Stick, partial slip and sliding in the plane strain micro contact of two elastic bodies

The plane strain problem of a curved elastic body pressed against an elastic half-space is considered. The effect of adhesion is included through the use of surface energy in a manner similar to the well-known JKR theory for spherical contacts. The compressive normal force is held constant while a tangential force is gradually increased from zero. The contact is characterized by complete stick up to a critical value of the tangential force when there is a transition either directly to complete sliding or to a partial slip state in which a central stick region is surrounded by two slip regions. In the latter case, at a finite value of the stick zone width, a second critical condition exists at which there is a transition from partial slip to complete sliding. This behaviour is determined for a range of dimensionless values of the work of adhesion, the assumed constant shear stress during slip/sliding and the initial compressive load.