Mean-field Concept Research Articles

Off-Axis Tensile Properties of CFRP Laminates and Non-Linear Lamination Theory Based on Micromechanics Approach.

This paper deals with the deformation and damage of CFRP cross-ply laminates under off-axis tension and develops a non-linear lamination theory. Off-axis tensile tests were carried out on five kinds of CFRP cross-ply laminates which were different in stacking lay-up. On the laminates under off-axis tension, the stress-strain response shows the non-linear deformation, while the ply-cracking damage is not remarkable except for the specimen with large fracture strain. Therefore, It is concluded that the non-linear deformation of the laminates under off-axis tension is mainly attributed to the non-linear deformation of the matrix resin. In order to describe the deformation of the laminates, a non-linear lamination theory is developed. An incremental constitutive relation of the unidirectional composite containing elastic long fibers in the elastic-plastic matrix is derived based on Eshelby's equivalent inclusion method and Mori-Tanaka mean field concept. Then, this constitutive relation is introduced Into the classical lamination theory. Numerical results by the present theory for off-axis tension of the CFRP unidirectional and cross-ply laminates well described the experimental stress-strain relations.

Crossover to Fermi-liquid behavior for weakly coupled Luttinger liquids in the anisotropic large-dimension limit

We study the problem of the crossover from one- to higher-dimensional metals by considering an array of Luttinger liquids (one-dimensional chains) coupled by a weak interchain hopping {\tp.} We evaluate the exact asymptotic low-energy behavior of the self-energy in the anisotropic infinite-dimension limit. This limit extends the dinamical mean field concept to the case of a chain embedded in a self-consistent medium. The system flows to a Fermi-liquid fixed point for energies below the dimensional crossover temperature, and the anomalous exponent $\al$ renormalizes to zero, in the case of equal spin and charge velocities. In particular, the single-particle spectral function shows sharp quasiparticle peaks with nonvanishing weight along the whole Fermi surface, in contrast to the lowest-order result. Our result is obtained by carring out a resummation of all diagrams of the expansion in \tp contributing to the anisotropic $D\to\infty$ limit. This is done by solving, in an almost completely analytic way, an asymptotically exact recursive equation for the renormalized vertices, within a skeleton expansion. Our outcome shows that perturbation expansions in \tp restricted to lowest orders are unreliable below the crossover temperature. The extension to finite dimensions is discussed. This work extends our recent Letter [Phys. Rev. Lett. {\bf 83}, 128 (1999)], and includes all mathematical details.

Nuclear spectroscopy, nuclear clustering and exotic shapes

Nuclear clustering has been a subject of intense study since the advent of heavy ion accelerators. Looking back more than 30 years, we are able today to see the connection between resonances in heavy ion reactions and extreme states in nuclei. In particular, excited states close to the decay thresholds into substructures show pronounced cluster structures. The ever repeated question about the possibility to describe such cluster phenomena in an extended (to a very large basis) and deformed shell model, has recently been revived in view of improved computational facilities. The new experimental facilities and the powerful new detector arrays for γ-spectroscopy and for charged particles have increased the sensitivity to study clustering phenomena by orders of magnitude. Today we are able to study nuclear structure at the limits of the mean field concept. With the advent of radioactive beams and the study of nuclei, which are weakly bound in their ground states, the question of the limits of mean field concepts has reached the low excitation energy region of nuclei.

Stern-Gerlach deflection of ferromagnetic cluster beams

Abstract The magnetic moments and heat capacities of small iron, cobalt and nickel clusters in a molecular beam have been measured as a function of their size and temperature using Stern-Gerlach deflections. Single-sided deflections are found indicating that spin relaxation occurs within the isolated clusters. Superparamagnetic behaviour is observed when all the degrees of freedom of the clusters are in equilibrium. Marked decreases in the magnetic moment are observed with increasing temperature and increasing size, slowly converging to the bulk magnetization curve as the cluster size increases. At a given temperature, oscillation of the moment is observed as a function of size, which suggests the filling of layers of atoms in the cluster. Heat capacity measurement of nickel and cobalt clusters in the beam reveals that the magnetic contribution to the heat capacity is well approximated using mean-field concepts, combined with measured magnetic properties. In contrast, iron clusters show anomalies both in the magnetic moments and in the heat capacities.

