Minimization of Fracture Parameters of a Composite at Bending

A thin elastic plate of an isotropic medium (matrix) containing inclusions of another material and subjected to bending is considered. It is assumed that the medium is weakened by rectilinear cracks arbitrarily placed near the inclusion. The service life of the composite plate depends on the distribution of stresses in the zones of interaction of its elements. The serviceability of the composite can be improved by changing the geometry of binder and inclusion joint. A fracture mechanics problem for determining the optimum form of inclusion which minimizes the stress intensity factors (moments) near crack tips is solved. A fracture criterion and a solution method for the problem on preventing the composite from fracture under the action of a given system of external bending loads are proposed. A closed system of equations permitting one to obtain a solution to the optimum design problem according to the geometrical and mechanical characteristics of the binder and inclusions is obtained. The cross-sectional shape found for the elastic foreign inclusion provides an increased load-carrying capacity of the composite.