Strength of Plate with the Filled Crack under Multiparameter Loading

The problem of stressed state of an elastic plate weakened by narrow rectilinear through crack (slit) filled with low-modulus material is considered within framework the classical two-dimensional plate theory. For the inclusion of small width the hypothesis of elastic Winkler's layer is accepted. The boundary problem for the pair of biharmonic equations with complicated boundary conditions on the cut is formulated. The analytical solution of singular integrodifferential equations of the problem is built for a case of elliptical form of slit and uniform multiparameter load (combined tension, shear, bending and twisting). The jumps of the displacements and the normal rotation angles on the cut, the stress intensity factors for crack tips and the stresses in the filler are obtained. Special attention is paid to the issue of limited equilibrium of composition. The two mechanisms of fracture are considered: cracking of the plate near the peak of a slit and breach of filler integrity. The first of them is described by the criterion of the linear mechanics of fracture and the second one is described by the classical theory of strength. The considered model of the filled slit allows analytically evaluating the results of the renovation of defective lamellar structures. The diagrams of limiting equilibrium of plate with filled slit are built for several options of two-parametric loading. The key parameters that determine the success of injection technology for repair of the cracked plate for a given loading trajectory are the relative stiffness and relative strength of the filler. (C) 2018 The Authors. Published by Elsevier B.V.