Elastic Stability Criteria and Structural Bifurcations in Crystals Under Load

Abstract

What happens when a crystalline material is deformed elastically to the point where it loses structural stability? Under what circumstances will it lose stability? Why are these questions important? The stress required to cause elastic instability is often considered to be the ultimate “theoretical strength” of a crystalline material, which is an inherently intriguing concept, in and of itself. The “theoretical strength” plays important roles in understanding and/or describing practical phenomena, e.g., it forms a basis for calculating the efficiency of grinding processes and it affects the stress distribution near the tip of a crack and thus influences whether a material will exhibit brittle or ductile behavior. From another viewpoint, structural phase change rather than loss of strength is the presumed outcome of elastic instability. New crystalline or amorphous structures that form under mechanical stress may remain elastically stable after the stress is released, and so may continue to exist indefinitely, even if not in the thermodynamic equilibrium state at zero stress. (An example of an elastically stable structure that is also not in the thermodynamic equilibrium state is the extremely hard, tetragonal crystalline form of ironcarbon alloy referred to as martensitic steel; such structures are sometimes called metastable.)