Geodesic
Refined study of stress-strain state near the crack tip under cyclic loading in a~damaged medium
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2011), pp. 105-115

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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.
Keywords: fatigue crack growth, coupled statement of the problem, elasticity–damage coupling, active damage accumulation zone (process zone), totally damaged zone. 
@article{VSGU_2011_2_a10,
     author = {L. V. Stepanova},
     title = {Refined study of stress-strain state near the crack tip under cyclic loading in a~damaged medium},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {105--115},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2011_2_a10/}
}
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L. V. Stepanova. Refined study of stress-strain state near the crack tip under cyclic loading in a~damaged medium. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 2 (2011), pp. 105-115. http://geodesic.mathdoc.fr/item/VSGU_2011_2_a10/