×

zbMATH — the first resource for mathematics

An analysis of texture and plastic spin for planar polycrystals. (English) Zbl 0780.73067
A major source of induced anisotropy in metals undergoing large strain is the preferential reorientation of single crystals. We present a macroscopic description of this textural anisotropy for an idealized planar aggregate of single crystals with two slip systems. We derive an analytical expression for the plastic spin associated with crystallographic slip and use it to obtain an equation of evolution for the single crystal orientation. The single microstructural parameter that appears in this equation is defined in terms of the slip system geometry. We introduce a continuous distribution function to describe orientation of crystals in an aggregate and obtain analytical solutions to the conservation equation governing its evolution. Using an orientation average, we determine the average plastic spin in terms of the microstructural parameter and a second rank tensor related to the anisotropy in the orientation distribution. Finally, for constant velocity gradients, we show that the eigenvectors of this tensor rotate with half the difference between the macroscopic and average plastic spins.

MSC:
74A60 Micromechanical theories
74M25 Micromechanics of solids
74E10 Anisotropy in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Advani, S.G.; Tucker, C.L., J. rheol., 31, 751, (1987)
[2] Advani, S.G.; Tucker, C.L., J. rheol., 34, 367, (1990)
[3] Aravas, N.; Aifantis, E.C., Int. J. plasticity, 7, 141, (1991)
[4] Arminjon, M., J. mech. theor. appl., 6, 511, (1987)
[5] Asaro, R.J., Adv. appl. mech., 23, 1, (1983)
[6] Bammann, D.J.; Aifantis, E.C., Acta mechanica, 69, 97, (1987)
[7] Bammann, D.J.; Johnson, G.C., Int. J. solids struct., 20, 725, (1984)
[8] Bammann, D.J.; Johnson, G.C., Acta mechanica, 70, 1, (1987)
[9] Clément, A., Mater. sci. engng, 55, 203, (1982)
[10] Dafalias, Y.F., Mech. mater., 3, 223, (1984)
[11] Dafalias, Y.F., J. appl. mech., 52, 865, (1985)
[12] Dafalias, Y.F., (), 135
[13] Dafalias, Y.F.; Aifantis, E.C., Acta mechanica, 82, 31, (1990)
[14] Dafalias, Y.F.; Rashid, M.M., Int. J. plasticity, 5, 227, (1989)
[15] Dienes, J.K., Acta mechanica, 32, 217, (1979)
[16] Goddard, J.D.; Miller, C., Rheologica acta, 5, 177, (1966)
[17] Hand, G.L., J. fluid mech., 13, 33, (1962)
[18] Harren, S.V.; Asaro, R.J., J. mech. phys. solids, 37, 191, (1989)
[19] Havner, K.S., Finite plastic deformation of crystalline solids, (1992), Cambridge University Press New York · Zbl 0774.73001
[20] Kocks, U.F, (), 81-115
[21] Kocks, U.F., (), 1-88
[22] Loret, B., Mech. mater., 2, 287, (1983)
[23] MacMillan, E.H., A theory of anisotropic fluids, ()
[24] MacMillan, E.H., J. rheol., 33, 1071, (1989)
[25] Mandel, J., Int. J. solids struct., 9, 725, (1973)
[26] Mandel, J., Proc. of the CNRS intl colloq. 319, (), 197-210
[27] Onat, E.T.; Leckie, F.A., J. appl. mech., 55, 1, (1988)
[28] Prantil, V.C., An analytical description of macroscopic anisotropy for planar polycrystalline aggregates, ()
[29] Rashid, M.M., J. mech. phys. solids, 40, 1009, (1992)
[30] Simo, J.C.; Vu Quoc, L., Electronics research laboratory memorandum no. UCB/ERL M85/31, ()
[31] Spencer, A.J.M., J. mech. phys. solids, 12, 337, (1964)
[32] Taylor, G.I., J. inst. metals, 62, 307, (1938)
[33] Truesdell, C., Kinematics of vorticity, (1954), Indiana University Press Bloomington · Zbl 0056.18606
[34] Van Der Giessen, E., Eur. J. mech., A/solids, 8, 15, (1989)
[35] Van Der Giessen, E., Eur. J. mech., A/solids, 8, 89, (1989)
[36] Van Der Giessen, E., Int. J. plasticity, 7, 365, (1991)
[37] Voyiadjis, G.Z.; Kattan, P.I., Acta mechanica, 88, 91, (1991)
[38] Voyiadjis, G.Z.; Kattan, P.I, Int. J. plasticity, 8, 365, (1992)
[39] Zbib, H.M.; Aifantis, E.C., Acta mechanica, 74, 15, (1988)
[40] Zbib, H.M.; Aifantis, E.C., Acta mechanica, 74, 35, (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.