Stern-Gerlach deflection of ferromagnetic cluster beams

Abstract The magnetic moments and heat capacities of small iron, cobalt and nickel clusters in a molecular beam have been measured as a function of their size and temperature using Stern-Gerlach deflections. Single-sided deflections are found indicating that spin relaxation occurs within the isolated clusters. Superparamagnetic behaviour is observed when all the degrees of freedom of the clusters are in equilibrium. Marked decreases in the magnetic moment are observed with increasing temperature and increasing size, slowly converging to the bulk magnetization curve as the cluster size increases. At a given temperature, oscillation of the moment is observed as a function of size, which suggests the filling of layers of atoms in the cluster. Heat capacity measurement of nickel and cobalt clusters in the beam reveals that the magnetic contribution to the heat capacity is well approximated using mean-field concepts, combined with measured magnetic properties. In contrast, iron clusters show anomalies both in the magnetic moments and in the heat capacities.

Theory of Reinforcement Damage in Discontinuously-Reinforced Composites and Its Application.

In particle or short-fiber reinforced composites, cracking or debonding of the reinforcements is a significant damage mode because the damaged reinforcements lose load carrying capacity. This paper deals with a theory of the reinforcement damage in discontinuously-reinforced composites and its application. The composite with progressive cracking damage contains intact and cracked reinforcements in a matrix. To describe the load carrying capacity of the cracked reinforcement, the average stress of a broken ellipsoidal inhomogeneity in an infinite body which was proposed in the previous paper is introduced. An incremental constitutive relation of the composites with progressive cracking damage of the reinforcements has been developed based on Eshelby's equivalent inclusion method and Mori and Tanaka's mean field concept. This damage theory can describe not only cracking damage but also debonding damage of the reinforcements by modifying teh load carrying capacity of damaged reinforcements. Influence of the reinforcement damage on the stress-strain response and elastic stiffness of the composites is discussed. It is noted that tha full-debonding damage gives the lower limit of the stress-strain relation of the composite with progressive reinforcement damage.

Incremental damage theory of particle or short-fiber reinforced composites

In particle or short-fiber reinforced ductile-matrix composites, cracking of reinforcements is a significant damage mode because cracked reinforcements lose load carrying capacity. This paper deals with an incremental damage theory of the composites. The composite in damage process contains intact and cracked reinforcements in a matrix. To describe the load carrying capacity of the cracked reinforcement, the average stress of a broken ellipsoidal inhomogeneity in an infinite body is introduced. An incremental constitutive relation of particle or short-fiber reinforced composites including the progressive’ cracking damage of reinforcements and the plasticity of matrix have been developed based on the Eshelby’s equivalent inclusion method and Mori and Tanaka s mean field concept. Influence of the reinforcement damage on the stress-strain response of the composites is demonstrated.

Thermal properties of ferromagnetic clusters

The magnetic moments and heat capacities of small iron, cobalt and nickel clusters in a molecular beam have been measured as a function of their size and temperature. The magnetic moment of nickel and cobalt clusters decreases with increasing size and with increasing temperature, slowly converging to the bulk magnetization curve as the cluster size increases. Heat capacity measurement of the clusters in the beam reveals that the magnetic contribution to the heat capacity is well approximated using mean field concepts, combined with measured magnetic properties. In contrast, iron clusters show anomalies, both in the magnetic moments as well as in the heat capacities. We speculate that these effects reflect a sensitivity of the magnetic order on structure as in bulk iron.

Investigation on the effective conductivities of carbon/carbon fiber composites with inhomogeneous interphase

Thermal conductivities of carbon/carbon fiber composites with inhomogeneous interphase are studied in thtis paper. The inhomogeneous interphase is modeled approximately as a multilayered structure consisting of many thin layers having homogeneous properties, and close-formed solution of the effective conductivities of the composites is obtained by using the Mori-Tanaka mean-field concept.

Shapes and rotational structures of neutron configurations in the XeBaCe region

Abstract Rotational bands built on neutron h 11 2 states are investigated within the Strutinsky mean-field concept. Calculated deformation trajectories of one-, three- and five-quasiparticle configurations are presented. The experimentally observed signature splitting and crossing frequencies in XeBaCe nuclei are compared to theoretical predictions. The systematics of the observed band structures can only be accounted for by allowing a smooth transition from prolate to oblate structure via triaxial shapes as the number of neutrons increases.

A survey of alpha-clustering

The concept of alpha-clustering has found many applications to nuclear reactions and nuclear structure. Calculations of the properties of nuclear matter indicate that condensation into alpha-particles occurs when the density is somewhat less than the central nuclear density, suggesting that alpha clustering is favoured in the nuclear surface. This provides an explanation of alpha-decay which is now quantitatively successful. The concept of the alpha-particle mean field is now widely used to unify the alpha-particle bound and unbound states found by alpha-transfer reactions, and the scattering of alpha-particles by nuclei. The analysis of the structure of 44Ti using the alpha-40Ca potential has been particularly successful. There are now several phenomenological alpha-alpha interactions that fit the low-energy phase shifts, and these are used to calculate the structure of light nuclei, particularly those composed of 2N protons and 2N neutrons. Many excited states of such nuclei can be studied in this way, and a particularly interesting class of states is those composed of a linear chain of alpha-particles, some of which have been identified experimentally.

PARTICLE SIZE AND ORIENTATION EFFECTS ON INTERPARTICLE INTERACTION

Interparticle interaction was discussed by measuring Henkel plots and delta M plaots for various magnetic media, such as Co-γ-iron oxide tape, metal particulate tape and Ba ferrite particulate tape. It was ascertaind that only negative interaction acts for the parallel and the transverse directions to the orientation direction, for both non-oriented and longitudinally oriented acicular particulate tapes, and that positive interaction acts for the orientation direction for platelet-shaped Ba ferrite tapes, negative interaction for their transverse direction, and almost zero interactin for non-oriented Ba ferrite tapes. Interaction field strength was estimated for these media, by means of linearization of Henkel plots, based on mean-field concept.

Transient Creep Strain of a Fiber-Reinforced Metal-Matrix Composite Under Transverse Loading

Based on the combination of Mori-Tanaka’s mean-field concept and Luo-Weng’s solution of a three-phase cylindrically concentric solid, a local-field theory is developed to study the evolution of stress distribution in the ductile matrix and the time-dependent creep strain of a fiber-reinforced metal-matrix composite. Due to the nonlinear stress dependence in the creep rate and the highly heterogeneous nature of the transverse deformation, this local theory is shown to provide a more accurate estimate for the overall transverse creep of the composite than the simpler meanfield theory (the difference between the two however is not significant in the axial tensile creep). The disclosed transverse stress field in the matrix is truly heterogeneous, with the 45 deg region exhibiting a substantially higher effective stress than the 0 deg and 90 deg regions. The stress in the higher stress region is found to decrease continuously; it is passed on to the fibers and thereby serves as an important creep-strengthening mechanism for the composite. The interfacial tensile stress at the pole, which is the highest stress point around the interface, is seen to grow continuously and becomes a potential site for a later creep debonding. The developed micromechanical theory is finally applied to predict the transverse tensile creepstrain of a Borsic/aluminum composite, and the result is found to be in close agreement with the test data.

The effective thermal conductivity of composites reinforced by coated cylindrically orthotropic fibers

The present paper is concerned with coated-fiber composites in which the fibers possess cylindrical orthotropy and may have an arbitrary orientation distribution. A micromechanics model is developed which predicts the effective thermal conductivity and estimates the local fields of such composites which may be subjected to uniform heat fluxes on its boundary. The micromechanics model is based on the Mori–Tanaka mean-field concept [T. Mori and K. Tanaka, Acta Metall. 21, 571 (1973)] and provides explicit expressions for the effective conductivity of the considered composite aggregate which is highly complicated. The analysis shows that special care is needed in formulating an effective theory of composites with constituents possessing curvilinear anisotropy.

Energy dependence of the mean-field potential for neutron scattering from 190,192Os and 194,196Pt.

An extensive set of neutron scattering cross sections for four shape-transitional nuclei, /sup 190,192/Os and /sup 194,196/Pt, have been examined to test recent mean-field concepts which relate scattering potentials to those which bind single particle levels in nuclei. Scattering observables for each of these four nuclei have been separately and exhaustively analyzed to fix the potential strengths and their dependence on incident neutron energy. The results of these analyses revealed potentials quite different than the usual ''Hartree-Fock type'' potentials arising from global analyses at higher particle energies. A dispersion relation, based on the imaginary parts of the optical model potential, is applied in these analyses. Not only can the nonlinear energy dependencies observed in the scattering potential be described with this method, the potential can be extrapolated to negative energies where it is constrained to fit bound states in the neutron-plus-nucleus system. This is the first report of dispersion corrections for potentials from coupled-channels analyses of scattering from highly collective nuclei.

