Surface outflow effect on dislocation structures in micrometer-sized metals

Abstract

Dislocations in metals often multiply and agglomerate into quasi-ordered structures with various morphologies in cyclic loading experiments. Specifically in face-centered cubic metals, the shapes of dislocation clusters change from dislocation bundle structures (called veins) to ladder-like periodic wall structures at a threshold of the applied shear strain that coincides with the fracture initiation threshold. In these ladder-like structures, the interval between adjacent walls is 1 or 2μm, regardless of the material dimensions. The robustness of such micrometer-sized wall intervals implies the impossibility of forming ladder-like structures in micrometer-sized metals. Nonetheless, the kind of dislocation structure that will occur is unclear because of a lack of knowledge about small-scale metal fatigue. In this study, we theoretically speculate the dislocation structures formed in micrometer-sized metals using differential equations that describe the reaction and diffusion of dislocations in the fatigue process. We find that micrometer-sized metals form few-walled structures due to the outflow of dislocations from their free surfaces, even under the parameter conditions under which vein structures form in macroscopic metals. The results indicate that the fracture initiation limit can be decreased by reducing the system size, which contradicts the well-established “smaller is stronger” consensus regarding the mechanics of small-volume single crystals.