Showing papers in "Journal De Physique Iv in 1998"

Mechanics of generalized continua: construction by homogenizaton

Abstract: La mecanique des milieux continus generalises fournit des outils pour decrire les effets d'echelle que presentent certains materiaux heterogenes. Cependant les liens entre les nouveaux degres de liberte que certains de ces milieux introduisent et la microstructure ne sont clairement etablis que pour quelques cas extremes (cristaux liquides...). Dans ce travail, on essaie de construire un milieu de Cosserat homogene equivalent a un milieu classique micro-heterogene, par des methodes d'homogeneisation generalisees. Ces techniques permettent alors de rendre compte des champs de contraintes et de deformation dans un materiau heterogene sollicite de telle sorte que la taille de l'element de volume representatif ne soit pas negligeable devant la longueur d'onde des sollicitations.

An experimental test of the Gallavotti-Cohen fluctuation theorem

Abstract: The chaotic hypothesis of the Gallavotti-Cohen theory is experimentally checked on turbulent Rayleigh-Benard convection. We find that the local temperature fluctuations verify the hypothesis prediction

Bending of marble with intrinsic length scales : A gradient theory with surface energy and size effects

Abstract: A gradient bending theory is developed based on a strain energy function that includes the classical Bernoulli-Euler term, the shape correction term (microstructural length scale) introduced by Timoshenko, and a term associated with surface energy (micromaterial length scale) accounting for the bending moment gradient effect. It is shown that the last term is capable to interpret the size effect in three-point bending (3PB), namely the decrease of the failure load with decreasing beam length for the same aspect ratio. This theory is used to describe the mechanical behaviour of Dionysos-Pentelikon marble in 3PR. Series of tests with prismatic marble beams of the same aperture but with different lengths were conducted and it was concluded that the present theory predicts well the size effect.

Duo-plasmaline, a surface wave sustained linearly extended discharge

Abstract: On decrit un dispositif a plasma, le Duo-Plasmaline. Le plasma y est produit par micro-ondes dans une chambre basse pression a l'exterieur d'un tube. Les ondes se propagent comme des ondes de surface en partie dans le tube et en partie dans le plasma. Elles sont excitees aux deux extremites du tube et produisent un plasma homogene qui s'etend axialement le long du tube. On etudie les proprietes des ondes en resolvant numeriquement l'equation d'onde. On presente des resultates experimentaux de profils radial et axial de la densite electronique ainsi que du champ de l'onde.

Identification of the characteristic length scale for fatigue cracking in fretting contacts

Abstract: Fretting damage consisting in cracking and wear generated by debris formation is induced by very small alternated displacements between contacting surfaces. It is often considered through the drastic drop in the fretting fatigue limit which is very detrimental for industrial applications. This paper focuses on the quantification of the fretting crack nucleation appearance by comparing fretting experiments obtained on well defined quenched 30NCD16 steel and a multiaxial fatigue approach. The plane/sphere configuration was studied under partial slip situations characterised by a central stick domain surrounded by an external sliding zone. Validated for classical fatigue conditions, the Dang Van's fatigue prediction is compared to fretting cracking mechanisms (10 6 cycles). The correlation is achieved according to some conditions: - the local friction coefficient operating in the annular partial slip contact has to be identified. It permits a more accurate estimation of the stress loading path evolution during the fretting cycle. - the loading states which are computed to determine the crack nucleation risk must be averaged on an elementary volume representative of the microstructure of the steel. It allows a convenient size effect consideration regarding the very small material volume stressed below the contact.

A unified concept of elastic-viscoplastic Cosserat and micromorphic continua

Abstract: The paper is concerned with a unified formulation and treatment of Cosserat, micromorphic, and more general continua. First the classical understanding of Cosserat and micromorphic continua is reviewed and critically examined. It is shown that the strain measures of the micromorphic continuum as suggested by Eringen and co-workers do exihibit shortcomings which become evident when discussing the Euler-Lagrange equations of a corresponding action, Assuming that invariance of the strain measures should be required with respect to the group SO(3) alone and not to that of GL + (3), new strain measures of the micromorphic continuum and corresponding field equations are derived. A new unified understanding of Cosserat and micromorphic continua is propagated which views the rotation field in case of the Cosserat continuum as a first approximation of a generalized displacement field. The unified treatment allows for a straightforward formulation of finite strain viscoplasticity of such continua. The formulation is based on a multiplicative decomposition of the micro stretch tensor. Furthermore it allows for the application of constitutive laws of the unified type generally formulated for classical continua.

