Deformation at the nanometer and micrometer length scales: Effects of strain gradients and dislocation starvation

Nanomechanical devices are certain to play an important role in future technologies. Already sensors and actuators based on MEMS technologies are common and new devices based on NEMS are just around the corner. These developments are part of a decade-long trend to build useful engineering devices and structures on a smaller and smaller scale. The creation of structures and devices calls for an understanding of the mechanical properties of materials at these small length scales. Here we examine some of the effects that arise when crystalline materials are mechanically deformed in small volumes. We show that indentation size effects at the micrometer scale can be understood in terms of the hardening associated with strain gradients and geometrically necessary dislocations, while indentation size effects at the nanometer scale involve the concepts of dislocation starvation and the nucleation of dislocations. We also describe uniaxial compression experiments on micrometer size pillars of single crystal gold and find surprisingly strong size effects, even though no significant strain gradients are present and the crystals are not initially dislocation free. We argue that these size effects are caused by dislocation starvation hardening, with dislocations leaving the crystal more quickly than they multiply and leading to the requirement of continual dislocation nucleation during the course of deformation. A new length scale for plasticity, the distance a dislocation travels before it creates another, arises naturally in this treatment. Hardening of crystals smaller than this characteristic size is expected to be dominated by dislocation starvation while crystals much larger than this size should exhibit conventional dislocation plasticity.