Abstract
In this work, based on the representation of the Papkovich –Neiber displacement and stress through 3 harmonic functions, dual integral equations are obtained, the solution of which is reduced to finding one Helder function. To find this function, a singular integral equation with a Cauchy kernel of the 1st kind is obtained. The solution of this integral equation, proposed by the method of V. D. Kuliyev, is reduced to the Fredholm integral equation of the 2nd kind with a continuous kernel. The main parameter of the mechanics of linear fracture of the stress intensity coefficient is determined and a numerical analysis is carried out. When the crack of a normal fracture is located in an infinite elastic medium, it is shown that both components of the displacement vector are nonzero. This result suggests that the crack is an oblate ellipsoid.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Kuliyev VD (2015) New effective methods for solving a class of mixed boundary value problems. Bull I. Ya. Yakovlev Chuvash State Pedagogical Univ Ser Mech Limit State 1(23):132–162
Kuliyev VD (2005) Singular boundary value problems (M.: Fizmatlit)
Kuliyev VD, Kurbanmagomedov AK (2013) On the theory of crack growth under cyclic loading. Bull I. Ya. Yakovlev Chuvash State Pedagogical Univ Ser Mech Limit State 4(18):52–67
Okolnikova GE, Grishin GE et al (2019) Experimental study of the modified high-strength coarse-grained concrete. Syst Tech 2(31):25–31
Okolnikova GE, Grishin GE, Kurbanmagomedov AK, Shchedrin NI (2019) Experimental study of the physical and mechanical properties of high-strength fine-grained modified ‘“powdery”’ concrete. Syst Technol 2(31):41–46
Radjabov Z, Kurbanmagomedov AK (2016) Calculation of visco-elastic properties of layered organoplastics. Syst Technol 3(20):101–104
Kurbanmagomedov AK (2017) Crack of a normal rupture in an elastic layer. Bull I. Ya. Yakovlev Chuvash State Pedag Univ Ser Mech Limit State 1(31):96–104
Carpinteri A, Mainardi F (eds) (2014) Fractals and fractional calculus in continuum mechanics. Springer, p 378
Gludovatz B et al (2014) A fracture-resistant high-entropy alloy for cryogenic applications. Science 345(6201):1153–1158
Ritchie RO (2011) The conflicts between strength and toughness. Nat Mater 10(11):817–822
Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements: basic concepts, theory and applications. Springer Science & Business Media
Grewal D, Roggeveen AL, Nordfält J (2017) The future of retailing. J Retail 93(1):1–6
Lyons JS, Liu J, Sutton MA (1996) High-temperature deformation measurements using digital-image correlation. Exp Mech 36(1):64–70
Chapetti MD (2022) Fracture mechanics for fatigue design of metallic components and small defect assessment. Int J Fatigue 154:106550. https://doi.org/10.1016/j.ijfatigue.2021.106550
Teh S et al (2021) Numerical fracture mechanics as a practical failure investigatory tool: the outlook of cracked round bars. Eng Failure An 128:105630. https://doi.org/10.1016/j.engfailanal.2021.105630
Reinoso J, Tavara L (2021) Non-classical numerical/experimental fracture mechanics methodologies for engineering materials and structures Forewords. Theor Appl Fract Mech 114
Hammad DA, Semary MS, Khattab AG (2022) Ten non-polynomial cubic splines for some classes of Fredholm integral equations. Ain Shams Eng J 13(4):101666. https://doi.org/10.1016/j.asej.2021.101666
Dean A et al (2020) A phase field approach for ductile fracture of short fibre reinforced composites. Theor Appl Fract Mech 106:102495. https://doi.org/10.1016/j.tafmec.2020.102495
Kotousov A et al (2012) Three dimensional finite element mixed fracture mode under anti-plane loading of a crack. Theor Appl Fract Mech 62:26–33. https://doi.org/10.1016/j.tafmec.2013.01.003
Afshar R, Berto F (2011) Stress concentration factors of periodic notches determined from the strain energy density. Theor Appl Fract Mech 56(3):127–139. https://doi.org/10.1016/j.tafmec.2011.11.001
Zhuang B-B, Du Y-N, Weng S, Zhu M-L, Xuan F-Z (2022) On the significance of transition behavior in fatigue crack growth. Eng Fract Mech 262:108271. https://doi.org/10.1016/j.engfracmech.2022.108271
Yu H, Hao L, Shen R, Guo L, Shen Z, Li Y (2022) A phase field model with the mixed-mode driving force of power-law relation. Eng Fracture Mech 264:108265. https://doi.org/10.1016/j.engfracmech.2022.108265
Paggi M, Carpinteri A, Wriggers P (2012) special issue on fracture and contact mechanics for interface problems. Eng Fract Mech. https://doi.org/10.1016/j.engfracmech.2012.01.002
Acknowledgements
The author expresses gratitude to his scientific supervisor, Professor V. D. Kuliyev, for the attention and discussion of this work.
This paper has been supported by the RUDN University Strategic Academic Leadership Program.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Kurbanmagomedov, A., Radzhabov, Z., Okolnikova, G. (2023). Investigation of Normal Fracture Cracks in an Infinite Elastic Medium. In: Guda, A. (eds) Networked Control Systems for Connected and Automated Vehicles. NN 2022. Lecture Notes in Networks and Systems, vol 509. Springer, Cham. https://doi.org/10.1007/978-3-031-11058-0_142
Download citation
DOI: https://doi.org/10.1007/978-3-031-11058-0_142
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-11057-3
Online ISBN: 978-3-031-11058-0
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)