The ductile/brittle transition of polycrystalline aggregates in terms of their single crystal cubic properties

Abstract

The Kröner solution is used to determine the shear modulus of any polycrystalline aggregate composed of cubic crystals. This solution from the self-consistent method takes the form of a cubic equation specified by the three elastic properties of the crystal. The ductile/brittle transition for homogeneous and isotropic materials in uniaxial tension is specified by terms of the shear modulus and the bulk modulus of the aggregate. These two basic results are then combined to specify the ductile/brittle transition of the polycrystalline aggregate in terms of its cubic crystal symmetry elastic properties. The various forms that the combined results take are developed and interpreted. Examples and detailed results are given for carbon-diamond, copper, tungsten, iron, silicon, lithium and platinum element type polycrystal materials. The tungsten and iron cases very closely bracket the ductile/brittle transition for all of the solids forming elements of the Periodic Table, one from the brittle side and the other from the ductile side.