Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University485810.18287/2541-7525-2011-17-2-105-115REFINED STUDY OF STRESS-STRAIN STATE NEAR THE CRACK TIP UNDER CYCLIC LOADING IN A DAMAGED MEDIUMStepanovaL.V.morenov.sv@ssau.ruSamara State University160620111721051151506201715062017Copyright © 2011, Stepanova L.2011<p>The article is devoted to the fatigue growing crack problems in damaged<br />media and mutual effects of damage on the evolution of the stress-strain state<br />near the crack tip and vice versa. The new asymptotic study of fatigue crack<br />growth in an isotropic linear elastic material based on the continuum damage<br />mechanics in the coupled (elasticity damage) formulation under plane strain<br />and plane stress conditions is proposed. 1) The new numerical solution of the<br />two-point boundary value problem for non-linear ordinary differential equations<br />to which the fatigue crack growing problem reduces is obtained; 2) The new<br />analytical presentation of stress, strain and continuity fields both for plane strain<br />and plane stress conditions is given. The results obtained differ from Zhao and<br />Zhang’s solution where the original formulation of the problem for plane stress<br />conditions has been proposed.</p>fatigue crack growth, coupled statement of the problem, elasticity damage coupling, active damage accumulation zone (process zone), totally damaged zoneусталостный рост трещинысвязанная постановка задачисвязка "упругость - поврежденность"область активного накопления поврежденийобласть полностью поврежденного материала