Assessment of tangential and normal stiffness of contact between rough surfaces using ultrasonic method

The acoustic model of contact, previously proposed for longitudinal ultrasonic waves, was adopted for shear waves. It was found that the measurements of the phase shift of coefficient of reflection from the contact interface, taken both for shear and longitudinal ultrasonic waves of the same frequency, allows us to find the tangential to normal contact stiffness ratio for the contact tested.

However, an analysis based on the Greenwood-Williamson model and the Hertz-Mindlin theory revealed that for a contact between rough surfaces with spherical asperities, the ratio of the tangential to the normal contact stiffness is independent of surface height distribution and is, moreover, equal to that ratio for an elementary contact.

In order to verify the theoretical predictions, measurements of the phase shift of longitudinal and shear ultrasonic waves of frequency 10 MHz were carried out for the loaded contact (up to 300 MPa) between ground quartz samples. It appeared that the value of the tangential to normal contact stiffness ratio resulting from the ultrasonic measurements is fairly close to that predicted by the Hertz-Mindlin theory.