Continuum Thermodynamic Modeling and Simulation of Additional Hardening due to Deformation Incompatibility

The purpose of this work is the formulation and investigation of a phenomenological constitutive model for the inelastic material behavior of single crystals and polycrystals including the possible effects of incompatibility in the local inelastic deformation on this behavior. In particular, attention is focused here on additional hardening caused by the production of additional dislocations (i.e., geometrically-necessary dislocations) accommodating such incompatibility. In the context of crystal plasticity, such local inelastic deformation is represented by the glide-system (scalar) slips. As it turns out, this quantity can be used as a basis on which to formulate a non-local continuum thermodynamic generalization of standard crystal plasticity in order to account for the effects of such incompatibility on the material behavior. The corresponding continuum thermodynamic formulation yields a generalized Ginzburg-Landau or Cahn-Allen-type evolution/field relation for the scalar glide-system slip whose form is determined by that of the free energy, a dissipation potential, and that of the evolution relations for the inelastic state variables. In the last part of the work, the behavior of the model is elucidated in the context of the constrained simple shear of a crystalline strip containing one or two glide systems.

[1]  Morton E. Gurtin,et al.  On the plasticity of single crystals: free energy, microforces, plastic-strain gradients , 2000 .

[2]  H. Stumpf,et al.  Nonlinear continuum theory of dislocations , 1996 .

[3]  van der Erik Giessen,et al.  Discrete dislocation plasticity: a simple planar model , 1995 .

[4]  M. Suffczyński,et al.  Selection rules for the double space group of the beta-Wolfram structure , 1977 .

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

[6]  M. Ashby.  The deformation of plastically non-homogeneous materials , 1970 .

[7]  Georges Cailletaud,et al.  A Cosserat theory for elastoviscoplastic single crystals at finite deformation , 1997 .

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

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

[10]  Paul Steinmann,et al.  Views on multiplicative elastoplasticity and the continuum theory of dislocations , 1996 .

[11]  B. Svendsen.  On the thermodynamics of thermoelastic materials with additional scalar degrees of freedom , 1999 .

[12]  J. Nye.  Some geometrical relations in dislocated crystals , 1953 .

[13]  P. M. Naghdi,et al.  Characterization of dislocations and their influence on plastic deformation in single crystals , 1994 .

[14]  E. Kröner,et al.  Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen , 1959 .

[15]  B. Svendsen.  Formulation of balance relations and configurational fields for continua with microstructure and moving point defects via invariance , 2001 .

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

[17]  J. Cahn,et al.  A Microscopic Theory for Domain Wall Motion and Its Experimental Verification in Fe‐Al Alloy Domain Growth Kinetics , 1977 .

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

[19]  Gérard A. Maugin,et al.  Infernal Variables and Dissipative Structures , 1990 .

[20]  Laurent Stainier,et al.  A theory of subgrain dislocation structures , 2000 .

[21]  H. Zbib,et al.  A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals , 1999 .

[22]  Norman A. Fleck,et al.  Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity , 2001 .

[23]  Bob Svendsen,et al.  Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations , 2002 .

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

[25]  Michael Ortiz,et al.  Computational modelling of single crystals , 1993 .