Selective symmetrization of the slip-system interaction matrix in crystal plasticity

• Autorzy: Petryk H. , Kursa M.
• Języki publikacji: EN

Abstrakty

EN

The symmetry issue of the interaction matrix between multiple slip-systems in the theory of crystal plasticity at finite deformation is revisited. By appealing to possibly non-uniform distribution of slip-system activity in a representative space-time element of a crystal, symmetry of the slip-system interaction matrix for the representative element is derived under assumptions that have a physical meaning. This conclusion refers to active slip-systems only. Accordingly, for any given hardening law, a new symmetrization rule is proposed that is restricted to active slip-systems and leaves the latent hardening of inactive slip-systems unchanged. Advantages of the proposal in comparison with full symmetrization are illustrated by a simple example of uniaxial tension.

Słowa kluczowe

EN

finite deformation; metal crystal; plasticity; hardening; symmetry

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2011
• Tom: Vol. 63, nr 3
• Strony: 287--287
• Opis fizyczny: –-310, Bibliogr. 26 poz.

Twórcy

autor

Petryk H.

autor

Kursa M.

• Institute of Fundamental Technological Research Polish Academy of Sciences Pawińskiego 5B 02-106 Warsaw, Poland,

Bibliografia

• 1. R. Hill, Generalized constitutive relations for incremental deformation of metal crystals by multislip, J. Mech. Phys. Solids, 14, 2, 95–102, 1966.
• 2. J.R. Rice, Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19, 433–455, 1971.
• 3. R. Hill, J.R. Rice, Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20, 401–413, 1972.
• 4. D. Peirce, R.J. Asaro, A. Needleman, An analysis of nonuniform and localized deformation in ductile single crystals, Acta Metall., 30, 1087–1119, 1982.
• 5. R.J. Asaro, Micromechanics of crystals and polycrystals, Adv. Appl. Mech., 23, 1–115, 1983.
• 6. K.S. Havner, Finite plastic deformation of crystalline solids, Cambridge University Press, Cambridge, 1992.
• 7. J.L. Bassani, Plastic flow of crystals, Adv. Appl. Mech., 30, 191–258, 1994.
• 8. F. Roters, P. Eisenlohr, L. Hantcherli, D.D. Tjahjanto, T.R. Bieler, D. Raabe, Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications, Acta Mater., 58, 1152–1211, 2010.
• 9. B. Svendsen, S. Bargmann, On the continuum thermodynamic rate variational formulation of models for extended crystal plasticity at large deformation, J. Mech. Phys. Solids, 58, 9, 1253–1271, 2010.
• 10. U.F. Kocks, H. Mecking, Physics and phenomenology of strain hardening: the FCC case, Progress Mater. Sci., 48, 171–273, 2003.
• 11. R. Hill, Aspects of invariance in solids mechanics, Adv. Appl. Mech., 18, Academic Press, New York, 1–75, 1978.
• 12. H. Petryk, Theory of material instability in incrementally nonlinear plasticity, [in:]Material instabilities in elastic and plastic solids, H. Petryk [Ed.], CISM courses and lectures, Vol. 414, Springer, Wien, New York, 261–331, 2000.
• 13. K.S. Havner, A.H. Shalaby, A simple mathematical theory of finite distortional latent hardening in single crystals, Proc. R. Soc. Lond., A358, 47–70, 1977.
• 14. K.S. Havner, P. Yu, Kinematic, stress, and hardening analysis in finite double slip, Int. J. Plasticity, 21, 83–99, 2005.
• 15. H. Petryk, General conditions for uniqueness in materials with multiple mechanisms of inelastic deformation, J. Mech. Phys. Solids, 48, 367–396, 2000.
• 16. J. Mandel, Plasticité classique et viscoplasticité, CISM courses and lectures, Vol. 97, Springer, Wien–New York, 1971.
• 17. U.F. Kocks, P. Franciosi, M. Kawai, A forest model of latent hardening and its application to polycrystal deformation, Textures and Microstructures, 14-18, 1103–1114, 1991.
• 18. U.F. Kocks, The relation between polycrystal deformation and single-crystal deformation, Metall. Trans, 1, 1121–1142, 1970.
• 19. P. Franciosi, M. Berveiller, A. Zaoui, Latent hardening in copper and aluminium single crystals, Acta Metall., 28, 3, 273–283, 1980.
• 20. P. Franciosi, A. Zaoui, Multislip in f.c.c. crystals a theoretical approach compared with experimental data, Acta Metall., 30, 9, 1627–1637, 1982.
• 21. A.V. Kumar, C. Yang, Study of work hardening models for single crystals using threedimensional finite element analysis, Int. J. Plasticity, 15, 737–754, 1999.
• 22. K.S. Havner, On lattice and material-frame rotations and crystal hardening in highsymmetry axial loading, Phil. Mag., 85, 25, 2861–2894, 2005.
• 23. R. Hill, On constitutive macro-variables for heterogeneous solids at finite strain, Proc. R. Soc. Lond., A326, 131–147, 1972.
• 24. H. Petryk, On constitutive inequalities and bifurcation in elastic-plastic solids with a yield-surface vertex, J. Mech. Phys. Solids, 37, 2, 265–291, 1989.
• 25. H. Petryk, On the second-order work in plasticity, Arch. Mech., 43, 2–3, 377–397, 1991.
• 26. L. Anand, M. Kothari, A computational procedure for rate-independent crystal plasticity, J. Mech. Phys. Solids, 44, 4, 525–558, 1996.