Nanoindentations in kinking nonlinear elastic solids

In this work we claim that all solids with high c/a ratios that do not twin are members of a large class of solids labeled kinking non-linear elastic, KNE, solids. These include materials such as micaceous solids, layered silicates and rocks that form the bulk of the earth's surface, graphite, layered ternary carbides and nitrides such as the M_[n+1]AX_n phases, layered oxides, super conductors and semiconductors, boron nitride and probably ice among others. These solids are typically layered and are characterized by fully or near fully reversible stress strain hysteresis loops exhibiting nonlinear elastic behavior, hysteresis and discrete memory. Many materials near earth's surface exhibiting such behavior are modeled phenomenologically by invoking the presence of hysteretic mesoscopic units, (HMUs), whose physical underpinnings are unknown. Similarly the underlying mechanisms of such response of other materials in these KNE solids are not well understood to date, even though some of them have been studied for over a century. Nanoindentation experiments with a spherical indenter were used to probe the mechanical properties of some of these materials - Ti₃SiC₂, single crystal graphite, mica single crystals and layered superconductor - tetragonal YBa2Cu3O6, at very high stresses at the crystal level. Multiple indents on the same location were carried out to study the effect of cycling and it was observed that the first indent usually resulted in a permanent deformation and the subsequent indents resulted in fully reversible, hysteretic response. Our results, together with much of the literature on the mechanical properties of these layered solids, can be explained by invoking the formation of dislocation based incipient kink bands, IKB's, that give way to mobile dislocation walls that, in turn, coalesce into kink boundaries with increasing stress. The IKB's are fully reversible; the dislocation walls result in plastic deformation, and the kink boundaries result in hardening. Herein we show microstructural evidence for kink bands and the formation of a multitude of subgrains under the indenter. Remarkably, these dislocation-based mechanisms allow repeated loading without damage, while dissipating significant amounts of energy during each cycle. Since the dislocations are confined to the basal planes, they cannot entangle and can thus move reversibly over relatively large distances resulting in the dissipation of substantial amounts (up to 300 MJ/m3) of energy (the work done Wd) during each cycle. The values of the work done Wd normalized by the corresponding modulus for these solids along the indenting direction measured herein were in excellent agreement for all these layered solids, confirming that the same mechanisms are operative for these materials despite their differences in the nature of their bonding and the stress levels.