BENDING OF AN ISOTROPIC PLATE WITH TWO IDENTICAL COAXIAL THROUGH CRACKS DEPENDING ON THE WIDTH OF THE CONTACT ZONE OF THEIR FACES AND IN THE PRESENCE OF PLASTIC ZONES NEAR THEIR TIPS

摘要

We formulate and solve the problem of biaxial bending of an isotropic plate with two coaxial through cracks of identical lengths by distributed bending moments applied at infinity under the action of external load symmetric about the cracks with regard for the contact zone of their faces and in the presence of plastic zones near the crack tips, where the Tresca plasticity conditions are satisfied in the form of a surface layer or a plastic hinge. By using complex potentials of the plane problem and the classical theory of bending of the plates, we obtain an analytic solution of the problem in the class of functions bounded in the vicinity of the vertices of the plastic zones. The length of the plastic zones and the crack-tip opening displacements are found numerically.