Biaxial tension of the plate softened by the Griffiths crack https://doi.org/10.33108/visnyk_tntu2017.04.088

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Vol. 88 No. 4 (2017)
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Published: 31-12-2019
DOI: https://doi.org/10.33108/visnyk_tntu2017.04.088
Keywords:
elliptical defect, crack tip opening, elastic approach, elastic-plastic approach, biaxial load, deformation criterion

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Igor Panko
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv, Ukraine
Stepan Shtayura
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv, Ukraine
Oleg Panko
Karpenko Physico-Mechanical Institute of the NAS of Ukraine, Lviv, Ukraine
Nataliya Shtayura
Ivan Franko National University of Lviv, Lviv, Ukraine

Abstract

According to the elastic approach the biaxial loading problem of the plane with an elliptical defect was solved. Using the obtained solution and the deformation approach [1, 3] the solution for the cracked plane under the biaxial load in the elastic-plastic statement has been obtained. Thereupon a deformation criterion
for the critical crack tip opening has been proposed. It was shown, that the tensile load applied parallely to the major defect axis results in the increase of the crack tip opening and the decrease of the crack shores displacement along the minor axis.

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Vol. 88 No. 4 (2017)

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References

1. Halatenko H.V. Upruhoplastycheskoe razrushenye yzotropnoy plastyny s treshchynoy pry dvukhosnom nahruzhenyy, Prykl. mekhanyka, 1989, V. 25, No 7, pp. 86 – 91 [in Russian].

2. Duqdale D.S. Yielding of steel sheets containing slits, D.S. Duqdale, J. mech. Phys. Solids, 1960, V. 8, No 2, pp. 100 - 108.

https://doi.org/10.1016/0022-5096(60)90013-2

3. Halatenko H.V. Ob odnom obobshchenyy modely treshchyny Dahdeila, Prykl. mekhanyka. 1989, V. 25, No 3, pp. 53 – 58 [in Russian].

4. Halatenko H.V. K upruhoplastycheskoi modely treshchyny v uslovyiakh ploskoi deformatsyy, Prykl. mekhanyka. 1992, V. 28, No 9, pp. 35 – 41 [in Russian].

5. Khoroshun L.P. Ob odnoi modely nelyneinoi mekhanyky treshchyn, Prykl. mekhanyka. 1994, V. 30, No 11, pp.3 – 9 [in Russian].

6. Stadnyk M.M. Sylovi kryterii hranychno-rivnovazhnoho stanu plastyny z trishchynoiu pid dvovisnym navantazhenniam, M.M. Stadnyk.-Fiz.-khim. mekhanika materialiv, 2007, No 6, pp. 14 – 16 [in Ukrainе].

7. Muskhelyshvyly M.M. Nekotorыe osnovnye zadachy matematycheskoi teoryy upruhosty, M.M. Musk-helyshvyly, M. Nauka, 1968, 707 p. [in Russian].

8. Panasiuk V.V. Predelnoe ravnovesye khrupkykh tel s treshchynamy, V.V. Panasiuk, Kyev: Naukova dumka, 1968, 245 p. [in Russian].