Backstresses in geologic materials quantified by nanoindentation load-drop experiments

ABSTRACT

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.

GRAPHICAL ABSTRACT

KEYWORDS:

• Rock deformation
• transient creep
• backstress

Acknowledgements

The authors declare no conflict of interest. C.A.T. designed the study and nanoindentation method, carried out experiments and data analysis, and wrote the initial manuscript draft. All authors contributed to editing and revising the manuscript. The authors would like to thank G. Pharr and D. Wallis for useful discussions. All data used in this study are available at https://upenn.box.com/s/mo9txpz9n6dzvdup6dt5yq8t6ltd80tt. Funding for this study was provided by NERC 1710DG008/JC4 to L.N.H. and C.A.T. and NSF EAR-1806791 to K.M.K.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by NSF: [grant number EAR-1806791]; Natural Environment Research Council: [grant number 1710DG008/JC4].