Refined study of stress-strain state near the crack tip under cyclic loading in a damaged medium

The article is devoted to the fatigue growing crack problems in damaged media and mutual effects of damage on the evolution of the stress-strain state near the crack tip and vice versa. The new asymptotic study of fatigue crack growth in an isotropic linear elastic material based on the continuum damage mechanics in the coupled (elasticity–damage) formulation under plane strain and plane stress conditions is proposed. 1) The new numerical solution of the two-point boundary value problem for non-linear ordinary differential equations to which the fatigue crack growing problem reduces is obtained; 2) The new analytical presentation of stress, strain and continuity fields both for plane strain and plane stress conditions is given. The results obtained differ from Zhao and Zhang's solution where the original formulation of the problem for plane stress conditions has been proposed.