Ductile and brittle crystals

Abstract An attempt is made to assess whether a crystal can break in a fully brittle manner or whether some plastic flow must accompany fracture. The criterion proposed is that, if the ratio of the largest tensile stress to the largest shear stress close to the tip of an equilibrium crack in the crystal is greater than the ratio of the ideal cleavage stress to the ideal shear stress, then a fully brittle fracture is possible. If the converse is the case, the crystal must always break with some plastic flow. Calculations are presented for sodium chloride, a Lennard-Jbnes solid, diamond, copper, silver, gold, nickel, iron and tungsten. The criterion appears to give results in broad qualitative agreement with experiment.