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  • 1
    Electronic Resource
    Electronic Resource
    The differential geometry of grain boundaries: tilt boundaries (1977)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 33 (1977), S. 865-872 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: A differential geometric analysis has been made of the various tensor quantities associated with a grain boundary. It is shown how these tensor quantities can be developed so as to give a unique and generalized formulation for the description of the dislocation content of such boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739477002150
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  • 2
    Electronic Resource
    Electronic Resource
    The differential geometry of two-phase interfaces (1977)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 33 (1977), S. 480-486 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Coherent as well as incoherent interfaces associated with simple two-phase boundaries have been analyzed in terms of the concepts of differential geometry. Such tensor quantities as distortion, torsion and curvature have been developed and are all shown to give significant insight in describing the Burgers circuits and dislocation content of such boundaries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S056773947700120X
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  • 3
    Electronic Resource
    Electronic Resource
    Theory of simple two-phase interfaces (1975)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 292-299 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The coincidence-site-lattice theory of grain boundaries has been applied to simple two-phase boundaries. Symmetric and unsymmetric tilt boundaries, pure twist boundaries and unrotated and untwisted boundaries have all been considered. It has been shown that each type of boundary can be described in terms of a characteristic coincidence-site lattice. In addition, the dislocation content within the interphase boundaries has been defined in terms of Burgers circuits described with respect to the original crystal lattices in the new coincidence-site lattices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739475000630
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  • 4
    Electronic Resource
    Electronic Resource
    Unification of the coincidence-site-lattice and continuum theories of grain boundaries (1975)
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 31 (1975), S. 280-292 
    Details
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The concepts embodied in the coincidence-site-lattice theory of grain boundaries are shown to be compatible with a large number of tensor quantities which have their origin in the continuum field theory of dislocations. More specifically such tensor quantities as distortion, grain-boundary dislocation density, and incompatibility have all been developed in terms of a general grain boundary for a continuum as well as for the discrete crystal. A generalized Burgers circuit about an arbitrary grain boundary is also shown to be a natural outcome of the present development.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1107/S0567739475000629
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  • 5
    Electronic Resource
    Electronic Resource
    The differential geometry of bending (1978)
    Springer
    Meccanica 13 (1978), S. 151-157 
    Details
    ISSN: 1572-9648
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Summary The deformation associated with uniform bending has been treated using the techniques of differential geometry. The Burgers circuit as well as various related tensor quantities such as torsion and dislocation density have all been determinated with respect to these various states of deformation.
    Notes: Sommario La deformazione associata con la flessione uniforme viene trattata usando le tecniche della geometria differenziale. Il circuito di Burgers e altre quantità tensoriali e la densità di dislocazione, vengono determinate nei vari stati di deformazione.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02128358
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  • 6
    Electronic Resource
    Electronic Resource
    Behaviour of an edge dislocation in a semi-infinite solid with surface energy effects (1979)
    Springer
    Journal of materials science 14 (1979), S. 1052-1070 
    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 method of continuously distributed dislocations and the method of discrete distribution of dislocations have been used to determine the effect of surface energy on the surface boundary conditions of a semi-infinite solid containing an edge dislocation. The surface dislocation model which incorporates two surface dislocation arrays, the primary and the secondary, in order of importance, is used to study the effect of surface energy. The surface dislocation model in conjunction with the method of continuously distributed dislocations enables the exact determination of the dislocation distribution function of the primary and secondary dislocation arrays and the effect of surface energy tends to lower both the total Burgers vector associated with the surface arrays and dislocations in evaluating the effect of surface energy is illustrated and is compared with the method of continuously distributed dislocations. It has been found that the surface energy tends to lower both the total Burgers vector associated with the surface arrays and the length of the region within which they are spread on the surface. Although the effect on the primary surface arrays is not very large, the secondary surface arrays are completely eliminated with normal values of surface energy encountered in real solids. Thus, the effect of surface energy is to bring non-vanishing stress components to the surface. The surface is also non-uniformly stressed. The superiority of the surface dislocation model over the other methods hitherto used in the literature is illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00561288
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  • 7
    Electronic Resource
    Electronic Resource
    Discrete dislocation analysis of pre-existing cracks (1980)
    Springer
    International journal of fracture 16 (1980), S. 193-206 
    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
    Description / Table of Contents: Résumé On utilise la méthode de dislocations discrètes pour déterminer la configuration des dislocations associées à une fissure plastique continue soumise à une charge et à déchargement. Le concept de dislocation d'anti-fissure est introduit en vue de satisfaire les conditions aux limites de surface libre sur les faces de la fissure non chargée, associées aux dislocations des réseaux dans la zône plastique. Des configurations variées de fissures non soumises à sollicitation qui comportent une action de fermeture des surfaces de fissure en vue de réduire l'énergie de surface, sont schématiquement illustrées dès lors que l'analyse par dislocations discrètes peut être utilisée. Des résultats sont obtenus pour des fissurations sous tension et sous cisaillement.
