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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 51 (1981), S. 139-149 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht In diesem Artikel wird eine analytische Methode zur Bestimmung von großen elastischen Verformungen eines schief gekrümmten Stabes durch exakte Formeln entwickelt. Dieses Problem wird durch ein System von fünfzehn nichtlinearen, gewöhnlichen Differentialgleichungen erster Ordnung beschrieben; die Unbekannten des Systems sind sowohl die endlichen Krümmungs- und Torsionsfunktionen als auch die verallgemeinerten inneren Kräfte und Verschiebungen des Stabes. Ferner wird das Problem des dünnen beidseitig gelagerten zylindrischen Stabes, welcher koplanaren Endlasten unterliegt, untersucht, und geschlossene Formeln werden erhalten. Schließlich werden die Effektivität und die Möglichkeiten der Methode durch mehrere numerische Anwendungen dargestellt.
    Notes: Summary In this paper an appropriate analytical treatment for the determination, through exact formulae, of large elastic deformations in thin skew-curved rods is presented. This problem is associated with a system of fifteen nonlinear, ordinary, differential equations of the first order; the unknowns of the system are the final curvature and torsion functions, as well as the generalized internal forces and displacements of the rod. Subsequently, the problem of a thin cantilever circular rod subjected to terminal co-planar forces is examined and closed formulae determining its generalized displacements are obtained. Finally, the effectiveness and the potentialities of the method are demonstrated by several numerical applications.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Archive of applied mechanics 52 (1982), S. 159-166 
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Das Konzept wegunabhängiger Integrale, welches für homogene Medien früher eingeführt wurde, wird für den Fall eines Risses in einer Grenzfläche zwischen zwei verschiedenen Halbebenen erweitert. Durch Verwendung eines der in dieser Arbeit definierten wegunabhängigen Integrale erhalten wir den Spannungsintensitätsfaktor, wenn die Eißlippen durch an beiden Lippen identisch verteilter Spannungen oder Einzelkräfte oder Momente belastet werden. Die oben genannten Integrale sind erweitert, um den Fall einer willkürlichen Zahl von kollinearen Bissen in der Grenzfläche der Halbebenen einzuschließen. Der Fall von periodischen Rissen kann aus dieser Analysis erhalten werden. Schließlich kann eine interessante Verallgemeinerung für den Fall erhalten werden, daß willkürliche Risse, Einschlüsse oder nicht unbedingt an den Rißlippen wirkende Einzelkräfte und Momente in Wechselwirkung stehen.
    Notes: Summary The concept of path independent integrals introduced previously for homogeneous media is extended to the case of a crack in the interface between dissimilar half planes. Using any of the pathindependent integrals defined in this paper we obtain the stress intensity factor when the lips of the crack are loaded by identical distributions of stresses in both lips, or by concentrated forces or couples. The above integrals are extended in order to include the case of an arbitrary number of collinear cracks in the interface of two half planes. The case of periodic cracks may be derived from the above analysis. Finally, an interesting generalization may be obtained for the case where arbitrary cracks, inclusions or concentrated forces and couples, not necessarily applied at the lips of the crack, interact.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 27 (1976), S. 801-814 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Es wird das ebene elastostatische Problem eines symmetrischen gegabelten Risses für den unendlichen, isotropen und mit senkrecht zur Riss-Hauptachse belasteten Körpers untersucht, und zwar unter Anwendung der Methode der komplexen Potentiale. Das Problem wird auf ein Systen von drei singulären Integralgleichungen reduziert und weiter auf ein System linearer Gleichungen transformiert, vermittelst einer Näherung der Integrale mit Hilfe des leicht lösbaren numerischen Quadraturverfahrens von Gauss und Lobatto. Die Spannungsintensitätsfaktoren in den Spitzen des gegabelten Risses werden rechnerisch ermittelt und mit experimentellen Ergebnissen verglichen.
    Notes: Summary The plane elastostatic problem of a symmetrically branched crack in an infinite isotropic body loaded by normal stresses perpendicular to the main crack axis at infinity was studied by using the method of complex potentials. The problem was reduced to a system of three singular integral equations. By means of an approximation of the integrals through the Gauss and Lobatto numerical quadrature procedures, these singular integral equations were transformed into a system of linear equations, which can be readily solved. The stress intensity factors at the tips of the branched crack were computed directly from the solution of the above system of linear equations and were compared with the already existing experimental solutions.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 28 (1977), S. 1085-1098 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Résumé Une équation intégrale du type de Cauchy singulière le long d'un intervalle fini réel et avec une fonction pondérante ayant des singularités complexes aux extremités de l'intervalle d'intégration peut être résolue numériquement par réduction à un système d'équations linéaires, en utilisant une règle appropriée d'intégration numérique associée aux polynômes de Jacobi, exactement de la même manière que dans le cas des singularités réelles. La façon la plus appropriée de trouver la solution numérique de cette équation telle qu'elle se présente dans les problèmes de fissure en élasticité plane et d'évaluer les facteurs de contrainte aux extremités da la fissure est la méthode d'intégration numérique de Lobatto-Jacobi.
    Notes: Summary A Cauchy type singular integral equation along a finite real interval and with a weight function with complex singularities at the end-points of the integration interval can be numerically solved by reduction to a system of linear equations, by using an appropriate numerical integration rule associated with the Jacobi polynomials, in exactly the same way used for the case of real singularities. For the numerical solution of such an equation arising in plane elasticity crack problems and the evaluation of stress intensity factors at crack tips, the Lobatto-Jacobi numerical integration rule is the most appropriate.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Zeitschrift für angewandte Mathematik und Physik 30 (1979), S. 728-728 
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1435-1536
    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: Summary The role of the boundary interphase on the adhesion efficiency between fiber and matrix in the case of polymers reinforced with unidirectional fibers was investigated. A theoretical model was introduced considering that the composite material consists of three phases; that is, the fiber, the matrix and the interphase, material which is the part of the polymer matrix lying at the close vicinity of the fiber surface. The interphase material, having different physical properties from those of the bulk matrix, affects the overall behavior of the composite. Moreover, the quality of adhesion between the two main phases depends greatly on the nature of the interphase material. In this study we have considered that the interphase material is inhomogeneous in nature, with properties varying continuously from the fiber surface to the bulk matrix. The theory developed resulted in a criterion of the adhesion quality and in a prediction of the longitudinal modulus of elasticity of the fiber-composite.
    Type of Medium: Electronic Resource
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  • 7
    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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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Colloid & polymer science 258 (1980), S. 1044-1051 
    ISSN: 1435-1536
    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: Summary A theoretical expression of the value of the glass-transition temperatureT g at any direction of orientation, defined by the angle ϑ subtended between this direction and the average axis of fibers; was introduced. Dilatometric, as well as dynamic tests were executed for a type of unidirectional composite in order to compare the respective values ofT g derived from these tests. The experimental results were also compared with theoretical values derived from the theoretical expression. A satisfactory agreement between, theory and experiment was established.
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Colloid & polymer science 262 (1984), S. 929-938 
    ISSN: 1435-1536
    Keywords: Fibrous composites ; mesophase ; unfolding models
    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 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.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Colloid & polymer science 262 (1984), S. 867-875 
    ISSN: 1435-1536
    Keywords: Polyimides ; polymers ; ductile fracture ; caustics ; K I -factor
    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 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.
    Type of Medium: Electronic Resource
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