We consider a problem of fracture mechanics for a hub of a friction pair during operation. It is assumed that near the friction surface the hub has a rectilinear crack of length 2ℓ1. A criterion and a method for solving the inverse problem of fracture mechanics on definition of the function of displacements of external contour points of the hub of a friction pair with regard to temperature drop in the details of friction pair is given. The found function of displacements of external contacts points of the hub provides increase of load-carrying capacity of the friction pair. Calculation for a friction pair applied to the borehole sucker-rod oil pumps was considered as an example.
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