Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape

The aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean-field homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori–Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed, which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are studied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites.     

Effect of particle shape and size on flow properties of lactose powders

The shape and size of particles are understood to affect the bulk behaviour of powders, though there are but few studies that present quantitative information on the relationship between particle shape and the flow properties of powder. This is due in part to the lack of techniques for rapidly determining both particle shape and the range of flow characteristics that describe the response of powders to the stress and shear experienced during their processing. This study presents data that quantifies the influence of particle shape/size of three different lactose powders on their respective flow and bulk characteristics. Two of the samples differ in size but have similar shapes; the third sample is more spherical but similar in size to one of the other two samples. The results demonstrate that in addition to particle size, particle shape significantly affect the flow characteristics of a powder over a wide range of stress conditions.     

Mean field calculation of effective permeability based on fractal pore space

Effective permeability for porous rocks is calculated using mean field theory. We make two simplifying assumptions about the internal conductances in a network representation of the porous rock: (i) Pore space is characterized by a uniform fractal scaling; (ii) the internal conductances depend only on the characteristic pore sizes. Within these approximations, it is possible to derive a simple probability density for the internal conductances which is used for calculating effective permeability. Good agreement between calculations and experimental data of permeability vs. porosity is achieved.     

Bounds and estimates for the effect of strain gradients upon the effective plastic properties of an isotropic two-phase composite

Predictions are made for the size effect on strength of a random, isotropic two-phase composite. Each phase is treated as an isotropic, elastic-plastic solid, with a response described by a modified deformation theory version of the Fleck-Hutchinson strain gradient plasticity formulation (Fleck and Hutchinson, J. Mech. Phys. Solids 49 (2001) 2245). The essential feature of the new theory is that the plastic strain tensor is treated as a primary unknown on the same footing as the displacement. Minimum principles for the energy and for the complementary energy are stated for a composite, and these lead directly to elementary bounds analogous to those of Reuss and Voigt. For the case of a linear hardening solid, Hashin-Shtrikman bounds and self-consistent estimates are derived. A non-linear variational principle is constructed by generalising that of Ponte Castañeda (J. Mech. Phys. Solids 40 (1992) 1757). The minimum principle is used to derive an upper bound, a lower estimate and a self-consistent estimate for the overall plastic response of a statistically homogeneous and isotropic strain gradient composite. Sample numerical calculations are performed to explore the dependence of the macroscopic uniaxial response upon the size scale of the microstructure, and upon the relative volume fraction of the two phases.     

Effect of high pressure on pore formation

A method of formation of duralumin plates from the melt under conditions of hydrostatic pressure is investigated. The mechanism of the action of high pressure on the structure of the metal during crystallization is discussed. Results from the measurement of density, strength, and specific electrical resistance are presented.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 6, pp. 110–113, November–December, 1970.     

Analysis method of planar cracks of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic magnetoelectroelastic medium

The hyper-singular boundary integral equation method of crack analysis in three-dimensional transversely isotropic magnetoelectroelastic media is proposed. Based on the fundamental solutions or Green’s functions of three-dimensional transversely isotropic magnetoelectroelastic media and the corresponding Somigliana identity, the boundary integral equations for a planar crack of arbitrary shape in the plane of isotropy are obtained in terms of the extended displacement discontinuities across crack faces. The extended displacement discontinuities include the displacement discontinuities, the electric potential discontinuity and the magnetic potential discontinuity, and correspondingly the extended tractions on crack face represent the conventional tractions, the electric displacement and the magnetic induction boundary values. The near crack tip fields and the intensity factors in terms of the extended displacement discontinuities are derived by boundary integral equation approach. A solution method is proposed by use of the analogy between the boundary integral equations of the magnetoelectroelastic media and the purely elastic materials. The influence of different electric and magnetic boundary conditions, i.e., electrically and magnetically impermeable and permeable conditions, electrically impermeable and magnetically permeable condition, and electrically permeable and magnetically impermeable condition, on the solutions is studied. The crack opening model is proposed to consider the real crack opening and the electric and magnetic fields in the crack cavity under combined mechanical-electric-magnetic loadings. An iteration approach is presented for the solution of the non-linear model. The exact solution is obtained for the case of uniformly applied loadings on the crack faces. Numerical results for a square crack under different electric and magnetic boundary conditions are displayed to demonstrate the proposed method.     

Effect of pore distribution on the statistics of peak stress and overall properties of porous material

This paper addresses the effect of pore distribution on the overall properties and local stress fields in a porous material. Thermal and elastic fields in materials with uniform microstructure are compared with those of materials containing distinguishable clusters of circular or elliptic shape. The numerical simulation combines multipole expansion of local fields with the multi-particle unit cell method. Our work demonstrates that statistics of the peak stresses follow Gumbel’s rule derived for statistics of extreme values and are directly related to statistics of nearest neighbors. Based on this correspondence, an analytical expression for statistics of maximal stresses in a porous material with arbitrary microstructure is constructed in terms of porosity and statistics of minimal distances between the nearest neighbors. At the same time, the numerical analysis indicates that overall elastic constants and thermal (or electrical) conductivity are almost insensitive to the actual distribution of pores – uniform or with distinguishable pore clusters – at least in the examined interval of porosity (up to 50%).     

