Refined estimatation of the mode~II crack tip stress field at plane stress conditions for a~steady state creep linear-fractional law

L. V. Stepanova

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 94-109.

Résumé

The approximate solution of the mode II crack problem in a linear-fractional law of creeping material under plane stress conditions is demonstrated. The stress field in the vicinity of the mode II crack tip is obtained. It is demonstrated that the near crack tip fields consist of four wedge-shape regions. The sectors can be assembled subject to the boundary conditions and continuity of tractions across the sectors boundaries. The comparison of the analytical and numerical solutions is given. The creep strain rate tensor components in the neighborhood of the crack tip are shown to be singular $\dot\varepsilon\sim r^{-\alpha}.$ The singularity exponent $\alpha$ varies discretely from 1 to 1/2.

Détail

Keywords: fracture mechanics, mode II crack, linear-fractional steady-state creep law, stress-strain state near a crack tip.

Bibliographie

[1] Boil Dzh., Spens Dzh., Analiz napryazhenii v konstruktsiyakh pri polzuchesti, Mir, M., 1986, 360 pp.

[2] Shesterikov S. A., Yumasheva M. A., “Konkretizatsiya uravnenii sostoyaniya v teorii polzuchesti”, Izv. AN SSSR. MTT, 1984, no. 1, 86–92

[3] Shesterikov S. A., Lebedev S. Yu., Yumasheva M. A., “O dlitelnoi prochnosti”, Problemy mekhaniki sploshnoi sredy, K 60-letiyu so dnya rozhdeniya V. P. Myasnikova, Vladivostok, 1996, 80–85

[4] Arshakuni A. L., Shesterikov S. A., “Prognozirovanie dlitelnoi prochnosti zharoprochnykh metallicheskikh materialov”, Izv. RAN. MTT, 1994, no. 3, 126–141

[5] Arshakuni A. L., “Prognozirovanie dlitelnoi prochnosti metallov”, Izv. RAN. MTT, 1997, no. 6, 126–135

[6] Lokoschenko A. M., Nazarov V. V., Platonov D. O., Shesterikov S. A., “Analiz kriteriev dlitelnoi prochnosti metallov pri slozhnom napryazhennom sostoyanii”, Izv. RAN. MTT, 2003, no. 2, 139–149

[7] Kashelkin V. V., Kuznetsova I. A., Shesterikov S. A., “Metod prognozirovaniya dlitelnoi prochnosti khromonikelevykh austenitnykh stalei”, Izv. RAN. MTT, 2004, no. 1, 182–187

[8] Shesterikov S. A., Stepanova L. V., “Analiz napryazhenno-deformirovannogo sostoyaniya v okrestnosti vershiny treschiny v usloviyakh polzuchesti”, Izv. RAN. MTT, 1995, no. 1, 96–103

[9] Astafev V. I., Shesterikov S. A., Stepanova L. V., “Asimptotika napryazhenno-deformirovannogo sostoyaniya v okrestnosti vershiny treschiny v usloviyakh polzuchesti”, Vestn. Samarsk. gos. un-ta. Estestvennonauchn. ser., Spets. vypusk (1995), 59–64

[10] Stepanova L. V., “Treschina antiploskogo sdviga v srede s drobno-lineinym zakonom polzuchesti”, Mat. modeli i metody mekhaniki sploshnykh sred, Sb. nauchn. tr. k 60-letiyu d. f.-m. n. A. A. Burenina, IAPU DVO RAN, Vladivostok, 2007, 244–258

[11] Hutchinson J. W., “Plastic stress and strain fields at a crack tip”, J. Mech. Phys. Solids, 16 (1968), 337–349 | DOI

[12] Hill R., “On discontinuos plastic states, with special reference to localized necking in thin sheets”, J. Mech. Phys. Solids, 1 (1952), 19–30 | DOI | MR

[13] Shih C. F., Elastic-plastic analysis of combined mode crack problems, Ph. D. Thesis, Harvard University, Cambridge, 1973

[14] Rahman M., Hancock J. W., “Elastic perfectly-plastic asymptotic mixed mode crack tip fields in plane stress”, Int. J. Solids and Structures, 43 (2006), 3692–3704 | DOI | Zbl

[15] Stepanova L. V., “Napryazheniya v okrestnosti vershiny treschiny poperechnogo sdviga v usloviyakh ploskogo napryazhennogo sostoyaniya v idealno plasticheskom materiale”, Vestn. Samarsk. gos. un-ta. Estestvennonauchn. ser., 2002, no. 2(24), 78–84 | Zbl

[16] Rice J. R., Rosengren G. F., “Plane strain deformation near a crack tip in a power-law hardening material”, J. Mech. Phys. Solids, 16:1 (1968), 1–12 | DOI | Zbl

[17] Hutchinson J. W., “Singular behaviour at the end of tensile crack in a harderning material”, J. Mech. Phys. Solids, 16 (1968), 13–31 | DOI | Zbl

[18] Astafev V. I., Radaev Yu. N., Stepanova L. V., Nelineinaya mekhanika razrusheniya, Samarskii universitet, Samara, 2001, 632 pp.

[19] Stepanova L. V., Matematicheskie metody mekhaniki razrusheniya, Samarskii universitet, Samara, 2006, 232 pp.