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  • 1
    Digitale Medien
    Digitale Medien
    Equivalence and convergence of direct and indirect methods for the numerical solution of singular integral equations (1981)
    Springer
    Computing 27 (1981), S. 71-80 
    Details
    ISSN: 1436-5057
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Direkte Methoden zur Lösung von singulären Integralgleichungen vom Cauchy-Typus (S. I. G.) beruhen auf der Gaussschen Regel für numerische Integration, wobei die S. I. G. durch Anwendung der resultierenden Funktionalgleichung an geeignet gewählten Kollokationspunkten auf ein lineares Gleichungssystem reduziert wird. In diesem Artikel wurde die Äquivalenz dieser Methode mit derjenigen, welche auf der Lagrangeschen Interpolations-Approximation der unbekannten Funktion, beruht, gezeigt. Indirekte Methoden zur Lösung von S. I. G. können durch Anwendung derselben numerischen Regel an der Fredholmschen Integralgleichung, auf welche die S. I. G. reduziert wird, erhalten werden. In diesem Artikel wurde gezeigt, daß beide Methoden, im Sinne, daß sie dieselben numerischen Resultate liefern, äquivalent sind. Schließlich wurde mit Hilfe dieser Resultate der, Fehler und die Konvergenz der Methoden festgestellt.
    Notizen: Abstract Direct methods for solving Cauchy-type singular integral equations (S.I.E.) are based on Gauss numerical integration rule [1] where the S.I.E. is reduced to a linear system of equations by applying the resulting functional equation at properly selected collocation points. The equivalence of this formulation with the one based on the Lagrange interpolatory approximation of the unknown function was shown in the paper. Indirect methods for the solution of S. I. E. may be obtained after a reduction of it to an equivalent Fredholm integral equation and an application of the same numerical technique to the latter. It was shown in this paper that both methods are equivalent in the sense that they give the same numerical results. Using these results the error estimate and the convergence of the methods was established.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02243439
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  • 2
    Digitale Medien
    Digitale Medien
    On the evaluation of adhesion between phases in fiber composites (1984)
    Springer
    Colloid & polymer science 262 (1984), S. 929-938 
    Details
    ISSN: 1435-1536
    Schlagwort(e): Fibrous composites ; mesophase ; unfolding models
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Notizen: Abstract A theoretical model was introduced for the evaluation of the boundary layer developed between the main phases during the preparation of unidirectional fiber composites. It has been shown that this thin layer influences considerably the physical properties of the composite. It was assumed that the physical properties of themesophase unfold from those of the hard-core fibers to those of the softer matrix. Thus, a multicylinder model was assumed improving the classical two-cylinder model introduced by Hashin and Rosen for the representative volume element of the composite. Based on thermodynamic phenomena appearing at the glass transition temperatures of the composite and concerning the positions and the sizes of the heat-capacity jumps there, as well as on the experimental values of the longitudinal elastic modulus of the composite, the extent of the mesophase and the mechanical properties of the composite may be accurately evaluated. This version of the model is based on a previous one concerning a multilayer model, but it is considerably improved in order to take into consideration, in a realistic manner, the physical phenomena developed in fiber reinforced composites.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01490025
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  • 3
    Digitale Medien
    Digitale Medien
    A ductile-brittle zone in polyimides depending on the reaction temperature (1984)
    Springer
    Colloid & polymer science 262 (1984), S. 867-875 
    Details
    ISSN: 1435-1536
    Schlagwort(e): Polyimides ; polymers ; ductile fracture ; caustics ; K I -factor
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Notizen: Abstract The mechanical and optical properties of polyimides were studied in this paper and the influence of the variation of the reaction temperature on the physico-chemical properties of the polymers was evaluated. From this the dependence of the stress-strain diagrams on the reaction temperature, as well as the stresses and strains at fracture were experimentally determined. Moreover, the elastic moduli and Poisson's ratios, as well as the refractive index of the polymers were evaluated for different temperatures of imidization. In order to define also the behaviour of the polymers as thin membranes at fracture, simple tension tests with edge-cracked thin strips were executed up to fracture. The method of caustics was used, with the specimens loaded inK I mode of deformation at different stress-levels to evaluate the stress intensity factors of the materials in the non-linear zone of loading. TheK I -factor was evaluated by applying the simple Dugdale-Barenblatt model for the ductile materials, whereas for brittle samples the elastic theory was used. Interesting results concerning the physico-mechanical properties of the polyimides were derived.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01452217
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  • 4
    Digitale Medien
    Digitale Medien
    The influence of the mesophase on the transverse and longitudinal moduli and the major poisson ratio in fibrous composites (1986)
    Springer
    Colloid & polymer science 264 (1986), S. 561-569 
    Details
    ISSN: 1435-1536
    Schlagwort(e): Fibrous composites ; mesophase ; longitudinal elastic modulus ; transverse elastic modulus ; major Poisson ratio
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Notizen: Abstract Expressions for the evaluation of the transverse and longitudinal elastic moduli and the major Poisson ratio of unidirectional fiber composites are derived. The model described is based on the correct version of Kerner's model, which in our case is conveniently modified by introducing a mesophase layer between the fiber and the matrix in the representative volume element surrounding the typical fiber. The expression for the longitudinal elastic modulus derived in this paper, and the law of mixtures already presented in previous papers, give concordant results. Therefore, the law of mixtures, taking the mesophase also into account, and the two-term unfolding model for the mesophase are used for the evaluation of its extent and its properties. The model was applied to a glass filament-epoxy resin composite and its predictions were found to be in good agreement with the experimental data.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01412593
