Asymptotics of stress and continuity fields near a fatigue growing crack in a damaged medium in conditions of state of plane stress

In the paper asymptotic solution to the problem of growth of fatigue crack in conditions of repeated loading in a damaged medium in the coupled elasticity-damage statement of the problem is given. Asymptotic expansions of stress fields and continuity fields in which two summands are retained in asymptotic representation are derived. The problems of determination of amplitude coefficients of obtained asymptotic expansions are discussed.