Anelastic Deformation of Geologic Materials from Nanoindentation Load-Drop Experiments

Rheological models are often used to constrain transient creep that occurs during post-seismic deformation or post-glacial rebound, yet the microphysical mechanisms that underlie the anelastic behavior of geological materials is not well-established. Recent work by Wallis et al. (2017) and Hansen et al. (2019) suggest that a "back stress" created by long-range dislocation interactions may control strain hardening and anelastic behavior in olivine, but it is unknown if similar mechanisms occur in other geologic materials.

We performed over 200 load-drop experiments on olivine, quartz, calcite, and halite at room temperature using nanoindentation. We used a diamond Berkovich indenter, which induces a constant strain of 8%, and varied the dislocation density in the plastically deforming volume beneath the indenter by controlling the size of the indent (i.e., by varying the applied load). Measurements of contact stiffness were made continuously throughout each experiment to determine the contact area between the tip and sample and thus whether the sample was creeping. After deforming a sample at a nominally constant strain rate then holding the load constant and measuring its creep behavior for 60 s, we reduced the applied load by 1% to 99% and held it constant for 1 hour to measure the anelastic response, if any, of the sample. For all materials, three deformation behaviors were observed: 1) small reductions in the applied load result in continued forward creep of the sample at a reduced rate; 2) moderate reductions result in negligible creep; and 3) large reductions result in reverse creep as the indenter tip is effectively pushed out of the sample. We calculate the stress at the transition between behaviors 2 and 3 to determine the "back stress" and find that it scales with the geometrically necessary dislocation density as σ_b ∝ ρ^2.02±0.20 for all materials tested. This relationship is remarkably consistent with the predicted exponent of 2 derived from the Taylor hardening equation, which is derived from the physics of long-range dislocation interactions. These data suggest that anelastic deformation caused by dislocation interactions plays an important role in the deformation of geologic materials and the microphysics of anelasticity should be included in transient rheological models applied to geodynamic processes.