Engineering Transactions, 49, 4, pp. 537–571, 2001

Evolution of Plastic Anisotropy for the Polycrystalline Materials in Large Deformation Processes

K. Kowalczyk
Institute of Fundamental Technological Research Polish Academy of Sciences

Model of evolution of plastic anisotropy due to crystallographic texture development in metals subjected to large deformation processes is presented. The rigid-plastic model of single grain with regularized Schmid law proposed by Gambin is used. Phenomenological and physical descriptions of plastic flow of polycrystals are discussed. Properties of any yield function for orthotropic material subjected to the plane stress state are outlined. Yield conditions of degree m proposed by Hill and Barlat with Lian are analyzed. Finally, phenomenological texture-dependent yield surface is proposed. Evolution of this yield surface is compared with phenomenological yield conditions for two processes: rolling and pure shear.


R.J. ASARO, Crystal plasticity, J. of Applied Mechanics, 50, 921–934, 1983.

R.J. ASARO, Micromechanics of crystals and polycrystals, Advances in Applied Mechanics, 23, 1983.

B. BUDIANSKY, T.T. Wu, Theoretical Prediction of plastic strains of polycrystals, Proc. 4th U.S. Nat. Congr. Appl. Mech., 1175–1185, ASME, New York 1962.

F. BARLAT, Crystallographies texture, anisotropic yield surfaces and forming limits of sheet metals, Materials Science and Engineering, 91, 55–72, 1987.

F. BARLAT, J. LIAN, Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions, Int. J. Plasticity, 5, 51–66, 1989.

F. BARLAT, D.J. LEGE, J.C. BREM, A six-component yield function for anisotropic materials, Int. J. Plasticity, 7, 693–712, 1991.

J.F. BISHOP, R. HILL, A theory of the plastic distortion of a polycrystalline aggregate under combined stresses, Philosophical Magazine, 42, Ser. VII, 414–427, 1951.

J.F. BISHOP, R. HILL, A theoretical derivation of the plastic properties of a polycrystalline face–centred metal, Philosophical Magazine, 42, Ser. VII, 1298–1307, 1951.

J.P. BOEHLER, A simple derivation of representation for non-polynomial constitutive equations in some cases of anisotropy, ZAMM, 59, 157–167, 1979.

J.P. BOEHLER, Applications of tensor functions in solid mechanics, CISM Courses and Lectures, 292, Springer-Verlag, Wien–New York 1987.

H.J. BUNGE, Texture analysis in material science, Mathematical Methods, London, Butterworths 1982.

A. CLEMENT, Prediction of deformation texture using a physical principle of conservation, Mater. Sci. Eng., 55, 203–210, 1982.

M. DARRIEULAT, D. PIOT, A method of generating analytical yield surfaces of crystalline materials, Int. J. Plasticity, 12, 5, 575–610, 1996.

J.D. ESHELBY, The determination of the elastic field of an ellipsoidal inclusion and related problems, Proc. Roy. Soc. London, A241, 376–296, 1957.

W. GAMBIN, Crystal plasticity based on yield surface with rounded-off corners, ZAMM, 71, 4, T265–T268, 1991.

W. GAMBIN, Plasticity of crystals with interacting slip systems, Enging. Trans., 39, 3–4, 303–324, 1991.

W. GAMBIN, Refined analysis of elastic-plastic crystals, Int. J. Solids Structures, 29, 16, 2013–2021, 1992.

W. GAMBIN, F. BARLAT, Modelling of deformation texture development based on rate independent crystal plasticity, Int. J. Plasticity, 13, 1/2, 75–85, 1997.

W. GAMBIN, K. KOWALCZYK, Evolution of plastic anisotropy due to deformation texture development, Mat. VII Inter. Symp. Plasticity'99, January 5–13, Mexico, Cancun 1999.

M. GOTOH, A theory of plastic anisotropy based on a yield function of fourth order (plane stress state) – I/II, Int. J. Mech. Sci., 19, 505–512, 513–520, 1977.

K.S. HAVNER, Finite Plastic deformation of crystalline solids, Cambridge University Press, 1992.

