This thesis is concerned with the continuum modeling and simulations of the structure, energy and dynamics of grain boundaries and dislocation arrays in crystalline materials.

In the first part of the thesis, the structure and energy of (111) twist boundaries in fcc Al, Cu and Ni are studied systematically by atomistic simulations with EAM potentials and generalized Peierls-Nabarro models. Compared with atomistic simulations, the generalized Peierls-Nabarro models work excellently for low angle grain boundaries and near twin grain boundaries. In these two regimes, dislocations and fault regions can be identified, based on which analytical energy expressions are derived, respectively. For the intermediate grain boundaries, a simple polynomial expression is proposed to fit the e...[ Read more ]

This thesis is concerned with the continuum modeling and simulations of the structure, energy and dynamics of grain boundaries and dislocation arrays in crystalline materials.

In the first part of the thesis, the structure and energy of (111) twist boundaries in fcc Al, Cu and Ni are studied systematically by atomistic simulations with EAM potentials and generalized Peierls-Nabarro models. Compared with atomistic simulations, the generalized Peierls-Nabarro models work excellently for low angle grain boundaries and near twin grain boundaries. In these two regimes, dislocations and fault regions can be identified, based on which analytical energy expressions are derived, respectively. For the intermediate grain boundaries, a simple polynomial expression is proposed to fit the energy from atomistic simulations. The resulting analytical energy formulas for twist boundaries over the full range of twist angles are in excellent agreement with atomistic simulations.

In the second part of the thesis, a continuum model is presented for the core relaxation of incoherent twin boundaries based on the Peierls-Nabarro framework, incorporating both the long-range strain field and the local atomic structure. The continuum model is employed to study the finite size effect of twin boundaries and interactions of dislocations with twin boundaries. Simulation results obtained using this continuum model agree well with those of experiments and atomistic simulations. This model provides a basis for quantitative study of structures and collective behaviors of twin boundaries within the continuum framework.

Finally in this thesis, a simulation method for the dynamics of dislocation arrays is presented. In this numerical method, dislocation arrays are considered as continuous surfaces in three dimensions, represented using the level set framework. The level set representation of the surfaces has the advantage of automatically handling the topological changes occurring during the evolution, and simple implementation using standard accurate finite difference schemes on a uniform grid. The driving force of the evolution of the dislocation array surfaces comes from both the long-range interaction of the constituent dislocations and their local curvature effect. The long-range interaction is calculated efficiently using the fast Fourier transform (FFT) method. Simulations are performed for dislocation arrays bypassing different particles under applied stress. The long-range nature of the stress fields of nonplanar infinite dislocation arrays is shown to be essentially different from that by a single dislocation.