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  • 5
    Digitale Medien
    Digitale Medien
    Phase transformation, at the boundary layers between polymers, and solid surfaces (1985)
    Springer
    Colloid & polymer science 263 (1985), S. 863-872 
    Details
    ISSN: 1435-1536
    Schlagwort(e): Composites ; mesophase ; unfolding models
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Notizen: Abstract The size of the mesophase, which constitutes a boundary layer between fillers and matrix in composites, has been efficiently evaluated by the modified two-term unfolding model, which was based on delicate DSC measurements of the heat capacity jumps at the glass transitions of the composite and its constituent phases [1,2]. This model is now used to evaluate the mesophase along the whole viscoelastic spectrum of the composite, by making measurements of the storage and loss compliances or moduli of the composite and matrix and without making recourse to any other type of special measurement at the glass transition temperature of the substances. By applying this model the following important results were derived: i) Lipatov's empirical formula for defining the mesophase atT g was shown to yield reasonable results and ii) the evaluation of the size of mesophase over the entire viscoelastic spectrum was shown to remain almost constant and in conformity with the values defined by the other versions of the model. Extensive application of the experimental results of the literature indicated the mutual proof of the validity of these affine models.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01469622
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  • 6
    Digitale Medien
    Digitale Medien
    Accurate evaluation of the transverse shear modulus in unidirectional fibrous composites (1987)
    Springer
    Rheologica acta 26 (1987), S. 182-192 
    Details
    ISSN: 1435-1528
    Schlagwort(e): Transverseshear modulus ; unidirectionalfiber composite ; mesophase
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: Abstract A new relation for the prediction of the transverse shear modulus in unidirectional fiber composites has been derived. The theoretical results of this relationship are in better agreement with the experiments than those of other relations, existing in the literature. The discrepancies, which are observed among the theoretical predictions and the experimental values, are explained by the consideration of the boundary layers existing between the matrix and the fibers of the composite. A new model, which includes the intermediate phase between the matrix and the fiber, called the mesophase, is considered in order to take into account the above-mentioned layers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01331976
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  • 7
    Digitale Medien
    Digitale Medien
    Time dependence of creep recovery in cross-linked polymers (1967)
    Springer
    Rheologica acta 6 (1967), S. 246-251 
    Details
    ISSN: 1435-1528
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: Summary Transient creep recovery tests in simple tension were performed in a series of cross-linked high polymers in pure and plasticized states. A loading cycle was adopted according to which each specimen was loaded in creep for a time period of 16′ followed by recovery for the same time period. This loading cycle was repeated for various steps of temperature from ambient temperature up to a temperature corresponding to the rubbery region of each polymer. It was shown that, while the 15″ measurements of deformation after loading or unloading were approximately equal, recovery individual curves were always lagging in time the corresponding creep curves. Composite curves of creep or recovery deformation in semi-log time scale reduced to a temperature of 30 °C were plotted by applying the method of reduced variables. The creepdeformation composite curve was always advancing in time relatively to the respective recovery composite curve. This phenomenon was an accumulation of the partial difference of the corresponding individual curves. Time-shift factor versus temperature curves for creep and recovery were plotted and compared. It was established that the remaining deformation after 16 minutes of a 16′ creep recovery normalized to the initial deformation at the beginning of recovery, if plotted versus temperature, presented the same shape of curves for all types of materials tested. The maxima of these curves were diminishing with addition of plasticizer according to a straight line.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01976441
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  • 8
    Digitale Medien
    Digitale Medien
    Higher spectra approximations derived from multistep loading (1967)
    Springer
    Colloid & polymer science 215 (1967), S. 149-157 
    Details
    ISSN: 1435-1536
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Ein Programm, bei dem ein vernetztes Polymeres mit diskontinuierlichen Sprüngen von gleichem zeitlichem Abstand und konstanter Amplitude in bezug auf Dehnung oder Spannung belastet wird, kann höhere Näherungen für Retardations- und Relaxationsspektra mit einem ausreichenden Grad an Genauigkeit liefern, vorausgesetzt, daß dasBoltzmannsche Superpositionsprinzip nicht verletzt wird. Im Falle der Retardationsspektren ist die Mehrstufenbelastung ersetzbar durch eine anfängliche Kriechbelastung, gefolgt durch Stufen der Entlastung mit gleichen Amplituden und gleichen Zeitabständen. In dem Fall, daß eine exakte Master-Kurve für das Material durch Anwendung des Prinzips der reduzierten Variablen erlangbar ist, gewährt diese Kurve genügend Information für die Ermittlung des Retardationsoder Relaxationsspektrum mit ausreichender Näherung. Beispiele werden für die Gewinnung von Retardations- und Relaxationsspektren bis zu ihrer dritten Näherung für ein Epoxidharz und für ein Polyurethan-Elastomeres unter Verwendung der Mehrstufenmethode gegeben. Drei Näherungen der Relaxationsspektren für N.B.S., Polyisobutylen und Polymethylmethacrylat werden aus den Master-Kurven abgelcitct.
