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  • 1985-1989  (7)
  • 1980-1984  (6)
  • Chemistry  (11)
  • Caustics  (1)
  • Lagrange polynomials
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Computing 31 (1983), S. 105-114 
    ISSN: 1436-5057
    Keywords: Primary 65D30 ; 65D32 ; secondary 41A55 ; Cauchy-principal values ; finite-part integrals ; convergence ; Jacobi quadratures ; Lagrange polynomials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Description / Table of Contents: Zusammenfassung In diesem Artikel sind hinreichende Bedingungen, welche die Konvergenz von Quadratursätzen des Elliott-und Hunter-Typus für die Bestimmung von gewichteten Cauchy Hauptwert-Integralen der Form sicherstellen, hergeleitet. Die gleichzeitige Konvergenz beider Quadraturen im Intervall (−1, +1) wurde für eine Klasse von Hölderstetigen Funktionenf(f∈H μ ) nachgewiesen. Im Artikel sind auch Korrekturen von gewissen früheren Darlegungen über die Konvergenz von solchen Quadraturen enthalten. Ferner wurde eine einfache Herleitung der Elliott-und Hunterschen Quadratursätze für die Bestimmung derp-ten Ableitung des obenstehenden Integrals gegeben und hinreichende Bedingungen für die Konvergenz der Hunterschen Quadratur wurden erhalten. Die Konvergenz dieses Integrals wurde somit für Funktionenf, für welchef (p) ∈H μ gilt, sichergestellt.
    Notes: Abstract In this paper sufficient conditions are derived to ensure the convergence of the Elliott and Hunter types of quadrature rules for the evaluation of weighted Cauchy principal-value integrals of the form: The simultaneous convergence in the interval (−1, 1) of both quadratures was established for a class of Hölder-continuous functionsf(f∈H μ ). Corrections of some previous statements on the subject of convergence of such quadratures are also included. Moreover, a simple derivation of the Hunter and Elliott types of quadrature rules for the evaluation of the derivative of thep-th-order of the abovestated integral was given and sufficient conditions for the convergence of the Hunter-type quadrature were obtained. Thus, the convergence of this integral was ensured for functionsf such thatf (p) ∈H μ .
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Colloid & polymer science 261 (1983), S. 825-833 
    ISSN: 1435-1536
    Keywords: Polymers ; Slow-brittle-fracture ; Toughness ; Caustics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A slow crack growth was achieved in initially edge-cracked specimens made of a high-molecular weight PMMA by regulating the cross-head speed of loading by a computer-driven testing machine. The strain rate $$\dot \varepsilon $$ used during the tests varied between $$\dot \varepsilon $$ =1× l0−6 s−1 and 1×10−4 s−1. It was shown that, in this zone of slow quasi-static loading of brittle polymethylmethacrylate specimens under conditions of plane stress, the crack initiated for a critical value of loading, at some characteristic zone of strain-rate variation at the crack tip. It was established that for strain rate between $$\dot \varepsilon $$ =0.18×10−5 s−1 and $$\dot \varepsilon $$ =0.45×10−4 s−1 brittle cracks were propagating always slowly with velocities in the range ofc=3 to 5×10−2 m/s. For values ofv s outside this transition zone fracture was typically brittle with high crack-propagation velocities. As the strain rate was varying beyond the stable low-velocity region, a two-step crack velocity pattern was operative, where the one step took always low values, and the other step corresponded to crack-propagation velocities significantly higher than these limits, tending to typical brittle-fracture velocities of the material. Oscillations of the velocityc at the transition zones, or, in many cases all over the zone of slow propagation of the crack, indicated the unstable character of crack propagation, influenced by different stress raisers and especially by the opposite longitudinal boundary of the specimen. Stress intensity factor values during crack propagation, evaluated from the front (cuspoid) and the rear (external) caustic, which remained alwaysk g-dominant, were following similar trends as the variation of the crack propagation velocity.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Stamford, Conn. [u.a.] : Wiley-Blackwell
    Polymer Engineering and Science 28 (1988), S. 610-625 
    ISSN: 0032-3888
    Keywords: Chemistry ; Chemical Engineering
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The influence of the hard or soft inclusions and the mesophase layers in either a soft-hard-soft or hard-soft-hard combination of biphase plates submitted to dynamic tensile loads on the fracture mode and bifurcation process in both phases was investigated in this paper. It was assumed that the soft or hard matrix is infolding the hard or soft inclusion of the plate, so that the plate constitutes a meridional section of the representative volume element of a unidirectional fiber composite, or a principal section of a particulate. The influence of the mechanical properties of either phase on the crack propagation velocity and the initiation of crack bifurcation was studied by using high-speed photography and dynamic caustics. The results showed that the propagating crack tended to bifurcate either in the brittle or in the mesophase layer under certain conditions of propagation velocity. It was shown that bifurcation of a propagating crack depends on the elastic moduli and Poisson's ratios of the phases, as well as on the extent of the mesophase layer, which depended on the adhesion quality of phases.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 27 (1982), S. 3019-3025 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The thermomechanical behavior of particle composites was investigated in their transition region. In particular, the value of the glass-transition temperature Tg, which constitutes an upper limit for the structurally important glassy region, was examined. According to experimental evidence existing in the literature the introduction of a reinforcing filler in a polymeric matrix causes Tg of the latter to increase, unless mechanical imperfections counterbalance the reinforcing effect or even produce a Tg for the composite which is lower than that of the matrix. Based on mechanical theories, valid for the mechanical moduli of viscoelastic particle composites, a model was introduced that explains why the glass transition of composite materials may be reduced in some cases, whereas it may be increased in others. The concept of interphase between inclusions and matrix was used for the development of the model. Interphase is assumed to be a region, which is created between the matrix material and the filler particles, both considered as homogeneous and isotropic, whose thermomechanical properties and volume fraction may be determined from the overall thermomechanical behavior of the composite.