mathrm{s}}\text{,) =}\text{A(a)}\text{√r}{}_{\mathrm{s}}\text{+ B(a) + C(a)√r}{}_{\mathrm{s}}\text{+ D(a)r}{}_{\mathrm{s}}$.Coefficients $\text{A(a)}$, $\text{B(a)}$, $\text{C(a)}$ and $\text{D(a)}$, which are functions of crack length ($\text{a}$), can be obtained by least-squares fitting procedures. The crack-face nodal weight functions for a new crack geometry can be approximated using cubic spline interpolation of the coefficients $\text{A, B, C}$ and $\text{D}$ of varying crack lengths. This approach, demonstrated on the calculation of stress intensity factors for single edge crack geometry resulted in total loss of accuracy of less than 1%.     

Propagation of waves in the interior of a thermoelastic dielectric half-space

This paper presents a plane Lamb problem for a semi-infinite thermoelastic dielectric body. The loading acting on the boundary is separated into two systems: the first is associated with the displacement field $\text{u}\text{?}\text{= (u}{}_1\text{, u}{}_2\text{, 0)}$, the polarization field, $\text{P}\text{?}\text{= (P}{}_1\text{, P}{}_2\text{, 0)}$, the electric potential field, φ, and the temperature field, θ; the second system is related to the components $\text{u}{}_3$ and $\text{P}{}_3$ only. A general solution for these systems is derived. The last section of the paper is devoted to 1-dimensional problems and the results therefrom are used to obtain a closed-form solution for the case in which the surface energy is assumed to vary harmonically and the boundary conditions are homogeneous.     

Elastodynamic near-tip fields for a crack propagating along the interface of two orthotropic solids

The elastodynamic stress field near a crack tip rapidly propagating along the interface between two dissimilar orthotropic elastic solids is solved numerically, for in-plane motion. The cartesian displacements are sought in the separated forms, $\text{r}{}^{\mathrm{p}}\text{U(θ)}$ and $\text{r}{}^{\mathrm{p}}\text{V(θ)}$, $\text{r}$ and θ being polar coordinates centered at the moving tip. This reduces the mathematical statement of the problem to two complex second-order linear ordinary differential equations for complex functions $\text{U(θ)}$ and $\text{V(θ)}$. By means of the finite difference method, a matrix eigenvalue problem of the type $\text{ΣA}{}_{\mathrm{ij}}\text{(p)X}{}_{\mathrm{j}}\text{= 0}$, is obtained where $\text{A}{}_{\mathrm{ij}}\text{(p)}$ are polynomials of the complex variable $\text{p}$ and $\text{X}{}_{\mathrm{j}}$, are complex unknowns. An iterative numerical scheme for determining $\text{Im(p)}$ is developed and the roots $\text{p}$ as well as angular stress and displacement distributions are calculated and plotted for various material combinations. Comparison with exact solutions for the case of dissimilar Isotropie solids indicates good accuracy of the numerical solution. The orthotropic nature of the materials is shown to have a significant effect on stress maximums.     

Electrical properties of ferromagnetic Gd3−xS4 near its Curie temperature

Nonstoichiometric $\text{Gd}{}_{\mathrm{<mtext>3?</mtext><mtext>x</mtext>}}\text{S}{}_4\text{(0 <}\text{x}\text{<}\text{1}\text{3}\text{)}$, which exhibits a metallic behavior, was obtained by heating an insulating Gd₂S₃ at various temperatures under a vacuum. Electrical and magnetic properties of the samples obtained have been investigated from 4.2 K to 300 K. A maximum in resistivity was observed in the curve of resistivity vs. temperature. The temperature T_P, at which the maximum emerged, was very close to the Curie temperature T_C for the sample. An increase in resistivity at T_P, Δ_?, is proportional to ?_P exp ($\text{E}\text{k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{P}}$), where ?_P is the resistivity obtained by the extrapolation from the linear portion to T_P in the ? vs. T curve. Using the relationship obtained, a model based on the formation of magnetic polaron was proposed for this system.     

