Crack nucleation in a strip of varying thickness under force loading

A mathematical model of crack nucleation in a strip of varying thickness under force loading is constructed. It is assumed that the loading of the strip by external forces gives rise to prefracture zones, which are modeled as regions of weakened interparticle bonds in the material. Solution of the problem of the equilibrium of an isotropic strip of varying thickness, with a crack nucleus reduces to solving a system of nonlinear singular integral equations with a Cauchy type kernel to determine the forces in the region of crack nucleation. The condition of crack nucleation in a strip of varying thickness is formulated using the criterion of the limiting stretching of material bonds.