Abstract:
This paper deals with the multi-parameter asymptotic description of the stress field near the crack tip of
a finite crack in an infinite isotropic elastic plane medium subject to 1) tensile stress; 2) in-plane shear; 3)
mixed mode loading for a wide range of mode-mixing situations (Mode I and Mode II). The multi-parameter
series expansion of the stress tensor components containing higher order terms has been constructed. All the
coefficients of the multi-parameter series expansion of the stress field are given. The main focus is on the
discussion of the influence of considering the higher-order terms of the Williams expansion. Analysis of the
higher order terms in the stress field is made. It is shown that the larger distance from the crack tip, the more
terms are necessary to be kept in the asymptotic series expansion.
Therefore, it can be concluded that several more higher-order terms of the Williams expansion must be
used for the stress field description when the distance from the crack tip is not small enough. The crack
propagation direction angle has been calculated. Two fracture criteria: maximum tangential stress criterion
and the strain energy density criterion, are used. The multi-parameter form of two commonly used fracture
criteria is introduced and tested. Thirty and more terms of the Williams expansion enable the angle to be
calculated more precisely.
Key words:
stress-strain state near the crack tip, multi-parameter asymptotic description of the stress field, mixed-mode loading, stress intensity factor, T-stress, coefficients of higher order terms.
Citation:
L. V. Stepanova, “Asymptotic analysis of the crack tip stress field (consideration of higher order terms)”, Sib. Zh. Vychisl. Mat., 22:3 (2019), 345–361; Num. Anal. Appl., 12:3 (2019), 284–296
\Bibitem{Ste19}
\by L.~V.~Stepanova
\paper Asymptotic analysis of the crack tip stress field (consideration of higher order terms)
\jour Sib. Zh. Vychisl. Mat.
\yr 2019
\vol 22
\issue 3
\pages 345--361
\mathnet{http://mi.mathnet.ru/sjvm719}
\crossref{https://doi.org/10.15372/SJNM20190307}
\elib{https://elibrary.ru/item.asp?id=38303552}
\transl
\jour Num. Anal. Appl.
\yr 2019
\vol 12
\issue 3
\pages 284--296
\crossref{https://doi.org/10.1134/S1995423919030078}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000485274000007}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85071739142}
Linking options:
https://www.mathnet.ru/eng/sjvm719
https://www.mathnet.ru/eng/sjvm/v22/i3/p345
This publication is cited in the following 10 articles:
Zhifeng Zhan, Yuchao Yu, Wei Yao, Kaiwen Xia, “Validity for measuring mode II fracture toughness using the short beam in compression method”, Engineering Fracture Mechanics, 308 (2024), 110381
Mehraban M.R., Ayatollahi M.R., Bahrami B., Berto F., “Higher Order Stress Terms in Sharp Notch Problems Under Pure-Out-of-Plane Loading”, Fatigue Fract. Eng. Mater. Struct., 45:2 (2022), 500–513
Yu. Li, K. Zheng, “Crack tip asymptotic field coefficients analyses based on extended finite element method using over-deterministic displacement field fitting method”, Theor. Appl. Fract. Mech., 113 (2021), 102971
R. M. Zhabbarov, L. V. Stepanova, “Sravnitelnyi analiz polei napryazhenii u vershiny treschiny i bokovykh nadrezov, poluchennykh s pomoschyu usechennykh razlozhenii Uilyamsa”, Vestn. SamU. Estestvennonauchn. ser., 27:4 (2021), 30–67
O. N. Belova, L. V. Stepanova, “Vychislenie koeffitsientov asimptoticheskogo razlozheniya polya napryazhenii vblizi vershiny treschiny. Smeshannoe nagruzhenie plastiny”, Vestn. SamU. Estestvennonauchn. ser., 26:3 (2020), 40–62
O. N. Belova, L. V. Stepanova, D. V. Chaplii, “Kompyuternoe modelirovanie rosta treschiny. Metod molekulyarnoi dinamiki”, Vestn. SamU. Estestvennonauchn. ser., 26:4 (2020), 44–55
V. S. Dolgikh, A. V. Pulkin, E. A. Mironova, A. A. Peksheva, L. V. Stepanova, “Teoretiko-eksperimentalnoe issledovanie napravleniya rosta treschiny. Chast I”, Vestn. SamU. Estestvennonauchn. ser., 25:2 (2019), 30–54
V. S. Dolgikh, A. V. Pulkin, E. A. Mironova, A. A. Peksheva, L. V. Stepanova, “Teoretiko-eksperimentalnoe issledovanie napravleniya rosta treschiny. Chast II”, Vestn. SamU. Estestvennonauchn. ser., 25:2 (2019), 55–74
A. N. Kosygin, L. N. Kosygina, “Tsifrovaya obrabotka eksperimentalnykh interferogramm, poluchennykh metodom fotouprugosti”, Vestn. SamU. Estestvennonauchn. ser., 25:2 (2019), 75–91
L. V. Stepanova, O. N. Belova, V. A. Turkova, “Opredelenie koeffitsientov razlozheniya M. Uilyamsa polya napryazhenii u vershiny treschiny s pomoschyu metoda tsifrovoi fotouprugosti i metoda konechnykh elementov”, Vestn. SamU. Estestvennonauchn. ser., 25:3 (2019), 62–82
Citation in format AMSBIB
Contact us: