Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents

The paper addresses the problem of calculation of the local stress field and effective elastic properties of a unidirectional fiber reinforced composite with anisotropic constituents. For this aim, the representative unit cell approach has been utilized. The micro geometry of the composite is modeled by a periodic structure with a unit cell containing multiple circular fibers. The number of fibers is sufficient to account for the micro structure statistics of composite. A new method based on the multipole expansion technique is developed to obtain the exact series solution for the micro stress field. The method combines the principle of superposition, technique of complex potentials and some new results in the theory of special functions. A proper choice of potentials and new results for their series expansions allow one to reduce the boundary-value problem for the multiple-connected domain to an ordinary, well-posed set of linear algebraic equations. This reduction provides high numerical efficiency of the developed method. Exact expressions for the components of the effective stiffness tensor have been obtained by analytical averaging of the strain and stress fields.     

Oxygen-distribution imaging with a novel two-tracer laser-induced fluorescence technique

We introduce a new technique for imaging oxygen concentrations in fuel/air mixtures that takes advantage of the different responses of toluene and 3-pentanone to collisional quenching by molecular oxygen. Since laser-induced fluorescence signals from both tracers upon excitation at 248 nm are spectrally well separated, simultaneous detection is possible. The technique is first applied to instantaneous imaging in turbulent mixing processes of interacting seeded air and nitrogen flows. Received: 1 August 2001 / Revised version: 29 October 2001 / Published online: 29 November 2001     

Field-theoretical three-body relativistic equations for the multichannel πN↔γN↔ππN↔γπN reactions

A new kind of the relativistic three-body equations for the coupled πN and γN scattering reactions with the ππN and γπN three particle final states are suggested. These equations are derived in the framework of the standard field-theoretical S-matrix approach in the time-ordered three-dimensional form. Therefore, corresponding relativistic covariant equations are three-dimensional from the beginning and the considered formulation is free of the ambiguities which appear due to a three dimensional reduction of the four dimensional Bethe-Salpeter equations. The solutions of the considered equations satisfy the unitarity condition and they are exactly gauge invariant even after the truncation of the multiparticle (n>3) intermediate states. Moreover, the form of these three-body equations does not depend on the choice of the model Lagrangian and it is the same for the formulations with and without quark degrees of freedom. The effective potential of the suggested equations is defined by the vertex functions with two on-mass shell particles. It is emphasized that these INPUT vertex functions can be constructed from experimental data. Special attention is given to the construction of the intermediate on shell and off shell Δ resonance states. These intermediate Δ states are obtained after separation of the Δ resonance pole contributions in the intermediate πN Green function. The resulting amplitudes for the Δ⇔Nπ; Δ⇔Nγ; Δ^′⇔Δγ transition have the same structure as the vertex functions for transitions between the on-mass shell particle states with spin 1/2 and 3/2. Therefore it is possible to introduce the real value for the magnetic momenta for the Δ^′⇔Δγ transition amplitudes in the same way as it is done for the N^′⇔Nγ vertex function.     

Debye temperature of cubic crystals

An algorithm for determination of the Debye temperature is presented, which enables the easy computation of the Debye temperature for arbitrary stable cubic crystal.     

Ab-initio simulation of elastic constants for some ceramic materials

Athermal elasticity for some ceramic materials (α-Al₂O₃, SiC (α and β phases), TiO₂ (rutile and anatase), hexagonal AlN and TiB₂, cubic BN and CaF₂, and monoclinic ZrO₂) have been investigated via density functional theory. Energy-volume equation-of-state computations to obtain the zero pressure equilibrium volume and bulk modulus as well as computations of the full elastic constant tensor of these ceramics at the experimental zero pressure volume have been performed. The present results for the single crystal elasticity are in good agreement with experiments both for the aggregate properties (bulk and shear modulus) and the elastic anisotropy. In contrast, a considerable discrepancy for the zero pressure bulk modulus of some ceramics evaluated from the energy-volume fit to the computational zero pressure volume has been observed.     

