The Ductile/Brittle Transition for Materials Failure—Atomic Scale to Macroscopic Scale

Abstract

This work is the continuation and completion to that initiated in the studies by Christensen (2022, “Perspective on the Bond Bending and Bond Stretching Effects of the Atomic Scale and Their Relationship to Ductile Versus Brittle Materials Failure,” J. Mech. Phys. Solids, 167, p. 104984; 2023, “Review of the Basic Elastic Mechanical Properties and Their Realignment to Establish Ductile Versus Brittle Failure Behaviors,” ASME Appl. Mech. Rev., 75(3), p. 031001) on the ductile/brittle transition for homogeneous and isotropic materials in uniaxial tensile failure. Starting here at the atomic level with the bonding involving both bond bending and bond stretching effects, there then is given the development of the ductile/brittle transition for a type of cubic symmetry in the individual crystals of the composing polycrystalline material. Thereafter, a complementary derivation is given for the ductile/brittle transition at the macroscopic level involving a specific form of the strain energy. The two results are found to be compatible and mutually verifying, thereby finishing the investigation.