Implementation of a Deformation Model for Pressure Tubes under Irradiation

Current semi-empiric deformation models for in-reactor deformation of Zr2.5Nb CANDU pressure tubes are based on the physical model of Christodoulou et al. (Proc. 11th Int. Symp. Zirc. Nucl. Ind., ASTM STP 1295 (1996), p. 518) and consider material texture effects via the code'SELFPOLY' introduced by Tomé et al. (Philos. Mag. A67 (1993), p. 917) and Turner et al. (Philos. Mag. A 79 (1999), p. 2505). This code makes use of a 'tangent' self-consistent approach proposed by Molinari et al. (Acta Metall. 35 (1987), p. 2983) to obtain the overall response of a viscoplastic polycrystalline system in terms of the local response of the single crystals and their microstructuralmorphology. More recently, Liu and Ponte Castañeda (J. Mech. Phys. Solids 52 (2004), p. 467)derived a 'generalized-secant' self-consistent approach which has been found to improve substantially on the earlier 'tangent' approach in some cases. In this work we study the influence of the linearization procedure on the predictions for the deformation of pressure tubes. The calculations are carried out by means of the VPSC code of Lebensohn et al. (14th International Conference on Textures of Materials 495-497 (2005), p. 955). It is found that the predictions based on the 'tangent' and 'generalized-secant' approaches are quite similar, and hence the use of a 'generalized-secant' approach is not recommended for this particular problem in view of its higher computational cost. Moreover, analyzing the current in-reactor deformation model reviewed by Holt (J. Nucl. Mat. 372 (2008), p. 182), a restriction in the stress state was found. The stress tensor components are projected to the material axes that are not guaranteed to be principal, for that reason the constitutive laws are not valid for a general stress state neglecting in particular the gravity forces. Based on the same constitutive law structure, a modification is proposed that accounts for a general stress state via coupling VPSC-FEM codes.Publicado en: Mecánica Computacional vol. XXXV no.32Facultad de Ingenierí

Stellar Population Gradients in Bulges along the Hubble Sequence: I. The Data

This is the first paper presenting our long-term project aimed at studying the nature of bulges through the analysis of their stellar population gradients. We present deep spectroscopic observations along the minor axis and the data reduction for a sample of 32 bulges of edge-on spiral galaxies. We explain in detail our procedures to measure their dynamical parameters (rotation curves and velocity dispersion profiles) and line-strength indices, including the conversion to the Lick/IDS system. Tables giving the values of the dynamical parameters and line-strength indices at each galactocentric radius are presented (in electronic form) for each galaxy of the sample. The derived line-strength gradients from this dataset will be analyzed in a forthcoming paper to set constraints on the different scenarios for the formation of the bulges.Comment: Accepted for publication in A&

The metallicity gradient as a tracer of history and structure : the Magellanic Clouds and M33 galaxies

Original article can be found at: http://www.aanda.org/ Copyright The European Southern Observatory (ESO) DOI: 10.1051/0004-6361/200912138Context. The stellar metallicity and its gradient place constraints on the formation and evolution of galaxies. Aims. This is a study of the metallicity gradient of the LMC, SMC and M33 galaxies derived from their asymptotic giant branch (AGB) stars. Methods. The [Fe/H] abundance was derived from the ratio between C- and M-type AGB stars and its variation analysed as a function of galactocentric distance. Galaxy structure parameters were adopted from the literature. Results. The metallicity of the LMC decreases linearly as −0.047±0.003 dex kpc−1 out to ∼8 kpc from the centre. In the SMC, [Fe/H] has a constant value of ∼−1.25 ± 0.01 dex up to ∼12 kpc. The gradient of the M33 disc, until ∼9 kpc, is −0.078 ± 0.003 dex kpc−1 while the outer disc/halo, out to ∼25 kpc, has [Fe/H] ∼ −1.7 dex. Conclusions. The metallicity of the LMC, as traced by different populations, bears the signature of two major star forming episodes: the first one constituting a thick disc/halo population and the second one a thin disc and bar due to a close encounter with the Milky Way and SMC. The [Fe/H] of the recent episode supports an LMC origin for the Stream. The metallicity of the SMC supports star formation, ∼3 Gyr ago, as triggered by LMC interaction and sustained by the bar in the outer region of the galaxy. The SMC [Fe/H] agrees with the present-day abundance in the Bridge and shows no significant gradient. The metallicity of M33 supports an “insideout” disc formation via accretion of metal poor gas from the interstellar medium.Peer reviewe

Double-Barred Galaxies: I. A Catalog of Barred Galaxies with Stellar Secondary Bars and Inner Disks

