SOME GENERAL RESULTS IN THE THEORY OF CRYSTALLOGRAPHIC SLIP
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abstract
Crystallographic slip of a Bravais lattice is analyzed utilizing the main results of a recently constructed theory of structured solids, where explicit account is taken of the influence of dislocation density identified in terms of Curl of plastic deformation Gp. In the present paper, the scope of the subject is enlarged to also include defects (other than dislocations) such as substitutional impurities and vacancies and it is shown that these point defects may also be characterized in terms of the plastic deformation field Gp. Several general results pertaining to the kinematics and kinetics of Crystallographic slip are proved within the scope of an appropriate constraint theory suitable for Crystallographic slip; the latter is motivated by the well-known basic mechanism of Crystallographic slip that constrains the admissible modes of plastic deformation. The constraint responses (or forces) that are necessary to maintain the active slip systems, as well as the conditions for the transitions between the slip systems, are determined. In spite of the nature of the assumption pertaining to the mechanism of Crystallographic slip on distinct slip systems, it is shown that the yield surface does not necessarily exhibit sharp corners. Instead, the shape of the yield surface is in the form of hyperplanes joined by round corners. In fact, the presence of sharp corners is mainly a result of the use of a special set of constitutive assumptions. The predictive capability of the theoretical results is further illustrated by using a two-dimensional crystal subjected to simple shear. The effect of the initial dislocation density on the response of the sheared-crystal is studied by carrying out detailed calculations for two substantially different initial dislocation densities. The calculations show that while the response of the crystal is sensitive to the initial dislocation density in the early stages of deformation, its influence diminishes with progressively larger deformations. Furthermore, the crystal exhibits a well-defined shear band which evolves naturally due to the presence of initial dislocation distribution and is easily visible at large deformations. 1994 Birkhuser Verlag.
