The accumulation of dislocations during the deformation of polycrystals

The accumulation of dislocations during work hardening of polycrystalline iron, copper, and 7030 brass have been investigated using stress relaxation techniques to monitor the variation of internal stress during work hardening as a function of grain size. It is shown that, for certain conditions dependent on the temperature and the nature of slip, the rate of accumulation of dislocations in a polycrystal is grain size dependent and can be expressed in terms of a modified Hall-Petch equation with a slope dependent on the degree of plastic strain. A simple dimensional argument is developed to show that under conditions of planar slip where the slip distance is equivalent to the grain diameter, the grain size dependent accumulation of dislocations is related to the development of strain gradients necessary for the contiguity of the polycrystal during deformation.The observation of a grain size dependent work hardening rate leads to the establishment of some important similarities between the deformation of polycrystals and two-phase materials containing rigid inclusions which deform in a non-homogeneous manner.