I present a catalog of 67 barred galaxies which contain distinct, elliptical stellar structures inside their bars. Fifty of these are double-barred galaxies: a small-scale, "inner" or "secondary" bar is embedded within a large-scale, "outer" or "primary" bar. I provide homogenized measurements of the sizes, ellipticities, and orientations of both inner and outer bars, along with with global parameters for the galaxies. The other 17 are classified as "inner-disk" galaxies, where a large-scale bar harbors an inner elliptical structure which is aligned with the galaxy's outer disk. Four of the double-barred galaxies also possess inner disks, located in between the inner and outer bars. While the inner-disk classification is ad-hoc -- and undoubtedly includes some inner bars with chance alignments (five such probable cases are identified) -- there is good evidence that inner disks form a statistically distinct population, and that at least some are indeed disks rather than bars. In addition, I list 36 galaxies which may be double-barred, but for which current observations are ambiguous or incomplete, and another 23 galaxies which have been previously suggested as potentially being double-barred, but which are probably *not*. False double-bar identifications are usually due to features such as nuclear rings and spirals being misclassified as bars; I provide some illustrated examples of how this can happen.Comment: LaTeX, 25 pages, 6 EPS figures. Typos fixed and title slightly altered; accepted by Astronomy & Astrophysics. Version with full-resolution figures available at http://www.iac.es/galeria/erwin/research

Comportement macroscopique et statistiques des champs dans les composites viscoplastiques.

We have developed nonlinear homogenization methods capable of delivering estimates not only for the macroscopic behavior but also for the field statistics in viscoplastic composites. These methods are based on suitably designed variational principles, which make use of an optimally chosen 'linear comparison composite', allowing direct conversion of linear estimates into corresponding estimates for the effective potentials of nonlinear composites. In order to extract estimates for the field statistics from these methods, a novel procedure is proposed, ! making use of suitably perturbed effective potentials. By means of this procedure, we obtain estimates for the first moments of the local fields in each phase that are entirely consistent with the corresponding estimates for the effective behavior. In addition, unlike earlier approaches, this procedure is not limited to first and second moments, and can be used to estimate higher-order moments as well as the phase average of more general convex functions of the fields. Sample results are given for two-phase composites with random 'particulate' microstructures exhibiting overall transversely isotropic and isotropic symmetry. Their accuracy is assessed by confronting them with corresponding exact results for nonlinear sequential laminates. Homogenization estimates are found to be in good agreement with the exact results, even for high nonlinearities, when the strain-rate fields are found to become strongly heterogeneous.La plus part des matériaux présentant un intérêt en ingénierie et sciences physiques sont intrinsèquement hétérogènes, comme par example les composites renforcés, les matériaux poreux, et les solides polycristallins (e.g., métaux, glace, plusieurs roches). Un problème fondamental en mécanique des matériaux réside dans l'estimation de la réponse macroscopique de tels matériaux hétérogènes à partir des propriétés et de l'arrangement géométrique (microstructure) de leurs constituants. En plus, l'incorporation de l'effet des processus locaux (e.g., évolution de la microstructure, endommagement, ecruisage, recristallisation) sur la réponse macroscopique exige des connaissances statistiques sur la distribution spatiale des champs locaux dans le matériau. A cet effet, nous avons développé des méthodes non-linéaires d'homogénéisation capables de fournir des estimations non seulement du comportement macroscopique mais également des statistiques des champs dans les composites viscoplastiques. Ces méthodes sont basées sur des principes variationnels convenablement conçus, qui se servent d'un composite linéaire de comparaison choisi de façon optimale, permettant une conversion directe des estimations linéaires aux estimations correspondantes pour les potentiels effectifs des composites non-linéaires. Afin d'extraire des estimations des statistiques des champs à partir de ces méthodes, nous proposons une nouvelle procédure basée sur l'utilisation de potentiels effectifs convenablement perturbés. Au moyen de cette procédure sont obtenues des estimations pour les premiers moments des champs locaux dans chaque phase, qui sont conformes aux estimations correspondantes pour le comportement effectif. De plus, contrairement aux approches précédantes, cette procédure n'est pas limité aux premiers et seconds moments, et peut être employée pour estimer les moments d'ordre supérieur, aussi bien que la moyenne par phase des fonctions (convexes) plus générales des champs. Des résultats sont donnés pour des composites biphasés à microstructures particulaires et aléatoires, isotropes transverse ou isotropes. La pertinence de ces résultats est évaluée en les comparant aux résultats exacts correspondant à des matériaux stratifiés séquentiels non-linéaires. Les estimations obtenues s'avèrent en bon accord avec les résultats exacts, même pour des non-linéarités élevées pour lesquelles les champs de déformation sont fortement hétérogènes

