Common edge contacts: Effect of interface line orientation

•Development of theory to solve common edge contacts.•Maps of incipient slip conditions.•Combined plane and anti-plane loading.

The problem of frictional contact between a finite triangular plane body in frictional contact with an elastically similar frustum, so that the combined geometry is that of a semi-infinite wedge, is studied under plane and anti-plane loading conditions, using a bilateral formulation. The limit of validity of this solution and, in particular the conditions for separation and first slip are found. These results are of relevance to more general contacts having a ‘common edge’ and suggest whether slip is interior or edge initiated. This is of practical relevance to contacts of this class subject to fretting loading.