Generalizing J 2 flow theory: Fundamental issues in strain gradient plasticity
Tóm tắt
It has not been a simple matter to obtain a sound extension of the classical J
2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J
2 theory have been proposed: one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhaus and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J
2 flow theory of plasticity to include a dependence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermodynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher order stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J
2 flow theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J
2 deformation theory of gradient plasticity for deformation histories characterized by proportional straining.
Tài liệu tham khảo
Gudmundson, P.A.: Unified treatment of strain gradient plasticity. J. Mech. Phys. Solids 52, 1379–1406 (2004)
Fleck, N.A., Hutchinson, J.W.: A reformulation of strain gradient plasticity. J. Mech. Phys. Solids 49, 2245–2271 (2001)
Muhlhaus, H.B., Aifantis, E.C.: A variational principle for gradient plasticity. Int. J. Solids Struct. 28, 845–857 (1991)
Gurtin, M.E., Anand, L.: Thermodynamics applied to gradient theories involving accumulated plastic strain. The theories of Aifantis and Fleck and Hutchinson and their generalizations. J. Mech. Phys. Solids 57, 405–421 (2009)
Gurtin, M.E., Anand, L.: A theory of strain-gradient plasticity for isotropic, plastically irrotational materials. Part I: Small deformations. J. Mech. Phys. Solids 53, 1624–1649 (2005)
Fleck, N.A., Willis, J.R.: A mathematical basis for strain gradient plasticity theory. Part I: scalar plastic multiplier. J. Mech. Phys. Solids 57, 161–177 (2009)
Acharya, A., Bassani, J.L.: Incompatibility and crystal plasticity. J. Mech. Phys. Solids 48, 1565–1595 (2000)
Chen, S.H., Wang, T.C.: A new hardening law for strain gradient plasticity. Acta Mater. 48, 3997–4005 (2000)
Huang, Y., Qu, S., Hwang, K.C., et al.: A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plast. 20, 753–782 (2004)
Fleck, N.A., Hutchinson, J.W.: Strain gradient plasticity. Adv. Appl. Mech. 33, 295–361 (1997)
Bittencourt, E., Needleman, A., Gurtin, M.E., et al.: A comparison of nonlocal continuum and discrete dislocation plasticity predictions. J. Mech. Phys. Solids 51, 281–310 (2003)
Reddy, D.B.: The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity. Continuum Mechanics and Thermodynamics 23, 527–549 (2011)
Aifantis, K.E., Soer, W.A., DeHosson, J.Th.M., et al.: Interfaces within strain gradient plasticity: Theory and experiments. Acta Mater. 54, 5077–5085 (2006)
Groma, I., Csikor, F.F., Zaiser, M.: Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics. Acta Mater. 51, 1271–1281 (2003)
Xiang, Y., Vlassak, J.J.: Bauschinger and size effects in thin-film plasticity. Acta Mater. 54, 5449–5460 (2006)
Lele, S.P., Anand, L.: A small deformation strain-gradient theory for isotropic viscoplastic materials. Phi. Mag. 88, 3655–3689 (2008)