Abstract
We propose a version of the deformation theory of plasticity for anisotropic media that allows us to consider the limiting strain (for example, in industrial processes involving pressure treatment of materials). The modified theory gives good agreement between the calculations and the experimental data not only with respect to the stress level but also with respect to the strains.
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B. I. Koval'chuk, V. V. Kosarchuk, and A. A. Lebedev, “Investigation of the scalar and vector properties of anisotropic materials under conditions of a complex stress state. Communication 2. Plastic strains of anisotropic materials under simple loading,” Probl. Prochn., No. 8, 114–121 (1982).
B. I. Koval'chuk, A. A. Lebedev, and S. É. Umanskii, Mechanics of Inelastic Deformation of Materials and Structural Elements [in Russian], Naukova Dumka, Kiev (1987).
E. E. Kurchakov, “Tensor linear constitutive equations for a nonlinear anisotropic medium,” Prikl. Mekh.,12, No. 4, 65–68 (1976).
E. E. Kurchakov, “Investigation of the relation between strains and stresses for a nonlinear anisotropic medium,” Prikl. Mekh.,15, No. 9, 19–24 (1979).
A. S. Kravchuk, “Plasticity theory for anisotropic materials,” Raschety na Prochnost', No. 27, 21–29 (1986).
A. I. Chanyshev, “Plasticity of anisotropic media,” Zh. Prikl. Mekh. Tekh. Fiz., No. 2, 149–151 (1984).
J. Ostrowska-Maciejewska and J. Rychlewski, “Plane elastic and limit states in anisotropic solids,” Arch. Mech.,40, No. 4, 379–386 (1988).
J. Rychlewski, Prikl. Matem. Mekh.,48, No. 3, 420–435 (1984).
A. A. Il'yushin, “Isomorphism of the elastoplastic properties of anisotropic bodies,” in: Abstracted Reports, Sixth All-Union Conference on Theoretical and Applied Mechanics [in Russian], FAN, Tashkent (1986), p. 312.
N. B. Alfutova. “Equivalency relation for the elastoplastic properties of anisotropic bodies,” Moscow (1987), Dep. in VINITI, No. 4159-V-87.
O. S. Sadakov, V. N. Madudin, and M. V. Apaichev, “A very simple version of deformation plasticity theory for anisotropic materials,” Chelyabinsk (1990), Dep. in VINITI, No. 3424-V90.
G. S. Pisarenko and A. A. Lebedev, Deformation and Strength of Materials for a Complex Stress State [in Russian], Naukova Dumka, Kiev (1976).
B. I. Koval'chuk, “Theory of plastic deformation of anisotropic materials,” Probl. Prochn., No. 9, 8–12 (1975).
V. P. Lamashevskii, A. A. Lebedev, and N. V. Novikov, “Investigation of the deformation and fracture of aluminum alloy for a complex stress state under low-temperature conditions,” Probl. Prochn., No. 6, 54–59 (1969).
B. E. Pobedrya, “Deformation theory of plasticity for anisotropic media,” Prikl. Matem. Mekh.,48, No. 1, 29–37 (1984).
B. E. Pobedrya, Mechanics of Composite Materials [in Russian], MGU, Moscow (1984).
M. I. Goikhman, “Characteristics of elastoplastic deformation of transversely isotropic bodies for simple loading processes,” Dissertation in competition for the academic degree of Candidate of the Technical Sciences, Institute of Mechanics, Academy of Sciences of the Ukrainian SSR (1990).
B. I. Koval'chuk, V. V. Kosarchuk, and A. A. Lebedev, “Plastic strains of initially anisotropic materials under simple and complex loading,” in: Strength, Plasticity, and Viscoelasticity of Materials and Constructions [in Russian], Sverdlovsk (1986), pp. 74–81.
U. F. Kocks and C. Tome, “Living with anisotropic plasticity: deformation mode maps, textures, polycrystal yield surfaces,” Abstracts, International Conference on Mech. Phys. and Struct. Mater. “Celebret. Aristotle's 23 Centuries,” Thessaloniki, August 19–24, 1990, Houghton, Michigan (1990), p. 11.
K.-H. Matucha and P. Wincierz, “Experimental determination of flow curves,” in: Mechanical Anisotropy [in German], Hrsg. Stuwe H. P., Vienna/New York (1974), Vol. VIII, pp. 201–229.
S. G. Lekhnitskii, Elasticity Theory for an Anisotropic Body [in Russian], Nauka, Moscow (1977).
H. Schiller, “Influence of the hydrostatic stress component on the yield stress,” Arch. Eisenhutenw.,53, No. 4, 369–372 (1982).
A. A. Il'yushin, Plasticity. Principles of the General Mathematical Theory [in Russian], Izdat. Akad. Nauk SSSR, Moscow (1963).
A. A. Lebedev, V. V. Kosarchuk, and B. I. Koval'chuk, “Investigation of scalar and vector properties of anisotropic materials under conditions of a complex stress state. Communication 1. Yield conditions for anisotropic materials,” Probl. Prochn., No. 3, 25–31 (1982).
V. V. Kosarchuk, B. I. Koval'chuk, and A. A. Lebedev, “Theory of plastic flow of anisotropic media. Communication 1. Constitutive relations,” Probl. Prochn., No. 4, 50–57 (1986).
F. Barlat, “Crystallographic texture, anisotropic yield surfaces and forming limits of sheet metals,” Mater. Sci. Eng.,91, 55–72 (1987).
J. Lian and J. Chen, “Isotropic polycrystal yield surfaces of b.c.c. and f.c.c. metals: crystallographic and continuum mechanics approaches,” Acta Met. Mater.,39, No. 10, 2285–2294 (1991).
V. V. Kosarchuk, “Elastoplastic deformation of anisotropic aluminum alloys in a complex stress state,” Dissertation in competition for the academic degree of Candidate of the Technical Sciences, Institute of Problems of Strength, Academy of Sciences of the Ukrainian SSR (1982).
B. I. Koval'chuk, “Loss of stability of plastic deformation in shells,” Probl. Prochn., No. 5, 11–16 (1983).
B. I. Koval'chuk, N. M. Kul'chitskii, and A. A. Lebedev, “Plasticity and strength of prestrained chromium steel in biaxial tension under low-temperature conditions,” Probl. Prochn., No. 10, 23–26 (1978).
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Translated from Problemy Prochnosti, No. 9, pp. 3–15, September, 1995.
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Kosaruchuk, V.V., Mel'nikov, S.A. Deformation theory of plasticity for initially anisotropic media. Strength Mater 27, 497–507 (1995). https://doi.org/10.1007/BF02208567
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DOI: https://doi.org/10.1007/BF02208567