A modified thickness criterion for fracture toughness testing

A modified criterion is developed on an empirical basis for the minimum thickness $\text{B}{}_{\min }$ of a plane strain fracture toughness test specimen: $\text{B}{}_{\mathrm{<mtext>min</mtext>}}\text{= 400}\text{K}{}_{\mathrm{Ic}}{}^2\text{Eδ}{}_{\mathrm{Y}}$ where $\text{K}{}_{\mathrm{Ic}}$ is the plane strain fracture toughness, $\text{E}$ is the Young's modulus and δ_Y is the yield stress of the material. The modified criterion is tested alongside the ASTM thickness criterion against published data on the variation of $\text{K}{}_{\mathrm{c}}$ with thickness, and shows significantly the better agreement with observed values of $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$ for a wide range of materials.An attempt has been made to rationalise this criterion. The expression is considered to take into account two major factors which determine $\text{B}{}_{\mathrm{<mtext>min</mtext>}}$, the attainment of plane strain in the specimen interior ahead of the crack tip, and the role of microstructure in determining how far the quasi-plane strain fracture (square fracture) extends beyond the region of true plane strain.     

Une modelisation du comportement magnetique d'un compose de l'iridium pentavalent: LaLi12Ir12O3

A new interpretation is proposed for the magnetic properties of perovskite-type iridium (+V) oxide $\text{LaLi}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{Ir}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{O}{}_3$. In its unusual +5 oxidation state iridium has a t⁴_2ge⁰_g configuration. The magnetic susceptibility has been calculated assuming cubic symmetry of the crystal field and a Coulomb repulsion of the same order of magnitude than spin-orbit coupling. Fitting of the experimental data leads to a single spin-orbit constant $\text{ζ ? 3470}\text{cm}{}^{\mathrm{?1}}$ close to that of previously investigated Ir(+V) compounds.     

On the thermal and mechanical properties of slender-fibre reinforced materials at non-dilute concentration

The slender-body theory as applied to a dilute suspension of nearly-rigid and nearly-perfect conducting fibres in an elastic matrix predicts an increase in the composite Young modulus and thermal conductivity along the direction of the applied field of the order $\text{l}{}^2\text{/R}{}_0{}^2$, where 2$\text{l}$ is the length of the fibre and $\text{R}{}_0$ is its representative radius. As a consequence of the diluteness assumption, the fibre-contributed stress or heat flux is never more than a perturbation of the stress or the heat flux due to the ma rix. At non-dilute concentration range, where the average distance between neighbouring fibres is very much less than $\text{l}$ but yet much greater than $\text{R}{}_0$, Batchelor's ideas can be applied to show that the dilute formulae continue to give accurate predictions, and that an order of magnitude increase in Young modulus or thermal conductivity is possible at this level of concentration.     

A comparison of the geometry dependence of several nonlinear fracture toughness parameters

A number of fracture toughness tests on compact tension specimens have been performed for the purpose of comparing several nonlinear fracture toughness methods; including the nonlinear energy ($\text{G}\text{?}{}_{\mathrm{I}}$), J-integral ($\text{J}{}_{\mathrm{I}}$), COD ($\text{G}{}_{\mathrm{\delta }}$), and linear (–$\text{G}{}_{\mathrm{I}}$) approaches. The effect of variations in specimen thickness ($\text{B}$) and width ($\text{w}$) on the fracture toughness was examined for 7075-T651, 2124-T851, 2048-T35I, and 2048-T851 aluminum alloys, Ti-6Al-4V, and 4340 steel. Fracture toughness values were evaluated at both the initiation of stable crack growth and the onset of unstable fracture (peak load).It was found that the peak load toughness values are quite geometry sensitive at thicknesses below the requirement for plane strain fracture. At the initiation of stable crack growth, the toughness values are constant over a much larger range of specimen thickness. However, the nonlinearity of the load displacement curve is quite limited at this point and the associated fracture toughness is only 30–50% of the peak-load values.     

