Multiparametric presentation of the crack-tip fields in the vicinity of longitudinal shear crack

Yu. N. Bachareva

Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 4, pp. 18-25

Résumé

The article is devoted to the study of the stress field at the tip of a longitudinal shear crack based on a multiparametric asymptotic representation of the stress field at the crack tip in a linearly elastic isotropic material. The performed asymptotic analysis of the fields at the tip of a longitudinal shear crack is a natural continuation of the studies conducted for multiparametric stress fields at the tips of cracks of normal separation and transverse shear, as well as mixed loading. Despite the simplicity of analyzing the contribution of higher approximations to the general representation of the stress field at the tip of a type III crack, multicoefficient representations of the stress field near this type of crack have not been previously studied. It is shown that higher-order approximations must necessarily be taken into account for 1) accurate representation of the stress field and 2) expansion of the range of asymptotic expansions. It has been found that the greater the distance from the crack tip, the more components of the series must be stored near the crack tip.

Détail

Keywords: longitudinal (antiplane shear) crack, multiparametric expansion, linearly elastic material, asymptotic presentation, higher order terms.
Mots-clés : exact solution

Bibliographie

[1] Williams M.L., “On the stress distribution at the base of a stationary crack”, Journal of Applied Mechanics, 24:1 (1957), 109–114 | DOI | MR | Zbl

[2] Hello G., Tahar M.B., Roelandt J.-M., “Analytical determination of coefficients in cracktip stress expansions for a finite crack in an infinite plane medium”, International Journal of Solids and Structures, 49:3-4 (2012), 556–566 | DOI

[3] Hello G., “Derivation of complete crack-tip stress expansions from Westergaard-Sanford solutions”, International Journal of Solids and Structures, 144–145 (2018), 265–275 | DOI

[4] Zhu F., Ji X., He P., Zheng B., Zhang K., “On the stress singularity at crack tip in elasticity”, Results in Physics, 13 (2019), 102210 | DOI

[5] Krepl O., Klusak J., “Multi-parameter average strain energy density factor criterion applied on the sharp material inclusion problem”, Procedia Structural Integrity, 13 (2018), 1279–1284 | DOI

[6] Moazzami M., Ayatollahi M.R., Chamani H.R., Guagliano Vergani L., “Determination of higher order stress terms in cracked Brazilian disc specimen under mode I loading using digital image correlation technique”, Optic and Laser Technology, 107 (2018), 344–352 | DOI

[7] Karihaloo B.L., Xiao Q.Z., “Asymptotic crack tip fields in linear and nonlinear materials and their role in crack propagation”, Fizicheskaya mezomekhanika, 21:6 (2018), 23–35 | DOI

[8] Berto F., Lazzarin P., “Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches”, Materials Science and Engineering: R: Reports, 75 (2014), 1–48 | DOI

[9] Malikova L., “Multi-parameter fracture criteria for the estimation of crack propagation direction applied to a mixed-mode geometry”, Engineering Fracture Mechanics, 143 (2015), 32–46 | DOI

[10] Malikova L., Vesely V., Seitl S., “Crack propagation direction in a mixed mode geometry estimated via multi-parameter fracture criteria”, International Journal of Fatigue, 89 (2016), 99–107 | DOI

[11] Stepanova L.V., “Asymptotics of stresses and strain rates near the tip of a transverse shear crack in a material whose behavior is described by a fractional-linear law”, Journal of Applied Mechanics and Technical Physics, 50:1 (2009), 137–146 | DOI | Zbl

[12] Stepanova L.V., Roslyakov P.S., “Multi-parameter description of the crack-tip stress field: Analytic determination of coefficients of crack-tip stress expansions in the vicinity of the crack tips of two finite cracks in an infinite plane medium”, International Journal of Solids and Structures, 100–101 (2016), 11–28 | DOI

[13] Vesely V., Sobek J., Seitl S., “Multi-parameter approximation of the stress field in a cracked body in the more distant surrounding of the crack tip”, International Journal of Fatigue, 89 (2016), 20–35 | DOI

[14] Stepanova L.V., Adylina E.M., “Stress-strain state in the vicinity of a crack tip under mixed loading”, Journal of Applied Mechanics and Technical Physics, 55:5 (2014), 885–895 | DOI | MR | Zbl

[15] Stepanova L.V., Yakovleva E.M., “Asymptotic stress field in the vicinity of a mixedmode crack under plane stress conditions for a power-law hardening material”, Journal of Mechanics of Materials and Structures, 10:3 (2015), 367–393 | DOI | MR

[16] Stepanova L.V., Mushankova K.A., “Atomistic and continuum Ascertainment of The crack tip stress fields in anisotropic elastic cubic media”, Theoretical and Applied Fracture Mechanics, 133 (2024), 104613 pp. | DOI

[17] Mushankova K.A., Stepanova L.V., “Opredelenie koeffitsientov asimptoticheskogo ryada dlya polei napryazhenii na osnovanii molekulyarno-dinamicheskikh vychislenii”, Prikladnaya mekhanika i tekhnicheskaya fizika, 2024 | DOI

[18] Anisimov G.S., Stepanova L.V., “Eksperimentalnoe opredelenie polei u vershiny treschiny: metod golograficheskoi interferometrii i metod korrelyatsii tsifrovykh izobrazhenii”, Vestnik Permskogo natsionalnogo issledovatelskogo politekhnicheskogo universiteta. Mekhanika, 2024, no. 3, 39–56 | DOI

[19] Muskhelishvili N.I., Nekotorye osnovnye zadachi matematicheskoi teorii uprugosti, Nauka, M., 1966, 708 pp. https://klex.ru/1fa4?ysclid=m5qsu4dvcj256999603 | MR