Abstract
This paper is devoted to a self-consistent derivation of the overall behaviour of multiphase materials from those of the constituent phases when these phases obey rate-dependent elastic-plastic constitutive equations. We have already proposed a solution to this still unsolved problem in the case of quite simple constitutive equations. In this paper, the formulation is extended to more general ones, including internal parameters: such a description can be specified for the case of rate-dependent elastic-plastic polycrystals and the classically associated constitutive equations. It is shown that the merits of the proposed formulation are saved at the expense of limited complication. A simple application is given as an illustration of the tractability of the method.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Kröner, E. (1961) Zur plastischen Verformung des Vielkristalls, Acta Metall, 9, 155–161.
Eshelby, J.D. (1957) The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. London, A 241, 376–396.
Hill, R. (1965) Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13, 89–101.
Hutchinson, J.W. (1976) Bounds and self-consistent estimates for creep of poly crystalline materials, Proc. Roy. Soc. London, A 348, 101–127.
Laws, N. and McLaughlin, R (1978) Self-consistent estimates for the viscoelastic creep compliances of composite materials, Proc. R. Soc. Lond., A 359, 251–273.
Zaoui, A. (1972) Effets de la désorientation des grains sur le comportement viscoplastique des polycristaux C.F.C., Int. J. Solids Structures, 8, 1089–1101.
Weng, G J. (1981) Self-consistent determination of time-dependent behaviour of metals, J. Appl. Mech., 48, 41–46.
Weng, G.J. (1982) A unified self-consistent theory for the plastic creep deformation of metals, J. Appl. Mech., 48, 41–46.
Nemat-Nasser, S. and Obata, M. (1986) Rate-dependent finite elastoplastic deformation of polycrystals, Proc. Roy. Soc. London, A 407, 343–375.
Harren, S.V. (1991) The finite deformation of rate-dependent polycrystals I, A self-consistent framework, J. Mech. Phys. Solids, 39, 345–360.
Rougier, Y., (1994) Ph. D. Dissertation, Ecole Polytechnique, Palaiseau (France).
Rougier, Y., Stolz C and Zaoui, A. (1994) Self-consistent modelling of elastic-viscoplastic polycrystals, C. R. Acad. Sci. Paris, II 318, 145–151.
Zaoui, A. and Raphanel, J.L. (1993) On the nature of the intergranular accommodation in the modelling of elastoviscoplastic behavior of polycrystalline aggregates, in C. Teodosiu, J.L. Raphanel and F. Sidoroff (eds), Large plastic deformations, Fundamentals and applications to metal forming, Balkema, Rotterdam, pp. 185–192.
Zaoui, A., Rougier, Y. and Stolz C., (1995) Micromechanical modelling based on morphological analysis; Application to viscoelasticity, in R. Pyrz (ed), Microstructure-Property Interactions in Composite Materials, Kluwer Academic Publishers, Dordrecht, 419–430.
Kröner, E. (1977) Bounds for effective elastic moduli of disordered materials, J. Mech. Phys. Solids, 25, 137–155.
Kröner, E. (1978) Self-consistent scheme and graded disorder in polycrystal elasticity, J. Phys. F: Metal Phys., 8, 2261–2267.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Kluwer Academic Publishers
About this paper
Cite this paper
Navidi, P., Rougier, Y., Zaoui, A. (1996). Self-Consistent Modelling of Elastic-Viscoplastic Multiphase Materials. In: Pineau, A., Zaoui, A. (eds) IUTAM Symposium on Micromechanics of Plasticity and Damage of Multiphase Materials. Solid Mechanics and its Applications, vol 46. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1756-9_16
Download citation
DOI: https://doi.org/10.1007/978-94-009-1756-9_16
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7285-4
Online ISBN: 978-94-009-1756-9
eBook Packages: Springer Book Archive