Discrete dislocation simulations and size dependent hardening in single slip

Abstract: Plastic deformation in two-dimensional monophase and composite materials is studied using a discrete dislocation dynamics method. In this method, dislocations are represented by line defects in a linear elastic medium, and their interactions with boundaries or second-phase elastic particles are incorporated through a complementary finite element solution. The formulation includes a set of simple constitutive rules to model the lattice resistance to dislocation glide, as well as the generation, annihilation and pinning of dislocations at point obstacles. The focus is on the predicted strain hardening of these materials when only a single slip system is active. When the particle morphology is such as to require geometrically necessary dislocations, hardening in the composite materials exhibits a distinct size effect. This size effect is weaker than that predicted by simple analytical estimates based on geometrically necessary dislocations.

A continuum model with microstructure for materials with flaws and inclusions

Abstract: A continuum endowed with affine microstructure is adopted for the macroscopic description of fiber composite materials. The microstructure is made of a rigid and of a deformable local structure. The former represents the fibers of the composite, perceived as rigid inclusions. The latter accounts for the presence of distributed flaws, considered as slit microcracks. In the framework of a degree one theory, a formula for the mechanical power is derived from a discrete microscopic model using an integral procedure of equivalence. Constitutive elastic stress-strain relationships, accounting for the geometry of the internal phases, are identified The balance equations for both the continuum macro and micro-actions are derived from the axiom of vanishing power and of invariance of power under change of observer. It is also shown that the material symmetries are preserved in the transition from fine to gross description.

A one-dimensional model for localized and distributed failure

Abstract: For an elastic body with limited strength, the equilibrium configurations can be obtained by minimization of an energy functional containing two contributions, bulk and cohesive: the bulk energy is a function of strain and the cohesive energy is a function of the relative displacement on a surface of discontinuity. In the present communication we consider the simplest one-dimensional problem for a bar with this type of energy in a hard device. We assume that the bulk energy is convex, and we vary the concavity propertiess of the cohesive energy, obtaining thereby three distinct modes of failure. If the cohesive energy is concave for all admissible displacements, failure occurs with the formation of a single crack, and the opening of the crack may be either abrupt or gradual, depending on the length of the bar. If the cohesive energy is concave at large displacements but convex at the origin, the deformation may progress at constant stress (yielding), through formation of an infinite numer of infinitesimal cracks (structured deformation). Finally, when the cohesive energy is characterized by two domains of concavity, (in the vicinity, and far away from the origin), separated by a domain of convexity, fracture procedes through a successive formation of a finite number of cracks of small but finite size. We conjecture that the different modes of fracture, produced by this simple model, may be associated with various experimentally well-documented regimes of localized and distributed damage. A standard model in fracture mechanics is based on the assumption that the total energy of a body is a sum of a bulk term, representing the strain energy, and of a surface term, representing the energy associated with the displacement discontinuity. This assumption was introduced by Griffith, and modified later by Barenblatt to account for the cohesive forces which oppose fracture opening. A one-dimensional model of this type with convex bulk energy and concave cohesive energy is capable of reproducing a phenomenon of localized fracture: for a bar subject to a prescribed elongation, the minimum of the total energy corresponds to configurations with a single crack 12, 4, 51. The overall response in this case may be either discontinous, with an abrupt drop of stress, or gradual, with a continuous decrease of stress, depending on the length of the bar. These two regimes, which one can loosely associate with brittle and ductile fracture, can also be obtained from a model of a chain made of nonlinear springs with a Lennard-Jones potential: for a sufficiently large number of springs, this discrete system can be approximated by a continuum model with a convex bulk and a concave cohesive energy (8). This type of behavior changes drastically if the cohesive energy is convex at the origin and concave away from the origin (5). In this case, for elongations belonging to a certain interval, there are no piecewise continuous minimizers, and the energy minimum is attained at a configuration with an infinite number of infinitesimal cracks. This situation can be described in the context of the theory of structured defomzations (6). The resulting expression of the energy minimum in the one-dimensional model agrees with the three- dimensional relaxation in the class of functions with this level of regularity (3). In the present communication we report some preliminary results for a one-dimensional model with a cohesive energy which is convex on a finite segment separated from the origin and concave outside. As we show, this model predicts the formation of a finite number of cracks, one after another, as the total elongation increases (7). This regime of distributed cracking can be viewed as a "quantized propagation of damage. When the concave region near the origin shrinks to zero the model recovers structured deformations, and when the convex region disappears a localized fracture appears as another limiting case.

