Role of Strain Hardening in Frictional Aging of Nanoscale Asperity Contacts

Frictional strength of a fault surface is controlled by the yield strength of microscopic asperities. During any quasi-stationary contact, these asperities transiently creep to a characteristic nm-to-μm length scale to achieve a steady-state strain-rate, which governs the “state” evolution of the fault interface. In the Low-Temperature Plasticity regime, asperities predominantly deform through dislocation creep which is controlled by the dislocation density at the junction. While the density of the statistically stored dislocations (ρ_SSD) controls the steady-state deformation of the asperities, density of the geometrically necessary dislocations (ρ_GND) governs the transient creep.

We have designed a novel nanoindentation based cyclic deformation experiment to assess the evolution of dislocation densities at asperity contact with progressive hardening. Experiments with normal load ranging from 1 to 8 mN and 10 continuous deformation cycles conducted on single crystals of San Carlos Olivine reveal that with increasing iteration of deformation cycle, and thus strain-hardening, Yield Stress and the percentage of anelastic recovery increases nonlinearly. We show that progressive hardening increases the ρ_GND at asperity contact that alters the root-mean-square curvature of the asperity, while a similar increment in the ρ_SSD reduces the characteristic length scale of deformation and increases the macroscopic strength of the material. These observations further validates that the “contact quality” controls the “contact quantity” of nanoscale asperities. Integrating the experimental observations with the existing theories on scale-dependent strength of asperities and nanoscale surface roughness, we have developed a semi-analytical model that relates coefficient of friction with the characteristic length scale of asperity deformation, dislocation densities and roughness parameters. Our model predicts that increasing strain-hardening can reduce the frictional aging for a given amount of fault-normal strain, which provides a microphysical basis for understanding the rate-and-state based friction laws of natural fault surfaces. This study provides a novel mechanistic interpretation of the frictional evolution of nanoscopic self-affine rough surfaces and has potential applications in understanding the transient deformation of the lithospheric mantle.