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

S. A. Igonin   ; L. V. Stepanova

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 9 (2013), pp. 97-108

Résumé

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.

Détail

Keywords: damaging, fatigue crack growth, fatigue damage, coupled formulation of the problem, damage accumulation near the crack tip, eigenfunction expansion method.

Bibliographie

[1] Lee Y. L., Barkey M. E., Kang H. T., Metal Fatigue Analysis Handbook Practical Problem-Solving Techniques for Computer-Aided Engineering, Elsevier, Boston, 2012 633 pp.

[2] Zehnder A. T., Fracture Mechanics, Springer, Dordrecht, 2012, 238 pp. | MR

[3] Zhao J., Zhao X., “The asymptotic study of fatigue crack growth based on damage mechanics”, Engn. Fracture Mechanics, 50:1 (1995), 131–141 | DOI

[4] Stepanova L. V., Matematicheskie metody mekhaniki razrusheniya, Fizmatlit, M., 2009, 336 pp.

[5] Stepanova L. V., “Utochnennyi raschet napryazhenno-deformirovannogo sostoyaniya u vershiny treschiny v usloviyakh tsiklicheskogo nagruzheniya”, Vestnik Samarskogo gosudarstvennogo universiteta, 2011, no. 2(83), 105–115

[6] Adylina E. M., Igonin S. A., Stepanova L. V., “O nelineinoi zadache na sobstvennye znacheniya, sleduyuschei iz analiza napryazhenii u vershiny ustalostnoi treschiny”, Vestnik Samarskogo gosudarstvennogo universiteta, 2012, no. 3/1(94), 83–102

[7] Murakami S., Continuum Damage Mechanics. A continuum mechanics approach to the analysis of damage and fracture, Springer, Dordrecht, 2012, 423 pp.

[8] Voyiadjis G. Z., Kattan P. I., “A comparative study of damage variables in continuum damage mechanics”, Int. J. Damage Mech., 18 (2009), 315–340 | DOI

[9] Pinna Ch., Doquet V., “The preferred fatigue crack propagation mode in a M250 maraging steel loaded in shear”, Fatigue Fract. Eng. Mater. Structure, 23 (1999), 173–183 | DOI

[10] Stepanova L. V., “O sobstvennykh znacheniyakh v zadache o treschine antiploskogo sdviga v materiale so stepennymi opredelyayuschimi uravneniyami”, Prikladnaya mekhanika i tekhnicheskaya fizika, 49:1 (2008), 173–180 | Zbl

[11] Stepanova L. V., “Analiz sobstvennykh znachenii v zadache o treschine v materiale so stepennym opredelyayuschim zakonom”, Zhurnal vychislitelnoi matematiki i matematicheskoi fiziki, 2009, no. 8, 1332–1347 | MR | Zbl

[12] Adylina E. A., Stepanova L. V., “O postroenii mnogomasshtabnykh modelei neuprugogo razrusheniya”, Vestnik Samarskogo gosudarstvennogo universiteta, 2012, no. 9(100), 70–83

[13] Ayatollahi M. R., Dehgany M., Nejati M., “Fracture analysis of V-notched components — Effects of first non-singular stress term”, International Journal of Solids and Structures, 48 (2011), 1579–1589 | DOI | Zbl

[14] Stepanova L. V., Fedina M. E., “O geometrii oblasti polnostyu povrezhdennogo materiala u vershiny treschiny antiploskogo sdviga v svyazannoi postanovke (svyazka “polzuchest–povrezhdennost”)”, Vestnik Samarskogo gosudarstvennogo universiteta, 2001, no. 2, 87–113 | MR | Zbl

[15] Astafev V. I., Shesterikov S. A., Stepanova L. V., “Asimptotika napryazhenno-deformirovannogo sostoyaniya v okrestnosti vershiny treschiny v usloviyakh polzuchesti”, Vestnik Samarskogo gosudarstvennogo universiteta, 1995, Spets. vypusk, 59–64

[16] Hello G., Tahar M. B., Roelandt J. M., “Analytical determination of coefficients in crack-tip stress expansions for a finite crack in an infinite plane medium”, Int. J. of Solids and Structures, 49 (2012), 556–566 | DOI

[17] J. Awrejcewicz, P. Hagedorn (eds.), Nonlinearity, bifurcation and chaos — theory and applications, InTech, Rijeka, 2012, 355 pp. | MR

[18] Andriyanov I. V., Danishevskii V. V., Ivankov A. O., Asimptoticheskie metody v teorii kolebanii plastin i obolochek, Pridneprovskaya gosudarstvennaya akademiya stroitelstva i arkhitektury, Dnepropetrovsk, 2010, 216 pp.

[19] Rao S. S., The finite element methods in engineering, Elsevier, Oxford, 2011, 727 pp. | Zbl