THEORETICALLY RECONSTRUCTED ISOCHROMATIC FRINGES IN THE VICINITY OF THE CRACK TIP



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Abstract

Theoretically reconstructed isochromatic fringe in the vicinity of the crack tip was received. The problem for a plate with central horizontal crack under uniaxial tension was considered. Isochromatic fringe in the vicinity of the crack tip image generating programme using complete asymptotic expansion of M. Williams stress field with scaling factor for infinity plate was developed. It was demonstrated that using large term of sum in the asymptotic expansion is necessary. If target isochromatic fringe is located far from the vicinity of the crack tip, then using many terms of sum in the asymptotic expansion of M. Williams is required.

About the authors

R. M. Zhabbarov

Samara National Research University

Author for correspondence.
Email: morenov@ssau.ru
ORCID iD: 0000-0001-9340-8512

postgraduate student of the Department of Mathematical Modelling in
Mechanics

References

  1. Broek D. Osnovy mekhaniki razrusheniya . M.: Vysshaya shkola, 1980, 368 p. Available at: https://www.studmed.ru/broek-d-osnovy-mehaniki-razrusheniya_95e0e618676.html .
  2. Williams M.L. Stress singularities resulting from various boundary conditions in angular corners of plates in tension. Journal of Applied Mechanics. 1952, Vol. 19, pp. 109–114. Available at: https://pdfs.semanticscholar.org/fec1/283d078a3d14bd0f3eee30bb482cefa70567.pdf .
  3. Igonin S.A., Stepanova L.V. Asimptotika polei napryazhenii i sploshnosti u vershiny ustalostnoi treshchiny v povrezhdennoi srede v usloviyakh ploskogo napryazhennogo sostoyaniya . Vestnik Samarskogo gosudarstvennogo universiteta , 2013, no. 9–2(110), pp. 97–108. Available at: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=vsgu&paperid=305&option_lang=rus .
  4. Kukushkin E.V., Menovshchikov V.A., Еrеsко Т.Т. Analiz sovremennykh predstavlenii i podkhodov pri issledovanii ustalostnykh razrushenii igol’chatykh podshipnikov . Reshetnevskie chteniya , 2013, no. 17, pp. 287–288. Available at: https : // cyberleninka.ru / article / n / analiz - sovremennyh - predstavleniy - i - podhodov -pri -issledovanii -ustalostnyhrazrusheniy- igolchatyh-podshipnikov .
  5. Stepanova L.V., Roslyakov P.S. Polnoe asimptoticheskoe razlozhenie M. Uil’yamsa u vershin dvukh kollinearnykh treshchin konechnoi dliny v beskonechnoi plastine . Vestnik Permskogo natsional’nogo tekhnicheskogo universiteta. Mekhanika , 2015, no. 4, pp. 188–225. doi: 10.15593/perm.mech/2015.4.12 .
  6. Godzhaev N.M. Optika . M.: Vysshaya shkola, 1977, 432 p. Available at: http://bookre.org/reader?file=636960 .
  7. Ramesh K., Gupta S., Kelkar A.A. Evaluation of stress field parameters in fracture mechanics by photoelastisity — revisited. Engineering Fracture Mechanics, Volume 56, Issue 1, January 1997, pp. 25–41, 43–45. doi: 10.1016/S0013-7944(96)00098-7 .
  8. Vivekannadan A., Ramesh K. Study of interaction effects of asymmetric cracks under biaxial loading using digital photoelasticity. Theoretical and Applied Fracture Mechanics, 2019, Vol. 99, pp. 104–117 .
  9. Carpinteri A., Paggi M. Asymptotic analysis in Linear Ealasticity: From the pioneering studies by Wieghardt and Irwin until today. Engineering Fracture Mechanics, 2009, Vol. 76, pp. 1771–1784. Available at: http://staff.polito.it/alberto.carpinteri/papers/CARPINTERI_2009_N.549_EFM.pdf .
  10. Ramesh K., Vivek, Dore P.T., Sanyal D. A Simple Approach to Photoelastic Calibration of Glass Using Digital Photoelasticity. Journal of Non-Crystalline Solids, 2013, Vol. 378, pp. 7–14. doi: 10.1016/j.jnoncrysol.2013.06.004 .
  11. Ramesh K., Pandey A. An improved normalization technique for white light photoelasticity. Optics and Lasers in Engineering, 2018, Vol. 109, pp. 7–16. doi: 10.1016/j.optlaseng.2018.05.004 .
  12. Ramesh K. , Vivek R. Digital photoelasticity of glass: A comprehensive review. Optics and Lasers in Engineering, 2016, Vol. 87, pp. 59–74. doi: 10.1016/j.optlaseng.2016.03.017 .
  13. Hello G., Tahar B., Roelandt J. Analytical determination of coefficients in crack-tip stress epansions for a finite crack in an infinite plane medium. International Journal of Solid and Structures, Volume 49, Issues 3–4, February 2012, pp. 556–566. doi: 10.1016/j.ijsolstr.2011.10.024 .
  14. Stepanova L.V., Dolgikh V.S. Tsifrovaya obrabotka rezul’tatov optoelektronnykh izmerenii. Metod fotouprugosti i ego primenenie dlya opredeleniya koeffitsientov mnogoparametricheskogo asimptoticheskogo razlozheniya M. Uil’yamsa polya napryazhenii . Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki , 2017, Vol. 21, no. 4, pp. 717–735. doi: 10.14498/vsgtu1544 .

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