Skip over navigation

 

An Internal State Variable Model of Micropolar Elasto-Vicoplasticity

DOUGLAS BAMMANN (MISSISSIPPI STATE UNIVERSITY)

Plasticity at Different Length Scales

Mon 4:20 - 5:40

CIT 219

An internal state variable theory of micorpolar elasto-viscoplasticity is developed based upon the physics associated with dislocations and disclinations. Elastic-plastic kinematics are modified to include an additional rotational degree of freedom from which non-symmetric elastic and plastic strains and curvatures are defined. Dislocations and disclinations can then be easily identified in terms of the incompatibilities associated with the elastic deformation and elastic curvature. The state variables introduced are the nonsymmetric internal elastic strain and elastic curvature resulting from the presence of the dislocations and disclinations, as well as scalar measure of the elastic strain field associated with the statistically stored dislocations. The conjugate thermodynamic internal micro-stress and micro-moment are required to satisfy micro linear and angular momentum balances, while the macro stress (the derivative of the free energy with the respect to the macro elastic strain) satisfies standard linear and angular (symmetry of stress tensor) momentum balance laws. Expressions for the plastic velocity gradient and plastic curvature are proposed as well as an equation describing the evolution of the statistically stored dislocation density. The resulting expression describing the dissipation associated with the micro and macro stress fields follows naturally as a result of the second law, and the ramifications these restrictions on localized deformation is discussed. This model has been implemented into ABAQUS and compared with dislocation dynamic codes and other gradient models, as well as the code FLEXPDE. Here, an internal state variable associated with the mobile dislocation density on each slip system of a double planar slip model is include, which as a result, leads to gradients in the mobile dislocation density. Deformation of a single crystal results in the formation of cell blocks and cell walls.