Bounds on the effective conductivity of statistically isotropic multicomponent materials and random cell polycrystals

Upper and lower bounds on the effective conductivity of statistically isotropic multicomponent materials in d dimensions (d=2 or 3) are constructed from the minimum energy principles and appropriate trial fields. The trial fields, involving harmonic potentials and free parameters to be optimized, lead to the bounds containing up to three-point correlation information about the microgeometry of a composite. The bounds are applied to give estimates for the symmetric cell materials, which are optimal over some ranges of parameters, and asymmetric multicoated spheres, which yield the exact effective conductivity in certain cases. The results also agree with many known ones. New bounds for random cell polycrystals are obtained and illustrated on a number of polycrystalline aggregates.     

Higher-order correction of effective permeability of heterogeneous isotropic formations of lognormal conductivity distribution

Steady flow of an incompressible fluid takes place in a porous formation of spatially variable hydraulic conductivityK. The latter is regarded as a lognormal stationary random space function and Y=ln(K/K _G ), whereK _G is the geometric mean ofK, is characterized by its variance ² and correlation scale I. Exact results are known for the effective conductivityK _eff in one- and two-dimensional flows. In contrast, only a first-order term in a perturbation expansion in ² has been derived exactly for the three-dimensional flow. A conjecture has been made in the past onK _eff for any ², but it was not yet proved exactly. This study derived the exact nonlinear correction, i.e. the termO(⁴) ofK _eff, which is found to be the one resulting from the conjecture, strengthening the confidence in it. It is also shown that the self-consistent approximation leads to the exact results for one-dimensional and two-dimensional flows, but underestimates the nonlinear correction ofK _eff for in the three-dimensional case.     

A non-convex lower bound on the effective energy of polycrystalline shape memory alloys

This paper addresses the estimation of the effective free energy of polycrystalline shape memory alloys, in the framework of nonlinear elasticity and infinitesimal strains. The translation method is combined with a Hashin-Shtrikman type variational formulation to provide rigorous lower bounds on the effective free energy. Those bounds incorporate both intra-grain compatibility conditions (resulting in a non-convex bound) and inter-grain constraints (by taking one- and two-point statistics into account). Some examples are given to compare the results obtained with other bounds from the literature.     

A crack of arbitrary shape inside an infinite transversely isotropic cylinder under arbitrary load

Summary  In the first part of the article an infinite circular cylinder is considered, made of transversely isotropic elastic material and weakened by a plane crack perpendicular to its axis O z. The crack is opened by an arbitrary normal stress. The second part is devoted to the same crack loaded by an arbitrary tangential stress. The complete solution in both cases is presented as a sum of the solution of a similar problem of a crack in an infinite space and an integral transform term, the parameters of which are determined from a set of linear algebraic equations derived from the boundary conditions. Governing integral equations with respect to the yet unknown crack displacement discontinuities are obtained. In the case of a circular crack, these equations can be inverted and solved by the method of consecutive interations. Received 30 November 2000; accepted for publication 3 May 2001     

Effect of pore concentration on localized plastic deformation in polycrystals

Presented is a mesomechanical model that simulates the behavior of localized plastic deformation in polycrystal subjected to uniaxial load. Edge effect and pore concentration are analyzed. Predicted results between the mechanical properties of polycrystal and pore concentration are inconclusive as porosity alone could not explain the increase or decrease of polycrystal strength. The model applies to low pore concentration of less than 5% and hence coalescence of pores is also neglected.     

Analysis method of planar interface cracks of arbitrary shape in three-dimensional transversely isotropic magnetoelectroelastic bimaterials

Using the fundamental solutions for three-dimensional transversely isotropic magnetoelectroelastic bimaterials, the extended displacements at any point for an internal crack parallel to the interface in a magnetoelectroelastic bimaterial are expressed in terms of the extended displacement discontinuities across the crack surfaces. The hyper-singular boundary integral–differential equations of the extended displacement discontinuities are obtained for planar interface cracks of arbitrary shape under impermeable and permeable boundary conditions in three-dimensional transversely isotropic magnetoelectroelastic bimaterials. An analysis method is proposed based on the analogy between the obtained boundary integral–differential equations and those for interface cracks in purely elastic media. The singular indexes and the singular behaviors of near crack-tip fields are studied. Three new extended stress intensity factors at crack tip related to the extended stresses are defined for interface cracks in three-dimensional transversely isotropic magnetoelectroelastic bimaterials. A penny-shaped interface crack in magnetoelectroelastic bimaterials is studied by using the proposed method.The results show that the extended stresses near the border of an impermeable interface crack possess the well-known oscillating singularity r^?1/2±iε or the non-oscillating singularity r^?1/2±κ. Three-dimensional transversely isotropic magnetoelectroelastic bimaterials are categorized into two groups, i.e., ε-group with non-zero value of ε and κ-group with non-zero value of κ. The two indexes ε and κ do not coexist for one bimaterial. However, the extended stresses near the border of a permeable interface crack have only oscillating singularity and depend only on the mechanical loadings.     

