  It is shown here that fracture after a brief plastic strain, typically of a
few percents, is a necessary consequence of the polycrystalline nature of the
materials. The polycrystal undergoing plastic deformation is modeled as a
flowing continuum of random deformable polyhedra, representing the grains,
which fill the space without leaving voids. Adjacent grains slide with a
relative velocity proportional to the local shear stress resolved on the plane
of the shared grain boundary, when greater than a finite threshold. The
polyhedral grains reshape continuously to preserve matter continuity, being the
forces causing grain sliding dominant over those reshaping the grains. It has
been shown in the past that this model does not conserve volume, causing a
monotonic hydrostatic pressure variation with strain. This effect introduces a
novel concept in the theory of plasticity because determines that any fine
grained polycrystalline material will fail after a finite plastic strain. Here
the hydrostatic pressure dependence on strain is explicitly calculated and
shown that has a logarithmic divergence which determines the strain to
fracture. Comparison of theoretical results with strains to fracture given by
mechanical tests of commercial alloys show very good agreement.
