Minimization of the Stress State and Fracture Parameters of a Composite in Bending

A plane inverse fracture mechanics problem for a composite in bending is considered. Its binder is weakened by rectilinear cracks located arbitrarily near fibers. To determine the optimum tightness of fiber-binder connection that reduces stress concentrations at the interface of material joints and minimizes the fracture parameters (stress intensity factor) of the composite, a theoretical analysis is carried out on the basis of the principle of equal strength. A closed system of algebraic equations allowing one to obtain a solution to the optimum design problem for the composite in relation to the geometric and mechanical characteristics of the binder and fibers is constructed.