Identification through mesoscopic simulations of macroscopic parameters of physically based constitutive equations for the plastic behaviour of fcc single crystats

Abstract: The objective of this work is to derive the parameters of macroscopie constitutive equations for the plasticity of fee single crystals with the help of simulations performed at a dislocation level. The macroscopic model is based on the leading physical mechanisms which are involved in the plastic deformation. The three involved constitutive laws use the total dislocation densities on each glide system as fundamental variables. Those three expressions are derived from physieal processes governing the behaviour of a single dislocation and adapted to be used at the macroscopic scale. Literature results could lie widely used for the identification of the material parameters for different fee materials but some of the parameters are mean values and must be seen as phenomenological parameters so that a good way to determine such values consists to use a numerical tool where each dislocation is individually simulated in a three dimensional network. Such a tool works at a mesoscopic scale (typically several microns ) and deals with dislocations discretized into pure screw and edge segments. It includes all the well-known elementary events governing the dislocation motion such as the line tension effect, the Frank-Read multiplication mechanisms, the cross-slip events and the function formations. The cross-analysis of several specif mesoscopic simulations allows to delerminate the values of some macroscopic parameters and also to check the validity of both models.

Fast analysis of traces and major elements with ED(P)XRF using polarized X-rays: TURBOQUANT

Abstract: Une nouvelle methode d'analyse elementaire quantitative par fluorescence X, utilisant la dispersion en energie et une excitation polarisee est dite TURBOQUANT. La flexibilite de la methode permet d'aborder aisement l'analyse d'echantillons dont les matrices sont tres differentes. Une correction automatique des effets de matrice assure la justesse des resultats pour une large gamme d'echantillons liquides ou solides. Des exemples d'analyses par TURBOQUANT illustrent les hautes performances de la technique presentee.

Non-local failure and damage evolution rule : Application to a dilatant crack model

Abstract: A non-local crack propagation and damage evolution criteria were discussed in detail by the authors in [13-15] and applied to predict crack initiation from sharp notches and damage accumulation for complex cyclic loading programs In the present paper the non-local condition is applied to the case of a cracked body subjected to compression and shear fractions inducing frictional slip and dilatancy at crack interfaces The crack propagation directions with critical loading conditions are obtained taking into account the crack asperity interaction and dilatancy induced by slip The material strength and compliance variation can be predicted from the model

Modeling the transitions from capacitive to inductive to wave-sustained rf discharges

Abstract: Radio frequency (rf) plasma sources used in the processing of thin films can be divided into three distinct categories: capacitive (E), inductive (H), and wave (W) -sustained (e.g., helicon) discharges. As the excitation power or voltage is increased, transitions from capacitive to inductive to helicon discharges are often observed, in some cases exhibiting hysteresis. A model is developed to determine these transitions based on the electron energy balance in the discharge and the coupling between capacitive, inductive, and helicon electron energy deposition. R6sum6: Les sources plasma radiofrequence (rf) qu'on utilise dans les processus de films minces peuvent se classer en trois categories : decharges capacitives (E), inductives 0 et entretenues par une onde CN) comme les decharges helicon. Lorsqu'on augmente la puissance ou la tension d'excitation, on observe souvent des transitions de regimes de decharges : capacitives - inductives - helicon. Dans certains cas, ces transitions presentent un hysteresis. Nous developpons un modele pour dderminer ces transitions a partir d'un bilan d'energie electronique dans la decharge et du couplage entre d&& d'energie electronique capacitif, inductif et helicon.

