Theoretical approach to the ductile fracture of polycrystalline solids

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.