  The plastic flow of a polycrystal is analyzed assuming grains as fine that
the rate limiting process is grain boundary sliding, and grains readily
accommodate their shapes by slip to preserve spatial continuity. It is shown
that thinking of a polycrystal with randomly oriented grains as an homogeneous
and isotropic continuum when dealing with it as a dynamical medium, even in a
scale much larger than the grain size, leads to gross errors. The polyhedral
nature of grains influences the plastic flow in a radical manner, as the
relative velocity of adjacent grains is constrained to the common boundary
plane, and only the in--plane shear stress contributes to their relative
motion. This constriction determines that the divergency of the velocity field
of the material medium does not vanish, and plastic deformation necessarily
involves grain volume variations, which can only be elastic. As this has a
limit, fracture follows as a necessary step of plastic flow. A theoretical
approach to plastic flow is developed, and emphasis is done in superplastic
deformation, from zero to fracture strain. The theory allows to quantitatively
explain the observed features of superplastic materials and responds to many
open questions in the field.