Effect of orifice shape on bubble formation mechanism

The effect of orifice shape on the mechanism of bubble formation in gas–liquid two-phase flow is investigated experimentally with three different orifice geometries regarding a circle, a square, and a triangle with same cross-sectional areas. The liquid and gas phases are purified water at 20 °C and air at room temperature, respectively. Gas is injected at the rate of 50–1200 mlph into a stagnant pool of liquid in distances of 5, 10, and 15 cm below the liquid surface. The position, velocity, and acceleration of bubbles are measured at bubbles’ centers of mass (CM) and the effects of these parameters on the bubble volume are investigated. Moreover, the forces acting on a bubble are balanced and the effects of geometry and gas flow rate on each force are presented. In addition, the changes of the acting forces versus time are plotted and discussed for a specific condition. Results show the bubbles formed with the square and circular orifice cross-sectional areas have the most and least volumes at detachment, respectively.     

Elastic fields generated by inhomogeneities: Far-field asymptotics,its shape dependence and relation to the effective elastic properties

We discuss connections between the effective elastic properties of a solid with inhomogeneities and the far-field asymptotics of the elastic fields generated by them. We focus on the dependence of the far-field asymptotics on the inhomogeneity shape. This shape dependence in the inhomogeneity problem is in contrast with shape independence of the far field in the eigenstrain problem. For the latter, the far field applies to inclusions of any shape. We show that the external fields in the eigenstrain – and the inhomogeneity problems are interrelated by the same tensor that characterizes the compliance contribution of an inhomogeneity.     

Size and shape effects on magnetic properties of Ni nanoparticles

Pure Ni nanoparticles ranging in size from 24 to 200 nm are prepared via thermal decomposition of nickel acetylacetonate in oleylamine. The as-prepared Ni particles change from spherical to dendritic or starlike with increasing precursor concentration. The particles are stable because the organic coating occurs in situ. Magnetic measurement reveals that all the Ni nanoparticles are ferromagnetic and show ferromagnetic–paramagnetic transitions at their Curie points. The saturation magnetization M_s is size-dependent, with a maximum value of 52.01 and 82.31 emu/g at room temperature and 5 K, respectively. The coercivity decreases at first and then increases with increasing particle size, which is attributed to the competition between size effect and shape anisotropy. The Curie temperature T_c is 593, 612, 622, 626 and 627 K for the 24, 50, 96, 165 and 200 nm Ni nanoparticles, respectively. A theoretical model is proposed to explain the size-dependence of Ni nanoparticle Curie temperature.     

Thin film reflection properties of isotropic and uni-axial plasma slabs

The maxima and minima of the power reflection coefficient as a function of the wave frequency of an electromagnetic wave obliquely incident on isotropic and uni-axial plasma slabs are discussed.     

The influence of constraints on the properties of acceleration waves in isotropic thermoelastic media

The properties of acceleration waves are investigated for situations in which the waves propagate in isotropic heat-conducting elastic media subject to arbitrary sets of constraints. Conditions under which waves may exist in the presence of constraints are investigated for classes of constraints broad enough to encompass all those encountered in practice. Attention is focussed on principal waves, and results are presented for the growth of the amplitudes of such waves first for fronts of arbitrary curvature, and subsequently by specialisation for plane, cylindrical and spherical waves travelling in material which has undergone one-dimensional plane deformation, cylindrically symmetric and spherically symmetric deformation, respectively.     

Prediction of the effective elastic moduli of materials with irregularly-shaped pores based on the pore projected areas

Statistical modeling is used to correlate geometric parameters of pores with their contributions to the overall Young’s moduli of linearly elastic solids. The statistical model is based on individual pore contribution parameters evaluated by finite element simulations for a small pore subset selected using the design of experiments approach, so there is no need to solve the elasticity problem for all pores in the material. A polynomial relating pore geometric parameters to the contribution parameters is then fitted to the results of the simulations. We found a good correlation between normalized projected areas of the pores on three coordinate planes and their contributions to the corresponding effective Young’s moduli. The model is applied and validated for two large sets of pore geometries obtained by X-ray microcomputed tomography of a carbon/carbon and a 3D woven carbon/epoxy composite specimens.     

Influence of a thin isotropic coating on the edge effect zone in isotropic and transversely isotropic materials

The effect of a thin isotropic coating on the edge effect zone in a representative element of a coated material is examined. Isotropic and transversely isotropic materials are considered. The transversely isotropic material has the elastic properties of unidirectional glass-fiber-reinforced plastic. The decay of the edge effect in the directions perpendicular to the coating plane and to the plane of isotropy is studied. A boundary-value problem of elasticity for piecewise-homogeneouse orthotropic bodies and a quantitative edge effect decay criterion for normal stresses are used as a design model. The problem is solved using the finite-difference method and base schemes. The results of evaluation of the edge effect zone in homogeneous and inhomogeneous materials are presented. It is shown that the presence of a thin isotropic coating blocks the edge effect, that is, decreases the edge effect zone in both isotropic and transversely isotropic materials __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 61–67, December 2007.