Transient field losses in multifilamentary composite conductors carrying dc transport currents

Theoretical studies are presented for transient field losses in multifilamentary composite conductors carrying a dc transport current. The analysis of the total loss is split into separate calculations of the magnetization loss and the loss due to the dynamic resistance. Analytical expressions are derived for a field change of trapezoidal shape. The parameter which characterizes the total loss is a dimensionless sweep rate of the external field $\text{β = τ}\text{B}\text{?}{}_{\mathrm{<mtext>e</mtext>}}\text{/B}{}_{\mathrm{<mtext>p</mtext>}}$, where τ is the relaxation time of the eddy current and B_p is the full-penetration field of the composite conductor. Graphs for a wide range of the field change rate are given and they reveal the strong influence of the transport current.     

The stress field near the blunt crack tip and the fracture criterion

The asymptotic expansion solution containing two terms for the stress field near the blunt crack tip is obtained. It is proposed that the slit be divided into the ideal crack, blunt crack I, blunt crack II and the notch in accordance with the geometrical structure of the slit tip. Whether the blunt crack can be considered as the ideal crack will depend mainly on the following three factors: $\text{√}\text{2R}{}_0\text{C}$, $\text{√}\text{R}{}_0\text{r}{}_{\mathrm{c}}$ and the profile of the crack. In this paper, the influence of the crack tip radius on the fracture criterion is studied and it is shown that the classical strength theories belong to the unconditional extremum criteria while the S criterion, etc. in fracture mechanics belong to the conditional extremum criteria. A modified maximum tension stress theory is developed, in which the fracture theories of the crack and the notch can be roughly unified.     

Control of the growth-induced magnetic anisotropy in ferrimagnetic garnet films grown by liquid-phase epitaxy

The influence of melt composition and growth temperature T_g on the growth-induced magnetic anisotropy constant K^g_u in Bi substituted LPE ferrimagnetic garnet films has been investigated. In films grown from Bi₂O₃ based and from $\text{PbO}\text{B}{}_2\text{O}{}_3$ based melts the value of K^g_u increased upon decreasing T_g, associated with an increasing incorporation of B1. However, at given Bi content the films grown from Bi₂O₃ based fluxes generally exhibited smaller values of K^g_u than those from $\text{PbO}\text{B}{}_2\text{O}{}_3$ based melts. The addition of small amounts of Ca²⁺ to the Bi₂O₃ based melts resulted in (Y,Bi)-garnet films changing from n- to p-type electrical conductivity at a minimum value of K^g_u. Additions of Si⁴⁺ to a $\text{PbO}\text{B}{}_2\text{O}{}_3$ based melt reduced the uniaxial magnetic anisotropy of La-YIG-Ga films accompanied by a change from p- to n-type conductivity. Similarly, (Gd,Bi)-garnet films from $\text{PbO}\text{B}{}_2\text{O}{}_3$ based melts changed from n- to p-type conductivity upon decreasing T_g where K^g_u changes sign from negative to positive. From the temperature dependence of the electrical conductivity the electron and hole concentrations in some of these films were estimated suggesting that the sign change of K^g_u in the investigated (Gd,Bi)-garnet films and the minimum of K^g_u in the investigated (Y,Bi)-garnet films and (La,Y)-garnet films occur at donor-acceptor compensation. This experimental evidence led us to conclude that the growth induced magnetic anisotropy may be correlated with the presence of donor and acceptor centers in the garnet structure.     

A correlation of critical points

Critical points were correlated for fluids which obey the three-parameter equation of state according to which the compressibility factor, $\text{Z=}\text{P}\text{dRT}$, is given by Z=1 + k_Bδκ (θ, δ), in which κ (θ, δ) is a universal function of reduced temperature, $\text{θ =}\text{T}\text{T}{}_{\mathrm{B}}$, and reduced density, $\text{δ =}\text{d}\text{d}{}_{\mathrm{<mtext>O</mtext>}}$. The three parameters which distinguish one fluid from another are k_B, T_B, and d_O. It is shown that experimental inflection points of the pressure versus density isotherms of gases obeying this equation of state all fall on the same reduced curve of θ versus δ. Critical points also must lie on this curve, at a location dependent on k_B. Critical densities are too uncertain experimentally to permit a definite correlation, but the critical temperatures of sixteen fluids are shown to fall on a common θ_c versus k_B curve with an average deviation of 0.4 degrees. The critical pressures of these same fluids lie within a few tenths of an atmosphere on a common π_c ($\text{π =}\text{P}\text{d}{}_{\mathrm{<mtext>O</mtext>}}\text{RT}{}_{\mathrm{<mtext>B</mtext>}}$) versus k_B line. This correlation of critical points is accomplished using values of the three parameters that had previously been determined by fitting supercritical PVT data to the equation of state.     

