Summary
The anisotropic plastic behavior of materials during finite deformation is partly due to the development of different types of textures or substructures. In order to describe phenomenologically this behavior, a two-component model of finite plasticity is proposed based on the scale invariance approach earlier advanced by Aifantis and co-workers. Each component follows its own evolution and rotation rules to account for the different textures occurring during the deformation process. A direct extension of this framework to consider viscoplastic effects is also developed. The model is applied to simulate the anisotropic deformation behavior of materials under tension, compression and torsion. The results are compared with available experimental data and related predictions of polycrystalline plasticity models. It is shown that the present continuum model has the advantages of both accuracy and simplicity as compared to polycrystalline calculations.
Similar content being viewed by others
References
Lowe, T. C., Harren, S., Asaro, R. J., Needleman, A.: Analysis of the evolution of texture and axial stresses in FCC polycrystals subject to large strain shear. In: Yielding, damage, and failure of anisotropic solids, EGF5 (Boehler, J. P., ed.), pp. 335–358, London: Mechanical Engineering Publications 1990.
Molinari, A., Canava, G. R., Ahzi, S.: A self-consistent approach to the large deformation polycrystal viscoplasticity. Acta Metall.35, 2983–2994 (1987).
Lowe, T. C., Lipkin, J.: Axial effects during reversed torsional deformation. In: Proc. of plasticity 89 (Kahn, A. S., Tokuda, M., eds.), pp. 625–628. The second international symposium on plasticity and its current applications. Tsu, Mie Prefacture, Japan 1989.
Dafalias, Y. F., Rashid, M. M.: The effect of plastic spin on anisotropic material behavior. Int. J. Plasticity5, 227–246 (1989).
Van der Giessen, E.: Micromechanical and thermodynamic aspects of the plastic spin. Int. J. Plasticity7, 365–386 (1991).
Loret, B.: On the effects of plastic rotation in the finite deformation of anisotropic elastoplastic materials. Mech. Mat.2, 287–301 (1983).
Zbib, H. M., Aifantis, E. C.: On the concept of relative spins and its implications to large deformation theories. Part I & Part II. Acta Mech.75, 15–56 (1988).
Shi, M. F., Gerdeen, J. C., Aifantis, E. C.: On finite deformation plasticity with directional softening. Part II. Two-component model. Acta Mech.101, 69–80 (1993).
Ning, J., Aifantis, E. C.: On anisotropic finite deformation plasticity. Part I. A two-back stress model. Acta Mech.106, 55–72 (1994).
Rice, J. R.: A note on the ‘small strain’ formulation for elastic-plastic problems. Tech. Rep. N00014-67-A-000318, Div. of Eng., Brown Univ. Providence 1970.
Ning, J.: An endochronic constitutive theory for material under nonproportional cyclic loading. Mech. Comm. Theory Appl.18, 187–198 (1991).
Rauch, E., Canova, G. R., Jonas, J. J., Semiatin, S. L.: An analysis of flow localization during torsion testing. Acta Metall.33, 465–476 (1985).
Kocks, U. F., Stout, M. G., Rollett, A. D.: The influence of texture on strain hardening. In: ICSMA 8 (Kettunen, P. O., Lepisto, T. K., Lehtonen, M. E., eds.), pp. 25–34. Tampere, Finland 1988.
Lipkin, J., Chiesa, M. L., Bammann, D. J.: Thermal softening of 3042 stainless steel: experimental results and numerical simulations. In: Impact loading and dynamic behavior of materials. (Chiem, C. Y., Kunze, H.-D., Meyer, L. W., eds.), pp. 687–697. DGM, Oberursel, FRG 1988.
Montheillet, F., Cohen, M., Jonas, J. J.: Axial torsion test of Al, Cu and α-Fe. Acta Metall.32, 2077–2089 (1984).
Johnson, G. R., Haegfeldt, J. M., Lindholm, U. S., Nagy, A.: Response of various metals to large torsional strains over a large range of strain rates. Part I. Ductile metals. J. Eng. Mat. Tech.105, 42–47 (1983).
Harren, S., Lowe, T. C., Asaro, R. J., Needleman, A.: Analysis of large-strain shear in rate-dependent FCC polycrystals: correlation of micro and macromechanics. Phil. Trans. R. Soc. London Ser.A 328, 443–500 (1989).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ning, J., Aifantis, E.C. On anisotropic finite deformation plasticity Part II. A two-component model. Acta Mechanica 106, 73–85 (1994). https://doi.org/10.1007/BF01300945
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01300945