Search

The purpose of this work is the numerical resolution, in the case of anisotropic elasticity, of the problem of a dislocation parallel and near to the two free surfaces of a thin bicrystal. This case is obtained while making the period of a network of misfit dislocations much greater than the thickness of the two foils. As a result, in the vicinity of the dislocation, the limiting bondary conditions will be close to that of Volterra translation dislocation. The elastic fields of displacement and stress are calculated for various orientations of the burgers vector. Before this calculation, we tested the precision of the results of the program by comparing the interfacial relative displacement obtained from this one to the results of the analytical expression describing this same displacement. The thin bicristal Al/Al2Cu, that made the object of several investigations, is treated like example. The results obtained are compared to those obtained in isotropic elasticity.Este trabajo aborda la resolución numérica en anisotropía elástica, del problema de una dislocación paralela cercana a las superficies libres de un bi-cristal delgado. Este problema se genera cuando el periodo de la red de dislocaciones desplazadas es mucho mayor que el espesor de la bi-lámina. Como resultados, en la vecindad de la dislocación, las condiciones de contorno estarán cercanas a la dislocación de traslación de Volterra. Los campos elásticos de desplazamiento y las tensiones se calcularon para distintas orientaciones del vector de burgers. Como paso previo a los cálculos, se comprobó la precisión de los resultados del programa comparando le desplazamiento relativo interracial obtenido con los resultados de la expresión analítica que describen dicho desplazamiento. Se emplearon como ejemplo bi-cristales de Al/Al2Cu, debido a su empleo en varias investigaciones. Los resultados fueron comparados con los obtenidos en elasticidad isótropa.

The elastic field of an angular dislocation line that has a branch placed in a crystal of a bi-material while the other branch is along a strongly bound or welded interface, is found when the two crystals have anisotropic properties. Since the field of this angular dislocation depends on the elastic constants of the two crystals, it can be called hybrid dislocation (HD). To face this problem already treated using isotropic elasticity, the analysis first formulates the elastic field of a closed dislocation loop whose surface S is that of a circular sector centred in a point O of the interface. By virtue of the Saint Venant principle, when the circular segment moves far away from O, the field induced by the loop near O tends towards that of a HD. The calculation is possible thanks to the knowledge of the Green's tensor of the bi-material which has already been the subject of several works. Thanks to the use of polar coordinates, the solution is reduced to convenient line-integral expressions which make the calculation faster. This work complements a previous approach to the HD problem based on the integral formalism. By combining two HD's, it also gives the solution to the problem of an interfacial angular dislocation. Some applications illustrate anisotropy effects and highlight an inability of integral formalism to deal with a interfacial branch strictly in the interface. [ABSTRACT FROM AUTHOR]

The 3D deformation of a bimaterial subjected to a dislocation composed of two straight semi‐infinite arms is known when the two arms are placed on each side of the interface. The resolution is possible taking into account an anisotropic elasticity for both media, thanks to the use of the concept of dislocation/force proposed by Belov (1992). By generalizing the analysis of this author, it is possible to solve a similar problem having an angular geometry, but which concerns a line force crossing the interface. For isotropic media, the solution can be formulated explicitly when the two arms are continuous and perpendicular to the interface. A few numerical applications illustrate the calculations for environments with different elastic properties and for different orientations of the two arms. [ABSTRACT FROM AUTHOR]

The elastic field of an angular dislocation determined by Yoffe ([The angular dislocation. Phil. Mag. 5(50) (1960), pp. 161–175]) using isotropic elasticity is a convenient tool for modelling defects in very different materials such as crystalline media or the Earth's crust deformed by internal shifts. We show that the anisotropy of the medium can be introduced in two ways to solve the same problem, one using an integral formalism and the other the Green's tensor attached to a homogeneous medium. β' CuZn brass, which has a strong elastic anisotropy, is treated with the two methods, and the results are compared. [ABSTRACT FROM AUTHOR]