Macroscopic behavior and field statistics in viscoplastic composites

Most man-made as well as natural materials of interest in engineering and physical sciences are intrinsically heterogeneous. Common examples are particle-reinforced composites, porous materials, and polycrystalline solids such as metals, ice, and many rocks. A fundamental problem in mechanics of materials is the estimation of the macroscopic response of such heterogeneous materials from the properties and geometrical arrangement (microstructure) of their constituents. In addition, incorporating the effect of local processes (e.g., microstructure evolution, damage, work hardening, recrystallization) on the macroscopic response requires statistical information about spatial distribution of the local fields within the material. To this end, we have developed nonlinear homogenization methods capable of delivering estimates not only for the macroscopic behavior but also for the field statistics in viscoplastic composites. These methods are based on suitably designed variational principles, which make use of an optimally chosen \u27linear comparison composite\u27, allowing direct conversion of linear estimates into corresponding estimates for the effective potentials of nonlinear composites. In order to extract estimates for the field statistics from these methods, a novel procedure is proposed, making use of suitably perturbed effective potentials. By means of this procedure, we obtain estimates for the first moments of the local fields in each phase that are entirely consistent with the corresponding estimates for the effective behavior. In addition, unlike earlier approaches, this procedure is not limited to first and second moments, and can be used to estimate higher-order moments as well as the phase average of more general convex functions of the fields. Sample results are given for two-phase composites with random \u27particulate\u27 microstructures exhibiting overall transversely isotropic and isotropic symmetry. Their accuracy is assessed by confronting them with corresponding exact results for nonlinear sequential laminates. Homogenization estimates are found to be in good agreement with the exact results, even for high nonlinearities, when the strain-rate fields are found to become strongly heterogeneous

Macroscopic behavior and field statistics in viscoplastic composites

Most man-made as well as natural materials of interest in engineering and physical sciences are intrinsically heterogeneous. Common examples are particle-reinforced composites, porous materials, and polycrystalline solids such as metals, ice, and many rocks. A fundamental problem in mechanics of materials is the estimation of the macroscopic response of such heterogeneous materials from the properties and geometrical arrangement (microstructure) of their constituents. In addition, incorporating the effect of local processes (e.g., microstructure evolution, damage, work hardening, recrystallization) on the macroscopic response requires statistical information about spatial distribution of the local fields within the material. To this end, we have developed nonlinear homogenization methods capable of delivering estimates not only for the macroscopic behavior but also for the field statistics in viscoplastic composites. These methods are based on suitably designed variational principles, which make use of an optimally chosen \u27linear comparison composite\u27, allowing direct conversion of linear estimates into corresponding estimates for the effective potentials of nonlinear composites. In order to extract estimates for the field statistics from these methods, a novel procedure is proposed, making use of suitably perturbed effective potentials. By means of this procedure, we obtain estimates for the first moments of the local fields in each phase that are entirely consistent with the corresponding estimates for the effective behavior. In addition, unlike earlier approaches, this procedure is not limited to first and second moments, and can be used to estimate higher-order moments as well as the phase average of more general convex functions of the fields. Sample results are given for two-phase composites with random \u27particulate\u27 microstructures exhibiting overall transversely isotropic and isotropic symmetry. Their accuracy is assessed by confronting them with corresponding exact results for nonlinear sequential laminates. Homogenization estimates are found to be in good agreement with the exact results, even for high nonlinearities, when the strain-rate fields are found to become strongly heterogeneous

Variational linear comparison bounds for nonlinear composites with anisotropic phases. I. General results

International audienceThis work is concerned with the development of bounds for nonlinear composites with anisotropic phases by means of an appropriate generalization of the ‘linear comparison’ variational method, introduced by Ponte Castañeda for composites with isotropic phases. The bounds can be expressed in terms of a convex (concave) optimization problem, requiring the computation of certain ‘error’ functions that, in turn, depend on the solution of a non-concave/non-convex optimization problem. A simple formula is derived for the overall stress–strain relation of the composite associated with the bound, and special, simpler forms are provided for power-law materials, as well as for ideally plastic materials, where the computation of the error functions simplifies dramatically. As will be seen in part II of this work in the specific context of composites with crystalline phases (e.g. polycrystals), the new bounds have the capability of improving on earlier bounds, such as the ones proposed by deBotton and Ponte Castañeda for these specific material systems

Field statistics in nonlinear composites. I. Theory

International audienceThis work presents a means for extracting the statistics of the local fields in nonlinear composites from the effective potential of suitably perturbed composites. The idea is to introduce a parameter in the local potentials, generally a tensor, such that differentiation of the corresponding effective potential with respect to the parameter yields the volume average of the desired quantity. In particular, this provides a generalization to the nonlinear case of well-known formulas in the context of linear composites, which express phase averages and second moments of the local fields in terms of derivatives of the effective potential. Such expressions are useful since they allow the generation of estimates for the field statistics in nonlinear composites, directly from homogenization estimates for appropriately defined effective potentials. Here, use is made of these expressions in the context of the ‘variational’, ‘tangent second-order’ and ‘second-order’ homogenization methods, to obtain rigorous estimates for the first and second moments of the fields in nonlinear composites. While the variational estimates for these quantities are found to be identical to those proposed in previous works, the tangent second-order and second-order estimates are found be different. In particular, the new estimates for the first moments given in this work are found to be entirely consistent with the corresponding estimates for the macroscopic behaviour. Sample results for two-phase, power-law composites are provided in part II of this work