Crack nucleation in circular disk under mixed boundary conditions

Abstract

A model of crack nucleation in a circular disk, based on consideration of cracking process zone is suggested. It is assumed that the cracking process zone is a finitelength layer containing a material with partially disturbed bonds between separate structural elements. Existence of bonds between the pre-fracture zone faces (the area of weakened interparticle bonds of the material) is simulated by application of cohesive forces caused by the existence of bonds to pre-fracture area surfaces. Analysis of limit equilibrium of the pre-fracture zone in a circular disk with mixed conditions on the boundary are fulfilled on the basis of ultimate stretching of material’s bonds and includes: 1) setting up the dependence of cohesive forces on opening of pre-fracture area faces, 2) estimation of stress state near the pre-fracture zone with regard to external loads and cohesive forces, 3) determination of dependence of critical external loads on geometrical parameters of the disk, under which the crack appears.