Continuous distributions of dislocations. Ill

Abstract

The theory of the continuously dislocated crystal is extended. It is shown that the general equations of the theory of Nye are applicable in full only when the lattice curvature (and so also the dislocation density) is small. The correct equations for large curvatures are formulated. The relation between the fundamental node theorem of dislocation theory and certain theorems of the theory of generalized space is considered in some detail. It is also shown that when the lattice lines of the dislocated crystal are treated as a system of independent congruences of curves, the tensor describing the local dislocation density may be expressed in terms of certain invariants connected with the system of congruences. For the rotation case, a relation between the dislocation density and Ricci’s coefficients of rotation is derived.