The solution of a problem in contact fracture mechanics on the nucleation and development of a bridged crack in the hub of a friction pair

The contact deformation of the hub of a plunger pair is considered. It is assumed that, during the repeated reciprocating motion of the plunger, a crack is initiated and fracture of the materials of the elements of the contact pair occurs. The problem of the equilibrium of the hub of a friction pair with a crack nucleus reduces to solving a system of non-linear singular integrodifferential equations with a Cauchy-type kernel. The normal and shear forces in the zone where the crack originates are found from the solution of this system of equations. The condition for the appearance of a crack is formulated, taking account of the criterion of the limit traction of the bonds in the material. A problem for the plunger of a friction pair as applied to a borehole sucker rod pump is considered as an example. In conclusion, the case when there are several arbitrarily distributed rectilinear bridged cracks, with bonds between the crack faces in the end zone, close to the contact surface of the hub is investigated.