By the method of singular integral equations, we solve a plane elastoplastic problem of fracture mechanics for an isotropic plane with an infinite series of curvilinear holes and plasticity bands at their tips. We study the influence of the shapes of smooth holes and the radii of rounding of the contours at their tips on the opening displacements and lengths of the plasticity bands. The solutions of the corresponding problems for semiinfinite bilateral rounded notches whose tips serve as the origins of plasticity bands are obtained by the limit transition in the case where the relative distance between the holes tends to zero. On the basis of the deformation criterion of fracture and solutions of the periodic elastoplastic problem, we approximately determine the strength of rectangular specimens with bilateral U-shaped notches.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. M. Vytvyts’kyi and M. Ya. Leonov, “Brittle fracture of a plate with circular hole,” Dop. Akad. Nauk Ukr. RSR, No. 2, 174–178 (1962).
B. A. Bilby, A. H. Cottrell, E. Smith, and K. H. Swinden, “Plastic yielding from sharp notches,” Proc. Royal Soc. London, A279, 1–9 (1964).
M. Shiratori, T. Miyoshi, and H. Matsushita, Computational Fracture Mechanics [Russian translation], Mir, Moscow (1986).
V. V. Panasyuk, Mechanics of Quasibrittle Fracture of Materials [in Russian], Naukova Dumka, Kiev (1991).
V. V. Panasyuk and M. P. Savruk, “Plastic strips model in elastic-plastic problems of fracture mechanics,” Adv. Mech., 15, Nos. 3–4, 123–147 (1992).
M. P. Savruk, P. N. Osiv, and I. V. Prokopchuk, Numerical Analysis in Plane Problems of the Theory of Cracks [in Russian], Naukova Dumka, Kiev (1989).
V. M. Mirsalimov, Elastoplastic Problems That Are Not One-Dimensional [in Russian], Nauka, Moscow (1987).
V. M. Mirsalimov, Fracture of Elastic and Elastoplastic Bodies with Cracks [in Russian], Élm, Baku (1984).
M. P. Savruk and A. Kazberuk, Stress Concentration in Solid Bodies with Notches, Vol. 14, in: V. V. Panasyuk (editor), Fracture Mechanics and Strength of Materials: A Handbook [in Ukrainian], Spolom, Lviv (2012).
M. P. Savruk and A. Kazberuk, Stress Concentration at Notches, Springer, Cham (2017).
V. S. Kravets’ and M. P. Savruk, “Two-dimensional periodic problem of the theory of elasticity for an isotropic plane with curvilinear holes and edge cracks,” Fiz.-Khim. Mekh. Mater., 54, No. 6, 102–109 (2018); English translation: Mater. Sci., 54, No. 6, 866–874 (2019).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 56, No. 3, pp. 15–23, May–June, 2020.
Rights and permissions
About this article
Cite this article
Kravets, V.S., Savruk, М.P. Deformation of an Isotropic Plate with Periodic System of Curvilinear Holes and Plasticity Bands. Mater Sci 56, 301–309 (2020). https://doi.org/10.1007/s11003-020-00430-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11003-020-00430-0