Equilibrium of a dissociated dislocation located in an elastically anisotropic thin foil

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 1/2 < 110 > screw dislocation dissociated into two 30 degrees 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). (c) 2006 Acaddmie des sciences. Publie par Elsevier SAS. Tons droits reserves.