Backstresses in geologic materials quantified by nanoindentation load-drop experiments

Transient creep of geologic materials is inferred to control many large-scale phenomena such as post-seismic deformation and post-glacial isostatic readjustment. Viscoelastic simulations can reproduce transient creep measured at Earth’s surface via GPS, but these approaches are entirely phenomenological, lacking a microphysical basis. This empirical nature limits our ability to extrapolate to future events and longer time scales. Recent experimental work has identified the importance of strain hardening and backstresses among dislocations in the transient deformation of geologic materials at both high and low temperatures, but very few experimental measurements of such backstresses exist. Here, we develop a nanoindentation load-drop method that can measure the magnitude of backstresses in a material. Using this method and a self-similar Berkovich tip, we measure backstresses in single crystals of olivine, quartz, and plagioclase feldspar at a range of indentation depths from 100–1750 nm, corresponding to geometrically necessary dislocation (GND) densities of order 10¹⁴–10¹⁵ m⁻². Our results reveal a power-law relationship between backstress and GND density with an exponent ranging from 0.44–0.55 for each material, in close agreement with the theoretical prediction (0.5) from Taylor hardening. This work supports the assertion that backstresses and their evolution must be considered in future models of both transient and steady-state deformation in the Earth.