Abstract
A model of a physical section that describes stress–strain states in elastic–plastic solids weakened by cracks is proposed. The problem of plane deformation and the stress state of a solid of an infinite size of an arbitrary geometry, weakened by a physical section, is solved. It comes down to a system of two variational equations with respect to displacement fields in the parts of the solid bordering the interaction layer. For a material whose properties are close to those of a D16T alloy, the linear parameter introduced into the crack model is estimated, and the critical conditions of solids with lateral cracks in the case of a normal detachment are determined.
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References
Engineering Fracture Mechanics, Vol. 70, No. 14 (Special Issue): Fundamentals and Applications of Cohesive Models (2003).
D. S. Dugdale, “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids 8 (2), 100–104 (1960).
R. V. Goldshtein and N. M. Osipenko, “Fracture and Formation of Structures,” Dokl. Akad. Nauk SSSR 240 (4), 111–126 (1978).
Yu. V. Petrov, “Quantum Analogy in Fracture Mechanics,” Fiz. Tv. Tela 38 (11), 3385–3393 (1996).
V. D. Kurguzov, N. S. Astapov, and I. S. Astapov, “Fracture Model for Structured Quasibrittle Materials,” Prikl. Mekh. Tekh. Fiz. 55 (6), 173–185 (2014) [J. Appl. Mech. Tech. Phys. 55 (6), 1055–1065 (2014)].
V. M. Kornev and V. D. Kurguzov, “Multiparametric Sufficient Criterion of Quasi-Brittle Fracture for Complicated Stress State,” Eng. Fracture Mech. 75 (5), 1099–1113.
H. Neuber, Kerbspannunglehre: Grunglagen für Genaue Spannungsrechnung (Springer-Verlag, 1937).
V. V. Novozhilov, “On a Necessary and Sufficient Criterion for Brittle Strength,” Prikl. Mat. Mekh. 33 (2), 212–222 (1969) [J. Appl. Math. Mech., 33 (2), 201–210 (1969)].
G. N. Savin, Plane Problem of Moment Theory of Elasticity (Izd. Kiev. Gos. Univ., Kiev, 1965) [in Russian].
A. L. Aero, “Essentially Nonlinear Micromechanics of a Medium with a Variable Periodic Structure,” Usp. Mekh., No. 3, 130–176 (2002).
B. E. Pobedrya and S. E. Omarov, “Constitutive Relations in the Moment Theory of Elasticity,” Vestn. Mosk. Gos. Univ., Ser 1: Mat., Mekh. No. 3, 56–58 (2007).
V. V. Vasil’ev and S. A. Lur’e, “New Solution of the Plane Problem of an Equilibrium Crack,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela 51 (5), 61–67 (2016).
A. F. Revuzhenko, “Version of the Linear Elasticity Theory with a Structural Parameter,” Prikl. Mekh. Tekh. Fiz. 57 (5), 45–52 (2016) [J. Appl. Mech. Tech. Phys. 57 (5), 801–807 (2016)].
S. E. Omarov, “Determining the Material Constant in the Problem of Equilibrium of an Infinite Elastic Plane Weakened by a Circular Hole,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela 44 (5), 144–149 (2009).
R. V. Goldshtein and N. M. Osipenko, “Estimating the Effective Strength of Solids under Compression,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela, No. 4, 80–93 (2017).
A. Needleman and E. van der Giessen, “Micromechanics of Fracture: Connecting Physics to Engineering,” MRS Bull. 26 (3), 211–214 (2001).
V. E. Panin, Yu. V. Grinyaev, V. I. Danilov, et al., Structural Levels of Plastic Strain and Fracture (Nauka, Novosibirsk, 1990) [in Russian].
L. I. Domozhirov and N. A. Makhutov, “Hierarchy of Cracks in Cyclic Fracture Mechanics,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela, No. 5, 17–26 (1999).
G. I. Barenblatt and G. S. Golitsyn, “Similarity Criteria and Scales for Crystals,” Fiz. Mezomekh. 20 (1), 116–119 (2017) [Phys. Mesomech. 20 (1), 111–114 (2017)].
J. D. Carrol, W. Z. Abuzaid, J. Lambros, and H. Sehitoglu, “On the Interactions between Strain Accumulation, Microstructure, and Fatigue Crack Behavior,” Int. J. Fracture 180, 223–241 (2013).
P. S. Volegov, D. S. Gribov, and P. V. Trusov, “Damage and Fracture: Classical Continuum Theories,” Fiz. Mezomekh. 18 (3), 11–24 (2015) [Phys. Mesomech. 20 (2), 157–173 (2017)].
V. V. Glagolev and A. A. Markin, “Finding the Elastic Strain Limit at the Tip Region of a Physical Cut with Arbitrarily Loaded Faces,” Prikl. Mekh. Tekh. Fiz. 53 (5), 174–183 (2012) [J. Appl. Mech. Tech. Phys. 53 (5), 784–792 (2012)].
V. V. Glagolev, L. V. Glagolev, and A. A. Markin, “Stress–Strain State of Elastoplastic Bodies with Crack,” Acta Mech. Solida Sinica 28 (4), 375–383 (2015).
A. A. Ilyushin, Plasticity, Vol. 1: Elastic–Plastic Deformations (Gostekhteoretizdat, Moscow–Leningrad, 1948) [in Russian].
I. I. Vorovich and Yu. P. Krasovskii, “Method of Plastic Solutions,” Dokl. Akad. Nauk SSSR 126 (4), 740–743 (1959).
H. G. Hahn, Elastizit¨atstheorie: Grundiagen der linearen Theorie und Anwendungen auf eindimensionale, ebene und r¨aumliche Probleme (Teubner, Stuttgart, 1985).
G. P. Cherepanov, Mechanics of Brittle Fracture (Nauka, Moscow, 1974; McGraw-Hill, New York, 1979).
V. Z. Parton and E. M. Morozov, Mechanics of Elastic–Plastic Fracture (Nauka, Moscow, 1985; Hemisphere, Washington, 1989).
G. V. Klevtsov and L. R. Botvina, “Microscopic and Macroscopic Plastic Deformation As a Criterion of the Limiting State of a Material during Fracture,” Probl. Prochn., No. 4, 24–28 (1984).[Strength Mater. 16 (4), 473–479 (1984)].
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Original Russian Text © V.V. Glagolev, L.V. Glagolev, A.A. Markin.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 6, pp. 143–154, November–December, 2018.
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Glagolev, V.V., Glagolev, L.V. & Markin, A.A. Determining The Stress–Strain State of Elastic–Plastic Solids With A Lateral Crack-Like Defect with the Use of a Model with a Linear Size. J Appl Mech Tech Phy 59, 1085–1094 (2018). https://doi.org/10.1134/S0021894418060147
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DOI: https://doi.org/10.1134/S0021894418060147