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.