L. V. Stepanova, E. M. Adylina, “Stress-strain state in the vicinity of a crack tip under mixed loading”, Prikl. Mekh. Tekh. Fiz., 55:5 (2014), 181–194; J. Appl. Mech. Tech. Phys., 55:5 (2014), 885

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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2014, Volume 55, Issue 5, Pages 181–194 (Mi pmtf1038)

This article is cited in 26 scientific papers (total in 26 papers)

Stress-strain state in the vicinity of a crack tip under mixed loading

L. V. Stepanova, E. M. Adylina

Samara State University, Samara, 443011, Russia

Full-text PDF (474 kB) Citations (26)

Abstract: A method is proposed to calculate the eigenvalues of the class of nonlinear eigenvalue problems resulting from the problem of determining the stress-strain state in the vicinity of a crack tip in power-law materials over the entire range of mixed modes of deformation, from the opening mode to pure shear. The proposed approach was used to found eigenvalues of the problem that differ from the well-known eigenvalue corresponding to the Hutchinson–Rice–Rosengren solution. The resulting asymptotic form of the stress field is a self-similar intermediate asymptotic solution of the problem of a crack in a damaged medium under mixed loading. Using the new asymptotic form of the stress field and introducing a self-similar variable, we obtained an asymptotic solution of the problem of a crack in a damaged medium and constructed the regions of dispersed material near the crack.

Keywords: mixed deformation, self-similar representation of solution, self-similarity of the second kind, intermediate asymptotic form.

Received: 26.04.2013
Revised: 15.08.2013

English version:
Journal of Applied Mechanics and Technical Physics, 2014, Volume 55, Issue 5, Pages 885–895
DOI: https://doi.org/10.1134/S0021894414050186

Bibliographic databases:

Document Type: Article

UDC: 539.376

Language: Russian

Citation: L. V. Stepanova, E. M. Adylina, “Stress-strain state in the vicinity of a crack tip under mixed loading”, Prikl. Mekh. Tekh. Fiz., 55:5 (2014), 181–194; J. Appl. Mech. Tech. Phys., 55:5 (2014), 885–895

Citation in format AMSBIB

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\pages 181--194

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\elib{https://elibrary.ru/item.asp?id=22318154}

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\jour J. Appl. Mech. Tech. Phys.

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Linking options:

https://www.mathnet.ru/eng/pmtf1038

https://www.mathnet.ru/eng/pmtf/v55/i5/p181

This publication is cited in the following 26 articles:

Yu. N. Bakhareva, “Multiparametric presentation of the crack-tip fields in the vicinity of longitudinal shear crack”, Vestnik of Samara University. Natural Science Series, 30:4 (2025), 18
Lyudmila Frishter, Lecture Notes in Networks and Systems, 706, Fundamental and Applied Scientific Research in the Development of Agriculture in the Far East (AFE-2022), 2023, 375
L.V. Stepanova, E.M. Yakovleva, “Nonlinear EigenProblems Arising From Nonlinear Fracture Mechanics Boundary Value Problems”, Procedia Structural Integrity, 37 (2022), 908
L.V. Stepanova, E.M. Yakovleva, “Nonlinear Eigenvalues Problems Engendered by Nonlinear Fracture Mechanics Boundary Value Problems”, Procedia Structural Integrity, 39 (2022), 735
Larisa V. Stepanova, “Methods of perturbation theory and their applications in nonlinear fracture mechanics: From the pioneering studies by Hutchinson, Rice and Rosengren until today”, Mat Design & Process Comms, 3:6 (2021)
S. A. Sokolov, D. E. Tulin, “Modeling of Elastoplastic Stress States in Crack Tip Regions”, Phys Mesomech, 24:3 (2021), 237
A N Kosygin, L N Kosygina, V N Usacheva, “One example of image digital processing of experimental data obtained by the method of photoelasticity”, J. Phys.: Conf. Ser., 1479:1 (2020), 012144
Larisa Stepanova, Sergey Bronnikov, “A computational study of the mixed–mode crack behavior by molecular dynamics method and the multi – Parameter crack field description of classical fracture mechanics”, Theoretical and Applied Fracture Mechanics, 109 (2020), 102691
L. V. Stepanova, “Influence of the higher order terms in Williams' series expansion of the stress field on the stress-strain state in the vicinity of the crack tip. Part II”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 25:1 (2019), 80–96
Xu Li, Xiaotao Li, Shihao Cao, Xiaoyu Jiang, “Analysis of different damage configurations at a macro-crack tip”, Arch Appl Mech, 89:7 (2019), 1259
L. V. Stepanova, “Influence of the higher order terms in Williams' series expansion of the stress field on the stress-strain state in the vicinity of the crack tip. Part I”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 25:1 (2019), 63–79
L. V. Stepanova, “Asymptotic analysis of the crack tip stress field (consideration of higher order terms)”, Num. Anal. Appl., 12:3 (2019), 284–296
A. N. Kosygin, L. N. Kosygina, “Digital processing of interferograms obtained by the photoelasticity method”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 25:2 (2019), 75–91
LV Stepanova, O N Belova, “Estimation of crack propagation direction angles under mixed mode loading in linear elastic isotropic materials by generalized fracture mechanics criteria and by molecular dynamics method”, J. Phys.: Conf. Ser., 1096 (2018), 012060
L. N. Kosygina, “Asymptotic representation of the stress field near the crack tip of an infinite plate with two semi-infinite symmetrical edge notches: theoretical study and computational experiment”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 24:2 (2018), 55–66
Stepanova Larisa, “Intermediate self-similar asymptotic presentation of stress and damage fields in the vicinity of mixed mode crack tip under creep regime”, Procedia Structural Integrity, 13 (2018), 255
L Stepanova, “Asymptotic methods and their applications in nonlinear fracture mechanics: a review”, J. Phys.: Conf. Ser., 1096 (2018), 012058
Larisa Stepanova, Sergej Bronnikov, “Mathematical modeling of the crack growth in linear elastic isotropic materials by conventional fracture mechanics approaches and by molecular dynamics method: crack propagation direction angle under mixed mode loading”, J. Phys.: Conf. Ser., 973 (2018), 012046
L V Stepanova, V S Dolgikh, “Interference-optical methods in mechanics for the multi-parameter description of the stress fields in the vicinity of the crack tip”, J. Phys.: Conf. Ser., 1096 (2018), 012117
L. V. Stepanova, AIP Conference Proceedings, 1915, 2017, 040059

Citing articles in Google Scholar: Russian citations, English citations
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