Abstract
Some characteristics of an initially anisotropic aluminum alloy are investigated. The coefficients of transverse elastoplastic and plastic strain are calculated. It is established that the coefficients of transverse plastic strain are much different from 0.5 in directions that are not in the plane of isotropy. It is also shown that the material is plastically incompressible. The possibility of using Hill’s theory of flow with isotropic hardening to describe the inelastic behavior of the material is examined
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REFERENCES
I. I. Gol’denblat. “Small elastoplastic deformation theory for anisotropic bodies,” Dokl. AN SSSR, 101, No.4, 619–622 (1955).
B. I. Koval’chuk, “The theory of plastic deformation of anisotropic materials,” Probl. Prochn., No. 9, 8–12 (1975).
V. A. Lomakin, “The theory of nonlinear elasticity and plasticity of anisotropic media,” Izv. AN SSSR, Mekh. Mashinostr., No. 4, 60–64 (1960).
S. V. Malashenko, O. N. Chekin, and M. Sh. Dyshel’, Pneumatic Gauging of Materials and Structural Members [in Russian], Naukova Dumka, Kiev (1983).
P. P. Petrishchev, “Elastoplastic deformation of anisotropic media,” Vestn. MGU, Ser. Fiz.-Mat. Estestvoved., No. 6, 63–69 (1952).
B. E. Pobedrya, “Deformation theory of plasticity of anisotropic media,” Prikl. Mat. Mekh., 48, No.4, 29–37 (1984).
M. E. Babeshko, “Thermoelastoplastic state of flexible laminated shells under axisymmetric loading along various plane paths,” Int. Appl. Mech., 39, No.2, 177–184 (2003).
M. E. Babeshko and Yu. N. Shevchenko, “Thermoelastoplastic stress-strain state of laminated transversely isotropic shells under axisymmetric loading,” Int. Appl. Mech., 40, No.8, 908–915 (2004).
M. E. Babeshko and Yu. N. Shevchenko, “Thermoelastoplastic axisymmetric stress-strain state of laminated orthotropic shells,” Int. Appl. Mech., 40, No.12, 1378–1384 (2004).
J. Betten, “Elementaren Ansatz zur beschreibung des orthotropen kompressiblen plastischen Fliessens unter Berucksichtigung des Bauschinger-Effekts,” Arch. Eisenhuttenw., 49, No.4, 179–182 (1978).
J. Betten, “Pressure-dependent yield behavior of isotropic and anisotropic materials,” Deform. Failure Granul. Mater., Rotterdam, 81–89 (1982).
A. D. Freed and B. I. Sandor, “The plastic compressibility of 7075-T651 aluminium-alloy plate,” Exp. Mech., 26, No.2, 119–121 (1986).
A. Z. Galishin and Yu. N. Shevchenko, “Determining the axisymmetric, geometrically nonlinear, thermoelastoplastic state of laminated orthotropic shells,” Int. Appl. Mech., 39, No.1, 56–63 (2003).
R. Hill, The Mathematical Theory of Plasticity, Claredon Press, Oxford (1950).
R. Hill, “Theoretical plasticity of texture aggregates,” Math. Proc. Cambridge Phil. Soc., 85, No.1, 179–191 (1979).
E. Krempe and P. Hewelt, “The constant volume hypothesis for the inelastic deformation of metals in the small strain range,” Mech. Res. Communs., 7, No.5, 283–288 (1980).
O.-G. Lademo, O. S. Hopperstad, and M. Langseth, “An evaluation of yield criteria and flow rules for aluminium alloys,” Int. J. Plasticity, 15, No.2, 191–208 (1999).
J. S. H. Lake, D. J. Willis, and H. G. Fleming, “The variation of plastic anisotropy during straining,” Met. Trans. A, 19, No.7–12, 2805–2817 (1988).
R. Mises, “Mechanik der plastischen Formanderung von Kristallen,” ZAMM, 8, No.3, 161–185 (1928).
K. Naruse, B. Dodd, and Y. Motoki, “An experimental investigation of yield criteria with planar anisotropy,” Trans. Jap. Soc. Mech. Eng., A 57, 543, 2659–2663 (1991).
O. Richmond and W. A. Spitzig, “Pressure dependence and dilatancy of plastic flow,” in: Proc. 15th Int. Congr. on Theoretical and Applied Mechanics, Toronto, Postprints, Amsterdam e.a. (1980), pp. 377–386.
Yu. N. Shevchenko and M. I. Goikhman, “Study of laws governing the elastoplastic deformation of transversely isotropic bodies,” Int. Appl. Mech., 26, No.9, 849–852 (1990).
W. A. Spitzig, R. J. Sober, and O. Richmond, “The effect of hydrostatic pressure on the deformation behavior of maraging and HY-80 steels and its implications for plasticity theory,” Met. Trans., A7, 11, 1703–1710 (1976).
W. A. Spitzig and O. Richmond, “The effect of pressure on the flow stress of metals,” Acta Met., 32, No.3, 453–457 (1984).
A. Troost and J. Betten, “Plastische Querzahlen anisotroper Werkstoffe,” Arch. Eisenhuttenw., 43, No.11, 811–812 (1972).
A. Troost and J. Betten, “Beitrag zum isotropen kompressiblen plastischen Fleissen,” Mech. Res. Communs., 2, No.1, 7–12 (1975).
A. Troost and M. Schlimmer, “ Fliessbedingung anisotroper, plastisch kompressibler Werkstoffe mit Anwendung auf Plastomere,” Mech. Res. Communs., 2, No.4, 165–169 (1975).
A. Troost and M. Schlimmer, “Isotropes und anisotropes Fliessen, plastisch kompressibler Werkstoffe, insbesondere von Plastomeren,” Mater. Sci. Eng., 26, No.1, 23–45 (1976).
A. Troost and M. Schlimmer, “Kurzzeitbeanspruchung isotroper und anisotroper, plastisch kompressibler Werkstoffe, insbesondere von Thermoplasten,” Kunststoffe, 67, No.5, 287–289 (1977).
P. I. Welch, L. Ratke, and H. J. Bunge, “Comparison of plastic anisotropic parameters for polycrystalline metals,” Sheet Metal Ind., 60, No.10, 594–597 (1983).
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The study was partially sponsored by the State Fund for Basic Research of the Ministry of Education and Science of Ukraine (Grant No. 01.07/00010).
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 38–45, March 2005.
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Babeshko, M.E., Shevchenko, Y.N. Plastic Incompressibility of Anisotropic Material. Int Appl Mech 41, 256–263 (2005). https://doi.org/10.1007/s10778-005-0082-8
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DOI: https://doi.org/10.1007/s10778-005-0082-8