285-6 Differential stress and strain rate from the perimeter-area fractal dimension of dynamically recrystallized quartz

Session: Rock Deformation and the Dynamics of Mountain Building: A Session Honoring the Scientific Contributions of John P. Platt, Part II

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Microstructures in deforming rocks and other crystalline solids evolve in response to deformation conditions (e.g., stress, strain rate, temperature) but identifying a single microstructural attribute that directly reflects these conditions has remained elusive. Here we show that the perimeter-area fractal dimension of monomineralic quartz aggregates, which we term the Grain Boundary Dimension (GBD), strongly correlates with both differential stress and strain rate in aggregates deformed by dislocation creep. Analysis of experimentally deformed Black Hills quartzite samples yields quantitative calibrations that show excellent agreement with published grain-size stress piezometers and flow laws. Unlike traditional methods of estimating differential stress, it does not require discrimination between relict and recrystallized grains nor identification of subgrains. As an empirical measure of strain rate, the GBD provides, for the first time, a direct comparison to strain rate estimates from existing flow laws. By quantifying the fractal nature of grain boundaries, the GBD offers new insights into the fundamental relations among macroscale thermomechanical loading and resulting microstructural processes and evolution.

Geological Society of America Abstracts with Program. Vol. 57, No. 6, 2025

doi: 10.1130/abs/2025AM-9805

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