Dependence of the contact heat conductivity of granular systems on the external load

An examination has been made of the dependence of the contact heat conductivity of granular systems on the external load. The calculation formulas proposed for contact heat conduction are applicable over a wide range of materials.Notation s_a area of actual contact of two particles in a granular material - _c conductivity of the contact between two particles - h_r height of a micro-roughness - _s thermal conductivity of the material of the particles - d=2r particle diameter - _c contact thermal conductivity of the granular material - p porosity of the system - S_a1, S_a2 area of contact of two particles in the freely poured state and under the action of a load - f thermal conductivity of the granular system in the freely poured state - () portion of the thermal conductivity of a granular material that depends on the external load - relative area of contact - s_n nominal area of contact of the two particles - external specific load - E modulus of elasticity of the particle material - E₀ effective modulus of elasticity of the granular material - k₁, k₂, k₃, k_m, k_b empirical coefficients     

Equations of generalized thermoelasticity of a Cosserat medium in stresses

Thermoelasticity equations in stresses are derived in this paper for a Cosserat medium taking into account the finiteness of the heat propagation velocity. A theorem is proved on the uniqueness of the solution for one of the obtained systems of such equations.Notation u displacement vector - small rotation vector - absolute temperature - ₀ initial temperature of the medium - relative deviation of the temperature from the initial value - , , , , , ,, m constants characterizing the mechanical or thermophysical properties of the medium - density - I dynamic characteristic of the medium reaction during rotation - k heat conduction coefficient - ₀ a constant characterizing the velocity of heat propagation - X external volume force vector - Y external volume moment vector - w density of the heat liberation sources distributed in the medium - E unit tensor - T force stress tensor - M moment stress tensor - nonsymmetric strain tensor - bending-torsion tensor - s entropy referred to unit volume - V volume occupied by the body - surface bounding the body - (T)_ki, (M)_ki components of the tensorsT andM - q thermal flux vector Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 482–488, March, 1981.     

An instability mechanism for the sliding motion of finite depth of bulk granular materials

Summary Field observations and experimental records indicate that the primary mode of motion of many large landslides is that ofsliding rather thanflowing. Most of shear during sliding is concentrated at the base of slides, with little or no mixing taking place away from the base. This sliding motion may generate strong pressure waves at the interface between the quasi-static deforming granular mass and the grain-inertia dominated rapid granular flow, thus inducing a Kelvin-Helmholtz type instability mechanism for large landslides. The existence of a transitional zone in granular flow is essential for the generation of this type of instability waves. A model using a finite depth of elastic sliding bulk granular materials riding on a basal granular shear flow layer is estabilished to represent the sliding motion of these large volume of bulk granular materials. The balance and the stability of this sliding system are investigated under the perturbation of internal pressure waves. The generated instability waves will force favorable phase shifts between the overburden pressure and the sliding velocity, leading to a net reduction in the total power loss due to friction. The depth of sliding mass will affect the generation of this type of instability waves. Both analytical and numerical results show that smaller depth slides can induce stronger instability waves than larger depth slides do.Notation a perturbation wave amplitude - C nondimensional instability wave speed - C _i growth rate, the imaginary part ofC - C _r wave phase speed, the real part ofC - c _p compressional wave speed in elastic medium - c _s shear wave speed in elastic medium - D nondimensional depth of sliding mass - d depth of sliding mass - G shear modulus of elastic medium - H nondimensional basal depth - h depth of basal shear zone - i - K Coulomb friction coefficient - P _xx, P_yy lateral and normal pressures in granular material, respectively - P _xy shear stress in granular material - p ₀ amplitude of perturbation pressure - p _yy perturbation pressure - r nondimensional complex wave number of instability wave - S nondimensional wave number of shear wave - t time scale - U uniform sliding velocity of a landslide inx direction - u, v velocities inx direction andy direction, respectively - u ₀ granular flow velocity in the basal shear zone - V, V _c nondimensional sliding velocity and its critical velocity, respectively - W power loss to friction - internal friction angle - , Lame's potentials, and are time-independent amplitudes of and , respectively - perturbation wave surface profile - wave number of perturbation wave, _r and _i are the real and imaginary parts of - Poisson's ratio of elastic medium - wave frequency of perturbation wave - , _g density of granular material - stress component in elastic medium - Rankine's earth pressure coefficient - -K ² - Re{}, Im{} the real and imaginary parts of complex quantity inside {}, respectively - , the divergence and the curl of perturbation wave velocities, respectively - Laplacian operator - _ij Kronecker delta; _ij =1 fori=j, _ij =0 forij - ()i, ()j, ()ij tensor - ()1, ()e in sliding mass - ()2, ()b in ground     