Homogenization of discrete media

Abstract: Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extand discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures: the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function.

An estimation of overall properties of heterogeneous Cosserat materials

Abstract: In this work, we try to answer the following question: What is the effective characteristic length of a mixture of Cosserat continua? More generally, homogenization methods for heterogeneous Cosserat media are proposed and applied to the case of linear elasticity. They first application deals with a beam network regarded as a discrete Cosserat medium and the second with a continuous heterogeneous Cosserat continuum.

Wave propagation and localisation in nonlocal and gradient-enhanced damage models

Abstract: Classical continuum descriptions of material degradation may cease to be mathematically meaningful in case of softening-induced localisation of deformation. Several enhancements of conventional models have been proposed to remove this deficiency. The properties of two of these so-called regularisation methods, the nonlocal and the gradient approaches, are examined and compared in a continuum damage context. It is shown that the enhanced models allow for the propagation of waves in the softening zone, in contrast to conventional damage models. For both types of enhancement wave propagation becomes dispersive. The behaviour under quasi-static loading conditions is studied numerically. Finite element simulations of a one-dimensional problem yield quite similar results for the nonlocal and a gradient-enhanced model. The gradient enhancement has been used to model concrete fracture, yielding results which are in good agreement with experimental data.

A dislocation based gradient plasticity model

Abstract: A crystal plasticity model including gradient terms was suggested for a double slip geometry. The dislocation densities for the two slip systems were considered as internal variables of the model. Diffusion-like second derivative terms were attributed to dislocation cross-slip. A relation between the 'diffusion coefficient' and the micromechanical quantities, such as the dislocation cross-slip probability and the cross-slip distance, was established. To demonstrate that a model of this type can be successfully used in conjunction with finite element analysis, a simplified case of a shear layer, with two slip systems sharing a common slip plane, was studied.

Computation of coarse grain structures using a homogeneous equivalent medium

Abstract: This paper deals with the improvement of concentration relations when some basic hypothesis of homogenization techniques are no longer valid inducing important errors in the deduced local fields. In the first part of this work we propose a new formalism of the standard concentration rules developed in the homogenization of periodic media framework. In a second part, we insist on the fact that a homogeneous equivalent medium replacing a coarse grain material is in fact expected to be a generalized continuum. Additional stiffnesses must be attributed to the unit cell and special non-homogeneous boundary conditions and their periodic counterparts are proposed. The resulting HEM turns out to be a Cosserat continuum.

Piezoelectric bimorph cantilever for actuating and sensing applications

Abstract: Back side bulk micromachining has been combined with front side ferroelectric technology for making a piezo-active microsystem including a sensor and an actuator on a silicon cantilever. Stress and thickness control of the thin (10μ) silicon beam are obtained by an original technology. The PZT piezoelectric material is deposited by the sol-gel spin coating technique. Due to the partial incompatibility of piezoelectric PZT capacitor with the methods of IC processing, a new processing route had to he found that is able to protect the sensitive area on the front side during back side micromachining. Additionally, a new method to pattern aluminum metallization in contact with platinum had to he developed to avoid electrochemical reactions in etching solutions The beam can he sensed and actuated by the piezoelectric direct and (resp) converse effects, Sensor voltage response and actuator displacement are given up to the resonance frequency of 2.6 kHz. The device is planned to he used in a self regulated closed loop where the feedback electronics will be integrated on the chip.

