Transitions of shear resistance in a single-asperity contact

The shear force required to emit circular dislocation loops from the edge of a circular adhesive-contact zone is calculated analytically as a function of contact-zone radii. The emission condition is based on the balance of the configurational force and the Peierls force on a dislocation loop initiated at the edge of the adhesive contact zone. The analysis suggests that there is a transition, for a nanometer-scale single-asperity contact, from concurrent (mobile-dislocation-free) slip to single-dislocation-assisted (SDA) slip. The nanometer-scale friction stress (shear force required for slip/contact area), which experimentally is observed independent of normal loading and contact-zone size, is believed to be the stress required for concurrent slip. The analysis also predicts a second transition from SDA slip to multiple-dislocation-cooperated (MDC) slip at the scale of tens of micrometers in contact size. The friction stress at this large length scale has also been observed experimentally to be independent of normal loading and contact size; however, the friction stress at the nanometer scale is about 30 times that at the scale of tens of micrometers. The analysis is consistent with these experimental observations.