Modeling of crack nucleation in a variable-thickness band under nonuniform heating

A mathematical model of crack nucleation in a variable-thickness band (rod) under nonuniform heating is constructed. As the band (rod) is thermally loaded, pre-fracture zones are assumed to appear; these zones are modeled as regions with attenuated bonds between material particles. The presence of bonds between the pre-fracture zone faces is modeled by adhesion forces applied to the pre-fracture zone surface. Solving the problem of equilibrium of an isotropic variable-thickness band with a prefracture zone is reduced to solving a nonlinear singular integrodifferential equation with a Cauchy-type kernel, which establishes the relation between the adhesion forces in the crack-nucleation zone and the distance between the crack faces. The condition of crack nucleation in a variable-thickness band is formulated with allowance for the criterion of ultimate tension of bonds in the material.