The origin of the main field

Early in the twentieth century Einstein described the problem of the origin of the earth's magnetic field as being one of the five most important unsolved problems in physics. Since then, major advances have been made and it is now generally accepted that the main field originates from some form of dynamo process taking place in the earth's outer core. However, the 'dynamo problem' has not yet been solved and remains one of the most challenging mathematical problems ever formulated. Significant progress was made during the 1950s and 1960s with the nearly axisymmetric model developed by Braginsky and the mean-field concept instituted by Krause and Radler. Since then dynamo theorists have continued to search for ways to simplify the mathematics.

Theory of the solar cycle

The properties of kinematic αω -dynamos are briefly reviewed. The mean field concept, including turbulent diffusivity, is defended against recent criticism. It is pointed out that although the Maunder minimum cannot be explained by kinematic dynamo theory alone, this does not invalidate dynamo theory in general. A special discussion is devoted to attempts to evaluate the coefficients of the mean field induction equation in the case of very large conductivity. The field then behaves intermittent, in the form of locally concentrated flux tubes, and the α-effect and the turbulent diffusivity may be determined by asymptotic techniques or with the help of an exact solution of the non-dissipative induction equation in Lagrangian co-ordinates.

Effects of interaction fields on the hysteretic properties of assemblies of randomly oriented magnetic or electric moments

Theoretical models of interacting magnetic or electric moments based on the concept of a uniform Lorentz-type internal spatial mean field predict results that are in conflict with experimental observations. Neglect of the nonuniformities in the interaction-field distribution can account for this. In order to test interaction theories, hysteresis measurements have been made on samples containing particles of known intrinsic magnetic properties. Coercivities, susceptibilities, and saturation remanences have been measured for randomly oriented uniaxial single-domained magnetites as a function of packing factor. On the basis of these results, a model is proposed which takes into account heterogeneity in the interaction-field distribution while retaining the simplicity of the mean-field approach. The model is based on the magnetization configuration which most effectively gives rise to internal pole cancellation and minimum anisotropy energy. This occurs when moments segregate into magnetically independent domains within which magnetic moments are nearly parallel and lie along particle easy axes, but which are themselves randomly oriented throughout the assembly. Particle moments would then be subjected to domain-magnetizing fields which are proportional to and oppositely directed to intrinsic demagnetizing fields. The model predicts a reduction of demagnetizing factors of (1−p), so that susceptibility is given by χ (p) = (2/3)[Nb−Na)(1−p)]−1 for particles of average demagnetizing factors Na, Nb, and also that the remanence remains constant with increased packing, i.e., IRS(p) =0.5IS both of which have been observed experimentally. The results lead to the general conclusions that for all noncrystalline polar interactions: moments will tend to form into the pole-cancelling domains described; the average internal field acting on a moment is a constant, which is independent of the net polarization; and, the spatial mean internal field of polarized assemblies of interacting moments exerts no torque on elementary moments and plays no part in determining the net polarization of the assembly.

Soft mode dynamics at the pressure-induced ferroelectric transition in sodium nitrate

Raman light scattering has been used in a room temperature study of sodium nitrate in which a ferroelectric transition has been induced by the application of hydrostatic pressure. In the ferroelectric phase above 45 kilobars, a soft lattice mode has been observed which evolves from underdamped to overdamped behavior as the pressure is reduced to within 1 kb of the transition. The transition appears second order and can be described using mean field concepts.

METHODS OF STUDYING THE SPATIAL STRUCTURE OF MARKET ZONES

The mean-field concept is used to derive an index μ that describes consumption conditions within a market zone by relating aggregate volumes of haul of a particular product to aggregate freight costs. The technique is illustrated in the case of the fuel-oil market zones of Soviet refineries. The highest values for μ, suggesting zones with optimal refinery locations, are found for the Novopolotsk refinery in Belorussia and the Kirishi refinery near Leningrad. The lowest values are found for the East Siberian refinery at Angarsk and the West Kazakhstan refinery at Gur'yev. The size of market zones tends to vary seasonally in some cases because the use of waterways in summer reduces the length of haul, thus raising the μ index for some refineries. The shape of fields of two interacting market zones will depend not only on the length of haul from producing centers but also on the μ index.