Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect

Abstract

A material strength depends on its microstructure, which in turn, is controlled by an engineering process. Strengthening mechanisms like work hardening, precipitate, and grain boundary strengthening can alter the strength of a material in a predictive, quantitative manner and are readily linked to the deformation mechanism. This quantification strongly depends on the characteristic length scale of a particular microstructure, thereby dictating bulk material’s strength as a function of, for example, grain or precipitate size, twin boundary spacing, or dislocation density. This microstructural, or intrinsic , size governs the mechanical properties and post-elastic material deformation at all sample dimensions, as the classical definition of “ultimate tensile strength” deems it to be “an intensive property, therefore its value does not depend on the size of the test specimen.” Yet in the last 5 years, the vast majority of uniaxial deformation experiments and computations on small-scale metallic structures unambiguously demonstrated that at the micron and sub-micron scales, this definition no longer holds true. In fact, it has been shown that in single crystals the ultimate tensile strength and the yield strength scale with external sample size in a power law fashion, sometimes attaining a significant fraction of material’s theoretical strength, and exhibiting the now-commonly-known phenomenon “smaller is stronger.” Understanding of this “extrinsic size effect” at small scales is not yet mature and is currently a topic of rigorous investigations. As both the intrinsic (i.e. microstructural) and extrinsic (i.e. sample size) dimensions play a non-trivial role in the mechanical properties and material deformation mechanisms, it is critical to develop an understanding of their interplay and mutual effects on the mechanical properties and material deformation, especially in small-scale structures. This review focuses on providing an overview of metal-based material classes whose properties as a function of external size have been investigated and provides a critical discussion on the combined effects of intrinsic and extrinsic sizes on the material deformation behavior.