A dislocation model of the plastic deformation of single crystals of ice

A new dislocation model is constructed on the basis of various characteristics of dislocations revealed by X-ray diffraction topography, for interpreting plastic deformation behaviour of ice single crystals in basal glide. The model of a pair of screw dislocation arrays of opposite sign exhibits resistance for the movement, which depends upon both the configuration and the stress. Orowan's relation between the macroscopic strain rate and characteristic of dislocations in the crystal (density and velocity) is rewritten in a dynamical style taking into account the resisting stress and the empirically established linear relationship between the dislocation velocity and the stress. In this formulation, a new concept of fractional dislocation density is introduced.Examples of fractional density as a function of maximum stress are obtained from our stress relaxation experiments. Assuming that the initial fractional density profile for a fresh ice single crystal is similar to those obtained above, stress-strain curves are calculated numerically for various crosshead speeds of the test machine. Computed results coincide well with the characteristic stress-strain curves previously obtained experimentally.