Continuum Dislocation Dynamics Modeling of Mesoscale Crystal Plasticity at Finite Deformation
Abstract
Over the past two decade, there have been renewed interests in the use of continuum models of dislocation to predict the plastic strength of metals from basic properties of dislocations. Such interests have been motivated by the unique self-organized dislocation microstructures that develop during plastic deformation of metals and the need to understand their origin and connection with strength of metals. This thesis effort focuses on the theoretical development of a vector-density based representation of dislocation dynamics on the mesoscale accounting for the kinematics of finite deformation. This model consists of two parts, the first is the development of the transport-reaction equations governing dislocation dynamics within the finite deformation setting, and the second focuses on the computational solution of the resulting model. The transport-reaction equations come in the form of a set of hyperbolic curl type transport equations, with reaction terms that nonlinearly couple these equations. The equations are also geometrically non-linear due to finite deformation kinematics and by their constitutive closure. The solution of the resulting model consists of two parts that are coupled in a staggered fashion, the crystal mechanics equations are lumped in the stress equilibrium equations, and the dislocation transport-reactions equations. The two sets of equations are solved by the Galerkin and First-Order System Least-Squares (FOSLS) finite element methods. A special attention is given to the accurate modeling of glissile dislocation junctions using de Rahm currents and graph theory ideas. The introduction of these measures requires the derivation of further transport relations. Using homogenization theory, we specialize the proposed model to a mean deformation gradient driven bulk plasticity model. Lastly, we simulate bulk plasticity behavior and compare our results against experiments.
Degree
Ph.D.
Advisors
El-Azab, Purdue University.
Subject Area
Mechanics|Mathematics
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