Out-of-plane instability and electron-phonon contribution tos- andd-wave pairing in high-temperature superconductors; LDA linear-response calculation for doped CaCuO2 and a generic tight-binding model

The equilibrium structure, energy bands, phonon dispersions, and s- and d-channel electron-phonon interactions (EPIs) are calculated for the infinite-layer superconductor CaCuO₂ doped with 0.12 holes per CuO₂. The LDA and the linear-response full-potential LMTO method were used. In the equilibrium structure, oxygen is found to buckle slightly out of the plane and, as a result, the characters of the energy bands near F are found to be similar to those of other optimally doped HTSCs. For the EPI we find _s ~ 0.4, in accord with previous LDA calculations for YBa₂ Cu₃O₇. This supports the common belief that the EPI mechanism alone is insufficient to explain HTSC. is found to be positive and nearly as large as _s. This is surprising and indicates that the EPI could enhance some other d-wave pairing mechanism. Like in YBa2 Cu3 O₇ the buckling modes contribute significantly to the EPI, although these contributions are proportional to the static buckling and would vanish for flat planes. These numerical results can be understood from a generic tight-binding model originally derived from the LDA bands of YBa₂ Cu₃O₇. In the future, the role of anharmonicity of the buckling-modes and the influence of the spin-fluctuations should be investigated.     

Cohesive crack models for semi-brittle materials derived from localization of damage coupled to plasticity

Based on discontinuous displacement approximation of the continuum and shear band kinematics, two cohesive crack models are derived within the constitutive framework of coupled damage and plasticity. The models employ the Rankine fracture criterion, and the model parameters are determined from a uniaxial tension test (mode I cracking). Bifurcation analysis is used in order to diagnose critical directions along which the crack will gradually develop and propagate. These directions depend on the actual stress state and are kept fixed after fracture has initiated, whereby a fixed crack model is obtained. A discrete crack strategy is employed at the finite element implementation in the sense that interfaces (that represent the cohesive crack) are introduced along inter-element boundaries. This implementation strategy calls for gradual realignment of the mesh as a key feature of the algorithm. Numerical results from the analysis of mixed mode fracture in a notched concrete plate are presented.     

The occurrence of stress-induced α′ martensite in an (α+γ) Fe-Cr-Ni alloy

The interaction of an applied stress with the displacive shear during the martensitic transformation determined theK-S variants which formed in three types of tensile specimens, with tensile directions of 0°, 45° and 90° to a rolling direction respectively. The 3–6, 4–5 and 1–3 variants in a 0°-specimen, 1–5 and 4–5 variants in a 45°-specimen and 4-4 and 3–6 variants in a 90°-specimen are chosen asK-S variants which have the maximum value ofU/ in respective tensile directions. These variants are related to the occurrence of martensite with particular orientations as (100), (110) and (211).     

Thermal Conductivity of the Four-Leg Spin-Ladder System La2Cu2O5 Single Crystal

We have investigated the magnetic susceptibility, , and the thermal conductivity, , in magnetic fields for the four-leg spin-ladder system La₂Cu₂O₅ single crystal. The in a magnetic field parallel to the ladder exhibits a kink at 130 K in correspondence to the magnetic ordering. The along the ladder exhibits a peak at 25 K and a shoulder at 14 K, which are probably related to the thermal conductivity due to magnons, _magnon, and that due to phonons, _phonon, respectively. The perpendicular to the ladder, on the other hand, exhibits only one broad peak related to _phonon. The observed large anisotropy of has been explained based upon the anisotropy of _magnon.     

