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https://hdl.handle.net/2142/72229
Description
Title
Continuity in Rigid Viscoplastic Flow
Author(s)
Mach, Justin C.
Issue Date
2009
Doctoral Committee Chair(s)
Beaudoin, Armand J.
Department of Study
Mechancial Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Mechanical
Abstract
Classical plasticity models evolve state variables in a spatially independent manner through (local) ordinary differential equations, such as in the update of the rotation field in crystal plasticity. This approach emanates from how the deformation has been described, e.g. the multiplicative decomposition of the deformation gradient. In the present work, a continuity condition is derived for the elastic spin field from a conservation law for Burgers vector content---a consequence of an averaged field theory of dislocation mechanics. This results in a nonlocal evolution equation for the rotation field in rigid viscoplasticity. The continuity condition provides a theoretical basis for assumptions of co-rotation models of crystal plasticity.
The prediction of texture evolution is improved without constitutive enhancements. This provides evidence for the importance of continuity in modeling of classical plasticity. Bulk rolling texture evolution predictions for f.c.c. metals exhibit a weaker overall intensity with a more uniform beta fiber. Single grain simulations show evidence of grain splitting and locally larger rotations with an average rotation less than a Taylor model prediction. Continuous elastic rotation fields with sharp gradients (as in grain splitting) are computationally demonstrated within rigid viscoplasticity and non-singular dislocation distributions are calculated from these rotation fields. Computational evidence is shown for the enhancement of stress fields in the vicinity of delamination-prone grain boundaries. All of these results suggest that even the problem of size-independent macroscopic plasticity is spatially nonlocal in nature.
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