A Cryogenic GaAs PHEMT/ Ferroelectric Ku-Band Tunable Oscillator

Abstract: A Ku-band tunable oscillator operated at and below 77 K is described. The oscillator is based on two separate technologies: a 0.25 mm GaAs pseudomorphic high electron mobility transistor (PHEMT) circuit optimized for cryogenic operation, and a gold microstrip ring resonator patterned on a thin ferroelectric (SrTiO3) film which was laser ablated onto a LaAlO3 substrate. A tuning range of up to 3% of the center frequency was achieved by applying dc bias between the ring resonator and ground plane. To the best of our knowledge, this is the first tunable oscillator based on a thin film ferroelectric structure demonstrated in the microwave frequency range. The design methodology of the oscillator and the performance characteristics of the tunable resonator are described.

On Ward-Takahashi identities for the Parisi spin glass

Abstract: The introduction of small permutations allows us to derive Ward-Takahashi identities for the spin-glass, in the Parisi limit of an infinite number of steps of replica symmetry breaking. The first identities express the emergence of a band of Goldstone modes. The next identities relate components of (the Replica Fourier Transformed) 3-point function to overlap derivatives of the 2-point function (inverse propagator). A jump in this last function is exhibited, when its two overlaps are crossing each other, in the special simpler case where one of the cross-overlaps is maximal.

Interface magnetism in Fe-based nanocrystalline alloys

Abstract: Nanoscale materials exhibit properties that can not be find in larger scale system due to the crystal size effects as well as structural variations between the interfacial regions and the crystalline interior. In this paper the consideration of the finite-size effects are limited to a special class of nonconventional granular materials produced by the devitrification of Fe-based amorphous ribbons. The complementary microstructural and magnetic studies show that in such mesoscopic systems the interfaces exhibit identifiable properties. The data presented do not provide the detailed picture of the internal structure of the boundary regions but bring information about their basic structural and magnetic properties. In particular the influence of the magnetic state of the intergranular amorphous matrix (ferro-or paramagnetic) on the local magnetic behavior of the interfaces is considered. The effect of the symmetry restriction at grain boundaries on the structurally sensitive parameter such as a magnetostriction is also presented and discussed.

Survey of magnetic properties during and after amorphous-nanocrystalline transformation

Abstract: In the first part of this paper, the metallurgical background of the amorphous-nanocrystalline transformation leading to the development of soft magnetic properties is discussed. The mechanisms of nucleation as well as grain growth hindering will be treated on the basis of metallurgical principles. The development of some technical magnetic properties during the nanocrystallization such as the loss characteristics and the change in the domain structure will be compared. Finally, the development of the field-induced anisotropy obtained during different heat treatments will be compared for the FINEMET-type and Fe-Zr based nanocrystalline alloys.

A continuum mechanical gradient theory with applications to fluid mechanics

Abstract: A gradient theory of grade two based on an axiomatic conception of a nonlocal continuum theory for materials of grade n is presentated. The total stress tensor of rank two in the equation of linear momentum contains two higher stress tensors of rank two and three. In the case of isotropic materials both the tensor of rank two and three are tensor-valued functions of the second order strain rate tensor and its first gradient so that the equation of motion is of order four. The necessary boundary conditions for real boundaries are generated by using so-called porosity tensors. This theory is applied to two experiments. To a velocity profile of a turbulent COUETTE flow of water and a POISEUILLE flow of a blood like suspension. On the basis of these experimental data the material and porosity coefficients are identified by numerical algorithms like evolution strategies.

Theoretical analysis of localized magnetic flux measurement by needle probe

Abstract: Analytical study of the needle probe measurement of magnetic flux was performed on the basis of the electromagnetic theory to provide an advanced theoretical backbone for the measuring method. Provided that the flux change in the specimen is homogeneous, the electromotive force induced between the needles represents exactly the flux change in the area between the needles. The measuring error in the needle probe measurement is caused by lack of homogeneity in the flux change postulated in the theory. Among several possible causes of flux non-homogeneity, the existence of domain structure is most intrinsic in Iocalized area measurements, so that in this study the measuring error due to this cause was calculated theoretically in detaiL It can be concluded that even in the cases of large domain size often occurring in oriented core materials, the localized measurements by the needle probe provide fairly reliable measure of the flux change in the area.

