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  • 1990-1994  (7)
  • 1993  (7)
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  • 1990-1994  (7)
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  • 1
    Electronic Resource
    Electronic Resource
    The stress intensity variation of an orthotropic perforated plate containing an internal crack (1993)
    Springer
    Archive of applied mechanics 63 (1993), S. 242-252 
    Details
    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: Zusammenfassung Das elastische Problem einer unendlichen, orthotropen Platte mit verschiedenen Wurzeln ihrer charakteristischen Gleichung wird im Falle, daß die Fasern senkrecht zu einem inneren Riß verlaufen und daß sie durch ein elliptisches Loch geschwächt sind, im Rahmen der Lekhnitskii-Theorie gelöst. Die Platte wird im Unendlichen einer vorgeschriebenen Spannung unterworfen, während die Randbedingungen an den Rißflanken, am Lochrand und im Unendlichen gegeben sind. Mit Hilfe der Methode der komplexen Variable wird die Lösung des Problems zurückgeführt auf die Berechnung von Cauchy-Integralen der analytischen Funktionen des Problems. Die numerische Lösung des Problems zeigt eine starke Abhängigkeit von Mode-I-Spannungsintensitätsfaktoren (SIF) an den Rißspitzen von der Rißlänge oder des Ligaments zwischen der Rißplatte und dem Loch. Weiterhin wurde gezeigt, daß Orthotropie starken Einfluß auf die Spannungsintensität hat. Diese Beobachtungen stehen in voller Übereinstimmung mit Resultaten aus der Arbeit [1] über ein ähnliches Problem für eine orthotrope Platte, wo allerdings die Wurzel der charakteristischen Gleichung identisch sind.
    Notes: Summary The elastic problem of an infinite orthotropic plate with different roots of its characteristic equation, when the fibers are oriented perpendicularly to an internal crack, and is weakened by an elliptic hole, is solved using Lekhnitskii's theory. The plate is subjected to prescribed stresses at infinity, while the boundary conditions are given at the flanks of the crack, at the rim of the perforation and at infinity. Using the complex-variable method, the solution of the problem is reduced to the evaluation of Cauchy-type integrals concerning the analytic functions of the problem. The numerical solution of the problem revealed an intense variation of mode-I stress intensity factors (SIF) at the crack tips due to the increase of either the crack length, or the distance of the near-by rack tip from the center of the hole. Furthermore, it was found that orthotropy strongly influences the intensity of stresses at the crack tips. These findings are in complete agreement with results given in a previous work by the authors, concerning a similar problem for an orthotropic plate, which, however, constitutes a special case, where the material presents equal roots for its characteristic equation [1].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00793891
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The beneficial influence of matrix anisotropy in fiber composites (1993)
    Springer
    Acta mechanica 97 (1993), S. 127-139 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary It has been recently shown [1] that the stress concentrations in anisotropic materials with distinct complex or imaginary roots of the respective characteristic function are much higher than in materials with equal roots. It was further shown [2] that anisotropic materials with equal roots behave like quasi-isotropic materials. Modern carbon-carbon and metal-ceramic composites are intuitively using these facts to create much stronger materials by reinforcing the matrix properties. A theory is presented in this paper where the coupling of strongly anisotropic fibers along their axis with strongly anisotropic matrices along either the fiber direction or the transverse plane to the direction of the fibers, either deteriorates, or improves perceptibly the mechanical behavior of the composites. It was shown that anisotropy of the matrix, increasing its mechanical properties on the transverse isotropic plane of the composite, increased the transverse Poisson's ratio, whereas decreased the longitudinal shear modulusG LC . This resulted in values of the eigenangleω c receding from the corresponding valueω ic for the respective isotropic, case. This resulted in a deterioration of the mechanical performance of the composite since the material now has the tendency to develop higher stress concentrations for equivalent loadings. On the contrary, a strong anisotropic matrix along the direction of the fibers yielded the inverse results for the various moduli of the anisotropic composite. The most important result is the increase of the longitudinal shear modulusG L , so that the ratioE L /2G L is consistently decreasing, thus yielding values of the eigenangleω c tending to approach the critical valueω c for the isotropic material. This decrease ofω c indicates the improvement of the quality of the composite, which develops relatively lower stress concentration factors approaching their respective isotropic values. This fact makes the anisotropic composite material to approach an equivalent state of quasi-isotropy and thus to improve the strength of the material by reducing considerably the eventual, anisotropic stress concentration factors of the respective structural elements. Examples with T300/N5208 Graphite-Epoxy composites and Borsic-1100 Aluminum metal-metal composites indicate clearly the beneficial effect of the anisotropy of their matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01176521
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  • 3
    Electronic Resource
    Electronic Resource
    On a family of quasi-isotropic fiber-reinforced composites (1993)
    Springer