    Notes: Abstract The discrete dislocation method is employed to determine the dislocation configurations associated with a continuous plastic crack subjected to both loading and unloading. The concept of anticrack dislocations is introduced in order to satisfy the free surface boundary conditions on the surfaces of the unloaded crack associated with lattice dislocations in its plastic zone. Various configurations of the unloaded crack, which incorporate a zipping action of the crack surfaces to reduce surface energy, are illustrated schematically wherein the discrete dislocation analysis is utilized. The results are obtained for both a tensile and a shear crack.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00013377
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  • 8
    Electronic Resource
    Electronic Resource
    Dislocation model of the interaction between a tensile crack and a hole (1978)
    Springer
    International journal of fracture 14 (1978), S. 155-171 
    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
    Description / Table of Contents: Résumé La représentation d'une fissure par des dislocation discrètes et d'un trou par des dislocations de surface est utilisée pour l'étude de l'interaction entre une fissure résultant d'un état de tension et un trou. On montre que pour une dimension et une forme données d'un trou préexistant dans un matériau homogène il ne peut exister une fissure que d'une seule dimension pour maintenir l'équilibre. Cette dimension d'équilibre de la fissure dépend de la dimension et de la forme du trou ainsi que de la distance entre la fissure et le trou. Toutes les fissures dont les dimensions sont supérieures ou inférieures à la dimension d'équilibre sont instables. L'effet de la dimension de la forme du trou sur la dimension d'équilibre de la fissure est illustré. L'assymétrie de la configuration des dislocations associée à la fissure et au trou est utile pour comprendre la concentration de contrainte qui existe au voisinage de l'extrémité d'une fissure et au bord d'un trou, ainsi que pour étudier d'une manière plus approfondie le mécanisme de croissance de la fissure et du trou.
    Notes: Abstract The representation of a crack by discrete dislocations and that of a hole by surface dislocations is used to study the interaction between a tensile crack and a hole. It is shown that for a given size and shape of a pre-existing hole in a homogeneous material, a crack of only one size can exist in equilibrium. This equilibrium size of the crack depends on the size and shape of the hole and also on the distance between the crack and the hole. All cracks whose size is greater than or lesser than the equilibrium size are unstable. The effect of the size and shape of the hole on the equilibrium size of the crack is illustrated. The asymmetry in the dislocation configuration of the crack and the hole is useful in understanding the stress concentration that exists around the crack tip and the corners of the hole and to further study the mechanism of the growth of the crack and the hole.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00032542
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  • 9
    Electronic Resource
    Electronic Resource
    The relationship between cracks, holes and surface dislocations (1974)
    Springer
    International journal of fracture 10 (1974), S. 181-200 
    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
    Description / Table of Contents: Résumé On a pu montrer que les fissures de surface, aussi bien que les cavités peuvent être représentés par des dislocations de surface. Celles-ci ont pour rôle d'empêcher que des efforts de traction n'agissent sur une surface libre se trouvant dans un corps sous contraintes. A l'aide des techniques numériques, on montre qu'il est possible de déterminer l'énergie et le champ de contrainte qui sont associés à des fissures ou à des cavités. Dès lors, en principe, tout problème de cavité ou de fissure peut être solutionné à quelque degré d'approximation que ce soit en utilisant la formulation en termes de dislocations qui est décrite dans l'article.
    Abstract: Zusammenfassung Man zeigt daß Oberflächenrisse sowohl als Löcher in Form von Oberflächendislokationen dargestellt werden können. Diese Oberflächendislokationen bestehen um zu versichern daß an keiner freien Oberfläche eines Körpers unter Spannung, Zugkräfte bestehen. Mittels numerischen Verfahren wird gezeigt daß die Energie sowohl als das durch Risse oder Löcher bedingte Spannungsfeld bestimmt werden können. So kann man dann grundsätzlich irgend ein Loch- oder Rißproblem mit jeglichem Annäherungsgrad lösen indem man das in diesem Bericht beschriebene Dislokationsverfahren anwendet.
    Notes: Abstract It has been shown that surface cracks as well as holes can be represented in terms of surface dislocations. These surface dislocations exist in order to insure that no tractions act on any free surface within a stressed body. Using numerical techniques, it is shown that the energy as well as the stress field associated with cracks or holes can be determined. In principle then, any hole or crack problem can be solved to any degree of approximation using the dislocation formulation described herein.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00113925
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  • 10
    Electronic Resource
    Electronic Resource
    Differential geometry of the coincidence site lattice (1979)
    Springer
    Journal of materials science 14 (1979), S. 205-220 
    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 tensor properties of simple internal surfaces, such as two-phase interfaces and grain boundaries, have been studied in detail. In particular, these tensor quantities have been defined with respect to the original crystal lattice as well as to a common coincidence site lattice that is a characteristic of the boundary. Such lattices allow a given type of distortion to be represented in either a Riemannian or a non-Riemannian (dislocated) space. This particular generality provides a powerful method of anlysing problems in continuum mechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01028345
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