Magnetostriction and its contribution to noise in a PWM inverter fed induction machine

Abstract: PWM inverter fed induction machines generate significant noise. The noise comes not only from radial air gap forces but also from magnetostriction. It turns out that magnetostrictive and radial air gap forces have about the same magnitude in medium sized induction machines. A FEM model, based on actual magnetostrictive data for electric steel sheet, has been derived for calculation of magnetostrictive deformation of the stator. The FEM model has been verified on a test machine in which the radial air gap force is eliminated. Measurements with the test machine connected to a PWM inverter reveal the same spectrum as from standard PWM inverter fed machines. Thus there is reason to believe that noise comes from magnetostrictive deformation and not from magneto acoustic emission (MAE).

Giant magnetoimpedance in soft magnetic amorphous and nanocrystalline materials

Abstract: Recent results on giant magnetoimpedance (GMI) are reviewed. After a brief outline on the existent theories which explain the phenomenon, a general overview of experimental data on amorphous wires and ribbons is given. Furthermore, the GMI effect is observed in soft magnetic crystalline and nanocrystalline samples, and few investigations done in different systems are presented. To conclude, a recently observed effect in amorphous materials, the so-called magnetoimpedance aftereffect, is reported and explained as a consequence of the relaxation of the circular magnetic permeability.

Relationship between precursor chemistry and microstructure of CSD derived PZT films

Abstract: The microstructure of CSD PZT based thin films is mainly controlled by the substrate, electrode and/or thermal treatment. However, it can be significantly altered by the choice of starting compounds and solution-precursor synthesis conditions. The choice of transition metal alkoxide, namely propoxide or butoxide in the methoxyethanol based PZT route, results in different reactions with lead acetate. While the propoxides predominantly react via the addition reaction, the esterification reaction is predominant for butoxides. A finer microstructure of PbZrO 3 films is attained from propoxides and a coarser one starting from butoxides. Lead acetate can be replaced by lead oxide in the methoxyethanol based PZT route. The crystallisation of the latter is characterised by easy nucleation of the perovskite phase as compared to acetate derived films. The type of lanthanum precursor, i.e. acetate or nitrate in the acetic acid based CSD PLZT route, influences the functional group content of formamide modified sots and consequently affects the microstructure of the thin films. La-nitrate based films consist of about 100 nm sized grains and La-acetate ones are characterised by the cluster-type microstructure.

Application of an exactly invertible hysteresis model to magnetic field computations

Abstract: We consider an hysteresis model recently proposed, where the magnetic constitutive law M(H) is derived from considerations on domain wall motion. For this model we show that it is possible to build up the inverse constitutive law H(M), exactly, The inverse constitutive relation is applied to one-dimensional numerical computation of flux distributions and eddy currents in a magnetic slab.

Deformation and compatibility for elasto-plastic micropolar materials with application to geomechanical problems

Abstract: The consideration of empty porous solid materials (e.g. granular skeletons) naturally falls into the macroscopic continuum mechanical concept of the Theory of Porous Media (TPM). It is well known from Various experiments that granular materials tend to localization phenomena (e. g. shear bands) as a result of local concentrations of plastic strains. The numerical simulation of these phenomena generally reveals an ill-posed problem with the consequence that the shear band width strongly depends on the chosen spatial discretization. To overcome this problem, an internal length scale must be introduced, which, in the present article, is a result of the inclusion of micropolar degrees of freedom in the sense of the Cosserat brothers. Based on this approach, the contribution of the present article is to show that the micropolar compatibility condition of the geometrically linear approach is a direct consequence of the general finite micropolar theory. Furthermore, as a result of the micropolar compatibility condition applied to elasto-plastic problems, there is no independent evolution equation for the rate of curvature tensor, since this quantity is uniquely determined by the the gradient of the plastic strain rate. Proceeding from the fact that micropolar theories are downward compatible to the usual standard approach, the numerical example is carried out on the basis of a model adaptive strategy, where an automatic switch between the standard and the micropolar approach guarantees that the additional micropolar degrees of freedom are only taken into consideration in those domains, where micropolar rotations occur, i.e. in the shear band zone.