Model of plastic anisotropy evolution with texture-dependent yield surface

Abstract Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.

[1]  Rodney Hill,et al.  Elastic potentials and the structure of inelastic constitutive laws , 1973 .

[2]  P. Houtte.  Fast calculation of average Taylor factors and Mandel spins for all possible strain modes , 2001 .

[3]  R. Asaro,et al.  Overview no. 42 Texture development and strain hardening in rate dependent polycrystals , 1985 .

[4]  F. Barlat,et al.  Modeling of deformation texture development based on rate independent crystal plasticity , 1997 .

[5]  L. Anand,et al.  A computational procedure for rate-independent crystal plasticity , 1996 .

[6]  R. Hill,et al.  XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. , 1951 .

[7]  Y. Dafalias.  The Plastic Spin , 1985 .

[8]  M. Arminjon.  A Regular Form of the Schmid Law. Application to the Ambiguity Problem , 1991 .

[9]  J. Jonas,et al.  Effect of rate sensitivity on the stability of torsion textures , 1988 .

[10]  R. Hill.  The mathematical theory of plasticity , 1950 .

[11]  F. Barlat,et al.  Yield function development for aluminum alloy sheets , 1997 .

[12]  D. Piot,et al.  A method of generating analytical yield surfaces of crystalline materials , 1996 .

[13]  M. Życzkowski,et al.  Combined Loadings in the Theory of Plasticity , 1981 .

[14]  W. Gambin.  Refined analysis of elastic-plastic crystals , 1992 .

[15]  F. Barlat,et al.  A six-component yield function for anisotropic materials , 1991 .

[16]  En-Jui Lee.  Elastic-Plastic Deformation at Finite Strains , 1969 .

[17]  R. Hill.  Constitutive modelling of orthotropic plasticity in sheet metals , 1990 .

[18]  B. Peeters,et al.  Assessment of crystal plasticity based calculation of the lattice spin of polycrystalline metals for FE implementation , 2001 .

[19]  Zenon Mróz,et al.  On the description of anisotropic workhardening , 1967 .

[20]  R. Hill.  A theory of the yielding and plastic flow of anisotropic metals , 1948, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[21]  A. Baltov,et al.  A rule of anisotropic hardening , 1965 .

[22]  Bernard Budiansky,et al.  THEORETICAL PREDICTION OF PLASTIC STRAINS OF POLYCRYSTALS , 1961 .

[23]  K. S. Havner,et al.  Finite Plastic Deformation of Crystalline Solids , 1992 .

[24]  Frédéric Barlat,et al.  A Yield Function for Orthotropic Sheets under Plane Stress Conditions , 1989 .

[25]  E. Kröner.  Zur plastischen verformung des vielkristalls , 1961 .

[26]  Rodney Hill,et al.  Continuum micro-mechanics of elastoplastic polycrystals , 1965 .

[27]  M. Gotoh.  A theory of plastic anisotropy based on a yield function of fourth order (plane stress state)—I , 1977 .

[28]  D. Imbault,et al.  A fourth-order plastic potential for anisotropic metals and its analytical calculation from the texture function , 1994 .

[29]  A. Bertram,et al.  The evolution of Hooke's law due to texture development in FCC polycrystals , 2001 .

[30]  R. Hill.  Theoretical plasticity of textured aggregates , 1979, Mathematical Proceedings of the Cambridge Philosophical Society.

[31]  J. Jonas,et al.  Large strain shear and torsion of rate-sensitive FCC polycrystals , 1990 .

[32]  Elisabeth Massoni,et al.  Rate-independent crystalline and polycrystalline plasticity, application to FCC materials , 2000 .

[33]  J. Boehler,et al.  A Simple Derivation of Representations for Non‐Polynomial Constitutive Equations in Some Cases of Anisotropy , 1979 .

[34]  André Zaoui,et al.  An extension of the self-consistent scheme to plastically-flowing polycrystals , 1978 .

[35]  M. Życzkowski,et al.  Evolution equations for distortional plastic hardening , 1996 .

[36]  Frédéric Barlat,et al.  Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions , 1989 .

[37]  R. Hill,et al.  A user-friendly theory of orthotropic plasticity in sheet metals , 1993 .

[38]  Richard Von Mises,et al.  Mechanik der plastischen Formänderung von Kristallen , 1928 .

[39]  J. Rice,et al.  Constitutive analysis of elastic-plastic crystals at arbitrary strain , 1972 .

[40]  A. Clément.  Prediction of deformation texture using a physical principle of conservatiol , 1982 .

[41]  R. Hill,et al.  CXXVIII. A theoretical derivation of the plastic properties of a polycrystalline face-centred metal , 1951 .

[42]  Albert Van Bael,et al.  Finite element modeling of plastic anisotropy induced by texture and strain-path change , 2003 .