Earthquakes are an integral and catastrophic part of the seismic cycle. Due to their disruptive impact on society, there is a public as well as a scientific interest in accurate modeling of this cycle. Part of this, is constraining the maximum strength of the crust in the transition region between brittle and ductile rheologies. This maximum strength of long-lived faults is important in geodynamic models governing e.g. mountain building and collapse and volcano activity. In seismic models the strength of faults controls the strain build up before it’s released in a seismic event. Ductile behavior is incorporated in such models via flow laws.
Phyllosilicates are abundant in faults and fault gouges. Incorporating their ductile behavior is necessary to accurately describe the behavior in long-lived faults. To date there are multiple flow laws for phyllosilicate creep, giving significantly different results in terms of stress and strain rate upon extrapolation from the laboratorial conditions under which they were established to nature. There are two groups of flow laws, one group with a power law relation between strain rate and stress (ε ̇ ∝ σ^n) based on geometrical relations. The other group has an exponential relation between strain rate and stress (ε ̇ ∝ e^ασ) and finds its origin in the elementary atomic jump theory.
To distinguish between these two flow laws, sheets of single crystals of muscovite were submitted to three point bending tests under constant stress and elevated temperatures conditions. TGA measurements were performed to establish the maximum experimental temperature of 600ᵒC to avoid dehydroxylation. The stresses employed varied between 0.1-0.4 MPa and temperatures between 500ᵒC and 600ᵒC. Strain and strain rates were calculated. Results were compared with previous work and both flow law approaches were fit to the data. After retrieval of the samples, they were examined with a Leica optical microscope and a scanning electron microscope. Microstructural observations displayed an array of different features that do not influence the deformation behavior, but are most likely shrinking features that form upon cooling.
The maximum of strain reached ranges between 0.6 – 1.0 %. After an initial period of thermal cooling due to the set-up, the initial strain rates are 10-6 s-1, but decrease with time to 10-8 to 10-10 s-1 (=strain hardening). When a power law relation was fitted to the data, our results gave a stress exponent (n) of 1, corresponding with Harper-Dorn creep which assumes a constant dislocation density. This linear relation between stress and strain rate is previously found in combination with strain rates slower than 10-5 s-1. At higher strain rates this value increased to ~18. When an exponential relation was fitted to the data, our results gave an exponential factor (α) of 4. Previous work found lower values of around 0.5.
There is too little data to conclusively distinguish between the two flow laws. However, from the Geometrically Necessary Dislocations (GND) theory it follows that in a bending geometry, dislocations of one sign need to accumulate in the crystal to accommodate the bend which conflicts with the assumption of a constant dislocation density. In addition, we also observed strain hardening, Harper-Dorn creep is therefore regarded unlikely. This leaves glide due to thermal vibration, as expressed by the exponential flow law, as the most likely operating mechanism.
This has implications for models that use a flow law with power law relation between stress and strain rate to incorporate phyllosilicate behavior. As the exponential relationship predicts higher strain rates for lower stresses, and therefore a weaker crust. This means that the strain will most likely be released aseismically before stresses necessary to initiate brittle behavior can build up.