Contact of faces of a rectilinear crack under complex loading and various contact conditions

The problem of partial contact of faces of a rectilinear crack in a uniform elastic plane under given tensile and shear stresses at infinity as well as two compressive concentrated forces applied near the crack is investigated. Three variants of problem statement are considered: smooth contact, sliding contact, and contact with slip and adhesion between the faces of the crack. Using Kolosov-Muskhelishvili complex potentials, the problem is reduced to a conjugation problem, and a solution of the last one is obtained in analytic form. Transcendental equations to determine the boundaries of contact area and adhesion zone are derived. Conditions are found for cases when the contact area of crack faces degenerates into a point or takes an entire crack. It is shown that an adhesion zone disappears and a mutual slip of crack faces occurs along an entire contact area, if a ratio of tangential and normal stresses given at infinity is larger than a certain value. The results of calculation of boundaries of contact area and adhesion zone, stress intensity factors, and distributions of normal and tangential contact stresses are presented.