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 28 (1983), S. 3641-3649 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Retardation spectra, derived from dynamic measurements of extension compliances along three decades on the logarithmic scale of frequencies in standard specimens prepared from a fiber-reinforced composite with their fibers parallel to the longitudinal axis of the specimens, have revealed the structure of the matrix material of the composite. The experimental results were used to prove that the physicochemical rearrangements in the vicinity of the inclusions, consisting of restrained development of the macromolecules and especially their side chains due to the presence of the other phase, concentration of voids and dirt, shrinkage stresses developed during curing and creating microcracks (radial as well as along the interface), are activated by the existence of high stress gradients and eventually stress singularities due to the strong adhesion developed between phases.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 30 (1985), S. 621-645 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The adhesion between matrix and inclusions (fibers or particulates) in a composite material is one of principal factors characterizing the mechanical and physical behavior of the modern composite materials. All theoretical models describing these substances neglect to consider the influence of the boundary layer developed between phases during the preparation of the composite. In this paper, two versions of a theoretical model were introduced for the evaluation of this mesophase layer. It had been shown that this thin layer influences considerably the physical properties of the composite. It was assumed that the physical properties of the mesophase 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. These versions of model are based on a previous one concerning a multilayer model, but they are considerably improved, in order to take into consideration, in a realistic manner, the physical phenomena developed in fiber-reinforced composites.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part A: Polymer Chemistry 25 (1987), S. 1285-1294 
    ISSN: 0887-624X
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Structural changes which take place in many amorphous polymers, when they are annealed at temperatures near the glass transition temperature, have important theoretical, physical, and mechanical consequences. In this paper the possible existence of some local ordering in highlycrosslinked epoxy resins is studied. Three kinds of tests - TMA, DSC, and dynamic experiments - are used for a type of epoxy resin, cured with six different amounts of curing agent. In order to study the effect of the thermal history on the behavior of the polymer at its transition region, as well as the morphology of the materials tested, three different thermal treatments have been followed. Interesting results were derived concerning the influence of these parameters to these parameters to the mechanical characterization of the polymer.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 28 (1983), S. 3145-3153 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The influence of moisture absorption on the extent of the boundary interphase in particulate composites is thoroughly studied. It was found that, during the process of moisture absorption there is a variation of the extent of the boundary interphase, closely related to the degradation of the mechanical behavior of the composite, as well as to the percentage amount of moisture absorbed. An explanation of the observed relationship was advanced, based on a theoretical mechanism of absorption. This study complements a previous one, where the observed degradation of the thermomechanical properties of particulate composites due to moisture absorption was shown to be intimately interrelated with the state and extent of the interphase between fillers and matrix.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 29 (1984), S. 2997-3011 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The static and dynamic elastic moduli of particulate composites, consisting of two phases, one of which has isotropic-elastic and the other linear viscoelastic properties, were studied. For this purpose a model defining the approximate equations for determining the elastic modulus of a composite from the properties of the constituent materials was used. Classical theory of elasticity was applied to this simplified model of a composite-unit cell. The following assumptions are made: (i) filler particles are spherical; (ii) fillers are completely dispersed; and (iii) the volume fraction of fillers is sufficiently small, so that any interaction among fillers may be neglected. A class of iron-filled epoxy composites was subjected to tests in order to compare the theoretical values with the experimental results. The elastic modulus calculated by the expression derived in this study seems to corroborate with the experimental results fairly well. Finally, by applying the correspondence principle to this expression, theoretical relationships for the dynamic storage and loss moduli were also derived.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Applied Polymer Science 30 (1985), S. 2979-2995 
    ISSN: 0021-8995
    Keywords: Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: The determination of the cubic thermal expansion coefficient of a two-phase particulate is presented in this paper. The model described is based on the well-known Kerner's model and takes into account the existence of mesophase, which constitutes a boundary layer between inclusions and the matrix in the composite. This layer is assumed as created by the substance of matrix during the preparation procedure of the composite, and it includes areas of imperfections around and near the inclusions. The influence of this layer on the effective properties of the composite has been proved to be significant. In order to take into consideration the influence of mesophase a spherical shell with the average properties of this layer is interposed between the spherical inclusion and the matrix. The evaluation of the average elastic and thermoelastic properties and also of the extent of mesophase is succeeded by considering the two-term unfolding model, introduced previously, for describing the change of the elastic modulus of the mesophase layer of fiber-reinforced and particulate composites. The two-term unfolding model was, in this paper, extended to incorporate the mode of variation of the thermal expansion coefficient and the bulk modulus in the mesophase. The model was applied to a polyurethane rubber filled with particles of sodium chloride, and its predictions were found to be in good agreement with the experimental data.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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