Rat-hole stress profiles for shear-index granular materials

Summary The formation of stable circular and almost vertical cylindrical holes in stockpiles and hoppers is a familiar phenomena in granular material industries and is often the cause of serious disruption to the industry. These holes are referred to as rat-holes and the precise conditions under which they may form or the stability of an existing rat-hole are two issues which have yet to be properly resolved in the literature. We do not address these issues here, but for an existing rat-hole, and assuming a shear-index granular material, we determine the limiting stress profiles. Existing theory applies only to the Coulomb-Mohr yield function. A shear-index granular material is one for which failure due to frictional slip between particles, occurs when the shear and normal components of stress and satisfy the so called Warren Spring equation (vv/C)ⁿ=1–(/t), wherec, t andn are positive constants which are referred to as the cohesion, tensile strength and shear-index respectively, and the known numerical values of the shear-index indicate that for certain materialsn lies between the values 1 and 2. The valuen=1 corresponds to the standard Coulomb-Mohr yield function while the valuen=2 permits some further analytical investigation, and stress profiles for these two values constitute bounds for those shear-index materials for which 1<n<2.     

On internal stress and activation volume in polymers

The two-site model is developed for the analysis of stress relaxation data. It is shown that the product of d In (– )/d and (- _i) is constant where is the applied stress, _i is the (deformation-induced) internal stress and = d/dt. The quantity d In ( )/d is often presented in the literature as the (experimental) activation volume, and there are many examples in which the above relationship with (- _i) holds true. This is in apparent contradiction to the arguments that lead to the association of the quantity d In (– )/d with the activation volume, since these normally start with the premise that the activation volume is independent of stress. In the modified theory presented here the source of this anomaly is apparent. Similar anomalies arise in the estimation of activation volume from creep or constant strain rate tests and these are also examined from the standpoint of the site model theory. In the derivation presented here full account is taken of the site population distribution and this is the major difference compared to most other analyses. The predicted behaviour is identical to that obtained with the standard linear solid. Consideration is also given to the orientation-dependence of stress-aided activation.     

Conventional Electronic Structure of MgB2 and ZrB2: LDA vs. de Haas-v. Alphen & ARPES Data

We compare full potential LDA band calculations of the Fermi surfaces areas and band masses of MgB₂ and ZrB₂ previously reported and new dHvA data. Discrepancies in areas in MgB₂ can be removed by a small shift of bands relative to bands. Comparison of effective masses lead to orbit averaged el-ph coupling constants =1.3 and =0.5, whereas for ZrB₂ only weak el-ph coupling with <0.3 is found. The ARPES data can be also well described by the LDA showing the presence of surface states.     

Radiation of internal waves during vertical motion of a body through a nonuniform liquid

Energy losses to radiation of internal waves during the vertical motion of a point dipole in two-dimensional and three-dimensional cases are computed.Notation _o(z), p_o(z) density and pressure of the ground state - z vertical coordinate - v, p, perturbed velocity, pressure, and density - H(d 1n _o/dz)^–1 characteristic length scale for stratification - N=(gH^–1–g²c _o ^–2 )^1/2 Weisel-Brent frequency - g acceleration of gravity - c_o speed of sound - vertical component of the perturbed velocity - V vector operator - k wave vector - frequency - d vector surface element - W magnitude of the energy losses - (t), (r) (x)(y)(z) Dirac functions - v_o velocity of motion of the source of perturbations - d dipole moment of the doublet - _o,l length dimension parameters - _o intensity of the source Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 619–623, October, 1980.     

