Finite element analysis of grain-by-grain deformation by crystal plasticity with couple stress

Abstract Rigid–plastic crystal plasticity with the rate-sensitive constitutive behavior of a slip system has been formulated within the framework of a two-dimensional finite element method to predict the grain-by-grain deformation of single- and polycrystalline FCC metals. For that purpose, individual grains are represented by several numbers of finite elements to describe the sub-grain deformation behavior, and couple stress has been introduced into the equilibrium equation to be able to describe the size effect as well as to prevent mesh-dependent predictions. A modified virtual work-rate principle with an approximate interface constraint has been suggested to use a C 0 -continuous element in the finite element implementation, and the couple stress work-rate has been formulated on the basis of an assumed constitutive behavior. Simulated plane-strain compressions of a single crystal cube show that the shearing and the deformation load are closely related to the imbedded lattice orientation of the crystal grain, and that the sub-grain deformation and the load magnitude can be controlled by the couple stress hardening. It is also confirmed that almost the same predictions are obtained for different mesh systems by considering the couple stress hardening. Simulated plane-strain compressions of a bi-crystal show considerably curved grain-by-grain surface profiles after large reduction for several combinations of the imbedded lattice orientation. The high couple stress hardening predicted around grain boundaries is supposed to be related to the grain size effect. It is also supposed that consideration of couple stress is necessary to predict the sub-grain or the grain-by-grain deformation, and the couple stress hardening may be used to describe the state of microstructures in grain.

[1]  Norman A. Fleck,et al.  A phenomenological theory for strain gradient effects in plasticity , 1993 .

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

[3]  Lallit Anand,et al.  The process of shear band formation in plane strain compression of fcc metals: Effects of crystallographic texture , 1994 .

[4]  Geoffrey Ingram Taylor,et al.  Bakerian Lecture. The Distortion of an Aluminium Crystal during a Tensile Test , 1923 .

[5]  N. Fleck,et al.  FINITE ELEMENTS FOR MATERIALS WITH STRAIN GRADIENT EFFECTS , 1999 .

[6]  Amit Acharya,et al.  Lattice incompatibility and a gradient theory of crystal plasticity , 2000 .

[7]  Paul R. Dawson,et al.  Effects of grain interaction on deformation in polycrystals , 1998 .

[8]  Norman A. Fleck,et al.  Strain gradient crystal plasticity: size-dependentdeformation of bicrystals , 1999 .

[9]  J. Hutchinson,et al.  Bounds and self-consistent estimates for creep of polycrystalline materials , 1976, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[10]  W. Drugan,et al.  Theory of plasticity , 1987 .

[11]  Paul R. Dawson,et al.  On modeling the development of crystallographic texture in bulk forming processes , 1989 .

[12]  Abhishek Bhattacharyya,et al.  Evolution of grain-scale microstructure during large strain simple compression of polycrystalline aluminum with quasi-columnar grains: OIM measurements and numerical simulations , 2001 .

[13]  P. Dawson,et al.  Polycrystal plasticity modeling of intracrystalline boundary textures , 1999 .

[14]  L. Anand,et al.  Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[15]  J. Harder,et al.  A crystallographic model for the study of local deformation processes in polycrystals , 1999 .

[16]  Hans Muhlhaus,et al.  A variational principle for gradient plasticity , 1991 .

[17]  R. Asaro,et al.  Micromechanics of Crystals and Polycrystals , 1983 .

[18]  F. Barbe,et al.  Intergranular and intragranular behavior of polycrystalline aggregates.Part 2: Results , 2001 .

[19]  Alan Needleman,et al.  Material rate dependence and localized deformation in crystalline solids , 1983 .

[20]  Paul Steinmann,et al.  On the continuum formulation of higher gradient plasticity for single and polycrystals , 2000 .

[21]  Amit Acharya,et al.  Consideration of grain-size effect and kinetics in the plastic deformation of metal polycrystals , 2000 .

[22]  L. Anand,et al.  Large deformation simple compression of a copper single crystal , 1993 .

[23]  J. C. Simo,et al.  A three-dimensional finite-strain rod model. Part II: Computational aspects , 1986 .

[24]  David L. McDowell,et al.  Polycrystal constraint and grain subdivision , 1998 .

[25]  D. Jeulin,et al.  Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model , 2001 .

[26]  N. Fleck,et al.  Strain gradient plasticity , 1997 .

[27]  Lallit Anand,et al.  Elasto-viscoplastic constitutive equations for polycrystalline metals: Application to tantalum , 1998 .

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

[29]  Morton E. Gurtin,et al.  A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations , 2002 .

[30]  H. Zbib,et al.  Crystal plasticity: micro-shear banding in polycrystals using voronoi tessellation , 1998 .

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

[32]  P. Dawson,et al.  Texture Development During Wire Drawing , 1990 .

[33]  N. O'Dowd,et al.  Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains , 2001 .

[34]  G. Taylor,et al.  The Plastic Extension and Fracture of Aluminium Crystals , 1925 .