SOME GENERAL RESULTS IN THE THEORY OF CRYSTALLOGRAPHIC SLIP

Crystallographic slip of a Bravais lattice is analyzed utilizing the m ain results of a recently constructed theory of structured solids, whe re explicit account is taken of the influence of dislocation density i dentified in terms of Curl of plastic deformation G(p). In the present paper, the scope of the subject is enlarged to also include defects ( other than dislocations) such as substitutional impurities and vacanci es and it is shown that these point defects may also be characterized in terms of the plastic deformation field G(p). Several general result s pertaining to the kinematics and kinetics of crystallographic slip a re proved within the scope of an appropriate constraint theory suitabl e for crystallographic slip; the latter is motivated by the well-known basic mechanism of crystallographic slip that constrains the admissib le 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 determin ed. In spite of the nature of the assumption pertaining to the mechani sm 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 r esult of the use of a special set of constitutive assumptions. The pre dictive capability of the theoretical results is further illustrated b y using a two-dimensional crystal subjected to simple shear. The effec t of the initial dislocation density on the response of the sheared-cr ystal is studied by carrying out detailed calculations for two substan tially different initial dislocation densities. The calculations show that while the response of the crystal is sensitive to the initial dis location density in the early stages of deformation, its influence dim inishes with progressively larger deformations. Furthermore, the cryst al exhibits a well-defined shear band which evolves naturally due to t he presence of initial dislocation distribution and is easily visible at large deformations.