Acoustic characteristics of Ni–Nb–Zr–H glassy alloys by ultrasonic shear waves

The propagation characteristics of shear horizontally polarized (SH) waves passing through (Ni₄₂Nb₂₈Zr₃₀)_100–x H_x (x = 0–15.2) glassy alloys were investigated as a function of hydrogen content. With an increase in hydrogen content, the propagation time and main frequency of the receiving waves show increase and decrease, respectively, indicating expan‐ sion in average atomic distance which comes from solution of hydrogen. In sharp contrast to crystalline alloys, the decrease in damping ratio and the delay in phase with increasing hydrogen suggest a strong settlement of hydrogen into four‐coordination sites surrounded tetrahedrally by four Zr atoms and the resulting increase in dynamic elasticity, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Point load determination of static elastic moduli using laser speckle interferometry

Electronic speckle interferometry (ESPI) is used to determine the Young's modulus E and Poisson ratio ν of an isotropic material. Micron scale deformations of the surface of the block of polymethyl-methacrylate (PMMA) are induced by normal application of a known near-point force. These deformations are recorded in speckle interferometric fringe patterns. An iterative minimum error inversion technique is developed to obtain the elastic properties from the positions of fringe peaks and troughs observed in the fringe patterns. Sensitivity tests of the method on calculated fringe patterns using measured experimental uncertainties suggest the technique will provide measures of the elastic moduli to better than 5%. In an experimental test on a bloc of PMMA (acrylic) the technique gave values of E and ν that differed from corresponding measures obtained using more conventional strain-gauge methods by less than 4%.     

Metastability of a circular o-ring due to intrinsic curvature

An o-ring takes spontaneously the shape of a chair when strong enough torsion is applied in its tangent plane. This state is metastable, since work has to be done on the o-ring to return to the circular shape. We show that this metastable state exists in a Hamiltonian where curvature and torsion are coupled via an intrinsic curvature term. If the o-ring is constrained to be planar (2d case), this metastable state displays a kink-anti-kink pair. This state is metastable if the ratio is less than , where C and A are the torsion and the bending elastic constants [#!landau!#]. In three dimensions, our variational approach shows that . This model can be generalized to the case where the bend is induced by a concentration field which follows the variations of the curvature. Received: 27 August 1997 / Revised: 23 October 1997 / Accepted: 12 November 1997     

After-Effects of Electrolytically diffused hydrogen in the second-order elastic coefficient of poynting’s effect in nickel and steel

Summary If hydrogen is diffused electrolytically in a metal, it subsequently escapes out if the metal is left to itself. However this hydrogen-treated metal does not totally regain the original magnitudes of its various physical properties,e. g., thermo e.m.f., electrical resistivity, elastic modulii etc. This effect has also been observed in the second-order elastic effect (the Poynting effect) in nickel and two varieties of steel. Measurements were carried out first before hydrogen diffusion. The samples were electrolytically diffused with hydrogen and the left to themselves for a few days and the measurements were repeated. The changed values of the coefficient of Poynting effect are discussed in terms of the dislocations created by in-and out-going hydrogen. Now retired     

Elasticity in nanocrystalline Nd2Fe14B+αFe magnetic composites

The dynamic Young modulus (E) of magnetic Nd₂Fe₁₄B+αFe nanocomposites is investigated with mechanical spectroscopy techniques (vibrating reed configuration, f≈1.5 kHz <10⁻⁶). Reduced values of E are obtained (88–152 GPa) as compared with that predicted by the rule of mixtures for the composite (164 GPa). Three contributions to this reduction are briefly discussed: a large volume fraction of the specimen with grain boundary like structure; internal pores, resulting from the high cooling rate during processing (10⁶ K/min) and magneto-mechanical effects. Even when porosity is identified as the principal cause of modulus reduction, magnetic effects are also detected.