The interfacial structure of a lamellar Al(α)-Al2Cu(θ) eutectic obtained by directional solidification is investigated using conventional transmission electron microscopy (TEM) and high-resolution TEM. The average lamellar habit plane is close to (2 3 3)αand lie 10° from the atomically densest planes (1 1 1)α//(2 –1 1)θ. Networks of linear contrasted features are observed along the interfaces, the lines being separated each other’s in a wide range of spacings, typically 6–500 nm. These features are identified as interfacial dislocations with 1/2<1 1 0>αBurgers vectors from image contrast analysis. According to previous works, they are associated with ledge-like defects, the heights of which can reach 3 nm. The high-resolution TEM images do not confirm the presence of atomic terraces parallel to the atomically dense plane (1 1 1)αor the habit plane (2 3 3)α. The interface ensures the quasi-continuity of atomically dense planes, which is a configuration corresponding to the plane-matching model. It is suggested thatα/θinterfaces can be considered as semi-coherent but in a particular sense since, according to our analysis, the theoretical length misfits between the fcc and bct lattices are too large to explain the presence of some loose dislocation networks. Their general irregular geometry suggests that these dislocation networks behave like non-equilibrated low-angle grain boundaries superposed on theα–θinterfaces. [ABSTRACT FROM PUBLISHER]

The elastic field generated by a semi-coherent interface formed by a succession of parallel terraces and nanoledges is investigated when the interface intersects the free surface of an isotropic half-space medium. The method uses the combination of semi-infinite Somigliana dislocations placed on each terrace and semi-infinite translation (or Volterra) dislocations placed at one or two corners of the nanoledges. Numerical examples depict the deformation fields nearby emerging regions of two semi-coherent interfaces; one is flat, while the other includes nanoledges. [ABSTRACT FROM PUBLISHER]

Abstract: The determination of the separation distance S between the two partials of a dissociated dislocation placed in an elastically anisotropic thin crystal is critically dependent on several parameters: the elastic constants, the Burgers vectors of the partials, the orientation of the fault plane in the crystal, the stacking fault energy per unit surface, the thickness h of the foil and the position of one partial in the crystal. The calculation of S is proposed from (i) an equation expressing the mechanical equilibrium of the two partials and (ii), the knowledge of the displacement field u of an isolated dislocation parallel to the free surfaces of a thin plate-like crystal. Since two theories are available in the literature to express u, both were tested for the calculation of S. One of them was preferred because of its better numerical efficiency and its fully explicit formulation in function of the space variables. This last property permits an easy derivation to be done and is useful to discuss the stability of the mechanical equilibrium of two partials. Numerical applications are presented for a screw dislocation dissociated into two 30° partials, located in a thin face cubic centred Cu-13.43 at.%Al crystal (anisotropy ratio=3.85). Assuming a fixed partial lying in the mid plane of the foil, around which turns a close-packed fault plane, the locus of the other partial is described by polar graphs. These graphs are quite different in the isotropic approximation. To cite this article: R. Bonnet, S. Youssef, C. R. Physique 7 (2006). [Copyright &y& Elsevier]

The elastic field of a crystalline defect parallel to the two free surfaces of an isotropic thin foil is studied, for plane strain, with a new approach using repeated applications of the classical solution of the Flamant''s problem. The case of an edge dislocation placed at any position in the foil and with a Burgers vector parallel to the surfaces is considered in greater detail. To cite this article: R. Bonnet, C. R. Physique 4 (2003). [Copyright &y& Elsevier]

A quantitative analysis of the image of a low angle (0 0 1) twist boundary in silicon is performed using the two-beam dynamical theory of electron diffraction. The contrast features are discussed as functions of the thickness of the foil and possible elastic relaxation effects of the low angle twist boundary in the thin foil. To cite this article: R. Bonnet et al., C. R. Physique 3 (2002) 657–663. [Copyright &y& Elsevier]