Effect of grain size upon flow and fracture in a precipitation-strengthened Ti-8 wt % Al-0.25 wt % Si alloy

The interaction of grain size and precipitation strengthening has been studied in a Ti-8 wt % Al-0.25 wt %Si alloy. Grain sizes varying from 9 to 90m were produced by warm-working and annealing the alloy in the single--phase field. A uniform distribution of the coherent ₂ particles in the matrix was produced by ageing the alloy in the two-phase ( + ₂) field. The yield strength Hall-Petch slopes of the alloys with and without the ₂ precipitates were found to be nearly equal, indicating that the precipitation and grain-boundary strengthening are linearly additive. While specimens containing no precipitates exhibited a high ductility for all grain sizes, the ductility of the specimens with the ₂ particles decreased drastically with increasing grain size. TEM examination of the specimens containing the precipitates revealed a highly planar, localized slip and SEM examination of the fracture surfaces of these specimens revealed a transition in fracture behaviour from highly dimpled to mixed cleavage and intergranular with increasing grain size.     

Boundary-layer similarity flows driven by a power-law shear over a permeable plane surface

Summary. The boundary-layer similarity flow driven over a semi-infinite permeable flat plate by a power-law shear with asymptotic velocity profile U(y)=y(y,>0) is considered in the presence of lateral suction or injection of the fluid (y denotes the coordinate normal to the plate). The analytically tractable cases =–2/3 and =–1/2 are examined in detail. It is shown that while for =–2/3 the adjustment of the flow over an impermeable plate to the power-law shear is not possible, in the permeable cases the presence of suction allows for a family of boundary-layer solutions with the proper algebraic decay. The value of the skin friction corresponding to this family of solutions is given by the parameter s=9³/(4f_w), where f_w denotes the suction parameter. In the limiting case of a vanishing suction and a properly vanishing value of the parameter (such that s=finite), this family of algebraically decaying solutions goes over into the (exponentially decaying) Glauert-jet. In the case =–1/2, solutions showing the proper algebraic decay were found both for suction ( f_w > 0) and injection ( f_w<0) in the whole range –<f_w<+. In this case the skin friction parameters s=2²/3 is independent of the suction/injection parameter f_w.     

Microstructural characterization of CO2 laser welds in the Al-Li based alloy 8090

The microstructural development of the Al-Li-Cu-Mg-Zr alloy 8090 has been studied after autogenous CO₂ laser welding. Sheets ranging in thickness from 1–4 mm were welded at speeds of between 20–120 mm s^–1 and powers from 1.5–3.8 kW. Optical microscopy, scanning and transmission electron microscopy were used to study the as-received base metal, the heat-affected zone and the solidified fusion zone. The base metal was supplied in a superplastically formable condition and thus had an unrecrystallized grain structure containing 1–2 m sized sub-grains with sub-micrometre and precipitates in the matrix. In the fusion zone, the as-solidified grain structure was columnar at the interface with the base metal but became equiaxed in the central region of the weld pool. The weld depth and top bead width both increased with decreasing welding speed and increasing beam power within the limits investigated. The fusion zone microstructure was cellular-dendritic. Intermetallic precipitates, which are rich in copper, magnesium, silicon (and presumably lithium), formed in the cell/dendrite boundaries. Very fine-scale precipitates were present in the as-solidified -Al matrix but there was no evidence for the , S and T₁ phases. The heat-affected zone was only 100 m wide and was characterized by regions of partial melting. Radiographs of welds reveal that porosity occurred predominantly along the weld centre-line. In partial penetration welds, two types of pores were observed: near spherical and irregular. However, in fully penetrating welds, only the spherical type of porosity was present. Overall volume fractions of porosity were measured from metallographic sections and were found to vary with welding speed and weld type, i.e. partial or full penetration.     