    Notizen: Summary A multistep loading programme for a cross-linked polymer with equidistant discontinuities jumping with constant amplitudes of stress or strain may yield higher approximations of the retardation or relaxation spectra to any degree of accuracy provided that theBoltzmann superposition principle is not violated. In the case of retardation spectra the multistep loading programme can be replaced by an initial creep loading followed by steps of recovery of equal amplitudes and time. In the case when an accurate composite curve of the material is available by application of the principle of reduced variables, this curve yields sufficient information for the tracing of retardation or relaxation spectra to any degree of approximation. Examples are given for the tracing of retardation and relaxation spectra up to their third approximation for an epoxy polymer and a polyurethane elastomer by using the multistep method. Three approximations of relaxation spectra for N.B.S. Polyisobutylene and Polymethylmethacrylate are also derived from their composite curves.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01520396
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  • 9
    Digitale Medien
    Digitale Medien
    Exotherm profiles of plasticized epoxy polymers in polymerization (1974)
    Springer
    Colloid & polymer science 252 (1974), S. 448-455 
    Details
    ISSN: 1435-1536
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Es wurde die Polymerisationsthermodynamik von plastifizierten Epoxydpolymeren untersucht unter Anwendung einer einfachen Meßvorrichtung welche die kontinuierliche Verfolgung der Polymerisationstemperatur ermöglicht. Hierbei wurde die Form der bei dieser exothermen Reaktion während der Polymerisation entstehenden Temperaturkurven ermittelt und ihr Verlauf in Abhängigkeit der Zeit graphisch dargestellt. Die aus diesen Ergebnissen erhaltenen charakteristischen Werte des Polymerisationsprozesses wie z. B. Gelier- und Härtungszeit, die zugehörigen und maximalen Temperaturen wurden zusammengestellt und verglichen. Die Untersuchung wurde für verschiedene Prozente plastifizierenden Materials in der Mischung durchgeführt und ihr Einfluß auf den Polymerisationsvorgang bestimmt.
    Notizen: Summary In this paper the thermodynamics of polymerization of a plasticized epoxy polymer were studied by applying a simple recording device for the instantaneous measurement of polymerization temperature. Especially, the forms of the characteristic exotherm profile during polymerization of a series of plasticized epoxy polymers were investigated, as well as its variation with respect to time. The characteristic points of the exothenn profile were determined, that is the gel point and the peak exotherm temperature as functions of time elapsed during the process of polymerization, as well as the temperature and time of hardening of mixture. The study was also extended to various percentages of plasticizer and to the functional influence of these percentages on the evolution of the polymerization process.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01554750
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  • 10
    Digitale Medien
    Digitale Medien
    Numerical inversion of Mellin transforms (1976)
    Springer
    BIT 16 (1976), S. 313-321 
    Details
    ISSN: 1572-9125
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A method is presented for the numerical inversion of Mellin transforms in which the inverse is obtained as an expansion in terms of Laguerre polynomials. The coefficients of this expansion are obtained as linear combinations of values of the transformed function or, equivalently, in terms of forward differences of this function. Thus, the Mellin transform of the series can be written as a forward interpolation series. Consequently the error of the numerical inversion procedure can be estimated. The practical advantage of the method is that values are needed for real arguments only.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01932274
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