    Acta mechanica 96 (1993), S. 163-180 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary The spectral decomposition of the compliance and the stiffness tensors for a transversely isotropic body (fiber-reinforced composite), and their eigenvalues derived from, define in a simple and efficient way the respective elastic eigenstates of loading of the material. It has been shown that, for the general orthotropic or transversely isotropic body, these eigenstates consist of two double components σ1 and σ2, which are shears, with σ2 a simple shear, and σ1 a suprposition of simple and pure shears, and they are associated with distortional components of energy. The remaining two eigenstates, with stress components σ3 and σ4 are the orthogonal supplement to the shear subspace of σ1 and σ2, and consist of an equilateral stressing in the plane of isotropy, superimposed with a prescribed tension or compression along the symmetry axis of the material. In this paper a particular class of transversely isotropic materials is studied, whose mechanical properties are conveniently selected to reduce the two last eigenstate components in such a manner, that the one is identified to contribute only a dilatational type of strain energy, whereas the other a distortional one. In this way the four eigenstates are clearly separated in two distinct groups creating either distortional or dilatational types of strain energy. It was shown that this family of materials behave like the isotropic body, in spite of their differences in the elastic constants along their principal axes of anisotropy. Since with fiber-composites it is possible to arrange their mechanical properties by selecting the appropriate ratios between matrix and inclusions, according to their properties, this possibility of selecting in advance the properties of the composite is feasible. Taking into consideration that quasi-isotropic materials develop the smallest stress concentrations in the structures, the development and selection of such composites with quasi-elastic properties becomes very important.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01340708
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  • 4
    Electronic Resource
    Electronic Resource
    Elastic-plastic analysis of cracked plates in plane stress: An experimental study (1993)
    Springer
    Acta mechanica 99 (1993), S. 75-93 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Summary An experimental method is presented for the complete solution of the elastic-plastic plane stress problem of an edge-cracked plate obeying the Mises yield criterion and the Prandtl-Reuss incremental stress-strain flow rule. The material of the plate is assumed as a strain-hardened one with different degrees of hardening. The elastic and plastic components of strain were determined by using the method of birefringent coatings cemented on the surface of the metallic specimens made of the material under study. Normal incidence of circularly polarized light yielded the isolinics and isochromatics of the coating which provided the principal elastic strain differences and strain-directions at the interface. Evaluation of the stress intensity factor at the crack tip, by using the Griffith-Irwin definition, gave the sum of principal stresses at the crack tip. These data were sufficient to separate the components of strain at the coating-plate interface by using the classical shear-difference method. The stress components on the partially plastically deformed cracked plate were determined by using the Prandtl-Reuss stress-strain relationships in a step-by-step process following the whole history of loading of the plate. Thus, a radial distribution law for the equivalent stress $$\bar \sigma $$ and strain in all directions of the plate was established which gave the instantaneous position of the elastic-plastic boundary and its evolution during loading, as well as the distribution of elastic and plastic components of stresses allover the plate. Four cases were solved for various amounts of strain-hardening from a quasi perfectly plastic material to an almost brittle strain hardened one. The values of the characteristic parameters defining each type of material were established. The results derived compare excellently with existing ones based either on experimental or numerical solutions and since they are based on both the theory of elasticity and the incremental theory of plasticity they constitute a sound basis for comparison. Moreover, the algorithm based on this hybrid method is fast and stable requiring a minimum computer time, memory and data preparation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01177236
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  • 5
    Electronic Resource
    Electronic Resource
    Local variations of the dynamic elastic modulus around running cracks (1993)
    Springer
    Journal of materials science 28 (1993), S. 4510-4514 
    Details
    ISSN: 1573-4803
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The variation of the dynamic elastic modulus in the immediate vicinity of the tip of the running crack was studied through an iterative procedure, based on the theoretical expressions for the stress-field components and the experimental relation between strain rate and elastic modulus. It was found that the elastic modulus varied strongly around the tip of the crack, both in radial and polar sense. Also it was observed that the polar distribution of the elastic modulus presented clear off-axis extrema in directions that were in good agreement with experimentally measured branching angles, thus indicating a possible relation between these two phenomena.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01154964
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  • 6
    Electronic Resource
    Electronic Resource
    Cracks of fractal geometry with unilateral contact and friction interface conditions (1993)
    Springer
    International journal of fracture 60 (1993), S. 293-310 
    Details
    ISSN: 1573-2673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Structures involving cracks of fractal geometry are studied here, on the assumption that at the interface unilateral contact and friction boundary conditions hold. Approximating the fractal by a sequence of classical surfaces or curves and combining this procedure with a two-level contact-friction algorithm based on the optimization of the potential and of the complementary energy, we get the solution of the problem after some appropriate transformations relying on the S.V.D.-decomposition of the equilibrium matrix. Numerical examples, using singular elements for the consideration of the crack singularity, illustrate the theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00034738
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    The ‘fractal assumption’ in cracks: Bilateral calculation methods (1993)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 1597-1604 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper considers the fractal nature of cracks by assuming the fractal as the fixed point of a given transformation. This concept enables the study of a sequence of classical-geometry crack problems whose limit gives the solution of the fractal-geometry crack problem. The method is illustrated by a numerical example. It was shown that the fractal nature of the cracks influences the value of the stress intensity factors.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620360911
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