A discrete dislocation plasticity study of the micro-cantilever size effect

Abstract

Micro-cantilevers are increasingly used to extract elastic and plastic material properties through controlled bending using a nanoindenter. Focused Ion Beam milling can be used to produce small scale single crystal cantilevers with cross-sectional dimensions on the order of microns, and electron backscatter diffraction (EBSD) allows cantilevers to be milled from a grain with a desired crystal orientation. Micro-cantilever bending experiments suggest that sufficiently smaller cantilevers are stronger, which is generally believed to be related to the effect of the neutral axis on the evolution of the dislocation structure. A planar model of discrete dislocation plasticity was used to simulate end-loaded cantilevers to interpret the behaviour observed in experiments. The model allowed correlation of the initial dislocation source density and resulting slip band spacing to the experimental load displacement curve. There are similarities between the predictions of this model and those of earlier discrete dislocation plasticity models of pure bending. However, there are notable differences, including a strong source density dependence of the size effect that cannot be explained by geometrically necessary dislocation (GND) arguments, and the effect of the cantilever stress distribution on the locations of soft pile-ups. The planar model was used to identify zero resolved shear stress isolines, rather than the neutral axis, as controlling the soft pile-up location, and source spacing as limiting the slip band spacing in the observed size effect; strengthening was much greater in the source-limited regime. The effect of sample dimensions and dislocation source density were investigated and compared to small scale mechanical tests conducted on titanium and zirconium. The calculations predict a scaling exponent n % 1 for the dependence of stress on size if size is normalised by the average source spacing and a term representing the size-independent flow stress is included, whereas the simple power-law form ordinarily used to fit experimental data significantly underestimates n.

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

“…Moreover, the bending stress in the plastic regime is size dependent with the smaller specimens exhibiting a larger bending stress. This is consistent with a wide body of both experimental [27,28] and computational [11,30,31] gations that suggest that the bending stress is size dependent in the micron size regime. We shall explore the origins of this size effect in more details in Sect.…”

“…Moreover, in this setting the imposed loads also generate shear stresses. In their study, Tarleton et al [31] performed small strain DDP Fig. 2 Sketch of the boundary value problem of the tip loading of the cantilever beam.…”

“…All bending experiments involve significant lattice rotations and changes in the specimen geometry. Discrete dislocation plasticity investigations of such experiments [11,30,31] have neglected these finite strain effects and usually attributed size effects in bending to GNDs.…”

Discrete Dislocation Plasticity Modeling of Hydrides in Zirconium under Thermal Cycling

“…Pa ⋅ s is the assumed edge drag coefficient in zirconium. Further details on DDP as applied to the mechanical behavior of small-scale zirconium can be found in the work of Tarleton et al [9]. Although the hydridematrix interface could impede dislocation motion in reality, this interaction is not included here for simplicity; the hydride dipole and matrix dislocations are only allowed to interact via their stress fields.…”

Evolution of surface grain structure and mechanical properties in orthogonal cutting of titanium alloy

“…For instance, Shishvan [15] showed the simpler two-dimensional DDD studies are more successful in a range of applications encompassing microstructure evolution and plastic mechanism. Tarleton [16] adopted a planar discrete dislocation dynamic model to simulate micro-cantilever bending for hcp crystals oriented for plane strain prismatic slip. The results showed that pure bending interpretations of the micro-cantilever size effect do not reveal its full behavior and the inhomogeneous, highly localized stress influence the strengthening mechanisms and mechanical property.…”