Aligned microstructure of some particulate polymer composites obtained with an electric field

Alignment by an electric field was obtained for a variety of particles dispersed in photopolymerizable fluids. The particle shapes studied were irregular, spherical, rhombohedral, rod-like (fibres), and platelet. The sizes ranged from sub-micrometres to tens of micrometres, and the dielectric constants of the particles varied from less than that of the lquid matrix to very much greater than that of the matrix. Polymerization or hardening of the matrix was possible at room temperature, required only a few seconds, and the aligned structures obtained were able to be examined by both light and scanning electron microscopy after fracture or sectioning. Nominally equiaxed particles, containing a statistical proportion of non-equiaxed particles, could be completely aligned at 48 vol% concentration in a fluid having a viscosity of about 2.5 Pa s, but at 57 vol%, the mixture behaved as a paste, and only particle rotation and local rearrangements were possible. The rate of alignment seemed to depend generally on the magnitude of 1(a)2, where 1 is the relative dielectric constant of the liquid resin, a is the particle radius, and is the particle dipole coefficient given by (2–1)/(2+21), where 2 is the relative dielectric constant of the particles. 1(a)2 emphasizes the importance of particle size and the relative unimportance of the particle dielectric constant for alignment, except when 21. Platelets were more rapidly aligned than fibres.     

Permeability of porous materials

A structural model and an approximate method for calculating the permeability of porous materials are proposed.Notation q volumetric flow rate of fluid - l, h, L, S width, thickness, length, and cross-sectional area of material - p pressure drop - coefficient of absolute viscosity - k, k₁, k₂ permeabilities - m₁, m₂ volume concentrations of components - R_t, R_e, R_f thermal, electrical, and filtration resistances - , thermal and electrical conductivities - c parameter - mean pore diameter - sinuousness - d fiber diameter Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 421–427, September, 1981.     

Steady-state creep in a 25 wt % Cr-20 wt % Ni austenitic stainless steel

Steady-state creep behaviour of a 25 wt % Cr-20 wt % Ni stainless steel without precipitates was studied in the stress range 9.8 to 39.2 MPa at temperatures between 1133 and 1193 K. The results of stress-drop tests indicate that, in the steady-state creep region, diffusion-controlled recovery creep is dominant. Such recovery creep can be accounted for in terms of the composition of the internal stress, _i=_s+_c, except in the case of fine-grained specimens where d<80 m, whered is the mean grain diameter, _s is possible to reduce easily and is comparable to the driving stress for creep, and _c is the persistent stress field due to metastable substructure. In the fine-grained specimens, it is suggested that the steady-state creep is dominantly controlled by grain boundaries.     

Hole pockets in the doped 2D Hubbard model

The electronic momentum distributionn(k) of the two dimensional Hubbard model is studied for different values of the couplingU/t, electronic density n, and temperature, using quantum Monte Carlo techniques. A detailed analysis of the data on 8 × 8 clusters shows that features consistent with hole pockets at momentak = (±/2,±/2) appear as the system is doped away from half-filling. Our results are consistent with recent experimental data for the cuprates discussed by Aebi et al. (Phys. Rev. Lett. 72, 5757 (1994)). In the range of couplings studied, the depth of the pockets is maximum at n 0.9,and it increases with decreasing temperature. The apparent absence of hole pockets in previous numerical studies of this model is explained.     

Phase Transformations and Melt Structure of Calcium Metasilicate

The phase transition, melting, crystallization, and vitrification of calcium metasilicate were studied by high-temperature Raman scattering spectroscopy. The results demonstrate that, in the course of melting, the [Si₃O₉] metasilicate rings, which form the structural basis of the phase, transform mainly into [SiO₃] anions. The structural similarity or dissimilarity of the CaO · SiO₂ melt to crystalline phases is shown to have a crucial effect on its crystallization/vitrification behavior.     

Thermal behavior of α-Ba(FeS2)2 and AgFeS2: quasi-unidimensional and 3D network compounds prepared from ion-exchange on the same precursor

Thermal behavior of AgFeS₂ and -Ba(FeS₂)₂ were studied under air atmosphere. Decomposition products of AgFeS₂ are Ag₂S, FeS₂ (pyrite form), Ag₂SO₄, -Fe₂O₃ and metallic silver. -Ba(FeS₂)₂ decomposes to pyrite, -Fe₂O₃ and BaSO₄. We propose that metallic sulfide formation on the initial step of the decomposition of these compounds is related to the packing of the metallic ions with sulfur and, hence, with metal-sulfur distances in the original material. Morphological information about AgFeS₂ and -Ba(FeS₂)₂ are presented for the first time.