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Multiscale Crystal Defect Dynamics: A Crystal Plasticity Theory Based on Dislocation Pattern Dynamics


Understanding the mechanism of plasticity is of great significance in material science,

structure design as well as manufacture. For example, the mechanism of fatigue, one critical

origin for mechanical failures, is governed by plastic deformation. In terms of simulating

plasticity, multiscale methods have drawn a lot of attention by bridging simulations at different

scales and yielding high-quality atomistic properties at affordable computational resources.

The main limitation of some multiscale methods is that the accuracy in much of the continuum

region is inherently limited to the accuracy of the coarse-scale model, even though much

effort has been made to improve the existing multiscale models by developing adaptive

refinement models. It is known that crystal defects play an important role in

determining material properties at macroscale. Crystal defects have microstructure,

and this microstructure should be related to the microstructure of the original

crystal. Hence each type of crystals may have similar defects due to the same failure

mechanism originated from the same microstructure, if they are under the same loading

conditions. In this dissertation, a multiscale crystal defect dynamics (MCDD) model

is proposed that modelling defects by considering their intrinsic microstructure derived

from the microstructure or dislocation patterns of the original perfect crystal. The main

novelties of present work are: (1) the discrete exterior calculus and algebraic topology

theory are used to construct a scale-up (coarse-grained) dual lattice model for crystal

defects, which may represent all possible defect modes inside a crystal; (2) a higher

order Cauchy-Born rule (up to the fourth order) is adopted to construct atomistic-informed

constitutive relations for various defect process zones, and (3) an hierarchical strain

gradient theory based finite element formulation is developed to support an hierarchical

multiscale process zone model for various defects in a unified formulation. The efficiency

of MCDD computational algorithm allows us to simulate dynamic defect evolution at large

scale while taking into account atomistic interaction. The MCDD model has been validated

by comparing the results of MCDD simulations with that of molecular dynamics (MD)in the

cases of nanoindentation, uniaxial tension and simple shear. Numerical simulations have

shown that MCDD can capture not only material failure but also inelastic deformation in

a multiscale continuum simulation by considering the atomistic interaction.

In addition, simulation of anisotropy demonstrates that MCDD is capable of capturing

the influence of loading axis orientation and the loading directionality on dislocation nucleation.

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