Continuous distributions of dislocations. V. Twisting under conditions of single glide

Abstract

The theory of continuous distributions of dislocations is applied to discuss the geometrical features of the twisting of a cylindrical crystal deforming by single glide. It is first assumed that the strains are small, and that the dislocations arrange themselves so as to produce no far-reaching stress, and explicit expressions for the shape changes, lattice rotations and dislocation distribution are derived. The theory is in reasonable agreement with the observations of Whapham & Wilman (1956) when the angle of twist per unit length is not too large. The expression for the shape of the glide surfaces is much simpler than that derived by Whapham & Wilman, who also applied a small strain approximation, but not consistently. It is shown that the consistent reduction of the complicated expression of these authors leads to the simple one of the present theory. Further, the correct shape of the glide surfaces for large strains is also derived using the boundary conditions employed by Whapham & Wilman. This predicts an asymmetry of the type observed in a severely twisted crystal before correction of the observations for macroscopic bending, although the predicted asymmetry is rather too large.