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  • 11
    Electronic Resource
    Electronic Resource
    The symmetric ellipsoid failure surface for the transversely isotropic body (1992)
    Springer
    Acta mechanica 92 (1992), S. 35-60 
    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 A realistic criterion in the 3D-principal stress space for describing failure of transversely isotropic bodies taking also into account the strength differential effect was shown to be the elliptic paraboloid failure surface (EPFS) [5]. The criterion, however, stipulates that in the compression-compression-compression octant these materials may sustain very high loadings. In order to remedy this ambiguous definition of failure in this zone for the compression strong materials or in the domain of the tension-tension octant for the tension strog materials an improved version of the EPFS was introduced in this paper. Based on the same principles as the EPFS a symmetric ellipsoid failure surface is defined whose symmetry axis is parallel to the hydrostatic axis, which is also passing through the three pairs of failure strengths in tension and compression along each of the principal stress axes. Since the symmetric ellipsoid failure criterion is a versatile one, based on the same hypotheses derived from assertions and long experrimental evidence as the EPFS, thus succeding to interrelate failure with the basic concepts and principles of mechanics, it constitutes a powerful and reliable general type of criterion. It was shown that extensive experimental evidence corroborates the results derived from this criterion along the basic intersections of this failure surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01174166
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  • 12
    Electronic Resource
    Electronic Resource
    Failure criteria for weak-axis quasi-orthotropic woven fabric composites (1992)
    Springer
    Acta mechanica 95 (1992), S. 69-86 
    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 failure behavior of woven fabric composites in the form of plain weave fiber unidirectional laminae is studied in this paper as defined by their failure stresses in simple tension and compression along the three principal stress directions. Since the transverse weave plane is the strong and isotropic plane of the composite, while the normal to it direction the weak one, the material is approximated as a weak-axis transversely isotropic composite. The elliptic paraboloid failure surface (EPFS) criterion, as introduced by the author [1], was shown to describe satisfactorily this type of interesting modern materials. It was shown that such weak-axis transversely isotropic composites correspond to tension strong composites and their failure surfaces consist of a single-sheet convex surface open to the tension-tension-tension octant of the principal stress space. The main characteristic of such surfaces is that they are oblate along the normal direction to the isotropic plane, in contrast with the typical (EPFS)-criterion for fiber composites, which, all of them, are prolate along the same direction. While the intersection of this (EPFS)-criterion by the (σ1,σ3) stress plane (σ3 is the weak axis) resembles closely the respective intersection for the unidirectional fiber composites the (σ1,σ2)-isotopic plane intersection, which coincides with the weaving strong plane approaches very closely a circle thus indicating that along this isotropic plane the failure stress is hydrostatic and independent of its orientation inside this plane. This property constitutes a significant and most promising property which makes this type of woven composites very attractive in applications. Experimental evidence of failure of such materials, which is very sparse, as derived from tests in a woven T-300 Carbon-epoxy composite corroborated excellently with the theory based on the (EPFS)-criterion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170805
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  • 13
    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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  • 14
    Electronic Resource
    Electronic Resource
    The elliptic paraboloid failure criterion for cellular solids and brittle foams (1991)
    Springer
    Acta mechanica 89 (1991), S. 93-121 
    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 Cellular solids and brittle foams are increasingly finding application in constructions mainly as core materials for loaded sandwich structures where the loading of the structure generates multiaxial stress states on them. It has been established that the principal mechanism of deformation is based on the cell-wall bending and closed-cell as well as open-cell foams present similar stiffnesses. Therefore simple relations are found for their tensile, compressive and shear strengths and their elastic properties. It has been established in this paper that the modes of failure of such materials can be satisfactorily described by the elliptic paraboloid failure criterion for the general orthotropic body. Then, as soon as the yield or failure stresses in simple tension and compression are measured along the three principal stress directions of the material the failure locus is unequivocally defined and all the properties of the material under any complicated load can be accurately established. However, since these materials fail in the compression-compression-compression octant of the principal stress space by elastic buckling, the EPFS-criterion is cut-off by an ellipsoid surface, with intercepts along the principal axes the respective compressive failure stresses. The criterion thus established yields satisfactory results. It has been tested among others in a reticulated vitreous carbon foam as well as in an aluminium foam. The experimental results for these foams existing in the literature are fitting better with this universal criterion than any other considered, thus indicating the validity of the elliptic paraboloid failure criterion also for this type of materials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01171249
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  • 15
    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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  • 16
    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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  • 17
    Electronic Resource
    Electronic Resource
    Some properties of generalized epicycloids applied to fracture mechanics (1971)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 22 (1971), S. 876-890 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Résumé La réflexion partielle d'un faisceau lumineux sur le revers d'une plaque mince en plexiglas comportant une fissure intérieure symétrique formant un angle quelconque avec l'axe d'application de la charge extérieure, crée des déviations des rayons réfléchis dans la zone contractée qui entoure l'extrémité de la fissure. Ces déviations forment une caustique. On montre, dans cet article, que cette caustique prend la forme d'une courbe épicycloïdale générale, valable pour tous les matériaux qui ont un comportement élastique. Cette courbe est créée par l'extremité du vecteur résultant qui représente les rayons de lumière réfléchis et déviés sur la plaque fissurée. On étudie ensuite les proprietés caractéristiques de ce type d'épicycloïdes en relation avec le facteur complexe d'intensité des contraintesK *. Les résultats des essais faits à l'aide des plaques munies des fissures intérieures symétriques d'orientation différente par rapport à l'axe d'application de la charge extérieure sont en parfait accord avec les résultats de la théorie.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01591815
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  • 18
    Electronic Resource
    Electronic Resource
    On the numerical solution of Cauchy type singular integral equations and the determination of stress intensity factors in case of complex singularities (1977)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 28 (1977), S. 1085-1098 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01601675
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  • 19
    Electronic Resource
    Electronic Resource
    Stress and displacement singularities near corners (1979)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 30 (1979), S. 728-728 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01590853
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  • 20
    Electronic Resource
    Electronic Resource
    The symmetrically branched crack in an infinite elastic medium (1976)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 27 (1976), S. 801-814 
    Details
    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
    URL: http://dx.doi.org/10.1007/BF01595131
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