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  • 1
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Eine frühere theoretische Studie [3], die den Effekt von Einschlusslänge und Geometrie auf den totalen Elastizitätsmodul von druch Fasern oder Whisker (Haarkristalle) verstärkte Verbundmaterialien behandelt, wird hier erweitert. Moduln, besonders für Stoffe, die geringe Dispersionen von ausgerichteten Einschlüssen schlanker, aber sonst willkürlicher axialer Geometrie haben ergeben mit der „Slender-Body”-Theorie für den elastischen Bereich $$\frac{{E^* }}{E}\kappa ^2 \ln 2/\kappa〈〈 1$$ , wobei, κ, die Aspektratio des Einschlusses, kein ist undE * undE Young's Moduln für den Einschluss und die Matrix sind. Um die Kontinuität mit den Resultaten [3] für den starren Bereich $$\frac{{E^* }}{E}\kappa ^2 \ln 2/\kappa〈〈 1$$ aufrechtzuerhalten, ist der Spezialfall schlanker, abgeplatteter sphärischer Einschlüsse betrachtet worden. Ausdrücke für die Moduln, gültig für alle Werte der oben angegebenen Parameter, werden von einer allgemeinen Lösung nach Eshelby abgeleitet. Diese analytischen Ergebnisse werden in kompakter graphischer Form dargestellt, mit der man bequem die Moduln abschätzen kann, wenn die schlanken Einschlüsse eine nicht gestreckte sphärische Geometrie besitzen.
    Notes: Abstract An earlier theoretical, study [3] regarding the effect of inclusion length, and geometry on the bulk elastic moduli of fiber-or whisker-reinforced composite materials is hereby extended. Specifically, with slender-body theory, moduli for materials containing dilute dispersions of aligned inclusions of slender, but otherwise arbitrary, axial geometry are found for the “elastic” range, $$\frac{{E^* }}{E}\kappa ^2 \ln 2/\kappa〈〈 1$$ , where κ, the aspect ratio of the inclusion, is small andE * andE are respectively, Young's moduli for the inclusion and the matrix. To provide continuity with the results of [3] for the rigid range, $$\frac{{E^* }}{E}\kappa ^2 \ln 2/\kappa 〉 〉 1$$ , the special case of slender prolate, spheroidal inclusions is considered and expressions for the moduli which are valid for all values of the above parameter are derived from a known general solution obtained by Eshelby. These analytic results are then presented in a compact graphical form which provides a useful means for estimating the moduli when the slender inclusions have non-prolate spheroidal geometries.
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  • 2
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Cet article donne les résultats d'une application de la théorie des corps élancés à la mécanique des milieux continus. On y analyse la réponse d'un milieu élastique infini, contenant une seule particular rigide et élancée, quand il est soumis à des efforts donnés. La théorie générale est resteinte à une classe de particules possédant une symmétrie de révolution, mais étant au moins aussi pointues que des sphéroïdes allongés. Dans certains cas les résultats peuvent néanmoins être appliqués approximativement à des inclusions cylindriques circulaires. A partir de cette solution, on a calculé les cinq modules d'élasticité indépendants qui caractérisent l'état global d'un milieu à faible concentration de particules, ces dernières étant toutes alignées dans une même direction. Les résultats sont donnés sous forme de développement de perturbation, en fonction du coefficient de forme,K, des particules. L'accroissement de la rigidité dû á leur présence est de l'ordre de $$\frac{\varphi }{{K^2 \log \tfrac{2}{K}}}$$ pour le module d'élongation de Young, et de l'ordre de π pour les quatre autres modules, où π représente le rapport du volume des particules au volume total.
    Notes: Summary Using slender-body theory the effective elastic moduli of a certain class of composite materials are determined by analyzing the response of an infinite elastic medium, containing a single slender rigid inclusion, to a given applied strain. Solutions are found as perturbation expansions in the slenderness ratio of the inclusion, κ, which is small. These then yield the five independent elastic moduli, which characterize the macroscopic state of a dilute dispersion of slender rigid inclusions aligned in a common direction. The increase in rigidity due to the inclusions is found to be of orderφ/κ 2 ln(2/κ) for the longitudinal Young's modulus and of order π for the other four moduli, where π is the volume fraction of inclusions. Although the general theory is restricted to axisymmetric inclusions having ends which are no more blunt than a prolate spheroid, the results are shown to be valid approximations for circular cylinders in certain cases.
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  • 3
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Die Elastizitätsmoduli von faserverstärkten Composites hängen bekanntlich u.a. von dem Modulverhältnis zwischen Kernmaterial und Fasern sowie von der Faserlänge ab. Diese Abhängigkeit wurde experimentell bei niedrigen Volumenkonzentrationen der Faser untersucht. Zu diesem Zweck wurden Modelle aus Epoxy-Gussharz und aus zerschnittenen Chromstahlfasern hergestellt. Die Elastizitätsmoduli liessen sich durch ein Ultraschall-Pulsverfahren messen. Die Resultate bestätigen zum Teil die von den Autoren früher hergeleiteten analytischen Ausdrücke für die Ersatzmoduli. Sie zeigen aber auch sogar bei niedriger Volumenkonzentration die primäre Bedeutung der Faserdispersion.
    Notes: Summary The dependence of the elastic moduli of chopped-fiber reinforced composites on the modulus ratio and the fiber length was studied experimentally at low volume fractions of fibers. For this purpose model composites were fabricated from an epoxy casting resin and chopped stainless steel fibers, and the elastic moduli of these samples were measured by an ultrasonic pulse technique. The results confirm in part the analytic expressions for the bulk moduli of such composites previously derived by the authors, but also emphasize the importance of fiber dispersion even at dilute concentrations.
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  • 4
    Electronic Resource
    Electronic Resource
    [s.l.] : Nature Publishing Group
    Nature 421 (2003), S. 490-491 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Fundamental advances in colloid science often depend on physical models, which are made by dispersing carefully tailored particles, less than a micrometre in size, in pure aqueous or organic liquids. Such dispersions can be characterized by methods such as light scattering and confocal microscopy, ...
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  • 5
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Process Engineering, Biotechnology, Nutrition Technology
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    [s.l.] : Macmillian Magazines Ltd.
    Nature 401 (1999), S. 893-895 
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Three-dimensional ordered colloidal systems with lattice constants comparable to the wavelength of visible light might find important application as photonic crystals, optic filters and switches, and chemical sensors. Colloidal crystallization has been actively studied, leading to the ...
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  • 7
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Macromolecules 22 (1989), S. 266-276 
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 8
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 10
    ISSN: 1520-5835
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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