R. HILL, A theory of the yielding and plastic flow of anisotropic metals, Proc. Roy. Soc., London, Ser. A, 193, 281–297, 1948.

R. HILL, Mathematical theory of plasticity, Oxford, Clarendon Press, 1950.

R. HILL, Continuum micro-mechanics of elastoplastic polycrystals, J. Mech. Phys. Solids, 13, 89–101, 1965.

R. HlLL, The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, 15, 79–95, 1967.

R. HILL, Theoretical plasticity of textured aggregates, Math. Proc. Camb. Phil. Soc., 85, 179–191, 1979.

R. HILL, Constitutive modelling of orthotropic plasticity in sheet metals, J. Mech. Phys. Solids, 38, 3, 405–417, 1990.

R. HILL, J.R. RICE, Constitutive analysis of elastic–plastic crystals at arbitrary strain, J. Mech. Phys. Solids, 20, 401–413, 1972.

R. HILL, J.R. RICE, Elastic potential and the structure of inelastic constitutive laws, SIAM J. Appl. Math., 25, 3, 1973.

R.W.K. HONEYCOMB, The plastic deformation of metals, E. Arnold Ltd, 1984.

D. HULL, Introduction to dislocations, Pergamon Press, Oxford, 1984.

S. JEMIOLO, J.J. TELEGA, Representations of tensor functions and applications in continuum mechanics, Prace IPPT, Warszawa, 3/1997.

S. JEMIOLO, K. KOWALCZYK, Invariant formulation and spectral decomposition of the Hill anisotropic yield criterion, (in Polish), Prace Naukowe PW, Budownictwo, z. 133, 87–123, 1999.

U.F. KOCKS, Constitutive behaviour based on crystal plasticity, Reprinted from United Constitutive Equations for Creep and Plasticity, A.K. MILLER [Ed.], Elsevier 1987.

K. KOWALCZYK, W. GAMBIN, Evolution of yield surface due to texture development, Volume of abstracts, 33rd Solid Mechanics Conference, Zakopane, September 5–9, 2000.

E. KRONER, Zur plastischen Verformung des Vielkristalls, Acta Met., 9, 155–161, 1961.

E.H. LEE, Elastic–plastic deformation at finite strains, J. Appl. Mech., 36, 1, 1969.

J. LIAN, F. BARLAT, B. BAUDELET. Plastic behaviour and strechability of sheet metals. Part II: Effect of yield surface shape on sheet forming limit, Int. J. Plasticity, 5, 131–147, 1989.

R. MISES, Mechanik der plastischen Formänderung von Kristallen, Zeitschrift für Angewandte Mathematik und Mechanik, 8, 161, 1928.

W. OLSZAK, W. URBANOWSKI, The plastic potential and generalized distorsion energy in the theory of non-homogeneous anisotropic elastic-plastic bodies, Arch. Mech. Stos., 8, 4, 671–694, 1956.

W. OLSZAK, J. OSTROWSKA-MACIEJEWSKA, The plastic potential in the theory of anisotropic elastic–plastic solids, Engng. Fracture Mech., 21, 4, 625–632, 1985.

J. OSTROWSKA-MACIEJEWSKA, Mechanics of deformable bodies [in Polish], PWN, Warszawa 1994.

J. RYCHLEWSKI, Elastic energy decomposition and limit criteria (in Russian), Advances in Mechanics, 7, 3, 1984.

G. SACHS, Zur Ableitung einer Fliessbedingung, Zeichschrift des Vereins deutcher Ingenieure, 72, 734, 1928.

G.I. TAYLOR, Plastic strain in metals, Journal of Institute of Metals, 62, 307–324, 1938.

C. TEODOSIU, J.L. RAPHANEL, L. TABOUROT, Finite element simulation of large elasto-plastic deformation in multicrystals, MECAMAT'91, THEODOSIU, RAPHANEL & SIDOROFF [Ed.], Balkema, Rotterdam 1993.

Copyright © 2014 by Institute of Fundamental Technological Research
Polish Academy of Sciences, Warsaw, Poland