Viscous dissipation effects on mixed convection about a rotating sphere

The effect of viscous dissipation on mixed convection flow about a rotating sphere is investigated analytically. A method based on Merk's type of series expansions is used to obtain the heat transfer rate and the skin-friction coefficients. Numerical computations were carried out for Eckert number Ec ranging from 0 to 0.1, rotation parameter B = 0, 1, 4 and buoyancy parameter ranging from 0 to 1 at various angular positions. As viscous dissipation increases heat transfer rate decreases. It is found that for Ec > 0, a critical value of B (say B_cri) exist such that $\text{Nu Re}{}_{\mathrm{R}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ increases as B increases up to B = B_cri and then decreases. B_cri decreases with Ec when the angle is fixed or decreases with angle when Ec is fixed. When Ec > 0, possibly there exist a λ, say λ_cri, such that $\text{Nu Re}{}_{\mathrm{R}}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ increases with λ up to λ = λ_cri and then decreases. Also the effect of viscous dissipation on skin friction is investigated.     

Identification of low energy ions (6 ≤ Z ≤ 10) in a plastic track detector CR-39

A method is developed for identifying low energy ions (6 ≤ Z ≤ 10) in a plastic track detector CR-39. After initial etching, rinsing in water and alcohol and final chemical etching of the detector, all in an ultrasound field, the etch rate ratio ($\text{V}{}_{\mathrm{<mtext>T</mtext>}}\text{V}{}_{\mathrm{<mtext>B</mtext>}}$) is directly measured at a defined distance from the end of the track. This method can be used to determine the etch rate ratio at several points along the track. The plastic track detector CR-39 is calibrated using ¹²C, ¹⁶O, ¹⁹F and ²²Ne ion energy in the interval from 2–7 MeV/amu.     

The use of small specimen strength ratio for measuring fracture toughness

The specimen strength ratio ($\text{R}{}_{\mathrm{s}}$), determined from small specimen tests was correlated with plane strain fracture toughness ($\text{K}{}_{\mathrm{Ic}}$) values for many heats of A533B-1 steel. A variety of loading rate and specimen size results suggest that $\text{K}{}_{\mathrm{Ic}}$ can be predicted from the small specimen strength ratio up to values of $\text{R}{}_{\mathrm{s}}$ near 2.0. Also, conservative estimates of cleavage-initiated, elastic-plastic fracture toughness can extend beyond $\text{R}{}_{\mathrm{s}}$ values of 2.0. The ASTM E399 size criterion appears to be too restrictive for the class of steel studied, and a more appropriate requirement would reduce the ASTM criterion by a factor of four.     

MHD flow in conducting circular expansions with strong transverse magnetic fields

This paper treats the steady, inertialess flow of an incompressible, electrically conducting fluid through perfectly conducting, variable-area ducts of circular cross section in the presence of strong transverse magnetic fields. The problem is of fundamental importance in the design of liquid-lithium cooling systems for fusion reactors, of liquid-metal MHD generators and of MHD machinery in metallurgy. First we find that, if a straight pipe of radius r is joined to an expansion or contraction, then the disturbance of the fully developed flow in the pipe dies out like exp ($\text{? 12.16¦x¦r}{}^{\mathrm{?1}}$), where x is distance from the join. Next we consider the flow in conical expansions with end effects neglected; and find that the flow becomes concentrated near the plane of symmetry as the divergence increases. Finally numerical schemes for determining the flow in more general expansions and contractions are outlined. Extension of the present analysis to non-circular sections is also discussed.